Finite Group Databasebeta

← #11776195

Subgroups — #11776195

Order 1152.

535 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595941C211yesmaximal, characteristic
2C3×#4925C211yesmaximal, characteristic
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
4#10589096C212yesmaximal, complemented
5#10589094C212yesmaximal, complemented
6#70776—31nomaximal
7#70437—31nomaximal
8C2×C32×C42C2211yescharacteristic
9#64135—21no—
10#64133—21no—
11#64133C412yes—
12#64079—21no—
13#64078C2211yescharacteristic
14#64078C2211yescharacteristic
15C4×#634—21no—
16C4×#634C412yes—
17C22×C3×C3⋊C8—21no—
18C3×#830—21no—
19C3×C4⋊(C3⋊C8)—21no—
20C3×C4⋊(C3⋊C8)C2212yes—
21C3×C4⋊(C3⋊C8)C2212yes—
22C3×C4×C3⋊C8—21no—
23#5470—31no—
24#5470—31no—
25#5470—61no—
26C3×#431—31no—
27C2×C3×C4⋊C8—31no—
28#4925D311yescharacteristic
29C2×C4⋊(C3⋊C8)D311yescharacteristic
30#4486—32no—
31#4482—32no—
32#4481—32no—
33#4481—32no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C2×#634—21no—
38C2×#634C2×C412yes—
39C32×C42C2×C411yescharacteristic
40C32×C42D411yescharacteristic
41C32×C42D411yescharacteristic
42C32×C42C2311yescharacteristic
43#3757—22no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)C2×C412yes—
48#3750—22no—
49#3750—22no—
50C4×C3⋊Dic3—22no—
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8—22no—
53C2×C3×C3⋊C8—42no—
54#1542—91noSylow
55C22×C3×C8—61no—
56C2×C3×C42—21no—
57C2×C3×C42C2×D311yescharacteristic
58C2×C3×C42C2×D311yescharacteristic
59#926—62no—
60#926—61no—
61#926—61no—
62#924—32no—
63#924—32no—
64#924—62no—
65#924—62no—
66#924—61no—
67#924—61no—
68C22×C3⋊C8—21no—
69#870—62no—
70#870—61no—
71#870—61no—
72#869—31no—
73#869—31no—
74#869—31no—
75#869—31no—
76#869—61no—
77#869—61no—
78C4×Dic6—32no—
79C4×Dic6—32no—
80C4×Dic6—62no—
81C4×Dic6—62no—
82C4×Dic6—61no—
83C4×Dic6—61no—
84C3×C4⋊C8—32no—
85C3×C4⋊C8—32no—
86C3×C4⋊C8—61no—
87C3×C22⋊C8—61no—
88C3×C4×C8—61no—
89#830—21no—
90C4⋊(C3⋊C8)—21no—
91C4⋊(C3⋊C8)C2×D312yes—
92C4⋊(C3⋊C8)C2×D312yes—
93C4×C3⋊C8—21no—
94C23×C32C22⋊C411yescharacteristic
95C2×C32×C4—22no—
96C2×C32×C4—41no—
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C22⋊C411yescharacteristic
100C2×C32×C4SD1612yes—
101C2×C32×C4Q1612yes—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—22no—
107#634—42no—
108#634—42no—
109C3×C3⋊C8—42no—
110C3×C3⋊C8—42no—
111#533—91no—
112#431—31no—
113C2×C4⋊C8—31no—
114#333—92no—
115#332—92no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4C4×D311yescharacteristic
120C22×C3×C4C4×D311yescharacteristic
121C22×C3×C4D1211yescharacteristic
122C22×C3×C4D1211yescharacteristic
123C22×C3×C4#6711yescharacteristic
124C22×C3×C4#6711yescharacteristic
125C2×Dic6—32no—
126C2×Dic6—32no—
127C2×Dic6—62no—
128C2×Dic6—62no—
129C2×Dic6—61no—
130C2×Dic6—61no—
131C2×C3×C8—62no—
132C2×C3×C8—62no—
133C2×C3×C8—122no—
134C3×C42—21no—
135C3×C42—21no—
136C3×C42—21no—
137C3×C42—21no—
138C3×C42C4×D311yescharacteristic
139C3×C42C4×D311yescharacteristic
140C3×C42D1211yescharacteristic
141C3×C42D1211yescharacteristic
142C3×C42#6711yescharacteristic
143C3×C42#6711yescharacteristic
144C3×C42C22×D311yescharacteristic
145C3×C42C22×D311yescharacteristic
146#217—64no—
147#217—62no—
148#217—62no—
149C4⋊Dic3—32no—
150C4⋊Dic3—32no—
151C4⋊Dic3—62no—
152C4⋊Dic3—62no—
153C4⋊Dic3—62no—
154C4⋊Dic3—62no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157C4⋊Dic3—61no—
158C4⋊Dic3—61no—
159C4⋊Dic3—61no—
160C4⋊Dic3—61no—
161Dic3⋊C4—64no—
162Dic3⋊C4—64no—
163Dic3⋊C4—62no—
164Dic3⋊C4—62no—
165Dic3⋊C4—62no—
166Dic3⋊C4—62no—
167C4×Dic3—64no—
168C4×Dic3—62no—
169C4×Dic3—62no—
170C2×C3⋊C8—22no—
171C2×C3⋊C8—22no—
172C2×C3⋊C8—42no—
173C22×C32—21no—
174C22×C32—21no—
175C22×C32#10312yes—
176C22×C32C2×C22⋊C411yescharacteristic
177C32×C4—21no—
178C32×C4—21no—
179C32×C4—21no—
180C32×C4#10312yes—
181C32×C4C2×SD1611yescharacteristic
182C32×C4C2×Q1611yescharacteristic
183C32×C4#13512yes—
184C3⋊Dic3—42no—
185C3⋊Dic3—42no—
186C22×C8—61no—
187C4⋊Q8—91no—
188C4⋊Q8—91no—
189#125—181no—
190C22⋊Q8—92no—
191C22⋊Q8—181no—
192C4×Q8—92no—
193C4×Q8—181no—
194#117—181no—
195C2×C42D3211yescharacteristic
196C4⋊C8—32no—
197C4⋊C8—32no—
198C4⋊C8—61no—
199C22⋊C8—61no—
200C4×C8—61no—
201C23×C3—21no—
202C23×C3(C2×D3)⋊C411yescharacteristic
203C23×C3(C2×D3)⋊C411yescharacteristic
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—42no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—42no—
218C2×C3×C4#20412yes—
219C2×C3×C4Dic1212yes—
220C2×C3×C4(C2×D3)⋊C411yescharacteristic
221C2×C3×C4(C2×D3)⋊C411yescharacteristic
222C2×C3×C4(C2×D3)⋊C411yescharacteristic
223C2×C3×C4(C2×D3)⋊C411yescharacteristic
224C2×C3×C4(C2×D3)⋊C411yescharacteristic
225C2×C3×C4(C2×D3)⋊C411yescharacteristic
226C2×C3×C4#21412yes—
227C2×C3×C4#21612yes—
228C2×C3×C4C2×C4×D311yescharacteristic
229C2×C3×C4C2×C4×D311yescharacteristic
230C2×C3×C4C2×D1211yescharacteristic
231C2×C3×C4C2×D1211yescharacteristic
232C2×C3×C4C2×#6711yescharacteristic
233C2×C3×C4C2×#6711yescharacteristic
234C2×Dic3—64no—
235C2×Dic3—64no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240Dic6—124no—
241Dic6—124no—
242Dic6—122no—
243Dic6—122no—
244Dic6—122no—
245Dic6—122no—
246C3×C8—122no—
247C3×C8—122no—
248C3⋊C8—42no—
249C3⋊C8—42no—
250C2×C32—22no—
251C2×C32#41311yescharacteristic
252C2×C32C2×#10311yescharacteristic
253C2×C32#41611yescharacteristic
254C2×Q8—92no—
255C2×Q8—181no—
256C22×C4#62411yescharacteristic
257C22×C4#62611yescharacteristic
258C22×C4#62611yescharacteristic
259C2×C8—62no—
260C2×C8—62no—
261C2×C8—122no—
262C4⋊C4—92no—
263C4⋊C4—182no—
264C4⋊C4—182no—
265C4⋊C4—181no—
266C4⋊C4—181no—
267C4⋊C4—181no—
268C22⋊C4—182no—
269C42—182no—
270C42#62411yescharacteristic
271C42#62611yescharacteristic
272C42#62611yescharacteristic
273C42C2×D3211yescharacteristic
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—22no—
279C22×C3—21no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3#81012yes—
283C22×C3#81612yes—
284C22×C3C2×(C2×D3)⋊C411yescharacteristic
285C22×C3C2×(C2×D3)⋊C411yescharacteristic
286C3×C4—22no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—22no—
294C3×C4—21no—
295C3×C4—22no—
296C3×C4—21no—
297C3×C4—41no—
298C3×C4—41no—
299C3×C4#81012yes—
300C3×C4#81612yes—
301C3×C4C2×#20411yescharacteristic
302C3×C4#90412yes—
303C3×C4C2×Dic1211yescharacteristic
304C3×C4C2×#21411yescharacteristic
305C3×C4C2×#21611yescharacteristic
306C3×C4#95012yes—
307Dic3—124no—
308Dic3—124no—
309Dic3—122no—
310Dic3—122no—
311Dic3—122no—
312Dic3—122no—
313C32#154211yescharacteristic, complemented, Sylow
314C23#372211yescharacteristic
315Q8—362no—
316Q8—362no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—182no—
320C2×C4—182no—
321C2×C4#371612yes—
322C2×C4#371912yes—
323C2×C4#372211yescharacteristic
324C2×C4#372211yescharacteristic
325C2×C4#372211yescharacteristic
326C2×C4C2×#62411yescharacteristic
327C2×C4C2×#62611yescharacteristic
328C2×C4C2×#62611yescharacteristic
329C8—122no—
330C8—122no—
331C2×C3—22no—
332C2×C3—22no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—42no—
337C2×C3C2×#81011yescharacteristic
338C2×C3#500211yescharacteristic
339C2×C3C2×#81611yescharacteristic
340C2×C3#511311yescharacteristic
341C2×C3#513211yescharacteristic
342C2×C3#513211yescharacteristic
343C22—21no—
344C22—21no—
345C22#6356712yes—
346C22C2×#372211yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—362no—
351C4—362no—
352C4#6356712yes—
353C4C2×#371611yescharacteristic
354C4#6382912yes—
355C4C2×#371911yescharacteristic
356C3—21no—
357C3#7043711yescharacteristic, complemented
358C3#7077611yescharacteristic, complemented
359C2—22no—
360C2#1059107811yescharacteristic
361C2C2×#6356711yescharacteristic
362C2#1059110511yescharacteristic
subgroupG/H
centerC2×C4#3722
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. #10589096C2semidirect
5. #10589094C2semidirect
313. C32#1542semidirect
357. C3#70437semidirect
358. C3#70776semidirect

Maximal subgroups

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

subgroupindex
#105959412
C3×#49252
C2×C3×C4⋊(C3⋊C8)2
#105890962
#105890942
#707763
#704373