Finite Group Databasebeta

← #30599065

Subgroups — #30599065

Order 15616.

320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 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#21461381C211yesmaximal, characteristic
2#21461379C211yesmaximal, characteristic
3#21461310C212yesmaximal
4#21460725C212yesmaximal
5#21454751C211yesmaximal, characteristic
6#16840783C2212yes—
7#16840783C2212yes—
8#16840626—21no—
9#16840625—21no—
10#16840624—21no—
11#16840623—21no—
12#16840619—22no—
13#16840619—22no—
14#16840315C2211yescharacteristic
15#16839890—21no—
16#16839890—21no—
17C8×Dic122—21no—
18C8×Dic122—21no—
19#16839790C411yescharacteristic
20#16839789C411yescharacteristic
21#16839785C2211yescharacteristic
22#16839717C411yescharacteristic
23C2×C8×Dic61C2211yescharacteristic
24C61×#405C411yescharacteristic
25C4⋊#92420—22no—
26C4⋊#92420—22no—
27C22⋊#92420—22no—
28C22⋊#92420—22no—
29#14519832—22no—
30#14519832—22no—
31C2×#11758194C2×C411yescharacteristic
32C22×#92418C2×C411yescharacteristic
33#14519776Q811yescharacteristic
34#14519776Q811yescharacteristic
35#14519768D411yescharacteristic
36#14519768D411yescharacteristic
37#14519754—21no—
38#14519754—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41#14519736C2×C411yescharacteristic
42C2×C4×Dic61C2311yescharacteristic
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45#14519706—21no—
46#14519706—21no—
47#14519706—21no—
48#14519706—21no—
49#14519687—21no—
50C8×Dic61—21no—
51C8×Dic61D411yescharacteristic
52C8×Dic61D411yescharacteristic
53C8×Dic61D411yescharacteristic
54C8×Dic61D411yescharacteristic
55C2×M16×C61C2×C411yescharacteristic
56C22×C8×C61C2×C411yescharacteristic
57#117×C61C2×C411yescharacteristic
58#97×C61—21no—
59C4×C8×C61—21no—
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61#4111yescharacteristic
62C22×Dic61#4111yescharacteristic
63C2×Dic122—21no—
64C2×Dic122—21no—
65C2×#92420—42no—
66C2×#92420—42no—
67M16×C61—41no—
68C2×C8×C61—22no—
69C2×C8×C61—21no—
70C2×C8×C61C22⋊C411yescharacteristic
71C2×C8×C61C22⋊C411yescharacteristic
72C4⋊C4×C61C4⋊C411yescharacteristic
73C4⋊C4×C61C4⋊C411yescharacteristic
74C22⋊C4×C61—21no—
75C42×C61—21no—
76C22⋊Dic61—21no—
77C4⋊Dic61—21no—
78C4⋊Dic61—21no—
79C4⋊Dic61C4⋊C411yescharacteristic
80C4⋊Dic61C4⋊C411yescharacteristic
81#11758196—21no—
82#11758196—21no—
83#11758196—21no—
84#11758196—21no—
85C4×Dic61—21no—
86C4×Dic61C2×D411yescharacteristic
87C4×Dic61C2×D411yescharacteristic
88C4×Dic61C2×D411yescharacteristic
89C4×Dic61C2×Q811yescharacteristic
90#11758194—41no—
91C2×#92418—21no—
92C2×#92418—41no—
93C2×#92418C22⋊C411yescharacteristic
94C2×#92418C22⋊C411yescharacteristic
95C23×C61#11711yescharacteristic
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61C2×C22⋊C411yescharacteristic
101C2×C4×C61C2×C4⋊C411yescharacteristic
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61#12111yescharacteristic
107C2×Dic61#12111yescharacteristic
108C2×Dic61C22⋊Q811yescharacteristic
109C2×Dic61C22⋊Q811yescharacteristic
110Dic122—42no—
111Dic122—42no—
112#92420—82no—
113#92420—82no—
114C8×C61—21no—
115C8×C61—41no—
116C8×C61#10112yes—
117#92418—21no—
118#92418—21no—
119#92418—41no—
120#8635—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61—21no—
124C22×C61#38011yescharacteristic
125C4×C61—21no—
126C4×C61—41no—
127C4×C61—41no—
128C4×C61C2×#10111yescharacteristic
129C4×C61#41311yescharacteristic
130Dic61—21no—
131Dic61—21no—
132Dic61—21no—
133Dic61—21no—
134Dic61—41no—
135Dic61—41no—
136#2960—611no—
137#1568—611no—
138#1568—611no—
139#1537—612no—
140#1307—612no—
141C2×C61—41no—
142C2×C61#180111yescharacteristic
143C2×C61#181411yescharacteristic
144C2×C61#181411yescharacteristic
145#533—611no—
146#446—1221no—
147#446—1221no—
148C8×Q8—1221no—
149C8×Q8—1221no—
150#432—612no—
151#432—612no—
152#424—611no—
153#424—611no—
154#423—611no—
155#405—611no—
156#405#692311yescharacteristic
157C2×C4×C8—611no—
158#335—1221no—
159#335—1221no—
160#334—1221no—
161#334—1221no—
162#330—1222no—
163#330—1222no—
164C61#863511yescharacteristic, complemented, Sylow
165C2×M16—611no—
166C2×M16C2×#692311yescharacteristic
167C22×C8—611no—
168C22×C8C2×#692311yescharacteristic
169C4⋊Q8—611no—
170C4⋊Q8—611no—
171#125—611no—
172#125—611no—
173C22⋊Q8—1221no—
174C22⋊Q8—1221no—
175C4×Q8—1221no—
176C4×Q8—1221no—
177#117—611no—
178#117C2×#692311yescharacteristic
179C2×C42—611no—
180C4⋊C8—1221no—
181C4⋊C8—1221no—
182C4⋊C8—1221no—
183C4⋊C8—1221no—
184C4⋊C8—1222no—
185C4⋊C8—1222no—
186C4⋊C8—1221no—
187C4⋊C8—1221no—
188C22⋊C8—1222no—
189C22⋊C8—1222no—
190#97—21no—
191#97—1222no—
192#97—1222no—
193#97—1221no—
194C4×C8—21no—
195C4×C8—611no—
196C4×C8—611no—
197C4×C8—611no—
198C4×C8—611no—
199C4×C8—1221no—
200C2×Q8—1221no—
201C2×Q8—1221no—
202C22×C4—611no—
203C22×C4—611no—
204C22×C4C22×#692311yescharacteristic
205M16—41no—
206M16—2441no—
207C2×C8—22no—
208C2×C8—21no—
209C2×C8—611no—
210C2×C8—611no—
211C2×C8—1221no—
212C2×C8—2441no—
213C2×C8—2442no—
214C2×C8—2442no—
215C2×C8C22⋊#692311yescharacteristic
216C2×C8C22⋊#692311yescharacteristic
217C4⋊C4—611no—
218C4⋊C4—611no—
219C4⋊C4—1221no—
220C4⋊C4—1221no—
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C4⋊C4—1221no—
224C4⋊C4—1221no—
225C4⋊C4C4⋊#692311yescharacteristic
226C4⋊C4C4⋊#692311yescharacteristic
227C22⋊C4—21no—
228C22⋊C4—1221no—
229C42—21no—
230C42—611no—
231C42—611no—
232C42—611no—
233C42—611no—
234C42—1221no—
235C23#1451985611yescharacteristic
236Q8—2442no—
237Q8—2442no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—611no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4C2×C22⋊#692311yescharacteristic
251C2×C4C2×C4⋊#692311yescharacteristic
252C8—21no—
253C8—41no—
254C8—1221no—
255C8—1221no—
256C8—4882no—
257C8—4882no—
258C8—2441no—
259C8#1451983812yes—
260C22—21no—
261C22—21no—
262C22—21no—
263C22#1684070411yescharacteristic
264C4—21no—
265C4—41no—
266C4—41no—
267C4—1221no—
268C4—1221no—
269C4—1221no—
270C4—1221no—
271C4—2441no—
272C4—2441no—
273C4C2×#1451983811yescharacteristic
274C4#1684074811yescharacteristic
275C2—41no—
276C2#2146168511yescharacteristic
277C2#2146170511yescharacteristic
278C2#2146170611yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#405C4
socleC22×C61#380
prime radicalC23×C61#117
cosocleC2×C4×Dic61C23
hypercenter#405#6923
hypocenterC61#8635
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #405

Complements

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

NH ≅ G/Ntype
164. C61#8635semidirect

Maximal subgroups

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

subgroupindex
#214613812
#214613792
#214613102
#214607252
#214547512
#863561