Finite Group Databasebeta

← #11808962

Subgroups — #11808962

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592348C211yesmaximal, characteristic
2C3×#4661C212yesmaximal
3#10591343C212yesmaximal
4#10591342C212yesmaximal
5#10591274C212yesmaximal
6#10591274C211yesmaximal, characteristic
7#10591252C211yesmaximal, characteristic
8#10591241C212yesmaximal
9#10591227C212yesmaximal
10#77741—32nomaximal
11C2×#3750C2212yes—
12C2×C4×C3⋊Dic3C2212yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×Dic3⋊C4C2212yes—
18C2×Dic3⋊Dic3C2212yes—
19C2×Dic32C2211yescharacteristic
20C2×Dic32C2212yes—
21C2×Dic32C2211yescharacteristic
22C32×#95C2211yescharacteristic
23#63658C2211yescharacteristic
24C3×C3⋊#95C2212yes—
25C3×C3⋊#95C2212yes—
26#63579C2212yes—
27#63579C2212yes—
28#63579C2211yescharacteristic
29#63579C2212yes—
30#63579C2212yes—
31#63579C2211yescharacteristic
32C3×#398—32no—
33#4986—32no—
34#4985—32no—
35#4982—32no—
36#4981—32no—
37Dic3×C4⋊C4—32no—
38Dic3×C4⋊C4—32no—
39Dic3×C4⋊C4—32no—
40Dic3×C4⋊C4—32no—
41#4661D312yes—
42#4660—32no—
43#4659—32no—
44#4649—32no—
45#4649—32no—
46#4649—61no—
47#4648—32no—
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2312yes—
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2311yescharacteristic
52C22×C3⋊Dic3C2311yescharacteristic
53C22×C3×Dic3C2312yes—
54C22×C3×Dic3C2312yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57#3750—24no—
58C4×C3⋊Dic3—24no—
59C4×C3⋊Dic3Q814yes—
60C3×C4⋊Dic3—24no—
61C3×C4⋊Dic3—24no—
62C3×C4⋊Dic3—24no—
63C3×Dic3⋊C4—24no—
64Dic3⋊Dic3—24no—
65Dic32—24no—
66Dic32—22no—
67Dic32—22no—
68#2402—91noSylow
69C2×C3×C4⋊C4—32no—
70C2×C3×C4⋊C4—32no—
71C2×C3×C4⋊C4—32no—
72C2×C3×C4⋊C4—32no—
73C2×C4⋊Dic3—32no—
74C2×C4⋊Dic3C2×D312yes—
75C2×C4⋊Dic3C2×D312yes—
76C2×C4⋊Dic3C2×D312yes—
77C2×Dic3⋊C4—32no—
78C2×Dic3⋊C4—32no—
79C2×Dic3⋊C4—32no—
80C2×Dic3⋊C4—62no—
81C2×Dic3⋊C4C2×D312yes—
82C2×C4×Dic3—32no—
83C2×C4×Dic3—32no—
84C2×C4×Dic3—32no—
85C2×C4×Dic3—32no—
86C2×C4×Dic3—32no—
87C2×C4×Dic3—32no—
88C2×C4×Dic3—32no—
89C2×C4×Dic3—61no—
90C2×C4×Dic3—62no—
91C3×#95—21no—
92C3×#95—32no—
93C3×#95—32no—
94C3×#95C2×D312yes—
95C3⋊#95—32no—
96C3⋊#95—32no—
97C3⋊#95—32no—
98C3⋊#95—32no—
99C3⋊#95—32no—
100C3⋊#95—32no—
101C3⋊#95—32no—
102C3⋊#95—32no—
103C3⋊#95—32no—
104C3⋊#95—32no—
105C3⋊#95—32no—
106C3⋊#95—61no—
107C3⋊#95C2×D312yes—
108C3⋊#95C2×D312yes—
109C23×C32C2411yescharacteristic
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4—22no—
113C2×C32×C4C2×Q812yes—
114C2×C32×C4#4114yes—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3C2×Q812yes—
120C2×C3⋊Dic3C2×Q812yes—
121C2×C3⋊Dic3#4112yes—
122C2×C3⋊Dic3#4112yes—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3#4114yes—
135#400—92no—
136#400—92no—
137#398—32no—
138#398—92no—
139C4×C4⋊C4—92no—
140C4×C4⋊C4—91no—
141C4×C4⋊C4—92no—
142C4×C4⋊C4—91no—
143#376—91no—
144C22×C3×C4—21no—
145C22×C3×C4—22no—
146C22×C3×C4—32no—
147C22×C3×C4—32no—
148C22×C3×C4—32no—
149C22×C3×C4—32no—
150C22×C3×C4C22×D312yes—
151C22×C3×C4C22×D312yes—
152C22×C3×C4C22×D312yes—
153C22×Dic3—32no—
154C22×Dic3—32no—
155C22×Dic3—32no—
156C22×Dic3—32no—
157C22×Dic3—61no—
158C22×Dic3—61no—
159C22×Dic3—62no—
160C22×Dic3C22×D312yes—
161C22×Dic3C22×D312yes—
162C22×Dic3C22×D312yes—
163C22×Dic3C22×D312yes—
164C3×C4⋊C4—64no—
165C3×C4⋊C4—64no—
166C3×C4⋊C4—64no—
167C3×C4⋊C4—64no—
168C4⋊Dic3—24no—
169C4⋊Dic3—24no—
170C4⋊Dic3—24no—
171C4⋊Dic3—64no—
172Dic3⋊C4—24no—
173Dic3⋊C4—68no—
174Dic3⋊C4—64no—
175Dic3⋊C4—64no—
176Dic3⋊C4—64no—
177C4×Dic3—38no—
178C4×Dic3—64no—
179C4×Dic3—64no—
180C4×Dic3—64no—
181C4×Dic3—64no—
182C4×Dic3—64no—
183C4×Dic3—64no—
184C4×Dic3—64no—
185C4×Dic3—124no—
186C22×C32C22×Q811yescharacteristic
187C22×C32C2×#4112yes—
188C22×C32C2×#4112yes—
189C22×C32C2×#4111yescharacteristic
190C22×C32C2×#4111yescharacteristic
191C32×C4—24no—
192C32×C4—22no—
193C3⋊Dic3—22no—
194C3⋊Dic3—42no—
195C3⋊Dic3#12514yes—
196C3×Dic3—24no—
197C3×Dic3—42no—
198C3×Dic3—42no—
199C3×Dic3—42no—
200C2×C4⋊C4—32no—
201C2×C4⋊C4—32no—
202C2×C4⋊C4—32no—
203C2×C4⋊C4—32no—
204C2×C4⋊C4—92no—
205C2×C4⋊C4—92no—
206C2×C42—91no—
207C2×C42—91no—
208C2×C42—91no—
209C2×C42—92no—
210C2×C42—92no—
211#95—32no—
212#95—32no—
213#95—92no—
214#95—91no—
215#95—92no—
216#95—92no—
217#95—91no—
218#95—92no—
219#95—91no—
220#95D3211yescharacteristic
221C23×C3—21no—
222C23×C3C23×D312yes—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—24no—
230C2×C3×C4—22no—
231C2×C3×C4—34no—
232C2×C3×C4—42no—
233C2×C3×C4—42no—
234C2×C3×C4—42no—
235C2×C3×C4—62no—
236C2×C3×C4—62no—
237C2×C3×C4—62no—
238C2×C3×C4—62no—
239C2×C3×C4—62no—
240C2×C3×C4—62no—
241C2×C3×C4—62no—
242C2×C3×C4—62no—
243C2×C3×C4—62no—
244C2×C3×C4—62no—
245C2×C3×C4—62no—
246C2×C3×C4#23714yes—
247C2×C3×C4D3×Q814yes—
248C2×C3×C4#23914yes—
249C2×Dic3—22no—
250C2×Dic3—22no—
251C2×Dic3—22no—
252C2×Dic3—22no—
253C2×Dic3—22no—
254C2×Dic3—22no—
255C2×Dic3—22no—
256C2×Dic3—22no—
257C2×Dic3—22no—
258C2×Dic3—22no—
259C2×Dic3—22no—
260C2×Dic3—34no—
261C2×Dic3—34no—
262C2×Dic3—34no—
263C2×Dic3—34no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—64no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—64no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280C2×Dic3#23714yes—
281C2×C32C2×#12511yescharacteristic
282C2×C32#52912yes—
283C2×C32#52912yes—
284C2×C32#53311yescharacteristic
285C2×C32#53311yescharacteristic
286C22×C4—32no—
287C22×C4—32no—
288C22×C4—32no—
289C22×C4—32no—
290C22×C4—91no—
291C22×C4—91no—
292C22×C4—92no—
293C22×C4C2×D3212yes—
294C22×C4C2×D3211yescharacteristic
295C4⋊C4—64no—
296C4⋊C4—64no—
297C4⋊C4—64no—
298C4⋊C4—64no—
299C4⋊C4—184no—
300C4⋊C4—184no—
301C42—94no—
302C42—184no—
303C42—184no—
304C42—182no—
305C42—182no—
306C22×C3—22no—
307C22×C3—21no—
308C22×C3—22no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3C2×#23712yes—
312C22×C3C2×#23712yes—
313C22×C3C2×D3×Q812yes—
314C22×C3C2×#23912yes—
315C22×C3D3×#4112yes—
316C22×C3D3×#4112yes—
317C22×C3D3×#4112yes—
318C3×C4—24no—
319C3×C4—24no—
320C3×C4—24no—
321C3×C4—44no—
322C3×C4—42no—
323C3×C4—64no—
324C3×C4—122no—
325C3×C4—122no—
326C3×C4—122no—
327Dic3—24no—
328Dic3—38no—
329Dic3—42no—
330Dic3—42no—
331Dic3—42no—
332Dic3—64no—
333Dic3—64no—
334Dic3—64no—
335Dic3—124no—
336Dic3—122no—
337Dic3—122no—
338C32#240211yescharacteristic, complemented, Sylow
339C23C22×D3211yescharacteristic
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—34no—
344C2×C4—62no—
345C2×C4—62no—
346C2×C4—62no—
347C2×C4—62no—
348C2×C4—62no—
349C2×C4—62no—
350C2×C4—62no—
351C2×C4—62no—
352C2×C4—62no—
353C2×C4—62no—
354C2×C4—62no—
355C2×C4—92no—
356C2×C4—92no—
357C2×C4—92no—
358C2×C4—92no—
359C2×C4—182no—
360C2×C4—182no—
361C2×C4—182no—
362C2×C4—182no—
363C2×C4#379614yes—
364C2×C4#379712yes—
365C2×C3—21no—
366C2×C3—22no—
367C2×C3—22no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3#560012yes—
371C2×C3#562212yes—
372C2×C3#562412yes—
373C2×C3#564912yes—
374C2×C3D3×#12512yes—
375C2×C3#569112yes—
376C2×C3#572812yes—
377C22C2×#379612yes—
378C22C2×#379711yescharacteristic
379C22D3×#23712yes—
380C22#6431211yescharacteristic
381C22#6431911yescharacteristic
382C4—24no—
383C4—22no—
384C4—64no—
385C4—94no—
386C4—122no—
387C4—122no—
388C4—122no—
389C4—182no—
390C4—362no—
391C3—21no—
392C3#7774112yescomplemented
393C2#1059386611yescharacteristic
394C2#1059403011yescharacteristic
395C2#1059414412yes—
396C2#1059442712yes—
397C2#1059448211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, prime radical, cosocleC23×C32C24
FittingC32×#95C22
hypercenter#95D32
hypocenterC32#2402
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
338. C32#2402semidirect
392. C3#77741semidirect

Maximal subgroups

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

subgroupindex
#105923482
C3×#46612
#105913432
#105913422
#105912742
#105912522
#105912412
#105912272
#777413