Finite Group Databasebeta

← #49133359

Subgroups — #49133359

Order 36224.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827155C211yesmaximal, characteristic, complemented
2#31827120C211yesmaximal, characteristic
3#31826834C211yesmaximal, characteristic, complemented
4#31826807C211yesmaximal, characteristic, complemented
5#31826801C211yesmaximal, characteristic, complemented
6#31826766C211yesmaximal, characteristic, complemented
7#31826723C211yesmaximal, characteristic, complemented
8#31826706C211yesmaximal, characteristic, complemented
9#31826676C211yesmaximal, characteristic, complemented
10#31826629C211yesmaximal, characteristic, complemented
11#31826629C211yesmaximal, characteristic, complemented
12#31826567C211yesmaximal, characteristic, complemented
13#31826467C211yesmaximal, characteristic, complemented
14#31826462C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985392C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×Dic1132C2211yescharacteristic
20C2×#17985381C2211yescharacteristic
21#22583610C2211yescharacteristic
22#22583603—21no—
23#22583602C2211yescharacteristic
24#22583600—21no—
25#22583592—21no—
26#22583592—21no—
27#22583591—21no—
28#22583589C2211yescharacteristic
29#22583589C2211yescharacteristic
30#22583589C2211yescharacteristic
31#22583589C2211yescharacteristic
32#22583581—21no—
33C4×Dic566C2211yescharacteristic
34C4×D1132C2211yescharacteristic
35#22583569C2211yescharacteristic
36#22583566—21no—
37C2×C4⋊Dic283C2211yescharacteristic
38C4⋊C4×D283—21no—
39#22583544C2211yescharacteristic
40#22583544C2211yescharacteristic
41#22583542C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583535C2211yescharacteristic
47#22583535C2211yescharacteristic
48#22583535C2211yescharacteristic
49#22583532C2211yescharacteristic
50#22583532C2211yescharacteristic
51#22583532C2211yescharacteristic
52C2×M16×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55C4⋊C8×C283C2211yescharacteristic
56C22⋊C8×C283C2211yescharacteristic
57C22⋊C8×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59#17985392—22no—
60#17985392—22no—
61#17985392—41no—
62#17985392—41no—
63C2×Dic566C2311yescharacteristic
64C2×Dic566C2311yescharacteristic
65C2×Dic566C2311yescharacteristic
66C2×D1132C2311yescharacteristic
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C22×Dic283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73Dic1132—41no—
74Dic1132—41no—
75#17985381—22no—
76C4⋊Dic283—21no—
77C4⋊Dic283—21no—
78C4⋊Dic283—21no—
79C4⋊Dic283C2311yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90C22⋊Dic283—21no—
91C22⋊Dic283—21no—
92C22⋊Dic283—21no—
93C22⋊Dic283—21no—
94C22⋊Dic283—21no—
95(C2×D283)⋊C4—21no—
96C4×Dic283—21no—
97C4×Dic283—21no—
98C2×D4×C283D411yescharacteristic
99C22×C4×C283C2311yescharacteristic
100C22×C4×C283C2311yescharacteristic
101M16×C283—41no—
102C2×C8×C283—41no—
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283D411yescharacteristic
108C22⋊C4×C283D411yescharacteristic
109C22⋊C4×C283D411yescharacteristic
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112Dic566—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—21no—
117Dic566—21no—
118D1132—21no—
119D1132#4112yes—
120C22⋊D283—42no—
121C22⋊D283—42no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—42no—
130C4×D283—42no—
131C4×D283—42no—
132C4×D283—42no—
133C23×C283C2×D411yescharacteristic
134C23×C283C2×D411yescharacteristic
135D4×C283—41no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2411yescharacteristic
145C8×C283—21no—
146C8×C283—21no—
147C8×C283—21no—
148C8×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283—21no—
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—21no—
155C22×C283C22×D411yescharacteristic
156C2×D283—22no—
157C2×D283—41no—
158C2×D283—41no—
159C4×C283—21no—
160C4×C283—21no—
161C4×C283—21no—
162C4×C283—21no—
163C4×C283C2×#4111yescharacteristic
164C4×C283H(5,𝔽2)11yescharacteristic
165Dic283—41no—
166Dic283—41no—
167Dic283—41no—
168Dic283—41no—
169Dic283—41no—
170Dic283—41no—
171Dic283—41no—
172C2×C283—41no—
173C2×C283—41no—
174C2×C283#54611yescharacteristic
175C2×C283#57511yescharacteristic
176C2×C283#57811yescharacteristic
177D283—42no—
178C283#331511yescharacteristic, complemented, Sylow
179#3315—2831nomaximal, Sylow
180#552—2831no—
181#547—2831no—
182#491—2831no—
183#485—2831no—
184#484—2831no—
185#478—2831no—
186#470—2831no—
187#467—2831no—
188#462—2831no—
189#452—2831no—
190#452—2831no—
191#440—2831no—
192#435D28311yescharacteristic, complemented
193#417—2831no—
194#416—2831no—
195C2×#41—2831no—
196C2×#41—2831no—
197C2×Q16—2831no—
198C2×Q16—2831no—
199C2×SD16—2831no—
200C2×M16C2×D28311yescharacteristic
201C22×C8C2×D28311yescharacteristic
202C4⋊Q8—2831no—
203#126—5661no—
204#125—2831no—
205#125—5661no—
206#123—5661no—
207#123—5661no—
208#123—5661no—
209C22⋊Q8—2831no—
210C22⋊Q8—2831no—
211C22⋊Q8—2831no—
212C22⋊Q8—2831no—
213#121—5661no—
214C4×Q8—2831no—
215C4×D4—2831no—
216C4×D4C2×D28311yescharacteristic
217#117—2831no—
218#117—5661no—
219C2×C4⋊C4—2831no—
220C2×C4⋊C4—5661no—
221#107—2831no—
222#107—2831no—
223#106—2831no—
224C4⋊C8C2×D28311yescharacteristic
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#103—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235C22⋊C8C2×D28311yescharacteristic
236C22⋊C8C2×D28311yescharacteristic
237#97C2×D28311yescharacteristic
238#41—5662no—
239#41—5662no—
240#41—11321no—
241#41—11321no—
242C2×Q8—2831no—
243C2×Q8—2831no—
244C2×Q8—2831no—
245C2×D4—2831no—
246C2×D4—5661no—
247C2×D4—5661no—
248C2×D4D113211yescharacteristic
249C22×C4—5661no—
250C22×C4—5661no—
251C22×C4—5661no—
252C22×C4—5661no—
253C22×C4C22×D28311yescharacteristic
254C22×C4C22×D28311yescharacteristic
255Q16—11321no—
256Q16—11321no—
257SD16—5662no—
258M16—41no—
259C2×C8—41no—
260C2×C8C22×D28311yescharacteristic
261C2×C8C22×D28311yescharacteristic
262C2×C8C22×D28311yescharacteristic
263C2×C8C22×D28311yescharacteristic
264C4⋊C4—2831no—
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4—5661no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4D113211yescharacteristic
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4D113211yescharacteristic
286C22⋊C4D113211yescharacteristic
287C42—5661no—
288C42—5661no—
289C42C22×D28311yescharacteristic
290C23—5661no—
291C23C2×D113211yescharacteristic
292C23C2×D113211yescharacteristic
293Q8—5661no—
294Q8—5661no—
295Q8—5661no—
296Q8—5661no—
297Q8—5661no—
298Q8—5661no—
299D4—41no—
300D4—2832no—
301D4—5661no—
302D4—11322no—
303D4—11322no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—5661no—
309C2×C4—5661no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—11322no—
316C2×C4—11322no—
317C2×C4—11322no—
318C2×C4—11322no—
319C2×C4C2×D113211yescharacteristic
320C2×C4C2×D113211yescharacteristic
321C2×C4C2×D113211yescharacteristic
322C2×C4C2×D113211yescharacteristic
323C2×C4C23×D28311yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—5662no—
335C22—11321no—
336C22—11321no—
337C22C22×D113211yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—11321no—
343C4—11321no—
344C4—11321no—
345C4—11321no—
346C4—11321no—
347C4—11321no—
348C4—11321no—
349C4#41×D28311yescharacteristic
350C4#2258365511yescharacteristic
351C2—41no—
352C2—41no—
353C2—11322no—
354C2#3182711011yescharacteristic
355C2#3182726511yescharacteristic
356C2#3182728211yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#435×C283C2
socleC22×C283C22×D4
prime radical#31827120C2
hypercenter#435D283
hypocenterC283#3315
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #31827155C2semidirect
3. #31826834C2semidirect
4. #31826807C2semidirect
5. #31826801C2semidirect
6. #31826766C2semidirect
7. #31826723C2semidirect
8. #31826706C2semidirect
9. #31826676C2semidirect
10. #31826629C2semidirect
11. #31826629C2semidirect
12. #31826567C2semidirect
13. #31826467C2semidirect
14. #31826462C2semidirect
15. #435×C283C2semidirect
178. C283#3315semidirect
192. #435D283semidirect

Maximal subgroups

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

subgroupindex
#318271552
#318271202
#318268342
#318268072
#318268012
#318267662
#318267232
#318267062
#318266762
#318266292
#318265672
#318264672
#318264622
#435×C2832
#3315283