Finite Group Databasebeta

← #30547641

Subgroups — #30547641

Order 15616.

2038 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459222C211yesmaximal, characteristic, complemented
2C2×#16840244C211yesmaximal, characteristic
3#21455684C214yesmaximal, complemented
4#21455678C214yesmaximal, complemented
5#21455673C214yesmaximal, complemented
6#21455667C214yesmaximal, complemented
7#21455624C211yesmaximal, characteristic, complemented
8#21455621C212yesmaximal, complemented
9#21455618C211yesmaximal, characteristic, complemented
10#21455615C212yesmaximal, complemented
11#21455612C211yesmaximal, characteristic, complemented
12#428×D61C212yesmaximal, complemented
13#21454381C211yesmaximal, characteristic, complemented
14#21454337C212yesmaximal
15C61×#3078C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C2×M16×D61C2212yes—
18#16840392C2212yescomplemented
19#16840392C2212yescomplemented
20#16840391—21no—
21#16840391—21no—
22#16840389C2212yescomplemented
23#16840389C2212yescomplemented
24#16840387—21no—
25#16840387—21no—
26#16840319C2211yescharacteristic
27#16840316—22no—
28#16840316—22no—
29#16840315C2212yes—
30#16840244—22no—
31#16840244—22no—
32#16840244C2214yes—
33#16840244C2214yes—
34C2×Q8×Dic61C2211yescharacteristic
35C2×C4×D244—21no—
36C2×C4×D244C2211yescharacteristic
37C2×#14519739—21no—
38C2×#14519739C2211yescharacteristic
39C2×#14519734—21no—
40C2×#14519734C2211yescharacteristic
41#117×D61C2212yes—
42C2×C4⋊C4×D61—21no—
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840071C2214yescomplemented
45#16840069C2214yescomplemented
46#16840067C2214yescomplemented
47#16840065C2214yescomplemented
48#16840063C2214yescomplemented
49#16840061C2214yescomplemented
50#16840059C2214yescomplemented
51#16840057C2212yescomplemented
52#16840055C2214yescomplemented
53#16840053C2212yescomplemented
54#16840051C2214yescomplemented
55#16840049C2212yescomplemented
56#16840047C2212yescomplemented
57#16840045C2214yescomplemented
58#16840043C2212yescomplemented
59#16840041C2214yescomplemented
60#16840039C2212yescomplemented
61#16839805C2212yes—
62#16839804C2212yes—
63#16839803C2214yescomplemented
64#16839802C2212yes—
65#16839801C2214yescomplemented
66#107×D61C2214yescomplemented
67#106×D61C2214yescomplemented
68#16839787C2214yescomplemented
69#16839787C2214yescomplemented
70#16839786C2211yescharacteristic
71#16839785C2212yes—
72#16839771C2212yes—
73#16839768C2212yes—
74#16839766C2212yes—
75#16839762C2214yes—
76#16839762C2214yes—
77#16839757C2214yes—
78#16839757C2214yes—
79C61×#533C2211yescharacteristic
80C2×C4×Q8×C61C2211yescharacteristic
81C61×#479C2214yescomplemented
82C61×#477C2212yescomplemented
83C61×#475C2212yescomplemented
84C61×#428C2212yes—
85C61×#423C2211yescharacteristic
86C61×#419C2212yes—
87C2×#11758226—22no—
88C2×#11758226—24no—
89C2×#11758226Q818yescomplemented
90C2×#11758226C2314yes—
91C22×D244—21no—
92C22×D244C2311yescharacteristic
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61C2311yescharacteristic
98C2×#11758194C2312yes—
99C2×#11758189C2314yes—
100M16×D61—28no—
101C2×C8×D61C2314yes—
102#14519777C2311yescharacteristic
103#14519777C2311yescharacteristic
104#14519776—22no—
105#14519776—22no—
106#14519776C2312yes—
107#14519776C2312yes—
108#14519775—22no—
109#14519775—22no—
110#14519769C2312yes—
111#14519768C2312yes—
112#14519768C2312yes—
113#14519767—22no—
114#14519767—22no—
115#14519767—22no—
116#14519767—22no—
117#14519757—22no—
118#14519757—22no—
119#14519756—21no—
120#14519756—21no—
121#14519755—22no—
122#14519755—22no—
123#14519755—22no—
124#14519755—22no—
125#14519754—22no—
126#14519754—22no—
127#14519753—22no—
128#14519753—22no—
129Q8×Dic61—22no—
130Q8×Dic61C2314yes—
131C4×Dic122—21no—
132C4×Dic122—21no—
133C4×Dic122—22no—
134C4×Dic122—22no—
135C4×D244—21no—
136C4×D244—21no—
137C4×D244—24no—
138C4×D244—24no—
139C4×D244C2312yes—
140C4×D244C2312yes—
141#14519739—24no—
142#14519739—24no—
143#14519739—22no—
144#14519739C2314yes—
145#14519736C2312yes—
146#14519735C2312yes—
147#14519735C2312yes—
148#14519734—22no—
149#14519734—24no—
150#14519734—24no—
151#14519734D412yes—
152#14519734D412yes—
153#14519734C2312yes—
154#14519734C2312yes—
155#14519733—22no—
156C2×C4⋊Dic61—21no—
157C2×C4⋊Dic61C2311yescharacteristic
158C2×#11758196—21no—
159C2×#11758196D411yescharacteristic
160C2×#11758196D411yescharacteristic
161C4⋊C4×D61—22no—
162C4⋊C4×D61—24no—
163C4⋊C4×D61—24no—
164C4⋊C4×D61C2314yes—
165C4⋊C4×D61C2312yes—
166C4⋊C4×D61C2312yes—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C2×#11758198D411yescharacteristic
170C2×#11758198D411yescharacteristic
171C22⋊C4×D61—22no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61C2311yescharacteristic
174C42×D61—22no—
175#14519711C2314yes—
176#14519710C2314yes—
177#14519710C2314yes—
178#14519709C2314yes—
179#14519708C2314yes—
180#14519708C2314yes—
181C4⋊#92418C2312yes—
182C4⋊#92418C2312yes—
183#14519706C2314yes—
184#14519706C2314yes—
185#14519701C2314yes—
186#14519701C2314yes—
187#14519699C2314yes—
188#14519699C2314yes—
189#14519697C2314yes—
190#14519697C2314yes—
191C22×Q8×C61C2311yescharacteristic
192C2×M16×C61C2312yes—
193C4⋊Q8×C61C2311yescharacteristic
194C4⋊Q8×C61C2311yescharacteristic
195#125×C61C2312yes—
196C22⋊Q8×C61—21no—
197C22⋊Q8×C61—21no—
198C4×Q8×C61—21no—
199C4×Q8×C61—21no—
200C4×Q8×C61—21no—
201C4×Q8×C61—21no—
202C4×Q8×C61C2312yes—
203C4×Q8×C61C2312yes—
204#117×C61C2312yes—
205C2×C4⋊C4×C61—21no—
206C2×C4⋊C4×C61C2311yescharacteristic
207C2×C42×C61—21no—
208C2×C42×C61C2311yescharacteristic
209#107×C61C2314yes—
210#106×C61C2314yes—
211C4⋊C8×C61C2312yes—
212C4⋊C8×C61C2312yes—
213#103×C61C2314yes—
214#103×C61C2314yes—
215C23×D61—21no—
216C23×D61C2×D411yescharacteristic
217C2×Q8×C61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61—21no—
220C2×Q8×C61—22no—
221C2×Q8×C61C2×Q814yes—
222C2×Q8×C61C2412yes—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2411yescharacteristic
228C22×Dic61—21no—
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232#11758226—216no—
233#11758226—28no—
234#11758226C2×Q8116yes—
235C2×D244—28no—
236C2×D244—24no—
237C2×D244—21no—
238C2×D244—22no—
239C2×D244C2×Q814yes—
240C2×D244C2412yes—
241C2×C4×D61—28no—
242C2×C4×D61—24no—
243C2×C4×D61—24no—
244C2×C4×D61—22no—
245C2×C4×D61—22no—
246C2×C4×D61—22no—
247C2×C4×D61—22no—
248C2×C4×D61—24no—
249C2×C4×D61—82no—
250C2×C4×D61—82no—
251C2×C4×D61—82no—
252C2×C4×D61C2×D412yes—
253C2×C4×D61C2×Q814yes—
254C2×C4×D61#4114yes—
255C2×C4×D61C2412yes—
256C2×Dic122—21no—
257C2×Dic122—21no—
258C2×Dic122—22no—
259C2×Dic122—22no—
260M16×C61—24no—
261C2×C8×C61C2414yes—
262C4⋊C4×C61—22no—
263C4⋊C4×C61—22no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—22no—
266C4⋊C4×C61—22no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61C2412yes—
270C4⋊C4×C61C2412yes—
271C4⋊C4×C61C2412yes—
272C22⋊C4×C61—22no—
273C42×C61—22no—
274C42×C61—22no—
275C42×C61—22no—
276C42×C61C2×D411yescharacteristic
277C42×C61C2×D411yescharacteristic
278C42×C61C2411yescharacteristic
279C42×C61C2411yescharacteristic
280C22⋊Dic61—22no—
281#11758198—22no—
282#11758198—22no—
283#11758198—22no—
284#11758198—22no—
285#11758198—24no—
286#11758198C2×D412yes—
287#11758198C2×D412yes—
288#11758198C2×D412yes—
289#11758198C2×D412yes—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61—24no—
294C4⋊Dic61—22no—
295C4⋊Dic61—22no—
296C4⋊Dic61C2412yes—
297C4⋊Dic61C2412yes—
298C4⋊Dic61C2412yes—
299#11758196—22no—
300#11758196—22no—
301#11758196—24no—
302#11758196—22no—
303#11758196—22no—
304#11758196—22no—
305#11758196—22no—
306#11758196—22no—
307#11758196—22no—
308#11758196C2×D412yes—
309#11758196C2×D412yes—
310#11758196C2×D412yes—
311#11758196C2×D412yes—
312C4×Dic61—22no—
313C4×Dic61—22no—
314C4×Dic61—22no—
315C4×Dic61—24no—
316C4×Dic61C2×D412yes—
317C4×Dic61C2412yes—
318#11758194—24no—
319C2×#92418C2414yes—
320#11758189—28no—
321C8×D61—28no—
322C23×C61C22×D411yescharacteristic
323C22×D61—24no—
324C22×D61—22no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61C22⋊Q814yes—
330C22×D61C22×D412yes—
331Q8×C61—24no—
332Q8×C61—22no—
333Q8×C61—81no—
334Q8×C61—81no—
335Q8×C61C22×Q814yes—
336C2×C4×C61—24no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—42no—
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C22×Q812yes—
350C2×C4×C61C2×#4112yes—
351C2×C4×C61C2511yescharacteristic
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—42no—
358C2×Dic61C22⋊Q814yes—
359C2×Dic61C22×D412yes—
360C2×Dic61C22×D412yes—
361C2×Dic61C22×D412yes—
362D244—216no—
363D244—24no—
364D244—22no—
365D244C22×Q814yes—
366C4×D61—216no—
367C4×D61—84no—
368C4×D61—82no—
369C4×D61—82no—
370C4×D61—82no—
371C4×D61—82no—
372C4×D61—84no—
373C4×D61C22⋊Q818yes—
374C4×D61C22×Q814yes—
375C4×D61C2×#4114yes—
376Dic122—82no—
377Dic122—82no—
378Dic122—81no—
379Dic122—81no—
380C8×C61—24no—
381#92418—24no—
382#60492—611nomaximal, Sylow
383C22×C61—21no—
384C22×C61—21no—
385C22×C61C2×C22⋊Q812yes—
386C22×C61C23×D411yescharacteristic
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—24no—
390C2×D61—44no—
391C2×D61—48no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61C2×C22⋊Q814yes—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—24no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61C2×C22⋊Q812yes—
404C4×C61C23×Q811yescharacteristic
405C4×C61C22×#4111yescharacteristic
406Dic61—22no—
407Dic61—22no—
408Dic61—42no—
409Dic61—42no—
410Dic61—42no—
411Dic61C2×C22⋊Q814yes—
412#3458—611no—
413C2×#520—611no—
414#3084—614no—
415#3084—614no—
416#3083—614no—
417#3083—614no—
418#3078—612no—
419#3078—611no—
420#3078D6111yescharacteristic, complemented
421#3077—612no—
422#3077—611no—
423#3077—611no—
424C2×#428—612no—
425#2905—611no—
426#2896—612no—
427C2×C61—22no—
428C2×C61C22×C22⋊Q811yescharacteristic
429C2×C61#358511yescharacteristic
430C2×C61#358611yescharacteristic
431D61—24no—
432D61—44no—
433C22×#41—611no—
434C22×M16—612no—
435#544—612no—
436#544—612no—
437#544—612no—
438#544—612no—
439#544—1221no—
440#544—1221no—
441#543—1221no—
442#543—1221no—
443#533—612no—
444#533—611no—
445#533—1222no—
446#533—1222no—
447#533C2×D6111yescharacteristic
448#520—614no—
449#520—614no—
450#520—1222no—
451#520—1222no—
452C2×C4×Q8—611no—
453C2×C4×Q8C2×D6111yescharacteristic
454C2×C4×D4—611no—
455C2×C4×D4—611no—
456C2×C4×D4—1221no—
457C2×C4×D4—1221no—
458C2×#117—611no—
459C2×#117—612no—
460C2×#117—1221no—
461C22×C4⋊C4—611no—
462C22×C4⋊C4—1221no—
463#479—614no—
464#479—614no—
465#479—614no—
466#479C2×D6114yescomplemented
467#478—614no—
468#478—614no—
469#478—614no—
470#478—614no—
471#477—612no—
472#477—614no—
473#477C2×D6112yescomplemented
474#476—612no—
475#476—614no—
476#476—612no—
477#475—612no—
478#475—614no—
479#475C2×D6112yescomplemented
480#474—612no—
481#474—614no—
482#474—612no—
483#428—612no—
484#428—612no—
485#428—612no—
486#428—614no—
487#428—614no—
488#428C2×D6112yes—
489C2×#107—614no—
490C2×#106—614no—
491#424—614no—
492#424—614no—
493#423—612no—
494#423—611no—
495#423C2×D6111yescharacteristic
496#419—612no—
497#419C2×D6112yes—
498#418—612no—
499#418—612no—
500#417—614no—
501#417—614no—
502#416—614no—
503#416—614no—
504C61#6049211yescharacteristic, complemented, Sylow
505C2×#41—618no—
506C2×#41—614no—
507C2×#41—1222no—
508C2×#41—1224no—
509C22×Q8C22×D6111yescharacteristic
510C22×D4—611no—
511C22×D4—1221no—
512C23×C4—611no—
513C23×C4—1221no—
514C23×C4—1221no—
515C23×C4—1221no—
516C23×C4—1221no—
517C2×M16—612no—
518C2×M16—614no—
519C2×M16—1228no—
520C2×M16C22×D6112yes—
521C22×C8—614no—
522C4⋊Q8—612no—
523C4⋊Q8—612no—
524C4⋊Q8—611no—
525C4⋊Q8—611no—
526C4⋊Q8—1222no—
527C4⋊Q8—1222no—
528C4⋊Q8—1222no—
529C4⋊Q8—1222no—
530C4⋊Q8C22×D6111yescharacteristic
531C4⋊Q8C22×D6111yescharacteristic
532#125—612no—
533#125—612no—
534#125—612no—
535#125—1222no—
536#125—1222no—
537#125—1222no—
538#125—1222no—
539#125C22×D6112yes—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—1222no—
543C22⋊Q8—1222no—
544C22⋊Q8—1222no—
545C22⋊Q8—1222no—
546C22⋊Q8—1222no—
547C22⋊Q8—1222no—
548C22⋊Q8—1222no—
549C22⋊Q8—1222no—
550C22⋊Q8—1222no—
551C22⋊Q8—1222no—
552C22⋊Q8—1221no—
553C22⋊Q8—1221no—
554C4×Q8—21no—
555C4×Q8—21no—
556C4×Q8—21no—
557C4×Q8—21no—
558C4×Q8—614no—
559C4×Q8—1222no—
560C4×Q8—1222no—
561C4×Q8—1222no—
562C4×Q8—1221no—
563C4×Q8—1221no—
564C4×Q8C22×D6112yes—
565C4×Q8C22×D6112yes—
566C4×D4—614no—
567C4×D4—612no—
568C4×D4—612no—
569C4×D4—1224no—
570C4×D4—1224no—
571C4×D4—1222no—
572C4×D4—1224no—
573C4×D4—1224no—
574C4×D4—1221no—
575C4×D4—1221no—
576#117—612no—
577#117—612no—
578#117—612no—
579#117—612no—
580#117—612no—
581#117—612no—
582#117—612no—
583#117—1224no—
584#117—1224no—
585#117—1222no—
586#117—1222no—
587#117C22×D6112yes—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—614no—
593C2×C4⋊C4—612no—
594C2×C4⋊C4—612no—
595C2×C4⋊C4—1224no—
596C2×C4⋊C4—1224no—
597C2×C4⋊C4—1222no—
598C2×C4⋊C4—1221no—
599C2×C4⋊C4—1221no—
600C2×C4⋊C4C22×D6111yescharacteristic
601C2×C22⋊C4—611no—
602C2×C22⋊C4—611no—
603C2×C22⋊C4—1222no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C42—21no—
607C2×C42—611no—
608C2×C42—1222no—
609C2×C42—1221no—
610C2×C42C22×D6111yescharacteristic
611#107—614no—
612#107—614no—
613#107—614no—
614#107C22×D6114yes—
615#106—614no—
616#106—614no—
617#106—614no—
618#106C22×D6114yes—
619C4⋊C8—614no—
620C4⋊C8—614no—
621C4⋊C8—612no—
622C4⋊C8—612no—
623C4⋊C8C22×D6112yes—
624C4⋊C8C22×D6112yes—
625#103—614no—
626#103—614no—
627#103C22×D6114yes—
628#103C22×D6114yes—
629#102—614no—
630#102—614no—
631#102—614no—
632#102—614no—
633C24—611no—
634C24—1221no—
635#41—6116no—
636#41—12216no—
637#41—1228no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—22no—
642C2×Q8—1222no—
643C2×Q8—1222no—
644C2×Q8—1221no—
645C2×Q8—1221no—
646C2×Q8Q8×D6114yes—
647C2×Q8C23×D6112yes—
648C2×D4—614no—
649C2×D4—612no—
650C2×D4—1224no—
651C2×D4—1228no—
652C2×D4—1221no—
653C2×D4—1222no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—611no—
657C22×C4—612no—
658C22×C4—614no—
659C22×C4—614no—
660C22×C4—612no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—1224no—
664C22×C4—1228no—
665C22×C4—1224no—
666C22×C4—1222no—
667C22×C4—1222no—
668C22×C4—1224no—
669C22×C4—1221no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—4882no—
673C22×C4—4882no—
674C22×C4—4882no—
675C22×C4D4×D6111yescharacteristic
676C22×C4D4×D6111yescharacteristic
677C22×C4C23×D6111yescharacteristic
678M16—24no—
679M16—1228no—
680M16—1224no—
681C2×C8—614no—
682C2×C8—1228no—
683C2×C8C23×D6114yes—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—612no—
692C4⋊C4—612no—
693C4⋊C4—612no—
694C4⋊C4—612no—
695C4⋊C4—612no—
696C4⋊C4—612no—
697C4⋊C4—612no—
698C4⋊C4—1224no—
699C4⋊C4—1222no—
700C4⋊C4—1222no—
701C4⋊C4—1224no—
702C4⋊C4—1222no—
703C4⋊C4—1222no—
704C4⋊C4—1222no—
705C4⋊C4—1222no—
706C4⋊C4—1222no—
707C4⋊C4—1222no—
708C4⋊C4—1221no—
709C4⋊C4—1222no—
710C4⋊C4—1222no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4C23×D6112yes—
714C4⋊C4C23×D6112yes—
715C4⋊C4C23×D6112yes—
716C22⋊C4—22no—
717C22⋊C4—612no—
718C22⋊C4—612no—
719C22⋊C4—612no—
720C22⋊C4—612no—
721C22⋊C4—1224no—
722C22⋊C4—1222no—
723C22⋊C4—1222no—
724C22⋊C4—1222no—
725C22⋊C4—1222no—
726C22⋊C4—1222no—
727C42—22no—
728C42—22no—
729C42—22no—
730C42—612no—
731C42—612no—
732C42—1222no—
733C42—1222no—
734C42—1224no—
735C42—1222no—
736C42D4×D6111yescharacteristic
737C42D4×D6111yescharacteristic
738C42C23×D6111yescharacteristic
739C42C23×D6111yescharacteristic
740C23—612no—
741C23—614no—
742C23—1224no—
743C23—1222no—
744C23—2441no—
745C23—2441no—
746C23—2442no—
747C23—2442no—
748C23C2×D4×D6111yescharacteristic
749Q8—24no—
750Q8—22no—
751Q8—81no—
752Q8—81no—
753Q8—4881no—
754Q8—4881no—
755Q8—4882no—
756Q8—4882no—
757Q8C2×Q8×D6114yes—
758D4—614no—
759D4—12216no—
760D4—1224no—
761D4—1222no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—614no—
771C2×C4—612no—
772C2×C4—618no—
773C2×C4—614no—
774C2×C4—614no—
775C2×C4—612no—
776C2×C4—612no—
777C2×C4—12216no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—4882no—
782C2×C4—4882no—
783C2×C4—4884no—
784C2×C4—4882no—
785C2×C4—4882no—
786C2×C4—4884no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2442no—
790C2×C4C2×D4×D6111yescharacteristic
791C2×C4C2×D4×D6111yescharacteristic
792C2×C4C2×D4×D6111yescharacteristic
793C2×C4C2×D4×D6111yescharacteristic
794C2×C4C2×D4×D6111yescharacteristic
795C2×C4C2×Q8×D6112yes—
796C2×C4#41×D6112yes—
797C2×C4C24×D6111yescharacteristic
798C8—24no—
799C8—1224no—
800C22—21no—
801C22—21no—
802C22—614no—
803C22—1222no—
804C22—1222no—
805C22—1224no—
806C22—2444no—
807C22—2448no—
808C22—2442no—
809C22—2442no—
810C22C22⋊Q8×D6112yes—
811C22C22×D4×D6111yescharacteristic
812C4—24no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—614no—
821C4—1222no—
822C4—1222no—
823C4—2442no—
824C4—2442no—
825C4—2442no—
826C4C22⋊Q8×D6112yes—
827C4C22×Q8×D6111yescharacteristic
828C4C2×#41×D6111yescharacteristic
829C2—22no—
830C2—1224no—
831C2—2444no—
832C2C2×C22⋊Q8×D6111yescharacteristic
833C2#2146059611yescharacteristic
834C2#2146060211yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3078C2
socleC22×C61C23×D4
prime radicalC22×#11758226C22
hypercenter#3078D61
hypocenterC61#60492
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
1. #21459222C2semidirect
3. #21455684C2semidirect
4. #21455678C2semidirect
5. #21455673C2semidirect
6. #21455667C2semidirect
7. #21455624C2semidirect
8. #21455621C2semidirect
9. #21455618C2semidirect
10. #21455615C2semidirect
11. #21455612C2semidirect
12. #428×D61C2semidirect
13. #21454381C2semidirect
15. C61×#3078C2semidirect
18. #16840392C22semidirect
19. #16840392C22semidirect
22. #16840389C22semidirect
23. #16840389C22semidirect
44. #16840071C22semidirect
45. #16840069C22semidirect
46. #16840067C22semidirect
47. #16840065C22semidirect
48. #16840063C22semidirect
49. #16840061C22semidirect
50. #16840059C22semidirect
51. #16840057C22semidirect
52. #16840055C22semidirect
53. #16840053C22semidirect
54. #16840051C22semidirect
55. #16840049C22semidirect
56. #16840047C22semidirect
57. #16840045C22semidirect
58. #16840043C22semidirect
59. #16840041C22semidirect
60. #16840039C22semidirect
63. #16839803C22semidirect
65. #16839801C22semidirect
66. #107×D61C22semidirect
67. #106×D61C22semidirect
68. #16839787C22semidirect
69. #16839787C22semidirect
81. C61×#479C22semidirect
82. C61×#477C22semidirect
83. C61×#475C22semidirect
89. C2×#11758226Q8semidirect
420. #3078D61semidirect
466. #479C2×D61semidirect
473. #477C2×D61semidirect
479. #475C2×D61semidirect
504. C61#60492semidirect

Maximal subgroups

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

subgroupindex
#214592222
C2×#168402442
#214556842
#214556782
#214556732
#214556672
#214556242
#214556212
#214556182
#214556152
#214556122
#428×D612
#214543812
#214543372
C61×#30782
#6049261