Finite Group Databasebeta

← #30544557

Subgroups — #30544557

Order 15616.

1962 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459116C211yesmaximal, characteristic
2#21454832C218yesmaximal, complemented
3#21454812C218yesmaximal, complemented
4#21454760C211yesmaximal, characteristic, complemented
5#21454538C211yesmaximal, characteristic, complemented
6#21454536C211yesmaximal, characteristic, complemented
7#21454515C212yesmaximal, complemented
8#21454512C212yesmaximal, complemented
9#21454469C212yesmaximal, complemented
10#21454451C211yesmaximal, characteristic, complemented
11#21454246C212yesmaximal, complemented
12C2×#97×D61C211yesmaximal, characteristic, complemented
13C61×#2961C211yesmaximal, characteristic, complemented
14C2×#14519785C2212yes—
15C2×#14519783C2212yes—
16C22×C8×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#16840317C412yes—
19#16840313C412yes—
20#16840312C2211yescharacteristic
21#16840299C2214yes—
22#16840298C414yes—
23#16840297C414yes—
24#16840275C414yes—
25#16840274C2212yes—
26C4×#11758226C2214yes—
27#16840230C2212yes—
28C2×C42×D61C2211yescharacteristic
29#16839893C2218yescomplemented
30#16839835C2218yes—
31#16839835C2218yescomplemented
32#16839832C2218yes—
33#16839832C2218yescomplemented
34C8×D244C2218yes—
35#16839827C2218yes—
36#16839822C2218yescomplemented
37#16839818C2214yes—
38#16839818C2218yescomplemented
39#16839814C2214yes—
40#16839789C2212yes—
41#16839786C2211yescharacteristic
42#16839730C2212yes—
43#16839728C2212yes—
44#16839725C2212yes—
45#16839719C2214yescomplemented
46#16839718C2212yes—
47#16839716C2214yescomplemented
48M16×Dic61C2212yes—
49C4×#11758189C2214yescomplemented
50C2×#14519688C2211yescharacteristic
51C2×#14519687C2211yescharacteristic
52C2×#14519687C2211yescharacteristic
53#97×D61C2214yes—
54#97×D61C2214yes—
55#97×D61C2214yescomplemented
56C61×#533C2211yescharacteristic
57C61×#446C2218yescomplemented
58C61×#424C2212yes—
59C61×#423C2211yescharacteristic
60C61×#405C2212yes—
61C2×#97×C61C2211yescharacteristic
62C2×#11758226C2×C414yes—
63C2×#11758222C2312yes—
64C22×C4×D61C2×C412yes—
65C22×C4×D61C2311yescharacteristic
66#14519785—28no—
67#14519783—28no—
68C2×#11758194C2312yes—
69C2×#11758189C2314yes—
70C2×#11758189C2314yes—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C2×C8×D61—24no—
74C2×C8×D61—24no—
75C2×C8×D61C2314yes—
76C2×C8×D61C2314yes—
77C2×C8×D61C2314yes—
78C2×C8×D61C2314yes—
79#14519777C2×C411yescharacteristic
80#14519774C2×C411yescharacteristic
81#14519772C2×C418yes—
82#14519768C2×C414yes—
83#14519766C2×C414yes—
84#14519765C2×C412yes—
85#14519762C2×C418yes—
86#14519761C2×C414yes—
87#14519757C2×C414yes—
88#14519753C2×C414yes—
89#14519752C2×C414yes—
90#14519752C2×C414yes—
91#14519751C2×C414yes—
92#14519747C2×C414yes—
93Q8×Dic61C2×C414yes—
94#14519742C2×C414yes—
95C4×D244C2318yes—
96C4×D244C2314yes—
97#14519739C2×C414yes—
98#14519739C2×C418yes—
99#14519739C2×C414yes—
100#14519737C2×C418yes—
101#14519735C2×C414yes—
102#14519735C2×C418yes—
103#14519734C2314yes—
104C2×C4×Dic61C2×C412yes—
105C2×C4×Dic61C2311yescharacteristic
106C42×D61C2×C412yes—
107C42×D61C2×C412yes—
108C42×D61C2312yes—
109C42×D61C2312yes—
110C42×D61C2314yes—
111C4⋊#92418C2314yes—
112C4⋊#92418C2318yes—
113#14519689C2318yes—
114#14519689C2318yes—
115#14519689C2318yes—
116#14519688C2314yes—
117#14519688C2314yes—
118#14519687C2312yes—
119#14519687C2312yes—
120#14519687C2312yes—
121#14519687C2312yes—
122#14519687C2314yes—
123C4×#92418C2314yes—
124C8×Dic61C2314yes—
125C2×M16×C61C2312yes—
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C4⋊Q8×C61C2×C412yes—
129#125×C61C2×C412yes—
130C22⋊Q8×C61C2×C414yes—
131C4×Q8×C61C2314yes—
132#117×C61C2312yes—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61C2314yes—
135C4⋊C8×C61C2318yes—
136#97×C61C2314yes—
137#97×C61C2314yes—
138C4×C8×C61C2314yes—
139C23×D61C22×C411yescharacteristic
140C2×Q8×C61C22×C414yes—
141C22×C4×C61C22×C412yes—
142C22×C4×C61C2411yescharacteristic
143C2×C22⋊D61C22×C414yes—
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C412yes—
146#11758226—48no—
147#11758222—24no—
148#11758222—24no—
149C2×D244C22×C412yes—
150C2×D244C22×C418yes—
151C2×D244C22×C414yes—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—44no—
155C2×C4×D61C22×C412yes—
156C2×C4×D61C22×C412yes—
157C2×C4×D61C22×C412yes—
158C2×C4×D61C22×C412yes—
159C2×C4×D61C22×C412yes—
160C2×C4×D61C22×C418yes—
161C2×C4×D61C2412yes—
162C2×C4×D61C2414yes—
163C2×Dic122C22×C412yes—
164M16×C61—24no—
165C2×C8×C61—22no—
166C2×C8×C61#4114yescomplemented
167C2×C8×C61C2414yes—
168C2×C8×C61C2412yes—
169C2×C8×C61C2412yes—
170C4⋊C4×C61C22×C414yes—
171C4⋊C4×C61C22×C418yes—
172C4⋊C4×C61C22×C414yes—
173C22⋊C4×C61C22×C414yes—
174C42×C61C22×C411yescharacteristic
175C42×C61C22×C411yescharacteristic
176C42×C61C2414yes—
177C42×C61C2412yes—
178#11758198C22×C418yes—
179#11758198C22×C418yes—
180#11758198C22×C418yes—
181#11758198C22×C418yes—
182C4⋊Dic61C22×C414yes—
183C4⋊Dic61C22×C418yes—
184#11758196C22×C418yes—
185C4×Dic61C22×C412yes—
186C4×Dic61C22×C412yes—
187C4×Dic61C22×C412yes—
188C4×Dic61C22×C412yes—
189C4×Dic61C22×C412yes—
190C4×Dic61C22×C418yes—
191C4×Dic61C2411yescharacteristic
192C4×Dic61C2411yescharacteristic
193#11758194—24no—
194C2×#92418—22no—
195C2×#92418#4114yescomplemented
196C2×#92418C2414yes—
197C2×#92418C2412yes—
198C2×#92418C2412yes—
199#11758189—28no—
200#11758189—28no—
201C8×D61—28no—
202C8×D61—28no—
203C8×D61—28no—
204C8×D61—28no—
205C23×C61C23×C411yescharacteristic
206C22×D61—22no—
207C22×D61—24no—
208C22×D61C23×C414yes—
209C22×D61C23×C412yes—
210Q8×C61—44no—
211C2×C4×C61—42no—
212C2×C4×C61C23×C412yes—
213C2×C4×C61C23×C412yes—
214C2×C4×C61C23×C418yes—
215C2×C4×C61C23×C411yescharacteristic
216C2×C4×C61C2×#4112yes—
217C2×C4×C61C2×#4112yes—
218C2×C4×C61C2511yescharacteristic
219C22⋊D61—28no—
220C2×Dic61—22no—
221C2×Dic61—42no—
222C2×Dic61C23×C412yes—
223C2×Dic61C23×C412yes—
224C2×Dic61C23×C412yes—
225C2×Dic61C23×C414yes—
226D244—216no—
227D244—24no—
228D244—44no—
229C4×D61—24no—
230C4×D61—24no—
231C4×D61—24no—
232C4×D61—22no—
233C4×D61—22no—
234C4×D61—24no—
235C4×D61—24no—
236C4×D61—42no—
237C4×D61—42no—
238C4×D61—48no—
239Dic122—24no—
240C8×C61—22no—
241C8×C61—24no—
242C8×C61C2×#4114yes—
243#92418—22no—
244#92418—24no—
245#92418C2×#4114yes—
246#60207—611nomaximal, Sylow
247C22×C61—22no—
248C22×C61C4×#4112yes—
249C22×C61C24×C411yescharacteristic
250C2×D61—28no—
251C2×D61—22no—
252C2×D61—22no—
253C2×D61—24no—
254C2×D61—28no—
255C2×D61#56814yes—
256C4×C61—22no—
257C4×C61—22no—
258C4×C61—28no—
259C4×C61C4×#4112yes—
260C4×C61C22×#4111yescharacteristic
261C4×C61C22×#4111yescharacteristic
262Dic61—24no—
263Dic61—22no—
264Dic61—22no—
265Dic61—22no—
266#3444—611no—
267#2970—618no—
268#2968—618no—
269#2961—611no—
270#2961D6111yescharacteristic, complemented
271#2932—611no—
272#2932—611no—
273#2929—612no—
274#2929—612no—
275#2923—612no—
276#2920—611no—
277#2875—612no—
278C22×#97—611no—
279C2×C61—22no—
280C2×C61C2×C4×#4111yescharacteristic
281C2×C61C2×#56812yes—
282D61—24no—
283D61—44no—
284C2×#131—612no—
285C2×#131—612no—
286C23×C8—611no—
287C23×C8—611no—
288#533—612no—
289#533C2×D6111yescharacteristic
290#532—612no—
291#532—611no—
292#529—614no—
293#529—614no—
294#529—614no—
295#525—614no—
296#525—612no—
297C4×#41—614no—
298C4×#41—612no—
299C22×C42—611no—
300#446—618no—
301#446C2×D6118yescomplemented
302#435—618no—
303#435—618no—
304#435—618no—
305#435—618no—
306C8×D4—618no—
307C8×D4—618no—
308#433—618no—
309#432—614no—
310#432—618no—
311#431—614no—
312#424—612no—
313#424C2×D6112yes—
314#423—611no—
315#423C2×D6111yescharacteristic
316#408—612no—
317#408—612no—
318#407—612no—
319#405—612no—
320#405—614no—
321#405—614no—
322#405C2×D6112yes—
323C4×M16—612no—
324C4×M16—614no—
325C2×#97—611no—
326C2×#97—611no—
327C2×#97—611no—
328C2×#97—614no—
329C2×#97—614no—
330C2×#97—614no—
331C2×#97C2×D6111yescharacteristic
332C61#6020711yescharacteristic, complemented, Sylow
333C2×#41—614no—
334C2×#41—612no—
335C23×C4—611no—
336C23×C4—612no—
337#131—1228no—
338#131—1228no—
339C2×M16—612no—
340C2×M16—614no—
341C2×M16—614no—
342C2×M16C22×D6112yes—
343C22×C8—611no—
344C22×C8—611no—
345C22×C8—614no—
346C22×C8—614no—
347C22×C8—614no—
348C22×C8—614no—
349C22×C8—1224no—
350C22×C8—1224no—
351C22×C8C22×D6111yescharacteristic
352C22×C8C22×D6111yescharacteristic
353C4⋊Q8—611no—
354C4⋊Q8C4×D6112yes—
355#127—611no—
356#126—618no—
357#125—614no—
358#125C4×D6112yes—
359#124—614no—
360#124—612no—
361#123—618no—
362#123—614no—
363C22⋊Q8—614no—
364C22⋊Q8—614no—
365C22⋊Q8C4×D6114yes—
366#121—614no—
367#121—614no—
368#121—614no—
369#120—614no—
370C4×Q8—614no—
371C4×Q8—614no—
372C4×Q8C22×D6114yes—
373C4×D4—618no—
374C4×D4—614no—
375C4×D4—614no—
376C4×D4—618no—
377C4×D4—618no—
378C4×D4—614no—
379#117—614no—
380#117—618no—
381#117—614no—
382#117C22×D6112yes—
383C2×C42—612no—
384C2×C42—611no—
385C2×C42—612no—
386C2×C42—612no—
387C2×C42—614no—
388C2×C42—612no—
389C2×C42—612no—
390C2×C42C22×D6111yescharacteristic
391C4⋊C8—614no—
392C4⋊C8—618no—
393C4⋊C8C22×D6114yes—
394C4⋊C8C22×D6118yes—
395C22⋊C8—618no—
396C22⋊C8—618no—
397C22⋊C8—618no—
398#97—612no—
399#97—612no—
400#97—612no—
401#97—612no—
402#97—614no—
403#97—614no—
404#97—614no—
405#97C22×D6114yes—
406#97C22×D6114yes—
407C4×C8—614no—
408C4×C8—614no—
409C4×C8C22×D6114yes—
410C24—611no—
411#41—1224no—
412#41—1224no—
413#41—2448no—
414C2×Q8—612no—
415C2×Q8C2×C4×D6114yes—
416C2×D4—614no—
417C2×D4—618no—
418C2×D4—612no—
419C2×D4—614no—
420C22×C4—611no—
421C22×C4—612no—
422C22×C4—612no—
423C22×C4—612no—
424C22×C4—612no—
425C22×C4—612no—
426C22×C4—614no—
427C22×C4—612no—
428C22×C4—612no—
429C22×C4—618no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—2444no—
433C22×C4C2×C4×D6112yes—
434C22×C4C23×D6111yescharacteristic
435M16—24no—
436M16—1228no—
437M16—1224no—
438M16—1228no—
439C2×C8—22no—
440C2×C8—614no—
441C2×C8—612no—
442C2×C8—614no—
443C2×C8—612no—
444C2×C8—1228no—
445C2×C8—1228no—
446C2×C8—1222no—
447C2×C8—1228no—
448C2×C8—1228no—
449C2×C8#1175822614yescomplemented
450C2×C8C23×D6114yes—
451C2×C8C23×D6112yes—
452C2×C8C23×D6112yes—
453C4⋊C4—618no—
454C4⋊C4—614no—
455C4⋊C4—618no—
456C4⋊C4C2×C4×D6114yes—
457C4⋊C4C2×C4×D6118yes—
458C4⋊C4C2×C4×D6114yes—
459C22⋊C4—618no—
460C22⋊C4—618no—
461C22⋊C4—618no—
462C22⋊C4—618no—
463C22⋊C4C2×C4×D6114yes—
464C42—612no—
465C42—612no—
466C42—612no—
467C42—612no—
468C42—612no—
469C42—618no—
470C42—611no—
471C42—611no—
472C42C2×C4×D6111yescharacteristic
473C42C2×C4×D6111yescharacteristic
474C42C23×D6114yes—
475C42C23×D6112yes—
476C23—612no—
477C23—614no—
478C23—1224no—
479C23—1222no—
480C23C22×C4×D6111yescharacteristic
481Q8—44no—
482Q8—1224no—
483D4—12216no—
484D4—1228no—
485D4—1224no—
486D4—2444no—
487C2×C4—42no—
488C2×C4—612no—
489C2×C4—612no—
490C2×C4—612no—
491C2×C4—614no—
492C2×C4—1224no—
493C2×C4—1224no—
494C2×C4—1222no—
495C2×C4—1224no—
496C2×C4—1222no—
497C2×C4—1224no—
498C2×C4—1222no—
499C2×C4—1224no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4—2448no—
503C2×C4—2442no—
504C2×C4C22×C4×D6112yes—
505C2×C4C22×C4×D6112yes—
506C2×C4C22×C4×D6118yes—
507C2×C4C22×C4×D6111yescharacteristic
508C2×C4#41×D6112yes—
509C2×C4C2×#1175822612yes—
510C2×C4C24×D6111yescharacteristic
511C8—22no—
512C8—24no—
513C8—614no—
514C8—1222no—
515C8—1224no—
516C8C2×#1175822614yes—
517C22—22no—
518C22—614no—
519C22—1228no—
520C22—1222no—
521C22—1222no—
522C22—1228no—
523C22—1224no—
524C22C4×#1175822612yes—
525C22C23×C4×D6111yescharacteristic
526C4—22no—
527C4—22no—
528C4—28no—
529C4—1222no—
530C4—1222no—
531C4—1222no—
532C4—1224no—
533C4C4×#1175822612yes—
534C4C2×#41×D6111yescharacteristic
535C4C22×#1175822611yescharacteristic
536C2—22no—
537C2—1224no—
538C2—2444no—
539C2C2×C4×#1175822611yescharacteristic
540C2#568×D6112yes—
subgroupG/H
center, FrattiniC2×C4C24×D61
commutator, socleC22×C61C24×C4
FittingC61×#2961C2
prime radical#21459116C2
cosocleC2×C4×C61C25
hypercenter#2961D61
hypocenterC61#60207
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. #21454832C2semidirect
3. #21454812C2semidirect
4. #21454760C2semidirect
5. #21454538C2semidirect
6. #21454536C2semidirect
7. #21454515C2semidirect
8. #21454512C2semidirect
9. #21454469C2semidirect
10. #21454451C2semidirect
11. #21454246C2semidirect
12. C2×#97×D61C2semidirect
13. C61×#2961C2semidirect
29. #16839893C22semidirect
31. #16839835C22semidirect
33. #16839832C22semidirect
36. #16839822C22semidirect
38. #16839818C22semidirect
45. #16839719C22semidirect
47. #16839716C22semidirect
49. C4×#11758189C22semidirect
55. #97×D61C22semidirect
57. C61×#446C22semidirect
166. C2×C8×C61#41semidirect
195. C2×#92418#41semidirect
270. #2961D61semidirect
301. #446C2×D61semidirect
332. C61#60207semidirect
449. C2×C8#11758226semidirect

Maximal subgroups

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

subgroupindex
#214591162
#214548322
#214548122
#214547602
#214545382
#214545362
#214545152
#214545122
#214544692
#214544512
#214542462
C2×#97×D612
C61×#29612
#6020761