Finite Group Databasebeta

← #49119814

Subgroups — #49119814

Order 36224.

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

normal subgroups only

This group has 284 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#31826975C211yesmaximal, characteristic
2C22⋊C8×D283C211yesmaximal, characteristic, complemented
3#31826327C211yesmaximal, characteristic, complemented
4#31826203C211yesmaximal, characteristic, complemented
5#31826201C211yesmaximal, characteristic, complemented
6#31826199C211yesmaximal, characteristic, complemented
7#327×C283C211yesmaximal, characteristic, complemented
8C2×#17985391C411yescharacteristic, complemented
9C22×C4×D283C2211yescharacteristic
10C2×C8×D283—21no—
11#22583592—21no—
12#22583590C411yescharacteristic, complemented
13#22583589C2211yescharacteristic
14#22583581C411yescharacteristic, complemented
15#22583578—21no—
16D4×Dic283—21no—
17(C22⋊D283)⋊C4—21no—
18#22583568C411yescharacteristic, complemented
19C2×(C2×D283)⋊C4—21no—
20C22⋊(C283⋊C8)C2211yescharacteristic
21(C2×D283)⋊C8—21no—
22C283⋊#95—21no—
23C283⋊#95C2211yescharacteristic
24#121×C283C2211yescharacteristic
25C22⋊C8×C283C2211yescharacteristic
26#95×C283C2211yescharacteristic
27C23×D283D411yescharacteristic
28#17985391—42no—
29C2×Dic566C2×C411yescharacteristic
30C2×C22⋊D283—21no—
31C2×C22⋊D283—21no—
32C22×Dic283—21no—
33C22×Dic283—21no—
34C22×Dic283D411yescharacteristic
35C2×C4×D283—42no—
36C2×C4×D283C2×C411yescharacteristic
37C2×C4×D283C2×C411yescharacteristic
38C2×C4×D283D411yescharacteristic
39C2×C4×D283D411yescharacteristic
40C2×C283⋊C8—21no—
41C8×D283—42no—
42C4⋊Dic283—21no—
43C4⋊Dic283C2×C411yescharacteristic
44Dic283⋊C4—21no—
45C22⋊Dic283—21no—
46C22⋊Dic283—21no—
47(C2×D283)⋊C4—21no—
48(C2×D283)⋊C4—21no—
49(C2×D283)⋊C4—42no—
50C4×Dic283—21no—
51C2×D4×C283—21no—
52C2×D4×C283C2×C411yescharacteristic
53C22×C4×C283—21no—
54C22×C4×C283C2311yescharacteristic
55C2×C8×C283—21no—
56C4⋊C4×C283C2×C411yescharacteristic
57C22⋊C4×C283—21no—
58C22×D283—21no—
59C22×D283—21no—
60C22×D283—22no—
61C22×D283—41no—
62C22×D283C22⋊C411yescharacteristic
63C22×D283C22⋊C411yescharacteristic
64Dic566—41no—
65C22⋊D283—42no—
66C22⋊D283—42no—
67C2×Dic283—21no—
68C2×Dic283—21no—
69C2×Dic283—41no—
70C2×Dic283—42no—
71C2×Dic283—41no—
72C2×Dic283—41no—
73C2×Dic283—41no—
74C2×Dic283C22⋊C411yescharacteristic
75C2×Dic283C22⋊C411yescharacteristic
76C4×D283—22no—
77C4×D283—22no—
78C4×D283—41no—
79C4×D283—41no—
80C283⋊C8—41no—
81C23×C283—21no—
82C23×C283C2×D411yescharacteristic
83D4×C283—41no—
84D4×C283—41no—
85D4×C283—41no—
86C2×C4×C283—21no—
87C2×C4×C283—41no—
88C2×C4×C283—41no—
89C2×C4×C283—41no—
90C2×C4×C283—41no—
91C2×C4×C283C22×C411yescharacteristic
92C2×C4×C283C2×D411yescharacteristic
93C8×C283—41no—
94C22×C283—21no—
95C22×C283—21no—
96C22×C283—41no—
97C22×C283—41no—
98C22×C283—41no—
99C22×C283C2×C22⋊C411yescharacteristic
100C22×C283#13511yescharacteristic
101C22×C283#13511yescharacteristic
102C2×D283—21no—
103C2×D283—21no—
104C2×D283—21no—
105C2×D283—21no—
106C2×D283—21no—
107C2×D283—42no—
108C2×D283—42no—
109C2×D283#9912yes—
110C4×C283—21no—
111C4×C283—21no—
112C4×C283—41no—
113C4×C283—81no—
114Dic283—21no—
115Dic283—21no—
116Dic283—41no—
117Dic283—41no—
118Dic283—81no—
119C2×C283—21no—
120C2×C283—21no—
121C2×C283—81no—
122C2×C283C2×#9911yescharacteristic
123C2×C283#41611yescharacteristic
124C2×C283#42111yescharacteristic
125D283—22no—
126D283—41no—
127C283#151611yescharacteristic, complemented, Sylow
128#1516—2831nomaximal, Sylow
129#525—2831no—
130C2×C22⋊C8—2831no—
131#381—2831no—
132#328—2831no—
133#328—2831no—
134#327—2831no—
135#327D28311yescharacteristic, complemented
136C2×#41—2831no—
137C23×C4—2831no—
138C22×C8—5661no—
139#123—5661no—
140C22⋊Q8—2831no—
141C22⋊Q8—2831no—
142#121—2831no—
143#121C2×D28311yescharacteristic
144#120—5661no—
145C4×D4—5661no—
146C4×D4—5661no—
147#117—2831no—
148C2×C22⋊C4—5661no—
149C22⋊C8—2831no—
150C22⋊C8—5661no—
151C22⋊C8C2×D28311yescharacteristic
152#95—2831no—
153#95—5661no—
154#95C2×D28311yescharacteristic
155C24—2831no—
156#41—11322no—
157C2×Q8—2831no—
158C2×D4—21no—
159C2×D4—5661no—
160C2×D4—5661no—
161C2×D4C4×D28311yescharacteristic
162C22×C4—21no—
163C22×C4—2831no—
164C22×C4—2831no—
165C22×C4—2831no—
166C22×C4—2831no—
167C22×C4—2831no—
168C22×C4—5661no—
169C22×C4—5661no—
170C22×C4—11322no—
171C22×C4C22×D28311yescharacteristic
172C2×C8—21no—
173C2×C8—5661no—
174C2×C8—11322no—
175C4⋊C4—2831no—
176C4⋊C4—5661no—
177C4⋊C4—5661no—
178C4⋊C4C4×D28311yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—5661no—
181C22⋊C4—5661no—
182C22⋊C4—5661no—
183C22⋊C4—5661no—
184C22⋊C4—11322no—
185C42—5661no—
186C23—21no—
187C23—2831no—
188C23—2831no—
189C23—5662no—
190C23—5661no—
191C23—5661no—
192C23—11321no—
193C23D4×D28311yescharacteristic
194Q8—11321no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—11322no—
199D4—11322no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—2831no—
206C2×C4—2831no—
207C2×C4—5662no—
208C2×C4—5662no—
209C2×C4—5661no—
210C2×C4—5661no—
211C2×C4—11321no—
212C2×C4—11321no—
213C2×C4—11321no—
214C2×C4—11322no—
215C2×C4—11321no—
216C2×C4—11321no—
217C2×C4—11321no—
218C2×C4C2×C4×D28311yescharacteristic
219C2×C4D4×D28311yescharacteristic
220C8—41no—
221C8—11321no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—2832no—
228C22—5661no—
229C22—5661no—
230C22—5661no—
231C22—5661no—
232C22—5661no—
233C22—11322no—
234C22—11322no—
235C22C22⋊C4×D28311yescharacteristic
236C22#2258362911yescharacteristic
237C22#2258363111yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—5661no—
243C4—5661no—
244C4—11321no—
245C4—11321no—
246C4—22641no—
247C2—21no—
248C2—21no—
249C2—81no—
250C2—5662no—
251C2—11321no—
252C2#99×D28311yescharacteristic
253C2#3182645811yescharacteristic
254C2#3182648011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#327×C283C2
socleC22×C283C2×C22⋊C4
prime radical#31826975C2
cosocleC22×C4×C283C23
hypercenter#327D283
hypocenterC283#1516
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. #31826327C2semidirect
4. #31826203C2semidirect
5. #31826201C2semidirect
6. #31826199C2semidirect
7. #327×C283C2semidirect
8. C2×#17985391C4semidirect
12. #22583590C4semidirect
14. #22583581C4semidirect
18. #22583568C4semidirect
127. C283#1516semidirect
135. #327D283semidirect

Maximal subgroups

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

subgroupindex
#318269752
C22⋊C8×D2832
#318263272
#318262032
#318262012
#318261992
#327×C2832
#1516283