Finite Group Databasebeta

← #37510686

Subgroups — #37510686

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#26039009C211yesmaximal, characteristic
2#101×D179C212yesmaximal, complemented
3#26038237C212yesmaximal, complemented
4#26038236C211yesmaximal, characteristic, complemented
5#355×C179C211yesmaximal, characteristic, complemented
6C2×#15668258C411yescharacteristic
7C2×Q8×D179C2211yescharacteristic
8M16×D179—22no—
9#19153113C411yescharacteristic
10#19153111C2211yescharacteristic
11#19153100C411yescharacteristic
12#19153095—22no—
13#19153090—22no—
14#19153070C411yescharacteristic
15#19153032C2212yes—
16#19153031—22no—
17#124×C179C2211yescharacteristic
18#101×C179C2212yes—
19#15668258—42no—
20C2×Dic358C2×C411yescharacteristic
21C2×Dic358C2×C411yescharacteristic
22C2×Dic358D412yes—
23Q8×D179—42no—
24C2×C22⋊D179—21no—
25C22×Dic179—21no—
26C2×C4×D179C2×C411yescharacteristic
27C2×C4×D179D412yes—
28#15668243—22no—
29#15668242—42no—
30C8×D179—42no—
31C4⋊Dic179—22no—
32Dic179⋊C4—21no—
33Dic179⋊C4—22no—
34C22⋊Dic179—22no—
35(C2×D179)⋊C4—21no—
36C4×Dic179C2×C411yescharacteristic
37C2×Q8×C179C2311yescharacteristic
38C2×D4×C179C2×C411yescharacteristic
39M16×C179—22no—
40C22⋊C4×C179—22no—
41C42×C179C2×C411yescharacteristic
42C22×D179C22⋊C411yescharacteristic
43Dic358—41no—
44Dic358—42no—
45Dic358—41no—
46C22⋊D179—42no—
47C2×Dic179—21no—
48C2×Dic179—21no—
49C2×Dic179—42no—
50C2×Dic179C22⋊C412yes—
51C2×Dic179C22⋊C411yescharacteristic
52C4×D179—22no—
53C4×D179—22no—
54C4×D179—22no—
55C179⋊C8—42no—
56C23×C179—21no—
57Q8×C179—41no—
58D4×C179—41no—
59C2×C4×C179—21no—
60C2×C4×C179C22×C411yescharacteristic
61C2×C4×C179C2×D412yes—
62C8×C179—42no—
63C22×C179—42no—
64C22×C179—41no—
65C22×C179C2×C22⋊C411yescharacteristic
66C2×D179—41no—
67C2×D179#9912yes—
68C4×C179—22no—
69C4×C179—21no—
70C4×C179—41no—
71Dic179—21no—
72Dic179—22no—
73Dic179—41no—
74Dic179—41no—
75C2×C179—21no—
76C2×C179—81no—
77C2×C179C2×#9911yescharacteristic
78D179—22no—
79C179#213311yescharacteristic, complemented, Sylow
80#2133—1791nomaximal, Sylow
81#536—1791no—
82C2×#101—1792no—
83#356—1792no—
84#355—1791no—
85#355D17911yescharacteristic, complemented
86C2×#41—1791no—
87C22×Q8—1791no—
88C2×M16—3582no—
89C4⋊Q8—1791no—
90C4⋊Q8—1791no—
91#124—1791no—
92#124C2×D17911yescharacteristic
93#123—3582no—
94C22⋊Q8—3582no—
95#117—1791no—
96#101—3582no—
97#101—1792no—
98#101C2×D17912yes—
99#41—7162no—
100C2×Q8—1791no—
101C2×Q8—1791no—
102C2×Q8—1792no—
103C2×Q8—7162no—
104C2×Q8C22×D17911yescharacteristic
105C2×D4—3581no—
106C2×D4C4×D17911yescharacteristic
107C22×C4—3581no—
108C22×C4—1791no—
109C22×C4—1792no—
110M16—22no—
111M16—3582no—
112M16—7162no—
113C2×C8—7162no—
114C4⋊C4—3581no—
115C4⋊C4—3582no—
116C4⋊C4—3582no—
117C22⋊C4—22no—
118C22⋊C4—3581no—
119C22⋊C4—3582no—
120C42—1791no—
121C42C4×D17911yescharacteristic
122C23—21no—
123C23—1791no—
124Q8—41no—
125Q8—7162no—
126Q8—7161no—
127Q8—7161no—
128D4—41no—
129D4—7162no—
130C2×C4—21no—
131C2×C4—3582no—
132C2×C4—3582no—
133C2×C4—3582no—
134C2×C4—3581no—
135C2×C4—3581no—
136C2×C4—1792no—
137C2×C4—1791no—
138C2×C4—7162no—
139C2×C4C2×C4×D17911yescharacteristic
140C2×C4D4×D17912yes—
141C8—42no—
142C8—7162no—
143C22—42no—
144C22—41no—
145C22—1792no—
146C22—7161no—
147C22C22⋊C4×D17911yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—3581no—
152C4—3582no—
153C4—7161no—
154C4—7161no—
155C2—21no—
156C2—81no—
157C2—3582no—
158C2#99×D17911yescharacteristic
subgroupG/H
centerC2#99×D179
commutatorC2×C4×C179C22×C4
FrattiniC2×Q8C22×D179
Fitting#355×C179C2
socleC2×C179C2×#99
prime radicalC2×#15668258C4
cosocleC2×Q8×C179C23
hypercenter#355D179
hypocenterC179#2133
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. #101×D179C2semidirect
3. #26038237C2semidirect
4. #26038236C2semidirect
5. #355×C179C2semidirect
79. C179#2133semidirect
85. #355D179semidirect

Maximal subgroups

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

subgroupindex
#260390092
#101×D1792
#260382372
#260382362
#355×C1792
#2133179