Finite Group Databasebeta

← #11861295

Subgroups — #11861295

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 353 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3797C211yesmaximal, characteristic
2C3⋊D3×C4⋊C8C211yesmaximal, characteristic
3C3×#4831C212yesmaximal, complemented
4#10590789C214yesmaximal, complemented
5#10590668C212yesmaximal
6#10590658C212yesmaximal
7C4×#3710C211yesmaximal, characteristic
8#10590258C212yesmaximal, complemented
9D3×#446—32nomaximal
10C2×#3797C411yescharacteristic
11C2×C8×C3⋊D3C2212yes—
12C42×C3⋊D3C2211yescharacteristic
13C3×C4×Dic6C2212yes—
14C4×#627C2212yes—
15#63900C411yescharacteristic
16#63883C412yes—
17C4×#624C2212yes—
18#63843C412yes—
19#63838C412yes—
20C2×#3710C2211yescharacteristic
21C2×#3710C2211yescharacteristic
22C32×C4⋊C8C2211yescharacteristic
23#63641C2212yes—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C3×#815C2214yes—
26C3×Dic3⋊C8C2214yes—
27C3×C4×C3⋊C8C2212yes—
28Dic3⋊(C3⋊C8)C2214yes—
29#63554C2214yes—
30#63553C2212yes—
31C4×D3×Q8—32no—
32C3×#446—32no—
33#5024—32no—
34D3×C4⋊C8—32no—
35D3×C4⋊C8—34no—
36D3×C4⋊C8—61no—
37#4831D312yescomplemented
38#4828—34no—
39D3×#97—34no—
40#4701—34no—
41C4×D3×C8—32no—
42#4679—32no—
43C2×C4×C3⋊D3C2×C411yescharacteristic
44C2×C4×C3⋊D3C2×C411yescharacteristic
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C3×Dic6C2×C412yes—
47C2×#627C2×C412yes—
48C2×#624C2×C412yes—
49C2×#624C2×C412yes—
50#3797—24no—
51C2×C32×C8C2312yes—
52C32×C42C2311yescharacteristic
53C4×C3⋊Dic3C2×C411yescharacteristic
54C4×C3⋊Dic3C2×C411yescharacteristic
55C4×C3⋊Dic3C2311yescharacteristic
56C2×C3⋊(C3⋊C8)C2312yes—
57C8×C3⋊D3—24no—
58C3×C4⋊Dic3C2×C412yes—
59C3×Dic3⋊C4C2×C414yes—
60C3×C4×Dic3C2314yes—
61C2×C3×C3⋊C8C2312yes—
62C2×C3×C3⋊C8C2312yes—
63#3724C2×C412yes—
64Dic3⋊Dic3C2×C414yes—
65Dic32C2×C414yes—
66#3710—22no—
67#3710Q814yescomplemented
68C2×#446—91noSylow
69C2×D3×Q8—32no—
70C3×C4×Q8—32no—
71Q8×Dic3—32no—
72C2×D3×C8—32no—
73C2×D3×C8—34no—
74C2×D3×C8—32no—
75C2×D3×C8—62no—
76D3×C4⋊C4—32no—
77D3×C4⋊C4—34no—
78#887—32no—
79#887—34no—
80C42×D3—32no—
81C42×D3—34no—
82C42×D3—61no—
83C4×Dic6—34no—
84C4×Dic6C2×D312yes—
85C3×C4⋊C8—21no—
86C3×C4⋊C8—34no—
87C3×C4⋊C8C2×D312yes—
88C3×#97—34no—
89C3×C4×C8—32no—
90#815—34no—
91#815C2×D314yes—
92Dic3⋊C8—34no—
93Dic3⋊C8—34no—
94Dic3⋊C8—62no—
95Dic3⋊C8C2×D314yes—
96C8×Dic3—32no—
97C8×Dic3—32no—
98C4⋊(C3⋊C8)—32no—
99C4⋊(C3⋊C8)—34no—
100C4⋊(C3⋊C8)—61no—
101#803—34no—
102C4×C3⋊C8C2×D312yes—
103C22×C3⋊D3C22×C411yescharacteristic
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2411yescharacteristic
107C2×C3⋊Dic3C22×C411yescharacteristic
108C2×C3⋊Dic3C22×C411yescharacteristic
109C2×C3⋊Dic3C22×C411yescharacteristic
110C4×C3⋊D3—22no—
111C4×C3⋊D3M1614yes—
112C4×C3⋊D3C2×Q812yes—
113C4×C3⋊D3#4112yes—
114C2×C3×Dic3C22×C414yes—
115C2×C3×Dic3C22×C414yes—
116C3×Dic6—24no—
117#627—24no—
118#624—24no—
119#624—24no—
120C32×C8—22no—
121C3⋊(C3⋊C8)—22no—
122C3×C3⋊C8—22no—
123C3×C3⋊C8C2×Q814yescomplemented
124C2×C4×Q8—91no—
125#446—32no—
126#446—92no—
127#446—94no—
128C2×C4⋊C8—92no—
129C2×C4⋊C8—91no—
130C2×#97—92no—
131C2×C4×C8—91no—
132C2×C3×Q8—32no—
133D3×Q8—68no—
134C2×C4×D3—32no—
135C2×C4×D3—32no—
136C2×C4×D3—32no—
137C2×C4×D3—34no—
138C2×C4×D3—34no—
139C2×C4×D3—61no—
140C2×C4×D3—61no—
141C2×C4×D3—61no—
142C2×Dic6—34no—
143C2×Dic6C4×D312yes—
144C2×C3×C8—22no—
145C2×C3×C8—32no—
146C2×C3×C8—32no—
147C2×C3×C8C22×D314yes—
148C3×C4⋊C4—34no—
149C3×C4⋊C4—32no—
150C3×C42—21no—
151C3×C42—34no—
152C3×C42C22×D312yes—
153C4⋊Dic3—34no—
154C4⋊Dic3C4×D312yes—
155Dic3⋊C4—34no—
156Dic3⋊C4—34no—
157Dic3⋊C4C4×D314yes—
158C4×Dic3—32no—
159C4×Dic3—32no—
160C4×Dic3—32no—
161C4×Dic3—34no—
162C4×Dic3—34no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—61no—
166C4×Dic3C22×D314yes—
167C2×C3⋊C8—34no—
168C2×C3⋊C8—62no—
169C2×C3⋊C8C22×D312yes—
170C2×C3⋊C8C22×D312yes—
171D3×C8—38no—
172D3×C8—64no—
173D3×C8—68no—
174D3×C8—124no—
175C22×C32C23×C411yescharacteristic
176C2×C3⋊D3C4×Q812yes—
177C2×C3⋊D3C2×M1612yes—
178C2×C3⋊D3#13112yes—
179C32×C4—21no—
180C32×C4C2×M1612yes—
181C32×C4C22×Q811yescharacteristic
182C32×C4C2×#4111yescharacteristic
183C3⋊Dic3—21no—
184C3⋊Dic3C4×Q812yes—
185C3⋊Dic3C2×M1612yes—
186C3×Dic3—24no—
187C3×Dic3—24no—
188C22×Q8—91no—
189C22×C8—91no—
190C22×C8—91no—
191C22×C8—92no—
192C4×Q8—32no—
193C4×Q8—92no—
194C4×Q8—92no—
195C4×Q8—92no—
196C2×C4⋊C4—92no—
197C2×C4⋊C4—91no—
198C2×C42—92no—
199C2×C42—91no—
200C4⋊C8—34no—
201C4⋊C8—94no—
202C4⋊C8—92no—
203C4⋊C8—91no—
204C4⋊C8D3211yescharacteristic
205#97—34no—
206#97—94no—
207C4×C8—32no—
208C4×C8—92no—
209C22×D3—32no—
210C22×D3—61no—
211C3×Q8—64no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—34no—
216C2×C3×C4—34no—
217C2×C3×C4C2×C4×D312yes—
218C2×C3×C4C2×C4×D312yes—
219C2×C3×C4C23×D312yes—
220C2×Dic3—32no—
221C2×Dic3—32no—
222C2×Dic3—32no—
223C2×Dic3—61no—
224C2×Dic3—61no—
225C2×Dic3—61no—
226C2×Dic3C2×C4×D314yes—
227C2×Dic3C2×C4×D314yes—
228C4×D3—38no—
229C4×D3—34no—
230C4×D3—34no—
231C4×D3—64no—
232C4×D3—62no—
233C4×D3—62no—
234C4×D3—68no—
235C4×D3—68no—
236C4×D3—64no—
237C4×D3—122no—
238Dic6—24no—
239Dic6—68no—
240C3×C8—24no—
241C3×C8—34no—
242C3×C8—42no—
243C3×C8—62no—
244C3⋊C8—22no—
245C3⋊C8—64no—
246C3⋊C8—122no—
247C3⋊C8D3×Q814yescomplemented
248C2×C32C2×C4×Q811yescharacteristic
249C2×C32C22×M1611yescharacteristic
250C2×C32C2×#13111yescharacteristic
251C3⋊D3#44614yescomplemented
252C2×Q8—32no—
253C2×Q8—92no—
254C2×Q8—184no—
255C22×C4—92no—
256C22×C4—92no—
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—91no—
260C2×C8—32no—
261C2×C8—32no—
262C2×C8—94no—
263C2×C8—92no—
264C2×C8—184no—
265C2×C8—182no—
266C2×C8C2×D3212yes—
267C4⋊C4—34no—
268C4⋊C4—32no—
269C4⋊C4—92no—
270C4⋊C4—94no—
271C42—34no—
272C42—94no—
273C42—91no—
274C42—91no—
275C42—91no—
276C42C2×D3211yescharacteristic
277C22×C3—21no—
278C22×C3C22×C4×D312yes—
279C2×D3—34no—
280C2×D3—34no—
281C2×D3—34no—
282C2×D3—62no—
283C2×D3—62no—
284C2×D3—62no—
285C3×C4—22no—
286C3×C4—22no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—64no—
291C3×C4—64no—
292C3×C4D3×M1614yes—
293C3×C4C2×D3×Q812yes—
294C3×C4D3×#4112yes—
295Dic3—24no—
296Dic3—24no—
297Dic3—34no—
298Dic3—34no—
299Dic3—62no—
300Dic3—62no—
301Dic3—62no—
302Dic3—121no—
303C32C2×#44611yescharacteristic, complemented, Sylow
304C23—91no—
305Q8—64no—
306Q8—184no—
307C2×C4—34no—
308C2×C4—34no—
309C2×C4—91no—
310C2×C4—91no—
311C2×C4—94no—
312C2×C4—92no—
313C2×C4—92no—
314C2×C4—91no—
315C2×C4—182no—
316C2×C4—184no—
317C2×C4—184no—
318C2×C4C4×D3211yescharacteristic
319C2×C4C4×D3211yescharacteristic
320C2×C4C22×D3211yescharacteristic
321C8—22no—
322C8—34no—
323C8—62no—
324C8—182no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3C4×D3×Q812yes—
329C2×C3C2×D3×M1612yes—
330C2×C3D3×#13112yes—
331D3—38no—
332D3—64no—
333C22—92no—
334C22—92no—
335C22—92no—
336C22C2×C4×D3211yescharacteristic
337C4—21no—
338C4—64no—
339C4—64no—
340C4—92no—
341C4—92no—
342C4—181no—
343C4#6379112yes—
344C4#6431211yescharacteristic
345C4D32×Q811yescharacteristic
346C3—21no—
347C3D3×#44612yescomplemented
348C2—94no—
349C2#1059436311yescharacteristic
350C2C2×#6379111yescharacteristic
351C2#1059470711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32C2×#446
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. C3×#4831C2semidirect
4. #10590789C2semidirect
8. #10590258C2semidirect
37. #4831D3semidirect
67. #3710Q8semidirect
123. C3×C3⋊C8C2×Q8semidirect
247. C3⋊C8D3×Q8semidirect
251. C3⋊D3#446semidirect
303. C32C2×#446semidirect
347. C3D3×#446semidirect

Maximal subgroups

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

subgroupindex
C4×#37972
C3⋊D3×C4⋊C82
C3×#48312
#105907892
#105906682
#105906582
C4×#37102
#105902582
D3×#4463