Finite Group Databasebeta

← #11787882

Subgroups — #11787882

Order 1152.

1137 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 1137 conjugacy classes of subgroups — too many to draw. Only its 132 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×#64149C211yesmaximal, characteristic
2#10594996C211yesmaximal, characteristic, complemented
3C3×#5215C212yesmaximal, complemented
4C2×#63559C211yesmaximal, characteristic, complemented
5#10589160C212yesmaximal, complemented
6#70323—32nomaximal
7C22×C32×D4C2211yescharacteristic
8C22×#638—22no—
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10#64149—22no—
11#64149C414yescomplemented
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C3×#926C2212yes—
14C2×C3×#208C2212yes—
15#63974—22no—
16#63894—24no—
17C3×#832—24no—
18#63559—22no—
19C2×#940—32no—
20C2×#940—61no—
21#5521—32no—
22C3×#418—32no—
23#5215D312yescomplemented
24C2×#823—32no—
25#4555—32no—
26#4532—32no—
27C24×C32—21no—
28C23×C3⋊D3D412yes—
29C2×C32×D4—22no—
30C2×C32×D4—21no—
31C2×C32×D4—22no—
32C2×C32×D4C2×C412yescomplemented
33C22×C32×C4C2311yescharacteristic
34C2×#638—28no—
35C2×#638—48no—
36C22×C3⋊Dic3—21no—
37C2×C4⋊(C3⋊D3)—22no—
38C2×C4⋊(C3⋊D3)—22no—
39C2×C4⋊(C3⋊D3)C2×C412yes—
40C2×C4⋊(C3⋊D3)D412yes—
41C2×#624—24no—
42C4×C3⋊Dic3—21no—
43C4×C3⋊Dic3C2×C412yescomplemented
44C3×#217—22no—
45C3×C4⋊Dic3D414yescomplemented
46C3×C4×Dic3—22no—
47C3×#208—22no—
48C3×#208—22no—
49C2×C3×C3⋊C8—22no—
50#3722—24no—
51#1887—91noSylow
52C22×C3×D4—21no—
53C22×C3×D4C2×D312yes—
54C22×#67—64no—
55C22×#67—64no—
56C22×D12—32no—
57C22×D12—61no—
58C2×C3×M16—32no—
59C3×#117—32no—
60#940—38no—
61#940—64no—
62#940—64no—
63#940—64no—
64#926C2×D312yes—
65C2×C4×Dic3—32no—
66C2×C4×Dic3—61no—
67C2×#208C2×D312yes—
68#893—64no—
69D3×C22⋊C4—64no—
70C4×D12—64no—
71C3×#102—64no—
72#832—24no—
73#823—64no—
74C23×C32—22no—
75C23×C32—44no—
76C23×C32—41no—
77C23×C32—41no—
78C23×C32C2×D411yescharacteristic
79C22×C3⋊D3—22no—
80C22×C3⋊D3—22no—
81C22×C3⋊D3—44no—
82C22×C3⋊D3C22⋊C414yes—
83C32×D4—24no—
84C32×D4—42no—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D412yes—
88C2×C32×C4#4112yes—
89#638—416no—
90C2×C3⋊Dic3—24no—
91C2×C3⋊Dic3—22no—
92C4⋊(C3⋊D3)—24no—
93C4⋊(C3⋊D3)—24no—
94C2×C3×Dic3—24no—
95#624—84no—
96C3×C3⋊C8—42no—
97C2×#127—91no—
98#518—91no—
99#418—32no—
100C2×#100—91no—
101#339—92no—
102C24×C3—22no—
103C24×C3—22no—
104C23×D3—34no—
105C23×D3—62no—
106C2×C3×D4—22no—
107C2×C3×D4—22no—
108C2×C3×D4—22no—
109C2×C3×D4—22no—
110C2×C3×D4—22no—
111C2×C3×D4—22no—
112C2×C3×D4—22no—
113C2×C3×D4—42no—
114C2×C3×D4—42no—
115C2×C3×D4C4×D314yescomplemented
116C22×C3×C4—21no—
117C22×C3×C4C22×D312yes—
118C2×#67—616no—
119C2×#67—616no—
120C2×#67—1216no—
121C2×#67—1216no—
122C22×Dic3—62no—
123C22×Dic3—62no—
124C2×D12—34no—
125C2×D12—34no—
126C2×D12—62no—
127C2×D12—62no—
128C2×D12—62no—
129C2×D12—62no—
130C2×D12—62no—
131C2×D12—62no—
132C2×D12—122no—
133C2×D12—122no—
134C2×C4×D3—68no—
135C3×M16—62no—
136C3×M16—62no—
137C2×C3×C8—62no—
138C3×C4⋊C4—34no—
139C3×C22⋊C4—62no—
140C3×C42—62no—
141#217—22no—
142(C2×D3)⋊C4—68no—
143C4⋊Dic3#6714yescomplemented
144C4×Dic3—22no—
145C4×Dic3—34no—
146C4×Dic3—62no—
147C4×Dic3—62no—
148C4×Dic3—62no—
149#208—22no—
150#208—22no—
151C2×C3⋊C8—22no—
152C22×C32—22no—
153C22×C32—44no—
154C22×C32—42no—
155C22×C32—82no—
156C22×C32—82no—
157C22×C32C2×C22⋊C411yescharacteristic
158C22×C32#12011yescharacteristic
159C22×C32#12311yescharacteristic
160C2×C3⋊D3—24no—
161C2×C3⋊D3—44no—
162C2×C3⋊D3—44no—
163C2×C3⋊D3—82no—
164C32×C4C4×D412yes—
165C32×C4#12112yes—
166C3⋊Dic3—24no—
167C3×Dic3—44no—
168C22×D4—91no—
169C22×D4—182no—
170C22×D4D3211yescharacteristic
171C2×M16—32no—
172#127—94no—
173#127—182no—
174C4×D4—184no—
175#117—32no—
176C2×C22⋊C4—182no—
177C2×C42—91no—
178#102—64no—
179#100—182no—
180C23×C3—24no—
181C23×C3—24no—
182C23×C3—21no—
183C23×C3—48no—
184C23×C3—48no—
185C23×C3—42no—
186C23×C3—42no—
187C23×C3—42no—
188C23×C3—42no—
189C23×C3D3×D412yes—
190C22×D3—38no—
191C22×D3—64no—
192C22×D3—64no—
193C22×D3—64no—
194C22×D3—122no—
195C22×D3—122no—
196C22×D3—128no—
197C22×D3—128no—
198C3×D4—24no—
199C3×D4—24no—
200C3×D4—44no—
201C3×D4—44no—
202C3×D4—42no—
203C3×D4—42no—
204C2×C3×C4—22no—
205C2×C3×C4—21no—
206C2×C3×C4—22no—
207C2×C3×C4—21no—
208C2×C3×C4—64no—
209C2×C3×C4C2×C4×D312yes—
210C2×C3×C4#23512yes—
211C2×C3×C4D3×D412yes—
212C2×C3×C4D3×D412yes—
213C2×C3×C4#23712yes—
214C2×C3×C4C2×#6712yes—
215#67—1232no—
216#67—1232no—
217C2×Dic3—24no—
218C2×Dic3—64no—
219C2×Dic3—68no—
220C2×Dic3—68no—
221C2×Dic3—64no—
222D12—64no—
223D12—64no—
224D12—64no—
225D12—64no—
226D12—124no—
227D12—124no—
228C4×D3—248no—
229C3×C8—122no—
230C3⋊C8—42no—
231C2×C32—21no—
232C2×C32—21no—
233C2×C32—82no—
234C2×C32#38611yescharacteristic
235C2×C32#45312yes—
236C3⋊D3—44no—
237C24—21no—
238C24—92no—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—21no—
242C2×D4—92no—
243C2×D4—92no—
244C2×D4—188no—
245C2×D4—182no—
246C2×D4—182no—
247C2×D4—368no—
248C2×D4#62412yescomplemented
249C22×C4—184no—
250C22×C4—181no—
251C22×C4C2×D3211yescharacteristic
252M16—62no—
253M16—62no—
254C2×C8—62no—
255C4⋊C4—34no—
256C22⋊C4—62no—
257C22⋊C4—184no—
258C42—62no—
259C42—92no—
260C42—181no—
261C22×C3—24no—
262C22×C3—24no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—48no—
267C22×C3—48no—
268C22×C3—44no—
269C22×C3—44no—
270C22×C3—84no—
271C22×C3—84no—
272C22×C3—84no—
273C22×C3—84no—
274C22×C3D3×C22⋊C412yes—
275C22×C3#88312yes—
276C22×C3#93712yes—
277C2×D3—68no—
278C2×D3—124no—
279C2×D3—128no—
280C2×D3—128no—
281C2×D3—128no—
282C2×D3—244no—
283C2×D3—244no—
284C2×D3—244no—
285C3×C4—22no—
286C3×C4—22no—
287C3×C4—124no—
288C3×C4#67⋊C412yes—
289C3×C4#88412yes—
290C3×C4C4×#6712yes—
291C3×C4#93812yes—
292Dic3—44no—
293Dic3—68no—
294Dic3—68no—
295C32#188711yescharacteristic, complemented, Sylow
296C23—22no—
297C23—44no—
298C23—41no—
299C23—41no—
300C23—94no—
301C23—182no—
302C23—182no—
303C23—364no—
304C23#381111yescharacteristic
305D4—24no—
306D4—42no—
307D4—184no—
308D4—184no—
309D4—3616no—
310C2×C4—64no—
311C2×C4—184no—
312C2×C4—182no—
313C2×C4—724no—
314C2×C4#380412yes—
315C2×C4C2×#62411yescharacteristic
316C2×C4D3×#6712yes—
317C2×C4#381111yescharacteristic
318C8—122no—
319C2×C3—22no—
320C2×C3—22no—
321C2×C3—22no—
322C2×C3—22no—
323C2×C3—22no—
324C2×C3—21no—
325C2×C3—84no—
326C2×C3—84no—
327C2×C3#495612yes—
328C2×C3#519814yes—
329D3—128no—
330D3—244no—
331C22—22no—
332C22—44no—
333C22—42no—
334C22—82no—
335C22—82no—
336C22—184no—
337C22—364no—
338C22—364no—
339C22—722no—
340C22#6397411yescharacteristic
341C22#6397511yescharacteristic
342C22#6398311yescharacteristic
343C4—124no—
344C4—184no—
345C4#6395212yes—
346C4#6395812yes—
347C3—21no—
348C3#7032312yescomplemented
349C2—21no—
350C2—21no—
351C2—82no—
352C2—364no—
353C2#1059152212yes—
354C2#1059172211yescharacteristic
subgroupG/H
centerC22#63983
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#120
prime radicalC2×#64149C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1887
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594996C2semidirect
3. C3×#5215C2semidirect
4. C2×#63559C2semidirect
5. #10589160C2semidirect
11. #64149C4semidirect
23. #5215D3semidirect
32. C2×C32×D4C2×C4semidirect
43. C4×C3⋊Dic3C2×C4semidirect
45. C3×C4⋊Dic3D4semidirect
115. C2×C3×D4C4×D3semidirect
143. C4⋊Dic3#67semidirect
248. C2×D4#624semidirect
295. C32#1887semidirect
348. C3#70323semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
#105949962
C3×#52152
C2×#635592
#105891602
#703233