Finite Group Databasebeta

← #11786674

Subgroups — #11786674

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#520C211yesmaximal, characteristic
2C2×#63664C211yesmaximal, characteristic
3#10592931C211yesmaximal, characteristic
4#10592694C211yesmaximal, characteristic, complemented
5#10592674C211yesmaximal, characteristic, complemented
6#10589398C211yesmaximal, characteristic, complemented
7#10589396C211yesmaximal, characteristic, complemented
8#71664—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C32×C4×Q8—21no—
11C32×C4×D4—21no—
12C32×C4×D4—22no—
13C32×#117—21no—
14C32×#117C2211yescharacteristic
15C2×C32×C4⋊C4—21no—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750—22no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×#3748C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22#63664C414yescomplemented
23#63662—21no—
24#63659—21no—
25#63635—21no—
26#63634—21no—
27C3×#520D314yes—
28C2×#837—34no—
29#5232—34no—
30#4995—34no—
31#4975—34no—
32#4532—34no—
33#4530—34no—
34C32×#41—21no—
35C32×#41—21no—
36C32×#41C2×C412yes—
37C32×#41Q812yes—
38C2×C32×Q8D411yescharacteristic
39C2×C32×D4—21no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C22×C32×C4—22no—
43C22×C32×C4D412yes—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C32×C4⋊C4—22no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4D411yescharacteristic
51C32×C4⋊C4D411yescharacteristic
52C32×C22⋊C4—22no—
53C32×C22⋊C4—21no—
54C32×C42—22no—
55C32×C42—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58#3750—44no—
59C4×C3⋊Dic3—21no—
60C4×C3⋊Dic3C2×C412yescomplemented
61#3748—21no—
62#3748—21no—
63#3748—21no—
64#3748C2×C412yescomplemented
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67#1859—91noSylow
68C2×C3×#41C2×D314yes—
69C3×C4×Q8—24no—
70C3×C4×D4—24no—
71C3×C4×D4—28no—
72C3×#117—24no—
73C3×#117C2×D314yes—
74C2×C3×C4⋊C4—24no—
75C2×C3×C4⋊C4C2×D314yes—
76C2×C4⋊Dic3—34no—
77C2×Dic3⋊C4—68no—
78C2×C4×Dic3—34no—
79C2×#208—34no—
80C2×#208—34no—
81#837—316no—
82#835—64no—
83#832—64no—
84#808—64no—
85#807—64no—
86C23×C32—21no—
87C23×C32C2×D411yescharacteristic
88C32×Q8—21no—
89C32×Q8C4⋊C412yescomplemented
90C32×D4—22no—
91C32×D4—22no—
92C32×D4—21no—
93C32×D4C4⋊C412yescomplemented
94C2×C32×C4—21no—
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4—21no—
98C2×C32×C4—22no—
99C2×C32×C4—21no—
100C2×C32×C4—42no—
101C2×C32×C4—82no—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×Q811yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—42no—
112C2×C3⋊Dic3—41no—
113C3⋊(C3⋊C8)—22no—
114C3⋊(C3⋊C8)—41no—
115#520C3⋊D311yescharacteristic
116#428—91no—
117C2×#104—91no—
118#417—91no—
119#384—91no—
120#343—91no—
121#339—91no—
122C3×#41—24no—
123C3×#41—24no—
124C3×#41Dic618yes—
125C3×#41C4×D318yes—
126C2×C3×Q8#6714yes—
127C2×C3×D4—24no—
128C2×C3×D4#6714yes—
129C22×C3×C4—24no—
130C22×C3×C4—28no—
131C22×C3×C4#6718yes—
132C22×C3×C4C22×D314yes—
133C22×Dic3—64no—
134C22×Dic3—64no—
135C3×C4⋊C4—28no—
136C3×C4⋊C4—24no—
137C3×C4⋊C4—24no—
138C3×C4⋊C4#6714yes—
139C3×C4⋊C4#6714yes—
140C3×C22⋊C4—28no—
141C3×C22⋊C4—24no—
142C3×C42—28no—
143C3×C42—24no—
144C4⋊Dic3—64no—
145C4⋊Dic3—64no—
146Dic3⋊C4—1216no—
147C4×Dic3—38no—
148C4×Dic3—64no—
149#208—38no—
150#208—64no—
151#208—64no—
152#208—64no—
153C2×C3⋊C8—64no—
154C2×C3⋊C8—64no—
155C22×C32—21no—
156C22×C32—21no—
157C22×C32—22no—
158C22×C32—41no—
159C22×C32—41no—
160C22×C32C4×D411yescharacteristic
161C22×C32#12011yescharacteristic
162C22×C32C22⋊Q811yescharacteristic
163C32×C4—22no—
164C32×C4—42no—
165C32×C4—41no—
166C32×C4—41no—
167C32×C4C2×C4⋊C411yescharacteristic
168C32×C4C4×D411yescharacteristic
169C32×C4C22⋊Q811yescharacteristic
170C32×C4#12311yescharacteristic
171C3⋊Dic3—24no—
172C3⋊Dic3—81no—
173C2×#41C2×C3⋊D311yescharacteristic
174C2×M16—91no—
175C2×M16—91no—
176C4×Q8—21no—
177C4×D4—21no—
178C4×D4—22no—
179#117—21no—
180#117C2×C3⋊D311yescharacteristic
181C2×C4⋊C4—21no—
182C2×C4⋊C4—91no—
183C2×C4⋊C4—182no—
184C2×C4⋊C4C2×C3⋊D311yescharacteristic
185C2×C42—91no—
186#107—181no—
187#106—181no—
188#104—94no—
189#103—181no—
190#102—181no—
191C23×C3—24no—
192C23×C3C2×#6714yes—
193C3×Q8—24no—
194C3×Q8Dic3⋊C418yescomplemented
195C3×D4—28no—
196C3×D4—28no—
197C3×D4—24no—
198C3×D4Dic3⋊C418yescomplemented
199C2×C3×C4—24no—
200C2×C3×C4—28no—
201C2×C3×C4—28no—
202C2×C3×C4—24no—
203C2×C3×C4—28no—
204C2×C3×C4—24no—
205C2×C3×C4—48no—
206C2×C3×C4—88no—
207C2×C3×C4C2×Dic614yes—
208C2×C3×C4C2×C4×D314yes—
209C2×C3×C4#23514yes—
210C2×C3×C4#23514yes—
211C2×C3×C4C2×#6714yes—
212C2×C3×C4C2×#6714yes—
213C2×Dic3—68no—
214C2×Dic3—68no—
215C2×Dic3—68no—
216C2×Dic3—128no—
217C2×Dic3—124no—
218C3⋊C8—68no—
219C3⋊C8—124no—
220C2×C32—21no—
221C2×C32—21no—
222C2×C32—42no—
223C2×C32#38511yescharacteristic
224C2×C32#45311yescharacteristic
225C2×C32#45611yescharacteristic
226#41—21no—
227#41—21no—
228#41#63412yes—
229#41C4×C3⋊D312yes—
230C2×Q8#63811yescharacteristic
231C2×D4—21no—
232C2×D4#63811yescharacteristic
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—181no—
236C22×C4—181no—
237C22×C4#63812yes—
238C22×C4C22×C3⋊D311yescharacteristic
239M16—92no—
240M16—181no—
241M16—181no—
242M16—181no—
243C2×C8—181no—
244C2×C8—181no—
245C4⋊C4—22no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—181no—
249C4⋊C4—181no—
250C4⋊C4—364no—
251C4⋊C4#63811yescharacteristic
252C4⋊C4#63811yescharacteristic
253C22⋊C4—22no—
254C22⋊C4—21no—
255C42—22no—
256C42—21no—
257C42—92no—
258C42—181no—
259C22×C3—24no—
260C22×C3—24no—
261C22×C3—28no—
262C22×C3—44no—
263C22×C3—44no—
264C22×C3#92414yes—
265C22×C3C4×#6714yes—
266C22×C3#95314yes—
267C3×C4—28no—
268C3×C4—48no—
269C3×C4—44no—
270C3×C4—44no—
271C3×C4C2×Dic3⋊C414yes—
272C3×C4#92414yes—
273C3×C4C4×#6714yes—
274C3×C4#92914yes—
275Dic3—616no—
276Dic3—244no—
277C32#185911yescharacteristic, complemented, Sylow
278C23—21no—
279C23C2×#63811yescharacteristic
280Q8—21no—
281Q8#375012yescomplemented
282D4—22no—
283D4—22no—
284D4—21no—
285D4#375012yescomplemented
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—82no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4—362no—
298C2×C4—361no—
299C2×C4C2×#63411yescharacteristic
300C2×C4C2×C4×C3⋊D311yescharacteristic
301C2×C4#382811yescharacteristic
302C2×C4#382811yescharacteristic
303C2×C4C2×#63811yescharacteristic
304C2×C4C2×#63811yescharacteristic
305C8—182no—
306C8—361no—
307C2×C3—24no—
308C2×C3—24no—
309C2×C3—48no—
310C2×C3#521014yes—
311C2×C3#524114yes—
312C2×C3#524614yes—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22#6413311yescharacteristic
319C22C4×#63811yescharacteristic
320C22#6416211yescharacteristic
321C4—22no—
322C4—42no—
323C4—41no—
324C4—41no—
325C4—184no—
326C4—721no—
327C4C2×#375011yescharacteristic
328C4#6413311yescharacteristic
329C4C4×#63811yescharacteristic
330C4#6413811yescharacteristic
331C3#7166414yescomplemented
332C2—21no—
333C2—21no—
334C2—42no—
335C2#1059290911yescharacteristic
336C2#1059294011yescharacteristic
337C2#1059294511yescharacteristic
subgroupG/H
centerC22#64162
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#520C2
socleC22×C32#120
prime radicalC2×C32×#41C22
cosocleC22×C32×C4C23
hypercenter#520C3⋊D3
hypocenterC32#1859
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #520

Complements

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

NH ≅ G/Ntype
4. #10592694C2semidirect
5. #10592674C2semidirect
6. #10589398C2semidirect
7. #10589396C2semidirect
22. #63664C4semidirect
60. C4×C3⋊Dic3C2×C4semidirect
64. #3748C2×C4semidirect
89. C32×Q8C4⋊C4semidirect
93. C32×D4C4⋊C4semidirect
194. C3×Q8Dic3⋊C4semidirect
198. C3×D4Dic3⋊C4semidirect
277. C32#1859semidirect
281. Q8#3750semidirect
285. D4#3750semidirect
331. C3#71664semidirect

Maximal subgroups

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

subgroupindex
C32×#5202
C2×#636642
#105929312
#105926942
#105926742
#105893982
#105893962
#716643