Finite Group Databasebeta

← #21456766

Subgroups — #21456766

Order 7808.

384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840316C211yesmaximal, characteristic
2C4⋊Q8×D61C211yesmaximal, characteristic
3#16840140C212yesmaximal, complemented
4#16840111C212yesmaximal, complemented
5#16839973C211yesmaximal, characteristic, complemented
6#16839972C211yesmaximal, characteristic, complemented
7#16839969C211yesmaximal, characteristic, complemented
8#16839919C212yesmaximal
9#16839916C212yesmaximal
10#16839814C211yesmaximal, characteristic
11C61×#462C211yesmaximal, characteristic, complemented
12C2×Q8×D61C2212yes—
13C2×Dic244C2212yes—
14C2×#11758202C2212yes—
15C2×#11758202C2212yes—
16#14519777C2211yescharacteristic
17#14519776—21no—
18#14519776—21no—
19#14519776C2211yescharacteristic
20#14519775C2212yes—
21#14519775C2211yescharacteristic
22#14519767—21no—
23#14519757C2211yescharacteristic
24#14519755—21no—
25#14519753C2211yescharacteristic
26C4×Dic122—21no—
27C4×Dic122C2211yescharacteristic
28#14519734—21no—
29C4⋊C4×D61—21no—
30C4⋊C4×D61—21no—
31C42×D61C2211yescharacteristic
32C4⋊#92418C2211yescharacteristic
33#14519702C2212yes—
34#14519701C2212yes—
35#14519700C2212yes—
36#14519689C2212yes—
37C8×Dic61C2212yes—
38C2×Q16×C61C2212yes—
39C4⋊Q8×C61C2211yescharacteristic
40C4×Q8×C61C2211yescharacteristic
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61C2312yes—
44C2×Q8×C61C2311yescharacteristic
45Q8×D61—42no—
46Q8×D61—42no—
47C2×C4×D61—22no—
48C2×C4×D61D411yescharacteristic
49C2×C4×D61D411yescharacteristic
50C2×C4×D61C2311yescharacteristic
51C2×Dic122—22no—
52C2×Dic122—21no—
53C2×Dic122C2312yes—
54C2×Dic122C2311yescharacteristic
55Q16×C61—42no—
56C2×C8×C61C2312yes—
57C4⋊C4×C61—21no—
58C4⋊C4×C61—21no—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2311yescharacteristic
61C42×C61—21no—
62C42×C61C2311yescharacteristic
63#11758202—42no—
64#11758202—42no—
65#11758198—21no—
66#11758198—21no—
67C4⋊Dic61—21no—
68C4⋊Dic61—21no—
69C4⋊Dic61—21no—
70C4⋊Dic61C2311yescharacteristic
71#11758196—21no—
72#11758196—22no—
73#11758196—22no—
74#11758196—21no—
75#11758196—21no—
76#11758196—21no—
77#11758196—21no—
78C4×Dic61—21no—
79C4×Dic61D411yescharacteristic
80C4×Dic61D411yescharacteristic
81C4×Dic61C2311yescharacteristic
82C2×#92418C2312yes—
83Dic244—42no—
84C22×D61C2×D411yescharacteristic
85Q8×C61—21no—
86Q8×C61—22no—
87Q8×C61—21no—
88Q8×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—21no—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2411yescharacteristic
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—22no—
98C2×Dic61C2×D411yescharacteristic
99C2×Dic61C2×D411yescharacteristic
100C2×Dic61C2×D411yescharacteristic
101C4×D61—21no—
102C4×D61—21no—
103C4×D61—22no—
104C4×D61—44no—
105C4×D61Q1614yescomplemented
106Dic122—21no—
107Dic122—22no—
108Dic122—21no—
109Dic122—22no—
110Dic122—44no—
111Dic122—42no—
112C8×C61—22no—
113#92418—22no—
114C22×C61C22×D411yescharacteristic
115C2×D61—21no—
116C2×D61—21no—
117C2×D61C2×Q1612yes—
118C4×C61—21no—
119C4×C61—42no—
120C4×C61—41no—
121C4×C61—41no—
122C4×C61C2×Q1612yes—
123C4×C61H(5,𝔽2)11yescharacteristic
124C4×C61H(5,𝔽2)11yescharacteristic
125Dic61—21no—
126Dic61—42no—
127Dic61—41no—
128Dic61—41no—
129Dic61C2×Q1612yes—
130Dic61#13712yes—
131#3209—611nomaximal, Sylow
132C2×C61#53511yescharacteristic
133C2×C61C22×Q1611yescharacteristic
134C2×C61C2×#13711yescharacteristic
135D61—22no—
136#533—611no—
137C2×C4⋊Q8—611no—
138#494—612no—
139#487—612no—
140#462—611no—
141#462—611no—
142#462—611no—
143#462D6111yescharacteristic, complemented
144#451—612no—
145#451—612no—
146#431—611no—
147C61#320911yescharacteristic, complemented, Sylow
148C22×Q8—612no—
149C2×Q16—612no—
150C2×Q16—612no—
151C2×Q16—612no—
152C2×Q16C2×D6112yes—
153C4⋊Q8—611no—
154C4⋊Q8—612no—
155C4⋊Q8—611no—
156C4⋊Q8—611no—
157C4⋊Q8—1221no—
158C4⋊Q8—1221no—
159C4⋊Q8C2×D6111yescharacteristic
160#125—1221no—
161C22⋊Q8—611no—
162C22⋊Q8—611no—
163C22⋊Q8—1221no—
164C4×Q8—611no—
165C4×Q8—1221no—
166C4×Q8C2×D6111yescharacteristic
167#117—1221no—
168C2×C4⋊C4—1221no—
169C2×C4⋊C4—1221no—
170C2×C42—611no—
171C4⋊C8—611no—
172C4⋊C8C2×D6111yescharacteristic
173#103—612no—
174#103—612no—
175#103—612no—
176#103C2×D6112yes—
177C22⋊C8—612no—
178C4×C8—612no—
179C2×Q8—612no—
180C2×Q8—611no—
181C2×Q8—1221no—
182C2×Q8—1222no—
183C2×Q8—2442no—
184C2×Q8—2442no—
185C2×Q8C22×D6112yes—
186C2×Q8C22×D6111yescharacteristic
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—1222no—
191Q16—42no—
192Q16—2442no—
193Q16—2442no—
194Q16—2442no—
195C2×C8—612no—
196C2×C8C22×D6112yes—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—611no—
201C4⋊C4—1222no—
202C4⋊C4—1222no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4—1221no—
211C4⋊C4C22×D6111yescharacteristic
212C22⋊C4—1221no—
213C22⋊C4—1221no—
214C42—21no—
215C42—611no—
216C42—611no—
217C42—611no—
218C42—1221no—
219C42C22×D6111yescharacteristic
220C23—611no—
221Q8—21no—
222Q8—22no—
223Q8—21no—
224Q8—22no—
225Q8—1221no—
226Q8—1222no—
227Q8—1221no—
228Q8—1222no—
229Q8—2442no—
230Q8—2444no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—611no—
235C2×C4—611no—
236C2×C4—614no—
237C2×C4—611no—
238C2×C4—1222no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—1222no—
244C2×C4—2444no—
245C2×C4D4×D6111yescharacteristic
246C2×C4D4×D6111yescharacteristic
247C2×C4C23×D6111yescharacteristic
248C8—22no—
249C8—1222no—
250C22—612no—
251C22—1221no—
252C22—1221no—
253C22C2×D4×D6111yescharacteristic
254C4—21no—
255C4—41no—
256C4—42no—
257C4—41no—
258C4—612no—
259C4—612no—
260C4—1221no—
261C4—2441no—
262C4—2442no—
263C4—2441no—
264C4Q16×D6112yes—
265C4#1451982211yescharacteristic
266C4#1451982311yescharacteristic
267C2—1222no—
268C2#1684032811yescharacteristic
269C2C2×Q16×D6111yescharacteristic
270C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#462C2
socleC22×C61C22×D4
hypercenter#462D61
hypocenterC61#3209
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #16840140C2semidirect
4. #16840111C2semidirect
5. #16839973C2semidirect
6. #16839972C2semidirect
7. #16839969C2semidirect
11. C61×#462C2semidirect
105. C4×D61Q16semidirect
143. #462D61semidirect
147. C61#3209semidirect