Finite Group Databasebeta

← #17199595

Subgroups — #17199595

Order 4352.

1940 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763536C211yesmaximal, characteristic
2#14531968C211yesmaximal, characteristic
3#14531967C211yesmaximal, characteristic
4#14531966C211yesmaximal, characteristic
5#14531877C211yesmaximal, characteristic
6#14531875C211yesmaximal, characteristic
7#14531839C211yesmaximal, characteristic
8#14531839C211yesmaximal, characteristic
9#14531837C211yesmaximal, characteristic
10#14531738C211yesmaximal, characteristic
11#14531738C211yesmaximal, characteristic
12#14531736C211yesmaximal, characteristic
13#14531703C211yesmaximal, characteristic
14#14531701C211yesmaximal, characteristic
15#14531698C211yesmaximal, characteristic
16#14531590C211yesmaximal, characteristic
17#14531586C211yesmaximal, characteristic
18#14531584C211yesmaximal, characteristic
19#14531582C211yesmaximal, characteristic
20#14531522C211yesmaximal, characteristic
21#14531522C211yesmaximal, characteristic
22#14531499C211yesmaximal, characteristic
23#14531499C211yesmaximal, characteristic
24#14531433C211yesmaximal, characteristic
25#14531433C211yesmaximal, characteristic
26#14531432C211yesmaximal, characteristic
27#14531432C211yesmaximal, characteristic
28#14531355C211yesmaximal, characteristic
29#14531257C211yesmaximal, characteristic
30#14531257C211yesmaximal, characteristic
31C17×#2382C211yesmaximal, characteristic
32#11763536C4116yescomplemented
33C2×#10587574C2211yescharacteristic
34C2×#10587574C2211yescharacteristic
35C2×#10587574C2211yescharacteristic
36C2×#10587576C2211yescharacteristic
37C2×#10587575C2211yescharacteristic
38C2×#10587575C2211yescharacteristic
39C2×#10587575C2211yescharacteristic
40C2×#10587575C2211yescharacteristic
41C2×C4×Dic34C2211yescharacteristic
42C2×C4×Dic34C2211yescharacteristic
43C2×C4×Dic34C2211yescharacteristic
44C2×C4×Dic34C2211yescharacteristic
45C2×#10587573C2211yescharacteristic
46C2×#10587573C2211yescharacteristic
47C2×#10587573C2211yescharacteristic
48C2×#10587573C2211yescharacteristic
49C2×#10587573C2211yescharacteristic
50C2×#10587573C2211yescharacteristic
51C2×#10587573C2211yescharacteristic
52C2×#10587573C2211yescharacteristic
53#11762713C2211yescharacteristic
54#11762713C2211yescharacteristic
55#11762713C2211yescharacteristic
56#11762713C2211yescharacteristic
57#11762713C2211yescharacteristic
58#11762713C2211yescharacteristic
59#11762713C2211yescharacteristic
60#11762713C2211yescharacteristic
61#11762713C2211yescharacteristic
62#11762713C2211yescharacteristic
63#11762708C2211yescharacteristic
64#11762708C2211yescharacteristic
65#11762707C2211yescharacteristic
66#11762706C2211yescharacteristic
67#11762706C2211yescharacteristic
68#11762706C2211yescharacteristic
69#11762706C2211yescharacteristic
70#11762706C2211yescharacteristic
71#11762706C2211yescharacteristic
72#11762706C2211yescharacteristic
73#11762706C2211yescharacteristic
74#11762706C2211yescharacteristic
75#11762705C2211yescharacteristic
76#11762705C2211yescharacteristic
77#11762705C2211yescharacteristic
78#11762704C2211yescharacteristic
79#11762704C2211yescharacteristic
80#11762704C2211yescharacteristic
81#11762704C2211yescharacteristic
82#11762704C2211yescharacteristic
83#11762704C2211yescharacteristic
84#11762704C2211yescharacteristic
85#11762704C2211yescharacteristic
86#11762704C2211yescharacteristic
87#11762696C2211yescharacteristic
88#11762696C2211yescharacteristic
89#11762696C2211yescharacteristic
90#11762695C2211yescharacteristic
91#11762695C2211yescharacteristic
92#11762695C2211yescharacteristic
93#11762695C2211yescharacteristic
94#11762695C2211yescharacteristic
95#11762695C2211yescharacteristic
96#11762695C2211yescharacteristic
97#11762695C2211yescharacteristic
98#11762694C2211yescharacteristic
99#11762694C2211yescharacteristic
100#11762694C2211yescharacteristic
101#11762694C2211yescharacteristic
102#11762693C2211yescharacteristic
103#11762693C2211yescharacteristic
104#11762693C2211yescharacteristic
105#11762693C2211yescharacteristic
106#11762693C2211yescharacteristic
107#11762692C2211yescharacteristic
108#11762692C2211yescharacteristic
109#11762692C2211yescharacteristic
110#11762692C2211yescharacteristic
111#11762692C2211yescharacteristic
112#11762692C2211yescharacteristic
113#11762691C2211yescharacteristic
114#11762691C2211yescharacteristic
115#11762691C2211yescharacteristic
116#11762691C2211yescharacteristic
117#11762691C2211yescharacteristic
118#11762691C2211yescharacteristic
119#11762691C2211yescharacteristic
120#11762690C2211yescharacteristic
121#11762690C2211yescharacteristic
122#11762690C2211yescharacteristic
123#11762690C2211yescharacteristic
124#11762690C2211yescharacteristic
125#11762690C2211yescharacteristic
126#11762690C2211yescharacteristic
127#11762678C2211yescharacteristic
128#11762678C2211yescharacteristic
129#11762678C2211yescharacteristic
130#11762677C2211yescharacteristic
131#11762676C2211yescharacteristic
132#11762676C2211yescharacteristic
133#11762676C2211yescharacteristic
134#11762674C2211yescharacteristic
135#11762674C2211yescharacteristic
136#11762673C2211yescharacteristic
137#11762673C2211yescharacteristic
138#11762673C2211yescharacteristic
139#11762673C2211yescharacteristic
140#11762673C2211yescharacteristic
141#11762673C2211yescharacteristic
142C4⋊C4×Dic17C2211yescharacteristic
143C4⋊C4×Dic17C2211yescharacteristic
144C4⋊C4×Dic17C2211yescharacteristic
145C4⋊C4×Dic17C2211yescharacteristic
146C4⋊C4×Dic17C2211yescharacteristic
147C4⋊C4×Dic17C2211yescharacteristic
148C4×#63225C2211yescharacteristic
149C4×#63225C2211yescharacteristic
150C4×#63225C2211yescharacteristic
151C4×#63225C2211yescharacteristic
152C4×#63225C2211yescharacteristic
153C4×#63225C2211yescharacteristic
154C4×C4⋊Dic17C2211yescharacteristic
155C4×C4⋊Dic17C2211yescharacteristic
156#11762660C2211yescharacteristic
157#11762660C2211yescharacteristic
158#11762660C2211yescharacteristic
159#11762660C2211yescharacteristic
160#11762660C2211yescharacteristic
161#11762660C2211yescharacteristic
162#11762660C2211yescharacteristic
163#11762660C2211yescharacteristic
164#11762660C2211yescharacteristic
165#11762660C2211yescharacteristic
166#11762660C2211yescharacteristic
167#11762660C2211yescharacteristic
168#11762654C2211yescharacteristic
169#11762654C2211yescharacteristic
170#11762654C2211yescharacteristic
171#11762654C2211yescharacteristic
172C42×Dic17C2211yescharacteristic
173C2×C17×#125C2211yescharacteristic
174C17×#389C2211yescharacteristic
175C17×#389C2211yescharacteristic
176C17×#389C2211yescharacteristic
177C17×#389C2211yescharacteristic
178C17×#387C2211yescharacteristic
179C17×#387C2211yescharacteristic
180C17×#387C2211yescharacteristic
181C17×#387C2211yescharacteristic
182C17×#387C2211yescharacteristic
183C17×#387C2211yescharacteristic
184C17×#387C2211yescharacteristic
185C17×#387C2211yescharacteristic
186C17×#382C2211yescharacteristic
187C17×#382C2211yescharacteristic
188C22×Dic34C2311yescharacteristic
189C22×Dic34C2311yescharacteristic
190C22×Dic34C2311yescharacteristic
191C22×Dic34C2311yescharacteristic
192C17×#125C2×C418yes—
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×C4⋊C4×C17C2311yescharacteristic
206C2×C4⋊C4×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×#63225C2311yescharacteristic
223C2×#63225C2311yescharacteristic
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×C4×Dic17C2311yescharacteristic
255C2×C4×Dic17C2311yescharacteristic
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#10587575C2×C418yes—
286#10587575C2×C418yes—
287#10587575C2×C418yes—
288#10587575C2×C418yes—
289#10587574C2×C418yes—
290#10587574C2×C418yes—
291#10587574C2×C418yes—
292#10587573—42no—
293#10587573—42no—
294#10587573—42no—
295#10587573—42no—
296#10587573C2×C418yes—
297#10587573C2×C418yes—
298#10587573C2×C418yes—
299#10587573C2×C418yes—
300C4×Dic34—42no—
301C4×Dic34—42no—
302C4×Dic34C2×C418yes—
303C4×Dic34C2×C418yes—
304C17×#95C2311yescharacteristic
305C17×#95C2311yescharacteristic
306C17×#95C2311yescharacteristic
307C17×#95C2311yescharacteristic
308C17×#95C2311yescharacteristic
309C17×#95C2311yescharacteristic
310C17×#95C2311yescharacteristic
311C17×#95C2311yescharacteristic
312C17×#95C2311yescharacteristic
313C17×#95C2311yescharacteristic
314C17×#95C2311yescharacteristic
315C17×#95C2311yescharacteristic
316C17×#95C2311yescharacteristic
317C17×#95C2311yescharacteristic
318C17×#95C2311yescharacteristic
319C17×#95C2311yescharacteristic
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
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×C4×C17C2411yescharacteristic
374C22×C4×C17C2411yescharacteristic
375C22×C4×C17C2411yescharacteristic
376C22×C4×C17C2411yescharacteristic
377C22×C4×C17C2411yescharacteristic
378C22×C4×C17C2411yescharacteristic
379C22×Dic17C2411yescharacteristic
380C22×Dic17C2411yescharacteristic
381C22×Dic17C2411yescharacteristic
382C22×Dic17C2411yescharacteristic
383C22×Dic17C2411yescharacteristic
384C22×Dic17C2411yescharacteristic
385C22×Dic17C2411yescharacteristic
386C22×Dic17C2411yescharacteristic
387C22×Dic17C2411yescharacteristic
388C22×Dic17C2411yescharacteristic
389C22×Dic17C2411yescharacteristic
390C22×Dic17C2411yescharacteristic
391C22×Dic17C2411yescharacteristic
392C22×Dic17C2411yescharacteristic
393C22×Dic17C2411yescharacteristic
394C22×Dic17C2411yescharacteristic
395C2×Dic34—22no—
396C2×Dic34—22no—
397C2×Dic34—22no—
398C2×Dic34—22no—
399C2×Dic34—22no—
400C2×Dic34—22no—
401C2×Dic34—22no—
402C2×Dic34—22no—
403C2×Dic34C22×C414yes—
404C2×Dic34C22×C414yes—
405C2×Dic34C22×C414yes—
406C2×Dic34C22×C414yes—
407C4⋊C4×C17—41no—
408C4⋊C4×C17—41no—
409C4⋊C4×C17—41no—
410C4⋊C4×C17—41no—
411C4⋊C4×C17—41no—
412C4⋊C4×C17—41no—
413C4⋊C4×C17—41no—
414C4⋊C4×C17—41no—
415C4⋊C4×C17C22×C414yes—
416C4⋊C4×C17C22×C414yes—
417C4⋊C4×C17C22×C414yes—
418C4⋊C4×C17C22×C414yes—
419C4⋊C4×C17C22×C414yes—
420C4⋊C4×C17C22×C414yes—
421C42×C17—41no—
422C42×C17—41no—
423C42×C17—41no—
424C42×C17—41no—
425C42×C17C22×C414yes—
426C4⋊Dic17—22no—
427C4⋊Dic17—22no—
428C4⋊Dic17—41no—
429C4⋊Dic17—41no—
430C4⋊Dic17—41no—
431C4⋊Dic17—41no—
432C4⋊Dic17C22×C414yes—
433C4⋊Dic17C22×C414yes—
434C4⋊Dic17C22×C414yes—
435C4⋊Dic17C22×C414yes—
436#63225—22no—
437#63225—22no—
438#63225—22no—
439#63225—22no—
440#63225—22no—
441#63225—22no—
442#63225—22no—
443#63225—22no—
444#63225—22no—
445#63225—22no—
446#63225—41no—
447#63225—41no—
448#63225—41no—
449#63225—41no—
450#63225—41no—
451#63225—41no—
452#63225—41no—
453#63225—41no—
454#63225—41no—
455#63225—41no—
456#63225C22×C414yes—
457#63225C22×C414yes—
458#63225C22×C414yes—
459#63225C22×C414yes—
460#63225C22×C414yes—
461#63225C22×C414yes—
462#63225C22×C414yes—
463#63225C22×C414yes—
464#63225C22×C414yes—
465#63225C22×C414yes—
466#63225C22×C414yes—
467#63225C22×C414yes—
468C4×Dic17—22no—
469C4×Dic17—22no—
470C4×Dic17—22no—
471C4×Dic17—22no—
472C4×Dic17—22no—
473C4×Dic17—22no—
474C4×Dic17—22no—
475C4×Dic17—22no—
476C4×Dic17—22no—
477C4×Dic17—41no—
478C4×Dic17—41no—
479C4×Dic17—41no—
480C4×Dic17—41no—
481C4×Dic17—41no—
482C4×Dic17—41no—
483C4×Dic17—41no—
484C4×Dic17—41no—
485C4×Dic17—41no—
486C4×Dic17—41no—
487C4×Dic17—41no—
488C4×Dic17—41no—
489C4×Dic17—41no—
490C4×Dic17C22×C414yes—
491C4×Dic17C22×C414yes—
492C4×Dic17C22×C414yes—
493C4×Dic17C22×C414yes—
494C4×Dic17C22×C414yes—
495C4×Dic17C22×C414yes—
496C4×Dic17C22×C414yes—
497C4×Dic17C22×C414yes—
498#34488—171nomaximal, Sylow
499C23×C17C2511yescharacteristic
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×C17—21no—
524C2×C4×C17—21no—
525C2×C4×C17—21no—
526C2×C4×C17—21no—
527C2×C4×C17—21no—
528C2×C4×C17—21no—
529C2×C4×C17—21no—
530C2×C4×C17—21no—
531C2×C4×C17—21no—
532C2×C4×C17—21no—
533C2×C4×C17—21no—
534C2×C4×C17—21no—
535C2×C4×C17—21no—
536C2×C4×C17—21no—
537C2×C4×C17—21no—
538C2×C4×C17C23×C412yes—
539C2×C4×C17C23×C412yes—
540C2×C4×C17C23×C412yes—
541C2×C4×C17C23×C412yes—
542C2×C4×C17C23×C412yes—
543C2×C4×C17C23×C412yes—
544C2×C4×C17C23×C412yes—
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×Dic17—21no—
570C2×Dic17—21no—
571C2×Dic17—21no—
572C2×Dic17—21no—
573C2×Dic17—21no—
574C2×Dic17—21no—
575C2×Dic17—21no—
576C2×Dic17—21no—
577C2×Dic17—21no—
578C2×Dic17—21no—
579C2×Dic17—21no—
580C2×Dic17C23×C412yes—
581C2×Dic17C23×C412yes—
582C2×Dic17C23×C412yes—
583C2×Dic17C23×C412yes—
584C2×Dic17C23×C412yes—
585C2×Dic17C23×C412yes—
586C2×Dic17C23×C412yes—
587C2×Dic17C23×C412yes—
588C2×Dic17H(5,𝔽2)12yes—
589C2×Dic172−1+412yes—
590C2×Dic172−1+412yes—
591C2×Dic172−1+412yes—
592C2×Dic172−1+412yes—
593Dic34—28no—
594Dic34—28no—
595Dic34—28no—
596Dic34—28no—
597C2×#557—171no—
598#2382—171no—
599#2382—171no—
600#2382—171no—
601#2382D1711yescharacteristic
602#2370—171no—
603#2370—171no—
604#2365—171no—
605#2365—171no—
606#2365—171no—
607#2355—171no—
608#2355—171no—
609#2355—171no—
610#2351—171no—
611#2351—171no—
612Q8×C4⋊C4—171no—
613#2336—171no—
614#2336—171no—
615#2336—171no—
616#2336—171no—
617#2330—171no—
618#2330—171no—
619#2327—171no—
620#2327—171no—
621#2320—171no—
622#2320—171no—
623#2320—171no—
624#2320—171no—
625C4×C4⋊Q8—171no—
626#2295—171no—
627#2295—171no—
628C22×C17C24×C411yescharacteristic
629C22×C17C2×H(5,𝔽2)11yescharacteristic
630C22×C17C2×2−1+411yescharacteristic
631C22×C17C2×2−1+411yescharacteristic
632C22×C17C2×2−1+411yescharacteristic
633C22×C17C2×2−1+411yescharacteristic
634C22×C17#58511yescharacteristic
635C4×C17—22no—
636C4×C17—22no—
637C4×C17—22no—
638C4×C17—22no—
639C4×C17—22no—
640C4×C17—22no—
641C4×C17—22no—
642C4×C17—41no—
643C4×C17—41no—
644C4×C17—41no—
645C4×C17—41no—
646C4×C17—41no—
647C4×C17—41no—
648C4×C17—41no—
649C4×C17—41no—
650Dic17—22no—
651Dic17—22no—
652Dic17—22no—
653Dic17—22no—
654Dic17—22no—
655Dic17—22no—
656Dic17—22no—
657Dic17—41no—
658Dic17—41no—
659Dic17—41no—
660Dic17—41no—
661Dic17—41no—
662Dic17—41no—
663Dic17—41no—
664Dic17#51914yes—
665Dic17#52014yes—
666#557—1716no—
667C2×C4⋊Q8—171no—
668C2×C4⋊Q8—171no—
669C2×C4⋊Q8—171no—
670C2×#125—171no—
671C2×#125—171no—
672C2×#125—171no—
673C2×#125—171no—
674C2×#125—171no—
675C2×#125C2×D1711yescharacteristic
676C2×C4×Q8—171no—
677C2×C4×Q8—171no—
678C2×C4×Q8—171no—
679C2×C4×Q8—171no—
680C2×C4×Q8—171no—
681C2×C4×Q8—171no—
682C2×C4×Q8—171no—
683C2×C4×Q8—171no—
684C2×C4×Q8—171no—
685C2×C4×Q8—171no—
686C2×C4×Q8—171no—
687C2×C4×Q8—171no—
688#391—171no—
689#391—171no—
690#391—171no—
691#391—171no—
692#391—171no—
693#391—171no—
694#391—171no—
695#391—171no—
696#391—171no—
697#391—171no—
698#389—171no—
699#389—171no—
700#389—171no—
701#389—171no—
702#389—171no—
703#389—171no—
704#389—171no—
705#389—171no—
706#389—171no—
707#389—171no—
708#389—171no—
709#389—171no—
710#389—171no—
711#389—171no—
712#389—171no—
713#389—171no—
714#389—171no—
715#389—171no—
716#389—171no—
717#389—171no—
718#389—171no—
719#389—171no—
720#389—171no—
721#389—171no—
722#389C2×D1711yescharacteristic
723#389C2×D1711yescharacteristic
724#389C2×D1711yescharacteristic
725#389C2×D1711yescharacteristic
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#387—171no—
751#387—171no—
752#387—171no—
753#387—171no—
754#387—171no—
755#387—171no—
756#387—171no—
757#387—171no—
758#387—171no—
759#387—171no—
760#387—171no—
761#387—171no—
762#387—171no—
763#387—171no—
764#387—171no—
765#387—171no—
766#387C2×D1711yescharacteristic
767#387C2×D1711yescharacteristic
768#387C2×D1711yescharacteristic
769#387C2×D1711yescharacteristic
770#387C2×D1711yescharacteristic
771#387C2×D1711yescharacteristic
772#387C2×D1711yescharacteristic
773#387C2×D1711yescharacteristic
774#384—171no—
775#384—171no—
776#384—171no—
777#383—171no—
778#383—171no—
779#383—171no—
780#383—171no—
781#382—171no—
782#382—171no—
783#382—171no—
784#382—171no—
785#382—171no—
786#382—171no—
787#382—171no—
788#382—171no—
789#382C2×D1711yescharacteristic
790#382C2×D1711yescharacteristic
791C4×C4⋊C4—171no—
792C4×C4⋊C4—171no—
793C4×C4⋊C4—171no—
794C4×C4⋊C4—171no—
795C4×C4⋊C4—171no—
796C4×C4⋊C4—171no—
797C4×C4⋊C4—171no—
798C4×C4⋊C4—171no—
799C4×C4⋊C4—171no—
800C4×C4⋊C4—171no—
801C4×C4⋊C4—171no—
802C4×C4⋊C4—171no—
803C4×C4⋊C4—171no—
804C4×C4⋊C4—171no—
805C4×C4⋊C4—171no—
806C4×C4⋊C4—171no—
807C4×C4⋊C4—171no—
808C4×C4⋊C4—171no—
809C4×C4⋊C4—171no—
810C4×C4⋊C4—171no—
811C4×C4⋊C4—171no—
812C4×C4⋊C4—171no—
813C4×C4⋊C4—171no—
814C4×C4⋊C4—171no—
815C4×C4⋊C4—171no—
816C4×C4⋊C4—171no—
817#376—171no—
818#376—171no—
819#376—171no—
820#376—171no—
821C43—171no—
822C2×C17C2×#51911yescharacteristic
823C2×C17C2×#52011yescharacteristic
824C2×C17C4×2−1+411yescharacteristic
825C2×C17#355211yescharacteristic
826C2×C17#355411yescharacteristic
827C2×C17#355511yescharacteristic
828C2×C17#355611yescharacteristic
829C22×Q8—171no—
830C22×Q8—171no—
831C22×Q8—171no—
832C22×Q8—171no—
833C4⋊Q8—178no—
834C4⋊Q8—178no—
835C4⋊Q8—178no—
836#125—178no—
837#125—178no—
838#125—178no—
839#125—178no—
840#125—178no—
841#125C4×D1718yes—
842C4×Q8—178no—
843C4×Q8—178no—
844C4×Q8—178no—
845C4×Q8—178no—
846C4×Q8—178no—
847C4×Q8—178no—
848C4×Q8—682no—
849C4×Q8—682no—
850C4×Q8—682no—
851C4×Q8—682no—
852C4×Q8—682no—
853C4×Q8—682no—
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⋊C4—171no—
871C2×C4⋊C4—171no—
872C2×C4⋊C4—171no—
873C2×C4⋊C4—171no—
874C2×C4⋊C4—171no—
875C2×C4⋊C4—171no—
876C2×C4⋊C4—171no—
877C2×C4⋊C4—171no—
878C2×C4⋊C4—171no—
879C2×C4⋊C4—171no—
880C2×C4⋊C4—171no—
881C2×C4⋊C4—171no—
882C2×C4⋊C4—171no—
883C2×C4⋊C4—171no—
884C2×C4⋊C4—171no—
885C2×C4⋊C4—171no—
886C2×C4⋊C4—171no—
887C2×C4⋊C4—171no—
888C2×C4⋊C4—171no—
889C2×C4⋊C4—171no—
890C2×C4⋊C4—171no—
891C2×C4⋊C4—171no—
892C2×C4⋊C4—171no—
893C2×C4⋊C4—171no—
894C2×C4⋊C4—171no—
895C2×C4⋊C4—171no—
896C2×C4⋊C4C22×D1711yescharacteristic
897C2×C4⋊C4C22×D1711yescharacteristic
898C2×C4⋊C4C22×D1711yescharacteristic
899C2×C4⋊C4C22×D1711yescharacteristic
900C2×C4⋊C4C22×D1711yescharacteristic
901C2×C4⋊C4C22×D1711yescharacteristic
902C2×C4⋊C4C22×D1711yescharacteristic
903C2×C4⋊C4C22×D1711yescharacteristic
904C2×C4⋊C4C22×D1711yescharacteristic
905C2×C4⋊C4C22×D1711yescharacteristic
906C2×C4⋊C4C22×D1711yescharacteristic
907C2×C4⋊C4C22×D1711yescharacteristic
908C2×C4⋊C4C22×D1711yescharacteristic
909C2×C4⋊C4C22×D1711yescharacteristic
910C2×C42—171no—
911C2×C42—171no—
912C2×C42—171no—
913C2×C42—171no—
914C2×C42—171no—
915C2×C42—171no—
916C2×C42—171no—
917C2×C42—171no—
918C2×C42—171no—
919C2×C42—171no—
920C2×C42—171no—
921C2×C42—171no—
922C2×C42—171no—
923C2×C42—171no—
924C2×C42—171no—
925C2×C42—171no—
926C2×C42—171no—
927C2×C42—171no—
928C2×C42—171no—
929C2×C42—171no—
930C2×C42—171no—
931C2×C42—171no—
932C2×C42—171no—
933C2×C42—171no—
934C2×C42—171no—
935C2×C42—171no—
936C2×C42—171no—
937C2×C42—171no—
938C2×C42—171no—
939C2×C42—171no—
940C2×C42C22×D1711yescharacteristic
941C2×C42C22×D1711yescharacteristic
942C2×C42C22×D1711yescharacteristic
943C2×C42C22×D1711yescharacteristic
944C2×C42C22×D1711yescharacteristic
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#95—171no—
970#95—171no—
971#95—171no—
972#95—171no—
973#95—171no—
974#95—171no—
975#95—171no—
976#95—171no—
977#95—171no—
978#95—171no—
979#95—171no—
980#95—171no—
981#95—171no—
982#95—171no—
983#95—171no—
984#95—171no—
985#95—171no—
986#95—171no—
987#95—171no—
988#95—171no—
989#95C22×D1711yescharacteristic
990#95C22×D1711yescharacteristic
991#95C22×D1711yescharacteristic
992#95C22×D1711yescharacteristic
993#95C22×D1711yescharacteristic
994#95C22×D1711yescharacteristic
995#95C22×D1711yescharacteristic
996#95C22×D1711yescharacteristic
997#95C22×D1711yescharacteristic
998#95C22×D1711yescharacteristic
999#95C22×D1711yescharacteristic
1000#95C22×D1711yescharacteristic
1001#95C22×D1711yescharacteristic
1002#95C22×D1711yescharacteristic
1003#95C22×D1711yescharacteristic
1004#95C22×D1711yescharacteristic
1005C17#3448811yescharacteristic, complemented, Sylow
1006C2×Q8—174no—
1007C2×Q8—174no—
1008C2×Q8—174no—
1009C2×Q8—174no—
1010C2×Q8—342no—
1011C2×Q8—342no—
1012C2×Q8—342no—
1013C2×Q8—342no—
1014C2×Q8—342no—
1015C2×Q8—342no—
1016C2×Q8—342no—
1017C2×Q8—342no—
1018C22×C4—171no—
1019C22×C4—171no—
1020C22×C4—171no—
1021C22×C4—171no—
1022C22×C4—171no—
1023C22×C4—171no—
1024C22×C4—171no—
1025C22×C4—171no—
1026C22×C4—171no—
1027C22×C4—171no—
1028C22×C4—171no—
1029C22×C4—171no—
1030C22×C4—171no—
1031C22×C4—171no—
1032C22×C4—171no—
1033C22×C4—171no—
1034C22×C4C23×D1711yescharacteristic
1035C22×C4C23×D1711yescharacteristic
1036C22×C4C23×D1711yescharacteristic
1037C22×C4C23×D1711yescharacteristic
1038C22×C4C23×D1711yescharacteristic
1039C22×C4C23×D1711yescharacteristic
1040C22×C4C23×D1711yescharacteristic
1041C22×C4C23×D1711yescharacteristic
1042C22×C4C23×D1711yescharacteristic
1043C22×C4C23×D1711yescharacteristic
1044C22×C4C23×D1711yescharacteristic
1045C22×C4C23×D1711yescharacteristic
1046C22×C4C23×D1711yescharacteristic
1047C22×C4C23×D1711yescharacteristic
1048C22×C4C23×D1711yescharacteristic
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—174no—
1058C4⋊C4—174no—
1059C4⋊C4—174no—
1060C4⋊C4—174no—
1061C4⋊C4—174no—
1062C4⋊C4—174no—
1063C4⋊C4—174no—
1064C4⋊C4—174no—
1065C4⋊C4—174no—
1066C4⋊C4—174no—
1067C4⋊C4—174no—
1068C4⋊C4—174no—
1069C4⋊C4—174no—
1070C4⋊C4—174no—
1071C4⋊C4—174no—
1072C4⋊C4—174no—
1073C4⋊C4—342no—
1074C4⋊C4—342no—
1075C4⋊C4—342no—
1076C4⋊C4—342no—
1077C4⋊C4—342no—
1078C4⋊C4—342no—
1079C4⋊C4—342no—
1080C4⋊C4—342no—
1081C4⋊C4—342no—
1082C4⋊C4—342no—
1083C4⋊C4—342no—
1084C4⋊C4—342no—
1085C4⋊C4—681no—
1086C4⋊C4—681no—
1087C4⋊C4—681no—
1088C4⋊C4—681no—
1089C4⋊C4—681no—
1090C4⋊C4—681no—
1091C4⋊C4—681no—
1092C4⋊C4—681no—
1093C4⋊C4—681no—
1094C4⋊C4—681no—
1095C4⋊C4—681no—
1096C4⋊C4—681no—
1097C4⋊C4—681no—
1098C4⋊C4—681no—
1099C4⋊C4C2×C4×D1714yes—
1100C4⋊C4C2×C4×D1714yes—
1101C4⋊C4C2×C4×D1714yes—
1102C4⋊C4C2×C4×D1714yes—
1103C4⋊C4C2×C4×D1714yes—
1104C4⋊C4C2×C4×D1714yes—
1105C42—41no—
1106C42—41no—
1107C42—41no—
1108C42—41no—
1109C42—174no—
1110C42—174no—
1111C42—174no—
1112C42—174no—
1113C42—174no—
1114C42—174no—
1115C42—174no—
1116C42—174no—
1117C42—342no—
1118C42—342no—
1119C42—342no—
1120C42—342no—
1121C42—342no—
1122C42—342no—
1123C42—342no—
1124C42—342no—
1125C42—342no—
1126C42—681no—
1127C42—681no—
1128C42—681no—
1129C42—681no—
1130C42—681no—
1131C42—681no—
1132C42—681no—
1133C42—681no—
1134C42—681no—
1135C42—681no—
1136C42—681no—
1137C42—681no—
1138C42—681no—
1139C42C2×C4×D1714yes—
1140C23C24×D1711yescharacteristic
1141Q8—348no—
1142Q8—348no—
1143Q8—348no—
1144Q8—348no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—172no—
1184C2×C4—172no—
1185C2×C4—172no—
1186C2×C4—172no—
1187C2×C4—172no—
1188C2×C4—172no—
1189C2×C4—172no—
1190C2×C4—172no—
1191C2×C4—172no—
1192C2×C4—172no—
1193C2×C4—172no—
1194C2×C4—172no—
1195C2×C4—172no—
1196C2×C4—341no—
1197C2×C4—341no—
1198C2×C4—341no—
1199C2×C4—341no—
1200C2×C4—341no—
1201C2×C4—341no—
1202C2×C4—341no—
1203C2×C4—341no—
1204C2×C4—341no—
1205C2×C4—341no—
1206C2×C4—341no—
1207C2×C4—341no—
1208C2×C4—341no—
1209C2×C4—341no—
1210C2×C4—341no—
1211C2×C4—341no—
1212C2×C4—341no—
1213C2×C4—341no—
1214C2×C4—341no—
1215C2×C4—341no—
1216C2×C4—341no—
1217C2×C4—341no—
1218C2×C4—341no—
1219C2×C4—341no—
1220C2×C4—341no—
1221C2×C4—341no—
1222C2×C4—341no—
1223C2×C4—341no—
1224C2×C4—341no—
1225C2×C4—341no—
1226C2×C4—341no—
1227C2×C4—341no—
1228C2×C4—341no—
1229C2×C4—341no—
1230C2×C4—341no—
1231C2×C4C22×C4×D1712yes—
1232C2×C4C22×C4×D1712yes—
1233C2×C4C22×C4×D1712yes—
1234C2×C4C22×C4×D1712yes—
1235C2×C4C22×C4×D1712yes—
1236C2×C4C22×C4×D1712yes—
1237C2×C4C22×C4×D1712yes—
1238C22C23×C4×D1711yescharacteristic
1239C22H(5,𝔽2)×D1711yescharacteristic
1240C222−1+4×D1711yescharacteristic
1241C222−1+4×D1711yescharacteristic
1242C222−1+4×D1711yescharacteristic
1243C222−1+4×D1711yescharacteristic
1244C22#1176364411yescharacteristic
1245C4—22no—
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—22no—
1251C4—22no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—174no—
1261C4—174no—
1262C4—342no—
1263C4—342no—
1264C4—342no—
1265C4—342no—
1266C4—342no—
1267C4—342no—
1268C4—342no—
1269C4—681no—
1270C4—681no—
1271C4—681no—
1272C4—681no—
1273C4—681no—
1274C4—681no—
1275C4—681no—
1276C2D17×#51911yescharacteristic
1277C2D17×#52011yescharacteristic
1278C2#1454199511yescharacteristic
1279C2#1454321811yescharacteristic
1280C2#1454324611yescharacteristic
1281C2#1454326311yescharacteristic
1282C2#1454327811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2382C2
socle, prime radical, cosocleC23×C17C25
hypercenter#2382D17
hypocenterC17#34488
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2382

Complements

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

NH ≅ G/Ntype
32. #11763536C4semidirect
1005. C17#34488semidirect

Maximal subgroups

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

subgroupindex
C2×#117635362
#145319682
#145319672
#145319662
#145318772
#145318752
#145318392
#145318372
#145317382
#145317362
#145317032
#145317012
#145316982
#145315902
#145315862
#145315842
#145315822
#145315222
#145314992
#145314332
#145314322
#145313552
#145312572
C17×#23822
#3448817