Finite Group Databasebeta

← #29647616

Subgroups — #29647616

Order 15616.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459542C211yesmaximal, characteristic
2#21454472C211yesmaximal, characteristic, complemented
3#21448680C211yesmaximal, characteristic, complemented
4#21444395C211yesmaximal, characteristic, complemented
5#21444380C211yesmaximal, characteristic, complemented
6#21444374C211yesmaximal, characteristic, complemented
7#21444364C211yesmaximal, characteristic, complemented
8#21444357C211yesmaximal, characteristic, complemented
9#21444346C211yesmaximal, characteristic, complemented
10#21444343C211yesmaximal, characteristic, complemented
11#21444326C211yesmaximal, characteristic, complemented
12#21444322C211yesmaximal, characteristic, complemented
13#21444312C211yesmaximal, characteristic, complemented
14#327×D61C211yesmaximal, characteristic, complemented
15C61×#1500C211yesmaximal, characteristic, complemented
16#16840475—21no—
17#16840463—21no—
18#16840461—21no—
19#16840437—21no—
20#16840436—21no—
21#16840410—21no—
22#16840407—21no—
23#16840404—21no—
24#16840392C411yescharacteristic, complemented
25#16840384C411yescharacteristic, complemented
26#16840381C411yescharacteristic, complemented
27#16840368C411yescharacteristic, complemented
28#16840363C411yescharacteristic, complemented
29#16840330C411yescharacteristic, complemented
30#16840312C2211yescharacteristic
31#16840307C2211yescharacteristic
32#16840298C2211yescharacteristic
33#16840275C2211yescharacteristic
34#121×D61C2211yescharacteristic
35#16840244C411yescharacteristic, complemented
36#16840234C411yescharacteristic, complemented
37C2×#14519734C2211yescharacteristic
38#16839822—21no—
39#16839821—21no—
40#16839819C2211yescharacteristic, complemented
41#16839816C2211yescharacteristic, complemented
42#16839812C2211yescharacteristic, complemented
43#16839787—21no—
44#16839724C2211yescharacteristic
45C22⋊C8×D61C2211yescharacteristic
46#16839716—21no—
47#16839649—21no—
48#16839646—21no—
49#16839636—21no—
50#16839629C2211yescharacteristic, complemented
51#16839628C2211yescharacteristic, complemented
52#16839624C2211yescharacteristic
53#16839613C2211yescharacteristic, complemented
54C4×#11758198—21no—
55#95×D61C2211yescharacteristic
56#16839499C2211yescharacteristic, complemented
57#16839499C2211yescharacteristic, complemented
58#16839497C2211yescharacteristic
59#16839497C2211yescharacteristic
60#16839497C2211yescharacteristic, complemented
61#16839497C2211yescharacteristic, complemented
62#16839496C2211yescharacteristic
63#16839496C2211yescharacteristic
64#16839495C2211yescharacteristic
65#16839495C2211yescharacteristic
66#16839495C2211yescharacteristic, complemented
67#16839495C2211yescharacteristic, complemented
68C61×#529C2211yescharacteristic
69C61×#431C2211yescharacteristic, complemented
70C61×#376C2211yescharacteristic, complemented
71C61×#328C2211yescharacteristic, complemented
72C61×#328C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758226C2×C411yescharacteristic
76C2×#11758222—21no—
77C2×#11758224—21no—
78C2×D4×D61—21no—
79C2×D4×D61C2×C411yescharacteristic
80C22×C4×D61—21no—
81C22×C4×D61C2311yescharacteristic
82C2×#11758189—21no—
83C2×C8×D61—21no—
84#14519777C2×C411yescharacteristic, complemented
85#14519776—21no—
86#14519776C2×C411yescharacteristic, complemented
87#14519774C2×C411yescharacteristic, complemented
88#14519773C2×C411yescharacteristic, complemented
89#14519772—21no—
90#14519771—21no—
91#14519770—21no—
92#14519768C2×C411yescharacteristic, complemented
93#14519767—21no—
94#14519766C2×C411yescharacteristic, complemented
95#14519765—21no—
96#14519765—21no—
97#14519763—21no—
98#14519763—21no—
99#14519762—21no—
100#14519762—21no—
101#14519762—21no—
102#14519762—21no—
103#14519761—21no—
104#14519761—21no—
105#14519760—21no—
106#14519759—21no—
107#14519757—21no—
108#14519755—21no—
109#14519755—21no—
110#14519754—21no—
111#14519753C2×C411yescharacteristic
112#14519752—21no—
113#14519752—21no—
114#14519752C2×C411yescharacteristic
115#14519752C2×C411yescharacteristic
116#14519751—21no—
117#14519751—21no—
118#14519751C2311yescharacteristic
119#14519751C2311yescharacteristic
120#14519750—21no—
121#14519750—21no—
122#14519750—21no—
123#14519750—21no—
124#14519749—21no—
125#14519749—21no—
126#14519748C2×C411yescharacteristic
127#14519747—21no—
128#14519747—21no—
129#14519747—21no—
130Q8×Dic61C2×C411yescharacteristic, complemented
131C4×D244—21no—
132C4×D244—21no—
133C4×D244C2×C411yescharacteristic, complemented
134C4×D244C2×C411yescharacteristic, complemented
135D4×Dic61C2×C411yescharacteristic, complemented
136#14519739—21no—
137#14519739—21no—
138#14519739C2×C411yescharacteristic, complemented
139#14519739C2×C411yescharacteristic, complemented
140C4×C22⋊D61—21no—
141#14519737—21no—
142#14519737—21no—
143#14519737—21no—
144#14519737—21no—
145#14519735—21no—
146#14519735C2×C411yescharacteristic
147#14519734—21no—
148#14519734C2×C411yescharacteristic
149#14519734C2×C411yescharacteristic
150#14519734C2×C411yescharacteristic
151#14519734C2×C411yescharacteristic
152#14519734D411yescharacteristic
153#14519734D411yescharacteristic
154#14519734D411yescharacteristic
155#14519734D411yescharacteristic
156C2×C4⋊Dic61—21no—
157C2×#11758196—21no—
158C2×#11758196D411yescharacteristic
159C2×#11758196D411yescharacteristic
160C4⋊C4×D61—21no—
161C4⋊C4×D61C2×C411yescharacteristic
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198D411yescharacteristic
165C2×#11758198D411yescharacteristic
166C22⋊C4×D61—21no—
167C22⋊C4×D61—21no—
168C2×C4×Dic61—21no—
169C2×C4×Dic61C2311yescharacteristic
170C4⋊#92418—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418C2311yescharacteristic
174C22⋊#92418C2311yescharacteristic
175#14519689—21no—
176#14519689—21no—
177#14519688—21no—
178#14519687—21no—
179C8×Dic61—21no—
180#14519684—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187#126×C61—21no—
188#125×C61C2×C411yescharacteristic, complemented
189#124×C61C2×C411yescharacteristic, complemented
190#123×C61—21no—
191C22⋊Q8×C61C2311yescharacteristic
192#121×C61C2311yescharacteristic
193C4×Q8×C61C2×C411yescharacteristic, complemented
194C4×D4×C61—21no—
195C4×D4×C61C2×C411yescharacteristic, complemented
196#117×C61—21no—
197C2×C42×C61—21no—
198C2×C42×C61C2311yescharacteristic
199C4⋊C8×C61—21no—
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202C4×C8×C61—21no—
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C23×D61—21no—
207C23×D61C2×D411yescharacteristic
208C2×Q8×C61C22×C411yescharacteristic
209C2×D4×C61—21no—
210C2×D4×C61C22×C411yescharacteristic
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2411yescharacteristic
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229#11758226—42no—
230#11758224—81no—
231#11758224—81no—
232D4×D61—42no—
233D4×D61—81no—
234D4×D61—81no—
235#11758222—81no—
236#11758222—81no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244—21no—
242C2×D244C22×C411yescharacteristic
243C2×D244C22×C411yescharacteristic
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61—42no—
253C2×C4×D61—81no—
254C2×C4×D61C22×C411yescharacteristic
255C2×C4×D61C22×C411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×Dic122—21no—
259C2×Dic122—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61C22×C411yescharacteristic
267C4⋊C4×C61C22×C411yescharacteristic
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C42×C61—21no—
274C42×C61—42no—
275C42×C61C22×C411yescharacteristic
276C42×C61C22×C411yescharacteristic
277C42×C61C2×D411yescharacteristic
278C42×C61C2×D411yescharacteristic
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—42no—
294#11758198C22⋊C411yescharacteristic
295#11758198C22⋊C411yescharacteristic
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—81no—
306C4⋊Dic61C22×C411yescharacteristic
307C4⋊Dic61C22×C411yescharacteristic
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—42no—
313#11758196C22⋊C411yescharacteristic
314#11758196C22⋊C411yescharacteristic
315#11758196C22⋊C411yescharacteristic
316#11758196C22⋊C411yescharacteristic
317#11758196C22⋊C411yescharacteristic
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320#11758196C22⋊C411yescharacteristic
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—81no—
324C4×Dic61C22×C411yescharacteristic
325C4×Dic61C22×C411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C2×#92418—21no—
329C2×#92418—21no—
330#11758189—42no—
331C8×D61—42no—
332C23×C61—21no—
333C23×C61C22×D411yescharacteristic
334C22×D61—21no—
335C22×D61—21no—
336C22×D61—22no—
337C22×D61—21no—
338C22×D61—21no—
339C22×D61—41no—
340C22×D61—42no—
341C22×D61—81no—
342C22×D61—81no—
343C22×D61C2×C22⋊C411yescharacteristic
344C22×D61C2×C22⋊C411yescharacteristic
345Q8×C61—41no—
346D4×C61—41no—
347D4×C61—41no—
348D4×C61—41no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—22no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—81no—
363C2×C4×C61C2×C22⋊C411yescharacteristic
364C2×C4×C61C2×C22⋊C411yescharacteristic
365C2×C4×C61C2×C22⋊C411yescharacteristic
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C23×C411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C22⋊D61—42no—
370C22⋊D61—41no—
371C22⋊D61—41no—
372C22⋊D61—41no—
373C22⋊D61—41no—
374C22⋊D61—81no—
375C22⋊D61—81no—
376C22⋊D61—81no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—81no—
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C2×C22⋊C411yescharacteristic
394C2×Dic61C2×C22⋊C411yescharacteristic
395C2×Dic61C2×C22⋊C411yescharacteristic
396D244—41no—
397D244—41no—
398D244—42no—
399D244—81no—
400D244—81no—
401D244—81no—
402D244—81no—
403C4×D61—22no—
404C4×D61—22no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—42no—
408C4×D61—81no—
409C4×D61—81no—
410C4×D61—81no—
411C4×D61—81no—
412C4×D61—81no—
413C4×D61—84no—
414Dic122—81no—
415Dic122—81no—
416C8×C61—41no—
417C8×C61—41no—
418#92418—41no—
419#92418—41no—
420#17604—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61C22×C22⋊C411yescharacteristic
427C22×C61#57611yescharacteristic
428C22×C61#57711yescharacteristic
429C2×D61—21no—
430C2×D61—21no—
431C2×D61—21no—
432C2×D61—21no—
433C2×D61—21no—
434C2×D61—42no—
435C2×D61—42no—
436C2×D61—41no—
437C2×D61—41no—
438C2×D61—41no—
439C2×D61—41no—
440C2×D61—41no—
441C2×D61—41no—
442C2×D61—162no—
443C2×D61#41012yes—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—21no—
449C4×C61—21no—
450C4×C61—42no—
451C4×C61—41no—
452C4×C61—41no—
453C4×C61—41no—
454C4×C61—81no—
455Dic61—21no—
456Dic61—21no—
457Dic61—21no—
458Dic61—21no—
459Dic61—21no—
460Dic61—21no—
461Dic61—41no—
462Dic61—41no—
463Dic61—81no—
464Dic61—81no—
465#3494—611no—
466#2924—611no—
467#2343—611no—
468#1521—611no—
469#1517—611no—
470#1516—611no—
471#1514—611no—
472#1512—611no—
473#1510—611no—
474#1509—611no—
475#1505—611no—
476#1504—611no—
477#1502—611no—
478#1500D6111yescharacteristic, complemented
479C2×#327—611no—
480C2×C61—21no—
481C2×C61—21no—
482C2×C61—81no—
483C2×C61C2×#41011yescharacteristic
484C2×C61#289711yescharacteristic
485C2×C61#290111yescharacteristic
486D61—22no—
487D61—41no—
488D61—81no—
489D61—81no—
490#555—1221no—
491#553—1221no—
492#553—1221no—
493#551—1221no—
494#551—1221no—
495#547—1221no—
496#546—1221no—
497#546—1221no—
498#544—611no—
499#542—611no—
500#542—611no—
501#540—611no—
502#540—611no—
503#535—611no—
504#532—611no—
505#532—611no—
506#529—611no—
507#529C2×D6111yescharacteristic
508#525—611no—
509C2×#121—611no—
510#520—611no—
511#518—611no—
512C2×#117—611no—
513#433—1221no—
514#433—1221no—
515#432—611no—
516#432—611no—
517#431—611no—
518#431C2×D6111yescharacteristic, complemented
519#424—1221no—
520#407—611no—
521C2×C22⋊C8—611no—
522#405—1221no—
523#387—1221no—
524#387—1221no—
525#385—1221no—
526#383—611no—
527#382—611no—
528#381—611no—
529C4×C4⋊C4—611no—
530C4×C22⋊C4—1221no—
531#376C2×D6111yescharacteristic, complemented
532C2×#95—611no—
533#328—611no—
534#328—611no—
535#328C2×D6111yescharacteristic, complemented
536#328C2×D6111yescharacteristic, complemented
537#327—611no—
538#327—611no—
539#327—611no—
540#327—611no—
541#327—611no—
542#327—611no—
543#327—611no—
544#327—611no—
545#327—611no—
546#327—611no—
547#327C2×D6111yescharacteristic
548#327C2×D6111yescharacteristic
549C61#1760411yescharacteristic, complemented, Sylow
550C2×#41—611no—
551C2×#41—1221no—
552C2×#41—1221no—
553C22×D4—611no—
554C22×D4—1221no—
555C23×C4—611no—
556C23×C4—1221no—
557C2×M16—1221no—
558C22×C8—1221no—
559C4⋊Q8—611no—
560C4⋊Q8—611no—
561C4⋊Q8—1221no—
562#127—611no—
563#127—611no—
564#126—21no—
565#126—1221no—
566#126—1221no—
567#126—1221no—
568#125—611no—
569#125—1221no—
570#125C4×D6111yescharacteristic, complemented
571#124—611no—
572#124—1221no—
573#124—1221no—
574#124—1221no—
575#124—1221no—
576#124C4×D6111yescharacteristic, complemented
577#123—21no—
578#123—1221no—
579#123—1221no—
580#123—1221no—
581#123—1221no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586C22⋊Q8—611no—
587C22⋊Q8—1221no—
588C22⋊Q8—1221no—
589C22⋊Q8—1221no—
590C22⋊Q8—1221no—
591C22⋊Q8C22×D6111yescharacteristic
592#121—611no—
593#121—611no—
594#121—611no—
595#121—611no—
596#121—611no—
597#121—1221no—
598#121—1221no—
599#121—1221no—
600#121—1221no—
601#121—1221no—
602#121—1221no—
603#121—1221no—
604#121—1221no—
605#121—1221no—
606#121—1221no—
607#121C22×D6111yescharacteristic
608#120—1221no—
609#120—1221no—
610#120—1221no—
611C4×Q8—611no—
612C4×Q8C4×D6111yescharacteristic, complemented
613C4×D4—21no—
614C4×D4—611no—
615C4×D4—611no—
616C4×D4—611no—
617C4×D4—611no—
618C4×D4—611no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4—1221no—
626C4×D4—1221no—
627C4×D4—1221no—
628C4×D4C4×D6111yescharacteristic, complemented
629#117—21no—
630#117—611no—
631#117—611no—
632#117—611no—
633#117—611no—
634#117—611no—
635#117—611no—
636#117—611no—
637#117—611no—
638#117—611no—
639#117—1221no—
640#117—1221no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—1221no—
645C2×C4⋊C4—1221no—
646C2×C4⋊C4—1221no—
647C2×C22⋊C4—611no—
648C2×C22⋊C4—611no—
649C2×C22⋊C4—1221no—
650C2×C22⋊C4—1221no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4—1221no—
653C2×C42—21no—
654C2×C42—611no—
655C2×C42—1221no—
656C2×C42C22×D6111yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—1221no—
659C4⋊C8—1221no—
660C4⋊C8—1221no—
661C22⋊C8—611no—
662C22⋊C8—611no—
663C22⋊C8—1221no—
664C22⋊C8—1221no—
665C22⋊C8C22×D6111yescharacteristic
666C22⋊C8C22×D6111yescharacteristic
667#97—1221no—
668#97—1221no—
669C4×C8—21no—
670C4×C8—1221no—
671#95—21no—
672#95—611no—
673#95—611no—
674#95—1221no—
675#95—1221no—
676#95—1221no—
677#95—1221no—
678#95—1221no—
679#95C22×D6111yescharacteristic
680#95C22×D6111yescharacteristic
681C24—611no—
682C24—1221no—
683#41—4881no—
684#41—4881no—
685#41—4881no—
686#41—4881no—
687#41—2442no—
688C2×Q8—1221no—
689C2×Q8—1221no—
690C2×Q8C2×C4×D6111yescharacteristic
691C2×D4—21no—
692C2×D4—611no—
693C2×D4—611no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—4881no—
706C2×D4—4881no—
707C2×D4—2442no—
708C2×D4C2×C4×D6111yescharacteristic
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—4881no—
729C22×C4—2442no—
730C22×C4—2442no—
731C22×C4—2442no—
732C22×C4D4×D6111yescharacteristic
733C22×C4D4×D6111yescharacteristic
734C22×C4C23×D6111yescharacteristic
735M16—2442no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—2442no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—611no—
753C4⋊C4—611no—
754C4⋊C4—611no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—4881no—
763C4⋊C4—2442no—
764C4⋊C4C2×C4×D6111yescharacteristic
765C4⋊C4C2×C4×D6111yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—611no—
772C22⋊C4—611no—
773C22⋊C4—611no—
774C22⋊C4—611no—
775C22⋊C4—611no—
776C22⋊C4—611no—
777C22⋊C4—611no—
778C22⋊C4—611no—
779C22⋊C4—1221no—
780C22⋊C4—1221no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—2442no—
794C42—21no—
795C42—42no—
796C42—611no—
797C42—611no—
798C42—611no—
799C42—611no—
800C42—1221no—
801C42—1221no—
802C42—4881no—
803C42C2×C4×D6111yescharacteristic
804C42C2×C4×D6111yescharacteristic
805C42D4×D6111yescharacteristic
806C42D4×D6111yescharacteristic
807C23—21no—
808C23—611no—
809C23—611no—
810C23—1222no—
811C23—1221no—
812C23—1221no—
813C23—1221no—
814C23—1221no—
815C23—4881no—
816C23—4881no—
817C23—2441no—
818C23—2442no—
819C23C2×D4×D6111yescharacteristic
820Q8—41no—
821Q8—4881no—
822Q8—4881no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—4881no—
827D4—4881no—
828D4—4881no—
829D4—4881no—
830D4—4881no—
831D4—4881no—
832D4—4881no—
833D4—2441no—
834D4—2441no—
835D4—2442no—
836D4—2442no—
837D4—2441no—
838D4—2441no—
839D4—2441no—
840D4—2441no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—81no—
855C2×C4—611no—
856C2×C4—611no—
857C2×C4—611no—
858C2×C4—611no—
859C2×C4—611no—
860C2×C4—611no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—4881no—
868C2×C4—4881no—
869C2×C4—4881no—
870C2×C4—4881no—
871C2×C4—4884no—
872C2×C4—4881no—
873C2×C4—4881no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2442no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4C22⋊C4×D6111yescharacteristic
886C2×C4C22⋊C4×D6111yescharacteristic
887C2×C4C22⋊C4×D6111yescharacteristic
888C2×C4C22⋊C4×D6111yescharacteristic
889C2×C4C22×C4×D6111yescharacteristic
890C2×C4C2×D4×D6111yescharacteristic
891C8—41no—
892C8—41no—
893C8—2441no—
894C8—2441no—
895C22—21no—
896C22—21no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—612no—
901C22—1221no—
902C22—1221no—
903C22—1221no—
904C22—1221no—
905C22—1221no—
906C22—9762no—
907C22—2442no—
908C22—2442no—
909C22—2441no—
910C22—2441no—
911C22—2441no—
912C22—2441no—
913C22—2441no—
914C22—2441no—
915C22C2×C22⋊C4×D6111yescharacteristic
916C22#1684056411yescharacteristic
917C22#1684056911yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—42no—
925C4—41no—
926C4—41no—
927C4—41no—
928C4—81no—
929C4—1221no—
930C4—1221no—
931C4—1221no—
932C4—1221no—
933C4—1221no—
934C4—1221no—
935C4—4881no—
936C4—4881no—
937C4—2441no—
938C4—2441no—
939C2—21no—
940C2—21no—
941C2—81no—
942C2—1222no—
943C2—4881no—
944C2—4881no—
945C2—2441no—
946C2#410×D6111yescharacteristic
947C2#2145434111yescharacteristic
948C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1500C2
socleC22×C61C22×C22⋊C4
prime radical#21459542C2
cosocleC22×C4×C61C24
hypercenter#1500D61
hypocenterC61#17604
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1500

Complements

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

NH ≅ G/Ntype
2. #21454472C2semidirect
3. #21448680C2semidirect
4. #21444395C2semidirect
5. #21444380C2semidirect
6. #21444374C2semidirect
7. #21444364C2semidirect
8. #21444357C2semidirect
9. #21444346C2semidirect
10. #21444343C2semidirect
11. #21444326C2semidirect
12. #21444322C2semidirect
13. #21444312C2semidirect
14. #327×D61C2semidirect
15. C61×#1500C2semidirect
24. #16840392C4semidirect
25. #16840384C4semidirect
26. #16840381C4semidirect
27. #16840368C4semidirect
28. #16840363C4semidirect
29. #16840330C4semidirect
35. #16840244C4semidirect
36. #16840234C4semidirect
40. #16839819C22semidirect
41. #16839816C22semidirect
42. #16839812C22semidirect
50. #16839629C22semidirect
51. #16839628C22semidirect
53. #16839613C22semidirect
56. #16839499C22semidirect
57. #16839499C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
66. #16839495C22semidirect
67. #16839495C22semidirect
69. C61×#431C22semidirect
70. C61×#376C22semidirect
71. C61×#328C22semidirect
72. C61×#328C22semidirect
84. #14519777C2×C4semidirect
86. #14519776C2×C4semidirect
87. #14519774C2×C4semidirect
88. #14519773C2×C4semidirect
92. #14519768C2×C4semidirect
94. #14519766C2×C4semidirect
130. Q8×Dic61C2×C4semidirect
133. C4×D244C2×C4semidirect
134. C4×D244C2×C4semidirect
135. D4×Dic61C2×C4semidirect
138. #14519739C2×C4semidirect
139. #14519739C2×C4semidirect
188. #125×C61C2×C4semidirect
189. #124×C61C2×C4semidirect
193. C4×Q8×C61C2×C4semidirect
195. C4×D4×C61C2×C4semidirect
478. #1500D61semidirect
518. #431C2×D61semidirect
531. #376C2×D61semidirect
535. #328C2×D61semidirect
536. #328C2×D61semidirect
549. C61#17604semidirect
570. #125C4×D61semidirect
576. #124C4×D61semidirect
612. C4×Q8C4×D61semidirect
628. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214595422
#214544722
#214486802
#214443952
#214443802
#214443742
#214443642
#214443572
#214443462
#214443432
#214443262
#214443222
#214443122
#327×D612
C61×#15002
#1760461