Finite Group Databasebeta

← #30620618

Subgroups — #30620618

Order 15616.

934 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462329C211yesmaximal, characteristic
2Q8×C22⋊#6923C211yesmaximal, characteristic
3#21461910C211yesmaximal, characteristic, complemented
4#21461908C211yesmaximal, characteristic, complemented
5#21461899C211yesmaximal, characteristic, complemented
6#21461898C211yesmaximal, characteristic, complemented
7#21461785C211yesmaximal, characteristic, complemented
8#21461783C211yesmaximal, characteristic, complemented
9#21461724C211yesmaximal, characteristic
10#21461697C211yesmaximal, characteristic
11#21461658C211yesmaximal, characteristic
12#21461592C211yesmaximal, characteristic, complemented
13#103×#6923C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic
15#419×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×#14519846C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519840C2211yescharacteristic
24D61⋊(C22⋊C8)C2211yescharacteristic
25C2×#14519831C2211yescharacteristic
26C2×C8×#6923C2211yescharacteristic
27(C2×#6923)⋊Q8—21no—
28(C2×#6923)⋊Q8—21no—
29(C2×#6923)⋊Q8C2211yescharacteristic
30(C2×#6923)⋊Q8C2211yescharacteristic
31#16840713C2211yescharacteristic
32#16840713C2211yescharacteristic
33#16840712—21no—
34#16840712—21no—
35#16840706—21no—
36#16840704—21no—
37#16840704C2211yescharacteristic
38#16840704C2211yescharacteristic
39C4⋊C4×#6923C2211yescharacteristic
40C4⋊C4×#6923C2211yescharacteristic
41C4×C22⋊#6923—21no—
42C4×C22⋊#6923C2211yescharacteristic
43#16840698—21no—
44#16840636C2211yescharacteristic
45#16840636C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C22×Q8×D61C2211yescharacteristic
53C2×M16×D61C2211yescharacteristic
54#117×D61C2211yescharacteristic
55#16839772C411yescharacteristic, complemented
56#16839771C411yescharacteristic, complemented
57#16839770C411yescharacteristic, complemented
58#16839769C411yescharacteristic, complemented
59#16839769C411yescharacteristic, complemented
60#16839769C411yescharacteristic, complemented
61#16839769C411yescharacteristic, complemented
62#103×D61C2211yescharacteristic
63#103×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#103×D61C2211yescharacteristic
66C61×#419C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69Q8×#6923—22no—
70Q8×#6923—22no—
71Q8×#6923—41no—
72Q8×#6923—41no—
73C2×C4⋊#6923—21no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923D411yescharacteristic
84C2×C22⋊#6923D411yescharacteristic
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923C2311yescharacteristic
90C2×C4×#6923C2311yescharacteristic
91#14519846—41no—
92#14519845—41no—
93#14519840—22no—
94#14519840—22no—
95#14519840—41no—
96#14519840—41no—
97#14519834—21no—
98C22⋊#92420—21no—
99#14519831—41no—
100C8×#6923—41no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4D411yescharacteristic
112(C2×#6923)⋊C4D411yescharacteristic
113C22×Dic122—21no—
114C22×Dic122C2×C411yescharacteristic
115C2×Q8×D61—21no—
116C2×Q8×D61—21no—
117C2×Q8×D61—22no—
118C2×Q8×D61—22no—
119C2×Q8×D61—41no—
120C2×Q8×D61—41no—
121C2×Q8×D61C2×C411yescharacteristic
122C2×Q8×D61C2×C411yescharacteristic
123C2×Q8×D61C2311yescharacteristic
124C2×Q8×D61C2311yescharacteristic
125C22×C4×D61—21no—
126C22×C4×D61C2311yescharacteristic
127C2×#11758194C2×C411yescharacteristic
128C2×#11758189C2×C411yescharacteristic
129C2×#11758189C2×C411yescharacteristic
130M16×D61—41no—
131M16×D61—41no—
132C2×C8×D61C2311yescharacteristic
133C2×C8×D61C2311yescharacteristic
134#14519736C2×C411yescharacteristic
135#14519735C2×C411yescharacteristic
136#14519735C2×C411yescharacteristic
137#14519734—21no—
138#14519733—21no—
139C4⋊C4×D61C2311yescharacteristic
140C4⋊C4×D61C2311yescharacteristic
141C22⋊C4×D61—21no—
142C42×D61—21no—
143#14519702C2×C411yescharacteristic
144#14519702C2×C411yescharacteristic
145#14519702C2×C411yescharacteristic
146#14519702C2×C411yescharacteristic
147#14519701C2×C411yescharacteristic
148#14519701C2×C411yescharacteristic
149#14519701C2×C411yescharacteristic
150#14519701C2×C411yescharacteristic
151#14519700C2×C411yescharacteristic
152#14519700C2×C411yescharacteristic
153#14519700C2×C411yescharacteristic
154#14519700C2×C411yescharacteristic
155C22×Q8×C61C2×C411yescharacteristic
156C2×M16×C61C2×C411yescharacteristic
157#117×C61C2×C411yescharacteristic
158#103×C61C2×C411yescharacteristic
159#103×C61C2×C411yescharacteristic
160#103×C61C2×C411yescharacteristic
161#103×C61C2×C411yescharacteristic
162C23×D61C2×D411yescharacteristic
163C22×#6923—21no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923C2×D411yescharacteristic
168C22×#6923C2×D411yescharacteristic
169C22×#6923C2×D411yescharacteristic
170C22×#6923C2×D411yescharacteristic
171C2×Q8×C61—21no—
172C2×Q8×C61—22no—
173C2×Q8×C61—41no—
174C2×Q8×C61C22×C411yescharacteristic
175C2×Q8×C61C22×C411yescharacteristic
176C22×C4×C61—21no—
177C22×C4×C61C22×C411yescharacteristic
178C22×Dic61—21no—
179C22×Dic61#4111yescharacteristic
180Q8×D61—21no—
181Q8×D61—21no—
182Q8×D61—22no—
183Q8×D61—21no—
184Q8×D61—21no—
185Q8×D61—21no—
186Q8×D61—21no—
187Q8×D61—22no—
188Q8×D61—41no—
189Q8×D61—41no—
190Q8×D61—42no—
191Q8×D61—42no—
192Q8×D61—42no—
193Q8×D61—42no—
194Q8×D61#4112yes—
195Q8×D61#4112yes—
196C2×C4×D61—21no—
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—21no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61C22×C411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61#4111yescharacteristic
211C2×C4×D61C2411yescharacteristic
212C2×Dic122—21no—
213C2×Dic122—22no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—41no—
219C2×Dic122—42no—
220C2×Dic122—42no—
221C2×Dic122C22×C411yescharacteristic
222C2×Dic122C22×C411yescharacteristic
223C22⋊#6923—22no—
224C22⋊#6923—41no—
225C22⋊#6923—42no—
226C22⋊#6923—81no—
227C2×#92420—21no—
228C2×#92420—21no—
229C4⋊#6923—21no—
230C4⋊#6923—21no—
231C4⋊#6923—21no—
232C4⋊#6923—21no—
233C4⋊#6923—21no—
234C4⋊#6923—21no—
235C4⋊#6923—21no—
236C4⋊#6923—21no—
237C4⋊#6923—42no—
238C4⋊#6923—42no—
239C4⋊#6923—81no—
240C4⋊#6923—81no—
241C4×#6923—21no—
242C4×#6923—21no—
243C4×#6923—21no—
244C4×#6923—21no—
245C4×#6923—42no—
246C4×#6923—42no—
247C4×#6923—42no—
248C4×#6923—42no—
249D61⋊C8—21no—
250D61⋊C8—21no—
251D61⋊C8—21no—
252D61⋊C8—21no—
253M16×C61—41no—
254C2×C8×C61C22×C411yescharacteristic
255C2×C8×C61C22×C411yescharacteristic
256C4⋊C4×C61C22×C411yescharacteristic
257C4⋊C4×C61C22×C411yescharacteristic
258C22⋊C4×C61—21no—
259C42×C61—21no—
260C22⋊Dic61—21no—
261#11758198—21no—
262#11758198—21no—
263C4⋊Dic61C22×C411yescharacteristic
264C4⋊Dic61C22×C411yescharacteristic
265#11758196—21no—
266#11758196—21no—
267C4×Dic61—21no—
268C4×Dic61—21no—
269C4×Dic61—21no—
270#11758194—41no—
271C2×#92418C22×C411yescharacteristic
272C2×#92418C22×C411yescharacteristic
273#11758189—41no—
274#11758189—41no—
275C8×D61—21no—
276C8×D61—21no—
277C8×D61—21no—
278C8×D61—21no—
279C23×C61C4×D411yescharacteristic
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61C4×D411yescharacteristic
287C22×D61C22×D411yescharacteristic
288C2×#6923—21no—
289C2×#6923—21no—
290C2×#6923—21no—
291C2×#6923—21no—
292C2×#6923—21no—
293C2×#6923—21no—
294C2×#6923—21no—
295C2×#6923—21no—
296C2×#6923—21no—
297C2×#6923—21no—
298C2×#6923—21no—
299C2×#6923—41no—
300C2×#6923—41no—
301C2×#6923—41no—
302C2×#6923—41no—
303C2×#6923—41no—
304C2×#6923—41no—
305C2×#6923—41no—
306C2×#6923—41no—
307C2×#6923—41no—
308C2×#6923—41no—
309C2×#6923—41no—
310C2×#6923—41no—
311C2×#6923#13712yes—
312Q8×C61—21no—
313Q8×C61—21no—
314Q8×C61—21no—
315Q8×C61—42no—
316Q8×C61#11712yes—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—42no—
324C2×C4×C61C4×D411yescharacteristic
325C2×C4×C61C23×C411yescharacteristic
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—42no—
333C2×Dic61C4×D411yescharacteristic
334C2×Dic61C2×#4111yescharacteristic
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—21no—
338C4×D61—21no—
339C4×D61—21no—
340C4×D61—21no—
341C4×D61—21no—
342C4×D61—21no—
343C4×D61—42no—
344C4×D61—42no—
345C4×D61—41no—
346C4×D61—41no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61C2×#4111yescharacteristic
352C4×D61C2×#4111yescharacteristic
353C4×D61H(5,𝔽2)11yescharacteristic
354C4×D61H(5,𝔽2)11yescharacteristic
355Dic122—21no—
356Dic122—22no—
357Dic122—22no—
358Dic122—21no—
359Dic122—21no—
360Dic122—42no—
361Dic122—42no—
362Dic122—42no—
363Dic122—41no—
364Dic122—41no—
365Dic122#11712yes—
366#92420—41no—
367#92420—41no—
368C8×C61—21no—
369C8×C61—21no—
370#92418—21no—
371#92418—21no—
372#22585—611nomaximal, Sylow
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—21no—
376C22×C61C2×C4×D411yescharacteristic
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61#54611yescharacteristic
385C2×D61#54611yescharacteristic
386C2×D61C2×#13711yescharacteristic
387C2×D61#57511yescharacteristic
388C2×D61#57711yescharacteristic
389C2×D61#57811yescharacteristic
390#6923—22no—
391#6923—41no—
392#6923—41no—
393#6923—41no—
394#6923—81no—
395#6923—81no—
396#6923—81no—
397#6923—81no—
398C4×C61—22no—
399C4×C61—21no—
400C4×C61—41no—
401C4×C61—41no—
402C4×C61—41no—
403C4×C61C2×#11711yescharacteristic
404C4×C61#51811yescharacteristic
405Dic61—22no—
406Dic61—21no—
407Dic61—41no—
408Dic61—41no—
409Dic61—41no—
410Dic61#55111yescharacteristic
411Dic61#55111yescharacteristic
412C2×#419—611no—
413#2346—611no—
414Q8×C22⋊C4—611no—
415#1935—611no—
416#1933—611no—
417#1928—611no—
418#1927—611no—
419#1865—611no—
420#1863—611no—
421#1825—611no—
422#1809—611no—
423#1787—611no—
424#1763—611no—
425C4×#103—611no—
426#1753—611no—
427C2×C61—41no—
428C2×C61#234211yescharacteristic
429C2×C61C4×#13711yescharacteristic
430C2×C61#294711yescharacteristic
431D61—41no—
432D61#331211yescharacteristic
433D61#332111yescharacteristic
434D61#332711yescharacteristic
435D61#332911yescharacteristic
436C23×Q8—611no—
437C22×M16—611no—
438C2×C4×Q8—611no—
439C2×C4×Q8—611no—
440C2×#117—611no—
441C2×#107—611no—
442C2×#106—611no—
443#419—611no—
444#419—611no—
445#419—611no—
446#419—611no—
447#419—611no—
448#419—611no—
449#419—611no—
450#419#692311yescharacteristic, complemented
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#103—611no—
455C2×#103—611no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×C22⋊C8—611no—
460C2×#97—611no—
461C2×C4×C8—611no—
462#391—611no—
463#391—611no—
464#391—1221no—
465#391—1221no—
466#389—611no—
467#389—611no—
468#388—1221no—
469#388—1221no—
470#382—1221no—
471#380—611no—
472#380—611no—
473#380—1221no—
474C4×C4⋊C4—611no—
475C4×C4⋊C4—611no—
476C4×C22⋊C4—611no—
477C4×C22⋊C4—1221no—
478#376—1221no—
479#340—611no—
480#340—611no—
481#340—611no—
482#340—611no—
483#340—611no—
484#340—611no—
485#336—611no—
486#336—611no—
487C61#2258511yescharacteristic, complemented, Sylow
488C22×Q8—611no—
489C22×Q8—611no—
490C22×Q8—611no—
491C22×Q8—611no—
492C22×Q8—611no—
493C22×Q8—1221no—
494C22×Q8—1221no—
495C22×Q8—1221no—
496C22×Q8—1222no—
497C22×Q8—1222no—
498C22×Q8—2441no—
499C22×Q8—2441no—
500C22×Q8C2×#692311yescharacteristic
501C23×C4—611no—
502C23×C4—1221no—
503C2×M16—611no—
504C2×M16—611no—
505C2×M16—611no—
506C2×M16—2441no—
507C2×M16—2441no—
508C2×M16C2×#692311yescharacteristic
509C22×C8—611no—
510C22×C8—611no—
511C22×C8—611no—
512C22×C8—611no—
513C4×Q8—1222no—
514C4×Q8—1222no—
515C4×Q8—2441no—
516C4×Q8—2441no—
517#117—611no—
518#117—611no—
519#117—611no—
520#117—1221no—
521#117—1221no—
522#117C2×#692311yescharacteristic
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C22⋊C4—611no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C42—611no—
539C2×C42—611no—
540C2×C42—1221no—
541C2×C42—1221no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42—1221no—
545#107—2441no—
546#106—2441no—
547#103—611no—
548#103—611no—
549#103—611no—
550#103—611no—
551#103—611no—
552#103—611no—
553#103—611no—
554#103—611no—
555#103—611no—
556#103—611no—
557#103—611no—
558#103—611no—
559#103—1222no—
560#103—1222no—
561#103—2441no—
562#103—2441no—
563#103C2×#692311yescharacteristic
564#103C2×#692311yescharacteristic
565#103C2×#692311yescharacteristic
566#103C2×#692311yescharacteristic
567C22⋊C8—1221no—
568C22⋊C8—1221no—
569#97—2441no—
570C4×C8—2441no—
571#95—611no—
572#95—611no—
573#95—1221no—
574#95—1221no—
575#95—1221no—
576#95—1221no—
577#95—1221no—
578#95—1221no—
579#95—1221no—
580#95—1221no—
581#95—1221no—
582#95—1221no—
583C24—611no—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—41no—
587C2×Q8—612no—
588C2×Q8—612no—
589C2×Q8—611no—
590C2×Q8—611no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1222no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×Q8—1222no—
604C2×Q8—1222no—
605C2×Q8—2441no—
606C2×Q8—2442no—
607C2×Q8—2442no—
608C2×Q8—2442no—
609C2×Q8—2442no—
610C2×Q8—2441no—
611C2×Q8—2441no—
612C2×Q8—2442no—
613C2×Q8—2442no—
614C2×Q8C22×#692311yescharacteristic
615C2×Q8C22×#692311yescharacteristic
616C22×C4—21no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
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—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—2442no—
642C22×C4—2442no—
643C22×C4C22×#692311yescharacteristic
644M16—41no—
645M16—2441no—
646M16—2441no—
647M16—2441no—
648C2×C8—611no—
649C2×C8—611no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8C22×#692311yescharacteristic
661C2×C8C22×#692311yescharacteristic
662C4⋊C4—611no—
663C4⋊C4—611no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—4881no—
675C4⋊C4—4881no—
676C4⋊C4—2442no—
677C4⋊C4—2442no—
678C4⋊C4C22×#692311yescharacteristic
679C4⋊C4C22×#692311yescharacteristic
680C22⋊C4—21no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1222no—
684C22⋊C4—1221no—
685C22⋊C4—4881no—
686C22⋊C4—2441no—
687C22⋊C4—2442no—
688C42—21no—
689C42—1221no—
690C42—1221no—
691C42—1221no—
692C42—1221no—
693C42—1221no—
694C42—1221no—
695C42—1221no—
696C42—2442no—
697C42—2442no—
698C42—2442no—
699C42—2442no—
700C23—611no—
701C23—611no—
702C23—1221no—
703C23—1221no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23D4×#692311yescharacteristic
709Q8—21no—
710Q8—21no—
711Q8—21no—
712Q8—42no—
713Q8—612no—
714Q8—1222no—
715Q8—1222no—
716Q8—1221no—
717Q8—1221no—
718Q8—1221no—
719Q8—2442no—
720Q8—2442no—
721Q8—2441no—
722Q8—2441no—
723Q8—2442no—
724Q8#1451985612yes—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—42no—
732C2×C4—611no—
733C2×C4—611no—
734C2×C4—611no—
735C2×C4—611no—
736C2×C4—611no—
737C2×C4—612no—
738C2×C4—611no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2442no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4—2441no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4D4×#692311yescharacteristic
786C2×C4C23×#692311yescharacteristic
787C8—21no—
788C8—21no—
789C8—1221no—
790C8—1221no—
791C8—2441no—
792C8—2441no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—611no—
797C22—611no—
798C22—611no—
799C22—611no—
800C22—611no—
801C22—611no—
802C22—1221no—
803C22—1221no—
804C22—1221no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22—2441no—
809C22C2×D4×#692311yescharacteristic
810C4—21no—
811C4—22no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—611no—
816C4—611no—
817C4—1222no—
818C4—1221no—
819C4—1222no—
820C4—4881no—
821C4—4881no—
822C4—4881no—
823C4—4881no—
824C4—2441no—
825C4—2441no—
826C4—2441no—
827C4—2441no—
828C4—2441no—
829C4—2441no—
830C4C2×#1451985611yescharacteristic
831C4#1684082911yescharacteristic
832C2—41no—
833C2—611no—
834C2—611no—
835C2—611no—
836C2—611no—
837C2—2441no—
838C2#2146232511yescharacteristic
839C2#137×#692311yescharacteristic
840C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#419C4
socleC22×C61C2×C4×D4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#419#6923
hypocenterC61#22585
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #21461910C2semidirect
4. #21461908C2semidirect
5. #21461899C2semidirect
6. #21461898C2semidirect
7. #21461785C2semidirect
8. #21461783C2semidirect
12. #21461592C2semidirect
13. #103×#6923C2semidirect
55. #16839772C4semidirect
56. #16839771C4semidirect
57. #16839770C4semidirect
58. #16839769C4semidirect
59. #16839769C4semidirect
60. #16839769C4semidirect
61. #16839769C4semidirect
66. C61×#419C4semidirect
450. #419#6923semidirect
487. C61#22585semidirect

Maximal subgroups

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

subgroupindex
#214623292
Q8×C22⋊#69232
#214619102
#214619082
#214618992
#214618982
#214617852
#214617832
#214617242
#214616972
#214616582
#214615922
#103×#69232
#214615592
#419×D612
#2258561