Finite Group Databasebeta

← #11793132

Subgroups — #11793132

Order 1152.

834 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 155 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#10595954C211yesmaximal, characteristic, complemented
2C2×#63633C211yesmaximal, characteristic
3C2×#63633C211yesmaximal, characteristic
4C2×#63633C211yesmaximal, characteristic
5C32×#342C211yesmaximal, characteristic, complemented
6#10589393C211yesmaximal, characteristic, complemented
7#10589392C211yesmaximal, characteristic, complemented
8#68967—34nomaximal
9C22×#638C2211yescharacteristic
10C2×C32×C22⋊C4C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×#3757C2211yescharacteristic
16#64133—22no—
17#64087—22no—
18#64087—22no—
19#63633—22no—
20#63633—22no—
21#63633—22no—
22#5483—34no—
23C2×#806—34no—
24C2×#806—34no—
25C2×#806—34no—
26C3×#342D314yescomplemented
27#4527—34no—
28#4526—34no—
29C24×C32C2311yescharacteristic
30C23×C3⋊D3Q811yescharacteristic, complemented
31C22×C32×C4—21no—
32C22×C32×C4—21no—
33C22×C32×C4—21no—
34C2×#638—21no—
35C2×#638—21no—
36C2×#638—21no—
37C2×#638—21no—
38C2×#638—21no—
39C2×#638—21no—
40C22×C3⋊Dic3—21no—
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3Q811yescharacteristic, complemented
44C2×#634—22no—
45C32×C22⋊C4—21no—
46C32×C22⋊C4—21no—
47C32×C22⋊C4—21no—
48C32×C22⋊C4—21no—
49C32×C22⋊C4—21no—
50C32×C22⋊C4D412yes—
51#3757—21no—
52#3757—21no—
53#3757—21no—
54#3757—21no—
55#3757D412yes—
56#3757D412yes—
57C4⋊(C3⋊Dic3)—22no—
58#3750—24no—
59#2032—91noSylow
60C22×#67—34no—
61C2×C3×C22⋊C4C2×D314yes—
62C2×C3×C22⋊C4C2×D314yes—
63C2×C3×C22⋊C4C2×D314yes—
64C2×#217—34no—
65C2×#217—34no—
66C2×#217—34no—
67#924—68no—
68#878—68no—
69#878—68no—
70#806—68no—
71#806—68no—
72#806—68no—
73C23×C32—81no—
74C23×C32C2×D411yescharacteristic
75C23×C32C2×D411yescharacteristic
76C23×C32C2×D411yescharacteristic
77C23×C32C2×Q811yescharacteristic
78C23×C32#4111yescharacteristic
79C23×C32#4111yescharacteristic
80C23×C32#4111yescharacteristic
81C22×C3⋊D3—21no—
82C22×C3⋊D3—21no—
83C22×C3⋊D3—21no—
84C22×C3⋊D3—81no—
85C2×C32×C4—22no—
86C2×C32×C4—41no—
87C2×C32×C4—41no—
88C2×C32×C4—81no—
89C2×C32×C4—81no—
90C2×C32×C4—81no—
91#638—41no—
92#638—41no—
93#638—41no—
94#638—41no—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—81no—
102C2×C3⋊Dic3—81no—
103C2×C3⋊Dic3—81no—
104#634—82no—
105#543—91no—
106C2×#99—91no—
107C2×#99—91no—
108C2×#99—91no—
109#342—91no—
110#342—91no—
111#342C3⋊D311yescharacteristic, complemented
112C24×C3C22×D314yes—
113C23×D3—34no—
114C22×C3×C4—24no—
115C22×C3×C4—24no—
116C22×C3×C4—24no—
117C2×#67—64no—
118C2×#67—64no—
119C2×#67—64no—
120C2×#67—64no—
121C2×#67—64no—
122C2×#67—64no—
123C22×Dic3—34no—
124C22×Dic3—64no—
125C22×Dic3—64no—
126C22×Dic3—64no—
127C2×Dic6—68no—
128C3×C22⋊C4—24no—
129C3×C22⋊C4—24no—
130C3×C22⋊C4—24no—
131C3×C22⋊C4—24no—
132C3×C22⋊C4—24no—
133C3×C22⋊C4D1218yes—
134#217—38no—
135#217—38no—
136#217—64no—
137#217—64no—
138#217—64no—
139#217—64no—
140C4⋊Dic3—68no—
141Dic3⋊C4—616no—
142C22×C32—41no—
143C22×C32—41no—
144C22×C32—41no—
145C22×C32—41no—
146C22×C32—41no—
147C22×C32—41no—
148C22×C32—41no—
149C22×C32#12011yescharacteristic
150C22×C32C22⋊Q811yescharacteristic
151C22×C32C22⋊Q811yescharacteristic
152C22×C32C22⋊Q811yescharacteristic
153C22×C32#12411yescharacteristic
154C22×C32#12411yescharacteristic
155C22×C32#12411yescharacteristic
156C2×C3⋊D3—41no—
157C2×C3⋊D3—81no—
158C2×C3⋊D3—81no—
159C2×C3⋊D3—81no—
160C32×C4—42no—
161C32×C4—81no—
162C32×C4—81no—
163C3⋊Dic3—42no—
164C3⋊Dic3—42no—
165C3⋊Dic3—41no—
166C3⋊Dic3—81no—
167C22×D4—91no—
168C22⋊Q8—182no—
169C22⋊Q8—182no—
170C22⋊Q8—182no—
171C2×C22⋊C4—91no—
172C2×C22⋊C4—91no—
173C2×C22⋊C4—91no—
174C2×C22⋊C4C2×C3⋊D311yescharacteristic
175C2×C22⋊C4C2×C3⋊D311yescharacteristic
176C2×C22⋊C4C2×C3⋊D311yescharacteristic
177#99—182no—
178#99—182no—
179#99—182no—
180C23×C3—84no—
181C23×C3C2×D1214yes—
182C23×C3#23514yes—
183C23×C3#23514yes—
184C23×C3D3×D414yes—
185C23×C3D3×D414yes—
186C23×C3#23714yes—
187C23×C3D3×Q814yes—
188C22×D3—64no—
189C22×D3—64no—
190C22×D3—64no—
191C22×D3—244no—
192C2×C3×C4—28no—
193C2×C3×C4—44no—
194C2×C3×C4—44no—
195C2×C3×C4—84no—
196C2×C3×C4—84no—
197C2×C3×C4—84no—
198#67—124no—
199#67—124no—
200#67—124no—
201#67—124no—
202C2×Dic3—68no—
203C2×Dic3—68no—
204C2×Dic3—64no—
205C2×Dic3—64no—
206C2×Dic3—64no—
207C2×Dic3—124no—
208C2×Dic3—244no—
209C2×Dic3—244no—
210C2×Dic3—244no—
211Dic6—248no—
212C2×C32—21no—
213C2×C32—21no—
214C2×C32—21no—
215C2×C32—21no—
216C2×C32—21no—
217C2×C32—21no—
218C2×C32—21no—
219C2×C32#39311yescharacteristic
220C3⋊D3—81no—
221C24—91no—
222C24C22×C3⋊D311yescharacteristic
223C2×Q8—182no—
224C2×D4—181no—
225C2×D4—181no—
226C2×D4—181no—
227C2×D4—181no—
228C2×D4—181no—
229C2×D4—181no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—91no—
234C22×C4—181no—
235C22×C4—181no—
236C22×C4—181no—
237C4⋊C4—184no—
238C4⋊C4—182no—
239C22⋊C4—21no—
240C22⋊C4—21no—
241C22⋊C4—21no—
242C22⋊C4—21no—
243C22⋊C4—21no—
244C22⋊C4—92no—
245C22⋊C4—92no—
246C22⋊C4—181no—
247C22⋊C4—181no—
248C22⋊C4—181no—
249C22⋊C4—181no—
250C22⋊C4C4⋊(C3⋊D3)12yes—
251C22×C3—44no—
252C22×C3—44no—
253C22×C3—44no—
254C22×C3—44no—
255C22×C3—44no—
256C22×C3—44no—
257C22×C3—44no—
258C22×C3#87514yes—
259C22×C3#88214yes—
260C22×C3#88514yes—
261C22×C3#88514yes—
262C22×C3#89614yes—
263C22×C3#89614yes—
264C22×C3#89714yes—
265C2×D3—124no—
266C2×D3—244no—
267C2×D3—244no—
268C2×D3—244no—
269C3×C4—48no—
270C3×C4—84no—
271C3×C4—84no—
272Dic3—128no—
273Dic3—128no—
274Dic3—124no—
275Dic3—244no—
276C32#203211yescharacteristic, complemented, Sylow
277C23—81no—
278C23—181no—
279C23—181no—
280C23—181no—
281C23—721no—
282C23C2×C4⋊(C3⋊D3)11yescharacteristic
283C23#382811yescharacteristic
284C23#382811yescharacteristic
285C23D4×C3⋊D311yescharacteristic
286C23D4×C3⋊D311yescharacteristic
287C23#383011yescharacteristic
288C23Q8×C3⋊D311yescharacteristic
289Q8—722no—
290D4—361no—
291D4—361no—
292D4—361no—
293D4—361no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4—181no—
303C2×C4—181no—
304C2×C4—181no—
305C2×C4—361no—
306C2×C4—721no—
307C2×C4—721no—
308C2×C4—721no—
309C2×C3—24no—
310C2×C3—24no—
311C2×C3—24no—
312C2×C3—24no—
313C2×C3—24no—
314C2×C3—24no—
315C2×C3—24no—
316C2×C3#467314yes—
317D3—244no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—361no—
326C22—721no—
327C22—721no—
328C22—721no—
329C22#6408411yescharacteristic
330C22#6409111yescharacteristic
331C22#6409411yescharacteristic
332C22#6409411yescharacteristic
333C22#6410511yescharacteristic
334C22#6410511yescharacteristic
335C22#6410611yescharacteristic
336C4—42no—
337C4—81no—
338C4—81no—
339C4—362no—
340C4—362no—
341C4—361no—
342C4—721no—
343C3#6896714yescomplemented
344C2—21no—
345C2—21no—
346C2—21no—
347C2—21no—
348C2—21no—
349C2—21no—
350C2—21no—
351C2—721no—
352C2#1059237211yescharacteristic
subgroupG/H
centerC2#10592372
commutator, cosocleC24×C32C23
FrattiniC24C22×C3⋊D3
FittingC32×#342C2
socleC2×C32#393
prime radicalC22×#638C22
hypercenter#342C3⋊D3
hypocenterC32#2032
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #10595954C2semidirect
5. C32×#342C2semidirect
6. #10589393C2semidirect
7. #10589392C2semidirect
26. C3×#342D3semidirect
30. C23×C3⋊D3Q8semidirect
43. C22×C3⋊Dic3Q8semidirect
111. #342C3⋊D3semidirect
276. C32#2032semidirect
343. C3#68967semidirect

Maximal subgroups

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

subgroupindex
#105959542
C2×#636332
C32×#3422
#105893932
#105893922
#689673