Finite Group Databasebeta

← #37507503

Subgroups — #37507503

Order 22912.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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#26038952C211yesmaximal, characteristic
2#26038401C211yesmaximal, characteristic, complemented
3#95×D179C211yesmaximal, characteristic, complemented
4#26038176C211yesmaximal, characteristic, complemented
5#26038174C211yesmaximal, characteristic, complemented
6#26038172C211yesmaximal, characteristic, complemented
7#328×C179C211yesmaximal, characteristic, complemented
8C2×#15668260C411yescharacteristic, complemented
9C22×C4×D179—21no—
10C22×C4×D179C2211yescharacteristic
11C2×#15668242—21no—
12#19153098—21no—
13#19153089C411yescharacteristic, complemented
14#19153088C411yescharacteristic, complemented
15#19153087C2211yescharacteristic
16#19153083—21no—
17#19153075—21no—
18(C22⋊D179)⋊C4—21no—
19#19153071C411yescharacteristic, complemented
20C22⋊(C179⋊C8)C2211yescharacteristic
21(C2×D179)⋊C8—21no—
22C179⋊#95—21no—
23C179⋊#95C2211yescharacteristic
24C22⋊Q8×C179C2211yescharacteristic
25C22⋊C8×C179C2211yescharacteristic
26#95×C179C2211yescharacteristic
27C23×D179D411yescharacteristic
28#15668260—42no—
29C2×D716—21no—
30C2×D716—21no—
31C2×D716C2×C411yescharacteristic, complemented
32C2×C22⋊D179—21no—
33C22×Dic179—21no—
34C22×Dic179D411yescharacteristic
35C2×C4×D179—24no—
36C2×C4×D179—21no—
37C2×C4×D179—42no—
38C2×C4×D179—42no—
39C2×C4×D179—42no—
40C2×C4×D179C2×C411yescharacteristic
41C2×C4×D179C2×C411yescharacteristic
42C2×C4×D179D411yescharacteristic
43C2×C4×D179D411yescharacteristic
44#15668242—42no—
45C2×C179⋊C8—21no—
46C4⋊Dic179C2×C411yescharacteristic, complemented
47Dic179⋊C4—21no—
48(C2×D179)⋊C4—21no—
49(C2×D179)⋊C4—21no—
50(C2×D179)⋊C4—21no—
51(C2×D179)⋊C4—21no—
52C4×Dic179—21no—
53C2×Q8×C179C2×C411yescharacteristic, complemented
54C22×C4×C179—21no—
55C22×C4×C179C2311yescharacteristic
56C2×C8×C179—21no—
57C4⋊C4×C179—21no—
58C4⋊C4×C179C2×C411yescharacteristic, complemented
59C22⋊C4×C179—21no—
60C22×D179—21no—
61C22×D179—21no—
62C22×D179—22no—
63C22×D179—22no—
64C22×D179—21no—
65C22×D179C22⋊C411yescharacteristic
66C22×D179C22⋊C411yescharacteristic
67D716—41no—
68D716—42no—
69D716—42no—
70C22⋊D179—41no—
71C22⋊D179—41no—
72C2×Dic179—22no—
73C2×Dic179—21no—
74C2×Dic179—41no—
75C2×Dic179—41no—
76C2×Dic179—41no—
77C2×Dic179C22⋊C411yescharacteristic
78C2×Dic179C22⋊C411yescharacteristic
79C4×D179—22no—
80C4×D179—22no—
81C4×D179—41no—
82C4×D179—41no—
83C4×D179—42no—
84C4×D179—48no—
85C179⋊C8—41no—
86C23×C179C2×D411yescharacteristic
87Q8×C179—41no—
88C2×C4×C179—22no—
89C2×C4×C179—21no—
90C2×C4×C179—21no—
91C2×C4×C179—41no—
92C2×C4×C179—41no—
93C2×C4×C179—41no—
94C2×C4×C179C22×C411yescharacteristic
95C2×C4×C179C2×D411yescharacteristic
96C8×C179—41no—
97C22×C179—21no—
98C22×C179—21no—
99C22×C179C2×C22⋊C411yescharacteristic
100C22×C179AGL(1,ℤ/8)11yescharacteristic
101C22×C179#13711yescharacteristic
102C2×D179—24no—
103C2×D179—24no—
104C2×D179—21no—
105C2×D179—21no—
106C2×D179—21no—
107C2×D179—21no—
108C2×D179—41no—
109C2×D179—41no—
110C2×D179—41no—
111C2×D179#9912yes—
112C2×D179#10412yes—
113C4×C179—21no—
114C4×C179—21no—
115C4×C179—42no—
116C4×C179—41no—
117C4×C179—41no—
118Dic179—21no—
119Dic179—21no—
120Dic179—42no—
121Dic179—41no—
122C2×C179—21no—
123C2×C179—21no—
124C2×C179C2×#9911yescharacteristic
125C2×C179#41711yescharacteristic
126C2×C179C2×#10411yescharacteristic
127D179—22no—
128D179—22no—
129D179—81no—
130C179#150411yescharacteristic, complemented, Sylow
131#1504—1791nomaximal, Sylow
132#525—1791no—
133#407—1791no—
134C2×#95—1791no—
135#328—1791no—
136#328D17911yescharacteristic, complemented
137#327—1791no—
138#327—1791no—
139C2×#41—1791no—
140C23×C4—3581no—
141C23×C4—1791no—
142C2×M16—3581no—
143#123—3581no—
144C22⋊Q8—1791no—
145C22⋊Q8C2×D17911yescharacteristic
146#121—1791no—
147#121—1791no—
148#120—3581no—
149C4×D4—3581no—
150C4×D4—3581no—
151#117—1791no—
152C22⋊C8—3581no—
153C22⋊C8—1791no—
154C22⋊C8C2×D17911yescharacteristic
155#95—3581no—
156#95—1791no—
157#95C2×D17911yescharacteristic
158C24—1791no—
159#41—7162no—
160C2×Q8C4×D17911yescharacteristic, complemented
161C2×D4—3581no—
162C2×D4—3581no—
163C2×D4—3581no—
164C2×D4—1791no—
165C22×C4—21no—
166C22×C4—3584no—
167C22×C4—3581no—
168C22×C4—3581no—
169C22×C4—1791no—
170C22×C4—1791no—
171C22×C4—1791no—
172C22×C4—1791no—
173C22×C4—1791no—
174C22×C4—7162no—
175C22×C4—7162no—
176C22×C4—7162no—
177C22×C4C22×D17911yescharacteristic
178M16—7162no—
179C2×C8—21no—
180C2×C8—3581no—
181C4⋊C4—21no—
182C4⋊C4—3581no—
183C4⋊C4—1791no—
184C4⋊C4C4×D17911yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—3581no—
187C22⋊C4—3581no—
188C22⋊C4—3581no—
189C22⋊C4—3581no—
190C42—3581no—
191C23—3582no—
192C23—3582no—
193C23—3581no—
194C23—3581no—
195C23—3581no—
196C23—1791no—
197C23—1791no—
198C23D4×D17911yescharacteristic
199Q8—41no—
200D4—7161no—
201D4—7162no—
202D4—7162no—
203D4—7161no—
204D4—7161no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—3582no—
212C2×C4—3582no—
213C2×C4—3582no—
214C2×C4—3581no—
215C2×C4—1791no—
216C2×C4—1791no—
217C2×C4—7161no—
218C2×C4—7161no—
219C2×C4—7162no—
220C2×C4—7168no—
221C2×C4—7161no—
222C2×C4—7161no—
223C2×C4—7161no—
224C2×C4C2×C4×D17911yescharacteristic
225C2×C4D4×D17911yescharacteristic
226C8—41no—
227C8—7161no—
228C22—21no—
229C22—21no—
230C22—3584no—
231C22—3584no—
232C22—3581no—
233C22—3581no—
234C22—3581no—
235C22—3581no—
236C22—1792no—
237C22—1792no—
238C22—7161no—
239C22—7161no—
240C22—7161no—
241C22C22⋊C4×D17911yescharacteristic
242C22#1915314011yescharacteristic
243C22#1915314511yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—41no—
249C4—3581no—
250C4—3581no—
251C4—7162no—
252C4—7161no—
253C2—21no—
254C2—21no—
255C2—3582no—
256C2—3582no—
257C2—14321no—
258C2#99×D17911yescharacteristic
259C2#2603843911yescharacteristic
260C2#104×D17911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D179
commutatorC2×C4×C179C22×C4
FrattiniC22×C4C22×D179
Fitting#328×C179C2
socleC22×C179C2×C22⋊C4
prime radical#26038952C2
cosocleC22×C4×C179C23
hypercenter#328D179
hypocenterC179#1504
LCSG ▷ C2×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #26038401C2semidirect
3. #95×D179C2semidirect
4. #26038176C2semidirect
5. #26038174C2semidirect
6. #26038172C2semidirect
7. #328×C179C2semidirect
8. C2×#15668260C4semidirect
13. #19153089C4semidirect
14. #19153088C4semidirect
19. #19153071C4semidirect
31. C2×D716C2×C4semidirect
46. C4⋊Dic179C2×C4semidirect
53. C2×Q8×C179C2×C4semidirect
58. C4⋊C4×C179C2×C4semidirect
130. C179#1504semidirect
136. #328D179semidirect
160. C2×Q8C4×D179semidirect
184. C4⋊C4C4×D179semidirect

Maximal subgroups

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

subgroupindex
#260389522
#260384012
#95×D1792
#260381762
#260381742
#260381722
#328×C1792
#1504179