Finite Group Databasebeta

← #21456710

Subgroups — #21456710

Order 7808.

378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840333C211yesmaximal, characteristic
2#16840103C212yesmaximal, complemented
3#16840100C212yesmaximal, complemented
4#16840018C212yesmaximal, complemented
5#16840001C212yesmaximal, complemented
6#16839918C212yesmaximal, complemented
7#16839917C212yesmaximal, complemented
8#16839729C211yesmaximal, characteristic
9C61×#536C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×#11758202C2212yes—
12C2×#11758202C2212yes—
13C2×#11758194C2211yescharacteristic
14C22×#92418C2211yescharacteristic
15#14519775—21no—
16#14519764—21no—
17#14519758—21no—
18#14519758—21no—
19#14519756C2212yes—
20#14519756C2212yes—
21#14519736C2211yescharacteristic
22#14519710C2212yes—
23#14519708C2212yes—
24#14519701C2212yes—
25#14519701C2212yes—
26#14519700C2212yes—
27#14519700C2212yes—
28C22⋊#92418C2212yes—
29C22⋊#92418C2212yes—
30C2×#41×C61C2211yescharacteristic
31C22×Q8×C61C2211yescharacteristic
32C4⋊Q8×C61—21no—
33#124×C61—21no—
34#123×C61—21no—
35#123×C61—21no—
36C22⋊Q8×C61C2212yes—
37C22⋊Q8×C61C2212yes—
38#117×C61C2211yescharacteristic
39#41×C61—41no—
40#41×C61—41no—
41C2×Q8×C61—21no—
42C2×Q8×C61—41no—
43C2×Q8×C61—41no—
44C2×Q8×C61D411yescharacteristic
45C2×Q8×C61C2312yes—
46C2×D4×C61D411yescharacteristic
47C2×D4×C61D411yescharacteristic
48C2×D4×C61D411yescharacteristic
49C22×C4×C61—21no—
50C22×C4×C61C2311yescharacteristic
51C22×C4×C61C2311yescharacteristic
52C22×C4×C61C2311yescharacteristic
53C22×Dic61—21no—
54C2×Dic122—21no—
55C2×Dic122—41no—
56C2×Dic122—41no—
57C2×Dic122C2312yes—
58C4⋊C4×C61—22no—
59C4⋊C4×C61—22no—
60C4⋊C4×C61C2312yes—
61C22⋊C4×C61—21no—
62C22⋊C4×C61—22no—
63C22⋊C4×C61—22no—
64C42×C61—21no—
65C22⋊Dic61—21no—
66C22⋊Dic61—22no—
67C22⋊Dic61—22no—
68#11758202—42no—
69#11758202—42no—
70C4⋊Dic61C2312yes—
71#11758196—22no—
72#11758196—22no—
73C4×Dic61—21no—
74#11758194—41no—
75C2×#92418—41no—
76C2×#92418C2312yes—
77C2×#92418C2312yes—
78C23×C61C2×D411yescharacteristic
79C23×C61C2×D411yescharacteristic
80C23×C61C2×D411yescharacteristic
81Q8×C61—22no—
82Q8×C61—22no—
83Q8×C61—41no—
84Q8×C61—42no—
85D4×C61—41no—
86D4×C61—41no—
87D4×C61—41no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—42no—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2411yescharacteristic
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—42no—
104Dic122—22no—
105Dic122—22no—
106Dic122—42no—
107#92418—22no—
108#92418—22no—
109C22×C61—21no—
110C22×C61—21no—
111C22×C61—21no—
112C22×C61—22no—
113C22×C61—22no—
114C22×C61—22no—
115C22×C61C22×D411yescharacteristic
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61—42no—
120C4×C61—42no—
121C4×C61H(5,𝔽2)11yescharacteristic
122C4×C61H(5,𝔽2)11yescharacteristic
123Dic61—42no—
124Dic61—42no—
125#3202—611nomaximal, Sylow
126C2×C61—41no—
127C2×C61—41no—
128C2×C61—41no—
129C2×C61#53411yescharacteristic
130C2×C61#57812yes—
131#536—611no—
132#536D6111yescharacteristic
133#485—612no—
134#485—612no—
135#470—612no—
136#467—612no—
137#451—612no—
138#451—612no—
139#408—611no—
140C61#320211yescharacteristic, complemented, Sylow
141C2×#41C2×D6111yescharacteristic
142C22×Q8—611no—
143C22×Q8C2×D6111yescharacteristic
144C2×Q16—612no—
145C2×Q16—612no—
146C2×M16—611no—
147C22×C8—611no—
148C4⋊Q8—21no—
149C4⋊Q8—1221no—
150#124—21no—
151#124—1221no—
152#123—21no—
153#123—21no—
154#123—1221no—
155#123—1221no—
156C22⋊Q8—612no—
157C22⋊Q8—612no—
158C22⋊Q8C2×D6112yes—
159C22⋊Q8C2×D6112yes—
160#117—611no—
161#117C2×D6111yescharacteristic
162#107—612no—
163#106—612no—
164#103—612no—
165#103—612no—
166#103—612no—
167#103—612no—
168C22⋊C8—612no—
169C22⋊C8—612no—
170#41—41no—
171#41—41no—
172C2×Q8—21no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—612no—
176C2×Q8—1221no—
177C2×Q8—2441no—
178C2×Q8—2441no—
179C2×Q8C22⋊D6111yescharacteristic
180C2×Q8C22×D6112yes—
181C2×D4C22⋊D6111yescharacteristic
182C2×D4C22⋊D6111yescharacteristic
183C2×D4C22⋊D6111yescharacteristic
184C22×C4—21no—
185C22×C4—1221no—
186C22×C4C22×D6111yescharacteristic
187C22×C4C22×D6111yescharacteristic
188C22×C4C22×D6111yescharacteristic
189Q16—2442no—
190Q16—2442no—
191M16—2441no—
192C2×C8—612no—
193C2×C8—612no—
194C2×C8—2441no—
195C4⋊C4—22no—
196C4⋊C4—22no—
197C4⋊C4—612no—
198C4⋊C4—1222no—
199C4⋊C4—1222no—
200C4⋊C4C22×D6112yes—
201C22⋊C4—21no—
202C22⋊C4—22no—
203C22⋊C4—22no—
204C22⋊C4—1221no—
205C22⋊C4—1222no—
206C22⋊C4—1222no—
207C42—21no—
208C42—1221no—
209C23C2×C22⋊D6111yescharacteristic
210C23C2×C22⋊D6111yescharacteristic
211C23C2×C22⋊D6111yescharacteristic
212Q8—22no—
213Q8—22no—
214Q8—41no—
215Q8—42no—
216Q8—1222no—
217Q8—1222no—
218Q8—2442no—
219D4—41no—
220D4—41no—
221D4—41no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—42no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—2442no—
234C2×C4C2×C22⋊D6111yescharacteristic
235C2×C4C2×C22⋊D6111yescharacteristic
236C2×C4C2×C22⋊D6111yescharacteristic
237C2×C4C23×D6111yescharacteristic
238C8—1222no—
239C8—1222no—
240C22—21no—
241C22—21no—
242C22—21no—
243C22—22no—
244C22—22no—
245C22—22no—
246C22C22×C22⋊D6111yescharacteristic
247C4—21no—
248C4—21no—
249C4—21no—
250C4—42no—
251C4—42no—
252C4—2442no—
253C4—2442no—
254C4#1451982211yescharacteristic
255C4#1451982211yescharacteristic
256C2—41no—
257C2—41no—
258C2—41no—
259C2#1684032111yescharacteristic
260C2#1684057712yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#536C2
socleC22×C61C22×D4
hypercenter#536D61
hypocenterC61#3202
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #16840103C2semidirect
3. #16840100C2semidirect
4. #16840018C2semidirect
5. #16840001C2semidirect
6. #16839918C2semidirect
7. #16839917C2semidirect
140. C61#3202semidirect