Finite Group Databasebeta

← #29650227

Subgroups — #29650227

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455856C211yesmaximal, characteristic
2#21454748C211yesmaximal, characteristic
3#446×D61C211yesmaximal, characteristic
4#21444716C211yesmaximal, characteristic, complemented
5#21444715C211yesmaximal, characteristic, complemented
6#21444713C211yesmaximal, characteristic, complemented
7#21444713C211yesmaximal, characteristic, complemented
8#21444671C211yesmaximal, characteristic, complemented
9#21444669C211yesmaximal, characteristic, complemented
10#21444667C211yesmaximal, characteristic, complemented
11#21444592C211yesmaximal, characteristic
12#21444246C211yesmaximal, characteristic
13#21444220C211yesmaximal, characteristic
14#21444104C211yesmaximal, characteristic
15C61×#1584C211yesmaximal, characteristic, complemented
16#16840316C2211yescharacteristic
17C4×Q8×D61C2211yescharacteristic
18#16840099C411yescharacteristic
19#16840096C411yescharacteristic
20#16840056C411yescharacteristic
21#16840055C411yescharacteristic
22#16839971C411yescharacteristic
23#16839970C411yescharacteristic
24#16839919C411yescharacteristic
25#16839916C411yescharacteristic
26#16839893C2211yescharacteristic
27#16839893C2211yescharacteristic
28#16839892C2211yescharacteristic
29#16839891—21no—
30#16839891—21no—
31#16839890—21no—
32#16839889C2211yescharacteristic
33#16839889C2211yescharacteristic
34C8×Dic122—21no—
35C8×Dic122C2211yescharacteristic
36C4×Dic244C2211yescharacteristic
37C4×#11758202C2211yescharacteristic
38C4×#11758202C2211yescharacteristic
39#16839813C2211yescharacteristic
40#16839813C2211yescharacteristic
41#16839787—21no—
42#16839784C2211yescharacteristic
43C4⋊C8×D61—21no—
44C4⋊C8×D61C2211yescharacteristic
45#16839716—21no—
46#97×D61—21no—
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839514C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54Q8⋊#92418C2211yescharacteristic
55#16839492C2211yescharacteristic
56#16839492C2211yescharacteristic
57#16839483C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C8×Q8×C61C2211yescharacteristic
62C4×Q16×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×Q8×D61C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×#11758202C2×C411yescharacteristic
70C2×#11758202C2×C411yescharacteristic
71C2×#11758189—21no—
72C2×C8×D61—21no—
73C2×C8×D61D411yescharacteristic
74C2×C8×D61D411yescharacteristic
75#14519776C2×C411yescharacteristic
76#14519775C2×C411yescharacteristic
77#14519767—21no—
78#14519757C2×C411yescharacteristic
79#14519755—21no—
80#14519753C2×C411yescharacteristic
81Q8×Dic61C2×C411yescharacteristic
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×Dic122C2311yescharacteristic
85C4×Dic122C2311yescharacteristic
86#14519742—21no—
87#14519742C2×C411yescharacteristic
88#14519734—21no—
89C4⋊C4×D61—21no—
90C4⋊C4×D61C2×C411yescharacteristic
91C42×D61—21no—
92C42×D61C2311yescharacteristic
93#14519711C2×C411yescharacteristic
94#14519710C2×C411yescharacteristic
95#14519710C2×C411yescharacteristic
96C4⋊#92418—21no—
97C4⋊#92418—21no—
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519706—21no—
101#14519706—21no—
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519706C2×C411yescharacteristic
108#14519706C2×C411yescharacteristic
109#14519702C2×C411yescharacteristic
110#14519702C2×C411yescharacteristic
111#14519701C2×C411yescharacteristic
112#14519701C2×C411yescharacteristic
113#14519700C2×C411yescharacteristic
114#14519700C2×C411yescharacteristic
115#14519689—21no—
116#14519689C2×C411yescharacteristic
117#14519689C2×C411yescharacteristic
118#14519688—21no—
119#14519688—21no—
120#14519687—21no—
121#14519687—21no—
122#14519687—21no—
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61D411yescharacteristic
128C8×Dic61D411yescharacteristic
129C2×Q16×C61C2×C411yescharacteristic
130C4×Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132#107×C61C2×C411yescharacteristic
133C4⋊C8×C61—21no—
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#103×C61C2×C411yescharacteristic
139#97×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146Q8×D61—41no—
147Q8×D61—41no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61C22×C411yescharacteristic
151C2×C4×D61C2×D411yescharacteristic
152C2×C4×D61#4111yescharacteristic
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122C22×C411yescharacteristic
156C2×Dic122C22×C411yescharacteristic
157Q16×C61—41no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61C22×C411yescharacteristic
162C2×C8×C61C22×C411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61C22×C411yescharacteristic
168C4⋊C4×C61C22×C411yescharacteristic
169C42×C61—21no—
170C42×C61—21no—
171C42×C61C2411yescharacteristic
172#11758202—41no—
173#11758202—41no—
174#11758198—21no—
175#11758198—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61C22×C411yescharacteristic
179C4⋊Dic61C22×C411yescharacteristic
180#11758196—21no—
181#11758196—21no—
182#11758196—21no—
183#11758196—21no—
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61C22×C411yescharacteristic
193C4×Dic61C2×D411yescharacteristic
194C4×Dic61#4111yescharacteristic
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418C22×C411yescharacteristic
199C2×#92418C22×C411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202Dic244—41no—
203#11758189—42no—
204C8×D61—22no—
205C8×D61—42no—
206C8×D61Q1614yescomplemented
207C22×D61C4×D411yescharacteristic
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61C23×C411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61C4×D411yescharacteristic
224C2×Dic61C4×D411yescharacteristic
225C2×Dic61C4×D411yescharacteristic
226C4×D61—21no—
227C4×D61—21no—
228C4×D61—41no—
229C4×D61—42no—
230C4×D61—42no—
231C4×D61C2×Q1612yes—
232C4×D61#13512yes—
233Dic122—21no—
234Dic122—21no—
235Dic122—21no—
236Dic122—21no—
237Dic122—42no—
238Dic122—42no—
239C8×C61—21no—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—41no—
243C8×C61—41no—
244C8×C61—41no—
245C8×C61C2×Q1612yes—
246#92418—21no—
247#92418—21no—
248#92418—21no—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#92418C2×Q1612yes—
253#17931—611nomaximal, Sylow
254C22×C61C2×C4×D411yescharacteristic
255C2×D61—21no—
256C2×D61—21no—
257C2×D61C4×Q1612yes—
258C4×C61—21no—
259C4×C61—41no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61#56811yescharacteristic
264C4×C61#56811yescharacteristic
265C4×C61C22×Q1611yescharacteristic
266C4×C61C2×#13511yescharacteristic
267Dic61—21no—
268Dic61—21no—
269Dic61—41no—
270Dic61—41no—
271Dic61—41no—
272Dic61—41no—
273Dic61C4×Q1612yes—
274#3104—611no—
275#2960—611no—
276C2×#446—611no—
277#1591—611no—
278#1591—611no—
279#1591—611no—
280#1591—611no—
281#1584—611no—
282#1584—611no—
283#1584—611no—
284#1584D6111yescharacteristic, complemented
285#1571—611no—
286#1487—611no—
287#1481—611no—
288#1450—611no—
289C2×C61#293011yescharacteristic
290C2×C61C2×C4×Q1611yescharacteristic
291C2×C61#295511yescharacteristic
292D61—22no—
293#533—611no—
294C2×C4×Q8—611no—
295#484—611no—
296#484—611no—
297#477—611no—
298#477—611no—
299#462—611no—
300#462—611no—
301#451—611no—
302#451—611no—
303#446—611no—
304#446—611no—
305#446—611no—
306#446—611no—
307#446—611no—
308#446—1221no—
309#446—1221no—
310#446—1221no—
311#446C2×D6111yescharacteristic
312C8×Q8—611no—
313C8×Q8—1221no—
314C8×Q8C2×D6111yescharacteristic
315C4×Q16—611no—
316C4×Q16—611no—
317C4×Q16—611no—
318C4×Q16C2×D6111yescharacteristic
319#431—611no—
320#431—611no—
321#424—1221no—
322#423—611no—
323C2×C4⋊C8—611no—
324C2×C4⋊C8—1221no—
325#405—1221no—
326C2×#97—1221no—
327C2×C4×C8—611no—
328#335—611no—
329#335—611no—
330#335—611no—
331#335C2×D6111yescharacteristic
332Q8⋊C8—611no—
333Q8⋊C8—611no—
334Q8⋊C8—611no—
335Q8⋊C8—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8C2×D6111yescharacteristic
339Q8⋊C8C2×D6111yescharacteristic
340#322—611no—
341#322C2×D6111yescharacteristic
342C82—611no—
343C82—611no—
344C61#1793111yescharacteristic, complemented, Sylow
345C22×Q8—611no—
346C2×Q16—611no—
347C2×Q16—611no—
348C2×Q16—611no—
349C2×Q16C4×D6111yescharacteristic
350C2×M16—1221no—
351C22×C8—611no—
352C22×C8—611no—
353C22×C8—1221no—
354C4⋊Q8—611no—
355C4⋊Q8—611no—
356#125—1221no—
357C22⋊Q8—611no—
358C22⋊Q8—611no—
359C22⋊Q8—1221no—
360C4×Q8—611no—
361C4×Q8—611no—
362C4×Q8—611no—
363C4×Q8—611no—
364C4×Q8—1221no—
365C4×Q8—1221no—
366C4×Q8—1221no—
367C4×Q8C22×D6111yescharacteristic
368C4×Q8C22×D6111yescharacteristic
369#117—1221no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—1221no—
372C2×C42—611no—
373C2×C42—1221no—
374#107—611no—
375#107—611no—
376#107—611no—
377#107C4×D6111yescharacteristic
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—611no—
381C4⋊C8—611no—
382C4⋊C8—611no—
383C4⋊C8—611no—
384C4⋊C8—1221no—
385C4⋊C8—1221no—
386C4⋊C8—1221no—
387C4⋊C8—1221no—
388C4⋊C8—1221no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8C22×D6111yescharacteristic
394C4⋊C8C22×D6111yescharacteristic
395#103—611no—
396#103—611no—
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103C4×D6111yescharacteristic
402#103C4×D6111yescharacteristic
403C22⋊C8—611no—
404C22⋊C8—611no—
405C22⋊C8—1221no—
406#97—21no—
407#97—1221no—
408#97—1221no—
409#97—1221no—
410#97—1221no—
411#97—1221no—
412C4×C8—21no—
413C4×C8—611no—
414C4×C8—611no—
415C4×C8—611no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—1221no—
419C4×C8C22×D6111yescharacteristic
420C4×C8C22×D6111yescharacteristic
421C4×C8C22×D6111yescharacteristic
422C2×Q8—611no—
423C2×Q8—611no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—2441no—
427C2×Q8—2441no—
428C2×Q8C2×C4×D6111yescharacteristic
429C2×Q8C2×C4×D6111yescharacteristic
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—1221no—
434C22×C4—1221no—
435Q16—41no—
436Q16—2441no—
437Q16—2441no—
438Q16—2441no—
439M16—2442no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—611no—
444C2×C8—614no—
445C2×C8—611no—
446C2×C8—611no—
447C2×C8—611no—
448C2×C8—1222no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—2442no—
453C2×C8C2×C4×D6111yescharacteristic
454C2×C8C2×C4×D6111yescharacteristic
455C2×C8D4×D6111yescharacteristic
456C2×C8D4×D6111yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—611no—
460C4⋊C4—611no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4C2×C4×D6111yescharacteristic
472C4⋊C4C2×C4×D6111yescharacteristic
473C22⋊C4—1221no—
474C22⋊C4—1221no—
475C42—21no—
476C42—21no—
477C42—611no—
478C42—611no—
479C42—611no—
480C42—1221no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42C23×D6111yescharacteristic
485C23—611no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—1221no—
491Q8—1221no—
492Q8—1221no—
493Q8—1221no—
494Q8—2442no—
495Q8—2442no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—611no—
501C2×C4—612no—
502C2×C4—612no—
503C2×C4—611no—
504C2×C4—611no—
505C2×C4—1221no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—2441no—
512C2×C4—2442no—
513C2×C4—2442no—
514C2×C4C22×C4×D6111yescharacteristic
515C2×C4C2×D4×D6111yescharacteristic
516C2×C4#41×D6111yescharacteristic
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—612no—
524C8—1221no—
525C8—1221no—
526C8—1221no—
527C8—2441no—
528C8—2441no—
529C8—2441no—
530C8Q16×D6112yes—
531C22—612no—
532C22—1221no—
533C22—1221no—
534C22C4×D4×D6111yescharacteristic
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—612no—
541C4—1221no—
542C4—1221no—
543C4—2441no—
544C4—2441no—
545C4—2441no—
546C4—2441no—
547C4#1684052711yescharacteristic
548C4#1684052811yescharacteristic
549C4C2×Q16×D6111yescharacteristic
550C4#135×D6111yescharacteristic
551C2—1222no—
552C2#2145451711yescharacteristic
553C2C4×Q16×D6111yescharacteristic
554C2#2145471911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1584C2
socleC22×C61C2×C4×D4
prime radicalC22×D61C4×D4
cosocleC42×C61C24
hypercenter#1584D61
hypocenterC61#17931
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #21444716C2semidirect
5. #21444715C2semidirect
6. #21444713C2semidirect
7. #21444713C2semidirect
8. #21444671C2semidirect
9. #21444669C2semidirect
10. #21444667C2semidirect
15. C61×#1584C2semidirect
206. C8×D61Q16semidirect
284. #1584D61semidirect
344. C61#17931semidirect

Maximal subgroups

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

subgroupindex
#214558562
#214547482
#446×D612
#214447162
#214447152
#214447132
#214446712
#214446692
#214446672
#214445922
#214442462
#214442202
#214441042
C61×#15842
#1793161