Finite Group Databasebeta

← #49124006

Subgroups — #49124006

Order 36224.

460 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583609C211yesmaximal, characteristic
2#31826371C211yesmaximal, characteristic
3#31826370C211yesmaximal, characteristic
4#31826369C211yesmaximal, characteristic
5#31826369C211yesmaximal, characteristic
6#31826362C211yesmaximal, characteristic
7#31826360C211yesmaximal, characteristic
8#31826351C211yesmaximal, characteristic
9#31826350C211yesmaximal, characteristic
10#31826348C211yesmaximal, characteristic
11#31826329C211yesmaximal, characteristic
12C4×Dic283⋊C4C211yesmaximal, characteristic
13#31826316C211yesmaximal, characteristic
14#31826310C211yesmaximal, characteristic
15#387×C283C211yesmaximal, characteristic
16C22×Dic566C2211yescharacteristic
17C22×Dic566C2211yescharacteristic
18#22583609C418yescomplemented
19C2×C4⋊Dic283C2211yescharacteristic
20C2×C4⋊Dic283C2211yescharacteristic
21C2×Dic283⋊C4C2211yescharacteristic
22C2×Dic283⋊C4C2211yescharacteristic
23C2×Dic283⋊C4C2211yescharacteristic
24C2×Dic283⋊C4C2211yescharacteristic
25C2×Dic283⋊C4C2211yescharacteristic
26C2×Dic283⋊C4C2211yescharacteristic
27C2×C4×Dic283C2211yescharacteristic
28C2×C4×Dic283C2211yescharacteristic
29C2×C4×Dic283C2211yescharacteristic
30C2×C4×Dic283C2211yescharacteristic
31C2×C4×Dic283C2211yescharacteristic
32C2×C4×Dic283C2211yescharacteristic
33C283⋊#95C2211yescharacteristic
34C283⋊#95C2211yescharacteristic
35C283⋊#95C2211yescharacteristic
36C283⋊#95C2211yescharacteristic
37C283⋊#95C2211yescharacteristic
38C283⋊#95C2211yescharacteristic
39C283⋊#95C2211yescharacteristic
40C283⋊#95C2211yescharacteristic
41C283⋊#95C2211yescharacteristic
42C283⋊#95C2211yescharacteristic
43C283⋊#95C2211yescharacteristic
44C283⋊#95C2211yescharacteristic
45C2×C4⋊C4×C283C2211yescharacteristic
46C2×C4⋊C4×C283C2211yescharacteristic
47C2×C42×C283C2211yescharacteristic
48#95×C283C2211yescharacteristic
49#95×C283C2211yescharacteristic
50#95×C283C2211yescharacteristic
51#95×C283C2211yescharacteristic
52C2×Dic566—41no—
53C2×Dic566—41no—
54C2×Dic566—41no—
55C2×Dic566—41no—
56C2×Dic566C2×C414yes—
57C2×Dic566C2×C414yes—
58C22×Dic283C2311yescharacteristic
59C22×Dic283C2311yescharacteristic
60C22×Dic283C2311yescharacteristic
61C22×Dic283C2311yescharacteristic
62C22×Dic283C2311yescharacteristic
63C22×Dic283C2311yescharacteristic
64C22×Dic283C2311yescharacteristic
65C22×Dic283C2311yescharacteristic
66C4⋊Dic283—41no—
67C4⋊Dic283C2×C414yes—
68Dic283⋊C4—22no—
69Dic283⋊C4—22no—
70Dic283⋊C4—41no—
71Dic283⋊C4—41no—
72Dic283⋊C4C2×C414yes—
73Dic283⋊C4C2×C414yes—
74C4×Dic283—22no—
75C4×Dic283—41no—
76C4×Dic283—41no—
77C4×Dic283—41no—
78C4×Dic283C2×C414yes—
79C4×Dic283Q814yescomplemented
80C22×C4×C283C2311yescharacteristic
81C22×C4×C283C2311yescharacteristic
82C22×C4×C283C2311yescharacteristic
83C22×C4×C283C2311yescharacteristic
84C22×C4×C283C2311yescharacteristic
85C22×C4×C283C2311yescharacteristic
86C22×C4×C283C2311yescharacteristic
87C4⋊C4×C283—41no—
88C4⋊C4×C283C2×C414yes—
89C42×C283—41no—
90Dic566—44no—
91Dic566—44no—
92C2×Dic283—21no—
93C2×Dic283—21no—
94C2×Dic283—21no—
95C2×Dic283—21no—
96C2×Dic283—21no—
97C2×Dic283—21no—
98C2×Dic283—21no—
99C2×Dic283—21no—
100C2×Dic283—21no—
101C2×Dic283—21no—
102C2×Dic283—21no—
103C2×Dic283—21no—
104C2×Dic283—21no—
105C2×Dic283—21no—
106C2×Dic283—21no—
107C2×Dic283—21no—
108C2×Dic283—21no—
109C2×Dic283C22×C412yes—
110C2×Dic283C22×C412yes—
111C2×Dic283C22×C412yes—
112C2×Dic283C22×C412yes—
113C2×Dic283C2×Q812yes—
114C2×Dic283C2×Q812yes—
115C2×Dic283#4112yes—
116C23×C283C2411yescharacteristic
117C2×C4×C283—21no—
118C2×C4×C283—21no—
119C2×C4×C283—21no—
120C2×C4×C283—21no—
121C2×C4×C283—21no—
122C2×C4×C283—21no—
123C2×C4×C283—21no—
124C2×C4×C283—21no—
125C2×C4×C283—21no—
126C2×C4×C283—21no—
127C2×C4×C283—21no—
128C2×C4×C283—21no—
129C2×C4×C283—21no—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283C22×C412yes—
135C2×C4×C283C22×C412yes—
136C2×C4×C283C22×C412yes—
137C2×C4×C283C2×Q812yes—
138C22×C283C23×C411yescharacteristic
139C22×C283C22×Q811yescharacteristic
140C22×C283C2×#4111yescharacteristic
141C22×C283H(5,𝔽2)11yescharacteristic
142C22×C283H(5,𝔽2)11yescharacteristic
143C22×C2832−1+411yescharacteristic
144C22×C2832−1+411yescharacteristic
145C4×C283—22no—
146C4×C283—22no—
147C4×C283—22no—
148C4×C283—22no—
149C4×C283—41no—
150C4×C283—41no—
151C4×C283—41no—
152Dic283—22no—
153Dic283—22no—
154Dic283—22no—
155Dic283—22no—
156Dic283—41no—
157Dic283—41no—
158Dic283—41no—
159Dic283C4×Q814yes—
160C2×C283C2×C4×Q811yescharacteristic
161C2×C283#51811yescharacteristic
162C2×C283#51911yescharacteristic
163C2×C283#54211yescharacteristic
164C2×C283#54211yescharacteristic
165C2×C283#54411yescharacteristic
166C2×C283#54411yescharacteristic
167C283#233111yescharacteristic, complemented, Sylow
168#2331—2831nomaximal, Sylow
169C2×C4⋊Q8—2831no—
170#391—2831no—
171#391—2831no—
172#391—2831no—
173#391—2831no—
174#389—2831no—
175#389—2831no—
176#387—2831no—
177#387—2831no—
178#387—2831no—
179#387D28311yescharacteristic
180#382—2831no—
181C4×C4⋊C4—2831no—
182C4×C4⋊C4—2831no—
183#376—2831no—
184C22×Q8—2831no—
185C22×Q8—2831no—
186C4⋊Q8—2838no—
187C2×C4⋊C4—2831no—
188C2×C4⋊C4—2831no—
189C2×C4⋊C4—2831no—
190C2×C4⋊C4—2831no—
191C2×C4⋊C4—2831no—
192C2×C4⋊C4—2831no—
193C2×C4⋊C4—2831no—
194C2×C4⋊C4—2831no—
195C2×C4⋊C4C2×D28311yescharacteristic
196C2×C4⋊C4C2×D28311yescharacteristic
197C2×C42—2831no—
198C2×C42—2831no—
199C2×C42—2831no—
200C2×C42—2831no—
201C2×C42—2831no—
202C2×C42—2831no—
203C2×C42C2×D28311yescharacteristic
204#95—2831no—
205#95—2831no—
206#95—2831no—
207#95—2831no—
208#95—2831no—
209#95—2831no—
210#95—2831no—
211#95—2831no—
212#95—2831no—
213#95—2831no—
214#95—2831no—
215#95—2831no—
216#95C2×D28311yescharacteristic
217#95C2×D28311yescharacteristic
218#95C2×D28311yescharacteristic
219#95C2×D28311yescharacteristic
220C2×Q8—2834no—
221C2×Q8—2834no—
222C2×Q8—11321no—
223C2×Q8—11321no—
224C2×Q8—11321no—
225C2×Q8—11321no—
226C22×C4—2831no—
227C22×C4—2831no—
228C22×C4—2831no—
229C22×C4—2831no—
230C22×C4—2831no—
231C22×C4—2831no—
232C22×C4—2831no—
233C22×C4—2831no—
234C22×C4C22×D28311yescharacteristic
235C22×C4C22×D28311yescharacteristic
236C22×C4C22×D28311yescharacteristic
237C22×C4C22×D28311yescharacteristic
238C22×C4C22×D28311yescharacteristic
239C22×C4C22×D28311yescharacteristic
240C22×C4C22×D28311yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—2834no—
243C4⋊C4—2834no—
244C4⋊C4—2834no—
245C4⋊C4—5662no—
246C4⋊C4—5662no—
247C4⋊C4—11321no—
248C4⋊C4—11321no—
249C4⋊C4—11321no—
250C4⋊C4C4×D28314yes—
251C42—41no—
252C42—2834no—
253C42—2834no—
254C42—5662no—
255C42—11321no—
256C42—11321no—
257C42—11321no—
258C23C23×D28311yescharacteristic
259Q8—11324no—
260Q8—11324no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—2832no—
279C2×C4—2832no—
280C2×C4—2832no—
281C2×C4—2832no—
282C2×C4—2832no—
283C2×C4—2832no—
284C2×C4—2832no—
285C2×C4—5661no—
286C2×C4—5661no—
287C2×C4—5661no—
288C2×C4—5661no—
289C2×C4—5661no—
290C2×C4—5661no—
291C2×C4—5661no—
292C2×C4—5661no—
293C2×C4—5661no—
294C2×C4—5661no—
295C2×C4—5661no—
296C2×C4—5661no—
297C2×C4—5661no—
298C2×C4—5661no—
299C2×C4—5661no—
300C2×C4—5661no—
301C2×C4—5661no—
302C2×C4C2×C4×D28312yes—
303C2×C4C2×C4×D28312yes—
304C2×C4C2×C4×D28312yes—
305C2×C4Q8×D28312yes—
306C22C22×C4×D28311yescharacteristic
307C22C2×Q8×D28311yescharacteristic
308C22#41×D28311yescharacteristic
309C22#2258365511yescharacteristic
310C22#2258365611yescharacteristic
311C22#2258365711yescharacteristic
312C22#2258365711yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—2834no—
321C4—5662no—
322C4—5662no—
323C4—5662no—
324C4—5662no—
325C4—11321no—
326C4—11321no—
327C4—11321no—
328C2C4×Q8×D28311yescharacteristic
329C2#3182693711yescharacteristic
330C2#3182694211yescharacteristic
331C2#3182708111yescharacteristic
332C2#3182708311yescharacteristic
333C2#3182709411yescharacteristic
334C2#3182709511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#387×C283C2
socle, prime radical, cosocleC23×C283C24
hypercenter#387D283
hypocenterC283#2331
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
18. #22583609C4semidirect
79. C4×Dic283Q8semidirect
167. C283#2331semidirect

Maximal subgroups

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

subgroupindex
C2×#225836092
#318263712
#318263702
#318263692
#318263622
#318263602
#318263512
#318263502
#318263482
#318263292
C4×Dic283⋊C42
#318263162
#318263102
#387×C2832
#2331283