Finite Group Databasebeta

← #49121708

Subgroups — #49121708

Order 36224.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#31826977C211yesmaximal, characteristic
2C2×#22583567C211yesmaximal, characteristic, complemented
3C2×#22583538C211yesmaximal, characteristic, complemented
4C2×#22583536C211yesmaximal, characteristic, complemented
5#31826428C211yesmaximal, characteristic, complemented
6#31826224C211yesmaximal, characteristic, complemented
7#339×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9C22×C4×D283C2211yescharacteristic
10C2×#17985376C2211yescharacteristic
11#22583594—21no—
12#22583590C412yescomplemented
13#22583585C412yescomplemented
14#22583580—21no—
15C4×D1132—22no—
16#22583567—22no—
17#22583567—22no—
18C2×Dic283⋊C4—21no—
19C2×(C2×D283)⋊C4—21no—
20C2×C4×Dic283C2211yescharacteristic
21#22583538—22no—
22#22583536—22no—
23(C2×D283)⋊C8—22no—
24C2×M16×C283C2211yescharacteristic
25#117×C283C2211yescharacteristic
26C2×C42×C283C2211yescharacteristic
27C23×D283D411yescharacteristic
28#17985392—21no—
29#17985392—21no—
30#17985392—21no—
31#17985392—21no—
32C2×Dic566C2×C411yescharacteristic
33C2×D1132—22no—
34C2×D1132C2×C411yescharacteristic
35C2×C22⋊D283—21no—
36C22×Dic283—21no—
37C22×Dic283D411yescharacteristic
38C2×C4×D283—21no—
39C2×C4×D283—21no—
40C2×C4×D283—21no—
41C2×C4×D283—21no—
42C2×C4×D283—21no—
43C2×C4×D283C2×C412yes—
44C2×C4×D283D412yes—
45#17985376—21no—
46#17985376—21no—
47C2×C283⋊C8—21no—
48C4⋊Dic283—22no—
49Dic283⋊C4—24no—
50(C2×D283)⋊C4—24no—
51(C2×D283)⋊C4—22no—
52(C2×D283)⋊C4—22no—
53C4×Dic283—21no—
54C4×Dic283D412yescomplemented
55C22×C4×C283—21no—
56C22×C4×C283C2311yescharacteristic
57M16×C283—21no—
58M16×C283—21no—
59C2×C8×C283—21no—
60C4⋊C4×C283C2×C412yes—
61C22⋊C4×C283—21no—
62C42×C283—21no—
63C42×C283—21no—
64C42×C283D412yescomplemented
65C22×D283—21no—
66C22×D283—21no—
67C22×D283—21no—
68C22×D283—42no—
69C22×D283C22⋊C412yes—
70Dic566—21no—
71Dic566—21no—
72D1132—21no—
73D1132—21no—
74D1132—44no—
75C22⋊D283—41no—
76C22⋊D283—41no—
77C2×Dic283—21no—
78C2×Dic283—21no—
79C2×Dic283—21no—
80C2×Dic283—22no—
81C2×Dic283—42no—
82C2×Dic283C22⋊C412yes—
83C4×D283—22no—
84C4×D283—22no—
85C4×D283—22no—
86C4×D283—22no—
87C4×D283—41no—
88C4×D283—41no—
89C283⋊C8—41no—
90C23×C283C2×D411yescharacteristic
91C2×C4×C283—22no—
92C2×C4×C283—22no—
93C2×C4×C283—42no—
94C2×C4×C283C22×C411yescharacteristic
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283C2×D411yescharacteristic
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283#4111yescharacteristic
99C2×C4×C283#4111yescharacteristic
100C8×C283—41no—
101C22×C283—22no—
102C22×C283C2×C22⋊C411yescharacteristic
103C22×C283#12011yescharacteristic
104C22×C283#12311yescharacteristic
105C2×D283—22no—
106C2×D283—22no—
107C2×D283—22no—
108C2×D283—42no—
109C2×D283—42no—
110C2×D283—41no—
111C2×D283—42no—
112C4×C283—42no—
113C4×C283—42no—
114C4×C283C4×D411yescharacteristic
115C4×C283C4×D411yescharacteristic
116C4×C283#12111yescharacteristic
117C4×C283#12111yescharacteristic
118Dic283—22no—
119Dic283—42no—
120Dic283—41no—
121C2×C283—21no—
122C2×C283—21no—
123C2×C283#38611yescharacteristic
124C2×C283#42112yes—
125D283—42no—
126D283—81no—
127C283#189711yescharacteristic, complemented, Sylow
128#1897—2831nomaximal, Sylow
129#525—2831no—
130C2×#117—2831no—
131C2×#104—2831no—
132C2×#104—2831no—
133#407—2831no—
134#339—2831no—
135#339D28311yescharacteristic, complemented
136C2×#41—2831no—
137C23×C4—2831no—
138C2×M16—2831no—
139C2×M16C2×D28311yescharacteristic
140#123—5661no—
141C22⋊Q8—2832no—
142#121—2832no—
143#120—5661no—
144C4×D4—5662no—
145#117—5662no—
146#117—5662no—
147#117C2×D28311yescharacteristic
148C2×C4⋊C4—5661no—
149C2×C22⋊C4—5661no—
150C2×C42—2831no—
151C2×C42C2×D28311yescharacteristic
152#104—5662no—
153#104—5662no—
154C22⋊C8—5662no—
155C24—2831no—
156#41—5661no—
157#41—5661no—
158#41—5661no—
159#41—5661no—
160C2×Q8—2831no—
161C2×D4—2831no—
162C2×D4—5662no—
163C2×D4—5661no—
164C22×C4—21no—
165C22×C4—2831no—
166C22×C4—2832no—
167C22×C4—2832no—
168C22×C4—5661no—
169C22×C4—5661no—
170C22×C4—5661no—
171C22×C4—5661no—
172C22×C4—5661no—
173C22×C4—5661no—
174C22×C4C22×D28311yescharacteristic
175M16—21no—
176M16—21no—
177M16—5661no—
178M16—5661no—
179C2×C8—21no—
180C2×C8—5661no—
181C4⋊C4—5662no—
182C4⋊C4—5664no—
183C4⋊C4C4×D28312yes—
184C22⋊C4—21no—
185C22⋊C4—5662no—
186C22⋊C4—5662no—
187C22⋊C4—5664no—
188C42—21no—
189C42—21no—
190C42—2832no—
191C42—5661no—
192C42D113212yescomplemented
193C23—2832no—
194C23—5661no—
195C23—5661no—
196C23—5661no—
197C23—11322no—
198C23D4×D28311yescharacteristic
199Q8—5661no—
200Q8—5661no—
201D4—5661no—
202D4—5661no—
203D4—11324no—
204D4—11321no—
205D4—11321no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—2832no—
210C2×C4—5661no—
211C2×C4—5661no—
212C2×C4—5662no—
213C2×C4—5662no—
214C2×C4—5662no—
215C2×C4—5662no—
216C2×C4—5661no—
217C2×C4—5662no—
218C2×C4—11322no—
219C2×C4—11321no—
220C2×C4—11321no—
221C2×C4C2×C4×D28311yescharacteristic
222C2×C4D4×D28311yescharacteristic
223C2×C4D4×D28311yescharacteristic
224C2×C4C2×D113211yescharacteristic
225C2×C4#1798539211yescharacteristic
226C2×C4#1798539311yescharacteristic
227C8—41no—
228C8—11321no—
229C22—22no—
230C22—5662no—
231C22—5662no—
232C22—5662no—
233C22—11322no—
234C22—11322no—
235C22—11322no—
236C22—11321no—
237C22C22⋊C4×D28311yescharacteristic
238C22#2258358011yescharacteristic
239C22#2258359511yescharacteristic
240C4—42no—
241C4—42no—
242C4—5662no—
243C4—11322no—
244C4—11321no—
245C4#2258357211yescharacteristic
246C4C4×D113211yescharacteristic
247C4#2258358311yescharacteristic
248C4#2258358511yescharacteristic
249C2—21no—
250C2—21no—
251C2—11322no—
252C2—22641no—
253C2#3182634311yescharacteristic
254C2#3182648012yes—
subgroupG/H
centerC2×C4D4×D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#339×C283C2
socleC22×C283C2×C22⋊C4
prime radical#31826977C2
cosocleC22×C4×C283C23
hypercenter#339D283
hypocenterC283#1897
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. C2×#22583567C2semidirect
3. C2×#22583538C2semidirect
4. C2×#22583536C2semidirect
5. #31826428C2semidirect
6. #31826224C2semidirect
7. #339×C283C2semidirect
12. #22583590C4semidirect
13. #22583585C4semidirect
54. C4×Dic283D4semidirect
64. C42×C283D4semidirect
127. C283#1897semidirect
135. #339D283semidirect
192. C42D1132semidirect

Maximal subgroups

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

subgroupindex
#318269772
C2×#225835672
C2×#225835382
C2×#225835362
#318264282
#318262242
#339×C2832
#1897283