Finite Group Databasebeta

← #49133231

Subgroups — #49133231

Order 36224.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827120C211yesmaximal, characteristic, complemented
2#31826835C211yesmaximal, characteristic, complemented
3#31826806C211yesmaximal, characteristic, complemented
4#31826795C211yesmaximal, characteristic, complemented
5#31826762C211yesmaximal, characteristic, complemented
6#31826709C211yesmaximal, characteristic, complemented
7#31826692C211yesmaximal, characteristic, complemented
8#31826670C211yesmaximal, characteristic, complemented
9#31826608C211yesmaximal, characteristic, complemented
10#31826608C211yesmaximal, characteristic, complemented
11#31826575C211yesmaximal, characteristic, complemented
12#31826537C211yesmaximal, characteristic, complemented
13#31826464C211yesmaximal, characteristic, complemented
14#31826459C211yesmaximal, characteristic, complemented
15#553×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985392C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
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#22583541C2211yescharacteristic
33#22583541C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35#22583533C2211yescharacteristic
36#22583533C2211yescharacteristic
37#22583533C2211yescharacteristic
38#22583533C2211yescharacteristic
39#22583533C2211yescharacteristic
40#22583533C2211yescharacteristic
41#22583531C2211yescharacteristic
42#22583530C2211yescharacteristic
43#22583530C2211yescharacteristic
44#22583530C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46C22⋊(C283⋊C8)C2211yescharacteristic
47#22583521C2211yescharacteristic
48#126×C283—21no—
49#125×C283C2211yescharacteristic
50#123×C283—21no—
51#121×C283—21no—
52#121×C283C2211yescharacteristic
53#121×C283C2211yescharacteristic
54C4×D4×C283—21no—
55C4×D4×C283C2211yescharacteristic
56C4×D4×C283C2211yescharacteristic
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#17985380—41no—
72#17985380—41no—
73#17985377—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×D4×C283—21no—
89C2×D4×C283—21no—
90C2×D4×C283D411yescharacteristic
91C2×D4×C283C2311yescharacteristic
92C22×C4×C283—21no—
93C22×C4×C283—21no—
94C22×C4×C283C2311yescharacteristic
95C22×C4×C283C2311yescharacteristic
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×C283—21no—
107C22⋊C4×C283D411yescharacteristic
108C22⋊C4×C283D411yescharacteristic
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×C283—21no—
131C23×C283C2×D411yescharacteristic
132C23×C283C2×D411yescharacteristic
133D4×C283—21no—
134D4×C283—21no—
135D4×C283—41no—
136D4×C283—42no—
137D4×C283—81no—
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—81no—
146C2×C4×C283—81no—
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2×D411yescharacteristic
150C2×C4×C283C2×D411yescharacteristic
151C2×C4×C283C2411yescharacteristic
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—21no—
155C22×C283—21no—
156C22×C283—21no—
157C22×C283—21no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283—41no—
161C22×C283C22×D411yescharacteristic
162C2×D283—22no—
163C2×D283—41no—
164C2×D283—41no—
165C4×C283—21no—
166C4×C283—21no—
167C4×C283—21no—
168C4×C283—21no—
169C4×C283—41no—
170C4×C283—41no—
171C4×C283—41no—
172C4×C283C2×#4111yescharacteristic
173C4×C283H(5,𝔽2)11yescharacteristic
174Dic283—41no—
175Dic283—41no—
176Dic283—41no—
177C2×C283—41no—
178C2×C283—41no—
179C2×C283—81no—
180C2×C283#54611yescharacteristic
181C2×C283#57511yescharacteristic
182C2×C283#57711yescharacteristic
183D283—42no—
184C283#330711yescharacteristic, complemented, Sylow
185#3307—2831nomaximal, Sylow
186#553D28311yescharacteristic, complemented
187#547—2831no—
188#491—2831no—
189#485—2831no—
190#483—2831no—
191#478—2831no—
192#468—2831no—
193#465—2831no—
194#461—2831no—
195#449—2831no—
196#449—2831no—
197#442—2831no—
198#435—2831no—
199#417—2831no—
200#416—2831no—
201C2×#41—2831no—
202C2×#41—2831no—
203C2×SD16—2831no—
204C2×SD16—2831no—
205C2×D8—2831no—
206C2×M16—2831no—
207C22×C8—2831no—
208C4⋊Q8—2831no—
209#126—21no—
210#125C2×D28311yescharacteristic
211#123—21no—
212#123—5661no—
213#123—5661no—
214C22⋊Q8—2831no—
215C22⋊Q8—2831no—
216#121—21no—
217#121—5661no—
218#121C2×D28311yescharacteristic
219#121C2×D28311yescharacteristic
220C4×D4—21no—
221C4×D4—2831no—
222C4×D4C2×D28311yescharacteristic
223C4×D4C2×D28311yescharacteristic
224#117C2×D28311yescharacteristic
225C2×C4⋊C4—5661no—
226C2×C4⋊C4C2×D28311yescharacteristic
227#107—2831no—
228#106—2831no—
229#106—2831no—
230C4⋊C8—2831no—
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#103—2831no—
235#103—2831no—
236#103—2831no—
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102—2831no—
241C22⋊C8—2831no—
242C22⋊C8—2831no—
243#97—2831no—
244#41—5662no—
245#41—5662no—
246#41—11321no—
247#41—11321no—
248C2×Q8—2831no—
249C2×Q8—2831no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—2831no—
253C2×D4—5661no—
254C2×D4—5661no—
255C2×D4C22⋊D28311yescharacteristic
256C2×D4C22×D28311yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—5661no—
260C22×C4—5661no—
261C22×C4—5661no—
262C22×C4C22×D28311yescharacteristic
263C22×C4C22×D28311yescharacteristic
264SD16—11321no—
265SD16—11321no—
266D8—5662no—
267M16—11321no—
268C2×C8—2831no—
269C2×C8—2831no—
270C2×C8—2831no—
271C2×C8—2831no—
272C2×C8—11321no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—2831no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4—5661no—
281C4⋊C4C22⋊D28311yescharacteristic
282C4⋊C4C22×D28311yescharacteristic
283C4⋊C4C22×D28311yescharacteristic
284C4⋊C4C22×D28311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4C22⋊D28311yescharacteristic
293C22⋊C4C22⋊D28311yescharacteristic
294C42—21no—
295C42C22×D28311yescharacteristic
296C23—21no—
297C23—5661no—
298C23C2×C22⋊D28311yescharacteristic
299C23C2×C22⋊D28311yescharacteristic
300Q8—5661no—
301Q8—5661no—
302Q8—5661no—
303Q8—5661no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—42no—
308D4—81no—
309D4—2832no—
310D4—5661no—
311D4—11322no—
312D4—11322no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—5661no—
323C2×C4—5661no—
324C2×C4—5661no—
325C2×C4—11322no—
326C2×C4—11322no—
327C2×C4—11322no—
328C2×C4C2×C22⋊D28311yescharacteristic
329C2×C4C2×C22⋊D28311yescharacteristic
330C2×C4C2×C22⋊D28311yescharacteristic
331C2×C4C2×C22⋊D28311yescharacteristic
332C2×C4C23×D28311yescharacteristic
333C8—5661no—
334C8—5661no—
335C8—5661no—
336C8—5661no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—5662no—
347C22—11321no—
348C22—11321no—
349C22C22×C22⋊D28311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—11321no—
358C4—11321no—
359C4—11321no—
360C4#41×D28311yescharacteristic
361C4#2258365611yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—11322no—
366C2#3182710311yescharacteristic
367C2#3182726311yescharacteristic
368C2#3182727611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#553×C283C2
socleC22×C283C22×D4
hypercenter#553D283
hypocenterC283#3307
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #31827120C2semidirect
2. #31826835C2semidirect
3. #31826806C2semidirect
4. #31826795C2semidirect
5. #31826762C2semidirect
6. #31826709C2semidirect
7. #31826692C2semidirect
8. #31826670C2semidirect
9. #31826608C2semidirect
10. #31826608C2semidirect
11. #31826575C2semidirect
12. #31826537C2semidirect
13. #31826464C2semidirect
14. #31826459C2semidirect
15. #553×C283C2semidirect
184. C283#3307semidirect
186. #553D283semidirect

Maximal subgroups

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

subgroupindex
#318271202
#318268352
#318268062
#318267952
#318267622
#318267092
#318266922
#318266702
#318266082
#318265752
#318265372
#318264642
#318264592
#553×C2832
#3307283