Finite Group Databasebeta

← #49131376

Subgroups — #49131376

Order 36224.

392 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#31827002C211yesmaximal, characteristic, complemented
2C4×#17985393C211yesmaximal, characteristic, complemented
3#31826804C211yesmaximal, characteristic, complemented
4#31826791C211yesmaximal, characteristic, complemented
5#31826770C211yesmaximal, characteristic, complemented
6#31826764C211yesmaximal, characteristic, complemented
7#31826689C211yesmaximal, characteristic, complemented
8#31826683C211yesmaximal, characteristic, complemented
9#31826626C211yesmaximal, characteristic, complemented
10#31826613C211yesmaximal, characteristic
11#31826578C211yesmaximal, characteristic, complemented
12#31826563C211yesmaximal, characteristic, complemented
13#31826563C211yesmaximal, characteristic, complemented
14#31826520C211yesmaximal, characteristic, complemented
15#441×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985379C2211yescharacteristic
18C2×#17985379C2211yescharacteristic
19C2×D2264C2211yescharacteristic
20#22583605—21no—
21#22583601C2211yescharacteristic
22#22583599C2211yescharacteristic
23#22583595—21no—
24#22583586C2211yescharacteristic
25#22583585C2211yescharacteristic
26Q8×Dic283C2211yescharacteristic
27C4×D1132—21no—
28C4×D1132—21no—
29C4×D1132C2211yescharacteristic
30C4×D1132C2211yescharacteristic
31#22583572—21no—
32#22583572C2211yescharacteristic
33#22583568—21no—
34#22583568C2211yescharacteristic
35#22583567—21no—
36C42×D283—21no—
37C42×D283C2211yescharacteristic
38#22583543C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583542C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583534C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583521C2211yescharacteristic
52C2×Q16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59#17985393—22no—
60#17985393—22no—
61C2×D1132—21no—
62C2×D1132—21no—
63C2×D1132C2311yescharacteristic
64C2×D1132C2311yescharacteristic
65C2×C4×D283—21no—
66C2×C4×D283—21no—
67C2×C4×D283—21no—
68C2×C4×D283—21no—
69C2×C4×D283D411yescharacteristic
70C2×C4×D283D411yescharacteristic
71C2×C4×D283C2311yescharacteristic
72#17985379—22no—
73#17985379—22no—
74D2264—22no—
75C2×C283⋊C8C2311yescharacteristic
76C2×C283⋊C8C2311yescharacteristic
77C4⋊Dic283—21no—
78C4⋊Dic283—21no—
79C4⋊Dic283C2311yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83(C2×D283)⋊C4—21no—
84(C2×D283)⋊C4—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283D411yescharacteristic
94C4×Dic283D411yescharacteristic
95C4×Dic283C2311yescharacteristic
96C2×Q8×C283C2311yescharacteristic
97C2×Q8×C283C2311yescharacteristic
98Q16×C283—22no—
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C4⋊C4×C283—21no—
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C42×C283—21no—
106C42×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283—21no—
110C22×D283C2×D411yescharacteristic
111D1132—24no—
112D1132—21no—
113D1132—21no—
114D1132—21no—
115D1132—42no—
116D1132#4112yes—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283C2×D411yescharacteristic
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C4×D283—24no—
123C4×D283—21no—
124C4×D283—21no—
125C4×D283—41no—
126C4×D283—41no—
127C4×D283—42no—
128C4×D283—42no—
129C4×D283—42no—
130C283⋊C8—21no—
131C283⋊C8—21no—
132Q8×C283—21no—
133Q8×C283—21no—
134Q8×C283—21no—
135Q8×C283#4112yes—
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×C283C2411yescharacteristic
143C8×C283—21no—
144C8×C283—21no—
145C22×C283C22×D411yescharacteristic
146C2×D283—21no—
147C2×D283—22no—
148C2×D283—21no—
149C2×D283—21no—
150C2×D283—41no—
151C2×D283—41no—
152C2×D283—41no—
153C2×D283—41no—
154C2×D283—41no—
155C4×C283—22no—
156C4×C283—21no—
157C4×C283—21no—
158C4×C283—41no—
159C4×C283—41no—
160C4×C283—41no—
161C4×C283C2×#4111yescharacteristic
162C4×C283C2×#4111yescharacteristic
163Dic283—21no—
164Dic283—21no—
165Dic283—21no—
166Dic283—41no—
167Dic283—41no—
168C2×C283#52511yescharacteristic
169C2×C283#57511yescharacteristic
170C2×C283#57511yescharacteristic
171D283—41no—
172D283—42no—
173D283—81no—
174C283#311111yescharacteristic, complemented, Sylow
175#3111—2831nomaximal, Sylow
176#529—2831no—
177C4×#41—2831no—
178#485—2831no—
179#482—2831no—
180#479—2831no—
181#478—2831no—
182#464—2831no—
183#463—2831no—
184#452—2831no—
185#449—2831no—
186#442—2831no—
187#441D28311yescharacteristic, complemented
188#440—2831no—
189#440—2831no—
190#432—2831no—
191C2×#41—2831no—
192C2×Q16C2×D28311yescharacteristic
193C2×SD16—2831no—
194C2×SD16—2831no—
195C2×D8—2831no—
196#126—5661no—
197#125—2831no—
198#124—2831no—
199#123—5661no—
200C22⋊Q8—2831no—
201#121—2831no—
202C4×Q8—2831no—
203C4×Q8C2×D28311yescharacteristic
204C4×Q8C2×D28311yescharacteristic
205C4×D4—2831no—
206C4×D4—2831no—
207C4×D4—2831no—
208C4×D4—5661no—
209C4×D4—5661no—
210C4×D4—5661no—
211#117—2831no—
212#117—5661no—
213#117—5661no—
214C2×C42—2831no—
215C2×C42—5661no—
216#107—2831no—
217#107—2831no—
218#106—2831no—
219#106C2×D28311yescharacteristic
220C4⋊C8—2831no—
221C4⋊C8—2831no—
222#103—2831no—
223#103—2831no—
224#103C2×D28311yescharacteristic
225#103C2×D28311yescharacteristic
226#102—2831no—
227#102—2831no—
228#102—2831no—
229#102—2831no—
230C22⋊C8—2831no—
231C22⋊C8—2831no—
232#97—2831no—
233#97C2×D28311yescharacteristic
234#41—5662no—
235#41—5662no—
236C2×Q8C22×D28311yescharacteristic
237C2×Q8C22×D28311yescharacteristic
238C2×D4—2831no—
239C2×D4—2831no—
240C2×D4—5661no—
241C2×D4—5661no—
242C22×C4—2831no—
243C22×C4—2831no—
244C22×C4—2831no—
245C22×C4—5661no—
246C22×C4—5661no—
247C22×C4—5661no—
248C22×C4—5661no—
249Q16—22no—
250SD16—5662no—
251SD16—5662no—
252D8—5662no—
253C2×C8—2831no—
254C2×C8—2831no—
255C2×C8C22×D28311yescharacteristic
256C2×C8C22×D28311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—2831no—
260C4⋊C4—2831no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4C22×D28311yescharacteristic
266C4⋊C4C22×D28311yescharacteristic
267C22⋊C4—5661no—
268C22⋊C4—5661no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C42—21no—
276C42—21no—
277C42—2831no—
278C42—2831no—
279C42—2831no—
280C42—5661no—
281C42—5661no—
282C42C22×D28311yescharacteristic
283C23—2831no—
284C23—5661no—
285C23—5661no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8#1798539212yes—
290D4—2832no—
291D4—5664no—
292D4—5661no—
293D4—5661no—
294D4—5661no—
295D4—11322no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—2831no—
301C2×C4—2831no—
302C2×C4—2831no—
303C2×C4—5664no—
304C2×C4—5661no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—11321no—
309C2×C4—11321no—
310C2×C4—11322no—
311C2×C4—11322no—
312C2×C4—11322no—
313C2×C4D4×D28311yescharacteristic
314C2×C4D4×D28311yescharacteristic
315C2×C4C23×D28311yescharacteristic
316C8—21no—
317C8—21no—
318C8—5661no—
319C8—5661no—
320C22—5662no—
321C22—5661no—
322C22—5661no—
323C22—5661no—
324C22—11321no—
325C22—11321no—
326C22—11321no—
327C22—11321no—
328C22—11321no—
329C22C2×D4×D28311yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—5661no—
337C4—5661no—
338C4—5661no—
339C4—11321no—
340C4—11321no—
341C4#41×D28311yescharacteristic
342C4C2×#1798539211yescharacteristic
343C2—11321no—
344C2—11322no—
345C2—22641no—
346C2#3182697411yescharacteristic
347C2#3182726411yescharacteristic
348C2#3182726411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#441×C283C2
socleC22×C283C22×D4
prime radical#31826613C2
hypercenter#441D283
hypocenterC283#3111
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #31827002C2semidirect
2. C4×#17985393C2semidirect
3. #31826804C2semidirect
4. #31826791C2semidirect
5. #31826770C2semidirect
6. #31826764C2semidirect
7. #31826689C2semidirect
8. #31826683C2semidirect
9. #31826626C2semidirect
11. #31826578C2semidirect
12. #31826563C2semidirect
13. #31826563C2semidirect
14. #31826520C2semidirect
15. #441×C283C2semidirect
174. C283#3111semidirect
187. #441D283semidirect

Maximal subgroups

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

subgroupindex
#318270022
C4×#179853932
#318268042
#318267912
#318267702
#318267642
#318266892
#318266832
#318266262
#318266132
#318265782
#318265632
#318265202
#441×C2832
#3111283