Finite Group Databasebeta

← #49134293

Subgroups — #49134293

Order 36224.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827193C211yesmaximal, characteristic, complemented
2#31827187C211yesmaximal, characteristic
3#31826859C211yesmaximal, characteristic
4#31826858C211yesmaximal, characteristic
5#31826843C211yesmaximal, characteristic, complemented
6#31826690C211yesmaximal, characteristic
7#31826687C211yesmaximal, characteristic
8#31826675C211yesmaximal, characteristic, complemented
9#31826674C211yesmaximal, characteristic, complemented
10#31826674C211yesmaximal, characteristic, complemented
11#31826669C211yesmaximal, characteristic
12#31826593C211yesmaximal, characteristic, complemented
13#31826571C211yesmaximal, characteristic, complemented
14#31826552C211yesmaximal, characteristic
15#441×C283C211yesmaximal, characteristic, complemented
16C2×Dic1132C2211yescharacteristic
17C2×Dic1132C2211yescharacteristic
18C2×#17985382C2211yescharacteristic
19C2×#17985382C2211yescharacteristic
20C2×#17985382C2211yescharacteristic
21C2×#17985381C2211yescharacteristic
22C2×#17985381C2211yescharacteristic
23C2×#17985379C2211yescharacteristic
24#22583610C2211yescharacteristic
25#22583608C2211yescharacteristic
26#22583608C2211yescharacteristic
27#22583608C2211yescharacteristic
28#22583605—21no—
29#22583604—21no—
30#22583602—21no—
31#22583600—21no—
32#22583600—21no—
33#22583599C2211yescharacteristic
34#22583598C2211yescharacteristic
35#22583588—21no—
36C4×Dic566—21no—
37C4×Dic566C2211yescharacteristic
38#22583575C2211yescharacteristic
39#22583575C2211yescharacteristic
40#22583575C2211yescharacteristic
41#22583572C2211yescharacteristic
42#22583567—21no—
43C4⋊(C283⋊C8)C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49#22583530C2211yescharacteristic
50#22583520C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×Q16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59C2×Dic566D411yescharacteristic
60C2×Dic566C2311yescharacteristic
61C2×Dic566C2311yescharacteristic
62C2×Dic566C2311yescharacteristic
63C2×D1132C2311yescharacteristic
64C2×C4×D283—21no—
65Dic1132—22no—
66Dic1132—41no—
67#17985382—41no—
68#17985382—41no—
69#17985382—41no—
70#17985381—22no—
71#17985381—41no—
72#17985379—41no—
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C4⋊Dic283—21no—
76C4⋊Dic283—21no—
77C4⋊Dic283D411yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4D411yescharacteristic
88Dic283⋊C4D411yescharacteristic
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283—21no—
97C4×Dic283C2311yescharacteristic
98C4×Dic283C2311yescharacteristic
99C2×Q8×C283C2311yescharacteristic
100C2×Q8×C283C2311yescharacteristic
101Q16×C283—22no—
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283—21no—
105C4⋊C4×C283—21no—
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C42×C283—21no—
109C42×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112Dic566—22no—
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—21no—
117Dic566—21no—
118Dic566—21no—
119D1132—21no—
120D1132—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C4×D283—42no—
129C283⋊C8—21no—
130C283⋊C8—21no—
131Q8×C283—21no—
132Q8×C283—21no—
133Q8×C283—21no—
134Q8×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2411yescharacteristic
142C8×C283—21no—
143C8×C283#4112yes—
144C22×C283C22×D411yescharacteristic
145C2×D283—41no—
146C2×D283—41no—
147C2×D283—41no—
148C4×C283—21no—
149C4×C283—21no—
150C4×C283—41no—
151C4×C283—41no—
152C4×C283—41no—
153C4×C283—41no—
154C4×C283C2×#4111yescharacteristic
155C4×C283H(5,𝔽2)11yescharacteristic
156Dic283—21no—
157Dic283—21no—
158Dic283—21no—
159Dic283—41no—
160Dic283—41no—
161Dic283—41no—
162Dic283#13712yes—
163C2×C283#55011yescharacteristic
164C2×C283C2×#13711yescharacteristic
165C2×C283#57811yescharacteristic
166D283—81no—
167C283#339811yescharacteristic, complemented, Sylow
168#3398—2831nomaximal, Sylow
169#557—2831no—
170#556—2831no—
171#497—2831no—
172#497—2831no—
173#494—2831no—
174#464—2831no—
175#464—2831no—
176#462—2831no—
177#462—2831no—
178#462—2831no—
179#461—2831no—
180#446—2831no—
181#441—2831no—
182#441D28311yescharacteristic, complemented
183C4×SD16—2831no—
184C2×Q16—2831no—
185C2×Q16—2831no—
186C2×Q16—2831no—
187C2×Q16—2831no—
188C2×Q16—2831no—
189C2×Q16C2×D28311yescharacteristic
190C2×SD16—2831no—
191C2×SD16—2831no—
192C2×SD16—2831no—
193C4⋊Q8—2831no—
194C4⋊Q8—2831no—
195C4⋊Q8—2831no—
196C4⋊Q8—2831no—
197#126—5661no—
198#126—5661no—
199#125—5661no—
200#125—5661no—
201#125—5661no—
202#124—2831no—
203#124—2831no—
204C22⋊Q8—5661no—
205C4×Q8—2831no—
206C4×Q8—2831no—
207C4×Q8—2831no—
208C4×Q8—2831no—
209C4×Q8—5661no—
210C4×Q8C2×D28311yescharacteristic
211C4×Q8C2×D28311yescharacteristic
212C4×D4—2831no—
213#117—5661no—
214#106C2×D28311yescharacteristic
215C4⋊C8—2831no—
216C4⋊C8—2831no—
217C4⋊C8—2831no—
218#103—2831no—
219#103—2831no—
220#103—2831no—
221#103C2×D28311yescharacteristic
222#103C2×D28311yescharacteristic
223#102—2831no—
224#97—2831no—
225#97C2×D28311yescharacteristic
226C4×C8—2831no—
227C2×Q8—2831no—
228C2×Q8—2831no—
229C2×Q8—2831no—
230C2×Q8—2831no—
231C2×Q8C22×D28311yescharacteristic
232C2×Q8C22×D28311yescharacteristic
233C2×D4—2831no—
234C22×C4—5661no—
235Q16—22no—
236Q16—5662no—
237Q16—11321no—
238Q16—11321no—
239Q16—11321no—
240Q16—11321no—
241SD16—5662no—
242SD16—11321no—
243SD16—11321no—
244C2×C8—2831no—
245C2×C8—2831no—
246C2×C8C22×D28311yescharacteristic
247C2×C8C22×D28311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—2831no—
251C4⋊C4—2831no—
252C4⋊C4—2831no—
253C4⋊C4—5661no—
254C4⋊C4—5661no—
255C4⋊C4—5661no—
256C4⋊C4—5661no—
257C4⋊C4—5661no—
258C4⋊C4—5661no—
259C4⋊C4—5661no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4C22×D28311yescharacteristic
265C4⋊C4C22×D28311yescharacteristic
266C22⋊C4—5661no—
267C22⋊C4—5661no—
268C22⋊C4—5661no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C42—21no—
272C42—21no—
273C42—2831no—
274C42—2831no—
275C42—5661no—
276C42—5661no—
277C42—5661no—
278C42C22×D28311yescharacteristic
279C23—5661no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—5662no—
285Q8—5661no—
286Q8—5661no—
287Q8—5661no—
288Q8—5661no—
289Q8—5661no—
290Q8—5661no—
291D4—5661no—
292D4—5661no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—2831no—
298C2×C4—2831no—
299C2×C4—2831no—
300C2×C4—2831no—
301C2×C4—5661no—
302C2×C4—5661no—
303C2×C4—5661no—
304C2×C4—11322no—
305C2×C4D4×D28311yescharacteristic
306C2×C4D4×D28311yescharacteristic
307C2×C4C23×D28311yescharacteristic
308C8—21no—
309C8—5661no—
310C8—5661no—
311C8#1798539212yes—
312C22—11321no—
313C22—11321no—
314C22—11321no—
315C22C2×D4×D28311yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—2832no—
323C4—5661no—
324C4—5661no—
325C4—5661no—
326C4—11321no—
327C4—11321no—
328C4—11321no—
329C4C2×#1798539211yescharacteristic
330C4#2258365611yescharacteristic
331C2—22641no—
332C2#3182713611yescharacteristic
333C2#137×D28311yescharacteristic
334C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#441×C283C2
socleC22×C283C22×D4
prime radicalC2×D1132C23
hypercenter#441D283
hypocenterC283#3398
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. #31827193C2semidirect
5. #31826843C2semidirect
8. #31826675C2semidirect
9. #31826674C2semidirect
10. #31826674C2semidirect
12. #31826593C2semidirect
13. #31826571C2semidirect
15. #441×C283C2semidirect
167. C283#3398semidirect
182. #441D283semidirect

Maximal subgroups

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

subgroupindex
#318271932
#318271872
#318268592
#318268582
#318268432
#318266902
#318266872
#318266752
#318266742
#318266692
#318265932
#318265712
#318265522
#441×C2832
#3398283