Finite Group Databasebeta

← #49119827

Subgroups — #49119827

Order 36224.

340 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 71 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×D283C211yesmaximal, characteristic
2C22⋊C8×D283C211yesmaximal, characteristic, complemented
3#31826324C211yesmaximal, characteristic, complemented
4#31826200C211yesmaximal, characteristic, complemented
5#31826199C211yesmaximal, characteristic, complemented
6#31826198C211yesmaximal, characteristic, complemented
7#327×C283C211yesmaximal, characteristic, complemented
8C2×D4×D283—21no—
9C2×D4×D283C411yescharacteristic, complemented
10C22×C4×D283C2211yescharacteristic
11C2×C8×D283—21no—
12#22583585C411yescharacteristic, complemented
13#22583584C2211yescharacteristic
14#22583583—21no—
15#22583582—21no—
16#22583581C411yescharacteristic, complemented
17C2×Dic283⋊C4—21no—
18C4⋊C4×D283C411yescharacteristic, complemented
19C2×(C2×D283)⋊C4—21no—
20C22⋊C4×D283—21no—
21C22⋊(C283⋊C8)C2211yescharacteristic, complemented
22(C2×D283)⋊C8—21no—
23C283⋊#95C2211yescharacteristic, complemented
24#121×C283C2211yescharacteristic
25C22⋊C8×C283C2211yescharacteristic, complemented
26#95×C283C2211yescharacteristic, complemented
27C23×D283—21no—
28C23×D283D411yescharacteristic
29C2×D1132—21no—
30C2×D1132C2×C411yescharacteristic
31C2×C22⋊D283—21no—
32C2×C22⋊D283—21no—
33C2×C22⋊D283—21no—
34D4×D283—42no—
35D4×D283—42no—
36D4×D283—42no—
37C22×Dic283—21no—
38C22×Dic283D411yescharacteristic
39C2×C4×D283—21no—
40C2×C4×D283—42no—
41C2×C4×D283C2×C411yescharacteristic
42C2×C4×D283C2×C411yescharacteristic
43C2×C4×D283D411yescharacteristic
44C2×C4×D283D411yescharacteristic
45C2×C283⋊C8—21no—
46C8×D283—42no—
47C4⋊Dic283C2×C411yescharacteristic
48Dic283⋊C4—21no—
49Dic283⋊C4—42no—
50C22⋊Dic283—21no—
51(C2×D283)⋊C4—21no—
52(C2×D283)⋊C4—21no—
53(C2×D283)⋊C4—42no—
54C2×D4×C283—21no—
55C2×D4×C283C2×C411yescharacteristic
56C22×C4×C283—21no—
57C22×C4×C283C2311yescharacteristic
58C2×C8×C283—21no—
59C4⋊C4×C283C2×C411yescharacteristic
60C22⋊C4×C283—21no—
61C22×D283—21no—
62C22×D283—41no—
63C22×D283—41no—
64C22×D283—42no—
65C22×D283—42no—
66C22×D283—42no—
67C22×D283C22⋊C411yescharacteristic
68C22×D283C22⋊C411yescharacteristic
69C22×D283D812yes—
70C22×D283SD1612yes—
71D1132—41no—
72D1132—42no—
73C22⋊D283—41no—
74C22⋊D283—41no—
75C22⋊D283—42no—
76C22⋊D283—42no—
77C2×Dic283—22no—
78C2×Dic283—21no—
79C2×Dic283—41no—
80C2×Dic283—41no—
81C2×Dic283—41no—
82C2×Dic283C22⋊C411yescharacteristic
83C2×Dic283C22⋊C411yescharacteristic
84C4×D283—22no—
85C4×D283—22no—
86C4×D283—41no—
87C4×D283—41no—
88C4×D283—42no—
89C283⋊C8—41no—
90C23×C283—21no—
91C23×C283C2×D411yescharacteristic
92D4×C283—41no—
93D4×C283—41no—
94D4×C283—41no—
95C2×C4×C283—21no—
96C2×C4×C283—41no—
97C2×C4×C283—41no—
98C2×C4×C283—41no—
99C2×C4×C283—41no—
100C2×C4×C283C22×C411yescharacteristic
101C2×C4×C283C2×D411yescharacteristic
102C8×C283—41no—
103C22×C283—21no—
104C22×C283—21no—
105C22×C283—41no—
106C22×C283—41no—
107C22×C283—41no—
108C22×C283C2×C22⋊C411yescharacteristic
109C22×C283C2×D811yescharacteristic
110C22×C283C2×SD1611yescharacteristic
111C2×D283—21no—
112C2×D283—21no—
113C2×D283—21no—
114C2×D283—21no—
115C2×D283—42no—
116C2×D283—42no—
117C2×D283—41no—
118C2×D283—41no—
119C2×D283—41no—
120C2×D283—84no—
121C2×D283#10212yes—
122C2×D283#10212yes—
123C4×C283—21no—
124C4×C283—21no—
125C4×C283—41no—
126C4×C283—81no—
127Dic283—21no—
128Dic283—41no—
129Dic283—81no—
130Dic283#9912yes—
131C2×C283—21no—
132C2×C283—21no—
133C2×C283—81no—
134C2×C283C2×#9911yescharacteristic
135C2×C283C2×#10211yescharacteristic
136C2×C283#42111yescharacteristic
137D283—22no—
138D283—22no—
139D283—81no—
140C283#151911yescharacteristic, complemented, Sylow
141#1519—2831nomaximal, Sylow
142C2×#121—2831no—
143C2×C22⋊C8—2831no—
144#380—2831no—
145#327—2831no—
146#327—2831no—
147#327—2831no—
148#327D28311yescharacteristic, complemented
149C22×D4—2831no—
150C22×D4—5661no—
151C23×C4—2831no—
152C22×C8—5661no—
153#121—2831no—
154#121—2831no—
155#121—2831no—
156#121—5661no—
157#121—5661no—
158#121C2×D28311yescharacteristic
159C2×C4⋊C4—2831no—
160C2×C4⋊C4—5661no—
161C2×C22⋊C4—5661no—
162C2×C22⋊C4—5661no—
163C22⋊C8—2831no—
164C22⋊C8—5661no—
165C22⋊C8C2×D28311yescharacteristic, complemented
166#95—2831no—
167#95C2×D28311yescharacteristic, complemented
168C24—2831no—
169C24—5661no—
170C2×D4—21no—
171C2×D4—2831no—
172C2×D4—5661no—
173C2×D4—5661no—
174C2×D4—5661no—
175C2×D4—5661no—
176C2×D4—11322no—
177C2×D4—11322no—
178C2×D4—11322no—
179C2×D4C4×D28311yescharacteristic
180C22×C4—21no—
181C22×C4—2831no—
182C22×C4—2831no—
183C22×C4—2831no—
184C22×C4—2831no—
185C22×C4—2831no—
186C22×C4—5661no—
187C22×C4—5661no—
188C22×C4—11322no—
189C22×C4C22×D28311yescharacteristic
190C2×C8—21no—
191C2×C8—5661no—
192C2×C8—11322no—
193C4⋊C4—2831no—
194C4⋊C4—5661no—
195C4⋊C4—11322no—
196C4⋊C4C4×D28311yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—5661no—
199C22⋊C4—5661no—
200C22⋊C4—5661no—
201C22⋊C4—11322no—
202C23—21no—
203C23—2831no—
204C23—2831no—
205C23—2832no—
206C23—2832no—
207C23—5661no—
208C23—11321no—
209C23—11321no—
210C23—11322no—
211C23—11322no—
212C23—11322no—
213C23D4×D28311yescharacteristic
214D4—41no—
215D4—41no—
216D4—41no—
217D4—11321no—
218D4—11322no—
219D4—11322no—
220D4—11322no—
221D4—11321no—
222D4—11321no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—2831no—
229C2×C4—2831no—
230C2×C4—5662no—
231C2×C4—5662no—
232C2×C4—5662no—
233C2×C4—5661no—
234C2×C4—11321no—
235C2×C4—11321no—
236C2×C4—11322no—
237C2×C4—11321no—
238C2×C4—11321no—
239C2×C4—11321no—
240C2×C4C2×C4×D28311yescharacteristic
241C2×C4D4×D28311yescharacteristic
242C8—41no—
243C8—11321no—
244C22—21no—
245C22—21no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—2832no—
250C22—2832no—
251C22—5661no—
252C22—5661no—
253C22—5661no—
254C22—5661no—
255C22—11322no—
256C22—11322no—
257C22—11321no—
258C22—11321no—
259C22—11321no—
260C22—22644no—
261C22C22⋊C4×D28311yescharacteristic
262C22D8×D28311yescharacteristic
263C22SD16×D28311yescharacteristic
264C4—21no—
265C4—21no—
266C4—41no—
267C4—81no—
268C4—2832no—
269C4—5661no—
270C4—11321no—
271C4—22641no—
272C2—21no—
273C2—21no—
274C2—81no—
275C2—5662no—
276C2—5662no—
277C2—22641no—
278C2#99×D28311yescharacteristic
279C2#102×D28311yescharacteristic
280C2#3182648011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#327×C283C2
socleC22×C283C2×C22⋊C4
prime radical#121×D283C2
cosocleC22×C4×C283C23
hypercenter#327D283
hypocenterC283#1519
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D283C2semidirect
3. #31826324C2semidirect
4. #31826200C2semidirect
5. #31826199C2semidirect
6. #31826198C2semidirect
7. #327×C283C2semidirect
9. C2×D4×D283C4semidirect
12. #22583585C4semidirect
16. #22583581C4semidirect
18. C4⋊C4×D283C4semidirect
21. C22⋊(C283⋊C8)C22semidirect
23. C283⋊#95C22semidirect
25. C22⋊C8×C283C22semidirect
26. #95×C283C22semidirect
140. C283#1519semidirect
148. #327D283semidirect
165. C22⋊C8C2×D283semidirect
167. #95C2×D283semidirect

Maximal subgroups

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

subgroupindex
#121×D2832
C22⋊C8×D2832
#318263242
#318262002
#318261992
#318261982
#327×C2832
#1519283