Finite Group Databasebeta

← #21446160

Subgroups — #21446160

Order 7808.

338 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 113 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×#11758202C211yesmaximal, characteristic
2C2×#14519701C211yesmaximal, characteristic
3C2×#14519700C211yesmaximal, characteristic
4#16839668C211yesmaximal, characteristic
5#16839524C211yesmaximal, characteristic
6#16839517C211yesmaximal, characteristic
7C2×C4×Q8×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758202—22no—
10C2×#11758202—22no—
11C2×#11758202C414yescomplemented
12C22×#92418C2211yescharacteristic
13C22×#92418C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15#14519701—22no—
16#14519700—22no—
17#14519684—21no—
18#14519684—21no—
19C22×Q8×C61C2211yescharacteristic
20C4×Q8×C61—22no—
21C4×Q8×C61—22no—
22C2×C4⋊C4×C61—21no—
23C2×C4⋊C4×C61C2211yescharacteristic
24C2×C42×C61—21no—
25C2×C42×C61C2211yescharacteristic
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61C2×C412yes—
30C2×Q8×C61D412yes—
31C2×Q8×C61D412yes—
32C22×C4×C61—21no—
33C22×C4×C61—21no—
34C22×C4×C61D411yescharacteristic
35C22×C4×C61D411yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×Dic61—21no—
38C22×Dic61—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122—21no—
42C2×Dic122—21no—
43C2×Dic122—21no—
44C2×Dic122C2×C412yes—
45C4⋊C4×C61—24no—
46C4⋊C4×C61—21no—
47C4⋊C4×C61D412yes—
48C42×C61—24no—
49C42×C61—21no—
50C42×C61—21no—
51#11758202—28no—
52C4⋊Dic61—21no—
53C4⋊Dic61—21no—
54C2×#92418—21no—
55C2×#92418—21no—
56C2×#92418—21no—
57C2×#92418—21no—
58C2×#92418—21no—
59C2×#92418C2×C412yes—
60C23×C61C2×D411yescharacteristic
61Q8×C61—22no—
62Q8×C61—22no—
63Q8×C61—22no—
64Q8×C61C22⋊C414yes—
65C2×C4×C61—22no—
66C2×C4×C61—21no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61Q1612yescomplemented
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—22no—
84C2×Dic61—41no—
85C2×Dic61—41no—
86C2×Dic61—41no—
87C2×Dic61—41no—
88C2×Dic61—41no—
89Dic122—22no—
90Dic122—22no—
91Dic122—41no—
92Dic122—41no—
93#92418—22no—
94#92418—41no—
95C22×C61C4×D411yescharacteristic
96C22×C61#12011yescharacteristic
97C22×C61#12111yescharacteristic
98C22×C61C2×Q1611yescharacteristic
99C22×C61#13511yescharacteristic
100C22×C61#13711yescharacteristic
101C22×C61#13711yescharacteristic
102C4×C61—24no—
103C4×C61—22no—
104C4×C61—41no—
105C4×C61—42no—
106C4×C61C2×C22⋊C411yescharacteristic
107C4×C61C4×D411yescharacteristic
108C4×C61#12111yescharacteristic
109C4×C61#12311yescharacteristic
110Dic61—42no—
111Dic61—81no—
112#1878—611nomaximal, Sylow
113C2×C61#38611yescharacteristic
114C2×C61C4×Q1611yescharacteristic
115C2×C61#44111yescharacteristic
116C2×C61#45111yescharacteristic
117C2×C61#45211yescharacteristic
118C2×C61#46211yescharacteristic
119C2×C61#46411yescharacteristic
120C22×Q16—611no—
121C2×C4×Q8D6111yescharacteristic
122C2×#103—611no—
123C2×#103—611no—
124#391—611no—
125#340—611no—
126#336—611no—
127C61#187811yescharacteristic, complemented, Sylow
128C22×Q8—611no—
129C22×Q8C2×D6111yescharacteristic
130C2×Q16—614no—
131C2×Q16—1222no—
132C2×Q16—1222no—
133C22×C8—611no—
134C22×C8—611no—
135C4×Q8—22no—
136C4×Q8—22no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—611no—
139C2×C4⋊C4C2×D6111yescharacteristic
140C2×C42—21no—
141C2×C42C2×D6111yescharacteristic
142#103—1222no—
143#103—1222no—
144#95—1221no—
145#95—1221no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—612no—
150C2×Q8—1221no—
151C2×Q8—1221no—
152C2×Q8—1221no—
153C2×Q8—1221no—
154C2×Q8—1221no—
155C2×Q8C4×D6112yes—
156C2×Q8D24412yes—
157C2×Q8C22⋊D6112yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—1221no—
161C22×C4—1221no—
162C22×C4C22⋊D6111yescharacteristic
163C22×C4C22⋊D6111yescharacteristic
164C22×C4C22×D6111yescharacteristic
165Q16—1228no—
166C2×C8—612no—
167C2×C8—1221no—
168C2×C8—1221no—
169C2×C8—1221no—
170C2×C8—1221no—
171C2×C8—1221no—
172C4⋊C4—24no—
173C4⋊C4—21no—
174C4⋊C4—1221no—
175C4⋊C4—1221no—
176C4⋊C4C22⋊D6112yes—
177C42—24no—
178C42—21no—
179C42—21no—
180C23C2×C22⋊D6111yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—22no—
184Q8—1222no—
185Q8—1222no—
186Q8—2441no—
187Q8—2441no—
188Q8#1175819814yes—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—1222no—
201C2×C4—2441no—
202C2×C4—2441no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4#1175820212yescomplemented
207C2×C4C2×C4×D6111yescharacteristic
208C2×C4C2×D24411yescharacteristic
209C2×C4#1175822211yescharacteristic
210C2×C4#1175822211yescharacteristic
211C2×C4C2×C22⋊D6111yescharacteristic
212C2×C4C2×C22⋊D6111yescharacteristic
213C8—1222no—
214C8—2441no—
215C22C4×C22⋊D6111yescharacteristic
216C22#1451974611yescharacteristic
217C22#1451975111yescharacteristic
218C22C2×#1175820211yescharacteristic
219C22#1451979711yescharacteristic
220C22#1451980711yescharacteristic
221C22#1451980811yescharacteristic
222C4—24no—
223C4—22no—
224C4—41no—
225C4—42no—
226C4—4881no—
227C4—2442no—
228C4C2×#1175819811yescharacteristic
229C4C4×C22⋊D6111yescharacteristic
230C4#1451975111yescharacteristic
231C4#1451976011yescharacteristic
232C2#1683964111yescharacteristic
233C2C4×#1175820211yescharacteristic
234C2#1683986711yescharacteristic
235C2#1683991811yescharacteristic
236C2#1683992411yescharacteristic
237C2#1683997211yescharacteristic
238C2#1683998411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×C4×Q8×C61C2
socleC23×C61C2×D4
hypercenterC2×C4×Q8D61
hypocenterC61#1878
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
11. C2×#11758202C4semidirect
76. C2×C4×C61Q16semidirect
127. C61#1878semidirect
206. C2×C4#11758202semidirect