Finite Group Databasebeta

← #44562097

Subgroups — #44562097

Order 32128.

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

normal subgroups only

This group has 494 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×#22548737C212yesmaximal, complemented
2#30632358C211yesmaximal, characteristic, complemented
3#30632342C211yesmaximal, characteristic, complemented
4#30632060C211yesmaximal, characteristic, complemented
5#30631916C212yesmaximal, complemented
6#30631898C211yesmaximal, characteristic, complemented
7#30631883C211yesmaximal, characteristic, complemented
8#30631851C212yesmaximal, complemented
9#30631834C212yesmaximal, complemented
10C4×#16860799C211yesmaximal, characteristic, complemented
11C8×D4×C251C211yesmaximal, characteristic, complemented
12C2×#16860810C2212yes—
13C2×#16860810C2212yes—
14#22548737—28no—
15C2×Dic1004C2212yes—
16C2×#16860799C2212yes—
17C2×#16860799C2212yes—
18C2×#16860799C2211yescharacteristic
19C2×D2008C2212yes—
20#22548715C2211yescharacteristic
21#22548712C2211yescharacteristic
22#22548711—21no—
23#22548697—22no—
24#22548694C2212yes—
25#22548689C2212yes—
26#22548688—22no—
27#22548686—21no—
28C4×Dic502C2211yescharacteristic
29C4×D1004C2211yescharacteristic
30#22548677—21no—
31C4⋊C4×D251—21no—
32#22548647C2211yescharacteristic
33#22548640C2211yescharacteristic
34#22548640C2212yes—
35#22548637C2211yescharacteristic
36#22548637C2212yes—
37C22×C8×C251C2212yes—
38C4×D4×C251C2211yescharacteristic
39C4⋊C8×C251C2211yescharacteristic
40C22⋊C8×C251C2212yes—
41C4×C8×C251C2211yescharacteristic
42#16860810—24no—
43#16860810—24no—
44#16860810—42no—
45#16860810—42no—
46C2×Dic502C2312yes—
47C2×Dic502C2311yescharacteristic
48C2×D1004—21no—
49C2×D1004—21no—
50C2×D1004C2312yes—
51C2×D1004C2311yescharacteristic
52C2×C22⋊D251—22no—
53C2×C22⋊D251—22no—
54C2×C22⋊D251—22no—
55C2×C4×D251—22no—
56C2×C4×D251—22no—
57C2×C4×D251—21no—
58Dic1004—24no—
59#16860799—24no—
60#16860799—42no—
61#16860799D414yescomplemented
62D2008—24no—
63C4⋊Dic251—21no—
64C4⋊Dic251—21no—
65C4⋊Dic251C2311yescharacteristic
66C4⋊Dic251C2311yescharacteristic
67Dic251⋊C4—22no—
68Dic251⋊C4—21no—
69C22⋊Dic251—22no—
70(C2×D251)⋊C4—22no—
71(C2×D251)⋊C4—21no—
72C4×Dic251—21no—
73C2×D4×C251D411yescharacteristic
74C22×C4×C251C2312yes—
75C2×C8×C251—24no—
76C2×C8×C251C2311yescharacteristic
77C2×C8×C251C2312yes—
78C2×C8×C251C2311yescharacteristic
79C4⋊C4×C251D411yescharacteristic
80C22⋊C4×C251D412yes—
81C42×C251C2311yescharacteristic
82C22×D251—21no—
83C22×D251—22no—
84Dic502—21no—
85Dic502—22no—
86Dic502—22no—
87Dic502C2×D412yes—
88D1004—22no—
89D1004—21no—
90D1004—22no—
91D1004—42no—
92D1004—81no—
93D1004C2×D412yes—
94C22⋊D251—44no—
95C22⋊D251—44no—
96C22⋊D251—82no—
97C2×Dic251—21no—
98C2×Dic251—21no—
99C2×Dic251—21no—
100C2×Dic251—22no—
101C4×D251—44no—
102C4×D251—44no—
103C4×D251—42no—
104C23×C251C2×D412yes—
105D4×C251—22no—
106C2×C4×C251—22no—
107C2×C4×C251—22no—
108C2×C4×C251C2×D411yescharacteristic
109C2×C4×C251C2×D412yes—
110C2×C4×C251C2×D411yescharacteristic
111C2×C4×C251C2411yescharacteristic
112C8×C251—22no—
113C8×C251—21no—
114C8×C251C2×D412yes—
115C22×C251—22no—
116C22×C251—22no—
117C22×C251—22no—
118C22×C251C22×D411yescharacteristic
119C2×D251—22no—
120C2×D251—41no—
121C2×D251—41no—
122C2×D251—42no—
123C2×D251—42no—
124C2×D251—42no—
125C4×C251—22no—
126C4×C251—21no—
127C4×C251#13512yescomplemented
128C4×C251C22×D411yescharacteristic
129C4×C251H(5,𝔽2)11yescharacteristic
130Dic251—22no—
131Dic251—42no—
132Dic251—41no—
133Dic251—41no—
134C2×C251—42no—
135C2×C251D4211yescharacteristic
136C2×C251C2×#13511yescharacteristic
137C2×C251#57711yescharacteristic
138D251—42no—
139D251—82no—
140C251#328411yescharacteristic, complemented, Sylow
141#3284—2511nomaximal, Sylow
142C2×#135—2512no—
143#550—2511no—
144#547—2511no—
145#492—2511no—
146#465—2512no—
147#462—2511no—
148#459—2511no—
149#452—2512no—
150#449—2512no—
151C4×SD16—2511no—
152C8×D4D25111yescharacteristic, complemented
153C2×#41—2512no—
154C2×#41—2512no—
155#135—5028no—
156C2×Q16—2512no—
157C2×SD16—2512no—
158C2×SD16—2512no—
159C2×SD16—2511no—
160C2×D8—2512no—
161C22×C8C2×D25112yes—
162C4⋊Q8—2511no—
163#127—5021no—
164#127—2511no—
165#123—5022no—
166C22⋊Q8—2512no—
167#121—5021no—
168#121—5022no—
169#121—2512no—
170C4×Q8—2511no—
171C4×D4—5021no—
172C4×D4—2511no—
173C4×D4C2×D25111yescharacteristic
174C2×C4⋊C4—5021no—
175#106—2511no—
176C4⋊C8C2×D25111yescharacteristic
177#103—2511no—
178#103—2512no—
179#102—2511no—
180#102—2512no—
181C22⋊C8C2×D25112yes—
182C4×C8C2×D25111yescharacteristic
183#41—10042no—
184#41—10042no—
185#41—5024no—
186#41—5024no—
187C2×Q8—2512no—
188C2×Q8—2511no—
189C2×D4—5022no—
190C2×D4—5022no—
191C2×D4—5022no—
192C2×D4—5021no—
193C2×D4—5021no—
194C2×D4—2512no—
195C2×D4—2511no—
196C2×D4D100411yescharacteristic
197C22×C4—5021no—
198C22×C4—5022no—
199C22×C4—5022no—
200C22×C4C22×D25112yes—
201Q16—5024no—
202SD16—10042no—
203SD16—5024no—
204SD16—2514no—
205D8—5024no—
206C2×C8—24no—
207C2×C8C22×D25111yescharacteristic
208C2×C8C22×D25112yes—
209C2×C8C22×D25111yescharacteristic
210C4⋊C4—5022no—
211C4⋊C4—5021no—
212C4⋊C4—5021no—
213C4⋊C4—5021no—
214C4⋊C4—2511no—
215C4⋊C4—2511no—
216C4⋊C4D100411yescharacteristic
217C22⋊C4—5022no—
218C22⋊C4—5022no—
219C22⋊C4—5021no—
220C22⋊C4D100412yes—
221C42—5021no—
222C42C22×D25111yescharacteristic
223C23—5022no—
224C23—5021no—
225C23C2×D100412yes—
226Q8—5022no—
227Q8—5022no—
228Q8—5021no—
229Q8—2512no—
230D4—22no—
231D4—20081no—
232D4—20082no—
233D4—10044no—
234D4—10044no—
235D4—10042no—
236D4—5022no—
237D4—5022no—
238D4—5021no—
239D4—2512no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—10044no—
243C2×C4—10044no—
244C2×C4—10042no—
245C2×C4—5021no—
246C2×C4—5021no—
247C2×C4—5022no—
248C2×C4—5021no—
249C2×C4C2×D100411yescharacteristic
250C2×C4C2×D100412yes—
251C2×C4C2×D100411yescharacteristic
252C2×C4C23×D25111yescharacteristic
253C8—22no—
254C8—21no—
255C8D4×D25112yes—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—10042no—
260C22—10042no—
261C22—10042no—
262C22—10041no—
263C22—10041no—
264C22—5022no—
265C22C22×D100411yescharacteristic
266C4—21no—
267C4—22no—
268C4—10041no—
269C4—10041no—
270C4—10042no—
271C4—5022no—
272C4#2254873712yescomplemented
273C4C2×D4×D25111yescharacteristic
274C4#2254876111yescharacteristic
275C2—42no—
276C2—20082no—
277C2—10042no—
278C2D4×D100411yescharacteristic
279C2C2×#2254873711yescharacteristic
280C2#3063249911yescharacteristic
subgroupG/H
centerC22C22×D1004
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
FittingC8×D4×C251C2
socleC22×C251C22×D4
hypercenterC8×D4D251
hypocenterC251#3284
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#22548737C2semidirect
2. #30632358C2semidirect
3. #30632342C2semidirect
4. #30632060C2semidirect
5. #30631916C2semidirect
6. #30631898C2semidirect
7. #30631883C2semidirect
8. #30631851C2semidirect
9. #30631834C2semidirect
10. C4×#16860799C2semidirect
11. C8×D4×C251C2semidirect
61. #16860799D4semidirect
127. C4×C251#135semidirect
140. C251#3284semidirect
152. C8×D4D251semidirect
272. C4#22548737semidirect

Maximal subgroups

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

subgroupindex
C2×#225487372
#306323582
#306323422
#306320602
#306319162
#306318982
#306318832
#306318512
#306318342
C4×#168607992
C8×D4×C2512
#3284251