Finite Group Databasebeta

← #30622741

Subgroups — #30622741

Order 15616.

1126 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840803C211yesmaximal, characteristic, complemented
2C2×SD16×#6923C211yesmaximal, characteristic, complemented
3#21462350C211yesmaximal, characteristic, complemented
4#21462349C211yesmaximal, characteristic, complemented
5#21461987C211yesmaximal, characteristic, complemented
6#21461986C211yesmaximal, characteristic, complemented
7#21461969C211yesmaximal, characteristic, complemented
8#21461966C211yesmaximal, characteristic, complemented
9#21461815C211yesmaximal, characteristic, complemented
10#21461814C211yesmaximal, characteristic, complemented
11#21461814C211yesmaximal, characteristic, complemented
12#21461812C211yesmaximal, characteristic, complemented
13#21461633C211yesmaximal, characteristic, complemented
14#21461617C211yesmaximal, characteristic, complemented
15#496×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923—21no—
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20C2×D4×#6923C2211yescharacteristic
21#16840803—24no—
22SD16×#6923—24no—
23C2×#14519846C2211yescharacteristic
24C2×#14519845C2211yescharacteristic
25D61⋊(C4⋊C8)C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519839C2211yescharacteristic
32C2×#14519839C2211yescharacteristic
33C2×#14519839C2211yescharacteristic
34C2×#14519831C2211yescharacteristic
35C2×C8×#6923C2211yescharacteristic
36(C2×#6923)⋊Q8C2211yescharacteristic
37#16840714—21no—
38#16840714C2211yescharacteristic
39#16840714C2211yescharacteristic
40#16840714C2211yescharacteristic
41#16840712—21no—
42#16840712—21no—
43#16840710—21no—
44#16840710—21no—
45#16840709—21no—
46C4×C4⋊#6923C2211yescharacteristic
47C4×C4⋊#6923C2211yescharacteristic
48C4×C4⋊#6923C2211yescharacteristic
49C22⋊C4×#6923—21no—
50#16840636C2211yescharacteristic
51#16840636C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×SD16×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56C2×D8×D61C2211yescharacteristic
57C2×D8×D61C2211yescharacteristic
58#127×D61C2211yescharacteristic
59#124×D61C2211yescharacteristic
60#16840152C411yescharacteristic, complemented
61#16840151C411yescharacteristic, complemented
62#16840150C411yescharacteristic, complemented
63#16840150C411yescharacteristic, complemented
64#16840149C411yescharacteristic, complemented
65#16840148C411yescharacteristic, complemented
66#16840148C411yescharacteristic, complemented
67#97×D61C2211yescharacteristic
68C61×#496C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C23×#6923—21no—
72C2×D61⋊C8C2311yescharacteristic
73C2×D61⋊C8C2311yescharacteristic
74Q8×#6923—22no—
75Q8×#6923—41no—
76D4×#6923—22no—
77D4×#6923—22no—
78D4×#6923—22no—
79D4×#6923—41no—
80D4×#6923—41no—
81D4×#6923—41no—
82D4×#6923—44no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923D411yescharacteristic
85C2×C4⋊#6923D411yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C22⋊#6923—21no—
97C2×C22⋊#6923—21no—
98C2×C22⋊#6923—21no—
99C2×C4×#6923—21no—
100C2×C4×#6923—21no—
101C2×C4×#6923—21no—
102C2×C4×#6923C2311yescharacteristic
103C2×C4×#6923C2311yescharacteristic
104#14519846—22no—
105#14519845D414yescomplemented
106#14519844—21no—
107C4⋊#92420—21no—
108#14519840—22no—
109#14519840—41no—
110#14519839—22no—
111#14519839—22no—
112#14519839—22no—
113#14519839—41no—
114#14519839—41no—
115#14519839—41no—
116#14519831—22no—
117C8×#6923—22no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4—21no—
122(C2×#6923)⋊C4D411yescharacteristic
123(C2×#6923)⋊C4D411yescharacteristic
124C2×Q8×D61C2311yescharacteristic
125C2×D4×D61—21no—
126C2×D4×D61—21no—
127C2×D4×D61C2311yescharacteristic
128C2×D4×D61C2311yescharacteristic
129C2×D4×D61C2311yescharacteristic
130C2×#11758190C2×C411yescharacteristic, complemented
131C2×#11758190C2×C411yescharacteristic, complemented
132C2×#11758200C2×C411yescharacteristic, complemented
133C2×#11758200C2×C411yescharacteristic, complemented
134C2×#11758201C2×C411yescharacteristic, complemented
135C2×#11758201C2×C411yescharacteristic, complemented
136SD16×D61—22no—
137SD16×D61—22no—
138SD16×D61—41no—
139SD16×D61—41no—
140C2×D488C2×C411yescharacteristic, complemented
141C2×D488C2×C411yescharacteristic, complemented
142C2×#11758199C2×C411yescharacteristic, complemented
143C2×#11758199C2×C411yescharacteristic, complemented
144C2×#11758199C2×C411yescharacteristic, complemented
145C2×#11758199C2×C411yescharacteristic, complemented
146D8×D61—22no—
147D8×D61—22no—
148D8×D61—41no—
149D8×D61—41no—
150C2×C8×D61C2311yescharacteristic
151C2×C8×D61C2311yescharacteristic
152#14519774C2×C411yescharacteristic, complemented
153#14519773—21no—
154#14519773—21no—
155#14519773C2×C411yescharacteristic, complemented
156#14519773C2×C411yescharacteristic, complemented
157#14519766C2×C411yescharacteristic, complemented
158#14519765C2×C411yescharacteristic, complemented
159#14519764C2×C411yescharacteristic, complemented
160#14519763—21no—
161#14519763—21no—
162C22⋊C4×D61—21no—
163C22⋊C4×D61—21no—
164C42×D61C2311yescharacteristic
165#14519688C2×C411yescharacteristic, complemented
166#14519687C2×C411yescharacteristic, complemented
167#14519687C2×C411yescharacteristic, complemented
168C2×SD16×C61C2×C411yescharacteristic, complemented
169C2×SD16×C61C2×C411yescharacteristic, complemented
170C2×D8×C61C2×C411yescharacteristic, complemented
171C2×D8×C61C2×C411yescharacteristic, complemented
172#127×C61C2×C411yescharacteristic, complemented
173#124×C61C2×C411yescharacteristic, complemented
174#97×C61C2×C411yescharacteristic, complemented
175C23×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—21no—
181C22×#6923—21no—
182C22×#6923—42no—
183C22×#6923—42no—
184C22×#6923—42no—
185C22×#6923—42no—
186C22×#6923—42no—
187C22×#6923—42no—
188C22×#6923—81no—
189C22×#6923—81no—
190C22×#6923—81no—
191C22×#6923C2×D411yescharacteristic
192C22×#6923C2×D411yescharacteristic
193C22×#6923C2×D411yescharacteristic
194C22×#6923C2×D411yescharacteristic
195C2×Q8×C61C22×C411yescharacteristic
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61C22×C411yescharacteristic
199C2×D4×C61C22×C411yescharacteristic
200C2×D4×C61C22×C411yescharacteristic
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C2×C22⋊D61—21no—
206C2×C22⋊D61—21no—
207C2×C22⋊D61—21no—
208Q8×D61—21no—
209Q8×D61—21no—
210Q8×D61—21no—
211Q8×D61—21no—
212D4×D61—21no—
213D4×D61—21no—
214D4×D61—21no—
215D4×D61—21no—
216D4×D61—21no—
217D4×D61—21no—
218D4×D61—21no—
219D4×D61—21no—
220D4×D61—21no—
221D4×D61—21no—
222D4×D61—21no—
223D4×D61—21no—
224D4×D61—42no—
225D4×D61—42no—
226D4×D61—81no—
227D4×D61—81no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244C22×C411yescharacteristic
231C2×D244C22×C411yescharacteristic
232C2×D244C22×C411yescharacteristic
233C2×C4×D61—21no—
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2411yescharacteristic
237C2×Dic122—21no—
238C2×Dic122C22×C411yescharacteristic
239C22⋊#6923—42no—
240C22⋊#6923—42no—
241C22⋊#6923—42no—
242C22⋊#6923—42no—
243C22⋊#6923—42no—
244C22⋊#6923—42no—
245C22⋊#6923—81no—
246C22⋊#6923—81no—
247C22⋊#6923—81no—
248C2×#92420—21no—
249C2×#92420—21no—
250C4⋊#6923—22no—
251C4⋊#6923—21no—
252C4⋊#6923—21no—
253C4⋊#6923—21no—
254C4⋊#6923—21no—
255C4⋊#6923—21no—
256C4⋊#6923—21no—
257C4⋊#6923—41no—
258C4⋊#6923—42no—
259C4⋊#6923C2×D412yes—
260C4⋊#6923C2×D412yes—
261C4×#6923—21no—
262C4×#6923—21no—
263C4×#6923—21no—
264C4×#6923—21no—
265C4×#6923—42no—
266C4×#6923—42no—
267C4×#6923—81no—
268D61⋊C8—21no—
269D61⋊C8—21no—
270D61⋊C8—21no—
271D61⋊C8—21no—
272SD16×C61—22no—
273SD16×C61—41no—
274D8×C61—22no—
275D8×C61—41no—
276C2×C8×C61C22×C411yescharacteristic
277C2×C8×C61C22×C411yescharacteristic
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C42×C61C22×C411yescharacteristic
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283#11758201—22no—
284#11758201—41no—
285#11758200—22no—
286#11758200—41no—
287#11758199—22no—
288#11758199—22no—
289#11758199—41no—
290#11758199—41no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295C4×Dic61C22×C411yescharacteristic
296C4×Dic61#4111yescharacteristic
297C4×Dic61#4111yescharacteristic
298C2×#92418C22×C411yescharacteristic
299C2×#92418C22×C411yescharacteristic
300D488—22no—
301D488—41no—
302#11758190—22no—
303#11758190—41no—
304C8×D61—21no—
305C8×D61—21no—
306C8×D61C2×D412yes—
307C8×D61#4112yes—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—41no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61C22×D411yescharacteristic
333C2×#6923—21no—
334C2×#6923—21no—
335C2×#6923—21no—
336C2×#6923—21no—
337C2×#6923—21no—
338C2×#6923—22no—
339C2×#6923—22no—
340C2×#6923—21no—
341C2×#6923—21no—
342C2×#6923—21no—
343C2×#6923—21no—
344C2×#6923—21no—
345C2×#6923—21no—
346C2×#6923—41no—
347C2×#6923—41no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—84no—
357C2×#6923—84no—
358C2×#6923—84no—
359C2×#6923AGL(1,ℤ/8)12yes—
360Q8×C61—21no—
361Q8×C61—21no—
362D4×C61—21no—
363D4×C61—21no—
364D4×C61—21no—
365D4×C61—21no—
366D4×C61—21no—
367D4×C61—21no—
368D4×C61—42no—
369D4×C61—81no—
370C2×C4×C61—21no—
371C2×C4×C61C4×D411yescharacteristic
372C2×C4×C61C4×D411yescharacteristic
373C2×C4×C61C23×C411yescharacteristic
374C22⋊D61—42no—
375C22⋊D61—42no—
376C22⋊D61—41no—
377C22⋊D61—41no—
378C22⋊D61—41no—
379C22⋊D61—41no—
380C22⋊D61—41no—
381C22⋊D61—41no—
382C22⋊D61—81no—
383C22⋊D61—81no—
384C2×Dic61—21no—
385C2×Dic61C4×D411yescharacteristic
386C2×Dic61C4×D411yescharacteristic
387C2×Dic61C2×#4111yescharacteristic
388D244—21no—
389D244—21no—
390D244—21no—
391D244—21no—
392D244—21no—
393D244—21no—
394D244—42no—
395D244—81no—
396C4×D61—21no—
397C4×D61—21no—
398C4×D61—21no—
399C4×D61—21no—
400C4×D61—41no—
401C4×D61—41no—
402C4×D61C22×D411yescharacteristic
403C4×D61C2×#4111yescharacteristic
404C4×D61H(5,𝔽2)11yescharacteristic
405C4×D61H(5,𝔽2)11yescharacteristic
406Dic122—21no—
407Dic122—21no—
408Dic122—41no—
409Dic122—41no—
410#92420—41no—
411#92420—41no—
412C8×C61—21no—
413C8×C61C4×D412yescomplemented
414#92418—21no—
415#92418C4×D412yescomplemented
416#23193—611nomaximal, Sylow
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61C2×C4×D411yescharacteristic
427C2×D61—41no—
428C2×D61—41no—
429C2×D61—41no—
430C2×D61—41no—
431C2×D61—41no—
432C2×D61—41no—
433C2×D61—41no—
434C2×D61—41no—
435C2×D61—41no—
436C2×D61—81no—
437C2×D61—81no—
438C2×D61—81no—
439C2×D61—81no—
440C2×D61—81no—
441C2×D61—81no—
442C2×D61—81no—
443C2×D61—81no—
444C2×D61—81no—
445C2×D61—81no—
446C2×D61—81no—
447C2×D61—81no—
448C2×D61D4211yescharacteristic
449C2×D61#55011yescharacteristic
450C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
451C2×D61#57511yescharacteristic
452C2×D61#57611yescharacteristic
453C2×D61#57711yescharacteristic
454#6923—22no—
455#6923—41no—
456#6923—42no—
457#6923—41no—
458#6923—41no—
459#6923—42no—
460#6923—81no—
461#6923—81no—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—41no—
465C4×C61C2×C4×D411yescharacteristic
466C4×C61#51811yescharacteristic
467Dic61—21no—
468Dic61—21no—
469Dic61—41no—
470Dic61#55011yescharacteristic
471Dic61#55911yescharacteristic
472C2×#496—611no—
473C2×#442—611no—
474C2×C4×SD16—611no—
475#2367—611no—
476#2366—611no—
477#1983—611no—
478#1982—611no—
479#1973—611no—
480#1970—611no—
481#1880—611no—
482#1879—611no—
483#1879—611no—
484#1877—611no—
485#1776—611no—
486#1771—611no—
487C2×C61—81no—
488C2×C61—81no—
489C2×C61—81no—
490C2×C61#236611yescharacteristic
491C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
492C2×C61#294611yescharacteristic
493D61—81no—
494D61—81no—
495D61—81no—
496D61#326511yescharacteristic
497D61#326811yescharacteristic
498D61#339911yescharacteristic
499D61#340111yescharacteristic
500C22×SD16—611no—
501C22×SD16—611no—
502C22×D8—611no—
503C22×D8—611no—
504C2×#127—611no—
505C2×#124—611no—
506C2×C4×Q8—611no—
507C2×C4×D4—611no—
508C2×C4×D4—611no—
509C2×C4×D4—611no—
510C2×C4×D4—1221no—
511#496—611no—
512#496—611no—
513#496—611no—
514#496—611no—
515#496—611no—
516#496—611no—
517#496—611no—
518#496#692311yescharacteristic, complemented
519#442—1224no—
520C4×SD16—1224no—
521C2×#107—611no—
522C2×#106—611no—
523C2×C4⋊C8—611no—
524C2×#103—611no—
525C2×#103—611no—
526C2×#102—611no—
527C2×#102—611no—
528C2×#102—611no—
529C2×#102—611no—
530C2×#102—611no—
531C2×#102—611no—
532C2×#97—611no—
533C2×#97—611no—
534C2×C4×C8—611no—
535#391—611no—
536#390—611no—
537#390—611no—
538#390—611no—
539#390—1221no—
540#388—1221no—
541#388—1221no—
542#386—1221no—
543#386—1221no—
544#385—1221no—
545C4×C4⋊C4—611no—
546C4×C4⋊C4—611no—
547C4×C4⋊C4—611no—
548C4×C22⋊C4—1221no—
549#340—611no—
550#340—611no—
551#336—611no—
552#336—611no—
553C61#2319311yescharacteristic, complemented, Sylow
554C22×Q8—611no—
555C22×D4—611no—
556C22×D4—611no—
557C22×D4—611no—
558C22×D4—1221no—
559C22×D4—1221no—
560C23×C4—1221no—
561C23×C4—1221no—
562C23×C4—1221no—
563C2×SD16—611no—
564C2×SD16—611no—
565C2×SD16—611no—
566C2×SD16—611no—
567C2×SD16—611no—
568C2×SD16—611no—
569C2×SD16—1222no—
570C2×SD16—1222no—
571C2×SD16—2441no—
572C2×SD16—2441no—
573C2×SD16C2×#692311yescharacteristic, complemented
574C2×SD16C2×#692311yescharacteristic, complemented
575C2×D8—611no—
576C2×D8—611no—
577C2×D8—611no—
578C2×D8—611no—
579C2×D8—611no—
580C2×D8—611no—
581C2×D8—1222no—
582C2×D8—1222no—
583C2×D8—2441no—
584C2×D8—2441no—
585C2×D8C2×#692311yescharacteristic, complemented
586C2×D8C2×#692311yescharacteristic, complemented
587C22×C8—611no—
588C22×C8—611no—
589C22×C8—611no—
590C22×C8—611no—
591#127—611no—
592#127—611no—
593#127—611no—
594#127—1221no—
595#127—1221no—
596#127C2×#692311yescharacteristic, complemented
597#124—611no—
598#124—611no—
599#124—611no—
600#124—1221no—
601#124—1221no—
602#124C2×#692311yescharacteristic, complemented
603C4×Q8—1222no—
604C4×Q8—2441no—
605C4×D4—1222no—
606C4×D4—1222no—
607C4×D4—1222no—
608C4×D4—2441no—
609C4×D4—2441no—
610C4×D4—2441no—
611C4×D4—2444no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—611no—
614C2×C4⋊C4—611no—
615C2×C4⋊C4—611no—
616C2×C4⋊C4—611no—
617C2×C4⋊C4—611no—
618C2×C4⋊C4—1221no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C42—611no—
631C2×C42—611no—
632C2×C42—611no—
633C2×C42—1221no—
634C2×C42—1221no—
635C2×C42—1221no—
636#107—1222no—
637#106—614no—
638C4⋊C8—1221no—
639C4⋊C8—1221no—
640#103—1222no—
641#103—2441no—
642#102—1222no—
643#102—1222no—
644#102—1222no—
645#102—2441no—
646#102—2441no—
647#102—2441no—
648#97—611no—
649#97—611no—
650#97—611no—
651#97—1222no—
652#97C2×#692311yescharacteristic, complemented
653C4×C8—1222no—
654#95—611no—
655#95—611no—
656#95—1221no—
657#95—1221no—
658#95—1221no—
659#95—1221no—
660C24—1221no—
661C24—1221no—
662C24—1221no—
663C2×Q8—611no—
664C2×Q8—1221no—
665C2×Q8—1221no—
666C2×Q8—1221no—
667C2×Q8—1221no—
668C2×Q8—1221no—
669C2×Q8C22×#692311yescharacteristic
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—611no—
673C2×D4—611no—
674C2×D4—611no—
675C2×D4—1221no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4—1221no—
691C2×D4—1221no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—4881no—
697C2×D4—4881no—
698C2×D4—2442no—
699C2×D4—2442no—
700C2×D4C22×#692311yescharacteristic
701C2×D4C22×#692311yescharacteristic
702C2×D4C22×#692311yescharacteristic
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—611no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—4881no—
716C22×C4—4881no—
717C22×C4—4881no—
718C22×C4—2442no—
719C22×C4—2442no—
720C22×C4—2442no—
721C22×C4—2442no—
722C22×C4—2442no—
723C22×C4—2442no—
724SD16—22no—
725SD16—41no—
726SD16—1222no—
727SD16—1222no—
728SD16—1222no—
729SD16—2441no—
730SD16—2441no—
731SD16—2441no—
732D8—22no—
733D8—41no—
734D8—1222no—
735D8—1222no—
736D8—1222no—
737D8—2441no—
738D8—2441no—
739D8—2441no—
740C2×C8—611no—
741C2×C8—612no—
742C2×C8—612no—
743C2×C8—611no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8—1221no—
750C2×C8—1221no—
751C2×C8—1221no—
752C2×C8C22×#692311yescharacteristic
753C2×C8C22×#692311yescharacteristic
754C4⋊C4—612no—
755C4⋊C4—612no—
756C4⋊C4—1221no—
757C4⋊C4—1222no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—2441no—
764C4⋊C4—2442no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4—1221no—
773C22⋊C4—4881no—
774C22⋊C4—4881no—
775C22⋊C4—4881no—
776C22⋊C4—2442no—
777C22⋊C4—2442no—
778C22⋊C4—2442no—
779C22⋊C4—2442no—
780C22⋊C4—2442no—
781C22⋊C4—2442no—
782C42—611no—
783C42—611no—
784C42—611no—
785C42—1221no—
786C42—1221no—
787C42—1221no—
788C42—1221no—
789C42—4881no—
790C42—2442no—
791C42—2442no—
792C42C22×#692311yescharacteristic
793C23—21no—
794C23—21no—
795C23—21no—
796C23—611no—
797C23—1221no—
798C23—1221no—
799C23—1221no—
800C23—2441no—
801C23—2441no—
802C23—2441no—
803C23—2441no—
804C23—2441no—
805C23—2441no—
806C23—2441no—
807C23—2441no—
808C23—2441no—
809C23—2441no—
810C23—2441no—
811C23—2441no—
812C23—2441no—
813C23—2441no—
814C23—2441no—
815C23—2441no—
816C23—2441no—
817C23—2441no—
818Q8—21no—
819Q8—21no—
820Q8—1221no—
821Q8—1221no—
822Q8—2441no—
823Q8—2441no—
824D4—21no—
825D4—21no—
826D4—21no—
827D4—21no—
828D4—21no—
829D4—21no—
830D4—42no—
831D4—81no—
832D4—1221no—
833D4—1221no—
834D4—1221no—
835D4—1221no—
836D4—1221no—
837D4—1221no—
838D4—4881no—
839D4—4881no—
840D4—4881no—
841D4—2442no—
842D4—2441no—
843D4—2441no—
844D4—2441no—
845D4—2441no—
846D4—2441no—
847D4—2441no—
848D4—2442no—
849D4—2442no—
850C2×C4—21no—
851C2×C4—611no—
852C2×C4—611no—
853C2×C4—611no—
854C2×C4—611no—
855C2×C4—611no—
856C2×C4—612no—
857C2×C4—611no—
858C2×C4—611no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1222no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1222no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—4884no—
878C2×C4—4884no—
879C2×C4—4884no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4D4×#692311yescharacteristic
893C2×C4D4×#692311yescharacteristic
894C2×C4C23×#692311yescharacteristic
895C8—21no—
896C8—612no—
897C8—1221no—
898C8—2441no—
899C8—2441no—
900C8D4×#692312yescomplemented
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—611no—
911C22—611no—
912C22—611no—
913C22—611no—
914C22—611no—
915C22—611no—
916C22—4881no—
917C22—4881no—
918C22—4881no—
919C22—4881no—
920C22—4881no—
921C22—4881no—
922C22—4881no—
923C22—4881no—
924C22—4881no—
925C22—4881no—
926C22—4881no—
927C22—4881no—
928C22—2441no—
929C22—2441no—
930C22—2441no—
931C22—2441no—
932C22—2441no—
933C22—2441no—
934C22—2441no—
935C22—2441no—
936C22—2441no—
937C22C2×D4×#692311yescharacteristic
938C4—21no—
939C4—21no—
940C4—41no—
941C4—611no—
942C4—611no—
943C4—1222no—
944C4—1221no—
945C4—1221no—
946C4—4881no—
947C4—4881no—
948C4—2441no—
949C4—2441no—
950C4—2441no—
951C4—2442no—
952C4—2442no—
953C4—2441no—
954C4C2×D4×#692311yescharacteristic
955C4#1684082911yescharacteristic
956C2—81no—
957C2—81no—
958C2—81no—
959C2—611no—
960C2—611no—
961C2—611no—
962C2—611no—
963C2—4881no—
964C2—4881no—
965C2—4881no—
966C2#2146234911yescharacteristic
967C2AGL(1,ℤ/8)×#692311yescharacteristic
968C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#496C4
socleC22×C61C2×C4×D4
prime radical#496×D61C2
cosocleC2×C4×D61C24
hypercenter#496#6923
hypocenterC61#23193
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#16840803C2semidirect
2. C2×SD16×#6923C2semidirect
3. #21462350C2semidirect
4. #21462349C2semidirect
5. #21461987C2semidirect
6. #21461986C2semidirect
7. #21461969C2semidirect
8. #21461966C2semidirect
9. #21461815C2semidirect
10. #21461814C2semidirect
11. #21461814C2semidirect
12. #21461812C2semidirect
13. #21461633C2semidirect
14. #21461617C2semidirect
60. #16840152C4semidirect
61. #16840151C4semidirect
62. #16840150C4semidirect
63. #16840150C4semidirect
64. #16840149C4semidirect
65. #16840148C4semidirect
66. #16840148C4semidirect
68. C61×#496C4semidirect
105. #14519845D4semidirect
130. C2×#11758190C2×C4semidirect
131. C2×#11758190C2×C4semidirect
132. C2×#11758200C2×C4semidirect
133. C2×#11758200C2×C4semidirect
134. C2×#11758201C2×C4semidirect
135. C2×#11758201C2×C4semidirect
140. C2×D488C2×C4semidirect
141. C2×D488C2×C4semidirect
142. C2×#11758199C2×C4semidirect
143. C2×#11758199C2×C4semidirect
144. C2×#11758199C2×C4semidirect
145. C2×#11758199C2×C4semidirect
152. #14519774C2×C4semidirect
155. #14519773C2×C4semidirect
156. #14519773C2×C4semidirect
157. #14519766C2×C4semidirect
158. #14519765C2×C4semidirect
159. #14519764C2×C4semidirect
165. #14519688C2×C4semidirect
166. #14519687C2×C4semidirect
167. #14519687C2×C4semidirect
168. C2×SD16×C61C2×C4semidirect
169. C2×SD16×C61C2×C4semidirect
170. C2×D8×C61C2×C4semidirect
171. C2×D8×C61C2×C4semidirect
172. #127×C61C2×C4semidirect
173. #124×C61C2×C4semidirect
174. #97×C61C2×C4semidirect
413. C8×C61C4×D4semidirect
415. #92418C4×D4semidirect
518. #496#6923semidirect
553. C61#23193semidirect
573. C2×SD16C2×#6923semidirect
574. C2×SD16C2×#6923semidirect
585. C2×D8C2×#6923semidirect
586. C2×D8C2×#6923semidirect
596. #127C2×#6923semidirect
602. #124C2×#6923semidirect
652. #97C2×#6923semidirect
900. C8D4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408032
C2×SD16×#69232
#214623502
#214623492
#214619872
#214619862
#214619692
#214619662
#214618152
#214618142
#214618122
#214616332
#214616172
#496×D612
#2319361