Finite Group Databasebeta

← #21445057

Subgroups — #21445057

Order 7808.

240 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 55 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#16840417C211yesmaximal, characteristic
2#16840167C211yesmaximal, characteristic, complemented
3#16840042C211yesmaximal, characteristic, complemented
4#16839968C211yesmaximal, characteristic, complemented
5#16839509C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758222—21no—
9C2×#11758190—21no—
10#14519777C2211yescharacteristic
11#14519777C2211yescharacteristic
12#14519759—22no—
13#14519756—21no—
14#14519748—21no—
15C4×D244C2211yescharacteristic
16C4⋊C4×D61—21no—
17#14519711—22no—
18#14519710—21no—
19C4⋊#92418C2211yescharacteristic
20#14519702—21no—
21#14519698—21no—
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×D4×C61D411yescharacteristic
26C22×C4×C61—21no—
27C2×C22⋊D61—22no—
28#11758222—42no—
29#11758222—42no—
30C2×D244D411yescharacteristic
31C2×C4×D61—22no—
32C2×C4×D61—21no—
33C2×Dic122—21no—
34C2×Dic122—21no—
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C4⋊C4×C61D411yescharacteristic
38C22⋊C4×C61—21no—
39C42×C61C2311yescharacteristic
40C22⋊Dic61—22no—
41#11758198—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61D411yescharacteristic
46C4⋊Dic61D412yes—
47#11758196—22no—
48C2×#92418—21no—
49#11758190—42no—
50C23×C61—21no—
51C22×D61—21no—
52D4×C61—21no—
53D4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C22⋊D61—44no—
61C2×Dic61—21no—
62C2×Dic61—22no—
63C2×Dic61—41no—
64D244—21no—
65D244D812yes—
66C4×D61—44no—
67C4×D61—41no—
68C4×D61—41no—
69Dic122—41no—
70Dic122—41no—
71Dic122—41no—
72Dic122—41no—
73C8×C61—22no—
74C8×C61—41no—
75#92418—41no—
76C22×C61—41no—
77C22×C61—41no—
78C22×C61—41no—
79C22×C61#12011yescharacteristic
80C2×D61—22no—
81C2×D61—41no—
82C2×D61—41no—
83C4×C61—21no—
84C4×C61—41no—
85C4×C61C2×D811yescharacteristic
86C4×C61#13511yescharacteristic
87C4×C61AGL(1,ℤ/8)11yescharacteristic
88C4×C61#13711yescharacteristic
89Dic61—42no—
90Dic61—41no—
91Dic61—81no—
92#1647—611nomaximal, Sylow
93C2×C61—81no—
94C2×C61#44711yescharacteristic
95C2×C61#45211yescharacteristic
96C2×C61#45611yescharacteristic
97D61—42no—
98#547—611no—
99#500—611no—
100#474—611no—
101#461—611no—
102#332—611no—
103D4⋊C8—611no—
104D4⋊C8D6111yescharacteristic, complemented
105C61#164711yescharacteristic, complemented, Sylow
106C2×#41—1221no—
107C2×SD16—1221no—
108C4⋊Q8—611no—
109C4⋊Q8—611no—
110#123—1222no—
111C22⋊Q8—1221no—
112#121—1221no—
113C4×D4—611no—
114C4×D4C2×D6111yescharacteristic
115C2×C4⋊C4—1221no—
116#107—1222no—
117#107—1221no—
118C4⋊C8—611no—
119C4⋊C8C2×D6111yescharacteristic
120#103—1221no—
121#102—1221no—
122C4×C8C2×D6111yescharacteristic
123#41—2442no—
124#41—2442no—
125C2×Q8—1221no—
126C2×Q8—1221no—
127C2×D4—611no—
128C2×D4—1222no—
129C2×D4D24411yescharacteristic
130C22×C4—21no—
131C22×C4—1222no—
132C22×C4—1221no—
133SD16—2442no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1221no—
137C4⋊C4—611no—
138C4⋊C4—612no—
139C4⋊C4—1222no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C4⋊C4D24411yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—1222no—
146C22⋊C4—1221no—
147C42C22×D6111yescharacteristic
148C23—21no—
149C23—1221no—
150Q8—2441no—
151Q8—2441no—
152Q8—2441no—
153Q8—2441no—
154D4—21no—
155D4—21no—
156D4—612no—
157D4—1221no—
158D4—2444no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—1221no—
163C2×C4—1222no—
164C2×C4—2444no—
165C2×C4—2441no—
166C2×C4—2441no—
167C2×C4—2441no—
168C2×C4C2×D24411yescharacteristic
169C2×C4D4×D6111yescharacteristic
170C2×C4D4×D6111yescharacteristic
171C8—22no—
172C8—41no—
173C8—2441no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22—1222no—
178C22—2441no—
179C22—2441no—
180C22#1451974711yescharacteristic
181C4—21no—
182C4—41no—
183C4—4881no—
184C4—2442no—
185C4—2441no—
186C4D8×D6111yescharacteristic
187C4#1451979911yescharacteristic
188C4#1451980411yescharacteristic
189C4#1451981011yescharacteristic
190C2—81no—
191C2—2442no—
192C2#1683989711yescharacteristic
193C2#1683992611yescharacteristic
194C2#1683994611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61#120
hypercenterD4⋊C8D61
hypocenterC61#1647
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #16840167C2semidirect
3. #16840042C2semidirect
4. #16839968C2semidirect
5. #16839509C2semidirect
6. #16839491C2semidirect
7. C61×D4⋊C8C2semidirect
104. D4⋊C8D61semidirect
105. C61#1647semidirect