Finite Group Databasebeta

← #37507488

Subgroups — #37507488

Order 22912.

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

normal subgroups only

This group has 304 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#26038949C211yesmaximal, characteristic
2C22⋊C8×D179C211yesmaximal, characteristic, complemented
3#26038286C211yesmaximal, characteristic, complemented
4#26038177C211yesmaximal, characteristic, complemented
5#26038175C211yesmaximal, characteristic, complemented
6#26038173C211yesmaximal, characteristic, complemented
7#327×C179C211yesmaximal, characteristic, complemented
8C2×#15668258C411yescharacteristic, complemented
9C22×C4×D179C2211yescharacteristic
10C2×C8×D179—21no—
11#19153095—21no—
12#19153093C411yescharacteristic, complemented
13#19153092C2211yescharacteristic
14#19153084C411yescharacteristic, complemented
15#19153081—21no—
16D4×Dic179—21no—
17(C22⋊D179)⋊C4—21no—
18#19153071C411yescharacteristic, complemented
19C2×(C2×D179)⋊C4—21no—
20C2×C4×Dic179—21no—
21C22⋊(C179⋊C8)C2211yescharacteristic
22(C2×D179)⋊C8—21no—
23C179⋊#95C2211yescharacteristic
24#121×C179C2211yescharacteristic
25C22⋊C8×C179C2211yescharacteristic
26#95×C179C2211yescharacteristic
27C23×D179D411yescharacteristic
28#15668258—42no—
29C2×Dic358C2×C411yescharacteristic
30C2×C22⋊D179—21no—
31C2×C22⋊D179—21no—
32C22×Dic179—21no—
33C22×Dic179—21no—
34C22×Dic179D411yescharacteristic
35C2×C4×D179—42no—
36C2×C4×D179C2×C411yescharacteristic
37C2×C4×D179C2×C411yescharacteristic
38C2×C4×D179D411yescharacteristic
39C2×C4×D179D411yescharacteristic
40C2×C179⋊C8—21no—
41C8×D179—42no—
42C4⋊Dic179—21no—
43C4⋊Dic179C2×C411yescharacteristic
44Dic179⋊C4—21no—
45C22⋊Dic179—21no—
46C22⋊Dic179—21no—
47(C2×D179)⋊C4—24no—
48(C2×D179)⋊C4—21no—
49(C2×D179)⋊C4—21no—
50C4×Dic179—21no—
51C4×Dic179—42no—
52C2×D4×C179—21no—
53C2×D4×C179C2×C411yescharacteristic
54C22×C4×C179—21no—
55C22×C4×C179C2311yescharacteristic
56C2×C8×C179—21no—
57C4⋊C4×C179C2×C411yescharacteristic
58C22⋊C4×C179—21no—
59C22×D179—21no—
60C22×D179—21no—
61C22×D179—22no—
62C22×D179—41no—
63C22×D179C22⋊C411yescharacteristic
64C22×D179C22⋊C411yescharacteristic
65Dic358—41no—
66C22⋊D179—42no—
67C22⋊D179—42no—
68C2×Dic179—22no—
69C2×Dic179—22no—
70C2×Dic179—21no—
71C2×Dic179—21no—
72C2×Dic179—41no—
73C2×Dic179—41no—
74C2×Dic179—42no—
75C2×Dic179C22⋊C411yescharacteristic
76C2×Dic179C22⋊C411yescharacteristic
77C4×D179—22no—
78C4×D179—22no—
79C4×D179—41no—
80C4×D179—41no—
81C179⋊C8—41no—
82C23×C179—21no—
83C23×C179C2×D411yescharacteristic
84D4×C179—41no—
85D4×C179—41no—
86D4×C179—41no—
87C2×C4×C179—22no—
88C2×C4×C179—21no—
89C2×C4×C179—41no—
90C2×C4×C179—41no—
91C2×C4×C179—41no—
92C2×C4×C179C22×C411yescharacteristic
93C2×C4×C179C2×D411yescharacteristic
94C8×C179—41no—
95C22×C179—21no—
96C22×C179—21no—
97C22×C179—41no—
98C22×C179—41no—
99C22×C179—41no—
100C22×C179C2×C22⋊C411yescharacteristic
101C22×C179#13511yescharacteristic
102C22×C179#13511yescharacteristic
103C2×D179—21no—
104C2×D179—21no—
105C2×D179—21no—
106C2×D179—21no—
107C2×D179—21no—
108C2×D179—42no—
109C2×D179—42no—
110C2×D179#10412yes—
111C4×C179—21no—
112C4×C179—21no—
113C4×C179—42no—
114C4×C179—41no—
115Dic179—21no—
116Dic179—42no—
117Dic179—41no—
118Dic179—41no—
119Dic179#9912yes—
120C2×C179—21no—
121C2×C179—21no—
122C2×C179—81no—
123C2×C179C2×#9911yescharacteristic
124C2×C179#41611yescharacteristic
125C2×C179C2×#10411yescharacteristic
126D179—22no—
127D179—41no—
128C179#150111yescharacteristic, complemented, Sylow
129#1501—1791nomaximal, Sylow
130#525—1791no—
131C2×C22⋊C8—1791no—
132C4×C22⋊C4—1791no—
133#328—1791no—
134#328—1791no—
135#327—1791no—
136#327D17911yescharacteristic, complemented
137C2×#41—1791no—
138C23×C4—1791no—
139C22×C8—3581no—
140#123—3581no—
141C22⋊Q8—1791no—
142C22⋊Q8—1791no—
143#121—1791no—
144#121C2×D17911yescharacteristic
145#120—3581no—
146C4×D4—3581no—
147C4×D4—3581no—
148#117—1791no—
149C2×C22⋊C4—3581no—
150C2×C42—3581no—
151C22⋊C8—3581no—
152C22⋊C8—1791no—
153C22⋊C8C2×D17911yescharacteristic
154#95—1791no—
155#95C2×D17911yescharacteristic
156C24—1791no—
157#41—7162no—
158C2×Q8—1791no—
159C2×D4—21no—
160C2×D4—3581no—
161C2×D4—3581no—
162C2×D4C4×D17911yescharacteristic
163C22×C4—21no—
164C22×C4—3581no—
165C22×C4—3581no—
166C22×C4—1791no—
167C22×C4—1791no—
168C22×C4—1791no—
169C22×C4—1791no—
170C22×C4—1791no—
171C22×C4—7162no—
172C22×C4C22×D17911yescharacteristic
173C2×C8—21no—
174C2×C8—3581no—
175C2×C8—7162no—
176C4⋊C4—3581no—
177C4⋊C4—3581no—
178C4⋊C4—1791no—
179C4⋊C4C4×D17911yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—3584no—
182C22⋊C4—3581no—
183C22⋊C4—3581no—
184C22⋊C4—3581no—
185C22⋊C4—3581no—
186C42—3581no—
187C42—7162no—
188C23—21no—
189C23—3582no—
190C23—3581no—
191C23—3581no—
192C23—1791no—
193C23—1791no—
194C23—7161no—
195C23D4×D17911yescharacteristic
196Q8—7161no—
197D4—41no—
198D4—41no—
199D4—41no—
200D4—7162no—
201D4—7162no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—3582no—
208C2×C4—3582no—
209C2×C4—3582no—
210C2×C4—3582no—
211C2×C4—3581no—
212C2×C4—3581no—
213C2×C4—1791no—
214C2×C4—1791no—
215C2×C4—7161no—
216C2×C4—7161no—
217C2×C4—7162no—
218C2×C4—7161no—
219C2×C4—7161no—
220C2×C4C2×C4×D17911yescharacteristic
221C2×C4D4×D17911yescharacteristic
222C8—41no—
223C8—7161no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—3581no—
230C22—3581no—
231C22—3581no—
232C22—3581no—
233C22—3581no—
234C22—1792no—
235C22—7162no—
236C22—7162no—
237C22C22⋊C4×D17911yescharacteristic
238C22#1915313211yescharacteristic
239C22#1915313411yescharacteristic
240C4—21no—
241C4—21no—
242C4—42no—
243C4—41no—
244C4—3581no—
245C4—1792no—
246C4—7162no—
247C4—7161no—
248C4—7161no—
249C2—21no—
250C2—21no—
251C2—81no—
252C2—3582no—
253C2—7161no—
254C2#99×D17911yescharacteristic
255C2#2603843211yescharacteristic
256C2#104×D17911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D179
commutatorC2×C4×C179C22×C4
FrattiniC22×C4C22×D179
Fitting#327×C179C2
socleC22×C179C2×C22⋊C4
prime radical#26038949C2
cosocleC22×C4×C179C23
hypercenter#327D179
hypocenterC179#1501
LCSG ▷ C2×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D179C2semidirect
3. #26038286C2semidirect
4. #26038177C2semidirect
5. #26038175C2semidirect
6. #26038173C2semidirect
7. #327×C179C2semidirect
8. C2×#15668258C4semidirect
12. #19153093C4semidirect
14. #19153084C4semidirect
18. #19153071C4semidirect
128. C179#1501semidirect
136. #327D179semidirect

Maximal subgroups

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

subgroupindex
#260389492
C22⋊C8×D1792
#260382862
#260381772
#260381752
#260381732
#327×C1792
#1501179