Finite Group Databasebeta

← #11773839

Subgroups — #11773839

Order 1152.

555 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2#10592624C211yesmaximal, characteristic
3C3×#4925C211yesmaximal, characteristic
4#10589147C214yesmaximal
5#71624—31nomaximal
6#70786—31nomaximal
7C22×C3×Dic6C411yescharacteristic
8C2×C32×C42C2211yescharacteristic
9C2×C3×C4⋊Dic3C411yescharacteristic
10C2×C3×Dic3⋊C4C2212yes—
11C2×C3×C4×Dic3C412yes—
12C3×C4×Dic6—21no—
13C3×C4×Dic6—21no—
14C3×C4×Dic6—21no—
15C3×C4×Dic6—21no—
16#63657C2212yes—
17C4⋊(C3⋊(C3⋊C8))—21no—
18C4×C3⋊(C3⋊C8)—21no—
19C3×#830C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21C3×C4×C3⋊C8—21no—
22C2×C3×C4×Q8—31no—
23C2×C4×Dic6D311yescharacteristic
24C3×#431—31no—
25#4925—31no—
26#4925—31no—
27#4925—61no—
28#4925D311yescharacteristic
29#4528—34no—
30#4469—34no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3×Dic3C2×C412yes—
35C22×C3×Dic3C2×C412yes—
36C2×C3×Dic6—21no—
37C2×C3×Dic6—21no—
38C2×C3×Dic6—22no—
39C2×C3×Dic6C814yescomplemented
40C32×C42D411yescharacteristic
41C32×C42D411yescharacteristic
42C32×C42D411yescharacteristic
43C32×C42D411yescharacteristic
44C2×C3⋊(C3⋊C8)—22no—
45C3×C4⋊Dic3—21no—
46C3×C4⋊Dic3—21no—
47C3×Dic3⋊C4—22no—
48C3×Dic3⋊C4—22no—
49C3×C4×Dic3—22no—
50C3×C4×Dic3—22no—
51C2×C3×C3⋊C8—22no—
52#1461—91noSylow
53C22×C3×Q8—31no—
54C22×Dic6Dic311yescharacteristic
55C3×C4×Q8—61no—
56C3×C4×Q8—61no—
57C3×C4×Q8—61no—
58C3×C4×Q8—61no—
59C2×C3×C4⋊C4—31no—
60C2×C3×C4⋊C4—32no—
61C2×C3×C42—21no—
62C2×C3×C42—32no—
63C2×C3×C42C2×D311yescharacteristic
64C2×C3×C42C2×D311yescharacteristic
65C2×C4⋊Dic3Dic311yescharacteristic
66C2×Dic3⋊C4C2×D312yes—
67C2×C4×Dic3Dic312yes—
68C4×Dic6—21no—
69C4×Dic6—21no—
70C4×Dic6—21no—
71C4×Dic6—21no—
72C3×C4⋊C8—61no—
73C3×C22⋊C8—32no—
74C3×C4×C8—61no—
75#830—32no—
76#830—32no—
77#830—62no—
78#830C2×D312yes—
79C4⋊(C3⋊C8)—21no—
80C4⋊(C3⋊C8)—62no—
81C4⋊(C3⋊C8)—61no—
82C4⋊(C3⋊C8)—61no—
83C4×C3⋊C8—21no—
84C4×C3⋊C8—62no—
85C4×C3⋊C8—61no—
86C4×C3⋊C8—61no—
87C23×C32C22×C411yescharacteristic
88C2×C32×C4—22no—
89C2×C32×C4—41no—
90C2×C32×C4C22⋊C411yescharacteristic
91C2×C32×C4C22⋊C411yescharacteristic
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C2×C812yes—
95C2×C32×C4M1612yes—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C3×Dic3—22no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3C2×C814yes—
103C3×Dic6—24no—
104C3×Dic6—24no—
105C3⋊(C3⋊C8)—42no—
106C3×C3⋊C8—42no—
107C2×C4×Q8—31no—
108#431—31no—
109#431—91no—
110#324—94no—
111C2×C3×Q8—34no—
112C2×C3×Q8—62no—
113C2×C3×Q8—61no—
114C2×C3×Q8—61no—
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—32no—
119C22×C3×C4—32no—
120C22×C3×C4C4×D311yescharacteristic
121C22×C3×C4C4×D311yescharacteristic
122C22×C3×C4C2×Dic311yescharacteristic
123C22×C3×C4C2×Dic311yescharacteristic
124C22×C3×C4C22×D311yescharacteristic
125C22×C3×C4C22×D311yescharacteristic
126C22×Dic3C2×Dic312yes—
127C22×Dic3C2×Dic312yes—
128C2×Dic6—22no—
129C2×Dic6—21no—
130C2×Dic6—21no—
131C2×Dic6C3⋊C814yescomplemented
132C2×C3×C8—62no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—62no—
136C3×C4⋊C4—62no—
137C3×C42—21no—
138C3×C42—21no—
139C3×C42—21no—
140C3×C42—21no—
141C3×C42—62no—
142C3×C42—62no—
143C3×C42D1211yescharacteristic
144C3×C42D1211yescharacteristic
145C3×C42#6711yescharacteristic
146C3×C42#6711yescharacteristic
147C3×C42#6711yescharacteristic
148C3×C42#6711yescharacteristic
149C3×C42#6711yescharacteristic
150C3×C42#6711yescharacteristic
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153Dic3⋊C4—22no—
154Dic3⋊C4—22no—
155C4×Dic3—22no—
156C4×Dic3—22no—
157C2×C3⋊C8—22no—
158C2×C3⋊C8—64no—
159C2×C3⋊C8—62no—
160C2×C3⋊C8—62no—
161C22×C32—21no—
162C22×C32—21no—
163C22×C32C2×C22⋊C411yescharacteristic
164C22×C32C22×C811yescharacteristic
165C22×C32C2×M1611yescharacteristic
166C32×C4—21no—
167C32×C4—21no—
168C32×C4—21no—
169C32×C4C22⋊C812yes—
170C32×C4C22⋊C812yes—
171C32×C4#10112yes—
172C3×Dic3—24no—
173C3×Dic3—42no—
174C22×Q8—31no—
175C4×Q8—61no—
176C4×Q8—61no—
177C4×Q8—61no—
178C4×Q8—61no—
179C2×C4⋊C4—31no—
180C2×C4⋊C4—32no—
181C2×C42—32no—
182C2×C42D3211yescharacteristic
183C4⋊C8—61no—
184C4⋊C8—181no—
185C22⋊C8—32no—
186C22⋊C8—92no—
187C4×C8—61no—
188C4×C8—181no—
189C23×C3—21no—
190C23×C3C2×C4×D311yescharacteristic
191C23×C3C22×Dic311yescharacteristic
192C3×Q8—64no—
193C3×Q8—64no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—34no—
205C2×C3×C4—42no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—42no—
209C2×C3×C4—62no—
210C2×C3×C4—62no—
211C2×C3×C4—62no—
212C2×C3×C4—122no—
213C2×C3×C4D3×C812yes—
214C2×C3×C4ΓL(1,𝔽25)12yes—
215C2×C3×C4C2×C3⋊C812yes—
216C2×C3×C4#20812yes—
217C2×C3×C4(C2×D3)⋊C411yescharacteristic
218C2×C3×C4(C2×D3)⋊C411yescharacteristic
219C2×C3×C4(C2×D3)⋊C411yescharacteristic
220C2×C3×C4(C2×D3)⋊C411yescharacteristic
221C2×C3×C4#21711yescharacteristic
222C2×C3×C4#21711yescharacteristic
223C2×C3×C4#21711yescharacteristic
224C2×C3×C4#21711yescharacteristic
225C2×C3×C4C2×D1211yescharacteristic
226C2×C3×C4C2×#6711yescharacteristic
227C2×C3×C4C2×#6711yescharacteristic
228C2×C3×C4C2×#6711yescharacteristic
229C2×Dic3—22no—
230C2×Dic3—22no—
231C2×Dic3—22no—
232C2×Dic3—42no—
233C2×Dic3C2×C3⋊C814yes—
234Dic6—24no—
235Dic6—24no—
236C3×C8—122no—
237C3⋊C8—42no—
238C3⋊C8—124no—
239C3⋊C8—122no—
240C3⋊C8—122no—
241C2×C32—21no—
242C2×C32—21no—
243C2×C32C2×C22⋊C811yescharacteristic
244C2×C32#41011yescharacteristic
245C2×C32C2×#10111yescharacteristic
246C2×Q8—34no—
247C2×Q8—62no—
248C2×Q8—61no—
249C2×Q8—61no—
250C22×C4—32no—
251C22×C4—32no—
252C22×C4D3×Dic311yescharacteristic
253C22×C4D3×Dic311yescharacteristic
254C22×C4C2×D3211yescharacteristic
255C2×C8—62no—
256C2×C8—182no—
257C4⋊C4—61no—
258C4⋊C4—61no—
259C4⋊C4—62no—
260C4⋊C4—62no—
261C42—62no—
262C42—62no—
263C42#62511yescharacteristic
264C42#62511yescharacteristic
265C42#62611yescharacteristic
266C42#62611yescharacteristic
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3C2×D3×C811yescharacteristic
277C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
278C22×C3C22×C3⋊C811yescharacteristic
279C22×C3C2×#20811yescharacteristic
280C22×C3C2×(C2×D3)⋊C411yescharacteristic
281C22×C3C2×#21711yescharacteristic
282C3×C4—22no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—22no—
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—64no—
295C3×C4—122no—
296C3×C4(C2×D3)⋊C812yes—
297C3×C4(C2×D3)⋊C812yes—
298C3×C4#82412yes—
299C3×C4#83012yes—
300C3×C4#83012yes—
301C3×C4#83612yes—
302Dic3—24no—
303Dic3—42no—
304C32#146111yescharacteristic, complemented, Sylow
305C23C2×D3×Dic311yescharacteristic
306Q8—64no—
307Q8—64no—
308C2×C4—22no—
309C2×C4—34no—
310C2×C4—41no—
311C2×C4—62no—
312C2×C4—62no—
313C2×C4—62no—
314C2×C4—122no—
315C2×C4D3×C3⋊C812yes—
316C2×C4#371112yes—
317C2×C4(C2×D3)⋊Dic311yescharacteristic
318C2×C4(C2×D3)⋊Dic311yescharacteristic
319C2×C4(C2×D3)⋊Dic311yescharacteristic
320C2×C4(C2×D3)⋊Dic311yescharacteristic
321C2×C4C2×#62511yescharacteristic
322C2×C4C2×#62611yescharacteristic
323C8—122no—
324C8—362no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—41no—
333C2×C3—41no—
334C2×C3#500611yescharacteristic
335C2×C3C2×(C2×D3)⋊C811yescharacteristic
336C2×C3C2×#82411yescharacteristic
337C2×C3C2×#83011yescharacteristic
338C2×C3C2×#83611yescharacteristic
339C2×C3#524011yescharacteristic
340C22—21no—
341C22—21no—
342C22C2×D3×C3⋊C811yescharacteristic
343C22C2×#371111yescharacteristic
344C22C2×(C2×D3)⋊Dic311yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—64no—
349C4—122no—
350C4(C2×D3)⋊(C3⋊C8)12yes—
351C4(C2×D3)⋊(C3⋊C8)12yes—
352C4#6356012yes—
353C3—21no—
354C3#7078611yescharacteristic, complemented
355C3#7162411yescharacteristic, complemented
356C2—21no—
357C2—21no—
358C2C2×(C2×D3)⋊(C3⋊C8)11yescharacteristic
359C2C2×#6356011yescharacteristic
360C2#1059123111yescharacteristic
subgroupG/H
centerC2×C4(C2×D3)⋊Dic3
commutatorC22×C32C22×C8
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1461
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
39. C2×C3×Dic6C8semidirect
131. C2×Dic6C3⋊C8semidirect
304. C32#1461semidirect
354. C3#70786semidirect
355. C3#71624semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
#105926242
C3×#49252
#105891472
#716243
#707863