Finite Group Databasebeta

← #11792795

Subgroups — #11792795

Order 1152.

1914 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1914 conjugacy classes of subgroups — too many to draw. Only its 181 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×#64162C212yesmaximal, complemented
2#10595964C211yesmaximal, characteristic, complemented
3C32×#379C211yesmaximal, characteristic, complemented
4C2×#63633C212yesmaximal, complemented
5#10589392C211yesmaximal, characteristic, complemented
6#69500—34nomaximal
7C25×C32C2211yescharacteristic
8C22×#638—22no—
9C22×#638C2212yes—
10C2×C32×C22⋊C4—22no—
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13#64162—24no—
14#64162—24no—
15C2×#3757—22no—
16C2×#3757C2212yes—
17#64139—22no—
18#64095—22no—
19#64091—22no—
20#63633—24no—
21C2×#953—38no—
22#5493—34no—
23C3×#379D314yescomplemented
24C2×#806—38no—
25#4526—34no—
26C24×C32—22no—
27C24×C32—21no—
28C24×C32—22no—
29C24×C32—21no—
30C24×C32—44no—
31C24×C32D412yescomplemented
32C24×C32C2311yescharacteristic
33C23×C3⋊D3D412yescomplemented
34C22×C32×C4—21no—
35C22×C32×C4D412yescomplemented
36C2×#638—28no—
37C2×#638—22no—
38C2×#638—22no—
39C2×#638—22no—
40C2×#638—22no—
41C2×#638—22no—
42C2×#638—22no—
43C2×#638—48no—
44C22×C3⋊Dic3—22no—
45C22×C3⋊Dic3D412yescomplemented
46C2×C4⋊(C3⋊D3)—22no—
47C32×C22⋊C4—22no—
48C32×C22⋊C4—22no—
49C32×C22⋊C4—44no—
50#3757—28no—
51#3757—22no—
52#3757D414yescomplemented
53#3752—24no—
54C4⋊(C3⋊Dic3)—22no—
55#2021—91noSylow
56C25×C3C2×D314yes—
57C22×#67—38no—
58C22×#67—68no—
59C2×C3×C22⋊C4—28no—
60C2×C3×C22⋊C4C2×D314yes—
61C2×C3×C22⋊C4C2×D314yes—
62#953—616no—
63#953—616no—
64C2×#217—38no—
65C2×#217—68no—
66#930—68no—
67#886—68no—
68#882—68no—
69#806—616no—
70C23×C32—24no—
71C23×C32—28no—
72C23×C32—24no—
73C23×C32—22no—
74C23×C32—44no—
75C23×C32—42no—
76C23×C32—44no—
77C23×C32—42no—
78C23×C32—48no—
79C23×C32—44no—
80C23×C32—41no—
81C23×C32—42no—
82C23×C32—41no—
83C23×C32C2×D411yescharacteristic
84C23×C32C2×D412yes—
85C23×C32C2×D412yes—
86C23×C32C2×D411yescharacteristic
87C23×C32#4111yescharacteristic
88C22×C3⋊D3—22no—
89C22×C3⋊D3—22no—
90C22×C3⋊D3—22no—
91C22×C3⋊D3—44no—
92C2×C32×C4—22no—
93C2×C32×C4—42no—
94C2×C32×C4—42no—
95C2×C32×C4—41no—
96#638—416no—
97#638—42no—
98#638—42no—
99#638—42no—
100#638—42no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—24no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—44no—
106C4⋊(C3⋊D3)—82no—
107#534—91no—
108C2×#120—92no—
109C2×#99—92no—
110#379C3⋊D311yescharacteristic, complemented
111#342—91no—
112C24×C3—28no—
113C24×C3—24no—
114C24×C3—24no—
115C24×C3—28no—
116C24×C3—416no—
117C24×C3D1218yescomplemented
118C24×C3C22×D314yes—
119C23×D3—38no—
120C22×C3×C4—24no—
121C22×C3×C4#6718yescomplemented
122C2×#67—632no—
123C2×#67—68no—
124C2×#67—68no—
125C2×#67—68no—
126C2×#67—68no—
127C2×#67—68no—
128C2×#67—68no—
129C2×#67—1232no—
130C22×Dic3—38no—
131C22×Dic3—68no—
132C2×D12—68no—
133C3×C22⋊C4—28no—
134C3×C22⋊C4—28no—
135C3×C22⋊C4—416no—
136#217—316no—
137#217—632no—
138#217—68no—
139(C2×D3)⋊C4—616no—
140C4⋊Dic3—68no—
141C22×C32—24no—
142C22×C32—22no—
143C22×C32—28no—
144C22×C32—24no—
145C22×C32—41no—
146C22×C32—42no—
147C22×C32—41no—
148C22×C32—44no—
149C22×C32—44no—
150C22×C32—48no—
151C22×C32—42no—
152C22×C32—42no—
153C22×C32—44no—
154C22×C32#12012yes—
155C22×C32#12011yescharacteristic
156C22×C32#12112yes—
157C22×C32#12111yescharacteristic
158C22×C32#12711yescharacteristic
159C2×C3⋊D3—44no—
160C2×C3⋊D3—42no—
161C2×C3⋊D3—44no—
162C2×C3⋊D3—82no—
163C32×C4—42no—
164C32×C4—81no—
165C3⋊Dic3—44no—
166C3⋊Dic3—42no—
167C25C2×C3⋊D311yescharacteristic
168C22×D4—92no—
169C22×D4—182no—
170#123—182no—
171#121—182no—
172#120—182no—
173#120—184no—
174#120—184no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—92no—
177C2×C22⋊C4—182no—
178C2×C22⋊C4C2×C3⋊D311yescharacteristic
179C2×C22⋊C4C2×C3⋊D311yescharacteristic
180#99—184no—
181C23×C3—216no—
182C23×C3—232no—
183C23×C3—216no—
184C23×C3—28no—
185C23×C3—416no—
186C23×C3—48no—
187C23×C3—416no—
188C23×C3—48no—
189C23×C3—432no—
190C23×C3—416no—
191C23×C3—48no—
192C23×C3—44no—
193C23×C3—44no—
194C23×C3C2×D1214yes—
195C23×C3#23514yes—
196C23×C3D3×D418yes—
197C23×C3D3×D418yes—
198C23×C3C2×#6714yes—
199C22×D3—68no—
200C22×D3—68no—
201C22×D3—68no—
202C22×D3—1216no—
203C2×C3×C4—28no—
204C2×C3×C4—48no—
205C2×C3×C4—48no—
206C2×C3×C4—44no—
207#67—1264no—
208#67—128no—
209#67—128no—
210#67—128no—
211#67—128no—
212C2×Dic3—616no—
213C2×Dic3—68no—
214C2×Dic3—68no—
215C2×Dic3—68no—
216C2×Dic3—1216no—
217D12—248no—
218C2×C32—22no—
219C2×C32—21no—
220C2×C32—22no—
221C2×C32—21no—
222C2×C32—44no—
223C2×C32#39211yescharacteristic
224C2×C32B(4,𝔽2)12yes—
225C3⋊D3—82no—
226C24—22no—
227C24—21no—
228C24—21no—
229C24—22no—
230C24—44no—
231C24—92no—
232C24C4⋊(C3⋊D3)12yescomplemented
233C24C22×C3⋊D311yescharacteristic
234C2×D4—182no—
235C2×D4—188no—
236C2×D4—182no—
237C2×D4—182no—
238C2×D4—182no—
239C2×D4—182no—
240C2×D4—182no—
241C2×D4—182no—
242C2×D4—368no—
243C22×C4—21no—
244C22×C4—92no—
245C22×C4—182no—
246C22×C4#63812yescomplemented
247C4⋊C4—182no—
248C22⋊C4—22no—
249C22⋊C4—22no—
250C22⋊C4—44no—
251C22⋊C4—94no—
252C22⋊C4—184no—
253C22⋊C4—188no—
254C22⋊C4—182no—
255C22×C3—216no—
256C22×C3—28no—
257C22×C3—232no—
258C22×C3—216no—
259C22×C3—44no—
260C22×C3—44no—
261C22×C3—48no—
262C22×C3—416no—
263C22×C3—416no—
264C22×C3—432no—
265C22×C3—48no—
266C22×C3—48no—
267C22×C3—416no—
268C22×C3#88218yes—
269C22×C3#88418yes—
270C22×C3#93014yes—
271C22×C3#93714yes—
272C22×C3#94014yes—
273C2×D3—1216no—
274C2×D3—128no—
275C2×D3—1216no—
276C2×D3—248no—
277C3×C4—48no—
278C3×C4—84no—
279Dic3—1216no—
280Dic3—128no—
281C32#202111yescharacteristic, complemented, Sylow
282C23—24no—
283C23—28no—
284C23—24no—
285C23—22no—
286C23—44no—
287C23—42no—
288C23—42no—
289C23—44no—
290C23—48no—
291C23—44no—
292C23—42no—
293C23—41no—
294C23—41no—
295C23—182no—
296C23—182no—
297C23—182no—
298C23—364no—
299C23C2×C4⋊(C3⋊D3)11yescharacteristic
300C23#382811yescharacteristic
301C23D4×C3⋊D312yes—
302C23D4×C3⋊D312yes—
303C23C2×#63811yescharacteristic
304D4—3616no—
305D4—362no—
306D4—362no—
307D4—362no—
308D4—362no—
309D4—722no—
310C2×C4—22no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—184no—
315C2×C4—182no—
316C2×C4—182no—
317C2×C4—182no—
318C2×C4—364no—
319C2×C3—28no—
320C2×C3—24no—
321C2×C3—28no—
322C2×C3—24no—
323C2×C3—416no—
324C2×C3#496014yes—
325C2×C3#503218yes—
326D3—248no—
327C22—22no—
328C22—24no—
329C22—28no—
330C22—24no—
331C22—41no—
332C22—41no—
333C22—42no—
334C22—44no—
335C22—44no—
336C22—42no—
337C22—48no—
338C22—42no—
339C22—44no—
340C22—364no—
341C22—362no—
342C22—364no—
343C22—722no—
344C22#6409112yes—
345C22#6409312yes—
346C22#6413911yescharacteristic
347C22#6414611yescharacteristic
348C22#6414911yescharacteristic
349C4—42no—
350C4—81no—
351C4—364no—
352C4—362no—
353C3#6950014yescomplemented
354C2—21no—
355C2—22no—
356C2—21no—
357C2—22no—
358C2—44no—
359C2—722no—
360C2#1059265911yescharacteristic
361C2#1059273112yes—
subgroupG/H
centerC22#64146
commutator, cosocleC24×C32C23
FrattiniC24C22×C3⋊D3
FittingC32×#379C2
socleC22×C32#120
hypercenter#379C3⋊D3
hypocenterC32#2021
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#64162C2semidirect
2. #10595964C2semidirect
3. C32×#379C2semidirect
4. C2×#63633C2semidirect
5. #10589392C2semidirect
23. C3×#379D3semidirect
31. C24×C32D4semidirect
33. C23×C3⋊D3D4semidirect
35. C22×C32×C4D4semidirect
45. C22×C3⋊Dic3D4semidirect
52. #3757D4semidirect
110. #379C3⋊D3semidirect
117. C24×C3D12semidirect
121. C22×C3×C4#67semidirect
232. C24C4⋊(C3⋊D3)semidirect
246. C22×C4#638semidirect
281. C32#2021semidirect
353. C3#69500semidirect

Maximal subgroups

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

subgroupindex
C2×#641622
#105959642
C32×#3792
C2×#636332
#105893922
#695003