Finite Group Databasebeta

← #37508108

Subgroups — #37508108

Order 22912.

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

normal subgroups only

This group has 216 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#26039159C211yesmaximal, characteristic, complemented
2#26038785C211yesmaximal, characteristic, complemented
3#26038636C211yesmaximal, characteristic, complemented
4#26038186C211yesmaximal, characteristic, complemented
5#26038169C211yesmaximal, characteristic, complemented
6D4⋊(C179⋊C8)C211yesmaximal, characteristic, complemented
7#459×C179C211yesmaximal, characteristic
8C2×#15668247—21no—
9#19153113C2211yescharacteristic
10#19153106—22no—
11#19153100—21no—
12#19153092—21no—
13C4×Dic358C2211yescharacteristic
14#19153078—21no—
15#19153072—21no—
16C4⋊(C179⋊C8)C2211yescharacteristic
17#19153034—22no—
18#19153034—21no—
19C4×C179⋊C8C2211yescharacteristic
20C2×D8×C179—21no—
21#127×C179C2211yescharacteristic
22C4×D4×C179C2211yescharacteristic
23C4⋊C8×C179C2211yescharacteristic
24#102×C179—21no—
25C2×Dic358—21no—
26C2×Dic358D411yescharacteristic
27#15668247—42no—
28C2×C179⋊C8—21no—
29C2×C179⋊C8—21no—
30C4⋊Dic179—21no—
31C4⋊Dic179D411yescharacteristic
32C4⋊Dic179D412yes—
33Dic179⋊C4—22no—
34Dic179⋊C4—21no—
35C22⋊Dic179—22no—
36C22⋊Dic179—22no—
37C4×Dic179—22no—
38C4×Dic179—21no—
39C2×D4×C179—21no—
40C2×D4×C179—21no—
41C2×D4×C179—21no—
42C2×D4×C179D411yescharacteristic
43C22×C4×C179—21no—
44D8×C179—42no—
45C2×C8×C179—21no—
46C4⋊C4×C179D411yescharacteristic
47C22⋊C4×C179—21no—
48C42×C179C2311yescharacteristic
49Dic358—21no—
50Dic358—21no—
51Dic358—41no—
52Dic358—41no—
53C2×Dic179—21no—
54C2×Dic179—21no—
55C2×Dic179—22no—
56C179⋊C8—41no—
57C179⋊C8—41no—
58C23×C179—21no—
59C23×C179—41no—
60D4×C179—21no—
61D4×C179—21no—
62D4×C179—42no—
63D4×C179—41no—
64D4×C179—41no—
65D4×C179—41no—
66D4×C179—41no—
67C2×C4×C179—21no—
68C2×C4×C179—41no—
69C2×C4×C179—41no—
70C2×C4×C179C2×D411yescharacteristic
71C2×C4×C179C2×D411yescharacteristic
72C2×C4×C179C2×D411yescharacteristic
73C8×C179—41no—
74C22×C179—41no—
75C22×C179—41no—
76C22×C179—41no—
77C22×C179—81no—
78C22×C179—81no—
79C22×C179—81no—
80C22×C179#12011yescharacteristic
81C4×C179—21no—
82C4×C179—41no—
83C4×C179#13511yescharacteristic
84C4×C179#13511yescharacteristic
85C4×C179AGL(1,ℤ/8)11yescharacteristic
86C4×C179AGL(1,ℤ/8)11yescharacteristic
87Dic179—41no—
88Dic179—42no—
89Dic179—41no—
90C2×C179—81no—
91C2×C179—161no—
92C2×C179#44911yescharacteristic
93C2×C179#44911yescharacteristic
94C2×C179#45411yescharacteristic
95C179#162811yescharacteristic, complemented, Sylow
96#1628—1791nomaximal, Sylow
97#556—1791no—
98#486—1791no—
99#460—1791no—
100#459D17911yescharacteristic
101#332—1791no—
102Q8⋊C8—1791no—
103D4⋊C8—1791no—
104C2×SD16—3581no—
105C2×D8—21no—
106C4⋊Q8—1791no—
107#127C2×D17911yescharacteristic
108#126—3582no—
109#124—3581no—
110C22⋊Q8—3581no—
111C4×Q8—3581no—
112C4×Q8—1791no—
113C4×D4C2×D17911yescharacteristic
114#117—3581no—
115C4⋊C8—1791no—
116C4⋊C8C2×D17911yescharacteristic
117#102—21no—
118#102—3581no—
119#102—3582no—
120C4×C8—1791no—
121C2×Q8—3581no—
122C2×Q8—1791no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4C22⋊D17911yescharacteristic
127C22×C4—21no—
128SD16—7162no—
129D8—42no—
130C2×C8—21no—
131C2×C8—3581no—
132C2×C8—3581no—
133C4⋊C4—3582no—
134C4⋊C4—3581no—
135C4⋊C4—3581no—
136C4⋊C4—1791no—
137C4⋊C4—1792no—
138C4⋊C4C22⋊D17911yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—3582no—
141C22⋊C4—3582no—
142C42—3582no—
143C42—3581no—
144C42C22×D17911yescharacteristic
145C23—21no—
146C23—41no—
147Q8—3581no—
148Q8—3581no—
149Q8—7161no—
150Q8—7161no—
151D4—21no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—3581no—
162C2×C4—3581no—
163C2×C4—3582no—
164C2×C4D4×D17911yescharacteristic
165C2×C4D4×D17911yescharacteristic
166C2×C4C2×C22⋊D17911yescharacteristic
167C8—41no—
168C8—7161no—
169C8—7161no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22#1915308111yescharacteristic
177C4—21no—
178C4—41no—
179C4—7161no—
180C4—7162no—
181C4—7161no—
182C4#1915313211yescharacteristic
183C4#1915313311yescharacteristic
184C4#1915313711yescharacteristic
185C4#1915313911yescharacteristic
186C2—81no—
187C2—161no—
188C2#2603858111yescharacteristic
189C2#2603858211yescharacteristic
190C2#2603861011yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting, prime radical#459×C179C2
socleC22×C179#120
hypercenter#459D179
hypocenterC179#1628
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #26039159C2semidirect
2. #26038785C2semidirect
3. #26038636C2semidirect
4. #26038186C2semidirect
5. #26038169C2semidirect
6. D4⋊(C179⋊C8)C2semidirect
95. C179#1628semidirect

Maximal subgroups

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

subgroupindex
#260391592
#260387852
#260386362
#260381862
#260381692
D4⋊(C179⋊C8)2
#459×C1792
#1628179