Finite Group Databasebeta

← #11860708

Subgroups — #11860708

Order 1152.

1113 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 1113 conjugacy classes of subgroups — too many to draw. Only its 224 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×#63797C211yesmaximal, characteristic
2#10594606C212yesmaximal, complemented
3#10592579C211yesmaximal, characteristic, complemented
4C3×#4872C212yesmaximal, complemented
5Dic3×D24C212yesmaximal, complemented
6#10590700C211yesmaximal, characteristic, complemented
7#10590594C212yesmaximal, complemented
8#10590455C214yesmaximal, complemented
9#79588—32nomaximal
10C2×#3802C2212yes—
11C2×C8×C3⋊D3C2211yescharacteristic
12#64101C2212yes—
13C2×C3×D24C2212yes—
14C3×#893C2214yescomplemented
15D3×(C2×D3)⋊C4—24no—
16#63902—22no—
17C4×#625—22no—
18Dic3×D12C2214yescomplemented
19#63874C2211yescharacteristic
20C2×#3713C2212yes—
21C2×#3712C2211yescharacteristic
22#63797C418yescomplemented
23C32×#107C2211yescharacteristic, complemented
24#63645C2211yescharacteristic, complemented
25#63635C2212yescomplemented
26C3×C8×Dic3C2212yescomplemented
27C3×#809C2214yescomplemented
28#63563C2214yescomplemented
29#63554C2212yescomplemented
30C2×D3×D8—32no—
31#5545—34no—
32C3×C4×D8—32no—
33Dic3×D8—32no—
34#5014—34no—
35#4880—32no—
36#4880—61no—
37#4872D312yescomplemented
38#4785—34no—
39#4770—34no—
40C4×D24—32no—
41#4689—32no—
42C22×D32—22no—
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×C3×D12C2314yes—
45C2×C3×C4×D3—24no—
46C2×#625—22no—
47C2×D3×Dic3—24no—
48#3802—24no—
49#3802C2×C418yescomplemented
50C2×C32×C8C2311yescharacteristic
51C32×C4⋊C4C2312yes—
52#3752—22no—
53C4⋊(C3⋊Dic3)C2312yes—
54C4×C3⋊Dic3—22no—
55C2×C3⋊(C3⋊C8)C2311yescharacteristic
56C8×C3⋊D3C2×C414yescomplemented
57C3×(C2×D3)⋊C4—24no—
58C3×C4×Dic3C2312yes—
59C2×C3×C3⋊C8C2312yes—
60C3×D24C2×C418yescomplemented
61#3724D411yescharacteristic
62#3724D411yescharacteristic
63#3722D412yes—
64(C2×D3)⋊Dic3—24no—
65#3713C2×C418yescomplemented
66#3712—22no—
67#2948—91noSylow
68C2×D3×D4—34no—
69C2×C3×D8—32no—
70C3×C4×D4—34no—
71D4×Dic3—34no—
72C2×#213—34no—
73C4×#67—64no—
74C2×(C2×D3)⋊C4—64no—
75D3×D8—316no—
76C2×D24C2×D312yes—
77C2×ΓL(1,𝔽25)—32no—
78C2×D3×C8—32no—
79C2×D3×C8—61no—
80#893C2×D314yescomplemented
81#892—34no—
82#892—62no—
83#67⋊C4—64no—
84D3×C22⋊C4—64no—
85C4×D12—34no—
86#872—32no—
87C3×#107—21no—
88C3×#107C2×D312yescomplemented
89C3×#102—34no—
90C3×C4×C8—32no—
91#832—34no—
92#821—34no—
93#818—32no—
94#818—61no—
95#815—32no—
96C8×Dic3C2×D312yescomplemented
97#809C2×D314yescomplemented
98#808—34no—
99#808—62no—
100#803—32no—
101C22×C3⋊D3C2×D411yescharacteristic
102C22×C3×D3—24no—
103C2×D32—28no—
104C2×D32—82no—
105C2×D32—82no—
106C2×C32×C4—22no—
107C2×C32×C4C2411yescharacteristic
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3C2×D411yescharacteristic
110C4×C3⋊D3C22×C412yes—
111C4×C3⋊D3#4112yes—
112C2×C3×Dic3C2×D412yes—
113C2×C3×Dic3C2×D412yes—
114C3×D12—24no—
115C3×D12C22×C418yes—
116C3×C4×D3—84no—
117#625—28no—
118D3×Dic3—84no—
119C32×C8C22×C412yes—
120C3⋊(C3⋊C8)C22×C412yes—
121C3×C3⋊C8—22no—
122C22×D8—91no—
123#518—92no—
124#442—94no—
125C4×D8—32no—
126C4×D8—92no—
127#427—91no—
128#418—92no—
129#405—91no—
130C23×D3—64no—
131C2×C3×D4—34no—
132C22×C3×C4—64no—
133C2×#67—64no—
134C22×Dic3—64no—
135D3×D4—316no—
136D3×D4—68no—
137C2×D12C22×D314yes—
138C2×C4×D3—24no—
139C2×C4×D3—32no—
140C2×C4×D3—61no—
141C2×C4×D3—64no—
142C3×D8—38no—
143C2×C3×C8—21no—
144C2×C3×C8—32no—
145C2×C3×C8C22×D312yes—
146C3×C4⋊C4—22no—
147C3×C4⋊C4C22×D314yes—
148C3×C22⋊C4—64no—
149C3×C42—32no—
150#217—64no—
151#213—316no—
152(C2×D3)⋊C4—24no—
153(C2×D3)⋊C4—32no—
154(C2×D3)⋊C4—32no—
155(C2×D3)⋊C4—64no—
156(C2×D3)⋊C4—64no—
157(C2×D3)⋊C4—122no—
158C4⋊Dic3—34no—
159C4⋊Dic3—62no—
160Dic3⋊C4—32no—
161Dic3⋊C4—32no—
162C4×Dic3—64no—
163C4×Dic3—122no—
164C4×Dic3C22×D312yes—
165C2×C3⋊C8—32no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8C22×D312yes—
168D24C4×D318yescomplemented
169ΓL(1,𝔽25)—64no—
170D3×C8—38no—
171D3×C8—64no—
172C22×C32C22×D411yescharacteristic
173C2×C3⋊D3—21no—
174C2×C3⋊D3—21no—
175C2×C3⋊D3C4×D412yes—
176C2×C3×D3—28no—
177C2×C3×D3—44no—
178C2×C3×D3—44no—
179D32—88no—
180C32×C4—42no—
181C32×C4C23×C411yescharacteristic
182C32×C4C2×#4111yescharacteristic
183C3⋊Dic3—42no—
184C3⋊Dic3C4×D412yes—
185C3×Dic3—22no—
186C3×Dic3—22no—
187C22×D4—92no—
188C2×D8—32no—
189C2×D8—98no—
190C2×D8—92no—
191C2×M16—91no—
192C22×C8—91no—
193C4×D4—34no—
194C4×D4—94no—
195C4×D4—182no—
196C4×D4—182no—
197#117—91no—
198#117—92no—
199C2×C22⋊C4—184no—
200#107—91no—
201#107D3211yescharacteristic, complemented
202#106—92no—
203#102—34no—
204#102—94no—
205#97—92no—
206C4×C8—32no—
207C23×C3—64no—
208C22×D3—24no—
209C22×D3—32no—
210C22×D3—61no—
211C22×D3—616no—
212C22×D3—244no—
213C22×D3—244no—
214C3×D4—38no—
215C3×D4—64no—
216C2×C3×C4—24no—
217C2×C3×C4—21no—
218C2×C3×C4—32no—
219C2×C3×C4—32no—
220C2×C3×C4—42no—
221C2×C3×C4—244no—
222C2×C3×C4C23×D312yes—
223#67—616no—
224C2×Dic3—32no—
225C2×Dic3—61no—
226C2×Dic3—64no—
227C2×Dic3—122no—
228C2×Dic3—244no—
229C2×Dic3D3×D412yes—
230C2×Dic3D3×D412yes—
231D12—24no—
232D12C2×C4×D318yes—
233C4×D3—34no—
234C4×D3—34no—
235C4×D3—62no—
236C4×D3—62no—
237C4×D3—84no—
238C4×D3—244no—
239C3×C8—22no—
240C3×C8—62no—
241C3×C8C2×C4×D314yes—
242C3⋊C8—22no—
243C3⋊C8—34no—
244C3⋊C8—62no—
245C2×C32C2×C4×D411yescharacteristic
246C2×C32#57611yescharacteristic
247C2×C32#57611yescharacteristic
248C3⋊D3—22no—
249C3×D3—48no—
250C24—182no—
251C2×D4—34no—
252C2×D4—98no—
253C2×D4—184no—
254C2×D4—182no—
255C22×C4—64no—
256C22×C4—91no—
257C22×C4—184no—
258D8—38no—
259D8—98no—
260M16—182no—
261C2×C8—32no—
262C2×C8—91no—
263C2×C8—94no—
264C2×C8C2×D3211yescharacteristic
265C4⋊C4—91no—
266C4⋊C4—91no—
267C4⋊C4—92no—
268C4⋊C4C2×D3212yes—
269C22⋊C4—64no—
270C22⋊C4—92no—
271C22⋊C4—182no—
272C22⋊C4—184no—
273C42—32no—
274C42—182no—
275C22×C3—21no—
276C22×C3—68no—
277C22×C3—124no—
278C22×C3—124no—
279C22×C3C2×D3×D412yes—
280C2×D3—28no—
281C2×D3—34no—
282C2×D3—44no—
283C2×D3—44no—
284C2×D3—62no—
285C2×D3—62no—
286C2×D3—62no—
287C2×D3—121no—
288C2×D3—121no—
289C2×D3—2416no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—44no—
293C3×C4—62no—
294C3×C4—62no—
295C3×C4—82no—
296C3×C4C22×C4×D312yes—
297C3×C4D3×#4112yes—
298Dic3—22no—
299Dic3—22no—
300Dic3—34no—
301Dic3—62no—
302Dic3—124no—
303Dic3—242no—
304C32#294811yescharacteristic, complemented, Sylow
305C23—64no—
306C23—91no—
307C23—188no—
308C23—722no—
309C23—722no—
310D4—38no—
311D4—64no—
312D4—188no—
313C2×C4—22no—
314C2×C4—32no—
315C2×C4—32no—
316C2×C4—91no—
317C2×C4—92no—
318C2×C4—92no—
319C2×C4—182no—
320C2×C4—244no—
321C2×C4—724no—
322C2×C4C22×D3211yescharacteristic
323C8—62no—
324C8—92no—
325C8C4×D3212yes—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—128no—
330C2×C3C4×D3×D412yes—
331C2×C3#575712yes—
332C2×C3#576912yes—
333D3—48no—
334D3—64no—
335D3—122no—
336C22—68no—
337C22—92no—
338C22—124no—
339C22—124no—
340C22—181no—
341C22—181no—
342C22—728no—
343C22D32×D411yescharacteristic
344C4—42no—
345C4—62no—
346C4—62no—
347C4—92no—
348C4—362no—
349C4C2×C4×D3211yescharacteristic
350C4#6431911yescharacteristic
351C3—21no—
352C3#7958812yescomplemented
353C2—128no—
354C2—182no—
355C2#1059460511yescharacteristic
356C2#1059473111yescharacteristic
357C2#1059477111yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#63797C2
cosocleC2×C32×C4C24
hypercenter#107D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594606C2semidirect
3. #10592579C2semidirect
4. C3×#4872C2semidirect
5. Dic3×D24C2semidirect
6. #10590700C2semidirect
7. #10590594C2semidirect
8. #10590455C2semidirect
14. C3×#893C22semidirect
18. Dic3×D12C22semidirect
22. #63797C4semidirect
23. C32×#107C22semidirect
24. #63645C22semidirect
25. #63635C22semidirect
26. C3×C8×Dic3C22semidirect
27. C3×#809C22semidirect
28. #63563C22semidirect
29. #63554C22semidirect
37. #4872D3semidirect
49. #3802C2×C4semidirect
56. C8×C3⋊D3C2×C4semidirect
60. C3×D24C2×C4semidirect
65. #3713C2×C4semidirect
80. #893C2×D3semidirect
88. C3×#107C2×D3semidirect
96. C8×Dic3C2×D3semidirect
97. #809C2×D3semidirect
168. D24C4×D3semidirect
201. #107D32semidirect
304. C32#2948semidirect
352. C3#79588semidirect

Maximal subgroups

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

subgroupindex
C2×#637972
#105946062
#105925792
C3×#48722
Dic3×D242
#105907002
#105905942
#105904552
#795883