Finite Group Databasebeta

← #49133351

Subgroups — #49133351

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#31827120C211yesmaximal, characteristic
2#31826835C211yesmaximal, characteristic, complemented
3#31826806C211yesmaximal, characteristic, complemented
4#31826800C211yesmaximal, characteristic, complemented
5#31826762C211yesmaximal, characteristic, complemented
6#31826721C211yesmaximal, characteristic, complemented
7#31826704C211yesmaximal, characteristic, complemented
8#31826675C211yesmaximal, characteristic, complemented
9#31826625C211yesmaximal, characteristic, complemented
10#31826625C211yesmaximal, characteristic, complemented
11#31826563C211yesmaximal, characteristic, complemented
12#31826537C211yesmaximal, characteristic, complemented
13#31826464C211yesmaximal, characteristic, complemented
14#31826459C211yesmaximal, characteristic, complemented
15#552×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985392C2211yescharacteristic
18C2×#17985382C2211yescharacteristic
19C2×#17985382C2211yescharacteristic
20C2×#17985379C2211yescharacteristic
21C2×#17985376C2211yescharacteristic
22C22×C283⋊C8C2211yescharacteristic
23#22583610C2211yescharacteristic
24#22583592—21no—
25#22583592—21no—
26#22583589C2211yescharacteristic
27#22583589C2211yescharacteristic
28#22583581—21no—
29C4×D1132C2211yescharacteristic
30C4⋊C4×D283—21no—
31#22583543C2211yescharacteristic
32#22583543C2211yescharacteristic
33#22583541C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35#22583534C2211yescharacteristic
36#22583533C2211yescharacteristic
37#22583533C2211yescharacteristic
38#22583533C2211yescharacteristic
39#22583533C2211yescharacteristic
40#22583533C2211yescharacteristic
41#22583533C2211yescharacteristic
42#22583530C2211yescharacteristic
43#22583530C2211yescharacteristic
44#22583530C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46C22⋊(C283⋊C8)C2211yescharacteristic
47#22583521C2211yescharacteristic
48#126×C283—21no—
49#125×C283—21no—
50#125×C283C2211yescharacteristic
51#123×C283—21no—
52C22⋊Q8×C283C2211yescharacteristic
53C22⋊Q8×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55C4×D4×C283C2211yescharacteristic
56#117×C283—21no—
57#117×C283C2211yescharacteristic
58C2×C4⋊C4×C283C2211yescharacteristic
59#17985392—22no—
60#17985392—22no—
61#17985392—41no—
62#17985392—41no—
63C2×Dic566C2311yescharacteristic
64C2×Dic566C2311yescharacteristic
65C2×D1132C2311yescharacteristic
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C4×D283—21no—
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71#17985382—41no—
72#17985382—41no—
73#17985379—22no—
74#17985376—41no—
75C2×C283⋊C8—41no—
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C4⋊Dic283—21no—
81C4⋊Dic283—21no—
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87(C2×D283)⋊C4—21no—
88C2×Q8×C283C2311yescharacteristic
89C2×D4×C283D411yescharacteristic
90C22×C4×C283—21no—
91C22×C4×C283C2311yescharacteristic
92C22×C4×C283C2311yescharacteristic
93C4⋊C4×C283—21no—
94C4⋊C4×C283—21no—
95C4⋊C4×C283—21no—
96C4⋊C4×C283—21no—
97C4⋊C4×C283—21no—
98C4⋊C4×C283—21no—
99C4⋊C4×C283D411yescharacteristic
100C4⋊C4×C283C2311yescharacteristic
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C22⋊C4×C283—21no—
104C22⋊C4×C283—21no—
105C22⋊C4×C283—21no—
106C22⋊C4×C283D411yescharacteristic
107C22⋊C4×C283D411yescharacteristic
108C42×C283—21no—
109C42×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112Dic566—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116D1132—21no—
117D1132#4112yes—
118C22⋊D283—42no—
119C22⋊D283—42no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C4×D283—42no—
124C4×D283—42no—
125C4×D283—42no—
126C283⋊C8—21no—
127C283⋊C8—21no—
128C283⋊C8—21no—
129C283⋊C8—21no—
130C23×C283C2×D411yescharacteristic
131C23×C283C2×D411yescharacteristic
132Q8×C283—21no—
133Q8×C283—21no—
134D4×C283—41no—
135C2×C4×C283—21no—
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—42no—
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2411yescharacteristic
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×C283—41no—
164C4×C283—41no—
165C4×C283—41no—
166C4×C283—41no—
167C4×C283C2×#4111yescharacteristic
168C4×C283H(5,𝔽2)11yescharacteristic
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#552D28311yescharacteristic, complemented
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#435—2831no—
193#417—2831no—
194#416—2831no—
195C2×#41—2831no—
196C2×#41—2831no—
197C2×Q16—2831no—
198C2×Q16—2831no—
199C2×SD16—2831no—
200C2×M16—2831no—
201C22×C8—2831no—
202C4⋊Q8—2831no—
203#126—21no—
204#125—21no—
205#125C2×D28311yescharacteristic
206#123—21no—
207#123—5661no—
208#123—5661no—
209C22⋊Q8—2831no—
210C22⋊Q8—2831no—
211C22⋊Q8C2×D28311yescharacteristic
212C22⋊Q8C2×D28311yescharacteristic
213#121—5661no—
214C4×Q8C2×D28311yescharacteristic
215C4×D4—2831no—
216C4×D4C2×D28311yescharacteristic
217#117—21no—
218#117C2×D28311yescharacteristic
219C2×C4⋊C4—5661no—
220C2×C4⋊C4C2×D28311yescharacteristic
221#107—2831no—
222#107—2831no—
223#106—2831no—
224C4⋊C8—2831no—
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⋊C8—2831no—
236C22⋊C8—2831no—
237#97—2831no—
238#41—5662no—
239#41—5662no—
240#41—11321no—
241#41—11321no—
242C2×Q8—2831no—
243C2×Q8—2831no—
244C2×Q8C22×D28311yescharacteristic
245C2×D4—2831no—
246C2×D4—5661no—
247C2×D4—5661no—
248C2×D4C22⋊D28311yescharacteristic
249C22×C4—21no—
250C22×C4—5661no—
251C22×C4—5661no—
252C22×C4—5661no—
253C22×C4C22×D28311yescharacteristic
254C22×C4C22×D28311yescharacteristic
255Q16—11321no—
256Q16—11321no—
257SD16—5662no—
258M16—11321no—
259C2×C8—2831no—
260C2×C8—2831no—
261C2×C8—2831no—
262C2×C8—2831no—
263C2×C8—11321no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—2831no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4C22⋊D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C4⋊C4C22×D28311yescharacteristic
278C4⋊C4C22×D28311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4C22⋊D28311yescharacteristic
286C22⋊C4C22⋊D28311yescharacteristic
287C42—21no—
288C42—21no—
289C42C22×D28311yescharacteristic
290C23—5661no—
291C23C2×C22⋊D28311yescharacteristic
292C23C2×C22⋊D28311yescharacteristic
293Q8—21no—
294Q8—21no—
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—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—11322no—
317C2×C4—11322no—
318C2×C4—11322no—
319C2×C4C2×C22⋊D28311yescharacteristic
320C2×C4C2×C22⋊D28311yescharacteristic
321C2×C4C2×C22⋊D28311yescharacteristic
322C2×C4C2×C22⋊D28311yescharacteristic
323C2×C4C23×D28311yescharacteristic
324C8—5661no—
325C8—5661no—
326C8—5661no—
327C8—5661no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—5662no—
335C22—11321no—
336C22—11321no—
337C22C22×C22⋊D28311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—11321no—
347C4—11321no—
348C4—11321no—
349C4#41×D28311yescharacteristic
350C4#2258365611yescharacteristic
351C2—41no—
352C2—41no—
353C2—11322no—
354C2#3182710311yescharacteristic
355C2#3182726311yescharacteristic
356C2#3182728011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#552×C283C2
socleC22×C283C22×D4
prime radical#31827120C2
hypercenter#552D283
hypocenterC283#3315
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #31826835C2semidirect
3. #31826806C2semidirect
4. #31826800C2semidirect
5. #31826762C2semidirect
6. #31826721C2semidirect
7. #31826704C2semidirect
8. #31826675C2semidirect
9. #31826625C2semidirect
10. #31826625C2semidirect
11. #31826563C2semidirect
12. #31826537C2semidirect
13. #31826464C2semidirect
14. #31826459C2semidirect
15. #552×C283C2semidirect
178. C283#3315semidirect
180. #552D283semidirect

Maximal subgroups

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

subgroupindex
#318271202
#318268352
#318268062
#318268002
#318267622
#318267212
#318267042
#318266752
#318266252
#318265632
#318265372
#318264642
#318264592
#552×C2832
#3315283