Finite Group Databasebeta

← #11755252

Subgroups — #11755252

Order 960.

424 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 132 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
1#91835C211yesmaximal, characteristic, complemented
2C5×Q8×Dic3C211yesmaximal, characteristic, complemented
3C3×#4092C211yesmaximal, characteristic, complemented
4#91469C211yesmaximal, characteristic, complemented
5C4×#1202C211yesmaximal, characteristic
6#91361C212yesmaximal, complemented
7#91358C211yesmaximal, characteristic, complemented
8#91353C212yesmaximal
9#91347C211yesmaximal, characteristic, complemented
10#91337C212yesmaximal, complemented
11#91324C212yesmaximal, complemented
12#65918—31nomaximal, Hall
13C2×C3×C5×Q8C2211yescharacteristic
14C2×C4×D15C2211yescharacteristic
15C2×C3×C4×D5C2211yescharacteristic
16C2×#1204C2212yes—
17C2×#1202C2211yescharacteristic
18#6714C2212yes—
19C4⋊Dic15C2211yescharacteristic
20#6712C2212yes—
21C5×C4⋊Dic3C2212yes—
22C5×C4⋊Dic3C2211yescharacteristic
23C4×C5×Dic3C2211yescharacteristic
24C4×C5×Dic3C2212yes—
25C3×#685C2212yes—
26C3×C4⋊Dic5C2211yescharacteristic
27C3×#683C2212yes—
28Dic3⋊Dic5C2211yescharacteristic
29Dic3⋊Dic5C2212yes—
30#6667C2211yescharacteristic
31#6667C2212yes—
32#6665C2211yescharacteristic
33#6665C2212yes—
34Dic3×Dic5C2212yes—
35Dic3×Dic5C2212yes—
36#5641—51nomaximal, Hall
37C4×C5×Q8—31no—
38#4092—31no—
39#4092D311yescharacteristic, complemented
40#4044—32no—
41#4044—32no—
42#4038—31no—
43#4038—31no—
44#4021—32no—
45C4×D20—31no—
46#4015—31no—
47C4×Dic10—32no—
48C22×D15C2311yescharacteristic
49C22×C3×D5C2311yescharacteristic
50C3×C5×Q8—22no—
51C2×C3×C4×C5C2312yes—
52C2×C3×C4×C5C2311yescharacteristic
53C2×Dic15C2311yescharacteristic
54C2×Dic15C2312yes—
55C4×D15—22no—
56C2×C5×Dic3C2312yes—
57C2×C5×Dic3C2311yescharacteristic
58C2×C5×Dic3C2311yescharacteristic
59C2×C3×Dic5C2311yescharacteristic
60C2×C3×Dic5C2312yes—
61C3×C4×D5—22no—
62#1204—24no—
63#1202—22no—
64C3×C22⋊Q8—51no—
65#946—51no—
66Q8×Dic3D511yescharacteristic, complemented
67C4×#67—51no—
68#926—51no—
69#898—52no—
70#892—51no—
71#888—51no—
72#887—52no—
73#885—52no—
74#879—52no—
75C2×C5×Q8C2×D311yescharacteristic
76C2×D20—31no—
77C2×C4×D5—31no—
78C2×C4×D5C2×D311yescharacteristic
79C2×Dic10—32no—
80C5×C4⋊C4—31no—
81C5×C4⋊C4—32no—
82C42×C5—32no—
83C42×C5—31no—
84#685—31no—
85#685—32no—
86#685—32no—
87#685—31no—
88#685—32no—
89#685C2×D312yes—
90C4⋊Dic5—31no—
91C4⋊Dic5—31no—
92C4⋊Dic5—32no—
93C4⋊Dic5C2×D311yescharacteristic
94#683—32no—
95#683C2×D312yes—
96C4×Dic5—32no—
97C4×Dic5—32no—
98#556—151noSylow
99C22×C3×C5C2411yescharacteristic
100C2×D15—21no—
101C2×D15—21no—
102C2×D15—21no—
103C2×C3×D5—21no—
104C2×C3×D5—21no—
105C2×C3×D5—21no—
106C3×C4×C5—22no—
107C3×C4×C5#4112yes—
108Dic15—22no—
109Dic15—21no—
110C3×Dic5—22no—
111C3×Dic5—21no—
112C5×Dic3—22no—
113C5×Dic3—21no—
114C5×Dic3#4112yes—
115C2×C3×Q8C2×D511yescharacteristic
116C22×C3×C4—51no—
117C2×#67—51no—
118C2×C4×D3—51no—
119C2×Dic6—52no—
120C3×C4⋊C4—52no—
121C3×C4⋊C4—51no—
122C3×C22⋊C4—52no—
123#217—51no—
124#217—52no—
125(C2×D3)⋊C4—52no—
126(C2×D3)⋊C4—52no—
127(C2×D3)⋊C4—51no—
128C4⋊Dic3—51no—
129C4⋊Dic3C2×D512yes—
130C4⋊Dic3C2×D511yescharacteristic
131Dic3⋊C4—52no—
132Dic3⋊C4—52no—
133Dic3⋊C4—51no—
134C4×Dic3—52no—
135C4×Dic3—52no—
136C4×Dic3C2×D512yes—
137C4×Dic3C2×D511yescharacteristic
138C22×D5—31no—
139C22×D5C22×D311yescharacteristic
140C5×Q8—22no—
141C2×C4×C5—31no—
142C2×C4×C5—32no—
143C2×C4×C5—31no—
144C2×C4×C5C22×D312yes—
145C2×C4×C5C22×D311yescharacteristic
146C2×Dic5—31no—
147C2×Dic5—32no—
148C2×Dic5C22×D311yescharacteristic
149C2×Dic5C22×D312yes—
150D20—62no—
151C4×D5—22no—
152C4×D5—62no—
153Dic10—64no—
154C4⋊Q8—151no—
155#126—152no—
156#126—152no—
157#124—152no—
158C22⋊Q8—51no—
159C22⋊Q8—151no—
160C4×Q8—31no—
161C4×Q8—152no—
162C4×D4—151no—
163#117—151no—
164#117—151no—
165C2×C3×C5C2×#4111yescharacteristic
166C2×C3×C5C2×#4111yescharacteristic
167C2×C3×C52−1+411yescharacteristic
168D15—41no—
169C3×D5—41no—
170C23×C3—51no—
171C22×D3—51no—
172C3×Q8—22no—
173C2×C3×C4—51no—
174C2×C3×C4—52no—
175C2×C3×C4—102no—
176C2×C3×C4C22×D512yes—
177C2×C3×C4C22×D511yescharacteristic
178#67—102no—
179C2×Dic3—51no—
180C2×Dic3—52no—
181C2×Dic3C22×D512yes—
182C2×Dic3C22×D511yescharacteristic
183C2×Dic3C22×D511yescharacteristic
184C4×D3—102no—
185Dic6—104no—
186C22×C5C23×D311yescharacteristic
187C2×D5—21no—
188C2×D5—21no—
189C2×D5—21no—
190C2×D5—61no—
191C2×D5—61no—
192C2×D5—61no—
193C4×C5—22no—
194C4×C5—32no—
195C4×C5—62no—
196C4×C5—61no—
197C4×C5#23712yes—
198Dic5—21no—
199Dic5—22no—
200Dic5—61no—
201Dic5—62no—
202C2×Q8—152no—
203C2×Q8D3×D511yescharacteristic
204C2×D4—151no—
205C22×C4—51no—
206C22×C4—151no—
207C4⋊C4—31no—
208C4⋊C4—32no—
209C4⋊C4—51no—
210C4⋊C4—52no—
211C4⋊C4—151no—
212C4⋊C4—152no—
213C4⋊C4—151no—
214C4⋊C4—152no—
215C22⋊C4—52no—
216C22⋊C4—152no—
217C22⋊C4—151no—
218C22⋊C4—152no—
219C22⋊C4—151no—
220C22⋊C4—152no—
221C42—31no—
222C42—32no—
223C42—152no—
224C42—152no—
225C3×C5#55611yescharacteristic, complemented, Hall
226C22×C3—101no—
227C22×C3—101no—
228C22×C3—101no—
229C22×C3C23×D511yescharacteristic
230C2×D3—101no—
231C2×D3—101no—
232C2×D3—101no—
233C3×C4—22no—
234C3×C4—101no—
235C3×C4—102no—
236C3×C4#70912yes—
237Dic3—22no—
238Dic3—21no—
239Dic3—101no—
240Dic3—102no—
241Dic3#71312yes—
242C2×C5C2×#23711yescharacteristic
243C2×C5#100711yescharacteristic
244C2×C5D3×#4111yescharacteristic
245D5—41no—
246D5—121no—
247C23—51no—
248C23—151no—
249Q8—22no—
250Q8—304no—
251D4—302no—
252C2×C4—31no—
253C2×C4—32no—
254C2×C4—31no—
255C2×C4—51no—
256C2×C4—52no—
257C2×C4—102no—
258C2×C4—151no—
259C2×C4—152no—
260C2×C4—302no—
261C2×C4C2×D3×D512yes—
262C2×C4C2×D3×D511yescharacteristic
263C2×C3—201no—
264C2×C3C2×#70911yescharacteristic
265C2×C3C2×#71311yescharacteristic
266C2×C3#415011yescharacteristic
267D3—201no—
268C5#564111yescharacteristic, complemented, Sylow
269C22—101no—
270C22—101no—
271C22—101no—
272C22—301no—
273C22—301no—
274C22—301no—
275C22C22×D3×D511yescharacteristic
276C4—22no—
277C4—32no—
278C4—62no—
279C4—61no—
280C4—102no—
281C4—101no—
282C4—302no—
283C4—301no—
284C4#677912yes—
285C3#6591811yescharacteristic, complemented, Sylow
286C2—201no—
287C2—601no—
288C2#9203011yescharacteristic
289C2D3×#71311yescharacteristic
290C2C2×#677911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×Q8C22
prime radicalC2×#1202C22
hypercenterC2×Q8D3×D5
hypocenterC3×C5#556
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. #91835C2semidirect
2. C5×Q8×Dic3C2semidirect
3. C3×#4092C2semidirect
4. #91469C2semidirect
6. #91361C2semidirect
7. #91358C2semidirect
9. #91347C2semidirect
10. #91337C2semidirect
11. #91324C2semidirect
39. #4092D3semidirect
66. Q8×Dic3D5semidirect
225. C3×C5#556semidirect
268. C5#5641semidirect
285. C3#65918semidirect

Maximal subgroups

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

subgroupindex
#918352
C5×Q8×Dic32
C3×#40922
#914692
C4×#12022
#913612
#913582
#913532
#913472
#913372
#913242
#659183
#56415