Finite Group Databasebeta

← #21457042

Subgroups — #21457042

Order 7808.

362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#14519777C211yesmaximal, characteristic, complemented
2#16840296C211yesmaximal, characteristic
3#16840171C212yesmaximal, complemented
4#16840122C212yesmaximal, complemented
5#16840093C212yesmaximal, complemented
6#16840076C212yesmaximal
7#16840058C212yesmaximal, complemented
8#16840053C212yesmaximal, complemented
9C61×#432C211yesmaximal, characteristic, complemented
10C22×Dic122—21no—
11#14519777—21no—
12#14519777—21no—
13#14519777C2212yes—
14#14519777C2212yes—
15#14519771—21no—
16#14519769C2211yescharacteristic
17#14519765C2211yescharacteristic
18#14519760—21no—
19#14519756C2211yescharacteristic
20#14519751C2211yescharacteristic
21C4×Dic122C2211yescharacteristic
22C4×D244C2211yescharacteristic
23C4×C22⋊D61—21no—
24#14519734—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2212yes—
27#14519711C2214yes—
28#14519709C2214yes—
29#14519702C2214yes—
30#14519699C2214yes—
31C2×C42×C61C2211yescharacteristic
32C4⋊C8×C61C2212yes—
33C22⋊C8×C61C2212yes—
34#97×C61C2212yes—
35C22×C4×C61D411yescharacteristic
36C22×C4×C61D411yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—21no—
39C22×Dic61—22no—
40C2×D244C2311yescharacteristic
41C2×C4×D61—21no—
42C2×Dic122—22no—
43C2×Dic122—22no—
44C2×Dic122—44no—
45C2×Dic122C2311yescharacteristic
46C2×C8×C61C2314yes—
47C42×C61D411yescharacteristic
48C42×C61D411yescharacteristic
49C42×C61C2311yescharacteristic
50C42×C61C2311yescharacteristic
51C22⋊Dic61—21no—
52#11758198—21no—
53#11758198—21no—
54#11758198—21no—
55#11758198—21no—
56C4⋊Dic61—22no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61C2314yes—
60C4⋊Dic61C2311yescharacteristic
61C4⋊Dic61C2311yescharacteristic
62#11758196—21no—
63#11758196—21no—
64#11758196—21no—
65#11758196—21no—
66C4×Dic61—21no—
67C23×C61C2×D411yescharacteristic
68C22×D61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2411yescharacteristic
78C22⋊D61—42no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—24no—
83C2×Dic61—44no—
84D244—22no—
85C4×D61—42no—
86Dic122—22no—
87Dic122—44no—
88Dic122—44no—
89C8×C61—24no—
90C22×C61—21no—
91C22×C61—21no—
92C22×C61AGL(1,ℤ/8)12yes—
93C22×C61C22×D411yescharacteristic
94C2×D61—41no—
95C2×D61—41no—
96C2×D61—41no—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61#13712yes—
102C4×C612−1+412yes—
103Dic61—41no—
104Dic61—44no—
105Dic61—41no—
106Dic61—41no—
107#3238—611nomaximal, Sylow
108C2×C61—22no—
109C2×C61#53611yescharacteristic
110C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C61C2×#13711yescharacteristic
112D61—81no—
113C2×C4⋊Q8—611no—
114#529—611no—
115#501—612no—
116#489—612no—
117#483—612no—
118#480—612no—
119#477—612no—
120#476—612no—
121#432D6111yescharacteristic, complemented
122C61#323811yescharacteristic, complemented, Sylow
123C22×Q8—1221no—
124C4⋊Q8—612no—
125C4⋊Q8—612no—
126C4⋊Q8—1221no—
127C4⋊Q8—1221no—
128#126—1221no—
129#125—611no—
130#124—611no—
131#123—1221no—
132C22⋊Q8—611no—
133#121—611no—
134C4×Q8—611no—
135C4×D4—611no—
136C4×D4—1221no—
137#117—1221no—
138C2×C4⋊C4—612no—
139C2×C4⋊C4—1221no—
140C2×C42C2×D6111yescharacteristic
141#107—614no—
142#106—614no—
143C4⋊C8C2×D6112yes—
144#103—614no—
145#102—614no—
146C22⋊C8C2×D6112yes—
147#97C2×D6112yes—
148C2×Q8—611no—
149C2×Q8—1222no—
150C2×Q8—1222no—
151C2×Q8—2444no—
152C2×D4—611no—
153C2×D4—1221no—
154C22×C4—1222no—
155C22×C4—1221no—
156C22×C4D24411yescharacteristic
157C22×C4D24411yescharacteristic
158C22×C4C22×D6111yescharacteristic
159C2×C8C22×D6114yes—
160C4⋊C4—614no—
161C4⋊C4—611no—
162C4⋊C4—611no—
163C4⋊C4—1222no—
164C4⋊C4—1222no—
165C4⋊C4—1222no—
166C4⋊C4—1221no—
167C4⋊C4—1221no—
168C4⋊C4—1221no—
169C4⋊C4—1221no—
170C22⋊C4—1221no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C22⋊C4—1221no—
174C22⋊C4—1221no—
175C42—1221no—
176C42D24411yescharacteristic
177C42D24411yescharacteristic
178C42C22×D6111yescharacteristic
179C42C22×D6111yescharacteristic
180C23—1221no—
181C23C2×D24411yescharacteristic
182Q8—1222no—
183Q8—2444no—
184Q8—2444no—
185D4—1222no—
186D4—2442no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1224no—
194C2×C4—2444no—
195C2×C4—2442no—
196C2×C4C2×D24411yescharacteristic
197C2×C4C2×D24411yescharacteristic
198C2×C4C2×D24411yescharacteristic
199C2×C4C2×D24411yescharacteristic
200C2×C4C2×D24411yescharacteristic
201C2×C4C23×D6111yescharacteristic
202C8—24no—
203C22—21no—
204C22—21no—
205C22—2441no—
206C22—2441no—
207C22—2441no—
208C22#1451980512yes—
209C22C22×D24411yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—2444no—
215C4—2441no—
216C4—2441no—
217C4—2441no—
218C4#1451981012yes—
219C4#1451982412yes—
220C2—22no—
221C2—4881no—
222C2#1684033811yescharacteristic
223C2C2×#1451980511yescharacteristic
224C2C2×#1451981011yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#432C2
socleC22×C61C22×D4
hypercenter#432D61
hypocenterC61#3238
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. C2×#14519777C2semidirect
3. #16840171C2semidirect
4. #16840122C2semidirect
5. #16840093C2semidirect
7. #16840058C2semidirect
8. #16840053C2semidirect
9. C61×#432C2semidirect
121. #432D61semidirect
122. C61#3238semidirect