Finite Group Databasebeta

← #49130221

Subgroups — #49130221

Order 36224.

412 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#17985391C211yesmaximal, characteristic
2#31826594C211yesmaximal, characteristic, complemented
3#31826593C211yesmaximal, characteristic, complemented
4#31826541C211yesmaximal, characteristic, complemented
5#31826540C211yesmaximal, characteristic, complemented
6#31826537C211yesmaximal, characteristic, complemented
7#31826536C211yesmaximal, characteristic, complemented
8#31826533C211yesmaximal, characteristic, complemented
9#31826517C211yesmaximal, characteristic, complemented
10#31826515C211yesmaximal, characteristic, complemented
11#31826515C211yesmaximal, characteristic, complemented
12#31826417C211yesmaximal, characteristic, complemented
13M16×Dic283C211yesmaximal, characteristic, complemented
14C2×C8×Dic283C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C411yescharacteristic
17C2×#17985376C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C2×#17985375C2211yescharacteristic
20C22×C283⋊C8C2211yescharacteristic
21C4×Dic566C2211yescharacteristic
22#22583575C411yescharacteristic
23D4×Dic283C411yescharacteristic
24C4×C22⋊D283C2211yescharacteristic
25C4×C22⋊D283C2211yescharacteristic
26(C22⋊D283)⋊C4C411yescharacteristic
27(C22⋊D283)⋊C4C411yescharacteristic
28#22583568C411yescharacteristic
29#22583566C411yescharacteristic
30#22583566C411yescharacteristic
31C2×C4×Dic283C2211yescharacteristic
32C2×C4×Dic283C2211yescharacteristic
33C42×D283C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35Dic283⋊C8C2211yescharacteristic
36Dic283⋊C8C2211yescharacteristic
37Dic283⋊C8C2211yescharacteristic
38Dic283⋊C8C2211yescharacteristic
39C22⋊(C283⋊C8)C2211yescharacteristic
40C22⋊(C283⋊C8)C2211yescharacteristic
41(C2×D283)⋊C8C2211yescharacteristic
42(C2×D283)⋊C8C2211yescharacteristic
43#22583521C2211yescharacteristic
44#22583520C2211yescharacteristic
45#22583520C2211yescharacteristic
46C8×Dic283C2211yescharacteristic
47C8×Dic283C2211yescharacteristic
48C8×Dic283C2211yescharacteristic
49C8×Dic283C2211yescharacteristic
50C8×Dic283C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×M16×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55C4⋊C8×C283C2211yescharacteristic
56C22⋊C8×C283C2211yescharacteristic
57C22⋊C8×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59#17985391—24no—
60C2×Dic566C2×C411yescharacteristic
61C2×C22⋊D283C2×C411yescharacteristic
62C2×C22⋊D283C2×C411yescharacteristic
63C22×Dic283C2×C411yescharacteristic
64C22×Dic283C2×C411yescharacteristic
65C22×Dic283C2×C411yescharacteristic
66C22×Dic283C2×C411yescharacteristic
67C2×C4×D283C2×C411yescharacteristic
68C2×C4×D283C2×C411yescharacteristic
69C2×C4×D283C2311yescharacteristic
70#17985376—22no—
71#17985375—22no—
72#17985375—22no—
73C2×C283⋊C8—22no—
74C2×C283⋊C8C2311yescharacteristic
75C2×C283⋊C8C2311yescharacteristic
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C4⋊Dic283C2×C411yescharacteristic
79Dic283⋊C4C2×C411yescharacteristic
80Dic283⋊C4C2×C411yescharacteristic
81Dic283⋊C4C2×C411yescharacteristic
82Dic283⋊C4C2×C411yescharacteristic
83C22⋊Dic283C2×C411yescharacteristic
84C22⋊Dic283C2×C411yescharacteristic
85(C2×D283)⋊C4C2×C411yescharacteristic
86(C2×D283)⋊C4C2×C411yescharacteristic
87C4×Dic283C2×C411yescharacteristic
88C4×Dic283C2×C411yescharacteristic
89C4×Dic283C2×C411yescharacteristic
90C4×Dic283C2×C411yescharacteristic
91C4×Dic283C2×C411yescharacteristic
92C4×Dic283C2×C411yescharacteristic
93C4×Dic283C2311yescharacteristic
94C4×Dic283C2311yescharacteristic
95C4×Dic283C2311yescharacteristic
96C2×D4×C283C2×C411yescharacteristic
97C22×C4×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99M16×C283—22no—
100C2×C8×C283—22no—
101C2×C8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C4⋊C4×C283C2×C411yescharacteristic
106C22⋊C4×C283C2×C411yescharacteristic
107C22⋊C4×C283C2×C411yescharacteristic
108C42×C283C2311yescharacteristic
109C22×D283C22×C411yescharacteristic
110Dic566—22no—
111C22⋊D283—22no—
112C22⋊D283—22no—
113C2×Dic283—22no—
114C2×Dic283—22no—
115C2×Dic283—22no—
116C2×Dic283M1614yescomplemented
117C2×Dic283C22×C411yescharacteristic
118C2×Dic283C22×C411yescharacteristic
119C2×Dic283C22×C411yescharacteristic
120C2×Dic283C22×C411yescharacteristic
121C2×Dic283C22×C411yescharacteristic
122C2×Dic283C22×C411yescharacteristic
123C2×Dic283C22×C411yescharacteristic
124C4×D283—21no—
125C4×D283—21no—
126C4×D283—22no—
127C4×D283—22no—
128C283⋊C8—21no—
129C283⋊C8—21no—
130C283⋊C8—21no—
131C283⋊C8#4112yescomplemented
132C23×C283C22×C411yescharacteristic
133C23×C283C22×C411yescharacteristic
134D4×C283—22no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283C22×C411yescharacteristic
140C2×C4×C283C22×C411yescharacteristic
141C2×C4×C283C22×C411yescharacteristic
142C2×C4×C283C22×C411yescharacteristic
143C2×C4×C283C2411yescharacteristic
144C8×C283—21no—
145C8×C283—21no—
146C8×C283—21no—
147C8×C283#4112yescomplemented
148C22×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283—21no—
152C22×C283—21no—
153C22×C283C2×M1612yes—
154C22×C283C23×C411yescharacteristic
155C2×D283—21no—
156C2×D283—21no—
157C2×D283—21no—
158C4×C283—21no—
159C4×C283—21no—
160C4×C283—21no—
161C4×C283—21no—
162C4×C283C2×#4111yescharacteristic
163C4×C283C2×#4111yescharacteristic
164Dic283—21no—
165Dic283—21no—
166Dic283—21no—
167Dic283—21no—
168Dic283C2×M1612yes—
169Dic283C2×M1612yes—
170Dic283#13112yes—
171C2×C283—22no—
172C2×C283—41no—
173C2×C283C4×#4111yescharacteristic
174C2×C283C22×M1611yescharacteristic
175C2×C283C2×#13111yescharacteristic
176D283—41no—
177C283#296511yescharacteristic, complemented, Sylow
178#2965—2831nomaximal, Sylow
179C4×#41—2831no—
180#446—2831no—
181#446—2831no—
182#436—2831no—
183#436—2831no—
184#435—2831no—
185#435—2831no—
186#435—2831no—
187#435D28311yescharacteristic, complemented
188#431—2831no—
189#431—2831no—
190#431—2831no—
191C4×M16—2831no—
192C4×M16—2831no—
193C2×C4×C8—2831no—
194C2×#41—2831no—
195C2×M16—2831no—
196C2×M16—2831no—
197C2×M16—2831no—
198C2×M16C2×D28311yescharacteristic
199C22×C8—2831no—
200C22×C8C2×D28311yescharacteristic
201C4×Q8—2831no—
202C4×Q8—2831no—
203C4×D4—2831no—
204C4×D4—2831no—
205C4×D4—2831no—
206C4×D4—2831no—
207C4×D4—2831no—
208C4×D4C2×D28311yescharacteristic
209#117—2831no—
210#117—2831no—
211#117—2831no—
212C2×C42—2831no—
213C2×C42—2831no—
214C2×C42—2831no—
215C4⋊C8—2831no—
216C4⋊C8—2831no—
217C4⋊C8—2831no—
218C4⋊C8—2831no—
219C4⋊C8—2831no—
220C4⋊C8C2×D28311yescharacteristic
221C22⋊C8—2831no—
222C22⋊C8—2831no—
223C22⋊C8—2831no—
224C22⋊C8—2831no—
225C22⋊C8C2×D28311yescharacteristic
226C22⋊C8C2×D28311yescharacteristic
227#97—2831no—
228#97—2831no—
229#97—2831no—
230#97C2×D28311yescharacteristic
231C4×C8—2831no—
232C4×C8—2831no—
233C4×C8—2831no—
234C4×C8—2831no—
235C4×C8—2831no—
236C4×C8—2831no—
237#41—5664no—
238C2×Q8—2831no—
239C2×D4—2831no—
240C2×D4—2831no—
241C2×D4C4×D28311yescharacteristic
242C22×C4—2831no—
243C22×C4—2831no—
244C22×C4—2831no—
245C22×C4—2831no—
246C22×C4—2831no—
247C22×C4—2831no—
248C22×C4—2831no—
249C22×C4C22×D28311yescharacteristic
250C22×C4C22×D28311yescharacteristic
251M16—22no—
252M16—5662no—
253M16—5662no—
254M16—5662no—
255C2×C8—22no—
256C2×C8—2831no—
257C2×C8—2831no—
258C2×C8—2831no—
259C2×C8—2831no—
260C2×C8—5662no—
261C2×C8C22×D28311yescharacteristic
262C2×C8C22×D28311yescharacteristic
263C2×C8C22×D28311yescharacteristic
264C2×C8C22×D28311yescharacteristic
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—2831no—
270C4⋊C4C4×D28311yescharacteristic
271C22⋊C4—2831no—
272C22⋊C4—2831no—
273C22⋊C4—2831no—
274C22⋊C4—2831no—
275C22⋊C4C4×D28311yescharacteristic
276C22⋊C4C4×D28311yescharacteristic
277C42—2831no—
278C42—2831no—
279C42—2831no—
280C42—2831no—
281C42—2831no—
282C42—2831no—
283C42—2831no—
284C42—2831no—
285C42—2831no—
286C42C22×D28311yescharacteristic
287C23—2831no—
288C23C2×C4×D28311yescharacteristic
289C23C2×C4×D28311yescharacteristic
290Q8—5662no—
291D4—22no—
292D4—5662no—
293D4—5662no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—2834no—
299C2×C4—2831no—
300C2×C4—2831no—
301C2×C4—2831no—
302C2×C4—2831no—
303C2×C4—2831no—
304C2×C4—2831no—
305C2×C4—2831no—
306C2×C4—5662no—
307C2×C4—5662no—
308C2×C4—5662no—
309C2×C4—5662no—
310C2×C4—5662no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4C2×C4×D28311yescharacteristic
314C2×C4C2×C4×D28311yescharacteristic
315C2×C4C2×C4×D28311yescharacteristic
316C2×C4C2×C4×D28311yescharacteristic
317C2×C4C23×D28311yescharacteristic
318C8—21no—
319C8—21no—
320C8—21no—
321C8—2832no—
322C8—5661no—
323C8—5661no—
324C8—5661no—
325C8#1798539112yescomplemented
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—5661no—
332C22—5661no—
333C22—5661no—
334C22M16×D28312yes—
335C22C22×C4×D28311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—2832no—
341C4—2832no—
342C4—2832no—
343C4—5661no—
344C4—5661no—
345C4—5661no—
346C4—5661no—
347C4#41×D28311yescharacteristic
348C4C2×#1798539111yescharacteristic
349C2—22no—
350C2—41no—
351C2—11321no—
352C2C4×#1798539111yescharacteristic
353C2C2×M16×D28311yescharacteristic
354C2#131×D28311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D283
commutator, socleC22×C283C23×C4
Fitting#435×C283C2
prime radicalC2×#17985391C4
cosocleC2×C4×C283C24
hypercenter#435D283
hypocenterC283#2965
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #31826594C2semidirect
3. #31826593C2semidirect
4. #31826541C2semidirect
5. #31826540C2semidirect
6. #31826537C2semidirect
7. #31826536C2semidirect
8. #31826533C2semidirect
9. #31826517C2semidirect
10. #31826515C2semidirect
11. #31826515C2semidirect
12. #31826417C2semidirect
13. M16×Dic283C2semidirect
14. C2×C8×Dic283C2semidirect
15. #435×C283C2semidirect
116. C2×Dic283M16semidirect
131. C283⋊C8#41semidirect
147. C8×C283#41semidirect
177. C283#2965semidirect
187. #435D283semidirect
325. C8#17985391semidirect

Maximal subgroups

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

subgroupindex
C4×#179853912
#318265942
#318265932
#318265412
#318265402
#318265372
#318265362
#318265332
#318265172
#318265152
#318264172
M16×Dic2832
C2×C8×Dic2832
#435×C2832
#2965283