Finite Group Databasebeta

← #11785792

Subgroups — #11785792

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4#10589164C214yesmaximal, complemented
5#69925—31nomaximal
6#69502—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3—21no—
9C2×C4⋊(C3⋊Dic3)—21no—
10C2×C4⋊(C3⋊Dic3)—22no—
11C2×C4⋊(C3⋊Dic3)C414yescomplemented
12C2×C4⋊(C3⋊Dic3)C2212yes—
13C2×C3×#217—21no—
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C3×C3⋊#95—21no—
17C3×#830—22no—
18C22×C4⋊Dic3—31no—
19C22×C4⋊Dic3—31no—
20C22×C4⋊Dic3—61no—
21C2×C3×C22⋊C8—31no—
22C3×#380—31no—
23#5212D311yescharacteristic
24C2×#830D311yescharacteristic
25#4551—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—44no—
36C22×C3×Dic3—22no—
37C4⋊(C3⋊Dic3)—24no—
38C4⋊(C3⋊Dic3)—22no—
39C4⋊(C3⋊Dic3)C2×C414yes—
40C3×#217—42no—
41C3×C4⋊Dic3—24no—
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8—24no—
44#1824—91noSylow
45C23×C3×C4—21no—
46C23×C3×C4C2×D311yescharacteristic
47C23×C3×C4C2×D311yescharacteristic
48C23×Dic3—62no—
49C23×Dic3—61no—
50C23×Dic3—61no—
51C22×C3×C8—32no—
52C2×C3×C4⋊C4—32no—
53C2×C3×C22⋊C4—61no—
54C2×#217—21no—
55C2×C4⋊Dic3—34no—
56C2×C4⋊Dic3—34no—
57C2×C4⋊Dic3—32no—
58C2×C4⋊Dic3—32no—
59C2×C4⋊Dic3—64no—
60C2×C4⋊Dic3—62no—
61C2×C4⋊Dic3—62no—
62C2×C4⋊Dic3—64no—
63C2×C4⋊Dic3—61no—
64C2×C4⋊Dic3—62no—
65C2×C4⋊Dic3—61no—
66C2×C4⋊Dic3—62no—
67C2×C4⋊Dic3C2×D312yes—
68C22×C3⋊C8C2×D312yes—
69C3×C22⋊C8—62no—
70C3×#95—61no—
71C3⋊#95—21no—
72#830—22no—
73C23×C32—22no—
74C23×C32—22no—
75C23×C32C22⋊C412yes—
76C23×C32SD1612yes—
77C23×C32Q1612yes—
78C23×C32C2×D411yescharacteristic
79C2×C32×C4—22no—
80C2×C32×C4—24no—
81C2×C32×C4—24no—
82C2×C32×C4C22⋊C412yes—
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4#4114yes—
86C2×C3⋊Dic3—24no—
87C2×C3⋊Dic3—48no—
88C2×C3⋊Dic3—44no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—42no—
92C3×C3⋊C8—42no—
93C22×C4⋊C4—91no—
94C2×C22⋊C8—31no—
95#380—31no—
96#340—94no—
97C24×C3—21no—
98C24×C3D1211yescharacteristic
99C24×C3#6711yescharacteristic
100C22×C3×C4—28no—
101C22×C3×C4—24no—
102C22×C3×C4—24no—
103C22×C3×C4—22no—
104C22×C3×C4—21no—
105C22×C3×C4—22no—
106C22×C3×C4—21no—
107C22×C3×C4—62no—
108C22×C3×C4C4×D312yes—
109C22×C3×C4C4×D312yes—
110C22×C3×C4D1211yescharacteristic
111C22×C3×C4D1212yes—
112C22×C3×C4#6711yescharacteristic
113C22×C3×C4#6712yes—
114C22×C3×C4C22×D311yescharacteristic
115C22×C3×C4C22×D311yescharacteristic
116C22×Dic3—22no—
117C22×Dic3—68no—
118C22×Dic3—64no—
119C22×Dic3—64no—
120C22×Dic3—64no—
121C22×Dic3—62no—
122C22×Dic3—62no—
123C22×Dic3—128no—
124C22×Dic3—124no—
125C22×Dic3—124no—
126C2×C3×C8—62no—
127C2×C3×C8—64no—
128C3×C4⋊C4—64no—
129C3×C22⋊C4—122no—
130#217—42no—
131C4⋊Dic3—24no—
132C4⋊Dic3—34no—
133C4⋊Dic3—34no—
134C4⋊Dic3—64no—
135C4⋊Dic3—68no—
136C4⋊Dic3—64no—
137C4⋊Dic3—64no—
138C4⋊Dic3—64no—
139C4⋊Dic3—62no—
140C4⋊Dic3—62no—
141C2×C3⋊C8—24no—
142C2×C3⋊C8—22no—
143C22×C32—22no—
144C22×C32—22no—
145C22×C32—24no—
146C22×C32—24no—
147C22×C32#10314yes—
148C22×C32C2×C22⋊C411yescharacteristic
149C22×C32#12312yes—
150C22×C32C2×SD1611yescharacteristic
151C22×C32C2×Q1611yescharacteristic
152C22×C32AGL(1,ℤ/8)12yes—
153C32×C4—22no—
154C32×C4#11712yes—
155C32×C4#12312yes—
156C3⋊Dic3—44no—
157C3×Dic3—82no—
158C23×C4—181no—
159C23×C4D3211yescharacteristic
160C22×C8—32no—
161C2×C4⋊C4—32no—
162C2×C4⋊C4—94no—
163C2×C4⋊C4—92no—
164C2×C4⋊C4—181no—
165C2×C4⋊C4—182no—
166C2×C22⋊C4—61no—
167C22⋊C8—62no—
168#95—61no—
169C23×C3—24no—
170C23×C3—24no—
171C23×C3—22no—
172C23×C3—22no—
173C23×C3—22no—
174C23×C3—22no—
175C23×C3—22no—
176C23×C3—22no—
177C23×C3—22no—
178C23×C3—21no—
179C23×C3#20412yes—
180C23×C3Dic1212yes—
181C23×C3(C2×D3)⋊C412yes—
182C23×C3(C2×D3)⋊C412yes—
183C23×C3#21412yes—
184C23×C3#21612yes—
185C23×C3C2×D1211yescharacteristic
186C23×C3C2×#6711yescharacteristic
187C2×C3×C4—24no—
188C2×C3×C4—28no—
189C2×C3×C4—28no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—24no—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
196C2×C3×C4—22no—
197C2×C3×C4—24no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—122no—
201C2×C3×C4—122no—
202C2×C3×C4—122no—
203C2×C3×C4(C2×D3)⋊C412yes—
204C2×C3×C4(C2×D3)⋊C412yes—
205C2×C3×C4C2×C4×D311yescharacteristic
206C2×C3×C4C2×C4×D311yescharacteristic
207C2×C3×C4C2×D1211yescharacteristic
208C2×C3×C4#23714yes—
209C2×C3×C4#23714yes—
210C2×C3×C4C2×#6711yescharacteristic
211C2×Dic3—42no—
212C2×Dic3—42no—
213C2×Dic3—42no—
214C2×Dic3—68no—
215C2×Dic3—64no—
216C2×Dic3—64no—
217C2×Dic3—1216no—
218C2×Dic3—128no—
219C2×Dic3—128no—
220C2×Dic3—128no—
221C2×Dic3—124no—
222C2×Dic3—124no—
223C3×C8—122no—
224C3⋊C8—42no—
225C2×C32—24no—
226C2×C32#38111yescharacteristic
227C2×C32C2×#10311yescharacteristic
228C2×C32#41811yescharacteristic
229C2×C32#48112yes—
230C2×C32#48412yes—
231C24#62611yescharacteristic
232C22×C4—24no—
233C22×C4—62no—
234C22×C4—184no—
235C22×C4—182no—
236C22×C4—364no—
237C22×C4#62412yes—
238C22×C4#62611yescharacteristic
239C22×C4#62612yes—
240C22×C4C2×D3211yescharacteristic
241C2×C8—64no—
242C2×C8—62no—
243C4⋊C4—64no—
244C4⋊C4—94no—
245C4⋊C4—184no—
246C4⋊C4—182no—
247C22⋊C4—122no—
248C22×C3—24no—
249C22×C3—24no—
250C22×C3—28no—
251C22×C3—28no—
252C22×C3—22no—
253C22×C3—22no—
254C22×C3—22no—
255C22×C3—24no—
256C22×C3—24no—
257C22×C3—22no—
258C22×C3—24no—
259C22×C3—24no—
260C22×C3—24no—
261C22×C3—22no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—22no—
265C22×C3—21no—
266C22×C3#81014yes—
267C22×C3#81614yes—
268C22×C3#88612yes—
269C22×C3C2×#20411yescharacteristic
270C22×C3C2×Dic1211yescharacteristic
271C22×C3#90812yes—
272C22×C3C2×(C2×D3)⋊C411yescharacteristic
273C22×C3C2×(C2×D3)⋊C411yescharacteristic
274C22×C3C2×#21411yescharacteristic
275C22×C3#93512yes—
276C22×C3C2×#21611yescharacteristic
277C22×C3#94912yes—
278C3×C4—24no—
279C3×C4—22no—
280C3×C4—22no—
281C3×C4—22no—
282C3×C4—22no—
283C3×C4—242no—
284C3×C4#87712yes—
285C3×C4#87712yes—
286C3×C4#88612yes—
287C3×C4#93512yes—
288Dic3—82no—
289Dic3—128no—
290Dic3—124no—
291Dic3—124no—
292C32#182411yescharacteristic, complemented, Sylow
293C23—22no—
294C23—22no—
295C23#371612yes—
296C23#371912yes—
297C23#372212yes—
298C23C2×#62611yescharacteristic
299C2×C4—22no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—122no—
303C2×C4—122no—
304C2×C4—122no—
305C2×C4—184no—
306C2×C4—368no—
307C2×C4—364no—
308C2×C4#372212yes—
309C2×C4#380514yes—
310C2×C4C2×#62411yescharacteristic
311C2×C4C2×#62611yescharacteristic
312C8—122no—
313C2×C3—28no—
314C2×C3—24no—
315C2×C3—24no—
316C2×C3—22no—
317C2×C3—21no—
318C2×C3—22no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3#472212yes—
322C2×C3#473512yes—
323C2×C3#494311yescharacteristic
324C2×C3#494311yescharacteristic
325C2×C3C2×#81011yescharacteristic
326C2×C3#500111yescharacteristic
327C2×C3#503412yes—
328C2×C3#504412yes—
329C2×C3C2×#81611yescharacteristic
330C2×C3#513111yescharacteristic
331C22—24no—
332C22—22no—
333C22—24no—
334C22—22no—
335C22#6356714yes—
336C22#6382512yes—
337C22C2×#371611yescharacteristic
338C22C2×#371911yescharacteristic
339C22#6396212yes—
340C22C2×#372211yescharacteristic
341C4—22no—
342C4—242no—
343C4—364no—
344C4#6395712yes—
345C4#6396212yes—
346C3—21no—
347C3#6950211yescharacteristic, complemented
348C3#6992511yescharacteristic, complemented
349C2—24no—
350C2#1059109212yes—
351C2#1059109611yescharacteristic
352C2#1059110312yes—
353C2C2×#6356711yescharacteristic
354C2#1059169711yescharacteristic
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#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. #10589164C2semidirect
11. C2×C4⋊(C3⋊Dic3)C4semidirect
292. C32#1824semidirect
347. C3#69502semidirect
348. C3#69925semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C3×#52122
C2×C3×#8302
#105891642
#699253
#695023