Finite Group Databasebeta

← #30598971

Subgroups — #30598971

Order 15616.

368 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 98 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#21461368C211yesmaximal, characteristic, complemented
2#21461366C211yesmaximal, characteristic, complemented
3#21461050C212yesmaximal
4#21460645C212yesmaximal, complemented
5C2×#16839820C211yesmaximal, characteristic
6#16840778C2212yes—
7#16840778C2212yes—
8#16840626—21no—
9#16840625—21no—
10#16840624—21no—
11#16840623—21no—
12#16840607—22no—
13#16840605—22no—
14C2×#14519736C2211yescharacteristic
15#16839820—21no—
16#16839820—21no—
17#16839820—21no—
18#16839820—21no—
19C2×#14519706C411yescharacteristic
20C2×#14519706C411yescharacteristic
21C2×C22⋊#92418C411yescharacteristic
22C2×#14519687C2211yescharacteristic
23C2×C8×Dic61C2211yescharacteristic
24C2×C22⋊C8×C61C411yescharacteristic
25C4⋊#92420—22no—
26C4⋊#92420—22no—
27C22⋊#92420—22no—
28C22⋊#92420—22no—
29C4×#92420—22no—
30C4×#92420—22no—
31C22×#92418C2×C411yescharacteristic
32C22×#92418C2×C411yescharacteristic
33#14519736—21no—
34#14519736—21no—
35#14519736—21no—
36#14519736—21no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61Q811yescharacteristic
39C2×C22⋊Dic61D411yescharacteristic
40C2×C22⋊Dic61Q811yescharacteristic
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61C2311yescharacteristic
43#14519706—21no—
44#14519706—21no—
45#14519706—21no—
46#14519706—21no—
47C22⋊#92418—21no—
48C22⋊#92418—21no—
49#14519687—21no—
50#14519687—21no—
51C8×Dic61D411yescharacteristic
52C8×Dic61D411yescharacteristic
53C8×Dic61D411yescharacteristic
54C8×Dic61D411yescharacteristic
55C23×C4×C61C2×C411yescharacteristic
56C22×C8×C61C2×C411yescharacteristic
57C22×C8×C61C2×C411yescharacteristic
58C22⋊C8×C61—21no—
59C22⋊C8×C61—21no—
60C24×C61C4⋊C411yescharacteristic
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—22no—
64C22×C4×C61—22no—
65C22×C4×C61C4⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61C4⋊C411yescharacteristic
68C22×Dic61C4⋊C411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C22×Dic61C2×Q811yescharacteristic
71C2×#92420—42no—
72C2×#92420—42no—
73C2×C8×C61—22no—
74C2×C8×C61—21no—
75C2×C8×C61—22no—
76C2×C8×C61C22⋊C411yescharacteristic
77C2×C8×C61C22⋊C411yescharacteristic
78C22⋊Dic61—21no—
79C22⋊Dic61—21no—
80C22⋊Dic61—21no—
81C22⋊Dic61—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4×Dic61—21no—
87C4×Dic61—21no—
88C4×Dic61C2×D411yescharacteristic
89C4×Dic61C2×D411yescharacteristic
90C4×Dic61#4111yescharacteristic
91C4×Dic61#4111yescharacteristic
92C2×#92418—22no—
93C2×#92418—21no—
94C2×#92418—22no—
95C2×#92418C22⋊C411yescharacteristic
96C2×#92418C22⋊C411yescharacteristic
97C23×C61—21no—
98C23×C61—22no—
99C23×C61—41no—
100C23×C61—41no—
101C23×C61C2×C4⋊C411yescharacteristic
102C2×C4×C61—21no—
103C2×C4×C61—22no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—42no—
107C2×C4×C61C2×C22⋊C411yescharacteristic
108C2×C4×C61#11711yescharacteristic
109C2×C4×C61#13112yes—
110C2×C4×C61#13112yes—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61#12111yescharacteristic
118C2×Dic61#12111yescharacteristic
119C2×Dic61C22⋊Q811yescharacteristic
120C2×Dic61C22⋊Q811yescharacteristic
121#92420—82no—
122#92420—82no—
123C8×C61—21no—
124C8×C61—21no—
125C8×C61—41no—
126#92418—21no—
127#92418—21no—
128#92418—41no—
129#8603—611nomaximal, Sylow
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61—82no—
136C22×C61#38011yescharacteristic
137C22×C61#42412yes—
138C4×C61—41no—
139C4×C61#40811yescharacteristic
140C4×C61#40811yescharacteristic
141C4×C61#43312yes—
142Dic61—21no—
143Dic61—21no—
144Dic61—21no—
145Dic61—21no—
146Dic61—41no—
147Dic61—41no—
148C2×#433—611no—
149#1564—611no—
150#1564—611no—
151#1458—612no—
152#1275—612no—
153C2×C61—22no—
154C2×C61—81no—
155C2×C61#179811yescharacteristic
156C2×C61#181211yescharacteristic
157C2×C61#181311yescharacteristic
158C2×#117—611no—
159#433—1221no—
160#433—1221no—
161#433—1221no—
162#433—1221no—
163#431—612no—
164#431—612no—
165C2×C4⋊C8—611no—
166C2×C4⋊C8—611no—
167C2×C22⋊C8—611no—
168C2×C22⋊C8#692311yescharacteristic
169C2×#97—611no—
170C2×C4×C8—611no—
171#335—1221no—
172#335—1221no—
173#334—1221no—
174#334—1221no—
175#324—1222no—
176#323—1222no—
177C61#860311yescharacteristic, complemented, Sylow
178C23×C4C2×#692311yescharacteristic
179C22×C8—611no—
180C22×C8—611no—
181C22×C8C2×#692311yescharacteristic
182C22×C8C2×#692311yescharacteristic
183#117—1221no—
184#117—1221no—
185#117—1221no—
186#117—1221no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—611no—
189C2×C22⋊C4—611no—
190C2×C22⋊C4—611no—
191C2×C42—611no—
192C2×C42—611no—
193C4⋊C8—1222no—
194C4⋊C8—1222no—
195C4⋊C8—1221no—
196C4⋊C8—1221no—
197C4⋊C8—1221no—
198C4⋊C8—1221no—
199C22⋊C8—21no—
200C22⋊C8—21no—
201C22⋊C8—1221no—
202C22⋊C8—1221no—
203C22⋊C8—1222no—
204C22⋊C8—1222no—
205#97—1221no—
206#97—1221no—
207C4×C8—611no—
208C4×C8—611no—
209C4×C8—611no—
210C4×C8—611no—
211C4×C8—1222no—
212C4×C8—1222no—
213C24C4⋊#692311yescharacteristic
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4C4⋊#692311yescharacteristic
223C22×C4C22×#692311yescharacteristic
224C2×C8—22no—
225C2×C8—21no—
226C2×C8—22no—
227C2×C8—611no—
228C2×C8—611no—
229C2×C8—1222no—
230C2×C8—1221no—
231C2×C8—1222no—
232C2×C8—2442no—
233C2×C8—2442no—
234C2×C8C22⋊#692311yescharacteristic
235C2×C8C22⋊#692311yescharacteristic
236C4⋊C4—1221no—
237C4⋊C4—1221no—
238C4⋊C4—1221no—
239C4⋊C4—1221no—
240C22⋊C4—1221no—
241C22⋊C4—1221no—
242C22⋊C4—1221no—
243C22⋊C4—1221no—
244C42—611no—
245C42—611no—
246C42—611no—
247C42—611no—
248C42—1221no—
249C42—1221no—
250C23—21no—
251C23—22no—
252C23—41no—
253C23—41no—
254C23C2×C4⋊#692311yescharacteristic
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—611no—
261C2×C4—611no—
262C2×C4—611no—
263C2×C4—611no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4C2×C22⋊#692311yescharacteristic
271C2×C4#1451985611yescharacteristic
272C2×C4#1451986412yes—
273C2×C4#1451986412yes—
274C8—21no—
275C8—21no—
276C8—41no—
277C8—1221no—
278C8—1221no—
279C8—4882no—
280C8—4882no—
281C8—2441no—
282C22—21no—
283C22—21no—
284C22—41no—
285C22—41no—
286C22—41no—
287C22—82no—
288C22#1684070411yescharacteristic
289C22#1684076812yes—
290C4—41no—
291C4—1221no—
292C4—1221no—
293C4—1221no—
294C4—1221no—
295C4—2441no—
296C4—2441no—
297C4#1684073511yescharacteristic
298C4#1684073611yescharacteristic
299C4#1684078612yes—
300C2—22no—
301C2—81no—
302C2#2146167711yescharacteristic
303C2#2146170111yescharacteristic
304C2#2146170411yescharacteristic
subgroupG/H
centerC2×C4#14519856
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#380
prime radicalC24×C61C4⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#8603
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #21461368C2semidirect
2. #21461366C2semidirect
4. #21460645C2semidirect
177. C61#8603semidirect

Maximal subgroups

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

subgroupindex
#214613682
#214613662
#214610502
#214606452
C2×#168398202
#860361