Finite Group Databasebeta

← #11788795

Subgroups — #11788795

Order 1152.

891 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 891 conjugacy classes of subgroups — too many to draw. Only its 124 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#10595996C211yesmaximal, characteristic
2#10594996C211yesmaximal, characteristic, complemented
3#10591113C212yesmaximal, complemented
4C2×#63559C211yesmaximal, characteristic, complemented
5C3×#4531C212yesmaximal, complemented
6#68705—32nomaximal
7C2×#3828C2211yescharacteristic
8C22×C4⋊(C3⋊D3)C2211yescharacteristic
9C32×#117C2211yescharacteristic
10#64104—22no—
11#64091—22no—
12#64084C412yescomplemented
13#64083C412yescomplemented
14C3×#926C2212yes—
15C2×C3×#208C2212yes—
16#63974—22no—
17#63894—24no—
18#63570—24no—
19#63559—22no—
20#5525—32no—
21#5525—61no—
22#5521—32no—
23#5139—32no—
24C2×#823—32no—
25#5005—32no—
26C3×H(3,ℤ/4)—32no—
27#4531D312yescomplemented
28C23×C3⋊D3D412yes—
29C22×C32×C4C2311yescharacteristic
30C2×#638—21no—
31#3828—22no—
32#3828—22no—
33C2×C4⋊(C3⋊D3)—22no—
34C2×C4⋊(C3⋊D3)—22no—
35C2×C4⋊(C3⋊D3)—24no—
36C2×C4⋊(C3⋊D3)C2×C412yes—
37C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
38C2×C4⋊(C3⋊D3)D412yes—
39C2×C4×C3⋊D3—21no—
40C2×#634C2×C411yescharacteristic, complemented
41C2×#624—24no—
42C32×C4⋊C4—21no—
43C32×C22⋊C4—21no—
44C32×C42C2×C412yescomplemented
45#3752—24no—
46C3×#217—22no—
47C3×C4⋊Dic3—22no—
48C3×C4×Dic3D414yescomplemented
49C3×#208—22no—
50C3×#208—22no—
51C2×C3×C3⋊C8—22no—
52#3722—24no—
53#1911—91noSylow
54C2×#235—32no—
55C2×#235—61no—
56C22×D12—32no—
57C22×D12—61no—
58C2×C3×M16—32no—
59C3×#117—21no—
60C3×#117—32no—
61C3×#117C2×D312yes—
62#926C2×D312yes—
63C2×#208C2×D312yes—
64#895—64no—
65#895—64no—
66#893—64no—
67#882—64no—
68#882—64no—
69D3×C22⋊C4—64no—
70#875—34no—
71#875—62no—
72#874—34no—
73#874—62no—
74C4×D12—64no—
75#825—64no—
76#823—64no—
77#805—64no—
78C23×C32C2×D411yescharacteristic
79C22×C3⋊D3—21no—
80C22×C3⋊D3—22no—
81C22×C3⋊D3—22no—
82C22×C3⋊D3—82no—
83C22×C3⋊D3C22⋊C414yes—
84C2×C32×C4—22no—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C2×D412yes—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4#4112yes—
89#638—41no—
90#638—41no—
91C2×C3⋊Dic3—21no—
92C4⋊(C3⋊D3)—24no—
93C4⋊(C3⋊D3)—22no—
94C4⋊(C3⋊D3)—24no—
95C4⋊(C3⋊D3)—84no—
96C4×C3⋊D3—42no—
97#634—22no—
98C2×C3×Dic3—24no—
99#624—84no—
100C3×C3⋊C8—42no—
101#535—91no—
102#518—91no—
103#421—92no—
104C2×#100—91no—
105H(3,ℤ/4)—32no—
106C23×D3—34no—
107C23×D3—62no—
108C22×C3×C4—21no—
109C22×C3×C4C22×D312yes—
110C2×#67—62no—
111C2×#67—62no—
112#235—62no—
113#235—62no—
114#235—62no—
115#235—62no—
116#235—122no—
117#235—122no—
118C2×D12—34no—
119C2×D12—32no—
120C2×D12—34no—
121C2×D12—61no—
122C2×D12—62no—
123C2×D12—62no—
124C2×D12—62no—
125C2×D12—62no—
126C2×D12—62no—
127C2×D12—62no—
128C2×D12—68no—
129C2×D12—68no—
130C2×D12—122no—
131C2×D12—122no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×C4×D3—68no—
135C2×Dic6—32no—
136C2×Dic6—61no—
137C3×M16—62no—
138C3×M16—62no—
139C2×C3×C8—62no—
140C3×C4⋊C4—22no—
141C3×C4⋊C4—22no—
142C3×C4⋊C4—62no—
143C3×C22⋊C4—22no—
144C3×C22⋊C4—22no—
145C3×C22⋊C4—62no—
146C3×C42—22no—
147C3×C42—34no—
148C3×C42C4×D314yescomplemented
149#217—22no—
150(C2×D3)⋊C4—68no—
151(C2×D3)⋊C4—68no—
152(C2×D3)⋊C4—68no—
153C4⋊Dic3—22no—
154C4×Dic3D1214yescomplemented
155#208—22no—
156#208—22no—
157C2×C3⋊C8—22no—
158C22×C32—41no—
159C22×C32C2×C22⋊C411yescharacteristic
160C22×C32#12011yescharacteristic
161C22×C32#12311yescharacteristic
162C2×C3⋊D3—24no—
163C2×C3⋊D3—44no—
164C2×C3⋊D3—42no—
165C2×C3⋊D3—41no—
166C2×C3⋊D3—44no—
167C2×C3⋊D3—82no—
168C32×C4—42no—
169C32×C4C4×D412yes—
170C32×C4#12112yes—
171C3⋊Dic3—41no—
172C3×Dic3—44no—
173C2×#41—91no—
174C22×D4—91no—
175C2×M16—32no—
176#127—92no—
177#124—92no—
178#121—182no—
179#120—182no—
180C4×D4—184no—
181#117—32no—
182#117D3211yescharacteristic
183C2×C22⋊C4—182no—
184#104—184no—
185#100—182no—
186C23×C3—21no—
187C23×C3D3×D412yes—
188C22×D3—38no—
189C22×D3—64no—
190C22×D3—64no—
191C22×D3—64no—
192C22×D3—62no—
193C22×D3—62no—
194C22×D3—122no—
195C22×D3—122no—
196C22×D3—244no—
197C22×D3—244no—
198C2×C3×C4—24no—
199C2×C3×C4—24no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—64no—
205C2×C3×C4C2×C4×D312yes—
206C2×C3×C4C2×D1212yes—
207C2×C3×C4#23512yes—
208C2×C3×C4D3×D412yes—
209C2×C3×C4D3×D412yes—
210C2×C3×C4#23912yes—
211#67—122no—
212#67—122no—
213#67—122no—
214#67—122no—
215C2×Dic3—24no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218D12—64no—
219D12—62no—
220D12—64no—
221D12—64no—
222D12—62no—
223D12—64no—
224D12—124no—
225D12—124no—
226D12—122no—
227D12—248no—
228D12—248no—
229C4×D3—124no—
230C4×D3—122no—
231C4×D3—122no—
232C4×D3—248no—
233Dic6—62no—
234Dic6—62no—
235Dic6—122no—
236C3×C8—122no—
237C3⋊C8—42no—
238C2×C32—21no—
239C2×C32—21no—
240C2×C32—21no—
241C2×C32#38611yescharacteristic
242C3⋊D3—44no—
243C3⋊D3—81no—
244C24—92no—
245#41—182no—
246#41—182no—
247C2×Q8—91no—
248C2×D4—92no—
249C2×D4—91no—
250C2×D4—92no—
251C2×D4—184no—
252C2×D4—181no—
253C2×D4—182no—
254C2×D4—182no—
255C22×C4—184no—
256C22×C4—181no—
257C22×C4C2×D3211yescharacteristic
258M16—62no—
259M16—62no—
260C2×C8—62no—
261C4⋊C4—21no—
262C4⋊C4—62no—
263C22⋊C4—21no—
264C22⋊C4—62no—
265C22⋊C4—184no—
266C22⋊C4—184no—
267C42—34no—
268C42#62412yescomplemented
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—42no—
273C22×C3—42no—
274C22×C3D3×C22⋊C412yes—
275C22×C3#88212yes—
276C22×C3#89412yes—
277C2×D3—68no—
278C2×D3—124no—
279C2×D3—128no—
280C2×D3—128no—
281C2×D3—122no—
282C2×D3—124no—
283C2×D3—124no—
284C2×D3—128no—
285C2×D3—122no—
286C2×D3—244no—
287C2×D3—244no—
288C2×D3—244no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—44no—
292C3×C4—44no—
293C3×C4—124no—
294C3×C4C4×D1212yes—
295C3×C4#88412yes—
296C3×C4#89312yes—
297C3×C4#89512yes—
298Dic3—44no—
299Dic3—122no—
300Dic3—122no—
301C32#191111yescharacteristic, complemented, Sylow
302C23—94no—
303C23—182no—
304C23—182no—
305C23—181no—
306C23—722no—
307C23#381111yescharacteristic
308Q8—182no—
309D4—184no—
310D4—182no—
311D4—184no—
312D4—361no—
313D4—361no—
314D4—724no—
315C2×C4—22no—
316C2×C4—64no—
317C2×C4—181no—
318C2×C4—362no—
319C2×C4—724no—
320C2×C4#379912yes—
321C2×C4D3×D1212yes—
322C2×C4C2×#62411yescharacteristic
323C2×C4#381111yescharacteristic
324C8—122no—
325C2×C3—22no—
326C2×C3—22no—
327C2×C3—22no—
328C2×C3—22no—
329C2×C3—21no—
330C2×C3—41no—
331C2×C3—41no—
332C2×C3#466512yes—
333D3—128no—
334D3—244no—
335D3—242no—
336D3—242no—
337C22—41no—
338C22—184no—
339C22—364no—
340C22—364no—
341C22—362no—
342C22—361no—
343C22—722no—
344C22#6389711yescharacteristic
345C22#6392311yescharacteristic
346C22#6397411yescharacteristic
347C4—42no—
348C4—124no—
349C4—361no—
350C4#6389412yes—
351C4#6391012yes—
352C3—21no—
353C3#6870512yescomplemented
354C2—21no—
355C2—21no—
356C2—21no—
357C2—364no—
358C2—721no—
359C2#1059138011yescharacteristic
subgroupG/H
centerC2#10591380
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radical#10595996C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1911
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10594996C2semidirect
3. #10591113C2semidirect
4. C2×#63559C2semidirect
5. C3×#4531C2semidirect
12. #64084C4semidirect
13. #64083C4semidirect
27. #4531D3semidirect
37. C2×C4⋊(C3⋊D3)C2×C4semidirect
40. C2×#634C2×C4semidirect
44. C32×C42C2×C4semidirect
48. C3×C4×Dic3D4semidirect
148. C3×C42C4×D3semidirect
154. C4×Dic3D12semidirect
268. C42#624semidirect
301. C32#1911semidirect
353. C3#68705semidirect

Maximal subgroups

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

subgroupindex
#105959962
#105949962
#105911132
C2×#635592
C3×#45312
#687053