Finite Group Databasebeta

← #11792789

Subgroups — #11792789

Order 1152.

1914 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1914 conjugacy classes of subgroups — too many to draw. Only its 191 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
1C32×#534C211yesmaximal, characteristic, complemented
2C2×#64146C212yesmaximal, complemented
3C2×#63661C212yesmaximal, complemented
4#10592654C211yesmaximal, characteristic, complemented
5#10589392C211yesmaximal, characteristic, complemented
6#71851—34nomaximal
7C24×C3⋊D3C2211yescharacteristic
8C22×C32×D4C2212yes—
9C22×#638—22no—
10C32×#123—22no—
11C32×#121—22no—
12C32×#120—22no—
13C2×C32×C22⋊C4C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×#3757C2212yes—
16#64146—24no—
17#64146—24no—
18C2×#3752—22no—
19C2×#3752—22no—
20#63661—24no—
21C3×#534D314yescomplemented
22C2×#937—38no—
23C2×#834—38no—
24#4955—34no—
25#4526—34no—
26C24×C32D412yescomplemented
27C24×C32C2311yescharacteristic
28C23×C3⋊D3—22no—
29C23×C3⋊D3—21no—
30C23×C3⋊D3—22no—
31C23×C3⋊D3—21no—
32C23×C3⋊D3—44no—
33C23×C3⋊D3D412yescomplemented
34C2×C32×D4—22no—
35C2×C32×D4—22no—
36C2×C32×D4—22no—
37C2×C32×D4—22no—
38C2×C32×D4—22no—
39C2×C32×D4—22no—
40C2×C32×D4—22no—
41C22×C32×C4D412yescomplemented
42C22×C32×C4D412yescomplemented
43C2×#638—28no—
44C2×#638—48no—
45C22×C3⋊Dic3—22no—
46C22×C3⋊Dic3—21no—
47C32×C4⋊C4—22no—
48C32×C22⋊C4—24no—
49C32×C22⋊C4—22no—
50#3757—22no—
51#3757—22no—
52#3757D414yescomplemented
53#3752—28no—
54#3752—44no—
55#2021—91noSylow
56C24×D3—34no—
57C22×C3×D4C2×D318yes—
58C22×#67—68no—
59C3×#123—28no—
60C3×#121—28no—
61C3×#120—28no—
62C2×C3×C22⋊C4C2×D314yes—
63C2×#217—38no—
64C2×#217—34no—
65#937—616no—
66#937—616no—
67C2×(C2×D3)⋊C4—68no—
68C2×(C2×D3)⋊C4—68no—
69#834—616no—
70C23×C32—22no—
71C23×C32—22no—
72C23×C32—22no—
73C23×C32—42no—
74C23×C32—44no—
75C23×C32C2×D411yescharacteristic
76C23×C32C2×D412yes—
77C23×C32C2×D412yes—
78C23×C32C2×D411yescharacteristic
79C23×C32#4111yescharacteristic
80C22×C3⋊D3—24no—
81C22×C3⋊D3—28no—
82C22×C3⋊D3—24no—
83C22×C3⋊D3—22no—
84C22×C3⋊D3—44no—
85C22×C3⋊D3—48no—
86C22×C3⋊D3—44no—
87C22×C3⋊D3—42no—
88C22×C3⋊D3—44no—
89C22×C3⋊D3—41no—
90C22×C3⋊D3—42no—
91C22×C3⋊D3—41no—
92C32×D4—42no—
93C32×D4—42no—
94C32×D4—42no—
95C32×D4—42no—
96C32×D4—82no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4—42no—
102#638—416no—
103C2×C3⋊Dic3—24no—
104C2×C3⋊Dic3—44no—
105C2×C3⋊Dic3—42no—
106C2×C3⋊Dic3—41no—
107#534C3⋊D311yescharacteristic, complemented
108C2×#120—92no—
109C2×#99—92no—
110#379—91no—
111#342—91no—
112C24×C3#6718yescomplemented
113C24×C3C22×D314yes—
114C23×D3—38no—
115C23×D3—64no—
116C23×D3—68no—
117C23×D3—68no—
118C23×D3—64no—
119C23×D3—1216no—
120C2×C3×D4—28no—
121C2×C3×D4—28no—
122C2×C3×D4—28no—
123C2×C3×D4—28no—
124C2×C3×D4—28no—
125C2×C3×D4—28no—
126C2×C3×D4—28no—
127C22×C3×C4#6718yescomplemented
128C22×C3×C4#6718yescomplemented
129C2×#67—632no—
130C2×#67—1232no—
131C22×Dic3—68no—
132C22×Dic3—64no—
133C3×C4⋊C4—28no—
134C3×C22⋊C4—216no—
135C3×C22⋊C4—28no—
136#217—316no—
137#217—68no—
138#217—68no—
139(C2×D3)⋊C4—632no—
140(C2×D3)⋊C4—1216no—
141C22×C32—22no—
142C22×C32—24no—
143C22×C32—41no—
144C22×C32—42no—
145C22×C32—41no—
146C22×C32—44no—
147C22×C32—42no—
148C22×C32—44no—
149C22×C32—82no—
150C22×C32#12012yes—
151C22×C32#12011yescharacteristic
152C22×C32#12111yescharacteristic
153C22×C32#12112yes—
154C22×C32#12711yescharacteristic
155C2×C3⋊D3—28no—
156C2×C3⋊D3—24no—
157C2×C3⋊D3—44no—
158C2×C3⋊D3—44no—
159C2×C3⋊D3—42no—
160C2×C3⋊D3—48no—
161C2×C3⋊D3—42no—
162C2×C3⋊D3—44no—
163C32×C4—42no—
164C32×C4—42no—
165C3⋊Dic3—44no—
166C3⋊Dic3—81no—
167C25—91no—
168C22×D4—182no—
169C22×D4C2×C3⋊D312yes—
170#123—22no—
171#121—22no—
172#120—22no—
173#120—184no—
174#120—184no—
175C2×C22⋊C4—92no—
176C2×C22⋊C4—91no—
177C2×C22⋊C4—182no—
178C2×C22⋊C4—182no—
179C2×C22⋊C4C2×C3⋊D311yescharacteristic
180#99—184no—
181C23×C3—28no—
182C23×C3—28no—
183C23×C3—28no—
184C23×C3—48no—
185C23×C3—416no—
186C23×C3D3×D414yes—
187C23×C3D3×D418yes—
188C23×C3#23714yes—
189C23×C3C2×#6718yes—
190C23×C3C2×#6714yes—
191C22×D3—616no—
192C22×D3—632no—
193C22×D3—616no—
194C22×D3—68no—
195C22×D3—1216no—
196C22×D3—1232no—
197C22×D3—1216no—
198C22×D3—128no—
199C22×D3—1216no—
200C22×D3—128no—
201C22×D3—124no—
202C22×D3—124no—
203C3×D4—48no—
204C3×D4—48no—
205C3×D4—48no—
206C3×D4—48no—
207C3×D4—88no—
208C2×C3×C4—28no—
209C2×C3×C4—28no—
210C2×C3×C4—28no—
211C2×C3×C4—28no—
212C2×C3×C4—48no—
213#67—1264no—
214C2×Dic3—616no—
215C2×Dic3—1216no—
216C2×Dic3—128no—
217C2×Dic3—124no—
218C2×C32—22no—
219C2×C32—21no—
220C2×C32—21no—
221C2×C32—22no—
222C2×C32—82no—
223C2×C32#39211yescharacteristic
224C2×C32B(4,𝔽2)12yes—
225C3⋊D3—44no—
226C24—92no—
227C24—181no—
228C24—182no—
229C24—182no—
230C24—181no—
231C24—364no—
232C24#63812yescomplemented
233C24C22×C3⋊D311yescharacteristic
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—188no—
242C2×D4—368no—
243C22×C4—182no—
244C22×C4—181no—
245C22×C4#63812yescomplemented
246C22×C4#63812yescomplemented
247C4⋊C4—22no—
248C22⋊C4—24no—
249C22⋊C4—22no—
250C22⋊C4—94no—
251C22⋊C4—188no—
252C22⋊C4—182no—
253C22⋊C4—182no—
254C22⋊C4—364no—
255C22×C3—28no—
256C22×C3—216no—
257C22×C3—44no—
258C22×C3—48no—
259C22×C3—44no—
260C22×C3—416no—
261C22×C3—48no—
262C22×C3—416no—
263C22×C3—88no—
264C22×C3#93718yes—
265C22×C3#93814yes—
266C22×C3#93918yes—
267C22×C3#94014yes—
268C22×C3#95314yes—
269C2×D3—632no—
270C2×D3—616no—
271C2×D3—1216no—
272C2×D3—1216no—
273C2×D3—128no—
274C2×D3—1232no—
275C2×D3—128no—
276C2×D3—1216no—
277C3×C4—48no—
278C3×C4—48no—
279Dic3—1216no—
280Dic3—244no—
281C32#202111yescharacteristic, complemented, Sylow
282C23—22no—
283C23—22no—
284C23—22no—
285C23—42no—
286C23—44no—
287C23—184no—
288C23—188no—
289C23—184no—
290C23—182no—
291C23—362no—
292C23—364no—
293C23—364no—
294C23—368no—
295C23—364no—
296C23—362no—
297C23—361no—
298C23—361no—
299C23D4×C3⋊D311yescharacteristic
300C23D4×C3⋊D312yes—
301C23#383011yescharacteristic
302C23C2×#63812yes—
303C23C2×#63811yescharacteristic
304D4—42no—
305D4—42no—
306D4—42no—
307D4—42no—
308D4—82no—
309D4—3616no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—42no—
315C2×C4—184no—
316C2×C4—364no—
317C2×C4—362no—
318C2×C4—361no—
319C2×C3—28no—
320C2×C3—24no—
321C2×C3—24no—
322C2×C3—28no—
323C2×C3—88no—
324C2×C3#522314yes—
325C2×C3#524418yes—
326D3—1216no—
327C22—22no—
328C22—24no—
329C22—41no—
330C22—42no—
331C22—41no—
332C22—44no—
333C22—42no—
334C22—44no—
335C22—82no—
336C22—188no—
337C22—184no—
338C22—364no—
339C22—364no—
340C22—368no—
341C22—362no—
342C22—362no—
343C22—364no—
344C22#6414612yes—
345C22#6414711yescharacteristic
346C22#6414812yes—
347C22#6414911yescharacteristic
348C22#6416211yescharacteristic
349C4—42no—
350C4—42no—
351C4—364no—
352C4—721no—
353C3#7185114yescomplemented
354C2—22no—
355C2—21no—
356C2—22no—
357C2—21no—
358C2—82no—
359C2—364no—
360C2#1059292211yescharacteristic
361C2#1059294312yes—
subgroupG/H
centerC22#64162
commutator, cosocleC24×C32C23
FrattiniC24C22×C3⋊D3
FittingC32×#534C2
socleC22×C32#120
hypercenter#534C3⋊D3
hypocenterC32#2021
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C32×#534C2semidirect
2. C2×#64146C2semidirect
3. C2×#63661C2semidirect
4. #10592654C2semidirect
5. #10589392C2semidirect
21. C3×#534D3semidirect
26. C24×C32D4semidirect
33. C23×C3⋊D3D4semidirect
41. C22×C32×C4D4semidirect
42. C22×C32×C4D4semidirect
52. #3757D4semidirect
107. #534C3⋊D3semidirect
112. C24×C3#67semidirect
127. C22×C3×C4#67semidirect
128. C22×C3×C4#67semidirect
232. C24#638semidirect
245. C22×C4#638semidirect
246. C22×C4#638semidirect
281. C32#2021semidirect
353. C3#71851semidirect

Maximal subgroups

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

subgroupindex
C32×#5342
C2×#641462
C2×#636612
#105926542
#105893922
#718513