Finite Group Databasebeta

← #11860133

Subgroups — #11860133

Order 1152.

1025 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 1025 conjugacy classes of subgroups — too many to draw. Only its 232 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×#63802C211yesmaximal, characteristic
2#10594363C212yesmaximal
3C3⋊D3×#106C211yesmaximal, characteristic
4C3×#4853C212yesmaximal, complemented
5#10590812C212yesmaximal, complemented
6#10590668C211yesmaximal, characteristic
7#10590601C212yesmaximal
8#10590477C214yesmaximal, complemented
9D3×#441—32nomaximal
10C2×#3797C2212yes—
11C2×C8×C3⋊D3C2211yescharacteristic
12C4⋊C4×C3⋊D3C2212yes—
13C2×C3×Dic12C2212yes—
14C3×#887C2214yes—
15#63883—22no—
16C4×#624—22no—
17C4×#624C2211yescharacteristic
18Dic3×Dic6C2214yes—
19#63837—24no—
20C2×#3718C2212yes—
21C2×#3710C2211yescharacteristic
22#63802C418yescomplemented
23C32×#106C2211yescharacteristic
24#63644C2211yescharacteristic
25#63635C2212yes—
26C3×#815C2212yes—
27C3×#810C2214yes—
28#63566C2214yes—
29#63554C2212yes—
30C2×D3×Q16—32no—
31C4×D3×Q8—34no—
32C3×#441—32no—
33#5184—32no—
34#5030—34no—
35D3×#106—32no—
36D3×#106—61no—
37#4853D312yescomplemented
38D3×#103—34no—
39#4789—34no—
40#4716—32no—
41D3×#97—32no—
42C2×C4×C3⋊D3—22no—
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×C3×Dic6C2314yes—
45C2×#627—22no—
46C2×#624—22no—
47C2×#624D412yes—
48#3797—24no—
49#3797C2×C418yes—
50C2×C32×C8C2311yescharacteristic
51C32×C4⋊C4C2312yes—
52C4⋊(C3⋊Dic3)C2312yes—
53#3750—22no—
54C2×C3⋊(C3⋊C8)C2311yescharacteristic
55C8×C3⋊D3C2×C414yes—
56C3×Dic3⋊C4—24no—
57C3×C4×Dic3—24no—
58C3×C4×Dic3C2312yes—
59C2×C3×C3⋊C8C2312yes—
60C3×Dic12C2×C418yescomplemented
61Dic3⋊Dic3—24no—
62Dic32—24no—
63Dic32D412yes—
64#3718C2×C418yescomplemented
65#3710—22no—
66C2×#441—91noSylow
67C2×D3×Q8—34no—
68C2×C3×Q16—32no—
69C3×C4×Q8—34no—
70Q8×Dic3—34no—
71C2×#216—34no—
72D3×Q16—316no—
73C2×Dic12C2×D312yes—
74C2×D3×C8—32no—
75C2×D3×C8—32no—
76C2×D3×C8—61no—
77D3×C4⋊C4—34no—
78D3×C4⋊C4—62no—
79D3×C4⋊C4—64no—
80#887—64no—
81#887C2×D314yes—
82C42×D3—32no—
83C42×D3—64no—
84C4×Dic6—34no—
85C4×Dic6—64no—
86C3×#106—21no—
87C3×#106C2×D312yes—
88C3×#103—34no—
89C3×#97—32no—
90#835—34no—
91#817—32no—
92#817—61no—
93#816—34no—
94#815—32no—
95#815C2×D312yes—
96#810C2×D314yes—
97#808—34no—
98#808—62no—
99#803—32no—
100C22×C3⋊D3C2×D411yescharacteristic
101C2×C32×C4—22no—
102C2×C32×C4C2411yescharacteristic
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3C2×D411yescharacteristic
105C4×C3⋊D3—44no—
106C4×C3⋊D3C22×C412yes—
107C4×C3⋊D3#4112yes—
108C2×C3×Dic3—24no—
109C2×C3×Dic3C2×D414yes—
110C3×Dic6—24no—
111C3×Dic6C22×C418yes—
112#627—28no—
113#624—28no—
114#624—24no—
115C32×C8C22×C412yes—
116C3⋊(C3⋊C8)C22×C412yes—
117C3×C3⋊C8—22no—
118C22×Q16—91no—
119C2×C4×Q8—92no—
120#441—32no—
121#441—92no—
122#441—94no—
123C2×#106—91no—
124C2×#103—92no—
125C2×#97—91no—
126C2×C3×Q8—34no—
127D3×Q8—316no—
128D3×Q8—68no—
129C2×C4×D3—32no—
130C2×C4×D3—34no—
131C2×C4×D3—61no—
132C2×C4×D3—64no—
133C2×C4×D3—64no—
134C2×C4×D3—122no—
135C2×Dic6—64no—
136C2×Dic6C22×D314yes—
137C3×Q16—38no—
138C2×C3×C8—21no—
139C2×C3×C8—32no—
140C2×C3×C8C22×D312yes—
141C3×C4⋊C4—22no—
142C3×C4⋊C4—64no—
143C3×C4⋊C4C22×D314yes—
144C3×C42—32no—
145C3×C42—64no—
146#216—316no—
147C4⋊Dic3—34no—
148C4⋊Dic3—62no—
149C4⋊Dic3—64no—
150Dic3⋊C4—24no—
151Dic3⋊C4—64no—
152Dic3⋊C4—64no—
153Dic3⋊C4—122no—
154C4×Dic3—24no—
155C4×Dic3—34no—
156C4×Dic3—64no—
157C4×Dic3—64no—
158C4×Dic3C22×D312yes—
159C2×C3⋊C8—32no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8C22×D312yes—
162Dic12C4×D318yescomplemented
163D3×C8—38no—
164D3×C8—64no—
165D3×C8—64no—
166C22×C32C22×D411yescharacteristic
167C2×C3⋊D3C4×D412yes—
168C2×C3⋊D3#13714yes—
169C32×C4—42no—
170C32×C4C23×C411yescharacteristic
171C32×C4C2×#4111yescharacteristic
172C3⋊Dic3—42no—
173C3⋊Dic3C4×D412yes—
174C3×Dic3—28no—
175C3×Dic3—24no—
176C22×Q8—92no—
177C2×Q16—32no—
178C2×Q16—98no—
179C2×Q16—92no—
180C22×C8—91no—
181C22×C8—91no—
182C4×Q8—34no—
183C4×Q8—94no—
184C4×Q8—184no—
185C2×C4⋊C4—92no—
186C2×C4⋊C4—182no—
187C2×C42—91no—
188C2×C42—182no—
189#106—91no—
190#106—92no—
191#106D3211yescharacteristic
192#103—34no—
193#103—94no—
194#97—32no—
195#97—92no—
196C22×D3—32no—
197C22×D3—61no—
198C3×Q8—38no—
199C3×Q8—64no—
200C2×C3×C4—24no—
201C2×C3×C4—21no—
202C2×C3×C4—34no—
203C2×C3×C4—42no—
204C2×C3×C4—64no—
205C2×C3×C4C23×D312yes—
206C2×Dic3—24no—
207C2×Dic3—32no—
208C2×Dic3—61no—
209C2×Dic3—64no—
210C2×Dic3—122no—
211C2×Dic3D3×D414yes—
212C4×D3—34no—
213C4×D3—34no—
214C4×D3—62no—
215C4×D3—62no—
216C4×D3—68no—
217C4×D3—616no—
218C4×D3—128no—
219C4×D3—244no—
220Dic6—24no—
221Dic6—616no—
222Dic6C2×C4×D318yes—
223C3×C8—22no—
224C3×C8—62no—
225C3×C8C2×C4×D314yes—
226C3⋊C8—22no—
227C3⋊C8—34no—
228C3⋊C8—62no—
229C2×C32C2×C4×D411yescharacteristic
230C2×C32C2×#13712yes—
231C3⋊D3#44114yescomplemented
232C2×Q8—34no—
233C2×Q8—98no—
234C2×Q8—182no—
235C2×Q8—184no—
236C22×C4—92no—
237C22×C4—91no—
238C22×C4—182no—
239C22×C4—182no—
240Q16—38no—
241Q16—98no—
242C2×C8—32no—
243C2×C8—91no—
244C2×C8—94no—
245C2×C8—182no—
246C2×C8C2×D3211yescharacteristic
247C4⋊C4—64no—
248C4⋊C4—92no—
249C4⋊C4—182no—
250C4⋊C4—184no—
251C4⋊C4C2×D3212yes—
252C42—32no—
253C42—64no—
254C42—92no—
255C42—184no—
256C22×C3—21no—
257C22×C3C2×D3×D412yes—
258C2×D3—38no—
259C2×D3—34no—
260C2×D3—62no—
261C2×D3—64no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—44no—
265C3×C4—64no—
266C3×C4—68no—
267C3×C4—82no—
268C3×C4C22×C4×D312yes—
269C3×C4D3×#4112yes—
270Dic3—24no—
271Dic3—28no—
272Dic3—34no—
273Dic3—62no—
274Dic3—124no—
275Dic3—242no—
276C32C2×#44111yescharacteristic, complemented, Sylow
277C23—91no—
278Q8—38no—
279Q8—64no—
280Q8—188no—
281C2×C4—22no—
282C2×C4—34no—
283C2×C4—64no—
284C2×C4—91no—
285C2×C4—92no—
286C2×C4—92no—
287C2×C4—184no—
288C2×C4—188no—
289C2×C4—182no—
290C2×C4—364no—
291C2×C4C22×D3211yescharacteristic
292C8—62no—
293C8—92no—
294C8C4×D3212yes—
295C2×C3—21no—
296C2×C3—22no—
297C2×C3C4×D3×D412yes—
298C2×C3D3×#13714yes—
299D3—38no—
300D3—64no—
301C22—92no—
302C22—94no—
303C22D32×D411yescharacteristic
304C4—42no—
305C4—68no—
306C4—64no—
307C4—92no—
308C4—362no—
309C4C2×C4×D3211yescharacteristic
310C4#6431911yescharacteristic
311C3—21no—
312C3D3×#44112yescomplemented
313C2—94no—
314C2#1059460511yescharacteristic
315C2#1059474212yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32C2×#441
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
4. C3×#4853C2semidirect
5. #10590812C2semidirect
8. #10590477C2semidirect
22. #63802C4semidirect
37. #4853D3semidirect
60. C3×Dic12C2×C4semidirect
64. #3718C2×C4semidirect
162. Dic12C4×D3semidirect
231. C3⋊D3#441semidirect
276. C32C2×#441semidirect
312. C3D3×#441semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
#105943632
C3⋊D3×#1062
C3×#48532
#105908122
#105906682
#105906012
#105904772
D3×#4413