Finite Group Databasebeta

← #11793093

Subgroups — #11793093

Order 1152.

732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595988C211yesmaximal, characteristic, complemented
2C32×#410C211yesmaximal, characteristic
3#10592935C211yesmaximal, characteristic
4C2×#63664C211yesmaximal, characteristic
5#10589399C211yesmaximal, characteristic, complemented
6#10589398C211yesmaximal, characteristic, complemented
7#10589397C211yesmaximal, characteristic, complemented
8#70038—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C32×#117C2211yescharacteristic
11C32×#117C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16#64099—21no—
17#64097—21no—
18#64087—22no—
19C4×#634—22no—
20C32×#99—22no—
21#63664—21no—
22#63664—21no—
23#63664—22no—
24#5517—34no—
25C3×#410D314yes—
26#5236—34no—
27C2×#837—34no—
28#4533—34no—
29#4532—34no—
30#4531—34no—
31C32×#41—21no—
32C32×#41—21no—
33C32×#41—21no—
34C32×#41—21no—
35C2×C32×Q8Q811yescharacteristic, complemented
36C2×C32×D4—21no—
37C2×C32×D4Q811yescharacteristic, complemented
38C22×C32×C4—21no—
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3—21no—
41C2×#634—22no—
42C32×C4⋊C4—21no—
43C32×C4⋊C4—21no—
44C32×C22⋊C4—21no—
45C32×C22⋊C4D412yes—
46C32×C42—21no—
47C32×C42—21no—
48#3757—21no—
49C4⋊(C3⋊Dic3)—22no—
50C4⋊(C3⋊Dic3)—21no—
51#3750—22no—
52#3750—22no—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3D412yes—
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57#3748—21no—
58#3748—21no—
59#3748—21no—
60#3748—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63#2031—91noSylow
64C2×C3×#41C2×D314yes—
65C3×#117C2×D314yes—
66C3×#117C2×D314yes—
67#926—34no—
68C2×C4×Dic3—34no—
69C2×#208—34no—
70C2×#208—34no—
71#890—64no—
72#888—64no—
73#878—68no—
74C4×Dic6—68no—
75C3×#99—28no—
76#837—64no—
77#837—64no—
78#837—68no—
79C23×C32—21no—
80C23×C32C2×D411yescharacteristic
81C32×Q8—21no—
82C32×Q8—21no—
83C32×D4—21no—
84C32×D4—21no—
85C32×D4—41no—
86C32×D4—41no—
87C2×C32×C4—22no—
88C2×C32×C4—21no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×Q811yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—42no—
102#634—44no—
103C3⋊(C3⋊C8)—41no—
104C3⋊(C3⋊C8)—41no—
105#533—91no—
106#421—91no—
107C2×#104—91no—
108#410C3⋊D311yescharacteristic
109#344—91no—
110#339—91no—
111H(3,ℤ/4)—91no—
112C3×#41—24no—
113C3×#41—24no—
114C3×#41—24no—
115C3×#41—24no—
116C2×C3×Q8Dic614yescomplemented
117C2×C3×D4—24no—
118C2×C3×D4Dic614yescomplemented
119C22×C3×C4—24no—
120C22×C3×C4C22×D314yes—
121C22×Dic3—64no—
122C2×Dic6—68no—
123C3×C4⋊C4—24no—
124C3×C4⋊C4—24no—
125C3×C22⋊C4—24no—
126C3×C22⋊C4#6718yes—
127C3×C42—24no—
128C3×C42—24no—
129#217—64no—
130C4⋊Dic3—68no—
131C4⋊Dic3—64no—
132Dic3⋊C4—68no—
133Dic3⋊C4—68no—
134C4×Dic3—38no—
135C4×Dic3—34no—
136C4×Dic3—34no—
137C4×Dic3—64no—
138#208—64no—
139#208—64no—
140#208—64no—
141#208—64no—
142C2×C3⋊C8—64no—
143C2×C3⋊C8—64no—
144C22×C32—41no—
145C22×C32—41no—
146C22×C32—81no—
147C22×C32#12011yescharacteristic
148C22×C32C22⋊Q811yescharacteristic
149C22×C32#12411yescharacteristic
150C32×C4—42no—
151C32×C4—41no—
152C32×C4—81no—
153C32×C4C22⋊Q811yescharacteristic
154C32×C4C22⋊Q811yescharacteristic
155C32×C4#12411yescharacteristic
156C32×C4#12411yescharacteristic
157C3⋊Dic3—22no—
158C3⋊Dic3—42no—
159C3⋊Dic3—41no—
160C2×#41C2×C3⋊D311yescharacteristic
161C2×M16—91no—
162C2×M16—91no—
163C4⋊Q8—181no—
164#125—181no—
165C22⋊Q8—182no—
166C4×Q8—182no—
167#117—91no—
168#117C2×C3⋊D311yescharacteristic
169#117C2×C3⋊D311yescharacteristic
170C2×C42—91no—
171#104—181no—
172#104—181no—
173#104—182no—
174#99—22no—
175C23×C3—24no—
176C23×C3C2×#6714yes—
177C3×Q8—24no—
178C3×Q8—24no—
179C3×D4—24no—
180C3×D4—24no—
181C3×D4—44no—
182C3×D4—44no—
183C2×C3×C4—24no—
184C2×C3×C4—28no—
185C2×C3×C4—44no—
186C2×C3×C4—44no—
187C2×C3×C4—44no—
188C2×C3×C4C2×Dic614yes—
189C2×C3×C4#23514yes—
190C2×C3×C4D3×D414yes—
191C2×C3×C4D3×D414yes—
192C2×C3×C4#23714yes—
193C2×C3×C4#23714yes—
194C2×Dic3—64no—
195C2×Dic3—64no—
196C2×Dic3—68no—
197C2×Dic3—128no—
198Dic6—1216no—
199C3⋊C8—124no—
200C3⋊C8—124no—
201C2×C32—21no—
202C2×C32—21no—
203C2×C32—21no—
204C2×C32—81no—
205C2×C32#39311yescharacteristic
206#41—21no—
207#41—21no—
208#41—21no—
209#41—21no—
210C2×Q8—182no—
211C2×Q8#63411yescharacteristic, complemented
212C2×D4—21no—
213C2×D4#63411yescharacteristic, complemented
214C22×C4—21no—
215C22×C4—181no—
216C22×C4C22×C3⋊D311yescharacteristic
217M16—181no—
218M16—181no—
219M16—181no—
220M16—181no—
221C2×C8—181no—
222C2×C8—181no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—182no—
226C4⋊C4—182no—
227C4⋊C4—182no—
228C4⋊C4—181no—
229C22⋊C4—21no—
230C22⋊C4—181no—
231C22⋊C4#63812yes—
232C42—21no—
233C42—21no—
234C42—91no—
235C42—91no—
236C42—92no—
237C42—181no—
238C22×C3—44no—
239C22×C3—44no—
240C22×C3—84no—
241C22×C3#92414yes—
242C22×C3#93614yes—
243C22×C3#93714yes—
244C3×C4—48no—
245C3×C4—44no—
246C3×C4—84no—
247C3×C4#87814yes—
248C3×C4#87814yes—
249C3×C4#88514yes—
250C3×C4#88514yes—
251Dic3—68no—
252Dic3—128no—
253Dic3—124no—
254C32#203111yescharacteristic, complemented, Sylow
255C23—21no—
256C23C2×#63811yescharacteristic
257Q8—21no—
258Q8—21no—
259Q8—364no—
260D4—21no—
261D4—21no—
262D4—41no—
263D4—41no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—181no—
270C2×C4—181no—
271C2×C4—182no—
272C2×C4—362no—
273C2×C4C2×#63411yescharacteristic
274C2×C4#382811yescharacteristic
275C2×C4D4×C3⋊D311yescharacteristic
276C2×C4D4×C3⋊D311yescharacteristic
277C2×C4#383011yescharacteristic
278C2×C4#383011yescharacteristic
279C8—361no—
280C8—361no—
281C2×C3—24no—
282C2×C3—24no—
283C2×C3—24no—
284C2×C3—84no—
285C2×C3#494714yes—
286C22—41no—
287C22—41no—
288C22—81no—
289C22#6413311yescharacteristic
290C22#6414511yescharacteristic
291C22#6414611yescharacteristic
292C4—42no—
293C4—41no—
294C4—81no—
295C4—182no—
296C4—361no—
297C4—362no—
298C4#6408711yescharacteristic
299C4#6408711yescharacteristic
300C4#6409411yescharacteristic
301C4#6409411yescharacteristic
302C3#7003814yescomplemented
303C2—21no—
304C2—21no—
305C2—21no—
306C2—81no—
307C2#1059264611yescharacteristic
subgroupG/H
centerC4#64094
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#410C2
socleC2×C32#393
prime radicalC2×C32×#41C22
hypercenter#410C3⋊D3
hypocenterC32#2031
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #10595988C2semidirect
5. #10589399C2semidirect
6. #10589398C2semidirect
7. #10589397C2semidirect
35. C2×C32×Q8Q8semidirect
37. C2×C32×D4Q8semidirect
116. C2×C3×Q8Dic6semidirect
118. C2×C3×D4Dic6semidirect
211. C2×Q8#634semidirect
213. C2×D4#634semidirect
254. C32#2031semidirect
302. C3#70038semidirect

Maximal subgroups

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

subgroupindex
#105959882
C32×#4102
#105929352
C2×#636642
#105893992
#105893982
#105893972
#700383