Finite Group Databasebeta

← #44450337

Subgroups — #44450337

Order 29824.

326 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 63 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#121×D233C211yesmaximal, characteristic
2#28416397C211yesmaximal, characteristic, complemented
3#28416297C211yesmaximal, characteristic, complemented
4#28416170C211yesmaximal, characteristic, complemented
5#28416169C211yesmaximal, characteristic, complemented
6#28416168C211yesmaximal, characteristic, complemented
7#327×C233C211yesmaximal, characteristic, complemented
8C2×D4×D233—21no—
9C2×D4×D233C411yescharacteristic, complemented
10C22×C4×D233C2211yescharacteristic
11C2×#16836577—21no—
12#21418510C411yescharacteristic, complemented
13#21418509C2211yescharacteristic
14#21418508—21no—
15#21418507—21no—
16#21418506C411yescharacteristic, complemented
17C4⋊C4×D233C411yescharacteristic, complemented
18C2×#16836571—21no—
19C22⋊C4×D233—21no—
20C22⋊#14272338C2211yescharacteristic, complemented
21#21418447—21no—
22#21418442—21no—
23#21418442C2211yescharacteristic, complemented
24#121×C233C2211yescharacteristic
25C22⋊C8×C233C2211yescharacteristic, complemented
26#95×C233C2211yescharacteristic, complemented
27C23×D233—21no—
28C23×D233D411yescharacteristic
29C2×D932—21no—
30C2×D932C2×C411yescharacteristic
31C2×C22⋊D233—21no—
32C2×C22⋊D233—21no—
33C2×C22⋊D233—21no—
34D4×D233—42no—
35D4×D233—42no—
36D4×D233—42no—
37C22×Dic233—21no—
38C22×Dic233D411yescharacteristic
39C2×C4×D233—21no—
40C2×C4×D233—42no—
41C2×C4×D233C2×C411yescharacteristic
42C2×C4×D233C2×C411yescharacteristic
43C2×C4×D233D411yescharacteristic
44C2×C4×D233D411yescharacteristic
45#16836577—42no—
46C2×#14272338—21no—
47C4⋊Dic233C2×C411yescharacteristic
48#16836573—21no—
49C22⋊Dic233—21no—
50#16836571—21no—
51#16836571—21no—
52#16836571—42no—
53C2×D4×C233—21no—
54C2×D4×C233C2×C411yescharacteristic
55C22×C4×C233—21no—
56C22×C4×C233C2311yescharacteristic
57C2×C8×C233—21no—
58C4⋊C4×C233C2×C411yescharacteristic
59C22⋊C4×C233—21no—
60C22×D233—21no—
61C22×D233—21no—
62C22×D233—22no—
63C22×D233—21no—
64C22×D233—41no—
65C22×D233—42no—
66C22×D233—42no—
67C22×D233—42no—
68C22×D233C22⋊C411yescharacteristic
69C22×D233C22⋊C411yescharacteristic
70D932—41no—
71D932—42no—
72C22⋊D233—42no—
73C22⋊D233—42no—
74C22⋊D233—41no—
75C22⋊D233—41no—
76C2×Dic233—21no—
77C2×Dic233—41no—
78C2×Dic233—41no—
79C2×Dic233—41no—
80C2×Dic233—41no—
81C2×Dic233C22⋊C411yescharacteristic
82C2×Dic233C22⋊C411yescharacteristic
83C4×D233—22no—
84C4×D233—22no—
85C4×D233—41no—
86C4×D233—41no—
87C4×D233—42no—
88#14272338—41no—
89C23×C233—21no—
90C23×C233C2×D411yescharacteristic
91D4×C233—41no—
92D4×C233—41no—
93D4×C233—41no—
94C2×C4×C233—21no—
95C2×C4×C233—41no—
96C2×C4×C233—41no—
97C2×C4×C233—41no—
98C2×C4×C233—41no—
99C2×C4×C233C22×C411yescharacteristic
100C2×C4×C233C2×D411yescharacteristic
101C8×C233—41no—
102C22×C233—21no—
103C22×C233—21no—
104C22×C233—41no—
105C22×C233—41no—
106C22×C233—41no—
107C22×C233C2×C22⋊C411yescharacteristic
108C22×C233AGL(1,ℤ/8)11yescharacteristic
109C22×C233AGL(1,ℤ/8)11yescharacteristic
110C2×D233—21no—
111C2×D233—21no—
112C2×D233—21no—
113C2×D233—21no—
114C2×D233—21no—
115C2×D233—42no—
116C2×D233—42no—
117C2×D233—41no—
118C2×D233—41no—
119C2×D233—41no—
120C2×D233—84no—
121C2×D233#9912yes—
122C4×C233—21no—
123C4×C233—21no—
124C4×C233—41no—
125C4×C233—81no—
126Dic233—21no—
127Dic233—21no—
128Dic233—41no—
129Dic233—81no—
130C2×C233—21no—
131C2×C233—21no—
132C2×C233—81no—
133C2×C233C2×#9911yescharacteristic
134C2×C233#41811yescharacteristic
135C2×C233#42111yescharacteristic
136D233—22no—
137D233—41no—
138D233—81no—
139C233#151011yescharacteristic, complemented, Sylow
140#1510—2331nomaximal, Sylow
141C2×#121—2331no—
142#407—2331no—
143#381—2331no—
144#327—2331no—
145#327—2331no—
146#327—2331no—
147#327D23311yescharacteristic, complemented
148C22×D4—4661no—
149C22×D4—2331no—
150C23×C4—2331no—
151C2×M16—4661no—
152#121—4661no—
153#121—4661no—
154#121—2331no—
155#121—2331no—
156#121—2331no—
157#121C2×D23311yescharacteristic
158C2×C4⋊C4—2331no—
159C2×C22⋊C4—4661no—
160C2×C22⋊C4—4661no—
161C22⋊C8—4661no—
162C22⋊C8—2331no—
163C22⋊C8C2×D23311yescharacteristic, complemented
164#95—4661no—
165#95—2331no—
166#95C2×D23311yescharacteristic, complemented
167C24—4661no—
168C24—2331no—
169C2×D4—21no—
170C2×D4—9322no—
171C2×D4—9322no—
172C2×D4—9322no—
173C2×D4—4661no—
174C2×D4—4661no—
175C2×D4—4661no—
176C2×D4—4661no—
177C2×D4—2331no—
178C2×D4C4×D23311yescharacteristic
179C22×C4—21no—
180C22×C4—9322no—
181C22×C4—4661no—
182C22×C4—4661no—
183C22×C4—2331no—
184C22×C4—2331no—
185C22×C4—2331no—
186C22×C4—2331no—
187C22×C4—2331no—
188C22×C4C22×D23311yescharacteristic
189M16—9322no—
190C2×C8—21no—
191C2×C8—4661no—
192C4⋊C4—4661no—
193C4⋊C4—2331no—
194C4⋊C4C4×D23311yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—9322no—
197C22⋊C4—4661no—
198C22⋊C4—4661no—
199C22⋊C4—4661no—
200C23—21no—
201C23—9321no—
202C23—9322no—
203C23—9322no—
204C23—9322no—
205C23—4662no—
206C23—4661no—
207C23—4661no—
208C23—4661no—
209C23—2331no—
210C23—2331no—
211C23D4×D23311yescharacteristic
212D4—41no—
213D4—41no—
214D4—41no—
215D4—9321no—
216D4—9322no—
217D4—9322no—
218D4—9321no—
219D4—9321no—
220D4—9322no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—9321no—
227C2×C4—9321no—
228C2×C4—9322no—
229C2×C4—9321no—
230C2×C4—9321no—
231C2×C4—9321no—
232C2×C4—9321no—
233C2×C4—4662no—
234C2×C4—4662no—
235C2×C4—4661no—
236C2×C4—2331no—
237C2×C4—2331no—
238C2×C4C2×C4×D23311yescharacteristic
239C2×C4D4×D23311yescharacteristic
240C8—41no—
241C8—9321no—
242C22—21no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—18644no—
248C22—9322no—
249C22—9322no—
250C22—9321no—
251C22—9321no—
252C22—9321no—
253C22—4661no—
254C22—4661no—
255C22—4661no—
256C22—4661no—
257C22—4661no—
258C22—2332no—
259C22C22⋊C4×D23311yescharacteristic
260C22#2141855911yescharacteristic
261C22#2141856211yescharacteristic
262C4—21no—
263C4—21no—
264C4—41no—
265C4—81no—
266C4—18641no—
267C4—9321no—
268C4—4661no—
269C4—4661no—
270C2—21no—
271C2—21no—
272C2—81no—
273C2—18641no—
274C2—9321no—
275C2—4662no—
276C2#99×D23311yescharacteristic
277C2#2841643811yescharacteristic
278C2#2841645011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D233
commutatorC2×C4×C233C22×C4
FrattiniC22×C4C22×D233
Fitting#327×C233C2
socleC22×C233C2×C22⋊C4
prime radical#121×D233C2
cosocleC22×C4×C233C23
hypercenter#327D233
hypocenterC233#1510
LCSG ▷ C2×C4×C233 ▷ C22×C233 ▷ C233
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #28416397C2semidirect
3. #28416297C2semidirect
4. #28416170C2semidirect
5. #28416169C2semidirect
6. #28416168C2semidirect
7. #327×C233C2semidirect
9. C2×D4×D233C4semidirect
12. #21418510C4semidirect
16. #21418506C4semidirect
17. C4⋊C4×D233C4semidirect
20. C22⋊#14272338C22semidirect
23. #21418442C22semidirect
25. C22⋊C8×C233C22semidirect
26. #95×C233C22semidirect
139. C233#1510semidirect
147. #327D233semidirect
163. C22⋊C8C2×D233semidirect
166. #95C2×D233semidirect

Maximal subgroups

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

subgroupindex
#121×D2332
#284163972
#284162972
#284161702
#284161692
#284161682
#327×C2332
#1510233