Finite Group Databasebeta

← #11776243

Subgroups — #11776243

Order 1152.

436 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
3#10590248C211yesmaximal, characteristic
4#10589352C211yesmaximal, characteristic, complemented
5C3×#4482C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589093C211yesmaximal, characteristic, complemented
8#70777—31nomaximal
9#68419—31nomaximal
10#64078C2211yescharacteristic
11C3×C42×D3C2211yescharacteristic
12C3×#869C2211yescharacteristic
13#63869C412yes—
14#63857—21no—
15#63856—21no—
16#63844—21no—
17Dic3×Dic6—21no—
18#63841C412yes—
19C32×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C3×(C2×D3)⋊C8—21no—
22C3×C8×Dic3—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25(C2×D3)⋊(C3⋊C8)—21no—
26Dic3×C3⋊C8—21no—
27#5728—31no—
28#5470—31no—
29C3×#431—31no—
30#4925—31no—
31#4833—31no—
32#4833D311yescharacteristic
33C3×#332—31no—
34#4547—31no—
35#4486—31no—
36#4486—31no—
37#4486—31no—
38#4486—61no—
39#4482—31no—
40#4482—31no—
41#4482D311yescharacteristic, complemented
42C2×#634—21no—
43C2×C3×C4×D3C2×C411yescharacteristic
44C2×C3×C4×D3D411yescharacteristic
45C2×C3×C4×D3D411yescharacteristic
46C2×C3×Dic6—21no—
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⋊Dic3C2×C412yes—
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—
63#1544—91noSylow
64C3×C4⋊Q8—31no—
65C2×C3×C42—31no—
66#946—61no—
67Q8×Dic3—61no—
68#926—32no—
69#924—61no—
70#924—61no—
71#897—61no—
72#892—32no—
73#890—32no—
74#887—61no—
75C42×D3C2×D311yescharacteristic
76#870—32no—
77#869—31no—
78#869—31no—
79#869—61no—
80#869C2×D311yescharacteristic
81C4×Dic6—61no—
82C4×Dic6—61no—
83C3×C4⋊C8—21no—
84C3×C4⋊C8—31no—
85C3×C4⋊C8—31no—
86C3×C4⋊C8C2×D311yescharacteristic
87C3×C4⋊C8C2×D311yescharacteristic
88C3×C22⋊C8—61no—
89C3×C4×C8—61no—
90#830—61no—
91(C2×D3)⋊C8—21no—
92(C2×D3)⋊C8—61no—
93C8×Dic3—21no—
94C8×Dic3—61no—
95C4⋊(C3⋊C8)—31no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—61no—
98C4⋊(C3⋊C8)C2×D311yescharacteristic
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4×C3⋊C8—61no—
101C22×C3×D3C22⋊C411yescharacteristic
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C3⋊Dic3—22no—
106#634—41no—
107#634—41no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3C22⋊C411yescharacteristic
110C2×C3×Dic3C22⋊C411yescharacteristic
111C2×C3×Dic3C22⋊C411yescharacteristic
112C3×C4×D3—21no—
113C3×C4×D3—21no—
114C3×C4×D3—21no—
115C3×C4×D3—21no—
116C3×C4×D3—22no—
117C3×Dic6—41no—
118C3×Dic6—41no—
119C32×C8—41no—
120C3⋊(C3⋊C8)—41no—
121C3×C3⋊C8—41no—
122C3×C3⋊C8—41no—
123#533—91no—
124#431—31no—
125#431—91no—
126#332—31no—
127#332—91no—
128#332—91no—
129#332—91no—
130C2×C3×Q8—61no—
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—21no—
138C2×Dic6—61no—
139C2×Dic6—61no—
140C2×Dic6—121no—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8—41no—
144C2×C3×C8—61no—
145C2×C3×C8—61no—
146C3×C4⋊C4—32no—
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—32no—
158C4⋊Dic3—32no—
159C4⋊Dic3—62no—
160C4⋊Dic3—61no—
161C4⋊Dic3—61no—
162C4⋊Dic3—62no—
163C4⋊Dic3—121no—
164C4⋊Dic3C4×D312yes—
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—
178C22×C32C2×C22⋊C411yescharacteristic
179C2×C3×D3—21no—
180C2×C3×D3—21no—
181C2×C3×D3—21no—
182C32×C4—21no—
183C32×C4#13511yescharacteristic
184C32×C4#13511yescharacteristic
185C32×C4#13511yescharacteristic
186C32×C4#13511yescharacteristic
187C3⋊Dic3—42no—
188C3×Dic3—21no—
189C3×Dic3—21no—
190C3×Dic3—42no—
191C3×Dic3#10112yes—
192C4⋊Q8—31no—
193C4⋊Q8—91no—
194#125—92no—
195C22⋊Q8—181no—
196C22⋊Q8—181no—
197C4×Q8—181no—
198C4×Q8—181no—
199#117—92no—
200C2×C42—31no—
201C4⋊C8—31no—
202C4⋊C8—31no—
203C4⋊C8—91no—
204C4⋊C8D3211yescharacteristic
205C22⋊C8—61no—
206C22⋊C8—181no—
207C4×C8—61no—
208C4×C8—181no—
209C23×C3—31no—
210C22×D3(C2×D3)⋊C411yescharacteristic
211C3×Q8—121no—
212C3×Q8—121no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—31no—
217C2×C3×C4—31no—
218C2×C3×C4—31no—
219C2×C3×C4—62no—
220C2×C3×C4—61no—
221C2×C3×C4—61no—
222C2×C3×C4—61no—
223C2×C3×C4—61no—
224C2×C3×C4—62no—
225C2×C3×C4C2×C4×D311yescharacteristic
226C2×C3×C4C2×C4×D311yescharacteristic
227C2×C3×C4C2×D1211yescharacteristic
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4C2×#6711yescharacteristic
231C2×Dic3—22no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—122no—
235C2×Dic3(C2×D3)⋊C411yescharacteristic
236C2×Dic3(C2×D3)⋊C411yescharacteristic
237C2×Dic3(C2×D3)⋊C411yescharacteristic
238C4×D3—21no—
239C4×D3—21no—
240C4×D3—21no—
241C4×D3—21no—
242C4×D3—22no—
243Dic6—41no—
244Dic6—41no—
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×C32C2×#10111yescharacteristic
262C2×C32#41611yescharacteristic
263C2×C32#41611yescharacteristic
264C3×D3—41no—
265C2×Q8—61no—
266C2×Q8—181no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—31no—
270C2×C8—21no—
271C2×C8—61no—
272C2×C8—61no—
273C2×C8—181no—
274C4⋊C4—32no—
275C4⋊C4—61no—
276C4⋊C4—92no—
277C4⋊C4—182no—
278C4⋊C4—182no—
279C4⋊C4—181no—
280C22⋊C4—182no—
281C42—31no—
282C42—31no—
283C42—31no—
284C42—182no—
285C42C2×D3211yescharacteristic
286C22×C3—21no—
287C22×C3—61no—
288C22×C3—61no—
289C22×C3—61no—
290C22×C3D3×C22⋊C411yescharacteristic
291C22×C3C2×(C2×D3)⋊C411yescharacteristic
292C2×D3—21no—
293C2×D3—21no—
294C2×D3—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—32no—
302C3×C4—41no—
303C3×C4—61no—
304C3×C4—61no—
305C3×C4—122no—
306C3×C4#90411yescharacteristic
307C3×C4#90411yescharacteristic
308C3×C4#91211yescharacteristic
309C3×C4#91611yescharacteristic
310C3×C4#91611yescharacteristic
311C3×C4#91911yescharacteristic
312C3×C4#95011yescharacteristic
313C3×C4#95011yescharacteristic
314Dic3—21no—
315Dic3—21no—
316Dic3—42no—
317Dic3—122no—
318Dic3—122no—
319Dic3—242no—
320Dic3#82412yes—
321C32#154411yescharacteristic, complemented, Sylow
322C23—31no—
323Q8—121no—
324Q8—121no—
325Q8—361no—
326Q8—361no—
327C2×C4—31no—
328C2×C4—31no—
329C2×C4—31no—
330C2×C4—62no—
331C2×C4—61no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4—62no—
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—121no—
348C2×C3D3×#10111yescharacteristic
349C2×C3#477211yescharacteristic
350C2×C3#480411yescharacteristic
351C2×C3#500211yescharacteristic
352C2×C3#511311yescharacteristic
353C2×C3C2×#82411yescharacteristic
354D3—41no—
355C22—61no—
356C22—61no—
357C22—61no—
358C22D3×(C2×D3)⋊C411yescharacteristic
359C4—21no—
360C4—32no—
361C4—61no—
362C4—61no—
363C4—122no—
364C4—362no—
365C4#6380611yescharacteristic
366C4#6380811yescharacteristic
367C4#6393311yescharacteristic
368C4#6394711yescharacteristic
369C3—21no—
370C3#6841911yescharacteristic, complemented
371C3#7077711yescharacteristic, complemented
372C2—121no—
373C2#1059060811yescharacteristic
374C2#1059069011yescharacteristic
375C2D3×#82411yescharacteristic
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#1544
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. #10589352C2semidirect
5. C3×#4482C2semidirect
6. #10589094C2semidirect
7. #10589093C2semidirect
41. #4482D3semidirect
321. C32#1544semidirect
370. C3#68419semidirect
371. C3#70777semidirect

Maximal subgroups

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

subgroupindex
#105938592
C3×#48332
#105902482
#105893522
C3×#44822
#105890942
#105890932
#707773
#684193