Finite Group Databasebeta

← #11798064

Subgroups — #11798064

Order 1152.

599 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 599 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C22×C3×D24C211yesmaximal, characteristic, complemented
2#10592814C211yesmaximal, characteristic, complemented
3C2×#63546C212yesmaximal, complemented
4C3×#4549C211yesmaximal, characteristic, complemented
5#10589115C212yesmaximal, complemented
6#72035—31nomaximal
7#69108—31nomaximal
8C22×C3×D12—21no—
9C22×C32×C8C2211yescharacteristic
10#64139—21no—
11C2×#3745C2211yescharacteristic, complemented
12C2×C3×D24—21no—
13C2×C3×D24—24no—
14C2×C3×D24C2212yes—
15#63648—21no—
16#63645C2211yescharacteristic, complemented
17C2×C3×C3⋊C16C2212yescomplemented
18#63546—24no—
19C22×C3×D8—31no—
20C22×D24D311yescharacteristic, complemented
21C2×#826—32no—
22#5115—31no—
23#5115—31no—
24#5115—61no—
25C2×D48—32no—
26C3×C22⋊C16—31no—
27#4562—32no—
28#4549D311yescharacteristic, complemented
29#4509—32no—
30C23×C3×D3—41no—
31C22×C32×C4D411yescharacteristic
32C2×#638—41no—
33C2×C4⋊(C3⋊D3)—21no—
34C2×C3×D12—24no—
35C2×C3×D12—22no—
36C2×C3×D12—42no—
37C2×C3×D12—41no—
38C2×C32×C8—22no—
39C2×C32×C8D411yescharacteristic
40C2×C32×C8C2311yescharacteristic
41#3752—41no—
42C4⋊(C3⋊Dic3)—21no—
43#3745—22no—
44C3×D24—24no—
45C3×D24—22no—
46C3×D24D414yescomplemented
47C3×C3⋊C16—22no—
48#2184—91noSylow
49C22×C3×D4—61no—
50C22×D12—21no—
51C2×C3×D8—32no—
52C2×C3×D8—64no—
53C2×C3×D8—61no—
54C22×C3×C8—21no—
55C22×C3×C8C2×D311yescharacteristic
56C22×C3×C8C2×D311yescharacteristic
57#930—62no—
58#930—61no—
59#930—61no—
60C2×D24—21no—
61C2×D24—24no—
62C2×D24—31no—
63C2×D24—31no—
64C2×D24—61no—
65C2×D24C2×D312yes—
66C2×C3×C16—32no—
67#826—64no—
68#821—62no—
69#821—61no—
70#821—61no—
71#818—31no—
72#818—31no—
73#818—61no—
74C2×C3⋊C16C2×D312yescomplemented
75D48—64no—
76C23×C32D811yescharacteristic
77C22×C3⋊D3—41no—
78C22×C3×D3—44no—
79C22×C3×D3—42no—
80C22×C3×D3—82no—
81C22×C3×D3—82no—
82C2×C32×C4—21no—
83C2×C32×C4—21no—
84C2×C32×C4D811yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86#638—82no—
87C2×C3⋊Dic3—41no—
88C4⋊(C3⋊D3)—41no—
89C4⋊(C3⋊D3)—41no—
90C3×D12—24no—
91C3×D12—44no—
92C3×D12—42no—
93C32×C8—21no—
94C32×C8C2×D412yes—
95C22×D8—31no—
96C2×D16—92no—
97#466—91no—
98#357—92no—
99C22⋊C16—31no—
100C24×C3—121no—
101C23×D3—41no—
102C2×C3×D4—64no—
103C2×C3×D4—62no—
104C2×C3×D4—122no—
105C2×C3×D4—121no—
106C22×C3×C4—21no—
107C22×C3×C4D1211yescharacteristic
108C22×C3×C4#6711yescharacteristic
109C2×#67—122no—
110C2×#67—121no—
111C2×#67—121no—
112C2×D12—24no—
113C2×D12—22no—
114C2×D12—42no—
115C2×D12—41no—
116C2×D12—62no—
117C2×D12—61no—
118C2×D12—61no—
119C3×D8—34no—
120C3×D8—64no—
121C3×D8—62no—
122C2×C3×C8—22no—
123C2×C3×C8—22no—
124C2×C3×C8—21no—
125C2×C3×C8—21no—
126C2×C3×C8—42no—
127C2×C3×C8D1211yescharacteristic
128C2×C3×C8#6711yescharacteristic
129C2×C3×C8C22×D311yescharacteristic
130C2×C3×C8C22×D311yescharacteristic
131(C2×D3)⋊C4—122no—
132(C2×D3)⋊C4—121no—
133(C2×D3)⋊C4—121no—
134C4⋊Dic3—62no—
135C4⋊Dic3—61no—
136C4⋊Dic3—61no—
137D24—24no—
138D24—22no—
139D24—62no—
140D24—62no—
141D24—122no—
142D24#6714yescomplemented
143C3×C16—62no—
144C3⋊C16—22no—
145C22×C32—21no—
146C22×C32—21no—
147C22×C32D1612yescomplemented
148C22×C32C2×D811yescharacteristic
149C2×C3⋊D3—81no—
150C2×C3⋊D3—81no—
151C2×C3⋊D3—81no—
152C2×C3×D3—44no—
153C2×C3×D3—88no—
154C2×C3×D3—82no—
155C2×C3×D3—82no—
156C32×C4—21no—
157C32×C4#12011yescharacteristic
158C32×C4AGL(1,ℤ/8)11yescharacteristic
159C3⋊Dic3—81no—
160C22×D4—61no—
161C2×D8—32no—
162C2×D8—64no—
163C2×D8—61no—
164C2×D8—91no—
165C22×C8D3211yescharacteristic
166#121—181no—
167D16—184no—
168C2×C16—32no—
169#107—91no—
170#102—181no—
171C23×C3—21no—
172C23×C3—124no—
173C23×C3—122no—
174C23×C3—242no—
175C23×C3—242no—
176C23×C3D2411yescharacteristic
177C23×C3#21311yescharacteristic
178C22×D3—44no—
179C22×D3—42no—
180C22×D3—82no—
181C22×D3—82no—
182C22×D3—122no—
183C22×D3—121no—
184C22×D3—121no—
185C3×D4—64no—
186C3×D4—124no—
187C3×D4—122no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—41no—
195C2×C3×C4—41no—
196C2×C3×C4D2411yescharacteristic
197C2×C3×C4#21311yescharacteristic
198C2×C3×C4C2×D1211yescharacteristic
199C2×C3×C4C2×#6711yescharacteristic
200#67—244no—
201#67—242no—
202#67—242no—
203C2×Dic3—122no—
204C2×Dic3—121no—
205C2×Dic3—121no—
206D12—24no—
207D12—44no—
208D12—42no—
209D12—122no—
210D12—122no—
211D12—121no—
212D12—121no—
213D12—121no—
214D12—121no—
215C3×C8—21no—
216C3×C8—21no—
217C3×C8—22no—
218C3×C8—41no—
219C3×C8D3×D412yes—
220C3×C8C2×#6712yes—
221C2×C32—22no—
222C2×C32#44711yescharacteristic
223C2×C32C2×D1611yescharacteristic
224C2×C32#50911yescharacteristic
225C3⋊D3—161no—
226C3×D3—84no—
227C24—121no—
228C2×D4—64no—
229C2×D4—62no—
230C2×D4—122no—
231C2×D4—121no—
232C2×D4—181no—
233C2×D4—361no—
234C22×C4#62611yescharacteristic
235D8—34no—
236D8—64no—
237D8—62no—
238D8—182no—
239C2×C8—22no—
240C2×C8#62611yescharacteristic
241C2×C8C2×D3211yescharacteristic
242C4⋊C4—181no—
243C22⋊C4—361no—
244C16—62no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—22no—
250C22×C3—21no—
251C22×C3—41no—
252C22×C3—41no—
253C22×C3—124no—
254C22×C3—248no—
255C22×C3—242no—
256C22×C3—242no—
257C22×C3D4812yescomplemented
258C22×C3#82612yescomplemented
259C22×C3C2×D2411yescharacteristic
260C22×C3C2×#21311yescharacteristic
261C2×D3—44no—
262C2×D3—88no—
263C2×D3—82no—
264C2×D3—82no—
265C2×D3—242no—
266C2×D3—242no—
267C2×D3—242no—
268C2×D3—241no—
269C2×D3—241no—
270C2×D3—241no—
271C2×D3—241no—
272C2×D3—241no—
273C2×D3—241no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4#88211yescharacteristic
280C3×C4#90811yescharacteristic
281C3×C4#93211yescharacteristic
282C3×C4#95311yescharacteristic
283Dic3—242no—
284Dic3—241no—
285Dic3—241no—
286C32#218411yescharacteristic, complemented, Sylow
287C23—124no—
288C23—122no—
289C23—242no—
290C23—242no—
291C23—361no—
292C23#371411yescharacteristic
293D4—64no—
294D4—124no—
295D4—122no—
296D4—361no—
297D4—361no—
298D4—722no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—361no—
302C2×C4#371411yescharacteristic
303C2×C4C2×#62611yescharacteristic
304C8—21no—
305C8D3×#6712yes—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—42no—
312C2×C3—244no—
313C2×C3#473211yescharacteristic
314C2×C3C2×D4811yescharacteristic
315C2×C3#490811yescharacteristic
316C2×C3C2×#82611yescharacteristic
317C2×C3#514711yescharacteristic
318C2×C3#521711yescharacteristic
319D3—84no—
320D3—482no—
321D3—481no—
322D3—481no—
323C22—21no—
324C22—21no—
325C22—124no—
326C22—248no—
327C22—242no—
328C22—242no—
329C22—721no—
330C22—721no—
331C22—721no—
332C22#6354612yescomplemented
333C22C2×#371411yescharacteristic
334C4—21no—
335C4—721no—
336C4#6383011yescharacteristic
337C4#6397711yescharacteristic
338C3—21no—
339C3#6910811yescharacteristic, complemented
340C3#7203511yescharacteristic, complemented
341C2—22no—
342C2—244no—
343C2—1441no—
344C2C2×#6354611yescharacteristic
345C2#1059063311yescharacteristic
346C2#1059116211yescharacteristic
subgroupG/H
centerC22C2×#3714
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC22×C32×C8C22
socleC22×C32C2×D8
hypercenterC22×C8D32
hypocenterC32#2184
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D24C2semidirect
2. #10592814C2semidirect
3. C2×#63546C2semidirect
4. C3×#4549C2semidirect
5. #10589115C2semidirect
11. C2×#3745C22semidirect
16. #63645C22semidirect
17. C2×C3×C3⋊C16C22semidirect
20. C22×D24D3semidirect
28. #4549D3semidirect
46. C3×D24D4semidirect
74. C2×C3⋊C16C2×D3semidirect
142. D24#67semidirect
147. C22×C32D16semidirect
257. C22×C3D48semidirect
258. C22×C3#826semidirect
286. C32#2184semidirect
332. C22#63546semidirect
339. C3#69108semidirect
340. C3#72035semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D242
#105928142
C2×#635462
C3×#45492
#105891152
#720353
#691083