Finite Group Databasebeta

← #49124200

Subgroups — #49124200

Order 36224.

588 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583572C211yesmaximal, characteristic
2#31826357C211yesmaximal, characteristic, complemented
3#31826355C211yesmaximal, characteristic, complemented
4#31826351C211yesmaximal, characteristic, complemented
5#31826343C211yesmaximal, characteristic
6#31826343C211yesmaximal, characteristic
7#31826332C211yesmaximal, characteristic, complemented
8#31826327C211yesmaximal, characteristic, complemented
9#31826322C211yesmaximal, characteristic, complemented
10C4×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
11C4×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
12#31826312C211yesmaximal, characteristic, complemented
13#31826310C211yesmaximal, characteristic, complemented
14#95×D283C211yesmaximal, characteristic, complemented
15#387×C283C211yesmaximal, characteristic, complemented
16C22×D1132C2211yescharacteristic
17C22×C4×D283C2211yescharacteristic
18C22×C4×D283C2211yescharacteristic
19C22×C4×D283C2211yescharacteristic
20C22×C4×D283C2211yescharacteristic
21#22583572C418yescomplemented
22C2×C4⋊Dic283C2211yescharacteristic
23C2×(C2×D283)⋊C4C2211yescharacteristic
24C2×(C2×D283)⋊C4C2211yescharacteristic
25C2×(C2×D283)⋊C4C2211yescharacteristic
26C2×(C2×D283)⋊C4C2211yescharacteristic
27C2×(C2×D283)⋊C4C2211yescharacteristic
28C2×(C2×D283)⋊C4C2211yescharacteristic
29C2×(C2×D283)⋊C4C2211yescharacteristic
30C2×(C2×D283)⋊C4C2211yescharacteristic
31C2×C4×Dic283C2211yescharacteristic
32C2×C4×Dic283C2211yescharacteristic
33C2×C4×Dic283C2211yescharacteristic
34C2×C4×Dic283C2211yescharacteristic
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
52C23×D283C2311yescharacteristic
53C23×D283C2311yescharacteristic
54C2×D1132—22no—
55C2×D1132—22no—
56C2×D1132C2×C414yes—
57C22×Dic283C2311yescharacteristic
58C22×Dic283C2311yescharacteristic
59C22×Dic283C2311yescharacteristic
60C22×Dic283C2311yescharacteristic
61C22×Dic283C2311yescharacteristic
62C22×Dic283C2311yescharacteristic
63C2×C4×D283—22no—
64C2×C4×D283—22no—
65C2×C4×D283—22no—
66C2×C4×D283—22no—
67C2×C4×D283—41no—
68C2×C4×D283—41no—
69C2×C4×D283—41no—
70C2×C4×D283—41no—
71C2×C4×D283—41no—
72C2×C4×D283—41no—
73C2×C4×D283C2×C414yes—
74C2×C4×D283C2×C414yescomplemented
75C4⋊Dic283—41no—
76(C2×D283)⋊C4—22no—
77(C2×D283)⋊C4—22no—
78(C2×D283)⋊C4—22no—
79(C2×D283)⋊C4—22no—
80(C2×D283)⋊C4—41no—
81(C2×D283)⋊C4—41no—
82(C2×D283)⋊C4C2×C414yes—
83(C2×D283)⋊C4C2×C414yescomplemented
84C4×Dic283—22no—
85C4×Dic283—22no—
86C4×Dic283—41no—
87C4×Dic283C2×C414yescomplemented
88C22×C4×C283C2311yescharacteristic
89C22×C4×C283C2311yescharacteristic
90C22×C4×C283C2311yescharacteristic
91C22×C4×C283C2311yescharacteristic
92C22×C4×C283C2311yescharacteristic
93C22×C4×C283C2311yescharacteristic
94C22×C4×C283C2311yescharacteristic
95C4⋊C4×C283—41no—
96C4⋊C4×C283C2×C414yescomplemented
97C42×C283—41no—
98C22×D283—21no—
99C22×D283—21no—
100C22×D283—21no—
101C22×D283—21no—
102C22×D283—21no—
103C22×D283—21no—
104C22×D283—21no—
105C22×D283—21no—
106C22×D283—21no—
107C22×D283—21no—
108C22×D283C22×C412yes—
109C22×D283C22×C412yes—
110C22×D283#4112yes—
111C22×D283#4112yes—
112D1132—28no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283C22×C412yes—
129C2×Dic283C22×C412yes—
130C2×Dic283#4112yes—
131C4×D283—44no—
132C4×D283—44no—
133C4×D283—44no—
134C4×D283—44no—
135C23×C283C2411yescharacteristic
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—21no—
151C2×C4×C283—21no—
152C2×C4×C283—21no—
153C2×C4×C283C22×C412yes—
154C2×C4×C283C22×C412yes—
155C2×C4×C283C22×C412yes—
156C2×C4×C283#4112yes—
157C22×C283C23×C411yescharacteristic
158C22×C283C2×#4111yescharacteristic
159C22×C283C2×#4111yescharacteristic
160C22×C283C2×#4111yescharacteristic
161C22×C283C2×#4111yescharacteristic
162C22×C283H(5,𝔽2)11yescharacteristic
163C22×C283H(5,𝔽2)11yescharacteristic
164C2×D283—22no—
165C2×D283—22no—
166C2×D283—22no—
167C2×D283—22no—
168C2×D283—22no—
169C2×D283—22no—
170C2×D283—22no—
171C2×D283—22no—
172C2×D283—22no—
173C2×D283—41no—
174C2×D283—41no—
175C2×D283—41no—
176C2×D283—41no—
177C2×D283#11714yes—
178C4×C283—22no—
179C4×C283—22no—
180C4×C283—22no—
181C4×C283—22no—
182C4×C283—41no—
183C4×C283—41no—
184C4×C283—41no—
185Dic283—22no—
186Dic283—22no—
187Dic283—22no—
188Dic283—41no—
189Dic283—41no—
190Dic283—41no—
191C2×C283C2×#11711yescharacteristic
192C2×C283C4×#4111yescharacteristic
193C2×C283#51811yescharacteristic
194C2×C283#55111yescharacteristic
195C2×C283#55111yescharacteristic
196C2×C283#55311yescharacteristic
197C2×C283#55311yescharacteristic
198D283—24no—
199D283—42no—
200C283#235311yescharacteristic, complemented, Sylow
201#2353—2831nomaximal, Sylow
202C2×C4×D4—2831no—
203#388—2831no—
204#388—2831no—
205#387—2831no—
206#387D28311yescharacteristic, complemented
207#386—2831no—
208#386—2831no—
209#383—2831no—
210#381—2831no—
211#380—2831no—
212C4×C22⋊C4—2831no—
213C4×C22⋊C4—2831no—
214C4×C22⋊C4—2831no—
215#376—2831no—
216C2×#95—2831no—
217C22×D4—2831no—
218C23×C4—2831no—
219C23×C4—2831no—
220C23×C4—2831no—
221C23×C4—2831no—
222C4×D4—2838no—
223C2×C4⋊C4—2831no—
224C2×C4⋊C4C2×D28311yescharacteristic
225C2×C4⋊C4C2×D28311yescharacteristic
226C2×C22⋊C4—2831no—
227C2×C22⋊C4—2831no—
228C2×C22⋊C4—2831no—
229C2×C22⋊C4—2831no—
230C2×C22⋊C4—2831no—
231C2×C22⋊C4—2831no—
232C2×C22⋊C4—2831no—
233C2×C22⋊C4—2831no—
234C2×C42—2831no—
235C2×C42—2831no—
236C2×C42—2831no—
237C2×C42—2831no—
238C2×C42C2×D28311yescharacteristic
239#95—2831no—
240#95—2831no—
241#95—2831no—
242#95—2831no—
243#95—2831no—
244#95—2831no—
245#95—2831no—
246#95—2831no—
247#95—2831no—
248#95—2831no—
249#95C2×D28311yescharacteristic
250#95C2×D28311yescharacteristic
251#95C2×D28311yescharacteristic
252#95C2×D28311yescharacteristic
253C24—2831no—
254C24—2831no—
255C2×D4—2834no—
256C2×D4—5662no—
257C2×D4—5662no—
258C22×C4—2831no—
259C22×C4—2831no—
260C22×C4—2831no—
261C22×C4—2834no—
262C22×C4—2834no—
263C22×C4—2831no—
264C22×C4—2831no—
265C22×C4—2831no—
266C22×C4—5662no—
267C22×C4—5662no—
268C22×C4—5662no—
269C22×C4—5662no—
270C22×C4—11321no—
271C22×C4—11321no—
272C22×C4—11321no—
273C22×C4—11321no—
274C22×C4—11321no—
275C22×C4—11321no—
276C22×C4C22×D28311yescharacteristic
277C22×C4C22×D28311yescharacteristic
278C22×C4C22×D28311yescharacteristic
279C22×C4C22×D28311yescharacteristic
280C22×C4C22×D28311yescharacteristic
281C22×C4C22×D28311yescharacteristic
282C22×C4C22×D28311yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—11321no—
285C4⋊C4C4×D28314yescomplemented
286C22⋊C4—2834no—
287C22⋊C4—2834no—
288C22⋊C4—5662no—
289C22⋊C4—5662no—
290C22⋊C4—5662no—
291C22⋊C4—5662no—
292C22⋊C4—11321no—
293C22⋊C4—11321no—
294C42—41no—
295C42—2834no—
296C42—5662no—
297C42—5662no—
298C42—11321no—
299C23—2832no—
300C23—2832no—
301C23—2832no—
302C23—2832no—
303C23—5661no—
304C23—5661no—
305C23—5661no—
306C23—5661no—
307C23—5661no—
308C23—5661no—
309C23—5661no—
310C23—5661no—
311C23—5661no—
312C23—5661no—
313C23C23×D28311yescharacteristic
314D4—5668no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—2832no—
333C2×C4—2832no—
334C2×C4—2832no—
335C2×C4—5661no—
336C2×C4—5661no—
337C2×C4—5661no—
338C2×C4—5661no—
339C2×C4—5661no—
340C2×C4—5661no—
341C2×C4—5661no—
342C2×C4—5661no—
343C2×C4—5661no—
344C2×C4—5661no—
345C2×C4—5661no—
346C2×C4—5661no—
347C2×C4—5661no—
348C2×C4—5661no—
349C2×C4—5661no—
350C2×C4—11324no—
351C2×C4—11324no—
352C2×C4—11324no—
353C2×C4—11324no—
354C2×C4C2×C4×D28312yes—
355C2×C4C2×C4×D28312yes—
356C2×C4C2×C4×D28312yes—
357C2×C4#1798539312yes—
358C22—2834no—
359C22—5662no—
360C22—5662no—
361C22—5662no—
362C22—5662no—
363C22—5662no—
364C22—5662no—
365C22—5662no—
366C22—5662no—
367C22—5662no—
368C22—11321no—
369C22—11321no—
370C22—11321no—
371C22—11321no—
372C22C22×C4×D28311yescharacteristic
373C22#41×D28311yescharacteristic
374C22#41×D28311yescharacteristic
375C22#41×D28311yescharacteristic
376C22C2×#1798539311yescharacteristic
377C22#2258365511yescharacteristic
378C22#2258365611yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—5662no—
387C4—5662no—
388C4—5662no—
389C4—11321no—
390C4—11321no—
391C4—11321no—
392C2—5664no—
393C2—11322no—
394C2#117×D28311yescharacteristic
395C2C4×#1798539311yescharacteristic
396C2#3182693711yescharacteristic
397C2#3182714011yescharacteristic
398C2#3182714211yescharacteristic
399C2#3182716011yescharacteristic
400C2#3182716811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#387×C283C2
socle, cosocleC23×C283C24
prime radicalC22×D1132C22
hypercenter#387D283
hypocenterC283#2353
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #31826357C2semidirect
3. #31826355C2semidirect
4. #31826351C2semidirect
7. #31826332C2semidirect
8. #31826327C2semidirect
9. #31826322C2semidirect
10. C4×(C2×D283)⋊C4C2semidirect
11. C4×(C2×D283)⋊C4C2semidirect
12. #31826312C2semidirect
13. #31826310C2semidirect
14. #95×D283C2semidirect
15. #387×C283C2semidirect
21. #22583572C4semidirect
74. C2×C4×D283C2×C4semidirect
83. (C2×D283)⋊C4C2×C4semidirect
87. C4×Dic283C2×C4semidirect
96. C4⋊C4×C283C2×C4semidirect
200. C283#2353semidirect
206. #387D283semidirect
285. C4⋊C4C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835722
#318263572
#318263552
#318263512
#318263432
#318263322
#318263272
#318263222
C4×(C2×D283)⋊C42
#318263122
#318263102
#95×D2832
#387×C2832
#2353283