Finite Group Databasebeta

← #11785292

Subgroups — #11785292

Order 1152.

733 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2#10591230C211yesmaximal, characteristic
3C2×#63572C211yesmaximal, characteristic
4C2×#63567C212yesmaximal
5C3×#4529C212yesmaximal
6#68905—32nomaximal
7C22×#634C2211yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×#3750—21no—
10C2×C4×C3⋊Dic3—21no—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64096—22no—
13#64096C414yescomplemented
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16#63579—21no—
17#63579—21no—
18#63572—22no—
19#63567—24no—
20C2×#887—32no—
21C2×#887—61no—
22C2×#816—32no—
23C2×Dic3⋊C8—32no—
24#4977—32no—
25C2×#810—32no—
26C3×#340—32no—
27#4529D312yes—
28C22×C32×C4—21no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C2×#634—21no—
34C2×#634—21no—
35C2×#634—21no—
36C2×#634C2×C412yes—
37C2×#634D412yes—
38C2×#634Q812yes—
39C22×C3×Dic3—22no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4C2×C412yes—
42#3750—24no—
43C4×C3⋊Dic3—24no—
44C4×C3⋊Dic3C2×C412yes—
45C4×C3⋊Dic3D412yes—
46C3×C4⋊Dic3—22no—
47C3×C4⋊Dic3—22no—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8—22no—
51#1805—91noSylow
52C22×Dic6—32no—
53C22×Dic6—61no—
54C22×C3×C8—32no—
55C2×C3×C4⋊C4—21no—
56C2×C3×C4⋊C4—32no—
57C2×C3×C4⋊C4C2×D312yes—
58C2×C4⋊Dic3C2×D312yes—
59C2×Dic3⋊C4—62no—
60C2×Dic3⋊C4—62no—
61C2×C4×Dic3—32no—
62C2×C4×Dic3—61no—
63C2×C4×Dic3—62no—
64C2×C4×Dic3—62no—
65C22×C3⋊C8C2×D312yes—
66#887—38no—
67#887—64no—
68#887—64no—
69#887—64no—
70C3⋊#95—62no—
71C3⋊#95—62no—
72#816—64no—
73Dic3⋊C8—64no—
74#810—64no—
75C23×C32C2×D411yescharacteristic
76C2×C32×C4—22no—
77C2×C32×C4—42no—
78C2×C32×C4C22×C411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×Q811yescharacteristic
82C2×C32×C4#4111yescharacteristic
83C2×C32×C4#4111yescharacteristic
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3C22⋊C412yes—
90C2×C3⋊Dic3C22⋊C412yes—
91#634—22no—
92#634—22no—
93#634—22no—
94#634C4⋊C414yes—
95C2×C3×Dic3—42no—
96C2×C3×Dic3—42no—
97C2×C3×Dic3—42no—
98C3×C3⋊C8—42no—
99C2×C4×Q8—91no—
100C2×C4⋊C8—91no—
101C2×#103—92no—
102#382—91no—
103#340—32no—
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C22×C3×C4—21no—
107C22×C3×C4—62no—
108C22×C3×C4C22×D312yes—
109C22×Dic3—22no—
110C22×Dic3—32no—
111C22×Dic3—32no—
112C22×Dic3—61no—
113C22×Dic3—61no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C2×Dic6—34no—
117C2×Dic6—34no—
118C2×Dic6—34no—
119C2×Dic6—62no—
120C2×Dic6—62no—
121C2×Dic6—62no—
122C2×Dic6—62no—
123C2×Dic6—62no—
124C2×Dic6—62no—
125C2×Dic6—62no—
126C2×Dic6—62no—
127C2×Dic6—62no—
128C2×C3×C8—62no—
129C2×C3×C8—62no—
130C2×C3×C8—62no—
131C3×C4⋊C4—22no—
132C3×C4⋊C4—22no—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—62no—
135C3×C4⋊C4—62no—
136C3×C4⋊C4C4×D314yes—
137C4⋊Dic3—22no—
138C4⋊Dic3—22no—
139Dic3⋊C4—68no—
140Dic3⋊C4—68no—
141C4×Dic3—34no—
142C4×Dic3—34no—
143C4×Dic3—62no—
144C4×Dic3—62no—
145C4×Dic3—68no—
146C4×Dic3—68no—
147C2×C3⋊C8—22no—
148C2×C3⋊C8—22no—
149C2×C3⋊C8—22no—
150C22×C32C2×C22⋊C411yescharacteristic
151C22×C32#12111yescharacteristic
152C22×C32C22⋊Q811yescharacteristic
153C22×C32#13512yes—
154C22×C32#13712yes—
155C32×C4—42no—
156C32×C4C2×C4⋊C411yescharacteristic
157C32×C4#11711yescharacteristic
158C32×C4#12111yescharacteristic
159C32×C4C22⋊Q811yescharacteristic
160C3⋊Dic3—24no—
161C3⋊Dic3—22no—
162C3⋊Dic3—22no—
163C3×Dic3—82no—
164C22×Q8—91no—
165C22×C8—32no—
166C4×Q8—94no—
167C4×Q8—182no—
168C2×C4⋊C4—32no—
169C2×C4⋊C4—181no—
170C2×C4⋊C4D3211yescharacteristic
171C2×C42—91no—
172C2×C42—181no—
173C4⋊C8—182no—
174#103—184no—
175#95—181no—
176#95—181no—
177C23×C3—21no—
178C23×C3D3×D412yes—
179C2×C3×C4—24no—
180C2×C3×C4—24no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—44no—
188C2×C3×C4—42no—
189C2×C3×C4—42no—
190C2×C3×C4—122no—
191C2×C3×C4—122no—
192C2×C3×C4—122no—
193C2×C3×C4C2×C4×D312yes—
194C2×C3×C4#23512yes—
195C2×C3×C4#23512yes—
196C2×C3×C4D3×D412yes—
197C2×C3×C4D3×D412yes—
198C2×C3×C4D3×Q812yes—
199C2×Dic3—34no—
200C2×Dic3—34no—
201C2×Dic3—42no—
202C2×Dic3—42no—
203C2×Dic3—42no—
204C2×Dic3—62no—
205C2×Dic3—62no—
206C2×Dic3—64no—
207C2×Dic3—64no—
208C2×Dic3—64no—
209C2×Dic3—64no—
210C2×Dic3—64no—
211C2×Dic3—64no—
212C2×Dic3—64no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—122no—
218Dic6—38no—
219Dic6—64no—
220Dic6—64no—
221Dic6—64no—
222Dic6—64no—
223Dic6—64no—
224Dic6—64no—
225Dic6—64no—
226C3×C8—122no—
227C3⋊C8—42no—
228C2×C32#38011yescharacteristic
229C2×C32#41611yescharacteristic
230C2×C32#41911yescharacteristic
231C2×C32#46412yes—
232C2×C32#47912yes—
233C2×Q8—92no—
234C2×Q8—92no—
235C2×Q8—92no—
236C2×Q8—181no—
237C2×Q8—181no—
238C2×Q8—181no—
239C22×C4—21no—
240C22×C4—62no—
241C22×C4—91no—
242C22×C4—91no—
243C22×C4—181no—
244C22×C4C2×D3211yescharacteristic
245C2×C8—62no—
246C2×C8—62no—
247C2×C8—62no—
248C4⋊C4—21no—
249C4⋊C4—62no—
250C4⋊C4—62no—
251C4⋊C4—184no—
252C4⋊C4#62412yes—
253C42—92no—
254C42—92no—
255C42—184no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3D3×C22⋊C412yes—
262C22×C3#88412yes—
263C22×C3#89612yes—
264C22×C3#91212yes—
265C22×C3#91512yes—
266C22×C3#91612yes—
267C22×C3#91812yes—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—44no—
273C3×C4—44no—
274C3×C4—242no—
275C3×C4#87212yes—
276C3×C4#88412yes—
277C3×C4D3×C4⋊C412yes—
278C3×C4#89612yes—
279Dic3—68no—
280Dic3—64no—
281Dic3—68no—
282Dic3—64no—
283Dic3—64no—
284Dic3—82no—
285Dic3—122no—
286C32#180511yescharacteristic, complemented, Sylow
287C23#381111yescharacteristic
288Q8—94no—
289Q8—182no—
290Q8—182no—
291Q8—182no—
292C2×C4—22no—
293C2×C4—42no—
294C2×C4—92no—
295C2×C4—92no—
296C2×C4—122no—
297C2×C4—122no—
298C2×C4—122no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4—182no—
304C2×C4#379711yescharacteristic
305C2×C4#379811yescharacteristic
306C2×C4#379811yescharacteristic
307C2×C4#380211yescharacteristic
308C2×C4C2×#62411yescharacteristic
309C2×C4#381111yescharacteristic
310C8—122no—
311C2×C3—22no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—22no—
316C2×C3#466712yes—
317C2×C3#476712yes—
318C2×C3#477212yes—
319C2×C3#479812yes—
320C2×C3#480212yes—
321C2×C3#485712yes—
322C2×C3#487712yes—
323C22#6386511yescharacteristic
324C22#6391211yescharacteristic
325C22#6393612yes—
326C22#6395112yes—
327C22#6397411yescharacteristic
328C4—42no—
329C4—182no—
330C4—184no—
331C4—182no—
332C4—242no—
333C4#6386511yescharacteristic
334C4#6387411yescharacteristic
335C4#6390011yescharacteristic
336C4#6391211yescharacteristic
337C3—21no—
338C3#6890512yescomplemented
339C2#1059043412yes—
340C2#1059053812yes—
341C2#1059135511yescharacteristic
342C2#1059142411yescharacteristic
343C2#1059156211yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1805
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
13. #64096C4semidirect
286. C32#1805semidirect
338. C3#68905semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
#105912302
C2×#635722
C2×#635672
C3×#45292
#689053