Finite Group Databasebeta

← #21461979

Subgroups — #21461979

Order 7808.

296 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 68 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⋊#108C211yesmaximal, characteristic, complemented
2#16840755C211yesmaximal, characteristic, complemented
3#16840754C211yesmaximal, characteristic
4D61⋊#101C211yesmaximal, characteristic, complemented
5D61⋊#100C211yesmaximal, characteristic
6#16840725C211yesmaximal, characteristic, complemented
7C2×SD16×D61C211yesmaximal, characteristic
8D61⋊M16C2211yescharacteristic
9D61⋊M16C2211yescharacteristic
10D61⋊M16C2211yescharacteristic
11#14519856C2211yescharacteristic
12#14519848—21no—
13#14519847—21no—
14#14519840—22no—
15#14519839—22no—
16#14519838—22no—
17#14519837—22no—
18#14519831—21no—
19C8×#6923—21no—
20C2×Q8×D61C2211yescharacteristic
21C2×D4×D61C2211yescharacteristic
22C2×#11758190C411yescharacteristic, complemented
23C2×#11758200C411yescharacteristic, complemented
24C2×#11758201C411yescharacteristic, complemented
25SD16×D61—21no—
26SD16×D61—21no—
27SD16×D61—21no—
28SD16×D61—21no—
29C2×C8×D61C2211yescharacteristic
30C2×SD16×C61C411yescharacteristic, complemented
31C23×D61—21no—
32C2×Q8×C61C2×C411yescharacteristic
33C2×D4×C61C2×C411yescharacteristic
34C2×C22⋊D61—21no—
35Q8×D61—21no—
36Q8×D61—21no—
37Q8×D61—21no—
38Q8×D61—21no—
39D4×D61—21no—
40D4×D61—21no—
41D4×D61—21no—
42D4×D61—21no—
43C2×D244C2×C411yescharacteristic
44C2×C4×D61—21no—
45C2×C4×D61C2311yescharacteristic
46C2×Dic122—21no—
47C2×Dic122C2×C411yescharacteristic
48C22⋊#6923—21no—
49#11758217—21no—
50#11758217—21no—
51#11758217D412yes—
52C4⋊#6923D412yes—
53C4×#6923—21no—
54#11758213—21no—
55#11758213—21no—
56#11758213—21no—
57D61⋊C8—21no—
58D61⋊C8—21no—
59D61⋊C8—21no—
60SD16×C61—21no—
61SD16×C61—21no—
62C2×C8×C61C2×C411yescharacteristic
63#11758201—21no—
64#11758201—21no—
65#11758200—21no—
66#11758200—21no—
67C2×#92418C2×C411yescharacteristic
68#11758190—21no—
69#11758190—21no—
70C8×D61D411yescharacteristic
71C8×D61D411yescharacteristic
72C8×D61D411yescharacteristic
73C8×D61D411yescharacteristic
74C23×C61—21no—
75C22×D61—21no—
76C22×D61—41no—
77C22×D61—41no—
78C22×D61—82no—
79C22×D61#4111yescharacteristic
80C2×#6923—22no—
81Q8×C61—21no—
82Q8×C61—21no—
83D4×C61—21no—
84D4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61C22×C411yescharacteristic
87C22⋊D61—41no—
88C22⋊D61—41no—
89C2×Dic61—21no—
90C2×Dic61C2×D411yescharacteristic
91D244—21no—
92D244—21no—
93C4×D61—41no—
94C4×D61—41no—
95C4×D61C2×D411yescharacteristic
96C4×D61C2×D411yescharacteristic
97C4×D61C2×D411yescharacteristic
98C4×D61#4111yescharacteristic
99Dic122—21no—
100Dic122—21no—
101Dic122—41no—
102Dic122—41no—
103#92420—22no—
104#92420—41no—
105#92420—41no—
106C8×C61C22⋊C411yescharacteristic
107C8×C61C22⋊C411yescharacteristic
108#92418C22⋊C411yescharacteristic
109#92418C22⋊C411yescharacteristic
110C22×C61—41no—
111C22×C61—81no—
112C22×C61C4×D411yescharacteristic
113C2×D61—22no—
114C2×D61—41no—
115C2×D61—82no—
116C2×D61—82no—
117C2×D61—81no—
118C2×D61#12111yescharacteristic
119C2×D61#12411yescharacteristic
120#6923—42no—
121C4×C61—41no—
122C4×C61C2×C22⋊C411yescharacteristic
123C4×C61C4×D411yescharacteristic
124Dic61—41no—
125Dic61#12111yescharacteristic
126Dic61#12711yescharacteristic
127#1977—611nomaximal, Sylow
128C2×C61—21no—
129C2×C61—81no—
130C2×C61#39011yescharacteristic
131D61—21no—
132D61—81no—
133D61#47112yes—
134C22×SD16—611no—
135C2×#108—611no—
136#419—611no—
137#418—611no—
138C2×#101—611no—
139C2×#100—611no—
140#405—611no—
141C61#197711yescharacteristic, complemented, Sylow
142C22×Q8—611no—
143C22×D4—611no—
144C2×SD16—611no—
145C2×SD16—611no—
146C2×SD16—611no—
147C2×SD16—1221no—
148C2×SD16—1221no—
149C2×SD16—1221no—
150C2×SD16—1221no—
151C2×SD16#692311yescharacteristic, complemented
152C2×M16—611no—
153C2×M16—611no—
154C2×M16—611no—
155C22×C8—611no—
156#117—611no—
157#108—1221no—
158#108—1221no—
159#103—1222no—
160#102—1222no—
161#101—1222no—
162#100—1222no—
163#97—1221no—
164C4×C8—1221no—
165C24—1221no—
166C2×Q8—611no—
167C2×Q8—1221no—
168C2×Q8—1221no—
169C2×Q8—1221no—
170C2×Q8—1221no—
171C2×Q8—1221no—
172C2×Q8C2×#692311yescharacteristic
173C2×D4—611no—
174C2×D4—1221no—
175C2×D4—1221no—
176C2×D4—1221no—
177C2×D4—1221no—
178C2×D4—1221no—
179C2×D4C2×#692311yescharacteristic
180C22×C4—611no—
181C22×C4—1221no—
182SD16—21no—
183SD16—21no—
184SD16—1221no—
185SD16—1221no—
186SD16—1221no—
187SD16—1221no—
188SD16—1221no—
189SD16—1221no—
190M16—612no—
191M16—1221no—
192M16—1221no—
193M16—1221no—
194M16—1221no—
195M16—1221no—
196C2×C8—611no—
197C2×C8—611no—
198C2×C8—611no—
199C2×C8—611no—
200C2×C8—611no—
201C2×C8—1221no—
202C2×C8—1221no—
203C2×C8—1221no—
204C2×C8C2×#692311yescharacteristic
205C4⋊C4—612no—
206C22⋊C4—1221no—
207C42—1221no—
208C23—21no—
209C23—611no—
210C23—1221no—
211C23—4882no—
212C23—2441no—
213C23—2441no—
214Q8—21no—
215Q8—21no—
216Q8—1221no—
217Q8—1221no—
218Q8—2441no—
219Q8—2441no—
220D4—21no—
221D4—21no—
222D4—1221no—
223D4—1221no—
224D4—2441no—
225D4—2441no—
226C2×C4—21no—
227C2×C4—611no—
228C2×C4—611no—
229C2×C4—611no—
230C2×C4—611no—
231C2×C4—611no—
232C2×C4—1222no—
233C2×C4—1221no—
234C2×C4—2441no—
235C2×C4—2441no—
236C2×C4C22×#692311yescharacteristic
237C8—611no—
238C8—611no—
239C8—1222no—
240C8—2441no—
241C8—2441no—
242C8C22⋊#692311yescharacteristic
243C8C22⋊#692311yescharacteristic
244C22—41no—
245C22—81no—
246C22—611no—
247C22—611no—
248C22—1222no—
249C22—4881no—
250C22—4882no—
251C22—4882no—
252C22—2441no—
253C22D4×#692311yescharacteristic
254C4—41no—
255C4—611no—
256C4—611no—
257C4—2442no—
258C4—2441no—
259C4C2×C22⋊#692311yescharacteristic
260C4D4×#692311yescharacteristic
261C2—21no—
262C2—81no—
263C2—612no—
264C2—1221no—
265C2—4881no—
266C2#1684071411yescharacteristic
subgroupG/H
centerC2#16840714
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×SD16×C61C4
socleC2×C61#390
hypercenterC2×SD16#6923
hypocenterC61#1977
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. D61⋊#108C2semidirect
2. #16840755C2semidirect
4. D61⋊#101C2semidirect
6. #16840725C2semidirect
22. C2×#11758190C4semidirect
23. C2×#11758200C4semidirect
24. C2×#11758201C4semidirect
30. C2×SD16×C61C4semidirect
141. C61#1977semidirect
151. C2×SD16#6923semidirect