Finite Group Databasebeta

← #27187320

Subgroups — #27187320

Order 12928.

244 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 70 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#20266182C211yesmaximal, characteristic
2#20266113C211yesmaximal, characteristic
3#20266047C214yesmaximal
4#20265732C211yesmaximal, characteristic
5C2×#13108084C2212yes—
6C2×C4×#87938C2212yes—
7#15692322—21no—
8#15692322—21no—
9(C2×#87938)⋊C4—21no—
10(C2×#87938)⋊C4—21no—
11#15692255C411yescharacteristic, complemented
12#15692246C412yescomplemented
13#15692235—21no—
14#15692231—21no—
15Q8×Dic101—21no—
16#15692220—21no—
17#15692213C2212yes—
18C42×D101C2211yescharacteristic
19C4⋊Q8×C101C411yescharacteristic, complemented
20C22×#87938—22no—
21#13108084—24no—
22C2×#11717581—22no—
23C4×#87938—22no—
24C4×#87938Q814yescomplemented
25C2×Dic202—21no—
26C2×C4×D101D411yescharacteristic
27C2×C4×D101D411yescharacteristic
28C2×C4×D101C2311yescharacteristic
29C4⋊Dic101—21no—
30C4⋊Dic101—22no—
31C4⋊Dic101C2×C412yes—
32#13108053—22no—
33#13108051—22no—
34C4×Dic101—22no—
35C4×Dic101C2×C411yescharacteristic
36C4×Dic101D411yescharacteristic
37C4×Dic101D411yescharacteristic
38C2×Q8×C101—21no—
39C4⋊C4×C101—21no—
40C4⋊C4×C101C2×C412yes—
41C42×C101C2×C411yescharacteristic
42C22×D101C2×D411yescharacteristic
43C2×#87938—24no—
44C2×#87938—42no—
45C2×#87938—42no—
46Q8×C101—42no—
47C2×C4×C101—22no—
48C2×C4×C101C22⋊C411yescharacteristic
49C2×C4×C101C22⋊C411yescharacteristic
50C2×C4×C101C22×C411yescharacteristic
51C2×Dic101—22no—
52C2×Dic101C22⋊C411yescharacteristic
53C2×Dic101C22⋊C411yescharacteristic
54C2×Dic101C2×D411yescharacteristic
55C4×D101—41no—
56C4×D101—41no—
57C4×D101C2×Q812yes—
58C4×D101#4112yes—
59Dic202—42no—
60#11717581—42no—
61C22×C101C2×C22⋊C411yescharacteristic
62C2×D101—21no—
63C2×D101—21no—
64C2×D101C22⋊Q812yes—
65#87938—44no—
66C4×C101—21no—
67C4×C101—21no—
68C4×C101—42no—
69C4×C101C4×Q812yes—
70Dic101—21no—
71Dic101—21no—
72Dic101—42no—
73Dic101#12411yescharacteristic
74Dic101C4⋊Q811yescharacteristic
75C2×C101#39111yescharacteristic
76C2×C101#42111yescharacteristic
77C2×C101#42111yescharacteristic
78D101—22no—
79#1995—1011nomaximal, Sylow
80C101#199511yescharacteristic, complemented, Sylow
81#533—1011no—
82#423—1011no—
83#376—1011no—
84#339—1014no—
85C2×M16—1012no—
86C4⋊Q8—1011no—
87C4⋊Q8#8793811yescharacteristic, complemented
88#125—1012no—
89C22⋊Q8—2021no—
90C22⋊Q8—2021no—
91C4×Q8—2021no—
92C4×Q8—2021no—
93#117—1012no—
94C2×C42—1011no—
95C2×C42—1012no—
96C4⋊C8—2021no—
97C4⋊C8—2021no—
98#95—2021no—
99#95—2021no—
100C2×Q8—21no—
101C2×Q8—2021no—
102C22×C4—1011no—
103C22×C4—1011no—
104C22×C4—1011no—
105C22×C4—2022no—
106M16—2024no—
107C2×C8—2022no—
108C4⋊C4—21no—
109C4⋊C4—1012no—
110C4⋊C4—2022no—
111C4⋊C4—2022no—
112C4⋊C4—2021no—
113C4⋊C4C2×#8793812yes—
114C22⋊C4—2022no—
115C42—1011no—
116C42—1011no—
117C42—1011no—
118C42—1014no—
119C42—2022no—
120C42—2022no—
121C42C2×#8793811yescharacteristic
122C23—1011no—
123Q8—42no—
124Q8—4042no—
125C2×C4—22no—
126C2×C4—1011no—
127C2×C4—1012no—
128C2×C4—1012no—
129C2×C4—1011no—
130C2×C4—1011no—
131C2×C4—4041no—
132C2×C4—4041no—
133C2×C4—4042no—
134C2×C4—4042no—
135C2×C4—2024no—
136C2×C4—2022no—
137C2×C4C22⋊#8793811yescharacteristic
138C2×C4C22⋊#8793811yescharacteristic
139C2×C4C22×#8793811yescharacteristic
140C8—4042no—
141C22—1012no—
142C22—2021no—
143C22—2021no—
144C22C2×C22⋊#8793811yescharacteristic
145C4—21no—
146C4—21no—
147C4—42no—
148C4—1011no—
149C4—1011no—
150C4—4044no—
151C4—4042no—
152C4—2021no—
153C4—2021no—
154C4Q8×#8793812yes—
155C2—2022no—
156C2(C2×#87938)⋊Q811yescharacteristic
157C2#2026617511yescharacteristic
158C2#2026617611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC4⋊Q8×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC22×D101C2×D4
cosocleC2×C4×D101C23
hypercenterC4⋊Q8#87938
hypocenterC101#1995
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
11. #15692255C4semidirect
12. #15692246C4semidirect
19. C4⋊Q8×C101C4semidirect
24. C4×#87938Q8semidirect
80. C101#1995semidirect
87. C4⋊Q8#87938semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202661822
#202661132
#202660472
#202657322
#1995101