Finite Group Databasebeta

← #11788511

Subgroups — #11788511

Order 1152.

930 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 179 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
1C2×#64118C211yesmaximal, characteristic
2#10595987C211yesmaximal, characteristic, complemented
3#10592838C211yesmaximal, characteristic
4#10592819C211yesmaximal, characteristic, complemented
5#10592705C211yesmaximal, characteristic
6C32×#344C211yesmaximal, characteristic, complemented
7#10589423C211yesmaximal, characteristic, complemented
8#69030—34nomaximal
9C2×#3828C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C32×#117C2211yescharacteristic
14#64135C2211yescharacteristic
15#64135C2211yescharacteristic
16#64118—22no—
17#64118—22no—
18C2×#3746C412yescomplemented
19C2×#3744C412yescomplemented
20#64096—22no—
21#64086—22no—
22C4×#634—22no—
23#63652—22no—
24#63643—22no—
25#63633—22no—
26C2×#909—34no—
27#5516—34no—
28#5139—34no—
29#5120—34no—
30#5006—34no—
31C3×#344D314yescomplemented
32#4557—34no—
33C22×C32×C4C2311yescharacteristic
34C2×#638—21no—
35C22×C3⋊Dic3—21no—
36#3828—21no—
37#3828—21no—
38#3828—21no—
39#3828—21no—
40C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
41C2×C4×C3⋊D3—21no—
42C2×#634—21no—
43C2×#634—21no—
44C2×#634—21no—
45C2×#634C2×C411yescharacteristic
46C2×#634C2×C412yes—
47C2×#634D412yes—
48C2×#634D412yes—
49C32×M16—21no—
50C32×M16—21no—
51C32×M16—21no—
52C32×M16—21no—
53C2×C32×C8—21no—
54C2×C32×C8C2×C412yes—
55C32×C4⋊C4—21no—
56C32×C22⋊C4D412yes—
57C32×C42—21no—
58#3757—21no—
59#3757—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62#3750—24no—
63C4×C3⋊Dic3—24no—
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3D412yes—
66#3746—24no—
67#3744—24no—
68#1905—91noSylow
69C2×#235—34no—
70C22×Dic6—34no—
71C2×C3×M16C2×D314yes—
72C2×C3×M16C2×D314yes—
73C3×#117C2×D314yes—
74#926—34no—
75#926—34no—
76#909—68no—
77#909—68no—
78C2×Dic12—38no—
79C2×#204—38no—
80#887—68no—
81#877—68no—
82C4×Dic6—68no—
83#825—68no—
84#816—68no—
85#806—68no—
86C23×C32C2×D411yescharacteristic
87C22×C3⋊D3—21no—
88C2×C32×C4—22no—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C32×C4#4111yescharacteristic
95#638—41no—
96#638—41no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—41no—
103C4⋊(C3⋊D3)—21no—
104C4⋊(C3⋊D3)—21no—
105C4×C3⋊D3—41no—
106C4×C3⋊D3—41no—
107#634—22no—
108#634—22no—
109#634—22no—
110#634—21no—
111#634—21no—
112#634C22⋊C414yes—
113C32×C8—22no—
114C32×C8—41no—
115C2×#137—91no—
116#519—91no—
117#421—91no—
118#419—91no—
119#410—91no—
120#344C3⋊D311yescharacteristic, complemented
121H(3,ℤ/4)—91no—
122C22×C3×C4C22×D314yes—
123C2×#67—64no—
124C22×Dic3—64no—
125#235—64no—
126#235—64no—
127#235—64no—
128#235—64no—
129C2×D12—34no—
130C2×C4×D3—64no—
131C2×Dic6—38no—
132C2×Dic6—38no—
133C2×Dic6—38no—
134C2×Dic6—34no—
135C2×Dic6—64no—
136C2×Dic6—64no—
137C2×Dic6—64no—
138C3×M16—24no—
139C3×M16—24no—
140C3×M16—24no—
141C3×M16—24no—
142C2×C3×C8—24no—
143C2×C3×C8C4×D318yes—
144C3×C4⋊C4—24no—
145C3×C22⋊C4D1218yes—
146C3×C42—24no—
147#217—64no—
148#217—64no—
149C4⋊Dic3—64no—
150C4⋊Dic3—64no—
151Dic3⋊C4—616no—
152C4×Dic3—38no—
153C4×Dic3—616no—
154C4×Dic3—64no—
155Dic12—616no—
156#204—616no—
157C22×C32—41no—
158C22×C32C4×D411yescharacteristic
159C22×C32#12011yescharacteristic
160C22×C32#12111yescharacteristic
161C2×C3⋊D3—41no—
162C2×C3⋊D3—81no—
163C32×C4—42no—
164C32×C4C2×C22⋊C411yescharacteristic
165C32×C4C4×D411yescharacteristic
166C32×C4#12111yescharacteristic
167C32×C4#12311yescharacteristic
168C3⋊Dic3—24no—
169C3⋊Dic3—42no—
170C3⋊Dic3—41no—
171C3⋊Dic3—81no—
172C2×#41—91no—
173C22×Q8—91no—
174#137—182no—
175#137—182no—
176C2×Q16—92no—
177C2×SD16—92no—
178C2×M16C2×C3⋊D311yescharacteristic
179C2×M16C2×C3⋊D311yescharacteristic
180C4×Q8—182no—
181C4×Q8—182no—
182#117—91no—
183#117—91no—
184#117—182no—
185#117C2×C3⋊D311yescharacteristic
186#104—182no—
187#103—182no—
188#99—182no—
189C23×C3C2×D1214yes—
190C22×D3—64no—
191C2×C3×C4—28no—
192C2×C3×C4C2×C4×D314yes—
193C2×C3×C4#23514yes—
194C2×C3×C4D3×D414yes—
195C2×C3×C4D3×D414yes—
196C2×C3×C4D3×D414yes—
197C2×C3×C4#23914yes—
198#67—124no—
199#67—124no—
200C2×Dic3—68no—
201C2×Dic3—68no—
202C2×Dic3—68no—
203C2×Dic3—64no—
204C2×Dic3—68no—
205C2×Dic3—124no—
206D12—64no—
207D12—64no—
208C4×D3—124no—
209C4×D3—124no—
210Dic6—316no—
211Dic6—68no—
212Dic6—68no—
213Dic6—68no—
214Dic6—64no—
215Dic6—64no—
216C3×C8—28no—
217C3×C8—44no—
218C2×C32—21no—
219C2×C32—21no—
220C2×C32—21no—
221C2×C32#38611yescharacteristic
222C3⋊D3—81no—
223#41—181no—
224#41—181no—
225#41—181no—
226#41—181no—
227C2×Q8—92no—
228C2×Q8—91no—
229C2×Q8—92no—
230C2×Q8—92no—
231C2×Q8—181no—
232C2×Q8—181no—
233C2×Q8—181no—
234C2×D4—91no—
235C2×D4—181no—
236C22×C4—181no—
237C22×C4—181no—
238C22×C4C22×C3⋊D311yescharacteristic
239Q16—184no—
240SD16—184no—
241M16—21no—
242M16—21no—
243M16—21no—
244M16—21no—
245C2×C8—21no—
246C2×C8C4×C3⋊D312yes—
247C4⋊C4—21no—
248C4⋊C4—184no—
249C4⋊C4—181no—
250C4⋊C4—181no—
251C22⋊C4—181no—
252C22⋊C4—181no—
253C22⋊C4C4⋊(C3⋊D3)12yes—
254C42—21no—
255C42—92no—
256C42—184no—
257C42—181no—
258C22×C3—44no—
259C22×C3C4×D1214yes—
260C22×C3#88214yes—
261C22×C3#89514yes—
262C2×D3—124no—
263C2×D3—244no—
264C3×C4—48no—
265C3×C4D3×C22⋊C414yes—
266C3×C4#88414yes—
267C3×C4#89314yes—
268C3×C4#89414yes—
269Dic3—616no—
270Dic3—128no—
271Dic3—124no—
272Dic3—244no—
273C32#190511yescharacteristic, complemented, Sylow
274C23—181no—
275C23C2×C4⋊(C3⋊D3)11yescharacteristic
276Q8—94no—
277Q8—182no—
278Q8—182no—
279Q8—182no—
280Q8—181no—
281Q8—181no—
282D4—181no—
283D4—181no—
284D4—361no—
285D4—361no—
286C2×C4—22no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4—182no—
290C2×C4—181no—
291C2×C4—182no—
292C2×C4—361no—
293C2×C4—361no—
294C2×C4—361no—
295C2×C4C2×C4×C3⋊D311yescharacteristic
296C2×C4#382811yescharacteristic
297C2×C4D4×C3⋊D311yescharacteristic
298C2×C4D4×C3⋊D311yescharacteristic
299C2×C4D4×C3⋊D311yescharacteristic
300C2×C4#383211yescharacteristic
301C8—22no—
302C8—41no—
303C2×C3—24no—
304C2×C3—24no—
305C2×C3—24no—
306C2×C3#466514yes—
307D3—244no—
308C22—41no—
309C22—361no—
310C22—721no—
311C22C4×C4⋊(C3⋊D3)11yescharacteristic
312C22#6409111yescharacteristic
313C22#6410411yescharacteristic
314C4—42no—
315C4—184no—
316C4—362no—
317C4—361no—
318C4—721no—
319C4C22⋊C4×C3⋊D311yescharacteristic
320C4#6409311yescharacteristic
321C4#6410211yescharacteristic
322C4#6410311yescharacteristic
323C3#6903014yescomplemented
324C2—21no—
325C2—21no—
326C2—21no—
327C2—721no—
328C2#1059236411yescharacteristic
subgroupG/H
centerC2#10592364
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#344C2
socleC2×C32#386
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#344C3⋊D3
hypocenterC32#1905
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #10595987C2semidirect
4. #10592819C2semidirect
6. C32×#344C2semidirect
7. #10589423C2semidirect
18. C2×#3746C4semidirect
19. C2×#3744C4semidirect
31. C3×#344D3semidirect
120. #344C3⋊D3semidirect
273. C32#1905semidirect
323. C3#69030semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
#105959872
#105928382
#105928192
#105927052
C32×#3442
#105894232
#690303