Finite Group Databasebeta

← #11786575

Subgroups — #11786575

Order 1152.

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

normal subgroups only

This group has 972 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#10595992C211yesmaximal, characteristic
2C2×#63650C211yesmaximal, characteristic
3#10592820C211yesmaximal, characteristic, complemented
4#10592694C211yesmaximal, characteristic, complemented
5#10592638C211yesmaximal, characteristic
6C32×#339C211yesmaximal, characteristic, complemented
7#10589389C211yesmaximal, characteristic, complemented
8#68758—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3752—22no—
14#64135C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17#64102—21no—
18#64102—21no—
19C22⋊C4×C3⋊D3—22no—
20C4×C4⋊(C3⋊D3)—21no—
21C4×C4⋊(C3⋊D3)—21no—
22#63650C414yescomplemented
23#63645—21no—
24#63644—21no—
25#63635—21no—
26#63634—21no—
27#5521—34no—
28C2×#823—34no—
29#5121—34no—
30#4995—34no—
31#4939—34no—
32C3×#339D314yescomplemented
33#4523—34no—
34C23×C3⋊D3D412yes—
35C22×C32×C4—21no—
36C22×C32×C4C2311yescharacteristic
37C22×C3⋊Dic3—21no—
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)C2×C412yes—
43C2×C4⋊(C3⋊D3)Q812yes—
44C2×C4×C3⋊D3—22no—
45C2×C4×C3⋊D3—22no—
46C32×M16—21no—
47C32×M16C2×C412yescomplemented
48C2×C32×C8—21no—
49C32×C4⋊C4D411yescharacteristic
50C32×C4⋊C4D411yescharacteristic
51C32×C22⋊C4—21no—
52C32×C42—21no—
53C32×C42—21no—
54C32×C42—21no—
55#3757—21no—
56#3752—22no—
57#3752—22no—
58#3752—44no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)D411yescharacteristic
62C4⋊(C3⋊Dic3)D411yescharacteristic
63C4×C3⋊Dic3—21no—
64#3748—21no—
65#3748C2×C412yescomplemented
66C2×C3⋊(C3⋊C8)—21no—
67#1856—91noSylow
68C22×D12—34no—
69C2×C3×M16C2×D314yes—
70C3×#117C2×D314yes—
71C2×C3×C42C2×D314yes—
72C2×(C2×D3)⋊C4—68no—
73#926—34no—
74C2×C4⋊Dic3—34no—
75C2×#208—34no—
76#893—64no—
77#893—64no—
78D3×C22⋊C4—68no—
79C4×D12—64no—
80C4×D12—64no—
81#823—316no—
82#818—64no—
83#817—64no—
84#808—64no—
85#807—64no—
86C23×C32C2×D411yescharacteristic
87C22×C3⋊D3—22no—
88C22×C3⋊D3—22no—
89C22×C3⋊D3—42no—
90C22×C3⋊D3—42no—
91C22×C3⋊D3C4⋊C414yes—
92C2×C32×C4—22no—
93C2×C32×C4—21no—
94C2×C32×C4—21no—
95C2×C32×C4—41no—
96C2×C32×C4—41no—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×Q811yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3—21no—
105C2×C3⋊Dic3—42no—
106C2×C3⋊Dic3—41no—
107C4⋊(C3⋊D3)—22no—
108C4⋊(C3⋊D3)—22no—
109C4⋊(C3⋊D3)—22no—
110C4⋊(C3⋊D3)—22no—
111C4×C3⋊D3—82no—
112C4×C3⋊D3—82no—
113C32×C8—22no—
114C3⋊(C3⋊C8)—22no—
115#518—91no—
116#428—91no—
117#428—91no—
118C2×#100—91no—
119#390—91no—
120#339—91no—
121#339C3⋊D311yescharacteristic, complemented
122C23×D3—38no—
123C22×C3×C4—24no—
124C22×C3×C4C22×D314yes—
125C22×Dic3—64no—
126C2×D12—38no—
127C2×D12—38no—
128C2×D12—64no—
129C2×D12—64no—
130C2×D12—64no—
131C2×D12—64no—
132C2×C4×D3—68no—
133C2×C4×D3—68no—
134C3×M16—24no—
135C3×M16C4×D318yescomplemented
136C2×C3×C8—24no—
137C3×C4⋊C4D1214yes—
138C3×C4⋊C4D1214yes—
139C3×C22⋊C4—24no—
140C3×C42—24no—
141C3×C42—24no—
142C3×C42—24no—
143#217—64no—
144(C2×D3)⋊C4—68no—
145(C2×D3)⋊C4—68no—
146(C2×D3)⋊C4—1216no—
147C4⋊Dic3—34no—
148C4⋊Dic3—34no—
149C4⋊Dic3—64no—
150C4⋊Dic3—64no—
151C4×Dic3—64no—
152#208—38no—
153#208—64no—
154C2×C3⋊C8—64no—
155C22×C32—21no—
156C22×C32—21no—
157C22×C32C2×C4⋊C411yescharacteristic
158C22×C32#12011yescharacteristic
159C22×C32#12311yescharacteristic
160C2×C3⋊D3—24no—
161C2×C3⋊D3—42no—
162C2×C3⋊D3—42no—
163C2×C3⋊D3—44no—
164C2×C3⋊D3—82no—
165C32×C4—42no—
166C32×C4—41no—
167C32×C4—41no—
168C32×C4C4×D411yescharacteristic
169C32×C4C4×D411yescharacteristic
170C32×C4C22⋊Q811yescharacteristic
171C32×C4C22⋊Q811yescharacteristic
172C3⋊Dic3—41no—
173C3⋊Dic3—41no—
174C3⋊Dic3—81no—
175C22×D4—91no—
176C2×M16—91no—
177C2×M16C2×C3⋊D311yescharacteristic
178C4×D4—181no—
179C4×D4—181no—
180C4×D4—181no—
181C4×D4—181no—
182#117—91no—
183#117C2×C3⋊D311yescharacteristic
184C2×C4⋊C4—91no—
185C2×C22⋊C4—182no—
186C2×C22⋊C4—182no—
187C2×C42C2×C3⋊D311yescharacteristic
188#107—181no—
189#107—181no—
190#106—181no—
191#106—181no—
192#100—94no—
193C23×C3D3×D414yes—
194C22×D3—316no—
195C22×D3—68no—
196C22×D3—68no—
197C22×D3—128no—
198C22×D3—128no—
199C2×C3×C4—28no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—44no—
203C2×C3×C4—44no—
204C2×C3×C4C2×C4×D314yes—
205C2×C3×C4C2×D1214yes—
206C2×C3×C4#23514yes—
207C2×C3×C4D3×D414yes—
208C2×C3×C4#23714yes—
209C2×C3×C4D3×Q814yes—
210C2×Dic3—64no—
211C2×Dic3—64no—
212C2×Dic3—128no—
213C2×Dic3—124no—
214D12—68no—
215D12—68no—
216D12—68no—
217D12—68no—
218C4×D3—248no—
219C4×D3—248no—
220C3×C8—28no—
221C3⋊C8—68no—
222C2×C32—21no—
223C2×C32—21no—
224C2×C32#38511yescharacteristic
225C2×C32#45311yescharacteristic
226C2×C32#45511yescharacteristic
227C3⋊D3—44no—
228C24—92no—
229C2×D4—92no—
230C2×D4—92no—
231C2×D4—181no—
232C2×D4—181no—
233C2×D4—181no—
234C2×D4—181no—
235C22×C4—21no—
236C22×C4—182no—
237C22×C4—182no—
238C22×C4—181no—
239C22×C4C22×C3⋊D311yescharacteristic
240M16—21no—
241M16—92no—
242M16—181no—
243M16C4×C3⋊D312yescomplemented
244C2×C8—21no—
245C2×C8—181no—
246C4⋊C4—91no—
247C4⋊C4—91no—
248C4⋊C4—181no—
249C4⋊C4—181no—
250C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
251C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—182no—
254C22⋊C4—182no—
255C22⋊C4—181no—
256C22⋊C4—364no—
257C42—21no—
258C42—21no—
259C42—21no—
260C42—181no—
261C22×C3—24no—
262C22×C3—24no—
263C22×C3#88214yes—
264C22×C3#88314yes—
265C22×C3D3×C4⋊C414yes—
266C2×D3—616no—
267C2×D3—128no—
268C2×D3—128no—
269C2×D3—1216no—
270C2×D3—248no—
271C3×C4—48no—
272C3×C4—44no—
273C3×C4—44no—
274C3×C4C4×D1214yes—
275C3×C4#67⋊C414yes—
276C3×C4#89614yes—
277C3×C4#89714yes—
278Dic3—124no—
279Dic3—124no—
280Dic3—244no—
281C32#185611yescharacteristic, complemented, Sylow
282C23—94no—
283C23—182no—
284C23—182no—
285C23—362no—
286C23—362no—
287C23D4×C3⋊D311yescharacteristic
288D4—182no—
289D4—182no—
290D4—182no—
291D4—182no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—181no—
298C2×C4—181no—
299C2×C4—362no—
300C2×C4—361no—
301C2×C4—722no—
302C2×C4—722no—
303C2×C4C2×C4×C3⋊D311yescharacteristic
304C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
305C2×C4#382811yescharacteristic
306C2×C4D4×C3⋊D311yescharacteristic
307C2×C4#383011yescharacteristic
308C2×C4Q8×C3⋊D311yescharacteristic
309C8—22no—
310C8—182no—
311C2×C3—24no—
312C2×C3—24no—
313C2×C3#466814yes—
314C2×C3#482214yes—
315C2×C3#482514yes—
316D3—1216no—
317C22—21no—
318C22—21no—
319C22—184no—
320C22—364no—
321C22—362no—
322C22—362no—
323C22—722no—
324C22#6409111yescharacteristic
325C22#6409211yescharacteristic
326C22C4⋊C4×C3⋊D311yescharacteristic
327C4—42no—
328C4—41no—
329C4—41no—
330C4—361no—
331C4—361no—
332C4—721no—
333C4C4×C4⋊(C3⋊D3)11yescharacteristic
334C4#6409011yescharacteristic
335C4#6410511yescharacteristic
336C4#6410611yescharacteristic
337C3#6875814yescomplemented
338C2—21no—
339C2—21no—
340C2—364no—
341C2#1059236711yescharacteristic
342C2#1059252111yescharacteristic
343C2#1059252411yescharacteristic
subgroupG/H
centerC22#64091
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#339C2
socleC22×C32#120
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenter#339C3⋊D3
hypocenterC32#1856
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
3. #10592820C2semidirect
4. #10592694C2semidirect
6. C32×#339C2semidirect
7. #10589389C2semidirect
22. #63650C4semidirect
32. C3×#339D3semidirect
47. C32×M16C2×C4semidirect
65. #3748C2×C4semidirect
121. #339C3⋊D3semidirect
135. C3×M16C4×D3semidirect
243. M16C4×C3⋊D3semidirect
281. C32#1856semidirect
337. C3#68758semidirect

Maximal subgroups

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

subgroupindex
#105959922
C2×#636502
#105928202
#105926942
#105926382
C32×#3392
#105893892
#687583