Finite Group Databasebeta

← #49121800

Subgroups — #49121800

Order 36224.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#31827024C211yesmaximal, characteristic
2#31826938C211yesmaximal, characteristic, complemented
3C2×#22583525C211yesmaximal, characteristic, complemented
4C2×#22583524C211yesmaximal, characteristic, complemented
5#31826232C211yesmaximal, characteristic, complemented
6#31826231C211yesmaximal, characteristic, complemented
7C2×#99×C283C211yesmaximal, characteristic, complemented
8C22×C22⋊D283C2211yescharacteristic
9#22583593C412yescomplemented
10#22583591—21no—
11#22583582—22no—
12#22583579C412yescomplemented
13#22583578—21no—
14C4×C22⋊D283—22no—
15(C22⋊D283)⋊C4—22no—
16#22583566—21no—
17C2×C22⋊Dic283C2211yescharacteristic
18C2×C22⋊Dic283C2211yescharacteristic
19C2×C22⋊Dic283C2211yescharacteristic
20C22⋊C4×D283—21no—
21#22583525—22no—
22#22583524—22no—
23C22×D4×C283C2211yescharacteristic
24C2×C22⋊C4×C283C2211yescharacteristic
25C2×C22⋊C4×C283C2211yescharacteristic
26#99×C283—22no—
27C23×D283D411yescharacteristic
28C2×C22⋊D283—22no—
29C2×C22⋊D283—21no—
30C2×C22⋊D283—21no—
31C2×C22⋊D283—21no—
32C2×C22⋊D283—21no—
33C2×C22⋊D283C2×C412yes—
34C2×C22⋊D283D412yes—
35C22×Dic283—21no—
36C22×Dic283—21no—
37C22×Dic283—21no—
38C22×Dic283D411yescharacteristic
39C2×C4×D283—22no—
40Dic283⋊C4—22no—
41Dic283⋊C4—22no—
42C22⋊Dic283—22no—
43C22⋊Dic283—21no—
44C22⋊Dic283—21no—
45C22⋊Dic283—21no—
46C22⋊Dic283—21no—
47C22⋊Dic283C2×C412yescomplemented
48C22⋊Dic283D412yescomplemented
49(C2×D283)⋊C4—22no—
50(C2×D283)⋊C4—22no—
51C4×Dic283—22no—
52C24×C283C2×C411yescharacteristic, complemented
53C24×C283C2311yescharacteristic
54C2×D4×C283—21no—
55C2×D4×C283—21no—
56C2×D4×C283—21no—
57C2×D4×C283—21no—
58C2×D4×C283—21no—
59C2×D4×C283—21no—
60C22×C4×C283—21no—
61C22×C4×C283—21no—
62C22×C4×C283C2×C411yescharacteristic, complemented
63C22⋊C4×C283—21no—
64C22⋊C4×C283—21no—
65C22⋊C4×C283—21no—
66C22⋊C4×C283D412yescomplemented
67C22×D283—21no—
68C22×D283—21no—
69C22×D283—81no—
70C22×D283C22⋊C412yes—
71C22⋊D283—22no—
72C22⋊D283—22no—
73C22⋊D283—22no—
74C22⋊D283—22no—
75C22⋊D283—82no—
76C2×Dic283—21no—
77C2×Dic283—21no—
78C2×Dic283—22no—
79C2×Dic283—22no—
80C2×Dic283—41no—
81C2×Dic283—81no—
82C2×Dic283—81no—
83C2×Dic283—81no—
84C2×Dic283C22⋊C412yes—
85C4×D283—82no—
86C23×C283—21no—
87C23×C283—21no—
88C23×C283—21no—
89C23×C283—81no—
90C23×C283—81no—
91C23×C283C22×C411yescharacteristic
92C23×C283C2×D411yescharacteristic
93C23×C283C2×D411yescharacteristic
94C23×C283C2×D411yescharacteristic
95C23×C283C2×D411yescharacteristic
96C23×C283#4111yescharacteristic
97C23×C283#4111yescharacteristic
98D4×C283—41no—
99D4×C283—41no—
100D4×C283—41no—
101D4×C283—41no—
102C2×C4×C283—21no—
103C2×C4×C283—21no—
104C2×C4×C283—21no—
105C2×C4×C283—22no—
106C2×C4×C283—41no—
107C2×C4×C283—81no—
108C2×C4×C283—81no—
109C22×C283—41no—
110C22×C283—41no—
111C22×C283—41no—
112C22×C283—41no—
113C22×C283—41no—
114C22×C283—41no—
115C22×C283—41no—
116C22×C283—42no—
117C22×C283—41no—
118C22×C283—81no—
119C22×C283—81no—
120C22×C283C2×C22⋊C411yescharacteristic
121C22×C283C4×D411yescharacteristic
122C22×C283C4×D411yescharacteristic
123C22×C283#12011yescharacteristic
124C22×C283#12111yescharacteristic
125C22×C283#12111yescharacteristic
126C22×C283#12311yescharacteristic
127C2×D283—22no—
128C2×D283—42no—
129C2×D283—42no—
130C2×D283—81no—
131C4×C283—42no—
132C4×C283—41no—
133C4×C283—81no—
134Dic283—22no—
135Dic283—42no—
136Dic283—42no—
137Dic283—81no—
138C2×C283—21no—
139C2×C283—21no—
140C2×C283—21no—
141C2×C283—21no—
142C2×C283—21no—
143C2×C283—21no—
144C2×C283—21no—
145C2×C283—81no—
146C2×C283#38611yescharacteristic
147D283—42no—
148C283#191311yescharacteristic, complemented, Sylow
149#1913—2831nomaximal, Sylow
150#534—2831no—
151#518—2831no—
152C2×#99—2831no—
153C2×#99—2831no—
154C2×#99D28311yescharacteristic, complemented
155#342—2831no—
156#342—2831no—
157C22×D4—2831no—
158C22×D4C2×D28311yescharacteristic
159#123—2832no—
160#123—5661no—
161#121—5662no—
162#120—2832no—
163#120—5661no—
164C4×D4—5662no—
165C4×D4—5662no—
166#117—5661no—
167C2×C22⋊C4—2831no—
168C2×C22⋊C4—2831no—
169C2×C22⋊C4—2831no—
170C2×C22⋊C4—5661no—
171C2×C22⋊C4C2×D28311yescharacteristic
172C2×C22⋊C4C2×D28311yescharacteristic
173#99—22no—
174#99—5662no—
175#99—5662no—
176C24—2831no—
177C24C4×D28311yescharacteristic, complemented
178C24C22×D28311yescharacteristic
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—2832no—
186C2×D4—2832no—
187C2×D4—5661no—
188C2×D4—5661no—
189C2×D4—5661no—
190C2×D4—5661no—
191C2×D4—5662no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—2831no—
195C22×C4—5662no—
196C22×C4—5661no—
197C22×C4—5661no—
198C22×C4—5661no—
199C22×C4C4×D28311yescharacteristic, complemented
200C4⋊C4—5662no—
201C4⋊C4—5662no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—21no—
205C22⋊C4—2832no—
206C22⋊C4—2832no—
207C22⋊C4—5662no—
208C22⋊C4—5662no—
209C22⋊C4—5662no—
210C22⋊C4—5661no—
211C22⋊C4—5661no—
212C22⋊C4—5661no—
213C22⋊C4—5661no—
214C22⋊C4C22⋊D28312yescomplemented
215C42—5662no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23—81no—
220C23—81no—
221C23—2832no—
222C23—5661no—
223C23—5661no—
224C23—22641no—
225C23C2×C4×D28311yescharacteristic
226C23D4×D28311yescharacteristic
227C23D4×D28311yescharacteristic
228C23D4×D28311yescharacteristic
229C23C2×C22⋊D28311yescharacteristic
230C23#1798539111yescharacteristic
231C23#1798539211yescharacteristic
232D4—41no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—5662no—
237D4—5662no—
238D4—5662no—
239D4—5662no—
240D4—22642no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—2832no—
249C2×C4—5661no—
250C2×C4—5661no—
251C2×C4—5662no—
252C2×C4—5662no—
253C2×C4—11321no—
254C2×C4—22642no—
255C2×C4—22641no—
256C2×C4—22641no—
257C2×C4—22641no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—42no—
266C22—41no—
267C22—81no—
268C22—81no—
269C22—5662no—
270C22—11322no—
271C22—11322no—
272C22—22641no—
273C22C22⋊C4×D28311yescharacteristic
274C22(C22⋊D283)⋊C411yescharacteristic
275C22C4×C22⋊D28311yescharacteristic
276C22#2258357811yescharacteristic
277C22#2258358111yescharacteristic
278C22#2258358311yescharacteristic
279C22#2258359211yescharacteristic
280C4—42no—
281C4—41no—
282C4—81no—
283C4—5662no—
284C4—11322no—
285C4—11322no—
286C4—22641no—
287C2—21no—
288C2—21no—
289C2—21no—
290C2—21no—
291C2—21no—
292C2—21no—
293C2—21no—
294C2—81no—
295C2—11322no—
296C2#3182634111yescharacteristic
subgroupG/H
centerC2#31826341
commutatorC23×C283C22×C4
FrattiniC24C22×D283
FittingC2×#99×C283C2
socleC2×C283#386
prime radical#31827024C2
cosocleC24×C283C23
hypercenterC2×#99D283
hypocenterC283#1913
LCSG ▷ C23×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. #31826938C2semidirect
3. C2×#22583525C2semidirect
4. C2×#22583524C2semidirect
5. #31826232C2semidirect
6. #31826231C2semidirect
7. C2×#99×C283C2semidirect
9. #22583593C4semidirect
12. #22583579C4semidirect
47. C22⋊Dic283C2×C4semidirect
48. C22⋊Dic283D4semidirect
52. C24×C283C2×C4semidirect
62. C22×C4×C283C2×C4semidirect
66. C22⋊C4×C283D4semidirect
148. C283#1913semidirect
154. C2×#99D283semidirect
177. C24C4×D283semidirect
199. C22×C4C4×D283semidirect
214. C22⋊C4C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318270242
#318269382
C2×#225835252
C2×#225835242
#318262322
#318262312
C2×#99×C2832
#1913283