Finite Group Databasebeta

← #11785793

Subgroups — #11785793

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic3C211yesmaximal, characteristic
2C2×#63657C211yesmaximal, characteristic
3C3×#5212C211yesmaximal, characteristic
4#10589163C214yesmaximal, complemented
5#71554—31nomaximal
6#69502—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3×Dic3—21no—
9C22×C3⋊(C3⋊C8)C2212yes—
10C2×C3×#217—21no—
11C2×C3×C4⋊Dic3—21no—
12C2×C3×C4⋊Dic3—22no—
13C2×C3×C4⋊Dic3C414yescomplemented
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×C4⋊Dic3C2212yes—
16#63657—22no—
17C3×C3⋊#95—21no—
18C22×C3×C4⋊C4—31no—
19C22×C4⋊Dic3D311yescharacteristic
20C3×#380—31no—
21#5212D311yescharacteristic
22C2×#830—31no—
23C2×#830—31no—
24C2×#830—61no—
25#4529—34no—
26#4529—34no—
27C24×C32D411yescharacteristic
28C22×C32×C4—24no—
29C22×C32×C4C2×C412yes—
30C22×C32×C4D411yescharacteristic
31C22×C32×C4D412yes—
32C22×C32×C4C2311yescharacteristic
33C22×C3×Dic3—24no—
34C22×C3×Dic3—22no—
35C22×C3×Dic3—22no—
36C22×C3×Dic3—44no—
37C2×C3⋊(C3⋊C8)—22no—
38C2×C3⋊(C3⋊C8)—24no—
39C3×#217—42no—
40C3×C4⋊Dic3—24no—
41C3×C4⋊Dic3—22no—
42C3×C4⋊Dic3—24no—
43C3×C4⋊Dic3C2×C414yes—
44#1824—91noSylow
45C23×C3×C4—21no—
46C23×C3×C4—61no—
47C23×C3×C4C2×D311yescharacteristic
48C23×C3×C4C2×D311yescharacteristic
49C23×Dic3—21no—
50C2×C3×C4⋊C4—34no—
51C2×C3×C4⋊C4—32no—
52C2×C3×C4⋊C4—32no—
53C2×C3×C4⋊C4—62no—
54C2×C3×C4⋊C4—61no—
55C2×C3×C22⋊C4—61no—
56C2×#217—21no—
57C2×C4⋊Dic3—21no—
58C2×C4⋊Dic3—22no—
59C2×C4⋊Dic3Dic314yescomplemented
60C2×C4⋊Dic3C2×D312yes—
61C2×C4⋊Dic3C2×D312yes—
62C22×C3⋊C8—32no—
63C22×C3⋊C8—32no—
64C22×C3⋊C8—62no—
65C3×#95—61no—
66C3⋊#95—21no—
67#830—64no—
68#830—62no—
69#830—62no—
70C23×C32—22no—
71C23×C32—22no—
72C23×C32C22⋊C412yes—
73C23×C32SD1612yes—
74C23×C32Q1612yes—
75C23×C32C2×D411yescharacteristic
76C2×C32×C4—22no—
77C2×C32×C4—24no—
78C2×C32×C4—24no—
79C2×C32×C4C22⋊C412yes—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4#4114yes—
83C2×C3×Dic3—24no—
84C2×C3×Dic3—48no—
85C2×C3×Dic3—44no—
86C2×C3×Dic3—42no—
87C2×C3×Dic3—42no—
88C2×C3×Dic3—42no—
89C3⋊(C3⋊C8)—42no—
90C22×C4⋊C4—31no—
91C2×C22⋊C8—91no—
92#380—31no—
93#340—94no—
94C24×C3—21no—
95C24×C3#6711yescharacteristic
96C24×C3#6711yescharacteristic
97C22×C3×C4—24no—
98C22×C3×C4—24no—
99C22×C3×C4—22no—
100C22×C3×C4—21no—
101C22×C3×C4—22no—
102C22×C3×C4—21no—
103C22×C3×C4—44no—
104C22×C3×C4—64no—
105C22×C3×C4—62no—
106C22×C3×C4—62no—
107C22×C3×C4—124no—
108C22×C3×C4C4×D312yes—
109C22×C3×C4D1212yes—
110C22×C3×C4C2×Dic312yes—
111C22×C3×C4#6711yescharacteristic
112C22×C3×C4#6711yescharacteristic
113C22×C3×C4#6712yes—
114C22×C3×C4C22×D311yescharacteristic
115C22×C3×C4C22×D311yescharacteristic
116C22×Dic3—24no—
117C22×Dic3—22no—
118C22×Dic3—22no—
119C22×Dic3—44no—
120C3×C4⋊C4—34no—
121C3×C4⋊C4—64no—
122C3×C4⋊C4—62no—
123C3×C4⋊C4—64no—
124C3×C22⋊C4—122no—
125#217—42no—
126C4⋊Dic3—24no—
127C4⋊Dic3—22no—
128C4⋊Dic3—24no—
129C4⋊Dic3C2×Dic314yes—
130C2×C3⋊C8—64no—
131C2×C3⋊C8—62no—
132C2×C3⋊C8—64no—
133C2×C3⋊C8—64no—
134C2×C3⋊C8—62no—
135C2×C3⋊C8—124no—
136C22×C32—22no—
137C22×C32—22no—
138C22×C32—24no—
139C22×C32—24no—
140C22×C32#10314yes—
141C22×C32C2×C22⋊C411yescharacteristic
142C22×C32#12312yes—
143C22×C32C2×SD1611yescharacteristic
144C22×C32C2×Q1611yescharacteristic
145C22×C32AGL(1,ℤ/8)12yes—
146C32×C4—22no—
147C32×C4#11712yes—
148C32×C4#12312yes—
149C3×Dic3—44no—
150C3×Dic3—82no—
151C23×C4—61no—
152C23×C4D3211yescharacteristic
153C22×C8—92no—
154C2×C4⋊C4—34no—
155C2×C4⋊C4—32no—
156C2×C4⋊C4—32no—
157C2×C4⋊C4—61no—
158C2×C4⋊C4—62no—
159C2×C22⋊C4—61no—
160C22⋊C8—182no—
161#95—61no—
162C23×C3—22no—
163C23×C3—22no—
164C23×C3—22no—
165C23×C3—22no—
166C23×C3—22no—
167C23×C3—22no—
168C23×C3—22no—
169C23×C3—21no—
170C23×C3—42no—
171C23×C3—42no—
172C23×C3(C2×D3)⋊C412yes—
173C23×C3#21412yes—
174C23×C3#21512yes—
175C23×C3#21612yes—
176C23×C3#21612yes—
177C23×C3#21712yes—
178C23×C3C2×#6711yescharacteristic
179C23×C3C2×#6711yescharacteristic
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—24no—
183C2×C3×C4—24no—
184C2×C3×C4—24no—
185C2×C3×C4—24no—
186C2×C3×C4—22no—
187C2×C3×C4—21no—
188C2×C3×C4—24no—
189C2×C3×C4—21no—
190C2×C3×C4—44no—
191C2×C3×C4—44no—
192C2×C3×C4—42no—
193C2×C3×C4—64no—
194C2×C3×C4—128no—
195C2×C3×C4—124no—
196C2×C3×C4—122no—
197C2×C3×C4—122no—
198C2×C3×C4—122no—
199C2×C3×C4(C2×D3)⋊C412yes—
200C2×C3×C4#21712yes—
201C2×C3×C4C2×C4×D311yescharacteristic
202C2×C3×C4C2×D1211yescharacteristic
203C2×C3×C4#23514yes—
204C2×C3×C4#23714yes—
205C2×C3×C4C22×Dic311yescharacteristic
206C2×C3×C4C2×#6711yescharacteristic
207C2×Dic3—24no—
208C2×Dic3—48no—
209C2×Dic3—44no—
210C2×Dic3—42no—
211C2×Dic3—42no—
212C2×Dic3—42no—
213C3⋊C8—124no—
214C3⋊C8—122no—
215C3⋊C8—122no—
216C2×C32—24no—
217C2×C32#38111yescharacteristic
218C2×C32C2×#10311yescharacteristic
219C2×C32#41811yescharacteristic
220C2×C32#48112yes—
221C2×C32#48412yes—
222C24#62511yescharacteristic
223C22×C4—24no—
224C22×C4—64no—
225C22×C4—62no—
226C22×C4—62no—
227C22×C4—124no—
228C22×C4D3×Dic312yes—
229C22×C4#62511yescharacteristic
230C22×C4#62612yes—
231C22×C4C2×D3211yescharacteristic
232C2×C8—184no—
233C2×C8—182no—
234C4⋊C4—34no—
235C4⋊C4—64no—
236C4⋊C4—62no—
237C4⋊C4—64no—
238C22⋊C4—122no—
239C22×C3—22no—
240C22×C3—22no—
241C22×C3—22no—
242C22×C3—24no—
243C22×C3—24no—
244C22×C3—22no—
245C22×C3—24no—
246C22×C3—24no—
247C22×C3—24no—
248C22×C3—22no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—22no—
253C22×C3—42no—
254C22×C3—42no—
255C22×C3—44no—
256C22×C3—44no—
257C22×C3#81014yes—
258C22×C3#83514yes—
259C22×C3C2×(C2×D3)⋊C411yescharacteristic
260C22×C3#92912yes—
261C22×C3#93212yes—
262C22×C3C2×#21411yescharacteristic
263C22×C3#93512yes—
264C22×C3C2×#21511yescharacteristic
265C22×C3C2×#21611yescharacteristic
266C22×C3C2×#21611yescharacteristic
267C22×C3#94912yes—
268C22×C3C2×#21711yescharacteristic
269C3×C4—22no—
270C3×C4—22no—
271C3×C4—22no—
272C3×C4—22no—
273C3×C4—42no—
274C3×C4—124no—
275C3×C4—242no—
276C3×C4#87712yes—
277C3×C4#88612yes—
278C3×C4#92612yes—
279C3×C4#92912yes—
280Dic3—44no—
281Dic3—82no—
282C32#182411yescharacteristic, complemented, Sylow
283C23—22no—
284C23—22no—
285C23#371512yes—
286C23#371812yes—
287C23(C2×D3)⋊Dic312yes—
288C23C2×#62511yescharacteristic
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—64no—
293C2×C4—128no—
294C2×C4—124no—
295C2×C4—122no—
296C2×C4—122no—
297C2×C4—122no—
298C2×C4(C2×D3)⋊Dic312yes—
299C2×C4C2×D3×Dic311yescharacteristic
300C2×C4#380414yes—
301C2×C4C2×#62611yescharacteristic
302C8—362no—
303C2×C3—24no—
304C2×C3—24no—
305C2×C3—21no—
306C2×C3—22no—
307C2×C3—21no—
308C2×C3—22no—
309C2×C3—21no—
310C2×C3—44no—
311C2×C3#494311yescharacteristic
312C2×C3#496812yes—
313C2×C3C2×#81011yescharacteristic
314C2×C3#497012yes—
315C2×C3#500111yescharacteristic
316C2×C3#503412yes—
317C2×C3#504412yes—
318C2×C3#521111yescharacteristic
319C2×C3#521511yescharacteristic
320C2×C3C2×#83511yescharacteristic
321C22—22no—
322C22—24no—
323C22—24no—
324C22—22no—
325C22#6356514yes—
326C22#6382312yes—
327C22C2×#371511yescharacteristic
328C22C2×#371811yescharacteristic
329C22C2×(C2×D3)⋊Dic311yescharacteristic
330C22#6396112yes—
331C4—22no—
332C4—124no—
333C4—242no—
334C4#6395512yes—
335C4#6396612yes—
336C3—21no—
337C3#6950211yescharacteristic, complemented
338C3#7155411yescharacteristic, complemented
339C2—24no—
340C2#1059108511yescharacteristic
341C2#1059109112yes—
342C2C2×#6356511yescharacteristic
343C2#1059113212yes—
344C2#1059169611yescharacteristic
subgroupG/H
centerC23C2×#625
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC24×C32D4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1824
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. #10589163C2semidirect
13. C2×C3×C4⋊Dic3C4semidirect
59. C2×C4⋊Dic3Dic3semidirect
282. C32#1824semidirect
337. C3#69502semidirect
338. C3#71554semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic32
C2×#636572
C3×#52122
#105891632
#715543
#695023