Finite Group Databasebeta

← #49130002

Subgroups — #49130002

Order 36224.

492 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583618C211yesmaximal, characteristic, complemented
2C2×#22583616C211yesmaximal, characteristic, complemented
3#31827012C211yesmaximal, characteristic
4#31826541C211yesmaximal, characteristic, complemented
5#31826540C211yesmaximal, characteristic, complemented
6#31826538C211yesmaximal, characteristic, complemented
7#31826537C211yesmaximal, characteristic, complemented
8#31826535C211yesmaximal, characteristic, complemented
9C8×C22⋊D283C211yesmaximal, characteristic, complemented
10(C22⋊D283)⋊C8C211yesmaximal, characteristic, complemented
11C4⋊C8×D283C211yesmaximal, characteristic, complemented
12#31826430C211yesmaximal, characteristic, complemented
13#31826430C211yesmaximal, characteristic, complemented
14#31826417C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985392C2211yescharacteristic
18#22583618—24no—
19#22583616—24no—
20C2×#17985376C2211yescharacteristic
21C2×#17985375C2211yescharacteristic
22C2×#17985375C2211yescharacteristic
23C2×#17985375C2211yescharacteristic
24C2×#17985375C2211yescharacteristic
25C22×C283⋊C8C2211yescharacteristic
26C2×C8×D283C2211yescharacteristic
27C2×C8×D283C2211yescharacteristic
28C2×C8×D283C2211yescharacteristic
29C2×C8×D283C2211yescharacteristic
30#22583609C411yescharacteristic
31#22583606C411yescharacteristic
32#22583596C411yescharacteristic
33#22583596C411yescharacteristic
34#22583585C411yescharacteristic
35#22583583C411yescharacteristic
36#22583583C411yescharacteristic
37#22583581C411yescharacteristic
38C4×D1132C2211yescharacteristic
39C4×C22⋊D283C2211yescharacteristic
40C4×C22⋊D283C2211yescharacteristic
41C42×D283C2211yescharacteristic
42C4⋊(C283⋊C8)C2211yescharacteristic
43Dic283⋊C8C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46C22⋊(C283⋊C8)C2211yescharacteristic
47(C2×D283)⋊C8C2211yescharacteristic
48(C2×D283)⋊C8C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583521C2211yescharacteristic
52C8×Dic283C2211yescharacteristic
53C8×Dic283C2211yescharacteristic
54C2×M16×C283C2211yescharacteristic
55C22×C8×C283C2211yescharacteristic
56C4×D4×C283C2211yescharacteristic
57C4⋊C8×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59C22⋊C8×C283C2211yescharacteristic
60#97×C283C2211yescharacteristic
61#17985392—22no—
62#17985392—22no—
63#17985392—22no—
64#17985392—22no—
65C2×Dic566C2×C411yescharacteristic
66C2×Dic566C2×C411yescharacteristic
67C2×D1132C2×C411yescharacteristic
68C2×D1132C2×C411yescharacteristic
69C2×D1132C2×C411yescharacteristic
70C2×C22⋊D283C2×C411yescharacteristic
71C2×C22⋊D283C2×C411yescharacteristic
72C2×C22⋊D283C2×C411yescharacteristic
73C2×C22⋊D283C2×C411yescharacteristic
74C2×C22⋊D283C2×C411yescharacteristic
75C2×C22⋊D283C2×C411yescharacteristic
76C2×C4×D283C2×C411yescharacteristic
77C2×C4×D283C2×C411yescharacteristic
78C2×C4×D283C2311yescharacteristic
79C2×C4×D283C2311yescharacteristic
80C2×C4×D283C2311yescharacteristic
81#17985376—22no—
82#17985375—22no—
83#17985375—22no—
84#17985375—22no—
85#17985375D414yescomplemented
86C2×C283⋊C8—22no—
87C2×C283⋊C8C2311yescharacteristic
88C2×C283⋊C8C2311yescharacteristic
89C2×C283⋊C8C2311yescharacteristic
90C2×C283⋊C8C2311yescharacteristic
91C8×D283—22no—
92C8×D283—22no—
93C8×D283—22no—
94C8×D283—22no—
95C4⋊Dic283C2×C411yescharacteristic
96Dic283⋊C4C2×C411yescharacteristic
97Dic283⋊C4C2×C411yescharacteristic
98C22⋊Dic283C2×C411yescharacteristic
99C22⋊Dic283C2×C411yescharacteristic
100(C2×D283)⋊C4C2×C411yescharacteristic
101(C2×D283)⋊C4C2×C411yescharacteristic
102(C2×D283)⋊C4C2×C411yescharacteristic
103(C2×D283)⋊C4C2×C411yescharacteristic
104C4×Dic283C2×C411yescharacteristic
105C4×Dic283C2×C411yescharacteristic
106C4×Dic283C2311yescharacteristic
107C2×D4×C283C2×C411yescharacteristic
108C22×C4×C283C2311yescharacteristic
109C22×C4×C283C2311yescharacteristic
110M16×C283—22no—
111C2×C8×C283—22no—
112C2×C8×C283C2311yescharacteristic
113C2×C8×C283C2311yescharacteristic
114C2×C8×C283C2311yescharacteristic
115C2×C8×C283C2311yescharacteristic
116C4⋊C4×C283C2×C411yescharacteristic
117C22⋊C4×C283C2×C411yescharacteristic
118C22⋊C4×C283C2×C411yescharacteristic
119C42×C283C2311yescharacteristic
120C22×D283C22×C411yescharacteristic
121C22×D283C22×C411yescharacteristic
122C22×D283C22×C411yescharacteristic
123Dic566—22no—
124Dic566—22no—
125D1132—22no—
126D1132—22no—
127D1132—41no—
128C22⋊D283—22no—
129C22⋊D283—22no—
130C22⋊D283—22no—
131C22⋊D283—22no—
132C22⋊D283—22no—
133C22⋊D283—22no—
134C2×Dic283C22×C411yescharacteristic
135C2×Dic283C22×C411yescharacteristic
136C2×Dic283C22×C411yescharacteristic
137C2×Dic283C22×C411yescharacteristic
138C2×Dic283C22×C411yescharacteristic
139C4×D283—21no—
140C4×D283—21no—
141C4×D283—21no—
142C4×D283—21no—
143C4×D283—22no—
144C4×D283—41no—
145C4×D283C2×D412yes—
146C4×D283#4112yes—
147C283⋊C8—21no—
148C283⋊C8—21no—
149C283⋊C8—21no—
150C283⋊C8C2×D412yes—
151C23×C283C22×C411yescharacteristic
152C23×C283C22×C411yescharacteristic
153D4×C283—41no—
154C2×C4×C283—21no—
155C2×C4×C283—21no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283C22×C411yescharacteristic
159C2×C4×C283C22×C411yescharacteristic
160C2×C4×C283C22×C411yescharacteristic
161C2×C4×C283C22×C411yescharacteristic
162C2×C4×C283C2411yescharacteristic
163C8×C283—21no—
164C8×C283—21no—
165C8×C283—21no—
166C8×C283C2×D412yes—
167C22×C283—21no—
168C22×C283—21no—
169C22×C283—21no—
170C22×C283—21no—
171C22×C283—21no—
172C22×C283—21no—
173C22×C283C23×C411yescharacteristic
174C2×D283—21no—
175C2×D283—21no—
176C2×D283—21no—
177C2×D283—21no—
178C2×D283—21no—
179C2×D283—21no—
180C2×D283—21no—
181C2×D283—21no—
182C2×D283C4×D412yes—
183C4×C283—21no—
184C4×C283—21no—
185C4×C283—21no—
186C4×C283—21no—
187C4×C283C22×D411yescharacteristic
188C4×C283C2×#4111yescharacteristic
189Dic283—21no—
190Dic283—21no—
191Dic283—21no—
192Dic283C4×D412yes—
193Dic283#13112yescomplemented
194C2×C283—41no—
195C2×C283—41no—
196C2×C283C2×C4×D411yescharacteristic
197C2×C283C2×#13111yescharacteristic
198C2×C283#56811yescharacteristic
199D283—22no—
200D283—41no—
201D283—41no—
202C283#293511yescharacteristic, complemented, Sylow
203#2935—2831nomaximal, Sylow
204C2×#131—2831no—
205C2×#131—2831no—
206#532—2831no—
207#436—2831no—
208#436—2831no—
209#435—2831no—
210#435—2831no—
211#435—2831no—
212#435D28311yescharacteristic, complemented
213C8×D4—2831no—
214C8×D4—2831no—
215C2×C4⋊C8—2831no—
216#408—2831no—
217#408—2831no—
218C4×M16—2831no—
219C2×#41—2831no—
220C2×#41—2831no—
221#131—5664no—
222#131—5664no—
223C2×M16—2831no—
224C2×M16—2831no—
225C2×M16—2831no—
226C2×M16—2831no—
227C2×M16—2831no—
228C2×M16C2×D28311yescharacteristic
229C22×C8—2831no—
230C22×C8—2831no—
231C22×C8—2831no—
232C22×C8—2831no—
233C22×C8—2831no—
234C22×C8C2×D28311yescharacteristic
235C4⋊Q8—2831no—
236#127—2831no—
237#124—2831no—
238#124—2831no—
239#121—2831no—
240#121—2831no—
241#121—2831no—
242#121—2831no—
243C4×D4—2831no—
244C4×D4—2831no—
245C4×D4—2831no—
246C4×D4C2×D28311yescharacteristic
247C2×C42—2831no—
248C4⋊C8—2831no—
249C4⋊C8—2831no—
250C4⋊C8—2831no—
251C4⋊C8C2×D28311yescharacteristic
252C22⋊C8—2831no—
253C22⋊C8—2831no—
254C22⋊C8—2831no—
255C22⋊C8—2831no—
256C22⋊C8—2831no—
257C22⋊C8—2831no—
258C22⋊C8C2×D28311yescharacteristic
259C22⋊C8C2×D28311yescharacteristic
260#97—2831no—
261#97C2×D28311yescharacteristic
262C4×C8—2831no—
263C4×C8—2831no—
264#41—5662no—
265#41—5662no—
266#41—5662no—
267#41—5662no—
268C2×Q8—2831no—
269C2×Q8—2831no—
270C2×D4—2831no—
271C2×D4—2831no—
272C2×D4—2831no—
273C2×D4—2831no—
274C2×D4—2831no—
275C2×D4—2831no—
276C2×D4—2831no—
277C2×D4—2831no—
278C2×D4—2831no—
279C2×D4C4×D28311yescharacteristic
280C22×C4—2831no—
281C22×C4—2831no—
282C22×C4—2831no—
283C22×C4—2831no—
284C22×C4—2831no—
285C22×C4C22×D28311yescharacteristic
286C22×C4C22×D28311yescharacteristic
287M16—22no—
288M16—2834no—
289M16—5662no—
290M16—5662no—
291M16—5662no—
292M16—5662no—
293C2×C8—22no—
294C2×C8—2831no—
295C2×C8—2831no—
296C2×C8—2831no—
297C2×C8—2831no—
298C2×C8—5662no—
299C2×C8—5662no—
300C2×C8—5662no—
301C2×C8—5662no—
302C2×C8—5662no—
303C2×C8C22×D28311yescharacteristic
304C2×C8C22×D28311yescharacteristic
305C2×C8C22×D28311yescharacteristic
306C2×C8C22×D28311yescharacteristic
307C4⋊C4—2831no—
308C4⋊C4—2831no—
309C4⋊C4—2831no—
310C4⋊C4C4×D28311yescharacteristic
311C22⋊C4—2831no—
312C22⋊C4—2831no—
313C22⋊C4—2831no—
314C22⋊C4—2831no—
315C22⋊C4—2831no—
316C22⋊C4—2831no—
317C22⋊C4C4×D28311yescharacteristic
318C22⋊C4C4×D28311yescharacteristic
319C42—2831no—
320C42—2831no—
321C42—2831no—
322C42C22×D28311yescharacteristic
323C23—2831no—
324C23—2831no—
325C23—2831no—
326C23C2×C4×D28311yescharacteristic
327C23C2×C4×D28311yescharacteristic
328Q8—5662no—
329Q8—5662no—
330D4—41no—
331D4—5662no—
332D4—5662no—
333D4—5662no—
334D4—5662no—
335D4—5662no—
336D4—5662no—
337D4—5662no—
338D4—5662no—
339D4—11321no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—2831no—
345C2×C4—2831no—
346C2×C4—2832no—
347C2×C4—2832no—
348C2×C4—2831no—
349C2×C4—2831no—
350C2×C4—2831no—
351C2×C4—5662no—
352C2×C4—5661no—
353C2×C4—5661no—
354C2×C4—5661no—
355C2×C4—5661no—
356C2×C4—11321no—
357C2×C4C2×C4×D28311yescharacteristic
358C2×C4C2×C4×D28311yescharacteristic
359C2×C4C2×C4×D28311yescharacteristic
360C2×C4C2×C4×D28311yescharacteristic
361C2×C4C23×D28311yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8—2832no—
366C8—5661no—
367C8—5661no—
368C8—5661no—
369C8D4×D28312yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—2832no—
377C22—5661no—
378C22—5661no—
379C22—5661no—
380C22—5661no—
381C22—5661no—
382C22—5661no—
383C22—5661no—
384C22—5661no—
385C22C22×C4×D28311yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—2832no—
391C4—2832no—
392C4—5661no—
393C4—5661no—
394C4—5661no—
395C4C2×D4×D28311yescharacteristic
396C4#41×D28311yescharacteristic
397C2—41no—
398C2—41no—
399C2—5662no—
400C2—11321no—
401C2—11321no—
402C2C4×D4×D28311yescharacteristic
403C2#131×D28311yescharacteristic
404C2#3182723111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D283
commutator, socleC22×C283C23×C4
Fitting#435×C283C2
prime radical#31827012C2
cosocleC2×C4×C283C24
hypercenter#435D283
hypocenterC283#2935
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#22583618C2semidirect
2. C2×#22583616C2semidirect
4. #31826541C2semidirect
5. #31826540C2semidirect
6. #31826538C2semidirect
7. #31826537C2semidirect
8. #31826535C2semidirect
9. C8×C22⋊D283C2semidirect
10. (C22⋊D283)⋊C8C2semidirect
11. C4⋊C8×D283C2semidirect
12. #31826430C2semidirect
13. #31826430C2semidirect
14. #31826417C2semidirect
15. #435×C283C2semidirect
85. #17985375D4semidirect
193. Dic283#131semidirect
202. C283#2935semidirect
212. #435D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836182
C2×#225836162
#318270122
#318265412
#318265402
#318265382
#318265372
#318265352
C8×C22⋊D2832
(C22⋊D283)⋊C82
C4⋊C8×D2832
#318264302
#318264172
#435×C2832
#2935283