Finite Group Databasebeta

← #37508169

Subgroups — #37508169

Order 22912.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#26039163C211yesmaximal, characteristic
2#26038731C211yesmaximal, characteristic, complemented
3#26038726C211yesmaximal, characteristic
4#26038185C211yesmaximal, characteristic, complemented
5#26038171C211yesmaximal, characteristic, complemented
6#26038168C211yesmaximal, characteristic
7#487×C179C211yesmaximal, characteristic, complemented
8#19153108—22no—
9#19153102—21no—
10#19153093—21no—
11Q8×Dic179—21no—
12C4×Dic358C2211yescharacteristic
13C4×D716C2211yescharacteristic
14#19153071—21no—
15#19153046—21no—
16#19153044—21no—
17C4⋊(C179⋊C8)C2211yescharacteristic
18C4⋊(C179⋊C8)C2211yescharacteristic
19#19153036—21no—
20#19153033—21no—
21C4⋊Q8×C179C2211yescharacteristic
22C4⋊Q8×C179C2211yescharacteristic
23#103×C179—22no—
24C4×C8×C179C2211yescharacteristic
25C2×Dic358D411yescharacteristic
26C2×D716D411yescharacteristic
27C2×C4×D179—21no—
28C2×C179⋊C8—21no—
29C2×C179⋊C8—21no—
30C4⋊Dic179—22no—
31C4⋊Dic179D411yescharacteristic
32C4⋊Dic179D411yescharacteristic
33Dic179⋊C4—21no—
34(C2×D179)⋊C4—22no—
35(C2×D179)⋊C4—22no—
36(C2×D179)⋊C4—21no—
37C4×Dic179—22no—
38C4×Dic179—21no—
39C2×Q8×C179—21no—
40C2×Q8×C179—21no—
41C2×C8×C179—21no—
42C4⋊C4×C179—21no—
43C4⋊C4×C179—21no—
44C4⋊C4×C179—21no—
45C4⋊C4×C179D412yes—
46C42×C179C2311yescharacteristic
47C22×D179—21no—
48Dic358—21no—
49Dic358—21no—
50D716—21no—
51D716—21no—
52C2×Dic179—21no—
53C2×Dic179—21no—
54C2×Dic179—21no—
55C4×D179—41no—
56C4×D179—41no—
57C179⋊C8—41no—
58C179⋊C8—41no—
59Q8×C179—42no—
60Q8×C179—41no—
61Q8×C179—41no—
62C2×C4×C179—22no—
63C2×C4×C179—41no—
64C2×C4×C179C2×D411yescharacteristic
65C2×C4×C179C2×D411yescharacteristic
66C2×C4×C179C2×D411yescharacteristic
67C8×C179—41no—
68C22×C179#12011yescharacteristic
69C2×D179—41no—
70C2×D179—41no—
71C2×D179—41no—
72C4×C179—21no—
73C4×C179—42no—
74C4×C179—81no—
75C4×C179#13511yescharacteristic
76C4×C179#13511yescharacteristic
77C4×C179#13711yescharacteristic
78C4×C179#13711yescharacteristic
79Dic179—41no—
80Dic179—41no—
81Dic179—41no—
82C2×C179#45211yescharacteristic
83C2×C179#45211yescharacteristic
84C2×C179#45411yescharacteristic
85D179—81no—
86C179#163811yescharacteristic, complemented, Sylow
87#1638—1791nomaximal, Sylow
88#556—1791no—
89#487D17911yescharacteristic, complemented
90#477—1791no—
91#476—1791no—
92#332—1791no—
93Q8⋊C8—1791no—
94D4⋊C8—1791no—
95C4⋊Q8C2×D17911yescharacteristic
96C4⋊Q8C2×D17911yescharacteristic
97#126—3582no—
98#124—3581no—
99C22⋊Q8—3581no—
100C4×Q8—3581no—
101C4×Q8—1791no—
102C4×D4—1791no—
103#117—3581no—
104#107—3581no—
105#106—3581no—
106C4⋊C8—1791no—
107C4⋊C8—1791no—
108#103—22no—
109#103—3581no—
110#102—3581no—
111C4×C8C2×D17911yescharacteristic
112C2×Q8—21no—
113C2×Q8—21no—
114C2×Q8—1791no—
115C2×D4—1791no—
116C22×C4—3581no—
117C2×C8—21no—
118C2×C8—3581no—
119C2×C8—3581no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—3582no—
124C4⋊C4—3581no—
125C4⋊C4—1791no—
126C4⋊C4—1791no—
127C4⋊C4C22⋊D17912yes—
128C22⋊C4—3582no—
129C22⋊C4—3582no—
130C22⋊C4—3581no—
131C42—3582no—
132C42—3581no—
133C42C22×D17911yescharacteristic
134C23—3581no—
135Q8—42no—
136Q8—41no—
137Q8—41no—
138Q8—3581no—
139Q8—3581no—
140D4—3581no—
141D4—3581no—
142C2×C4—22no—
143C2×C4—41no—
144C2×C4—3581no—
145C2×C4—3581no—
146C2×C4—3581no—
147C2×C4—7161no—
148C2×C4—7161no—
149C2×C4D4×D17911yescharacteristic
150C2×C4D4×D17911yescharacteristic
151C2×C4C2×C22⋊D17911yescharacteristic
152C8—41no—
153C8—7161no—
154C8—7161no—
155C22—7161no—
156C22—7161no—
157C22—7161no—
158C22#1915308111yescharacteristic
159C4—21no—
160C4—42no—
161C4—81no—
162C4—7161no—
163C4—7161no—
164C4—7161no—
165C4#1915313411yescharacteristic
166C4#1915313611yescharacteristic
167C4#1915314211yescharacteristic
168C4#1915314511yescharacteristic
169C2—14321no—
170C2#2603859811yescharacteristic
171C2#2603860011yescharacteristic
172C2#2603861111yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#487×C179C2
socleC22×C179#120
prime radicalC2×D716D4
hypercenter#487D179
hypocenterC179#1638
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #26038731C2semidirect
4. #26038185C2semidirect
5. #26038171C2semidirect
7. #487×C179C2semidirect
86. C179#1638semidirect
89. #487D179semidirect

Maximal subgroups

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

subgroupindex
#260391632
#260387312
#260387262
#260381852
#260381712
#260381682
#487×C1792
#1638179