Finite Group Databasebeta

← #11771099

Subgroups — #11771099

Order 1152.

621 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3757C211yesmaximal, characteristic
2C3×C4×#217C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4#67683—31nomaximal
5#67618—31nomaximal
6C23×C32×C4C2211yescharacteristic
7C2×#3757—21no—
8C2×C4×C3⋊Dic3—21no—
9C2×C3×#217—21no—
10C2×C3×C4×Dic3—21no—
11C2×C3×#208C412yescomplemented
12#63658C412yescomplemented
13C3×C3⋊#95C412yescomplemented
14C3×#830—21no—
15C3×#830—21no—
16C3×#407—31no—
17C3×C4×C22⋊C4—31no—
18C4×#217—31no—
19C4×#217—31no—
20C4×#217—61no—
21C4×#217D311yescharacteristic
22#5207D311yescharacteristic
23C24×C32D411yescharacteristic
24C22×C32×C4—42no—
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4Q811yescharacteristic
31C22×C3⋊Dic3—22no—
32C22×C3×Dic3—22no—
33#3757—24no—
34C4×C3⋊Dic3—42no—
35C3×#217—24no—
36C3×C4×Dic3—42no—
37C3×#208—42no—
38C2×C3×C3⋊C8—22no—
39#1297—91noSylow
40C23×C3×C4—21no—
41C23×C3×C4C2×D311yescharacteristic
42C23×C3×C4C2×D311yescharacteristic
43C2×C3×M16—32no—
44C2×C3×C22⋊C4—61no—
45C2×C3×C42—61no—
46C2×#217—21no—
47C2×#217—62no—
48C2×#217—61no—
49C2×#217—61no—
50C2×C4×Dic3—21no—
51C2×C4×Dic3—62no—
52C2×C4×Dic3—61no—
53C2×C4×Dic3—61no—
54C2×#208Dic312yescomplemented
55C3×C22⋊C8—61no—
56C3×C22⋊C8—61no—
57C3×#95—32no—
58C3⋊#95—32no—
59C3⋊#95—32no—
60C3⋊#95—62no—
61C3⋊#95Dic312yescomplemented
62#830—21no—
63#830—21no—
64C23×C32—22no—
65C23×C32—22no—
66C23×C32—41no—
67C23×C32C22⋊C411yescharacteristic
68C23×C32C22⋊C411yescharacteristic
69C23×C32C4⋊C411yescharacteristic
70C2×C32×C4—22no—
71C2×C32×C4—22no—
72C2×C32×C4—22no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4C4211yescharacteristic
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C4⋊C411yescharacteristic
79C2×C32×C4C4⋊C411yescharacteristic
80C2×C3⋊Dic3—24no—
81C2×C3⋊Dic3—42no—
82C2×C3⋊Dic3—42no—
83C2×C3×Dic3—24no—
84C2×C3×Dic3—42no—
85C2×C3×Dic3—42no—
86C3×C3⋊C8—42no—
87#407—31no—
88C4×C22⋊C4—31no—
89C4×C22⋊C4—91no—
90C24×C3—21no—
91C24×C3D1211yescharacteristic
92C24×C3#6711yescharacteristic
93C22×C3×C4—21no—
94C22×C3×C4—21no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4—42no—
100C22×C3×C4—42no—
101C22×C3×C4—44no—
102C22×C3×C4—62no—
103C22×C3×C4Dic611yescharacteristic
104C22×C3×C4Dic611yescharacteristic
105C22×C3×C4C4×D311yescharacteristic
106C22×C3×C4C4×D311yescharacteristic
107C22×C3×C4C4×D311yescharacteristic
108C22×C3×C4C4×D311yescharacteristic
109C22×C3×C4D1211yescharacteristic
110C22×C3×C4C2×Dic311yescharacteristic
111C22×C3×C4C2×Dic311yescharacteristic
112C22×C3×C4#6711yescharacteristic
113C22×C3×C4#6711yescharacteristic
114C22×C3×C4#6711yescharacteristic
115C22×Dic3—22no—
116C22×Dic3—64no—
117C22×Dic3—62no—
118C22×Dic3—62no—
119C3×M16—122no—
120C2×C3×C8—62no—
121C3×C22⋊C4—64no—
122C3×C42—122no—
123#217—24no—
124#217—68no—
125#217—64no—
126#217—64no—
127C4×Dic3—42no—
128C4×Dic3—124no—
129C4×Dic3—122no—
130C4×Dic3—122no—
131#208—42no—
132C2×C3⋊C8—22no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32—21no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32—44no—
141C22×C32#9511yescharacteristic
142C22×C32#10412yes—
143C22×C32#10412yes—
144C32×C4—21no—
145C32×C4—21no—
146C32×C4—21no—
147C32×C4#9912yes—
148C3⋊Dic3—44no—
149C3×Dic3—44no—
150C23×C4D3211yescharacteristic
151C2×M16—32no—
152C2×C22⋊C4—61no—
153C2×C22⋊C4—181no—
154C2×C42—61no—
155C2×C42—181no—
156C22⋊C8—61no—
157C22⋊C8—61no—
158#95—32no—
159#95—92no—
160C23×C3—24no—
161C23×C3—22no—
162C23×C3—22no—
163C23×C3—22no—
164C23×C3—22no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3—42no—
169C23×C3—41no—
170C23×C3—41no—
171C23×C3—42no—
172C23×C3Dic3⋊C411yescharacteristic
173C23×C3C4⋊Dic311yescharacteristic
174C23×C3(C2×D3)⋊C411yescharacteristic
175C23×C3(C2×D3)⋊C411yescharacteristic
176C23×C3(C2×D3)⋊C411yescharacteristic
177C23×C3#21711yescharacteristic
178C2×C3×C4—24no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—42no—
190C2×C3×C4—42no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×C3×C4—41no—
194C2×C3×C4—41no—
195C2×C3×C4—41no—
196C2×C3×C4—41no—
197C2×C3×C4—42no—
198C2×C3×C4—42no—
199C2×C3×C4—42no—
200C2×C3×C4—64no—
201C2×C3×C4—122no—
202C2×C3×C4—122no—
203C2×C3×C4C4×Dic311yescharacteristic
204C2×C3×C4C4×Dic311yescharacteristic
205C2×C3×C4Dic3⋊C411yescharacteristic
206C2×C3×C4Dic3⋊C411yescharacteristic
207C2×C3×C4Dic3⋊C411yescharacteristic
208C2×C3×C4C4⋊Dic311yescharacteristic
209C2×C3×C4(C2×D3)⋊C411yescharacteristic
210C2×C3×C4#21711yescharacteristic
211C2×Dic3—24no—
212C2×Dic3—42no—
213C2×Dic3—42no—
214C2×Dic3—68no—
215C2×Dic3—64no—
216C2×Dic3—64no—
217C2×Dic3—124no—
218C2×Dic3—122no—
219C2×Dic3—122no—
220C2×Dic3—124no—
221C2×Dic3—122no—
222C2×Dic3—122no—
223C3×C8—122no—
224C3⋊C8—42no—
225C2×C32—22no—
226C2×C32—22no—
227C2×C32—41no—
228C2×C32#33911yescharacteristic
229C2×C32#33911yescharacteristic
230C2×C32#34211yescharacteristic
231C24#62611yescharacteristic
232C22×C4—42no—
233C22×C4—62no—
234C22×C4—182no—
235C22×C4D3×Dic311yescharacteristic
236C22×C4D3×Dic311yescharacteristic
237C22×C4#62411yescharacteristic
238C22×C4#62511yescharacteristic
239C22×C4#62611yescharacteristic
240C22×C4#62711yescharacteristic
241M16—122no—
242C2×C8—62no—
243C22⋊C4—64no—
244C22⋊C4—184no—
245C42—122no—
246C42—362no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—22no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—21no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—44no—
272C22×C3—44no—
273C22×C3—48no—
274C22×C3#80512yes—
275C22×C3#82512yes—
276C22×C3#82512yes—
277C22×C3C3⋊#9511yescharacteristic
278C22×C3C3⋊#9511yescharacteristic
279C22×C3#83712yes—
280C3×C4—22no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—22no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—124no—
291C3×C4#80612yes—
292C3×C4#83412yes—
293Dic3—44no—
294Dic3—128no—
295Dic3—124no—
296Dic3—124no—
297C32#129711yescharacteristic, complemented, Sylow
298C23—22no—
299C23—22no—
300C23—41no—
301C23(C2×D3)⋊Dic311yescharacteristic
302C23#372211yescharacteristic
303C23Dic3⋊Dic311yescharacteristic
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—64no—
311C2×C4—122no—
312C2×C4—122no—
313C2×C4—184no—
314C2×C4—362no—
315C2×C4—362no—
316C2×C4Dic3211yescharacteristic
317C2×C4(C2×D3)⋊Dic311yescharacteristic
318C2×C4Dic3⋊Dic311yescharacteristic
319C2×C4#372411yescharacteristic
320C8—122no—
321C2×C3—24no—
322C2×C3—22no—
323C2×C3—22no—
324C2×C3—22no—
325C2×C3—22no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—42no—
330C2×C3—42no—
331C2×C3—41no—
332C2×C3—41no—
333C2×C3#452311yescharacteristic
334C2×C3#452611yescharacteristic
335C2×C3#452711yescharacteristic
336C2×C3#453211yescharacteristic
337C2×C3#455511yescharacteristic
338C2×C3#455511yescharacteristic
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22#6356812yes—
348C22#6357012yes—
349C22#6357911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—124no—
354C4—364no—
355C4#6358012yes—
356C3—21no—
357C3#6761811yescharacteristic, complemented
358C3#6768311yescharacteristic, complemented
359C2—22no—
360C2—22no—
361C2—41no—
362C2#1058916011yescharacteristic
363C2#1058916211yescharacteristic
364C2#1058918611yescharacteristic
subgroupG/H
centerC2×C4(C2×D3)⋊Dic3
commutatorC2×C32×C4C42
Frattini, hypercenterC23×C4D32
Fitting, cosocleC23×C32×C4C22
socleC22×C32#95
prime radicalC24×C32D4
hypocenterC32#1297
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
11. C2×C3×#208C4semidirect
12. #63658C4semidirect
13. C3×C3⋊#95C4semidirect
54. C2×#208Dic3semidirect
61. C3⋊#95Dic3semidirect
297. C32#1297semidirect
357. C3#67618semidirect
358. C3#67683semidirect

Maximal subgroups

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

subgroupindex
C4×#37572
C3×C4×#2172
C3×#52072
#676833
#676183