Finite Group Databasebeta

← #21456765

Subgroups — #21456765

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#16840314C211yesmaximal, characteristic
2C2×#14519775C211yesmaximal, characteristic
3#16840140C212yesmaximal, complemented
4#16840111C212yesmaximal, complemented
5#16839971C212yesmaximal, complemented
6#16839970C212yesmaximal, complemented
7#16839920C211yesmaximal, characteristic
8#16839918C211yesmaximal, characteristic
9#16839917C211yesmaximal, characteristic
10#16839812C211yesmaximal, characteristic
11C61×#451C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13C2×Dic244C2212yes—
14C2×#11758202C2212yes—
15C2×#11758202C2212yes—
16#14519776C2211yescharacteristic
17#14519775—21no—
18#14519775—21no—
19#14519775C2212yes—
20#14519775C2212yes—
21#14519775C2211yescharacteristic
22#14519767—21no—
23#14519756C2211yescharacteristic
24#14519754—21no—
25Q8×Dic61C2211yescharacteristic
26#14519742—21no—
27#14519742C2211yescharacteristic
28#14519733—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×C4×Dic61C2211yescharacteristic
32#14519706C2212yes—
33#14519702C2212yes—
34#14519701C2212yes—
35#14519700C2212yes—
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yes—
38C22×Q8×C61C2211yescharacteristic
39C2×Q16×C61C2212yes—
40C22⋊Q8×C61C2211yescharacteristic
41#103×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44C2×Q8×C61—42no—
45C2×Q8×C61C2312yes—
46C2×Q8×C61C2311yescharacteristic
47C22×C4×C61—21no—
48C22×C4×C61C2311yescharacteristic
49C22×Dic61—21no—
50C22×Dic61D411yescharacteristic
51C22×Dic61D411yescharacteristic
52C2×Dic122—21no—
53C2×Dic122—21no—
54C2×Dic122—42no—
55C2×Dic122C2312yes—
56C2×Dic122C2311yescharacteristic
57Q16×C61—42no—
58C2×C8×C61C2312yes—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2311yescharacteristic
61C22⋊C4×C61—21no—
62C22⋊Dic61—21no—
63#11758202—42no—
64#11758202—42no—
65C4⋊Dic61—21no—
66C4⋊Dic61C2311yescharacteristic
67#11758196—21no—
68#11758196—22no—
69#11758196—22no—
70#11758196—22no—
71#11758196—22no—
72#11758196—21no—
73#11758196—21no—
74#11758196—21no—
75#11758196—21no—
76C4×Dic61—21no—
77C4×Dic61—21no—
78C4×Dic61D411yescharacteristic
79C4×Dic61D411yescharacteristic
80C4×Dic61C2311yescharacteristic
81C4×Dic61C2311yescharacteristic
82C2×#92418C2312yes—
83Dic244—42no—
84C23×C61C2×D411yescharacteristic
85Q8×C61—22no—
86Q8×C61—22no—
87Q8×C61—22no—
88Q8×C61—42no—
89C2×C4×C61—22no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—42no—
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2411yescharacteristic
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—22no—
100C2×Dic61—42no—
101C2×Dic61Q1614yescomplemented
102C2×Dic61C2×D411yescharacteristic
103C2×Dic61C2×D411yescharacteristic
104C2×Dic61C2×D411yescharacteristic
105C2×Dic61C2×D411yescharacteristic
106Dic122—22no—
107Dic122—22no—
108Dic122—22no—
109Dic122—42no—
110Dic122—42no—
111C8×C61—22no—
112#92418—22no—
113C22×C61—21no—
114C22×C61—21no—
115C22×C61C2×Q1612yes—
116C22×C61C22×D411yescharacteristic
117C4×C61—21no—
118C4×C61—42no—
119C4×C61—41no—
120C4×C61—41no—
121C4×C61H(5,𝔽2)12yes—
122Dic61—21no—
123Dic61—42no—
124Dic61—41no—
125Dic61—41no—
126Dic61C2×Q1612yes—
127Dic61C2×Q1612yes—
128Dic61#13712yes—
129#3209—611nomaximal, Sylow
130C2×C61—22no—
131C2×C61#53511yescharacteristic
132C2×C61C22×Q1611yescharacteristic
133C2×C61C2×#13711yescharacteristic
134#533—611no—
135C2×C4⋊Q8—611no—
136#494—612no—
137#487—612no—
138#462—612no—
139#462—612no—
140#451—611no—
141#451—611no—
142#451—611no—
143#451D6111yescharacteristic
144#431—611no—
145C61#320911yescharacteristic, complemented, Sylow
146C22×Q8—611no—
147C22×Q8C2×D6111yescharacteristic
148C2×Q16—612no—
149C2×Q16—612no—
150C2×Q16—612no—
151C2×Q16C2×D6112yes—
152C4⋊Q8—611no—
153C4⋊Q8—612no—
154C4⋊Q8—612no—
155C4⋊Q8—611no—
156C4⋊Q8—1221no—
157C4⋊Q8—1221no—
158#125—1221no—
159C22⋊Q8—611no—
160C22⋊Q8—1221no—
161C22⋊Q8C2×D6111yescharacteristic
162C4×Q8—611no—
163C4×Q8—611no—
164C4×Q8—1221no—
165#117—1221no—
166C2×C4⋊C4—1221no—
167C2×C4⋊C4—1221no—
168C2×C42—611no—
169C4⋊C8—612no—
170#103—612no—
171#103—612no—
172#103—612no—
173#103C2×D6112yes—
174C22⋊C8—611no—
175C22⋊C8C2×D6111yescharacteristic
176C4×C8—612no—
177C2×Q8—21no—
178C2×Q8—42no—
179C2×Q8—612no—
180C2×Q8—611no—
181C2×Q8—1221no—
182C2×Q8—1221no—
183C2×Q8—2442no—
184C2×Q8C22×D6112yes—
185C2×Q8C22×D6111yescharacteristic
186C22×C4—21no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—1221no—
190C22×C4C22×D6111yescharacteristic
191Q16—42no—
192Q16—2442no—
193Q16—2442no—
194Q16—2442no—
195C2×C8—612no—
196C2×C8C22×D6112yes—
197C4⋊C4—21no—
198C4⋊C4—611no—
199C4⋊C4—1222no—
200C4⋊C4—1222no—
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⋊C4C22×D6111yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—1221no—
212C42—611no—
213C42—611no—
214C42—611no—
215C42—611no—
216C42—1221no—
217C42—1221no—
218C23D4×D6111yescharacteristic
219Q8—22no—
220Q8—22no—
221Q8—22no—
222Q8—42no—
223Q8—1222no—
224Q8—1222no—
225Q8—1222no—
226Q8—2442no—
227Q8—2442no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—42no—
233C2×C4—611no—
234C2×C4—611no—
235C2×C4—611no—
236C2×C4—614no—
237C2×C4—611no—
238C2×C4—1222no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1222no—
242C2×C4—2442no—
243C2×C4D4×D6111yescharacteristic
244C2×C4C23×D6111yescharacteristic
245C8—22no—
246C8—1222no—
247C22—21no—
248C22—21no—
249C22Q16×D6112yes—
250C22C2×D4×D6111yescharacteristic
251C4—21no—
252C4—41no—
253C4—42no—
254C4—41no—
255C4—612no—
256C4—612no—
257C4—612no—
258C4—1221no—
259C4—2441no—
260C4—2442no—
261C4—2441no—
262C4#1451982212yes—
263C2—22no—
264C2#1684032711yescharacteristic
265C2C2×Q16×D6111yescharacteristic
266C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#451C2
socleC22×C61C22×D4
hypercenter#451D61
hypocenterC61#3209
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #16840140C2semidirect
4. #16840111C2semidirect
5. #16839971C2semidirect
6. #16839970C2semidirect
101. C2×Dic61Q16semidirect
145. C61#3209semidirect