Finite Group Databasebeta

← #29646997

Subgroups — #29646997

Order 15616.

1022 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459436C211yesmaximal, characteristic
2#21454941C211yesmaximal, characteristic, complemented
3C4×#14519783C211yesmaximal, characteristic, complemented
4#21444280C211yesmaximal, characteristic, complemented
5#21444278C211yesmaximal, characteristic, complemented
6#21444272C211yesmaximal, characteristic, complemented
7#21444266C211yesmaximal, characteristic, complemented
8#21444264C211yesmaximal, characteristic, complemented
9#21444257C211yesmaximal, characteristic, complemented
10#21444238C211yesmaximal, characteristic, complemented
11#21444231C211yesmaximal, characteristic, complemented
12#21444230C211yesmaximal, characteristic, complemented
13#21444200C211yesmaximal, characteristic, complemented
14Q8⋊C8×D61C211yesmaximal, characteristic, complemented
15C2×C61×Q8⋊C8C211yesmaximal, characteristic, complemented
16C2×#14519783—21no—
17#16840488C411yescharacteristic
18#16840484—21no—
19#16840484C411yescharacteristic
20#16840453—21no—
21#16840453C411yescharacteristic
22#16840447—21no—
23#16840447C411yescharacteristic
24Q8×C22⋊D61C411yescharacteristic
25#16840424C411yescharacteristic
26#16840423C411yescharacteristic
27#16840413—21no—
28#16840413C411yescharacteristic
29#16840316—21no—
30#16840316C2211yescharacteristic
31#16840299—21no—
32#16840299C2211yescharacteristic
33#16840296—21no—
34#16840296C2211yescharacteristic
35C4×#11758226C2211yescharacteristic
36C4×#11758222—21no—
37C4×#11758222C2211yescharacteristic
38C4×Q8×D61C2211yescharacteristic
39#16839891—21no—
40#16839833—21no—
41#16839832—21no—
42C8×C22⋊D61—21no—
43#16839819C2211yescharacteristic
44#16839818C2211yescharacteristic
45#16839814C2211yescharacteristic
46#16839784C2211yescharacteristic
47C4⋊C8×D61C2211yescharacteristic
48#16839717—21no—
49#16839716—21no—
50#16839716—21no—
51C4×#11758194C2211yescharacteristic
52C4×#11758189C2211yescharacteristic
53C4×#11758189C2211yescharacteristic
54C4×C8×D61C2211yescharacteristic
55C4×C8×D61C2211yescharacteristic
56#16839494C2211yescharacteristic
57#16839494C2211yescharacteristic
58Q8⋊#92418C2211yescharacteristic
59Q8⋊#92418C2211yescharacteristic
60Q8⋊#92418C2211yescharacteristic
61Q8⋊#92418C2211yescharacteristic
62#16839492C2211yescharacteristic
63#16839492C2211yescharacteristic
64#16839491C2211yescharacteristic
65#16839491C2211yescharacteristic
66#16839489C2211yescharacteristic
67#16839489C2211yescharacteristic
68C2×C4×Q8×C61C2211yescharacteristic
69C2×C4⋊C8×C61C2211yescharacteristic
70C2×C4×C8×C61C2211yescharacteristic
71C61×Q8⋊C8C2211yescharacteristic
72C61×Q8⋊C8C2211yescharacteristic
73C61×Q8⋊C8C2211yescharacteristic
74C61×Q8⋊C8C2211yescharacteristic
75C2×#11758226C2×C411yescharacteristic
76C2×#11758222—21no—
77C2×#11758222D411yescharacteristic
78C2×Q8×D61C2×C411yescharacteristic
79#14519783—28no—
80C2×#11758194—21no—
81C2×#11758189—21no—
82C2×#11758189—21no—
83C2×#11758189—21no—
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87#14519776—21no—
88#14519776C2×C411yescharacteristic
89#14519775—21no—
90#14519775C2×C411yescharacteristic
91#14519772—21no—
92#14519772—21no—
93#14519772—21no—
94#14519771—21no—
95#14519771—21no—
96#14519771—21no—
97#14519769—21no—
98#14519769C2×C411yescharacteristic
99#14519768—21no—
100#14519768C2×C411yescharacteristic
101#14519767—21no—
102#14519767—21no—
103#14519767—21no—
104#14519766—21no—
105#14519766C2×C411yescharacteristic
106#14519765—21no—
107#14519765C2×C411yescharacteristic
108#14519762—21no—
109#14519762—21no—
110#14519762—21no—
111#14519760—21no—
112#14519760—21no—
113#14519760—21no—
114#14519757—21no—
115#14519757C2×C411yescharacteristic
116#14519756—21no—
117#14519756C2×C411yescharacteristic
118#14519755—21no—
119#14519755—21no—
120#14519755—21no—
121#14519753—21no—
122#14519753—21no—
123#14519753C2×C411yescharacteristic
124#14519753C2×C411yescharacteristic
125#14519752—21no—
126#14519752C2×C411yescharacteristic
127#14519751—21no—
128#14519751C2×C411yescharacteristic
129Q8×Dic61C2×C411yescharacteristic
130Q8×Dic61C2×C411yescharacteristic
131C4×Dic122—21no—
132C4×Dic122—21no—
133C4×Dic122—21no—
134C4×Dic122C2×C411yescharacteristic
135C4×Dic122D411yescharacteristic
136C4×Dic122C2311yescharacteristic
137#14519742—21no—
138#14519742C2×C411yescharacteristic
139C4×D244—21no—
140C4×D244—21no—
141C4×D244—21no—
142C4×D244C2×C411yescharacteristic
143C4×D244D411yescharacteristic
144C4×D244C2311yescharacteristic
145#14519739—21no—
146#14519739C2×C411yescharacteristic
147C4×C22⋊D61—21no—
148C4×C22⋊D61—21no—
149C4×C22⋊D61—21no—
150C4×C22⋊D61C2×C411yescharacteristic
151C4×C22⋊D61C2×C411yescharacteristic
152C4×C22⋊D61D411yescharacteristic
153C4×C22⋊D61D411yescharacteristic
154#14519736—21no—
155#14519736D411yescharacteristic
156#14519735—21no—
157#14519735C2×C411yescharacteristic
158#14519734—21no—
159#14519734—21no—
160#14519734—21no—
161#14519734—21no—
162#14519734—21no—
163#14519734D411yescharacteristic
164#14519734D411yescharacteristic
165C4⋊C4×D61—21no—
166C4⋊C4×D61C2×C411yescharacteristic
167C42×D61—21no—
168C42×D61—21no—
169C42×D61C2311yescharacteristic
170C42×D61C2311yescharacteristic
171C4⋊#92418C2311yescharacteristic
172C4⋊#92418C2311yescharacteristic
173#14519706—21no—
174#14519706—21no—
175C22⋊#92418—21no—
176#14519689—21no—
177#14519689—21no—
178#14519688—21no—
179#14519688—21no—
180#14519687—21no—
181#14519687—21no—
182#14519687—21no—
183C4×#92418C2311yescharacteristic
184C4×#92418C2311yescharacteristic
185C8×Dic61—21no—
186C8×Dic61—21no—
187C8×Dic61—21no—
188C22×Q8×C61C2×C411yescharacteristic
189C22×C8×C61—21no—
190C22×C8×C61—21no—
191C4×Q8×C61—21no—
192C4×Q8×C61—21no—
193C4×Q8×C61C2×C411yescharacteristic
194C4×Q8×C61C2×C411yescharacteristic
195C4×Q8×C61C2311yescharacteristic
196C4×Q8×C61C2311yescharacteristic
197C2×C4⋊C4×C61—21no—
198C2×C4⋊C4×C61C2×C411yescharacteristic
199C2×C42×C61—21no—
200C2×C42×C61C2311yescharacteristic
201C4⋊C8×C61—21no—
202C4⋊C8×C61C2311yescharacteristic
203C4⋊C8×C61C2311yescharacteristic
204C4×C8×C61—21no—
205C4×C8×C61C2311yescharacteristic
206C4×C8×C61C2311yescharacteristic
207C2×Q8×C61—21no—
208C2×Q8×C61—22no—
209C2×Q8×C61—41no—
210C2×Q8×C61C22×C411yescharacteristic
211C2×Q8×C61C22×C411yescharacteristic
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C2×C22⋊D61—21no—
218C2×C22⋊D61C22⋊C411yescharacteristic
219C2×C22⋊D61C22⋊C411yescharacteristic
220#11758226—22no—
221#11758226—41no—
222Q8×D61—22no—
223Q8×D61—41no—
224#11758222—24no—
225#11758222—44no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244C22⋊C411yescharacteristic
229C2×D244C22×C411yescharacteristic
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61C22×C411yescharacteristic
236C2×C4×D61C22×C411yescharacteristic
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61C2×D411yescharacteristic
240C2×C4×D61C2×D411yescharacteristic
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122C22⋊C411yescharacteristic
244C2×Dic122C22×C411yescharacteristic
245C2×C8×C61—24no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—81no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61C22×C411yescharacteristic
257C4⋊C4×C61C22×C411yescharacteristic
258C42×C61—21no—
259C42×C61—21no—
260C42×C61—21no—
261C42×C61—21no—
262C42×C61C22×C411yescharacteristic
263C42×C61C2×D411yescharacteristic
264C42×C61C2×D411yescharacteristic
265C42×C61C2411yescharacteristic
266C22⋊Dic61—21no—
267C22⋊Dic61C22⋊C411yescharacteristic
268C22⋊Dic61C22⋊C411yescharacteristic
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198C22⋊C411yescharacteristic
282#11758198C22⋊C411yescharacteristic
283#11758198C22⋊C411yescharacteristic
284#11758198C22⋊C411yescharacteristic
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61C22⋊C411yescharacteristic
290C4⋊Dic61C22⋊C411yescharacteristic
291C4⋊Dic61C22×C411yescharacteristic
292C4⋊Dic61C22×C411yescharacteristic
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61C22×C411yescharacteristic
315C4×Dic61C22×C411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320#11758194—24no—
321C2×#92418—21no—
322C2×#92418—21no—
323C2×#92418—21no—
324C2×#92418—21no—
325#11758189—24no—
326#11758189—24no—
327#11758189—81no—
328C8×D61—24no—
329C8×D61—24no—
330C8×D61—81no—
331C23×C61C2×C22⋊C411yescharacteristic
332C22×D61—21no—
333C22×D61C2×C22⋊C411yescharacteristic
334C22×D61C2×C22⋊C411yescharacteristic
335Q8×C61—21no—
336Q8×C61—21no—
337Q8×C61—21no—
338Q8×C61—42no—
339Q8×C61#13112yescomplemented
340C2×C4×C61—21no—
341C2×C4×C61—22no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—42no—
350C2×C4×C61—42no—
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C2×C22⋊C411yescharacteristic
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C23×C411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C22⋊D61—22no—
358C22⋊D61—42no—
359C22⋊D61#10414yes—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61C2×C22⋊C411yescharacteristic
364C2×Dic61C2×C22⋊C411yescharacteristic
365C2×Dic61C2×C22⋊C411yescharacteristic
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369D244—22no—
370D244—21no—
371D244—21no—
372D244—42no—
373D244—42no—
374C4×D61—22no—
375C4×D61—21no—
376C4×D61—21no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—21no—
380C4×D61—21no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—22no—
384C4×D61—42no—
385C4×D61—42no—
386C4×D61—42no—
387C4×D61—41no—
388C4×D61—41no—
389C4×D61—42no—
390Dic122—22no—
391Dic122—21no—
392Dic122—21no—
393Dic122—42no—
394Dic122—42no—
395C8×C61—22no—
396C8×C61—22no—
397C8×C61—41no—
398C8×C61—41no—
399#92418—22no—
400#92418—22no—
401#92418—41no—
402#92418—41no—
403#17519—611nomaximal, Sylow
404C22×C61—21no—
405C22×C61—21no—
406C22×C61C2×#10412yes—
407C22×C61C22×C22⋊C411yescharacteristic
408C2×D61—21no—
409C2×D61—21no—
410C2×D61—21no—
411C2×D61—21no—
412C2×D61—21no—
413C2×D61—41no—
414C2×D61—41no—
415C2×D61—41no—
416C2×D61C2×#10412yes—
417C4×C61—22no—
418C4×C61—21no—
419C4×C61—21no—
420C4×C61—21no—
421C4×C61—21no—
422C4×C61—41no—
423C4×C61—41no—
424C4×C61—41no—
425C4×C61C2×#13111yescharacteristic
426C4×C61#56811yescharacteristic
427C4×C61#57711yescharacteristic
428C4×C61#57811yescharacteristic
429Dic61—21no—
430Dic61—21no—
431Dic61—21no—
432Dic61—21no—
433Dic61—21no—
434Dic61—41no—
435Dic61—41no—
436Dic61—41no—
437Dic61C2×#10412yes—
438#3482—611no—
439#2990—611no—
440C4×#131—611no—
441#1494—611no—
442#1494—611no—
443#1493—611no—
444#1491—611no—
445#1491—611no—
446#1489—611no—
447#1485—611no—
448#1483—611no—
449#1483—611no—
450#1476—611no—
451C2×Q8⋊C8—611no—
452C2×Q8⋊C8D6111yescharacteristic, complemented
453C2×C61—22no—
454C2×C61#288011yescharacteristic
455C2×C61#289811yescharacteristic
456C2×C61C22×#10411yescharacteristic
457D61—22no—
458D61—41no—
459D61—81no—
460C2×#131—1221no—
461#557—611no—
462#556—611no—
463#556—1221no—
464#552—611no—
465#552—611no—
466#552—1221no—
467#552—1221no—
468D4×Q8—611no—
469#548—611no—
470#548—611no—
471#547—611no—
472#547—1221no—
473#533—611no—
474#533—1221no—
475#529—611no—
476#529—611no—
477#529—1221no—
478#529—1221no—
479C4×#41—611no—
480C4×#41—611no—
481C4×#41—1221no—
482C2×C4×Q8—611no—
483C2×C4×Q8C2×D6111yescharacteristic
484#446—1221no—
485#435—1221no—
486#435—1221no—
487C8×D4—1221no—
488#432—611no—
489#432—611no—
490#431—611no—
491#423—611no—
492C2×C4⋊C8—611no—
493C2×C4⋊C8C2×D6111yescharacteristic
494#405—1221no—
495#405—1221no—
496#405—1221no—
497C4×M16—611no—
498C4×M16—611no—
499C4×M16—611no—
500C2×C4×C8—611no—
501C2×C4×C8—611no—
502C2×C4×C8C2×D6111yescharacteristic
503Q8⋊C8—611no—
504Q8⋊C8—611no—
505Q8⋊C8—611no—
506Q8⋊C8—611no—
507Q8⋊C8—611no—
508Q8⋊C8—611no—
509Q8⋊C8—611no—
510Q8⋊C8—611no—
511Q8⋊C8C2×D6111yescharacteristic
512Q8⋊C8C2×D6111yescharacteristic
513Q8⋊C8C2×D6111yescharacteristic
514Q8⋊C8C2×D6111yescharacteristic
515D4⋊C8—611no—
516D4⋊C8—611no—
517D4⋊C8—611no—
518D4⋊C8—611no—
519C61#1751911yescharacteristic, complemented, Sylow
520C2×#41—611no—
521C2×#41—611no—
522C2×#41—1221no—
523C22×Q8—611no—
524C22×Q8C4×D6111yescharacteristic
525#131—1228no—
526C2×M16—1221no—
527C2×M16—1221no—
528C2×M16—1221no—
529C2×M16—1221no—
530C22×C8—21no—
531C22×C8—21no—
532C22×C8—1221no—
533C22×C8—1221no—
534C22×C8—1221no—
535C4⋊Q8—611no—
536C4⋊Q8—611no—
537C4⋊Q8—1221no—
538C4⋊Q8—1221no—
539#126—1221no—
540#126—1221no—
541#126—1221no—
542#126—1221no—
543#126—1221no—
544#126—1221no—
545#125—611no—
546#125—611no—
547#125—1221no—
548#125—1221no—
549#125—1221no—
550#125—1221no—
551#125—1221no—
552#124—611no—
553#124—611no—
554#124—1221no—
555#124—1221no—
556#123—1221no—
557#123—1221no—
558#123—1221no—
559#123—1221no—
560#123—1221no—
561#123—1221no—
562C22⋊Q8—611no—
563C22⋊Q8—611no—
564C22⋊Q8—611no—
565C22⋊Q8—611no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573#121—611no—
574#121—611no—
575#121—1221no—
576#121—1221no—
577C4×Q8—21no—
578C4×Q8—21no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—611no—
583C4×Q8—611no—
584C4×Q8—611no—
585C4×Q8—1221no—
586C4×Q8—1221no—
587C4×Q8—1221no—
588C4×Q8—1221no—
589C4×Q8C4×D6111yescharacteristic
590C4×Q8C4×D6111yescharacteristic
591C4×Q8C22×D6111yescharacteristic
592C4×Q8C22×D6111yescharacteristic
593C4×D4—611no—
594C4×D4—611no—
595C4×D4—611no—
596C4×D4—611no—
597C4×D4—611no—
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—1221no—
602C4×D4—1221no—
603C4×D4—1221no—
604C4×D4—1221no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4—1221no—
608#117—611no—
609#117—611no—
610#117—611no—
611#117—611no—
612#117—1221no—
613#117—1221no—
614#117—1221no—
615#117—1221no—
616#117—1221no—
617#117—1221no—
618#117—1221no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—1221no—
622C2×C4⋊C4C4×D6111yescharacteristic
623C2×C42—21no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42—1221no—
627C2×C42—1221no—
628C2×C42C22×D6111yescharacteristic
629C4⋊C8—21no—
630C4⋊C8—611no—
631C4⋊C8—611no—
632C4⋊C8—1221no—
633C4⋊C8—1221no—
634C4⋊C8C22×D6111yescharacteristic
635C4⋊C8C22×D6111yescharacteristic
636C22⋊C8—1221no—
637C22⋊C8—1221no—
638C22⋊C8—1221no—
639#97—1221no—
640#97—1221no—
641#97—1221no—
642#97—1221no—
643#97—1221no—
644C4×C8—21no—
645C4×C8—611no—
646C4×C8—611no—
647C4×C8—1221no—
648C4×C8—1221no—
649C4×C8—1221no—
650C4×C8C22×D6111yescharacteristic
651C4×C8C22×D6111yescharacteristic
652#41—1224no—
653#41—1222no—
654#41—2444no—
655#41—2441no—
656C2×Q8—21no—
657C2×Q8—22no—
658C2×Q8—41no—
659C2×Q8—611no—
660C2×Q8—611no—
661C2×Q8—1221no—
662C2×Q8—1221no—
663C2×Q8—1222no—
664C2×Q8—2441no—
665C2×Q8C2×C4×D6111yescharacteristic
666C2×Q8C2×C4×D6111yescharacteristic
667C2×D4—611no—
668C2×D4—611no—
669C2×D4—611no—
670C2×D4—611no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—1221no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4C2×C4×D6111yescharacteristic
688C22×C4D4×D6111yescharacteristic
689C22×C4D4×D6111yescharacteristic
690M16—1224no—
691M16—1224no—
692M16—1224no—
693M16—4881no—
694C2×C8—24no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—81no—
700C2×C8—1224no—
701C2×C8—1224no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—4881no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—611no—
713C4⋊C4—611no—
714C4⋊C4—611no—
715C4⋊C4—611no—
716C4⋊C4—611no—
717C4⋊C4—611no—
718C4⋊C4—611no—
719C4⋊C4—611no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4C2×C4×D6111yescharacteristic
737C4⋊C4C2×C4×D6111yescharacteristic
738C22⋊C4—611no—
739C22⋊C4—611no—
740C22⋊C4—611no—
741C22⋊C4—611no—
742C22⋊C4—611no—
743C22⋊C4—611no—
744C22⋊C4—1221no—
745C22⋊C4—1221no—
746C22⋊C4—1221no—
747C22⋊C4—1221no—
748C22⋊C4—1221no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—1221no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—611no—
762C42—611no—
763C42—611no—
764C42—611no—
765C42—611no—
766C42—611no—
767C42—1221no—
768C42—1221no—
769C42—1221no—
770C42—1221no—
771C42—1221no—
772C42C2×C4×D6111yescharacteristic
773C42D4×D6111yescharacteristic
774C42D4×D6111yescharacteristic
775C42C23×D6111yescharacteristic
776C23—611no—
777C23—611no—
778C23—1221no—
779C23C22⋊C4×D6111yescharacteristic
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—42no—
784Q8—1222no—
785Q8—1221no—
786Q8—1221no—
787Q8—2442no—
788Q8—2442no—
789Q8#1451978312yescomplemented
790D4—614no—
791D4—1222no—
792D4—1222no—
793D4—1221no—
794D4—1221no—
795D4—2442no—
796D4—2442no—
797D4—2442no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—611no—
810C2×C4—611no—
811C2×C4—611no—
812C2×C4—611no—
813C2×C4—611no—
814C2×C4—611no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—2442no—
829C2×C4—2442no—
830C2×C4—2442no—
831C2×C4—2442no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4C22⋊C4×D6111yescharacteristic
835C2×C4C22⋊C4×D6111yescharacteristic
836C2×C4C22⋊C4×D6111yescharacteristic
837C2×C4C22×C4×D6111yescharacteristic
838C2×C4C2×D4×D6111yescharacteristic
839C2×C4C2×D4×D6111yescharacteristic
840C8—22no—
841C8—22no—
842C8—41no—
843C8—41no—
844C8—1222no—
845C8—1222no—
846C8—2441no—
847C8—2441no—
848C22—21no—
849C22—21no—
850C22—612no—
851C22—1221no—
852C22—1221no—
853C22—1221no—
854C22—1221no—
855C22—1221no—
856C22—2441no—
857C22—2441no—
858C22—2441no—
859C22#104×D6112yes—
860C22C2×C22⋊C4×D6111yescharacteristic
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—22no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—612no—
870C4—1221no—
871C4—1221no—
872C4—1221no—
873C4—1221no—
874C4—1221no—
875C4—2441no—
876C4—2441no—
877C4—2441no—
878C4C2×#1451978311yescharacteristic
879C4#1684052811yescharacteristic
880C4#1684056811yescharacteristic
881C4#1684057511yescharacteristic
882C2—22no—
883C2—1222no—
884C2—4881no—
885C2—2441no—
886C2#2145426511yescharacteristic
887C2#2145434711yescharacteristic
888C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC2×C61×Q8⋊C8C2
socleC22×C61C22×C22⋊C4
prime radical#21459436C2
cosocleC42×C61C24
hypercenterC2×Q8⋊C8D61
hypocenterC61#17519
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #21454941C2semidirect
3. C4×#14519783C2semidirect
4. #21444280C2semidirect
5. #21444278C2semidirect
6. #21444272C2semidirect
7. #21444266C2semidirect
8. #21444264C2semidirect
9. #21444257C2semidirect
10. #21444238C2semidirect
11. #21444231C2semidirect
12. #21444230C2semidirect
13. #21444200C2semidirect
14. Q8⋊C8×D61C2semidirect
15. C2×C61×Q8⋊C8C2semidirect
339. Q8×C61#131semidirect
452. C2×Q8⋊C8D61semidirect
519. C61#17519semidirect
789. Q8#14519783semidirect

Maximal subgroups

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

subgroupindex
#214594362
#214549412
C4×#145197832
#214442802
#214442782
#214442722
#214442662
#214442642
#214442572
#214442382
#214442312
#214442302
#214442002
Q8⋊C8×D612
C2×C61×Q8⋊C82
#1751961