Finite Group Databasebeta

← #37510693

Subgroups — #37510693

Order 22912.

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

normal subgroups only

This group has 230 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#26039014C211yesmaximal, characteristic
2#26038422C212yesmaximal
3#26038238C211yesmaximal, characteristic, complemented
4#26038237C212yesmaximal, complemented
5#356×C179C211yesmaximal, characteristic, complemented
6C2×#15668260C2211yescharacteristic
7C2×Q8×D179C411yescharacteristic
8M16×D179—22no—
9#19153111C2211yescharacteristic
10#19153102C411yescharacteristic
11#19153101C411yescharacteristic
12#19153098—22no—
13#19153091—22no—
14#19153070C411yescharacteristic
15#19153032C2212yes—
16#19153029—22no—
17C4⋊Q8×C179C2211yescharacteristic
18#101×C179C2212yes—
19#15668260—42no—
20C2×Dic358—21no—
21C2×Dic358C2×C411yescharacteristic
22Q8×D179—42no—
23C2×D716C2×C411yescharacteristic
24C2×D716D412yes—
25C2×C4×D179—21no—
26C2×C4×D179C2×C411yescharacteristic
27C2×C4×D179D412yes—
28#15668243—22no—
29#15668242—42no—
30C8×D179—42no—
31Dic179⋊C4—21no—
32Dic179⋊C4—22no—
33(C2×D179)⋊C4—21no—
34(C2×D179)⋊C4—22no—
35(C2×D179)⋊C4—22no—
36C4×Dic179C2×C411yescharacteristic
37C2×Q8×C179C2×C411yescharacteristic
38C2×Q8×C179C2311yescharacteristic
39M16×C179—22no—
40C4⋊C4×C179—22no—
41C42×C179C2×C411yescharacteristic
42C22×D179C22⋊C412yes—
43C22×D179C22⋊C411yescharacteristic
44Dic358—42no—
45Dic358—41no—
46D716—41no—
47D716—42no—
48C2×Dic179—21no—
49C2×Dic179—21no—
50C2×Dic179C22⋊C411yescharacteristic
51C4×D179—22no—
52C4×D179—22no—
53C4×D179—22no—
54C4×D179—42no—
55C179⋊C8—42no—
56Q8×C179—41no—
57Q8×C179—41no—
58C2×C4×C179—21no—
59C2×C4×C179—21no—
60C2×C4×C179C22×C411yescharacteristic
61C2×C4×C179C2×D412yes—
62C8×C179—42no—
63C22×C179C2×C22⋊C411yescharacteristic
64C2×D179—21no—
65C2×D179—22no—
66C2×D179—42no—
67C2×D179—41no—
68C4×C179—22no—
69C4×C179—21no—
70C4×C179—41no—
71C4×C179—41no—
72Dic179—41no—
73Dic179—41no—
74Dic179#9912yes—
75C2×C179—21no—
76C2×C179C2×#9911yescharacteristic
77D179—41no—
78D179—42no—
79C179#213511yescharacteristic, complemented, Sylow
80#2135—1791nomaximal, Sylow
81#536—1791no—
82#413—1792no—
83#356—1791no—
84#356—1792no—
85#356D17911yescharacteristic, complemented
86C2×#41—1791no—
87C22×Q8—1791no—
88C2×M16—3582no—
89C4⋊Q8—1791no—
90C4⋊Q8C2×D17911yescharacteristic
91#124—1791no—
92#124—1791no—
93#123—3582no—
94C22⋊Q8—3582no—
95#117—1791no—
96#101—1792no—
97#101C2×D17912yes—
98#100—3582no—
99#41—7162no—
100C2×Q8—3581no—
101C2×Q8—1791no—
102C2×Q8—7162no—
103C2×Q8C4×D17911yescharacteristic
104C2×Q8C22×D17911yescharacteristic
105C2×D4—1791no—
106C2×D4—1792no—
107C22×C4—3581no—
108C22×C4—1791no—
109C22×C4—1792no—
110M16—22no—
111M16—3582no—
112M16—7162no—
113C2×C8—7162no—
114C4⋊C4—22no—
115C4⋊C4—3581no—
116C4⋊C4—3582no—
117C22⋊C4—3581no—
118C22⋊C4—3582no—
119C22⋊C4—3582no—
120C42—1791no—
121C42C4×D17911yescharacteristic
122C23—1792no—
123C23—1791no—
124Q8—41no—
125Q8—41no—
126Q8—7161no—
127Q8—7162no—
128D4—7162no—
129D4—7161no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—3582no—
133C2×C4—3582no—
134C2×C4—3582no—
135C2×C4—3581no—
136C2×C4—3581no—
137C2×C4—1791no—
138C2×C4—7162no—
139C2×C4C2×C4×D17911yescharacteristic
140C2×C4D4×D17912yes—
141C8—42no—
142C8—7162no—
143C22—3581no—
144C22—3582no—
145C22—7162no—
146C22—7161no—
147C22C22⋊C4×D17911yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—1792no—
153C4—7161no—
154C4—7161no—
155C2—21no—
156C2—7161no—
157C2—7162no—
158C2#99×D17911yescharacteristic
subgroupG/H
centerC2#99×D179
commutatorC2×C4×C179C22×C4
FrattiniC2×Q8C22×D179
Fitting#356×C179C2
socleC2×C179C2×#99
prime radicalC2×#15668260C22
cosocleC2×Q8×C179C23
hypercenter#356D179
hypocenterC179#2135
LCSG ▷ C2×C4×C179 ▷ C22×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
3. #26038238C2semidirect
4. #26038237C2semidirect
5. #356×C179C2semidirect
79. C179#2135semidirect
85. #356D179semidirect

Maximal subgroups

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

subgroupindex
#260390142
#260384222
#260382382
#260382372
#356×C1792
#2135179