Finite Group Databasebeta

← #29689114

Subgroups — #29689114

Order 15616.

1326 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840335C211yesmaximal, characteristic
2C2×#16839728C211yesmaximal, characteristic
3#21448408C211yesmaximal, characteristic
4#21446253C211yesmaximal, characteristic, complemented
5#21446250C211yesmaximal, characteristic, complemented
6#21446242C211yesmaximal, characteristic, complemented
7#21446130C211yesmaximal, characteristic, complemented
8#21446128C211yesmaximal, characteristic, complemented
9#21446125C211yesmaximal, characteristic, complemented
10#21446123C211yesmaximal, characteristic, complemented
11#21445913C211yesmaximal, characteristic, complemented
12#21445912C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445752C211yesmaximal, characteristic, complemented
15C61×#1892C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19#16840335—24no—
20#16840335C418yescomplemented
21C2×#14519776—21no—
22C2×#14519763—21no—
23C2×#14519762—21no—
24C2×#14519759—21no—
25C2×#14519757C2211yescharacteristic
26C2×#14519756C2211yescharacteristic
27C2×#14519753C2211yescharacteristic
28C2×#14519735C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37#16839728—24no—
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42#16839666—21no—
43#16839662—21no—
44#16839640—21no—
45#16839638—21no—
46#16839622C2211yescharacteristic
47#16839619C2211yescharacteristic
48#16839619C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C2×#11758222—41no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222C2×C414yes—
67C2×#11758222D414yes—
68C22×Dic122—21no—
69C22×Dic122D411yescharacteristic
70C22×Dic122C2311yescharacteristic
71C2×Q8×D61—22no—
72C2×Q8×D61—41no—
73C2×Q8×D61—41no—
74C2×Q8×D61—41no—
75C2×Q8×D61—41no—
76C2×Q8×D61C2×C414yescomplemented
77C22×D244D411yescharacteristic
78C22×C22⋊D61D411yescharacteristic
79C22×C22⋊D61D411yescharacteristic
80C22×C4×D61—21no—
81C22×C4×D61—21no—
82C22×C4×D61C2311yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C2×#11758194—22no—
85C2×#11758194—41no—
86C2×#11758194—41no—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89#14519776—28no—
90#14519763—28no—
91#14519762—28no—
92#14519759—28no—
93#14519757—22no—
94#14519757C2×C414yes—
95#14519756—22no—
96#14519756C2×C414yescomplemented
97#14519753—22no—
98#14519753C2×C414yes—
99#14519735—22no—
100#14519735—41no—
101#14519735—41no—
102#14519735C2×C414yescomplemented
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C4⋊C4×D61—41no—
111C4⋊C4×D61—41no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122#14519702—41no—
123#14519702—41no—
124#14519701—41no—
125#14519701—41no—
126#14519700—41no—
127#14519700—41no—
128#14519689—22no—
129#14519689—22no—
130#14519689—22no—
131#14519689—22no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C22×Q8×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C22×C8×C61—22no—
138C22×C8×C61—41no—
139C22×C8×C61—41no—
140C22×C8×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C22⋊Q8×C61—22no—
143C22⋊Q8×C61C2×C414yescomplemented
144C2×C4⋊C4×C61—21no—
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150#103×C61—41no—
151#103×C61—41no—
152#95×C61—21no—
153C24×C61C2×D411yescharacteristic
154C23×D61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61C22×C412yes—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61C22×C412yes—
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D412yes—
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—41no—
175C2×C22⋊D61—41no—
176C2×C22⋊D61—41no—
177C2×C22⋊D61—41no—
178C2×C22⋊D61C22⋊C414yes—
179C2×C22⋊D61C22⋊C414yes—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186Q8×D61—44no—
187Q8×D61—44no—
188Q8×D61—44no—
189Q8×D61—44no—
190#11758222—44no—
191#11758222—44no—
192#11758222—44no—
193#11758222—44no—
194C2×D244—41no—
195C2×D244—41no—
196C2×D244C22⋊C414yes—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—24no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—81no—
210C2×C4×D61—81no—
211C2×C4×D61C22×C412yes—
212C2×C4×D61C22×C412yes—
213C2×C4×D61C2×D412yes—
214C2×C4×D61C2×D412yes—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122—24no—
221C2×Dic122—41no—
222C2×Dic122—41no—
223C2×Dic122—42no—
224C2×Dic122—42no—
225C2×Dic122C22⋊C414yes—
226C2×Dic122C22×C412yes—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—44no—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61C22×C412yes—
241C22⋊C4×C61—24no—
242C22⋊C4×C61—81no—
243C22⋊Dic61—24no—
244C22⋊Dic61—81no—
245#11758198—24no—
246#11758198—24no—
247#11758198—24no—
248#11758198—42no—
249#11758198—81no—
250#11758198—81no—
251C4⋊Dic61—21no—
252C4⋊Dic61—24no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61C22×C412yes—
258#11758196—24no—
259#11758196—24no—
260#11758196—42no—
261C4×Dic61—24no—
262C4×Dic61—42no—
263#11758194—44no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61C2×C22⋊C412yes—
277C23×C61C22×D411yescharacteristic
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61C2×C22⋊C412yes—
291C22×D61C2×C22⋊C412yes—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—41no—
295Q8×C61—41no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61C2×C22⋊C412yes—
315C2×C4×C61C23×C411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61H(5,𝔽2)11yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C22⋊D61—44no—
322C22⋊D61—44no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61C2×C22⋊C412yes—
340C2×Dic61C2×C22⋊C412yes—
341D244—44no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—48no—
351C4×D61—84no—
352Dic122—22no—
353Dic122—22no—
354Dic122—44no—
355Dic122—48no—
356Dic122—41no—
357Dic122—41no—
358C8×C61—41no—
359C8×C61—41no—
360#92418—41no—
361#92418—41no—
362#21771—611nomaximal, Sylow
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61C22×C22⋊C411yescharacteristic
371C22×C61#53411yescharacteristic
372C22×C61#53411yescharacteristic
373C22×C61#57711yescharacteristic
374C22×C61#57711yescharacteristic
375C22×C61#57811yescharacteristic
376C22×C61#57811yescharacteristic
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C4×C61—22no—
392C4×C61—42no—
393C4×C61—42no—
394C4×C61—81no—
395C4×C61—81no—
396C4×C61#51811yescharacteristic
397C4×C61#51811yescharacteristic
398C4×C61#53411yescharacteristic
399C4×C61#53411yescharacteristic
400Dic61—22no—
401Dic61—22no—
402Dic61—42no—
403Dic61—42no—
404Dic61—81no—
405Dic61—81no—
406C2×#536—611no—
407C2×#408—611no—
408#2311—611no—
409#1894—611no—
410#1894—611no—
411#1892—611no—
412#1892D6111yescharacteristic, complemented
413#1873—611no—
414#1873—611no—
415#1872—611no—
416#1872—611no—
417#1825—611no—
418#1825—611no—
419#1787—611no—
420#1787—611no—
421C2×C61—42no—
422C2×C61#230811yescharacteristic
423C2×C61#289811yescharacteristic
424C2×C61#289811yescharacteristic
425C2×C61#320011yescharacteristic
426C2×C61#320111yescharacteristic
427C2×C61#320111yescharacteristic
428C2×C61#320211yescharacteristic
429D61—42no—
430D61—42no—
431C22×#41—611no—
432C23×Q8—611no—
433C22×M16—611no—
434C23×C8C2×D6111yescharacteristic
435#536—618no—
436#536—1224no—
437C2×C4⋊Q8—1221no—
438C2×#124—1221no—
439C2×#123—1221no—
440C2×#123—1221no—
441C2×C22⋊Q8—611no—
442C2×C22⋊Q8—611no—
443C2×C22⋊Q8—611no—
444C2×C22⋊Q8C2×D6111yescharacteristic
445C2×#117—611no—
446C2×#117—611no—
447C22×C4⋊C4—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#103C2×D6111yescharacteristic
455C2×#103C2×D6111yescharacteristic
456#408—1224no—
457C2×C22⋊C8—611no—
458C2×C22⋊C8—611no—
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461#391—1221no—
462#390—1221no—
463#386—1221no—
464#386—1221no—
465#380—611no—
466#380—611no—
467#380—611no—
468#380C2×D6111yescharacteristic
469#340—611no—
470#340—611no—
471#340—611no—
472#340—611no—
473#340—611no—
474#340—611no—
475#340C2×D6111yescharacteristic
476#340C2×D6111yescharacteristic
477C61#2177111yescharacteristic, complemented, Sylow
478C2×#41—614no—
479C2×#41—614no—
480C2×#41—2441no—
481C2×#41—2441no—
482C2×#41—2441no—
483C2×#41—2441no—
484C22×Q8—611no—
485C22×Q8—614no—
486C22×Q8—611no—
487C22×Q8—1221no—
488C22×Q8—1222no—
489C22×Q8—2441no—
490C22×Q8—2441no—
491C22×Q8—2441no—
492C22×Q8—2441no—
493C22×Q8C22×D6111yescharacteristic
494C22×D4—611no—
495C22×D4—611no—
496C22×D4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—1221no—
500C23×C4—1221no—
501C23×C4C22×D6111yescharacteristic
502C2×M16—1222no—
503C2×M16—2441no—
504C2×M16—2441no—
505C22×C8—22no—
506C22×C8—41no—
507C22×C8—41no—
508C22×C8—611no—
509C22×C8—611no—
510C22×C8C22×D6111yescharacteristic
511C22×C8C22×D6111yescharacteristic
512C4⋊Q8—1228no—
513#124—1228no—
514#123—1228no—
515#123—1228no—
516C22⋊Q8—22no—
517C22⋊Q8—614no—
518C22⋊Q8—614no—
519C22⋊Q8—614no—
520C22⋊Q8—1222no—
521C22⋊Q8—1222no—
522C22⋊Q8—1222no—
523C22⋊Q8C4×D6114yescomplemented
524#117—614no—
525#117—1222no—
526#117—2441no—
527#117—2441no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4—2441no—
537C2×C4⋊C4—2441no—
538C2×C4⋊C4C22×D6111yescharacteristic
539C2×C4⋊C4C22×D6111yescharacteristic
540C2×C4⋊C4C22×D6111yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C42—1221no—
552C2×C42—1221no—
553#103—41no—
554#103—41no—
555#103—2441no—
556#103—2441no—
557#103—2441no—
558#103—2441no—
559#103—2441no—
560#103—2441no—
561C22⋊C8—1222no—
562C22⋊C8—1222no—
563C22⋊C8—1222no—
564C22⋊C8—1222no—
565#95—21no—
566#95—1221no—
567#95—1221no—
568#95—1221no—
569C24—611no—
570C24—611no—
571C24D4×D6111yescharacteristic
572#41—2444no—
573#41—2444no—
574#41—2444no—
575#41—2444no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—614no—
582C2×Q8—612no—
583C2×Q8—1224no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—2441no—
590C2×Q8—2441no—
591C2×Q8—2442no—
592C2×Q8—2442no—
593C2×Q8—2444no—
594C2×Q8—2444no—
595C2×Q8—2444no—
596C2×Q8—2444no—
597C2×Q8C2×C4×D6112yes—
598C2×D4—614no—
599C2×D4—614no—
600C2×D4—614no—
601C2×D4—2441no—
602C2×D4—2441no—
603C2×D4—2441no—
604C2×D4—2441no—
605C2×D4—2441no—
606C2×D4—2441no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—612no—
618C22×C4—612no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—1224no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—4881no—
635C22×C4—4881no—
636C22×C4—2442no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4C2×C4×D6112yes—
640C22×C4D4×D6112yes—
641C22×C4D4×D6111yescharacteristic
642C22×C4C23×D6111yescharacteristic
643M16—2444no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—44no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C4⋊C4—21no—
658C4⋊C4—24no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—612no—
664C4⋊C4—1224no—
665C4⋊C4—1224no—
666C4⋊C4—1221no—
667C4⋊C4—1224no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—2442no—
673C4⋊C4C2×C4×D6112yes—
674C22⋊C4—24no—
675C22⋊C4—81no—
676C22⋊C4—1224no—
677C22⋊C4—1224no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C22⋊C4—4881no—
681C22⋊C4—4881no—
682C22⋊C4—4881no—
683C22⋊C4—2442no—
684C42—1224no—
685C42—2442no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—612no—
693C23—612no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23—1221no—
698C23—1221no—
699C23—1221no—
700C23—1221no—
701C23—1221no—
702C23—1221no—
703C23—1221no—
704C23—1221no—
705C23—1221no—
706C23C22⋊C4×D6112yes—
707C23C2×D4×D6111yescharacteristic
708Q8—22no—
709Q8—22no—
710Q8—41no—
711Q8—41no—
712Q8—1222no—
713Q8—1222no—
714Q8—2444no—
715Q8—2448no—
716Q8—2441no—
717Q8—2441no—
718D4—2444no—
719D4—2444no—
720D4—2444no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—612no—
740C2×C4—612no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—4884no—
756C2×C4—2448no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4C22⋊C4×D6112yes—
768C2×C4C22×C4×D6111yescharacteristic
769C2×C4C2×D4×D6111yescharacteristic
770C2×C4#1451982211yescharacteristic
771C2×C4#1451982211yescharacteristic
772C2×C4#1451982311yescharacteristic
773C2×C4#1451982311yescharacteristic
774C8—41no—
775C8—41no—
776C8—2441no—
777C8—2441no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—1222no—
786C22—1222no—
787C22—1222no—
788C22—1222no—
789C22—1222no—
790C22—1222no—
791C22—2441no—
792C22—2441no—
793C22—2441no—
794C22—2441no—
795C22—2441no—
796C22—2441no—
797C22—2441no—
798C22—2441no—
799C22C2×C22⋊C4×D6111yescharacteristic
800C22#1684032011yescharacteristic
801C22#1684032011yescharacteristic
802C22#1684056811yescharacteristic
803C22#1684056911yescharacteristic
804C22#1684057511yescharacteristic
805C22#1684057611yescharacteristic
806C4—22no—
807C4—42no—
808C4—42no—
809C4—81no—
810C4—81no—
811C4—1222no—
812C4—1222no—
813C4—4881no—
814C4—4881no—
815C4—2442no—
816C4—2442no—
817C4#1684023411yescharacteristic
818C4#1684023411yescharacteristic
819C4#1684032211yescharacteristic
820C4#1684032311yescharacteristic
821C2—42no—
822C2—2442no—
823C2—2442no—
824C2#2144839311yescharacteristic
825C2#2145434711yescharacteristic
826C2#2145434811yescharacteristic
827C2#2145668511yescharacteristic
828C2#2145669411yescharacteristic
829C2#2145670411yescharacteristic
830C2#2145670911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1892C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1892D61
hypocenterC61#21771
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
4. #21446253C2semidirect
5. #21446250C2semidirect
6. #21446242C2semidirect
7. #21446130C2semidirect
8. #21446128C2semidirect
9. #21446125C2semidirect
10. #21446123C2semidirect
11. #21445913C2semidirect
12. #21445912C2semidirect
13. #21445752C2semidirect
14. #21445752C2semidirect
15. C61×#1892C2semidirect
20. #16840335C4semidirect
76. C2×Q8×D61C2×C4semidirect
96. #14519756C2×C4semidirect
102. #14519735C2×C4semidirect
143. C22⋊Q8×C61C2×C4semidirect
412. #1892D61semidirect
477. C61#21771semidirect
523. C22⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403352
C2×#168397282
#214484082
#214462532
#214462502
#214462422
#214461302
#214461282
#214461252
#214461232
#214459132
#214459122
#214457522
C61×#18922
#2177161