Finite Group Databasebeta

← #49130745

Subgroups — #49130745

Order 36224.

480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22583642C212yesmaximal
2C4⋊Q8×D283C211yesmaximal, characteristic, complemented
3C4×#17985393C211yesmaximal, characteristic
4#31826675C211yesmaximal, characteristic, complemented
5#31826673C212yesmaximal, complemented
6#31826671C211yesmaximal, characteristic, complemented
7#31826669C212yesmaximal, complemented
8#31826667C211yesmaximal, characteristic, complemented
9#31826487C211yesmaximal, characteristic, complemented
10#31826472C212yesmaximal, complemented
11#462×C283C211yesmaximal, characteristic, complemented
12C2×#17985393C2211yescharacteristic
13C2×Q8×D283C2212yes—
14#22583642—28no—
15C2×#17985382C2212yes—
16C2×#17985381C2212yes—
17C2×#17985379C2212yes—
18C2×#17985375C2212yes—
19#22583610C2211yescharacteristic
20#22583609—21no—
21#22583609—21no—
22#22583608C2212yes—
23Q8×Dic283C2211yescharacteristic
24C4×D1132—21no—
25C4×D1132C2211yescharacteristic
26#22583572—21no—
27#22583572C2211yescharacteristic
28#22583568—21no—
29#22583568C2211yescharacteristic
30C4⋊C4×D283—21no—
31C4⋊C4×D283—21no—
32C42×D283—21no—
33C42×D283C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35Dic283⋊C8C2212yes—
36#22583535C2212yes—
37#22583534C2212yes—
38#22583533C2212yes—
39C2×Q16×C283C2212yes—
40C4⋊Q8×C283C2211yescharacteristic
41C4×Q8×C283C2211yescharacteristic
42C4⋊C8×C283C2211yescharacteristic
43#103×C283C2212yes—
44#17985393—22no—
45#17985393D414yes—
46C2×Dic566—22no—
47C2×Dic566C2312yes—
48Q8×D283—24no—
49Q8×D283—24no—
50C2×D1132—21no—
51C2×D1132C2311yescharacteristic
52C2×C4×D283—21no—
53C2×C4×D283—22no—
54C2×C4×D283—21no—
55C2×C4×D283—21no—
56C2×C4×D283D411yescharacteristic
57C2×C4×D283D411yescharacteristic
58C2×C4×D283C2311yescharacteristic
59#17985382—24no—
60#17985381—24no—
61#17985379—24no—
62#17985375—24no—
63C2×C283⋊C8C2312yes—
64C4⋊Dic283—21no—
65C4⋊Dic283—21no—
66C4⋊Dic283—21no—
67C4⋊Dic283C2311yescharacteristic
68Dic283⋊C4—22no—
69Dic283⋊C4—22no—
70(C2×D283)⋊C4—21no—
71(C2×D283)⋊C4—21no—
72(C2×D283)⋊C4—21no—
73C4×Dic283—21no—
74C4×Dic283—21no—
75C4×Dic283D411yescharacteristic
76C4×Dic283D411yescharacteristic
77C4×Dic283C2311yescharacteristic
78C2×Q8×C283C2312yes—
79C2×Q8×C283C2311yescharacteristic
80Q16×C283—24no—
81C2×C8×C283C2312yes—
82C4⋊C4×C283—21no—
83C4⋊C4×C283—21no—
84C4⋊C4×C283—21no—
85C4⋊C4×C283C2311yescharacteristic
86C42×C283—21no—
87C42×C283C2311yescharacteristic
88C22×D283—21no—
89C22×D283C2×D411yescharacteristic
90Dic566—22no—
91Dic566—22no—
92Dic566—44no—
93D1132—24no—
94D1132—21no—
95D1132C2×D412yes—
96C2×Dic283—21no—
97C2×Dic283—22no—
98C2×Dic283C2×D411yescharacteristic
99C2×Dic283C2×D411yescharacteristic
100C2×Dic283C2×D411yescharacteristic
101C4×D283—22no—
102C4×D283—24no—
103C4×D283—22no—
104C4×D283—44no—
105C4×D283—42no—
106C4×D283—42no—
107C4×D283C2×D412yes—
108C4×D283#4112yes—
109C283⋊C8—22no—
110Q8×C283—21no—
111Q8×C283—22no—
112Q8×C283—22no—
113Q8×C283C2×D412yes—
114C2×C4×C283—21no—
115C2×C4×C283—21no—
116C2×C4×C283—22no—
117C2×C4×C283C2×D411yescharacteristic
118C2×C4×C283C2×D411yescharacteristic
119C2×C4×C283C2411yescharacteristic
120C8×C283—22no—
121C22×C283C22×D411yescharacteristic
122C2×D283—21no—
123C2×D283—21no—
124C2×D283—22no—
125C2×D283—41no—
126C2×D283—41no—
127C2×D283#12112yes—
128C4×C283—22no—
129C4×C283—21no—
130C4×C283—42no—
131C4×C283—41no—
132C4×C283#13712yescomplemented
133C4×C283C22×D411yescharacteristic
134C4×C283C2×#4111yescharacteristic
135Dic283—21no—
136Dic283—42no—
137Dic283—41no—
138Dic283#12112yes—
139Dic283#13712yescomplemented
140C2×C283C2×#12111yescharacteristic
141C2×C283C2×#13711yescharacteristic
142C2×C283C2×#13711yescharacteristic
143D283—22no—
144D283—42no—
145C283#303911yescharacteristic, complemented, Sylow
146#3039—2831nomaximal, Sylow
147C2×#137—2832no—
148C2×C4⋊Q8—2831no—
149C4×#41—2831no—
150#462—2832no—
151#462—2831no—
152#462D28311yescharacteristic, complemented
153#461—2831no—
154#461—2831no—
155#461—2832no—
156#423—2831no—
157#419—2832no—
158C2×#41—2831no—
159C22×Q8—2832no—
160#137—5668no—
161C2×Q16—2832no—
162C2×Q16C2×D28312yes—
163C2×SD16—2832no—
164C2×SD16—2832no—
165C2×M16—2832no—
166C4⋊Q8—2832no—
167C4⋊Q8—2831no—
168C4⋊Q8—5661no—
169C4⋊Q8—5661no—
170C4⋊Q8C2×D28311yescharacteristic
171C4×Q8—2831no—
172C4×Q8C2×D28311yescharacteristic
173C4×D4—2831no—
174C4×D4—2831no—
175C4×D4—5661no—
176C4×D4—5661no—
177#117—2831no—
178#117—5661no—
179C2×C4⋊C4—5661no—
180C2×C4⋊C4—5661no—
181C2×C42—2831no—
182C2×C42—5661no—
183C4⋊C8—2832no—
184C4⋊C8—2831no—
185C4⋊C8C2×D28311yescharacteristic
186#103—2832no—
187#103—2832no—
188#103—2832no—
189#103C2×D28312yes—
190#41—2834no—
191#41—5662no—
192C2×Q8—2832no—
193C2×Q8—5662no—
194C2×Q8—5664no—
195C2×Q8—5664no—
196C2×Q8C22×D28312yes—
197C2×Q8C22×D28311yescharacteristic
198C2×D4—2831no—
199C2×D4—5661no—
200C22×C4—2831no—
201C22×C4—2831no—
202C22×C4—2831no—
203C22×C4—5661no—
204C22×C4—5661no—
205C22×C4—5662no—
206C22×C4—5661no—
207Q16—24no—
208Q16—5664no—
209SD16—5664no—
210SD16—5664no—
211M16—5664no—
212C2×C8—2832no—
213C2×C8C22×D28312yes—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—2831no—
218C4⋊C4—5662no—
219C4⋊C4—5662no—
220C4⋊C4—5661no—
221C4⋊C4—5661no—
222C4⋊C4—5661no—
223C4⋊C4C22×D28311yescharacteristic
224C22⋊C4—5661no—
225C22⋊C4—5661no—
226C22⋊C4—5661no—
227C42—21no—
228C42—2831no—
229C42—2831no—
230C42—2831no—
231C42—5661no—
232C42—5661no—
233C42C22×D28311yescharacteristic
234C23—2831no—
235C23—5661no—
236Q8—21no—
237Q8—22no—
238Q8—22no—
239Q8—5662no—
240Q8—5662no—
241Q8—11324no—
242Q8D4×D28312yes—
243D4—2832no—
244D4—5664no—
245D4—5661no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—2831no—
250C2×C4—2831no—
251C2×C4—2832no—
252C2×C4—2832no—
253C2×C4—2831no—
254C2×C4—5662no—
255C2×C4—5664no—
256C2×C4—5662no—
257C2×C4—5661no—
258C2×C4—5662no—
259C2×C4—11322no—
260C2×C4—11324no—
261C2×C4—11322no—
262C2×C4D4×D28311yescharacteristic
263C2×C4D4×D28311yescharacteristic
264C2×C4C23×D28311yescharacteristic
265C8—22no—
266C8—5662no—
267C22—2832no—
268C22—5661no—
269C22—5661no—
270C22—5662no—
271C22—11321no—
272C22—11321no—
273C22C2×D4×D28311yescharacteristic
274C4—22no—
275C4—21no—
276C4—42no—
277C4—41no—
278C4—2832no—
279C4—2832no—
280C4—5661no—
281C4—11322no—
282C4—11321no—
283C4#2258364212yescomplemented
284C4C2×D4×D28311yescharacteristic
285C4#41×D28311yescharacteristic
286C2—5662no—
287C2—11322no—
288C2#121×D28311yescharacteristic
289C2#137×D28311yescharacteristic
290C2C2×#2258364211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#462×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985393C22
hypercenter#462D283
hypocenterC283#3039
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D283C2semidirect
4. #31826675C2semidirect
5. #31826673C2semidirect
6. #31826671C2semidirect
7. #31826669C2semidirect
8. #31826667C2semidirect
9. #31826487C2semidirect
10. #31826472C2semidirect
11. #462×C283C2semidirect
132. C4×C283#137semidirect
139. Dic283#137semidirect
145. C283#3039semidirect
152. #462D283semidirect
283. C4#22583642semidirect

Maximal subgroups

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

subgroupindex
C2×#225836422
C4⋊Q8×D2832
C4×#179853932
#318266752
#318266732
#318266712
#318266692
#318266672
#318264872
#318264722
#462×C2832
#3039283