Finite Group Databasebeta

← #11859956

Subgroups — #11859956

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63802C211yesmaximal, characteristic
2#10594363C212yesmaximal
3C3⋊D3×#107C211yesmaximal, characteristic
4C3×#4873C212yesmaximal, complemented
5Dic3×Dic12C212yesmaximal, complemented
6C8×#624C211yesmaximal, characteristic
7#10590601C212yesmaximal
8#10590476C214yesmaximal, complemented
9C4×D3×Q16—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×#107C2211yescharacteristic
24#63645C2211yescharacteristic
25#63634C2212yes—
26C3×C8×Dic3C2212yes—
27C3×#810C2214yes—
28#63566C2214yes—
29Dic3×C3⋊C8C2212yes—
30C2×D3×Q16—32no—
31C4×D3×Q8—34no—
32C3×C4×Q16—32no—
33Dic3×Q16—32no—
34C4×#216—34no—
35D3×#107—32no—
36D3×#107—61no—
37#4873D312yescomplemented
38D3×#103—34no—
39#4790—34no—
40C4×Dic12—32no—
41C4×D3×C8—32no—
42C2×C4×C3⋊D3—22no—
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×C3×Dic6C2314yes—
45C2×#627—22no—
46C2×#624—22no—
47C2×#624D411yescharacteristic
48C2×#624D411yescharacteristic
49#3797—24no—
50#3797C2×C418yes—
51C2×C32×C8C2311yescharacteristic
52C32×C4⋊C4C2312yes—
53C4⋊(C3⋊Dic3)C2312yes—
54#3750—22no—
55C2×C3⋊(C3⋊C8)C2311yescharacteristic
56C8×C3⋊D3C2×C414yes—
57C3×Dic3⋊C4—24no—
58C3×C4×Dic3—24no—
59C3×C4×Dic3C2312yes—
60C2×C3×C3⋊C8C2312yes—
61C3×Dic12C2×C418yescomplemented
62Dic3⋊Dic3—24no—
63Dic32—24no—
64Dic32D412yes—
65#3718C2×C418yescomplemented
66#3710—22no—
67C2×C4×Q16—91noSylow
68C2×D3×Q8—34no—
69C2×C3×Q16—32no—
70C3×C4×Q8—34no—
71Q8×Dic3—34no—
72C2×#216—34no—
73D3×Q16—316no—
74C2×Dic12C2×D312yes—
75C2×D3×C8—32no—
76C2×D3×C8—32no—
77C2×D3×C8—61no—
78D3×C4⋊C4—34no—
79D3×C4⋊C4—62no—
80D3×C4⋊C4—64no—
81#887—64no—
82#887C2×D314yes—
83C42×D3—32no—
84C42×D3—64no—
85C4×Dic6—34no—
86C4×Dic6—64no—
87C3×#107—21no—
88C3×#107C2×D312yes—
89C3×#103—34no—
90C3×C4×C8—32no—
91#835—34no—
92#818—32no—
93#818—61no—
94#816—34no—
95C8×Dic3—32no—
96C8×Dic3C2×D312yes—
97#810C2×D314yes—
98#807—34no—
99#807—62no—
100C4×C3⋊C8—32no—
101C22×C3⋊D3C2×D411yescharacteristic
102C2×C32×C4—22no—
103C2×C32×C4C2411yescharacteristic
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3C2×D411yescharacteristic
106C4×C3⋊D3—44no—
107C4×C3⋊D3C22×C412yes—
108C4×C3⋊D3#4112yes—
109C2×C3×Dic3—24no—
110C2×C3×Dic3C2×D412yes—
111C2×C3×Dic3C2×D412yes—
112C3×Dic6—24no—
113C3×Dic6C22×C418yes—
114#627—28no—
115#624—28no—
116#624—22no—
117#624Q1614yescomplemented
118C32×C8C22×C412yes—
119C3⋊(C3⋊C8)C22×C412yes—
120C3×C3⋊C8—22no—
121C22×Q16—91no—
122C2×C4×Q8—92no—
123C4×Q16—32no—
124C4×Q16—92no—
125C4×Q16—94no—
126C2×#107—91no—
127C2×#103—92no—
128C2×C4×C8—91no—
129C2×C3×Q8—34no—
130D3×Q8—316no—
131D3×Q8—68no—
132C2×C4×D3—32no—
133C2×C4×D3—32no—
134C2×C4×D3—32no—
135C2×C4×D3—61no—
136C2×C4×D3—64no—
137C2×C4×D3—64no—
138C2×C4×D3—122no—
139C2×Dic6—64no—
140C2×Dic6C22×D314yes—
141C3×Q16—38no—
142C2×C3×C8—21no—
143C2×C3×C8—32no—
144C2×C3×C8C22×D312yes—
145C3×C4⋊C4—22no—
146C3×C4⋊C4—64no—
147C3×C4⋊C4C22×D314yes—
148C3×C42—32no—
149C3×C42—64no—
150#216—316no—
151C4⋊Dic3—34no—
152C4⋊Dic3—62no—
153C4⋊Dic3—64no—
154Dic3⋊C4—24no—
155Dic3⋊C4—64no—
156Dic3⋊C4—64no—
157Dic3⋊C4—122no—
158C4×Dic3—24no—
159C4×Dic3—32no—
160C4×Dic3—32no—
161C4×Dic3—64no—
162C4×Dic3—64no—
163C4×Dic3C22×D312yes—
164C2×C3⋊C8—32no—
165C2×C3⋊C8—61no—
166C2×C3⋊C8C22×D312yes—
167Dic12C4×D318yescomplemented
168D3×C8—38no—
169D3×C8—64no—
170D3×C8—64no—
171C22×C32C22×D411yescharacteristic
172C2×C3⋊D3C4×D412yes—
173C2×C3⋊D3C2×Q1612yes—
174C2×C3⋊D3#13512yes—
175C32×C4—42no—
176C32×C4C23×C411yescharacteristic
177C32×C4C2×#4111yescharacteristic
178C3⋊Dic3—42no—
179C3⋊Dic3C4×D412yes—
180C3×Dic3—28no—
181C3×Dic3—22no—
182C3×Dic3C2×Q1614yescomplemented
183C22×Q8—92no—
184C2×Q16—32no—
185C2×Q16—98no—
186C2×Q16—92no—
187C22×C8—91no—
188C22×C8—91no—
189C4×Q8—34no—
190C4×Q8—94no—
191C4×Q8—184no—
192C2×C4⋊C4—92no—
193C2×C4⋊C4—182no—
194C2×C42—91no—
195C2×C42—182no—
196#107—91no—
197#107—92no—
198#107D3211yescharacteristic
199#103—34no—
200#103—94no—
201C4×C8—32no—
202C4×C8—92no—
203C22×D3—32no—
204C22×D3—61no—
205C3×Q8—38no—
206C3×Q8—64no—
207C2×C3×C4—24no—
208C2×C3×C4—21no—
209C2×C3×C4—32no—
210C2×C3×C4—32no—
211C2×C3×C4—42no—
212C2×C3×C4—64no—
213C2×C3×C4C23×D312yes—
214C2×Dic3—24no—
215C2×Dic3—32no—
216C2×Dic3—61no—
217C2×Dic3—64no—
218C2×Dic3—122no—
219C2×Dic3D3×D412yes—
220C2×Dic3D3×D412yes—
221C4×D3—34no—
222C4×D3—34no—
223C4×D3—38no—
224C4×D3—62no—
225C4×D3—62no—
226C4×D3—64no—
227C4×D3—616no—
228C4×D3—128no—
229C4×D3—244no—
230Dic6—24no—
231Dic6—616no—
232Dic6C2×C4×D318yes—
233C3×C8—22no—
234C3×C8—62no—
235C3×C8C2×C4×D314yes—
236C3⋊C8—22no—
237C3⋊C8—34no—
238C3⋊C8—62no—
239C2×C32C2×C4×D411yescharacteristic
240C2×C32C22×Q1611yescharacteristic
241C2×C32C2×#13511yescharacteristic
242C3⋊D3C4×Q1614yescomplemented
243C2×Q8—34no—
244C2×Q8—98no—
245C2×Q8—182no—
246C2×Q8—184no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—182no—
251C22×C4—182no—
252Q16—38no—
253Q16—98no—
254C2×C8—32no—
255C2×C8—91no—
256C2×C8—94no—
257C2×C8—182no—
258C2×C8C2×D3211yescharacteristic
259C4⋊C4—64no—
260C4⋊C4—92no—
261C4⋊C4—182no—
262C4⋊C4—184no—
263C4⋊C4C2×D3212yes—
264C42—32no—
265C42—64no—
266C42—92no—
267C42—184no—
268C22×C3—21no—
269C22×C3C2×D3×D412yes—
270C2×D3—34no—
271C2×D3—34no—
272C2×D3—34no—
273C2×D3—62no—
274C2×D3—62no—
275C2×D3—62no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—34no—
279C3×C4—44no—
280C3×C4—62no—
281C3×C4—68no—
282C3×C4—82no—
283C3×C4C22×C4×D312yes—
284C3×C4D3×#4112yes—
285Dic3—22no—
286Dic3—28no—
287Dic3—34no—
288Dic3—62no—
289Dic3—124no—
290Dic3—242no—
291Dic3D3×Q1614yescomplemented
292C32C2×C4×Q1611yescharacteristic, complemented, Sylow
293C23—91no—
294Q8—38no—
295Q8—64no—
296Q8—188no—
297C2×C4—22no—
298C2×C4—32no—
299C2×C4—32no—
300C2×C4—64no—
301C2×C4—94no—
302C2×C4—91no—
303C2×C4—92no—
304C2×C4—92no—
305C2×C4—182no—
306C2×C4—188no—
307C2×C4—182no—
308C2×C4—364no—
309C2×C4C22×D3211yescharacteristic
310C8—62no—
311C8—92no—
312C8C4×D3212yes—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3C4×D3×D412yes—
317C2×C3C2×D3×Q1612yes—
318C2×C3D3×#13512yes—
319D3—38no—
320D3—64no—
321C22—92no—
322C22—92no—
323C22—92no—
324C22D32×D411yescharacteristic
325C4—34no—
326C4—42no—
327C4—68no—
328C4—62no—
329C4—92no—
330C4—362no—
331C4C2×C4×D3211yescharacteristic
332C4#6431911yescharacteristic
333C3—21no—
334C3C4×D3×Q1612yescomplemented
335C2—94no—
336C2#1059460511yescharacteristic
337C2#1059473011yescharacteristic
338C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C32×C4C24
hypercenter#107D32
hypocenterC32C2×C4×Q16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
4. C3×#4873C2semidirect
5. Dic3×Dic12C2semidirect
8. #10590476C2semidirect
22. #63802C4semidirect
37. #4873D3semidirect
61. C3×Dic12C2×C4semidirect
65. #3718C2×C4semidirect
117. #624Q16semidirect
167. Dic12C4×D3semidirect
182. C3×Dic3C2×Q16semidirect
242. C3⋊D3C4×Q16semidirect
291. Dic3D3×Q16semidirect
292. C32C2×C4×Q16semidirect
334. C3C4×D3×Q16semidirect

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×#1072
C3×#48732
Dic3×Dic122
C8×#6242
#105906012
#105904762
C4×D3×Q163