Finite Group Databasebeta

← #49121666

Subgroups — #49121666

Order 36224.

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

normal subgroups only

This group has 578 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
1C2×#22583579C211yesmaximal, characteristic
2#31826938C211yesmaximal, characteristic, complemented
3C2×#22583524C211yesmaximal, characteristic, complemented
4#31826321C211yesmaximal, characteristic, complemented
5#31826232C211yesmaximal, characteristic, complemented
6#31826231C211yesmaximal, characteristic, complemented
7#379×C283C211yesmaximal, characteristic, complemented
8C22×C22⋊D283—21no—
9C22×C22⋊D283C2211yescharacteristic
10#22583579—22no—
11#22583579C414yescomplemented
12C4×C22⋊D283—22no—
13(C22⋊D283)⋊C4—22no—
14#22583566—21no—
15C2×C22⋊Dic283—21no—
16C2×C22⋊Dic283—22no—
17C2×C22⋊Dic283C2211yescharacteristic
18C2×C22⋊Dic283C2211yescharacteristic
19C2×C22⋊Dic283C2211yescharacteristic
20C22⋊C4×D283—21no—
21#22583524—22no—
22C25×C283C2211yescharacteristic
23C2×C22⋊C4×C283—22no—
24C2×C22⋊C4×C283C2211yescharacteristic
25C2×C22⋊C4×C283C2211yescharacteristic
26C23×D283D411yescharacteristic
27C2×C22⋊D283—24no—
28C2×C22⋊D283—21no—
29C2×C22⋊D283—21no—
30C2×C22⋊D283—21no—
31C2×C22⋊D283—21no—
32C2×C22⋊D283—44no—
33C2×C22⋊D283C2×C412yes—
34C2×C22⋊D283D412yes—
35C22×Dic283—21no—
36C22×Dic283—21no—
37C22×Dic283D411yescharacteristic
38C22×Dic283D412yescomplemented
39C2×C4×D283—22no—
40Dic283⋊C4—22no—
41C22⋊Dic283—24no—
42C22⋊Dic283—21no—
43C22⋊Dic283—21no—
44C22⋊Dic283—21no—
45C22⋊Dic283—21no—
46C22⋊Dic283—21no—
47C22⋊Dic283—44no—
48C22⋊Dic283C2×C412yescomplemented
49(C2×D283)⋊C4—22no—
50C4×Dic283—22no—
51C24×C283—21no—
52C24×C283—21no—
53C24×C283—21no—
54C24×C283—21no—
55C24×C283—21no—
56C24×C283—21no—
57C24×C283—44no—
58C24×C283C2×C412yescomplemented
59C24×C283C2311yescharacteristic
60C22×C4×C283—21no—
61C22×C4×C283D412yescomplemented
62C22⋊C4×C283—21no—
63C22⋊C4×C283—21no—
64C22⋊C4×C283—21no—
65C22⋊C4×C283—21no—
66C22⋊C4×C283—44no—
67C22×D283—21no—
68C22×D283—21no—
69C22×D283—42no—
70C22×D283C22⋊C412yescomplemented
71C22⋊D283—22no—
72C22⋊D283—22no—
73C22⋊D283—22no—
74C22⋊D283—22no—
75C22⋊D283—48no—
76C2×Dic283—21no—
77C2×Dic283—21no—
78C2×Dic283—22no—
79C2×Dic283—22no—
80C2×Dic283—42no—
81C2×Dic283—42no—
82C2×Dic283—42no—
83C2×Dic283—41no—
84C2×Dic283C22⋊C412yescomplemented
85C4×D283—82no—
86C23×C283—24no—
87C23×C283—24no—
88C23×C283—24no—
89C23×C283—22no—
90C23×C283—22no—
91C23×C283—22no—
92C23×C283—44no—
93C23×C283—42no—
94C23×C283—42no—
95C23×C283—42no—
96C23×C283—42no—
97C23×C283—44no—
98C23×C283—44no—
99C23×C283—44no—
100C23×C283—41no—
101C23×C283—41no—
102C23×C283—41no—
103C23×C283—41no—
104C23×C283C22×C411yescharacteristic
105C23×C283C2×D411yescharacteristic
106C23×C283C2×D411yescharacteristic
107C23×C283C2×D411yescharacteristic
108C23×C283C2×D411yescharacteristic
109C23×C283#4111yescharacteristic
110C23×C283#4111yescharacteristic
111C2×C4×C283—22no—
112C2×C4×C283—42no—
113C2×C4×C283—42no—
114C2×C4×C283—41no—
115C22×C283—22no—
116C22×C283—22no—
117C22×C283—22no—
118C22×C283—24no—
119C22×C283—24no—
120C22×C283—24no—
121C22×C283—41no—
122C22×C283—41no—
123C22×C283—41no—
124C22×C283—41no—
125C22×C283—42no—
126C22×C283—44no—
127C22×C283—44no—
128C22×C283—44no—
129C22×C283—42no—
130C22×C283—42no—
131C22×C283—42no—
132C22×C283—44no—
133C22×C283C2×C22⋊C411yescharacteristic
134C22×C283C4×D411yescharacteristic
135C22×C283C4×D411yescharacteristic
136C22×C283#12011yescharacteristic
137C22×C283#12111yescharacteristic
138C22×C283#12111yescharacteristic
139C22×C283#12311yescharacteristic
140C2×D283—22no—
141C2×D283—42no—
142C2×D283—42no—
143C2×D283—81no—
144C4×C283—42no—
145C4×C283—81no—
146Dic283—22no—
147Dic283—42no—
148Dic283—42no—
149Dic283—81no—
150C2×C283—21no—
151C2×C283—21no—
152C2×C283—21no—
153C2×C283—21no—
154C2×C283—21no—
155C2×C283—21no—
156C2×C283—44no—
157C2×C283#38611yescharacteristic
158C2×C283B(4,𝔽2)12yes—
159D283—42no—
160C283#188911yescharacteristic, complemented, Sylow
161#1889—2831nomaximal, Sylow
162C2×#120—2831no—
163#518—2831no—
164C2×#99—2831no—
165#379—2831no—
166#379D28311yescharacteristic, complemented
167#342—2831no—
168#342—2831no—
169C25C2×D28311yescharacteristic
170C22×D4—2831no—
171C22×D4—5661no—
172#120—2834no—
173#120—5662no—
174C4×D4—5662no—
175C4×D4—5662no—
176#117—5661no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—2831no—
179C2×C22⋊C4—2831no—
180C2×C22⋊C4—2831no—
181C2×C22⋊C4—5661no—
182C2×C22⋊C4—5661no—
183C2×C22⋊C4—5662no—
184C2×C22⋊C4C2×D28311yescharacteristic
185C2×C22⋊C4C2×D28311yescharacteristic
186#99—5662no—
187C24—21no—
188C24—21no—
189C24—21no—
190C24—21no—
191C24—21no—
192C24—21no—
193C24—44no—
194C24—2831no—
195C24C4×D28312yescomplemented
196C24C22×D28311yescharacteristic
197C2×D4—2832no—
198C2×D4—2832no—
199C2×D4—5661no—
200C2×D4—5661no—
201C2×D4—5661no—
202C2×D4—5661no—
203C2×D4—5664no—
204C2×D4—11324no—
205C22×C4—21no—
206C22×C4—2831no—
207C22×C4—2832no—
208C22×C4—5662no—
209C22×C4—5661no—
210C22×C4—5661no—
211C22×C4C22⋊D28312yescomplemented
212C4⋊C4—5662no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—44no—
218C22⋊C4—2832no—
219C22⋊C4—5662no—
220C22⋊C4—5664no—
221C22⋊C4—5661no—
222C22⋊C4—5661no—
223C22⋊C4—5661no—
224C22⋊C4—5661no—
225C22⋊C4—5661no—
226C22⋊C4—11324no—
227C42—5662no—
228C23—24no—
229C23—24no—
230C23—24no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—44no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—44no—
240C23—44no—
241C23—44no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—2832no—
247C23—5661no—
248C23—5661no—
249C23—11322no—
250C23C2×C4×D28311yescharacteristic
251C23D4×D28311yescharacteristic
252C23D4×D28311yescharacteristic
253C23D4×D28311yescharacteristic
254C23C2×C22⋊D28311yescharacteristic
255C23#1798539111yescharacteristic
256C23#1798539211yescharacteristic
257D4—5662no—
258D4—5662no—
259D4—5662no—
260D4—5662no—
261D4—11328no—
262C2×C4—22no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—2832no—
267C2×C4—5661no—
268C2×C4—5661no—
269C2×C4—5662no—
270C2×C4—5662no—
271C2×C4—11322no—
272C2×C4—11322no—
273C2×C4—11322no—
274C2×C4—11321no—
275C2×C4—22642no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—24no—
280C22—24no—
281C22—24no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—44no—
287C22—42no—
288C22—44no—
289C22—42no—
290C22—42no—
291C22—44no—
292C22—42no—
293C22—44no—
294C22—5662no—
295C22—11322no—
296C22—11322no—
297C22—22641no—
298C22C22⋊C4×D28311yescharacteristic
299C22(C22⋊D283)⋊C411yescharacteristic
300C22C4×C22⋊D28311yescharacteristic
301C22#2258357811yescharacteristic
302C22#2258358111yescharacteristic
303C22#2258358311yescharacteristic
304C22#2258359211yescharacteristic
305C4—42no—
306C4—81no—
307C4—5662no—
308C4—11322no—
309C4—11322no—
310C4—22641no—
311C2—21no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2—21no—
317C2—44no—
318C2—11322no—
319C2#3182634111yescharacteristic
320C2#3182665112yes—
subgroupG/H
centerC22#22583578
commutatorC23×C283C22×C4
FrattiniC24C22×D283
Fitting#379×C283C2
socleC22×C283#120
prime radicalC2×#22583579C2
cosocleC24×C283C23
hypercenter#379D283
hypocenterC283#1889
LCSG ▷ C23×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #31826938C2semidirect
3. C2×#22583524C2semidirect
4. #31826321C2semidirect
5. #31826232C2semidirect
6. #31826231C2semidirect
7. #379×C283C2semidirect
11. #22583579C4semidirect
38. C22×Dic283D4semidirect
48. C22⋊Dic283C2×C4semidirect
58. C24×C283C2×C4semidirect
61. C22×C4×C283D4semidirect
70. C22×D283C22⋊C4semidirect
84. C2×Dic283C22⋊C4semidirect
160. C283#1889semidirect
166. #379D283semidirect
195. C24C4×D283semidirect
211. C22×C4C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835792
#318269382
C2×#225835242
#318263212
#318262322
#318262312
#379×C2832
#1889283