Finite Group Databasebeta

← #21444286

Subgroups — #21444286

Order 7808.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#16840309C211yesmaximal, characteristic
2#16839818C211yesmaximal, characteristic, complemented
3#16839813C211yesmaximal, characteristic, complemented
4#16839491C211yesmaximal, characteristic, complemented
5D4⋊#92418C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758222—21no—
9#14519776C411yescharacteristic
10#14519773C411yescharacteristic
11#14519763—21no—
12#14519752C411yescharacteristic
13#14519750—21no—
14#14519748C411yescharacteristic
15C4×D244C2211yescharacteristic
16C4×C22⋊D61—21no—
17C42×D61C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519706—21no—
20#14519689—21no—
21#14519689—21no—
22#14519687—21no—
23C4×#92418C2211yescharacteristic
24C4×D4×C61C2211yescharacteristic
25C4⋊C8×C61C2211yescharacteristic
26C4×C8×C61C2211yescharacteristic
27C2×D4×C61C2×C411yescharacteristic
28C22×C4×C61—21no—
29C2×C22⋊D61—21no—
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32#11758222—42no—
33#11758222—42no—
34C2×D244—21no—
35C2×D244C2×C411yescharacteristic
36C2×C4×D61—21no—
37C2×C4×D61C2×C411yescharacteristic
38C2×C4×D61D411yescharacteristic
39C2×C4×D61D411yescharacteristic
40C2×Dic122—21no—
41C2×C8×C61—21no—
42C2×C8×C61—21no—
43C4⋊C4×C61C2×C411yescharacteristic
44C22⋊C4×C61—21no—
45C42×C61C2311yescharacteristic
46C22⋊Dic61—21no—
47#11758198—21no—
48#11758198—21no—
49C4⋊Dic61C2×C411yescharacteristic
50#11758196—21no—
51C4×Dic61C2×C411yescharacteristic
52C4×Dic61D411yescharacteristic
53C4×Dic61D411yescharacteristic
54C2×#92418—21no—
55C2×#92418—21no—
56C23×C61—21no—
57C22×D61—21no—
58C22×D61C22⋊C411yescharacteristic
59D4×C61—21no—
60D4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61C22×C411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C22⋊D61—42no—
68C22⋊D61—42no—
69C22⋊D61—42no—
70C2×Dic61—21no—
71C2×Dic61C22⋊C411yescharacteristic
72C2×Dic61C22⋊C411yescharacteristic
73C2×Dic61C22⋊C411yescharacteristic
74D244—21no—
75D244—21no—
76D244—42no—
77C4×D61—21no—
78C4×D61—21no—
79C4×D61—21no—
80C4×D61—21no—
81C4×D61—41no—
82C4×D61—41no—
83C4×D61—41no—
84Dic122—42no—
85C8×C61—41no—
86C8×C61—41no—
87#92418—41no—
88#92418—41no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61C2×C22⋊C411yescharacteristic
93C2×D61—21no—
94C2×D61—21no—
95C2×D61—21no—
96C2×D61—41no—
97C2×D61—41no—
98C2×D61—41no—
99C4×C61—21no—
100C4×C61—41no—
101C4×C61#13111yescharacteristic
102C4×C61#13111yescharacteristic
103C4×C61AGL(1,ℤ/8)11yescharacteristic
104C4×C61AGL(1,ℤ/8)11yescharacteristic
105Dic61—21no—
106Dic61—21no—
107Dic61—21no—
108Dic61—41no—
109#1496—611nomaximal, Sylow
110C2×C61—81no—
111C2×C61#40811yescharacteristic
112C2×C61#41811yescharacteristic
113C2×C61#42111yescharacteristic
114D61—41no—
115D61—81no—
116#532—611no—
117#432—611no—
118#431—611no—
119D4⋊C8—611no—
120D4⋊C8—611no—
121D4⋊C8—611no—
122D4⋊C8D6111yescharacteristic, complemented
123C61#149611yescharacteristic, complemented, Sylow
124C2×#41—1221no—
125C4⋊Q8—611no—
126#127—611no—
127#124—1221no—
128#121—611no—
129#121—611no—
130#121—1221no—
131C4×D4—611no—
132C4×D4—1221no—
133C4×D4C2×D6111yescharacteristic
134C2×C42—611no—
135C4⋊C8—611no—
136C4⋊C8—1221no—
137C4⋊C8C2×D6111yescharacteristic
138C22⋊C8—1221no—
139C22⋊C8—1221no—
140#97—1221no—
141C4×C8—611no—
142C4×C8C2×D6111yescharacteristic
143#41—2442no—
144#41—2442no—
145C2×Q8—1221no—
146C2×D4—611no—
147C2×D4—1221no—
148C2×D4—1221no—
149C2×D4—1221no—
150C2×D4—1221no—
151C2×D4C4×D6111yescharacteristic
152C22×C4—21no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—1221no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—1221no—
160C2×C8—1221no—
161C4⋊C4—611no—
162C4⋊C4—1221no—
163C4⋊C4C4×D6111yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C42—611no—
169C42—611no—
170C42—611no—
171C42C22×D6111yescharacteristic
172C23—21no—
173C23—611no—
174C23—1221no—
175Q8—2442no—
176D4—21no—
177D4—21no—
178D4—1221no—
179D4—1221no—
180D4—2442no—
181D4—2442no—
182D4—2442no—
183D4—2442no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4—2441no—
198C2×C4C2×C4×D6111yescharacteristic
199C2×C4D4×D6111yescharacteristic
200C2×C4D4×D6111yescharacteristic
201C8—41no—
202C8—41no—
203C8—2441no—
204C8—2441no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—1221no—
209C22—1221no—
210C22—1221no—
211C22—2441no—
212C22—2441no—
213C22—2441no—
214C22C22⋊C4×D6111yescharacteristic
215C4—21no—
216C4—41no—
217C4—1221no—
218C4—1221no—
219C4—1221no—
220C4—2441no—
221C4#1451978311yescharacteristic
222C4#1451978511yescharacteristic
223C4#1451980111yescharacteristic
224C4#1451980411yescharacteristic
225C2—81no—
226C2—4881no—
227C2—2441no—
228C2#1683972711yescharacteristic
229C2#1683976511yescharacteristic
230C2#1683977711yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61C2×C22⋊C4
hypercenterD4⋊C8D61
hypocenterC61#1496
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #16839818C2semidirect
3. #16839813C2semidirect
4. #16839491C2semidirect
5. D4⋊#92418C2semidirect
6. #16839489C2semidirect
7. C61×D4⋊C8C2semidirect
122. D4⋊C8D61semidirect
123. C61#1496semidirect