Finite Group Databasebeta

← #11791664

Subgroups — #11791664

Order 1152.

589 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#870C211yesmaximal, characteristic
2C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic
4#10589163C212yesmaximal
5#10589163C212yesmaximal
6#71738—31nomaximal
7#69491—31nomaximal
8C2×C32×C42C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2212yes—
10C2×C3×C4⋊Dic3C2211yescharacteristic
11C2×C3×C4⋊Dic3C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13C2×C3×Dic3⋊C4—21no—
14C2×C3×Dic3⋊C4—21no—
15C2×C3×C4×Dic3—21no—
16C3×#870—22no—
17C3×#870C414yescomplemented
18C4⋊(C3⋊(C3⋊C8))—22no—
19C3×C3⋊#95—21no—
20C2×C3×#125—31no—
21C2×#870D311yescharacteristic
22C3×C4×C4⋊C4—31no—
23C4×C4⋊Dic3D311yescharacteristic
24C2×C4⋊(C3⋊C8)—31no—
25C2×C4⋊(C3⋊C8)—31no—
26C2×C4⋊(C3⋊C8)—61no—
27#4529—32no—
28#4529—32no—
29#4529—32no—
30#4529—32no—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3×Dic3—22no—
35C22×C3×Dic3—21no—
36C22×C3×Dic3—21no—
37C32×C42C2×C412yes—
38C32×C42D412yes—
39C2×C3⋊(C3⋊C8)—22no—
40C2×C3⋊(C3⋊C8)—24no—
41C3×C4⋊Dic3—21no—
42C3×C4⋊Dic3—21no—
43C3×C4⋊Dic3—22no—
44C3×C4⋊Dic3C2×C412yes—
45C3×C4⋊Dic3C2×C412yes—
46C3×C4⋊Dic3Q814yes—
47C3×Dic3⋊C4—24no—
48C3×Dic3⋊C4—24no—
49C3×C4×Dic3—42no—
50#1989—91noSylow
51C3×#125—34no—
52C3×#125—62no—
53C2×C3×C4⋊C4—32no—
54C2×C3×C4⋊C4—31no—
55C2×C3×C4⋊C4—31no—
56C2×C3×C4⋊C4—61no—
57C2×C3×C4⋊C4—61no—
58C2×C3×C42—21no—
59C2×C3×C42—61no—
60C2×C3×C42C2×D311yescharacteristic
61C2×C3×C42C2×D311yescharacteristic
62C2×C4⋊Dic3C2×D312yes—
63C2×C4⋊Dic3C2×D311yescharacteristic
64C2×C4⋊Dic3C2×D311yescharacteristic
65C2×Dic3⋊C4—21no—
66C2×Dic3⋊C4—21no—
67C2×C4×Dic3—21no—
68C22×C3⋊C8—32no—
69C22×C3⋊C8—32no—
70C22×C3⋊C8—62no—
71#870—22no—
72#870Dic314yescomplemented
73C3×#95—61no—
74C3⋊#95—21no—
75C4⋊(C3⋊C8)—64no—
76C4⋊(C3⋊C8)—62no—
77C4⋊(C3⋊C8)—62no—
78C23×C32C2×D411yescharacteristic
79C2×C32×C4—22no—
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4C22⋊C412yes—
83C2×C32×C4C22⋊C412yes—
84C2×C32×C4C22×C411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×Q812yes—
87C2×C32×C4#4112yes—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—24no—
91C2×C3×Dic3—42no—
92C2×C3×Dic3—42no—
93C2×C3×Dic3—42no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3—41no—
96C3⋊(C3⋊C8)—42no—
97C2×#125—31no—
98C2×C4⋊C8—91no—
99C4×C4⋊C4—31no—
100#340—92no—
101#340—92no—
102C22×C3×C4—21no—
103C22×C3×C4—21no—
104C22×C3×C4—21no—
105C22×C3×C4—62no—
106C22×C3×C4—61no—
107C22×C3×C4—61no—
108C22×C3×C4#6711yescharacteristic
109C22×C3×C4#6711yescharacteristic
110C22×C3×C4#6711yescharacteristic
111C22×C3×C4#6711yescharacteristic
112C22×C3×C4C22×D311yescharacteristic
113C22×C3×C4C22×D311yescharacteristic
114C22×Dic3—22no—
115C22×Dic3—21no—
116C22×Dic3—21no—
117C3×C4⋊C4—32no—
118C3×C4⋊C4—32no—
119C3×C4⋊C4—34no—
120C3×C4⋊C4—64no—
121C3×C4⋊C4—64no—
122C3×C4⋊C4—61no—
123C3×C4⋊C4—61no—
124C3×C4⋊C4—62no—
125C3×C42—22no—
126C3×C42—22no—
127C3×C42—122no—
128C3×C42C4×D312yes—
129C3×C42D1212yes—
130C3×C42C2×Dic312yes—
131C3×C42#6712yes—
132C4⋊Dic3—22no—
133C4⋊Dic3—21no—
134C4⋊Dic3—21no—
135C4⋊Dic3Dic614yes—
136C4⋊Dic3C2×Dic312yes—
137C4⋊Dic3C2×Dic312yes—
138Dic3⋊C4—24no—
139Dic3⋊C4—24no—
140C4×Dic3—42no—
141C2×C3⋊C8—64no—
142C2×C3⋊C8—62no—
143C2×C3⋊C8—64no—
144C2×C3⋊C8—64no—
145C2×C3⋊C8—62no—
146C2×C3⋊C8—124no—
147C22×C32C2×C22⋊C411yescharacteristic
148C22×C32C22⋊Q812yes—
149C22×C32#13512yes—
150C22×C32AGL(1,ℤ/8)11yescharacteristic
151C22×C32#13711yescharacteristic
152C32×C4—22no—
153C32×C4—22no—
154C32×C4C4×Q812yes—
155C32×C4#12411yescharacteristic
156C32×C4C4⋊Q811yescharacteristic
157C3×Dic3—42no—
158C3×Dic3—42no—
159C3×Dic3—44no—
160C22×C8—92no—
161#125—34no—
162#125—62no—
163C2×C4⋊C4—31no—
164C2×C4⋊C4—31no—
165C2×C4⋊C4—32no—
166C2×C4⋊C4—61no—
167C2×C4⋊C4—61no—
168C2×C42—61no—
169C2×C42D3211yescharacteristic
170C4⋊C8—182no—
171#95—61no—
172C23×C3—21no—
173C23×C3C2×#6711yescharacteristic
174C23×C3C2×#6711yescharacteristic
175C2×C3×C4—24no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—21no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—41no—
189C2×C3×C4—41no—
190C2×C3×C4—62no—
191C2×C3×C4—62no—
192C2×C3×C4—64no—
193C2×C3×C4—121no—
194C2×C3×C4—121no—
195C2×C3×C4—122no—
196C2×C3×C4—122no—
197C2×C3×C4—122no—
198C2×C3×C4(C2×D3)⋊C412yes—
199C2×C3×C4(C2×D3)⋊C412yes—
200C2×C3×C4#21712yes—
201C2×C3×C4#21712yes—
202C2×C3×C4C2×Dic612yes—
203C2×C3×C4C2×C4×D311yescharacteristic
204C2×C3×C4C2×D1211yescharacteristic
205C2×C3×C4#23512yes—
206C2×C3×C4D3×Q812yes—
207C2×C3×C4#23912yes—
208C2×C3×C4C22×Dic311yescharacteristic
209C2×C3×C4C2×#6711yescharacteristic
210C2×Dic3—24no—
211C2×Dic3—22no—
212C2×Dic3—22no—
213C2×Dic3—42no—
214C2×Dic3—41no—
215C2×Dic3—42no—
216C2×Dic3—42no—
217C2×Dic3—41no—
218C3⋊C8—124no—
219C3⋊C8—122no—
220C3⋊C8—122no—
221C2×C32#39111yescharacteristic
222C2×C32#41611yescharacteristic
223C2×C32#41711yescharacteristic
224C2×C32#47812yes—
225C2×C32#47912yes—
226C22×C4—62no—
227C22×C4—61no—
228C22×C4—61no—
229C22×C4#62511yescharacteristic
230C22×C4#62511yescharacteristic
231C22×C4C2×D3211yescharacteristic
232C2×C8—184no—
233C2×C8—182no—
234C4⋊C4—34no—
235C4⋊C4—32no—
236C4⋊C4—32no—
237C4⋊C4—64no—
238C4⋊C4—64no—
239C4⋊C4—62no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C42—122no—
243C42D3×Dic312yes—
244C42#62612yes—
245C22×C3—22no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—22no—
249C22×C3—21no—
250C22×C3#92412yes—
251C22×C3C2×(C2×D3)⋊C411yescharacteristic
252C22×C3#93211yescharacteristic
253C22×C3#94211yescharacteristic
254C22×C3#94612yes—
255C22×C3#94911yescharacteristic
256C22×C3#95012yes—
257C22×C3#95012yes—
258C22×C3#95111yescharacteristic
259C22×C3C2×#21711yescharacteristic
260C3×C4—24no—
261C3×C4—22no—
262C3×C4—22no—
263C3×C4—22no—
264C3×C4—22no—
265C3×C4—22no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—42no—
269C3×C4—122no—
270C3×C4—122no—
271C3×C4—124no—
272C3×C4C4×Dic612yes—
273C3×C4#86911yescharacteristic
274C3×C4#87511yescharacteristic
275C3×C4#94411yescharacteristic
276C3×C4Q8×Dic312yes—
277C3×C4#94711yescharacteristic
278Dic3—42no—
279Dic3—42no—
280Dic3—44no—
281C32#198911yescharacteristic, complemented, Sylow
282C23C2×#62511yescharacteristic
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—64no—
287C2×C4—62no—
288C2×C4—62no—
289C2×C4—122no—
290C2×C4—122no—
291C2×C4—122no—
292C2×C4—121no—
293C2×C4—121no—
294C2×C4(C2×D3)⋊Dic312yes—
295C2×C4(C2×D3)⋊Dic312yes—
296C2×C4D3×Dic612yes—
297C2×C4#379912yes—
298C2×C4C2×D3×Dic311yescharacteristic
299C2×C4C2×#62611yescharacteristic
300C8—362no—
301C2×C3—22no—
302C2×C3—22no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3#492911yescharacteristic
307C2×C3#496611yescharacteristic
308C2×C3#500211yescharacteristic
309C2×C3#500912yes—
310C2×C3#502212yes—
311C2×C3#506312yes—
312C2×C3#506612yes—
313C2×C3#522911yescharacteristic
314C2×C3#523211yescharacteristic
315C2×C3#523311yescharacteristic
316C22#6382212yes—
317C22#6382311yescharacteristic
318C22#6382711yescharacteristic
319C22#6385612yes—
320C22C2×(C2×D3)⋊Dic311yescharacteristic
321C4—22no—
322C4—22no—
323C4—124no—
324C4—122no—
325C4—122no—
326C4Dic3×Dic612yes—
327C4#6386411yescharacteristic
328C4#6386611yescharacteristic
329C3—21no—
330C3#6949111yescharacteristic, complemented
331C3#7173811yescharacteristic, complemented
332C2#1059027012yes—
333C2#1059028612yes—
334C2#1059108311yescharacteristic
335C2#1059108711yescharacteristic
336C2#1059122011yescharacteristic
subgroupG/H
centerC23C2×#625
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1989
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
17. C3×#870C4semidirect
72. #870Dic3semidirect
281. C32#1989semidirect
330. C3#69491semidirect
331. C3#71738semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8702
C2×C4⋊(C3⋊(C3⋊C8))2
C3×C4×C4⋊Dic32
#105891632
#717383
#694913