Finite Group Databasebeta

← #37510150

Subgroups — #37510150

Order 22912.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#19153104C211yesmaximal, characteristic
2C2×#19153038C211yesmaximal, characteristic
3C2×#19153036C211yesmaximal, characteristic
4#26038344C211yesmaximal, characteristic
5#26038201C211yesmaximal, characteristic
6#26038193C211yesmaximal, characteristic
7#340×C179C211yesmaximal, characteristic
8C22×Dic358C2211yescharacteristic
9C22×C179⋊C8C2211yescharacteristic
10#19153104—22no—
11#19153104—22no—
12C2×C4⋊Dic179—21no—
13C2×C4⋊Dic179C2211yescharacteristic
14C2×Dic179⋊C4—21no—
15C2×C4×Dic179C2211yescharacteristic
16#19153038—22no—
17#19153036—22no—
18C179⋊#95—21no—
19C179⋊#95—21no—
20C22×C8×C179C2211yescharacteristic
21C2×C4⋊C4×C179C2211yescharacteristic
22C2×C4⋊C4×C179C2211yescharacteristic
23C2×Dic358—21no—
24C2×Dic358—21no—
25C2×Dic358—21no—
26C2×Dic358—21no—
27C2×Dic358—21no—
28C2×Dic358Q812yes—
29C22×Dic179—21no—
30C22×Dic179—21no—
31C22×Dic179D411yescharacteristic
32C22×Dic179D411yescharacteristic
33C2×C179⋊C8—21no—
34C2×C179⋊C8—21no—
35C2×C179⋊C8—21no—
36C4⋊Dic179—24no—
37C4⋊Dic179—21no—
38C4⋊Dic179D412yes—
39Dic179⋊C4—24no—
40C4×Dic179—21no—
41C4×Dic179—21no—
42C22×C4×C179—21no—
43C22×C4×C179—21no—
44C22×C4×C179C2311yescharacteristic
45C2×C8×C179—21no—
46C2×C8×C179—21no—
47C2×C8×C179—21no—
48C4⋊C4×C179—21no—
49C4⋊C4×C179—21no—
50C4⋊C4×C179—21no—
51C4⋊C4×C179D412yes—
52Dic358—22no—
53Dic358—22no—
54Dic358—41no—
55Dic358—41no—
56C2×Dic179—21no—
57C2×Dic179—21no—
58C2×Dic179—22no—
59C2×Dic179—22no—
60C2×Dic179—21no—
61C2×Dic179—21no—
62C2×Dic179—21no—
63C2×Dic179—21no—
64C2×Dic179—41no—
65C2×Dic179—41no—
66C2×Dic179—41no—
67C2×Dic179—41no—
68C179⋊C8—41no—
69C23×C179C2×D411yescharacteristic
70C2×C4×C179—22no—
71C2×C4×C179—41no—
72C2×C4×C179—41no—
73C2×C4×C179—41no—
74C2×C4×C179—41no—
75C2×C4×C179—41no—
76C2×C4×C179C2×D411yescharacteristic
77C2×C4×C179C2×D411yescharacteristic
78C2×C4×C179C2×Q811yescharacteristic
79C2×C4×C179#4111yescharacteristic
80C2×C4×C179#4111yescharacteristic
81C2×C4×C179#4111yescharacteristic
82C8×C179—41no—
83C22×C179#12011yescharacteristic
84C22×C179C22⋊Q811yescharacteristic
85C22×C179#12411yescharacteristic
86C22×C179#13511yescharacteristic
87C22×C179#13511yescharacteristic
88C22×C179#13711yescharacteristic
89C22×C179#13711yescharacteristic
90C4×C179—42no—
91C4×C179—81no—
92C4×C179C22⋊Q811yescharacteristic
93C4×C179C22⋊Q811yescharacteristic
94C4×C179#12411yescharacteristic
95C4×C179#12411yescharacteristic
96Dic179—42no—
97Dic179—41no—
98Dic179—41no—
99Dic179—42no—
100C2×C179#39311yescharacteristic
101C2×C179#45211yescharacteristic
102C2×C179#45211yescharacteristic
103C2×C179#47911yescharacteristic
104C2×C179#47911yescharacteristic
105C2×C179#48811yescharacteristic
106C2×C179#49111yescharacteristic
107C179#202611yescharacteristic, complemented, Sylow
108#2026—1791nomaximal, Sylow
109C2×#125—1791no—
110C2×#103—1791no—
111C2×#103—1791no—
112#391—1791no—
113#340—1791no—
114#340D17911yescharacteristic
115#336—1791no—
116C22×Q8—1791no—
117C22×C8—1791no—
118C22×C8C2×D17911yescharacteristic
119#125—3582no—
120#125—3582no—
121C2×C4⋊C4—3581no—
122C2×C4⋊C4—3581no—
123C2×C4⋊C4—1791no—
124C2×C4⋊C4C2×D17911yescharacteristic
125C2×C4⋊C4C2×D17911yescharacteristic
126C2×C42—1791no—
127#103—3582no—
128#103—3582no—
129#95—3581no—
130#95—3581no—
131C2×Q8—3581no—
132C2×Q8—3581no—
133C2×Q8—3581no—
134C2×Q8—3581no—
135C2×Q8—3581no—
136C2×Q8—1792no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—3581no—
140C22×C4—3581no—
141C22×C4—1791no—
142C22×C4—1791no—
143C22×C4C22×D17911yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—3581no—
148C2×C8—3581no—
149C2×C8—3581no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—3584no—
154C4⋊C4—3584no—
155C4⋊C4—3581no—
156C4⋊C4—1792no—
157C4⋊C4D71612yes—
158C42—3581no—
159C42—3581no—
160C23D4×D17911yescharacteristic
161Q8—3582no—
162Q8—3582no—
163Q8—7161no—
164Q8—7161no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—3581no—
172C2×C4—3581no—
173C2×C4—3582no—
174C2×C4—3582no—
175C2×C4—3581no—
176C2×C4—3581no—
177C2×C4—3581no—
178C2×C4—3581no—
179C2×C4—7161no—
180C2×C4—7161no—
181C2×C4—7161no—
182C2×C4—7161no—
183C2×C4D4×D17911yescharacteristic
184C2×C4C2×D71611yescharacteristic
185C2×C4Q8×D17911yescharacteristic
186C2×C4#1566825811yescharacteristic
187C2×C4#1566825911yescharacteristic
188C2×C4#1566825911yescharacteristic
189C8—41no—
190C8—7161no—
191C22#1915308311yescharacteristic
192C22#1915309111yescharacteristic
193C22#1915309911yescharacteristic
194C22#1915313211yescharacteristic
195C22#1915313411yescharacteristic
196C22#1915314211yescharacteristic
197C22#1915314511yescharacteristic
198C4—42no—
199C4—81no—
200C4—7161no—
201C4—7161no—
202C4—7162no—
203C4—7162no—
204C4#1915309111yescharacteristic
205C4#1915309311yescharacteristic
206C4#1915309911yescharacteristic
207C4#1915310111yescharacteristic
208C2#2603835211yescharacteristic
209C2#2603860211yescharacteristic
210C2#2603860411yescharacteristic
211C2#2603874511yescharacteristic
212C2#2603874911yescharacteristic
213C2#2603879211yescharacteristic
214C2#2603880611yescharacteristic
subgroupG/H
centerC23D4×D179
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#340×C179C2
socle, prime radicalC23×C179C2×D4
hypercenter#340D179
hypocenterC179#2026
LCSG ▷ C22×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
107. C179#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#191531042
C2×#191530382
C2×#191530362
#260383442
#260382012
#260381932
#340×C1792
#2026179