Finite Group Databasebeta

← #11788793

Subgroups — #11788793

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#10596301C211yesmaximal, characteristic
2#10594996C211yesmaximal, characteristic, complemented
3C3×#5236C212yesmaximal, complemented
4C2×#63559C211yesmaximal, characteristic, complemented
5#10589158C212yesmaximal, complemented
6#70408—32nomaximal
7C2×C32×#41C2211yescharacteristic
8C22×C4⋊(C3⋊D3)C2211yescharacteristic
9#64156C412yescomplemented
10#64149C412yescomplemented
11#64146—22no—
12#64139—22no—
13#64135C2211yescharacteristic
14C3×#926C2212yes—
15C2×C3×#208C2212yes—
16#63974—22no—
17#63894—24no—
18C3×#837—24no—
19#63559—22no—
20#5830—32no—
21#5830—61no—
22#5521—32no—
23C3×#421—32no—
24#5236D312yescomplemented
25C2×#823—32no—
26#4557—32no—
27#4531—32no—
28C23×C3⋊D3D412yes—
29C32×#41—22no—
30C32×#41—22no—
31C2×C32×Q8C2×C411yescharacteristic, complemented
32C2×C32×D4—21no—
33C2×C32×D4C2×C411yescharacteristic, complemented
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C2×#638—24no—
37C2×C4⋊(C3⋊D3)—22no—
38C2×C4⋊(C3⋊D3)—22no—
39C2×C4⋊(C3⋊D3)C2×C412yes—
40C2×C4⋊(C3⋊D3)D412yes—
41C2×#624—24no—
42#3757—21no—
43#3752—24no—
44C4⋊(C3⋊Dic3)—21no—
45C4×C3⋊Dic3C2×C412yescomplemented
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×C3×#41—21no—
55C2×C3×#41C2×D312yes—
56C22×D12—32no—
57C22×D12—61no—
58C2×C3×M16—32no—
59C3×#117—32no—
60#947—34no—
61#947—62no—
62#940—34no—
63#940—62no—
64#937—64no—
65#937—64no—
66#930—64no—
67#930—64no—
68#926—32no—
69#926—61no—
70#926C2×D312yes—
71C2×#208C2×D312yes—
72#893—64no—
73D3×C22⋊C4—64no—
74C4×D12—64no—
75C3×#104—64no—
76#837—24no—
77#823—64no—
78C23×C32—21no—
79C23×C32C2×D411yescharacteristic
80C22×C3⋊D3—22no—
81C22×C3⋊D3—22no—
82C22×C3⋊D3—82no—
83C22×C3⋊D3C22⋊C414yes—
84C32×Q8—22no—
85C32×D4—22no—
86C32×D4—41no—
87C32×D4—41no—
88C2×C32×C4—21no—
89C2×C32×C4—42no—
90C2×C32×C4C22×C411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D412yes—
93C2×C32×C4#4112yes—
94#638—84no—
95C2×C3⋊Dic3—22no—
96C4⋊(C3⋊D3)—24no—
97C4⋊(C3⋊D3)—24no—
98C2×C3×Dic3—24no—
99#624—84no—
100C3×C3⋊C8—42no—
101#535—91no—
102#518—91no—
103#421—32no—
104C2×#100—91no—
105H(3,ℤ/4)—92no—
106C23×D3—34no—
107C23×D3—62no—
108C3×#41—22no—
109C3×#41—22no—
110C3×#41—22no—
111C3×#41—22no—
112C3×#41—42no—
113C3×#41—42no—
114C2×C3×Q8—21no—
115C2×C3×Q8C4×D312yescomplemented
116C2×C3×D4—22no—
117C2×C3×D4—22no—
118C2×C3×D4—21no—
119C2×C3×D4C4×D312yescomplemented
120C22×C3×C4—22no—
121C22×C3×C4—22no—
122C22×C3×C4—21no—
123C22×C3×C4C22×D312yes—
124C2×#67—68no—
125C2×#67—68no—
126C2×D12—34no—
127C2×D12—34no—
128C2×D12—62no—
129C2×D12—62no—
130C2×D12—62no—
131C2×D12—62no—
132C2×D12—62no—
133C2×D12—62no—
134C2×D12—122no—
135C2×D12—122no—
136C2×C4×D3—68no—
137C3×M16—62no—
138C3×M16—62no—
139C2×C3×C8—62no—
140C3×C4⋊C4—62no—
141C3×C22⋊C4—62no—
142C3×C42—34no—
143#217—22no—
144#217—62no—
145#217—62no—
146(C2×D3)⋊C4—68no—
147(C2×D3)⋊C4—68no—
148(C2×D3)⋊C4—68no—
149C4⋊Dic3—22no—
150C4⋊Dic3—62no—
151C4⋊Dic3—62no—
152C4×Dic3—34no—
153C4×Dic3—62no—
154C4×Dic3#6714yescomplemented
155#208—22no—
156#208—22no—
157C2×C3⋊C8—22no—
158C22×C32—41no—
159C22×C32—42no—
160C22×C32—41no—
161C22×C32C2×C22⋊C411yescharacteristic
162C22×C32#12011yescharacteristic
163C22×C32#12311yescharacteristic
164C2×C3⋊D3—24no—
165C2×C3⋊D3—44no—
166C2×C3⋊D3—44no—
167C2×C3⋊D3—82no—
168C32×C4—41no—
169C32×C4C4×D412yes—
170C32×C4#12112yes—
171C3⋊Dic3—42no—
172C3×Dic3—44no—
173C2×#41D3211yescharacteristic
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#117—91no—
183C2×C22⋊C4—182no—
184#104—64no—
185#100—182no—
186C23×C3—22no—
187C23×C3—22no—
188C23×C3—21no—
189C23×C3D3×D412yes—
190C22×D3—38no—
191C22×D3—64no—
192C22×D3—64no—
193C22×D3—64no—
194C22×D3—122no—
195C22×D3—122no—
196C22×D3—244no—
197C22×D3—244no—
198C3×Q8—22no—
199C3×Q8—22no—
200C3×Q8—42no—
201C3×D4—22no—
202C3×D4—22no—
203C3×D4—42no—
204C3×D4—42no—
205C3×D4—42no—
206C3×D4—42no—
207C3×D4—42no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—21no—
212C2×C3×C4—22no—
213C2×C3×C4—21no—
214C2×C3×C4—44no—
215C2×C3×C4—42no—
216C2×C3×C4—42no—
217C2×C3×C4—64no—
218C2×C3×C4C2×C4×D312yes—
219C2×C3×C4#23512yes—
220C2×C3×C4D3×D412yes—
221C2×C3×C4D3×D412yes—
222C2×C3×C4#23712yes—
223C2×C3×C4C2×#6712yes—
224#67—248no—
225#67—248no—
226C2×Dic3—24no—
227C2×Dic3—64no—
228C2×Dic3—64no—
229D12—64no—
230D12—64no—
231D12—64no—
232D12—64no—
233D12—124no—
234D12—124no—
235C4×D3—248no—
236C3×C8—122no—
237C3⋊C8—42no—
238C2×C32—21no—
239C2×C32—21no—
240C2×C32—21no—
241C2×C32—81no—
242C2×C32#38611yescharacteristic
243C3⋊D3—44no—
244C24—92no—
245#41—22no—
246#41—22no—
247C2×Q8#62411yescharacteristic, complemented
248C2×D4—21no—
249C2×D4—92no—
250C2×D4—92no—
251C2×D4—184no—
252C2×D4—182no—
253C2×D4—182no—
254C2×D4#62411yescharacteristic, complemented
255C22×C4—21no—
256C22×C4—184no—
257C22×C4C2×D3211yescharacteristic
258M16—62no—
259M16—62no—
260C2×C8—62no—
261C4⋊C4—62no—
262C4⋊C4—181no—
263C22⋊C4—62no—
264C22⋊C4—184no—
265C22⋊C4—184no—
266C22⋊C4—181no—
267C42—34no—
268C42—92no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—42no—
273C22×C3—42no—
274C22×C3—44no—
275C22×C3—44no—
276C22×C3—42no—
277C22×C3—42no—
278C22×C3D3×C22⋊C412yes—
279C22×C3#88312yes—
280C22×C3#93712yes—
281C2×D3—68no—
282C2×D3—124no—
283C2×D3—128no—
284C2×D3—128no—
285C2×D3—128no—
286C2×D3—244no—
287C2×D3—244no—
288C2×D3—244no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—42no—
292C3×C4—42no—
293C3×C4—124no—
294C3×C4#67⋊C412yes—
295C3×C4#88412yes—
296C3×C4C4×#6712yes—
297C3×C4#93812yes—
298Dic3—44no—
299Dic3—124no—
300Dic3—124no—
301C32#191111yescharacteristic, complemented, Sylow
302C23—21no—
303C23—94no—
304C23—182no—
305C23—182no—
306C23—722no—
307C23#381111yescharacteristic
308Q8—22no—
309D4—22no—
310D4—41no—
311D4—41no—
312D4—184no—
313D4—184no—
314D4—724no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—64no—
318C2×C4—182no—
319C2×C4—724no—
320C2×C4#380412yes—
321C2×C4C2×#62411yescharacteristic
322C2×C4D3×#6712yes—
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—82no—
333C2×C3—82no—
334C2×C3#495612yes—
335D3—128no—
336D3—244no—
337C22—41no—
338C22—42no—
339C22—41no—
340C22—184no—
341C22—364no—
342C22—364no—
343C22—722no—
344C22#6397411yescharacteristic
345C22#6397511yescharacteristic
346C22#6398311yescharacteristic
347C4—41no—
348C4—124no—
349C4—362no—
350C4#6395212yes—
351C4#6395812yes—
352C3—21no—
353C3#7040812yescomplemented
354C2—21no—
355C2—21no—
356C2—21no—
357C2—81no—
358C2—364no—
359C2#1059172211yescharacteristic
subgroupG/H
centerC2#10591722
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#386
prime radical#10596301C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1911
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594996C2semidirect
3. C3×#5236C2semidirect
4. C2×#63559C2semidirect
5. #10589158C2semidirect
9. #64156C4semidirect
10. #64149C4semidirect
24. #5236D3semidirect
31. C2×C32×Q8C2×C4semidirect
33. C2×C32×D4C2×C4semidirect
45. C4×C3⋊Dic3C2×C4semidirect
48. C3×C4×Dic3D4semidirect
115. C2×C3×Q8C4×D3semidirect
119. C2×C3×D4C4×D3semidirect
154. C4×Dic3#67semidirect
247. C2×Q8#624semidirect
254. C2×D4#624semidirect
301. C32#1911semidirect
353. C3#70408semidirect

Maximal subgroups

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

subgroupindex
#105963012
#105949962
C3×#52362
C2×#635592
#105891582
#704083