Finite Group Databasebeta

← #30616420

Subgroups — #30616420

Order 15616.

738 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462506C212yesmaximal, complemented
2#21461974C211yesmaximal, characteristic
3#21461972C211yesmaximal, characteristic
4#21461929C211yesmaximal, characteristic, complemented
5#21461926C211yesmaximal, characteristic, complemented
6#21461915C212yesmaximal, complemented
7#21461913C212yesmaximal, complemented
8#21461639C211yesmaximal, characteristic, complemented
9C4×#14519841C212yesmaximal, complemented
10#97×#6923C211yesmaximal, characteristic, complemented
11#21454616C211yesmaximal, characteristic
12#16840786—22no—
13#16840786—22no—
14#16840783—22no—
15#16840782—22no—
16C2×#14519848C2211yescharacteristic
17C2×#14519847C2211yescharacteristic
18#16840769C2212yes—
19#16840769C2212yes—
20C2×#14519841C2212yes—
21C2×#14519841C2212yes—
22#16840736C2212yes—
23#16840736C2212yes—
24C4×#11758213C2212yes—
25#16840721C2211yescharacteristic
26C2×#14519831C2211yescharacteristic
27C2×#14519831C2211yescharacteristic
28C2×C8×#6923C2211yescharacteristic
29C2×C8×#6923C2211yescharacteristic
30C42×#6923C2211yescharacteristic
31#16840638C2212yes—
32#16840632C2212yes—
33#16840632C2212yes—
34C2×#14519796C2211yescharacteristic
35C4×#11758224C2212yes—
36#16839874C411yescharacteristic, complemented
37#16839870C411yescharacteristic, complemented
38#16839868C411yescharacteristic, complemented
39#16839862C412yescomplemented
40#16839859C412yescomplemented
41#16839797C2211yescharacteristic
42#16839755C2212yes—
43#97×D61C2211yescharacteristic
44C61×#442C411yescharacteristic, complemented
45C2×#11758213C2312yes—
46C2×#11758213C2312yes—
47C2×D61⋊C8C2311yescharacteristic
48C2×D61⋊C8C2311yescharacteristic
49C2×C4×#6923—22no—
50C2×C4×#6923C2311yescharacteristic
51C2×C4×#6923C2311yescharacteristic
52#14519848—22no—
53#14519847—22no—
54#14519844—22no—
55#14519844—22no—
56C4⋊#92420—22no—
57C4⋊#92420—22no—
58#14519841—24no—
59#14519841—24no—
60C22⋊#92420—22no—
61C22⋊#92420—22no—
62C22⋊#92420—22no—
63C22⋊#92420—22no—
64#14519832—22no—
65#14519832D412yes—
66#14519832D412yes—
67#14519831—22no—
68#14519831—22no—
69C4×#92420—22no—
70C8×#6923—22no—
71C8×#6923—22no—
72C2×#11758224C2312yes—
73#14519796—22no—
74#14519796—22no—
75C2×Dic244C2×C411yescharacteristic
76C2×#11758200C2×C412yes—
77C2×C8×D61C2311yescharacteristic
78C2×C8×D61C2311yescharacteristic
79C4×Dic122C2×C412yes—
80#14519742C2×C412yes—
81D4×Dic61C2×C412yes—
82C4×C22⋊D61—22no—
83#14519737—22no—
84#14519735C2312yes—
85#14519733—22no—
86C2×C4×Dic61—22no—
87C42×D61C2311yescharacteristic
88#14519710C2×C412yes—
89#14519709C2×C411yescharacteristic
90#14519702C2×C412yes—
91#14519700C2×C412yes—
92#14519698C2×C412yes—
93#14519688C2×C411yescharacteristic
94#14519687C2×C411yescharacteristic
95#14519687C2×C411yescharacteristic
96C2×D8×C61C2×C411yescharacteristic
97C4×D4×C61C2×C412yes—
98#106×C61C2×C411yescharacteristic
99#102×C61C2×C412yes—
100#97×C61C2×C411yescharacteristic
101C22×#6923—21no—
102C22×#6923—21no—
103C2×D4×C61C22×C412yes—
104C22×C4×C61—22no—
105C2×C22⋊D61—22no—
106C22×Dic61—22no—
107C22×Dic61—22no—
108#11758224—22no—
109#11758224—22no—
110#11758224—22no—
111#11758224—22no—
112C2×C4×D61#4112yes—
113C2×C4×D61C2411yescharacteristic
114C2×Dic122C22×C412yes—
115C2×#92420—22no—
116C2×#92420—22no—
117C2×#92420C2×D411yescharacteristic
118C2×#92420C2×D412yes—
119C2×#92420C2×D411yescharacteristic
120C4×#6923—21no—
121C4×#6923—21no—
122C4×#6923—44no—
123C4×#6923#4112yes—
124C4×#6923#4112yes—
125#11758213—22no—
126#11758213—22no—
127#11758213—22no—
128#11758213—22no—
129D61⋊C8—21no—
130D61⋊C8—21no—
131D61⋊C8—21no—
132D61⋊C8—21no—
133D8×C61—22no—
134C2×C8×C61C22×C411yescharacteristic
135C2×C8×C61C22×C411yescharacteristic
136C4⋊C4×C61C22×C412yes—
137C22⋊C4×C61—22no—
138C42×C61C22×C411yescharacteristic
139C22⋊Dic61—22no—
140#11758200—24no—
141#11758198—22no—
142C4⋊Dic61C22×C412yes—
143#11758196—22no—
144#11758196—22no—
145C4×Dic61—22no—
146C4×Dic61—22no—
147C4×Dic61—22no—
148C4×Dic61C22×C411yescharacteristic
149C4×Dic61C2×D412yes—
150C2×#92418C22×C411yescharacteristic
151C2×#92418C22×C411yescharacteristic
152Dic244—22no—
153C8×D61—21no—
154C8×D61—21no—
155C8×D61#4112yes—
156C8×D61#4112yes—
157C23×C61—22no—
158C22×D61C2×#4111yescharacteristic
159C2×#6923—24no—
160C2×#6923—22no—
161C2×#6923—22no—
162C2×#6923—42no—
163D4×C61—22no—
164D4×C61—22no—
165C2×C4×C61—22no—
166C2×C4×C61—82no—
167C2×C4×C61C4×D412yes—
168C2×C4×C61C23×C411yescharacteristic
169C22⋊D61—42no—
170C22⋊D61—42no—
171C2×Dic61—22no—
172C2×Dic61—22no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61—82no—
176C2×Dic61C4×D412yes—
177C2×Dic61C22×D411yescharacteristic
178C4×D61—42no—
179C4×D61C2×#4111yescharacteristic
180C4×D61C2×#4111yescharacteristic
181C4×D61C2×#4111yescharacteristic
182C4×D61C2×#4111yescharacteristic
183Dic122—22no—
184Dic122—22no—
185#92420—21no—
186#92420—22no—
187#92420—21no—
188#92420—42no—
189#92420—42no—
190C8×C61—21no—
191C8×C61#11712yes—
192#92418—21no—
193#92418#11712yes—
194#21297—611nomaximal, Sylow
195C22×C61—42no—
196C22×C61—42no—
197C22×C61—42no—
198C22×C61C2×C4×D411yescharacteristic
199C2×D61—22no—
200C2×D61#52911yescharacteristic
201C2×D61#52911yescharacteristic
202#6923—24no—
203#6923—42no—
204C4×C61—22no—
205C4×C61—42no—
206C4×C61C2×#11711yescharacteristic
207C4×C61C4×#4111yescharacteristic
208Dic61—22no—
209Dic61—42no—
210Dic61—42no—
211Dic61#53211yescharacteristic
212Dic61#53211yescharacteristic
213#2943—611no—
214#2923—612no—
215#1975—611no—
216#1974—611no—
217#1946—611no—
218#1945—611no—
219#1938—612no—
220#1937—612no—
221#1778—611no—
222C4×#104—612no—
223C4×#97—611no—
224C2×C61—82no—
225C2×C61#229311yescharacteristic
226C2×C61#295612yes—
227D61—21no—
228D61—21no—
229C2×#135—611no—
230C4×#41—612no—
231#442—611no—
232#442#692311yescharacteristic, complemented
233#441—611no—
234#441—611no—
235#440—612no—
236#440—612no—
237#433—1222no—
238#433—1222no—
239#432—1222no—
240#432—1222no—
241C2×#108—611no—
242C2×#108—611no—
243#427—611no—
244#424—612no—
245#424—612no—
246C2×#104—612no—
247C2×#104—612no—
248#416—612no—
249#408—612no—
250#408—612no—
251C4×M16—612no—
252C2×#97—611no—
253C2×#97—611no—
254C2×#97—611no—
255C2×#97—611no—
256C2×C4×C8—611no—
257C2×C4×C8—611no—
258C43—611no—
259#341—612no—
260#339—612no—
261#339—612no—
262C61#2129711yescharacteristic, complemented, Sylow
263C2×#41—612no—
264#135—1222no—
265#135—1222no—
266C2×Q16—611no—
267C2×SD16—612no—
268C2×D8C2×#692311yescharacteristic
269C2×M16—612no—
270C2×M16—612no—
271C22×C8—611no—
272C22×C8—611no—
273C22×C8—611no—
274C22×C8—611no—
275C4×Q8—612no—
276C4×Q8—612no—
277C4×D4—612no—
278C4×D4—1222no—
279C4×D4—1222no—
280C4×D4C2×#692312yes—
281#117—612no—
282#117—1222no—
283C2×C42—611no—
284C2×C42—611no—
285C2×C42—611no—
286C2×C42—1222no—
287C2×C42—1222no—
288#108—1222no—
289#108—1222no—
290#107—612no—
291#106—611no—
292#106C2×#692311yescharacteristic
293C4⋊C8—1222no—
294C4⋊C8—1222no—
295C4⋊C8—1222no—
296C4⋊C8—1222no—
297#104—1224no—
298#104—1224no—
299#103—612no—
300#103—612no—
301#102—612no—
302#102C2×#692312yes—
303C22⋊C8—1222no—
304C22⋊C8—1222no—
305C22⋊C8—1222no—
306C22⋊C8—1222no—
307#97—612no—
308#97—612no—
309#97—611no—
310#97—611no—
311#97—611no—
312#97—1222no—
313#97—1222no—
314#97—1222no—
315#97C2×#692311yescharacteristic
316C4×C8—1222no—
317C4×C8—1222no—
318C4×C8—1222no—
319#41—1222no—
320#41—1222no—
321#41—1222no—
322#41—1222no—
323C2×Q8—612no—
324C2×D4—1222no—
325C2×D4C22×#692312yes—
326C22×C4—22no—
327C22×C4—611no—
328C22×C4—612no—
329C22×C4—1222no—
330C22×C4—1222no—
331C22×C4—1221no—
332C22×C4—1221no—
333Q16—1222no—
334SD16—1224no—
335D8—22no—
336M16—1222no—
337M16—1222no—
338M16—1222no—
339M16—1222no—
340C2×C8—611no—
341C2×C8—612no—
342C2×C8—612no—
343C2×C8—611no—
344C2×C8—612no—
345C2×C8—611no—
346C2×C8—611no—
347C2×C8—1221no—
348C2×C8—1221no—
349C2×C8—1221no—
350C2×C8—1221no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—1222no—
354C2×C8—1222no—
355C2×C8C22×#692311yescharacteristic
356C2×C8C22×#692311yescharacteristic
357C4⋊C4—612no—
358C4⋊C4—1222no—
359C4⋊C4—1222no—
360C4⋊C4C22×#692312yes—
361C22⋊C4—22no—
362C22⋊C4—1222no—
363C22⋊C4—1222no—
364C42—612no—
365C42—611no—
366C42—612no—
367C42—612no—
368C42—1222no—
369C42—1222no—
370C42—1221no—
371C42—1221no—
372C42—1222no—
373C42—2444no—
374C42C22×#692311yescharacteristic
375C23—22no—
376C23—611no—
377Q8—1222no—
378Q8—1222no—
379D4—22no—
380D4—22no—
381D4—2442no—
382D4—2442no—
383C2×C4—22no—
384C2×C4—82no—
385C2×C4—611no—
386C2×C4—611no—
387C2×C4—611no—
388C2×C4—611no—
389C2×C4—611no—
390C2×C4—612no—
391C2×C4—1222no—
392C2×C4—1224no—
393C2×C4—1222no—
394C2×C4—1222no—
395C2×C4—1222no—
396C2×C4—4882no—
397C2×C4—2442no—
398C2×C4—2442no—
399C2×C4—2442no—
400C2×C4—2442no—
401C2×C4D4×#692312yes—
402C2×C4C23×#692311yescharacteristic
403C8—21no—
404C8—612no—
405C8—1221no—
406C8—1222no—
407C8—1221no—
408C8—1221no—
409C8—2442no—
410C8—2442no—
411C8#1451985612yes—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—611no—
416C22—611no—
417C22—1222no—
418C22C2×D4×#692311yescharacteristic
419C4—22no—
420C4—42no—
421C4—611no—
422C4—611no—
423C4—1224no—
424C4—1222no—
425C4—2442no—
426C4—2442no—
427C4—2442no—
428C4C2×#1451985611yescharacteristic
429C4#41×#692311yescharacteristic
430C2—82no—
431C2—1221no—
432C2—1221no—
433C2#2146227611yescharacteristic
434C2#2146259312yes—
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#442C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519796C22
cosocleC2×C4×D61C24
hypercenter#442#6923
hypocenterC61#21297
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #21462506C2semidirect
4. #21461929C2semidirect
5. #21461926C2semidirect
6. #21461915C2semidirect
7. #21461913C2semidirect
8. #21461639C2semidirect
9. C4×#14519841C2semidirect
10. #97×#6923C2semidirect
36. #16839874C4semidirect
37. #16839870C4semidirect
38. #16839868C4semidirect
39. #16839862C4semidirect
40. #16839859C4semidirect
44. C61×#442C4semidirect
232. #442#6923semidirect
262. C61#21297semidirect

Maximal subgroups

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

subgroupindex
#214625062
#214619742
#214619722
#214619292
#214619262
#214619152
#214619132
#214616392
C4×#145198412
#97×#69232
#214546162
#2129761