Finite Group Databasebeta

← #11791665

Subgroups — #11791665

Order 1152.

617 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#870C211yesmaximal, characteristic
2C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
4#10589164C212yesmaximal
5#10589164C212yesmaximal
6#71738—31nomaximal
7#70461—31nomaximal
8C2×C32×C42C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2212yes—
10C2×C4×C3⋊Dic3—21no—
11C2×C3×C4⋊Dic3C2211yescharacteristic
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C2×C3×Dic3⋊C4—21no—
14C2×C3×Dic3⋊C4—21no—
15C22×C3×C3⋊C8C2212yes—
16C3×#870—22no—
17C3×#870C414yescomplemented
18#63658—21no—
19C3×C4⋊(C3⋊C8)—22no—
20C2×C3×#125—31no—
21C2×#870D311yescharacteristic
22C2×C3×C4⋊C8—31no—
23C4×C4⋊Dic3—31no—
24C4×C4⋊Dic3—31no—
25C4×C4⋊Dic3—61no—
26C2×C4⋊(C3⋊C8)D311yescharacteristic
27#4551—32no—
28#4551—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—
39C4⋊(C3⋊Dic3)—22no—
40C4⋊(C3⋊Dic3)Q814yes—
41C4×C3⋊Dic3—42no—
42C3×C4⋊Dic3—21no—
43C3×C4⋊Dic3—21no—
44C3×C4⋊Dic3C2×C412yes—
45C3×C4⋊Dic3C2×C412yes—
46C3×Dic3⋊C4—24no—
47C3×Dic3⋊C4—24no—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—24no—
50#1989—91noSylow
51C22×C3×C8—32no—
52C3×#125—34no—
53C3×#125—62no—
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×C42C2×D311yescharacteristic
60C2×C3×C42C2×D311yescharacteristic
61C2×C4⋊Dic3—32no—
62C2×C4⋊Dic3—32no—
63C2×C4⋊Dic3—62no—
64C2×C4⋊Dic3C2×D311yescharacteristic
65C2×C4⋊Dic3C2×D311yescharacteristic
66C2×Dic3⋊C4—21no—
67C2×Dic3⋊C4—21no—
68C2×C4×Dic3—62no—
69C2×C4×Dic3—61no—
70C2×C4×Dic3—61no—
71C22×C3⋊C8C2×D312yes—
72#870—22no—
73#870Dic314yescomplemented
74C3×C4⋊C8—62no—
75C3⋊#95—62no—
76C3⋊#95—61no—
77C3⋊#95—61no—
78C4⋊(C3⋊C8)—22no—
79C23×C32C2×D411yescharacteristic
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4—22no—
83C2×C32×C4C22⋊C412yes—
84C2×C32×C4C22⋊C412yes—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×Q812yes—
88C2×C32×C4#4112yes—
89C2×C3⋊Dic3—24no—
90C2×C3⋊Dic3—42no—
91C2×C3⋊Dic3—42no—
92C2×C3×Dic3—22no—
93C2×C3×Dic3—22no—
94C2×C3×Dic3—42no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C3×C3⋊C8—42no—
98C2×#125—31no—
99C2×C4⋊C8—31no—
100C4×C4⋊C4—91no—
101#340—92no—
102#340—92no—
103C22×C3×C4—21no—
104C22×C3×C4—21no—
105C22×C3×C4—21no—
106C22×C3×C4—61no—
107C22×C3×C4—61no—
108C22×C3×C4D1211yescharacteristic
109C22×C3×C4D1211yescharacteristic
110C22×C3×C4#6711yescharacteristic
111C22×C3×C4#6711yescharacteristic
112C22×C3×C4C22×D311yescharacteristic
113C22×C3×C4C22×D311yescharacteristic
114C22×Dic3—21no—
115C22×Dic3—21no—
116C22×Dic3—64no—
117C22×Dic3—62no—
118C22×Dic3—62no—
119C2×C3×C8—64no—
120C2×C3×C8—62no—
121C3×C4⋊C4—32no—
122C3×C4⋊C4—32no—
123C3×C4⋊C4—64no—
124C3×C4⋊C4—64no—
125C3×C4⋊C4—61no—
126C3×C4⋊C4—61no—
127C3×C42—22no—
128C3×C42—22no—
129C3×C42C4×D312yes—
130C3×C42C2×Dic312yes—
131C3×C42#6712yes—
132C3×C42#6712yes—
133C4⋊Dic3—21no—
134C4⋊Dic3—21no—
135C4⋊Dic3—34no—
136C4⋊Dic3—34no—
137C4⋊Dic3—64no—
138C4⋊Dic3—64no—
139C4⋊Dic3—62no—
140C4⋊Dic3—62no—
141C4⋊Dic3C2×Dic312yes—
142C4⋊Dic3C2×Dic312yes—
143Dic3⋊C4—24no—
144Dic3⋊C4—24no—
145C4×Dic3—124no—
146C4×Dic3—122no—
147C4×Dic3—122no—
148C2×C3⋊C8—24no—
149C2×C3⋊C8—22no—
150C22×C32C2×C22⋊C411yescharacteristic
151C22×C32C22⋊Q812yes—
152C22×C32#13512yes—
153C22×C32AGL(1,ℤ/8)11yescharacteristic
154C22×C32#13711yescharacteristic
155C32×C4—22no—
156C32×C4—22no—
157C32×C4C4×Q812yes—
158C32×C4#12411yescharacteristic
159C32×C4C4⋊Q811yescharacteristic
160C3⋊Dic3—44no—
161C3×Dic3—42no—
162C3×Dic3—42no—
163C22×C8—32no—
164#125—34no—
165#125—62no—
166C2×C4⋊C4—31no—
167C2×C4⋊C4—31no—
168C2×C4⋊C4—61no—
169C2×C4⋊C4—61no—
170C2×C4⋊C4—92no—
171C2×C42—181no—
172C2×C42D3211yescharacteristic
173C4⋊C8—62no—
174#95—181no—
175C23×C3—21no—
176C23×C3C2×D1211yescharacteristic
177C23×C3C2×#6711yescharacteristic
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—22no—
185C2×C3×C4—21no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—42no—
193C2×C3×C4—62no—
194C2×C3×C4—62no—
195C2×C3×C4—122no—
196C2×C3×C4—121no—
197C2×C3×C4—121no—
198C2×C3×C4(C2×D3)⋊C412yes—
199C2×C3×C4(C2×D3)⋊C412yes—
200C2×C3×C4#21712yes—
201C2×C3×C4#21712yes—
202C2×C3×C4C2×C4×D311yescharacteristic
203C2×C3×C4#23712yes—
204C2×C3×C4D3×Q812yes—
205C2×C3×C4D3×Q812yes—
206C2×C3×C4#23912yes—
207C2×C3×C4C22×Dic311yescharacteristic
208C2×C3×C4C2×#6711yescharacteristic
209C2×C3×C4C2×#6711yescharacteristic
210C2×Dic3—22no—
211C2×Dic3—22no—
212C2×Dic3—41no—
213C2×Dic3—42no—
214C2×Dic3—41no—
215C2×Dic3—68no—
216C2×Dic3—64no—
217C2×Dic3—64no—
218C2×Dic3—124no—
219C2×Dic3—124no—
220C2×Dic3—122no—
221C2×Dic3—122no—
222C2×Dic3—122no—
223C2×Dic3—122no—
224C3×C8—122no—
225C3⋊C8—42no—
226C2×C32#39111yescharacteristic
227C2×C32#41611yescharacteristic
228C2×C32#41711yescharacteristic
229C2×C32#47812yes—
230C2×C32#47912yes—
231C22×C4—61no—
232C22×C4—61no—
233C22×C4—182no—
234C22×C4#62611yescharacteristic
235C22×C4#62611yescharacteristic
236C22×C4C2×D3211yescharacteristic
237C2×C8—64no—
238C2×C8—62no—
239C4⋊C4—32no—
240C4⋊C4—32no—
241C4⋊C4—64no—
242C4⋊C4—64no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—94no—
246C4⋊C4—182no—
247C42—362no—
248C42D3×Dic312yes—
249C42#62512yes—
250C22×C3—21no—
251C22×C3—22no—
252C22×C3—21no—
253C22×C3—22no—
254C22×C3—21no—
255C22×C3#89712yes—
256C22×C3#90412yes—
257C22×C3#90811yescharacteristic
258C22×C3#90911yescharacteristic
259C22×C3C2×(C2×D3)⋊C411yescharacteristic
260C22×C3#94612yes—
261C22×C3#94911yescharacteristic
262C22×C3#95012yes—
263C22×C3#95111yescharacteristic
264C22×C3C2×#21711yescharacteristic
265C3×C4—24no—
266C3×C4—22no—
267C3×C4—22no—
268C3×C4—22no—
269C3×C4—22no—
270C3×C4—22no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—42no—
274C3×C4—122no—
275C3×C4—122no—
276C3×C4#88712yes—
277C3×C4#93611yescharacteristic
278C3×C4#94411yescharacteristic
279C3×C4#94411yescharacteristic
280C3×C4Q8×Dic312yes—
281C3×C4#94711yescharacteristic
282Dic3—42no—
283Dic3—42no—
284Dic3—128no—
285Dic3—124no—
286Dic3—124no—
287C32#198911yescharacteristic, complemented, Sylow
288C23C2×#62611yescharacteristic
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—62no—
293C2×C4—62no—
294C2×C4—121no—
295C2×C4—122no—
296C2×C4—121no—
297C2×C4—184no—
298C2×C4—362no—
299C2×C4—362no—
300C2×C4(C2×D3)⋊Dic312yes—
301C2×C4(C2×D3)⋊Dic312yes—
302C2×C4#379612yes—
303C2×C4#379712yes—
304C2×C4C2×D3×Dic311yescharacteristic
305C2×C4C2×#62511yescharacteristic
306C8—122no—
307C2×C3—22no—
308C2×C3—22no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3#482912yes—
313C2×C3#484712yes—
314C2×C3#497311yescharacteristic
315C2×C3#506312yes—
316C2×C3#506612yes—
317C2×C3#511311yescharacteristic
318C2×C3#513311yescharacteristic
319C2×C3#522911yescharacteristic
320C2×C3#523211yescharacteristic
321C2×C3#523311yescharacteristic
322C22#6382511yescharacteristic
323C22#6382912yes—
324C22#6383111yescharacteristic
325C22#6387112yes—
326C22C2×(C2×D3)⋊Dic311yescharacteristic
327C4—22no—
328C4—22no—
329C4—122no—
330C4—122no—
331C4—364no—
332C4#6384312yes—
333C4#6386311yescharacteristic
334C4#6387311yescharacteristic
335C3—21no—
336C3#7046111yescharacteristic, complemented
337C3#7173811yescharacteristic, complemented
338C2#1059029212yes—
339C2#1059030812yes—
340C2#1059108411yescharacteristic
341C2#1059108811yescharacteristic
342C2#1059122111yescharacteristic
subgroupG/H
centerC23C2×#626
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
73. #870Dic3semidirect
287. C32#1989semidirect
336. C3#70461semidirect
337. 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
C4×C4⋊(C3⋊Dic3)2
C2×C3×C4⋊(C3⋊C8)2
#105891642
#717383
#704613