Finite Group Databasebeta

← #11785767

Subgroups — #11785767

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 354 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#71553—31nomaximal
6#69501—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—42no—
37C22×C3×Dic3—42no—
38C2×C3⋊(C3⋊C8)—22no—
39C2×C3⋊(C3⋊C8)—24no—
40C3×#217—42no—
41C3×C4⋊Dic3—24no—
42C3×C4⋊Dic3—22no—
43C3×C4⋊Dic3—24no—
44C3×C4⋊Dic3C2×C414yes—
45#1823—91noSylow
46C23×C3×C4—21no—
47C23×C3×C4—61no—
48C23×C3×C4C2×D311yescharacteristic
49C23×C3×C4C2×D311yescharacteristic
50C23×Dic3—21no—
51C2×C3×C4⋊C4—34no—
52C2×C3×C4⋊C4—32no—
53C2×C3×C4⋊C4—32no—
54C2×C3×C4⋊C4—62no—
55C2×C3×C4⋊C4—61no—
56C2×C3×C22⋊C4—61no—
57C2×#217—21no—
58C2×C4⋊Dic3—21no—
59C2×C4⋊Dic3—22no—
60C2×C4⋊Dic3Dic314yescomplemented
61C2×C4⋊Dic3C2×D312yes—
62C2×C4⋊Dic3C2×D312yes—
63C22×C3⋊C8—32no—
64C22×C3⋊C8—32no—
65C22×C3⋊C8—62no—
66C3×#95—61no—
67C3⋊#95—21no—
68#830—64no—
69#830—62no—
70#830—62no—
71C23×C32—22no—
72C23×C32—22no—
73C23×C32C22⋊C412yes—
74C23×C32D812yes—
75C23×C32SD1612yes—
76C23×C32C2×D411yescharacteristic
77C2×C32×C4—22no—
78C2×C32×C4—24no—
79C2×C32×C4—24no—
80C2×C32×C4C22⋊C412yes—
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4#4114yes—
84C2×C3×Dic3—24no—
85C2×C3×Dic3—48no—
86C2×C3×Dic3—42no—
87C2×C3×Dic3—42no—
88C2×C3×Dic3—42no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—42no—
91C3⋊(C3⋊C8)—42no—
92C22×C4⋊C4—31no—
93C2×C22⋊C8—91no—
94#380—31no—
95#340—94no—
96C24×C3—21no—
97C24×C3#6711yescharacteristic
98C24×C3#6711yescharacteristic
99C22×C3×C4—24no—
100C22×C3×C4—24no—
101C22×C3×C4—22no—
102C22×C3×C4—21no—
103C22×C3×C4—22no—
104C22×C3×C4—21no—
105C22×C3×C4—44no—
106C22×C3×C4—64no—
107C22×C3×C4—62no—
108C22×C3×C4—62no—
109C22×C3×C4—122no—
110C22×C3×C4—122no—
111C22×C3×C4C4×D312yes—
112C22×C3×C4D1212yes—
113C22×C3×C4C2×Dic312yes—
114C22×C3×C4#6711yescharacteristic
115C22×C3×C4#6711yescharacteristic
116C22×C3×C4#6712yes—
117C22×C3×C4C22×D311yescharacteristic
118C22×C3×C4C22×D311yescharacteristic
119C22×Dic3—24no—
120C22×Dic3—22no—
121C22×Dic3—22no—
122C22×Dic3—42no—
123C22×Dic3—42no—
124C3×C4⋊C4—34no—
125C3×C4⋊C4—64no—
126C3×C4⋊C4—62no—
127C3×C4⋊C4—64no—
128C3×C22⋊C4—122no—
129#217—42no—
130C4⋊Dic3—24no—
131C4⋊Dic3—22no—
132C4⋊Dic3—24no—
133C4⋊Dic3C2×Dic314yes—
134C2×C3⋊C8—64no—
135C2×C3⋊C8—62no—
136C2×C3⋊C8—64no—
137C2×C3⋊C8—64no—
138C2×C3⋊C8—62no—
139C2×C3⋊C8—124no—
140C22×C32—22no—
141C22×C32—22no—
142C22×C32—24no—
143C22×C32—24no—
144C22×C32#10214yes—
145C22×C32C2×C22⋊C411yescharacteristic
146C22×C32#12312yes—
147C22×C32C2×D811yescharacteristic
148C22×C32C2×SD1611yescharacteristic
149C22×C32#13712yes—
150C32×C4—22no—
151C32×C4#11712yes—
152C32×C4#12312yes—
153C3×Dic3—44no—
154C3×Dic3—82no—
155C23×C4—61no—
156C23×C4D3211yescharacteristic
157C22×C8—92no—
158C2×C4⋊C4—34no—
159C2×C4⋊C4—32no—
160C2×C4⋊C4—32no—
161C2×C4⋊C4—61no—
162C2×C4⋊C4—62no—
163C2×C22⋊C4—61no—
164C22⋊C8—182no—
165#95—61no—
166C23×C3—22no—
167C23×C3—22no—
168C23×C3—22no—
169C23×C3—22no—
170C23×C3—22no—
171C23×C3—22no—
172C23×C3—22no—
173C23×C3—21no—
174C23×C3—42no—
175C23×C3—42no—
176C23×C3(C2×D3)⋊C412yes—
177C23×C3#21312yes—
178C23×C3#21312yes—
179C23×C3#21412yes—
180C23×C3#21512yes—
181C23×C3#21712yes—
182C23×C3C2×#6711yescharacteristic
183C23×C3C2×#6711yescharacteristic
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—24no—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4—22no—
191C2×C3×C4—21no—
192C2×C3×C4—24no—
193C2×C3×C4—21no—
194C2×C3×C4—44no—
195C2×C3×C4—44no—
196C2×C3×C4—42no—
197C2×C3×C4—64no—
198C2×C3×C4—128no—
199C2×C3×C4—122no—
200C2×C3×C4—122no—
201C2×C3×C4—122no—
202C2×C3×C4—122no—
203C2×C3×C4—122no—
204C2×C3×C4(C2×D3)⋊C412yes—
205C2×C3×C4#21712yes—
206C2×C3×C4C2×C4×D311yescharacteristic
207C2×C3×C4C2×D1211yescharacteristic
208C2×C3×C4#23514yes—
209C2×C3×C4#23714yes—
210C2×C3×C4C22×Dic311yescharacteristic
211C2×C3×C4C2×#6711yescharacteristic
212C2×Dic3—24no—
213C2×Dic3—48no—
214C2×Dic3—42no—
215C2×Dic3—42no—
216C2×Dic3—42no—
217C2×Dic3—42no—
218C2×Dic3—42no—
219C3⋊C8—124no—
220C3⋊C8—122no—
221C3⋊C8—122no—
222C2×C32—24no—
223C2×C32#38111yescharacteristic
224C2×C32C2×#10211yescharacteristic
225C2×C32#41911yescharacteristic
226C2×C32#48012yes—
227C2×C32#48312yes—
228C24#62511yescharacteristic
229C22×C4—24no—
230C22×C4—64no—
231C22×C4—62no—
232C22×C4—62no—
233C22×C4—122no—
234C22×C4—122no—
235C22×C4D3×Dic312yes—
236C22×C4#62511yescharacteristic
237C22×C4#62612yes—
238C22×C4C2×D3211yescharacteristic
239C2×C8—184no—
240C2×C8—182no—
241C4⋊C4—34no—
242C4⋊C4—64no—
243C4⋊C4—62no—
244C4⋊C4—64no—
245C22⋊C4—122no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—24no—
249C22×C3—22no—
250C22×C3—24no—
251C22×C3—22no—
252C22×C3—24no—
253C22×C3—24no—
254C22×C3—24no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—22no—
258C22×C3—21no—
259C22×C3—22no—
260C22×C3—42no—
261C22×C3—44no—
262C22×C3—42no—
263C22×C3—44no—
264C22×C3#80914yes—
265C22×C3#83214yes—
266C22×C3C2×(C2×D3)⋊C411yescharacteristic
267C22×C3#92912yes—
268C22×C3C2×#21311yescharacteristic
269C22×C3C2×#21311yescharacteristic
270C22×C3C2×#21411yescharacteristic
271C22×C3#93512yes—
272C22×C3C2×#21511yescharacteristic
273C22×C3#94212yes—
274C22×C3#95112yes—
275C22×C3C2×#21711yescharacteristic
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—22no—
280C3×C4—42no—
281C3×C4—124no—
282C3×C4—242no—
283C3×C4#87712yes—
284C3×C4#88612yes—
285C3×C4#92612yes—
286C3×C4#92912yes—
287Dic3—44no—
288Dic3—82no—
289C32#182311yescharacteristic, complemented, Sylow
290C23—22no—
291C23—22no—
292C23#371312yes—
293C23#371512yes—
294C23(C2×D3)⋊Dic312yes—
295C23C2×#62511yescharacteristic
296C2×C4—22no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—64no—
300C2×C4—128no—
301C2×C4—122no—
302C2×C4—122no—
303C2×C4—122no—
304C2×C4—122no—
305C2×C4—122no—
306C2×C4(C2×D3)⋊Dic312yes—
307C2×C4C2×D3×Dic311yescharacteristic
308C2×C4#380414yes—
309C2×C4C2×#62611yescharacteristic
310C8—362no—
311C2×C3—24no—
312C2×C3—24no—
313C2×C3—21no—
314C2×C3—22no—
315C2×C3—21no—
316C2×C3—22no—
317C2×C3—21no—
318C2×C3—44no—
319C2×C3#494311yescharacteristic
320C2×C3C2×#80911yescharacteristic
321C2×C3#496712yes—
322C2×C3#497112yes—
323C2×C3#500411yescharacteristic
324C2×C3#503312yes—
325C2×C3#504312yes—
326C2×C3#521111yescharacteristic
327C2×C3C2×#83211yescharacteristic
328C2×C3#522511yescharacteristic
329C22—24no—
330C22—22no—
331C22—24no—
332C22—22no—
333C22#6356214yes—
334C22C2×#371311yescharacteristic
335C22C2×#371511yescharacteristic
336C22#6382712yes—
337C22C2×(C2×D3)⋊Dic311yescharacteristic
338C22#6396112yes—
339C4—22no—
340C4—124no—
341C4—242no—
342C4#6395512yes—
343C4#6396612yes—
344C3—21no—
345C3#6950111yescharacteristic, complemented
346C3#7155311yescharacteristic, complemented
347C2—24no—
348C2C2×#6356211yescharacteristic
349C2#1059108912yes—
350C2#1059109911yescharacteristic
351C2#1059110112yes—
352C2#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#1823
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
60. C2×C4⋊Dic3Dic3semidirect
289. C32#1823semidirect
345. C3#69501semidirect
346. C3#71553semidirect

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
#715533
#695013