Finite Group Databasebeta

← #49131273

Subgroups — #49131273

Order 36224.

396 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
1C4×#17985392C211yesmaximal, characteristic, complemented
2#31826803C211yesmaximal, characteristic, complemented
3#31826786C211yesmaximal, characteristic, complemented
4#31826769C211yesmaximal, characteristic, complemented
5#31826762C211yesmaximal, characteristic, complemented
6#31826684C211yesmaximal, characteristic, complemented
7#31826677C211yesmaximal, characteristic, complemented
8#31826625C211yesmaximal, characteristic, complemented
9#31826608C211yesmaximal, characteristic
10C4×#17985382C211yesmaximal, characteristic, complemented
11C4×#17985379C211yesmaximal, characteristic, complemented
12C4×#17985380C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14#31826518C211yesmaximal, characteristic, complemented
15#529×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21C4×Dic566C2211yescharacteristic
22C4×Dic566C2211yescharacteristic
23C4×D1132C2211yescharacteristic
24C4×D1132C2211yescharacteristic
25C4×C22⋊D283—21no—
26C4×C22⋊D283—21no—
27#22583569C2211yescharacteristic
28#22583567—21no—
29C42×D283—21no—
30#22583543C2211yescharacteristic
31#22583543C2211yescharacteristic
32#22583541C2211yescharacteristic
33#22583541C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35C4⋊(C283⋊C8)C2211yescharacteristic
36#22583534C2211yescharacteristic
37#22583534C2211yescharacteristic
38#22583533C2211yescharacteristic
39#22583533C2211yescharacteristic
40#22583531C2211yescharacteristic
41#22583531C2211yescharacteristic
42#22583530C2211yescharacteristic
43#22583530C2211yescharacteristic
44C22⋊(C283⋊C8)C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46C4×C283⋊C8C2211yescharacteristic
47C4×C283⋊C8C2211yescharacteristic
48#126×C283—21no—
49#125×C283C2211yescharacteristic
50#124×C283C2211yescharacteristic
51#123×C283—21no—
52C22⋊Q8×C283C2211yescharacteristic
53#121×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55C4×D4×C283—21no—
56C4×D4×C283C2211yescharacteristic
57#117×C283—21no—
58C2×C42×C283C2211yescharacteristic
59#17985392—22no—
60#17985392—22no—
61C2×Dic566C2311yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C4×D283—21no—
65C2×C4×D283—21no—
66C2×C4×D283—21no—
67#17985382—22no—
68#17985380—22no—
69#17985379—22no—
70#17985377—22no—
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79C22⋊Dic283—21no—
80(C2×D283)⋊C4—21no—
81(C2×D283)⋊C4—21no—
82C4×Dic283—21no—
83C4×Dic283—21no—
84C4×Dic283—21no—
85C2×Q8×C283C2311yescharacteristic
86C2×D4×C283—21no—
87C2×D4×C283C2311yescharacteristic
88C22×C4×C283—21no—
89C22×C4×C283D411yescharacteristic
90C22×C4×C283D411yescharacteristic
91C22×C4×C283C2311yescharacteristic
92C4⋊C4×C283—21no—
93C4⋊C4×C283—21no—
94C4⋊C4×C283—21no—
95C4⋊C4×C283—21no—
96C4⋊C4×C283C2311yescharacteristic
97C4⋊C4×C283C2311yescharacteristic
98C22⋊C4×C283—21no—
99C22⋊C4×C283—21no—
100C22⋊C4×C283—21no—
101C22⋊C4×C283—21no—
102C22⋊C4×C283—21no—
103C42×C283—21no—
104C42×C283D411yescharacteristic
105C42×C283D411yescharacteristic
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109Dic566—21no—
110Dic566#4112yes—
111D1132—21no—
112D1132#4112yes—
113C22⋊D283—24no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C4×D283—24no—
118C4×D283—42no—
119C4×D283—42no—
120C283⋊C8—21no—
121C283⋊C8—21no—
122C283⋊C8—21no—
123C283⋊C8—21no—
124C23×C283—21no—
125C23×C283C2×D411yescharacteristic
126Q8×C283—21no—
127Q8×C283—21no—
128D4×C283—21no—
129D4×C283—21no—
130D4×C283—42no—
131C2×C4×C283—22no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—41no—
138C2×C4×C283—42no—
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2411yescharacteristic
145C22×C283—21no—
146C22×C283—21no—
147C22×C283—21no—
148C22×C283—41no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283C22×D411yescharacteristic
152C2×D283—22no—
153C2×D283—41no—
154C2×D283—41no—
155C4×C283—21no—
156C4×C283—21no—
157C4×C283—21no—
158C4×C283—21no—
159C4×C283—41no—
160C4×C283—41no—
161C4×C283—41no—
162C4×C283#13512yes—
163C4×C283C2×#4111yescharacteristic
164C4×C283C2×#4111yescharacteristic
165Dic283—22no—
166Dic283—41no—
167Dic283—41no—
168C2×C283—41no—
169C2×C283—81no—
170C2×C283#52511yescharacteristic
171C2×C283C2×#13511yescharacteristic
172C2×C283#57511yescharacteristic
173D283—42no—
174C283#310211yescharacteristic, complemented, Sylow
175#3102—2831nomaximal, Sylow
176#529D28311yescharacteristic, complemented
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—
186C4×Q16—2831no—
187C4×SD16—2831no—
188C4×SD16—2831no—
189C4×D8—2831no—
190#431—2831no—
191C2×#41—2831no—
192C2×Q16—2831no—
193C2×SD16—2831no—
194C2×SD16—2831no—
195C2×D8—2831no—
196#126—21no—
197#125C2×D28311yescharacteristic
198#124C2×D28311yescharacteristic
199#123—21no—
200C22⋊Q8C2×D28311yescharacteristic
201#121C2×D28311yescharacteristic
202C4×Q8—2831no—
203C4×Q8—2831no—
204C4×Q8C2×D28311yescharacteristic
205C4×D4—21no—
206C4×D4—2831no—
207C4×D4—2831no—
208C4×D4—5661no—
209C4×D4—5661no—
210C4×D4C2×D28311yescharacteristic
211#117—21no—
212#117—2831no—
213#117—5661no—
214C2×C42—5661no—
215C2×C42C2×D28311yescharacteristic
216#107—2831no—
217#107—2831no—
218#106—2831no—
219#106—2831no—
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#102—2831no—
229#102—2831no—
230C22⋊C8—2831no—
231C22⋊C8—2831no—
232C4×C8—2831no—
233C4×C8—2831no—
234#41—5662no—
235#41—5662no—
236C2×Q8—2831no—
237C2×Q8C22×D28311yescharacteristic
238C2×D4—21no—
239C2×D4—2831no—
240C2×D4—5661no—
241C2×D4C22×D28311yescharacteristic
242C22×C4—21no—
243C22×C4—5661no—
244C22×C4—5661no—
245C22×C4—5661no—
246C22×C4C22⋊D28311yescharacteristic
247C22×C4C22⋊D28311yescharacteristic
248C22×C4C22×D28311yescharacteristic
249Q16—5662no—
250SD16—5662no—
251SD16—5662no—
252D8—5662no—
253C2×C8—2831no—
254C2×C8—2831no—
255C2×C8—2831no—
256C2×C8—2831no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—2831no—
262C4⋊C4—2831no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4C22×D28311yescharacteristic
266C4⋊C4C22×D28311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C42—21no—
276C42—5661no—
277C42—5661no—
278C42—5661no—
279C42C22⋊D28311yescharacteristic
280C42C22⋊D28311yescharacteristic
281C42C22×D28311yescharacteristic
282C42C22×D28311yescharacteristic
283C23—21no—
284C23—5661no—
285C23C2×C22⋊D28311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—2832no—
289Q8—5661no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—2832no—
294D4—5664no—
295D4—5661no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—5664no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—11322no—
309C2×C4—11322no—
310C2×C4C2×C22⋊D28311yescharacteristic
311C2×C4C2×C22⋊D28311yescharacteristic
312C2×C4C2×C22⋊D28311yescharacteristic
313C2×C4C2×C22⋊D28311yescharacteristic
314C2×C4C2×C22⋊D28311yescharacteristic
315C2×C4C23×D28311yescharacteristic
316C8—5661no—
317C8—5661no—
318C8—5661no—
319C8—5661no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—5662no—
327C22—11321no—
328C22—11321no—
329C22C22×C22⋊D28311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—5662no—
338C4—11321no—
339C4—11321no—
340C4#2258363012yes—
341C4#41×D28311yescharacteristic
342C4#41×D28311yescharacteristic
343C2—41no—
344C2—81no—
345C2—11322no—
346C2#3182697211yescharacteristic
347C2C2×#2258363011yescharacteristic
348C2#3182726311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#529×C283C2
socleC22×C283C22×D4
prime radical#31826608C2
hypercenter#529D283
hypocenterC283#3102
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×#17985392C2semidirect
2. #31826803C2semidirect
3. #31826786C2semidirect
4. #31826769C2semidirect
5. #31826762C2semidirect
6. #31826684C2semidirect
7. #31826677C2semidirect
8. #31826625C2semidirect
10. C4×#17985382C2semidirect
11. C4×#17985379C2semidirect
12. C4×#17985380C2semidirect
13. C4×#17985377C2semidirect
14. #31826518C2semidirect
15. #529×C283C2semidirect
174. C283#3102semidirect
176. #529D283semidirect

Maximal subgroups

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

subgroupindex
C4×#179853922
#318268032
#318267862
#318267692
#318267622
#318266842
#318266772
#318266252
#318266082
C4×#179853822
C4×#179853792
C4×#179853802
C4×#179853772
#318265182
#529×C2832
#3102283