Finite Group Databasebeta

← #21455860

Subgroups — #21455860

Order 7808.

384 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 127 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
1#16840317C211yesmaximal, characteristic
2C4×Q8×D61C211yesmaximal, characteristic
3#16840099C212yesmaximal
4#16840054C211yesmaximal, characteristic, complemented
5#16839973C211yesmaximal, characteristic, complemented
6#16839972C211yesmaximal, characteristic, complemented
7#16839919C212yesmaximal
8#16839856C212yesmaximal, complemented
9#16839854C212yesmaximal, complemented
10#16839814C211yesmaximal, characteristic
11C61×#477C211yesmaximal, characteristic, complemented
12C2×Q8×D61C2211yescharacteristic
13C2×Dic244C2212yes—
14C2×#11758202C2212yes—
15#14519777C2211yescharacteristic
16#14519768—21no—
17#14519757C2212yes—
18#14519753—21no—
19Q8×Dic61—21no—
20Q8×Dic61C2211yescharacteristic
21C4×Dic122—21no—
22C4×Dic122C2211yescharacteristic
23#14519742—21no—
24#14519742C2211yescharacteristic
25#14519742C2212yes—
26#14519735—21no—
27C4⋊C4×D61—21no—
28C4⋊C4×D61C2211yescharacteristic
29C42×D61—21no—
30C42×D61C2211yescharacteristic
31#14519710C2212yes—
32C4⋊#92418C2211yescharacteristic
33#14519702C2212yes—
34#14519700C2212yes—
35#14519700C2212yes—
36#14519689C2212yes—
37C8×Dic61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×Q8×C61C2211yescharacteristic
40#107×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45Q8×D61—22no—
46Q8×D61—22no—
47C2×C4×D61—21no—
48C2×C4×D61—21no—
49C2×C4×D61D411yescharacteristic
50C2×C4×D61D411yescharacteristic
51C2×C4×D61C2311yescharacteristic
52C2×Dic122—21no—
53C2×Dic122C2312yes—
54C2×Dic122C2311yescharacteristic
55C2×C8×C61C2312yes—
56C4⋊C4×C61—21no—
57C4⋊C4×C61—21no—
58C4⋊C4×C61C2312yes—
59C4⋊C4×C61C2311yescharacteristic
60C42×C61—21no—
61C42×C61C2311yescharacteristic
62#11758202—24no—
63#11758198—22no—
64C4⋊Dic61—21no—
65C4⋊Dic61—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61—22no—
68C4⋊Dic61C2311yescharacteristic
69#11758196—21no—
70#11758196—21no—
71#11758196—21no—
72#11758196—22no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C4×Dic61—21no—
76C4×Dic61—22no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81Dic244—24no—
82C22×D61C2×D411yescharacteristic
83Q8×C61—21no—
84Q8×C61—42no—
85Q8×C61#4112yes—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2411yescharacteristic
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—22no—
95C2×Dic61C2×D411yescharacteristic
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98C4×D61—24no—
99C4×D61—21no—
100C4×D61—21no—
101C4×D61—41no—
102C4×D61—42no—
103C4×D61Q1614yescomplemented
104Dic122—24no—
105Dic122—21no—
106Dic122—22no—
107Dic122—22no—
108Dic122#4112yes—
109C8×C61—22no—
110#92418—22no—
111C22×C61C22×D411yescharacteristic
112C2×D61—21no—
113C2×D61—21no—
114C2×D61C2×Q1612yes—
115C4×C61—22no—
116C4×C61—21no—
117C4×C61—41no—
118C4×C61—42no—
119C4×C61C2×Q1612yes—
120C4×C61C2×#4111yescharacteristic
121C4×C61C2×#4111yescharacteristic
122Dic61—21no—
123Dic61—22no—
124Dic61—21no—
125Dic61—42no—
126Dic61—41no—
127Dic61C2×Q1612yes—
128#3104—611nomaximal, Sylow
129C2×C61#52511yescharacteristic
130C2×C61C22×Q1611yescharacteristic
131C2×C61#57511yescharacteristic
132D61—22no—
133#533—611no—
134C2×C4×Q8—611no—
135#484—612no—
136#477—611no—
137#477D6111yescharacteristic, complemented
138#462—611no—
139#462—611no—
140#451—612no—
141C4×Q16—612no—
142C4×Q16—612no—
143#431—611no—
144C61#310411yescharacteristic, complemented, Sylow
145C22×Q8—611no—
146C2×Q16—612no—
147C2×Q16—612no—
148C4⋊Q8—611no—
149C4⋊Q8C2×D6111yescharacteristic
150#125—1221no—
151C22⋊Q8—612no—
152C22⋊Q8—1221no—
153C4×Q8—611no—
154C4×Q8—611no—
155C4×Q8—612no—
156C4×Q8—611no—
157C4×Q8—1221no—
158C4×Q8—1221no—
159C4×Q8—1221no—
160C4×Q8C2×D6111yescharacteristic
161#117—1221no—
162C2×C4⋊C4—611no—
163C2×C4⋊C4—1221no—
164C2×C42—611no—
165C2×C42—1221no—
166#107—612no—
167#107C2×D6112yes—
168C4⋊C8—611no—
169C4⋊C8C2×D6111yescharacteristic
170#103—612no—
171#103—612no—
172#103—612no—
173#103C2×D6112yes—
174C22⋊C8—612no—
175C4×C8—612no—
176C2×Q8—21no—
177C2×Q8—611no—
178C2×Q8—612no—
179C2×Q8—1221no—
180C2×Q8—1222no—
181C2×Q8—1222no—
182C2×Q8C22×D6111yescharacteristic
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—1221no—
187C22×C4—1221no—
188Q16—1224no—
189Q16—1224no—
190C2×C8—612no—
191C2×C8C22×D6112yes—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—611no—
195C4⋊C4—1221no—
196C4⋊C4—1221no—
197C4⋊C4—1221no—
198C4⋊C4—1222no—
199C4⋊C4—1222no—
200C4⋊C4—1221no—
201C4⋊C4—1221no—
202C4⋊C4—1221no—
203C4⋊C4C22×D6111yescharacteristic
204C4⋊C4C22×D6112yes—
205C22⋊C4—1222no—
206C42—21no—
207C42—611no—
208C42—611no—
209C42—611no—
210C42—1221no—
211C42—1221no—
212C42—1222no—
213C42—1221no—
214C42C22×D6111yescharacteristic
215C23—611no—
216Q8—21no—
217Q8—42no—
218Q8—612no—
219Q8—1224no—
220Q8—1221no—
221Q8—1222no—
222Q8—1222no—
223Q8#1175822612yes—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—611no—
228C2×C4—614no—
229C2×C4—611no—
230C2×C4—611no—
231C2×C4—1224no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—1222no—
237C2×C4—2441no—
238C2×C4—2442no—
239C2×C4D4×D6111yescharacteristic
240C2×C4D4×D6111yescharacteristic
241C2×C4C23×D6111yescharacteristic
242C8—22no—
243C8—1222no—
244C22—612no—
245C22—1221no—
246C22—1221no—
247C22C2×D4×D6111yescharacteristic
248C4—22no—
249C4—21no—
250C4—41no—
251C4—42no—
252C4—612no—
253C4—1221no—
254C4—1222no—
255C4—1221no—
256C4—2442no—
257C4—2441no—
258C4Q16×D6112yes—
259C4#41×D6111yescharacteristic
260C4C2×#1175822611yescharacteristic
261C2—1222no—
262C2#1684027511yescharacteristic
263C2C2×Q16×D6111yescharacteristic
264C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#477C2
socleC22×C61C22×D4
hypercenter#477D61
hypocenterC61#3104
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
4. #16840054C2semidirect
5. #16839973C2semidirect
6. #16839972C2semidirect
8. #16839856C2semidirect
9. #16839854C2semidirect
11. C61×#477C2semidirect
103. C4×D61Q16semidirect
137. #477D61semidirect
144. C61#3104semidirect