Finite Group Databasebeta

← #17963070

Subgroups — #17963070

Order 4352.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763760C211yesmaximal, characteristic
2C2×#11763758C211yesmaximal, characteristic
3C2×C4⋊C4×#595C211yesmaximal, characteristic
4C2×C4×C4⋊#595C211yesmaximal, characteristic
5#14543964C211yesmaximal, characteristic
6#14543964C211yesmaximal, characteristic
7#14543964C211yesmaximal, characteristic
8#14543964C211yesmaximal, characteristic
9#14543964C211yesmaximal, characteristic
10#14543963C211yesmaximal, characteristic
11C4×(C2×#595)⋊C4C211yesmaximal, characteristic
12#95×#595C211yesmaximal, characteristic
13#95×#595C211yesmaximal, characteristic
14#95×#595C211yesmaximal, characteristic
15D17×#387C211yesmaximal, characteristic
16C22×C4⋊#595C2211yescharacteristic
17C22×C4⋊#595C2211yescharacteristic
18C22×C4⋊#595C2211yescharacteristic
19C22×C4⋊#595C2211yescharacteristic
20C22×C4×#595C2211yescharacteristic
21C22×C4×#595C2211yescharacteristic
22C22×C4×#595C2211yescharacteristic
23C22×C4×#595C2211yescharacteristic
24C22×C4×#595C2211yescharacteristic
25C22×C4×#595C2211yescharacteristic
26C22×C4×#595C2211yescharacteristic
27C22×C4×#595C2211yescharacteristic
28#11763760C418yescomplemented
29#11763758C418yescomplemented
30C4⋊C4×#595—24no—
31C4×C4⋊#595—24no—
32C2×(C2×#595)⋊C4C2211yescharacteristic
33C2×(C2×#595)⋊C4C2211yescharacteristic
34C2×(C2×#595)⋊C4C2211yescharacteristic
35C2×(C2×#595)⋊C4C2211yescharacteristic
36C2×(C2×#595)⋊C4C2211yescharacteristic
37C2×(C2×#595)⋊C4C2211yescharacteristic
38C2×(C2×#595)⋊C4C2211yescharacteristic
39C2×(C2×#595)⋊C4C2211yescharacteristic
40C2×(C2×#595)⋊C4C2211yescharacteristic
41C2×(C2×#595)⋊C4C2211yescharacteristic
42C2×(C2×#595)⋊C4C2211yescharacteristic
43C2×(C2×#595)⋊C4C2211yescharacteristic
44C2×(C2×#595)⋊C4C2211yescharacteristic
45C2×(C2×#595)⋊C4C2211yescharacteristic
46C2×(C2×#595)⋊C4C2211yescharacteristic
47C2×(C2×#595)⋊C4C2211yescharacteristic
48C2×C4⋊C4×D17C2211yescharacteristic
49C2×C4⋊C4×D17C2211yescharacteristic
50C2×C42×D17C2211yescharacteristic
51#11762696C411yescharacteristic, complemented
52#11762695C411yescharacteristic, complemented
53#11762694C411yescharacteristic, complemented
54#11762693C411yescharacteristic, complemented
55#11762692C411yescharacteristic, complemented
56#11762691C411yescharacteristic, complemented
57#11762690C411yescharacteristic, complemented
58#95×D17C2211yescharacteristic
59#95×D17C2211yescharacteristic
60#95×D17C2211yescharacteristic
61#95×D17C2211yescharacteristic
62C17×#387C411yescharacteristic, complemented
63C23×#595C2311yescharacteristic
64C23×#595C2311yescharacteristic
65C23×#595C2311yescharacteristic
66C23×#595C2311yescharacteristic
67C23×#595C2311yescharacteristic
68C23×#595C2311yescharacteristic
69C23×#595C2311yescharacteristic
70C23×#595C2311yescharacteristic
71C22×C4×D17C2311yescharacteristic
72C22×C4×D17C2311yescharacteristic
73C22×C4×D17C2311yescharacteristic
74C22×C4×D17C2311yescharacteristic
75C22×C4×D17C2311yescharacteristic
76C22×C4×D17C2311yescharacteristic
77C22×C4×D17C2311yescharacteristic
78C2×C4⋊#595—22no—
79C2×C4⋊#595—22no—
80C2×C4⋊#595—22no—
81C2×C4⋊#595—22no—
82C2×C4⋊#595—22no—
83C2×C4⋊#595—22no—
84C2×C4⋊#595—41no—
85C2×C4⋊#595—41no—
86C2×C4⋊#595C2×C414yes—
87C2×C4⋊#595C2×C414yes—
88C2×C4⋊#595C2×C414yes—
89C2×C4⋊#595C2×C414yes—
90C2×C4×#595—22no—
91C2×C4×#595—22no—
92C2×C4×#595—22no—
93C2×C4×#595—22no—
94C2×C4×#595—22no—
95C2×C4×#595—22no—
96C2×C4×#595—22no—
97C2×C4×#595—22no—
98C2×C4×#595—22no—
99C2×C4×#595—22no—
100C2×C4×#595—22no—
101C2×C4×#595—22no—
102C2×C4×#595—22no—
103C2×C4×#595—22no—
104C2×C4×#595—41no—
105C2×C4×#595—41no—
106C2×C4×#595—41no—
107C2×C4×#595—41no—
108C2×C4×#595—41no—
109C2×C4×#595—41no—
110C2×C4×#595—41no—
111C2×C4×#595—41no—
112C2×C4×#595C2×C414yes—
113C2×C4×#595C2×C414yes—
114C2×C4⋊C4×C17C2×C411yescharacteristic
115C2×C4⋊C4×C17C2×C411yescharacteristic
116C2×C42×C17C2×C411yescharacteristic
117C2×C4⋊Dic17C2×C411yescharacteristic
118C2×C4⋊Dic17C2×C411yescharacteristic
119C2×#63225C2×C411yescharacteristic
120C2×#63225C2×C411yescharacteristic
121C2×#63225C2×C411yescharacteristic
122C2×#63225C2×C411yescharacteristic
123C2×C4×Dic17C2×C411yescharacteristic
124C2×C4×Dic17C2×C411yescharacteristic
125C2×C4×Dic17C2×C411yescharacteristic
126C4⋊C4×D17—22no—
127C4⋊C4×D17—22no—
128C4⋊C4×D17C2×C414yes—
129C4⋊C4×D17C2×C414yes—
130C42×D17—22no—
131C42×D17—22no—
132(C2×#595)⋊C4—22no—
133(C2×#595)⋊C4—22no—
134(C2×#595)⋊C4—22no—
135(C2×#595)⋊C4—22no—
136(C2×#595)⋊C4—22no—
137(C2×#595)⋊C4—22no—
138(C2×#595)⋊C4—41no—
139(C2×#595)⋊C4—41no—
140(C2×#595)⋊C4C2×C414yes—
141(C2×#595)⋊C4C2×C414yes—
142(C2×#595)⋊C4C2×C414yes—
143(C2×#595)⋊C4C2×C414yes—
144(C2×#595)⋊C4C2×C414yes—
145(C2×#595)⋊C4C2×C414yes—
146(C2×#595)⋊C4D414yes—
147(C2×#595)⋊C4Q814yes—
148C17×#95C2×C411yescharacteristic
149C17×#95C2×C411yescharacteristic
150C17×#95C2×C411yescharacteristic
151C17×#95C2×C411yescharacteristic
152#10587502C2×C411yescharacteristic
153#10587502C2×C411yescharacteristic
154#10587502C2×C411yescharacteristic
155#10587502C2×C411yescharacteristic
156#10587502C2×C411yescharacteristic
157#10587502C2×C411yescharacteristic
158#10587502C2×C411yescharacteristic
159#10587502C2×C411yescharacteristic
160#10587502C2×C411yescharacteristic
161#10587502C2×C411yescharacteristic
162#10587502C2×C411yescharacteristic
163#10587502C2×C411yescharacteristic
164C23×D17C2411yescharacteristic
165C22×#595—21no—
166C22×#595—21no—
167C22×#595—21no—
168C22×#595—21no—
169C22×#595—21no—
170C22×#595—21no—
171C22×#595—21no—
172C22×#595—21no—
173C22×#595—21no—
174C22×#595—21no—
175C22×#595—21no—
176C22×#595—21no—
177C22×#595—21no—
178C22×#595—21no—
179C22×#595—21no—
180C22×#595—21no—
181C22×#595—21no—
182C22×#595—21no—
183C22×#595—21no—
184C22×#595—21no—
185C22×#595—21no—
186C22×#595—21no—
187C22×#595—21no—
188C22×#595—21no—
189C22×#595—21no—
190C22×#595—21no—
191C22×#595—21no—
192C22×#595—21no—
193C22×#595—21no—
194C22×#595—21no—
195C22×#595—21no—
196C22×#595—21no—
197C22×#595—21no—
198C22×#595—21no—
199C22×#595—21no—
200C22×#595—21no—
201C22×#595—21no—
202C22×#595—21no—
203C22×#595—21no—
204C22×#595—21no—
205C22×#595C22×C412yes—
206C22×#595C22×C412yes—
207C22×#595C22×C412yes—
208C22×#595C22×C412yes—
209C22×#595C22×C412yes—
210C22×#595C22×C412yes—
211C22×#595C22×C412yes—
212C22×#595C22×C412yes—
213C22×#595C2×D412yes—
214C22×#595C2×D412yes—
215C22×#595C2×Q812yes—
216C22×#595C2×Q812yes—
217C22×#595#4112yes—
218C22×#595#4112yes—
219C22×#595#4112yes—
220C22×#595#4112yes—
221C22×C4×C17C22×C411yescharacteristic
222C22×C4×C17C22×C411yescharacteristic
223C22×C4×C17C22×C411yescharacteristic
224C22×C4×C17C22×C411yescharacteristic
225C22×C4×C17C22×C411yescharacteristic
226C22×C4×C17C22×C411yescharacteristic
227C22×C4×C17C22×C411yescharacteristic
228C22×Dic17C22×C411yescharacteristic
229C22×Dic17C22×C411yescharacteristic
230C22×Dic17C22×C411yescharacteristic
231C22×Dic17C22×C411yescharacteristic
232C22×Dic17C22×C411yescharacteristic
233C22×Dic17C22×C411yescharacteristic
234C22×Dic17C22×C411yescharacteristic
235C2×C4×D17—21no—
236C2×C4×D17—21no—
237C2×C4×D17—21no—
238C2×C4×D17—21no—
239C2×C4×D17—21no—
240C2×C4×D17—21no—
241C2×C4×D17—21no—
242C2×C4×D17—21no—
243C2×C4×D17—21no—
244C2×C4×D17—21no—
245C2×C4×D17—21no—
246C2×C4×D17—21no—
247C2×C4×D17—21no—
248C2×C4×D17—21no—
249C2×C4×D17—21no—
250C2×C4×D17—21no—
251C2×C4×D17—21no—
252C2×C4×D17—21no—
253C2×C4×D17—21no—
254C2×C4×D17—21no—
255C2×C4×D17—21no—
256C2×C4×D17—21no—
257C2×C4×D17—21no—
258C2×C4×D17—21no—
259C2×C4×D17—21no—
260C2×C4×D17—21no—
261C2×C4×D17—21no—
262C2×C4×D17—21no—
263C2×C4×D17—21no—
264C2×C4×D17—21no—
265C2×C4×D17—21no—
266C2×C4×D17—21no—
267C2×C4×D17C22×C412yes—
268C2×C4×D17C22×C412yes—
269C2×C4×D17C22×C412yes—
270C2×C4×D17C22×C412yes—
271C2×C4×D17C22×C412yes—
272C2×C4×D17C22×C412yes—
273C2×C4×D17C2×D412yes—
274C2×C4×D17C2×Q812yes—
275C2×C4×D17#4112yes—
276C2×C4×D17#4112yes—
277C4⋊#595—28no—
278C4⋊#595—28no—
279C4⋊#595—28no—
280C4⋊#595—44no—
281C4×#595—28no—
282C4×#595—44no—
283C4×#595—44no—
284C4×#595—44no—
285C4×#595—44no—
286C4×#595—44no—
287C4×#595—44no—
288C4×#595—44no—
289C4⋊C4×C17—22no—
290C4⋊C4×C17C4214yescomplemented
291C42×C17—22no—
292C4⋊Dic17—22no—
293C4⋊Dic17C4214yescomplemented
294#63225—22no—
295#63225—22no—
296#63225C4214yescomplemented
297#63225C4214yescomplemented
298C4×Dic17—22no—
299C4×Dic17—22no—
300C4×Dic17—22no—
301#13825—171nomaximal, Sylow
302C23×C17C23×C411yescharacteristic
303C22×D17C23×C411yescharacteristic
304C22×D17C23×C411yescharacteristic
305C22×D17C22×D411yescharacteristic
306C22×D17C22×Q811yescharacteristic
307C22×D17C2×#4111yescharacteristic
308C22×D17C2×#4111yescharacteristic
309C22×D17C2×#4111yescharacteristic
310C22×D17C2×#4111yescharacteristic
311C22×D17C2×#4111yescharacteristic
312C22×D17C2×#4111yescharacteristic
313C22×D17H(5,𝔽2)11yescharacteristic
314C22×D17H(5,𝔽2)11yescharacteristic
315C22×D172−1+411yescharacteristic
316C22×D172−1+411yescharacteristic
317C2×#595—22no—
318C2×#595—22no—
319C2×#595—22no—
320C2×#595—22no—
321C2×#595—22no—
322C2×#595—22no—
323C2×#595—22no—
324C2×#595—22no—
325C2×#595—22no—
326C2×#595—22no—
327C2×#595—22no—
328C2×#595—22no—
329C2×#595—22no—
330C2×#595—22no—
331C2×#595—22no—
332C2×#595—22no—
333C2×#595—22no—
334C2×#595—22no—
335C2×#595—22no—
336C2×#595—22no—
337C2×#595—22no—
338C2×#595—22no—
339C2×#595—22no—
340C2×#595—22no—
341C2×#595—22no—
342C2×#595—22no—
343C2×#595—22no—
344C2×#595—22no—
345C2×#595—22no—
346C2×#595—22no—
347C2×#595—22no—
348C2×#595—22no—
349C2×#595—22no—
350C2×#595—22no—
351C2×#595—22no—
352C2×#595—22no—
353C2×#595—41no—
354C2×#595—41no—
355C2×#595—41no—
356C2×#595—41no—
357C2×#595—41no—
358C2×#595—41no—
359C2×#595—41no—
360C2×#595—41no—
361C2×#595—41no—
362C2×#595—41no—
363C2×#595—41no—
364C2×#595—41no—
365C2×#595—41no—
366C2×#595—41no—
367C2×#595—41no—
368C2×#595—41no—
369C2×#595C4×D414yes—
370C2×#595C4×D414yes—
371C2×#595C4×Q814yes—
372C2×#595C4×Q814yes—
373C2×C4×C17—21no—
374C2×C4×C17—21no—
375C2×C4×C17—21no—
376C2×C4×C17—21no—
377C2×C4×C17—21no—
378C2×C4×C17—21no—
379C2×C4×C17—21no—
380C2×C4×C17—21no—
381C2×C4×C17—21no—
382C2×C4×C17—21no—
383C2×C4×C17—21no—
384C2×C4×C17—21no—
385C2×C4×C17—21no—
386C2×C4×C17—21no—
387C2×C4×C17—21no—
388C2×C4×C17—21no—
389C2×C4×C17C2×C4212yes—
390C2×C4×C17C2×C4212yes—
391C2×C4×C17C2×C4212yes—
392C2×C4×C17C4×D412yes—
393C2×C4×C17C4×Q812yes—
394C2×Dic17—21no—
395C2×Dic17—21no—
396C2×Dic17—21no—
397C2×Dic17—21no—
398C2×Dic17—21no—
399C2×Dic17—21no—
400C2×Dic17—21no—
401C2×Dic17—21no—
402C2×Dic17—21no—
403C2×Dic17—21no—
404C2×Dic17—21no—
405C2×Dic17—21no—
406C2×Dic17—21no—
407C2×Dic17—21no—
408C2×Dic17—21no—
409C2×Dic17—21no—
410C2×Dic17C2×C4212yes—
411C2×Dic17C2×C4212yes—
412C2×Dic17C2×C4212yes—
413C2×Dic17C4×D412yes—
414C2×Dic17C4×Q812yes—
415C4×D17—22no—
416C4×D17—22no—
417C4×D17—22no—
418C4×D17—22no—
419C4×D17—22no—
420C4×D17—22no—
421C4×D17—22no—
422C4×D17—22no—
423C4×D17—22no—
424C4×D17—22no—
425C4×D17—22no—
426C4×D17—22no—
427C4×D17—22no—
428C4×D17—22no—
429C4×D17—22no—
430C4×D17—22no—
431C4×D17—22no—
432C4×D17—22no—
433C4×D17—22no—
434C4×D17—22no—
435C4×D17—41no—
436C4×D17—41no—
437C4×D17—41no—
438C4×D17—41no—
439C4×D17—41no—
440C4×D17—41no—
441C4×D17—41no—
442C4×D17—41no—
443C2×#389—171no—
444C2×#387—171no—
445C2×#387—171no—
446C2×C4×C4⋊C4—171no—
447C2×C4×C4⋊C4—171no—
448#1436—171no—
449#1436—171no—
450#1436—171no—
451#1436—171no—
452#1436—171no—
453#1436—171no—
454C4×#95—171no—
455C4×#95—171no—
456C4×#95—171no—
457C4×#95—171no—
458C22×C17C22×C4211yescharacteristic
459C22×C17C2×C4×D411yescharacteristic
460C22×C17C2×C4×Q811yescharacteristic
461C22×C17C4×#4111yescharacteristic
462C22×C17C4×#4111yescharacteristic
463C22×C17#52011yescharacteristic
464C22×C17#52011yescharacteristic
465C2×D17C2×C4×D411yescharacteristic
466C2×D17C2×C4×D411yescharacteristic
467C2×D17C2×C4×Q811yescharacteristic
468C2×D17C2×C4×Q811yescharacteristic
469C2×D17C4×#4111yescharacteristic
470C2×D17C4×#4111yescharacteristic
471C2×D17C4×#4111yescharacteristic
472C2×D17C4×#4111yescharacteristic
473C2×D17#51811yescharacteristic
474C2×D17#51911yescharacteristic
475C2×D17#52011yescharacteristic
476C2×D17#52011yescharacteristic
477C2×D17#54611yescharacteristic
478C2×D17#54611yescharacteristic
479C2×D17#54711yescharacteristic
480C2×D17D4×Q811yescharacteristic
481C2×D17#55111yescharacteristic
482C2×D17#55111yescharacteristic
483C2×D17#55211yescharacteristic
484C2×D17#55211yescharacteristic
485C2×D17#55211yescharacteristic
486C2×D17#55211yescharacteristic
487C2×D17#55311yescharacteristic
488C2×D17#55311yescharacteristic
489C2×D17#55411yescharacteristic
490C2×D17#55411yescharacteristic
491C2×D17#55611yescharacteristic
492C2×D17#55711yescharacteristic
493#595—24no—
494#595—24no—
495#595—24no—
496#595—24no—
497#595—42no—
498#595—42no—
499#595—42no—
500#595—42no—
501C4×C17—22no—
502C4×C17—22no—
503C4×C17—22no—
504C4×C17—22no—
505C4×C17—22no—
506C4×C17—41no—
507C4×C17—41no—
508Dic17—22no—
509Dic17—22no—
510Dic17—22no—
511Dic17—22no—
512Dic17—22no—
513Dic17—41no—
514Dic17—41no—
515C22×C4⋊C4—171no—
516C22×C4⋊C4—171no—
517C22×C4⋊C4—171no—
518C22×C4⋊C4—171no—
519C22×C4⋊C4—171no—
520C22×C4⋊C4—171no—
521C22×C42—171no—
522C22×C42—171no—
523C22×C42—171no—
524C22×C42—171no—
525C22×C42—171no—
526C22×C42—171no—
527C22×C42—171no—
528C22×C42—171no—
529C22×C42—171no—
530#389—178no—
531#387—178no—
532#387—171no—
533#387—171no—
534#387—171no—
535#387—171no—
536#387—171no—
537#387—171no—
538#387—171no—
539#387#59511yescharacteristic, complemented
540C4×C4⋊C4—344no—
541C4×C4⋊C4—344no—
542C2×#95—171no—
543C2×#95—171no—
544C2×#95—171no—
545C2×#95—171no—
546C2×#95—171no—
547C2×#95—171no—
548C2×#95—171no—
549C2×#95—171no—
550C2×#95—171no—
551C2×#95—171no—
552C2×#95—171no—
553C2×#95—171no—
554C2×#95—171no—
555C2×#95—171no—
556C2×#95—171no—
557C2×#95—171no—
558C2×#95—171no—
559C2×#95—171no—
560C2×#95—171no—
561C2×#95—171no—
562C2×C17C42×D411yescharacteristic
563C2×C17C42×Q811yescharacteristic
564C2×C17#227411yescharacteristic
565C2×C17#235911yescharacteristic
566C2×C17#236011yescharacteristic
567C2×C17#237011yescharacteristic
568C2×C17#237311yescharacteristic
569D17#235911yescharacteristic
570D17#236011yescharacteristic
571D17#236411yescharacteristic
572D17#236511yescharacteristic
573D17#236811yescharacteristic
574D17#237011yescharacteristic
575D17#237111yescharacteristic
576D17#237311yescharacteristic
577C23×C4—171no—
578C23×C4—171no—
579C23×C4—171no—
580C23×C4—171no—
581C23×C4—171no—
582C23×C4—171no—
583C23×C4—171no—
584C23×C4—171no—
585C23×C4—171no—
586C23×C4—171no—
587C23×C4—171no—
588C23×C4—171no—
589C23×C4—171no—
590C23×C4—171no—
591C23×C4—171no—
592C2×C4⋊C4—171no—
593C2×C4⋊C4—171no—
594C2×C4⋊C4—171no—
595C2×C4⋊C4—174no—
596C2×C4⋊C4—174no—
597C2×C4⋊C4—174no—
598C2×C4⋊C4—174no—
599C2×C4⋊C4—174no—
600C2×C4⋊C4—171no—
601C2×C4⋊C4—171no—
602C2×C4⋊C4—171no—
603C2×C4⋊C4—174no—
604C2×C4⋊C4—342no—
605C2×C4⋊C4—342no—
606C2×C4⋊C4—342no—
607C2×C4⋊C4—342no—
608C2×C4⋊C4—342no—
609C2×C4⋊C4—342no—
610C2×C4⋊C4—342no—
611C2×C4⋊C4—342no—
612C2×C4⋊C4—681no—
613C2×C4⋊C4—681no—
614C2×C4⋊C4C2×#59511yescharacteristic
615C2×C4⋊C4C2×#59511yescharacteristic
616C2×C42—174no—
617C2×C42—171no—
618C2×C42—171no—
619C2×C42—171no—
620C2×C42—174no—
621C2×C42—342no—
622C2×C42—342no—
623C2×C42—342no—
624C2×C42—342no—
625C2×C42—342no—
626C2×C42—342no—
627C2×C42—342no—
628C2×C42—342no—
629C2×C42—342no—
630C2×C42—342no—
631C2×C42—342no—
632C2×C42—342no—
633C2×C42—342no—
634C2×C42—342no—
635C2×C42—342no—
636C2×C42—342no—
637C2×C42—681no—
638C2×C42—681no—
639C2×C42—681no—
640C2×C42—681no—
641C2×C42—681no—
642C2×C42—681no—
643C2×C42—681no—
644C2×C42—681no—
645C2×C42C2×#59511yescharacteristic
646#95—174no—
647#95—174no—
648#95—174no—
649#95—174no—
650#95—174no—
651#95—174no—
652#95—174no—
653#95—174no—
654#95—171no—
655#95—171no—
656#95—171no—
657#95—171no—
658#95—171no—
659#95—171no—
660#95—171no—
661#95—171no—
662#95—171no—
663#95—171no—
664#95—171no—
665#95—171no—
666#95—342no—
667#95—342no—
668#95—342no—
669#95—342no—
670#95—342no—
671#95—342no—
672#95—681no—
673#95—681no—
674#95C2×#59511yescharacteristic
675#95C2×#59511yescharacteristic
676#95C2×#59511yescharacteristic
677#95C2×#59511yescharacteristic
678C17#1382511yescharacteristic, complemented, Sylow
679C24—171no—
680C22×C4—172no—
681C22×C4—172no—
682C22×C4—172no—
683C22×C4—172no—
684C22×C4—172no—
685C22×C4—172no—
686C22×C4—172no—
687C22×C4—172no—
688C22×C4—172no—
689C22×C4—172no—
690C22×C4—172no—
691C22×C4—172no—
692C22×C4—171no—
693C22×C4—171no—
694C22×C4—171no—
695C22×C4—171no—
696C22×C4—171no—
697C22×C4—172no—
698C22×C4—172no—
699C22×C4—172no—
700C22×C4—172no—
701C22×C4—172no—
702C22×C4—172no—
703C22×C4—172no—
704C22×C4—172no—
705C22×C4—172no—
706C22×C4—172no—
707C22×C4—172no—
708C22×C4—172no—
709C22×C4—172no—
710C22×C4—172no—
711C22×C4—171no—
712C22×C4—171no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—341no—
737C22×C4—341no—
738C22×C4—341no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4—341no—
746C22×C4—341no—
747C22×C4—341no—
748C22×C4—341no—
749C22×C4—341no—
750C22×C4—341no—
751C22×C4—341no—
752C22×C4—341no—
753C22×C4—341no—
754C22×C4—341no—
755C22×C4—341no—
756C22×C4—341no—
757C22×C4—341no—
758C22×C4—341no—
759C22×C4—341no—
760C22×C4—341no—
761C22×C4—341no—
762C22×C4—341no—
763C22×C4—341no—
764C22×C4—341no—
765C22×C4—341no—
766C22×C4—341no—
767C22×C4—341no—
768C22×C4—341no—
769C22×C4—341no—
770C22×C4—341no—
771C22×C4—341no—
772C22×C4—341no—
773C22×C4—341no—
774C22×C4—341no—
775C22×C4—341no—
776C22×C4—341no—
777C22×C4—341no—
778C22×C4—341no—
779C22×C4—341no—
780C22×C4—341no—
781C22×C4—341no—
782C22×C4—341no—
783C22×C4—341no—
784C22×C4—341no—
785C22×C4C22×#59511yescharacteristic
786C22×C4C22×#59511yescharacteristic
787C22×C4C22×#59511yescharacteristic
788C22×C4C22×#59511yescharacteristic
789C22×C4C22×#59511yescharacteristic
790C22×C4C22×#59511yescharacteristic
791C22×C4C22×#59511yescharacteristic
792C4⋊C4—22no—
793C4⋊C4—174no—
794C4⋊C4—174no—
795C4⋊C4—174no—
796C4⋊C4—342no—
797C4⋊C4—342no—
798C4⋊C4—348no—
799C4⋊C4—348no—
800C4⋊C4—348no—
801C4⋊C4—342no—
802C4⋊C4—684no—
803C4⋊C4C4×#59514yescomplemented
804C42—22no—
805C42—342no—
806C42—342no—
807C42—348no—
808C42—342no—
809C42—684no—
810C42—684no—
811C42—684no—
812C42—684no—
813C42—684no—
814C42—684no—
815C42—684no—
816C23—171no—
817C23—171no—
818C23—171no—
819C23—171no—
820C23—171no—
821C23—171no—
822C23—171no—
823C23—171no—
824C23—171no—
825C23—171no—
826C23—171no—
827C23—171no—
828C23—171no—
829C23—171no—
830C23C23×#59511yescharacteristic
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—174no—
848C2×C4—174no—
849C2×C4—174no—
850C2×C4—174no—
851C2×C4—172no—
852C2×C4—172no—
853C2×C4—172no—
854C2×C4—172no—
855C2×C4—172no—
856C2×C4—342no—
857C2×C4—342no—
858C2×C4—342no—
859C2×C4—342no—
860C2×C4—342no—
861C2×C4—342no—
862C2×C4—342no—
863C2×C4—342no—
864C2×C4—342no—
865C2×C4—342no—
866C2×C4—342no—
867C2×C4—342no—
868C2×C4—342no—
869C2×C4—342no—
870C2×C4—342no—
871C2×C4—342no—
872C2×C4—342no—
873C2×C4—342no—
874C2×C4—342no—
875C2×C4—342no—
876C2×C4—342no—
877C2×C4—342no—
878C2×C4—342no—
879C2×C4—342no—
880C2×C4—342no—
881C2×C4—342no—
882C2×C4—342no—
883C2×C4—342no—
884C2×C4—342no—
885C2×C4—342no—
886C2×C4—342no—
887C2×C4—342no—
888C2×C4—342no—
889C2×C4—342no—
890C2×C4—342no—
891C2×C4—342no—
892C2×C4—342no—
893C2×C4—342no—
894C2×C4—342no—
895C2×C4—342no—
896C2×C4—342no—
897C2×C4—342no—
898C2×C4—342no—
899C2×C4—342no—
900C2×C4—341no—
901C2×C4—341no—
902C2×C4—341no—
903C2×C4—341no—
904C2×C4—341no—
905C2×C4—341no—
906C2×C4—341no—
907C2×C4—341no—
908C2×C4—341no—
909C2×C4—341no—
910C2×C4—342no—
911C2×C4—342no—
912C2×C4—342no—
913C2×C4—342no—
914C2×C4—342no—
915C2×C4—342no—
916C2×C4—342no—
917C2×C4—342no—
918C2×C4—342no—
919C2×C4—342no—
920C2×C4—342no—
921C2×C4—342no—
922C2×C4—341no—
923C2×C4—341no—
924C2×C4—341no—
925C2×C4—341no—
926C2×C4—341no—
927C2×C4—341no—
928C2×C4—681no—
929C2×C4—681no—
930C2×C4—681no—
931C2×C4—681no—
932C2×C4—681no—
933C2×C4—681no—
934C2×C4—681no—
935C2×C4—681no—
936C2×C4—681no—
937C2×C4—681no—
938C2×C4—681no—
939C2×C4—681no—
940C2×C4—681no—
941C2×C4—681no—
942C2×C4—681no—
943C2×C4—681no—
944C2×C4—681no—
945C2×C4—681no—
946C2×C4—681no—
947C2×C4—681no—
948C2×C4—681no—
949C2×C4—681no—
950C2×C4—681no—
951C2×C4—681no—
952C2×C4C2×C4×#59512yes—
953C2×C4C2×C4×#59512yes—
954C2×C4C2×C4×#59512yes—
955C2×C4D4×#59512yes—
956C2×C4Q8×#59512yes—
957C22—171no—
958C22—171no—
959C22—171no—
960C22—171no—
961C22—171no—
962C22—171no—
963C22—171no—
964C22—171no—
965C22—171no—
966C22—171no—
967C22—171no—
968C22—171no—
969C22—171no—
970C22—171no—
971C22—171no—
972C22—171no—
973C22—171no—
974C22—171no—
975C22—171no—
976C22—171no—
977C22—171no—
978C22—171no—
979C22—171no—
980C22—171no—
981C22—171no—
982C22—171no—
983C22—171no—
984C22—171no—
985C22C22×C4×#59511yescharacteristic
986C22C2×D4×#59511yescharacteristic
987C22C2×Q8×#59511yescharacteristic
988C22#41×#59511yescharacteristic
989C22#41×#59511yescharacteristic
990C22#1176387811yescharacteristic
991C22#1176387811yescharacteristic
992C4—22no—
993C4—22no—
994C4—22no—
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—344no—
1000C4—344no—
1001C4—344no—
1002C4—344no—
1003C4—342no—
1004C4—342no—
1005C4—342no—
1006C4—342no—
1007C4—342no—
1008C4—682no—
1009C4—682no—
1010C4—682no—
1011C4—682no—
1012C4—681no—
1013C4—681no—
1014C2—171no—
1015C2—171no—
1016C2—171no—
1017C2—171no—
1018C2—171no—
1019C2—171no—
1020C2—171no—
1021C2—171no—
1022C2C4×D4×#59511yescharacteristic
1023C2C4×Q8×#59511yescharacteristic
1024C2#1454522111yescharacteristic
1025C2#1454530711yescharacteristic
1026C2#1454530811yescharacteristic
1027C2#1454531811yescharacteristic
1028C2#1454532111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC17×#387C4
socleC23×C17C23×C4
prime radical, cosocleC23×D17C24
hypercenter#387#595
hypocenterC17#13825
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
28. #11763760C4semidirect
29. #11763758C4semidirect
51. #11762696C4semidirect
52. #11762695C4semidirect
53. #11762694C4semidirect
54. #11762693C4semidirect
55. #11762692C4semidirect
56. #11762691C4semidirect
57. #11762690C4semidirect
62. C17×#387C4semidirect
290. C4⋊C4×C17C42semidirect
293. C4⋊Dic17C42semidirect
296. #63225C42semidirect
297. #63225C42semidirect
539. #387#595semidirect
678. C17#13825semidirect
803. C4⋊C4C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637602
C2×#117637582
C2×C4⋊C4×#5952
C2×C4×C4⋊#5952
#145439642
#145439632
C4×(C2×#595)⋊C42
#95×#5952
D17×#3872
#1382517