Finite Group Databasebeta

← #21446162

Subgroups — #21446162

Order 7808.

338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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×Q8×Dic61C211yesmaximal, characteristic
2C2×#14519701C211yesmaximal, characteristic
3C2×#14519701C211yesmaximal, characteristic
4#16839669C211yesmaximal, characteristic
5#16839525C211yesmaximal, characteristic
6#16839516C211yesmaximal, characteristic
7C22×Q16×C61C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9Q8×Dic61—22no—
10Q8×Dic61—22no—
11C2×C4⋊Dic61—21no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4×Dic61—21no—
15C2×C4×Dic61C2211yescharacteristic
16#14519701—22no—
17#14519701—22no—
18#14519684—21no—
19#14519684—21no—
20C22×Q8×C61C2211yescharacteristic
21C22×Q8×C61C2211yescharacteristic
22C2×Q16×C61—22no—
23C2×Q16×C61—22no—
24C2×Q16×C61C414yescomplemented
25C22×C8×C61C2211yescharacteristic
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61—21no—
34C2×Q8×C61C2×C412yes—
35C2×Q8×C61C2×C412yes—
36C2×Q8×C61D412yes—
37C2×Q8×C61D412yes—
38C22×C4×C61—21no—
39C22×C4×C61—21no—
40C22×C4×C61C2311yescharacteristic
41C22×Dic61—21no—
42C22×Dic61—21no—
43C22×Dic61D411yescharacteristic
44C22×Dic61D411yescharacteristic
45Q16×C61—28no—
46C2×C8×C61—21no—
47C2×C8×C61—21no—
48C2×C8×C61C2×C412yes—
49C4⋊Dic61—24no—
50C4⋊Dic61—21no—
51C4⋊Dic61—21no—
52C4⋊Dic61—21no—
53C4⋊Dic61D412yes—
54C4×Dic61—24no—
55C4×Dic61—21no—
56C4×Dic61—21no—
57C2×#92418—21no—
58C2×#92418—21no—
59C2×#92418—21no—
60C23×C61C2×D411yescharacteristic
61Q8×C61—22no—
62Q8×C61—22no—
63Q8×C61—22no—
64Q8×C61—22no—
65Q8×C61—22no—
66Q8×C61—41no—
67Q8×C61—41no—
68Q8×C61C22⋊C414yes—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61C22×C411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61#4111yescharacteristic
80C2×C4×C61#4111yescharacteristic
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—22no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—41no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—41no—
92C2×Dic61Q1612yescomplemented
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—24no—
103C4×C61—42no—
104C4×C61C2×C22⋊C411yescharacteristic
105C4×C61C4×D411yescharacteristic
106C4×C61#12111yescharacteristic
107C4×C61#12311yescharacteristic
108Dic61—22no—
109Dic61—41no—
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×Q16D6111yescharacteristic
121C2×C4×Q8—611no—
122C2×#103—611no—
123C2×#103—611no—
124#391—611no—
125#340—611no—
126#336—611no—
127C61#187811yescharacteristic, complemented, Sylow
128C22×Q8C2×D6111yescharacteristic
129C22×Q8C2×D6111yescharacteristic
130C2×Q16—22no—
131C2×Q16—22no—
132C2×Q16Dic6114yescomplemented
133C22×C8—611no—
134C22×C8C2×D6111yescharacteristic
135C4×Q8—1222no—
136C4×Q8—1222no—
137C2×C4⋊C4—611no—
138C2×C4⋊C4—611no—
139C2×C4⋊C4—1221no—
140C2×C42—611no—
141C2×C42—1221no—
142#103—1222no—
143#103—1222no—
144#95—1221no—
145#95—1221no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8C2×Dic6112yes—
155C2×Q8C2×Dic6112yes—
156C2×Q8C22⋊D6112yes—
157C2×Q8C22⋊D6112yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—1221no—
163C22×C4—1221no—
164C22×C4C22×D6111yescharacteristic
165Q16—28no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—1221no—
169C2×C8—1221no—
170C2×C8—1221no—
171C2×C8C2×Dic6112yes—
172C4⋊C4—612no—
173C4⋊C4—1224no—
174C4⋊C4—1221no—
175C4⋊C4—1221no—
176C4⋊C4—1221no—
177C42—1224no—
178C42—1221no—
179C42—1221no—
180C23D4×D6111yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—22no—
184Q8—22no—
185Q8—22no—
186Q8—41no—
187Q8—41no—
188Q8C22⋊Dic6114yes—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—612no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—1222no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—2441no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4—2441no—
207C2×C4D4×D6111yescharacteristic
208C2×C4#1175822411yescharacteristic
209C2×C4#1175822411yescharacteristic
210C2×C4C22×Dic6111yescharacteristic
211C2×C4C2×C22⋊D6111yescharacteristic
212C2×C4C2×C22⋊D6111yescharacteristic
213C8—22no—
214C8—2441no—
215C22D4×Dic6111yescharacteristic
216C22#1451974511yescharacteristic
217C22#1451974911yescharacteristic
218C22Q16×D6111yescharacteristic
219C22#1451980011yescharacteristic
220C22#1451980911yescharacteristic
221C22#1451980911yescharacteristic
222C4—24no—
223C4—42no—
224C4—1222no—
225C4—4881no—
226C4—2441no—
227C4—2442no—
228C4C2×C22⋊Dic6111yescharacteristic
229C4D4×Dic6111yescharacteristic
230C4#1451974911yescharacteristic
231C4#1451975811yescharacteristic
232C2#1683964211yescharacteristic
233C2Q16×Dic6111yescharacteristic
234C2#1683986911yescharacteristic
235C2#1683991611yescharacteristic
236C2#1683992311yescharacteristic
237C2#1683997011yescharacteristic
238C2#1683998611yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC22×Q16×C61C2
socleC23×C61C2×D4
hypercenterC22×Q16D61
hypocenterC61#1878
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
24. C2×Q16×C61C4semidirect
92. C2×Dic61Q16semidirect
127. C61#1878semidirect
132. C2×Q16Dic61semidirect