Finite Group Databasebeta

← #37508229

Subgroups — #37508229

Order 22912.

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

normal subgroups only

This group has 212 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#26039155C211yesmaximal, characteristic
2#26038789C211yesmaximal, characteristic, complemented
3#26038720C211yesmaximal, characteristic, complemented
4#26038645C211yesmaximal, characteristic, complemented
5#26038166C211yesmaximal, characteristic, complemented
6#26038166C211yesmaximal, characteristic, complemented
7#333×C179C211yesmaximal, characteristic, complemented
8C2×#15668248—21no—
9#19153113C2211yescharacteristic
10#19153102—22no—
11#19153088—21no—
12#19153088—21no—
13C4×D716C2211yescharacteristic
14C4×D716C2211yescharacteristic
15#19153071—21no—
16#19153071—21no—
17#19153047—21no—
18#19153038—21no—
19#19153037—22no—
20#19153035—21no—
21C4×C179⋊C8C2211yescharacteristic
22C4⋊Q8×C179C2211yescharacteristic
23C4⋊C8×C179C2211yescharacteristic
24C4⋊C8×C179C2211yescharacteristic
25C2×Dic358—21no—
26C2×D716—22no—
27C2×D716D411yescharacteristic
28C2×D716D411yescharacteristic
29C2×C4×D179—21no—
30C2×C4×D179—21no—
31#15668248—42no—
32C2×C179⋊C8—21no—
33C4⋊Dic179—21no—
34C4⋊Dic179—21no—
35C4⋊Dic179D411yescharacteristic
36C4⋊Dic179D411yescharacteristic
37(C2×D179)⋊C4—22no—
38(C2×D179)⋊C4—22no—
39(C2×D179)⋊C4—21no—
40(C2×D179)⋊C4—21no—
41C4×Dic179—22no—
42C2×Q8×C179D412yes—
43C2×C8×C179—21no—
44C2×C8×C179—21no—
45C4⋊C4×C179—21no—
46C4⋊C4×C179—21no—
47C42×C179C2311yescharacteristic
48C22×D179—21no—
49C22×D179—21no—
50Dic358—41no—
51Dic358—41no—
52D716—21no—
53D716—21no—
54D716—21no—
55D716—21no—
56D716—82no—
57C2×Dic179—21no—
58C2×Dic179—21no—
59C2×Dic179—41no—
60C4×D179—41no—
61C4×D179—41no—
62C4×D179—41no—
63C4×D179—41no—
64C179⋊C8—41no—
65Q8×C179—42no—
66C2×C4×C179—22no—
67C2×C4×C179C2×D411yescharacteristic
68C2×C4×C179C2×D411yescharacteristic
69C2×C4×C179C2×D411yescharacteristic
70C8×C179—41no—
71C8×C179—41no—
72C22×C179#12011yescharacteristic
73C2×D179—41no—
74C2×D179—41no—
75C2×D179—41no—
76C2×D179—41no—
77C2×D179—41no—
78C2×D179—41no—
79C4×C179—21no—
80C4×C179—42no—
81C4×C179#13511yescharacteristic
82C4×C179#13511yescharacteristic
83C4×C179AGL(1,ℤ/8)11yescharacteristic
84C4×C179#13711yescharacteristic
85Dic179—41no—
86Dic179—41no—
87Dic179—81no—
88C2×C179#44911yescharacteristic
89C2×C179#45211yescharacteristic
90C2×C179#45511yescharacteristic
91D179—81no—
92D179—81no—
93C179#164611yescharacteristic, complemented, Sylow
94#1646—1791nomaximal, Sylow
95#555—1791no—
96#487—1791no—
97#474—1791no—
98#461—1791no—
99#333D17911yescharacteristic, complemented
100D4⋊C8—1791no—
101D4⋊C8—1791no—
102C2×SD16—3581no—
103C4⋊Q8—1791no—
104C4⋊Q8C2×D17911yescharacteristic
105#124—3582no—
106#121—3581no—
107#121—3581no—
108C4×D4—1791no—
109C4×D4—1791no—
110#117—3581no—
111#117—3581no—
112#107—3581no—
113C4⋊C8C2×D17911yescharacteristic
114C4⋊C8C2×D17911yescharacteristic
115#103—3582no—
116#103—3581no—
117#102—3581no—
118C4×C8—1791no—
119C2×Q8—3581no—
120C2×Q8D71612yes—
121C2×D4—3582no—
122C2×D4—1791no—
123C2×D4—1791no—
124C22×C4—3581no—
125C22×C4—3581no—
126SD16—7162no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—3581no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—3581no—
133C4⋊C4—3581no—
134C4⋊C4—1791no—
135C4⋊C4—1791no—
136C22⋊C4—3582no—
137C22⋊C4—3582no—
138C22⋊C4—3581no—
139C22⋊C4—3581no—
140C42—3582no—
141C42C22×D17911yescharacteristic
142C23—3581no—
143C23—3581no—
144Q8—42no—
145Q8—7161no—
146Q8—7161no—
147D4—3581no—
148D4—3581no—
149D4—3581no—
150D4—3581no—
151D4—14322no—
152C2×C4—22no—
153C2×C4—3581no—
154C2×C4—3581no—
155C2×C4—7161no—
156C2×C4—7161no—
157C2×C4—7161no—
158C2×C4—7161no—
159C2×C4—7161no—
160C2×C4D4×D17911yescharacteristic
161C2×C4D4×D17911yescharacteristic
162C2×C4C2×D71611yescharacteristic
163C8—41no—
164C8—41no—
165C8—7161no—
166C22—7161no—
167C22—7161no—
168C22—7161no—
169C22—7161no—
170C22—7161no—
171C22—7161no—
172C22#1915308311yescharacteristic
173C4—21no—
174C4—42no—
175C4—14321no—
176C4—7161no—
177C4—7161no—
178C4#1915313411yescharacteristic
179C4#1915313611yescharacteristic
180C4#1915314011yescharacteristic
181C4#1915314511yescharacteristic
182C2—14321no—
183C2—14321no—
184C2#2603858711yescharacteristic
185C2#2603860411yescharacteristic
186C2#2603861911yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#333×C179C2
socleC22×C179#120
prime radical#26039155C2
hypercenter#333D179
hypocenterC179#1646
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #26038789C2semidirect
3. #26038720C2semidirect
4. #26038645C2semidirect
5. #26038166C2semidirect
6. #26038166C2semidirect
7. #333×C179C2semidirect
93. C179#1646semidirect
99. #333D179semidirect

Maximal subgroups

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

subgroupindex
#260391552
#260387892
#260387202
#260386452
#260381662
#333×C1792
#1646179