Finite Group Databasebeta

← #11785308

Subgroups — #11785308

Order 1152.

936 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic
2C2×#63664C212yesmaximal
3C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4#10592623C211yesmaximal, characteristic, complemented
5#10589398C212yesmaximal, complemented
6#71646—34nomaximal
7C2×C32×#41C2211yescharacteristic
8C32×C4×Q8C411yescharacteristic, complemented
9C32×C4×Q8C411yescharacteristic, complemented
10C32×C4×D4—21no—
11C32×C4×D4—21no—
12C32×C4×D4C411yescharacteristic, complemented
13C32×C4×D4C411yescharacteristic, complemented
14C32×#117—21no—
15C32×#117C2211yescharacteristic
16C2×C32×C42—21no—
17C2×C32×C42C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)—21no—
19C2×C4×C3⋊Dic3C2212yes—
20C2×#3748C2212yes—
21#63664—24no—
22#63658—21no—
23C4⋊(C3⋊(C3⋊C8))—21no—
24C4⋊(C3⋊(C3⋊C8))—21no—
25C3×C4×#41D314yes—
26C2×#837—38no—
27C4×C4⋊Dic3—34no—
28#4924—34no—
29#4532—38no—
30C32×#41—21no—
31C32×#41—21no—
32C32×#41D412yes—
33C32×#41Q812yes—
34C2×C32×Q8C2×C411yescharacteristic
35C2×C32×D4—21no—
36C2×C32×D4C2×C411yescharacteristic
37C22×C32×C4—21no—
38C22×C32×C4—21no—
39C22×C32×C4—21no—
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—22no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4C2×C411yescharacteristic
47C32×C4⋊C4C2×C411yescharacteristic
48C32×C22⋊C4—21no—
49C32×C22⋊C4—21no—
50C32×C22⋊C4—21no—
51C32×C42—21no—
52C32×C42—21no—
53C32×C42—21no—
54C32×C42C2×C411yescharacteristic
55C32×C42C2×C411yescharacteristic
56C32×C42D411yescharacteristic
57C32×C42D411yescharacteristic
58C4⋊(C3⋊Dic3)—24no—
59C4×C3⋊Dic3—22no—
60C4×C3⋊Dic3—22no—
61#3748—22no—
62#3748—22no—
63C2×C3⋊(C3⋊C8)—22no—
64#1806—91noSylow
65C2×C3×#41C2×D314yes—
66C3×C4×Q8Dic314yescomplemented
67C3×C4×Q8Dic314yescomplemented
68C3×C4×D4—24no—
69C3×C4×D4—24no—
70C3×C4×D4Dic314yescomplemented
71C3×C4×D4Dic314yescomplemented
72C3×#117—24no—
73C3×#117C2×D314yes—
74C2×C3×C42—24no—
75C2×C3×C42C2×D314yes—
76C2×C4⋊Dic3—64no—
77C2×C4×Dic3—38no—
78C2×#208—38no—
79#837—616no—
80C3⋊#95—64no—
81C4⋊(C3⋊C8)—64no—
82C4⋊(C3⋊C8)—64no—
83C23×C32—21no—
84C23×C32C2×D411yescharacteristic
85C32×Q8—21no—
86C32×Q8C4⋊C412yescomplemented
87C32×D4—22no—
88C32×D4—22no—
89C32×D4—21no—
90C32×D4C4⋊C412yescomplemented
91C2×C32×C4—21no—
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4—41no—
98C2×C32×C4—42no—
99C2×C32×C4—42no—
100C2×C32×C4C22⋊C411yescharacteristic
101C2×C32×C4C22⋊C411yescharacteristic
102C2×C32×C4C22⋊C411yescharacteristic
103C2×C32×C4C22⋊C411yescharacteristic
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×Q811yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C3⋊Dic3—24no—
111C2×C3⋊Dic3—42no—
112C2×C3⋊Dic3—42no—
113C3⋊(C3⋊C8)—42no—
114C4×#41C3⋊D311yescharacteristic
115#423—91no—
116C2×#104—92no—
117C4×C4⋊C4—91no—
118#339—92no—
119C3×#41—24no—
120C3×#41—24no—
121C3×#41Dic618yes—
122C3×#41D1218yes—
123C2×C3×Q8C2×Dic314yes—
124C2×C3×D4—24no—
125C2×C3×D4C2×Dic314yes—
126C22×C3×C4—24no—
127C22×C3×C4—24no—
128C22×C3×C4—24no—
129C22×C3×C4#6714yes—
130C22×C3×C4#6714yes—
131C22×C3×C4C22×D314yes—
132C22×Dic3—68no—
133C3×C4⋊C4—24no—
134C3×C4⋊C4—24no—
135C3×C4⋊C4C2×Dic314yes—
136C3×C4⋊C4C2×Dic314yes—
137C3×C22⋊C4—24no—
138C3×C22⋊C4—24no—
139C3×C22⋊C4—24no—
140C3×C42—24no—
141C3×C42—24no—
142C3×C42—24no—
143C3×C42C2×Dic314yes—
144C3×C42C2×Dic314yes—
145C3×C42#6714yes—
146C3×C42#6714yes—
147C4⋊Dic3—616no—
148C4×Dic3—68no—
149C4×Dic3—68no—
150#208—68no—
151#208—68no—
152C2×C3⋊C8—68no—
153C22×C32—21no—
154C22×C32—21no—
155C22×C32—22no—
156C22×C32—41no—
157C22×C32—41no—
158C22×C32C2×C22⋊C411yescharacteristic
159C22×C32#12111yescharacteristic
160C22×C32C22⋊Q811yescharacteristic
161C32×C4—22no—
162C32×C4—21no—
163C32×C4—21no—
164C32×C4—21no—
165C32×C4—41no—
166C32×C4—41no—
167C32×C4#10412yescomplemented
168C32×C4C2×C4⋊C411yescharacteristic
169C32×C4#11711yescharacteristic
170C32×C4#12111yescharacteristic
171C32×C4C22⋊Q811yescharacteristic
172C3⋊Dic3—44no—
173C2×#41C2×C3⋊D311yescharacteristic
174C2×M16—92no—
175C4×Q8C3⋊Dic311yescharacteristic, complemented
176C4×Q8C3⋊Dic311yescharacteristic, complemented
177C4×D4—21no—
178C4×D4—21no—
179C4×D4C3⋊Dic311yescharacteristic, complemented
180C4×D4C3⋊Dic311yescharacteristic, complemented
181#117—21no—
182#117C2×C3⋊D311yescharacteristic
183C2×C4⋊C4—181no—
184C2×C42—21no—
185C2×C42—92no—
186C2×C42C2×C3⋊D311yescharacteristic
187C4⋊C8—181no—
188C4⋊C8—181no—
189#104—184no—
190#95—181no—
191C23×C3—24no—
192C23×C3C2×#6714yes—
193C3×Q8—24no—
194C3×Q8C4⋊Dic318yescomplemented
195C3×D4—28no—
196C3×D4—28no—
197C3×D4—24no—
198C3×D4C4⋊Dic318yescomplemented
199C2×C3×C4—24no—
200C2×C3×C4—28no—
201C2×C3×C4—28no—
202C2×C3×C4—28no—
203C2×C3×C4—24no—
204C2×C3×C4—24no—
205C2×C3×C4—44no—
206C2×C3×C4—48no—
207C2×C3×C4—48no—
208C2×C3×C4#21714yes—
209C2×C3×C4#21714yes—
210C2×C3×C4#21714yes—
211C2×C3×C4#21714yes—
212C2×C3×C4C2×Dic614yes—
213C2×C3×C4C2×D1214yes—
214C2×C3×C4#23514yes—
215C2×C3×C4#23514yes—
216C2×C3×C4C22×Dic314yes—
217C2×C3×C4C2×#6714yes—
218C2×Dic3—616no—
219C2×Dic3—128no—
220C2×Dic3—128no—
221C3⋊C8—128no—
222C2×C32—21no—
223C2×C32—21no—
224C2×C32—42no—
225C2×C32#38011yescharacteristic
226C2×C32C2×#10411yescharacteristic
227C2×C32#42111yescharacteristic
228#41—21no—
229#41—21no—
230#41#63412yes—
231#41C4⋊(C3⋊D3)12yes—
232C2×Q8C2×C3⋊Dic311yescharacteristic
233C2×D4—21no—
234C2×D4C2×C3⋊Dic311yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—182no—
239C22×C4#63811yescharacteristic
240C22×C4#63811yescharacteristic
241C22×C4C22×C3⋊D311yescharacteristic
242M16—182no—
243M16—182no—
244C2×C8—182no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—184no—
248C4⋊C4C2×C3⋊Dic311yescharacteristic
249C4⋊C4C2×C3⋊Dic311yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—182no—
257C42—182no—
258C42C2×C3⋊Dic311yescharacteristic
259C42C2×C3⋊Dic311yescharacteristic
260C42#63811yescharacteristic
261C42#63811yescharacteristic
262C22×C3—24no—
263C22×C3—24no—
264C22×C3—28no—
265C22×C3—44no—
266C22×C3—44no—
267C22×C3#92414yes—
268C22×C3#93014yes—
269C22×C3C2×#21714yes—
270C3×C4—28no—
271C3×C4—24no—
272C3×C4—24no—
273C3×C4—24no—
274C3×C4—44no—
275C3×C4—44no—
276C3×C4#83718yescomplemented
277C3×C4#92414yes—
278C3×C4C2×C4⋊Dic314yes—
279C3×C4#92614yes—
280C3×C4#93014yes—
281Dic3—1216no—
282C32#180611yescharacteristic, complemented, Sylow
283C23—21no—
284C23C2×#63811yescharacteristic
285Q8—21no—
286Q8C4⋊(C3⋊Dic3)12yescomplemented
287D4—22no—
288D4—22no—
289D4—21no—
290D4C4⋊(C3⋊Dic3)12yescomplemented
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—184no—
301C2×C4—362no—
302C2×C4—362no—
303C2×C4#375711yescharacteristic
304C2×C4#375711yescharacteristic
305C2×C4#375711yescharacteristic
306C2×C4#375711yescharacteristic
307C2×C4C2×#63411yescharacteristic
308C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
309C2×C4#382811yescharacteristic
310C2×C4#382811yescharacteristic
311C2×C4C22×C3⋊Dic311yescharacteristic
312C2×C4C2×#63811yescharacteristic
313C8—362no—
314C2×C3—24no—
315C2×C3—24no—
316C2×C3—48no—
317C2×C3#521214yes—
318C2×C3C2×#83714yes—
319C2×C3#523614yes—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22#6413311yescharacteristic
326C22#6413911yescharacteristic
327C22C2×#375711yescharacteristic
328C4—22no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—364no—
335C4#6366412yescomplemented
336C4#6413311yescharacteristic
337C4C2×C4⋊(C3⋊Dic3)11yescharacteristic
338C4#6413511yescharacteristic
339C4#6413911yescharacteristic
340C3#7164614yescomplemented
341C2—21no—
342C2—21no—
343C2—42no—
344C2#1059291111yescharacteristic
345C2C2×#6366411yescharacteristic
346C2#1059293511yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×C4×#41C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C32×#41C22
cosocleC22×C32×C4C23
hypercenterC4×#41C3⋊D3
hypocenterC32#1806
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
3. C4×C4⋊(C3⋊Dic3)C2semidirect
4. #10592623C2semidirect
5. #10589398C2semidirect
8. C32×C4×Q8C4semidirect
9. C32×C4×Q8C4semidirect
12. C32×C4×D4C4semidirect
13. C32×C4×D4C4semidirect
66. C3×C4×Q8Dic3semidirect
67. C3×C4×Q8Dic3semidirect
70. C3×C4×D4Dic3semidirect
71. C3×C4×D4Dic3semidirect
86. C32×Q8C4⋊C4semidirect
90. C32×D4C4⋊C4semidirect
167. C32×C4#104semidirect
175. C4×Q8C3⋊Dic3semidirect
176. C4×Q8C3⋊Dic3semidirect
179. C4×D4C3⋊Dic3semidirect
180. C4×D4C3⋊Dic3semidirect
194. C3×Q8C4⋊Dic3semidirect
198. C3×D4C4⋊Dic3semidirect
276. C3×C4#837semidirect
282. C32#1806semidirect
286. Q8C4⋊(C3⋊Dic3)semidirect
290. D4C4⋊(C3⋊Dic3)semidirect
335. C4#63664semidirect
340. C3#71646semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C2×#636642
C4×C4⋊(C3⋊Dic3)2
#105926232
#105893982
#716463