Finite Group Databasebeta

← #49134393

Subgroups — #49134393

Order 36224.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583629C211yesmaximal, characteristic, complemented
2#135×D283C211yesmaximal, characteristic, complemented
3#31826908C211yesmaximal, characteristic, complemented
4#31826905C211yesmaximal, characteristic, complemented
5#31826904C212yesmaximal, complemented
6#31826901C211yesmaximal, characteristic, complemented
7#31826899C212yesmaximal, complemented
8#31826896C212yesmaximal, complemented
9#31826894C212yesmaximal, complemented
10M32×D283C211yesmaximal, characteristic, complemented
11#509×C283C211yesmaximal, characteristic, complemented
12C2×#17985391—21no—
13#41×D283—21no—
14#22583633C2211yescharacteristic, complemented
15#22583632C2211yescharacteristic
16#22583631—21no—
17#22583630—21no—
18#22583629—21no—
19#22583629—21no—
20#22583629C2212yes—
21#22583629C2211yescharacteristic, complemented
22#22583629C2212yescomplemented
23C2×Dic1132C2211yescharacteristic, complemented
24Q16×D283C2211yescharacteristic, complemented
25C2×#17985380—21no—
26SD16×D283—21no—
27D8×D283C2211yescharacteristic, complemented
28C2×C8×D283C2211yescharacteristic
29Dic2264C2212yescomplemented
30#22583556C2212yescomplemented
31#22583555C2212yescomplemented
32#22583554C2212yescomplemented
33#22583554C2212yescomplemented
34#22583551C2212yescomplemented
35#22583550C2211yescharacteristic, complemented
36#22583549C2212yescomplemented
37C16×D283C2212yescomplemented
38#135×C283C2211yescharacteristic
39C2×D8×C283C2211yescharacteristic, complemented
40SD32×C283C2212yescomplemented
41D16×C283C2212yescomplemented
42M32×C283C2211yescharacteristic, complemented
43#17985393—21no—
44#17985392—21no—
45#17985392—41no—
46#17985391—22no—
47#17985391—22no—
48#17985391—21no—
49#17985391—41no—
50#17985391—41no—
51#17985391—41no—
52C2×Dic566—21no—
53Q8×D283—21no—
54C2×C22⋊D283—41no—
55D4×D283—21no—
56D4×D283—41no—
57C22×Dic283—41no—
58C2×C4×D283—41no—
59C2×C4×D283D411yescharacteristic
60Dic1132—21no—
61Dic1132C2311yescharacteristic
62Dic1132C2312yes—
63#17985382—21no—
64#17985381—21no—
65#17985380—21no—
66#17985380—22no—
67#17985380—22no—
68#17985379—21no—
69D2264C2311yescharacteristic
70#17985377—21no—
71C2×C283⋊C8D411yescharacteristic
72C8×D283D411yescharacteristic
73C8×D283D411yescharacteristic
74C8×D283C2311yescharacteristic
75C8×D283C2311yescharacteristic
76C283⋊C16C2312yes—
77#41×C283—21no—
78C2×D4×C283—21no—
79Q16×C283C2311yescharacteristic
80SD16×C283—21no—
81D8×C283—21no—
82D8×C283C2311yescharacteristic
83D8×C283C2312yes—
84C2×C8×C283C2311yescharacteristic
85C16×C283C2312yes—
86C22×D283—41no—
87C22×D283D811yescharacteristic
88Dic566—22no—
89Dic566—21no—
90Dic566—41no—
91Dic566—41no—
92D1132—21no—
93D1132—41no—
94C22⋊D283—41no—
95C22⋊D283—41no—
96C22⋊D283—42no—
97C22⋊D283—42no—
98C22⋊D283—41no—
99C2×Dic283—41no—
100C2×Dic283—41no—
101C2×Dic283—42no—
102C2×Dic283—42no—
103C2×Dic283D811yescharacteristic
104C4×D283—41no—
105C4×D283—41no—
106C4×D283—41no—
107C4×D283D811yescharacteristic
108C4×D283D811yescharacteristic
109C4×D283C2×D411yescharacteristic
110C4×D283C2×D411yescharacteristic
111C283⋊C8C2×D411yescharacteristic
112C283⋊C8C2×D411yescharacteristic
113C23×C283—41no—
114Q8×C283—21no—
115D4×C283—22no—
116D4×C283—21no—
117D4×C283—41no—
118D4×C283—41no—
119C2×C4×C283—41no—
120C2×C4×C283C2×D411yescharacteristic
121C8×C283C2×D411yescharacteristic
122C8×C283C2411yescharacteristic
123C22×C283—41no—
124C22×C283—42no—
125C22×C283—82no—
126C22×C283C2×D811yescharacteristic
127C2×D283—41no—
128C2×D283—41no—
129C2×D283—82no—
130C2×D283C2×D811yescharacteristic
131C2×D283C2×D811yescharacteristic
132C4×C283—41no—
133C4×C283C2×D811yescharacteristic
134C4×C283C22×D411yescharacteristic
135Dic283—41no—
136Dic283—42no—
137Dic283C2×D811yescharacteristic
138Dic283C2×D811yescharacteristic
139C2×C283—21no—
140C2×C283—81no—
141C2×C283—82no—
142C2×C283C22×D811yescharacteristic
143D283—21no—
144D283—21no—
145D283—81no—
146C283#341411yescharacteristic, complemented, Sylow
147#3414—2831nomaximal, Sylow
148C2×#135—2831no—
149C2×#135—2831no—
150#510—2831no—
151#510—2832no—
152#510—2831no—
153#509—2831no—
154#509—2832no—
155#509D28311yescharacteristic, complemented
156#508—2832no—
157#508—2832no—
158C2×M32—2831no—
159C2×#41—5661no—
160C2×#41—5661no—
161#135—2831no—
162#135—2832no—
163#135—2832no—
164#135—2831no—
165#135—2831no—
166#135—5661no—
167#135—5661no—
168#135—5661no—
169#135—5661no—
170#135C2×D28311yescharacteristic
171C2×Q16—2831no—
172C2×Q16—2831no—
173C2×SD16—5661no—
174C2×SD16—5661no—
175C2×D8—2831no—
176C2×D8C2×D28311yescharacteristic, complemented
177C22×C8—2831no—
178Q32—2832no—
179Q32—2832no—
180SD32—2832no—
181SD32—2832no—
182SD32—2832no—
183SD32C2×D28312yescomplemented
184D16—2832no—
185D16C2×D28312yescomplemented
186M32—2831no—
187M32—2832no—
188M32C2×D28311yescharacteristic, complemented
189C2×C16—2832no—
190#41—21no—
191#41—5662no—
192#41—5662no—
193#41—5661no—
194#41—5661no—
195#41—5661no—
196#41—11321no—
197#41—11321no—
198#41—11321no—
199#41—11321no—
200C2×Q8—5661no—
201C2×Q8—5661no—
202C2×D4—21no—
203C2×D4—5661no—
204C2×D4—11321no—
205C2×D4—11321no—
206C22×C4—2831no—
207C22×C4—11321no—
208C22×C4—11321no—
209Q16—2831no—
210Q16—2832no—
211Q16—5661no—
212Q16—5661no—
213Q16C22×D28311yescharacteristic
214SD16—21no—
215SD16—5662no—
216SD16—5662no—
217SD16—5661no—
218SD16—5661no—
219SD16—5661no—
220D8—21no—
221D8—2831no—
222D8—5661no—
223D8C22×D28312yes—
224D8C22×D28311yescharacteristic
225C2×C8—2831no—
226C2×C8—2831no—
227C2×C8—2831no—
228C2×C8—2831no—
229C2×C8—2831no—
230C2×C8C22×D28311yescharacteristic
231C16—2832no—
232C16C22×D28312yes—
233C23—41no—
234C23—2831no—
235C23—11321no—
236Q8—21no—
237Q8—5662no—
238Q8—5661no—
239Q8—11321no—
240Q8—11321no—
241D4—22no—
242D4—21no—
243D4—41no—
244D4—41no—
245D4—5661no—
246D4—11321no—
247D4—11321no—
248D4—11321no—
249D4—11322no—
250D4—11322no—
251D4—11321no—
252C2×C4—41no—
253C2×C4—2831no—
254C2×C4—2831no—
255C2×C4—2831no—
256C2×C4—2831no—
257C2×C4—2831no—
258C2×C4—11321no—
259C2×C4—11321no—
260C2×C4—11321no—
261C2×C4—11322no—
262C2×C4—11322no—
263C2×C4—11321no—
264C2×C4—11321no—
265C2×C4D4×D28311yescharacteristic
266C8—2831no—
267C8—2831no—
268C8D4×D28311yescharacteristic
269C8C23×D28311yescharacteristic
270C22—41no—
271C22—42no—
272C22—82no—
273C22—2831no—
274C22—2831no—
275C22—11321no—
276C22—11321no—
277C22—22642no—
278C22D8×D28311yescharacteristic
279C4—41no—
280C4—2831no—
281C4—2831no—
282C4—11321no—
283C4—11322no—
284C4D8×D28311yescharacteristic
285C4C2×D4×D28311yescharacteristic
286C2—21no—
287C2—82no—
288C2—81no—
289C2—5661no—
290C2—5661no—
291C2—22641no—
292C2C2×D8×D28311yescharacteristic
subgroupG/H
centerC2C2×D8×D283
commutator, cosocleC8×C283C24
FrattiniC8C23×D283
Fitting#509×C283C2
socleC2×C283C22×D8
hypercenter#509D283
hypocenterC283#3414
LCSG ▷ C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. C2×#22583629C2semidirect
2. #135×D283C2semidirect
3. #31826908C2semidirect
4. #31826905C2semidirect
5. #31826904C2semidirect
6. #31826901C2semidirect
7. #31826899C2semidirect
8. #31826896C2semidirect
9. #31826894C2semidirect
10. M32×D283C2semidirect
11. #509×C283C2semidirect
14. #22583633C22semidirect
21. #22583629C22semidirect
22. #22583629C22semidirect
23. C2×Dic1132C22semidirect
24. Q16×D283C22semidirect
27. D8×D283C22semidirect
29. Dic2264C22semidirect
30. #22583556C22semidirect
31. #22583555C22semidirect
32. #22583554C22semidirect
33. #22583554C22semidirect
34. #22583551C22semidirect
35. #22583550C22semidirect
36. #22583549C22semidirect
37. C16×D283C22semidirect
39. C2×D8×C283C22semidirect
40. SD32×C283C22semidirect
41. D16×C283C22semidirect
42. M32×C283C22semidirect
146. C283#3414semidirect
155. #509D283semidirect
176. C2×D8C2×D283semidirect
183. SD32C2×D283semidirect
185. D16C2×D283semidirect
188. M32C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836292
#135×D2832
#318269082
#318269052
#318269042
#318269012
#318268992
#318268962
#318268942
M32×D2832
#509×C2832
#3414283