Finite Group Databasebeta

← #11785354

Subgroups — #11785354

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C3⋊C8C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic
3C3×#5212C211yesmaximal, characteristic
4C2×#63573C212yesmaximal, complemented
5#10589164C212yesmaximal, complemented
6#71970—31nomaximal
7#69511—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×#3757—21no—
10C2×C4⋊(C3⋊Dic3)C2212yes—
11C2×C3×#217—21no—
12C2×C3×C4⋊Dic3C2212yes—
13C22×C3×C3⋊C8—24no—
14C22×C3×C3⋊C8C414yescomplemented
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63658—21no—
18C3×C3⋊#95—21no—
19#63573—24no—
20C23×C3×C8—31no—
21C23×C3⋊C8D311yescharacteristic
22C3×#380—31no—
23#5212—31no—
24#5212—31no—
25#5212—61no—
26#5212D311yescharacteristic
27C2×#817—32no—
28C2×#808—32no—
29#4551—32no—
30#4529—32no—
31C24×C32D411yescharacteristic
32C22×C32×C4—22no—
33C22×C32×C4—22no—
34C22×C32×C4C2×C412yes—
35C22×C32×C4D411yescharacteristic
36C22×C32×C4Q812yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—22no—
39C22×C3×Dic3—22no—
40#3757—42no—
41C4⋊(C3⋊Dic3)—22no—
42C4⋊(C3⋊Dic3)—22no—
43C3×#217—42no—
44C3×C4⋊Dic3—22no—
45C3×C4⋊Dic3—22no—
46C2×C3×C3⋊C8—22no—
47C2×C3×C3⋊C8—28no—
48C2×C3×C3⋊C8C2×C412yes—
49C2×C3×C3⋊C8C2×C412yes—
50C2×C3×C3⋊C8D414yes—
51#1807—91noSylow
52C23×C3×C4—21no—
53C23×C3×C4C2×D311yescharacteristic
54C23×C3×C4C2×D311yescharacteristic
55C22×C3×C8—31no—
56C22×C3×C8—34no—
57C22×C3×C8—31no—
58C22×C3×C8—64no—
59C2×C3×C4⋊C4—32no—
60C2×C3×C22⋊C4—61no—
61C2×#217—21no—
62C2×#217—62no—
63C2×#217—61no—
64C2×#217—61no—
65C2×C4⋊Dic3—32no—
66C2×C4⋊Dic3—32no—
67C2×C4⋊Dic3—62no—
68C2×C4⋊Dic3C2×D312yes—
69C22×C3⋊C8—24no—
70C22×C3⋊C8Dic314yescomplemented
71C22×C3⋊C8C2×D311yescharacteristic
72C22×C3⋊C8C2×D311yescharacteristic
73C3×#95—61no—
74C3⋊#95—21no—
75C3⋊#95—62no—
76C3⋊#95—61no—
77C3⋊#95—61no—
78#817—64no—
79#808—64no—
80C23×C32—22no—
81C23×C32—22no—
82C23×C32C4⋊C412yes—
83C23×C32SD1612yes—
84C23×C32SD1612yes—
85C23×C32C2×D411yescharacteristic
86C2×C32×C4—22no—
87C2×C32×C4—22no—
88C2×C32×C4—22no—
89C2×C32×C4—24no—
90C2×C32×C4C4⋊C412yes—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D412yes—
93C2×C32×C4C2×Q811yescharacteristic
94C2×C32×C4#4112yes—
95C2×C3⋊Dic3—42no—
96C2×C3⋊Dic3—42no—
97C2×C3⋊Dic3—42no—
98C2×C3×Dic3—42no—
99C2×C3×Dic3—42no—
100C2×C3×Dic3—42no—
101C3×C3⋊C8—22no—
102C3×C3⋊C8C22⋊C414yescomplemented
103C23×C8—31no—
104C2×#106—92no—
105#380—31no—
106#380—91no—
107#340—92no—
108C24×C3—21no—
109C24×C3D1211yescharacteristic
110C24×C3#6711yescharacteristic
111C22×C3×C4—22no—
112C22×C3×C4—22no—
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×C3×C4—21no—
117C22×C3×C4—22no—
118C22×C3×C4—21no—
119C22×C3×C4—42no—
120C22×C3×C4—42no—
121C22×C3×C4—62no—
122C22×C3×C4Dic612yes—
123C22×C3×C4Dic612yes—
124C22×C3×C4C4×D312yes—
125C22×C3×C4D1211yescharacteristic
126C22×C3×C4C2×Dic312yes—
127C22×C3×C4#6711yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C22×C3×C4C22×D311yescharacteristic
130C22×Dic3—22no—
131C22×Dic3—64no—
132C22×Dic3—62no—
133C22×Dic3—62no—
134C2×C3×C8—32no—
135C2×C3×C8—34no—
136C2×C3×C8—32no—
137C2×C3×C8—68no—
138C2×C3×C8—62no—
139C3×C4⋊C4—62no—
140C3×C4⋊C4—62no—
141C3×C22⋊C4—122no—
142#217—42no—
143#217—124no—
144#217—122no—
145#217—122no—
146C4⋊Dic3—22no—
147C4⋊Dic3—22no—
148C4⋊Dic3—62no—
149C4⋊Dic3—62no—
150C4⋊Dic3—62no—
151C4⋊Dic3—62no—
152C4⋊Dic3—122no—
153C4⋊Dic3—122no—
154C2×C3⋊C8—22no—
155C2×C3⋊C8—28no—
156C2×C3⋊C8C2×Dic312yes—
157C2×C3⋊C8C2×Dic312yes—
158C2×C3⋊C8#6714yes—
159C22×C32—22no—
160C22×C32—22no—
161C22×C32—24no—
162C22×C32—24no—
163C22×C32#10614yescomplemented
164C22×C32C2×C4⋊C411yescharacteristic
165C22×C32#12112yes—
166C22×C32C2×SD1611yescharacteristic
167C22×C32C2×SD1611yescharacteristic
168C22×C32#13512yes—
169C32×C4—22no—
170C32×C4C2×C22⋊C411yescharacteristic
171C32×C4#11711yescharacteristic
172C32×C4C22⋊Q812yes—
173C3⋊Dic3—82no—
174C3×Dic3—82no—
175C23×C4D3211yescharacteristic
176C22×C8—31no—
177C22×C8—34no—
178C22×C8—31no—
179C22×C8—64no—
180C2×C4⋊C4—32no—
181C2×C4⋊C4—92no—
182C2×C22⋊C4—61no—
183C2×C22⋊C4—181no—
184#106—184no—
185#95—61no—
186#95—181no—
187C23×C3—22no—
188C23×C3—22no—
189C23×C3—22no—
190C23×C3—22no—
191C23×C3—22no—
192C23×C3—22no—
193C23×C3—22no—
194C23×C3—21no—
195C23×C3—42no—
196C23×C3—42no—
197C23×C3#20412yes—
198C23×C3#20412yes—
199C23×C3Dic3⋊C412yes—
200C23×C3C4⋊Dic312yes—
201C23×C3#21412yes—
202C23×C3#21512yes—
203C23×C3C2×D1211yescharacteristic
204C23×C3C2×#6711yescharacteristic
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—24no—
209C2×C3×C4—22no—
210C2×C3×C4—24no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—21no—
215C2×C3×C4—22no—
216C2×C3×C4—21no—
217C2×C3×C4—22no—
218C2×C3×C4—42no—
219C2×C3×C4—44no—
220C2×C3×C4—42no—
221C2×C3×C4—42no—
222C2×C3×C4—122no—
223C2×C3×C4—122no—
224C2×C3×C4—122no—
225C2×C3×C4Dic3⋊C412yes—
226C2×C3×C4C4⋊Dic312yes—
227C2×C3×C4C2×Dic611yescharacteristic
228C2×C3×C4C2×Dic611yescharacteristic
229C2×C3×C4C2×C4×D311yescharacteristic
230C2×C3×C4#23512yes—
231C2×C3×C4D3×D412yes—
232C2×C3×C4#23712yes—
233C2×C3×C4C22×Dic311yescharacteristic
234C2×C3×C4C2×#6712yes—
235C2×Dic3—42no—
236C2×Dic3—42no—
237C2×Dic3—42no—
238C2×Dic3—124no—
239C2×Dic3—124no—
240C2×Dic3—124no—
241C2×Dic3—122no—
242C2×Dic3—122no—
243C2×Dic3—122no—
244C2×Dic3—122no—
245C2×Dic3—122no—
246C2×Dic3—122no—
247C3×C8—34no—
248C3×C8—62no—
249C3⋊C8—22no—
250C3⋊C8#21714yescomplemented
251C2×C32—24no—
252C2×C32#38011yescharacteristic
253C2×C32C2×#10611yescharacteristic
254C2×C32#42711yescharacteristic
255C2×C32#46512yes—
256C2×C32#46512yes—
257C24#62611yescharacteristic
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—62no—
261C22×C4—182no—
262C22×C4D3×Dic312yes—
263C22×C4#62611yescharacteristic
264C22×C4#62712yes—
265C22×C4C2×D3211yescharacteristic
266C2×C8—32no—
267C2×C8—34no—
268C2×C8—32no—
269C2×C8—68no—
270C2×C8—62no—
271C4⋊C4—62no—
272C4⋊C4—62no—
273C4⋊C4—182no—
274C4⋊C4—182no—
275C22⋊C4—122no—
276C22⋊C4—362no—
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3—24no—
281C22×C3—24no—
282C22×C3—22no—
283C22×C3—24no—
284C22×C3—24no—
285C22×C3—21no—
286C22×C3—24no—
287C22×C3—22no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—22no—
291C22×C3—42no—
292C22×C3—42no—
293C22×C3—44no—
294C22×C3—44no—
295C22×C3#80814yescomplemented
296C22×C3#81714yescomplemented
297C22×C3C2×#20411yescharacteristic
298C22×C3C2×#20411yescharacteristic
299C22×C3#90412yes—
300C22×C3C2×Dic3⋊C411yescharacteristic
301C22×C3C2×C4⋊Dic311yescharacteristic
302C22×C3#93012yes—
303C22×C3C2×#21411yescharacteristic
304C22×C3#93912yes—
305C22×C3C2×#21511yescharacteristic
306C22×C3#95012yes—
307C3×C4—22no—
308C3×C4—22no—
309C3×C4—21no—
310C3×C4—22no—
311C3×C4—21no—
312C3×C4—42no—
313C3×C4—242no—
314C3×C4#87711yescharacteristic
315C3×C4#87812yes—
316C3×C4D3×C22⋊C411yescharacteristic
317C3×C4#92412yes—
318C3×C4#92611yescharacteristic
319C3×C4C2×#21711yescharacteristic
320Dic3—82no—
321Dic3—244no—
322Dic3—242no—
323Dic3—242no—
324C32#180711yescharacteristic, complemented, Sylow
325C23—22no—
326C23—22no—
327C23#371612yes—
328C23#371712yes—
329C23Dic3⋊Dic312yes—
330C23C2×#62611yescharacteristic
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—122no—
336C2×C4—122no—
337C2×C4—122no—
338C2×C4—362no—
339C2×C4—362no—
340C2×C4—362no—
341C2×C4Dic3⋊Dic312yes—
342C2×C4C2×D3×Dic311yescharacteristic
343C2×C4#380412yes—
344C2×C4C2×#62711yescharacteristic
345C2×C4D3×#6712yes—
346C8—34no—
347C8—62no—
348C2×C3—24no—
349C2×C3—24no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—22no—
353C2×C3—22no—
354C2×C3—21no—
355C2×C3—44no—
356C2×C3#494211yescharacteristic
357C2×C3C2×#80811yescharacteristic
358C2×C3#499811yescharacteristic
359C2×C3#504112yes—
360C2×C3#504812yes—
361C2×C3C2×#81711yescharacteristic
362C2×C3#510611yescharacteristic
363C2×C3#511412yes—
364C2×C3#511412yes—
365C2×C3#521211yescharacteristic
366C22—22no—
367C22—24no—
368C22—24no—
369C22—22no—
370C22#6357314yescomplemented
371C22C2×#371611yescharacteristic
372C22#6382912yes—
373C22C2×#371711yescharacteristic
374C22C2×Dic3⋊Dic311yescharacteristic
375C22#6397812yes—
376C4—22no—
377C4—242no—
378C4—722no—
379C4#6395511yescharacteristic
380C4#6396412yes—
381C4D3×#21711yescharacteristic
382C3—21no—
383C3#6951111yescharacteristic, complemented
384C3#7197011yescharacteristic, complemented
385C2—24no—
386C2#1059112211yescharacteristic
387C2C2×#6357311yescharacteristic
388C2#1059117512yes—
389C2#1059117712yes—
390C2#1059171611yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC24×C32D4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1807
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63573C2semidirect
5. #10589164C2semidirect
14. C22×C3×C3⋊C8C4semidirect
70. C22×C3⋊C8Dic3semidirect
102. C3×C3⋊C8C22⋊C4semidirect
163. C22×C32#106semidirect
250. C3⋊C8#217semidirect
295. C22×C3#808semidirect
296. C22×C3#817semidirect
324. C32#1807semidirect
370. C22#63573semidirect
383. C3#69511semidirect
384. C3#71970semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C3⋊C82
#105929112
C3×#52122
C2×#635732
#105891642
#719703
#695113