Finite Group Databasebeta

← #11783851

Subgroups — #11783851

Order 1152.

647 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#948C211yesmaximal, characteristic
2#10592939C211yesmaximal, characteristic
3C3×#5237C211yesmaximal, characteristic
4#10591059C212yesmaximal, complemented
5#10589171C212yesmaximal, complemented
6#72011—31nomaximal
7#70133—31nomaximal
8C2×C32×#41C2211yescharacteristic
9#64135C2212yes—
10C3×#948—22no—
11C3×#948—22no—
12C2×C3×#208C412yescomplemented
13C2×C3×#208C2212yes—
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C412yescomplemented
16C22×C3×C3⋊C8C2211yescharacteristic
17#63661C414yes—
18C3×#836C412yescomplemented
19C3×#833C412yescomplemented
20#63555—22no—
21#63553—22no—
22C2×C3×#131—31no—
23C2×#948D311yescharacteristic
24C3×#413—31no—
25#5240—31no—
26#5240—31no—
27#5240—61no—
28#5237D311yescharacteristic
29#5122—32no—
30#5101—32no—
31#4559—32no—
32#4556—32no—
33C32×#41—22no—
34C32×#41—22no—
35C2×C32×Q8C2×C411yescharacteristic
36C2×C32×D4C2×C412yes—
37C2×C32×D4C2×C411yescharacteristic
38C22×C32×C4C2×C412yes—
39C22×C32×C4C2311yescharacteristic
40#3757C2×C414yes—
41C4⋊(C3⋊Dic3)—22no—
42C4×C3⋊Dic3—22no—
43C3×#208—22no—
44C3×#208—22no—
45C3×#208—24no—
46C3×#208C2×C414yes—
47C2×C3×C3⋊C8—22no—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8C2×C412yes—
51C2×C3×C3⋊C8C2×C411yescharacteristic
52C2×C3×C3⋊C8C2×C411yescharacteristic
53C2×C3×C3⋊C8D412yes—
54C2×C3×C3⋊C8D412yes—
55#1757—91noSylow
56C2×C3×#41—21no—
57C2×C3×#41C2×D311yescharacteristic
58C2×C3×#41C2×D311yescharacteristic
59C3×#131—62no—
60C3×#131—62no—
61C2×C3×M16—32no—
62C2×C3×M16—31no—
63C2×C3×M16—32no—
64C22×C3×C8—31no—
65C22×C3×C8—32no—
66#948—22no—
67#948—22no—
68#926—32no—
69#926—32no—
70#926—62no—
71C2×#208Dic312yescomplemented
72C2×#208C2×D312yes—
73C2×#208C2×D311yescharacteristic
74C22×C3⋊C8Dic312yescomplemented
75C22×C3⋊C8C2×D311yescharacteristic
76C3×#101—32no—
77C3×#100—32no—
78#836Dic312yescomplemented
79#834—34no—
80#834—34no—
81#834—64no—
82#833Dic312yescomplemented
83#815—62no—
84#815—62no—
85C8×Dic3—62no—
86C8×Dic3—62no—
87C23×C32C4212yes—
88C23×C32C22×C411yescharacteristic
89C32×Q8—22no—
90C32×D4—24no—
91C32×D4—22no—
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4C4212yes—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D412yes—
98C2×C32×C4#4112yes—
99C2×C3⋊Dic3—24no—
100C3×C3⋊C8—22no—
101C3×C3⋊C8—24no—
102C3×C3⋊C8C22⋊C411yescharacteristic
103C3×C3⋊C8C22⋊C411yescharacteristic
104C3×C3⋊C8C22⋊C412yes—
105C2×#131—31no—
106#413—31no—
107#410—91no—
108#405—92no—
109#344—92no—
110C3×#41—22no—
111C3×#41—22no—
112C3×#41—22no—
113C3×#41—22no—
114C3×#41—42no—
115C3×#41—42no—
116C2×C3×Q8—21no—
117C2×C3×Q8C4×D311yescharacteristic
118C2×C3×Q8C2×Dic311yescharacteristic
119C2×C3×D4—21no—
120C2×C3×D4—22no—
121C2×C3×D4C4×D311yescharacteristic
122C2×C3×D4C4×D312yes—
123C2×C3×D4C4×D312yes—
124C2×C3×D4C2×Dic311yescharacteristic
125C22×C3×C4—22no—
126C22×C3×C4—21no—
127C22×C3×C4C4×D312yes—
128C22×C3×C4C2×Dic312yes—
129C22×C3×C4C22×D311yescharacteristic
130C22×C3×C4C22×D311yescharacteristic
131C3×M16—34no—
132C3×M16—64no—
133C3×M16—62no—
134C3×M16—62no—
135C2×C3×C8—31no—
136C2×C3×C8—31no—
137C2×C3×C8—32no—
138C2×C3×C8—32no—
139C2×C3×C8—32no—
140C2×C3×C8—62no—
141C2×C3×C8—62no—
142C2×C3×C8—62no—
143#217—34no—
144#217—34no—
145#217—64no—
146C4⋊Dic3—62no—
147C4⋊Dic3—62no—
148C4⋊Dic3—122no—
149C4×Dic3—62no—
150C4×Dic3—62no—
151C4×Dic3—122no—
152#208—22no—
153#208—22no—
154#208—24no—
155#208C2×Dic314yes—
156C2×C3⋊C8—22no—
157C2×C3⋊C8—22no—
158C2×C3⋊C8—22no—
159C2×C3⋊C8C2×Dic312yes—
160C2×C3⋊C8C2×Dic311yescharacteristic
161C2×C3⋊C8C2×Dic311yescharacteristic
162C2×C3⋊C8#6712yes—
163C2×C3⋊C8#6712yes—
164C22×C32—22no—
165C22×C32—41no—
166C22×C32—42no—
167C22×C32C2×C4211yescharacteristic
168C22×C32C4×D412yes—
169C32×C4—22no—
170C32×C4C2×C22⋊C411yescharacteristic
171C32×C4#11711yescharacteristic
172C32×C4C4×D412yes—
173C3⋊Dic3—44no—
174C2×#41D3211yescharacteristic
175#131—62no—
176#131—62no—
177C2×M16—32no—
178C2×M16—31no—
179C2×M16—32no—
180C22×C8—31no—
181C22×C8—32no—
182#117—92no—
183#101—32no—
184#100—32no—
185#99—94no—
186#97—182no—
187C4×C8—182no—
188C23×C3—22no—
189C23×C3—21no—
190C23×C3C4×Dic312yes—
191C23×C3C4×Dic312yes—
192C23×C3C2×C4×D311yescharacteristic
193C23×C3C2×C4×D311yescharacteristic
194C3×Q8—22no—
195C3×Q8—22no—
196C3×Q8—42no—
197C3×D4—24no—
198C3×D4—24no—
199C3×D4—22no—
200C3×D4—22no—
201C3×D4—42no—
202C3×D4—44no—
203C2×C3×C4—22no—
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—22no—
211C2×C3×C4—22no—
212C2×C3×C4—42no—
213C2×C3×C4—42no—
214C2×C3×C4C4×Dic312yes—
215C2×C3×C4C4×Dic312yes—
216C2×C3×C4C2×C4×D311yescharacteristic
217C2×C3×C4C2×C4×D311yescharacteristic
218C2×C3×C4#23512yes—
219C2×C3×C4D3×D412yes—
220C2×C3×C4#23712yes—
221C2×C3×C4C22×Dic311yescharacteristic
222C2×C3×C4C22×Dic311yescharacteristic
223C2×C3×C4C2×#6712yes—
224C2×Dic3—64no—
225C2×Dic3—64no—
226C2×Dic3—124no—
227C3×C8—31no—
228C3×C8—31no—
229C3×C8—32no—
230C3×C8—62no—
231C3×C8—64no—
232C3⋊C8—24no—
233C3⋊C8—22no—
234C3⋊C8#21711yescharacteristic
235C3⋊C8#21711yescharacteristic
236C3⋊C8#21712yes—
237C2×C32—22no—
238C2×C32—21no—
239C2×C32—42no—
240C2×C32C4×C22⋊C411yescharacteristic
241#41—22no—
242#41—22no—
243C2×Q8D3×Dic311yescharacteristic
244C2×D4D3×Dic311yescharacteristic
245C2×D4#62412yes—
246C22×C4D3×Dic312yes—
247C22×C4C2×D3211yescharacteristic
248M16—34no—
249M16—64no—
250M16—62no—
251M16—62no—
252C2×C8—31no—
253C2×C8—31no—
254C2×C8—32no—
255C2×C8—32no—
256C2×C8—32no—
257C2×C8—62no—
258C2×C8—62no—
259C2×C8—62no—
260C4⋊C4—182no—
261C22⋊C4—94no—
262C42—182no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—21no—
267C22×C3—42no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—42no—
271C22×C3—42no—
272C22×C3—81no—
273C22×C3—82no—
274C22×C3#67⋊C412yes—
275C22×C3C2×C4×Dic311yescharacteristic
276C22×C3C2×C4×Dic311yescharacteristic
277C22×C3C4×#6712yes—
278C3×C4—22no—
279C3×C4—22no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—22no—
283C3×C4—42no—
284C3×C4#87711yescharacteristic
285C3×C4D3×C22⋊C411yescharacteristic
286C3×C4#92611yescharacteristic
287C3×C4C4×#6712yes—
288C3×C4D4×Dic312yes—
289C3×C4C2×#21711yescharacteristic
290Dic3—124no—
291Dic3—124no—
292Dic3—244no—
293C32#175711yescharacteristic, complemented, Sylow
294C23Dic3212yes—
295C23C2×#62411yescharacteristic
296Q8—22no—
297D4—24no—
298D4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—184no—
302C2×C4Dic3212yes—
303C2×C4C2×D3×Dic311yescharacteristic
304C2×C4C2×D3×Dic311yescharacteristic
305C2×C4#380412yes—
306C2×C4D3×#6712yes—
307C8—31no—
308C8—31no—
309C8—32no—
310C8—62no—
311C8—64no—
312C2×C3—22no—
313C2×C3—21no—
314C2×C3—22no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—42no—
318C2×C3—41no—
319C2×C3—42no—
320C2×C3—42no—
321C2×C3—82no—
322C2×C3Dic3×C22⋊C411yescharacteristic
323C2×C3C4×#21711yescharacteristic
324C22—22no—
325C22—41no—
326C22—42no—
327C22#6395212yes—
328C22C2×Dic3211yescharacteristic
329C4—22no—
330C4—364no—
331C4#6395511yescharacteristic
332C4D3×#21711yescharacteristic
333C4Dic3×#6712yes—
334C3—21no—
335C3#7013311yescharacteristic, complemented
336C3#7201111yescharacteristic, complemented
337C2—22no—
338C2—21no—
339C2—42no—
340C2Dic3×#21711yescharacteristic
subgroupG/H
centerC4D3×#217
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32C4×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1757
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591059C2semidirect
5. #10589171C2semidirect
12. C2×C3×#208C4semidirect
15. C22×C3×C3⋊C8C4semidirect
18. C3×#836C4semidirect
19. C3×#833C4semidirect
71. C2×#208Dic3semidirect
74. C22×C3⋊C8Dic3semidirect
78. #836Dic3semidirect
82. #833Dic3semidirect
293. C32#1757semidirect
335. C3#70133semidirect
336. C3#72011semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9482
#105929392
C3×#52372
#105910592
#105891712
#720113
#701333