Finite Group Databasebeta

← #11786732

Subgroups — #11786732

Order 1152.

858 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 858 conjugacy classes of subgroups — too many to draw. Only its 191 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#10595975C211yesmaximal, characteristic
2C2×#63652C211yesmaximal, characteristic
3#10592832C211yesmaximal, characteristic
4#10592820C211yesmaximal, characteristic, complemented
5#10592676C211yesmaximal, characteristic, complemented
6C32×#343C211yesmaximal, characteristic, complemented
7#10589421C211yesmaximal, characteristic, complemented
8#69003—34nomaximal
9C2×#3828C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C4×#638—22no—
14#64135C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17#64102—21no—
18#64101—21no—
19C4⋊C4×C3⋊D3—21no—
20#64096—21no—
21#63658—22no—
22#63652C414yescomplemented
23#63648—21no—
24#63645—21no—
25#63644—21no—
26#63643—21no—
27#5504—34no—
28C2×#825—34no—
29#5133—34no—
30#5121—34no—
31#4977—34no—
32C3×#343D314yescomplemented
33#4555—34no—
34C22×C32×C4D412yes—
35C22×C32×C4C2311yescharacteristic
36C2×#638—21no—
37C22×C3⋊Dic3—21no—
38C22×C3⋊Dic3—21no—
39#3828—21no—
40#3828—21no—
41#3828C2×C412yes—
42#3828Q812yes—
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—22no—
46C2×#634D411yescharacteristic
47C32×M16—21no—
48C32×M16—21no—
49C32×M16—21no—
50C32×M16C2×C412yescomplemented
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55#3757—21no—
56#3752—22no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)D411yescharacteristic
60C4⋊(C3⋊Dic3)D411yescharacteristic
61#3750—22no—
62C4×C3⋊Dic3—22no—
63C4×C3⋊Dic3—21no—
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3C2×C412yescomplemented
66#1860—91noSylow
67C2×#235—34no—
68C2×C3×M16C2×D314yes—
69C2×C3×M16C2×D314yes—
70C2×C3×C4⋊C4C2×D314yes—
71C4×#67—68no—
72#926—34no—
73C2×C4⋊Dic3—34no—
74C2×C4×Dic3—34no—
75#893—64no—
76#892—64no—
77D3×C4⋊C4—64no—
78#887—64no—
79C3⋊#95—68no—
80#825—316no—
81#821—64no—
82#818—64no—
83#817—64no—
84#816—64no—
85C23×C32C2×D411yescharacteristic
86C22×C3⋊D3—21no—
87C2×C32×C4—22no—
88C2×C32×C4—42no—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×Q811yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C32×C4#4111yescharacteristic
95#638—22no—
96#638—22no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—42no—
104C2×C3⋊Dic3—41no—
105C4⋊(C3⋊D3)—21no—
106C4⋊(C3⋊D3)C4⋊C412yes—
107C4×C3⋊D3—22no—
108C4×C3⋊D3—22no—
109C4×C3⋊D3—82no—
110#634—21no—
111#634C4⋊C412yes—
112C32×C8—22no—
113C32×C8—41no—
114#520—91no—
115#428—91no—
116C2×#104—91no—
117#417—91no—
118#382—91no—
119#343C3⋊D311yescharacteristic, complemented
120#339—91no—
121C22×C3×C4D1218yes—
122C22×C3×C4C22×D314yes—
123C2×#67—64no—
124C22×Dic3—64no—
125C22×Dic3—64no—
126#235—38no—
127#235—38no—
128#235—64no—
129#235—64no—
130C2×D12—34no—
131C2×C4×D3—64no—
132C2×C4×D3—68no—
133C2×Dic6—34no—
134C3×M16—24no—
135C3×M16—24no—
136C3×M16—24no—
137C3×M16C4×D318yescomplemented
138C2×C3×C8—24no—
139C2×C3×C8—24no—
140C3×C4⋊C4—24no—
141C3×C4⋊C4—24no—
142#217—64no—
143(C2×D3)⋊C4—68no—
144C4⋊Dic3—34no—
145C4⋊Dic3—34no—
146C4⋊Dic3—64no—
147C4⋊Dic3—64no—
148Dic3⋊C4—68no—
149C4×Dic3—38no—
150C4×Dic3—68no—
151C4×Dic3—64no—
152C4×Dic3—64no—
153C22×C32—21no—
154C22×C32—21no—
155C22×C32C4×D411yescharacteristic
156C22×C32#12011yescharacteristic
157C22×C32C22⋊Q811yescharacteristic
158C2×C3⋊D3—22no—
159C2×C3⋊D3—41no—
160C2×C3⋊D3—41no—
161C32×C4—42no—
162C32×C4C2×C4⋊C411yescharacteristic
163C32×C4C4×D411yescharacteristic
164C32×C4C22⋊Q811yescharacteristic
165C32×C4#12311yescharacteristic
166C3⋊Dic3—22no—
167C3⋊Dic3—42no—
168C3⋊Dic3—41no—
169C3⋊Dic3—41no—
170C3⋊Dic3—81no—
171C2×#41—91no—
172C2×M16C2×C3⋊D311yescharacteristic
173C2×M16C2×C3⋊D311yescharacteristic
174C4×Q8—181no—
175C4×D4—181no—
176C4×D4—182no—
177#117—91no—
178#117—181no—
179C2×C4⋊C4—91no—
180C2×C4⋊C4—181no—
181C2×C4⋊C4C2×C3⋊D311yescharacteristic
182C2×C42—91no—
183#107—181no—
184#106—181no—
185#104—94no—
186#103—181no—
187#102—181no—
188#95—182no—
189C23×C3C2×D1214yes—
190C22×D3—64no—
191C2×C3×C4—28no—
192C2×C3×C4—48no—
193C2×C3×C4C2×C4×D314yes—
194C2×C3×C4#23514yes—
195C2×C3×C4D3×D414yes—
196C2×C3×C4D3×D414yes—
197C2×C3×C4#23714yes—
198C2×C3×C4D3×Q814yes—
199#67—68no—
200#67—68no—
201C2×Dic3—64no—
202C2×Dic3—68no—
203C2×Dic3—64no—
204C2×Dic3—64no—
205C2×Dic3—124no—
206C2×Dic3—124no—
207C2×Dic3—128no—
208C2×Dic3—124no—
209D12—38no—
210D12—64no—
211C4×D3—68no—
212C4×D3—68no—
213C4×D3—248no—
214Dic6—38no—
215Dic6—64no—
216C3×C8—28no—
217C3×C8—44no—
218C2×C32—21no—
219C2×C32—21no—
220C2×C32#38511yescharacteristic
221C2×C32#45411yescharacteristic
222C2×C32#45511yescharacteristic
223C3⋊D3—42no—
224#41—92no—
225#41—92no—
226#41—181no—
227#41—181no—
228C2×Q8—91no—
229C2×D4—91no—
230C2×D4—181no—
231C22×C4—182no—
232C22×C4—181no—
233C22×C4—181no—
234C22×C4—181no—
235C22×C4C4⋊(C3⋊D3)12yes—
236C22×C4C22×C3⋊D311yescharacteristic
237M16—21no—
238M16—21no—
239M16—21no—
240M16C4×C3⋊D312yescomplemented
241C2×C8—21no—
242C2×C8—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—91no—
246C4⋊C4—91no—
247C4⋊C4—182no—
248C4⋊C4—181no—
249C4⋊C4—181no—
250C22⋊C4—182no—
251C22⋊C4—181no—
252C42—92no—
253C42—182no—
254C42—181no—
255C42—181no—
256C22×C3—24no—
257C22×C3—24no—
258C22×C3C4×D1214yes—
259C22×C3#88214yes—
260C22×C3#89714yes—
261C2×D3—68no—
262C2×D3—124no—
263C2×D3—124no—
264C3×C4—48no—
265C3×C4#67⋊C414yes—
266C3×C4#88314yes—
267C3×C4D3×C4⋊C414yes—
268C3×C4#89614yes—
269Dic3—68no—
270Dic3—128no—
271Dic3—124no—
272Dic3—124no—
273Dic3—244no—
274C32#186011yescharacteristic, complemented, Sylow
275C23—181no—
276C23C2×C4⋊(C3⋊D3)11yescharacteristic
277Q8—92no—
278Q8—181no—
279D4—92no—
280D4—182no—
281D4—182no—
282D4—181no—
283C2×C4—22no—
284C2×C4—42no—
285C2×C4—181no—
286C2×C4—182no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4—181no—
290C2×C4—181no—
291C2×C4—361no—
292C2×C4—361no—
293C2×C4—362no—
294C2×C4—361no—
295C2×C4—722no—
296C2×C4C2×C4×C3⋊D311yescharacteristic
297C2×C4#382811yescharacteristic
298C2×C4D4×C3⋊D311yescharacteristic
299C2×C4D4×C3⋊D311yescharacteristic
300C2×C4#383011yescharacteristic
301C2×C4Q8×C3⋊D311yescharacteristic
302C8—22no—
303C8—41no—
304C2×C3—24no—
305C2×C3—24no—
306C2×C3#466814yes—
307C2×C3#474614yes—
308C2×C3#475314yes—
309D3—128no—
310C22—21no—
311C22—21no—
312C22—182no—
313C22—361no—
314C22—361no—
315C22C4×C4⋊(C3⋊D3)11yescharacteristic
316C22#6409111yescharacteristic
317C22#6410611yescharacteristic
318C4—42no—
319C4—182no—
320C4—362no—
321C4—361no—
322C4—361no—
323C4—721no—
324C4#6409011yescharacteristic
325C4#6409211yescharacteristic
326C4C4⋊C4×C3⋊D311yescharacteristic
327C4#6410511yescharacteristic
328C3#6900314yescomplemented
329C2—21no—
330C2—21no—
331C2—362no—
332C2#1059236711yescharacteristic
333C2#1059244511yescharacteristic
334C2#1059245211yescharacteristic
subgroupG/H
centerC22#64091
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32#120
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#343C3⋊D3
hypocenterC32#1860
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
4. #10592820C2semidirect
5. #10592676C2semidirect
6. C32×#343C2semidirect
7. #10589421C2semidirect
22. #63652C4semidirect
32. C3×#343D3semidirect
50. C32×M16C2×C4semidirect
65. C4×C3⋊Dic3C2×C4semidirect
119. #343C3⋊D3semidirect
137. C3×M16C4×D3semidirect
240. M16C4×C3⋊D3semidirect
274. C32#1860semidirect
328. C3#69003semidirect

Maximal subgroups

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

subgroupindex
#105959752
C2×#636522
#105928322
#105928202
#105926762
C32×#3432
#105894212
#690033