Finite Group Databasebeta

← #11770883

Subgroups — #11770883

Order 1152.

561 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 561 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592910C211yesmaximal, characteristic
2C3×C4×#217C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4#67682—31nomaximal
5#67616—31nomaximal
6C23×C32×C4C2211yescharacteristic
7C2×#3757—21no—
8C2×C3×#217—21no—
9C2×C3×C4×Dic3C412yescomplemented
10C2×C3×#208—21no—
11#63658—21no—
12#63658C412yescomplemented
13C3×C3⋊#95—21no—
14C3×#830—21no—
15C3×#830C412yescomplemented
16C3×#407—31no—
17C3×C4×C22⋊C4—31no—
18#5211—31no—
19#5211—31no—
20#5211—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—42no—
34C3×#217—24no—
35C3×C4×Dic3—42no—
36C3×#208—42no—
37C2×C3×C3⋊C8—22no—
38#1284—91noSylow
39C23×C3×C4—21no—
40C23×C3×C4C2×D311yescharacteristic
41C23×C3×C4C2×D311yescharacteristic
42C2×C3×M16—61no—
43C2×C3×C22⋊C4—61no—
44C2×C3×C42—32no—
45C2×#217—21no—
46C2×#217—62no—
47C2×#217—61no—
48C2×#217—61no—
49C2×C4×Dic3Dic312yescomplemented
50C2×#208—21no—
51C3×C22⋊C8—32no—
52C3×C22⋊C8—61no—
53C3×#95—61no—
54C3⋊#95—21no—
55C3⋊#95—32no—
56C3⋊#95—32no—
57C3⋊#95—62no—
58C3⋊#95—62no—
59C3⋊#95—61no—
60C3⋊#95—61no—
61#830—21no—
62#830Dic312yescomplemented
63C23×C32—22no—
64C23×C32—22no—
65C23×C32—41no—
66C23×C32C22⋊C411yescharacteristic
67C23×C32C22⋊C411yescharacteristic
68C23×C32C4⋊C411yescharacteristic
69C2×C32×C4—22no—
70C2×C32×C4—22no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4C4211yescharacteristic
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C4⋊C411yescharacteristic
78C2×C32×C4C4⋊C411yescharacteristic
79C2×C3⋊Dic3—42no—
80C2×C3⋊Dic3—42no—
81C2×C3⋊Dic3—42no—
82C2×C3×Dic3—24no—
83C2×C3×Dic3—42no—
84C2×C3×Dic3—42no—
85C3×C3⋊C8—42no—
86#407—31no—
87#381—91no—
88C4×C22⋊C4—31no—
89C24×C3—21no—
90C24×C3D1211yescharacteristic
91C24×C3#6711yescharacteristic
92C22×C3×C4—21no—
93C22×C3×C4—21no—
94C22×C3×C4—21no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×C3×C4—42no—
99C22×C3×C4—42no—
100C22×C3×C4—44no—
101C22×C3×C4—62no—
102C22×C3×C4Dic611yescharacteristic
103C22×C3×C4Dic611yescharacteristic
104C22×C3×C4C4×D311yescharacteristic
105C22×C3×C4C4×D311yescharacteristic
106C22×C3×C4C4×D311yescharacteristic
107C22×C3×C4C4×D311yescharacteristic
108C22×C3×C4D1211yescharacteristic
109C22×C3×C4C2×Dic311yescharacteristic
110C22×C3×C4C2×Dic311yescharacteristic
111C22×C3×C4#6711yescharacteristic
112C22×C3×C4#6711yescharacteristic
113C22×C3×C4#6711yescharacteristic
114C22×Dic3—22no—
115C22×Dic3—64no—
116C22×Dic3—62no—
117C22×Dic3—62no—
118C3×M16—122no—
119C2×C3×C8—62no—
120C3×C22⋊C4—64no—
121C3×C42—122no—
122#217—24no—
123#217—124no—
124#217—122no—
125#217—122no—
126C4×Dic3—42no—
127#208—42no—
128C2×C3⋊C8—22no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32—21no—
136C22×C32—44no—
137C22×C32#9511yescharacteristic
138C22×C32#9912yes—
139C22×C32#10412yes—
140C32×C4—21no—
141C32×C4—21no—
142C32×C4—21no—
143C32×C4—21no—
144C3⋊Dic3—82no—
145C3×Dic3—44no—
146C23×C4D3211yescharacteristic
147C2×M16—61no—
148C2×C22⋊C4—61no—
149C2×C22⋊C4—181no—
150C2×C42—32no—
151C22⋊C8—32no—
152C22⋊C8—61no—
153#95—61no—
154#95—92no—
155#95—181no—
156C23×C3—24no—
157C23×C3—22no—
158C23×C3—22no—
159C23×C3—22no—
160C23×C3—22no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—42no—
165C23×C3—41no—
166C23×C3—41no—
167C23×C3—42no—
168C23×C3Dic3⋊C411yescharacteristic
169C23×C3C4⋊Dic311yescharacteristic
170C23×C3(C2×D3)⋊C411yescharacteristic
171C23×C3(C2×D3)⋊C411yescharacteristic
172C23×C3(C2×D3)⋊C411yescharacteristic
173C23×C3#21711yescharacteristic
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—42no—
183C2×C3×C4—42no—
184C2×C3×C4—41no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4—41no—
189C2×C3×C4—41no—
190C2×C3×C4—41no—
191C2×C3×C4—41no—
192C2×C3×C4—42no—
193C2×C3×C4—42no—
194C2×C3×C4—42no—
195C2×C3×C4—42no—
196C2×C3×C4—64no—
197C2×C3×C4—122no—
198C2×C3×C4—122no—
199C2×C3×C4C4×Dic311yescharacteristic
200C2×C3×C4C4×Dic311yescharacteristic
201C2×C3×C4Dic3⋊C411yescharacteristic
202C2×C3×C4Dic3⋊C411yescharacteristic
203C2×C3×C4Dic3⋊C411yescharacteristic
204C2×C3×C4C4⋊Dic311yescharacteristic
205C2×C3×C4(C2×D3)⋊C411yescharacteristic
206C2×C3×C4#21711yescharacteristic
207C2×Dic3—24no—
208C2×Dic3—42no—
209C2×Dic3—42no—
210C2×Dic3—124no—
211C2×Dic3—122no—
212C2×Dic3—122no—
213C2×Dic3—124no—
214C2×Dic3—122no—
215C2×Dic3—122no—
216C2×Dic3—124no—
217C2×Dic3—122no—
218C2×Dic3—122no—
219C3×C8—122no—
220C3⋊C8—42no—
221C2×C32—22no—
222C2×C32—22no—
223C2×C32—41no—
224C2×C32H(3,ℤ/4)11yescharacteristic
225C2×C32#33911yescharacteristic
226C2×C32#34211yescharacteristic
227C24#62611yescharacteristic
228C22×C4—42no—
229C22×C4—62no—
230C22×C4—182no—
231C22×C4D3×Dic311yescharacteristic
232C22×C4D3×Dic311yescharacteristic
233C22×C4#62411yescharacteristic
234C22×C4#62511yescharacteristic
235C22×C4#62611yescharacteristic
236C22×C4#62711yescharacteristic
237M16—122no—
238C2×C8—62no—
239C22⋊C4—64no—
240C22⋊C4—362no—
241C42—122no—
242C22×C3—22no—
243C22×C3—22no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—22no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—22no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—44no—
267C22×C3—44no—
268C22×C3—48no—
269C22×C3#80512yes—
270C22×C3#80612yes—
271C22×C3#82512yes—
272C22×C3C3⋊#9511yescharacteristic
273C22×C3C3⋊#9511yescharacteristic
274C22×C3#83412yes—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—41no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—124no—
288Dic3—44no—
289Dic3—244no—
290Dic3—242no—
291Dic3—242no—
292C32#128411yescharacteristic, complemented, Sylow
293C23—22no—
294C23—22no—
295C23—41no—
296C23(C2×D3)⋊Dic311yescharacteristic
297C23#372211yescharacteristic
298C23Dic3⋊Dic311yescharacteristic
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—64no—
306C2×C4—122no—
307C2×C4—122no—
308C2×C4—362no—
309C2×C4—362no—
310C2×C4—362no—
311C2×C4Dic3211yescharacteristic
312C2×C4(C2×D3)⋊Dic311yescharacteristic
313C2×C4Dic3⋊Dic311yescharacteristic
314C2×C4#372411yescharacteristic
315C8—122no—
316C2×C3—24no—
317C2×C3—22no—
318C2×C3—22no—
319C2×C3—22no—
320C2×C3—22no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—42no—
325C2×C3—42no—
326C2×C3—41no—
327C2×C3—41no—
328C2×C3#452311yescharacteristic
329C2×C3#452611yescharacteristic
330C2×C3#452711yescharacteristic
331C2×C3#453111yescharacteristic
332C2×C3#455511yescharacteristic
333C2×C3#455711yescharacteristic
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—44no—
342C22#6357012yes—
343C22#6357911yescharacteristic
344C22#6358012yes—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—124no—
350C4—722no—
351C3—21no—
352C3#6761611yescharacteristic, complemented
353C3#6768211yescharacteristic, complemented
354C2—22no—
355C2—22no—
356C2—41no—
357C2#1058915811yescharacteristic
358C2#1058916211yescharacteristic
359C2#1058918611yescharacteristic
subgroupG/H
centerC22#63579
commutatorC2×C32×C4C42
Frattini, hypercenterC23×C4D32
Fitting, cosocleC23×C32×C4C22
socleC22×C32#95
prime radicalC24×C32D4
hypocenterC32#1284
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
9. C2×C3×C4×Dic3C4semidirect
12. #63658C4semidirect
15. C3×#830C4semidirect
49. C2×C4×Dic3Dic3semidirect
62. #830Dic3semidirect
292. C32#1284semidirect
352. C3#67616semidirect
353. C3#67682semidirect

Maximal subgroups

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

subgroupindex
#105929102
C3×C4×#2172
C3×#52072
#676823
#676163