Finite Group Databasebeta

← #11786966

Subgroups — #11786966

Order 1152.

894 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic
2C2×#63662C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic
4C2×#63635C211yesmaximal, characteristic
5#10592627C211yesmaximal, characteristic
6#10589395C211yesmaximal, characteristic
7#10589390C211yesmaximal, characteristic
8#71629—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C32×C4×Q8—22no—
11C32×C4×Q8—22no—
12C2×C32×C4⋊C4—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C42—21no—
15C2×C32×C42C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750—21no—
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21#63662—22no—
22#63662C414yescomplemented
23#63658—21no—
24#63635—22no—
25C2×C3×C4×Q8D314yes—
26C2×#835—34no—
27C2×#835—34no—
28C2×#808—34no—
29#4928—34no—
30#4529—34no—
31#4524—34no—
32C2×C32×Q8—21no—
33C2×C32×Q8—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8C2×C412yes—
36C2×C32×Q8D412yes—
37C2×C32×Q8Q812yes—
38C22×C32×C4—21no—
39C22×C32×C4—21no—
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3—21no—
45C32×C4⋊C4—24no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4D412yes—
48C32×C42—24no—
49C32×C42—21no—
50C32×C42—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)C2×C412yes—
55#3750—42no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)C2×C412yes—
62#1865—91noSylow
63C22×C3×Q8C2×D314yes—
64C3×C4×Q8—28no—
65C3×C4×Q8—28no—
66C2×C3×C4⋊C4—24no—
67C2×C3×C4⋊C4C2×D314yes—
68C2×C3×C42—24no—
69C2×C3×C42C2×D314yes—
70C2×C4⋊Dic3—34no—
71C2×C4⋊Dic3—34no—
72C2×Dic3⋊C4—64no—
73C22×C3⋊C8—34no—
74C22×C3⋊C8—34no—
75#835—316no—
76#835—68no—
77C3⋊#95—64no—
78#808—68no—
79C23×C32C2×D411yescharacteristic
80C32×Q8—22no—
81C32×Q8—22no—
82C32×Q8—22no—
83C32×Q8C4⋊C414yescomplemented
84C2×C32×C4—22no—
85C2×C32×C4—21no—
86C2×C32×C4—22no—
87C2×C32×C4—22no—
88C2×C32×C4—21no—
89C2×C32×C4—21no—
90C2×C32×C4—22no—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
95C2×C32×C4SD1612yes—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×Q811yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3—41no—
108C3⋊(C3⋊C8)—22no—
109C3⋊(C3⋊C8)—41no—
110C2×C4×Q8C3⋊D311yescharacteristic
111C2×#106—91no—
112C2×#103—91no—
113C2×#103—91no—
114#389—91no—
115#340—91no—
116#336—91no—
117C2×C3×Q8—24no—
118C2×C3×Q8—24no—
119C2×C3×Q8—24no—
120C2×C3×Q8Dic618yes—
121C2×C3×Q8C4×D318yes—
122C2×C3×Q8#6718yes—
123C22×C3×C4—24no—
124C22×C3×C4—24no—
125C22×C3×C4#6714yes—
126C22×C3×C4#6714yes—
127C22×C3×C4C22×D314yes—
128C22×Dic3—64no—
129C22×Dic3—64no—
130C3×C4⋊C4—216no—
131C3×C4⋊C4—24no—
132C3×C4⋊C4#6718yes—
133C3×C42—216no—
134C3×C42—24no—
135C3×C42—24no—
136C4⋊Dic3—38no—
137C4⋊Dic3—64no—
138C4⋊Dic3—64no—
139C4⋊Dic3—64no—
140Dic3⋊C4—128no—
141C2×C3⋊C8—38no—
142C2×C3⋊C8—64no—
143C2×C3⋊C8—64no—
144C2×C3⋊C8—64no—
145C2×C3⋊C8—64no—
146C2×C3⋊C8—64no—
147C22×C32C4×D411yescharacteristic
148C22×C32#12011yescharacteristic
149C22×C32C22⋊Q811yescharacteristic
150C22×C32C2×SD1611yescharacteristic
151C22×C32#13511yescharacteristic
152C22×C32#13711yescharacteristic
153C22×C32#13711yescharacteristic
154C32×C4—24no—
155C32×C4—22no—
156C32×C4—41no—
157C32×C4—42no—
158C32×C4C2×C4⋊C411yescharacteristic
159C32×C4C4×D411yescharacteristic
160C32×C4C22⋊Q811yescharacteristic
161C32×C4#12311yescharacteristic
162C3⋊Dic3—42no—
163C3⋊Dic3—81no—
164C22×Q8C2×C3⋊D311yescharacteristic
165C22×C8—91no—
166C22×C8—91no—
167C4×Q8—22no—
168C4×Q8—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—91no—
171C2×C4⋊C4—91no—
172C2×C4⋊C4—181no—
173C2×C4⋊C4C2×C3⋊D311yescharacteristic
174C2×C42—21no—
175C2×C42C2×C3⋊D311yescharacteristic
176#106—182no—
177#103—94no—
178#103—182no—
179#95—181no—
180C23×C3C2×#6714yes—
181C3×Q8—28no—
182C3×Q8—28no—
183C3×Q8—28no—
184C3×Q8Dic3⋊C4116yescomplemented
185C2×C3×C4—28no—
186C2×C3×C4—28no—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—28no—
190C2×C3×C4—24no—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4—28no—
194C2×C3×C4—44no—
195C2×C3×C4—44no—
196C2×C3×C4#21518yes—
197C2×C3×C4C2×Dic614yes—
198C2×C3×C4C2×C4×D314yes—
199C2×C3×C4#23514yes—
200C2×C3×C4#23514yes—
201C2×C3×C4C2×#6714yes—
202C2×C3×C4C2×#6714yes—
203C2×Dic3—68no—
204C2×Dic3—124no—
205C2×Dic3—124no—
206C2×Dic3—124no—
207C2×Dic3—124no—
208C2×Dic3—124no—
209C3⋊C8—68no—
210C3⋊C8—124no—
211C2×C32#38511yescharacteristic
212C2×C32C4×SD1611yescharacteristic
213C2×C32#44111yescharacteristic
214C2×C32#44811yescharacteristic
215C2×C32#45211yescharacteristic
216C2×C32#47511yescharacteristic
217C2×C32#47911yescharacteristic
218C2×Q8—21no—
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8#63412yes—
222C2×Q8C4×C3⋊D312yes—
223C2×Q8#63812yes—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—181no—
227C22×C4—181no—
228C22×C4#63811yescharacteristic
229C22×C4#63811yescharacteristic
230C22×C4C22×C3⋊D311yescharacteristic
231C2×C8—92no—
232C2×C8—181no—
233C2×C8—181no—
234C2×C8—181no—
235C2×C8—181no—
236C2×C8—181no—
237C4⋊C4—24no—
238C4⋊C4—21no—
239C4⋊C4—92no—
240C4⋊C4—181no—
241C4⋊C4—181no—
242C4⋊C4—181no—
243C4⋊C4—362no—
244C4⋊C4#63812yes—
245C42—24no—
246C42—21no—
247C42—21no—
248C22×C3#92414yes—
249C22×C3C4×#6714yes—
250C22×C3C2×#21514yes—
251C22×C3#94214yes—
252C22×C3#95014yes—
253C22×C3#95114yes—
254C22×C3#95314yes—
255C3×C4—216no—
256C3×C4—28no—
257C3×C4—44no—
258C3×C4—48no—
259C3×C4C2×Dic3⋊C414yes—
260C3×C4#92414yes—
261C3×C4C4×#6714yes—
262C3×C4#92914yes—
263Dic3—128no—
264Dic3—244no—
265C32#186511yescharacteristic, complemented, Sylow
266C23C2×#63811yescharacteristic
267Q8—22no—
268Q8—22no—
269Q8—22no—
270Q8#375014yescomplemented
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—182no—
283C2×C4—361no—
284C2×C4—361no—
285C2×C4—361no—
286C2×C4—361no—
287C2×C4—361no—
288C2×C4#375512yes—
289C2×C4C2×#63411yescharacteristic
290C2×C4C2×C4×C3⋊D311yescharacteristic
291C2×C4#382811yescharacteristic
292C2×C4#382811yescharacteristic
293C2×C4C2×#63811yescharacteristic
294C2×C4C2×#63811yescharacteristic
295C8—182no—
296C8—361no—
297C2×C3#502014yes—
298C2×C3#502214yes—
299C2×C3C4×#21514yes—
300C2×C3#503014yes—
301C2×C3#521014yes—
302C2×C3#522714yes—
303C2×C3#523914yes—
304C22#6413311yescharacteristic
305C22C4×#63811yescharacteristic
306C22C2×#375511yescharacteristic
307C22#6415111yescharacteristic
308C22#6415911yescharacteristic
309C22#6416011yescharacteristic
310C22#6416211yescharacteristic
311C4—24no—
312C4—22no—
313C4—41no—
314C4—42no—
315C4—362no—
316C4—721no—
317C4C2×#375011yescharacteristic
318C4#6413311yescharacteristic
319C4C4×#63811yescharacteristic
320C4#6413811yescharacteristic
321C3#7162914yescomplemented
322C2#1059271911yescharacteristic
323C2#1059272111yescharacteristic
324C2C4×#375511yescharacteristic
325C2#1059272911yescharacteristic
326C2#1059290911yescharacteristic
327C2#1059292611yescharacteristic
328C2#1059293811yescharacteristic
subgroupG/H
centerC23C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×C4×Q8C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C4×Q8C3⋊D3
hypocenterC32#1865
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
22. #63662C4semidirect
83. C32×Q8C4⋊C4semidirect
184. C3×Q8Dic3⋊C4semidirect
265. C32#1865semidirect
270. Q8#3750semidirect
321. C3#71629semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C2×#636622
C2×#636352
#105926272
#105893952
#105893902
#716293