Finite Group Databasebeta

← #11776191

Subgroups — #11776191

Order 1152.

456 conjugacy classes of subgroups.

The subgroup lattice has 377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593859C211yesmaximal, characteristic
2C3×#4833C211yesmaximal, characteristic
3D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
4#10589348C211yesmaximal, characteristic, complemented
5C3×#4481C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#70776—31nomaximal
9#68481—31nomaximal
10#64078C2211yescharacteristic
11C3×C42×D3C2211yescharacteristic
12C3×#869C2211yescharacteristic
13#63869—21no—
14#63857—21no—
15#63856C412yes—
16#63844—21no—
17Dic3×Dic6C412yes—
18#63841—21no—
19C2×D3×C3⋊C8—21no—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×(C2×D3)⋊C8—21no—
23C3×C8×Dic3—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26Dic3⋊(C3⋊C8)—21no—
27#5728—31no—
28#5470—31no—
29C3×#431—31no—
30C2×C4⋊(C3⋊C8)—31no—
31#4833D311yescharacteristic
32D3×C4⋊C8—31no—
33C3×#333—31no—
34#4546—31no—
35#4486—31no—
36#4482—31no—
37#4482—31no—
38#4482—31no—
39#4482—61no—
40#4481—31no—
41#4481D311yescharacteristic, complemented
42C2×#634—21no—
43C2×C3×C4×D3C2×C411yescharacteristic
44C2×C3×C4×D3D411yescharacteristic
45C2×C3×C4×D3D411yescharacteristic
46C2×C3×Dic6C2×C412yes—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)C2×C412yes—
51C2×C3⋊(C3⋊C8)—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4×Dic3C2×C411yescharacteristic
55C3×C4×Dic3D411yescharacteristic
56C3×C4×Dic3D411yescharacteristic
57C2×C3×C3⋊C8—21no—
58C2×C3×C3⋊C8—21no—
59#3724—22no—
60Dic3⋊Dic3—22no—
61(C2×D3)⋊Dic3—22no—
62Dic32—22no—
63D3×C3⋊C8—42no—
64#1542—91noSylow
65C3×C4⋊Q8—31no—
66C2×C3×C42—31no—
67#946—32no—
68Q8×Dic3—32no—
69#926—61no—
70#924—32no—
71#924—61no—
72C22×C3⋊C8—61no—
73C2×D3×C8—61no—
74#897—61no—
75#892—61no—
76#890—61no—
77#887—61no—
78C42×D3C2×D311yescharacteristic
79#870—61no—
80#869—31no—
81#869—31no—
82#869—61no—
83#869C2×D311yescharacteristic
84C4×Dic6—32no—
85C4×Dic6—61no—
86C3×C4⋊C8—21no—
87C3×C4⋊C8—31no—
88C3×C4⋊C8—31no—
89C3×C4⋊C8C2×D311yescharacteristic
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C22⋊C8—61no—
92C3×C4×C8—61no—
93(C2×D3)⋊C8—21no—
94Dic3⋊C8—61no—
95C8×Dic3—21no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—61no—
99C4⋊(C3⋊C8)—61no—
100C4⋊(C3⋊C8)C2×D311yescharacteristic
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C22×C3×D3C22⋊C411yescharacteristic
103C2×C32×C4C22×C411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C3⋊Dic3—22no—
107#634—41no—
108#634—41no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3C22⋊C411yescharacteristic
111C2×C3×Dic3C22⋊C411yescharacteristic
112C2×C3×Dic3C22⋊C411yescharacteristic
113C3×C4×D3—21no—
114C3×C4×D3—21no—
115C3×C4×D3—41no—
116C3×C4×D3SD1612yes—
117C3×C4×D3Q1612yes—
118C3×Dic6—42no—
119C32×C8—41no—
120C3⋊(C3⋊C8)—41no—
121C3×C3⋊C8—41no—
122C3×C3⋊C8—41no—
123#533—91no—
124#431—31no—
125C2×C4⋊C8—91no—
126#333—31no—
127#333—91no—
128#332—91no—
129#332—91no—
130C2×C3×Q8—32no—
131C22×C3×C4—31no—
132C22×C3×C4—31no—
133C22×C3×C4—31no—
134C2×C4×D3C4×D311yescharacteristic
135C2×C4×D3D1211yescharacteristic
136C2×C4×D3#6711yescharacteristic
137C2×Dic6—61no—
138C2×Dic6—61no—
139C2×Dic6—121no—
140C2×Dic6C4×D312yes—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8—41no—
144C2×C3×C8—61no—
145C2×C3×C8—61no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C42—21no—
149C3×C42—31no—
150C3×C42—31no—
151C3×C42—31no—
152C3×C42C22×D311yescharacteristic
153C3×C42C22×D311yescharacteristic
154#217—62no—
155(C2×D3)⋊C4—62no—
156C4⋊Dic3—21no—
157C4⋊Dic3—21no—
158C4⋊Dic3—32no—
159C4⋊Dic3—32no—
160C4⋊Dic3—62no—
161C4⋊Dic3—61no—
162C4⋊Dic3—61no—
163C4⋊Dic3—62no—
164C4⋊Dic3—121no—
165Dic3⋊C4—62no—
166Dic3⋊C4—62no—
167Dic3⋊C4—62no—
168C4×Dic3—62no—
169C4×Dic3—62no—
170C4×Dic3C4×D311yescharacteristic
171C4×Dic3D1211yescharacteristic
172C4×Dic3#6711yescharacteristic
173C2×C3⋊C8—21no—
174C2×C3⋊C8—21no—
175C2×C3⋊C8—61no—
176C2×C3⋊C8—61no—
177C2×C3⋊C8—121no—
178C2×C3⋊C8—122no—
179D3×C8—122no—
180C22×C32C2×C22⋊C411yescharacteristic
181C2×C3×D3—21no—
182C2×C3×D3—21no—
183C2×C3×D3#10312yes—
184C32×C4—21no—
185C32×C4C2×SD1611yescharacteristic
186C32×C4C2×Q1611yescharacteristic
187C32×C4#13511yescharacteristic
188C32×C4#13511yescharacteristic
189C3⋊Dic3—42no—
190C3×Dic3—21no—
191C3×Dic3—21no—
192C3×Dic3—42no—
193C3×Dic3#10312yes—
194C22×C8—181no—
195C4⋊Q8—31no—
196C4⋊Q8—91no—
197#125—181no—
198C22⋊Q8—92no—
199C22⋊Q8—181no—
200C4×Q8—92no—
201C4×Q8—181no—
202#117—181no—
203C2×C42—31no—
204C4⋊C8—31no—
205C4⋊C8—31no—
206C4⋊C8—91no—
207C4⋊C8—181no—
208C4⋊C8D3211yescharacteristic
209C22⋊C8—61no—
210C4×C8—61no—
211C23×C3—31no—
212C22×D3(C2×D3)⋊C411yescharacteristic
213C3×Q8—122no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—31no—
218C2×C3×C4—32no—
219C2×C3×C4—32no—
220C2×C3×C4—31no—
221C2×C3×C4—31no—
222C2×C3×C4—61no—
223C2×C3×C4—61no—
224C2×C3×C4—62no—
225C2×C3×C4—121no—
226C2×C3×C4C2×C4×D311yescharacteristic
227C2×C3×C4C2×C4×D311yescharacteristic
228C2×C3×C4C2×D1211yescharacteristic
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4D3×D411yescharacteristic
231C2×C3×C4C2×#6711yescharacteristic
232C2×Dic3—22no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—122no—
236C2×Dic3(C2×D3)⋊C411yescharacteristic
237C2×Dic3(C2×D3)⋊C411yescharacteristic
238C2×Dic3(C2×D3)⋊C411yescharacteristic
239C4×D3—21no—
240C4×D3—21no—
241C4×D3—41no—
242C4×D3#20412yes—
243C4×D3Dic1212yes—
244Dic6—42no—
245Dic6—121no—
246Dic6—121no—
247Dic6—121no—
248Dic6—121no—
249Dic6—241no—
250Dic6—241no—
251C3×C8—41no—
252C3×C8—41no—
253C3×C8—81no—
254C3×C8—121no—
255C3×C8—121no—
256C3⋊C8—41no—
257C3⋊C8—41no—
258C3⋊C8—121no—
259C3⋊C8—121no—
260C3⋊C8—241no—
261C2×C32#41311yescharacteristic
262C2×C32C2×#10311yescharacteristic
263C2×C32#41611yescharacteristic
264C3×D3—22no—
265C2×Q8—32no—
266C2×Q8—181no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—31no—
270C2×C8—21no—
271C2×C8—61no—
272C2×C8—61no—
273C2×C8—181no—
274C2×C8—362no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—92no—
278C4⋊C4—182no—
279C4⋊C4—182no—
280C4⋊C4—181no—
281C22⋊C4—182no—
282C42—31no—
283C42—31no—
284C42—31no—
285C42—182no—
286C42C2×D3211yescharacteristic
287C22×C3—21no—
288C22×C3—32no—
289C22×C3—61no—
290C22×C3—61no—
291C22×C3D3×C22⋊C411yescharacteristic
292C22×C3C2×(C2×D3)⋊C411yescharacteristic
293C2×D3—21no—
294C2×D3—21no—
295C2×D3#81612yes—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—32no—
303C3×C4—41no—
304C3×C4—61no—
305C3×C4—61no—
306C3×C4—122no—
307C3×C4C2×#20411yescharacteristic
308C3×C4C2×Dic1211yescharacteristic
309C3×C4D3×SD1611yescharacteristic
310C3×C4#91611yescharacteristic
311C3×C4D3×Q1611yescharacteristic
312C3×C4#91911yescharacteristic
313C3×C4#95011yescharacteristic
314C3×C4#95011yescharacteristic
315Dic3—21no—
316Dic3—21no—
317Dic3—42no—
318Dic3—122no—
319Dic3—122no—
320Dic3—242no—
321Dic3#81612yes—
322C32#154211yescharacteristic, complemented, Sylow
323C23—31no—
324Q8—122no—
325Q8—361no—
326Q8—361no—
327C2×C4—31no—
328C2×C4—32no—
329C2×C4—32no—
330C2×C4—31no—
331C2×C4—31no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—62no—
335C2×C4—121no—
336C2×C4—182no—
337C2×C4C4×D3211yescharacteristic
338C2×C4D3×D1211yescharacteristic
339C2×C4D3×#6711yescharacteristic
340C8—41no—
341C8—121no—
342C8—121no—
343C8—361no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—62no—
348C2×C3#474511yescharacteristic
349C2×C3D3×#10311yescharacteristic
350C2×C3#480411yescharacteristic
351C2×C3#500211yescharacteristic
352C2×C3C2×#81611yescharacteristic
353C2×C3#513211yescharacteristic
354D3—22no—
355C22—32no—
356C22—61no—
357C22—61no—
358C22D3×(C2×D3)⋊C411yescharacteristic
359C4—21no—
360C4—32no—
361C4—61no—
362C4—61no—
363C4—122no—
364C4—362no—
365C4D3×#20411yescharacteristic
366C4D3×Dic1211yescharacteristic
367C4#6393511yescharacteristic
368C4#6394911yescharacteristic
369C3—21no—
370C3#6848111yescharacteristic, complemented
371C3#7077611yescharacteristic, complemented
372C2—62no—
373C2#1059061011yescharacteristic
374C2D3×#81611yescharacteristic
375C2#1059100611yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1542
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #10589348C2semidirect
5. C3×#4481C2semidirect
6. #10589095C2semidirect
7. #10589094C2semidirect
41. #4481D3semidirect
322. C32#1542semidirect
370. C3#68481semidirect
371. C3#70776semidirect

Maximal subgroups

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

subgroupindex
#105938592
C3×#48332
D3×C4⋊(C3⋊C8)2
#105893482
C3×#44812
#105890952
#105890942
#707763
#684813