Finite Group Databasebeta

← #49121280

Subgroups — #49121280

Order 36224.

312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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#31826933C211yesmaximal, characteristic
2#31826488C211yesmaximal, characteristic, complemented
3C2×#22583538C211yesmaximal, characteristic
4C2×#22583536C211yesmaximal, characteristic
5C4×Dic283⋊C4C211yesmaximal, characteristic, complemented
6#31826224C211yesmaximal, characteristic, complemented
7#339×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9C2×#17985376C2211yescharacteristic
10#22583575C411yescharacteristic, complemented
11#22583575C411yescharacteristic, complemented
12#22583572C411yescharacteristic, complemented
13#22583572C411yescharacteristic, complemented
14(C22⋊D283)⋊C4—21no—
15(C22⋊D283)⋊C4—21no—
16#22583567—21no—
17C2×Dic283⋊C4—21no—
18C2×C4×Dic283C2211yescharacteristic
19C2×C4×Dic283C2211yescharacteristic
20C42×D283—21no—
21Dic283⋊C8—21no—
22Dic283⋊C8—21no—
23#22583538—22no—
24#22583536—22no—
25C283⋊#95—21no—
26C2×M16×C283C2211yescharacteristic
27#117×C283C2211yescharacteristic
28C2×C42×C283C2211yescharacteristic
29#17985392—21no—
30#17985392—21no—
31#17985392D412yes—
32#17985392Q812yes—
33C2×Dic566C2×C411yescharacteristic
34C2×D1132C2×C411yescharacteristic
35C2×C22⋊D283—21no—
36C22×Dic283—21no—
37C22×Dic283D411yescharacteristic
38C22×Dic283D411yescharacteristic
39C2×C4×D283—21no—
40C2×C4×D283—21no—
41C2×C4×D283—21no—
42#17985376—21no—
43#17985376—21no—
44C2×C283⋊C8—21no—
45Dic283⋊C4—24no—
46Dic283⋊C4—21no—
47Dic283⋊C4—21no—
48(C2×D283)⋊C4—21no—
49(C2×D283)⋊C4—21no—
50C4×Dic283—21no—
51C4×Dic283—21no—
52C4×Dic283—21no—
53C4×Dic283—21no—
54C4×Dic283C2×C411yescharacteristic
55C4×Dic283C2×C411yescharacteristic
56C4×Dic283D411yescharacteristic
57C4×Dic283D411yescharacteristic
58C22×C4×C283—21no—
59C22×C4×C283C2311yescharacteristic
60M16×C283—21no—
61M16×C283—21no—
62C2×C8×C283—21no—
63C4⋊C4×C283C2×C411yescharacteristic
64C4⋊C4×C283C2×C411yescharacteristic
65C22⋊C4×C283—21no—
66C42×C283—21no—
67C42×C283—21no—
68C42×C283—21no—
69C22×D283—21no—
70Dic566—21no—
71Dic566C4⋊C412yescomplemented
72D1132—21no—
73D1132C4⋊C412yescomplemented
74C22⋊D283—22no—
75C22⋊D283—22no—
76C2×Dic283—21no—
77C2×Dic283—22no—
78C2×Dic283—22no—
79C2×Dic283—41no—
80C2×Dic283—41no—
81C2×Dic283—41no—
82C2×Dic283C22⋊C411yescharacteristic
83C2×Dic283C22⋊C411yescharacteristic
84C2×Dic283C22⋊C411yescharacteristic
85C2×Dic283C22⋊C411yescharacteristic
86C4×D283—22no—
87C4×D283—22no—
88C4×D283—42no—
89C4×D283—42no—
90C283⋊C8—41no—
91C23×C283C2×D411yescharacteristic
92C2×C4×C283—22no—
93C2×C4×C283—21no—
94C2×C4×C283—21no—
95C2×C4×C283—41no—
96C2×C4×C283—41no—
97C2×C4×C283C22×C411yescharacteristic
98C2×C4×C283C2×D411yescharacteristic
99C2×C4×C283C2×D411yescharacteristic
100C2×C4×C283C2×Q811yescharacteristic
101C2×C4×C283#4111yescharacteristic
102C2×C4×C283#4111yescharacteristic
103C8×C283—41no—
104C22×C283—21no—
105C22×C283—21no—
106C22×C283C2×C22⋊C411yescharacteristic
107C22×C283#12111yescharacteristic
108C22×C283C22⋊Q811yescharacteristic
109C2×D283—22no—
110C2×D283—41no—
111C2×D283—41no—
112C4×C283—42no—
113C4×C283—41no—
114C4×C283—41no—
115C4×C283C2×C4⋊C411yescharacteristic
116C4×C283#11711yescharacteristic
117C4×C283#12111yescharacteristic
118C4×C283C22⋊Q811yescharacteristic
119Dic283—22no—
120Dic283—21no—
121Dic283—21no—
122Dic283—21no—
123Dic283—42no—
124Dic283#10412yescomplemented
125C2×C283—21no—
126C2×C283—21no—
127C2×C283#38011yescharacteristic
128C2×C283C2×#10411yescharacteristic
129C2×C283#42111yescharacteristic
130D283—42no—
131C283#180611yescharacteristic, complemented, Sylow
132#1806—2831nomaximal, Sylow
133C4×#41—2831no—
134#423—2831no—
135C2×#104—2831no—
136C2×#104—2831no—
137C4×C4⋊C4—2831no—
138#339—2831no—
139#339D28311yescharacteristic, complemented
140C2×#41—2831no—
141C2×M16—2831no—
142C2×M16C2×D28311yescharacteristic
143C4×Q8—2831no—
144C4×Q8—2831no—
145C4×D4—2831no—
146C4×D4—2831no—
147C4×D4—5661no—
148C4×D4—5661no—
149#117—5661no—
150#117C2×D28311yescharacteristic
151C2×C4⋊C4—5661no—
152C2×C42—2831no—
153C2×C42—2831no—
154C2×C42—5661no—
155C2×C42C2×D28311yescharacteristic
156C4⋊C8—5661no—
157C4⋊C8—5661no—
158#104—5662no—
159#104—5662no—
160#95—5661no—
161#41—2832no—
162#41—2832no—
163#41—5661no—
164#41—5661no—
165C2×Q8—2831no—
166C2×D4—2831no—
167C2×D4—5661no—
168C22×C4—21no—
169C22×C4—2831no—
170C22×C4—2831no—
171C22×C4—5661no—
172C22×C4—5661no—
173C22×C4—5661no—
174C22×C4—5661no—
175C22×C4C22×D28311yescharacteristic
176M16—21no—
177M16—21no—
178M16—5661no—
179M16—5661no—
180C2×C8—21no—
181C2×C8—5661no—
182C4⋊C4—5661no—
183C4⋊C4—5661no—
184C4⋊C4—5664no—
185C4⋊C4C4×D28311yescharacteristic
186C4⋊C4C4×D28311yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—5661no—
189C22⋊C4—5661no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—2831no—
194C42—2831no—
195C42—2831no—
196C42—2831no—
197C42—5661no—
198C42—5661no—
199C42—5661no—
200C42—5661no—
201C23—5661no—
202C23D4×D28311yescharacteristic
203Q8—2832no—
204Q8—5661no—
205D4—2832no—
206D4—5662no—
207D4—5662no—
208D4—5661no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—2831no—
215C2×C4—2831no—
216C2×C4—2831no—
217C2×C4—2831no—
218C2×C4—5662no—
219C2×C4—5661no—
220C2×C4—5662no—
221C2×C4—5662no—
222C2×C4—5662no—
223C2×C4—11322no—
224C2×C4—11322no—
225C2×C4—11321no—
226C2×C4—11321no—
227C2×C4—11321no—
228C2×C4C2×C4×D28311yescharacteristic
229C2×C4D4×D28311yescharacteristic
230C2×C4D4×D28311yescharacteristic
231C2×C4Q8×D28311yescharacteristic
232C2×C4#1798539211yescharacteristic
233C2×C4#1798539211yescharacteristic
234C8—41no—
235C8—11321no—
236C22—21no—
237C22—21no—
238C22—5662no—
239C22—11321no—
240C22—11321no—
241C22C22⋊C4×D28311yescharacteristic
242C22#2258358311yescharacteristic
243C22#2258358811yescharacteristic
244C4—42no—
245C4—41no—
246C4—41no—
247C4—2832no—
248C4—5661no—
249C4—5661no—
250C4—5661no—
251C4—5662no—
252C4—11322no—
253C4C4⋊C4×D28311yescharacteristic
254C4#2258356711yescharacteristic
255C4#2258358311yescharacteristic
256C4#2258358811yescharacteristic
257C2—21no—
258C2—21no—
259C2—11322no—
260C2#3182632411yescharacteristic
261C2#104×D28311yescharacteristic
262C2#3182648011yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#339×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC2×#17985392C22
cosocleC22×C4×C283C23
hypercenter#339D283
hypocenterC283#1806
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #31826488C2semidirect
5. C4×Dic283⋊C4C2semidirect
6. #31826224C2semidirect
7. #339×C283C2semidirect
10. #22583575C4semidirect
11. #22583575C4semidirect
12. #22583572C4semidirect
13. #22583572C4semidirect
71. Dic566C4⋊C4semidirect
73. D1132C4⋊C4semidirect
124. Dic283#104semidirect
131. C283#1806semidirect
139. #339D283semidirect

Maximal subgroups

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

subgroupindex
#318269332
#318264882
C2×#225835382
C2×#225835362
C4×Dic283⋊C42
#318262242
#339×C2832
#1806283