Finite Group Databasebeta

← #21461801

Subgroups — #21461801

Order 7808.

376 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 72 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×D61⋊M16C211yesmaximal, characteristic, complemented
2C2×#14519842C212yesmaximal, complemented
3C4×C22⋊#6923C211yesmaximal, characteristic, complemented
4#16840632C212yesmaximal, complemented
5#16840275C211yesmaximal, characteristic
6C2×#11758213C2212yes—
7D61⋊M16—24no—
8C2×#11758217—21no—
9C2×D61⋊C8—21no—
10C2×C22⋊#6923—21no—
11C2×C4×#6923C2212yes—
12#14519842—24no—
13(C2×#6923)⋊C4—21no—
14C2×#11758226C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519762—21no—
17#14519753C411yescharacteristic, complemented
18#14519752C411yescharacteristic, complemented
19#14519751C411yescharacteristic, complemented
20#14519747—21no—
21#14519739—21no—
22#14519737—21no—
23#14519735C2211yescharacteristic
24C22⋊Q8×C61C411yescharacteristic, complemented
25C23×D61D411yescharacteristic
26C22×#6923—22no—
27C2×Q8×C61C2×C411yescharacteristic
28C22×C4×C61C2×C411yescharacteristic
29C2×C22⋊D61—21no—
30C22×Dic61D411yescharacteristic
31#11758226—22no—
32#11758226—22no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244C2×C411yescharacteristic
36C2×C4×D61—22no—
37C2×C4×D61—22no—
38C2×C4×D61—21no—
39C2×C4×D61C2×C411yescharacteristic
40C2×C4×D61D411yescharacteristic
41C2×C4×D61D411yescharacteristic
42C2×C4×D61C2311yescharacteristic
43C22⋊#6923—24no—
44#11758217—24no—
45C2×#92420—22no—
46C4×#6923—22no—
47C4×#6923—22no—
48#11758213—22no—
49#11758213D414yescomplemented
50D61⋊C8—24no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61C2×C411yescharacteristic
53C22⋊C4×C61—21no—
54#11758198—21no—
55#11758198—21no—
56#11758198—21no—
57#11758198—21no—
58C4⋊Dic61C2×C411yescharacteristic
59#11758196—21no—
60C4×Dic61—21no—
61C23×C61C22⋊C411yescharacteristic
62C22×D61—22no—
63C22×D61—22no—
64C22×D61—21no—
65C22×D61—41no—
66C22×D61C22⋊C411yescharacteristic
67C22×D61C2×D411yescharacteristic
68C2×#6923—24no—
69C2×#6923—42no—
70C2×#6923—42no—
71Q8×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61C22⋊C411yescharacteristic
76C2×C4×C61C22×C411yescharacteristic
77C22⋊D61—42no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61C22⋊C411yescharacteristic
82C2×Dic61C2×D411yescharacteristic
83D244—22no—
84D244—42no—
85D244—42no—
86C4×D61—22no—
87C4×D61—22no—
88C4×D61—21no—
89C4×D61—21no—
90C4×D61—41no—
91C4×D61—41no—
92C4×D61C2×D412yes—
93C4×D61#4112yes—
94#92420—24no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61C2×C22⋊C411yescharacteristic
99C2×D61—21no—
100C2×D61—21no—
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—44no—
104C2×D61—41no—
105C2×D61—41no—
106C2×D61—41no—
107C2×D61#10412yescomplemented
108C2×D61#12112yes—
109#6923—44no—
110C4×C61—21no—
111C4×C61—41no—
112C4×C61—41no—
113C4×C61C4×D412yes—
114Dic61—21no—
115Dic61—41no—
116Dic61#12011yescharacteristic
117Dic61#12311yescharacteristic
118#1871—611nomaximal, Sylow
119C2×C61—41no—
120C2×C61#38611yescharacteristic
121C2×C61C2×#10411yescharacteristic
122C2×C61#42111yescharacteristic
123D61—22no—
124D61—22no—
125D61—81no—
126C22×M16—611no—
127#525—611no—
128C2×#104—612no—
129C4×C22⋊C4—611no—
130#339—612no—
131C61#187111yescharacteristic, complemented, Sylow
132C2×#41—611no—
133C23×C4—611no—
134C2×M16—612no—
135C2×M16—1224no—
136C2×M16—1221no—
137C22×C8—1221no—
138#123—1221no—
139C22⋊Q8—611no—
140C22⋊Q8#692311yescharacteristic, complemented
141#121—611no—
142#121—611no—
143#120—1221no—
144C4×D4—1221no—
145C4×D4—1221no—
146#117—611no—
147C2×C22⋊C4—1221no—
148C2×C42—612no—
149#104—1224no—
150#95—1221no—
151C24—611no—
152#41—1222no—
153#41—1222no—
154C2×Q8C2×#692311yescharacteristic
155C2×D4—611no—
156C2×D4—1221no—
157C2×D4—1221no—
158C2×D4—1221no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4—611no—
164C22×C4—1222no—
165C22×C4—1222no—
166C22×C4—1221no—
167C22×C4—1222no—
168C22×C4C2×#692311yescharacteristic
169M16—614no—
170M16—1222no—
171M16—1224no—
172C2×C8—1222no—
173C2×C8—1224no—
174C4⋊C4—21no—
175C4⋊C4—611no—
176C4⋊C4—1221no—
177C4⋊C4C2×#692311yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—1221no—
180C22⋊C4—1221no—
181C22⋊C4—1221no—
182C22⋊C4—1224no—
183C22⋊C4—1221no—
184C42—1221no—
185C42—1222no—
186C42—1222no—
187C23—611no—
188C23—611no—
189C23—1222no—
190C23—1222no—
191C23—1221no—
192C23—2441no—
193C23C22⋊#692311yescharacteristic
194Q8—22no—
195D4—1222no—
196D4—2442no—
197D4—2442no—
198D4—2442no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—611no—
203C2×C4—612no—
204C2×C4—612no—
205C2×C4—611no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1222no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1222no—
212C2×C4—1224no—
213C2×C4—1221no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4—2442no—
217C2×C4—2442no—
218C2×C4C22⋊#692311yescharacteristic
219C2×C4C22×#692311yescharacteristic
220C8—1224no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—612no—
225C22—612no—
226C22—1221no—
227C22—1221no—
228C22—1221no—
229C22—1221no—
230C22—2444no—
231C22—2441no—
232C22—2441no—
233C22—2441no—
234C22C2×C22⋊#692311yescharacteristic
235C4—21no—
236C4—41no—
237C4—41no—
238C4—611no—
239C4—611no—
240C4—1221no—
241C4—2444no—
242C4—2441no—
243C4D4×#692312yes—
244C2—41no—
245C2—1222no—
246C2—1222no—
247C2—4881no—
248C2#1684071011yescharacteristic
249C2D61⋊#10411yescharacteristic
250C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22⋊Q8#6923
hypocenterC61#1871
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×D61⋊M16C2semidirect
2. C2×#14519842C2semidirect
3. C4×C22⋊#6923C2semidirect
4. #16840632C2semidirect
17. #14519753C4semidirect
18. #14519752C4semidirect
19. #14519751C4semidirect
24. C22⋊Q8×C61C4semidirect
49. #11758213D4semidirect
107. C2×D61#104semidirect
131. C61#1871semidirect
140. C22⋊Q8#6923semidirect