Finite Group Databasebeta

← #21461809

Subgroups — #21461809

Order 7808.

324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×#14519865C211yesmaximal, characteristic, complemented
2C2×#14519842C211yesmaximal, characteristic, complemented
3C2×#14519842C211yesmaximal, characteristic, complemented
4#16840737C211yesmaximal, characteristic, complemented
5#16840638C211yesmaximal, characteristic, complemented
6(C2×#6923)⋊C8C211yesmaximal, characteristic, complemented
7C2×#14519800C211yesmaximal, characteristic
8#14519865—22no—
9#14519865—22no—
10C2×#11758213—21no—
11C2×#11758213C2211yescharacteristic
12C2×#11758213C2211yescharacteristic
13C2×D61⋊C8—21no—
14C2×D61⋊C8C2211yescharacteristic
15C2×C4×#6923C2211yescharacteristic
16#14519842—22no—
17#14519842—22no—
18#14519834—21no—
19#14519834—21no—
20C2×#11758226C2211yescharacteristic
21C2×#11758226C2211yescharacteristic
22#14519800—22no—
23#14519800—22no—
24C2×#11758201C411yescharacteristic, complemented
25C2×#11758201C411yescharacteristic, complemented
26C2×D488C411yescharacteristic, complemented
27C2×C8×D61C2211yescharacteristic
28C2×Q16×C61C411yescharacteristic, complemented
29C22×#6923—21no—
30C2×Q8×C61C2×C411yescharacteristic
31C2×Q8×C61C2×C411yescharacteristic
32#11758226—21no—
33#11758226—21no—
34#11758226—21no—
35#11758226—21no—
36#11758226—21no—
37#11758226—21no—
38#11758226D412yes—
39#11758226D412yes—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244C2×C411yescharacteristic
43C2×D244C2×C411yescharacteristic
44C2×C4×D61—21no—
45C2×C4×D61—21no—
46C2×C4×D61C2311yescharacteristic
47C2×#92420—21no—
48C2×#92420—21no—
49C2×#92420D411yescharacteristic
50C2×#92420D411yescharacteristic
51C4×#6923—21no—
52C4×#6923—21no—
53#11758213—24no—
54#11758213—21no—
55#11758213—21no—
56#11758213—21no—
57#11758213D412yes—
58D61⋊C8—24no—
59D61⋊C8—21no—
60D61⋊C8—21no—
61Q16×C61—22no—
62C2×C8×C61C2×C411yescharacteristic
63#11758201—22no—
64#11758201—22no—
65C2×#92418C2×C411yescharacteristic
66D488—22no—
67C8×D61—21no—
68C8×D61—21no—
69C22×D61—21no—
70C22×D61—21no—
71C22×D61#4111yescharacteristic
72C2×#6923—22no—
73C2×#6923—41no—
74C2×#6923—41no—
75Q8×C61—21no—
76Q8×C61—21no—
77Q8×C61—21no—
78Q8×C61C22⋊C412yes—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61C22×C411yescharacteristic
82C2×Dic61C2×D411yescharacteristic
83D244—22no—
84D244—22no—
85D244—21no—
86D244—21no—
87D244—21no—
88D244—41no—
89D244—41no—
90D244C22⋊C412yes—
91C4×D61—22no—
92C4×D61—22no—
93C4×D61—41no—
94C4×D61—41no—
95C4×D61C2×D411yescharacteristic
96C4×D61C2×D411yescharacteristic
97C4×D61C2×D411yescharacteristic
98C4×D61#4111yescharacteristic
99#92420—21no—
100#92420—21no—
101#92420—22no—
102#92420—41no—
103C8×C61—21no—
104#92418—21no—
105C22×C61C4×D411yescharacteristic
106C2×D61—21no—
107C2×D61—21no—
108C2×D61—22no—
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—41no—
112C2×D61—41no—
113C2×D61—41no—
114C2×D61#12111yescharacteristic
115C2×D61#12311yescharacteristic
116#6923—42no—
117C4×C61—22no—
118C4×C61—41no—
119C4×C61C2×C22⋊C411yescharacteristic
120C4×C61C4×D411yescharacteristic
121Dic61#12011yescharacteristic
122Dic61#12111yescharacteristic
123#1876—611nomaximal, Sylow
124C2×C61#38611yescharacteristic
125C2×C61#44311yescharacteristic
126C2×C61#44411yescharacteristic
127D61—21no—
128D61—21no—
129D61—42no—
130D61—81no—
131C2×#135—611no—
132C2×#131—611no—
133C2×#104—611no—
134C2×#104—611no—
135#408—611no—
136#341—611no—
137#336—611no—
138C61#187611yescharacteristic, complemented, Sylow
139C2×#41—611no—
140C2×#41—611no—
141#135—1222no—
142#135—1222no—
143C2×Q16#692311yescharacteristic, complemented
144C2×SD16—611no—
145C2×SD16—611no—
146C2×D8—611no—
147#131—1222no—
148#131—1222no—
149C2×M16—611no—
150C2×M16—611no—
151C2×M16—1221no—
152C22×C8—611no—
153C22×C8—611no—
154C22×C8—1221no—
155C2×C42—611no—
156#104—1222no—
157#104—1222no—
158C22⋊C8—1221no—
159C22⋊C8—1221no—
160#41—612no—
161#41—612no—
162#41—1221no—
163#41—1221no—
164#41—1221no—
165#41—1221no—
166#41—1221no—
167#41—1221no—
168C2×Q8C2×#692311yescharacteristic
169C2×Q8C2×#692311yescharacteristic
170C2×D4—611no—
171C2×D4—611no—
172C2×D4—1221no—
173C2×D4—1221no—
174C22×C4—611no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4—1221no—
178Q16—22no—
179SD16—1222no—
180SD16—1222no—
181D8—1222no—
182M16—612no—
183M16—1221no—
184M16—1224no—
185M16—1221no—
186M16—1221no—
187C2×C8—611no—
188C2×C8—611no—
189C2×C8—611no—
190C2×C8—1221no—
191C2×C8—1221no—
192C2×C8—1221no—
193C2×C8—1221no—
194C2×C8—1221no—
195C2×C8—1224no—
196C2×C8—1221no—
197C2×C8C2×#692311yescharacteristic
198C42—1221no—
199C42—1221no—
200C23—611no—
201C23—1221no—
202C23—1221no—
203Q8—21no—
204Q8—21no—
205Q8—21no—
206Q8C22⋊#692312yes—
207D4—612no—
208D4—1222no—
209D4—1222no—
210D4—1221no—
211D4—1221no—
212D4—1221no—
213D4—2441no—
214D4—2441no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—611no—
218C2×C4—611no—
219C2×C4—611no—
220C2×C4—611no—
221C2×C4—611no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—2441no—
226C2×C4—2441no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4C22×#692311yescharacteristic
230C8—21no—
231C8—1221no—
232C8—1221no—
233C8—1222no—
234C8—1221no—
235C8—2441no—
236C22—611no—
237C22—611no—
238C22—1221no—
239C22—1221no—
240C22—1222no—
241C22—2441no—
242C22—2441no—
243C22—2441no—
244C22—2441no—
245C22—2441no—
246C22D4×#692311yescharacteristic
247C4—22no—
248C4—41no—
249C4—611no—
250C4—611no—
251C4—2442no—
252C4C2×C22⋊#692311yescharacteristic
253C4D4×#692311yescharacteristic
254C2—1221no—
255C2—1221no—
256C2—4881no—
257C2—2442no—
258C2#1684071011yescharacteristic
259C2#1684080611yescharacteristic
260C2#1684080811yescharacteristic
subgroupG/H
centerC22D4×#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×Q16×C61C4
socleC22×C61C4×D4
hypercenterC2×Q16#6923
hypocenterC61#1876
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#14519865C2semidirect
2. C2×#14519842C2semidirect
3. C2×#14519842C2semidirect
4. #16840737C2semidirect
5. #16840638C2semidirect
6. (C2×#6923)⋊C8C2semidirect
24. C2×#11758201C4semidirect
25. C2×#11758201C4semidirect
26. C2×D488C4semidirect
28. C2×Q16×C61C4semidirect
138. C61#1876semidirect
143. C2×Q16#6923semidirect