Finite Group Databasebeta

← #49130272

Subgroups — #49130272

Order 36224.

406 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#17985392C211yesmaximal, characteristic
2#31826593C212yesmaximal, complemented
3#31826538C212yesmaximal, complemented
4#31826536C212yesmaximal, complemented
5C8×C22⋊D283C212yesmaximal, complemented
6#31826522C211yesmaximal, characteristic, complemented
7#31826520C211yesmaximal, characteristic, complemented
8#31826520C211yesmaximal, characteristic, complemented
9#31826417C211yesmaximal, characteristic, complemented
10#97×D283C211yesmaximal, characteristic, complemented
11C2×#97×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C411yescharacteristic
13C2×#17985375C2212yes—
14C2×C8×D283C2212yes—
15C4×Dic566C411yescharacteristic
16C4×Dic566C2211yescharacteristic
17C4×D1132C411yescharacteristic
18C4×D1132C2211yescharacteristic
19C4×C22⋊D283C411yescharacteristic
20C4×C22⋊D283C411yescharacteristic
21C4×C22⋊D283C2211yescharacteristic
22C4×C22⋊D283C2211yescharacteristic
23#22583569C411yescharacteristic
24#22583567C411yescharacteristic
25#22583567C411yescharacteristic
26C42×D283C2211yescharacteristic
27C42×D283C2211yescharacteristic
28C4⋊(C283⋊C8)C2212yes—
29Dic283⋊C8C2212yes—
30Dic283⋊C8C2212yes—
31C22⋊(C283⋊C8)C2212yes—
32(C2×D283)⋊C8C2212yes—
33(C2×D283)⋊C8C2212yes—
34#22583521C2211yescharacteristic
35#22583521C2211yescharacteristic
36#22583520C2212yes—
37C8×Dic283C2212yes—
38C22×C8×C283C2212yes—
39C2×C42×C283C2211yescharacteristic
40#97×C283C2211yescharacteristic
41#97×C283C2212yes—
42#97×C283C2211yescharacteristic
43#17985392—24no—
44C2×Dic566C2×C411yescharacteristic
45C2×D1132C2×C411yescharacteristic
46C2×C22⋊D283C2×C411yescharacteristic
47C2×C22⋊D283C2×C411yescharacteristic
48C2×C4×D283C2×C411yescharacteristic
49C2×C4×D283C2×C411yescharacteristic
50C2×C4×D283C2×C411yescharacteristic
51C2×C4×D283C2×C411yescharacteristic
52C2×C4×D283C2311yescharacteristic
53C2×C4×D283C2311yescharacteristic
54#17985375—24no—
55C2×C283⋊C8C2312yes—
56C2×C283⋊C8C2312yes—
57C8×D283—24no—
58C4⋊Dic283C2×C411yescharacteristic
59C4⋊Dic283C2×C411yescharacteristic
60Dic283⋊C4C2×C411yescharacteristic
61Dic283⋊C4C2×C411yescharacteristic
62Dic283⋊C4C2×C411yescharacteristic
63Dic283⋊C4C2×C411yescharacteristic
64C22⋊Dic283C2×C411yescharacteristic
65C22⋊Dic283C2×C411yescharacteristic
66(C2×D283)⋊C4C2×C411yescharacteristic
67(C2×D283)⋊C4C2×C411yescharacteristic
68(C2×D283)⋊C4C2×C411yescharacteristic
69(C2×D283)⋊C4C2×C411yescharacteristic
70C4×Dic283C2×C411yescharacteristic
71C4×Dic283C2×C411yescharacteristic
72C4×Dic283C2×C411yescharacteristic
73C4×Dic283C2×C411yescharacteristic
74C4×Dic283C2311yescharacteristic
75C4×Dic283C2311yescharacteristic
76C22×C4×C283C2×C411yescharacteristic
77C22×C4×C283C2×C411yescharacteristic
78C22×C4×C283C2311yescharacteristic
79C2×C8×C283—24no—
80C2×C8×C283C2312yes—
81C2×C8×C283C2312yes—
82C42×C283C2×C411yescharacteristic
83C42×C283C2×C411yescharacteristic
84C42×C283C2311yescharacteristic
85C42×C283C2311yescharacteristic
86C22×D283C22×C411yescharacteristic
87C22×D283C22×C411yescharacteristic
88Dic566—22no—
89D1132—22no—
90C22⋊D283—22no—
91C22⋊D283M1614yescomplemented
92C2×Dic283C22×C411yescharacteristic
93C2×Dic283C22×C411yescharacteristic
94C2×Dic283C22×C411yescharacteristic
95C2×Dic283C22×C411yescharacteristic
96C2×Dic283C22×C411yescharacteristic
97C2×Dic283C22×C411yescharacteristic
98C4×D283—22no—
99C4×D283—22no—
100C4×D283—22no—
101C4×D283—22no—
102C4×D283—41no—
103C4×D283—41no—
104C283⋊C8—22no—
105C283⋊C8—22no—
106C23×C283C22×C411yescharacteristic
107C2×C4×C283—22no—
108C2×C4×C283—22no—
109C2×C4×C283—41no—
110C2×C4×C283C22×C411yescharacteristic
111C2×C4×C283C22×C411yescharacteristic
112C2×C4×C283C22×C411yescharacteristic
113C2×C4×C283C22×C411yescharacteristic
114C2×C4×C283C22×C411yescharacteristic
115C2×C4×C283C2411yescharacteristic
116C8×C283—22no—
117C8×C283#4114yescomplemented
118C22×C283—21no—
119C22×C283—21no—
120C22×C283C2×M1612yes—
121C22×C283C23×C411yescharacteristic
122C2×D283—21no—
123C2×D283—21no—
124C2×D283—21no—
125C2×D283—21no—
126C2×D283—21no—
127C2×D283C2×M1612yes—
128C4×C283—21no—
129C4×C283—21no—
130C4×C283—21no—
131C4×C283—21no—
132C4×C283—21no—
133C4×C283C2×#4112yes—
134Dic283—21no—
135Dic283—21no—
136Dic283—21no—
137Dic283—21no—
138Dic283—21no—
139Dic283C2×M1612yes—
140C2×C283—22no—
141C2×C283C4×#4111yescharacteristic
142C2×C283C22×M1611yescharacteristic
143C2×C283#56811yescharacteristic
144D283—22no—
145D283—41no—
146C283#297011yescharacteristic, complemented, Sylow
147#2970—2831nomaximal, Sylow
148C4×#41—2831no—
149#446—2832no—
150#435—2832no—
151#435—2832no—
152C8×D4—2832no—
153#432—2831no—
154#432—2831no—
155#432—2831no—
156C4×M16—2831no—
157C2×#97—2831no—
158C2×#97D28311yescharacteristic, complemented
159C2×#41—2831no—
160C2×M16—2832no—
161C22×C8—2832no—
162C22×C8C2×D28312yes—
163C4×Q8—2831no—
164C4×Q8—2831no—
165C4×D4—2831no—
166C4×D4—2831no—
167C4×D4—2831no—
168C4×D4—2831no—
169C4×D4—2831no—
170C4×D4—2831no—
171#117—2831no—
172#117—2831no—
173#117—2831no—
174C2×C42—2831no—
175C2×C42—2831no—
176C2×C42C2×D28311yescharacteristic
177C4⋊C8—2832no—
178C4⋊C8—2832no—
179C4⋊C8—2832no—
180C22⋊C8—2832no—
181C22⋊C8—2832no—
182C22⋊C8—2832no—
183#97—2832no—
184#97—2831no—
185#97—2831no—
186#97C2×D28311yescharacteristic
187#97C2×D28311yescharacteristic
188#97C2×D28312yes—
189C4×C8—2832no—
190#41—5664no—
191C2×Q8—2831no—
192C2×D4—2831no—
193C2×D4—2831no—
194C2×D4—2831no—
195C22×C4—2831no—
196C22×C4—2831no—
197C22×C4—2831no—
198C22×C4—2831no—
199C22×C4—2831no—
200C22×C4—2831no—
201C22×C4C4×D28311yescharacteristic
202C22×C4C4×D28311yescharacteristic
203C22×C4C22×D28311yescharacteristic
204M16—5664no—
205C2×C8—24no—
206C2×C8—2832no—
207C2×C8—2832no—
208C2×C8—5664no—
209C2×C8C22×D28312yes—
210C2×C8C22×D28312yes—
211C4⋊C4—2831no—
212C4⋊C4—2831no—
213C4⋊C4—2831no—
214C4⋊C4—2831no—
215C4⋊C4—2831no—
216C4⋊C4—2831no—
217C22⋊C4—2831no—
218C22⋊C4—2831no—
219C22⋊C4—2831no—
220C22⋊C4—2831no—
221C22⋊C4—2831no—
222C22⋊C4—2831no—
223C42—2831no—
224C42—2831no—
225C42—2831no—
226C42—2831no—
227C42—2831no—
228C42—2831no—
229C42C4×D28311yescharacteristic
230C42C4×D28311yescharacteristic
231C42C22×D28311yescharacteristic
232C42C22×D28311yescharacteristic
233C23—2831no—
234C23—2831no—
235C23C2×C4×D28311yescharacteristic
236Q8—5662no—
237D4—2834no—
238D4—5662no—
239D4—5662no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—2831no—
244C2×C4—2831no—
245C2×C4—2831no—
246C2×C4—2831no—
247C2×C4—2831no—
248C2×C4—2831no—
249C2×C4—5662no—
250C2×C4—5662no—
251C2×C4—5662no—
252C2×C4—5662no—
253C2×C4—11321no—
254C2×C4—11321no—
255C2×C4C2×C4×D28311yescharacteristic
256C2×C4C2×C4×D28311yescharacteristic
257C2×C4C2×C4×D28311yescharacteristic
258C2×C4C2×C4×D28311yescharacteristic
259C2×C4C2×C4×D28311yescharacteristic
260C2×C4C23×D28311yescharacteristic
261C8—22no—
262C8—5662no—
263C8—5662no—
264C8#1798539214yescomplemented
265C22—21no—
266C22—21no—
267C22—2832no—
268C22—5661no—
269C22—5661no—
270C22—5661no—
271C22—5661no—
272C22—5661no—
273C22M16×D28312yes—
274C22C22×C4×D28311yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—2832no—
281C4—5661no—
282C4—5661no—
283C4—5661no—
284C4—5661no—
285C4—5661no—
286C4C2×#1798539212yes—
287C2—22no—
288C2—5662no—
289C2—11321no—
290C2C4×#1798539211yescharacteristic
291C2C2×M16×D28311yescharacteristic
292C2#3182723111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D283
commutator, socleC22×C283C23×C4
FittingC2×#97×C283C2
prime radicalC2×#17985392C4
cosocleC2×C4×C283C24
hypercenterC2×#97D283
hypocenterC283#2970
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. #31826593C2semidirect
3. #31826538C2semidirect
4. #31826536C2semidirect
5. C8×C22⋊D283C2semidirect
6. #31826522C2semidirect
7. #31826520C2semidirect
8. #31826520C2semidirect
9. #31826417C2semidirect
10. #97×D283C2semidirect
11. C2×#97×C283C2semidirect
91. C22⋊D283M16semidirect
117. C8×C283#41semidirect
146. C283#2970semidirect
158. C2×#97D283semidirect
264. C8#17985392semidirect

Maximal subgroups

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

subgroupindex
C4×#179853922
#318265932
#318265382
#318265362
C8×C22⋊D2832
#318265222
#318265202
#318264172
#97×D2832
C2×#97×C2832
#2970283