Finite Group Databasebeta

← #49121570

Subgroups — #49121570

Order 36224.

360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#22583586C211yesmaximal, characteristic
2C2×#22583568C211yesmaximal, characteristic
3C2×#22583534C211yesmaximal, characteristic, complemented
4C2×(C2×D283)⋊C8C211yesmaximal, characteristic
5#31826228C211yesmaximal, characteristic, complemented
6#31826227C211yesmaximal, characteristic, complemented
7C2×#103×C283C211yesmaximal, characteristic, complemented
8C22×C4×D283C2211yescharacteristic
9C22×C283⋊C8C2211yescharacteristic
10#22583586—22no—
11#22583586C414yescomplemented
12#22583568—22no—
13#22583568—22no—
14C2×C4⋊Dic283C2211yescharacteristic
15C2×C4⋊Dic283C2211yescharacteristic
16C2×Dic283⋊C4—21no—
17C2×(C2×D283)⋊C4—21no—
18C2×(C2×D283)⋊C4—21no—
19C2×C4×Dic283—21no—
20#22583534—22no—
21(C2×D283)⋊C8—22no—
22C22×Q8×C283C2211yescharacteristic
23C22×C8×C283C2211yescharacteristic
24C2×C4⋊C4×C283C2211yescharacteristic
25#103×C283—22no—
26C23×D283D411yescharacteristic
27C22×Dic283—21no—
28C22×Dic283—21no—
29C22×Dic283D411yescharacteristic
30C2×C4×D283—21no—
31C2×C4×D283—21no—
32C2×C4×D283—21no—
33C2×C4×D283—21no—
34C2×C4×D283C2×C412yes—
35C2×C4×D283D412yes—
36C2×C283⋊C8—21no—
37C2×C283⋊C8—21no—
38C2×C283⋊C8—21no—
39C4⋊Dic283—21no—
40C4⋊Dic283—21no—
41C4⋊Dic283C2×C412yes—
42C4⋊Dic283D412yes—
43Dic283⋊C4—24no—
44(C2×D283)⋊C4—24no—
45(C2×D283)⋊C4—24no—
46C4×Dic283—24no—
47C2×Q8×C283—21no—
48C2×Q8×C283—21no—
49C2×Q8×C283—21no—
50C2×Q8×C283—21no—
51C2×Q8×C283—21no—
52C2×Q8×C283C2×C412yes—
53C22×C4×C283—21no—
54C22×C4×C283—21no—
55C22×C4×C283C2311yescharacteristic
56C2×C8×C283—21no—
57C2×C8×C283—21no—
58C2×C8×C283—21no—
59C4⋊C4×C283—21no—
60C4⋊C4×C283D412yes—
61C22×D283—21no—
62C22×D283—21no—
63C22×D283—21no—
64C22×D283—21no—
65C22×D283—21no—
66C22×D283—21no—
67C22×D283C22⋊C412yes—
68C2×Dic283—21no—
69C2×Dic283—21no—
70C2×Dic283—22no—
71C2×Dic283—22no—
72C2×Dic283—41no—
73C2×Dic283—41no—
74C2×Dic283—41no—
75C2×Dic283—41no—
76C2×Dic283C22⋊C412yes—
77C4×D283—22no—
78C4×D283—22no—
79C4×D283—22no—
80C4×D283—22no—
81C283⋊C8—41no—
82C23×C283C2×D411yescharacteristic
83Q8×C283—22no—
84Q8×C283—22no—
85Q8×C283—41no—
86Q8×C283—41no—
87C2×C4×C283—22no—
88C2×C4×C283—22no—
89C2×C4×C283—41no—
90C2×C4×C283—41no—
91C2×C4×C283—41no—
92C2×C4×C283—41no—
93C2×C4×C283C22×C411yescharacteristic
94C2×C4×C283C2×D411yescharacteristic
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283C2×D411yescharacteristic
97C2×C4×C283#4111yescharacteristic
98C2×C4×C283#4111yescharacteristic
99C8×C283—41no—
100C22×C283C2×C22⋊C411yescharacteristic
101C22×C283#12011yescharacteristic
102C22×C283#12311yescharacteristic
103C22×C283#13511yescharacteristic
104C22×C283#13511yescharacteristic
105C22×C283#13711yescharacteristic
106C22×C283#13711yescharacteristic
107C2×D283—22no—
108C2×D283—22no—
109C2×D283—22no—
110C2×D283—41no—
111C2×D283—41no—
112C2×D283—41no—
113C2×D283—41no—
114C4×C283—42no—
115C4×C283—42no—
116C4×C283C4×D411yescharacteristic
117C4×C283C4×D411yescharacteristic
118C4×C283#12111yescharacteristic
119C4×C283#12111yescharacteristic
120Dic283—22no—
121Dic283—42no—
122Dic283—42no—
123C2×C283#38611yescharacteristic
124C2×C283#41611yescharacteristic
125C2×C283#41911yescharacteristic
126C2×C283#45211yescharacteristic
127C2×C283#45211yescharacteristic
128C2×C283#48511yescharacteristic
129C2×C283#48511yescharacteristic
130D283—42no—
131C283#187311yescharacteristic, complemented, Sylow
132#1873—2831nomaximal, Sylow
133C2×C22⋊Q8—2831no—
134C2×#117—2831no—
135C2×#103—2831no—
136C2×#103D28311yescharacteristic, complemented
137C2×C22⋊C8—2831no—
138#340—2831no—
139#340—2831no—
140C22×Q8C2×D28311yescharacteristic
141C23×C4—2831no—
142C22×C8—2831no—
143C22×C8C2×D28311yescharacteristic
144C22⋊Q8—2834no—
145C22⋊Q8—5662no—
146#117—5662no—
147#117—5662no—
148C2×C4⋊C4—2831no—
149C2×C4⋊C4—2831no—
150C2×C4⋊C4—5661no—
151C2×C4⋊C4C2×D28311yescharacteristic
152C2×C22⋊C4—5661no—
153C2×C22⋊C4—5661no—
154C2×C42—5661no—
155#103—22no—
156#103—5662no—
157C22⋊C8—5662no—
158C24—2831no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8C4×D28312yes—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—2831no—
168C22×C4—2832no—
169C22×C4—2832no—
170C22×C4—5661no—
171C22×C4—5661no—
172C22×C4—5661no—
173C22×C4—5661no—
174C22×C4—5661no—
175C22×C4—5661no—
176C22×C4C22×D28311yescharacteristic
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—5661no—
181C2×C8—5661no—
182C2×C8—5661no—
183C4⋊C4—21no—
184C4⋊C4—2832no—
185C4⋊C4—2832no—
186C4⋊C4—5664no—
187C4⋊C4—5661no—
188C4⋊C4—5661no—
189C4⋊C4C22⋊D28312yes—
190C22⋊C4—5664no—
191C22⋊C4—5664no—
192C42—5664no—
193C23—2832no—
194C23—5661no—
195C23—5661no—
196C23—5661no—
197C23—5661no—
198C23—5661no—
199C23—5661no—
200C23D4×D28311yescharacteristic
201Q8—22no—
202Q8—22no—
203Q8—41no—
204Q8—41no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—2832no—
212C2×C4—5661no—
213C2×C4—5661no—
214C2×C4—5662no—
215C2×C4—5662no—
216C2×C4—5662no—
217C2×C4—5662no—
218C2×C4—5662no—
219C2×C4—5662no—
220C2×C4—11321no—
221C2×C4—11321no—
222C2×C4—11321no—
223C2×C4—11321no—
224C2×C4C2×C4×D28311yescharacteristic
225C2×C4D4×D28311yescharacteristic
226C2×C4D4×D28311yescharacteristic
227C2×C4C2×C22⋊D28311yescharacteristic
228C2×C4#1798539111yescharacteristic
229C2×C4#1798539211yescharacteristic
230C8—41no—
231C8—11321no—
232C22—5662no—
233C22—5662no—
234C22—5662no—
235C22—11321no—
236C22—11321no—
237C22—11321no—
238C22—11321no—
239C22C22⋊C4×D28311yescharacteristic
240C22#2258357811yescharacteristic
241C22#2258359211yescharacteristic
242C22#2258363111yescharacteristic
243C22#2258363311yescharacteristic
244C22#2258363911yescharacteristic
245C22#2258364211yescharacteristic
246C4—42no—
247C4—42no—
248C4—5662no—
249C4—11322no—
250C4—11322no—
251C4(C22⋊D283)⋊C411yescharacteristic
252C4C4×C22⋊D28311yescharacteristic
253C4#2258358111yescharacteristic
254C4#2258358311yescharacteristic
255C2—11322no—
256C2#3182634111yescharacteristic
257C2#3182646011yescharacteristic
258C2#3182647211yescharacteristic
259C2#3182662411yescharacteristic
260C2#3182662611yescharacteristic
261C2#3182680411yescharacteristic
262C2#3182680511yescharacteristic
subgroupG/H
centerC23D4×D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingC2×#103×C283C2
socleC23×C283C2×D4
prime radicalC23×D283D4
cosocleC22×C4×C283C23
hypercenterC2×#103D283
hypocenterC283#1873
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#22583534C2semidirect
5. #31826228C2semidirect
6. #31826227C2semidirect
7. C2×#103×C283C2semidirect
11. #22583586C4semidirect
131. C283#1873semidirect
136. C2×#103D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835862
C2×#225835682
C2×#225835342
C2×(C2×D283)⋊C82
#318262282
#318262272
C2×#103×C2832
#1873283