Finite Group Databasebeta

← #49133305

Subgroups — #49133305

Order 36224.

376 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#31827149C211yesmaximal, characteristic
2Q8×C22⋊D283C211yesmaximal, characteristic
3#31826832C211yesmaximal, characteristic, complemented
4#31826807C211yesmaximal, characteristic, complemented
5#31826794C211yesmaximal, characteristic, complemented
6#31826774C211yesmaximal, characteristic, complemented
7#31826721C211yesmaximal, characteristic, complemented
8#31826703C211yesmaximal, characteristic, complemented
9#31826673C211yesmaximal, characteristic, complemented
10#31826619C211yesmaximal, characteristic, complemented
11#31826572C211yesmaximal, characteristic, complemented
12#31826539C211yesmaximal, characteristic
13#31826474C211yesmaximal, characteristic, complemented
14#103×D283C211yesmaximal, characteristic, complemented
15#451×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985376C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20#22583608—21no—
21#22583608C2211yescharacteristic
22#22583603—21no—
23#22583601C2211yescharacteristic
24#22583600—21no—
25#22583592—21no—
26#22583589—21no—
27#22583589C2211yescharacteristic
28#22583586—21no—
29#22583586C2211yescharacteristic
30#22583586C2211yescharacteristic
31Q8×Dic283C2211yescharacteristic
32Q8×Dic283C2211yescharacteristic
33C4×C22⋊D283—21no—
34C4×C22⋊D283C2211yescharacteristic
35#22583569C2211yescharacteristic
36#22583568—21no—
37C4⋊C4×D283C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583542C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583534C2211yescharacteristic
48#22583534C2211yescharacteristic
49#22583533C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic
52C22×Q8×C283C2211yescharacteristic
53C2×Q16×C283C2211yescharacteristic
54C2×Q16×C283C2211yescharacteristic
55C22⋊Q8×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61Q8×D283—22no—
62Q8×D283—41no—
63C2×C22⋊D283D411yescharacteristic
64C2×C4×D283—21no—
65C2×C4×D283—21no—
66C2×C4×D283C2311yescharacteristic
67#17985382—41no—
68#17985376—41no—
69C2×C283⋊C8C2311yescharacteristic
70C2×C283⋊C8C2311yescharacteristic
71C8×D283—41no—
72C4⋊Dic283—21no—
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4D411yescharacteristic
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283D411yescharacteristic
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4D411yescharacteristic
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96C2×Q8×C283—21no—
97C2×Q8×C283—22no—
98C2×Q8×C283—41no—
99C2×Q8×C283C2311yescharacteristic
100C2×Q8×C283C2311yescharacteristic
101C2×Q8×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283C2311yescharacteristic
104Q16×C283—22no—
105Q16×C283—41no—
106C2×C8×C283C2311yescharacteristic
107C2×C8×C283C2311yescharacteristic
108C4⋊C4×C283—21no—
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C22×D283C2×D411yescharacteristic
112Dic566—21no—
113Dic566—21no—
114Dic566—42no—
115C22⋊D283—22no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C4×D283—21no—
124C4×D283—21no—
125C4×D283—42no—
126C4×D283—42no—
127C283⋊C8—21no—
128C283⋊C8—21no—
129C23×C283C2×D411yescharacteristic
130Q8×C283—21no—
131Q8×C283—21no—
132Q8×C283—21no—
133Q8×C283—21no—
134Q8×C283—21no—
135Q8×C283—42no—
136Q8×C283#4112yes—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—42no—
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2411yescharacteristic
146C8×C283—21no—
147C8×C283—21no—
148C22×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283C22×D411yescharacteristic
152C2×D283—21no—
153C2×D283—21no—
154C2×D283#13712yes—
155C4×C283—21no—
156C4×C283—22no—
157C4×C283—41no—
158C4×C283—41no—
159C4×C283—41no—
160C4×C283C2×#4111yescharacteristic
161C4×C283H(5,𝔽2)11yescharacteristic
162Dic283—21no—
163Dic283—21no—
164Dic283—21no—
165Dic283—41no—
166Dic283—41no—
167Dic283—41no—
168Dic283—41no—
169C2×C283—41no—
170C2×C283#54611yescharacteristic
171C2×C283C2×#13711yescharacteristic
172C2×C283#57811yescharacteristic
173D283—22no—
174C283#331211yescharacteristic, complemented, Sylow
175#3312—2831nomaximal, Sylow
176#552—2831no—
177D4×Q8—2831no—
178#491—2831no—
179#485—2831no—
180#483—2831no—
181#479—2831no—
182#470—2831no—
183#467—2831no—
184#462—2831no—
185#451—2831no—
186#451D28311yescharacteristic, complemented
187#441—2831no—
188#435—2831no—
189#419—2831no—
190C2×#103—2831no—
191C22×Q8—2831no—
192C22×Q8C2×D28311yescharacteristic
193C2×Q16—2831no—
194C2×Q16C2×D28311yescharacteristic
195C2×Q16C2×D28311yescharacteristic
196C2×M16—2831no—
197C22×C8—2831no—
198C4⋊Q8—2831no—
199C4⋊Q8—5661no—
200#126—5661no—
201#125—2831no—
202#125—5661no—
203#123—5661no—
204C22⋊Q8—2831no—
205C22⋊Q8—2831no—
206C22⋊Q8—2831no—
207C22⋊Q8—5661no—
208C22⋊Q8—5661no—
209C22⋊Q8C2×D28311yescharacteristic
210C4×Q8—2831no—
211C4×Q8—2831no—
212C4×D4—2831no—
213C4×D4—5661no—
214#117—2831no—
215#117—5661no—
216C2×C4⋊C4—2831no—
217#107—2831no—
218#106—2831no—
219#106—2831no—
220C4⋊C8—2831no—
221#103—2831no—
222#103—2831no—
223#103—2831no—
224#103—2831no—
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103C2×D28311yescharacteristic
230#103C2×D28311yescharacteristic
231C22⋊C8—2831no—
232C22⋊C8C2×D28311yescharacteristic
233#97—2831no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—2831no—
238C2×Q8—5661no—
239C2×Q8—5662no—
240C2×Q8—11321no—
241C2×Q8C22×D28311yescharacteristic
242C2×Q8C22×D28311yescharacteristic
243C2×Q8C22×D28311yescharacteristic
244C2×D4—2831no—
245C22×C4—21no—
246C22×C4—2831no—
247C22×C4—5661no—
248C22×C4—5661no—
249C22×C4C22×D28311yescharacteristic
250Q16—22no—
251Q16—41no—
252Q16—11321no—
253M16—11321no—
254C2×C8—2831no—
255C2×C8—2831no—
256C2×C8—11321no—
257C2×C8C22×D28311yescharacteristic
258C2×C8C22×D28311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—2831no—
261C4⋊C4—2831no—
262C4⋊C4—2831no—
263C4⋊C4—2831no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4—5661no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4C22×D28311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—2831no—
277C22⋊C4—2831no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C42—2831no—
283C42—5661no—
284C42—5661no—
285C42—5661no—
286C23—2831no—
287C23D4×D28311yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—42no—
294Q8—5661no—
295Q8—5661no—
296Q8—11322no—
297Q8#1798539112yes—
298D4—5662no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—2831no—
307C2×C4—2831no—
308C2×C4—2831no—
309C2×C4—5661no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—11322no—
316C2×C4—11322no—
317C2×C4D4×D28311yescharacteristic
318C2×C4C23×D28311yescharacteristic
319C8—21no—
320C8—21no—
321C8—5661no—
322C8—5661no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—2832no—
327C22—5661no—
328C22—5661no—
329C22C2×D4×D28311yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—5661no—
336C4—5661no—
337C4—5661no—
338C4—11321no—
339C4—11321no—
340C4—11321no—
341C4—11321no—
342C4C2×#1798539111yescharacteristic
343C4#2258365511yescharacteristic
344C2—41no—
345C2—5662no—
346C2#3182710211yescharacteristic
347C2#137×D28311yescharacteristic
348C2#3182727811yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#451×C283C2
socleC22×C283C22×D4
prime radicalC2×C22⋊D283D4
hypercenter#451D283
hypocenterC283#3312
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #31826832C2semidirect
4. #31826807C2semidirect
5. #31826794C2semidirect
6. #31826774C2semidirect
7. #31826721C2semidirect
8. #31826703C2semidirect
9. #31826673C2semidirect
10. #31826619C2semidirect
11. #31826572C2semidirect
13. #31826474C2semidirect
14. #103×D283C2semidirect
15. #451×C283C2semidirect
174. C283#3312semidirect
186. #451D283semidirect

Maximal subgroups

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

subgroupindex
#318271492
Q8×C22⋊D2832
#318268322
#318268072
#318267942
#318267742
#318267212
#318267032
#318266732
#318266192
#318265722
#318265392
#318264742
#103×D2832
#451×C2832
#3312283