Finite Group Databasebeta

← #21456711

Subgroups — #21456711

Order 7808.

378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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#16840335C212yesmaximal
2#16840106C212yesmaximal, complemented
3#16840101C212yesmaximal, complemented
4#16840020C211yesmaximal, characteristic, complemented
5#16840001C212yesmaximal, complemented
6#16839919C212yesmaximal, complemented
7#16839916C212yesmaximal, complemented
8#16839730C211yesmaximal, characteristic
9C61×#470C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11C2×Q8×D61C2212yes—
12C2×Dic244C2211yescharacteristic
13C2×#11758202C2212yes—
14C22×#92418C2211yescharacteristic
15#14519776—22no—
16#14519763—22no—
17#14519762—22no—
18#14519759—22no—
19#14519757C2212yes—
20#14519756C2212yes—
21#14519753C2212yes—
22#14519735C2212yes—
23#14519710C2212yes—
24#14519709C2211yescharacteristic
25#14519702C2212yes—
26#14519701C2212yes—
27#14519700C2212yes—
28#14519689C2212yes—
29#14519689C2212yes—
30C2×Q16×C61C2211yescharacteristic
31C2×M16×C61C2211yescharacteristic
32C22⋊Q8×C61C2212yes—
33#106×C61C2211yescharacteristic
34#103×C61C2212yes—
35C2×Q8×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61D412yes—
38Q8×D61—42no—
39Q8×D61—42no—
40#11758222—41no—
41#11758222—41no—
42C2×D244D411yescharacteristic
43C2×C4×D61—22no—
44C2×C4×D61C2312yes—
45C2×Dic122—22no—
46C2×Dic122D411yescharacteristic
47C2×Dic122C2312yes—
48Q16×C61—41no—
49M16×C61—41no—
50C2×C8×C61C2311yescharacteristic
51C2×C8×C61C2311yescharacteristic
52C4⋊C4×C61—22no—
53C4⋊C4×C61C2312yes—
54C22⋊C4×C61—22no—
55C22⋊Dic61—22no—
56#11758202—42no—
57#11758198—22no—
58#11758198—22no—
59#11758198—22no—
60C4⋊Dic61—22no—
61C4⋊Dic61C2312yes—
62#11758196—22no—
63#11758196—22no—
64C4×Dic61—22no—
65C2×#92418—41no—
66C2×#92418C2312yes—
67Dic244—41no—
68C23×C61C2×D411yescharacteristic
69C22×D61C2×D412yes—
70Q8×C61—22no—
71Q8×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2411yescharacteristic
78C22⋊D61—42no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61C2×D412yes—
82D244—41no—
83C4×D61—22no—
84C4×D61—22no—
85C4×D61—44no—
86Dic122—22no—
87Dic122—22no—
88Dic122—41no—
89Dic122—44no—
90C8×C61—21no—
91C8×C61—21no—
92#92418—22no—
93C22×C61—21no—
94C22×C61—22no—
95C22×C61C22×D411yescharacteristic
96C2×D61—22no—
97C2×D61—24no—
98C4×C61—21no—
99C4×C61—42no—
100C4×C61—42no—
101C4×C61H(5,𝔽2)11yescharacteristic
102C4×C61H(5,𝔽2)11yescharacteristic
103Dic61—22no—
104Dic61—42no—
105Dic61—42no—
106#3202—611nomaximal, Sylow
107C2×C61—41no—
108C2×C61#53411yescharacteristic
109C2×C61#57812yes—
110D61—42no—
111#536—612no—
112#485—612no—
113#485—612no—
114#470—611no—
115#470D6111yescharacteristic, complemented
116#467—612no—
117#451—612no—
118#451—612no—
119#408—611no—
120C61#320211yescharacteristic, complemented, Sylow
121C2×#41—611no—
122C22×Q8—612no—
123C2×Q16—612no—
124C2×Q16—611no—
125C2×Q16C2×D6111yescharacteristic
126C2×M16C2×D6111yescharacteristic
127C22×C8—611no—
128C4⋊Q8—1222no—
129#124—1222no—
130#123—1222no—
131#123—1222no—
132C22⋊Q8—612no—
133C22⋊Q8—612no—
134C22⋊Q8—612no—
135C22⋊Q8C2×D6112yes—
136#117—612no—
137#107—612no—
138#106—611no—
139#106C2×D6111yescharacteristic
140#103—612no—
141#103—612no—
142#103—612no—
143#103C2×D6112yes—
144C22⋊C8—612no—
145C22⋊C8—612no—
146#41—2441no—
147#41—2441no—
148C2×Q8—611no—
149C2×Q8—612no—
150C2×Q8—1222no—
151C2×Q8—2442no—
152C2×Q8—2442no—
153C2×Q8C22×D6112yes—
154C2×D4—612no—
155C2×D4—611no—
156C22×C4—612no—
157C22×C4—1222no—
158C22×C4C22×D6111yescharacteristic
159Q16—41no—
160Q16—2441no—
161Q16—2442no—
162M16—41no—
163C2×C8—612no—
164C2×C8—2441no—
165C2×C8C22×D6111yescharacteristic
166C2×C8C22×D6111yescharacteristic
167C4⋊C4—22no—
168C4⋊C4—612no—
169C4⋊C4—1222no—
170C4⋊C4—1222no—
171C4⋊C4—1222no—
172C4⋊C4C22×D6112yes—
173C22⋊C4—22no—
174C22⋊C4—1222no—
175C22⋊C4—1222no—
176C22⋊C4—1222no—
177C22⋊C4—1222no—
178C42—1222no—
179C23—612no—
180C23D4×D6111yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—1222no—
184Q8—1222no—
185Q8—2441no—
186Q8—2444no—
187D4—2441no—
188D4—2442no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—612no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—2444no—
199C2×C4D4×D6111yescharacteristic
200C2×C4C23×D6111yescharacteristic
201C8—21no—
202C8—21no—
203C8—1222no—
204C22—21no—
205C22—22no—
206C22—1222no—
207C22—1224no—
208C22C2×D4×D6111yescharacteristic
209C4—21no—
210C4—42no—
211C4—42no—
212C4—1222no—
213C4—2442no—
214C4—2442no—
215C4#1451982211yescharacteristic
216C4#1451982311yescharacteristic
217C2—41no—
218C2—2442no—
219C2#1684032011yescharacteristic
220C2#1684057812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#470C2
socleC22×C61C22×D4
hypercenter#470D61
hypocenterC61#3202
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #16840106C2semidirect
3. #16840101C2semidirect
4. #16840020C2semidirect
5. #16840001C2semidirect
6. #16839919C2semidirect
7. #16839916C2semidirect
9. C61×#470C2semidirect
115. #470D61semidirect
120. C61#3202semidirect