Finite Group Databasebeta

← #30552007

Subgroups — #30552007

Order 15616.

2008 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459604C211yesmaximal, characteristic, complemented
2#21456922C214yesmaximal, complemented
3#21456896C214yesmaximal, complemented
4#21456843C212yesmaximal, complemented
5#21456826C212yesmaximal, complemented
6#21456791C212yesmaximal, complemented
7#21456764C212yesmaximal, complemented
8#21456310C212yesmaximal, complemented
9#21456189C212yesmaximal, complemented
10#21455306C211yesmaximal, characteristic, complemented
11#21455291C211yesmaximal, characteristic, complemented
12#21455274C211yesmaximal, characteristic, complemented
13C2×#16839972C211yesmaximal, characteristic, complemented
14#21455131C212yesmaximal, complemented
15#21455112C212yesmaximal, complemented
16#21454485C211yesmaximal, characteristic, complemented
17C61×#3461C211yesmaximal, characteristic, complemented
18C2×#14519824C2212yes—
19C2×#14519808C2212yes—
20C2×#14519807C2212yes—
21C2×#14519797C2212yes—
22C22×#11758202C2212yes—
23Q8×D244—21no—
24Q8×D244—21no—
25#16840416—22no—
26#16840416—21no—
27#16840416—22no—
28#16840416—21no—
29#16840338C2214yes—
30#16840338C2212yes—
31#16840312C2212yes—
32#16840312C2211yescharacteristic
33C2×#14519777C2212yes—
34C2×#14519777C2211yescharacteristic
35#16840157C2214yes—
36#16840154C2214yes—
37#16840144C2214yes—
38#16840141C2214yes—
39#16840132C2214yes—
40#16840124C2214yes—
41#16840119C2214yes—
42#16840114C2214yes—
43#16839984C2212yes—
44#16839984C2214yes—
45#16839977C2212yes—
46#16839972C2212yes—
47#16839972C2214yes—
48#16839972C2211yescharacteristic
49#16839972C2212yes—
50#16839972C2212yes—
51#16839972C2212yes—
52#16839972C2212yes—
53#16839967C2212yes—
54#16839967C2212yes—
55#16839967C2211yescharacteristic
56#16839962C2212yes—
57#16839962C2211yescharacteristic
58#16839957C2211yescharacteristic
59#16839922C2214yes—
60#16839922C2214yes—
61#16839922C2214yes—
62#16839917C2214yes—
63#16839917C2214yes—
64#16839917C2214yes—
65#16839905C2214yes—
66#16839900C2214yes—
67#16839823C2214yes—
68#16839819C2212yes—
69#16839815C2212yes—
70#16839786C2211yescharacteristic
71C2×C4⋊#92418C2211yescharacteristic
72#16839770C2212yes—
73#16839761C2212yes—
74#16839756C2212yes—
75C2×#14519700C2212yes—
76#16839729C2212yes—
77#16839718C2212yes—
78C61×#544C2211yescharacteristic
79C61×#542—21no—
80C61×#542C2212yes—
81C61×#541—21no—
82C61×#541C2212yes—
83C61×#539—22no—
84C61×#537C2211yescharacteristic
85C61×#536C2211yescharacteristic
86C61×#536C2211yescharacteristic
87C61×#533—21no—
88C61×#533C2212yes—
89C61×#529—22no—
90C61×#529—21no—
91C61×#529C2212yes—
92C4×#41×C61C2211yescharacteristic
93C4×#41×C61C2211yescharacteristic
94C2×C4×Q8×C61C2211yescharacteristic
95#14519824—44no—
96#14519824—44no—
97C2×#11758222C2312yes—
98C2×#11758222C2314yes—
99C2×#11758224—24no—
100C2×#11758224—22no—
101C22×Dic122C2312yes—
102C22×Dic122C2314yes—
103C2×Q8×D61—22no—
104#14519808—44no—
105#14519807—44no—
106#14519797—44no—
107C2×#11758202—44no—
108C2×#11758202C2314yes—
109C2×#11758202C2314yes—
110C2×#11758202C2314yes—
111C2×#11758202C2312yes—
112C2×#11758202C2314yes—
113C2×#11758200C2314yes—
114C2×#11758200C2312yes—
115C2×#11758201C2312yes—
116C2×#11758201C2314yes—
117C2×#11758199C2312yes—
118C2×#11758194C2312yes—
119C22×#92418C2312yes—
120#14519777—21no—
121#14519777—22no—
122#14519777—21no—
123#14519777—22no—
124#14519777C2312yes—
125#14519777C2311yescharacteristic
126#14519777C2312yes—
127#14519777C2314yes—
128#14519774C2311yescharacteristic
129#14519765C2312yes—
130#14519765C2314yes—
131#14519761—24no—
132#14519761—24no—
133#14519761—24no—
134#14519757—24no—
135#14519757—22no—
136#14519757—22no—
137#14519757—24no—
138#14519751—21no—
139#14519751—22no—
140#14519751—21no—
141#14519751—22no—
142C4×D244—21no—
143C4×D244—22no—
144C4×D244—21no—
145C4×D244—22no—
146C2×C4⋊Dic61—21no—
147C2×C4⋊Dic61—22no—
148C2×C4⋊Dic61—21no—
149C2×C4⋊Dic61—22no—
150C4⋊#92418C2311yescharacteristic
151C4⋊#92418C2311yescharacteristic
152C4⋊#92418C2312yes—
153C4⋊#92418C2312yes—
154C4⋊#92418C2312yes—
155#14519700C2314yes—
156#14519700C2314yes—
157#14519700C2312yes—
158#14519700C2314yes—
159#14519700C2314yes—
160#14519700C2312yes—
161#14519700C2314yes—
162#14519697C2312yes—
163#14519697C2312yes—
164#14519697C2314yes—
165C22⋊#92418C2314yes—
166C22⋊#92418C2314yes—
167#14519688C2314yes—
168C4×#92418C2314yes—
169C2×#41×C61C2311yescharacteristic
170C2×#41×C61C2311yescharacteristic
171C22×Q8×C61C2311yescharacteristic
172C4⋊Q8×C61—21no—
173C4⋊Q8×C61—21no—
174C4⋊Q8×C61C2312yes—
175C4⋊Q8×C61C2312yes—
176#126×C61—22no—
177#126×C61—22no—
178#126×C61—22no—
179#126×C61—22no—
180#125×C61—22no—
181#125×C61—22no—
182#125×C61—21no—
183#125×C61—22no—
184#125×C61C2312yes—
185#124×C61—21no—
186#124×C61—22no—
187#124×C61C2312yes—
188#123×C61—22no—
189#123×C61—22no—
190#123×C61—22no—
191#123×C61—22no—
192C22⋊Q8×C61—21no—
193C22⋊Q8×C61—22no—
194C22⋊Q8×C61—21no—
195C22⋊Q8×C61—22no—
196C22⋊Q8×C61—21no—
197C22⋊Q8×C61—22no—
198C22⋊Q8×C61C2312yes—
199C22⋊Q8×C61C2312yes—
200C22⋊Q8×C61C2312yes—
201#121×C61—22no—
202#121×C61—21no—
203#121×C61C2312yes—
204C4×Q8×C61—22no—
205C4×Q8×C61—21no—
206C4×Q8×C61—21no—
207C4×Q8×C61D411yescharacteristic
208C4×Q8×C61D411yescharacteristic
209C4×Q8×C61C2311yescharacteristic
210C4×Q8×C61C2312yes—
211C4×Q8×C61C2311yescharacteristic
212C4×Q8×C61C2312yes—
213C4×D4×C61—21no—
214C4×D4×C61—21no—
215C4×D4×C61—22no—
216C4×D4×C61D412yes—
217C4×D4×C61D411yescharacteristic
218C4×D4×C61D411yescharacteristic
219C4×D4×C61D412yes—
220C4×D4×C61C2311yescharacteristic
221C4×D4×C61C2311yescharacteristic
222#117×C61—22no—
223#117×C61—22no—
224#117×C61—21no—
225#117×C61C2311yescharacteristic
226#117×C61C2311yescharacteristic
227#117×C61C2312yes—
228C2×C4⋊C4×C61—21no—
229C2×C4⋊C4×C61C2311yescharacteristic
230C2×C42×C61—21no—
231C2×C42×C61—21no—
232C2×C42×C61C2312yes—
233C2×C42×C61C2311yescharacteristic
234#41×C61—22no—
235#41×C61—22no—
236#41×C61—22no—
237#41×C61—22no—
238C2×Q8×C61—21no—
239C2×Q8×C61—22no—
240C2×Q8×C61—22no—
241C2×Q8×C61—22no—
242C2×Q8×C61C2×D411yescharacteristic
243C2×Q8×C61C2412yes—
244C2×Q8×C61C2411yescharacteristic
245C2×D4×C61—21no—
246C2×D4×C61—22no—
247C2×D4×C61C2×D412yes—
248C2×D4×C61C2×D411yescharacteristic
249C2×D4×C61C2411yescharacteristic
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61C2×D411yescharacteristic
256C22×C4×C61C2×D412yes—
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2×D412yes—
259C22×C4×C61C2412yes—
260C22×C4×C61C2411yescharacteristic
261C2×C22⋊D61—24no—
262C2×C22⋊D61—22no—
263C22×Dic61—24no—
264C22×Dic61—22no—
265Q8×D61—48no—
266#11758224—416no—
267#11758224—48no—
268#11758222—24no—
269#11758222—24no—
270#11758222—44no—
271#11758222—44no—
272C2×D244—21no—
273C2×D244—21no—
274C2×D244C2412yes—
275C2×C4×D61—24no—
276C2×C4×D61—22no—
277C2×Dic122—24no—
278C2×Dic122—24no—
279C2×Dic122—24no—
280C2×Dic122—22no—
281C2×Dic122—44no—
282C2×Dic122—44no—
283C2×Dic122C2414yes—
284C2×Dic122C2412yes—
285C4⋊C4×C61—22no—
286C4⋊C4×C61—22no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61—22no—
291C4⋊C4×C61—22no—
292C4⋊C4×C61—22no—
293C4⋊C4×C61—22no—
294C4⋊C4×C61—22no—
295C4⋊C4×C61—22no—
296C4⋊C4×C61—22no—
297C4⋊C4×C61—22no—
298C4⋊C4×C61C2×D412yes—
299C4⋊C4×C61C2×D411yescharacteristic
300C4⋊C4×C61C2×D411yescharacteristic
301C4⋊C4×C61C2×D412yes—
302C4⋊C4×C61C2412yes—
303C4⋊C4×C61C2411yescharacteristic
304C4⋊C4×C61C2411yescharacteristic
305C22⋊C4×C61—22no—
306C22⋊C4×C61—22no—
307C22⋊C4×C61—21no—
308C22⋊C4×C61—22no—
309C22⋊C4×C61—21no—
310C22⋊C4×C61—21no—
311C22⋊C4×C61—22no—
312C22⋊C4×C61—22no—
313C22⋊C4×C61—22no—
314C22⋊C4×C61C2×D412yes—
315C22⋊C4×C61C2×D412yes—
316C22⋊C4×C61C2×D412yes—
317C42×C61—22no—
318C42×C61—21no—
319C42×C61—21no—
320C42×C61—21no—
321C42×C61—22no—
322C42×C61C2×D411yescharacteristic
323C42×C61C2×D411yescharacteristic
324C42×C61C2×D412yes—
325C42×C61C2×D412yes—
326C42×C61C2411yescharacteristic
327C42×C61C2411yescharacteristic
328C42×C61C2412yes—
329#11758202—44no—
330#11758202—44no—
331#11758202—44no—
332#11758202—42no—
333#11758202—44no—
334#11758201—44no—
335#11758201—42no—
336#11758200—42no—
337#11758200—44no—
338#11758199—42no—
339#11758198—22no—
340#11758198—22no—
341#11758198—24no—
342#11758198—24no—
343C4⋊Dic61—22no—
344C4⋊Dic61—21no—
345C4⋊Dic61—22no—
346C4⋊Dic61—21no—
347C4⋊Dic61—22no—
348C4⋊Dic61—22no—
349C4⋊Dic61—24no—
350C4⋊Dic61—24no—
351#11758194—24no—
352C2×#92418—24no—
353C2×#92418C2412yes—
354C2×#92418C2414yes—
355C2×#92418C2412yes—
356C23×C61—21no—
357C23×C61C22×D412yes—
358C23×C61C22×D411yescharacteristic
359C22×D61—22no—
360Q8×C61—22no—
361Q8×C61—22no—
362Q8×C61—21no—
363Q8×C61—22no—
364Q8×C61—21no—
365Q8×C61—42no—
366Q8×C61—82no—
367D4×C61—24no—
368D4×C61—22no—
369D4×C61—21no—
370D4×C61—21no—
371D4×C61—42no—
372D4×C61—82no—
373C2×C4×C61—22no—
374C2×C4×C61—24no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—21no—
378C2×C4×C61—22no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—22no—
382C2×C4×C61—41no—
383C2×C4×C61—42no—
384C2×C4×C61—42no—
385C2×C4×C61—42no—
386C2×C4×C61—42no—
387C2×C4×C61—81no—
388C2×C4×C61—81no—
389C2×C4×C61C22×D411yescharacteristic
390C2×C4×C61C22×D411yescharacteristic
391C2×C4×C61C22×D411yescharacteristic
392C2×C4×C61C22×D412yes—
393C2×C4×C61C22×D412yes—
394C2×C4×C61C22×D412yes—
395C2×C4×C61C22×D411yescharacteristic
396C2×C4×C61C22×D411yescharacteristic
397C2×C4×C61H(5,𝔽2)12yes—
398C2×C4×C61H(5,𝔽2)12yes—
399C2×C4×C61C2511yescharacteristic
400C22⋊D61—48no—
401C22⋊D61—44no—
402C2×Dic61—24no—
403C2×Dic61—22no—
404C2×Dic61—48no—
405C2×Dic61—44no—
406D244—22no—
407D244—22no—
408D244—42no—
409D244—42no—
410C4×D61—48no—
411C4×D61—44no—
412Dic122—24no—
413Dic122—22no—
414Dic122—24no—
415Dic122—22no—
416Dic122—48no—
417Dic122—44no—
418#92418—22no—
419#92418—22no—
420#92418—24no—
421#60837—611nomaximal, Sylow
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—22no—
425C22×C61—22no—
426C22×C61—22no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61#53512yes—
431C22×C61C23×D411yescharacteristic
432C2×D61—42no—
433C2×D61—42no—
434C2×D61—42no—
435C4×C61—21no—
436C4×C61—21no—
437C4×C61—22no—
438C4×C61—22no—
439C4×C61—21no—
440C4×C61—22no—
441C4×C61—42no—
442C4×C61—41no—
443C4×C61—41no—
444C4×C61—42no—
445C4×C61—41no—
446C4×C61#53512yes—
447C4×C61#57812yes—
448C4×C61C2×H(5,𝔽2)11yescharacteristic
449C4×C61C2×H(5,𝔽2)11yescharacteristic
450Dic61—44no—
451Dic61—42no—
452#3499—611no—
453#3461D6111yescharacteristic, complemented
454#3225—614no—
455#3223—614no—
456#3218—612no—
457#3216—612no—
458#3212—612no—
459#3209—612no—
460#3156—612no—
461#3137—612no—
462#3039—611no—
463#3037—611no—
464#3035—611no—
465C2×#462—611no—
466#3013—612no—
467#3011—612no—
468#2925—611no—
469C2×C61—22no—
470C2×C61—42no—
471C2×C61—81no—
472C2×C61C2×#53511yescharacteristic
473C2×C61C2×#57811yescharacteristic
474C2×C61#358611yescharacteristic
475D61—82no—
476C2×2−1+4—612no—
477C2×#137—612no—
478C2×#137—612no—
479C2×#135—612no—
480C22×Q16—612no—
481D4×Q8—1221no—
482D4×Q8—1221no—
483#547—1222no—
484#547—1221no—
485#547—1222no—
486#547—1221no—
487#544C2×D6111yescharacteristic
488#542—21no—
489#542C2×D6112yes—
490#541—21no—
491#541C2×D6112yes—
492#539—22no—
493#537C2×D6111yescharacteristic
494#536—612no—
495#536—614no—
496#536C2×D6111yescharacteristic
497#536C2×D6111yescharacteristic
498#533—21no—
499#533C2×D6112yes—
500#532—612no—
501#532—611no—
502C2×C4⋊Q8—612no—
503C2×C4⋊Q8—611no—
504#529—22no—
505#529—21no—
506#529C2×D6112yes—
507C4×#41C2×D6111yescharacteristic
508C4×#41C2×D6111yescharacteristic
509C2×C4×Q8C2×D6111yescharacteristic
510#497—614no—
511#497—614no—
512#495—614no—
513#494—614no—
514#491—614no—
515#489—614no—
516#488—614no—
517#487—614no—
518#464—612no—
519#464—614no—
520#463—612no—
521#462—611no—
522#462—612no—
523#462—612no—
524#462—612no—
525#462—612no—
526#462—612no—
527#462—614no—
528#461—612no—
529#461—611no—
530#461—612no—
531#460—612no—
532#460—611no—
533#459—611no—
534#452—614no—
535#452—614no—
536#452—614no—
537#451—614no—
538#451—614no—
539#451—614no—
540#449—614no—
541#448—614no—
542#433—614no—
543#432—612no—
544#431—612no—
545#423—611no—
546C2×C4⋊C8—611no—
547#419—612no—
548#417—612no—
549#416—612no—
550C2×#103—612no—
551#408—612no—
552#405—612no—
553C61#6083711yescharacteristic, complemented, Sylow
5542−1+4—2444no—
5552−1+4—2444no—
556C2×#41—612no—
557C2×#41—614no—
558C2×#41—1224no—
559C2×#41—1222no—
560C2×#41C22×D6111yescharacteristic
561C2×#41C22×D6111yescharacteristic
562C22×Q8—612no—
563C22×Q8—614no—
564C22×Q8—1222no—
565C22×Q8C22×D6111yescharacteristic
566#137—2444no—
567#137—2444no—
568#135—2444no—
569C2×Q16—614no—
570C2×Q16—614no—
571C2×Q16—612no—
572C2×Q16—614no—
573C2×Q16—614no—
574C2×Q16—2444no—
575C2×SD16—612no—
576C2×SD16—614no—
577C2×SD16—612no—
578C2×SD16—614no—
579C2×D8—612no—
580C2×M16—612no—
581C22×C8—612no—
582C4⋊Q8—21no—
583C4⋊Q8—21no—
584C4⋊Q8—611no—
585C4⋊Q8—612no—
586C4⋊Q8—612no—
587C4⋊Q8—614no—
588C4⋊Q8—1221no—
589C4⋊Q8—1222no—
590C4⋊Q8—1221no—
591C4⋊Q8—1222no—
592C4⋊Q8C22×D6112yes—
593C4⋊Q8C22×D6112yes—
594#127—611no—
595#126—22no—
596#126—22no—
597#126—22no—
598#126—22no—
599#125—22no—
600#125—21no—
601#125—22no—
602#125—22no—
603#125C22×D6112yes—
604#124—21no—
605#124—22no—
606#124—612no—
607#124—614no—
608#124C22×D6112yes—
609#123—22no—
610#123—22no—
611#123—22no—
612#123—22no—
613#123—1224no—
614#123—1224no—
615#123—1224no—
616C22⋊Q8—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8—22no—
621C22⋊Q8—22no—
622C22⋊Q8—1222no—
623C22⋊Q8—1224no—
624C22⋊Q8—1222no—
625C22⋊Q8—1224no—
626C22⋊Q8C22×D6112yes—
627C22⋊Q8C22×D6112yes—
628C22⋊Q8C22×D6112yes—
629#121—22no—
630#121—21no—
631#121—1221no—
632#121—1222no—
633#121—1221no—
634#121—1222no—
635#121C22×D6112yes—
636C4×Q8—21no—
637C4×Q8—21no—
638C4×Q8—22no—
639C4×Q8C22⋊D6111yescharacteristic
640C4×Q8C22⋊D6111yescharacteristic
641C4×Q8C22×D6112yes—
642C4×Q8C22×D6112yes—
643C4×Q8C22×D6111yescharacteristic
644C4×Q8C22×D6111yescharacteristic
645C4×D4—21no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—1221no—
649C4×D4—1222no—
650C4×D4—1221no—
651C4×D4—1222no—
652C4×D4C22⋊D6111yescharacteristic
653C4×D4C22⋊D6112yes—
654C4×D4C22⋊D6112yes—
655C4×D4C22⋊D6111yescharacteristic
656C4×D4C22×D6111yescharacteristic
657C4×D4C22×D6111yescharacteristic
658#117—22no—
659#117—21no—
660#117—22no—
661#117C22×D6111yescharacteristic
662#117C22×D6111yescharacteristic
663#117C22×D6112yes—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—1221no—
666C2×C4⋊C4—1222no—
667C2×C4⋊C4—1221no—
668C2×C4⋊C4—1222no—
669C2×C4⋊C4C22×D6111yescharacteristic
670C2×C42—21no—
671C2×C42—21no—
672C2×C42C22×D6111yescharacteristic
673C2×C42C22×D6112yes—
674C4⋊C8—611no—
675C4⋊C8—611no—
676C4⋊C8—612no—
677C4⋊C8—612no—
678C4⋊C8—612no—
679#103—614no—
680#103—614no—
681#103—612no—
682#103—612no—
683#103—614no—
684#103—614no—
685#103—614no—
686#102—612no—
687#102—612no—
688#102—614no—
689C22⋊C8—614no—
690C22⋊C8—614no—
691#97—614no—
692C4×C8—614no—
693#41—22no—
694#41—22no—
695#41—22no—
696#41—22no—
697#41—1224no—
698#41—1224no—
699#41—2444no—
700#41—2444no—
701#41—24416no—
702#41—2448no—
703C2×Q8—21no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—22no—
707C2×Q8—614no—
708C2×Q8—612no—
709C2×Q8—1224no—
710C2×Q8—1222no—
711C2×Q8—1224no—
712C2×Q8—1224no—
713C2×Q8—2444no—
714C2×Q8—2444no—
715C2×Q8—2448no—
716C2×Q8C2×C22⋊D6111yescharacteristic
717C2×Q8C23×D6112yes—
718C2×Q8C23×D6111yescharacteristic
719C2×D4—21no—
720C2×D4—22no—
721C2×D4—612no—
722C2×D4—1224no—
723C2×D4—1222no—
724C2×D4—1221no—
725C2×D4—1221no—
726C2×D4C2×C22⋊D6112yes—
727C2×D4C2×C22⋊D6111yescharacteristic
728C2×D4C23×D6111yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—1224no—
735C22×C4—1222no—
736C22×C4—1224no—
737C22×C4—1222no—
738C22×C4C2×C22⋊D6111yescharacteristic
739C22×C4C2×C22⋊D6112yes—
740C22×C4C2×C22⋊D6111yescharacteristic
741C22×C4C2×C22⋊D6112yes—
742C22×C4C23×D6112yes—
743C22×C4C23×D6111yescharacteristic
744Q16—2444no—
745Q16—2444no—
746Q16—2442no—
747Q16—2444no—
748Q16—2444no—
749SD16—2442no—
750SD16—2444no—
751SD16—2442no—
752SD16—2444no—
753D8—2442no—
754M16—1224no—
755C2×C8—612no—
756C2×C8—614no—
757C2×C8—612no—
758C2×C8—1224no—
759C4⋊C4—22no—
760C4⋊C4—22no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—22no—
765C4⋊C4—22no—
766C4⋊C4—22no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—22no—
771C4⋊C4—22no—
772C4⋊C4—1222no—
773C4⋊C4—1221no—
774C4⋊C4—1222no—
775C4⋊C4—1221no—
776C4⋊C4—1222no—
777C4⋊C4—1222no—
778C4⋊C4—1224no—
779C4⋊C4—1224no—
780C4⋊C4C2×C22⋊D6112yes—
781C4⋊C4C2×C22⋊D6111yescharacteristic
782C4⋊C4C2×C22⋊D6111yescharacteristic
783C4⋊C4C2×C22⋊D6112yes—
784C4⋊C4C23×D6112yes—
785C4⋊C4C23×D6111yescharacteristic
786C4⋊C4C23×D6111yescharacteristic
787C22⋊C4—22no—
788C22⋊C4—22no—
789C22⋊C4—21no—
790C22⋊C4—22no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—1222no—
797C22⋊C4—1222no—
798C22⋊C4—1224no—
799C22⋊C4—1224no—
800C22⋊C4C2×C22⋊D6112yes—
801C22⋊C4C2×C22⋊D6112yes—
802C22⋊C4C2×C22⋊D6112yes—
803C42—22no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—22no—
808C42C2×C22⋊D6111yescharacteristic
809C42C2×C22⋊D6111yescharacteristic
810C42C2×C22⋊D6112yes—
811C42C2×C22⋊D6112yes—
812C42C23×D6112yes—
813C42C23×D6111yescharacteristic
814C42C23×D6111yescharacteristic
815C23—21no—
816C23—1222no—
817C23C22×C22⋊D6112yes—
818C23C22×C22⋊D6111yescharacteristic
819Q8—22no—
820Q8—22no—
821Q8—21no—
822Q8—22no—
823Q8—21no—
824Q8—42no—
825Q8—82no—
826Q8—1224no—
827Q8—1222no—
828Q8—1224no—
829Q8—1222no—
830Q8—2448no—
831Q8—2444no—
832D4—24no—
833D4—22no—
834D4—21no—
835D4—21no—
836D4—42no—
837D4—82no—
838D4—1222no—
839D4—1222no—
840D4—2442no—
841D4—2448no—
842D4—2444no—
843D4—2442no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—41no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—1224no—
861C2×C4—1222no—
862C2×C4—2448no—
863C2×C4—2448no—
864C2×C4—2444no—
865C2×C4—2444no—
866C2×C4C22×C22⋊D6111yescharacteristic
867C2×C4C22×C22⋊D6111yescharacteristic
868C2×C4C22×C22⋊D6111yescharacteristic
869C2×C4C22×C22⋊D6112yes—
870C2×C4C22×C22⋊D6112yes—
871C2×C4C22×C22⋊D6112yes—
872C2×C4C22×C22⋊D6111yescharacteristic
873C2×C4C22×C22⋊D6111yescharacteristic
874C2×C4#1451982312yes—
875C2×C4#1451982312yes—
876C2×C4C24×D6111yescharacteristic
877C8—1222no—
878C8—1222no—
879C8—1224no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—2442no—
889C22—2442no—
890C22—2442no—
891C22#1684032612yes—
892C22C23×C22⋊D6111yescharacteristic
893C4—21no—
894C4—22no—
895C4—21no—
896C4—21no—
897C4—22no—
898C4—22no—
899C4—41no—
900C4—42no—
901C4—41no—
902C4—41no—
903C4—42no—
904C4—2444no—
905C4—2442no—
906C4#1684032612yes—
907C4#1684057712yes—
908C4C2×#1451982311yescharacteristic
909C4C2×#1451982311yescharacteristic
910C2—22no—
911C2—42no—
912C2—81no—
913C2—4882no—
914C2C2×#1684032611yescharacteristic
915C2C2×#1684057711yescharacteristic
916C2#2146060511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3461C2
socleC22×C61C23×D4
hypercenter#3461D61
hypocenterC61#60837
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #21459604C2semidirect
2. #21456922C2semidirect
3. #21456896C2semidirect
4. #21456843C2semidirect
5. #21456826C2semidirect
6. #21456791C2semidirect
7. #21456764C2semidirect
8. #21456310C2semidirect
9. #21456189C2semidirect
10. #21455306C2semidirect
11. #21455291C2semidirect
12. #21455274C2semidirect
13. C2×#16839972C2semidirect
14. #21455131C2semidirect
15. #21455112C2semidirect
16. #21454485C2semidirect
17. C61×#3461C2semidirect
453. #3461D61semidirect
553. C61#60837semidirect

Maximal subgroups

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

subgroupindex
#214596042
#214569222
#214568962
#214568432
#214568262
#214567912
#214567642
#214563102
#214561892
#214553062
#214552912
#214552742
C2×#168399722
#214551312
#214551122
#214544852
C61×#34612
#6083761