Finite Group Databasebeta

← #30599174

Subgroups — #30599174

Order 15616.

346 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 92 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#21461744C211yesmaximal, characteristic
2D61⋊#335C211yesmaximal, characteristic
3#21461336C212yesmaximal
4#21460688C212yesmaximal
5#21454750C211yesmaximal, characteristic
6#16840767C2212yes—
7D61⋊(C4⋊C8)C2212yes—
8#16840638—21no—
9#16840638—21no—
10#16840626—21no—
11#16840625—21no—
12#16840622—22no—
13#16840621—22no—
14#16840316C2211yescharacteristic
15#16839892C411yescharacteristic
16#16839890—21no—
17Q8×#92418C411yescharacteristic
18#16839886—21no—
19#16839886C411yescharacteristic
20#16839787—21no—
21#16839784C2211yescharacteristic
22#16839719—21no—
23C4×C8×D61C2211yescharacteristic
24C61×#446C411yescharacteristic
25C2×#11758213—22no—
26C2×D61⋊C8—22no—
27#14519844—22no—
28#14519844—22no—
29#14519844—22no—
30C4⋊#92420—22no—
31C2×#11758189—21no—
32C2×C8×D61D411yescharacteristic
33C2×C8×D61D411yescharacteristic
34#14519776D411yescharacteristic
35#14519775D411yescharacteristic
36#14519767—21no—
37#14519757Q811yescharacteristic
38#14519755—21no—
39#14519753Q811yescharacteristic
40C4×Dic122—21no—
41C4×Dic122C2×C411yescharacteristic
42#14519734—21no—
43C42×D61C2311yescharacteristic
44C4⋊#92418—21no—
45C4⋊#92418C2×C411yescharacteristic
46#14519706—21no—
47#14519706—21no—
48#14519706—21no—
49#14519687—21no—
50C4×#92418—21no—
51C4×#92418C2×C411yescharacteristic
52C8×Dic61—21no—
53C8×Dic61D411yescharacteristic
54C8×Dic61D411yescharacteristic
55C4×Q8×C61C2×C411yescharacteristic
56C4⋊C8×C61—21no—
57C4⋊C8×C61C2×C411yescharacteristic
58#97×C61—21no—
59C4×C8×C61C2×C411yescharacteristic
60C2×Q8×C61C4⋊C411yescharacteristic
61C2×C4×D61C2×D411yescharacteristic
62C2×C4×D61C2×Q811yescharacteristic
63C2×C4×D61#4111yescharacteristic
64C2×Dic122—21no—
65C2×Dic122C4⋊C411yescharacteristic
66C2×#92420—42no—
67C2×#92420—42no—
68#11758213—42no—
69#11758213—42no—
70D61⋊C8—82no—
71C2×C8×C61—21no—
72C2×C8×C61C22⋊C411yescharacteristic
73C2×C8×C61C22⋊C411yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61C4⋊C411yescharacteristic
76C42×C61—21no—
77C42×C61C22×C411yescharacteristic
78#11758198—21no—
79#11758198—21no—
80C4⋊Dic61—21no—
81C4⋊Dic61C4⋊C411yescharacteristic
82#11758196—21no—
83#11758196—21no—
84#11758196—21no—
85#11758196—21no—
86#11758196—21no—
87C4×Dic61—21no—
88C4×Dic61C2×D411yescharacteristic
89C4×Dic61C2×D411yescharacteristic
90C4×Dic61#4111yescharacteristic
91C2×#92418—21no—
92C2×#92418C22⋊C411yescharacteristic
93C2×#92418C22⋊C411yescharacteristic
94#11758189—42no—
95C8×D61—22no—
96C8×D61—22no—
97C22×D61C22⋊Q811yescharacteristic
98Q8×C61—41no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61C2×C22⋊C411yescharacteristic
102C2×C4×C61C2×C4⋊C411yescharacteristic
103C2×C4×C61#11711yescharacteristic
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61#12111yescharacteristic
107C2×Dic61#12111yescharacteristic
108C2×Dic61C22⋊Q811yescharacteristic
109C4×D61—21no—
110C4×D61—21no—
111C4×D61—41no—
112C4×D61#13512yes—
113C4×D61#13712yes—
114Dic122—41no—
115Dic122—41no—
116Dic122—41no—
117#92420—82no—
118#92420—82no—
119C8×C61—21no—
120C8×C61—21no—
121C8×C61—41no—
122#92418—21no—
123#92418—21no—
124#92418—41no—
125#8689—611nomaximal, Sylow
126C22×C61#38011yescharacteristic
127C2×D61—21no—
128C2×D61—21no—
129C2×D61#47912yes—
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—41no—
133C4×C61—41no—
134C4×C61#41611yescharacteristic
135C4×C61#41911yescharacteristic
136Dic61—21no—
137Dic61—41no—
138Dic61—41no—
139Dic61#46412yes—
140Dic61#47211yescharacteristic
141Dic61#47311yescharacteristic
142#2960—611no—
143#1837—611no—
144C2×#335—611no—
145#1550—612no—
146#1292—612no—
147C2×C61#180511yescharacteristic
148C2×C61#181311yescharacteristic
149C2×C61#181611yescharacteristic
150D61—22no—
151#533—611no—
152#446—611no—
153#446—1221no—
154#446#692311yescharacteristic
155C8×Q8—611no—
156C8×Q8—611no—
157C8×Q8—1221no—
158#424—1221no—
159#423—611no—
160#423—612no—
161C2×C4⋊C8—612no—
162#405—1221no—
163C2×C4×C8—611no—
164#341—1221no—
165#341—1221no—
166#335—1221no—
167#335—1221no—
168#333—1222no—
169#332—1222no—
170C61#868911yescharacteristic, complemented, Sylow
171C2×M16—1221no—
172C2×M16—1222no—
173C22×C8—611no—
174C22×C8—611no—
175C22×C8—1222no—
176C4⋊Q8—611no—
177C4⋊Q8—611no—
178#125—1221no—
179C22⋊Q8—611no—
180C22⋊Q8—611no—
181C22⋊Q8—1221no—
182C4×Q8—611no—
183C4×Q8—1221no—
184C4×Q8C2×#692311yescharacteristic
185#117—1221no—
186C2×C42—611no—
187C4⋊C8—21no—
188C4⋊C8—611no—
189C4⋊C8—1221no—
190C4⋊C8—1221no—
191C4⋊C8—1222no—
192C4⋊C8—1222no—
193C4⋊C8—1222no—
194C4⋊C8—1222no—
195C4⋊C8—1221no—
196C4⋊C8—1221no—
197C4⋊C8C2×#692311yescharacteristic
198#97—21no—
199#97—1221no—
200C4×C8—611no—
201C4×C8—611no—
202C4×C8—611no—
203C4×C8—1221no—
204C4×C8—1221no—
205C4×C8C2×#692311yescharacteristic
206C2×Q8—611no—
207C2×Q8—1221no—
208C2×Q8C4⋊#692311yescharacteristic
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—611no—
212M16—2442no—
213M16—2442no—
214M16—2442no—
215C2×C8—21no—
216C2×C8—611no—
217C2×C8—611no—
218C2×C8—1222no—
219C2×C8—1222no—
220C2×C8—1221no—
221C2×C8—4882no—
222C2×C8—2442no—
223C2×C8—2442no—
224C2×C8C22⋊#692311yescharacteristic
225C2×C8C22⋊#692311yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—611no—
228C4⋊C4—1221no—
229C4⋊C4—1221no—
230C4⋊C4—1221no—
231C4⋊C4—1221no—
232C4⋊C4—1221no—
233C4⋊C4—1221no—
234C4⋊C4C4⋊#692311yescharacteristic
235C22⋊C4—1221no—
236C22⋊C4—1221no—
237C42—21no—
238C42—611no—
239C42—611no—
240C42—611no—
241C42—1221no—
242C42C22×#692311yescharacteristic
243C23—611no—
244Q8—41no—
245Q8—2441no—
246Q8—2441no—
247Q8—2441no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—611no—
251C2×C4—611no—
252C2×C4—612no—
253C2×C4—612no—
254C2×C4—611no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—2441no—
260C2×C4C2×C22⋊#692311yescharacteristic
261C2×C4C2×C4⋊#692311yescharacteristic
262C2×C4#1451985611yescharacteristic
263C8—21no—
264C8—21no—
265C8—41no—
266C8—1221no—
267C8—1221no—
268C8—4882no—
269C8—4882no—
270C8—2441no—
271C22—612no—
272C22—1221no—
273C22—1221no—
274C22#1684070411yescharacteristic
275C4—21no—
276C4—21no—
277C4—41no—
278C4—41no—
279C4—612no—
280C4—611no—
281C4—611no—
282C4—1221no—
283C4—2441no—
284C4—2441no—
285C4#1684075211yescharacteristic
286C4#1684075511yescharacteristic
287C2—1222no—
288C2#2146169011yescharacteristic
289C2#2146170411yescharacteristic
290C2#2146170811yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#446C4
socleC22×C61#380
prime radicalC22×D61C22⋊Q8
cosocleC42×D61C23
hypercenter#446#6923
hypocenterC61#8689
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #446

Complements

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

NH ≅ G/Ntype
170. C61#8689semidirect

Maximal subgroups

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

subgroupindex
#214617442
D61⋊#3352
#214613362
#214606882
#214547502
#868961