Finite Group Databasebeta

← #21452825

Subgroups — #21452825

Order 7808.

492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519766C211yesmaximal, characteristic
2#16839684C212yesmaximal, complemented
3#16839679C212yesmaximal
4#16839673C212yesmaximal, complemented
5#16839669C211yesmaximal, characteristic, complemented
6#16839653C212yesmaximal, complemented
7#16839652C212yesmaximal, complemented
8#16839643C212yesmaximal, complemented
9C2×C4⋊Q8×C61C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11#14519766—24no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C2212yes—
14C2×#11758198C2212yes—
15C2×#11758198C2212yes—
16C2×#11758198C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×C4×Dic61C2211yescharacteristic
21C2×C4×Dic61C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C22×Q8×C61C2211yescharacteristic
28C22×Q8×C61C2211yescharacteristic
29C4⋊Q8×C61—24no—
30C2×C4⋊C4×C61C2212yes—
31C2×C4⋊C4×C61C2212yes—
32C2×C42×C61C2211yescharacteristic
33C23×D61C2312yes—
34C2×Q8×C61—22no—
35C2×Q8×C61—41no—
36C2×Q8×C61—41no—
37C2×Q8×C61—41no—
38C2×Q8×C61—41no—
39C2×Q8×C61D414yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C22×Dic61C2312yes—
48C2×D244—22no—
49C2×D244—41no—
50C2×D244—41no—
51C4⋊C4×C61—24no—
52C4⋊C4×C61—24no—
53C42×C61—22no—
54#11758198—24no—
55#11758198—24no—
56#11758198—24no—
57#11758198—24no—
58#11758198—42no—
59#11758198—42no—
60C4⋊Dic61—41no—
61#11758196—24no—
62C4×Dic61—22no—
63C4×Dic61—41no—
64C23×C61C2411yescharacteristic
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—22no—
72Q8×C61—44no—
73Q8×C61—44no—
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61C2×D412yes—
86C2×C4×C61C2×D412yes—
87C2×C4×C61C2×D412yes—
88C2×C4×C61#4114yes—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98D244—44no—
99C22×C61C22×D411yescharacteristic
100C22×C61C2×#4112yes—
101C22×C61H(5,𝔽2)11yescharacteristic
102C22×C61H(5,𝔽2)11yescharacteristic
103C22×C612−1+412yes—
104C2×D61—42no—
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—42no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—42no—
111C4×C61—22no—
112C4×C61—22no—
113C4×C61—22no—
114C4×C61—24no—
115C4×C61—42no—
116Dic61—42no—
117Dic61—42no—
118Dic61—42no—
119#2731—611nomaximal, Sylow
120C2×C61#53411yescharacteristic
121C2×C61#54212yes—
122C2×C61#54812yes—
123C2×C61#55511yescharacteristic
124C2×C61#56311yescharacteristic
125D61—82no—
126C2×C4⋊Q8D6111yescharacteristic, complemented
127C2×#124—611no—
128#396—612no—
129#394—612no—
130#393—612no—
131#391—611no—
132#388—612no—
133#388—612no—
134#387—612no—
135C61#273111yescharacteristic, complemented, Sylow
136C22×Q8C2×D6111yescharacteristic
137C22×Q8C2×D6111yescharacteristic
138C22×D4—611no—
139C4⋊Q8—24no—
140#124—1224no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—611no—
143C2×C4⋊C4C2×D6112yes—
144C2×C4⋊C4C2×D6112yes—
145C2×C22⋊C4—612no—
146C2×C22⋊C4—612no—
147C2×C22⋊C4—612no—
148C2×C22⋊C4—612no—
149C2×C22⋊C4—612no—
150C2×C22⋊C4—612no—
151C2×C42—611no—
152C2×C42—611no—
153C2×C42C2×D6111yescharacteristic
154#95—612no—
155#95—612no—
156#95—612no—
157#95—612no—
158#95—612no—
159C24—612no—
160C2×Q8—22no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8C22⋊D6114yes—
166C2×D4—1222no—
167C2×D4—2441no—
168C2×D4—2441no—
169C22×C4—612no—
170C22×C4—612no—
171C22×C4—612no—
172C22×C4C22×D6112yes—
173C22×C4C22×D6112yes—
174C22×C4C22×D6111yescharacteristic
175C22×C4C22×D6111yescharacteristic
176C22×C4C22×D6111yescharacteristic
177C4⋊C4—24no—
178C4⋊C4—24no—
179C4⋊C4—1224no—
180C4⋊C4—2441no—
181C22⋊C4—1224no—
182C22⋊C4—1224no—
183C22⋊C4—1224no—
184C22⋊C4—1224no—
185C22⋊C4—2442no—
186C22⋊C4—2442no—
187C42—22no—
188C42—1222no—
189C42—2441no—
190C23—1222no—
191C23—1222no—
192C23—1222no—
193C23—1222no—
194C23—1222no—
195C23—1222no—
196C23—1222no—
197C23C23×D6111yescharacteristic
198Q8—44no—
199Q8—44no—
200D4—2444no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4#1175822614yes—
222C2×C4C2×C22⋊D6112yes—
223C2×C4C2×C22⋊D6112yes—
224C2×C4C2×C22⋊D6112yes—
225C22—2442no—
226C22—2442no—
227C22—2442no—
228C22—2442no—
229C22—2442no—
230C22—2442no—
231C22—2442no—
232C22C22×C22⋊D6111yescharacteristic
233C22C2×#1175822612yes—
234C22#1451982211yescharacteristic
235C22#1451982211yescharacteristic
236C22#1451982512yes—
237C4—22no—
238C4—22no—
239C4—22no—
240C4—24no—
241C4—42no—
242C4—2442no—
243C4—2442no—
244C4—2442no—
245C2—4882no—
246C2#1684032111yescharacteristic
247C2#1684038612yes—
248C2#1684042312yes—
249C2#1684047811yescharacteristic
250C2#1684051111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4⋊Q8×C61C2
hypercenterC2×C4⋊Q8D61
hypocenterC61#2731
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16839684C2semidirect
4. #16839673C2semidirect
5. #16839669C2semidirect
6. #16839653C2semidirect
7. #16839652C2semidirect
8. #16839643C2semidirect
9. C2×C4⋊Q8×C61C2semidirect
126. C2×C4⋊Q8D61semidirect
135. C61#2731semidirect