Finite Group Databasebeta

← #21446151

Subgroups — #21446151

Order 7808.

402 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C22×#11758200C211yesmaximal, characteristic
2C2×D4×Dic61C211yesmaximal, characteristic
3C2×#14519702C211yesmaximal, characteristic, complemented
4#16839667C211yesmaximal, characteristic, complemented
5#16839524C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C2×#102×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C23×Dic61—21no—
10C2×#11758200—22no—
11C2×#11758200—22no—
12C2×#11758200C414yescomplemented
13C22×#92418C2211yescharacteristic
14D4×Dic61—22no—
15D4×Dic61—22no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C22⋊Dic61—21no—
18C2×C4×Dic61C2211yescharacteristic
19#14519702—22no—
20#14519684—21no—
21#14519684—21no—
22C22×D4×C61C2211yescharacteristic
23C22×C8×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25#102×C61—22no—
26C24×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61C2×C412yes—
31C2×D4×C61D412yes—
32C2×D4×C61D412yes—
33C22×C4×C61—21no—
34C22×C4×C61C2311yescharacteristic
35C22×Dic61—24no—
36C22×Dic61—21no—
37C22×Dic61—21no—
38C22×Dic61—42no—
39C22×Dic61—42no—
40C22×Dic61D411yescharacteristic
41C22×Dic61D411yescharacteristic
42C2×Dic122—21no—
43C2×Dic122—21no—
44C2×Dic122—21no—
45C2×Dic122—21no—
46C2×Dic122—21no—
47C2×Dic122C2×C412yescomplemented
48C2×C8×C61—21no—
49C2×C8×C61—21no—
50C2×C8×C61—21no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C22⋊Dic61—24no—
54#11758200—28no—
55C4⋊Dic61—21no—
56C4⋊Dic61D412yes—
57C4×Dic61—21no—
58C4×Dic61—21no—
59C2×#92418—21no—
60C2×#92418—21no—
61C2×#92418C2×C412yescomplemented
62C23×C61—22no—
63C23×C61—22no—
64C23×C61—22no—
65C23×C61—41no—
66C23×C61—41no—
67C23×C61—41no—
68C23×C61—41no—
69C23×C61C2×D411yescharacteristic
70D4×C61—22no—
71D4×C61—22no—
72D4×C61—22no—
73D4×C61C22⋊C414yes—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61C22×C411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61#4111yescharacteristic
82C2×C4×C61#4111yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—22no—
86C2×Dic61—21no—
87C2×Dic61—22no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—48no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—41no—
95C2×Dic61SD1612yescomplemented
96Dic122—22no—
97Dic122—22no—
98Dic122—41no—
99Dic122—41no—
100C8×C61—41no—
101#92418—22no—
102C22×C61—24no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61—42no—
109C22×C61C4×D411yescharacteristic
110C22×C61#12011yescharacteristic
111C22×C61#12111yescharacteristic
112C22×C61C2×SD1611yescharacteristic
113C22×C61#13511yescharacteristic
114C22×C61AGL(1,ℤ/8)11yescharacteristic
115C22×C61#13711yescharacteristic
116C4×C61—81no—
117C4×C61C2×C22⋊C411yescharacteristic
118C4×C61C4×D411yescharacteristic
119C4×C61#12111yescharacteristic
120C4×C61#12311yescharacteristic
121Dic61—22no—
122Dic61—42no—
123Dic61—42no—
124Dic61—41no—
125#1877—611nomaximal, Sylow
126C2×C61—44no—
127C2×C61#38611yescharacteristic
128C2×C61C4×SD1611yescharacteristic
129C2×C61#44011yescharacteristic
130C2×C61#45011yescharacteristic
131C2×C61#45211yescharacteristic
132C2×C61#46111yescharacteristic
133C2×C61#46311yescharacteristic
134C22×SD16—611no—
135C2×C4×D4—611no—
136C2×#103—611no—
137C2×#102D6111yescharacteristic
138#391—611no—
139#340—611no—
140#336—611no—
141C61#187711yescharacteristic, complemented, Sylow
142C22×Q8—611no—
143C22×D4C2×D6111yescharacteristic
144C23×C4—1221no—
145C2×SD16—614no—
146C2×SD16—1222no—
147C2×SD16—1222no—
148C22×C8—611no—
149C22×C8C2×D6111yescharacteristic
150C4×D4—1222no—
151C4×D4—1222no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4C2×D6111yescharacteristic
154C2×C22⋊C4—1221no—
155C2×C42—611no—
156#103—1222no—
157#102—22no—
158#95—1221no—
159#95—1221no—
160C24—21no—
161C2×Q8—612no—
162C2×Q8—1221no—
163C2×Q8—1221no—
164C2×Q8—1221no—
165C2×Q8—1221no—
166C2×Q8—1221no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4C4×D6112yes—
171C2×D4D24412yes—
172C2×D4C22⋊D6112yes—
173C22×C4—21no—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—1224no—
177C22×C4—1221no—
178C22×C4—1221no—
179C22×C4—2442no—
180C22×C4—2442no—
181C22×C4C22×D6111yescharacteristic
182SD16—1228no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—612no—
187C2×C8—1221no—
188C2×C8—1221no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—612no—
192C4⋊C4—1221no—
193C22⋊C4—1224no—
194C42—1221no—
195C42—1221no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23D4×D6111yescharacteristic
204Q8—1222no—
205Q8—1222no—
206Q8—2441no—
207Q8—2441no—
208D4—22no—
209D4—22no—
210D4—22no—
211D4#1175819814yes—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—612no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1222no—
219C2×C4—1221no—
220C2×C4—1222no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—2448no—
224C2×C4—2441no—
225C2×C4—2441no—
226C2×C4—2441no—
227C2×C4—2441no—
228C2×C4C2×C4×D6111yescharacteristic
229C2×C4C2×D24411yescharacteristic
230C2×C4D4×D6111yescharacteristic
231C2×C4#1175822411yescharacteristic
232C2×C4#1175822411yescharacteristic
233C2×C4C2×C22⋊D6111yescharacteristic
234C8—41no—
235C8—1222no—
236C22—24no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22#1451973711yescharacteristic
244C22#1451974711yescharacteristic
245C22#1451974911yescharacteristic
246C22SD16×D6111yescharacteristic
247C22#1451979611yescharacteristic
248C22#1451980111yescharacteristic
249C22#1451980611yescharacteristic
250C4—81no—
251C4—1222no—
252C4—2442no—
253C4—2442no—
254C4—2441no—
255C4C2×#1175819811yescharacteristic
256C4#1451973711yescharacteristic
257C4#1451974911yescharacteristic
258C4#1451976111yescharacteristic
259C2—44no—
260C2#1683963911yescharacteristic
261C2#1683985311yescharacteristic
262C2#1683985911yescharacteristic
263C2#1683991411yescharacteristic
264C2#1683992511yescharacteristic
265C2#1683996511yescharacteristic
266C2#1683997511yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC23×C61C2×D4
hypercenterC2×#102D61
hypocenterC61#1877
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
3. C2×#14519702C2semidirect
4. #16839667C2semidirect
5. #16839524C2semidirect
6. #16839516C2semidirect
12. C2×#11758200C4semidirect
47. C2×Dic122C2×C4semidirect
61. C2×#92418C2×C4semidirect
95. C2×Dic61SD16semidirect
141. C61#1877semidirect