Finite Group Databasebeta

← #11802866

Subgroups — #11802866

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic
2C3×#5212C212yesmaximal
3#10591703C214yesmaximal
4#10591359C211yesmaximal, characteristic, complemented
5#10591274C212yesmaximal, complemented
6#10591271C214yesmaximal, complemented
7#10591230C211yesmaximal, characteristic, complemented
8#73868—32nomaximal
9C23×C32×C4C2211yescharacteristic
10C2×#3757C2212yes—
11#64135C418yescomplemented
12C2×C4⋊(C3⋊Dic3)C2212yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×#217C2214yes—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×C4⋊Dic3C2212yes—
18C2×#3724C2214yes—
19C2×Dic32C2214yes—
20C3×C3⋊#95C2214yes—
21#63579C2214yes—
22#63579C2214yes—
23C2×#926—32no—
24C2×#926—61no—
25C3×#380—32no—
26#5212D312yes—
27#4977—32no—
28#4975—32no—
29Dic3×C4⋊C4—32no—
30Dic3×C4⋊C4—32no—
31#4945—34no—
32#4944—34no—
33#4654—34no—
34#4653—34no—
35C24×C32C2311yescharacteristic
36C22×C32×C4—22no—
37C22×C32×C4—22no—
38C22×C32×C4C2×C414yes—
39C22×C32×C4C2311yescharacteristic
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3C2312yes—
42C22×C3⋊Dic3C2312yes—
43C22×C3×Dic3C2314yes—
44C22×C3×Dic3C2314yes—
45#3757C2×C418yes—
46C4⋊(C3⋊Dic3)C2×C418yes—
47C4×C3⋊Dic3C2×C414yes—
48C4×C3⋊Dic3C2×C414yes—
49C3×#217—44no—
50C3×C4⋊Dic3—24no—
51C3×C4⋊Dic3—24no—
52#3724—44no—
53Dic32—44no—
54#2314—91noSylow
55C23×C3×C4—21no—
56C23×C3×C4C2×D312yes—
57C2×C3×C4⋊C4—32no—
58C2×C3×C4⋊C4—32no—
59C2×C3×C22⋊C4—34no—
60C2×#217—32no—
61C2×#217—32no—
62C2×#217—62no—
63C2×#217C2×D314yes—
64#926—316no—
65#926—68no—
66C2×C4⋊Dic3—32no—
67C2×C4⋊Dic3—32no—
68C2×C4⋊Dic3—62no—
69C2×C4⋊Dic3C2×D312yes—
70C2×C4⋊Dic3C2×D312yes—
71C2×Dic3⋊C4—34no—
72C2×Dic3⋊C4—34no—
73C2×C4×Dic3—32no—
74C2×C4×Dic3—32no—
75C2×C4×Dic3—34no—
76C2×C4×Dic3—34no—
77C2×C4×Dic3—61no—
78C2×C4×Dic3—61no—
79C3×#95—34no—
80C3⋊#95—34no—
81C3⋊#95—34no—
82C3⋊#95—34no—
83C3⋊#95—34no—
84C3⋊#95C2×D314yes—
85C23×C32—21no—
86C23×C32—21no—
87C23×C32—22no—
88C23×C32—22no—
89C23×C32C22×C412yes—
90C23×C32C2411yescharacteristic
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—28no—
94C2×C32×C4C22×C412yes—
95C2×C32×C4C22×C412yes—
96C2×C32×C4#4112yes—
97C2×C32×C4#4112yes—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3C22×C414yes—
103C2×C3⋊Dic3C22×C414yes—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×#117—91no—
111#388—94no—
112#387—94no—
113#384—91no—
114#382—91no—
115#380—32no—
116C4×C4⋊C4—92no—
117C24×C3—21no—
118C24×C3C22×D312yes—
119C22×C3×C4—24no—
120C22×C3×C4—24no—
121C22×C3×C4—24no—
122C22×C3×C4—24no—
123C22×C3×C4—24no—
124C22×C3×C4—21no—
125C22×C3×C4—21no—
126C22×C3×C4—34no—
127C22×C3×C4—34no—
128C22×C3×C4C4×D318yes—
129C22×C3×C4C22×D312yes—
130C22×C3×C4C22×D312yes—
131C22×Dic3—32no—
132C22×Dic3—32no—
133C22×Dic3—32no—
134C22×Dic3—32no—
135C22×Dic3—62no—
136C22×Dic3—62no—
137C22×Dic3C22×D314yes—
138C22×Dic3C22×D314yes—
139C3×C4⋊C4—64no—
140C3×C4⋊C4—64no—
141C3×C22⋊C4—124no—
142#217—38no—
143#217—38no—
144#217—44no—
145#217—68no—
146C4⋊Dic3—24no—
147C4⋊Dic3—24no—
148C4⋊Dic3—38no—
149C4⋊Dic3—38no—
150C4⋊Dic3—68no—
151Dic3⋊C4—124no—
152Dic3⋊C4—124no—
153C4×Dic3—38no—
154C4×Dic3—38no—
155C4×Dic3—64no—
156C4×Dic3—64no—
157C4×Dic3—124no—
158C4×Dic3—124no—
159C22×C32—22no—
160C22×C32—24no—
161C22×C32—41no—
162C22×C32—41no—
163C22×C32—42no—
164C22×C32C23×C411yescharacteristic
165C22×C32C2×#4111yescharacteristic
166C22×C32C2×#4111yescharacteristic
167C22×C32H(5,𝔽2)12yes—
168C22×C322−1+412yes—
169C32×C4—22no—
170C32×C4#11714yes—
171C3⋊Dic3—24no—
172C3⋊Dic3—24no—
173C3×Dic3—44no—
174C3×Dic3—44no—
175C23×C4D3211yescharacteristic
176#117—98no—
177C2×C4⋊C4—32no—
178C2×C4⋊C4—32no—
179C2×C4⋊C4—92no—
180C2×C4⋊C4—94no—
181C2×C22⋊C4—34no—
182C2×C22⋊C4—92no—
183C2×C42—91no—
184C2×C42—91no—
185C2×C42—94no—
186#95—34no—
187#95—94no—
188#95—94no—
189C23×C3—22no—
190C23×C3—22no—
191C23×C3—22no—
192C23×C3—22no—
193C23×C3—22no—
194C23×C3—22no—
195C23×C3—22no—
196C23×C3—22no—
197C23×C3—21no—
198C23×C3—22no—
199C23×C3—42no—
200C23×C3—42no—
201C23×C3C2×C4×D314yes—
202C23×C3C23×D312yes—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—216no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—216no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—64no—
214C2×C3×C4—64no—
215C2×C3×C4—64no—
216C2×C3×C4—64no—
217C2×C3×C4—64no—
218C2×C3×C4—64no—
219C2×C3×C4C2×C4×D314yes—
220C2×C3×C4C2×C4×D314yes—
221C2×C3×C4#23714yes—
222C2×C3×C4#23714yes—
223C2×Dic3—24no—
224C2×Dic3—24no—
225C2×Dic3—24no—
226C2×Dic3—24no—
227C2×Dic3—24no—
228C2×Dic3—24no—
229C2×Dic3—34no—
230C2×Dic3—34no—
231C2×Dic3—34no—
232C2×Dic3—34no—
233C2×Dic3—64no—
234C2×Dic3—64no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—122no—
244C2×Dic3—122no—
245C2×Dic3—122no—
246C2×Dic3—122no—
247C2×C32—42no—
248C2×C32C2×#11711yescharacteristic
249C2×C32#52012yes—
250C2×C32#54011yescharacteristic
251C2×C32#54111yescharacteristic
252C2×C32#54212yes—
253C24C2×D3211yescharacteristic
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—34no—
257C22×C4—34no—
258C22×C4—92no—
259C22×C4—92no—
260C22×C4#62414yes—
261C22×C4C2×D3211yescharacteristic
262C22×C4C2×D3211yescharacteristic
263C4⋊C4—64no—
264C4⋊C4—64no—
265C4⋊C4—98no—
266C4⋊C4—364no—
267C22⋊C4—98no—
268C22⋊C4—124no—
269C42—94no—
270C42—94no—
271C42—364no—
272C22×C3—24no—
273C22×C3—24no—
274C22×C3—24no—
275C22×C3—24no—
276C22×C3—22no—
277C22×C3—22no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—44no—
282C22×C3—42no—
283C22×C3—44no—
284C22×C3—42no—
285C22×C3—42no—
286C22×C3—42no—
287C22×C3—42no—
288C22×C3—42no—
289C22×C3C22×C4×D312yes—
290C22×C3C2×#23712yes—
291C22×C3C2×#23712yes—
292C22×C3#100412yes—
293C22×C3#100712yes—
294C22×C3#100912yes—
295C22×C3#101012yes—
296C3×C4—24no—
297C3×C4—24no—
298C3×C4—24no—
299C3×C4—124no—
300C3×C4—124no—
301C3×C4#87718yes—
302Dic3—44no—
303Dic3—44no—
304Dic3—64no—
305Dic3—64no—
306Dic3—64no—
307Dic3—64no—
308Dic3—124no—
309Dic3—124no—
310C32#231411yescharacteristic, complemented, Sylow
311C23—22no—
312C23—22no—
313C23—21no—
314C23—21no—
315C23C2×#62412yes—
316C23C22×D3211yescharacteristic
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—28no—
320C2×C4—64no—
321C2×C4—64no—
322C2×C4—64no—
323C2×C4—64no—
324C2×C4—64no—
325C2×C4—64no—
326C2×C4—94no—
327C2×C4—94no—
328C2×C4—182no—
329C2×C4—182no—
330C2×C4—182no—
331C2×C4—182no—
332C2×C4#380512yes—
333C2×C4#380512yes—
334C2×C4C2×#62412yes—
335C2×C4C2×#62412yes—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—22no—
339C2×C3—22no—
340C2×C3—21no—
341C2×C3—44no—
342C2×C3—44no—
343C2×C3C2×#87712yes—
344C2×C3#550412yes—
345C2×C3#552312yes—
346C2×C3#560312yes—
347C2×C3#561912yes—
348C2×C3#562512yes—
349C2×C3#564312yes—
350C22—22no—
351C22—24no—
352C22—41no—
353C22—42no—
354C22—41no—
355C22#6429712yes—
356C22#6430712yes—
357C22C2×#380511yescharacteristic
358C22C2×#380511yescharacteristic
359C22C22×#62411yescharacteristic
360C4—22no—
361C4—124no—
362C4—124no—
363C4—184no—
364C4—184no—
365C4#6395714yes—
366C3—21no—
367C3#7386812yescomplemented
368C2—42no—
369C2#1059482611yescharacteristic
370C2#1059498412yes—
371C2#1059499012yes—
372C2#1059504111yescharacteristic
373C2C2×#6395711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2314
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #10591359C2semidirect
5. #10591274C2semidirect
6. #10591271C2semidirect
7. #10591230C2semidirect
11. #64135C4semidirect
310. C32#2314semidirect
367. C3#73868semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C3×#52122
#105917032
#105913592
#105912742
#105912712
#105912302
#738683