Finite Group Databasebeta

← #30601018

Subgroups — #30601018

Order 15616.

470 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462714C211yesmaximal, characteristic
2#21461686C211yesmaximal, characteristic
3#21461334C212yesmaximal
4#21460717C212yesmaximal
5#21451030C211yesmaximal, characteristic
6#16840811—24no—
7#16840779—21no—
8#16840779C2212yes—
9#16840778—21no—
10#16840765C2212yes—
11C2×#14519838—21no—
12#16840642—21no—
13#16840621—24no—
14C2×#14519776C2211yescharacteristic
15C2×#14519742C2211yescharacteristic
16#16839702C411yescharacteristic
17#16839701C411yescharacteristic
18#16839700C411yescharacteristic
19#16839666—21no—
20#16839666—21no—
21#16839666—21no—
22#16839626—21no—
23#16839613C2211yescharacteristic
24C61×#400C411yescharacteristic
25C2×#11758217—22no—
26#14519844—22no—
27#14519844—22no—
28#14519844D414yes—
29C4⋊#92420—22no—
30C4⋊#92420—22no—
31#14519838—42no—
32C22⋊#92420—22no—
33C4×#92420—22no—
34C4×#92420—22no—
35C4×#92420—22no—
36C22×Dic122—21no—
37C22×Dic122D411yescharacteristic
38#14519776—22no—
39#14519776—22no—
40#14519742—22no—
41#14519742—22no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196C2×C411yescharacteristic
46C2×#11758196D411yescharacteristic
47C2×C4×Dic61—21no—
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61C2311yescharacteristic
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684C2×C411yescharacteristic
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2×C411yescharacteristic
60#95×C61—21no—
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×Dic122—22no—
75C2×Dic122—22no—
76C2×Dic122—44no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122SD1612yes—
80C2×Dic122Q1612yes—
81#11758217—42no—
82#11758217—42no—
83C2×#92420—24no—
84C2×#92420—42no—
85C4⋊C4×C61—22no—
86C4⋊C4×C61—22no—
87C4⋊Dic61—22no—
88#11758196—22no—
89#11758196—22no—
90#11758196—42no—
91#11758196—42no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—42no—
97C4×Dic61C2×D412yes—
98C4×Dic61#4112yes—
99C23×C61C2×C22⋊C411yescharacteristic
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—42no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61#10312yes—
111C2×C4×C61C4×D412yes—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—22no—
115C2×Dic61—21no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—42no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61#10312yes—
123C2×Dic61#12011yescharacteristic
124C2×Dic61#12112yes—
125C2×Dic61#12311yescharacteristic
126C2×Dic61C2×SD1611yescharacteristic
127C2×Dic61C2×Q1611yescharacteristic
128C2×Dic61#13512yes—
129Dic122—24no—
130Dic122—24no—
131Dic122—82no—
132Dic122—82no—
133#92420—44no—
134#92420—82no—
135#9396—611nomaximal, Sylow
136C22×C61—21no—
137C22×C61—21no—
138C22×C61#38611yescharacteristic
139C22×C61C2×#10311yescharacteristic
140C22×C61#41611yescharacteristic
141C4×C61—22no—
142C4×C61—22no—
143C4×C61—41no—
144C4×C61—81no—
145C4×C61—81no—
146Dic61—21no—
147Dic61—22no—
148Dic61—41no—
149Dic61—81no—
150Dic61—81no—
151Dic61#45412yes—
152Dic61#46512yes—
153Dic61#46712yes—
154#2982—611no—
155#2568—611no—
156#1801—611no—
157#1549—612no—
158#1303—612no—
159C2×C61—21no—
160C2×C61—21no—
161C2×C61#188811yescharacteristic
162C2×C61#189211yescharacteristic
163C2×C61#191511yescharacteristic
164C2×C4⋊Q8—611no—
165C2×C4×Q8—611no—
166C8×Q8—1224no—
167#431—612no—
168#431—1221no—
169#431—1221no—
170#423—612no—
171C2×#101—1221no—
172#400—611no—
173#400—611no—
174#400—611no—
175#400#692311yescharacteristic
176#391—1221no—
177#391—1221no—
178#391—1221no—
179#382—1221no—
180C4×C4⋊C4—611no—
181#343—1221no—
182#332—1224no—
183C61#939611yescharacteristic, complemented, Sylow
184C22×Q8—611no—
185C22×Q8—1221no—
186C2×M16—1222no—
187C4⋊Q8—1222no—
188C4⋊Q8—1222no—
189C4×Q8—1222no—
190C4×Q8—1222no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4C2×#692311yescharacteristic
197C2×C4⋊C4C2×#692311yescharacteristic
198C2×C42—611no—
199C2×C42—611no—
200C2×C42—611no—
201C2×C42—1221no—
202C4⋊C8—614no—
203C4⋊C8—1222no—
204C4⋊C8—1222no—
205C4⋊C8—1222no—
206C4⋊C8—1222no—
207#101—2442no—
208C22⋊C8—1222no—
209C4×C8—1222no—
210C4×C8—1222no—
211C4×C8—1222no—
212#95—21no—
213#95—21no—
214#95—611no—
215#95—1221no—
216#95—1221no—
217#95—1221no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95C2×#692311yescharacteristic
222C2×Q8—612no—
223C2×Q8—612no—
224C2×Q8—1222no—
225C2×Q8—1222no—
226C2×Q8—2441no—
227C2×Q8—2441no—
228C2×Q8—2444no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4C22⋊#692311yescharacteristic
238C22×C4C22⋊#692311yescharacteristic
239C22×C4C22×#692311yescharacteristic
240M16—2442no—
241M16—2442no—
242C2×C8—1224no—
243C2×C8—2442no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—1222no—
247C4⋊C4—1222no—
248C4⋊C4—1222no—
249C4⋊C4—2442no—
250C4⋊C4—2442no—
251C42—612no—
252C42—612no—
253C42—1221no—
254C42—1221no—
255C42—1221no—
256C42—1221no—
257C42—2442no—
258C23C2×C22⋊#692311yescharacteristic
259Q8—1224no—
260Q8—1224no—
261Q8—4882no—
262Q8—4882no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—611no—
274C2×C4—612no—
275C2×C4—611no—
276C2×C4—611no—
277C2×C4—612no—
278C2×C4—611no—
279C2×C4—612no—
280C2×C4—1222no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2442no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4#1451984012yes—
291C2×C4D4×#692312yes—
292C8—4882no—
293C8—2444no—
294C22—21no—
295C22—21no—
296C22#1684071011yescharacteristic
297C22C2×#1451984011yescharacteristic
298C22#1684075211yescharacteristic
299C4—22no—
300C4—22no—
301C4—41no—
302C4—81no—
303C4—81no—
304C4—612no—
305C4—612no—
306C4—612no—
307C4—1221no—
308C4—1222no—
309C4—4881no—
310C4—4881no—
311C4—2441no—
312C2—21no—
313C2—21no—
314C2#2146182711yescharacteristic
315C2#2146183211yescharacteristic
316C2#2146187111yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#400C4
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#400#6923
hypocenterC61#9396
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
183. C61#9396semidirect

Maximal subgroups

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

subgroupindex
#214627142
#214616862
#214613342
#214607172
#214510302
#939661