Finite Group Databasebeta

← #49133308

Subgroups — #49133308

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#31827150C211yesmaximal, characteristic
2Q8×C22⋊D283C211yesmaximal, characteristic
3#31826832C211yesmaximal, characteristic, complemented
4#31826805C211yesmaximal, characteristic, complemented
5#31826795C211yesmaximal, characteristic, complemented
6#31826774C211yesmaximal, characteristic, complemented
7#31826722C211yesmaximal, characteristic, complemented
8#31826706C211yesmaximal, characteristic, complemented
9#31826674C211yesmaximal, characteristic, complemented
10#31826622C211yesmaximal, characteristic, complemented
11#31826621C211yesmaximal, characteristic, complemented
12#31826569C211yesmaximal, characteristic, complemented
13#31826536C211yesmaximal, characteristic
14#31826472C211yesmaximal, characteristic, complemented
15C2×#103×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×Dic1132C2211yescharacteristic
18C2×#17985382C2211yescharacteristic
19C2×#17985382C2211yescharacteristic
20C2×#17985375C2211yescharacteristic
21#22583608—21no—
22#22583608C2211yescharacteristic
23#22583605—21no—
24#22583601C2211yescharacteristic
25#22583600—21no—
26#22583593—21no—
27#22583590C2211yescharacteristic
28#22583589—21no—
29#22583589C2211yescharacteristic
30#22583589C2211yescharacteristic
31#22583586—21no—
32#22583586C2211yescharacteristic
33Q8×Dic283C2211yescharacteristic
34#22583575C2211yescharacteristic
35C4×C22⋊D283—21no—
36C4×C22⋊D283C2211yescharacteristic
37#22583569—21no—
38#22583568C2211yescharacteristic
39#22583544C2211yescharacteristic
40#22583541C2211yescharacteristic
41#22583541C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic
52C22×Q8×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54C2×C4⋊C4×C283C2211yescharacteristic
55#103×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61C2×Dic566C2311yescharacteristic
62Q8×D283—22no—
63Q8×D283—41no—
64C2×C22⋊D283D411yescharacteristic
65C2×C4×D283—21no—
66C2×C4×D283C2311yescharacteristic
67Dic1132—41no—
68#17985382—22no—
69#17985382—41no—
70#17985375—41no—
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283—21no—
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)⋊C4—21no—
92(C2×D283)⋊C4D411yescharacteristic
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283C2311yescharacteristic
97C2×Q8×C283—21no—
98C2×Q8×C283—22no—
99C2×Q8×C283—41no—
100C2×Q8×C283C2311yescharacteristic
101C2×Q8×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283—21no—
104C22×C4×C283C2311yescharacteristic
105C2×C8×C283—41no—
106C2×C8×C283C2311yescharacteristic
107C2×C8×C283C2311yescharacteristic
108C4⋊C4×C283—21no—
109C4⋊C4×C283C2311yescharacteristic
110C4⋊C4×C283C2311yescharacteristic
111C22×D283C2×D411yescharacteristic
112Dic566—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—42no—
117C22⋊D283—22no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C4×D283—21no—
126C4×D283—21no—
127C4×D283—42no—
128C283⋊C8—21no—
129C283⋊C8—21no—
130C23×C283C2×D411yescharacteristic
131Q8×C283—21no—
132Q8×C283—21no—
133Q8×C283—21no—
134Q8×C283—42no—
135Q8×C283#4112yes—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—42no—
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#13712yes—
151C22×C283C22×D411yescharacteristic
152C2×D283—21no—
153C2×D283—21no—
154C2×D283—21no—
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—22no—
170C2×C283#54611yescharacteristic
171C2×C283C2×#13711yescharacteristic
172C2×C283#57811yescharacteristic
173D283—41no—
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#451—2831no—
187#441—2831no—
188#435—2831no—
189#419—2831no—
190C2×#103D28311yescharacteristic, complemented
191C22×Q8—2831no—
192C22×Q8C2×D28311yescharacteristic
193C2×Q16—2831no—
194C2×Q16—2831no—
195C2×Q16—2831no—
196C2×M16—2831no—
197C22×C8C2×D28311yescharacteristic
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—2831no—
208C22⋊Q8—5661no—
209C22⋊Q8—5661no—
210C4×Q8—2831no—
211C4×Q8—2831no—
212C4×D4—2831no—
213C4×D4—5661no—
214#117—2831no—
215#117—5661no—
216C2×C4⋊C4C2×D28311yescharacteristic
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#103C2×D28311yescharacteristic
228#103C2×D28311yescharacteristic
229#103C2×D28311yescharacteristic
230#103C2×D28311yescharacteristic
231C22⋊C8—2831no—
232C22⋊C8—2831no—
233#97—2831no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—2831no—
238C2×Q8—2831no—
239C2×Q8—5661no—
240C2×Q8—5662no—
241C2×Q8—11321no—
242C2×Q8C22×D28311yescharacteristic
243C2×Q8C22×D28311yescharacteristic
244C2×D4—2831no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—2831no—
248C22×C4—5661no—
249C22×C4C22×D28311yescharacteristic
250Q16—5662no—
251Q16—11321no—
252Q16—11321no—
253M16—11321no—
254C2×C8—41no—
255C2×C8—2831no—
256C2×C8—2831no—
257C2×C8C22×D28311yescharacteristic
258C2×C8C22×D28311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—2831no—
261C4⋊C4—2831no—
262C4⋊C4—2831no—
263C4⋊C4—5661no—
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⋊C4C22×D28311yescharacteristic
274C4⋊C4C22×D28311yescharacteristic
275C22⋊C4—2831no—
276C22⋊C4—2831no—
277C22⋊C4—5661no—
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—42no—
292Q8—5661no—
293Q8—5661no—
294Q8—5661no—
295Q8—5661no—
296Q8—11322no—
297Q8#1798539212yes—
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—42no—
307C2×C4—2831no—
308C2×C4—2831no—
309C2×C4—2831no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—11322no—
317C2×C4D4×D28311yescharacteristic
318C2×C4C23×D28311yescharacteristic
319C8—21no—
320C8—21no—
321C8—5661no—
322C8—5661no—
323C22—21no—
324C22—21no—
325C22—5661no—
326C22—5661no—
327C22—5661no—
328C22#2258363912yes—
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×#1798539211yescharacteristic
343C4#2258365511yescharacteristic
344C2—22no—
345C2—11321no—
346C2#3182710511yescharacteristic
347C2C2×#2258363911yescharacteristic
348C2#3182727811yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#103×C283C2
socleC22×C283C22×D4
prime radicalC2×C22⋊D283D4
hypercenterC2×#103D283
hypocenterC283#3312
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #31826832C2semidirect
4. #31826805C2semidirect
5. #31826795C2semidirect
6. #31826774C2semidirect
7. #31826722C2semidirect
8. #31826706C2semidirect
9. #31826674C2semidirect
10. #31826622C2semidirect
11. #31826621C2semidirect
12. #31826569C2semidirect
14. #31826472C2semidirect
15. C2×#103×C283C2semidirect
174. C283#3312semidirect
190. C2×#103D283semidirect

Maximal subgroups

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

subgroupindex
#318271502
Q8×C22⋊D2832
#318268322
#318268052
#318267952
#318267742
#318267222
#318267062
#318266742
#318266222
#318266212
#318265692
#318265362
#318264722
C2×#103×C2832
#3312283