Finite Group Databasebeta

← #30560612

Subgroups — #30560612

Order 15616.

1782 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459397C211yesmaximal, characteristic
2C2×Q8×Dic122C211yesmaximal, characteristic, complemented
3#21458754C214yesmaximal, complemented
4#21458750C212yesmaximal, complemented
5#21458732C214yesmaximal, complemented
6#21458728C212yesmaximal, complemented
7#21458700C212yesmaximal, complemented
8#21458678C212yesmaximal, complemented
9#21456366C211yesmaximal, characteristic, complemented
10#21456363C212yesmaximal, complemented
11#21455635C211yesmaximal, characteristic
12#21455632C212yesmaximal
13#21455621C212yesmaximal, complemented
14#21454770C211yesmaximal, characteristic, complemented
15C4×#14519808C211yesmaximal, characteristic
16#21454634C212yesmaximal
17C61×#3078C211yesmaximal, characteristic, complemented
18C2×#14519808C2211yescharacteristic
19Q8×Dic122—21no—
20Q8×Dic122—21no—
21Q8×Dic122—22no—
22Q8×Dic122C2212yes—
23Q8×Dic122C2212yes—
24Q8×Dic122C2214yes—
25#16840492C2211yescharacteristic
26#16840489C2212yes—
27#16840487C2211yescharacteristic
28#16840473C2211yescharacteristic
29#16840470—21no—
30#16840468C2212yes—
31#16840466—22no—
32#16840427C2211yescharacteristic
33#16840425—21no—
34#16840316—21no—
35#16840316—22no—
36#16840315C2212yes—
37C2×#14519777—21no—
38C2×#14519777C2211yescharacteristic
39C2×#14519776—22no—
40C2×#14519776C2212yes—
41C4×#11758222C2211yescharacteristic
42#16840230C2212yes—
43C2×Q8×Dic61C2212yes—
44C2×C4×Dic122—21no—
45C2×C4×Dic122C2211yescharacteristic
46C4×Q8×D61—21no—
47#16840172C2214yes—
48#16840170C2214yes—
49#16840169C2214yes—
50#16840166C2214yes—
51#16840165C2212yes—
52#16840159C2214yes—
53#16840158C2212yes—
54#16840071C2214yes—
55#16840067C2214yes—
56#16840058C2212yes—
57#16840056C2214yes—
58#16840055C2214yes—
59#16840053C2212yes—
60#16840051C2214yes—
61#16840048C2212yes—
62#16840046C2214yes—
63#16840045C2214yes—
64#16840043C2212yes—
65#16840041C2214yes—
66#16839891C2214yes—
67#16839889C2212yes—
68#16839886C2212yes—
69#16839867C2212yes—
70#16839866C2214yes—
71#16839865C2214yes—
72#16839860C2212yes—
73C4×#11758202C2212yes—
74#16839854C2214yes—
75C4×#11758201C2212yes—
76#16839847C2214yes—
77#16839805C2212yes—
78#16839805C2212yes—
79#16839804C2212yes—
80#16839802C2211yescharacteristic
81#16839785C2212yes—
82#16839771C2211yescharacteristic
83#16839764C2212yes—
84#16839761C2211yescharacteristic
85C4×#11758194C2211yescharacteristic
86M16×Dic61C2212yes—
87C61×#533C2211yescharacteristic
88C2×C4×Q8×C61C2211yescharacteristic
89C61×#479C2214yes—
90C61×#477C2212yes—
91C61×#475C2212yes—
92C61×#428C2212yes—
93C61×#423C2211yescharacteristic
94C61×#419C2212yes—
95C2×#11758222C2311yescharacteristic
96C22×Dic122—21no—
97C22×Dic122—22no—
98C22×Dic122D411yescharacteristic
99C2×Q8×D61—21no—
100#14519808Q818yescomplemented
101C2×#11758202C2312yes—
102C2×#11758201C2312yes—
103C2×#11758194C2311yescharacteristic
104C2×#11758194C2311yescharacteristic
105#14519777—21no—
106#14519777—21no—
107#14519777—22no—
108#14519777—22no—
109#14519777—24no—
110#14519777C2312yes—
111#14519777C2312yes—
112#14519776—22no—
113#14519776—21no—
114#14519776—24no—
115#14519776—24no—
116#14519776—24no—
117#14519776—24no—
118#14519776—22no—
119#14519776—22no—
120#14519776C2312yes—
121#14519776C2312yes—
122#14519776C2314yes—
123#14519776C2314yes—
124#14519775—21no—
125#14519775—22no—
126#14519768C2312yes—
127#14519768C2312yes—
128#14519767—22no—
129#14519767—22no—
130#14519767—22no—
131#14519757—21no—
132#14519757—22no—
133#14519755—22no—
134#14519755—22no—
135#14519755—22no—
136#14519754—22no—
137#14519754—22no—
138#14519753—21no—
139#14519753—22no—
140Q8×Dic61—21no—
141Q8×Dic61—22no—
142Q8×Dic61—22no—
143Q8×Dic61C2314yes—
144Q8×Dic61C2314yes—
145C4×Dic122—24no—
146C4×Dic122—22no—
147C4×Dic122—22no—
148C4×Dic122—22no—
149C4×Dic122—22no—
150C4×Dic122D411yescharacteristic
151C4×Dic122D412yes—
152C4×Dic122D411yescharacteristic
153C4×Dic122C2311yescharacteristic
154C4×Dic122C2311yescharacteristic
155C4×Dic122C2312yes—
156C4×Dic122C2311yescharacteristic
157C4×Dic122C2311yescharacteristic
158#14519742—21no—
159#14519742—22no—
160#14519742C2312yes—
161#14519742C2312yes—
162C4×D244C2311yescharacteristic
163C4×D244C2311yescharacteristic
164#14519739C2312yes—
165#14519739C2312yes—
166C4×C22⋊D61—21no—
167C4×C22⋊D61—21no—
168#14519737—22no—
169#14519737—22no—
170#14519736C2311yescharacteristic
171#14519734—21no—
172#14519734—22no—
173C2×C4⋊Dic61—21no—
174C2×C4⋊Dic61—22no—
175C2×C4⋊Dic61D411yescharacteristic
176C2×C4⋊Dic61C2312yes—
177C2×#11758196—22no—
178C2×#11758196D412yes—
179C4⋊C4×D61—21no—
180C4⋊C4×D61—22no—
181C2×C4×Dic61—22no—
182C2×C4×Dic61C2312yes—
183C42×D61—21no—
184C42×D61—22no—
185#14519711C2314yes—
186#14519710C2314yes—
187#14519710C2312yes—
188#14519710C2314yes—
189#14519709C2314yes—
190#14519708C2314yes—
191#14519708C2312yes—
192#14519708C2314yes—
193#14519706C2314yes—
194#14519706C2314yes—
195#14519702C2314yes—
196#14519701C2312yes—
197#14519701C2312yes—
198#14519700C2312yes—
199#14519699C2314yes—
200#14519697C2312yes—
201#14519688C2312yes—
202#14519687C2314yes—
203C4×#92418C2312yes—
204C8×Dic61C2314yes—
205C22×Q8×C61C2311yescharacteristic
206C2×M16×C61C2312yes—
207C4⋊Q8×C61C2311yescharacteristic
208C4⋊Q8×C61C2311yescharacteristic
209#125×C61C2312yes—
210C22⋊Q8×C61—21no—
211C22⋊Q8×C61—21no—
212C4×Q8×C61—21no—
213C4×Q8×C61—21no—
214C4×Q8×C61—21no—
215C4×Q8×C61—21no—
216C4×Q8×C61C2312yes—
217C4×Q8×C61C2312yes—
218#117×C61C2312yes—
219C2×C4⋊C4×C61—21no—
220C2×C4⋊C4×C61C2311yescharacteristic
221C2×C42×C61—21no—
222C2×C42×C61C2311yescharacteristic
223#107×C61C2314yes—
224#106×C61C2314yes—
225C4⋊C8×C61C2312yes—
226C4⋊C8×C61C2312yes—
227#103×C61C2314yes—
228#103×C61C2314yes—
229C2×Q8×C61—21no—
230C2×Q8×C61—21no—
231C2×Q8×C61—21no—
232C2×Q8×C61—22no—
233C2×Q8×C61C2×Q814yescomplemented
234C2×Q8×C61C2412yes—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2411yescharacteristic
240C2×C22⋊D61—21no—
241C22×Dic61—22no—
242C22×Dic61C2×D412yes—
243C22×Dic61C2×D412yes—
244Q8×D61—44no—
245#11758222—22no—
246#11758222C2×Q814yes—
247C2×D244C2411yescharacteristic
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—22no—
251C2×C4×D61—21no—
252C2×C4×D61—22no—
253C2×Dic122—24no—
254C2×Dic122—22no—
255C2×Dic122—22no—
256C2×Dic122—22no—
257C2×Dic122—24no—
258C2×Dic122—24no—
259C2×Dic122—22no—
260C2×Dic122—84no—
261C2×Dic122—82no—
262C2×Dic122C2×D412yes—
263C2×Dic122C2×D411yescharacteristic
264C2×Dic122C2×D411yescharacteristic
265C2×Dic122C2411yescharacteristic
266M16×C61—24no—
267C2×C8×C61C2414yes—
268C4⋊C4×C61—22no—
269C4⋊C4×C61—22no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—22no—
272C4⋊C4×C61—22no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61C2412yes—
276C4⋊C4×C61C2412yes—
277C4⋊C4×C61C2412yes—
278C22⋊C4×C61—22no—
279C42×C61—22no—
280C42×C61—22no—
281C42×C61—22no—
282C42×C61C2×D411yescharacteristic
283C42×C61C2×D411yescharacteristic
284C42×C61C2411yescharacteristic
285C42×C61C2411yescharacteristic
286C22⋊Dic61—21no—
287#11758202C2×Q818yescomplemented
288#11758201C2×Q818yescomplemented
289#11758198—21no—
290#11758198—21no—
291#11758198—22no—
292#11758198—22no—
293C4⋊Dic61—22no—
294C4⋊Dic61—22no—
295C4⋊Dic61—22no—
296C4⋊Dic61—22no—
297C4⋊Dic61—24no—
298C4⋊Dic61—24no—
299C4⋊Dic61—22no—
300C4⋊Dic61C2×D411yescharacteristic
301C4⋊Dic61C2×D411yescharacteristic
302C4⋊Dic61C2×D412yes—
303C4⋊Dic61C2414yes—
304C4⋊Dic61C2411yescharacteristic
305C4⋊Dic61C2411yescharacteristic
306#11758196—21no—
307#11758196—21no—
308#11758196—22no—
309#11758196—22no—
310#11758196—24no—
311#11758196—24no—
312#11758196—22no—
313#11758196—22no—
314#11758196—22no—
315#11758196—22no—
316#11758196C2×D412yes—
317#11758196C2×D412yes—
318#11758196C2×D412yes—
319#11758196C2×D412yes—
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—22no—
324C4×Dic61—22no—
325C4×Dic61—24no—
326C4×Dic61—24no—
327C4×Dic61C2×D412yes—
328C4×Dic61C2×D412yes—
329C4×Dic61C2412yes—
330C4×Dic61C2412yes—
331#11758194—22no—
332#11758194C2×Q814yescomplemented
333C2×#92418C2412yes—
334C2×#92418C2412yes—
335C23×C61C22×D411yescharacteristic
336C22×D61—21no—
337Q8×C61—24no—
338Q8×C61—22no—
339Q8×C61—42no—
340Q8×C61—81no—
341Q8×C61C22×Q814yes—
342C2×C4×C61—24no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—41no—
349C2×C4×C61—42no—
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×Q812yes—
356C2×C4×C612−1+412yes—
357C2×C4×C61C2511yescharacteristic
358C22⋊D61—24no—
359C2×Dic61—21no—
360C2×Dic61—24no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—24no—
364C2×Dic61—42no—
365C2×Dic61—44no—
366C2×Dic61C22×D412yes—
367C2×Dic61C22×D412yes—
368C2×Dic61C22×D412yes—
369C2×Dic61C22×D412yes—
370D244—21no—
371D244C22×Q812yes—
372C4×D61—24no—
373C4×D61—42no—
374C4×D61—44no—
375C4×D61—82no—
376C4×D61—81no—
377Dic122—22no—
378Dic122—21no—
379Dic122—24no—
380Dic122—44no—
381Dic122—82no—
382Dic122—84no—
383Dic122—84no—
384Dic122—82no—
385Dic122—82no—
386Dic122#13714yescomplemented
387Dic122C22×Q812yes—
388C8×C61—24no—
389#92418—22no—
390#92418C22×Q814yes—
391Q8×#137—611nomaximal, Sylow
392C22×C61—21no—
393C22×C61—21no—
394C22×C61D4×Q812yes—
395C22×C61C23×D411yescharacteristic
396C2×D61—22no—
397C2×D61—41no—
398C2×D61—41no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—24no—
402C4×C61—21no—
403C4×C61—42no—
404C4×C61—42no—
405C4×C61—42no—
406C4×C61D4×Q812yes—
407C4×C61C2×#13712yes—
408C4×C61C23×Q811yescharacteristic
409C4×C61C2×2−1+411yescharacteristic
410Dic61—22no—
411Dic61—22no—
412Dic61—22no—
413Dic61—22no—
414Dic61—44no—
415Dic61—41no—
416Dic61—41no—
417Dic61C2×#13714yes—
418Q8×#41—611no—
419C2×Q82—611no—
420#3387—614no—
421#3387—612no—
422#3385—614no—
423#3385—612no—
424Q8×Q16—612no—
425Q8×SD16—612no—
426#3165—612no—
427#3165—611no—
428#3079—612no—
429#3079—611no—
430#3078—612no—
431#3078D6111yescharacteristic, complemented
432Q8×M16—611no—
433C4×#137—612no—
434C4×#137—611no—
435C2×C61—22no—
436C2×C61C2×D4×Q811yescharacteristic
437C2×C61C22×#13711yescharacteristic
438C2×C61#358511yescharacteristic
439D61—42no—
440C2×#137—611no—
441Q82—611no—
442Q82—612no—
443Q82—614no—
444Q82—612no—
445Q82—1221no—
446Q82—1221no—
447Q82—1222no—
448#557—611no—
449#557—612no—
450#554—611no—
451#554—612no—
452#554—1222no—
453#554—1221no—
454D4×Q8—611no—
455D4×Q8—1221no—
456#533—612no—
457#533—1222no—
458#533—1221no—
459#533C2×D6111yescharacteristic
460C2×C4⋊Q8—612no—
461C2×C4⋊Q8—611no—
462C2×C4⋊Q8—1221no—
463C2×C4⋊Q8—1222no—
464C4×#41—612no—
465C4×#41—611no—
466C2×C4×Q8—611no—
467C2×C4×Q8—612no—
468C2×C4×Q8—1221no—
469C2×C4×Q8—1221no—
470C2×C4×Q8C2×D6111yescharacteristic
471#501—614no—
472#501—614no—
473#501—614no—
474#500—612no—
475#500—614no—
476#498—612no—
477#498—614no—
478#479—614no—
479#479—614no—
480#479C2×D6114yes—
481#477—614no—
482#477—612no—
483#477—614no—
484#477C2×D6112yes—
485#476—614no—
486#476—612no—
487#475—614no—
488#475—612no—
489#475—614no—
490#475C2×D6112yes—
491#474—614no—
492#474—612no—
493#446—612no—
494#446—614no—
495C8×Q8—612no—
496#441—612no—
497#441—614no—
498#440—612no—
499#440—614no—
500C4×Q16—612no—
501C4×Q16—614no—
502C4×SD16—612no—
503C4×SD16—614no—
504#428—612no—
505#428—612no—
506#428—612no—
507#428—611no—
508#428C2×D6112yes—
509#423—612no—
510#423C2×D6111yescharacteristic
511#419—611no—
512#419C2×D6112yes—
513#417—612no—
514#417—611no—
515C4×M16—612no—
516C4×M16—611no—
517C61Q8×#13711yescharacteristic, complemented, Sylow
518C2×#41—611no—
519C22×Q8—611no—
520C22×Q8—1222no—
521C22×Q8—1221no—
522C22×Q8—1221no—
523C22×Q8C22×D6111yescharacteristic
524#137—618no—
525C2×Q16—612no—
526C2×SD16—612no—
527C2×M16—611no—
528C2×M16—611no—
529C2×M16C22×D6112yes—
530C4⋊Q8—614no—
531C4⋊Q8—614no—
532C4⋊Q8—612no—
533C4⋊Q8—612no—
534C4⋊Q8—612no—
535C4⋊Q8—612no—
536C4⋊Q8—1222no—
537C4⋊Q8—1224no—
538C4⋊Q8—1222no—
539C4⋊Q8—1222no—
540C4⋊Q8—1222no—
541C4⋊Q8—1224no—
542C4⋊Q8—1224no—
543C4⋊Q8—1224no—
544C4⋊Q8—1224no—
545C4⋊Q8—1221no—
546C4⋊Q8—1222no—
547C4⋊Q8—1222no—
548C4⋊Q8—1221no—
549C4⋊Q8—1221no—
550C4⋊Q8—1221no—
551C4⋊Q8C22×D6111yescharacteristic
552C4⋊Q8C22×D6111yescharacteristic
553#125—612no—
554#125—612no—
555#125—1222no—
556#125—1222no—
557#125—1222no—
558#125C22×D6112yes—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—1222no—
562C22⋊Q8—1222no—
563C22⋊Q8—1222no—
564C22⋊Q8—1222no—
565C22⋊Q8—1222no—
566C22⋊Q8—1222no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1222no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8—21no—
574C4×Q8—611no—
575C4×Q8—612no—
576C4×Q8—611no—
577C4×Q8—611no—
578C4×Q8—612no—
579C4×Q8—611no—
580C4×Q8—614no—
581C4×Q8—614no—
582C4×Q8—612no—
583C4×Q8—612no—
584C4×Q8—611no—
585C4×Q8—611no—
586C4×Q8—1222no—
587C4×Q8—1222no—
588C4×Q8—1222no—
589C4×Q8—1224no—
590C4×Q8—1222no—
591C4×Q8—1222no—
592C4×Q8—1222no—
593C4×Q8—1222no—
594C4×Q8—1221no—
595C4×Q8—1221no—
596C4×Q8C22×D6112yes—
597C4×Q8C22×D6112yes—
598C4×D4—612no—
599C4×D4—612no—
600C4×D4—611no—
601C4×D4—611no—
602C4×D4—1222no—
603C4×D4—1222no—
604C4×D4—1221no—
605C4×D4—1221no—
606#117—611no—
607#117—1222no—
608#117—1221no—
609#117C22×D6112yes—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—612no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—612no—
614C2×C4⋊C4—1222no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1222no—
617C2×C4⋊C4—1222no—
618C2×C4⋊C4—1221no—
619C2×C4⋊C4C22×D6111yescharacteristic
620C2×C42—21no—
621C2×C42—612no—
622C2×C42—1222no—
623C2×C42—1222no—
624C2×C42—1221no—
625C2×C42C22×D6111yescharacteristic
626#107—614no—
627#107—614no—
628#107—612no—
629#107—614no—
630#107C22×D6114yes—
631#106—614no—
632#106—614no—
633#106—612no—
634#106—614no—
635#106C22×D6114yes—
636C4⋊C8—614no—
637C4⋊C8—614no—
638C4⋊C8C22×D6112yes—
639C4⋊C8C22×D6112yes—
640#103—612no—
641#103—612no—
642#103—614no—
643#103—612no—
644#103C22×D6114yes—
645#103C22×D6114yes—
646#102—614no—
647#102—612no—
648#97—614no—
649#97—612no—
650C4×C8—614no—
651C4×C8—612no—
652#41—614no—
653#41—1222no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—22no—
658C2×Q8—611no—
659C2×Q8—612no—
660C2×Q8—611no—
661C2×Q8—611no—
662C2×Q8—1222no—
663C2×Q8—1224no—
664C2×Q8—1224no—
665C2×Q8—1222no—
666C2×Q8—1224no—
667C2×Q8—1222no—
668C2×Q8—1222no—
669C2×Q8—4882no—
670C2×Q8—4884no—
671C2×Q8—2444no—
672C2×Q8Q8×D6114yescomplemented
673C2×Q8C23×D6112yes—
674C2×D4—611no—
675C2×D4—1221no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—612no—
679C22×C4—612no—
680C22×C4—1222no—
681C22×C4—1222no—
682C22×C4—1221no—
683C22×C4—1222no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4D4×D6111yescharacteristic
687C22×C4D4×D6111yescharacteristic
688C22×C4C23×D6111yescharacteristic
689Q16—618no—
690SD16—618no—
691M16—24no—
692M16—614no—
693M16—1222no—
694C2×C8—612no—
695C2×C8—612no—
696C2×C8C23×D6114yes—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—22no—
704C4⋊C4—612no—
705C4⋊C4—611no—
706C4⋊C4—612no—
707C4⋊C4—612no—
708C4⋊C4—612no—
709C4⋊C4—612no—
710C4⋊C4—611no—
711C4⋊C4—614no—
712C4⋊C4—611no—
713C4⋊C4—611no—
714C4⋊C4—1222no—
715C4⋊C4—1222no—
716C4⋊C4—1224no—
717C4⋊C4—1224no—
718C4⋊C4—1224no—
719C4⋊C4—1224no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4—1222no—
723C4⋊C4—1222no—
724C4⋊C4—1222no—
725C4⋊C4—1222no—
726C4⋊C4—1222no—
727C4⋊C4—1222no—
728C4⋊C4—1222no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4C23×D6112yes—
732C4⋊C4C23×D6112yes—
733C4⋊C4C23×D6112yes—
734C22⋊C4—22no—
735C22⋊C4—1222no—
736C22⋊C4—1222no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C42—22no—
741C42—22no—
742C42—22no—
743C42—612no—
744C42—612no—
745C42—612no—
746C42—612no—
747C42—1222no—
748C42—1222no—
749C42—1224no—
750C42—1224no—
751C42—1221no—
752C42—1221no—
753C42—1221no—
754C42D4×D6111yescharacteristic
755C42D4×D6111yescharacteristic
756C42C23×D6111yescharacteristic
757C42C23×D6111yescharacteristic
758C23—1221no—
759C23C2×D4×D6111yescharacteristic
760Q8—22no—
761Q8—24no—
762Q8—42no—
763Q8—81no—
764Q8—614no—
765Q8—612no—
766Q8—1224no—
767Q8—1222no—
768Q8—1221no—
769Q8—4882no—
770Q8—4882no—
771Q8—4882no—
772Q8—4884no—
773Q8—4884no—
774Q8—2444no—
775Q8C2×Q8×D6114yes—
776D4—612no—
777D4—1224no—
778D4—1221no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—612no—
788C2×C4—612no—
789C2×C4—612no—
790C2×C4—612no—
791C2×C4—1224no—
792C2×C4—1221no—
793C2×C4—1224no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1224no—
797C2×C4—4881no—
798C2×C4—4882no—
799C2×C4—2444no—
800C2×C4—2442no—
801C2×C4—2444no—
802C2×C4—2442no—
803C2×C4C2×D4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C2×D4×D6111yescharacteristic
806C2×C4C2×D4×D6111yescharacteristic
807C2×C4C2×D4×D6111yescharacteristic
808C2×C4C2×Q8×D6112yes—
809C2×C4#1451982412yes—
810C2×C4C24×D6111yescharacteristic
811C8—24no—
812C8—614no—
813C8—1222no—
814C22—21no—
815C22—21no—
816C22—1222no—
817C22—2441no—
818C22—2441no—
819C22#1684042512yes—
820C22C22×D4×D6111yescharacteristic
821C4—21no—
822C4—24no—
823C4—21no—
824C4—21no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—614no—
829C4—1222no—
830C4—1222no—
831C4—1222no—
832C4—1222no—
833C4—2441no—
834C4—2441no—
835C4—2444no—
836C4#1684042512yes—
837C4#137×D6112yes—
838C4C22×Q8×D6111yescharacteristic
839C4C2×#1451982411yescharacteristic
840C2—22no—
841C2—2442no—
842C2C2×#1684042511yescharacteristic
843C2C2×#137×D6111yescharacteristic
844C2#2146059611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3078C2
socleC22×C61C23×D4
prime radicalC2×#11758222C23
hypercenter#3078D61
hypocenterC61Q8×#137
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
2. C2×Q8×Dic122C2semidirect
3. #21458754C2semidirect
4. #21458750C2semidirect
5. #21458732C2semidirect
6. #21458728C2semidirect
7. #21458700C2semidirect
8. #21458678C2semidirect
9. #21456366C2semidirect
10. #21456363C2semidirect
13. #21455621C2semidirect
14. #21454770C2semidirect
17. C61×#3078C2semidirect
100. #14519808Q8semidirect
233. C2×Q8×C61C2×Q8semidirect
287. #11758202C2×Q8semidirect
288. #11758201C2×Q8semidirect
332. #11758194C2×Q8semidirect
386. Dic122#137semidirect
431. #3078D61semidirect
517. C61Q8×#137semidirect
672. C2×Q8Q8×D61semidirect

Maximal subgroups

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

subgroupindex
#214593972
C2×Q8×Dic1222
#214587542
#214587502
#214587322
#214587282
#214587002
#214586782
#214563662
#214563632
#214556352
#214556322
#214556212
#214547702
C4×#145198082
#214546342
C61×#30782
Q8×#13761