Finite Group Databasebeta

← #21461774

Subgroups — #21461774

Order 7808.

324 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 68 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#16840829C211yesmaximal, characteristic
2#16840773C212yesmaximal, complemented
3#16840714C211yesmaximal, characteristic
4#16840634C212yesmaximal, complemented
5#100×D61C211yesmaximal, characteristic
6D4×#6923—22no—
7D4×#6923—22no—
8#14519856C2212yes—
9C2×C4⋊#6923C2211yescharacteristic
10C2×C22⋊#6923—22no—
11C2×C22⋊#6923—22no—
12C2×C4×#6923C2211yescharacteristic
13#14519846—22no—
14#14519845—22no—
15C2×D4×D61C2211yescharacteristic
16M16×D61C2212yes—
17#14519694C411yescharacteristic, complemented
18#14519693C412yescomplemented
19#100×C61C411yescharacteristic, complemented
20C23×D61D412yes—
21C22×#6923—21no—
22C22×#6923—22no—
23C22×#6923—22no—
24C22×#6923—21no—
25C2×D4×C61C2×C411yescharacteristic
26C2×C22⋊D61Q812yes—
27D4×D61—22no—
28D4×D61—22no—
29C2×D244C2×C411yescharacteristic
30C2×C4×D61C2311yescharacteristic
31C22⋊#6923—24no—
32C22⋊#6923—22no—
33C22⋊#6923—44no—
34C4⋊#6923—22no—
35C4⋊#6923D412yes—
36C4⋊#6923D412yes—
37C4×#6923—22no—
38C4×#6923—22no—
39M16×C61C2×C412yescomplemented
40#11758194C2×C412yescomplemented
41#11758189—22no—
42C8×D61—22no—
43C23×C61C4⋊C412yes—
44C22×D61—22no—
45C22×D61—22no—
46C22×D61—42no—
47C22×D61—42no—
48C22×D61C4⋊C412yes—
49C22×D61C2×D411yescharacteristic
50C2×#6923—22no—
51C2×#6923—22no—
52C2×#6923—22no—
53C2×#6923—41no—
54C2×#6923—41no—
55C2×#6923—42no—
56C2×#6923—41no—
57C2×#6923—82no—
58C2×#6923—82no—
59D4×C61—22no—
60C2×C4×C61C22×C411yescharacteristic
61C22⋊D61—24no—
62C2×Dic61C2×Q811yescharacteristic
63D244—22no—
64C4×D61C2×D412yes—
65C4×D61#4112yes—
66C8×C61—22no—
67#92418—22no—
68C22×C61—22no—
69C22×C61—42no—
70C22×C61C2×C4⋊C411yescharacteristic
71C2×D61—21no—
72C2×D61—21no—
73C2×D61—22no—
74C2×D61—42no—
75C2×D61—42no—
76C2×D61—42no—
77C2×D61—82no—
78C2×D61#12011yescharacteristic
79C2×D61#12311yescharacteristic
80#6923—42no—
81#6923—42no—
82#6923—42no—
83#6923—81no—
84C4×C61C4×D412yes—
85Dic61C22⋊Q812yes—
86#1856—611nomaximal, Sylow
87C2×C61—21no—
88C2×C61—42no—
89C2×C61#38511yescharacteristic
90D61—21no—
91D61—42no—
92D61#45311yescharacteristic
93D61#45511yescharacteristic
94#518—611no—
95#428—612no—
96C2×#100—611no—
97#390—611no—
98#339—612no—
99C61#185611yescharacteristic, complemented, Sylow
100C22×D4—611no—
101C2×M16—612no—
102C4×D4—1222no—
103C4×D4—1222no—
104#117—612no—
105C2×C4⋊C4—611no—
106C2×C22⋊C4—1222no—
107C2×C22⋊C4—1222no—
108C2×C42—611no—
109#107—1222no—
110#106—1222no—
111#100—611no—
112#100—612no—
113#100#692311yescharacteristic, complemented
114C24—612no—
115C2×D4—612no—
116C2×D4—611no—
117C2×D4—1222no—
118C2×D4—1222no—
119C2×D4C2×#692311yescharacteristic
120C22×C4—611no—
121C22×C4—1222no—
122C22×C4—1222no—
123C22×C4—1221no—
124C22×C4—1221no—
125M16—612no—
126M16—1222no—
127M16C2×#692312yescomplemented
128C2×C8—1222no—
129C4⋊C4—612no—
130C4⋊C4—612no—
131C4⋊C4—1222no—
132C22⋊C4—1222no—
133C22⋊C4—1224no—
134C22⋊C4—2444no—
135C42—1222no—
136C42—1222no—
137C23—611no—
138C23—612no—
139C23—1222no—
140C23—1222no—
141C23—2442no—
142C23—2442no—
143C23C4⋊#692312yes—
144D4—22no—
145D4—1224no—
146D4—1222no—
147C2×C4—611no—
148C2×C4—612no—
149C2×C4—612no—
150C2×C4—1222no—
151C2×C4—1222no—
152C2×C4—1222no—
153C2×C4—4882no—
154C2×C4—4882no—
155C2×C4—2441no—
156C2×C4—2442no—
157C2×C4—2441no—
158C2×C4—2441no—
159C2×C4C22×#692311yescharacteristic
160C8—22no—
161C8—1222no—
162C22—22no—
163C22—42no—
164C22—611no—
165C22—611no—
166C22—1221no—
167C22—1221no—
168C22—1222no—
169C22—4882no—
170C22—2442no—
171C22—2442no—
172C22—2442no—
173C22C2×C4⋊#692311yescharacteristic
174C4—612no—
175C4—4881no—
176C4—2442no—
177C4—2442no—
178C4—2442no—
179C4D4×#692312yes—
180C2—21no—
181C2—42no—
182C2—611no—
183C2—611no—
184C2—1221no—
185C2—2442no—
186C2#1684070911yescharacteristic
subgroupG/H
centerC2#16840709
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#100×C61C4
socleC2×C61#385
hypercenter#100#6923
hypocenterC61#1856
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
2. #16840773C2semidirect
4. #16840634C2semidirect
17. #14519694C4semidirect
18. #14519693C4semidirect
19. #100×C61C4semidirect
39. M16×C61C2×C4semidirect
40. #11758194C2×C4semidirect
99. C61#1856semidirect
113. #100#6923semidirect
127. M16C2×#6923semidirect