Finite Group Databasebeta

← #21461977

Subgroups — #21461977

Order 7808.

284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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#16840772C211yesmaximal, characteristic, complemented
2#16840761C211yesmaximal, characteristic, complemented
3#16840760C211yesmaximal, characteristic, complemented
4#16840743C211yesmaximal, characteristic, complemented
5#16840742C211yesmaximal, characteristic, complemented
6#16840725C211yesmaximal, characteristic, complemented
7C2×#14519798C211yesmaximal, characteristic
8D61⋊M16C2211yescharacteristic
9#14519856C2211yescharacteristic
10#14519856C2211yescharacteristic
11#14519856C2211yescharacteristic
12#14519846—21no—
13#14519845—21no—
14#14519842—22no—
15#14519841—22no—
16#14519836—22no—
17#14519835—22no—
18#14519831—21no—
19C8×#6923—21no—
20C2×#11758226C2211yescharacteristic
21C2×#11758224C2211yescharacteristic
22#14519798—21no—
23#14519798—21no—
24#14519798—21no—
25#14519798—21no—
26C2×#11758202C411yescharacteristic, complemented
27C2×#11758190C411yescharacteristic, complemented
28C2×#11758199C411yescharacteristic, complemented
29C2×C8×D61C2211yescharacteristic
30C2×SD16×C61C411yescharacteristic, complemented
31C2×Q8×C61C2×C411yescharacteristic
32C2×D4×C61C2×C411yescharacteristic
33C2×C22⋊D61—21no—
34C22×Dic61—21no—
35#11758226—21no—
36#11758226—21no—
37#11758226—21no—
38#11758226—21no—
39#11758224—21no—
40#11758224—21no—
41#11758224—21no—
42#11758224—21no—
43C2×D244—21no—
44C2×D244C2×C411yescharacteristic
45C2×C4×D61—21no—
46C2×C4×D61C2311yescharacteristic
47C2×Dic122C2×C411yescharacteristic
48C22⋊#6923—21no—
49C22⋊#6923—21no—
50C22⋊#6923D412yes—
51#11758217—21no—
52C4⋊#6923—21no—
53C4⋊#6923—21no—
54C4⋊#6923—21no—
55C4×#6923—21no—
56C4×#6923—21no—
57C4×#6923—21no—
58#11758213D412yes—
59D61⋊C8—21no—
60SD16×C61—21no—
61SD16×C61—21no—
62C2×C8×C61C2×C411yescharacteristic
63#11758202—21no—
64#11758202—21no—
65#11758199—21no—
66#11758199—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×D61C2×D411yescharacteristic
77C2×#6923—22no—
78C2×#6923—41no—
79C2×#6923—41no—
80Q8×C61—21no—
81Q8×C61—21no—
82D4×C61—21no—
83D4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61C22×C411yescharacteristic
86C22⋊D61—41no—
87C22⋊D61—41no—
88C2×Dic61—21no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61#4111yescharacteristic
92D244—21no—
93D244—21no—
94D244—41no—
95D244—41no—
96C4×D61—41no—
97C4×D61—41no—
98C4×D61C2×D411yescharacteristic
99C4×D61C2×D411yescharacteristic
100C4×D61C2×D411yescharacteristic
101C4×D61#4111yescharacteristic
102Dic122—21no—
103Dic122—21no—
104#92420—22no—
105C8×C61C22⋊C411yescharacteristic
106C8×C61C22⋊C411yescharacteristic
107#92418C22⋊C411yescharacteristic
108#92418C22⋊C411yescharacteristic
109C22×C61—41no—
110C22×C61—81no—
111C22×C61C4×D411yescharacteristic
112C2×D61—41no—
113C2×D61—41no—
114C2×D61—81no—
115C2×D61#12111yescharacteristic
116C2×D61#12711yescharacteristic
117#6923—42no—
118#6923—81no—
119#6923—81no—
120C4×C61—41no—
121C4×C61C2×C22⋊C411yescharacteristic
122C4×C61C4×D411yescharacteristic
123Dic61—41no—
124Dic61#12111yescharacteristic
125Dic61#12411yescharacteristic
126#1976—611nomaximal, Sylow
127C2×C61—21no—
128C2×C61—81no—
129C2×C61#39011yescharacteristic
130D61—21no—
131D61—21no—
132D61—81no—
133C2×#135—611no—
134#427—611no—
135#421—611no—
136#421—611no—
137#410—611no—
138#410—611no—
139#405—611no—
140C61#197611yescharacteristic, complemented, Sylow
141C2×#41—611no—
142C2×#41—611no—
143#135—1221no—
144#135—1221no—
145#135—1221no—
146#135—1221no—
147C2×Q16—611no—
148C2×SD16—611no—
149C2×SD16#692311yescharacteristic, complemented
150C2×D8—611no—
151C2×M16—611no—
152C22×C8—611no—
153#117—611no—
154#117—611no—
155#117—611no—
156#107—1221no—
157#106—1221no—
158#104—1222no—
159#104—1222no—
160#99—1222no—
161#99—1222no—
162#97—1221no—
163C4×C8—1221no—
164#41—1221no—
165#41—1221no—
166#41—1221no—
167#41—1221no—
168#41—1221no—
169#41—1221no—
170#41—1221no—
171#41—1221no—
172C2×Q8—611no—
173C2×Q8C2×#692311yescharacteristic
174C2×D4—611no—
175C2×D4—1221no—
176C2×D4—1221no—
177C2×D4C2×#692311yescharacteristic
178C22×C4—611no—
179C22×C4—1221no—
180C22×C4—1221no—
181Q16—1221no—
182Q16—1221no—
183SD16—21no—
184SD16—21no—
185SD16—1221no—
186SD16—1221no—
187D8—1221no—
188D8—1221no—
189M16—612no—
190M16—1221no—
191C2×C8—611no—
192C2×C8—611no—
193C2×C8—611no—
194C2×C8—611no—
195C2×C8—611no—
196C2×C8—1221no—
197C2×C8C2×#692311yescharacteristic
198C4⋊C4—1221no—
199C4⋊C4—1221no—
200C4⋊C4—1221no—
201C22⋊C4—612no—
202C22⋊C4—1221no—
203C22⋊C4—1221no—
204C42—1221no—
205C42—1221no—
206C42—1221no—
207C23—21no—
208C23—611no—
209C23—1221no—
210Q8—21no—
211Q8—21no—
212Q8—1221no—
213Q8—1221no—
214D4—21no—
215D4—21no—
216D4—1221no—
217D4—1221no—
218D4—2441no—
219D4—2441no—
220D4—2441no—
221D4—2441no—
222C2×C4—21no—
223C2×C4—611no—
224C2×C4—611no—
225C2×C4—611no—
226C2×C4—611no—
227C2×C4—611no—
228C2×C4—1222no—
229C2×C4—1221no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4—2441no—
233C2×C4—2441no—
234C2×C4—2441no—
235C2×C4—2441no—
236C2×C4C22×#692311yescharacteristic
237C8—611no—
238C8—611no—
239C8—1222no—
240C8C22⋊#692311yescharacteristic
241C8C22⋊#692311yescharacteristic
242C22—41no—
243C22—81no—
244C22—611no—
245C22—611no—
246C22—4881no—
247C22—2441no—
248C22—2441no—
249C22D4×#692311yescharacteristic
250C4—41no—
251C4—611no—
252C4—611no—
253C4—4881no—
254C4—4881no—
255C4—2442no—
256C4—2441no—
257C4C2×C22⋊#692311yescharacteristic
258C4D4×#692311yescharacteristic
259C2—21no—
260C2—81no—
261C2—1221no—
262C2—1221no—
263C2—4881no—
264C2#1684071411yescharacteristic
subgroupG/H
centerC2#16840714
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×SD16×C61C4
socleC2×C61#390
hypercenterC2×SD16#6923
hypocenterC61#1976
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. #16840772C2semidirect
2. #16840761C2semidirect
3. #16840760C2semidirect
4. #16840743C2semidirect
5. #16840742C2semidirect
6. #16840725C2semidirect
26. C2×#11758202C4semidirect
27. C2×#11758190C4semidirect
28. C2×#11758199C4semidirect
30. C2×SD16×C61C4semidirect
140. C61#1976semidirect
149. C2×SD16#6923semidirect