Finite Group Databasebeta

← #21446161

Subgroups — #21446161

Order 7808.

338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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×Dic244C211yesmaximal, characteristic
2C2×#14519742C211yesmaximal, characteristic
3C2×#14519700C211yesmaximal, characteristic
4C2×#14519700C211yesmaximal, characteristic
5#16839667C211yesmaximal, characteristic
6#16839516C211yesmaximal, characteristic
7C61×#340C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10C2×Dic244—22no—
11C2×Dic244—22no—
12C2×Dic244C414yescomplemented
13C22×#92418C2211yescharacteristic
14#14519742—22no—
15#14519742—22no—
16C2×#11758196—21no—
17C2×C4×Dic61—21no—
18C2×C4×Dic61C2211yescharacteristic
19#14519700—22no—
20#14519700—22no—
21#14519684—21no—
22#14519684—21no—
23C22×C8×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25C2×C4⋊C4×C61C2211yescharacteristic
26C22×C4×C61—21no—
27C22×C4×C61—21no—
28C22×C4×C61C2311yescharacteristic
29C22×Dic61—21no—
30C22×Dic61—21no—
31C22×Dic61D411yescharacteristic
32C22×Dic61D411yescharacteristic
33C2×Dic122—21no—
34C2×Dic122—21no—
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122C2×C412yes—
42C2×Dic122C2×C412yes—
43C2×Dic122D412yes—
44C2×Dic122D412yes—
45C2×C8×C61—21no—
46C2×C8×C61—21no—
47C2×C8×C61C2×C412yes—
48C4⋊C4×C61—21no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—21no—
51C4⋊C4×C61D412yes—
52#11758196—24no—
53C4×Dic61—24no—
54C4×Dic61—21no—
55C4×Dic61—21no—
56C2×#92418—21no—
57C2×#92418—21no—
58C2×#92418—21no—
59Dic244—28no—
60C23×C61C2×D411yescharacteristic
61C2×C4×C61—22no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61C22×C411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61#4111yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×Dic61—22no—
74C2×Dic61—21no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—21no—
78C2×Dic61—22no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84C2×Dic61Q1612yescomplemented
85Dic122—22no—
86Dic122—22no—
87Dic122—22no—
88Dic122—22no—
89Dic122—22no—
90Dic122—41no—
91Dic122—41no—
92Dic122C22⋊C414yes—
93C8×C61—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—42no—
103C4×C61—81no—
104C4×C61C2×C22⋊C411yescharacteristic
105C4×C61C4×D411yescharacteristic
106C4×C61#12111yescharacteristic
107C4×C61#12311yescharacteristic
108Dic61—24no—
109Dic61—22no—
110Dic61—42no—
111Dic61—41no—
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×Q8—611no—
122C2×#103—611no—
123C2×#103—611no—
124#391—611no—
125#340D6111yescharacteristic
126#336—611no—
127C61#187811yescharacteristic, complemented, Sylow
128C22×Q8—611no—
129C22×Q8—611no—
130C2×Q16—614no—
131C2×Q16—1222no—
132C2×Q16—1222no—
133C22×C8—611no—
134C22×C8C2×D6111yescharacteristic
135C4×Q8—1222no—
136C4×Q8—1222no—
137C2×C4⋊C4—1221no—
138C2×C4⋊C4C2×D6111yescharacteristic
139C2×C4⋊C4C2×D6111yescharacteristic
140C2×C42—611no—
141C2×C42—1221no—
142#103—1222no—
143#103—1222no—
144#95—1221no—
145#95—1221no—
146C2×Q8—612no—
147C2×Q8—612no—
148C2×Q8—612no—
149C2×Q8—612no—
150C2×Q8—1221no—
151C2×Q8—1221no—
152C2×Q8—1221no—
153C2×Q8—1221no—
154C2×Q8—1221no—
155C2×Q8—1221no—
156C2×Q8—1221no—
157C2×Q8—1221no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—1221no—
163C22×C4—1221no—
164C22×C4C22×D6111yescharacteristic
165Q16—1228no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—1221no—
169C2×C8—1221no—
170C2×C8—1221no—
171C2×C8C4×D6112yes—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—1224no—
176C4⋊C4D24412yes—
177C42—1224no—
178C42—1221no—
179C42—1221no—
180C23D4×D6111yescharacteristic
181Q8—614no—
182Q8—1222no—
183Q8—1222no—
184Q8—1222no—
185Q8—1222no—
186Q8—1222no—
187Q8—2441no—
188Q8—2441no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—612no—
196C2×C4—1222no—
197C2×C4—1221no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1221no—
201C2×C4—1222no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—2441no—
206C2×C4—2441no—
207C2×C4C2×C4×D6111yescharacteristic
208C2×C4C2×D24411yescharacteristic
209C2×C4#1175822211yescharacteristic
210C2×C4D4×D6111yescharacteristic
211C2×C4D4×D6111yescharacteristic
212C2×C4#1175822611yescharacteristic
213C8—22no—
214C8—2441no—
215C22#1451973911yescharacteristic
216C22#1451974711yescharacteristic
217C22#1451975011yescharacteristic
218C22Q16×D6111yescharacteristic
219C22#1451979611yescharacteristic
220C22#1451980611yescharacteristic
221C22#1451980611yescharacteristic
222C4—42no—
223C4—81no—
224C4—1224no—
225C4—1222no—
226C4—2442no—
227C4—2441no—
228C4C22⋊C4×D6111yescharacteristic
229C4C4×D24411yescharacteristic
230C4#1451975211yescharacteristic
231C4#1451976211yescharacteristic
232C2#1683964011yescharacteristic
233C2#1683985611yescharacteristic
234C2#1683986811yescharacteristic
235C2#1683991911yescharacteristic
236C2#1683992511yescharacteristic
237C2#1683997111yescharacteristic
238C2#1683998311yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#1878
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
12. C2×Dic244C4semidirect
84. C2×Dic61Q16semidirect
127. C61#1878semidirect