Finite Group Databasebeta

← #30611923

Subgroups — #30611923

Order 15616.

896 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462742C211yesmaximal, characteristic
2#21462516C211yesmaximal, characteristic
3#21461355C212yesmaximal, complemented
4#21461352C212yesmaximal, complemented
5#21461345C212yesmaximal, complemented
6#21461336C211yesmaximal, characteristic, complemented
7#21461333C211yesmaximal, characteristic, complemented
8#21461332C212yesmaximal, complemented
9#21461320C211yesmaximal, characteristic, complemented
10D61⋊#333C211yesmaximal, characteristic, complemented
11#21459630C211yesmaximal, characteristic
12#16840812—21no—
13#16840797—21no—
14#16840794—22no—
15#16840786—22no—
16#16840782C2212yes—
17#16840782C2212yes—
18#16840780C2211yescharacteristic
19#16840779C2212yes—
20#16840767C2211yescharacteristic
21#16840765C2212yes—
22D61⋊(C4⋊C8)C2211yescharacteristic
23D61⋊(C4⋊C8)C2211yescharacteristic
24#16840736—21no—
25#16840727—21no—
26#16840622C2212yes—
27#16840622C2212yes—
28#16840622C2211yescharacteristic
29#16840622C2211yescharacteristic
30#16840622C2212yes—
31#16840622C2212yes—
32#16840622C2212yes—
33#16840621C2211yescharacteristic
34#16840621C2211yescharacteristic
35#16840621C2212yes—
36#16840492—21no—
37#16840490C411yescharacteristic
38#16840487C411yescharacteristic
39#16840471—21no—
40#16840466—22no—
41D4×Dic122C411yescharacteristic
42Q8×C22⋊D61C412yes—
43#16840425C412yes—
44#16840391—22no—
45#16840389—21no—
46#16840316C2211yescharacteristic
47#16840314C2212yes—
48C2×#14519775C2212yes—
49C4⋊Q8×D61C2211yescharacteristic
50#16840241—21no—
51C4×#11758224C2211yescharacteristic
52D4×Q8×C61C411yescharacteristic
53C2×#11758213—21no—
54C2×#11758217—22no—
55C2×D61⋊C8—21no—
56C2×D61⋊C8—21no—
57#14519844—21no—
58#14519844C2312yes—
59#14519844C2311yescharacteristic
60#14519844C2311yescharacteristic
61#14519844C2311yescharacteristic
62#14519844C2312yes—
63#14519844C2311yescharacteristic
64C4⋊#92420—21no—
65C4⋊#92420—21no—
66C4⋊#92420—22no—
67#14519834—21no—
68C22⋊#92420—22no—
69C22⋊#92420—22no—
70C22⋊#92420—22no—
71#14519832—22no—
72#14519832—22no—
73C4×#92420—22no—
74C4×#92420—21no—
75C2×#11758224D411yescharacteristic
76C22×Dic122C2×C412yes—
77C2×Q8×D61C2×C412yes—
78#14519777C2×C411yescharacteristic
79#14519776—21no—
80#14519776—22no—
81#14519776—21no—
82#14519776—21no—
83#14519776C2311yescharacteristic
84#14519775—22no—
85#14519775—22no—
86#14519775—22no—
87#14519775C2×C412yes—
88#14519775C2×C412yes—
89#14519775C2312yes—
90#14519775C2311yescharacteristic
91#14519769—21no—
92#14519768—21no—
93#14519767—22no—
94#14519767—22no—
95#14519767—22no—
96#14519767—21no—
97#14519757C2×C411yescharacteristic
98#14519756—22no—
99#14519756C2×C412yes—
100#14519755—21no—
101#14519755—22no—
102#14519754—22no—
103#14519754—22no—
104#14519754—22no—
105#14519753—22no—
106#14519753C2×C411yescharacteristic
107Q8×Dic61C2×C412yes—
108C4×Dic122—21no—
109C4×Dic122—21no—
110C4×Dic122C2×C411yescharacteristic
111C4×Dic122C2×C411yescharacteristic
112#14519742—21no—
113#14519742—22no—
114#14519742C2×C412yes—
115#14519742D411yescharacteristic
116D4×Dic61—21no—
117D4×Dic61D411yescharacteristic
118C4×C22⋊D61—22no—
119C4×C22⋊D61C2×C412yes—
120#14519737—22no—
121#14519737D412yes—
122#14519735D411yescharacteristic
123#14519734—21no—
124#14519733—22no—
125#14519733D412yes—
126C2×#11758196—22no—
127C2×#11758196—22no—
128C4⋊C4×D61—21no—
129C4⋊C4×D61—21no—
130C2×C4×Dic61C2312yes—
131C42×D61C2311yescharacteristic
132C22×Q8×C61C2×C412yes—
133C4⋊Q8×C61—21no—
134C4⋊Q8×C61C2×C411yescharacteristic
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61C2×C412yes—
137C4×Q8×C61C2×C411yescharacteristic
138C4×D4×C61—21no—
139C4×D4×C61C2×C411yescharacteristic
140C2×Q8×C61—22no—
141C2×Q8×C61—82no—
142C2×Q8×C61C22×C412yes—
143C2×Q8×C61C22×C411yescharacteristic
144C2×D4×C61C22⋊C411yescharacteristic
145C22×C4×C61—22no—
146C22×C4×C61C22×C412yes—
147C2×C22⋊D61C22⋊C412yes—
148C22×Dic61—22no—
149C22×Dic61C2×D412yes—
150C22×Dic61C2×D412yes—
151Q8×D61—82no—
152#11758224—22no—
153#11758224—22no—
154C2×C4×D61—22no—
155C2×C4×D61C22×C411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×Dic122—21no—
159C2×Dic122—22no—
160C2×Dic122—22no—
161C2×Dic122—82no—
162C2×Dic122C22⋊C411yescharacteristic
163C2×Dic122C22×C412yes—
164C2×Dic122C22×C411yescharacteristic
165#11758217—82no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—22no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—22no—
172#11758213—42no—
173D61⋊C8—42no—
174D61⋊C8—81no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61C22⋊C411yescharacteristic
180C4⋊C4×C61C22×C411yescharacteristic
181C22⋊C4×C61—22no—
182C22⋊C4×C61C22⋊C412yes—
183C42×C61—21no—
184C42×C61C22×C411yescharacteristic
185C22⋊Dic61—22no—
186C22⋊Dic61C22⋊C412yes—
187#11758198—21no—
188#11758198—21no—
189#11758198C22⋊C412yes—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—22no—
194C4⋊Dic61C22⋊C411yescharacteristic
195C4⋊Dic61C22×C411yescharacteristic
196#11758196—22no—
197#11758196—21no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—21no—
204#11758196—22no—
205#11758196—22no—
206#11758196—21no—
207#11758196—21no—
208#11758196—21no—
209#11758196C22⋊C412yes—
210#11758196C22⋊C412yes—
211C4×Dic61—21no—
212C4×Dic61—22no—
213C4×Dic61—22no—
214C4×Dic61C22×C412yes—
215C4×Dic61C2×D412yes—
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D412yes—
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2411yescharacteristic
220C23×C61C2×C22⋊C412yes—
221C22×D61C2×C22⋊C411yescharacteristic
222Q8×C61—42no—
223Q8×C61—41no—
224Q8×C61—82no—
225D4×C61—22no—
226C2×C4×C61—21no—
227C2×C4×C61—22no—
228C2×C4×C61—21no—
229C2×C4×C61—42no—
230C2×C4×C61—82no—
231C2×C4×C61C2×C22⋊C412yes—
232C2×C4×C61C2×C22⋊C411yescharacteristic
233C2×C4×C61C2×C22⋊C411yescharacteristic
234C2×C4×C61C23×C411yescharacteristic
235C22⋊D61—24no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—22no—
243C2×Dic61—82no—
244C2×Dic61C2×C22⋊C412yes—
245C2×Dic61C2×C22⋊C412yes—
246C2×Dic61C2×C22⋊C411yescharacteristic
247C2×Dic61C22×D411yescharacteristic
248C2×Dic61C22×D411yescharacteristic
249C4×D61—21no—
250C4×D61—21no—
251C4×D61—41no—
252C4×D61—82no—
253C4×D61#13712yes—
254C4×D61#13712yes—
255Dic122—22no—
256Dic122—41no—
257Dic122—41no—
258Dic122—41no—
259Dic122—42no—
260Dic122—82no—
261Dic122—82no—
262#92420—41no—
263#92420—41no—
264#92420—42no—
265#92420—42no—
266#92420—41no—
267#92420—41no—
268#17760—611nomaximal, Sylow
269C22×C61—22no—
270C22×C61—22no—
271C22×C61—22no—
272C22×C61C22×C22⋊C411yescharacteristic
273C2×D61—21no—
274C2×D61—21no—
275C2×D61#41912yes—
276C4×C61—21no—
277C4×C61—22no—
278C4×C61—21no—
279C4×C61—42no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61#41912yes—
283Dic61—21no—
284Dic61—22no—
285Dic61—22no—
286Dic61—42no—
287Dic61—41no—
288Dic61—41no—
289Dic61C2×#13711yescharacteristic
290Dic61C2×#13711yescharacteristic
291Dic61#57711yescharacteristic
292Dic61#57811yescharacteristic
293#3503—611no—
294#2989—611no—
295#2925—611no—
296#1559—612no—
297#1558—612no—
298#1554—612no—
299#1550—611no—
300#1548—612no—
301#1548—611no—
302#1542—611no—
303C2×#333—611no—
304C2×C61—42no—
305C2×C61#288811yescharacteristic
306C2×C61C2×#41911yescharacteristic
307C2×C61#289811yescharacteristic
308D61—22no—
309Q82—1221no—
310#557—611no—
311#557—611no—
312#554—1221no—
313#554—1222no—
314D4×Q8—612no—
315D4×Q8—612no—
316D4×Q8—611no—
317D4×Q8#692311yescharacteristic
318#544—1222no—
319#544—1221no—
320#533—612no—
321#533—611no—
322C2×C4⋊Q8—612no—
323C2×C4⋊Q8—611no—
324#520—1221no—
325C4×#41—611no—
326#446—1221no—
327#436—1221no—
328#435—1222no—
329#433—1222no—
330#432—612no—
331#432—612no—
332#431—611no—
333#431—612no—
334#423—611no—
335#423—612no—
336C2×C4⋊C8—611no—
337C2×C4⋊C8—611no—
338#408—1221no—
339#405—1221no—
340#333—612no—
341#333—612no—
342#333—611no—
343#333—611no—
344#333—612no—
345#333—612no—
346#333—612no—
347#332—611no—
348#332—611no—
349#332—612no—
350C61#1776011yescharacteristic, complemented, Sylow
351C2×#41—611no—
352C22×Q8—612no—
353C22×Q8—612no—
354C22×Q8C2×#692312yes—
355C2×M16—1222no—
356C2×M16—1221no—
357C22×C8—1221no—
358C22×C8—1221no—
359C4⋊Q8—21no—
360C4⋊Q8—611no—
361C4⋊Q8—612no—
362C4⋊Q8—611no—
363C4⋊Q8—612no—
364C4⋊Q8—612no—
365C4⋊Q8—611no—
366C4⋊Q8—1221no—
367C4⋊Q8—1221no—
368C4⋊Q8—1222no—
369C4⋊Q8—1222no—
370C4⋊Q8—1222no—
371C4⋊Q8—1222no—
372C4⋊Q8—1221no—
373C4⋊Q8C2×#692311yescharacteristic
374#125—1221no—
375#125—1222no—
376#125—1221no—
377#125—1222no—
378#125—1222no—
379#125—1221no—
380C22⋊Q8—22no—
381C22⋊Q8—611no—
382C22⋊Q8—612no—
383C22⋊Q8—611no—
384C22⋊Q8—1222no—
385C22⋊Q8—1222no—
386C22⋊Q8—1222no—
387C22⋊Q8—1222no—
388C22⋊Q8—1222no—
389C22⋊Q8—1221no—
390C22⋊Q8—1222no—
391C22⋊Q8C2×#692312yes—
392C4×Q8—611no—
393C4×Q8—611no—
394C4×Q8—612no—
395C4×Q8—612no—
396C4×Q8—611no—
397C4×Q8—1221no—
398C4×Q8—1221no—
399C4×Q8—1222no—
400C4×Q8—1221no—
401C4×Q8C2×#692311yescharacteristic
402C4×D4—21no—
403C4×D4—611no—
404C4×D4—612no—
405C4×D4—612no—
406C4×D4—1222no—
407C4×D4—1222no—
408C4×D4—1221no—
409C4×D4C2×#692311yescharacteristic
410#117—611no—
411#117—612no—
412#117—1221no—
413#117—1222no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—1222no—
417C2×C4⋊C4—1222no—
418C2×C42—612no—
419C2×C42—611no—
420C4⋊C8—612no—
421C4⋊C8—611no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—612no—
425C4⋊C8—611no—
426C4⋊C8—1221no—
427C4⋊C8—1221no—
428C4⋊C8—1222no—
429C4⋊C8—1221no—
430C22⋊C8—1222no—
431C22⋊C8—1222no—
432C22⋊C8—1222no—
433C22⋊C8—1221no—
434#97—1222no—
435#97—1222no—
436C4×C8—1222no—
437C4×C8—1221no—
438#41—1222no—
439#41—1222no—
440C2×Q8—22no—
441C2×Q8—82no—
442C2×Q8—611no—
443C2×Q8—612no—
444C2×Q8—611no—
445C2×Q8—1222no—
446C2×Q8—1221no—
447C2×Q8—1222no—
448C2×Q8—4882no—
449C2×Q8—4882no—
450C2×Q8C22×#692312yes—
451C2×Q8C22×#692311yescharacteristic
452C2×D4—612no—
453C2×D4C22⋊#692311yescharacteristic
454C22×C4—22no—
455C22×C4—611no—
456C22×C4—612no—
457C22×C4—612no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4C22×#692312yes—
463M16—4882no—
464M16—2442no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1222no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1222no—
471C2×C8—4881no—
472C2×C8—2442no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—612no—
478C4⋊C4—612no—
479C4⋊C4—611no—
480C4⋊C4—611no—
481C4⋊C4—1221no—
482C4⋊C4—1222no—
483C4⋊C4—1221no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1221no—
490C4⋊C4—1222no—
491C4⋊C4—1221no—
492C4⋊C4—1222no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1222no—
498C4⋊C4C22⋊#692311yescharacteristic
499C4⋊C4C22×#692311yescharacteristic
500C22⋊C4—22no—
501C22⋊C4—612no—
502C22⋊C4—612no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1222no—
506C22⋊C4C22⋊#692312yes—
507C42—21no—
508C42—612no—
509C42—611no—
510C42—612no—
511C42—611no—
512C42—611no—
513C42—612no—
514C42—1222no—
515C42—1222no—
516C42—1221no—
517C42C22×#692311yescharacteristic
518C23—611no—
519C23C2×C22⋊#692312yes—
520Q8—41no—
521Q8—42no—
522Q8—82no—
523Q8—1222no—
524Q8—4882no—
525Q8—4882no—
526Q8—2441no—
527Q8—2442no—
528Q8—2441no—
529Q8—2441no—
530D4—22no—
531D4—1224no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—42no—
536C2×C4—82no—
537C2×C4—611no—
538C2×C4—611no—
539C2×C4—612no—
540C2×C4—612no—
541C2×C4—612no—
542C2×C4—612no—
543C2×C4—611no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1222no—
547C2×C4—1222no—
548C2×C4—1222no—
549C2×C4—1222no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1222no—
553C2×C4—4882no—
554C2×C4—4882no—
555C2×C4—2441no—
556C2×C4C2×C22⋊#692312yes—
557C2×C4C2×C22⋊#692311yescharacteristic
558C2×C4C2×C22⋊#692311yescharacteristic
559C2×C4C23×#692311yescharacteristic
560C8—2441no—
561C8—2442no—
562C8—2441no—
563C8—2441no—
564C8—2441no—
565C8—2442no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—612no—
570C22—1221no—
571C22—1221no—
572C22C22×C22⋊#692311yescharacteristic
573C4—21no—
574C4—22no—
575C4—21no—
576C4—41no—
577C4—42no—
578C4—41no—
579C4—611no—
580C4—611no—
581C4—611no—
582C4—611no—
583C4—1221no—
584C4—1222no—
585C4—1222no—
586C4—2442no—
587C4—2441no—
588C4—2441no—
589C4#1684075512yes—
590C2—42no—
591C2—1222no—
592C2#2146242911yescharacteristic
593C2C2×#1684075511yescharacteristic
594C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758224D4
cosocleC4×Dic61C24
hypercenterD4×Q8#6923
hypocenterC61#17760
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
3. #21461355C2semidirect
4. #21461352C2semidirect
5. #21461345C2semidirect
6. #21461336C2semidirect
7. #21461333C2semidirect
8. #21461332C2semidirect
9. #21461320C2semidirect
10. D61⋊#333C2semidirect
350. C61#17760semidirect

Maximal subgroups

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

subgroupindex
#214627422
#214625162
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