Finite Group Databasebeta

← #17199944

Subgroups — #17199944

Order 4352.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531976C211yesmaximal, characteristic, complemented
2#14531950C211yesmaximal, characteristic, complemented
3#14531932C211yesmaximal, characteristic, complemented
4#14531925C211yesmaximal, characteristic
5#14531920C211yesmaximal, characteristic, complemented
6#14531908C211yesmaximal, characteristic, complemented
7#14531859C211yesmaximal, characteristic, complemented
8#14531815C211yesmaximal, characteristic, complemented
9#14531780C211yesmaximal, characteristic, complemented
10#14531733C211yesmaximal, characteristic, complemented
11#14531724C211yesmaximal, characteristic, complemented
12#14531677C211yesmaximal, characteristic, complemented
13#14531677C211yesmaximal, characteristic, complemented
14#14531633C211yesmaximal, characteristic, complemented
15#14531633C211yesmaximal, characteristic, complemented
16#14531599C211yesmaximal, characteristic, complemented
17#14531578C211yesmaximal, characteristic, complemented
18#14531578C211yesmaximal, characteristic, complemented
19#14531578C211yesmaximal, characteristic, complemented
20#14531563C211yesmaximal, characteristic, complemented
21#14531542C211yesmaximal, characteristic, complemented
22#14531468C211yesmaximal, characteristic, complemented
23#14531445C211yesmaximal, characteristic
24#14531417C211yesmaximal, characteristic, complemented
25#14531393C211yesmaximal, characteristic, complemented
26#14531382C211yesmaximal, characteristic, complemented
27#14531382C211yesmaximal, characteristic, complemented
28#126×Dic17C211yesmaximal, characteristic, complemented
29#14531282C211yesmaximal, characteristic, complemented
30#14531249C211yesmaximal, characteristic, complemented
31C2×C17×#551C211yesmaximal, characteristic
32C2×Q8×Dic17C2211yescharacteristic, complemented
33C2×D4×Dic17C2211yescharacteristic
34C2×#10587612C2211yescharacteristic
35C2×#10587612C2211yescharacteristic
36C2×#10587612C2211yescharacteristic, complemented
37C22×C22⋊Dic17C2211yescharacteristic
38#11762716C2211yescharacteristic, complemented
39#11762716C2211yescharacteristic, complemented
40#11762716C2211yescharacteristic, complemented
41#11762712C2211yescharacteristic
42#11762712C2211yescharacteristic
43#11762712C2211yescharacteristic
44#11762712C2211yescharacteristic
45#11762712C2211yescharacteristic
46#11762708C2211yescharacteristic, complemented
47#11762708C2211yescharacteristic, complemented
48#11762708C2211yescharacteristic, complemented
49#11762708C2211yescharacteristic, complemented
50#11762708C2211yescharacteristic, complemented
51#11762708C2211yescharacteristic, complemented
52#11762708C2211yescharacteristic, complemented
53#11762708C2211yescharacteristic, complemented
54#11762702C2211yescharacteristic
55#11762702C2211yescharacteristic
56#11762702C2211yescharacteristic
57#11762702C2211yescharacteristic
58#11762702C2211yescharacteristic
59#11762702C2211yescharacteristic
60#11762702C2211yescharacteristic
61#11762702C2211yescharacteristic
62#11762702C2211yescharacteristic
63#11762702C2211yescharacteristic
64#11762702C2211yescharacteristic
65#11762702C2211yescharacteristic
66#11762702C2211yescharacteristic
67#11762702C2211yescharacteristic
68#11762702C2211yescharacteristic
69#11762702C2211yescharacteristic
70#11762702C2211yescharacteristic
71#11762702C2211yescharacteristic
72#11762702C2211yescharacteristic
73#11762702C2211yescharacteristic
74#11762702C2211yescharacteristic
75#11762702C2211yescharacteristic
76#11762702C2211yescharacteristic
77#11762702C2211yescharacteristic
78#11762702C2211yescharacteristic
79#11762702C2211yescharacteristic
80#11762702C2211yescharacteristic
81#11762702C2211yescharacteristic
82#11762702C2211yescharacteristic
83#11762702C2211yescharacteristic
84#11762702C2211yescharacteristic
85#11762702C2211yescharacteristic
86#11762702C2211yescharacteristic
87#11762702C2211yescharacteristic
88#11762702C2211yescharacteristic, complemented
89#11762702C2211yescharacteristic, complemented
90#11762702C2211yescharacteristic, complemented
91#11762702C2211yescharacteristic, complemented
92#11762702C2211yescharacteristic, complemented
93#11762702C2211yescharacteristic, complemented
94#11762695C2211yescharacteristic, complemented
95#11762695C2211yescharacteristic, complemented
96#11762695C2211yescharacteristic, complemented
97#11762695C2211yescharacteristic, complemented
98#11762695C2211yescharacteristic, complemented
99#11762695C2211yescharacteristic, complemented
100#11762695C2211yescharacteristic, complemented
101#11762695C2211yescharacteristic, complemented
102#11762695C2211yescharacteristic, complemented
103#11762695C2211yescharacteristic, complemented
104#11762695C2211yescharacteristic, complemented
105#11762695C2211yescharacteristic, complemented
106#11762695C2211yescharacteristic, complemented
107#11762695C2211yescharacteristic, complemented
108#11762695C2211yescharacteristic, complemented
109#11762695C2211yescharacteristic, complemented
110#11762689C2211yescharacteristic
111#11762689C2211yescharacteristic
112#11762689C2211yescharacteristic
113#11762689C2211yescharacteristic
114#11762689C2211yescharacteristic
115#11762689C2211yescharacteristic
116#11762684C2211yescharacteristic
117#11762684C2211yescharacteristic
118#11762684C2211yescharacteristic
119#11762684C2211yescharacteristic
120#11762684C2211yescharacteristic
121#11762684C2211yescharacteristic, complemented
122#11762684C2211yescharacteristic, complemented
123#11762684C2211yescharacteristic, complemented
124#11762679C2211yescharacteristic, complemented
125#11762677C2211yescharacteristic, complemented
126#11762677C2211yescharacteristic, complemented
127#11762677C2211yescharacteristic, complemented
128#11762675C2211yescharacteristic, complemented
129#11762672C2211yescharacteristic
130#11762672C2211yescharacteristic
131#11762669C2211yescharacteristic
132#11762669C2211yescharacteristic
133#11762669C2211yescharacteristic
134#11762669C2211yescharacteristic
135#11762669C2211yescharacteristic
136#11762669C2211yescharacteristic
137#11762669C2211yescharacteristic, complemented
138#11762665C2211yescharacteristic
139#11762665C2211yescharacteristic
140#11762665C2211yescharacteristic
141C4⋊C4×Dic17C2211yescharacteristic, complemented
142C4⋊C4×Dic17C2211yescharacteristic, complemented
143C4⋊C4×Dic17C2211yescharacteristic, complemented
144C4⋊C4×Dic17C2211yescharacteristic, complemented
145C4⋊C4×Dic17C2211yescharacteristic, complemented
146C4⋊C4×Dic17C2211yescharacteristic, complemented
147C4⋊C4×Dic17C2211yescharacteristic, complemented
148C4⋊C4×Dic17C2211yescharacteristic, complemented
149C4×C4⋊Dic17C2211yescharacteristic, complemented
150C4×C4⋊Dic17C2211yescharacteristic, complemented
151C4×C4⋊Dic17C2211yescharacteristic, complemented
152C4×C4⋊Dic17C2211yescharacteristic, complemented
153C4×C4⋊Dic17C2211yescharacteristic, complemented
154C22⋊C4×Dic17C2211yescharacteristic
155C22⋊C4×Dic17C2211yescharacteristic
156C22⋊C4×Dic17C2211yescharacteristic
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic, complemented
160C22⋊C4×Dic17C2211yescharacteristic, complemented
161C22⋊C4×Dic17C2211yescharacteristic, complemented
162C4×C22⋊Dic17C2211yescharacteristic
163C4×C22⋊Dic17C2211yescharacteristic
164C4×C22⋊Dic17C2211yescharacteristic
165C4×C22⋊Dic17C2211yescharacteristic
166C4×C22⋊Dic17C2211yescharacteristic
167C4×C22⋊Dic17C2211yescharacteristic
168C4×C22⋊Dic17C2211yescharacteristic, complemented
169#11762655C2211yescharacteristic, complemented
170C2×#10587502C2211yescharacteristic, complemented
171C42×Dic17C2211yescharacteristic, complemented
172C17×#551C4116yescomplemented
173C2×C17×#126C2211yescharacteristic
174C2×C17×#126C2211yescharacteristic
175C2×C17×#124C2211yescharacteristic
176C2×C17×#123C2211yescharacteristic
177C2×C17×#123C2211yescharacteristic
178C2×C17×#123C2211yescharacteristic
179C2×C17×C22⋊Q8C2211yescharacteristic
180C2×C17×C22⋊Q8C2211yescharacteristic
181C2×C17×#120C2211yescharacteristic
182C2×C4×D4×C17C2211yescharacteristic
183C2×C4×D4×C17C2211yescharacteristic
184C2×C17×#117C2211yescharacteristic
185C2×C17×#117C2211yescharacteristic
186C22×C22⋊C4×C17C2211yescharacteristic
187C22×C22⋊C4×C17C2211yescharacteristic
188C25×C17C2311yescharacteristic
189C22×Q8×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C17×#126C2×C418yescomplemented
203C17×#126C2×C418yescomplemented
204C17×#124C2×C418yes—
205C17×#123C2×C418yes—
206C17×#123C2×C418yescomplemented
207C17×#123C2×C418yescomplemented
208C17×C22⋊Q8C2×C418yescomplemented
209C17×C22⋊Q8C2×C418yescomplemented
210C17×#120C2×C418yes—
211C4×D4×C17C2×C418yescomplemented
212C4×D4×C17C2×C418yescomplemented
213C17×#117C2×C418yescomplemented
214C17×#117C2×C418yescomplemented
215C2×C4⋊C4×C17C2311yescharacteristic
216C2×C4⋊C4×C17C2311yescharacteristic
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2×C418yescomplemented
224C2×C22⋊C4×C17C2×C418yescomplemented
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C42×C17C2311yescharacteristic
240C2×C42×C17C2311yescharacteristic
241C2×C42×C17C2311yescharacteristic
242C2×C22⋊Dic17—42no—
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267C2×C22⋊Dic17C2311yescharacteristic
268C2×C22⋊Dic17C2311yescharacteristic
269C2×C22⋊Dic17C2311yescharacteristic
270C2×C22⋊Dic17C2311yescharacteristic
271Q8×Dic17—42no—
272D4×Dic17—42no—
273#10587612—42no—
274#10587612—42no—
275#10587612—42no—
276C2×C4⋊Dic17C2311yescharacteristic
277C2×C4⋊Dic17C2311yescharacteristic
278C2×C4⋊Dic17C2311yescharacteristic
279C2×C4⋊Dic17C2311yescharacteristic
280C2×C4⋊Dic17C2311yescharacteristic
281C2×C4⋊Dic17C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
284C2×C4⋊Dic17C2311yescharacteristic
285C2×C4⋊Dic17C2311yescharacteristic
286C2×C4⋊Dic17C2311yescharacteristic
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2311yescharacteristic
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×C4×Dic17C2311yescharacteristic
299C2×C4×Dic17C2311yescharacteristic
300C2×C4×Dic17C2311yescharacteristic
301C2×C4×Dic17C2311yescharacteristic
302C2×C4×Dic17C2311yescharacteristic
303C2×C4×Dic17C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320#10587502C2311yescharacteristic
321#10587502C2311yescharacteristic
322#10587502C2311yescharacteristic
323#10587502C2311yescharacteristic
324#10587502C2311yescharacteristic
325#10587502C2311yescharacteristic
326#10587502C2311yescharacteristic
327#10587502C2311yescharacteristic
328#10587502C2311yescharacteristic
329#10587502C2311yescharacteristic
330#10587502C2311yescharacteristic
331#10587502C2311yescharacteristic
332#10587502C2311yescharacteristic
333#10587502C2311yescharacteristic
334#10587502C2311yescharacteristic
335#10587502C2311yescharacteristic
336#10587502C2311yescharacteristic
337#10587502C2311yescharacteristic
338#10587502C2311yescharacteristic
339#10587502C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364C24×C17—41no—
365C24×C17—41no—
366C24×C17—41no—
367C24×C17—41no—
368C24×C17—41no—
369C24×C17—41no—
370C24×C17C22×C414yes—
371C24×C17C2411yescharacteristic
372C24×C17C2411yescharacteristic
373C24×C17C2411yescharacteristic
374C24×C17C2411yescharacteristic
375C2×Q8×C17—41no—
376C2×Q8×C17—41no—
377C2×Q8×C17C22×C414yes—
378C2×D4×C17—41no—
379C2×D4×C17—41no—
380C2×D4×C17—41no—
381C2×D4×C17—41no—
382C2×D4×C17—41no—
383C2×D4×C17—41no—
384C2×D4×C17C22×C414yes—
385C2×D4×C17C22×C414yes—
386C2×D4×C17C22×C414yes—
387C22×C4×C17—41no—
388C22×C4×C17—41no—
389C22×C4×C17—41no—
390C22×C4×C17—41no—
391C22×C4×C17—41no—
392C22×C4×C17—41no—
393C22×C4×C17—41no—
394C22×C4×C17—41no—
395C22×C4×C17—41no—
396C22×C4×C17—41no—
397C22×C4×C17C22×C414yes—
398C22×C4×C17C22×C414yes—
399C22×C4×C17C22×C414yes—
400C22×C4×C17C22×C414yes—
401C22×C4×C17C22×C414yes—
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C22×Dic17—22no—
414C22×Dic17—41no—
415C22×Dic17—41no—
416C22×Dic17—41no—
417C22×Dic17—41no—
418C22×Dic17—41no—
419C22×Dic17—41no—
420C22×Dic17—41no—
421C22×Dic17—41no—
422C22×Dic17—41no—
423C22×Dic17—41no—
424C22×Dic17—41no—
425C22×Dic17C2411yescharacteristic
426C22×Dic17C2411yescharacteristic
427C22×Dic17C2411yescharacteristic
428C22×Dic17C2411yescharacteristic
429C22×Dic17C2411yescharacteristic
430C22×Dic17C2411yescharacteristic
431C22×Dic17C2411yescharacteristic
432C22×Dic17C2411yescharacteristic
433C22×Dic17C2411yescharacteristic
434C22×Dic17C2411yescharacteristic
435C22×Dic17C2411yescharacteristic
436C22×Dic17C2411yescharacteristic
437C22×Dic17C2411yescharacteristic
438C22×Dic17C2411yescharacteristic
439C22×Dic17C2411yescharacteristic
440C22×Dic17C2411yescharacteristic
441C4⋊C4×C17C22×C414yes—
442C4⋊C4×C17C22×C414yes—
443C4⋊C4×C17C22×C414yes—
444C4⋊C4×C17C22×C414yes—
445C4⋊C4×C17C22×C414yes—
446C4⋊C4×C17C22×C414yes—
447C4⋊C4×C17C22×C414yes—
448C4⋊C4×C17C22×C414yes—
449C22⋊C4×C17C22×C414yes—
450C22⋊C4×C17C22×C414yes—
451C22⋊C4×C17C22×C414yes—
452C22⋊C4×C17C22×C414yes—
453C22⋊C4×C17C22×C414yes—
454C22⋊C4×C17C22×C414yes—
455C22⋊C4×C17C22×C414yes—
456C22⋊C4×C17C22×C414yes—
457C22⋊C4×C17C22×C414yes—
458C22⋊C4×C17C22×C414yes—
459C22⋊C4×C17C22×C414yes—
460C22⋊C4×C17C22×C414yes—
461C22⋊C4×C17C22×C414yes—
462C22⋊C4×C17C22×C414yes—
463C42×C17C22×C414yes—
464C42×C17C22×C414yes—
465C42×C17C22×C414yes—
466C22⋊Dic17—22no—
467C22⋊Dic17—22no—
468C22⋊Dic17—22no—
469C22⋊Dic17—41no—
470C22⋊Dic17—41no—
471C22⋊Dic17—41no—
472C22⋊Dic17—41no—
473C22⋊Dic17—41no—
474C22⋊Dic17—41no—
475C22⋊Dic17—41no—
476C22⋊Dic17—41no—
477C22⋊Dic17—41no—
478C22⋊Dic17—41no—
479C22⋊Dic17—41no—
480C22⋊Dic17—41no—
481C22⋊Dic17—41no—
482C22⋊Dic17—41no—
483C22⋊Dic17—41no—
484C22⋊Dic17—41no—
485C22⋊Dic17—41no—
486C22⋊Dic17—41no—
487C22⋊Dic17—41no—
488C22⋊Dic17—41no—
489C22⋊Dic17—41no—
490C22⋊Dic17—41no—
491C22⋊Dic17—41no—
492C22⋊Dic17—41no—
493C22⋊Dic17—41no—
494C4⋊Dic17—22no—
495C4⋊Dic17—22no—
496C4⋊Dic17—22no—
497C4⋊Dic17—41no—
498C4⋊Dic17—41no—
499C4⋊Dic17—41no—
500C4⋊Dic17—41no—
501C4⋊Dic17—41no—
502C4⋊Dic17—41no—
503C4⋊Dic17—41no—
504C4⋊Dic17—41no—
505C4⋊Dic17—41no—
506C4⋊Dic17—41no—
507C4⋊Dic17—41no—
508C4⋊Dic17—41no—
509C4⋊Dic17—41no—
510C4⋊Dic17—41no—
511C4⋊Dic17—41no—
512C4⋊Dic17—41no—
513C4⋊Dic17—41no—
514C4⋊Dic17—41no—
515C4⋊Dic17—41no—
516C4×Dic17—22no—
517C4×Dic17—22no—
518C4×Dic17—41no—
519C4×Dic17—41no—
520C4×Dic17—41no—
521C4×Dic17—41no—
522C4×Dic17—41no—
523C4×Dic17—41no—
524C4×Dic17—41no—
525C4×Dic17—41no—
526C4×Dic17—41no—
527C4×Dic17—41no—
528C4×Dic17—41no—
529C4×Dic17—41no—
530C4×Dic17—41no—
531C4×Dic17—41no—
532C4×Dic17—41no—
533C4×Dic17—41no—
534C4×Dic17—41no—
535C4×Dic17—41no—
536C4×Dic17—41no—
537C4×Dic17—41no—
538#34504—171nomaximal, Sylow
539C23×C17—21no—
540C23×C17—21no—
541C23×C17—21no—
542C23×C17—21no—
543C23×C17—21no—
544C23×C17—21no—
545C23×C17—21no—
546C23×C17—21no—
547C23×C17—21no—
548C23×C17—21no—
549C23×C17—21no—
550C23×C17—21no—
551C23×C17—21no—
552C23×C17—21no—
553C23×C17—21no—
554C23×C17—21no—
555C23×C17—21no—
556C23×C17—21no—
557C23×C17—21no—
558C23×C17—21no—
559C23×C17—21no—
560C23×C17—21no—
561C23×C17—21no—
562C23×C17—21no—
563C23×C17—44no—
564C23×C17—44no—
565C23×C17—44no—
566C23×C17—82no—
567C23×C17—82no—
568C23×C17—82no—
569C23×C17—82no—
570C23×C17C23×C412yes—
571C23×C17C23×C412yes—
572C23×C17C23×C412yes—
573C23×C17C23×C412yes—
574C23×C17C2511yescharacteristic
575Q8×C17—44no—
576D4×C17—44no—
577D4×C17—44no—
578D4×C17—44no—
579C2×C4×C17—21no—
580C2×C4×C17—21no—
581C2×C4×C17—21no—
582C2×C4×C17—21no—
583C2×C4×C17—21no—
584C2×C4×C17—21no—
585C2×C4×C17—21no—
586C2×C4×C17—21no—
587C2×C4×C17—21no—
588C2×C4×C17—21no—
589C2×C4×C17—21no—
590C2×C4×C17—21no—
591C2×C4×C17—21no—
592C2×C4×C17—21no—
593C2×C4×C17—21no—
594C2×C4×C17—21no—
595C2×C4×C17—21no—
596C2×C4×C17—21no—
597C2×C4×C17—21no—
598C2×C4×C17—21no—
599C2×C4×C17—21no—
600C2×C4×C17—21no—
601C2×C4×C17—44no—
602C2×C4×C17—44no—
603C2×C4×C17—44no—
604C2×C4×C17—44no—
605C2×C4×C17—44no—
606C2×C4×C17C23×C412yes—
607C2×C4×C17C23×C412yes—
608C2×C4×C17C23×C412yes—
609C2×C4×C17C23×C412yes—
610C2×C4×C17C23×C412yes—
611C2×C4×C17C23×C412yes—
612C2×C4×C17C23×C412yes—
613C2×C4×C17C23×C412yes—
614C2×C4×C17C23×C412yes—
615C2×C4×C17C23×C412yes—
616C2×C4×C17C23×C412yes—
617C2×Dic17—21no—
618C2×Dic17—21no—
619C2×Dic17—21no—
620C2×Dic17—21no—
621C2×Dic17—21no—
622C2×Dic17—21no—
623C2×Dic17—21no—
624C2×Dic17—21no—
625C2×Dic17—21no—
626C2×Dic17—21no—
627C2×Dic17—21no—
628C2×Dic17—21no—
629C2×Dic17—21no—
630C2×Dic17—21no—
631C2×Dic17—21no—
632C2×Dic17—21no—
633C2×Dic17—21no—
634C2×Dic17—21no—
635C2×Dic17—21no—
636C2×Dic17—21no—
637C2×Dic17—21no—
638C2×Dic17—21no—
639C2×Dic17—21no—
640C2×Dic17—21no—
641C2×Dic17—21no—
642C2×Dic17—21no—
643C2×Dic17—21no—
644C2×Dic17—21no—
645C2×Dic17—21no—
646C2×Dic17—21no—
647C2×Dic17—21no—
648C2×Dic17—21no—
649C2×Dic17—21no—
650C2×Dic17—21no—
651C2×Dic17—21no—
652C2×Dic17—21no—
653C2×Dic17—21no—
654C2×Dic17—21no—
655C2×Dic17—21no—
656C2×Dic17—21no—
657C2×Dic17—21no—
658C2×Dic17—21no—
659C2×Dic17—21no—
660C2×Dic17—21no—
661C2×Dic17—21no—
662C2×Dic17—21no—
663C2×Dic17—21no—
664C2×Dic17—82no—
665C2×Dic17—82no—
666C2×Dic17—82no—
667C2×Dic17—82no—
668C2×Dic17H(5,𝔽2)12yes—
669C2×#551D1711yescharacteristic
670#2383—171no—
671#2378—171no—
672#2376—171no—
673#2375—171no—
674#2374—171no—
675#2373—171no—
676#2367—171no—
677#2362—171no—
678#2359—171no—
679#2354—171no—
680#2353—171no—
681#2347—171no—
682#2347—171no—
683#2342—171no—
684#2342—171no—
685#2337—171no—
686#2335—171no—
687#2335—171no—
688#2335—171no—
689#2334—171no—
690#2332—171no—
691#2323—171no—
692#2321—171no—
693#2318—171no—
694#2314—171no—
695#2312—171no—
696#2312—171no—
697C4×#126—171no—
698#2298—171no—
699#2293—171no—
700C22×C17—22no—
701C22×C17—22no—
702C22×C17—22no—
703C22×C17—22no—
704C22×C17—22no—
705C22×C17—22no—
706C22×C17—22no—
707C22×C17—22no—
708C22×C17—22no—
709C22×C17—22no—
710C22×C17—22no—
711C22×C17—22no—
712C22×C17—41no—
713C22×C17—41no—
714C22×C17—41no—
715C22×C17—41no—
716C22×C17—41no—
717C22×C17—41no—
718C22×C17—41no—
719C22×C17—41no—
720C22×C17—41no—
721C22×C17—41no—
722C22×C17—41no—
723C22×C17—41no—
724C22×C17—41no—
725C22×C17—41no—
726C22×C17—41no—
727C22×C17—41no—
728C22×C17—88no—
729C22×C17C24×C411yescharacteristic
730C22×C17C2×H(5,𝔽2)11yescharacteristic
731C22×C17#58511yescharacteristic
732C22×C17#58511yescharacteristic
733C22×C17#58511yescharacteristic
734C22×C17#58511yescharacteristic
735C22×C17#58511yescharacteristic
736C4×C17—22no—
737C4×C17—22no—
738C4×C17—22no—
739C4×C17—22no—
740C4×C17—22no—
741C4×C17—22no—
742C4×C17—22no—
743C4×C17—22no—
744C4×C17—22no—
745C4×C17—22no—
746C4×C17—22no—
747Dic17—22no—
748Dic17—41no—
749Dic17—41no—
750Dic17—41no—
751Dic17—41no—
752Dic17—41no—
753Dic17—41no—
754Dic17—41no—
755Dic17—41no—
756Dic17—41no—
757Dic17—41no—
758Dic17—41no—
759Dic17—41no—
760Dic17—41no—
761Dic17—41no—
762Dic17—41no—
763#551Dic17116yescomplemented
764C2×#126C2×D1711yescharacteristic
765C2×#126C2×D1711yescharacteristic
766C2×#124C2×D1711yescharacteristic
767C2×#123C2×D1711yescharacteristic
768C2×#123C2×D1711yescharacteristic
769C2×#123C2×D1711yescharacteristic
770C2×C22⋊Q8C2×D1711yescharacteristic
771C2×C22⋊Q8C2×D1711yescharacteristic
772C2×#120C2×D1711yescharacteristic
773C2×C4×Q8—171no—
774C2×C4×D4—171no—
775C2×C4×D4C2×D1711yescharacteristic
776C2×C4×D4C2×D1711yescharacteristic
777C2×#117—171no—
778C2×#117—171no—
779C2×#117—171no—
780C2×#117C2×D1711yescharacteristic
781C2×#117C2×D1711yescharacteristic
782C22×C22⋊C4—171no—
783C22×C22⋊C4C2×D1711yescharacteristic
784C22×C22⋊C4C2×D1711yescharacteristic
785#391—171no—
786#391—171no—
787#391—171no—
788#390—171no—
789#390—171no—
790#390—171no—
791#390—171no—
792#390—171no—
793#389—171no—
794#389—171no—
795#389—171no—
796#389—171no—
797#389—171no—
798#389—171no—
799#389—171no—
800#389—171no—
801#388—171no—
802#388—171no—
803#388—171no—
804#388—171no—
805#388—171no—
806#388—171no—
807#388—171no—
808#388—171no—
809#388—171no—
810#388—171no—
811#388—171no—
812#388—171no—
813#388—171no—
814#388—171no—
815#388—171no—
816#388—171no—
817#388—171no—
818#388—171no—
819#388—171no—
820#388—171no—
821#388—171no—
822#388—171no—
823#388—171no—
824#388—171no—
825#388—171no—
826#388—171no—
827#388—171no—
828#388—171no—
829#388—171no—
830#388—171no—
831#388—171no—
832#388—171no—
833#388—171no—
834#388—171no—
835#388—171no—
836#388—171no—
837#388—171no—
838#388—171no—
839#388—171no—
840#388—171no—
841#387—171no—
842#387—171no—
843#387—171no—
844#387—171no—
845#387—171no—
846#387—171no—
847#387—171no—
848#387—171no—
849#387—171no—
850#387—171no—
851#387—171no—
852#387—171no—
853#387—171no—
854#387—171no—
855#387—171no—
856#387—171no—
857#386—171no—
858#386—171no—
859#386—171no—
860#386—171no—
861#386—171no—
862#386—171no—
863#385—171no—
864#385—171no—
865#385—171no—
866#385—171no—
867#385—171no—
868#385—171no—
869#385—171no—
870#385—171no—
871#384—171no—
872#383—171no—
873#383—171no—
874#383—171no—
875#382—171no—
876#381—171no—
877#381—171no—
878#380—171no—
879#380—171no—
880#380—171no—
881#380—171no—
882#380—171no—
883#380—171no—
884#380—171no—
885#379—171no—
886#379—171no—
887#379—171no—
888C4×C4⋊C4—171no—
889C4×C4⋊C4—171no—
890C4×C4⋊C4—171no—
891C4×C4⋊C4—171no—
892C4×C4⋊C4—171no—
893C4×C4⋊C4—171no—
894C4×C4⋊C4—171no—
895C4×C4⋊C4—171no—
896C4×C4⋊C4—171no—
897C4×C4⋊C4—171no—
898C4×C4⋊C4—171no—
899C4×C4⋊C4—171no—
900C4×C4⋊C4—171no—
901C4×C22⋊C4—171no—
902C4×C22⋊C4—171no—
903C4×C22⋊C4—171no—
904C4×C22⋊C4—171no—
905C4×C22⋊C4—171no—
906C4×C22⋊C4—171no—
907C4×C22⋊C4—171no—
908C4×C22⋊C4—171no—
909C4×C22⋊C4—171no—
910C4×C22⋊C4—171no—
911C4×C22⋊C4—171no—
912C4×C22⋊C4—171no—
913C4×C22⋊C4—171no—
914C4×C22⋊C4—171no—
915C4×C22⋊C4—171no—
916#376—171no—
917C2×#95—171no—
918C43—171no—
919C2×C17—42no—
920C2×C17—42no—
921C2×C17—42no—
922C2×C17—42no—
923C2×C17#342811yescharacteristic
924C2×C17#342811yescharacteristic
925C2×C17C4×H(5,𝔽2)11yescharacteristic
926C2×C17#356011yescharacteristic
927C2×C17#356211yescharacteristic
928C2×C17#356611yescharacteristic
929C2×C17#356811yescharacteristic
930C25C22×D1711yescharacteristic
931C22×Q8C22×D1711yescharacteristic
932C22×D4C22×D1711yescharacteristic
933C22×D4C22×D1711yescharacteristic
934C22×D4C22×D1711yescharacteristic
935C23×C4—171no—
936C23×C4—171no—
937C23×C4—171no—
938C23×C4—171no—
939C23×C4C22×D1711yescharacteristic
940C23×C4C22×D1711yescharacteristic
941C23×C4C22×D1711yescharacteristic
942C23×C4C22×D1711yescharacteristic
943C23×C4C22×D1711yescharacteristic
944#126C2×Dic1718yescomplemented
945#126C2×Dic1718yescomplemented
946#124C2×Dic1718yes—
947#123C2×Dic1718yes—
948#123C2×Dic1718yescomplemented
949#123C2×Dic1718yescomplemented
950C22⋊Q8C2×Dic1718yescomplemented
951C22⋊Q8C2×Dic1718yescomplemented
952#120C2×Dic1718yes—
953C4×Q8—682no—
954C4×D4—682no—
955C4×D4C2×Dic1718yescomplemented
956C4×D4C2×Dic1718yescomplemented
957#117—682no—
958#117—682no—
959#117—682no—
960#117C2×Dic1718yescomplemented
961#117C2×Dic1718yescomplemented
962C2×C4⋊C4—171no—
963C2×C4⋊C4—171no—
964C2×C4⋊C4—171no—
965C2×C4⋊C4—171no—
966C2×C4⋊C4—171no—
967C2×C4⋊C4—171no—
968C2×C4⋊C4—171no—
969C2×C4⋊C4—171no—
970C2×C4⋊C4—171no—
971C2×C4⋊C4—171no—
972C2×C4⋊C4—171no—
973C2×C4⋊C4—171no—
974C2×C4⋊C4—171no—
975C2×C4⋊C4—171no—
976C2×C4⋊C4—171no—
977C2×C4⋊C4—171no—
978C2×C4⋊C4—171no—
979C2×C4⋊C4—171no—
980C2×C4⋊C4—171no—
981C2×C4⋊C4—171no—
982C2×C4⋊C4—171no—
983C2×C4⋊C4—171no—
984C2×C4⋊C4C22×D1711yescharacteristic
985C2×C4⋊C4C22×D1711yescharacteristic
986C2×C4⋊C4C22×D1711yescharacteristic
987C2×C4⋊C4C22×D1711yescharacteristic
988C2×C4⋊C4C22×D1711yescharacteristic
989C2×C4⋊C4C22×D1711yescharacteristic
990C2×C4⋊C4C22×D1711yescharacteristic
991C2×C4⋊C4C22×D1711yescharacteristic
992C2×C22⋊C4—171no—
993C2×C22⋊C4—171no—
994C2×C22⋊C4—171no—
995C2×C22⋊C4—171no—
996C2×C22⋊C4—171no—
997C2×C22⋊C4—171no—
998C2×C22⋊C4—171no—
999C2×C22⋊C4—171no—
1000C2×C22⋊C4—171no—
1001C2×C22⋊C4—171no—
1002C2×C22⋊C4—171no—
1003C2×C22⋊C4—171no—
1004C2×C22⋊C4—171no—
1005C2×C22⋊C4—171no—
1006C2×C22⋊C4—171no—
1007C2×C22⋊C4—171no—
1008C2×C22⋊C4—171no—
1009C2×C22⋊C4—171no—
1010C2×C22⋊C4—171no—
1011C2×C22⋊C4—171no—
1012C2×C22⋊C4—171no—
1013C2×C22⋊C4—171no—
1014C2×C22⋊C4—171no—
1015C2×C22⋊C4—171no—
1016C2×C22⋊C4—171no—
1017C2×C22⋊C4—171no—
1018C2×C22⋊C4—171no—
1019C2×C22⋊C4—171no—
1020C2×C22⋊C4—682no—
1021C2×C22⋊C4C2×Dic1718yescomplemented
1022C2×C22⋊C4C2×Dic1718yescomplemented
1023C2×C22⋊C4C22×D1711yescharacteristic
1024C2×C22⋊C4C22×D1711yescharacteristic
1025C2×C22⋊C4C22×D1711yescharacteristic
1026C2×C22⋊C4C22×D1711yescharacteristic
1027C2×C22⋊C4C22×D1711yescharacteristic
1028C2×C22⋊C4C22×D1711yescharacteristic
1029C2×C22⋊C4C22×D1711yescharacteristic
1030C2×C22⋊C4C22×D1711yescharacteristic
1031C2×C22⋊C4C22×D1711yescharacteristic
1032C2×C22⋊C4C22×D1711yescharacteristic
1033C2×C22⋊C4C22×D1711yescharacteristic
1034C2×C22⋊C4C22×D1711yescharacteristic
1035C2×C22⋊C4C22×D1711yescharacteristic
1036C2×C22⋊C4C22×D1711yescharacteristic
1037C2×C42—171no—
1038C2×C42—171no—
1039C2×C42—171no—
1040C2×C42—171no—
1041C2×C42—171no—
1042C2×C42—171no—
1043C2×C42—171no—
1044C2×C42—171no—
1045C2×C42—171no—
1046C2×C42—171no—
1047C2×C42—171no—
1048C2×C42—171no—
1049C2×C42—171no—
1050C2×C42—171no—
1051C2×C42—171no—
1052C2×C42—171no—
1053C2×C42—171no—
1054C2×C42—171no—
1055C2×C42—171no—
1056C2×C42—171no—
1057C2×C42—171no—
1058C2×C42—171no—
1059C2×C42C22×D1711yescharacteristic
1060C2×C42C22×D1711yescharacteristic
1061C2×C42C22×D1711yescharacteristic
1062#95—171no—
1063#95—171no—
1064#95—171no—
1065#95—171no—
1066#95—171no—
1067#95—171no—
1068#95—171no—
1069#95—171no—
1070#95—171no—
1071#95—171no—
1072#95—171no—
1073#95—171no—
1074#95—171no—
1075#95—171no—
1076#95—171no—
1077#95—171no—
1078#95—171no—
1079#95—171no—
1080#95—171no—
1081#95—171no—
1082#95—171no—
1083#95—171no—
1084#95—171no—
1085#95—171no—
1086#95—171no—
1087#95—171no—
1088#95—171no—
1089#95—171no—
1090#95—171no—
1091#95—171no—
1092#95—171no—
1093#95—171no—
1094#95—171no—
1095#95—171no—
1096#95—171no—
1097#95—171no—
1098#95—171no—
1099#95—171no—
1100#95—171no—
1101#95—171no—
1102#95—171no—
1103#95—171no—
1104#95—171no—
1105#95—171no—
1106C17#3450411yescharacteristic, complemented, Sylow
1107C24—41no—
1108C24—41no—
1109C24—41no—
1110C24—41no—
1111C24—41no—
1112C24—41no—
1113C24C22×Dic1714yes—
1114C24C23×D1711yescharacteristic
1115C24C23×D1711yescharacteristic
1116C24C23×D1711yescharacteristic
1117C24C23×D1711yescharacteristic
1118C2×Q8—41no—
1119C2×Q8—41no—
1120C2×Q8C22×Dic1714yes—
1121C2×D4—41no—
1122C2×D4—41no—
1123C2×D4—41no—
1124C2×D4—41no—
1125C2×D4—41no—
1126C2×D4—41no—
1127C2×D4C22×Dic1714yes—
1128C2×D4C22×Dic1714yes—
1129C2×D4C22×Dic1714yes—
1130C22×C4—41no—
1131C22×C4—41no—
1132C22×C4—41no—
1133C22×C4—41no—
1134C22×C4—41no—
1135C22×C4—41no—
1136C22×C4—41no—
1137C22×C4—41no—
1138C22×C4—41no—
1139C22×C4—41no—
1140C22×C4—171no—
1141C22×C4—171no—
1142C22×C4—171no—
1143C22×C4—171no—
1144C22×C4—171no—
1145C22×C4—171no—
1146C22×C4—171no—
1147C22×C4—171no—
1148C22×C4—171no—
1149C22×C4—171no—
1150C22×C4—171no—
1151C22×C4—171no—
1152C22×C4—171no—
1153C22×C4—171no—
1154C22×C4—171no—
1155C22×C4—171no—
1156C22×C4—342no—
1157C22×C4—681no—
1158C22×C4—681no—
1159C22×C4—681no—
1160C22×C4—681no—
1161C22×C4—681no—
1162C22×C4—681no—
1163C22×C4—681no—
1164C22×C4—681no—
1165C22×C4—681no—
1166C22×C4—681no—
1167C22×C4—681no—
1168C22×C4C22×Dic1714yes—
1169C22×C4C22×Dic1714yes—
1170C22×C4C22×Dic1714yes—
1171C22×C4C22×Dic1714yes—
1172C22×C4C22×Dic1714yes—
1173C22×C4C23×D1711yescharacteristic
1174C22×C4C23×D1711yescharacteristic
1175C22×C4C23×D1711yescharacteristic
1176C22×C4C23×D1711yescharacteristic
1177C22×C4C23×D1711yescharacteristic
1178C22×C4C23×D1711yescharacteristic
1179C22×C4C23×D1711yescharacteristic
1180C22×C4C23×D1711yescharacteristic
1181C22×C4C23×D1711yescharacteristic
1182C22×C4C23×D1711yescharacteristic
1183C22×C4C23×D1711yescharacteristic
1184C4⋊C4—342no—
1185C4⋊C4—342no—
1186C4⋊C4—342no—
1187C4⋊C4—681no—
1188C4⋊C4—681no—
1189C4⋊C4—681no—
1190C4⋊C4—681no—
1191C4⋊C4—681no—
1192C4⋊C4—681no—
1193C4⋊C4—681no—
1194C4⋊C4—681no—
1195C4⋊C4—681no—
1196C4⋊C4—681no—
1197C4⋊C4—681no—
1198C4⋊C4—681no—
1199C4⋊C4—681no—
1200C4⋊C4—681no—
1201C4⋊C4—681no—
1202C4⋊C4—681no—
1203C4⋊C4—681no—
1204C4⋊C4—681no—
1205C4⋊C4—681no—
1206C4⋊C4C22×Dic1714yes—
1207C4⋊C4C22×Dic1714yes—
1208C4⋊C4C22×Dic1714yes—
1209C4⋊C4C22×Dic1714yes—
1210C4⋊C4C22×Dic1714yes—
1211C4⋊C4C22×Dic1714yes—
1212C4⋊C4C22×Dic1714yes—
1213C4⋊C4C22×Dic1714yes—
1214C22⋊C4—342no—
1215C22⋊C4—342no—
1216C22⋊C4—342no—
1217C22⋊C4—681no—
1218C22⋊C4—681no—
1219C22⋊C4—681no—
1220C22⋊C4—681no—
1221C22⋊C4—681no—
1222C22⋊C4—681no—
1223C22⋊C4—681no—
1224C22⋊C4—681no—
1225C22⋊C4—681no—
1226C22⋊C4—681no—
1227C22⋊C4—681no—
1228C22⋊C4—681no—
1229C22⋊C4—681no—
1230C22⋊C4—681no—
1231C22⋊C4—681no—
1232C22⋊C4—681no—
1233C22⋊C4—681no—
1234C22⋊C4—681no—
1235C22⋊C4—681no—
1236C22⋊C4—681no—
1237C22⋊C4—681no—
1238C22⋊C4—681no—
1239C22⋊C4—681no—
1240C22⋊C4—681no—
1241C22⋊C4—681no—
1242C22⋊C4C22×Dic1714yes—
1243C22⋊C4C22×Dic1714yes—
1244C22⋊C4C22×Dic1714yes—
1245C22⋊C4C22×Dic1714yes—
1246C22⋊C4C22×Dic1714yes—
1247C22⋊C4C22×Dic1714yes—
1248C22⋊C4C22×Dic1714yes—
1249C22⋊C4C22×Dic1714yes—
1250C22⋊C4C22×Dic1714yes—
1251C22⋊C4C22×Dic1714yes—
1252C22⋊C4C22×Dic1714yes—
1253C22⋊C4C22×Dic1714yes—
1254C22⋊C4C22×Dic1714yes—
1255C22⋊C4C22×Dic1714yes—
1256C42—342no—
1257C42—342no—
1258C42—681no—
1259C42—681no—
1260C42—681no—
1261C42—681no—
1262C42—681no—
1263C42—681no—
1264C42—681no—
1265C42—681no—
1266C42—681no—
1267C42—681no—
1268C42—681no—
1269C42—681no—
1270C42—681no—
1271C42—681no—
1272C42—681no—
1273C42—681no—
1274C42—681no—
1275C42—681no—
1276C42—681no—
1277C42—681no—
1278C42C22×Dic1714yes—
1279C42C22×Dic1714yes—
1280C42C22×Dic1714yes—
1281C23—21no—
1282C23—21no—
1283C23—21no—
1284C23—21no—
1285C23—21no—
1286C23—21no—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—21no—
1296C23—21no—
1297C23—21no—
1298C23—21no—
1299C23—21no—
1300C23—21no—
1301C23—21no—
1302C23—21no—
1303C23—21no—
1304C23—21no—
1305C23—44no—
1306C23—44no—
1307C23—44no—
1308C23—82no—
1309C23—82no—
1310C23—82no—
1311C23—82no—
1312C23C23×Dic1712yes—
1313C23C23×Dic1712yes—
1314C23C23×Dic1712yes—
1315C23C23×Dic1712yes—
1316C23C24×D1711yescharacteristic
1317Q8—44no—
1318D4—44no—
1319D4—44no—
1320D4—44no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—44no—
1344C2×C4—44no—
1345C2×C4—44no—
1346C2×C4—44no—
1347C2×C4—44no—
1348C2×C4—172no—
1349C2×C4—341no—
1350C2×C4—341no—
1351C2×C4—341no—
1352C2×C4—341no—
1353C2×C4—341no—
1354C2×C4—341no—
1355C2×C4—341no—
1356C2×C4—341no—
1357C2×C4—341no—
1358C2×C4—341no—
1359C2×C4—341no—
1360C2×C4—341no—
1361C2×C4—341no—
1362C2×C4—341no—
1363C2×C4—341no—
1364C2×C4—341no—
1365C2×C4—341no—
1366C2×C4—341no—
1367C2×C4—341no—
1368C2×C4—341no—
1369C2×C4—341no—
1370C2×C4—341no—
1371C2×C4—341no—
1372C2×C4—341no—
1373C2×C4—341no—
1374C2×C4—341no—
1375C2×C4—341no—
1376C2×C4—341no—
1377C2×C4—341no—
1378C2×C4—341no—
1379C2×C4—341no—
1380C2×C4—341no—
1381C2×C4—341no—
1382C2×C4—341no—
1383C2×C4—341no—
1384C2×C4—341no—
1385C2×C4—341no—
1386C2×C4—341no—
1387C2×C4—341no—
1388C2×C4—341no—
1389C2×C4—341no—
1390C2×C4—341no—
1391C2×C4—341no—
1392C2×C4—341no—
1393C2×C4—341no—
1394C2×C4—341no—
1395C2×C4—341no—
1396C2×C4—1362no—
1397C2×C4—1362no—
1398C2×C4—1362no—
1399C2×C4—1362no—
1400C2×C4C23×Dic1712yes—
1401C2×C4C23×Dic1712yes—
1402C2×C4C23×Dic1712yes—
1403C2×C4C23×Dic1712yes—
1404C2×C4C23×Dic1712yes—
1405C2×C4C23×Dic1712yes—
1406C2×C4C23×Dic1712yes—
1407C2×C4C23×Dic1712yes—
1408C2×C4C23×Dic1712yes—
1409C2×C4C23×Dic1712yes—
1410C2×C4C23×Dic1712yes—
1411C22—22no—
1412C22—22no—
1413C22—22no—
1414C22—22no—
1415C22—22no—
1416C22—22no—
1417C22—22no—
1418C22—22no—
1419C22—22no—
1420C22—22no—
1421C22—22no—
1422C22—22no—
1423C22—41no—
1424C22—41no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—41no—
1429C22—41no—
1430C22—41no—
1431C22—41no—
1432C22—41no—
1433C22—41no—
1434C22—41no—
1435C22—41no—
1436C22—41no—
1437C22—41no—
1438C22—41no—
1439C22—88no—
1440C22C24×Dic1711yescharacteristic
1441C22H(5,𝔽2)×D1711yescharacteristic
1442C22#1176364411yescharacteristic
1443C22#1176364511yescharacteristic
1444C22#1176364511yescharacteristic
1445C22#1176364511yescharacteristic
1446C22#1176364511yescharacteristic
1447C4—22no—
1448C4—22no—
1449C4—22no—
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—22no—
1454C4—22no—
1455C4—22no—
1456C4—22no—
1457C4—22no—
1458C4—342no—
1459C4—681no—
1460C4—681no—
1461C4—681no—
1462C4—681no—
1463C4—681no—
1464C4—681no—
1465C4—681no—
1466C4—681no—
1467C4—681no—
1468C4—681no—
1469C4—681no—
1470C4—681no—
1471C4—681no—
1472C4—681no—
1473C4—681no—
1474C2—42no—
1475C2—42no—
1476C2—42no—
1477C2—42no—
1478C2#1454198711yescharacteristic
1479C2#1454198711yescharacteristic
1480C2H(5,𝔽2)×Dic1711yescharacteristic
1481C2#1454333111yescharacteristic
1482C2#1454336511yescharacteristic
1483C2#1454344211yescharacteristic
1484C2#1454347511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC2×C17×#551C2
socle, cosocleC23×C17C25
prime radicalC2×C17×#120C22
hypercenterC2×#551D17
hypocenterC17#34504
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#551

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14531976C2semidirect
2. #14531950C2semidirect
3. #14531932C2semidirect
5. #14531920C2semidirect
6. #14531908C2semidirect
7. #14531859C2semidirect
8. #14531815C2semidirect
9. #14531780C2semidirect
10. #14531733C2semidirect
11. #14531724C2semidirect
12. #14531677C2semidirect
13. #14531677C2semidirect
14. #14531633C2semidirect
15. #14531633C2semidirect
16. #14531599C2semidirect
17. #14531578C2semidirect
18. #14531578C2semidirect
19. #14531578C2semidirect
20. #14531563C2semidirect
21. #14531542C2semidirect
22. #14531468C2semidirect
24. #14531417C2semidirect
25. #14531393C2semidirect
26. #14531382C2semidirect
27. #14531382C2semidirect
28. #126×Dic17C2semidirect
29. #14531282C2semidirect
30. #14531249C2semidirect
32. C2×Q8×Dic17C22semidirect
36. C2×#10587612C22semidirect
38. #11762716C22semidirect
39. #11762716C22semidirect
40. #11762716C22semidirect
46. #11762708C22semidirect
47. #11762708C22semidirect
48. #11762708C22semidirect
49. #11762708C22semidirect
50. #11762708C22semidirect
51. #11762708C22semidirect
52. #11762708C22semidirect
53. #11762708C22semidirect
88. #11762702C22semidirect
89. #11762702C22semidirect
90. #11762702C22semidirect
91. #11762702C22semidirect
92. #11762702C22semidirect
93. #11762702C22semidirect
94. #11762695C22semidirect
95. #11762695C22semidirect
96. #11762695C22semidirect
97. #11762695C22semidirect
98. #11762695C22semidirect
99. #11762695C22semidirect
100. #11762695C22semidirect
101. #11762695C22semidirect
102. #11762695C22semidirect
103. #11762695C22semidirect
104. #11762695C22semidirect
105. #11762695C22semidirect
106. #11762695C22semidirect
107. #11762695C22semidirect
108. #11762695C22semidirect
109. #11762695C22semidirect
121. #11762684C22semidirect
122. #11762684C22semidirect
123. #11762684C22semidirect
124. #11762679C22semidirect
125. #11762677C22semidirect
126. #11762677C22semidirect
127. #11762677C22semidirect
128. #11762675C22semidirect
137. #11762669C22semidirect
141. C4⋊C4×Dic17C22semidirect
142. C4⋊C4×Dic17C22semidirect
143. C4⋊C4×Dic17C22semidirect
144. C4⋊C4×Dic17C22semidirect
145. C4⋊C4×Dic17C22semidirect
146. C4⋊C4×Dic17C22semidirect
147. C4⋊C4×Dic17C22semidirect
148. C4⋊C4×Dic17C22semidirect
149. C4×C4⋊Dic17C22semidirect
150. C4×C4⋊Dic17C22semidirect
151. C4×C4⋊Dic17C22semidirect
152. C4×C4⋊Dic17C22semidirect
153. C4×C4⋊Dic17C22semidirect
159. C22⋊C4×Dic17C22semidirect
160. C22⋊C4×Dic17C22semidirect
161. C22⋊C4×Dic17C22semidirect
168. C4×C22⋊Dic17C22semidirect
169. #11762655C22semidirect
170. C2×#10587502C22semidirect
171. C42×Dic17C22semidirect
172. C17×#551C4semidirect
202. C17×#126C2×C4semidirect
203. C17×#126C2×C4semidirect
206. C17×#123C2×C4semidirect
207. C17×#123C2×C4semidirect
208. C17×C22⋊Q8C2×C4semidirect
209. C17×C22⋊Q8C2×C4semidirect
211. C4×D4×C17C2×C4semidirect
212. C4×D4×C17C2×C4semidirect
213. C17×#117C2×C4semidirect
214. C17×#117C2×C4semidirect
223. C2×C22⋊C4×C17C2×C4semidirect
224. C2×C22⋊C4×C17C2×C4semidirect
763. #551Dic17semidirect
944. #126C2×Dic17semidirect
945. #126C2×Dic17semidirect
948. #123C2×Dic17semidirect
949. #123C2×Dic17semidirect
950. C22⋊Q8C2×Dic17semidirect
951. C22⋊Q8C2×Dic17semidirect
955. C4×D4C2×Dic17semidirect
956. C4×D4C2×Dic17semidirect
960. #117C2×Dic17semidirect
961. #117C2×Dic17semidirect
1021. C2×C22⋊C4C2×Dic17semidirect
1022. C2×C22⋊C4C2×Dic17semidirect
1106. C17#34504semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145319762
#145319502
#145319322
#145319252
#145319202
#145319082
#145318592
#145318152
#145317802
#145317332
#145317242
#145316772
#145316332
#145315992
#145315782
#145315632
#145315422
#145314682
#145314452
#145314172
#145313932
#145313822
#126×Dic172
#145312822
#145312492
C2×C17×#5512
#3450417