Finite Group Databasebeta

← #49131275

Subgroups — #49131275

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
1#31826997C211yesmaximal, characteristic, complemented
2C4×#17985391C211yesmaximal, characteristic, complemented
3#31826808C211yesmaximal, characteristic, complemented
4#31826787C211yesmaximal, characteristic, complemented
5#31826771C211yesmaximal, characteristic, complemented
6#31826763C211yesmaximal, characteristic, complemented
7#31826686C211yesmaximal, characteristic, complemented
8#31826678C211yesmaximal, characteristic, complemented
9#31826628C211yesmaximal, characteristic, complemented
10#31826607C211yesmaximal, characteristic
11C4×Dic1132C211yesmaximal, characteristic, complemented
12C4×#17985380C211yesmaximal, characteristic, complemented
13C4×#17985380C211yesmaximal, characteristic, complemented
14#31826516C211yesmaximal, characteristic, complemented
15C4×D8×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×Dic1132C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20#22583603—21no—
21#22583601C2211yescharacteristic
22#22583597C2211yescharacteristic
23#22583592—21no—
24#22583590C2211yescharacteristic
25#22583581C2211yescharacteristic
26C4×Dic566C2211yescharacteristic
27C4×Dic566C2211yescharacteristic
28#22583575C2211yescharacteristic
29D4×Dic283C2211yescharacteristic
30C4×C22⋊D283—21no—
31C4×C22⋊D283—21no—
32(C22⋊D283)⋊C4—21no—
33#22583569—21no—
34#22583568C2211yescharacteristic
35#22583566—21no—
36C2×C4×Dic283—21no—
37C42×D283C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583541C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583531C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C4×C283⋊C8C2211yescharacteristic
52C2×D8×C283C2211yescharacteristic
53C4×D4×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59#17985391—22no—
60#17985391—22no—
61C2×Dic566C2311yescharacteristic
62C2×Dic566C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C22×Dic283—21no—
66C22×Dic283—21no—
67C2×C4×D283D411yescharacteristic
68C2×C4×D283D411yescharacteristic
69C2×C4×D283C2311yescharacteristic
70Dic1132—22no—
71#17985380—22no—
72#17985380—22no—
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C4⋊Dic283—21no—
76C4⋊Dic283—21no—
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283D411yescharacteristic
94C4×Dic283D411yescharacteristic
95C4×Dic283C2311yescharacteristic
96C2×D4×C283C2311yescharacteristic
97C2×D4×C283C2311yescharacteristic
98C22×C4×C283—21no—
99C22×C4×C283—21no—
100D8×C283—22no—
101C2×C8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283C2×D411yescharacteristic
109Dic566—21no—
110Dic566—21no—
111Dic566—21no—
112Dic566#4112yes—
113C22⋊D283—24no—
114C22⋊D283—42no—
115C2×Dic283—24no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—42no—
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C4×D283—22no—
125C4×D283—21no—
126C4×D283—21no—
127C4×D283—41no—
128C283⋊C8—21no—
129C283⋊C8—21no—
130C23×C283—21no—
131C23×C283—21no—
132D4×C283—21no—
133D4×C283—21no—
134D4×C283—21no—
135D4×C283#4112yes—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—42no—
139C2×C4×C283—42no—
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2411yescharacteristic
143C8×C283—21no—
144C8×C283—21no—
145C22×C283—22no—
146C22×C283—41no—
147C22×C283—41no—
148C22×C283—41no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283C22×D411yescharacteristic
152C2×D283—21no—
153C2×D283—21no—
154C2×D283—21no—
155C4×C283—21no—
156C4×C283—41no—
157C4×C283—41no—
158C4×C283#13512yes—
159C4×C283C2×#4111yescharacteristic
160C4×C283C2×#4111yescharacteristic
161Dic283—21no—
162Dic283—22no—
163Dic283—21no—
164Dic283—21no—
165Dic283—41no—
166Dic283—41no—
167Dic283—41no—
168C2×C283—42no—
169C2×C283—81no—
170C2×C283#52511yescharacteristic
171C2×C283C2×#13511yescharacteristic
172C2×C283#57511yescharacteristic
173D283—41no—
174C283#310211yescharacteristic, complemented, Sylow
175#3102—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—
186C4×Q16—2831no—
187C4×SD16—2831no—
188C4×SD16—2831no—
189C4×D8D28311yescharacteristic, complemented
190#431—2831no—
191C2×#41—2831no—
192C2×Q16—2831no—
193C2×SD16—2831no—
194C2×SD16—2831no—
195C2×D8C2×D28311yescharacteristic
196#126—5661no—
197#125—2831no—
198#124—2831no—
199#123—5661no—
200C22⋊Q8—2831no—
201#121—2831no—
202C4×Q8—2831no—
203C4×Q8—2831no—
204C4×Q8—2831no—
205C4×D4—2831no—
206C4×D4—5661no—
207C4×D4—5661no—
208C4×D4—5661no—
209C4×D4C2×D28311yescharacteristic
210C4×D4C2×D28311yescharacteristic
211#117—2831no—
212#117—5661no—
213#117—5661no—
214C2×C42—2831no—
215C2×C42—5661no—
216#107—2831no—
217#107C2×D28311yescharacteristic
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#102C2×D28311yescharacteristic
229#102C2×D28311yescharacteristic
230C22⋊C8—2831no—
231C22⋊C8—2831no—
232C4×C8—2831no—
233C4×C8C2×D28311yescharacteristic
234#41—5662no—
235#41—5662no—
236C2×Q8—2831no—
237C2×Q8—2831no—
238C2×D4—5661no—
239C2×D4—5661no—
240C2×D4C22×D28311yescharacteristic
241C2×D4C22×D28311yescharacteristic
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—2831no—
245C22×C4—2831no—
246C22×C4—2831no—
247C22×C4—5661no—
248C22×C4—5661no—
249Q16—5662no—
250SD16—5662no—
251SD16—5662no—
252D8—22no—
253C2×C8—2831no—
254C2×C8—2831no—
255C2×C8C22×D28311yescharacteristic
256C2×C8C22×D28311yescharacteristic
257C4⋊C4—2831no—
258C4⋊C4—2831no—
259C4⋊C4—5661no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4C22×D28311yescharacteristic
266C4⋊C4C22×D28311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C42—2831no—
276C42—2831no—
277C42—2831no—
278C42—5661no—
279C42—5661no—
280C42—5661no—
281C42—5661no—
282C42C22×D28311yescharacteristic
283C23—21no—
284C23—21no—
285C23—2831no—
286Q8—2832no—
287Q8—5661no—
288Q8—5661no—
289Q8—5661no—
290D4—21no—
291D4—21no—
292D4—21no—
293D4—5664no—
294D4—11322no—
295D4#1798539212yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—2831no—
301C2×C4—2831no—
302C2×C4—2831no—
303C2×C4—5664no—
304C2×C4—5661no—
305C2×C4—5662no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—5661no—
309C2×C4—5661no—
310C2×C4—5661no—
311C2×C4—11321no—
312C2×C4—11322no—
313C2×C4D4×D28311yescharacteristic
314C2×C4D4×D28311yescharacteristic
315C2×C4C23×D28311yescharacteristic
316C8—21no—
317C8—21no—
318C8—5661no—
319C8—5661no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—5661no—
327C22—5661no—
328C22—5661no—
329C22C2×D4×D28311yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—5661no—
334C4—5662no—
335C4—5661no—
336C4—5661no—
337C4—11321no—
338C4—11321no—
339C4—11321no—
340C4#2258362912yes—
341C4#41×D28311yescharacteristic
342C4C2×#1798539211yescharacteristic
343C2—42no—
344C2—81no—
345C2—11321no—
346C2#3182697411yescharacteristic
347C2C2×#2258362911yescharacteristic
348C2#3182726211yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC4×D8×C283C2
socleC22×C283C22×D4
prime radical#31826607C2
hypercenterC4×D8D283
hypocenterC283#3102
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #31826997C2semidirect
2. C4×#17985391C2semidirect
3. #31826808C2semidirect
4. #31826787C2semidirect
5. #31826771C2semidirect
6. #31826763C2semidirect
7. #31826686C2semidirect
8. #31826678C2semidirect
9. #31826628C2semidirect
11. C4×Dic1132C2semidirect
12. C4×#17985380C2semidirect
13. C4×#17985380C2semidirect
14. #31826516C2semidirect
15. C4×D8×C283C2semidirect
174. C283#3102semidirect
189. C4×D8D283semidirect

Maximal subgroups

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

subgroupindex
#318269972
C4×#179853912
#318268082
#318267872
#318267712
#318267632
#318266862
#318266782
#318266282
#318266072
C4×Dic11322
C4×#179853802
#318265162
C4×D8×C2832
#3102283