Finite Group Databasebeta

← #11868727

Subgroups — #11868727

Order 1152.

1128 conjugacy classes of subgroups.

The subgroup lattice has 321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595941C211yesmaximal, characteristic
2C2×C4×#634C211yesmaximal, characteristic
3C32×#423C211yesmaximal, characteristic
4#10592820C212yesmaximal
5#10592819C212yesmaximal
6#10592550C212yesmaximal, complemented
7#10592549C212yesmaximal, complemented
8#10592528C214yesmaximal, complemented
9#79068—34nomaximal
10C22×#634C2211yescharacteristic
11C2×C32×M16C2212yes—
12C2×C32×C42C2211yescharacteristic
13#64135C2212yes—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15#64133—21no—
16#64133—21no—
17C2×#3750—21no—
18C2×C4×C3⋊Dic3—21no—
19#64079C2212yes—
20#64078C2211yescharacteristic
21#64078C2211yescharacteristic
22C4×#634—21no—
23C4×#634—21no—
24C4×#634—21no—
25C4×#634—21no—
26C4×#634C2212yes—
27C4×#634C2212yes—
28C32×C4⋊C8C2212yes—
29C32×C4⋊C8C2212yes—
30#63645C2214yes—
31#63644C2214yes—
32#63643C2214yes—
33#63643C2214yes—
34#5470—34no—
35C2×C4×Dic6—34no—
36C3×#423D314yes—
37#5121—38no—
38#5120—38no—
39#4851—38no—
40#4850—38no—
41#4829—316no—
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C2×#634—21no—
48C2×#634—22no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634Q814yescomplemented
52C2×#634C2312yes—
53C32×M16—24no—
54C2×C32×C8C2314yes—
55C32×C42D411yescharacteristic
56C32×C42D411yescharacteristic
57C32×C42C2311yescharacteristic
58C32×C42C2311yescharacteristic
59#3757—22no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)C2312yes—
64C4⋊(C3⋊Dic3)C2312yes—
65C4⋊(C3⋊Dic3)C2312yes—
66#3750—22no—
67#3750—22no—
68#3750—22no—
69#3750—22no—
70C4×C3⋊Dic3—22no—
71C4×C3⋊Dic3—22no—
72C4×C3⋊Dic3—22no—
73#3078—91noSylow
74C22×Dic6—34no—
75C2×C3×M16C2×D318yes—
76C2×C3×C42C2×D314yes—
77#926—38no—
78C2×C4⋊Dic3—34no—
79#924—64no—
80#924—64no—
81C2×Dic3⋊C4—64no—
82C2×C4×Dic3—64no—
83#870—38no—
84#869—34no—
85#869—34no—
86C4×Dic6—38no—
87C4×Dic6—38no—
88C4×Dic6—64no—
89C4×Dic6—64no—
90C4×Dic6—64no—
91C4×Dic6—64no—
92C3×C4⋊C8C2×D318yes—
93C3×C4⋊C8C2×D318yes—
94#818—316no—
95#817—316no—
96#816—316no—
97#816—316no—
98C23×C32C2×D411yescharacteristic
99C2×C32×C4—22no—
100C2×C32×C4—41no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×Q812yes—
107C2×C32×C4#4112yes—
108C2×C32×C4C2411yescharacteristic
109C2×C3⋊Dic3—24no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—42no—
115#634—24no—
116#634—22no—
117#634—42no—
118#634—42no—
119#634C2×Q814yes—
120C32×C8—24no—
121#533—91no—
122C2×C4×Q8—91no—
123#479—94no—
124#477—92no—
125#475—92no—
126#428—92no—
127#423C3⋊D311yescharacteristic
128#419—92no—
129C22×C3×C4D1214yes—
130C22×C3×C4D1214yes—
131C22×C3×C4C22×D314yes—
132C22×Dic3—64no—
133C22×Dic3—64no—
134C2×Dic6—316no—
135C2×Dic6—38no—
136C2×Dic6—64no—
137C2×Dic6—68no—
138C2×Dic6—64no—
139C2×Dic6—64no—
140C3×M16—216no—
141C2×C3×C8C22×D3116yes—
142C3×C42D1214yes—
143C3×C42D1214yes—
144C3×C42C22×D314yes—
145C3×C42C22×D314yes—
146#217—68no—
147C4⋊Dic3—38no—
148C4⋊Dic3—38no—
149C4⋊Dic3—38no—
150C4⋊Dic3—64no—
151C4⋊Dic3—64no—
152C4⋊Dic3—64no—
153Dic3⋊C4—68no—
154Dic3⋊C4—68no—
155Dic3⋊C4—68no—
156Dic3⋊C4—68no—
157C4×Dic3—68no—
158C4×Dic3—68no—
159C4×Dic3—68no—
160C22×C32—21no—
161C22×C32—21no—
162C22×C32C22⋊Q812yes—
163C22×C32C22×D411yescharacteristic
164C32×C4—21no—
165C32×C4—21no—
166C32×C4—21no—
167C32×C4C22⋊Q812yes—
168C32×C4#13712yes—
169C32×C4C22×Q811yescharacteristic
170C32×C4C2×#4111yescharacteristic
171C3⋊Dic3—24no—
172C3⋊Dic3—42no—
173C3⋊Dic3—42no—
174C3⋊Dic3—42no—
175C22×Q8—91no—
176C2×M16C2×C3⋊D312yes—
177C4⋊Q8—91no—
178C4⋊Q8—91no—
179#125—92no—
180C22⋊Q8—181no—
181C22⋊Q8—181no—
182C4×Q8—92no—
183C4×Q8—92no—
184C4×Q8—181no—
185C4×Q8—181no—
186C4×Q8—181no—
187C4×Q8—181no—
188#117—92no—
189C2×C4⋊C4—91no—
190C2×C4⋊C4—181no—
191C2×C42—181no—
192C2×C42C2×C3⋊D311yescharacteristic
193#107—94no—
194#106—94no—
195C4⋊C8C2×C3⋊D312yes—
196C4⋊C8C2×C3⋊D312yes—
197#103—94no—
198#103—94no—
199C23×C3C2×D1214yes—
200C2×C3×C4—28no—
201C2×C3×C4—44no—
202C2×C3×C4C2×D1214yes—
203C2×C3×C4C2×D1214yes—
204C2×C3×C4C2×D1214yes—
205C2×C3×C4C2×D1214yes—
206C2×C3×C4C2×D1214yes—
207C2×C3×C4#23718yes—
208C2×C3×C4D3×Q818yes—
209C2×C3×C4C23×D314yes—
210C2×Dic3—616no—
211C2×Dic3—68no—
212C2×Dic3—68no—
213C2×Dic3—68no—
214C2×Dic3—68no—
215C2×Dic3—128no—
216Dic6—316no—
217Dic6—616no—
218Dic6—68no—
219Dic6—128no—
220Dic6—128no—
221C3×C8—216no—
222C2×C32—22no—
223C2×C32C2×C22⋊Q811yescharacteristic
224C2×C32C2×#13711yescharacteristic
225C2×C32#57511yescharacteristic
226C2×Q8—92no—
227C2×Q8—94no—
228C2×Q8—181no—
229C2×Q8—181no—
230C2×Q8—181no—
231C2×Q8—182no—
232C22×C4—181no—
233C22×C4—181no—
234C22×C4C4⋊(C3⋊D3)11yescharacteristic
235C22×C4C4⋊(C3⋊D3)11yescharacteristic
236C22×C4C22×C3⋊D311yescharacteristic
237M16—24no—
238C2×C8C22×C3⋊D314yes—
239C4⋊C4—92no—
240C4⋊C4—92no—
241C4⋊C4—92no—
242C4⋊C4—181no—
243C4⋊C4—182no—
244C4⋊C4—182no—
245C4⋊C4—182no—
246C4⋊C4—182no—
247C4⋊C4—181no—
248C4⋊C4—181no—
249C22⋊C4—182no—
250C42—182no—
251C42—182no—
252C42—182no—
253C42C4⋊(C3⋊D3)11yescharacteristic
254C42C4⋊(C3⋊D3)11yescharacteristic
255C42C22×C3⋊D311yescharacteristic
256C42C22×C3⋊D311yescharacteristic
257C22×C3—24no—
258C22×C3—24no—
259C22×C3#89718yes—
260C22×C3C22×D1214yes—
261C3×C4—24no—
262C3×C4—24no—
263C3×C4—24no—
264C3×C4#89718yes—
265C3×C4#90918yes—
266C3×C4C2×#23714yes—
267C3×C4C2×D3×Q814yes—
268Dic3—616no—
269Dic3—128no—
270Dic3—128no—
271Dic3—128no—
272C32#307811yescharacteristic, complemented, Sylow
273C23C2×C4⋊(C3⋊D3)11yescharacteristic
274Q8—94no—
275Q8—182no—
276Q8—184no—
277Q8—362no—
278Q8—362no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—182no—
282C2×C4—184no—
283C2×C4—182no—
284C2×C4—182no—
285C2×C4—182no—
286C2×C4—362no—
287C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
288C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
289C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
290C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
291C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
292C2×C4#383012yes—
293C2×C4Q8×C3⋊D312yes—
294C2×C4C23×C3⋊D311yescharacteristic
295C8—24no—
296C2×C3—28no—
297C2×C3C2×#89714yes—
298C2×C3C2×#90914yes—
299C2×C3#574814yes—
300C22—21no—
301C22—21no—
302C22#6410612yes—
303C22C22×C4⋊(C3⋊D3)11yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—184no—
308C4—362no—
309C4—362no—
310C4—362no—
311C4#6410612yes—
312C4#6411812yes—
313C4C2×#383011yescharacteristic
314C4C2×Q8×C3⋊D311yescharacteristic
315C3#7906814yescomplemented
316C2—22no—
317C2C2×#6410611yescharacteristic
318C2C2×#6411811yescharacteristic
319C2#1059621911yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#423C2
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenter#423C3⋊D3
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
6. #10592550C2semidirect
7. #10592549C2semidirect
8. #10592528C2semidirect
51. C2×#634Q8semidirect
272. C32#3078semidirect
315. C3#79068semidirect

Maximal subgroups

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

subgroupindex
#105959412
C2×C4×#6342
C32×#4232
#105928202
#105928192
#105925502
#105925492
#105925282
#790683