Finite Group Databasebeta

← #37510682

Subgroups — #37510682

Order 22912.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#26038988C211yesmaximal, characteristic
2#26038422C212yesmaximal, complemented
3#26038237C212yesmaximal, complemented
4#26038236C211yesmaximal, characteristic, complemented
5#355×C179C211yesmaximal, characteristic, complemented
6C2×#15668260C2211yescharacteristic
7C2×#15668258C411yescharacteristic
8M16×D179—22no—
9#19153111C2211yescharacteristic
10#19153109C411yescharacteristic
11#19153101C411yescharacteristic
12#19153086—22no—
13(C22⋊D179)⋊C4—22no—
14C42×D179C411yescharacteristic
15#19153032C2212yes—
16#19153029—22no—
17#124×C179C2211yescharacteristic
18#101×C179C2212yes—
19#15668260—41no—
20#15668260—41no—
21#15668258—41no—
22#15668258—41no—
23C2×Dic358C2×C411yescharacteristic
24C2×D716C2×C411yescharacteristic
25C2×D716D412yes—
26C2×C22⋊D179—21no—
27C2×C22⋊D179—22no—
28C22×Dic179—21no—
29C2×C4×D179—21no—
30C2×C4×D179C2×C411yescharacteristic
31C2×C4×D179D412yes—
32#15668243—22no—
33#15668242—42no—
34C8×D179—42no—
35Dic179⋊C4—22no—
36(C2×D179)⋊C4—22no—
37C4×Dic179—21no—
38C4×Dic179C2×C411yescharacteristic
39C2×Q8×C179C2311yescharacteristic
40C2×D4×C179C2×C411yescharacteristic
41M16×C179—22no—
42C22⋊C4×C179—22no—
43C42×C179C2×C411yescharacteristic
44C22×D179C22⋊C412yes—
45C22×D179C22⋊C411yescharacteristic
46Dic358—41no—
47D716—41no—
48D716—42no—
49C22⋊D179—44no—
50C22⋊D179—42no—
51C2×Dic179—21no—
52C2×Dic179—21no—
53C2×Dic179—41no—
54C2×Dic179—41no—
55C2×Dic179C22⋊C411yescharacteristic
56C4×D179—22no—
57C4×D179—22no—
58C4×D179—21no—
59C4×D179—21no—
60C4×D179—42no—
61C179⋊C8—42no—
62C23×C179—21no—
63Q8×C179—41no—
64D4×C179—41no—
65C2×C4×C179—21no—
66C2×C4×C179C22×C411yescharacteristic
67C2×C4×C179C2×D412yes—
68C8×C179—42no—
69C22×C179—42no—
70C22×C179—41no—
71C22×C179C2×C22⋊C411yescharacteristic
72C2×D179—21no—
73C2×D179—22no—
74C2×D179—41no—
75C2×D179—42no—
76C4×C179—22no—
77C4×C179—21no—
78C4×C179—41no—
79Dic179—22no—
80Dic179—41no—
81Dic179#9911yescharacteristic
82Dic179#9911yescharacteristic
83C2×C179—21no—
84C2×C179—81no—
85C2×C179C2×#9911yescharacteristic
86D179—41no—
87D179—42no—
88C179#213211yescharacteristic, complemented, Sylow
89#2132—1791nomaximal, Sylow
90#532—1791no—
91#413—1792no—
92#356—1792no—
93#355—1791no—
94#355D17911yescharacteristic, complemented
95C2×#41—1791no—
96C2×#41—1791no—
97C2×M16—3582no—
98C4⋊Q8—1791no—
99#127—1791no—
100#124—1791no—
101#124C2×D17911yescharacteristic
102#121—3582no—
103C4×D4—3582no—
104C2×C42—1791no—
105#101—1792no—
106#101C2×D17912yes—
107#100—3582no—
108#41—7161no—
109#41—7161no—
110#41—7161no—
111#41—7161no—
112C2×Q8—1791no—
113C2×Q8C22×D17911yescharacteristic
114C2×D4—3582no—
115C2×D4—3581no—
116C2×D4—1791no—
117C2×D4—1792no—
118C2×D4C4×D17911yescharacteristic
119C22×C4—3581no—
120C22×C4—3581no—
121C22×C4—1791no—
122C22×C4—1792no—
123M16—22no—
124M16—3582no—
125M16—7162no—
126C2×C8—7162no—
127C4⋊C4—3582no—
128C22⋊C4—22no—
129C22⋊C4—3582no—
130C42—3581no—
131C42—1791no—
132C42C4×D17911yescharacteristic
133C23—21no—
134C23—1792no—
135C23—1791no—
136Q8—41no—
137Q8—7161no—
138D4—41no—
139D4—7162no—
140D4—7161no—
141D4—7164no—
142D4—7162no—
143C2×C4—21no—
144C2×C4—3582no—
145C2×C4—3582no—
146C2×C4—3581no—
147C2×C4—3581no—
148C2×C4—3581no—
149C2×C4—3581no—
150C2×C4—1791no—
151C2×C4—7162no—
152C2×C4—7161no—
153C2×C4—7161no—
154C2×C4C2×C4×D17911yescharacteristic
155C2×C4D4×D17912yes—
156C8—42no—
157C8—7162no—
158C22—42no—
159C22—41no—
160C22—3581no—
161C22—3582no—
162C22—7161no—
163C22—7162no—
164C22C22⋊C4×D17911yescharacteristic
165C4—22no—
166C4—21no—
167C4—41no—
168C4—3582no—
169C4—1791no—
170C4—1791no—
171C4—7161no—
172C2—21no—
173C2—81no—
174C2—7161no—
175C2—7162no—
176C2#99×D17911yescharacteristic
subgroupG/H
centerC2#99×D179
commutatorC2×C4×C179C22×C4
FrattiniC2×Q8C22×D179
Fitting#355×C179C2
socleC2×C179C2×#99
prime radical#26038988C2
cosocleC2×Q8×C179C23
hypercenter#355D179
hypocenterC179#2132
LCSG ▷ C2×C4×C179 ▷ C22×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #26038422C2semidirect
3. #26038237C2semidirect
4. #26038236C2semidirect
5. #355×C179C2semidirect
88. C179#2132semidirect
94. #355D179semidirect

Maximal subgroups

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

subgroupindex
#260389882
#260384222
#260382372
#260382362
#355×C1792
#2132179