Finite Group Databasebeta

← #11793129

Subgroups — #11793129

Order 1152.

834 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 165 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×C32×#99C211yesmaximal, characteristic
3C2×#63661C211yesmaximal, characteristic
4C2×#63661C211yesmaximal, characteristic
5#10589393C211yesmaximal, characteristic, complemented
6#10589393C211yesmaximal, characteristic, complemented
7#10589392C211yesmaximal, characteristic, complemented
8#70025—34nomaximal
9C22×C32×D4C2211yescharacteristic
10C2×C32×C22⋊C4C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×#3757C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×#3757C2211yescharacteristic
16#64133—22no—
17#64087—22no—
18#64087—22no—
19C32×#99—22no—
20#63661—22no—
21#63661—22no—
22#5483—34no—
23C2×C3×#99D314yes—
24C2×#834—34no—
25C2×#834—34no—
26#4527—34no—
27#4527—34no—
28#4526—34no—
29C24×C32Q811yescharacteristic, complemented
30C24×C32C2311yescharacteristic
31C2×C32×D4—21no—
32C2×C32×D4—21no—
33C2×C32×D4—21no—
34C2×C32×D4—21no—
35C2×C32×D4—21no—
36C2×C32×D4—21no—
37C22×C32×C4—21no—
38C22×C32×C4—21no—
39C22×C32×C4Q811yescharacteristic, complemented
40C22×C3⋊Dic3—21no—
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3—21no—
44C2×#634—22no—
45C32×C22⋊C4—21no—
46C32×C22⋊C4—21no—
47C32×C22⋊C4—21no—
48C32×C22⋊C4D412yes—
49#3757—21no—
50#3757—21no—
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×C3×D4C2×D314yes—
61C2×C3×C22⋊C4C2×D314yes—
62C2×C3×C22⋊C4C2×D314yes—
63C2×#217—34no—
64C2×#217—34no—
65C2×#217—34no—
66C2×#217—34no—
67#924—68no—
68#878—68no—
69#878—68no—
70C3×#99—28no—
71#834—68no—
72#834—68no—
73C23×C32—21no—
74C23×C32—21no—
75C23×C32—21no—
76C23×C32—81no—
77C23×C32—81no—
78C23×C32C2×D411yescharacteristic
79C23×C32C2×D411yescharacteristic
80C23×C32C2×D411yescharacteristic
81C23×C32C2×Q811yescharacteristic
82C23×C32#4111yescharacteristic
83C23×C32#4111yescharacteristic
84C23×C32#4111yescharacteristic
85C32×D4—41no—
86C32×D4—41no—
87C32×D4—41no—
88C32×D4—41no—
89C2×C32×C4—22no—
90C2×C32×C4—21no—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—41no—
94C2×C32×C4—81no—
95C2×C32×C4—81no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—81no—
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×#99C3⋊D311yescharacteristic
109#342—91no—
110#342—91no—
111#342—91no—
112C24×C3Dic614yescomplemented
113C24×C3C22×D314yes—
114C2×C3×D4—24no—
115C2×C3×D4—24no—
116C2×C3×D4—24no—
117C2×C3×D4—24no—
118C2×C3×D4—24no—
119C2×C3×D4—24no—
120C22×C3×C4—24no—
121C22×C3×C4—24no—
122C22×C3×C4Dic614yescomplemented
123C22×Dic3—64no—
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#6718yes—
132#217—38no—
133#217—38no—
134#217—64no—
135#217—64no—
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—41no—
150C22×C32—81no—
151C22×C32—81no—
152C22×C32—81no—
153C22×C32#12011yescharacteristic
154C22×C32C22⋊Q811yescharacteristic
155C22×C32C22⋊Q811yescharacteristic
156C22×C32C22⋊Q811yescharacteristic
157C22×C32#12411yescharacteristic
158C22×C32#12411yescharacteristic
159C22×C32#12411yescharacteristic
160C32×C4—42no—
161C32×C4—41no—
162C32×C4—81no—
163C3⋊Dic3—42no—
164C3⋊Dic3—42no—
165C3⋊Dic3—81no—
166C3⋊Dic3—81no—
167C22×D4C2×C3⋊D311yescharacteristic
168C22⋊Q8—182no—
169C22⋊Q8—182no—
170C22⋊Q8—182no—
171C2×C22⋊C4—91no—
172C2×C22⋊C4—91no—
173C2×C22⋊C4—91no—
174C2×C22⋊C4—91no—
175C2×C22⋊C4C2×C3⋊D311yescharacteristic
176C2×C22⋊C4C2×C3⋊D311yescharacteristic
177#99—22no—
178#99—182no—
179#99—182no—
180C23×C3—24no—
181C23×C3—24no—
182C23×C3—24no—
183C23×C3—84no—
184C23×C3—84no—
185C23×C3C2×Dic614yes—
186C23×C3#23514yes—
187C23×C3D3×D414yes—
188C23×C3D3×D414yes—
189C23×C3#23714yes—
190C23×C3#23714yes—
191C23×C3C2×#6714yes—
192C3×D4—44no—
193C3×D4—44no—
194C3×D4—44no—
195C3×D4—44no—
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4—24no—
199C2×C3×C4—28no—
200C2×C3×C4—44no—
201C2×C3×C4—84no—
202C2×C3×C4—84no—
203C2×Dic3—68no—
204C2×Dic3—68no—
205C2×Dic3—124no—
206C2×Dic3—124no—
207C2×Dic3—244no—
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—81no—
220C2×C32#39311yescharacteristic
221C24#63411yescharacteristic, complemented
222C24C22×C3⋊D311yescharacteristic
223C2×Q8—182no—
224C2×D4—21no—
225C2×D4—21no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—181no—
233C22×C4—181no—
234C22×C4—181no—
235C22×C4—181no—
236C22×C4#63411yescharacteristic, complemented
237C4⋊C4—184no—
238C4⋊C4—182no—
239C22⋊C4—21no—
240C22⋊C4—21no—
241C22⋊C4—21no—
242C22⋊C4—92no—
243C22⋊C4—92no—
244C22⋊C4—181no—
245C22⋊C4—181no—
246C22⋊C4—181no—
247C22⋊C4—181no—
248C22⋊C4—181no—
249C22⋊C4—181no—
250C22⋊C4#63812yes—
251C22×C3—44no—
252C22×C3—44no—
253C22×C3—44no—
254C22×C3—44no—
255C22×C3—44no—
256C22×C3—44no—
257C22×C3—44no—
258C22×C3—44no—
259C22×C3—84no—
260C22×C3—84no—
261C22×C3—84no—
262C22×C3#87814yes—
263C22×C3#87814yes—
264C22×C3#88514yes—
265C22×C3#88514yes—
266C22×C3#92414yes—
267C22×C3#93614yes—
268C22×C3#93714yes—
269C3×C4—48no—
270C3×C4—44no—
271C3×C4—84no—
272Dic3—128no—
273Dic3—128no—
274Dic3—244no—
275Dic3—244no—
276C32#203211yescharacteristic, complemented, Sylow
277C23—21no—
278C23—21no—
279C23—21no—
280C23—81no—
281C23—81no—
282C23C2×#63411yescharacteristic
283C23#382811yescharacteristic
284C23D4×C3⋊D311yescharacteristic
285C23D4×C3⋊D311yescharacteristic
286C23#383011yescharacteristic
287C23#383011yescharacteristic
288C23C2×#63811yescharacteristic
289Q8—722no—
290D4—41no—
291D4—41no—
292D4—41no—
293D4—41no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4—361no—
304C2×C4—361no—
305C2×C4—721no—
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—84no—
317C2×C3#494714yes—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22#6408711yescharacteristic
330C22#6408711yescharacteristic
331C22#6409411yescharacteristic
332C22#6409411yescharacteristic
333C22#6413311yescharacteristic
334C22#6414511yescharacteristic
335C22#6414611yescharacteristic
336C4—42no—
337C4—41no—
338C4—81no—
339C4—362no—
340C4—362no—
341C4—721no—
342C4—721no—
343C3#7002514yescomplemented
344C2—21no—
345C2—21no—
346C2—21no—
347C2—21no—
348C2—21no—
349C2—21no—
350C2—21no—
351C2—81no—
352C2#1059264611yescharacteristic
subgroupG/H
centerC2#10592646
commutator, cosocleC24×C32C23
FrattiniC24C22×C3⋊D3
FittingC2×C32×#99C2
socleC2×C32#393
prime radicalC22×C32×D4C22
hypercenterC2×#99C3⋊D3
hypocenterC32#2032
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. #10595954C2semidirect
5. #10589393C2semidirect
6. #10589393C2semidirect
7. #10589392C2semidirect
29. C24×C32Q8semidirect
39. C22×C32×C4Q8semidirect
112. C24×C3Dic6semidirect
122. C22×C3×C4Dic6semidirect
221. C24#634semidirect
236. C22×C4#634semidirect
276. C32#2032semidirect
343. C3#70025semidirect

Maximal subgroups

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

subgroupindex
#105959542
C2×C32×#992
C2×#636612
#105893932
#105893922
#700253