Finite Group Databasebeta

← #30616895

Subgroups — #30616895

Order 15616.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840840C211yesmaximal, characteristic, complemented
2C2×#16840809C211yesmaximal, characteristic, complemented
3C2×#16840804C211yesmaximal, characteristic, complemented
4#21462537C211yesmaximal, characteristic, complemented
5#21461810C211yesmaximal, characteristic, complemented
6#21461810C211yesmaximal, characteristic, complemented
7#21461803C211yesmaximal, characteristic, complemented
8#21461788C211yesmaximal, characteristic, complemented
9#21461786C211yesmaximal, characteristic, complemented
10#21461773C211yesmaximal, characteristic, complemented
11#21461660C211yesmaximal, characteristic, complemented
12#21461598C211yesmaximal, characteristic, complemented
13#21461594C211yesmaximal, characteristic, complemented
14#21461562C211yesmaximal, characteristic, complemented
15#21455032C211yesmaximal, characteristic
16#16840840—24no—
17#16840840—24no—
18C2×#14519864—21no—
19C2×#14519864—21no—
20C2×#14519864C2211yescharacteristic
21C2×#14519864C2211yescharacteristic
22C2×#14519864C2211yescharacteristic
23C2×#14519864C2211yescharacteristic
24C2×#14519864C2211yescharacteristic, complemented
25C2×D61⋊M16C2211yescharacteristic
26C2×D61⋊M16C2211yescharacteristic
27C22×#11758217—21no—
28C22×#11758217—21no—
29#16840809—24no—
30#16840804—24no—
31#16840797—21no—
32#16840795—21no—
33#16840793—21no—
34#16840791—21no—
35C2×#14519848C2211yescharacteristic, complemented
36C2×#14519847C2211yescharacteristic, complemented
37#16840769C2211yescharacteristic, complemented
38C2×#14519841C2211yescharacteristic
39C2×#14519841C2211yescharacteristic
40C2×#14519841C2211yescharacteristic
41C2×#14519841C2211yescharacteristic
42C2×#14519841C2211yescharacteristic, complemented
43C2×#14519841C2211yescharacteristic, complemented
44#16840736C2211yescharacteristic, complemented
45#16840733C2211yescharacteristic
46#16840727C2211yescharacteristic, complemented
47C2×#14519831C2211yescharacteristic, complemented
48C2×C8×#6923C2211yescharacteristic, complemented
49C4×C22⋊#6923C2211yescharacteristic
50#16840638C2211yescharacteristic, complemented
51#16840638C2211yescharacteristic, complemented
52#16840632C2211yescharacteristic, complemented
53#16840632C2211yescharacteristic, complemented
54(C2×#6923)⋊C8C2211yescharacteristic, complemented
55(C2×#6923)⋊C8C2211yescharacteristic, complemented
56C22×#11758224C2211yescharacteristic
57C2×#14519796C2211yescharacteristic
58C2×#14519796C2211yescharacteristic
59#16840272C2211yescharacteristic
60#16839925C411yescharacteristic, complemented
61#16839925C411yescharacteristic, complemented
62#16839920C411yescharacteristic, complemented
63#16839913C411yescharacteristic, complemented
64#16839904C411yescharacteristic, complemented
65#16839904C411yescharacteristic, complemented
66#16839900C411yescharacteristic, complemented
67#16839755C2211yescharacteristic
68#16839755C2211yescharacteristic
69C22⋊C8×D61C2211yescharacteristic
70C61×#447C411yescharacteristic, complemented
71#14519864—28no—
72#14519864—28no—
73#14519864—22no—
74#14519864—22no—
75#14519864—22no—
76#14519864—22no—
77#14519864—22no—
78#14519864—22no—
79#14519864—22no—
80#14519864—22no—
81#14519864D414yescomplemented
82#14519864D414yescomplemented
83C2×#11758213D411yescharacteristic
84C2×#11758213D411yescharacteristic
85C2×#11758213C2311yescharacteristic
86C2×#11758213C2311yescharacteristic
87C2×#11758213C2311yescharacteristic
88C2×#11758213C2311yescharacteristic
89D61⋊M16—22no—
90D61⋊M16—22no—
91D61⋊M16—22no—
92D61⋊M16—22no—
93C2×#11758217—28no—
94C2×#11758217—28no—
95C2×#11758217—21no—
96C2×#11758217—21no—
97C2×#11758217—21no—
98C2×#11758217—21no—
99C2×#11758217—21no—
100C2×#11758217—21no—
101C2×#11758217D411yescharacteristic
102C2×#11758217D411yescharacteristic
103C2×D61⋊C8—21no—
104C2×D61⋊C8C2311yescharacteristic
105C2×D61⋊C8C2311yescharacteristic
106C22×#92420—21no—
107C22×#92420—21no—
108C22×#92420—21no—
109C22×#92420—21no—
110C22×#92420—21no—
111C2×C22⋊#6923—21no—
112C2×C4×#6923C2311yescharacteristic
113C2×C4×#6923C2311yescharacteristic
114#14519848—22no—
115#14519847—22no—
116#14519844—21no—
117C4⋊#92420—21no—
118#14519841—22no—
119#14519841—22no—
120#14519841—22no—
121#14519841—22no—
122#14519841—22no—
123#14519841—22no—
124#14519834—21no—
125C22⋊#92420—21no—
126C22⋊#92420—21no—
127C22⋊#92420—21no—
128#14519832—21no—
129#14519831—22no—
130C4×#92420—21no—
131C8×#6923—22no—
132(C2×#6923)⋊C4—21no—
133C2×#11758224—22no—
134C2×#11758224—22no—
135C2×#11758224—22no—
136C2×#11758224—22no—
137C2×#11758224—21no—
138C2×#11758224—21no—
139C2×#11758224C2×C411yescharacteristic
140C2×#11758224C2×C411yescharacteristic
141C2×#11758224C2311yescharacteristic
142C2×#11758224C2311yescharacteristic
143C2×#11758224C2311yescharacteristic
144C22×Dic122C2×C411yescharacteristic
145C22×C22⋊D61—21no—
146C23×Dic61—21no—
147C22×C4×D61C2311yescharacteristic
148#14519796—22no—
149#14519796—22no—
150#14519796—22no—
151#14519796—22no—
152C2×Dic244C2×C411yescharacteristic
153C2×Dic244C2×C411yescharacteristic
154C2×#11758200C2×C411yescharacteristic
155C2×#11758200C2×C411yescharacteristic
156C2×#11758200C2×C411yescharacteristic
157C2×#11758200C2×C411yescharacteristic
158C2×C8×D61C2311yescharacteristic
159C2×C8×D61C2311yescharacteristic
160#14519759—21no—
161#14519757C2×C411yescharacteristic
162#14519756C2×C411yescharacteristic
163#14519748C2×C411yescharacteristic
164#14519745—21no—
165D4×Dic61—21no—
166#14519737—21no—
167#14519735C2311yescharacteristic
168#14519702C2×C411yescharacteristic
169#14519702C2×C411yescharacteristic
170#14519700C2×C411yescharacteristic
171#14519700C2×C411yescharacteristic
172#14519698C2×C411yescharacteristic
173#14519698C2×C411yescharacteristic
174C22⋊#92418C2×C411yescharacteristic
175#14519689C2×C411yescharacteristic
176#14519689C2×C411yescharacteristic
177C22×D4×C61C2×C411yescharacteristic
178C2×D8×C61C2×C411yescharacteristic
179C2×D8×C61C2×C411yescharacteristic
180#121×C61C2×C411yescharacteristic
181#102×C61C2×C411yescharacteristic
182#102×C61C2×C411yescharacteristic
183C22⋊C8×C61C2×C411yescharacteristic
184C24×C61—21no—
185C23×D61#4111yescharacteristic
186C22×#6923—21no—
187C22×#6923—21no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61C22×C411yescharacteristic
193C2×D4×C61C22×C411yescharacteristic
194C2×D4×C61C22×C411yescharacteristic
195C22×C4×C61C22×C411yescharacteristic
196C2×C22⋊D61—24no—
197C2×C22⋊D61—24no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C22×Dic61—24no—
205C22×Dic61—24no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61C2×D411yescharacteristic
213#11758224—24no—
214#11758224—24no—
215#11758224—24no—
216#11758224—24no—
217#11758224—22no—
218#11758224—22no—
219#11758224—21no—
220#11758224—21no—
221#11758224—21no—
222#11758224—21no—
223#11758224—21no—
224#11758224—21no—
225#11758224—21no—
226#11758224—21no—
227#11758224—22no—
228#11758224—22no—
229#11758224C2×D412yes—
230#11758224C2×D412yes—
231#11758224#4112yes—
232#11758224#4112yes—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61C22×C411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61#4111yescharacteristic
240C2×C4×D61C2411yescharacteristic
241C2×Dic122—21no—
242C2×Dic122—22no—
243C2×Dic122—22no—
244C2×Dic122C22×C411yescharacteristic
245C2×Dic122C22×C411yescharacteristic
246C2×Dic122C22×C411yescharacteristic
247C22⋊#6923—42no—
248#11758217—24no—
249#11758217—24no—
250#11758217—24no—
251#11758217—22no—
252#11758217—22no—
253#11758217—24no—
254#11758217—24no—
255#11758217—42no—
256C2×#92420—24no—
257C2×#92420—24no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—24no—
261C2×#92420—24no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—42no—
265C2×#92420C2×D411yescharacteristic
266C2×#92420C2×D411yescharacteristic
267C2×#92420C2×D411yescharacteristic
268C2×#92420C2×D411yescharacteristic
269C4×#6923—21no—
270C4×#6923—21no—
271C4×#6923—21no—
272C4×#6923—21no—
273#11758213—21no—
274#11758213—21no—
275#11758213—22no—
276#11758213—22no—
277#11758213—21no—
278#11758213—21no—
279#11758213—21no—
280#11758213—21no—
281#11758213C2×D412yes—
282#11758213C2×D412yes—
283D61⋊C8—24no—
284D61⋊C8—21no—
285D61⋊C8—21no—
286D61⋊C8C2×D412yes—
287D61⋊C8C2×D412yes—
288D8×C61—22no—
289D8×C61—22no—
290C2×C8×C61C22×C411yescharacteristic
291C2×C8×C61C22×C411yescharacteristic
292C4⋊C4×C61C22×C411yescharacteristic
293C22⋊C4×C61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296#11758200—22no—
297#11758200—22no—
298#11758200—22no—
299#11758200—22no—
300#11758198—21no—
301#11758198—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61C22×C411yescharacteristic
304#11758196—21no—
305C4×Dic61—21no—
306C2×#92418C22×C411yescharacteristic
307C2×#92418C22×C411yescharacteristic
308Dic244—22no—
309Dic244—22no—
310C8×D61—21no—
311C8×D61—21no—
312C8×D61—21no—
313C8×D61—21no—
314C23×C61—24no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61—81no—
319C23×C61—81no—
320C23×C61C4×D411yescharacteristic
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—41no—
324C22×D61—41no—
325C22×D61C4×D411yescharacteristic
326C22×D61C2×#4111yescharacteristic
327C2×#6923—22no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333D4×C61—24no—
334D4×C61—21no—
335D4×C61—21no—
336D4×C61—21no—
337D4×C61—21no—
338D4×C61—81no—
339D4×C61C4×D412yes—
340D4×C61C4×D412yes—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61C4×D411yescharacteristic
345C2×C4×C61C23×C411yescharacteristic
346C22⋊D61—24no—
347C22⋊D61—24no—
348C22⋊D61—22no—
349C22⋊D61—22no—
350C22⋊D61—22no—
351C22⋊D61—22no—
352C22⋊D61—41no—
353C22⋊D61—41no—
354C22⋊D61—81no—
355C2×Dic61—24no—
356C2×Dic61—24no—
357C2×Dic61—24no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61C4×D411yescharacteristic
371C2×Dic61C22×D411yescharacteristic
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—21no—
375C4×D61—21no—
376C4×D61—21no—
377C4×D61—21no—
378C4×D61C22×D411yescharacteristic
379C4×D61C22×D411yescharacteristic
380C4×D61C2×#4111yescharacteristic
381C4×D61C2×#4111yescharacteristic
382Dic122—24no—
383Dic122—21no—
384Dic122—21no—
385Dic122—21no—
386Dic122—21no—
387Dic122C4×D412yes—
388Dic122C4×D412yes—
389#92420—21no—
390#92420—21no—
391#92420—22no—
392#92420—22no—
393#92420—41no—
394#92420—41no—
395#92420#12012yes—
396#92420#12012yes—
397C8×C61—21no—
398C8×C61—21no—
399#92418—21no—
400#92418—21no—
401#21468—611nomaximal, Sylow
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—22no—
406C22×C61—22no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—84no—
415C22×C61C2×C4×D411yescharacteristic
416C2×D61—21no—
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—21no—
420C2×D61—21no—
421C2×D61—81no—
422C2×D61—81no—
423C2×D61#52511yescharacteristic
424C2×D61#52511yescharacteristic
425#6923—42no—
426#6923—81no—
427C4×C61—21no—
428C4×C61—41no—
429C4×C61C2×C4×D411yescharacteristic
430C4×C61C2×C4×D411yescharacteristic
431Dic61—22no—
432Dic61—22no—
433Dic61—21no—
434Dic61—41no—
435Dic61—41no—
436Dic61C2×#12011yescharacteristic
437Dic61#52511yescharacteristic
438C2×#568—611no—
439#3002—611no—
440C2×#444—611no—
441C2×#443—611no—
442#2930—611no—
443#1876—611no—
444#1876—611no—
445#1871—611no—
446#1866—611no—
447#1866—611no—
448#1855—611no—
449#1789—611no—
450#1765—611no—
451#1764—611no—
452#1753—611no—
453C2×C61—41no—
454C2×C61—42no—
455C2×C61—42no—
456C2×C61—81no—
457C2×C61C4×#12011yescharacteristic
458C2×C61#295611yescharacteristic
459C2×C61#295711yescharacteristic
460D61—21no—
461D61—21no—
462D61—41no—
463C22×#41—611no—
464C2×#135—611no—
465C2×#135—611no—
466#568—1224no—
467#568—1224no—
468C2×#131—611no—
469C2×#131—611no—
470C2×#131—611no—
471C2×#131—611no—
472C2×#131—611no—
473C2×#131—1221no—
474C2×#131—1221no—
475C22×M16—611no—
476C22×M16—611no—
477C22×M16—1221no—
478C22×M16—1221no—
479#525—611no—
480#452—611no—
481#452—611no—
482#451—611no—
483#450—611no—
484#449—611no—
485#449—611no—
486#448—611no—
487#447#692311yescharacteristic, complemented
488#444—1224no—
489#443—1224no—
490#436—1221no—
491#436—1221no—
492#435—1221no—
493#435—1221no—
494C2×#108—611no—
495C2×#108—611no—
496#424—611no—
497C2×#104—611no—
498C2×#104—611no—
499C2×#104—611no—
500C2×#104—611no—
501C2×#104—611no—
502C2×#104—611no—
503#416—611no—
504#416—611no—
505#408—611no—
506#407—611no—
507C2×C22⋊C8—611no—
508#405—611no—
509C2×#97—611no—
510C2×C4×C8—611no—
511C4×C22⋊C4—611no—
512#341—611no—
513#341—611no—
514#339—611no—
515#339—611no—
516#336—611no—
517#336—611no—
518C61#2146811yescharacteristic, complemented, Sylow
519C2×#41—611no—
520C2×#41—611no—
521C2×#41—611no—
522C2×#41—611no—
523C2×#41—611no—
524C2×#41—1221no—
525C2×#41—1221no—
526C2×#41—1222no—
527C2×#41—1222no—
528C2×#41—1222no—
529C2×#41—1222no—
530C22×Q8—611no—
531C22×D4—1221no—
532C22×D4C2×#692311yescharacteristic
533C23×C4—611no—
534C23×C4—1221no—
535#135—1222no—
536#135—1222no—
537#135—1222no—
538#135—1222no—
539C2×Q16—611no—
540C2×Q16—611no—
541C2×SD16—611no—
542C2×SD16—611no—
543C2×SD16—611no—
544C2×SD16—611no—
545C2×D8C2×#692311yescharacteristic
546C2×D8C2×#692311yescharacteristic
547#131—614no—
548#131—614no—
549#131—1222no—
550#131—1222no—
551#131—1222no—
552#131—1222no—
553#131—1222no—
554#131—1222no—
555#131—1222no—
556#131—1222no—
557#131—1228no—
558#131—1228no—
559C2×M16—611no—
560C2×M16—611no—
561C2×M16—611no—
562C2×M16—611no—
563C2×M16—611no—
564C2×M16—611no—
565C2×M16—611no—
566C2×M16—611no—
567C2×M16—1221no—
568C2×M16—1221no—
569C2×M16—1221no—
570C2×M16—1221no—
571C2×M16—1222no—
572C2×M16—1222no—
573C2×M16—1221no—
574C2×M16—1222no—
575C2×M16—1222no—
576C2×M16—1221no—
577C2×M16—1228no—
578C2×M16—1228no—
579C22×C8—611no—
580C22×C8—611no—
581C22×C8—611no—
582C22×C8—611no—
583C22×C8—1221no—
584C22×C8—1221no—
585C22×C8—1221no—
586C22×C8—1221no—
587C22×C8—1221no—
588C22×C8—1221no—
589#123—1221no—
590C22⋊Q8—611no—
591C22⋊Q8—611no—
592#121—611no—
593#121C2×#692311yescharacteristic
594#120—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597#117—611no—
598C2×C22⋊C4—1221no—
599C2×C42—611no—
600C2×C42—611no—
601#108—1222no—
602#108—1222no—
603C4⋊C8—1221no—
604C4⋊C8—1221no—
605#104—1222no—
606#104—1222no—
607#104—1222no—
608#104—1222no—
609#104—1222no—
610#104—1222no—
611#103—611no—
612#103—611no—
613#103—611no—
614#103—611no—
615#102—611no—
616#102—611no—
617#102C2×#692311yescharacteristic
618#102C2×#692311yescharacteristic
619C22⋊C8—611no—
620C22⋊C8—611no—
621C22⋊C8—611no—
622C22⋊C8—1221no—
623C22⋊C8—1221no—
624C22⋊C8—1221no—
625C22⋊C8—1221no—
626C22⋊C8C2×#692311yescharacteristic
627#97—1222no—
628#97—1221no—
629C4×C8—1222no—
630C4×C8—1221no—
631#95—1221no—
632C24—21no—
633C24—611no—
634#41—612no—
635#41—612no—
636#41—612no—
637#41—612no—
638#41—1221no—
639#41—1221no—
640#41—1221no—
641#41—1221no—
642#41—1221no—
643#41—1221no—
644#41—1221no—
645#41—1221no—
646#41—1222no—
647#41—1222no—
648#41—1224no—
649#41—1224no—
650#41—1224no—
651#41—1224no—
652#41—1222no—
653#41—1222no—
654C2×Q8—611no—
655C2×Q8—611no—
656C2×Q8—611no—
657C2×Q8—1222no—
658C2×Q8—1222no—
659C2×Q8—1221no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—1224no—
669C2×D4—1224no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4C22×#692311yescharacteristic
673C2×D4C22×#692311yescharacteristic
674C2×D4C22×#692311yescharacteristic
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1224no—
690C22×C4—1224no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4C22×#692311yescharacteristic
695Q16—1222no—
696Q16—1222no—
697SD16—1222no—
698SD16—1222no—
699SD16—1222no—
700SD16—1222no—
701D8—22no—
702D8—22no—
703M16—612no—
704M16—612no—
705M16—1222no—
706M16—1222no—
707M16—1222no—
708M16—1222no—
709M16—1224no—
710M16—1224no—
711M16—1221no—
712M16—1221no—
713M16—1224no—
714M16—1224no—
715M16—1224no—
716M16—1221no—
717M16—1221no—
718M16—1221no—
719M16—1221no—
720M16—2442no—
721C2×C8—611no—
722C2×C8—612no—
723C2×C8—611no—
724C2×C8—612no—
725C2×C8—611no—
726C2×C8—611no—
727C2×C8—611no—
728C2×C8—611no—
729C2×C8—1221no—
730C2×C8—1221no—
731C2×C8—1221no—
732C2×C8—1221no—
733C2×C8—1224no—
734C2×C8—1224no—
735C2×C8—1221no—
736C2×C8—1221no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1224no—
740C2×C8—1224no—
741C2×C8—1224no—
742C2×C8—1221no—
743C2×C8—1221no—
744C2×C8—2442no—
745C2×C8C22×#692311yescharacteristic
746C2×C8C22×#692311yescharacteristic
747C4⋊C4—611no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4C22×#692311yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—2442no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C23—24no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—81no—
767C23—81no—
768C23—611no—
769C23—611no—
770C23—1221no—
771C23—1221no—
772C23—2441no—
773C23—2441no—
774C23D4×#692311yescharacteristic
775Q8—612no—
776Q8—612no—
777Q8—1224no—
778Q8—1221no—
779Q8—1221no—
780Q8—1221no—
781Q8—1221no—
782D4—24no—
783D4—21no—
784D4—21no—
785D4—21no—
786D4—21no—
787D4—81no—
788D4—1222no—
789D4—1222no—
790D4—1222no—
791D4—1222no—
792D4—1224no—
793D4—1224no—
794D4—4881no—
795D4—2441no—
796D4—2441no—
797D4D4×#692312yes—
798D4D4×#692312yes—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—611no—
803C2×C4—611no—
804C2×C4—611no—
805C2×C4—611no—
806C2×C4—611no—
807C2×C4—611no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1224no—
819C2×C4—1224no—
820C2×C4—1224no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1222no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4D4×#692311yescharacteristic
836C2×C4C23×#692311yescharacteristic
837C8—21no—
838C8—21no—
839C8—612no—
840C8—612no—
841C8—1221no—
842C8—1221no—
843C8—1222no—
844C8—1222no—
845C8—1221no—
846C8—1221no—
847C8—2441no—
848C8—2441no—
849C22—21no—
850C22—22no—
851C22—22no—
852C22—21no—
853C22—21no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—84no—
862C22—611no—
863C22—611no—
864C22—1221no—
865C22—1221no—
866C22—1221no—
867C22—1221no—
868C22—1221no—
869C22—4881no—
870C22—4881no—
871C22C2×D4×#692311yescharacteristic
872C4—21no—
873C4—41no—
874C4—611no—
875C4—611no—
876C4—1221no—
877C4—1222no—
878C4—1222no—
879C4—4881no—
880C4—2442no—
881C4—2441no—
882C4—2441no—
883C4C2×D4×#692311yescharacteristic
884C4C2×D4×#692311yescharacteristic
885C2—41no—
886C2—42no—
887C2—42no—
888C2—81no—
889C2—1221no—
890C2—1221no—
891C2—2441no—
892C2#120×#692311yescharacteristic
893C2#2146259311yescharacteristic
894C2#2146259511yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#447C4
socleC22×C61C2×C4×D4
prime radical#21455032C2
cosocleC2×C4×D61C24
hypercenter#447#6923
hypocenterC61#21468
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#16840840C2semidirect
2. C2×#16840809C2semidirect
3. C2×#16840804C2semidirect
4. #21462537C2semidirect
5. #21461810C2semidirect
6. #21461810C2semidirect
7. #21461803C2semidirect
8. #21461788C2semidirect
9. #21461786C2semidirect
10. #21461773C2semidirect
11. #21461660C2semidirect
12. #21461598C2semidirect
13. #21461594C2semidirect
14. #21461562C2semidirect
24. C2×#14519864C22semidirect
35. C2×#14519848C22semidirect
36. C2×#14519847C22semidirect
37. #16840769C22semidirect
42. C2×#14519841C22semidirect
43. C2×#14519841C22semidirect
44. #16840736C22semidirect
46. #16840727C22semidirect
47. C2×#14519831C22semidirect
48. C2×C8×#6923C22semidirect
50. #16840638C22semidirect
51. #16840638C22semidirect
52. #16840632C22semidirect
53. #16840632C22semidirect
54. (C2×#6923)⋊C8C22semidirect
55. (C2×#6923)⋊C8C22semidirect
60. #16839925C4semidirect
61. #16839925C4semidirect
62. #16839920C4semidirect
63. #16839913C4semidirect
64. #16839904C4semidirect
65. #16839904C4semidirect
66. #16839900C4semidirect
70. C61×#447C4semidirect
81. #14519864D4semidirect
82. #14519864D4semidirect
487. #447#6923semidirect
518. C61#21468semidirect

Maximal subgroups

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

subgroupindex
C2×#168408402
C2×#168408092
C2×#168408042
#214625372
#214618102
#214618032
#214617882
#214617862
#214617732
#214616602
#214615982
#214615942
#214615622
#214550322
#2146861