Finite Group Databasebeta

← #17200496

Subgroups — #17200496

Order 4352.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17⋊#564C211yesmaximal, characteristic
2#14531967C211yesmaximal, characteristic
3#14531966C211yesmaximal, characteristic
4#14531966C211yesmaximal, characteristic
5#14531890C211yesmaximal, characteristic
6#14531889C211yesmaximal, characteristic
7#14531889C211yesmaximal, characteristic
8#14531888C211yesmaximal, characteristic
9#14531887C211yesmaximal, characteristic
10#14531886C211yesmaximal, characteristic
11#14531885C211yesmaximal, characteristic
12#14531883C211yesmaximal, characteristic
13#14531883C211yesmaximal, characteristic
14#14531881C211yesmaximal, characteristic
15#14531879C211yesmaximal, characteristic
16#14531875C211yesmaximal, characteristic
17#14531587C211yesmaximal, characteristic
18#14531586C211yesmaximal, characteristic
19#14531584C211yesmaximal, characteristic
20#14531583C211yesmaximal, characteristic
21#14531582C211yesmaximal, characteristic
22#14531582C211yesmaximal, characteristic
23#14531524C211yesmaximal, characteristic
24#14531523C211yesmaximal, characteristic
25#14531523C211yesmaximal, characteristic
26#14531522C211yesmaximal, characteristic
27#14531522C211yesmaximal, characteristic
28#14531343C211yesmaximal, characteristic
29#14531341C211yesmaximal, characteristic
30C4×#10587575C211yesmaximal, characteristic
31C17×#2330C211yesmaximal, characteristic
32C17⋊#564C4116yescomplemented
33C2×#10587556C2211yescharacteristic
34C2×#10587556C2211yescharacteristic
35C2×#10587576C2211yescharacteristic
36C2×#10587576C2211yescharacteristic
37C2×#10587576C2211yescharacteristic
38C2×#10587576C2211yescharacteristic
39C2×#10587575C2211yescharacteristic
40C2×#10587575C2211yescharacteristic
41C2×#10587575C2211yescharacteristic
42C2×#10587575C2211yescharacteristic
43C2×#10587575C2211yescharacteristic
44C2×#10587575C2211yescharacteristic
45C2×#10587575C2211yescharacteristic
46C2×#10587575C2211yescharacteristic
47#11762707C2211yescharacteristic
48#11762707C2211yescharacteristic
49#11762706C2211yescharacteristic
50#11762706C2211yescharacteristic
51#11762706C2211yescharacteristic
52#11762706C2211yescharacteristic
53#11762705C2211yescharacteristic
54#11762705C2211yescharacteristic
55#11762705C2211yescharacteristic
56#11762705C2211yescharacteristic
57#11762705C2211yescharacteristic
58#11762705C2211yescharacteristic
59#11762704C2211yescharacteristic
60#11762704C2211yescharacteristic
61#11762704C2211yescharacteristic
62#11762704C2211yescharacteristic
63#11762704C2211yescharacteristic
64#11762704C2211yescharacteristic
65#11762704C2211yescharacteristic
66#11762704C2211yescharacteristic
67#11762704C2211yescharacteristic
68#11762704C2211yescharacteristic
69#11762704C2211yescharacteristic
70#11762704C2211yescharacteristic
71#11762696C2211yescharacteristic
72#11762696C2211yescharacteristic
73#11762696C2211yescharacteristic
74#11762696C2211yescharacteristic
75#11762695C2211yescharacteristic
76#11762695C2211yescharacteristic
77#11762695C2211yescharacteristic
78#11762695C2211yescharacteristic
79#11762695C2211yescharacteristic
80#11762695C2211yescharacteristic
81#11762695C2211yescharacteristic
82#11762695C2211yescharacteristic
83#11762694C2211yescharacteristic
84#11762694C2211yescharacteristic
85#11762694C2211yescharacteristic
86#11762694C2211yescharacteristic
87#11762694C2211yescharacteristic
88#11762694C2211yescharacteristic
89#11762694C2211yescharacteristic
90#11762694C2211yescharacteristic
91#11762693C2211yescharacteristic
92#11762693C2211yescharacteristic
93#11762693C2211yescharacteristic
94#11762693C2211yescharacteristic
95#11762693C2211yescharacteristic
96#11762693C2211yescharacteristic
97#11762693C2211yescharacteristic
98#11762693C2211yescharacteristic
99#11762692C2211yescharacteristic
100#11762692C2211yescharacteristic
101#11762692C2211yescharacteristic
102#11762692C2211yescharacteristic
103#11762692C2211yescharacteristic
104#11762692C2211yescharacteristic
105#11762692C2211yescharacteristic
106#11762692C2211yescharacteristic
107#11762691C2211yescharacteristic
108#11762691C2211yescharacteristic
109#11762691C2211yescharacteristic
110#11762691C2211yescharacteristic
111#11762691C2211yescharacteristic
112#11762691C2211yescharacteristic
113#11762691C2211yescharacteristic
114#11762691C2211yescharacteristic
115#11762690C2211yescharacteristic
116#11762690C2211yescharacteristic
117#11762690C2211yescharacteristic
118#11762690C2211yescharacteristic
119#11762690C2211yescharacteristic
120#11762690C2211yescharacteristic
121#11762690C2211yescharacteristic
122#11762690C2211yescharacteristic
123#11762690C2211yescharacteristic
124#11762690C2211yescharacteristic
125#11762690C2211yescharacteristic
126#11762690C2211yescharacteristic
127#11762678C2211yescharacteristic
128#11762676C2211yescharacteristic
129#11762676C2211yescharacteristic
130#11762674C2211yescharacteristic
131#11762673C2211yescharacteristic
132#11762673C2211yescharacteristic
133C4⋊C4×Dic17C2211yescharacteristic
134C4⋊C4×Dic17C2211yescharacteristic
135C4⋊C4×Dic17C2211yescharacteristic
136C4⋊C4×Dic17C2211yescharacteristic
137C4⋊C4×Dic17C2211yescharacteristic
138C4⋊C4×Dic17C2211yescharacteristic
139C4⋊C4×Dic17C2211yescharacteristic
140C4⋊C4×Dic17C2211yescharacteristic
141C4⋊C4×Dic17C2211yescharacteristic
142C4⋊C4×Dic17C2211yescharacteristic
143C4⋊C4×Dic17C2211yescharacteristic
144C4⋊C4×Dic17C2211yescharacteristic
145C4×#63225C2211yescharacteristic
146C4×#63225C2211yescharacteristic
147C4×#63225C2211yescharacteristic
148C4×#63225C2211yescharacteristic
149C4×#63225C2211yescharacteristic
150C4×#63225C2211yescharacteristic
151C4×#63225C2211yescharacteristic
152C4×#63225C2211yescharacteristic
153C4×#63225C2211yescharacteristic
154C4×#63225C2211yescharacteristic
155C4×C4⋊Dic17C2211yescharacteristic
156C4×C4⋊Dic17C2211yescharacteristic
157#11762660C2211yescharacteristic
158#11762660C2211yescharacteristic
159#11762660C2211yescharacteristic
160#11762660C2211yescharacteristic
161#11762660C2211yescharacteristic
162#11762660C2211yescharacteristic
163#11762660C2211yescharacteristic
164#11762660C2211yescharacteristic
165#11762660C2211yescharacteristic
166#11762660C2211yescharacteristic
167#11762655C2211yescharacteristic
168#11762655C2211yescharacteristic
169#11762655C2211yescharacteristic
170#11762654C2211yescharacteristic
171#11762654C2211yescharacteristic
172C42×Dic17C2211yescharacteristic
173C2×C17×#125C2211yescharacteristic
174C17×#389C2211yescharacteristic
175C17×#389C2211yescharacteristic
176C17×#389C2211yescharacteristic
177C17×#389C2211yescharacteristic
178C17×#389C2211yescharacteristic
179C17×#389C2211yescharacteristic
180C17×#387C2211yescharacteristic
181C17×#387C2211yescharacteristic
182C17×#387C2211yescharacteristic
183C17×#387C2211yescharacteristic
184C17×#384C2211yescharacteristic
185C4×C4⋊C4×C17C2211yescharacteristic
186C4×C4⋊C4×C17C2211yescharacteristic
187C17×#376C2211yescharacteristic
188C17×#125C2×C418yes—
189C2×C4⋊C4×C17C2311yescharacteristic
190C2×C4⋊C4×C17C2311yescharacteristic
191C2×C4⋊C4×C17C2311yescharacteristic
192C2×C4⋊C4×C17C2311yescharacteristic
193C2×C4⋊C4×C17C2311yescharacteristic
194C2×C4⋊C4×C17C2311yescharacteristic
195C2×C4⋊C4×C17C2311yescharacteristic
196C2×C4⋊C4×C17C2311yescharacteristic
197C2×C4⋊C4×C17C2311yescharacteristic
198C2×C4⋊C4×C17C2311yescharacteristic
199C2×C4⋊C4×C17C2311yescharacteristic
200C2×C4⋊C4×C17C2311yescharacteristic
201C2×C4⋊C4×C17C2311yescharacteristic
202C2×C4⋊C4×C17C2311yescharacteristic
203C2×C4⋊C4×C17C2311yescharacteristic
204C2×C4⋊C4×C17C2311yescharacteristic
205C2×C42×C17C2311yescharacteristic
206C2×C42×C17C2311yescharacteristic
207C2×C42×C17C2311yescharacteristic
208C2×C42×C17C2311yescharacteristic
209C2×C42×C17C2311yescharacteristic
210C2×C42×C17C2311yescharacteristic
211C2×C42×C17C2311yescharacteristic
212C2×C4⋊Dic17C2311yescharacteristic
213C2×C4⋊Dic17C2311yescharacteristic
214C2×C4⋊Dic17C2311yescharacteristic
215C2×C4⋊Dic17C2311yescharacteristic
216C2×C4⋊Dic17C2311yescharacteristic
217C2×C4⋊Dic17C2311yescharacteristic
218C2×C4⋊Dic17C2311yescharacteristic
219C2×C4⋊Dic17C2311yescharacteristic
220C2×C4⋊Dic17C2311yescharacteristic
221C2×C4⋊Dic17C2311yescharacteristic
222C2×C4⋊Dic17C2311yescharacteristic
223C2×C4⋊Dic17C2311yescharacteristic
224C2×#63225C2311yescharacteristic
225C2×#63225C2311yescharacteristic
226C2×#63225C2311yescharacteristic
227C2×#63225C2311yescharacteristic
228C2×#63225C2311yescharacteristic
229C2×#63225C2311yescharacteristic
230C2×#63225C2311yescharacteristic
231C2×#63225C2311yescharacteristic
232C2×#63225C2311yescharacteristic
233C2×#63225C2311yescharacteristic
234C2×#63225C2311yescharacteristic
235C2×#63225C2311yescharacteristic
236C2×#63225C2311yescharacteristic
237C2×#63225C2311yescharacteristic
238C2×#63225C2311yescharacteristic
239C2×#63225C2311yescharacteristic
240C2×#63225C2311yescharacteristic
241C2×#63225C2311yescharacteristic
242C2×#63225C2311yescharacteristic
243C2×#63225C2311yescharacteristic
244C2×#63225C2311yescharacteristic
245C2×#63225C2311yescharacteristic
246C2×#63225C2311yescharacteristic
247C2×#63225C2311yescharacteristic
248C2×#63225C2311yescharacteristic
249C2×#63225C2311yescharacteristic
250C2×#63225C2311yescharacteristic
251C2×#63225C2311yescharacteristic
252C2×#63225C2311yescharacteristic
253C2×#63225C2311yescharacteristic
254C2×#63225C2311yescharacteristic
255C2×#63225C2311yescharacteristic
256C2×C4×Dic17C2311yescharacteristic
257C2×C4×Dic17C2311yescharacteristic
258C2×C4×Dic17C2311yescharacteristic
259C2×C4×Dic17C2311yescharacteristic
260C2×C4×Dic17C2311yescharacteristic
261C2×C4×Dic17C2311yescharacteristic
262C2×C4×Dic17C2311yescharacteristic
263C2×C4×Dic17C2311yescharacteristic
264C2×C4×Dic17C2311yescharacteristic
265C2×C4×Dic17C2311yescharacteristic
266C2×C4×Dic17C2311yescharacteristic
267C2×C4×Dic17C2311yescharacteristic
268C2×C4×Dic17C2311yescharacteristic
269C2×C4×Dic17C2311yescharacteristic
270C2×C4×Dic17C2311yescharacteristic
271C2×C4×Dic17C2311yescharacteristic
272C2×C4×Dic17C2311yescharacteristic
273C2×C4×Dic17C2311yescharacteristic
274C2×C4×Dic17C2311yescharacteristic
275C2×C4×Dic17C2311yescharacteristic
276C2×C4×Dic17C2311yescharacteristic
277C2×C4×Dic17C2311yescharacteristic
278C2×C4×Dic17C2311yescharacteristic
279C2×C4×Dic17C2311yescharacteristic
280C2×C4×Dic17C2311yescharacteristic
281C2×C4×Dic17C2311yescharacteristic
282C2×C4×Dic17C2311yescharacteristic
283C2×C4×Dic17C2311yescharacteristic
284#10587576C2×C418yes—
285#10587576C2×C418yes—
286#10587576C2×C418yes—
287#10587576C2×C418yes—
288#10587575C2×C418yes—
289#10587575C2×C418yes—
290#10587575C2×C418yes—
291#10587575C2×C418yes—
292#10587575C2×C418yes—
293#10587575C2×C418yes—
294#10587575C2×C418yes—
295#10587575C2×C418yes—
296#10587556C2×C418yes—
297#10587556C2×C418yes—
298C17×#95C2311yescharacteristic
299C17×#95C2311yescharacteristic
300C17×#95C2311yescharacteristic
301C17×#95C2311yescharacteristic
302C17×#95C2311yescharacteristic
303C17×#95C2311yescharacteristic
304C17×#95C2311yescharacteristic
305C17×#95C2311yescharacteristic
306C17×#95C2311yescharacteristic
307C17×#95C2311yescharacteristic
308C17×#95C2311yescharacteristic
309C17×#95C2311yescharacteristic
310#10587502C2311yescharacteristic
311#10587502C2311yescharacteristic
312#10587502C2311yescharacteristic
313#10587502C2311yescharacteristic
314#10587502C2311yescharacteristic
315#10587502C2311yescharacteristic
316#10587502C2311yescharacteristic
317#10587502C2311yescharacteristic
318#10587502C2311yescharacteristic
319#10587502C2311yescharacteristic
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
358C22×C4×C17C2411yescharacteristic
359C22×C4×C17C2411yescharacteristic
360C22×C4×C17C2411yescharacteristic
361C22×C4×C17C2411yescharacteristic
362C22×C4×C17C2411yescharacteristic
363C22×C4×C17C2411yescharacteristic
364C22×C4×C17C2411yescharacteristic
365C22×C4×C17C2411yescharacteristic
366C22×C4×C17C2411yescharacteristic
367C22×C4×C17C2411yescharacteristic
368C22×C4×C17C2411yescharacteristic
369C22×C4×C17C2411yescharacteristic
370C22×C4×C17C2411yescharacteristic
371C22×C4×C17C2411yescharacteristic
372C22×C4×C17C2411yescharacteristic
373C22×Dic17C2411yescharacteristic
374C22×Dic17C2411yescharacteristic
375C22×Dic17C2411yescharacteristic
376C22×Dic17C2411yescharacteristic
377C22×Dic17C2411yescharacteristic
378C22×Dic17C2411yescharacteristic
379C22×Dic17C2411yescharacteristic
380C22×Dic17C2411yescharacteristic
381C22×Dic17C2411yescharacteristic
382C22×Dic17C2411yescharacteristic
383C22×Dic17C2411yescharacteristic
384C22×Dic17C2411yescharacteristic
385C22×Dic17C2411yescharacteristic
386C22×Dic17C2411yescharacteristic
387C22×Dic17C2411yescharacteristic
388C22×Dic17C2411yescharacteristic
389C4⋊C4×C17—41no—
390C4⋊C4×C17—41no—
391C4⋊C4×C17—41no—
392C4⋊C4×C17—41no—
393C4⋊C4×C17—41no—
394C4⋊C4×C17—41no—
395C4⋊C4×C17—41no—
396C4⋊C4×C17—41no—
397C4⋊C4×C17—41no—
398C4⋊C4×C17—41no—
399C4⋊C4×C17C22×C414yes—
400C4⋊C4×C17C22×C414yes—
401C4⋊C4×C17C22×C414yes—
402C4⋊C4×C17C22×C414yes—
403C4⋊C4×C17C22×C414yes—
404C4⋊C4×C17C22×C414yes—
405C42×C17—22no—
406C42×C17—41no—
407C42×C17—41no—
408C42×C17—41no—
409C42×C17—41no—
410C42×C17—41no—
411C42×C17C22×C414yes—
412C4⋊Dic17—22no—
413C4⋊Dic17—22no—
414C4⋊Dic17—41no—
415C4⋊Dic17—41no—
416C4⋊Dic17C22×C414yes—
417C4⋊Dic17C22×C414yes—
418C4⋊Dic17C22×C414yes—
419C4⋊Dic17C22×C414yes—
420C4⋊Dic17C22×C414yes—
421C4⋊Dic17C22×C414yes—
422C4⋊Dic17C22×C414yes—
423C4⋊Dic17C22×C414yes—
424#63225—22no—
425#63225—22no—
426#63225—22no—
427#63225—22no—
428#63225—41no—
429#63225—41no—
430#63225—41no—
431#63225—41no—
432#63225—41no—
433#63225—41no—
434#63225—41no—
435#63225—41no—
436#63225—41no—
437#63225—41no—
438#63225—41no—
439#63225—41no—
440#63225C22×C414yes—
441#63225C22×C414yes—
442#63225C22×C414yes—
443#63225C22×C414yes—
444#63225C22×C414yes—
445#63225C22×C414yes—
446#63225C22×C414yes—
447#63225C22×C414yes—
448#63225C22×C414yes—
449#63225C22×C414yes—
450#63225C22×C414yes—
451#63225C22×C414yes—
452#63225C22×C414yes—
453#63225C22×C414yes—
454#63225C22×C414yes—
455#63225C22×C414yes—
456C4×Dic17—22no—
457C4×Dic17—22no—
458C4×Dic17—22no—
459C4×Dic17—22no—
460C4×Dic17—22no—
461C4×Dic17—22no—
462C4×Dic17—22no—
463C4×Dic17—22no—
464C4×Dic17—41no—
465C4×Dic17—41no—
466C4×Dic17—41no—
467C4×Dic17—41no—
468C4×Dic17—41no—
469C4×Dic17—41no—
470C4×Dic17—41no—
471C4×Dic17—41no—
472C4×Dic17—41no—
473C4×Dic17—41no—
474C4×Dic17—41no—
475C4×Dic17—41no—
476C4×Dic17—41no—
477C4×Dic17—41no—
478C4×Dic17—41no—
479C4×Dic17—41no—
480C4×Dic17C22×C414yes—
481C4×Dic17C22×C414yes—
482C4×Dic17C22×C414yes—
483C4×Dic17C22×C414yes—
484#34530—171nomaximal, Sylow
485C23×C17C2511yescharacteristic
486C2×C4×C17—21no—
487C2×C4×C17—21no—
488C2×C4×C17—21no—
489C2×C4×C17—21no—
490C2×C4×C17—21no—
491C2×C4×C17—21no—
492C2×C4×C17—21no—
493C2×C4×C17—21no—
494C2×C4×C17—21no—
495C2×C4×C17—21no—
496C2×C4×C17—21no—
497C2×C4×C17—21no—
498C2×C4×C17—21no—
499C2×C4×C17—21no—
500C2×C4×C17—21no—
501C2×C4×C17—21no—
502C2×C4×C17—21no—
503C2×C4×C17—21no—
504C2×C4×C17—21no—
505C2×C4×C17—21no—
506C2×C4×C17—21no—
507C2×C4×C17—21no—
508C2×C4×C17—21no—
509C2×C4×C17—21no—
510C2×C4×C17—21no—
511C2×C4×C17—21no—
512C2×C4×C17—21no—
513C2×C4×C17—21no—
514C2×C4×C17—21no—
515C2×C4×C17—21no—
516C2×C4×C17—21no—
517C2×C4×C17—21no—
518C2×C4×C17—21no—
519C2×C4×C17—21no—
520C2×C4×C17—21no—
521C2×C4×C17—21no—
522C2×C4×C17—21no—
523C2×C4×C17C23×C412yes—
524C2×C4×C17C23×C412yes—
525C2×C4×C17C23×C412yes—
526C2×C4×C17C23×C412yes—
527C2×C4×C17C23×C412yes—
528C2×C4×C17C23×C412yes—
529C2×C4×C17C23×C412yes—
530C2×C4×C172−1+412yes—
531C2×Dic17—21no—
532C2×Dic17—21no—
533C2×Dic17—21no—
534C2×Dic17—21no—
535C2×Dic17—21no—
536C2×Dic17—21no—
537C2×Dic17—21no—
538C2×Dic17—21no—
539C2×Dic17—21no—
540C2×Dic17—21no—
541C2×Dic17—21no—
542C2×Dic17—21no—
543C2×Dic17—21no—
544C2×Dic17—21no—
545C2×Dic17—21no—
546C2×Dic17—21no—
547C2×Dic17—21no—
548C2×Dic17—21no—
549C2×Dic17—21no—
550C2×Dic17—21no—
551C2×Dic17—21no—
552C2×Dic17—21no—
553C2×Dic17—21no—
554C2×Dic17—21no—
555C2×Dic17—21no—
556C2×Dic17—21no—
557C2×Dic17—21no—
558C2×Dic17—21no—
559C2×Dic17—21no—
560C2×Dic17—21no—
561C2×Dic17—21no—
562C2×Dic17—21no—
563C2×Dic17—21no—
564C2×Dic17—21no—
565C2×Dic17—21no—
566C2×Dic17—21no—
567C2×Dic17—21no—
568C2×Dic17—21no—
569C2×Dic17C23×C412yes—
570C2×Dic17C23×C412yes—
571C2×Dic17C23×C412yes—
572C2×Dic17C23×C412yes—
573C2×Dic17C23×C412yes—
574C2×Dic17C23×C412yes—
575C2×Dic17C23×C412yes—
576C2×Dic17C23×C412yes—
577C2×Dic172−1+412yes—
578C2×Dic172−1+412yes—
579C2×#564—171no—
580#2382—171no—
581#2382—171no—
582#2382—171no—
583#2371—171no—
584#2371—171no—
585#2371—171no—
586#2371—171no—
587#2371—171no—
588#2371—171no—
589#2370—171no—
590#2370—171no—
591#2370—171no—
592#2370—171no—
593#2370—171no—
594#2370—171no—
595#2336—171no—
596#2336—171no—
597#2336—171no—
598#2336—171no—
599#2336—171no—
600#2336—171no—
601#2330—171no—
602#2330—171no—
603#2330—171no—
604#2330—171no—
605#2330—171no—
606#2330D1711yescharacteristic
607C4×#125—171no—
608C4×#125—171no—
609C4×#125—171no—
610C22×C17C24×C411yescharacteristic
611C22×C17C2×2−1+411yescharacteristic
612C22×C17C2×2−1+411yescharacteristic
613C22×C17C2×2−1+411yescharacteristic
614C22×C17#58511yescharacteristic
615C22×C17#58511yescharacteristic
616C22×C17#58511yescharacteristic
617C4×C17—22no—
618C4×C17—22no—
619C4×C17—22no—
620C4×C17—22no—
621C4×C17—22no—
622C4×C17—22no—
623C4×C17—22no—
624C4×C17—22no—
625C4×C17—41no—
626C4×C17—41no—
627C4×C17—41no—
628C4×C17—41no—
629C4×C17—41no—
630C4×C17—41no—
631C4×C17—41no—
632Dic17—22no—
633Dic17—22no—
634Dic17—22no—
635Dic17—22no—
636Dic17—22no—
637Dic17—22no—
638Dic17—22no—
639Dic17—22no—
640Dic17—22no—
641Dic17—22no—
642Dic17—41no—
643Dic17—41no—
644Dic17—41no—
645Dic17—41no—
646Dic17—41no—
647Dic17—41no—
648#564—1716no—
649C2×#125—171no—
650C2×#125—171no—
651C2×#125—171no—
652C2×#125—171no—
653C2×#125—171no—
654C2×#125—171no—
655C2×#125—171no—
656C2×#125—171no—
657C2×#125—171no—
658C2×#125—171no—
659C2×#125—171no—
660C2×#125—171no—
661C2×#125—171no—
662C2×#125—171no—
663C2×#125C2×D1711yescharacteristic
664#389—171no—
665#389—171no—
666#389—171no—
667#389—171no—
668#389—171no—
669#389—171no—
670#389—171no—
671#389—171no—
672#389—171no—
673#389—171no—
674#389—171no—
675#389—171no—
676#389—171no—
677#389—171no—
678#389—171no—
679#389—171no—
680#389—171no—
681#389—171no—
682#389—171no—
683#389—171no—
684#389—171no—
685#389—171no—
686#389—171no—
687#389—171no—
688#389C2×D1711yescharacteristic
689#389C2×D1711yescharacteristic
690#389C2×D1711yescharacteristic
691#389C2×D1711yescharacteristic
692#389C2×D1711yescharacteristic
693#389C2×D1711yescharacteristic
694#387—171no—
695#387—171no—
696#387—171no—
697#387—171no—
698#387—171no—
699#387—171no—
700#387—171no—
701#387—171no—
702#387—171no—
703#387—171no—
704#387—171no—
705#387—171no—
706#387—171no—
707#387—171no—
708#387—171no—
709#387—171no—
710#387—171no—
711#387—171no—
712#387—171no—
713#387—171no—
714#387—171no—
715#387—171no—
716#387—171no—
717#387—171no—
718#387—171no—
719#387—171no—
720#387—171no—
721#387—171no—
722#387—171no—
723#387—171no—
724#387—171no—
725#387—171no—
726#387—171no—
727#387—171no—
728#387—171no—
729#387—171no—
730#387—171no—
731#387—171no—
732#387—171no—
733#387—171no—
734#387—171no—
735#387—171no—
736#387—171no—
737#387—171no—
738#387—171no—
739#387—171no—
740#387—171no—
741#387—171no—
742#387—171no—
743#387—171no—
744#387—171no—
745#387—171no—
746#387—171no—
747#387—171no—
748#387—171no—
749#387—171no—
750#387C2×D1711yescharacteristic
751#387C2×D1711yescharacteristic
752#387C2×D1711yescharacteristic
753#387C2×D1711yescharacteristic
754#384—171no—
755#384C2×D1711yescharacteristic
756#383—171no—
757#383—171no—
758#382—171no—
759#382—171no—
760#382—171no—
761C4×C4⋊C4—171no—
762C4×C4⋊C4—171no—
763C4×C4⋊C4—171no—
764C4×C4⋊C4—171no—
765C4×C4⋊C4—171no—
766C4×C4⋊C4—171no—
767C4×C4⋊C4—171no—
768C4×C4⋊C4—171no—
769C4×C4⋊C4—171no—
770C4×C4⋊C4—171no—
771C4×C4⋊C4—171no—
772C4×C4⋊C4—171no—
773C4×C4⋊C4—171no—
774C4×C4⋊C4—171no—
775C4×C4⋊C4—171no—
776C4×C4⋊C4—171no—
777C4×C4⋊C4—171no—
778C4×C4⋊C4—171no—
779C4×C4⋊C4—171no—
780C4×C4⋊C4—171no—
781C4×C4⋊C4—171no—
782C4×C4⋊C4—171no—
783C4×C4⋊C4—171no—
784C4×C4⋊C4—171no—
785C4×C4⋊C4—171no—
786C4×C4⋊C4—171no—
787C4×C4⋊C4—171no—
788C4×C4⋊C4—171no—
789C4×C4⋊C4—171no—
790C4×C4⋊C4—171no—
791C4×C4⋊C4—171no—
792C4×C4⋊C4—171no—
793C4×C4⋊C4—171no—
794C4×C4⋊C4—171no—
795C4×C4⋊C4C2×D1711yescharacteristic
796C4×C4⋊C4C2×D1711yescharacteristic
797#376—171no—
798#376—171no—
799#376—171no—
800#376—171no—
801#376—171no—
802#376C2×D1711yescharacteristic
803C43—171no—
804C2×C17C4×2−1+411yescharacteristic
805C2×C17C4×2−1+411yescharacteristic
806C2×C17C4×2−1+411yescharacteristic
807C2×C17#356311yescharacteristic
808C2×C17#356311yescharacteristic
809C2×C17#356311yescharacteristic
810C2×C17#356711yescharacteristic
811#125—178no—
812#125—178no—
813#125—178no—
814#125—178no—
815#125—178no—
816#125—178no—
817#125—178no—
818#125—178no—
819#125—178no—
820#125—178no—
821#125—178no—
822#125—178no—
823#125—178no—
824#125—178no—
825#125C4×D1718yes—
826C2×C4⋊C4—171no—
827C2×C4⋊C4—171no—
828C2×C4⋊C4—171no—
829C2×C4⋊C4—171no—
830C2×C4⋊C4—171no—
831C2×C4⋊C4—171no—
832C2×C4⋊C4—171no—
833C2×C4⋊C4—171no—
834C2×C4⋊C4—171no—
835C2×C4⋊C4—171no—
836C2×C4⋊C4—171no—
837C2×C4⋊C4—171no—
838C2×C4⋊C4—171no—
839C2×C4⋊C4—171no—
840C2×C4⋊C4—171no—
841C2×C4⋊C4—171no—
842C2×C4⋊C4—171no—
843C2×C4⋊C4—171no—
844C2×C4⋊C4—171no—
845C2×C4⋊C4—171no—
846C2×C4⋊C4—171no—
847C2×C4⋊C4—171no—
848C2×C4⋊C4—171no—
849C2×C4⋊C4—171no—
850C2×C4⋊C4—171no—
851C2×C4⋊C4—171no—
852C2×C4⋊C4—171no—
853C2×C4⋊C4—171no—
854C2×C4⋊C4—171no—
855C2×C4⋊C4—171no—
856C2×C4⋊C4—171no—
857C2×C4⋊C4—171no—
858C2×C4⋊C4—171no—
859C2×C4⋊C4—171no—
860C2×C4⋊C4—171no—
861C2×C4⋊C4—171no—
862C2×C4⋊C4—171no—
863C2×C4⋊C4—171no—
864C2×C4⋊C4—171no—
865C2×C4⋊C4—171no—
866C2×C4⋊C4—171no—
867C2×C4⋊C4—171no—
868C2×C4⋊C4—171no—
869C2×C4⋊C4—171no—
870C2×C4⋊C4C22×D1711yescharacteristic
871C2×C4⋊C4C22×D1711yescharacteristic
872C2×C4⋊C4C22×D1711yescharacteristic
873C2×C4⋊C4C22×D1711yescharacteristic
874C2×C4⋊C4C22×D1711yescharacteristic
875C2×C4⋊C4C22×D1711yescharacteristic
876C2×C4⋊C4C22×D1711yescharacteristic
877C2×C4⋊C4C22×D1711yescharacteristic
878C2×C4⋊C4C22×D1711yescharacteristic
879C2×C4⋊C4C22×D1711yescharacteristic
880C2×C4⋊C4C22×D1711yescharacteristic
881C2×C4⋊C4C22×D1711yescharacteristic
882C2×C4⋊C4C22×D1711yescharacteristic
883C2×C4⋊C4C22×D1711yescharacteristic
884C2×C4⋊C4C22×D1711yescharacteristic
885C2×C4⋊C4C22×D1711yescharacteristic
886C2×C42—171no—
887C2×C42—171no—
888C2×C42—171no—
889C2×C42—171no—
890C2×C42—171no—
891C2×C42—171no—
892C2×C42—171no—
893C2×C42—171no—
894C2×C42—171no—
895C2×C42—171no—
896C2×C42—171no—
897C2×C42—171no—
898C2×C42—171no—
899C2×C42—171no—
900C2×C42—171no—
901C2×C42—171no—
902C2×C42—171no—
903C2×C42—171no—
904C2×C42—171no—
905C2×C42—171no—
906C2×C42—171no—
907C2×C42—171no—
908C2×C42—171no—
909C2×C42—171no—
910C2×C42—171no—
911C2×C42—171no—
912C2×C42—171no—
913C2×C42—171no—
914C2×C42C22×D1711yescharacteristic
915C2×C42C22×D1711yescharacteristic
916C2×C42C22×D1711yescharacteristic
917C2×C42C22×D1711yescharacteristic
918C2×C42C22×D1711yescharacteristic
919C2×C42C22×D1711yescharacteristic
920C2×C42C22×D1711yescharacteristic
921#95—171no—
922#95—171no—
923#95—171no—
924#95—171no—
925#95—171no—
926#95—171no—
927#95—171no—
928#95—171no—
929#95—171no—
930#95—171no—
931#95—171no—
932#95—171no—
933#95—171no—
934#95—171no—
935#95—171no—
936#95—171no—
937#95—171no—
938#95—171no—
939#95—171no—
940#95—171no—
941#95—171no—
942#95—171no—
943#95—171no—
944#95—171no—
945#95—171no—
946#95—171no—
947#95—171no—
948#95—171no—
949#95—171no—
950#95—171no—
951#95—171no—
952#95—171no—
953#95—171no—
954#95—171no—
955#95—171no—
956#95—171no—
957#95—171no—
958#95—171no—
959#95—171no—
960#95—171no—
961#95—171no—
962#95—171no—
963#95—171no—
964#95—171no—
965#95—171no—
966#95—171no—
967#95—171no—
968#95—171no—
969#95C22×D1711yescharacteristic
970#95C22×D1711yescharacteristic
971#95C22×D1711yescharacteristic
972#95C22×D1711yescharacteristic
973#95C22×D1711yescharacteristic
974#95C22×D1711yescharacteristic
975#95C22×D1711yescharacteristic
976#95C22×D1711yescharacteristic
977#95C22×D1711yescharacteristic
978#95C22×D1711yescharacteristic
979#95C22×D1711yescharacteristic
980#95C22×D1711yescharacteristic
981C17#3453011yescharacteristic, complemented, Sylow
982C22×C4—171no—
983C22×C4—171no—
984C22×C4—171no—
985C22×C4—171no—
986C22×C4—171no—
987C22×C4—171no—
988C22×C4—171no—
989C22×C4—171no—
990C22×C4—171no—
991C22×C4—171no—
992C22×C4—171no—
993C22×C4—171no—
994C22×C4—171no—
995C22×C4—171no—
996C22×C4—171no—
997C22×C4—171no—
998C22×C4C23×D1711yescharacteristic
999C22×C4C23×D1711yescharacteristic
1000C22×C4C23×D1711yescharacteristic
1001C22×C4C23×D1711yescharacteristic
1002C22×C4C23×D1711yescharacteristic
1003C22×C4C23×D1711yescharacteristic
1004C22×C4C23×D1711yescharacteristic
1005C22×C4C23×D1711yescharacteristic
1006C22×C4C23×D1711yescharacteristic
1007C22×C4C23×D1711yescharacteristic
1008C22×C4C23×D1711yescharacteristic
1009C22×C4C23×D1711yescharacteristic
1010C22×C4C23×D1711yescharacteristic
1011C22×C4C23×D1711yescharacteristic
1012C22×C4C23×D1711yescharacteristic
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—174no—
1024C4⋊C4—174no—
1025C4⋊C4—174no—
1026C4⋊C4—174no—
1027C4⋊C4—174no—
1028C4⋊C4—174no—
1029C4⋊C4—174no—
1030C4⋊C4—174no—
1031C4⋊C4—174no—
1032C4⋊C4—174no—
1033C4⋊C4—174no—
1034C4⋊C4—174no—
1035C4⋊C4—174no—
1036C4⋊C4—174no—
1037C4⋊C4—174no—
1038C4⋊C4—174no—
1039C4⋊C4—174no—
1040C4⋊C4—174no—
1041C4⋊C4—174no—
1042C4⋊C4—174no—
1043C4⋊C4—174no—
1044C4⋊C4—174no—
1045C4⋊C4—174no—
1046C4⋊C4—174no—
1047C4⋊C4—342no—
1048C4⋊C4—342no—
1049C4⋊C4—342no—
1050C4⋊C4—342no—
1051C4⋊C4—342no—
1052C4⋊C4—342no—
1053C4⋊C4—681no—
1054C4⋊C4—681no—
1055C4⋊C4—681no—
1056C4⋊C4—681no—
1057C4⋊C4—681no—
1058C4⋊C4—681no—
1059C4⋊C4—681no—
1060C4⋊C4—681no—
1061C4⋊C4—681no—
1062C4⋊C4—681no—
1063C4⋊C4—681no—
1064C4⋊C4—681no—
1065C4⋊C4—681no—
1066C4⋊C4—681no—
1067C4⋊C4C2×C4×D1714yes—
1068C4⋊C4C2×C4×D1714yes—
1069C4⋊C4C2×C4×D1714yes—
1070C4⋊C4C2×C4×D1714yes—
1071C4⋊C4C2×C4×D1714yes—
1072C4⋊C4C2×C4×D1714yes—
1073C42—22no—
1074C42—41no—
1075C42—41no—
1076C42—41no—
1077C42—41no—
1078C42—41no—
1079C42—174no—
1080C42—174no—
1081C42—174no—
1082C42—174no—
1083C42—342no—
1084C42—342no—
1085C42—342no—
1086C42—342no—
1087C42—342no—
1088C42—342no—
1089C42—342no—
1090C42—342no—
1091C42—681no—
1092C42—681no—
1093C42—681no—
1094C42—681no—
1095C42—681no—
1096C42—681no—
1097C42—681no—
1098C42—681no—
1099C42—681no—
1100C42—681no—
1101C42—681no—
1102C42—681no—
1103C42—681no—
1104C42—681no—
1105C42—681no—
1106C42—681no—
1107C42C2×C4×D1714yes—
1108C23C24×D1711yescharacteristic
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—172no—
1147C2×C4—172no—
1148C2×C4—172no—
1149C2×C4—172no—
1150C2×C4—172no—
1151C2×C4—172no—
1152C2×C4—172no—
1153C2×C4—172no—
1154C2×C4—172no—
1155C2×C4—172no—
1156C2×C4—341no—
1157C2×C4—341no—
1158C2×C4—341no—
1159C2×C4—341no—
1160C2×C4—341no—
1161C2×C4—341no—
1162C2×C4—341no—
1163C2×C4—341no—
1164C2×C4—341no—
1165C2×C4—341no—
1166C2×C4—341no—
1167C2×C4—341no—
1168C2×C4—341no—
1169C2×C4—341no—
1170C2×C4—341no—
1171C2×C4—341no—
1172C2×C4—341no—
1173C2×C4—341no—
1174C2×C4—341no—
1175C2×C4—341no—
1176C2×C4—341no—
1177C2×C4—341no—
1178C2×C4—341no—
1179C2×C4—341no—
1180C2×C4—341no—
1181C2×C4—341no—
1182C2×C4—341no—
1183C2×C4—341no—
1184C2×C4—341no—
1185C2×C4—341no—
1186C2×C4—341no—
1187C2×C4—341no—
1188C2×C4—341no—
1189C2×C4—341no—
1190C2×C4—341no—
1191C2×C4—341no—
1192C2×C4—341no—
1193C2×C4—341no—
1194C2×C4C22×C4×D1712yes—
1195C2×C4C22×C4×D1712yes—
1196C2×C4C22×C4×D1712yes—
1197C2×C4C22×C4×D1712yes—
1198C2×C4C22×C4×D1712yes—
1199C2×C4C22×C4×D1712yes—
1200C2×C4C22×C4×D1712yes—
1201C2×C4#1058769412yes—
1202C22C23×C4×D1711yescharacteristic
1203C222−1+4×D1711yescharacteristic
1204C222−1+4×D1711yescharacteristic
1205C22C2×#1058769411yescharacteristic
1206C22#1176364411yescharacteristic
1207C22#1176364411yescharacteristic
1208C22#1176364511yescharacteristic
1209C4—22no—
1210C4—22no—
1211C4—22no—
1212C4—22no—
1213C4—22no—
1214C4—22no—
1215C4—22no—
1216C4—22no—
1217C4—41no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—342no—
1225C4—342no—
1226C4—342no—
1227C4—342no—
1228C4—342no—
1229C4—342no—
1230C4—342no—
1231C4—342no—
1232C4—342no—
1233C4—342no—
1234C4—681no—
1235C4—681no—
1236C4—681no—
1237C4—681no—
1238C4—681no—
1239C4—681no—
1240C2#1454199511yescharacteristic
1241C2#1454199511yescharacteristic
1242C2C4×#1058769411yescharacteristic
1243C2#1454338211yescharacteristic
1244C2#1454338311yescharacteristic
1245C2#1454338611yescharacteristic
1246C2#1454346911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2330C2
socle, prime radical, cosocleC23×C17C25
hypercenter#2330D17
hypocenterC17#34530
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2330

Complements

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

NH ≅ G/Ntype
32. C17⋊#564C4semidirect
981. C17#34530semidirect

Maximal subgroups

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

subgroupindex
C2×C17⋊#5642
#145319672
#145319662
#145318902
#145318892
#145318882
#145318872
#145318862
#145318852
#145318832
#145318812
#145318792
#145318752
#145315872
#145315862
#145315842
#145315832
#145315822
#145315242
#145315232
#145315222
#145313432
#145313412
C4×#105875752
C17×#23302
#3453017