Finite Group Databasebeta

← #28605067

Subgroups — #28605067

Order 15104.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837474C211yesmaximal, characteristic
2#21427025C211yesmaximal, characteristic
3#21425070C211yesmaximal, characteristic, complemented
4#21425049C211yesmaximal, characteristic, complemented
5#21424530C211yesmaximal, characteristic, complemented
6#21424520C211yesmaximal, characteristic, complemented
7#21424409C211yesmaximal, characteristic, complemented
8#21424404C211yesmaximal, characteristic, complemented
9#21424186C211yesmaximal, characteristic, complemented
10#21424182C211yesmaximal, characteristic, complemented
11#21424111C211yesmaximal, characteristic, complemented
12#21423926C211yesmaximal, characteristic, complemented
13#21423815C211yesmaximal, characteristic, complemented
14C2×#16837164C211yesmaximal, characteristic, complemented
15C2×C59×#554C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×#14273686C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20#16837474—24no—
21C2×C4⋊(C59⋊C8)C2211yescharacteristic
22C2×#14273651C2211yescharacteristic
23C2×#14273651C2211yescharacteristic
24C2×#14273651C2211yescharacteristic
25C2×#14273651C2211yescharacteristic
26C2×C22⋊(C59⋊C8)C2211yescharacteristic
27C2×C22⋊(C59⋊C8)C2211yescharacteristic
28C2×#14273638C2211yescharacteristic
29#16837295—21no—
30#16837288—21no—
31#16837282—21no—
32#16837268C2211yescharacteristic
33#16837262C2211yescharacteristic
34#16837262C2211yescharacteristic
35C4×C4⋊Dic59C2211yescharacteristic
36C22⋊C4×Dic59—21no—
37#16837164C2211yescharacteristic
38#16837164C2211yescharacteristic
39#16837164C2211yescharacteristic
40#16837164C2211yescharacteristic
41#16837164C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49C59×#554—24no—
50C59×#554C418yescomplemented
51C2×C4⋊Q8×C59C2211yescharacteristic
52C2×#125×C59—21no—
53C2×C22⋊Q8×C59—21no—
54C2×C22⋊Q8×C59—21no—
55C2×C22⋊Q8×C59C2211yescharacteristic
56C2×C22⋊Q8×C59C2211yescharacteristic
57C2×C4×Q8×C59C2211yescharacteristic
58C2×C4×D4×C59—21no—
59C2×C4×D4×C59C2211yescharacteristic
60C22×C4⋊C4×C59C2211yescharacteristic
61C22×C4⋊C4×C59C2211yescharacteristic
62C23×Dic59—21no—
63C2×#11745664—22no—
64C2×#11745664—22no—
65C2×#11745664—41no—
66C22×C59⋊C8—22no—
67C22×C59⋊C8—22no—
68C22×C59⋊C8—41no—
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73#14273686—22no—
74#14273686—41no—
75C2×C4⋊Dic59—22no—
76C2×C4⋊Dic59—21no—
77C2×C4⋊Dic59—41no—
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85C2×C4×Dic59—21no—
86C2×C4×Dic59—21no—
87C4⋊(C59⋊C8)—22no—
88#14273651—22no—
89#14273651—22no—
90#14273651—41no—
91#14273651—41no—
92C22⋊(C59⋊C8)—22no—
93C22⋊(C59⋊C8)—22no—
94#14273638—22no—
95C59⋊#95—21no—
96C59⋊#95—21no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C22×Q8×C59—21no—
101C22×Q8×C59C2311yescharacteristic
102C22×D4×C59D411yescharacteristic
103C23×C4×C59—21no—
104C23×C4×C59—21no—
105C23×C4×C59C2311yescharacteristic
106C23×C4×C59C2311yescharacteristic
107C4⋊Q8×C59—22no—
108C4⋊Q8×C59C2×C414yescomplemented
109#125×C59—28no—
110C22⋊Q8×C59—22no—
111C22⋊Q8×C59—22no—
112C22⋊Q8×C59—28no—
113C22⋊Q8×C59—28no—
114C22⋊Q8×C59C2×C414yes—
115C22⋊Q8×C59C2×C414yescomplemented
116C4×Q8×C59—22no—
117C4×Q8×C59C2×C414yescomplemented
118C4×D4×C59—28no—
119C4×D4×C59C2×C414yes—
120C4×D4×C59D414yes—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59—21no—
123C2×C4⋊C4×C59—22no—
124C2×C4⋊C4×C59—22no—
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59—21no—
127C2×C4⋊C4×C59—21no—
128C2×C4⋊C4×C59—21no—
129C2×C4⋊C4×C59C2×C414yes—
130C2×C4⋊C4×C59C2×C414yescomplemented
131C2×C4⋊C4×C59D411yescharacteristic
132C2×C4⋊C4×C59C2311yescharacteristic
133C2×C4⋊C4×C59C2311yescharacteristic
134C2×C4⋊C4×C59C2311yescharacteristic
135C2×C22⋊C4×C59—21no—
136C2×C22⋊C4×C59—21no—
137C2×C22⋊C4×C59D411yescharacteristic
138C2×C22⋊C4×C59D411yescharacteristic
139C2×C42×C59—21no—
140C2×C42×C59C2311yescharacteristic
141C24×C59C2×D411yescharacteristic
142C24×C59C2×D411yescharacteristic
143C2×Q8×C59—24no—
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—81no—
150C2×Q8×C59—81no—
151C2×Q8×C59C22×C412yes—
152C2×D4×C59—22no—
153C2×D4×C59—22no—
154C2×D4×C59C22⋊C414yes—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—24no—
168C22×C4×C59—24no—
169C22×C4×C59—81no—
170C22×C4×C59—81no—
171C22×C4×C59—81no—
172C22×C4×C59—81no—
173C22×C4×C59C22×C412yes—
174C22×C4×C59C22×C412yes—
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59C2×D411yescharacteristic
178C22×C4×C59C2×D411yescharacteristic
179C22×C4×C59C2×D412yes—
180C22×C4×C59C2×D412yes—
181C22×C4×C59C2411yescharacteristic
182C22×Dic59—21no—
183C22×Dic59—21no—
184C22×Dic59—21no—
185C22×Dic59—21no—
186C22×Dic59—42no—
187C22×Dic59—42no—
188C22×Dic59—81no—
189C4⋊C4×C59—24no—
190C4⋊C4×C59—24no—
191C4⋊C4×C59—24no—
192C4⋊C4×C59—24no—
193C4⋊C4×C59—24no—
194C4⋊C4×C59—24no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59C22⋊C414yes—
199C4⋊C4×C59C22×C412yes—
200C4⋊C4×C59C22×C412yes—
201C4⋊C4×C59C22×C412yes—
202C22⋊C4×C59—24no—
203C22⋊C4×C59—24no—
204C22⋊C4×C59C22⋊C414yes—
205C22⋊C4×C59C22⋊C414yes—
206C42×C59—24no—
207C42×C59C22×C412yes—
208C42×C59C2×D412yes—
209C22⋊Dic59—42no—
210C22⋊Dic59—42no—
211C22⋊Dic59—81no—
212C4⋊Dic59—21no—
213C4⋊Dic59—21no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—42no—
220C4⋊Dic59#4112yes—
221C4×Dic59—42no—
222C4×Dic59—81no—
223#11745664—44no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—44no—
236C2×C59⋊C8#4112yes—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59C2×C22⋊C412yes—
248C23×C59C2×C22⋊C412yes—
249C23×C59#13712yes—
250C23×C59#13712yes—
251C23×C59C22×D411yescharacteristic
252Q8×C59—22no—
253Q8×C59—22no—
254Q8×C59—41no—
255Q8×C59—41no—
256Q8×C59—84no—
257D4×C59—28no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—84no—
287C2×C4×C59—84no—
288C2×C4×C59C2×C22⋊C412yes—
289C2×C4×C59C2×C22⋊C412yes—
290C2×C4×C59C2×C22⋊C412yes—
291C2×C4×C59C2×C22⋊C412yes—
292C2×C4×C59C23×C411yescharacteristic
293C2×C4×C59C22×D411yescharacteristic
294C2×C4×C59C2×#4111yescharacteristic
295C2×C4×C59C2×#4111yescharacteristic
296C2×C4×C59H(5,𝔽2)11yescharacteristic
297C2×C4×C592−1+411yescharacteristic
298C2×Dic59—22no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—84no—
311C59⋊C8—22no—
312C59⋊C8—41no—
313C59⋊C8—41no—
314C59⋊C8—41no—
315#22497—591nomaximal, Sylow
316C22×C59—22no—
317C22×C59—22no—
318C22×C59—22no—
319C22×C59—22no—
320C22×C59—22no—
321C22×C59—22no—
322C22×C59—22no—
323C22×C59—22no—
324C22×C59—22no—
325C22×C59—41no—
326C22×C59—41no—
327C22×C59—41no—
328C22×C59—41no—
329C22×C59#41914yes—
330C22×C59C22×C22⋊C411yescharacteristic
331C22×C59#54611yescharacteristic
332C22×C59#54711yescharacteristic
333C22×C59C2×#13711yescharacteristic
334C22×C59C2×#13711yescharacteristic
335C22×C59#57611yescharacteristic
336C22×C59#57711yescharacteristic
337C4×C59—22no—
338C4×C59—22no—
339C4×C59—22no—
340C4×C59—22no—
341C4×C59—42no—
342C4×C59—42no—
343C4×C59—42no—
344C4×C59—42no—
345C4×C59C4×#4111yescharacteristic
346C4×C59#52011yescharacteristic
347C4×C59#54611yescharacteristic
348C4×C59#54711yescharacteristic
349Dic59—42no—
350Dic59—81no—
351Dic59—81no—
352Dic59—81no—
353C2×#554D5911yescharacteristic
354C2×#435—591no—
355#2352—591no—
356#1993—591no—
357#1988—591no—
358#1894—591no—
359#1892—591no—
360#1873—591no—
361#1872—591no—
362#1824—591no—
363#1823—591no—
364#1805—591no—
365#1763—591no—
366#1736—591no—
367C2×#340—591no—
368C2×C59—24no—
369C2×C59—42no—
370C2×C59#233911yescharacteristic
371C2×C59C2×#41911yescharacteristic
372C2×C59#289711yescharacteristic
373C2×C59#331411yescharacteristic
374C2×C59#331611yescharacteristic
375C2×C59#334411yescharacteristic
376C2×C59#334611yescharacteristic
377C22×M16—591no—
378C23×C8—591no—
379#554—24no—
380#554Dic5918yescomplemented
381C2×C4⋊Q8C2×D5911yescharacteristic
382C2×#125—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8C2×D5911yescharacteristic
386C2×C22⋊Q8C2×D5911yescharacteristic
387C2×C4×Q8C2×D5911yescharacteristic
388C2×C4×D4—21no—
389C2×C4×D4C2×D5911yescharacteristic
390C2×#117—591no—
391C22×C4⋊C4—591no—
392C22×C4⋊C4C2×D5911yescharacteristic
393C22×C4⋊C4C2×D5911yescharacteristic
394#435—1184no—
395C2×C4⋊C8—591no—
396C2×#103—591no—
397C2×#103—591no—
398C2×#103—591no—
399C2×#103—591no—
400C2×C22⋊C8—591no—
401C2×C22⋊C8—591no—
402C2×#97—591no—
403#388—1181no—
404#387—1181no—
405#386—1181no—
406#382—591no—
407#380—591no—
408#380—591no—
409C4×C4⋊C4—591no—
410C4×C22⋊C4—1181no—
411#340—591no—
412#340—591no—
413#340—591no—
414#340—591no—
415#340—591no—
416#340—591no—
417#340—591no—
418#340—591no—
419#340—591no—
420#340—591no—
421#340—591no—
422#340—591no—
423C59#2249711yescharacteristic, complemented, Sylow
424C22×Q8—21no—
425C22×Q8C22×D5911yescharacteristic
426C22×D4C22⋊D5911yescharacteristic
427C23×C4—21no—
428C23×C4—21no—
429C23×C4—1181no—
430C23×C4C22×D5911yescharacteristic
431C23×C4C22×D5911yescharacteristic
432C2×M16—1182no—
433C2×M16—1182no—
434C2×M16—2361no—
435C22×C8—591no—
436C22×C8—591no—
437C22×C8—591no—
438C22×C8—591no—
439C22×C8—1182no—
440C22×C8—1182no—
441C22×C8—2361no—
442C4⋊Q8—22no—
443C4⋊Q8C2×Dic5914yescomplemented
444#125—28no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—28no—
448C22⋊Q8—28no—
449C22⋊Q8C2×Dic5914yes—
450C22⋊Q8C2×Dic5914yescomplemented
451C4×Q8—22no—
452C4×Q8C2×Dic5914yescomplemented
453C4×D4—28no—
454C4×D4C2×Dic5914yes—
455C4×D4C22⋊D5914yes—
456#117—1182no—
457#117—2361no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—591no—
467C2×C4⋊C4—591no—
468C2×C4⋊C4—591no—
469C2×C4⋊C4—591no—
470C2×C4⋊C4—1182no—
471C2×C4⋊C4—1181no—
472C2×C4⋊C4—2361no—
473C2×C4⋊C4C2×Dic5914yes—
474C2×C4⋊C4C2×Dic5914yescomplemented
475C2×C4⋊C4C22⋊D5911yescharacteristic
476C2×C4⋊C4C22×D5911yescharacteristic
477C2×C4⋊C4C22×D5911yescharacteristic
478C2×C4⋊C4C22×D5911yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—1181no—
482C2×C22⋊C4—1181no—
483C2×C22⋊C4—1181no—
484C2×C22⋊C4C22⋊D5911yescharacteristic
485C2×C22⋊C4C22⋊D5911yescharacteristic
486C2×C42—21no—
487C2×C42—1181no—
488C2×C42—1181no—
489C2×C42C22×D5911yescharacteristic
490C4⋊C8—1182no—
491#103—1182no—
492#103—1182no—
493#103—2361no—
494#103—2361no—
495C22⋊C8—1182no—
496C22⋊C8—1182no—
497#97—1182no—
498#95—1181no—
499#95—1181no—
500#95—1181no—
501#95—1181no—
502#95—1181no—
503C24C2×C22⋊D5911yescharacteristic
504C24C2×C22⋊D5911yescharacteristic
505C2×Q8—24no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—81no—
512C2×Q8—81no—
513C2×Q8C22×Dic5912yes—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4C22⋊Dic5914yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—1181no—
536C22×C4—1181no—
537C22×C4—1181no—
538C22×C4—1181no—
539C22×C4—4721no—
540C22×C4—2362no—
541C22×C4—2362no—
542C22×C4C22×Dic5912yes—
543C22×C4C22×Dic5912yes—
544C22×C4C2×C22⋊D5911yescharacteristic
545C22×C4C2×C22⋊D5911yescharacteristic
546C22×C4C2×C22⋊D5911yescharacteristic
547C22×C4C2×C22⋊D5911yescharacteristic
548C22×C4C2×C22⋊D5912yes—
549C22×C4C2×C22⋊D5912yes—
550C22×C4C23×D5911yescharacteristic
551M16—2364no—
552C2×C8—592no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8—1181no—
557C2×C8—1181no—
558C2×C8—1181no—
559C2×C8—1181no—
560C2×C8—1181no—
561C2×C8—1181no—
562C2×C8—1181no—
563C2×C8—1181no—
564C2×C8—2364no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—592no—
575C4⋊C4—1181no—
576C4⋊C4—1181no—
577C4⋊C4—1181no—
578C4⋊C4—1181no—
579C4⋊C4—1181no—
580C4⋊C4—1181no—
581C4⋊C4—1181no—
582C4⋊C4—2362no—
583C4⋊C4C22⋊Dic5914yes—
584C4⋊C4C22×Dic5912yes—
585C4⋊C4C22×Dic5912yes—
586C4⋊C4C22×Dic5912yes—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—4721no—
590C22⋊C4—2362no—
591C22⋊C4—2362no—
592C22⋊C4C22⋊Dic5914yes—
593C22⋊C4C22⋊Dic5914yes—
594C42—24no—
595C42—4721no—
596C42—2362no—
597C42C22×Dic5912yes—
598C42C2×C22⋊D5912yes—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23C2×C22⋊Dic5912yes—
610C23C2×C22⋊Dic5912yes—
611C23#1427375812yes—
612C23#1427375812yes—
613C23C22×C22⋊D5911yescharacteristic
614Q8—22no—
615Q8—22no—
616Q8—41no—
617Q8—41no—
618Q8—84no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4—1182no—
651C2×C4—4724no—
652C2×C4—2361no—
653C2×C4—2361no—
654C2×C4—2361no—
655C2×C4—2361no—
656C2×C4—2361no—
657C2×C4—2361no—
658C2×C4—2361no—
659C2×C4—2361no—
660C2×C4—2361no—
661C2×C4—2361no—
662C2×C4—2361no—
663C2×C4C2×C22⋊Dic5912yes—
664C2×C4C2×C22⋊Dic5912yes—
665C2×C4C2×C22⋊Dic5912yes—
666C2×C4C2×C22⋊Dic5912yes—
667C2×C4C23×Dic5911yescharacteristic
668C2×C4C22×C22⋊D5911yescharacteristic
669C2×C4#41×D5911yescharacteristic
670C2×C4#41×D5911yescharacteristic
671C2×C4#1427377311yescharacteristic
672C2×C4#1427377411yescharacteristic
673C8—1182no—
674C8—2361no—
675C8—2361no—
676C8—2361no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1683741114yes—
691C22C22×C22⋊Dic5911yescharacteristic
692C22#1683804011yescharacteristic
693C22#1683805111yescharacteristic
694C22C2×#1427375811yescharacteristic
695C22C2×#1427375811yescharacteristic
696C22#1683820511yescharacteristic
697C22#1683821311yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—4721no—
707C4—4721no—
708C4—4721no—
709C4—2362no—
710C4#41×Dic5911yescharacteristic
711C4#1683788511yescharacteristic
712C4#1683804011yescharacteristic
713C4#1683805111yescharacteristic
714C2—24no—
715C2—42no—
716C2#2142692611yescharacteristic
717C2C2×#1683741111yescharacteristic
718C2#2143262211yescharacteristic
719C2#2143617111yescharacteristic
720C2#2143620111yescharacteristic
721C2#2143654511yescharacteristic
722C2#2143657511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#554C2
socleC23×C59C22×D4
prime radicalC22×D4×C59D4
cosocleC22×C4×C59C24
hypercenterC2×#554D59
hypocenterC59#22497
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
3. #21425070C2semidirect
4. #21425049C2semidirect
5. #21424530C2semidirect
6. #21424520C2semidirect
7. #21424409C2semidirect
8. #21424404C2semidirect
9. #21424186C2semidirect
10. #21424182C2semidirect
11. #21424111C2semidirect
12. #21423926C2semidirect
13. #21423815C2semidirect
14. C2×#16837164C2semidirect
50. C59×#554C4semidirect
108. C4⋊Q8×C59C2×C4semidirect
115. C22⋊Q8×C59C2×C4semidirect
117. C4×Q8×C59C2×C4semidirect
130. C2×C4⋊C4×C59C2×C4semidirect
380. #554Dic59semidirect
423. C59#22497semidirect
443. C4⋊Q8C2×Dic59semidirect
450. C22⋊Q8C2×Dic59semidirect
452. C4×Q8C2×Dic59semidirect
474. C2×C4⋊C4C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#168374742
#214270252
#214250702
#214250492
#214245302
#214245202
#214244092
#214244042
#214241862
#214241822
#214241112
#214239262
#214238152
C2×#168371642
C2×C59×#5542
#2249759