Finite Group Databasebeta

← #49130197

Subgroups — #49130197

Order 36224.

348 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827019C211yesmaximal, characteristic
2#31826596C211yesmaximal, characteristic, complemented
3#31826595C211yesmaximal, characteristic, complemented
4#31826594C211yesmaximal, characteristic, complemented
5#31826594C211yesmaximal, characteristic, complemented
6#31826593C211yesmaximal, characteristic, complemented
7#31826593C211yesmaximal, characteristic, complemented
8#31826592C211yesmaximal, characteristic, complemented
9#31826490C211yesmaximal, characteristic
10#31826490C211yesmaximal, characteristic
11#31826487C211yesmaximal, characteristic
12#31826422C211yesmaximal, characteristic
13#31826419C211yesmaximal, characteristic
14#97×D283C211yesmaximal, characteristic
15#446×C283C211yesmaximal, characteristic, complemented
16C2×#17985375C2211yescharacteristic
17C2×#17985375C2211yescharacteristic
18C2×C8×D283C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20#22583609C411yescharacteristic
21#22583608C411yescharacteristic
22#22583600C411yescharacteristic
23#22583600C411yescharacteristic
24#22583590C411yescharacteristic
25#22583588C411yescharacteristic
26#22583588C411yescharacteristic
27#22583586C411yescharacteristic
28C4×Dic566C2211yescharacteristic
29C4×Dic566C2211yescharacteristic
30C4×Dic566C2211yescharacteristic
31#22583567C2211yescharacteristic
32#22583567C2211yescharacteristic
33C42×D283C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35C4⋊(C283⋊C8)C2211yescharacteristic
36C4⋊(C283⋊C8)C2211yescharacteristic
37Dic283⋊C8C2211yescharacteristic
38Dic283⋊C8C2211yescharacteristic
39Dic283⋊C8C2211yescharacteristic
40Dic283⋊C8C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583521C2211yescharacteristic
44#22583521C2211yescharacteristic
45#22583520C2211yescharacteristic
46#22583520C2211yescharacteristic
47#22583520C2211yescharacteristic
48#22583520C2211yescharacteristic
49C4×C283⋊C8C2211yescharacteristic
50C8×Dic283C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C4×Q8×C283C2211yescharacteristic
53C4⋊C8×C283C2211yescharacteristic
54C4⋊C8×C283C2211yescharacteristic
55C4⋊C8×C283C2211yescharacteristic
56#97×C283C2211yescharacteristic
57#97×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59C2×Dic566C2×C411yescharacteristic
60C2×Dic566C2×C411yescharacteristic
61C2×Dic566C2×C411yescharacteristic
62C2×C4×D283C2×C411yescharacteristic
63C2×C4×D283C2×C411yescharacteristic
64C2×C4×D283C2311yescharacteristic
65#17985375—22no—
66#17985375—22no—
67C2×C283⋊C8C2311yescharacteristic
68C2×C283⋊C8C2311yescharacteristic
69C2×C283⋊C8C2311yescharacteristic
70C2×C283⋊C8C2311yescharacteristic
71C8×D283—22no—
72C8×D283Q814yescomplemented
73C4⋊Dic283C2×C411yescharacteristic
74C4⋊Dic283C2×C411yescharacteristic
75C4⋊Dic283C2×C411yescharacteristic
76Dic283⋊C4C2×C411yescharacteristic
77Dic283⋊C4C2×C411yescharacteristic
78Dic283⋊C4C2×C411yescharacteristic
79Dic283⋊C4C2×C411yescharacteristic
80Dic283⋊C4C2×C411yescharacteristic
81Dic283⋊C4C2×C411yescharacteristic
82Dic283⋊C4C2×C411yescharacteristic
83Dic283⋊C4C2×C411yescharacteristic
84Dic283⋊C4C2×C411yescharacteristic
85Dic283⋊C4C2×C411yescharacteristic
86(C2×D283)⋊C4C2×C411yescharacteristic
87(C2×D283)⋊C4C2×C411yescharacteristic
88(C2×D283)⋊C4C2×C411yescharacteristic
89(C2×D283)⋊C4C2×C411yescharacteristic
90C4×Dic283C2×C411yescharacteristic
91C4×Dic283C2×C411yescharacteristic
92C4×Dic283C2311yescharacteristic
93C4×Dic283C2311yescharacteristic
94C4×Dic283C2311yescharacteristic
95C2×Q8×C283C2×C411yescharacteristic
96C2×C8×C283C2311yescharacteristic
97C2×C8×C283C2311yescharacteristic
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C4⋊C4×C283C2×C411yescharacteristic
101C4⋊C4×C283C2×C411yescharacteristic
102C4⋊C4×C283C2×C411yescharacteristic
103C42×C283C2311yescharacteristic
104C42×C283C2311yescharacteristic
105C42×C283C2311yescharacteristic
106C22×D283C22×C411yescharacteristic
107Dic566—41no—
108Dic566—41no—
109Dic566—41no—
110C2×Dic283C22×C411yescharacteristic
111C2×Dic283C22×C411yescharacteristic
112C2×Dic283C22×C411yescharacteristic
113C2×Dic283C22×C411yescharacteristic
114C2×Dic283C22×C411yescharacteristic
115C2×Dic283C22×C411yescharacteristic
116C2×Dic283C22×C411yescharacteristic
117C4×D283—41no—
118C4×D283—41no—
119C4×D283C2×Q812yes—
120C4×D283#4112yes—
121C283⋊C8—21no—
122C283⋊C8—21no—
123C283⋊C8—21no—
124C283⋊C8C2×Q812yes—
125Q8×C283—41no—
126C2×C4×C283C22×C411yescharacteristic
127C2×C4×C283C22×C411yescharacteristic
128C2×C4×C283C22×C411yescharacteristic
129C2×C4×C283C22×C411yescharacteristic
130C2×C4×C283C22×C411yescharacteristic
131C2×C4×C283C22×C411yescharacteristic
132C2×C4×C283C2411yescharacteristic
133C8×C283—21no—
134C8×C283—21no—
135C8×C283—21no—
136C8×C283C2×Q812yes—
137C22×C283C23×C411yescharacteristic
138C2×D283—21no—
139C2×D283—21no—
140C2×D283C4×Q812yes—
141C4×C283—21no—
142C4×C283—21no—
143C4×C283—21no—
144C4×C283—21no—
145C4×C283—21no—
146C4×C283—21no—
147C4×C283C22×Q811yescharacteristic
148C4×C283C2×#4111yescharacteristic
149Dic283—21no—
150Dic283—21no—
151Dic283—21no—
152Dic283—21no—
153Dic283—21no—
154Dic283—21no—
155Dic283C4×Q812yes—
156C2×C283C2×C4×Q811yescharacteristic
157C2×C283#56811yescharacteristic
158C2×C283#56811yescharacteristic
159D283—22no—
160C283#296111yescharacteristic, complemented, Sylow
161#2961—2831nomaximal, Sylow
162#533—2831no—
163#446—2831no—
164#446—2831no—
165#446—2831no—
166#446—2831no—
167#446—2831no—
168#446—2831no—
169#446—2831no—
170#446D28311yescharacteristic, complemented
171#424—2831no—
172#424—2831no—
173#423—2831no—
174#405—2831no—
175#405—2831no—
176C2×#97—2831no—
177C2×M16—2831no—
178C2×M16—2831no—
179C22×C8—2831no—
180C22×C8—2831no—
181C4⋊Q8—2831no—
182C4⋊Q8—2831no—
183#125—2831no—
184#125—2831no—
185C22⋊Q8—2831no—
186C22⋊Q8—2831no—
187C22⋊Q8—2831no—
188C22⋊Q8—2831no—
189C4×Q8—2831no—
190C4×Q8—2831no—
191C4×Q8—2831no—
192C4×Q8C2×D28311yescharacteristic
193#117—2831no—
194#117—2831no—
195C2×C42—2831no—
196C4⋊C8—2831no—
197C4⋊C8—2831no—
198C4⋊C8—2831no—
199C4⋊C8—2831no—
200C4⋊C8—2831no—
201C4⋊C8—2831no—
202C4⋊C8—2831no—
203C4⋊C8—2831no—
204C4⋊C8—2831no—
205C4⋊C8C2×D28311yescharacteristic
206C4⋊C8C2×D28311yescharacteristic
207C4⋊C8C2×D28311yescharacteristic
208#97—2831no—
209#97—2831no—
210#97—2831no—
211#97—2831no—
212#97—2831no—
213#97—2831no—
214#97C2×D28311yescharacteristic
215#97C2×D28311yescharacteristic
216C4×C8—2831no—
217C4×C8—2831no—
218C4×C8—2831no—
219C4×C8C2×D28311yescharacteristic
220C2×Q8—2831no—
221C2×Q8—2831no—
222C2×Q8—2831no—
223C2×Q8C4×D28311yescharacteristic
224C22×C4—2831no—
225C22×C4—2831no—
226C22×C4—2831no—
227M16—5662no—
228M16—5662no—
229C2×C8—2831no—
230C2×C8—2834no—
231C2×C8—2831no—
232C2×C8—2831no—
233C2×C8—2831no—
234C2×C8—5662no—
235C2×C8C22×D28311yescharacteristic
236C2×C8C22×D28311yescharacteristic
237C2×C8C22×D28311yescharacteristic
238C2×C8C22×D28311yescharacteristic
239C4⋊C4—2831no—
240C4⋊C4—2831no—
241C4⋊C4—2831no—
242C4⋊C4—2831no—
243C4⋊C4—2831no—
244C4⋊C4—2831no—
245C4⋊C4—2831no—
246C4⋊C4—2831no—
247C4⋊C4—2831no—
248C4⋊C4—2831no—
249C4⋊C4—2831no—
250C4⋊C4—2831no—
251C4⋊C4—2831no—
252C4⋊C4C4×D28311yescharacteristic
253C4⋊C4C4×D28311yescharacteristic
254C4⋊C4C4×D28311yescharacteristic
255C22⋊C4—2831no—
256C22⋊C4—2831no—
257C22⋊C4—2831no—
258C22⋊C4—2831no—
259C42—2831no—
260C42—2831no—
261C42—2831no—
262C42—2831no—
263C42—2831no—
264C42C22×D28311yescharacteristic
265C42C22×D28311yescharacteristic
266C42C22×D28311yescharacteristic
267C23—2831no—
268Q8—41no—
269Q8—11321no—
270Q8—11321no—
271Q8—11321no—
272C2×C4—2831no—
273C2×C4—2832no—
274C2×C4—2832no—
275C2×C4—2831no—
276C2×C4—2831no—
277C2×C4—2831no—
278C2×C4—2831no—
279C2×C4—2831no—
280C2×C4—2831no—
281C2×C4—11321no—
282C2×C4—11321no—
283C2×C4C2×C4×D28311yescharacteristic
284C2×C4C2×C4×D28311yescharacteristic
285C2×C4C2×C4×D28311yescharacteristic
286C2×C4C2×C4×D28311yescharacteristic
287C2×C4C2×C4×D28311yescharacteristic
288C2×C4C2×C4×D28311yescharacteristic
289C2×C4C23×D28311yescharacteristic
290C8—21no—
291C8—21no—
292C8—21no—
293C8—2832no—
294C8—5661no—
295C8—5661no—
296C8—5661no—
297C8Q8×D28312yes—
298C22—2832no—
299C22—5661no—
300C22—5661no—
301C22C22×C4×D28311yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—2832no—
309C4—5661no—
310C4—5661no—
311C4—5661no—
312C4—5661no—
313C4—5661no—
314C4—5661no—
315C4C2×Q8×D28311yescharacteristic
316C4#41×D28311yescharacteristic
317C2—5662no—
318C2C4×Q8×D28311yescharacteristic
319C2#3182723011yescharacteristic
320C2#3182723111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D283
commutator, socleC22×C283C23×C4
Fitting#446×C283C2
prime radicalC22×D283C22×C4
cosocleC2×C4×C283C24
hypercenter#446D283
hypocenterC283#2961
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #31826596C2semidirect
3. #31826595C2semidirect
4. #31826594C2semidirect
5. #31826594C2semidirect
6. #31826593C2semidirect
7. #31826593C2semidirect
8. #31826592C2semidirect
15. #446×C283C2semidirect
72. C8×D283Q8semidirect
160. C283#2961semidirect
170. #446D283semidirect

Maximal subgroups

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

subgroupindex
#318270192
#318265962
#318265952
#318265942
#318265932
#318265922
#318264902
#318264872
#318264222
#318264192
#97×D2832
#446×C2832
#2961283