Finite Group Databasebeta

← #21445079

Subgroups — #21445079

Order 7808.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#16840427C211yesmaximal, characteristic
2#16840044C211yesmaximal, characteristic, complemented
3#16839964C211yesmaximal, characteristic
4#16839508C211yesmaximal, characteristic, complemented
5#16839494C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic
7C61×#498C211yesmaximal, characteristic, complemented
8C2×Q8×D61—21no—
9C2×#11758201—21no—
10#14519776—21no—
11#14519755—22no—
12#14519753—21no—
13C4×Dic122C2211yescharacteristic
14C4×D244C2211yescharacteristic
15#14519739—21no—
16#14519708—21no—
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519701—21no—
20#14519700—21no—
21C4⋊Q8×C61C2211yescharacteristic
22C4⋊Q8×C61C2211yescharacteristic
23#106×C61—22no—
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27Q8×D61—42no—
28Q8×D61—42no—
29C2×D244D411yescharacteristic
30C2×C4×D61—22no—
31C2×C4×D61—21no—
32C2×Dic122—22no—
33C2×Dic122D411yescharacteristic
34C2×C8×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61D412yes—
39C42×C61C2311yescharacteristic
40#11758201—42no—
41#11758198—22no—
42#11758198—21no—
43C4⋊Dic61D411yescharacteristic
44C4⋊Dic61D411yescharacteristic
45#11758196—22no—
46#11758196—21no—
47C4×Dic61—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C22×D61—21no—
51Q8×C61—41no—
52Q8×C61—41no—
53Q8×C61—41no—
54Q8×C61—41no—
55C2×C4×C61—22no—
56C2×C4×C61—41no—
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—21no—
63D244—21no—
64D244SD1612yes—
65C4×D61—44no—
66C4×D61—41no—
67C4×D61—41no—
68Dic122—21no—
69Dic122—44no—
70Dic122SD1612yescomplemented
71C8×C61—22no—
72#92418—41no—
73#92418—41no—
74C22×C61#12011yescharacteristic
75C2×D61—22no—
76C2×D61—41no—
77C2×D61—41no—
78C4×C61—21no—
79C4×C61—42no—
80C4×C61—81no—
81C4×C61C2×SD1611yescharacteristic
82C4×C61C2×SD1611yescharacteristic
83C4×C61AGL(1,ℤ/8)11yescharacteristic
84C4×C61#13711yescharacteristic
85Dic61—22no—
86Dic61—41no—
87Dic61—41no—
88#1651—611nomaximal, Sylow
89C2×C61#44811yescharacteristic
90C2×C61#45011yescharacteristic
91C2×C61#45611yescharacteristic
92D61—42no—
93D4×Q8—611no—
94#498D6111yescharacteristic, complemented
95#475—611no—
96#461—611no—
97#332—611no—
98Q8⋊C8—611no—
99D4⋊C8—611no—
100C61#165111yescharacteristic, complemented, Sylow
101C22×Q8—1221no—
102C2×SD16—1221no—
103C4⋊Q8—1221no—
104C4⋊Q8C2×D6111yescharacteristic
105C4⋊Q8C2×D6111yescharacteristic
106C22⋊Q8—1221no—
107C22⋊Q8—1222no—
108C4×Q8—611no—
109C4×D4—611no—
110C4×D4—1221no—
111#106—22no—
112#106—1221no—
113C4⋊C8—611no—
114C4⋊C8—611no—
115#103—1221no—
116#103—1221no—
117C4×C8C2×D6111yescharacteristic
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—611no—
121C2×Q8—1222no—
122C2×Q8—2442no—
123C2×Q8—2442no—
124C2×D4—611no—
125C22×C4—1222no—
126C22×C4—1221no—
127SD16—2442no—
128C2×C8—21no—
129C2×C8—1221no—
130C2×C8—1221no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—611no—
135C4⋊C4—611no—
136C4⋊C4—1222no—
137C4⋊C4—1221no—
138C4⋊C4C22⋊D6112yes—
139C22⋊C4—1222no—
140C22⋊C4—1221no—
141C42—1221no—
142C42C22×D6111yescharacteristic
143C23—1221no—
144Q8—41no—
145Q8—41no—
146Q8—41no—
147Q8—41no—
148Q8—612no—
149Q8—1221no—
150Q8—2444no—
151D4—612no—
152D4—1221no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—1221no—
156C2×C4—1221no—
157C2×C4—1221no—
158C2×C4—2444no—
159C2×C4—2441no—
160C2×C4—2441no—
161C2×C4D4×D6111yescharacteristic
162C2×C4D4×D6111yescharacteristic
163C2×C4C2×C22⋊D6111yescharacteristic
164C8—22no—
165C8—2441no—
166C8—2441no—
167C22—1222no—
168C22—2441no—
169C22—2441no—
170C22#1451974511yescharacteristic
171C4—21no—
172C4—42no—
173C4—81no—
174C4—1222no—
175C4—2441no—
176C4—2441no—
177C4SD16×D6111yescharacteristic
178C4SD16×D6111yescharacteristic
179C4#1451980411yescharacteristic
180C4#1451980611yescharacteristic
181C2—2442no—
182C2#1683989911yescharacteristic
183C2#1683991111yescharacteristic
184C2#1683994411yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#498C2
socleC22×C61#120
hypercenter#498D61
hypocenterC61#1651
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. #16840044C2semidirect
4. #16839508C2semidirect
5. #16839494C2semidirect
7. C61×#498C2semidirect
70. Dic122SD16semidirect
94. #498D61semidirect
100. C61#1651semidirect