Finite Group Databasebeta

← #17963657

Subgroups — #17963657

Order 4352.

1390 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×#11763760C211yesmaximal, characteristic
3C2×#11763758C211yesmaximal, characteristic
4C2×#11763755C211yesmaximal, characteristic
5#14543972C211yesmaximal, characteristic
6#14543972C211yesmaximal, characteristic
7#14543972C211yesmaximal, characteristic
8#14543972C211yesmaximal, characteristic
9#14543970C211yesmaximal, characteristic
10#14543969C211yesmaximal, characteristic
11#14543964C211yesmaximal, characteristic
12#14543964C211yesmaximal, characteristic
13#14543964C211yesmaximal, characteristic
14#14543960C211yesmaximal, 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#11763760—24no—
29#11763760—24no—
30#11763758—24no—
31#11763755—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—22no—
85C2×C4⋊#595—22no—
86C2×C4⋊#595—22no—
87C2×C4⋊#595—22no—
88C2×C4⋊#595—22no—
89C2×C4⋊#595—22no—
90C2×C4⋊#595—22no—
91C2×C4⋊#595—41no—
92C2×C4⋊#595—41no—
93C2×C4⋊#595—41no—
94C2×C4⋊#595—41no—
95C2×C4⋊#595—41no—
96C2×C4⋊#595—41no—
97C2×C4⋊#595—41no—
98C2×C4⋊#595—41no—
99C2×C4⋊#595—41no—
100C2×C4⋊#595—41no—
101C2×C4⋊#595—41no—
102C2×C4⋊#595—41no—
103C2×C4⋊#595—41no—
104C2×C4⋊#595—41no—
105C2×C4⋊#595—41no—
106C2×C4⋊#595—41no—
107C2×C4⋊#595D414yes—
108C2×C4×#595—22no—
109C2×C4×#595—22no—
110C2×C4×#595—22no—
111C2×C4×#595—41no—
112C2×C4×#595—41no—
113C2×C4×#595—41no—
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×D17D414yes—
129C4⋊C4×D17Q814yes—
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—22no—
139(C2×#595)⋊C4—22no—
140(C2×#595)⋊C4—22no—
141(C2×#595)⋊C4—22no—
142(C2×#595)⋊C4—41no—
143(C2×#595)⋊C4—41no—
144(C2×#595)⋊C4—41no—
145(C2×#595)⋊C4—41no—
146(C2×#595)⋊C4—41no—
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×#595—21no—
206C22×#595—21no—
207C22×#595—21no—
208C22×#595—21no—
209C22×#595—21no—
210C22×#595—21no—
211C22×#595—21no—
212C22×#595—21no—
213C22×#595—21no—
214C22×#595—21no—
215C22×#595—21no—
216C22×#595—21no—
217C22×#595C2×D412yes—
218C22×#595C2×D412yes—
219C22×#595C2×Q812yes—
220C22×#595C2×Q812yes—
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×D17C2×D412yes—
268C2×C4×D17C2×D412yes—
269C2×C4×D17C2×D412yes—
270C2×C4×D17C2×D412yes—
271C2×C4×D17C2×Q812yes—
272C2×C4×D17C2×Q812yes—
273C2×C4×D17C2×Q812yes—
274C2×C4×D17C2×Q812yes—
275C2×C4×D17#4112yes—
276C2×C4×D17#4112yes—
277C4⋊#595—44no—
278C4⋊#595—44no—
279C4⋊#595—44no—
280C4⋊#595—44no—
281C4⋊#595—44no—
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×C17C4⋊C414yescomplemented
291C42×C17—22no—
292C4⋊Dic17—22no—
293C4⋊Dic17C4⋊C414yescomplemented
294#63225—22no—
295#63225—22no—
296#63225C4⋊C414yescomplemented
297#63225C4⋊C414yescomplemented
298C4×Dic17—22no—
299C4×Dic17—22no—
300C4×Dic17—22no—
301#14406—171nomaximal, Sylow
302C23×C17C23×C411yescharacteristic
303C22×D17C22×D411yescharacteristic
304C22×D17C22×D411yescharacteristic
305C22×D17C22×Q811yescharacteristic
306C22×D17C22×Q811yescharacteristic
307C22×D17C2×#4111yescharacteristic
308C22×D17C2×#4111yescharacteristic
309C22×D17H(5,𝔽2)11yescharacteristic
310C22×D17H(5,𝔽2)11yescharacteristic
311C22×D17H(5,𝔽2)11yescharacteristic
312C22×D17H(5,𝔽2)11yescharacteristic
313C22×D172−1+411yescharacteristic
314C22×D172−1+411yescharacteristic
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—41no—
330C2×#595—41no—
331C2×#595—41no—
332C2×#595—41no—
333C2×#595—41no—
334C2×#595—41no—
335C2×#595—41no—
336C2×#595—41no—
337C2×#595—41no—
338C2×#595—41no—
339C2×#595—41no—
340C2×#595—41no—
341C2×#595—41no—
342C2×#595—41no—
343C2×#595—41no—
344C2×#595—41no—
345C2×#595—41no—
346C2×#595—41no—
347C2×#595—41no—
348C2×#595—41no—
349C2×#595—41no—
350C2×#595—41no—
351C2×#595—41no—
352C2×#595—41no—
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×#595—41no—
370C2×#595—41no—
371C2×#595—41no—
372C2×#595—41no—
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×C4⋊C412yes—
390C2×C4×C17C2×C4⋊C412yes—
391C2×C4×C17C2×C4⋊C412yes—
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×C4⋊C412yes—
411C2×Dic17C2×C4⋊C412yes—
412C2×Dic17C2×C4⋊C412yes—
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×#389—171no—
445C2×#387—171no—
446C2×#387—171no—
447C2×#384—171no—
448#1444—171no—
449#1444—171no—
450#1444—171no—
451#1444—171no—
452#1442—171no—
453#1441—171no—
454#1436—171no—
455#1436—171no—
456#1436—171no—
457#1434—171no—
458C22×C17C22×C4⋊C411yescharacteristic
459C22×C17C2×C4×D411yescharacteristic
460C22×C17C2×C4×Q811yescharacteristic
461C22×C17#52011yescharacteristic
462C22×C17#52011yescharacteristic
463C22×C17#52011yescharacteristic
464C22×C17#52011yescharacteristic
465C2×D17#53411yescharacteristic
466C2×D17#53511yescharacteristic
467C2×D17#53611yescharacteristic
468C2×D17#53611yescharacteristic
469C2×D17#53911yescharacteristic
470C2×D17#53911yescharacteristic
471C2×D17#54011yescharacteristic
472C2×D17#54111yescharacteristic
473C2×D17#54411yescharacteristic
474C2×D17#54411yescharacteristic
475C2×D17#54411yescharacteristic
476C2×D17#54411yescharacteristic
477C2×D17D4211yescharacteristic
478C2×D17#54611yescharacteristic
479C2×D17#54711yescharacteristic
480C2×D17D4×Q811yescharacteristic
481C2×D17D4×Q811yescharacteristic
482C2×D17D4×Q811yescharacteristic
483C2×D17#55011yescharacteristic
484C2×D17#55211yescharacteristic
485C2×D17#55411yescharacteristic
486C2×D17#55411yescharacteristic
487C2×D17#55711yescharacteristic
488C2×D17Q8211yescharacteristic
489C2×D17#56011yescharacteristic
490C2×D17#56311yescharacteristic
491C2×D17#56311yescharacteristic
492C2×D17#56311yescharacteristic
493#595—42no—
494#595—42no—
495#595—42no—
496#595—42no—
497#595—81no—
498#595—81no—
499#595—81no—
500#595—81no—
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×C4⋊C4—171no—
522C22×C4⋊C4—171no—
523C22×C4⋊C4—171no—
524C22×C4⋊C4—171no—
525C22×C4⋊C4—171no—
526C22×C4⋊C4—171no—
527C22×C42—171no—
528C22×C42—171no—
529C22×C42—171no—
530#389—344no—
531#389—344no—
532#387—171no—
533#387—171no—
534#387—171no—
535#387—171no—
536#387—171no—
537#387—171no—
538#387—171no—
539#387—344no—
540#387#59511yescharacteristic, complemented
541#384—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×C17#231711yescharacteristic
563C2×C17#232211yescharacteristic
564C2×C17#233011yescharacteristic
565C2×C17D4×C4⋊C411yescharacteristic
566C2×C17Q8×C4⋊C411yescharacteristic
567C2×C17#236011yescharacteristic
568C2×C17#238311yescharacteristic
569D17#267311yescharacteristic
570D17#267711yescharacteristic
571D17#271311yescharacteristic
572D17#272011yescharacteristic
573D17#272111yescharacteristic
574D17#273411yescharacteristic
575D17#279111yescharacteristic
576D17#279211yescharacteristic
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—171no—
598C2×C4⋊C4—171no—
599C2×C4⋊C4—171no—
600C2×C4⋊C4—174no—
601C2×C4⋊C4—342no—
602C2×C4⋊C4—342no—
603C2×C4⋊C4—342no—
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—342no—
613C2×C4⋊C4—342no—
614C2×C4⋊C4—342no—
615C2×C4⋊C4—342no—
616C2×C4⋊C4—681no—
617C2×C4⋊C4—681no—
618C2×C4⋊C4—681no—
619C2×C4⋊C4—681no—
620C2×C4⋊C4—681no—
621C2×C4⋊C4—681no—
622C2×C4⋊C4—681no—
623C2×C4⋊C4—681no—
624C2×C4⋊C4—681no—
625C2×C4⋊C4—681no—
626C2×C4⋊C4—681no—
627C2×C4⋊C4—681no—
628C2×C4⋊C4—681no—
629C2×C4⋊C4—681no—
630C2×C4⋊C4—681no—
631C2×C4⋊C4—681no—
632C2×C4⋊C4C2×#59511yescharacteristic
633C2×C4⋊C4C2×#59511yescharacteristic
634C2×C42—171no—
635C2×C42—171no—
636C2×C42—171no—
637C2×C42—342no—
638C2×C42—342no—
639C2×C42—342no—
640C2×C42—342no—
641C2×C42—342no—
642C2×C42—681no—
643C2×C42—681no—
644C2×C42—681no—
645C2×C42C2×#59511yescharacteristic
646#95—174no—
647#95—171no—
648#95—171no—
649#95—171no—
650#95—171no—
651#95—171no—
652#95—171no—
653#95—171no—
654#95—171no—
655#95—171no—
656#95—171no—
657#95—171no—
658#95—171no—
659#95—342no—
660#95—342no—
661#95—342no—
662#95—342no—
663#95—342no—
664#95—342no—
665#95—342no—
666#95—342no—
667#95—342no—
668#95—342no—
669#95—681no—
670#95—681no—
671#95—681no—
672#95—681no—
673#95—681no—
674#95C2×#59511yescharacteristic
675#95C2×#59511yescharacteristic
676#95C2×#59511yescharacteristic
677#95C2×#59511yescharacteristic
678C17#1440611yescharacteristic, complemented, Sylow
679C24—171no—
680C22×C4—171no—
681C22×C4—171no—
682C22×C4—171no—
683C22×C4—171no—
684C22×C4—171no—
685C22×C4—172no—
686C22×C4—172no—
687C22×C4—172no—
688C22×C4—172no—
689C22×C4—172no—
690C22×C4—172no—
691C22×C4—172no—
692C22×C4—172no—
693C22×C4—172no—
694C22×C4—172no—
695C22×C4—172no—
696C22×C4—172no—
697C22×C4—172no—
698C22×C4—172no—
699C22×C4—171no—
700C22×C4—171no—
701C22×C4—341no—
702C22×C4—341no—
703C22×C4—341no—
704C22×C4—341no—
705C22×C4—341no—
706C22×C4—341no—
707C22×C4—341no—
708C22×C4—341no—
709C22×C4—341no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
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—342no—
799C4⋊C4—684no—
800C4⋊C4—684no—
801C4⋊C4—684no—
802C4⋊C4—684no—
803C4⋊C4—684no—
804C4⋊C4—684no—
805C4⋊C4—684no—
806C4⋊C4—684no—
807C4⋊C4—684no—
808C4⋊C4—684no—
809C4⋊C4C4⋊#59514yescomplemented
810C42—22no—
811C42—342no—
812C42—342no—
813C42—342no—
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—172no—
848C2×C4—172no—
849C2×C4—172no—
850C2×C4—172no—
851C2×C4—172no—
852C2×C4—342no—
853C2×C4—342no—
854C2×C4—342no—
855C2×C4—342no—
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—341no—
873C2×C4—341no—
874C2×C4—341no—
875C2×C4—341no—
876C2×C4—341no—
877C2×C4—341no—
878C2×C4—341no—
879C2×C4—341no—
880C2×C4—341no—
881C2×C4—341no—
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—341no—
895C2×C4—341no—
896C2×C4—341no—
897C2×C4—341no—
898C2×C4—341no—
899C2×C4—341no—
900C2×C4—681no—
901C2×C4—681no—
902C2×C4—681no—
903C2×C4—681no—
904C2×C4—681no—
905C2×C4—681no—
906C2×C4—681no—
907C2×C4—681no—
908C2×C4—681no—
909C2×C4—681no—
910C2×C4—681no—
911C2×C4—681no—
912C2×C4—681no—
913C2×C4—681no—
914C2×C4—681no—
915C2×C4—681no—
916C2×C4—681no—
917C2×C4—681no—
918C2×C4—681no—
919C2×C4—681no—
920C2×C4—681no—
921C2×C4—681no—
922C2×C4—681no—
923C2×C4—681no—
924C2×C4—681no—
925C2×C4—681no—
926C2×C4—681no—
927C2×C4—681no—
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#1176387811yescharacteristic
989C22#1176387811yescharacteristic
990C22#1176387811yescharacteristic
991C22#1176387811yescharacteristic
992C4—22no—
993C4—22no—
994C4—22no—
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—342no—
1000C4—342no—
1001C4—342no—
1002C4—342no—
1003C4—342no—
1004C4—682no—
1005C4—682no—
1006C4—682no—
1007C4—682no—
1008C4—681no—
1009C4—681no—
1010C4—1361no—
1011C4—1361no—
1012C4—1361no—
1013C4—1361no—
1014C2—171no—
1015C2—171no—
1016C2—171no—
1017C2—171no—
1018C2—171no—
1019C2—171no—
1020C2—171no—
1021C2—171no—
1022C2#1454526511yescharacteristic
1023C2#1454527011yescharacteristic
1024C2#1454527811yescharacteristic
1025C2D4×C4⋊#59511yescharacteristic
1026C2Q8×C4⋊#59511yescharacteristic
1027C2#1454530811yescharacteristic
1028C2#1454533111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutator, socleC23×C17C23×C4
FittingC17×#387C4
prime radical, cosocleC23×D17C24
hypercenter#387#595
hypocenterC17#14406
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
51. #11762696C4semidirect
52. #11762695C4semidirect
53. #11762694C4semidirect
54. #11762693C4semidirect
55. #11762692C4semidirect
56. #11762691C4semidirect
57. #11762690C4semidirect
62. C17×#387C4semidirect
290. C4⋊C4×C17C4⋊C4semidirect
293. C4⋊Dic17C4⋊C4semidirect
296. #63225C4⋊C4semidirect
297. #63225C4⋊C4semidirect
540. #387#595semidirect
678. C17#14406semidirect
809. 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×#117637552
#145439722
#145439702
#145439692
#145439642
#145439602
D17×#3872
#1440617