Finite Group Databasebeta

← #49131548

Subgroups — #49131548

Order 36224.

382 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827068C211yesmaximal, characteristic
2#31826942C211yesmaximal, characteristic, complemented
3#31826789C211yesmaximal, characteristic, complemented
4#31826775C211yesmaximal, characteristic, complemented
5#31826771C211yesmaximal, characteristic, complemented
6#31826664C211yesmaximal, characteristic, complemented
7#31826664C211yesmaximal, characteristic, complemented
8#31826606C211yesmaximal, characteristic, complemented
9#31826603C211yesmaximal, characteristic, complemented
10#31826564C211yesmaximal, characteristic, complemented
11#31826562C211yesmaximal, characteristic, complemented
12#31826556C211yesmaximal, characteristic, complemented
13#31826552C211yesmaximal, characteristic, complemented
14#31826523C211yesmaximal, characteristic, complemented
15#482×C283C211yesmaximal, characteristic, complemented
16C22×Dic566C2211yescharacteristic
17C2×#17985381C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×#17985380C2211yescharacteristic
21#22583606C2211yescharacteristic
22#22583601C2211yescharacteristic
23#22583594—21no—
24#22583592—21no—
25#22583584C2211yescharacteristic
26#22583582—21no—
27#22583581—21no—
28C4×Dic566—21no—
29C4×Dic566—21no—
30#22583575C2211yescharacteristic
31#22583575C2211yescharacteristic
32#22583575C2211yescharacteristic
33#22583575C2211yescharacteristic
34D4×Dic283C2211yescharacteristic
35#22583572C2211yescharacteristic
36#22583569C2211yescharacteristic
37#22583566—21no—
38#22583566—21no—
39#22583543C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50#22583520C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52#121×C283C2211yescharacteristic
53#117×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59C2×Dic566—22no—
60C2×Dic566—22no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63C2×Dic566C2311yescharacteristic
64C2×D1132C2311yescharacteristic
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C22×Dic283—21no—
69C22×Dic283—21no—
70C2×C4×D283—21no—
71#17985381—22no—
72#17985381—22no—
73#17985380—22no—
74#17985380—22no—
75C2×C283⋊C8C2311yescharacteristic
76C2×C283⋊C8C2311yescharacteristic
77C4⋊Dic283—21no—
78C4⋊Dic283D411yescharacteristic
79C4⋊Dic283D411yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283D411yescharacteristic
88C22⋊Dic283D411yescharacteristic
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96C4×Dic283C2311yescharacteristic
97C2×D4×C283—21no—
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C42×C283—21no—
108C22×D283—21no—
109Dic566—24no—
110Dic566—21no—
111Dic566—21no—
112Dic566#4112yes—
113Dic566#4112yes—
114D1132—21no—
115D1132—21no—
116C22⋊D283—81no—
117C22⋊D283—81no—
118C22⋊D283—81no—
119C2×Dic283—24no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—81no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C4×D283—81no—
129C283⋊C8—21no—
130C283⋊C8—21no—
131C23×C283—21no—
132C23×C283C2×D411yescharacteristic
133D4×C283—21no—
134D4×C283—21no—
135D4×C283—81no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2411yescharacteristic
143C8×C283—21no—
144C8×C283—21no—
145C22×C283—21no—
146C22×C283—21no—
147C22×C283—21no—
148C22×C283—41no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283C22×D411yescharacteristic
152C2×D283—41no—
153C2×D283—41no—
154C2×D283—41no—
155C4×C283—21no—
156C4×C283—41no—
157C4×C283—41no—
158C4×C283—41no—
159C4×C283C2×#4111yescharacteristic
160C4×C283C2×#4111yescharacteristic
161Dic283—22no—
162Dic283—22no—
163Dic283—21no—
164Dic283—21no—
165Dic283—21no—
166Dic283—21no—
167Dic283—41no—
168C2×C283—41no—
169C2×C283—81no—
170C2×C283#52511yescharacteristic
171C2×C283#57711yescharacteristic
172C2×C283#57711yescharacteristic
173D283—81no—
174C283#312611yescharacteristic, complemented, Sylow
175#3126—2831nomaximal, Sylow
176#540—2831no—
177#519—2831no—
178#482—2831no—
179#482D28311yescharacteristic, complemented
180#479—2831no—
181#479—2831no—
182#460—2831no—
183#460—2831no—
184#448—2831no—
185#448—2831no—
186#440—2831no—
187#440—2831no—
188C4×SD16—2831no—
189C4×SD16—2831no—
190#433—2831no—
191C22×Q8—2831no—
192C2×SD16—2831no—
193C2×SD16—2831no—
194C2×SD16—2831no—
195C2×SD16—2831no—
196#127—2831no—
197#125—2831no—
198#123—5661no—
199#123—5661no—
200#121—2831no—
201#121—5661no—
202#121—5661no—
203#121C2×D28311yescharacteristic
204C4×Q8—2831no—
205C4×Q8—2831no—
206C4×Q8—2831no—
207C4×Q8—2831no—
208C4×Q8—5661no—
209C4×Q8—5661no—
210C4×D4—2831no—
211C4×D4—2831no—
212#117—2831no—
213#117—5661no—
214#117—5661no—
215#117C2×D28311yescharacteristic
216#107—2831no—
217#107C2×D28311yescharacteristic
218#106—2831no—
219#106C2×D28311yescharacteristic
220C4⋊C8—2831no—
221C4⋊C8—2831no—
222#103—2831no—
223#103—2831no—
224#103—2831no—
225#103—2831no—
226#102—2831no—
227#102—2831no—
228#102C2×D28311yescharacteristic
229#102C2×D28311yescharacteristic
230C22⋊C8—2831no—
231C22⋊C8C2×D28311yescharacteristic
232#97—2831no—
233C4×C8—2831no—
234C2×Q8—2831no—
235C2×Q8—2831no—
236C2×Q8—5662no—
237C2×Q8—5662no—
238C2×Q8—5661no—
239C2×D4—21no—
240C2×D4—2831no—
241C2×D4—5661no—
242C2×D4—5661no—
243C2×D4—5661no—
244C2×D4C22×D28311yescharacteristic
245C22×C4—5661no—
246C22×C4—5661no—
247C22×C4—5661no—
248C22×C4C22×D28311yescharacteristic
249SD16—5662no—
250SD16—5662no—
251SD16—5662no—
252SD16—5662no—
253C2×C8—2831no—
254C2×C8—2831no—
255C2×C8C22×D28311yescharacteristic
256C2×C8C22×D28311yescharacteristic
257C4⋊C4—2831no—
258C4⋊C4—2831no—
259C4⋊C4—2831no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4C22×D28311yescharacteristic
267C4⋊C4C22×D28311yescharacteristic
268C4⋊C4C22×D28311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—2831no—
272C22⋊C4—2831no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C42—21no—
277C42—2831no—
278C42—2831no—
279C42—5661no—
280C42—5661no—
281C42—5661no—
282C42—5661no—
283C23—21no—
284C23—5661no—
285C23D4×D28311yescharacteristic
286Q8—2832no—
287Q8—2832no—
288Q8—5664no—
289Q8—5661no—
290Q8—5661no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—5661no—
295D4—5661no—
296D4—22641no—
297D4—22641no—
298D4—22641no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—2831no—
305C2×C4—2831no—
306C2×C4—2831no—
307C2×C4—2831no—
308C2×C4—5664no—
309C2×C4—5661no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—22641no—
313C2×C4—22641no—
314C2×C4D4×D28311yescharacteristic
315C2×C4C23×D28311yescharacteristic
316C8—21no—
317C8—21no—
318C8—5661no—
319C8—5661no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—11321no—
327C22—11321no—
328C22—11321no—
329C22C2×D4×D28311yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—5662no—
335C4—5662no—
336C4—5661no—
337C4—5661no—
338C4—5661no—
339C4—5661no—
340C4—11321no—
341C4#41×D28311yescharacteristic
342C4#41×D28311yescharacteristic
343C2—41no—
344C2—81no—
345C2—22641no—
346C2#3182697311yescharacteristic
347C2#3182727211yescharacteristic
348C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#482×C283C2
socleC22×C283C22×D4
prime radical#31827068C2
hypercenter#482D283
hypocenterC283#3126
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #31826942C2semidirect
3. #31826789C2semidirect
4. #31826775C2semidirect
5. #31826771C2semidirect
6. #31826664C2semidirect
7. #31826664C2semidirect
8. #31826606C2semidirect
9. #31826603C2semidirect
10. #31826564C2semidirect
11. #31826562C2semidirect
12. #31826556C2semidirect
13. #31826552C2semidirect
14. #31826523C2semidirect
15. #482×C283C2semidirect
174. C283#3126semidirect
179. #482D283semidirect

Maximal subgroups

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

subgroupindex
#318270682
#318269422
#318267892
#318267752
#318267712
#318266642
#318266062
#318266032
#318265642
#318265622
#318265562
#318265522
#318265232
#482×C2832
#3126283