Finite Group Databasebeta

← #30604448

Subgroups — #30604448

Order 15616.

330 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 104 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
1D61⋊(C4⋊C16)C211yesmaximal, characteristic
2C4×#14519852C211yesmaximal, characteristic
3#21460786C212yesmaximal, complemented
4Q8⋊#11758187C212yesmaximal, complemented
5#21454750C211yesmaximal, characteristic
6C2×#14519852—21no—
7C2×D61⋊C16—21no—
8#16840683—21no—
9C4⋊#11758187C2212yes—
10#16840651—21no—
11C4×#11758187C2212yes—
12#16840316C411yescharacteristic
13#16839892C411yescharacteristic
14#16839890—21no—
15Q8×#92418C2211yescharacteristic
16#16839886—21no—
17#16839886C2211yescharacteristic
18#16839787—21no—
19#16839784C411yescharacteristic
20#16839719—21no—
21C4×C8×D61C2211yescharacteristic
22C61×#446C411yescharacteristic
23#14519852—24no—
24D61⋊C16—42no—
25C2×#11758187—22no—
26C2×#11758187—22no—
27C2×#11758189—21no—
28C2×C8×D61D411yescharacteristic
29C2×C8×D61D411yescharacteristic
30#14519776C811yescharacteristic
31#14519775C811yescharacteristic
32#14519767—21no—
33#14519757C811yescharacteristic
34#14519755—21no—
35#14519753C811yescharacteristic
36C4×Dic122—21no—
37C4×Dic122C2×C411yescharacteristic
38#14519734—21no—
39C42×D61C2×C411yescharacteristic
40C4⋊#92418—21no—
41C4⋊#92418C2×C411yescharacteristic
42#14519706—21no—
43#14519706—21no—
44#14519706—21no—
45#14519687—21no—
46C4×#92418—21no—
47C4×#92418C2311yescharacteristic
48C8×Dic61—21no—
49C8×Dic61D411yescharacteristic
50C8×Dic61D411yescharacteristic
51C4×Q8×C61C2×C411yescharacteristic
52C4⋊C8×C61—21no—
53C4⋊C8×C61C2×C411yescharacteristic
54#97×C61—21no—
55C4×C8×C61C2×C411yescharacteristic
56C2×Q8×C61C2×C811yescharacteristic
57C2×C4×D61C22⋊C411yescharacteristic
58C2×C4×D61C2×C811yescharacteristic
59C2×C4×D61M1611yescharacteristic
60C2×Dic122—21no—
61C2×Dic122C2×C811yescharacteristic
62C2×C8×C61—21no—
63C2×C8×C61C22⋊C411yescharacteristic
64C2×C8×C61C22⋊C411yescharacteristic
65C4⋊C4×C61—21no—
66C4⋊C4×C61C2×C811yescharacteristic
67C42×C61—21no—
68C42×C61C22×C411yescharacteristic
69#11758198—21no—
70#11758198—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61C2×C811yescharacteristic
73#11758196—21no—
74#11758196—21no—
75#11758196—21no—
76#11758196—21no—
77#11758196—21no—
78C4×Dic61—21no—
79C4×Dic61C22⋊C411yescharacteristic
80C4×Dic61C2×C811yescharacteristic
81C4×Dic61M1611yescharacteristic
82C2×#92418—21no—
83C2×#92418C2×D411yescharacteristic
84C2×#92418C2×D411yescharacteristic
85#11758189—42no—
86C8×D61—22no—
87C8×D61SD1612yes—
88C8×D61Q1612yes—
89#11758187—24no—
90#11758187—42no—
91C22×D61C22⋊C811yescharacteristic
92Q8×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61C22×C811yescharacteristic
97C2×C4×C61C2×M1611yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61C22⋊C811yescharacteristic
101C2×Dic61C22⋊C811yescharacteristic
102C2×Dic61C22⋊C811yescharacteristic
103C4×D61—22no—
104C4×D61—41no—
105C4×D61#10312yes—
106C4×D61#10412yes—
107Dic122—22no—
108Dic122—42no—
109C8×C61—21no—
110C8×C61—41no—
111C8×C61#10312yes—
112#92418—21no—
113#92418—41no—
114#92418C2×SD1611yescharacteristic
115#92418C2×Q1611yescharacteristic
116#11606—611nomaximal, Sylow
117C22×C61C2×C22⋊C811yescharacteristic
118C2×D61—21no—
119C2×D61—21no—
120C2×D61Q8⋊C812yes—
121C4×C61—21no—
122C4×C61—41no—
123C4×C61—41no—
124C4×C61C2×#10311yescharacteristic
125C4×C61C2×#10411yescharacteristic
126C4×C61#50412yes—
127Dic61—21no—
128Dic61—21no—
129Dic61—41no—
130Dic61—41no—
131Dic61Q8⋊C812yes—
132#2960—611no—
133C2×C4⋊C16—611no—
134C4×M32—611no—
135Q8⋊C16—612no—
136Q8⋊C16—612no—
137C2×C61C2×Q8⋊C811yescharacteristic
138C2×C61#211311yescharacteristic
139C2×C61#211711yescharacteristic
140D61—22no—
141#533—611no—
142C2×M32—1221no—
143C22×C16—1221no—
144#446—611no—
145#446—1221no—
146#446#692311yescharacteristic
147C8×Q8—611no—
148C8×Q8—611no—
149C8×Q8—1221no—
150#424—1221no—
151#423—611no—
152#405—1221no—
153C2×C4×C8—611no—
154C4⋊C16—612no—
155C4⋊C16—1221no—
156#346—1221no—
157C4×C16—612no—
158C61#1160611yescharacteristic, complemented, Sylow
159C2×M16—1221no—
160C22×C8—611no—
161C22×C8—611no—
162C4⋊Q8—611no—
163C4⋊Q8—611no—
164#125—1221no—
165C22⋊Q8—611no—
166C22⋊Q8—611no—
167C22⋊Q8—1221no—
168C4×Q8—611no—
169C4×Q8—1221no—
170C4×Q8C2×#692311yescharacteristic
171#117—1221no—
172C2×C42—611no—
173M32—1224no—
174C2×C16—1222no—
175C2×C16—1222no—
176C2×C16—2442no—
177C4⋊C8—21no—
178C4⋊C8—611no—
179C4⋊C8—1221no—
180C4⋊C8—1221no—
181C4⋊C8—1221no—
182C4⋊C8—1221no—
183C4⋊C8C2×#692311yescharacteristic
184#97—21no—
185#97—1221no—
186C4×C8—611no—
187C4×C8—611no—
188C4×C8—611no—
189C4×C8—1221no—
190C4×C8—1221no—
191C4×C8C2×#692311yescharacteristic
192C2×Q8—611no—
193C2×Q8—1221no—
194C2×Q8D61⋊C811yescharacteristic
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—611no—
198M16—2442no—
199C2×C8—21no—
200C2×C8—611no—
201C2×C8—612no—
202C2×C8—612no—
203C2×C8—611no—
204C2×C8—1222no—
205C2×C8—1221no—
206C2×C8C22⋊#692311yescharacteristic
207C2×C8C22⋊#692311yescharacteristic
208C4⋊C4—21no—
209C4⋊C4—611no—
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C4⋊C4—1221no—
215C4⋊C4—1221no—
216C4⋊C4D61⋊C811yescharacteristic
217C22⋊C4—1221no—
218C22⋊C4—1221no—
219C42—21no—
220C42—611no—
221C42—611no—
222C42—611no—
223C42—1221no—
224C42C22×#692311yescharacteristic
225C16—1224no—
226C16—2442no—
227C23—611no—
228Q8—22no—
229Q8—1222no—
230Q8—2442no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—611no—
234C2×C4—612no—
235C2×C4—612no—
236C2×C4—611no—
237C2×C4—611no—
238C2×C4—1222no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—2441no—
242C2×C4C2×C22⋊#692311yescharacteristic
243C2×C4C2×D61⋊C811yescharacteristic
244C2×C4D61⋊M1611yescharacteristic
245C8—21no—
246C8—41no—
247C8—611no—
248C8—611no—
249C8—1221no—
250C8—2441no—
251C8#1451984012yes—
252C22—612no—
253C22—1221no—
254C22—1221no—
255C22D61⋊(C22⋊C8)11yescharacteristic
256C4—21no—
257C4—41no—
258C4—41no—
259C4—612no—
260C4—1221no—
261C4—1221no—
262C4—2441no—
263C4—2441no—
264C4C2×#1451984011yescharacteristic
265C4D61⋊#10411yescharacteristic
266C4#1684082112yes—
267C2—1222no—
268C2D61⋊(Q8⋊C8)11yescharacteristic
269C2#2146205011yescharacteristic
270C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC61×#446C4
socleC22×C61C2×C22⋊C8
prime radicalC22×D61C22⋊C8
cosocleC4×#92418C23
hypercenter#446#6923
hypocenterC61#11606
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #446

Complements

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

NH ≅ G/Ntype
3. #21460786C2semidirect
4. Q8⋊#11758187C2semidirect
158. C61#11606semidirect

Maximal subgroups

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

subgroupindex
D61⋊(C4⋊C16)2
C4×#145198522
#214607862
Q8⋊#117581872
#214547502
#1160661