Finite Group Databasebeta

← #11776196

Subgroups — #11776196

Order 1152.

493 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5470C211yesmaximal, characteristic
2C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic
3C3×#4925C211yesmaximal, characteristic
4#10589095C212yesmaximal, complemented
5#10589093C212yesmaximal, complemented
6#71828—31nomaximal
7#70776—31nomaximal
8C2×C32×C42C2211yescharacteristic
9C22×C3⋊(C3⋊C8)—21no—
10C3×#926—21no—
11C3×#924—21no—
12C3×#924C412yes—
13C3×#870—21no—
14C3×#869C2211yescharacteristic
15C3×#869C2211yescharacteristic
16C3×C4×Dic6—21no—
17C3×C4×Dic6C412yes—
18C4⋊(C3⋊(C3⋊C8))—21no—
19C4⋊(C3⋊(C3⋊C8))C2212yes—
20C3×#830—21no—
21C3×C4⋊(C3⋊C8)C2212yes—
22C3×C4×C3⋊C8—21no—
23C3×#533—31no—
24#5470D311yescharacteristic
25C3×#431—31no—
26#4925D311yescharacteristic
27C2×C4⋊(C3⋊C8)—31no—
28C2×C4⋊(C3⋊C8)—31no—
29C2×C4⋊(C3⋊C8)—61no—
30#4547—32no—
31#4546—32no—
32#4482—32no—
33#4481—32no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C2×C3×Dic6—21no—
38C2×C3×Dic6C2×C412yes—
39C32×C42C2×C411yescharacteristic
40C32×C42D411yescharacteristic
41C32×C42D411yescharacteristic
42C32×C42C2311yescharacteristic
43C2×C3⋊(C3⋊C8)—22no—
44C2×C3⋊(C3⋊C8)—42no—
45C3×#217—22no—
46C3×C4⋊Dic3—21no—
47C3×C4⋊Dic3—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3C2×C412yes—
50C3×Dic3⋊C4—22no—
51C3×Dic3⋊C4—22no—
52C3×C4×Dic3—22no—
53C2×C3×C3⋊C8—22no—
54#1542—91noSylow
55C3×C4⋊Q8—31no—
56C3×C4⋊Q8—31no—
57C3×#125—61no—
58C3×C22⋊Q8—32no—
59C3×C22⋊Q8—61no—
60C3×C4×Q8—32no—
61C3×C4×Q8—61no—
62C3×#117—61no—
63C2×C3×C42—21no—
64C2×C3×C42C2×D311yescharacteristic
65C2×C3×C42C2×D311yescharacteristic
66#926—21no—
67#924—21no—
68#924Dic312yes—
69C22×C3⋊C8—62no—
70C22×C3⋊C8—61no—
71C22×C3⋊C8—61no—
72#870—21no—
73#869C2×D311yescharacteristic
74#869C2×D311yescharacteristic
75C4×Dic6—21no—
76C4×Dic6Dic312yes—
77C3×C4⋊C8—32no—
78C3×C22⋊C8—61no—
79C3×C4×C8—61no—
80#830—21no—
81C4⋊(C3⋊C8)—32no—
82C4⋊(C3⋊C8)—32no—
83C4⋊(C3⋊C8)—62no—
84C4⋊(C3⋊C8)—62no—
85C4⋊(C3⋊C8)—61no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)C2×D312yes—
88C4×C3⋊C8—21no—
89C23×C32C22⋊C411yescharacteristic
90C2×C32×C4—22no—
91C2×C32×C4—41no—
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4SD1612yes—
96C2×C32×C4Q1612yes—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C3×Dic6—42no—
103C3×Dic6—42no—
104C3⋊(C3⋊C8)—42no—
105C3×C3⋊C8—42no—
106#533—31no—
107#431—31no—
108C2×C4⋊C8—91no—
109#333—92no—
110#332—92no—
111C2×C3×Q8—32no—
112C2×C3×Q8—61no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4C4×D311yescharacteristic
117C22×C3×C4D1211yescharacteristic
118C22×C3×C4C2×Dic311yescharacteristic
119C22×C3×C4#6711yescharacteristic
120C22×C3×C4#6711yescharacteristic
121C22×C3×C4#6711yescharacteristic
122C2×Dic6—21no—
123C2×Dic6C2×Dic312yes—
124C2×C3×C8—62no—
125C3×C4⋊C4—32no—
126C3×C4⋊C4—62no—
127C3×C4⋊C4—62no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C22⋊C4—62no—
132C3×C42—21no—
133C3×C42—21no—
134C3×C42—21no—
135C3×C42—21no—
136C3×C42—62no—
137C3×C42C4×D311yescharacteristic
138C3×C42D1211yescharacteristic
139C3×C42C2×Dic311yescharacteristic
140C3×C42#6711yescharacteristic
141C3×C42#6711yescharacteristic
142C3×C42#6711yescharacteristic
143C3×C42C22×D311yescharacteristic
144C3×C42C22×D311yescharacteristic
145#217—22no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3—21no—
149C4⋊Dic3C2×Dic312yes—
150Dic3⋊C4—22no—
151Dic3⋊C4—22no—
152C4×Dic3—22no—
153C2×C3⋊C8—22no—
154C2×C3⋊C8—64no—
155C2×C3⋊C8—62no—
156C2×C3⋊C8—62no—
157C2×C3⋊C8—124no—
158C2×C3⋊C8—122no—
159C2×C3⋊C8—122no—
160C22×C32—21no—
161C22×C32—21no—
162C22×C32#10312yes—
163C22×C32C2×C22⋊C411yescharacteristic
164C32×C4—21no—
165C32×C4—21no—
166C32×C4—21no—
167C32×C4#10312yes—
168C32×C4C2×SD1611yescharacteristic
169C32×C4C2×Q1611yescharacteristic
170C32×C4#13512yes—
171C3×Dic3—42no—
172C3×Dic3—42no—
173C22×C8—181no—
174C4⋊Q8—31no—
175C4⋊Q8—31no—
176#125—61no—
177C22⋊Q8—32no—
178C22⋊Q8—61no—
179C4×Q8—32no—
180C4×Q8—61no—
181#117—61no—
182C2×C42D3211yescharacteristic
183C4⋊C8—32no—
184C4⋊C8—92no—
185C4⋊C8—181no—
186C22⋊C8—61no—
187C4×C8—61no—
188C23×C3—21no—
189C23×C3(C2×D3)⋊C411yescharacteristic
190C23×C3#21711yescharacteristic
191C3×Q8—122no—
192C3×Q8—122no—
193C2×C3×C4—24no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4—42no—
207C2×C3×C4—62no—
208C2×C3×C4—62no—
209C2×C3×C4#20412yes—
210C2×C3×C4Dic1212yes—
211C2×C3×C4(C2×D3)⋊C411yescharacteristic
212C2×C3×C4(C2×D3)⋊C411yescharacteristic
213C2×C3×C4(C2×D3)⋊C411yescharacteristic
214C2×C3×C4#21512yes—
215C2×C3×C4#21612yes—
216C2×C3×C4#21711yescharacteristic
217C2×C3×C4#21711yescharacteristic
218C2×C3×C4#21711yescharacteristic
219C2×C3×C4C2×C4×D311yescharacteristic
220C2×C3×C4C2×D1211yescharacteristic
221C2×C3×C4C22×Dic311yescharacteristic
222C2×C3×C4C2×#6711yescharacteristic
223C2×C3×C4C2×#6711yescharacteristic
224C2×C3×C4C2×#6711yescharacteristic
225C2×Dic3—22no—
226C2×Dic3—22no—
227Dic6—42no—
228Dic6—42no—
229C3×C8—122no—
230C3⋊C8—42no—
231C3⋊C8—124no—
232C3⋊C8—122no—
233C3⋊C8—122no—
234C2×C32—22no—
235C2×C32#41311yescharacteristic
236C2×C32C2×#10311yescharacteristic
237C2×C32#41611yescharacteristic
238C2×Q8—32no—
239C2×Q8—61no—
240C22×C4D3×Dic311yescharacteristic
241C22×C4#62511yescharacteristic
242C22×C4#62611yescharacteristic
243C2×C8—62no—
244C2×C8—182no—
245C2×C8—362no—
246C4⋊C4—32no—
247C4⋊C4—62no—
248C4⋊C4—62no—
249C4⋊C4—61no—
250C4⋊C4—61no—
251C4⋊C4—61no—
252C22⋊C4—62no—
253C42—62no—
254C42D3×Dic311yescharacteristic
255C42#62511yescharacteristic
256C42#62611yescharacteristic
257C42C2×D3211yescharacteristic
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—22no—
265C22×C3—21no—
266C22×C3#81612yes—
267C22×C3#83512yes—
268C22×C3C2×(C2×D3)⋊C411yescharacteristic
269C22×C3C2×#21711yescharacteristic
270C3×C4—22no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—41no—
282C3×C4—41no—
283C3×C4—122no—
284C3×C4—122no—
285C3×C4#81612yes—
286C3×C4#83512yes—
287C3×C4C2×#20411yescharacteristic
288C3×C4C2×Dic1211yescharacteristic
289C3×C4C2×#21511yescharacteristic
290C3×C4C2×#21611yescharacteristic
291C3×C4#95012yes—
292C3×C4#95012yes—
293Dic3—42no—
294Dic3—42no—
295C32#154211yescharacteristic, complemented, Sylow
296C23(C2×D3)⋊Dic311yescharacteristic
297Q8—122no—
298Q8—122no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—62no—
302C2×C4—62no—
303C2×C4#371712yes—
304C2×C4#371912yes—
305C2×C4(C2×D3)⋊Dic311yescharacteristic
306C2×C4(C2×D3)⋊Dic311yescharacteristic
307C2×C4(C2×D3)⋊Dic311yescharacteristic
308C2×C4C2×D3×Dic311yescharacteristic
309C2×C4C2×#62511yescharacteristic
310C2×C4C2×#62611yescharacteristic
311C8—122no—
312C8—362no—
313C2×C3—24no—
314C2×C3—22no—
315C2×C3—22no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3#500211yescharacteristic
320C2×C3C2×#81611yescharacteristic
321C2×C3#513211yescharacteristic
322C2×C3C2×#83511yescharacteristic
323C2×C3#523311yescharacteristic
324C2×C3#523711yescharacteristic
325C22—21no—
326C22—21no—
327C22#6356612yes—
328C22C2×(C2×D3)⋊Dic311yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—122no—
333C4—122no—
334C4#6356612yes—
335C4#6382212yes—
336C4C2×#371711yescharacteristic
337C4C2×#371911yescharacteristic
338C3—21no—
339C3#7077611yescharacteristic, complemented
340C3#7182811yescharacteristic, complemented
341C2—22no—
342C2#1059107611yescharacteristic
343C2#1059108311yescharacteristic
344C2C2×#6356611yescharacteristic
subgroupG/H
centerC2×C4(C2×D3)⋊Dic3
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1542
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #10589095C2semidirect
5. #10589093C2semidirect
295. C32#1542semidirect
339. C3#70776semidirect
340. C3#71828semidirect

Maximal subgroups

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

subgroupindex
C3×#54702
C2×C4⋊(C3⋊(C3⋊C8))2
C3×#49252
#105890952
#105890932
#718283
#707763