Finite Group Databasebeta

← #21461967

Subgroups — #21461967

Order 7808.

304 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 78 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×#14519845C211yesmaximal, characteristic
2C2×#14519840C212yesmaximal
3C2×#14519831C211yesmaximal, characteristic
4(C2×#6923)⋊Q8C212yesmaximal
5C2×Q16×D61C211yesmaximal, characteristic
6C2×D61⋊C8C2211yescharacteristic
7C2×C4⋊#6923C2212yes—
8C2×C4×#6923C2211yescharacteristic
9#14519845—22no—
10#14519840—24no—
11#14519831—22no—
12(C2×#6923)⋊C4—24no—
13C2×Q8×D61C2212yes—
14C2×Dic244C411yescharacteristic, complemented
15C2×#11758202C412yescomplemented
16Q16×D61—22no—
17Q16×D61—22no—
18C2×C8×D61C2211yescharacteristic
19C2×Q16×C61C411yescharacteristic, complemented
20C22×#6923—22no—
21C22×#6923D412yes—
22C2×Q8×C61C2×C412yes—
23Q8×D61—22no—
24Q8×D61—22no—
25Q8×D61—22no—
26Q8×D61—22no—
27C2×C4×D61—22no—
28C2×C4×D61C2311yescharacteristic
29C2×Dic122—22no—
30C2×Dic122C2×C412yes—
31C2×#92420—21no—
32C4⋊#6923—22no—
33C4⋊#6923—22no—
34C4×#6923—21no—
35C4×#6923—21no—
36D61⋊C8—21no—
37D61⋊C8D412yes—
38Q16×C61—22no—
39C2×C8×C61C2×C411yescharacteristic
40#11758202—24no—
41C2×#92418C2×C411yescharacteristic
42Dic244—22no—
43C8×D61D412yes—
44C8×D61D412yes—
45C22×D61C2×D411yescharacteristic
46C2×#6923—22no—
47C2×#6923—24no—
48C2×#6923—42no—
49C2×#6923—44no—
50Q8×C61—22no—
51Q8×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61C22×C411yescharacteristic
54C2×Dic61—22no—
55C2×Dic61#4111yescharacteristic
56C4×D61—42no—
57C4×D61—42no—
58C4×D61C2×D411yescharacteristic
59C4×D61C2×D411yescharacteristic
60C4×D61C2×D411yescharacteristic
61C4×D61#4111yescharacteristic
62Dic122—22no—
63Dic122—22no—
64Dic122—42no—
65Dic122—42no—
66#92420—22no—
67C8×C61C22⋊C412yes—
68#92418C22⋊C412yes—
69C22×C61C4×D411yescharacteristic
70C2×D61#12111yescharacteristic
71C2×D61#12711yescharacteristic
72C2×D61#13714yes—
73#6923—42no—
74#6923—82no—
75C4×C61—42no—
76C4×C61C2×C22⋊C411yescharacteristic
77C4×C61C4×D411yescharacteristic
78Dic61—42no—
79Dic61#12111yescharacteristic
80Dic61#12411yescharacteristic
81#1971—611nomaximal, Sylow
82C2×C61#39011yescharacteristic
83C2×C61#44112yes—
84D61#47012yes—
85D61#49712yes—
86C22×Q16—611no—
87C2×#106—611no—
88C2×#103—612no—
89C2×#97—611no—
90#391—612no—
91C61#197111yescharacteristic, complemented, Sylow
92C22×Q8—612no—
93C2×Q16—612no—
94C2×Q16—611no—
95C2×Q16—1222no—
96C2×Q16—1222no—
97C2×Q16#692311yescharacteristic, complemented
98C22×C8—611no—
99C22×C8—611no—
100C2×C4⋊C4—612no—
101C2×C42—611no—
102#106—1222no—
103#103—1224no—
104#97—1222no—
105#95—1224no—
106C2×Q8—612no—
107C2×Q8—1222no—
108C2×Q8—1222no—
109C2×Q8—1222no—
110C2×Q8—1222no—
111C2×Q8—1222no—
112C2×Q8C2×#692312yes—
113C22×C4—611no—
114C22×C4—612no—
115C22×C4—1222no—
116C22×C4—1222no—
117Q16—22no—
118Q16—1224no—
119Q16—1222no—
120C2×C8—611no—
121C2×C8—612no—
122C2×C8—612no—
123C2×C8—612no—
124C2×C8—1221no—
125C2×C8—1221no—
126C2×C8C2×#692311yescharacteristic
127C4⋊C4—1222no—
128C4⋊C4—1222no—
129C42—1221no—
130C42—1221no—
131C23—611no—
132Q8—22no—
133Q8—22no—
134Q8—1222no—
135Q8—1222no—
136Q8—2442no—
137Q8—2442no—
138C2×C4—22no—
139C2×C4—611no—
140C2×C4—611no—
141C2×C4—611no—
142C2×C4—611no—
143C2×C4—611no—
144C2×C4—1222no—
145C2×C4—1224no—
146C2×C4—1222no—
147C2×C4—2442no—
148C2×C4—2442no—
149C2×C4—2442no—
150C2×C4—2444no—
151C2×C4C22×#692311yescharacteristic
152C8—612no—
153C8—1222no—
154C8C22⋊#692312yes—
155C22—611no—
156C22—611no—
157C22—614no—
158C22D4×#692311yescharacteristic
159C4—42no—
160C4—611no—
161C4—611no—
162C4—4882no—
163C4—2442no—
164C4—2442no—
165C4C2×C22⋊#692311yescharacteristic
166C4D4×#692311yescharacteristic
167C2—612no—
168C2—612no—
169C2#1684071411yescharacteristic
170C2#1684080212yes—
subgroupG/H
centerC22D4×#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×Q16×C61C4
socleC22×C61C4×D4
hypercenterC2×Q16#6923
hypocenterC61#1971
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
14. C2×Dic244C4semidirect
15. C2×#11758202C4semidirect
19. C2×Q16×C61C4semidirect
91. C61#1971semidirect
97. C2×Q16#6923semidirect