Finite Group Databasebeta

← #29718006

Subgroups — #29718006

Order 15616.

1404 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic122C211yesmaximal, characteristic
2C2×#16840018C211yesmaximal, characteristic, complemented
3C2×#16839917C211yesmaximal, characteristic, complemented
4C2×#16839917C211yesmaximal, characteristic, complemented
5C2×#16839770C211yesmaximal, characteristic, complemented
6#21447065C211yesmaximal, characteristic, complemented
7#21447015C211yesmaximal, characteristic, complemented
8#21446918C211yesmaximal, characteristic, complemented
9#21446827C211yesmaximal, characteristic, complemented
10#21446163C211yesmaximal, characteristic, complemented
11#21446131C211yesmaximal, characteristic, complemented
12#21446117C211yesmaximal, characteristic
13#21446086C211yesmaximal, characteristic, complemented
14#21445753C211yesmaximal, characteristic, complemented
15C61×#2415C211yesmaximal, characteristic
16C23×Dic122C2211yescharacteristic
17C23×Dic122C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21C22×#11758194C2211yescharacteristic
22D4×Dic122—24no—
23D4×Dic122—24no—
24C2×#14519777C2211yescharacteristic
25C2×#14519776—21no—
26C2×#14519756C2211yescharacteristic
27C2×#14519756C2211yescharacteristic
28C2×#14519754—21no—
29C2×#14519754—21no—
30C2×C4×Dic122C2211yescharacteristic
31C2×D4×Dic61—21no—
32#16840018—24no—
33#16839917—24no—
34#16839917—24no—
35C2×#14519708C2211yescharacteristic
36#16839770—24no—
37C2×#14519701C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44C2×#14519700C2211yescharacteristic
45C2×#14519700C2211yescharacteristic
46C2×#14519700C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic
48C2×C22⋊#92418C2211yescharacteristic
49C2×C22⋊#92418C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839517C2211yescharacteristic
53#16839517C2211yescharacteristic
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C2×#117×C61C2211yescharacteristic
58C61×#397—21no—
59C61×#394—21no—
60C61×#391C2211yescharacteristic
61C61×#389—21no—
62C61×#389C2211yescharacteristic
63C61×#388—21no—
64C61×#380C2211yescharacteristic
65C22×Dic122—22no—
66C22×Dic122—22no—
67C22×Dic122—21no—
68C22×Dic122—21no—
69C22×Dic122—22no—
70C22×Dic122—22no—
71C22×Dic122—22no—
72C22×Dic122—22no—
73C22×Dic122—22no—
74C22×Dic122—41no—
75C22×Dic122—41no—
76C22×Dic122—41no—
77C22×Dic122—41no—
78C22×Dic122D414yes—
79C22×Dic122C2311yescharacteristic
80C22×Dic122C2311yescharacteristic
81C22×Dic122C2311yescharacteristic
82C23×Dic61—21no—
83C23×Dic61—21no—
84C2×#11758202—22no—
85C2×#11758202—22no—
86C2×#11758202—22no—
87C2×#11758202—22no—
88C2×#11758202—22no—
89C2×#11758202—22no—
90C2×#11758202—41no—
91C2×#11758202—41no—
92C2×#11758202—41no—
93C2×#11758194—22no—
94C2×#11758194—22no—
95C2×#11758194—41no—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100#14519777—22no—
101#14519777—22no—
102#14519776—28no—
103#14519756—22no—
104#14519756—22no—
105#14519756—22no—
106#14519756D414yes—
107#14519754—28no—
108#14519754—28no—
109C4×Dic122—22no—
110C4×Dic122—22no—
111D4×Dic61—28no—
112C2×C4⋊Dic61—21no—
113C2×C4⋊Dic61—21no—
114C2×C4⋊Dic61C2311yescharacteristic
115C2×#11758196—21no—
116C2×#11758196—21no—
117C2×#11758196—21no—
118C2×C22⋊Dic61—21no—
119C2×C22⋊Dic61—21no—
120C2×C4×Dic61—21no—
121#14519708—22no—
122#14519701—22no—
123#14519700—22no—
124#14519700—22no—
125#14519700—22no—
126#14519700—22no—
127#14519700—22no—
128#14519700—22no—
129#14519700—22no—
130#14519700—41no—
131#14519700D414yescomplemented
132C22⋊#92418—22no—
133C22⋊#92418—22no—
134C22⋊#92418—41no—
135C22×Q8×C61C2311yescharacteristic
136C22×D4×C61D411yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C22⋊Q8×C61—22no—
140C22⋊Q8×C61—22no—
141C22⋊Q8×C61—22no—
142C22⋊Q8×C61—41no—
143C4×D4×C61—22no—
144C4×D4×C61—22no—
145#117×C61—22no—
146#117×C61—41no—
147C2×C4⋊C4×C61—21no—
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61—21no—
150C2×C4⋊C4×C61D411yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156C2×C22⋊C4×C61—21no—
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61D411yescharacteristic
159C2×C22⋊C4×C61D411yescharacteristic
160C2×C42×C61—21no—
161C2×C42×C61C2311yescharacteristic
162#95×C61—21no—
163#95×C61—21no—
164#95×C61—21no—
165#95×C61—21no—
166C24×C61C2×D411yescharacteristic
167C24×C61C2×D411yescharacteristic
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×D4×C61—22no—
175C2×D4×C61—22no—
176C2×D4×C61—22no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D412yes—
195C22×C4×C61C2×D412yes—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2411yescharacteristic
198C22×Dic61—21no—
199C22×Dic61—24no—
200C22×Dic61—24no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—42no—
205C22×Dic61—42no—
206C22×Dic61—42no—
207C22×Dic61—42no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—28no—
220C2×Dic122—24no—
221C2×Dic122—24no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—44no—
225C2×Dic122—44no—
226C2×Dic122—44no—
227C2×Dic122—44no—
228C2×Dic122—44no—
229C2×Dic122—44no—
230C2×Dic122—42no—
231C2×Dic122—42no—
232C2×Dic122—42no—
233C2×Dic122—42no—
234C2×Dic122—44no—
235C2×Dic122C2×D412yes—
236C2×Dic122C2×D412yes—
237C2×Dic122C2×D412yes—
238C2×Dic122C2×D412yes—
239C2×Dic122#4112yes—
240C4⋊C4×C61—22no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—42no—
247C4⋊C4×C61—42no—
248C4⋊C4×C61—42no—
249C4⋊C4×C61C2×D412yes—
250C22⋊C4×C61—22no—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—42no—
255C22⋊C4×C61—42no—
256C42×C61—21no—
257C42×C61—21no—
258C42×C61—42no—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261#11758202—44no—
262#11758202—44no—
263#11758202—44no—
264C4⋊Dic61—24no—
265C4⋊Dic61—24no—
266C4⋊Dic61—21no—
267C4⋊Dic61C2×D412yes—
268#11758196—24no—
269#11758196—24no—
270#11758196—24no—
271C4×Dic61—24no—
272#11758194—44no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418C2×D412yes—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61#12012yes—
298C23×C61#13712yes—
299C23×C61C22×D411yescharacteristic
300Q8×C61—41no—
301Q8×C61—41no—
302Q8×C61—41no—
303Q8×C61—41no—
304D4×C61—28no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—22no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61#12012yes—
336C2×C4×C61#13712yes—
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—48no—
350C2×Dic61—48no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357Dic122—22no—
358Dic122—22no—
359Dic122—22no—
360Dic122—22no—
361Dic122—22no—
362Dic122—22no—
363Dic122—22no—
364Dic122—48no—
365Dic122—48no—
366Dic122—41no—
367Dic122—41no—
368Dic122—41no—
369Dic122—41no—
370Dic122#12114yes—
371#92418—22no—
372#92418—41no—
373#92418—41no—
374#92418—41no—
375#24453—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61C2×#12011yescharacteristic
391C22×C61D4211yescharacteristic
392C22×C61#54611yescharacteristic
393C22×C61C2×#13711yescharacteristic
394C22×C61C2×#13711yescharacteristic
395C22×C61#57811yescharacteristic
396C22×C61#57811yescharacteristic
397C4×C61—22no—
398C4×C61—22no—
399C4×C61—41no—
400C4×C61—41no—
401C4×C61—42no—
402C4×C61—81no—
403C4×C61—81no—
404C4×C61—81no—
405C4×C61C2×#12111yescharacteristic
406C4×C61#53411yescharacteristic
407C4×C61D4211yescharacteristic
408C4×C61#54611yescharacteristic
409Dic61—24no—
410Dic61—42no—
411Dic61—42no—
412Dic61—42no—
413C2×D4×Q8—611no—
414C2×#470—611no—
415C2×#451—611no—
416C2×#451—611no—
417C2×#419—611no—
418#2415D6111yescharacteristic
419#2043—611no—
420#2035—611no—
421#2016—611no—
422#2001—611no—
423#1878—611no—
424#1873—611no—
425#1870—611no—
426#1865—611no—
427#1787—611no—
428C2×C61—42no—
429C2×C61—42no—
430C2×C61#241011yescharacteristic
431C2×C61#300411yescharacteristic
432C2×C61#301111yescharacteristic
433C2×C61#327011yescharacteristic
434C2×C61#327611yescharacteristic
435C2×C61#331211yescharacteristic
436C2×C61#332811yescharacteristic
437C23×Q8—611no—
438C23×Q8—611no—
439C22×Q16—611no—
440C22×Q16—611no—
441C22×Q16—611no—
442C22×M16—611no—
443D4×Q8—1224no—
444D4×Q8—1224no—
445C2×C4⋊Q8—611no—
446C2×C4⋊Q8—1221no—
447C2×C22⋊Q8—611no—
448C2×C22⋊Q8—611no—
449C2×C22⋊Q8—1221no—
450C2×C22⋊Q8—1221no—
451C2×C22⋊Q8C2×D6111yescharacteristic
452C2×C22⋊Q8C2×D6111yescharacteristic
453C2×C4×Q8—611no—
454C2×C4×D4—1221no—
455C2×C4×D4C2×D6111yescharacteristic
456C2×#117C2×D6111yescharacteristic
457#470—1224no—
458#451—1224no—
459#451—1224no—
460C2×#106—611no—
461#419—1224no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#103—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×C22⋊C8—611no—
473C2×C22⋊C8—611no—
474C2×C22⋊C8—611no—
475#397—21no—
476#394—21no—
477#391C2×D6111yescharacteristic
478#389—21no—
479#389C2×D6111yescharacteristic
480#388—21no—
481#380C2×D6111yescharacteristic
482#340—611no—
483#340—611no—
484#336—611no—
485#336—611no—
486C61#2445311yescharacteristic, complemented, Sylow
487C22×Q8—614no—
488C22×Q8—611no—
489C22×Q8—611no—
490C22×Q8—611no—
491C22×Q8—1222no—
492C22×Q8—1222no—
493C22×Q8—1222no—
494C22×Q8—1222no—
495C22×Q8—1222no—
496C22×Q8—1222no—
497C22×Q8—1222no—
498C22×Q8—1221no—
499C22×Q8—1221no—
500C22×Q8—2441no—
501C22×Q8—2441no—
502C22×Q8—2441no—
503C22×Q8—2441no—
504C22×Q8C22×D6111yescharacteristic
505C22×D4C22⋊D6111yescharacteristic
506C23×C4—1221no—
507C23×C4—1221no—
508C23×C4C22×D6111yescharacteristic
509C23×C4C22×D6111yescharacteristic
510C2×Q16—1222no—
511C2×Q16—1222no—
512C2×Q16—1222no—
513C2×Q16—1222no—
514C2×Q16—1222no—
515C2×Q16—1222no—
516C2×Q16—2441no—
517C2×Q16—2441no—
518C2×Q16—2441no—
519C2×M16—1222no—
520C2×M16—1222no—
521C2×M16—2441no—
522C22×C8—611no—
523C22×C8—611no—
524C22×C8—611no—
525C22×C8—611no—
526C4⋊Q8—1222no—
527C4⋊Q8—1222no—
528C4⋊Q8—1228no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—41no—
533C22⋊Q8—614no—
534C22⋊Q8—1228no—
535C22⋊Q8—1228no—
536C22⋊Q8—1222no—
537C22⋊Q8—1222no—
538C22⋊Q8—1222no—
539C4×Q8—1222no—
540C4×Q8—1222no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—1228no—
544#117—22no—
545#117—41no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4C22⋊D6111yescharacteristic
556C2×C4⋊C4C22×D6111yescharacteristic
557C2×C4⋊C4C22×D6111yescharacteristic
558C2×C4⋊C4C22×D6111yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4C22⋊D6111yescharacteristic
566C2×C22⋊C4C22⋊D6111yescharacteristic
567C2×C42—21no—
568C2×C42—1221no—
569C2×C42C22×D6111yescharacteristic
570#106—1222no—
571#103—614no—
572#103—1222no—
573#103—1222no—
574#103—1222no—
575#103—1222no—
576#103—1222no—
577#103—1222no—
578#103—1222no—
579#103—1222no—
580#103—2441no—
581C22⋊C8—1222no—
582C22⋊C8—1222no—
583C22⋊C8—2441no—
584#95—21no—
585#95—21no—
586#95—21no—
587#95—21no—
588C24C2×C22⋊D6111yescharacteristic
589C24C2×C22⋊D6111yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—612no—
597C2×Q8—612no—
598C2×Q8—612no—
599C2×Q8—612no—
600C2×Q8—612no—
601C2×Q8—1224no—
602C2×Q8—1228no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—1224no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×Q8—1221no—
613C2×Q8—1221no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—2442no—
618C2×Q8—2442no—
619C2×Q8—2442no—
620C2×Q8—2442no—
621C2×Q8—2444no—
622C2×Q8—2444no—
623C2×Q8—2444no—
624C2×Q8—2444no—
625C2×Q8—2444no—
626C2×Q8—2444no—
627C2×Q8—2444no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—22no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—1221no—
646C22×C4—1224no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1224no—
651C22×C4—2442no—
652C22×C4—2442no—
653C22×C4—2442no—
654C22×C4—2442no—
655C22×C4D4×D6112yes—
656C22×C4D4×D6112yes—
657C22×C4C2×C22⋊D6111yescharacteristic
658C22×C4C2×C22⋊D6111yescharacteristic
659C22×C4C2×C22⋊D6111yescharacteristic
660C22×C4C2×C22⋊D6111yescharacteristic
661C22×C4C23×D6111yescharacteristic
662Q16—2444no—
663Q16—2444no—
664Q16—2444no—
665M16—2444no—
666C2×C8—612no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C4⋊C4—21no—
679C4⋊C4—22no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—612no—
688C4⋊C4—1224no—
689C4⋊C4—1224no—
690C4⋊C4—1224no—
691C4⋊C4—1224no—
692C4⋊C4—1221no—
693C4⋊C4—1224no—
694C4⋊C4D4×D6112yes—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—1224no—
702C22⋊C4—1224no—
703C42—21no—
704C42—21no—
705C42—42no—
706C42—1224no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23#1451974512yes—
720C23#1451980712yes—
721C23C22×C22⋊D6111yescharacteristic
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726Q8—614no—
727Q8—1222no—
728Q8—1222no—
729Q8—1222no—
730Q8—1222no—
731Q8—1222no—
732Q8—1222no—
733Q8—1222no—
734Q8—2448no—
735Q8—2448no—
736Q8—2441no—
737Q8—2441no—
738Q8—2441no—
739Q8—2441no—
740D4—28no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—2448no—
778C2×C4—2448no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4#1451974512yes—
786C2×C4#1451980712yes—
787C2×C4C2×D4×D6111yescharacteristic
788C2×C4C2×D4×D6111yescharacteristic
789C2×C4C2×D4×D6111yescharacteristic
790C2×C4#41×D6111yescharacteristic
791C2×C4#1451982211yescharacteristic
792C2×C4#1451982311yescharacteristic
793C8—1222no—
794C8—2441no—
795C8—2441no—
796C8—2441no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22C2×#1451974511yescharacteristic
812C22D4×C22⋊D6111yescharacteristic
813C22#1684040011yescharacteristic
814C22C2×#1451980711yescharacteristic
815C22C2×#1451980711yescharacteristic
816C22#1684057711yescharacteristic
817C22#1684057711yescharacteristic
818C4—22no—
819C4—22no—
820C4—41no—
821C4—42no—
822C4—41no—
823C4—81no—
824C4—81no—
825C4—81no—
826C4—1224no—
827C4—2442no—
828C4—2442no—
829C4—2442no—
830C4#121×D6111yescharacteristic
831C4#1684032011yescharacteristic
832C4#1684039611yescharacteristic
833C4#1684040111yescharacteristic
834C2—42no—
835C2—42no—
836C2#2144919011yescharacteristic
837C2#2145505211yescharacteristic
838C2#2145511211yescharacteristic
839C2#2145738511yescharacteristic
840C2#2145746111yescharacteristic
841C2#2145786411yescharacteristic
842C2#2145809611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2415C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenter#2415D61
hypocenterC61#24453
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2415

Complements

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

NH ≅ G/Ntype
2. C2×#16840018C2semidirect
3. C2×#16839917C2semidirect
4. C2×#16839917C2semidirect
5. C2×#16839770C2semidirect
6. #21447065C2semidirect
7. #21447015C2semidirect
8. #21446918C2semidirect
9. #21446827C2semidirect
10. #21446163C2semidirect
11. #21446131C2semidirect
13. #21446086C2semidirect
14. #21445753C2semidirect
131. #14519700D4semidirect
486. C61#24453semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic1222
C2×#168400182
C2×#168399172
C2×#168397702
#214470652
#214470152
#214469182
#214468272
#214461632
#214461312
#214461172
#214460862
#214457532
C61×#24152
#2445361