Finite Group Databasebeta

← #11866965

Subgroups — #11866965

Order 1152.

1257 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 1257 conjugacy classes of subgroups — too many to draw. Only its 176 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, complemented
2C2×#63791C211yesmaximal, characteristic, complemented
3#10594612C212yesmaximal, complemented
4C3⋊D3×#106C211yesmaximal, characteristic, complemented
5C3×#4865C212yesmaximal, complemented
6#10590836C212yesmaximal, complemented
7#10590593C212yesmaximal, complemented
8#10590504C214yesmaximal, complemented
9D3×#469—32nomaximal
10C2×#3802—22no—
11C2×#3802C2212yes—
12C2×C4×D32C2211yescharacteristic
13C2×C8×C3⋊D3C2211yescharacteristic
14C4⋊C4×C3⋊D3C2212yes—
15C2×C3×D24C2212yescomplemented
16C2×C3×ΓL(1,𝔽25)C2212yescomplemented
17C3×#895C2214yescomplemented
18#63921—22no—
19#63908C2214yescomplemented
20#63885—24no—
21C2×#3713C2212yescomplemented
22C2×#3711C2212yescomplemented
23C2×#3710C2211yescharacteristic
24#63797—24no—
25#63791—24no—
26C32×#106C2211yescharacteristic, complemented
27#63644C2211yescharacteristic, complemented
28#63635C2212yescomplemented
29C3×#809C2214yescomplemented
30#63563C2214yescomplemented
31C2×D3×D8—32no—
32C2×D3×M16—32no—
33D3×#121—34no—
34C3×#469—32no—
35#5159—32no—
36#5135—32no—
37#5039—34no—
38#4865D312yescomplemented
39D3×#106—32no—
40D3×#106—61no—
41#4782—34no—
42D3×#102—34no—
43C22×D32—22no—
44C22×D32D411yescharacteristic
45C2×C4×C3⋊D3—22no—
46C2×C4×C3⋊D3C2311yescharacteristic
47C2×C3×D12—24no—
48C2×C3×D12C2314yes—
49C2×C3×C4×D3C2312yes—
50C2×#625—24no—
51C2×#625—22no—
52C2×#624D411yescharacteristic
53C2×D3×Dic3D412yes—
54#3802—24no—
55#3802—24no—
56#3802—48no—
57C4×D32—22no—
58C4×D32—22no—
59C2×C32×C8C2311yescharacteristic
60C32×C4⋊C4C2312yes—
61C4⋊(C3⋊Dic3)C2312yes—
62#3750—22no—
63C2×C3⋊(C3⋊C8)C2311yescharacteristic
64C8×C3⋊D3D414yescomplemented
65C3×(C2×D3)⋊C4—24no—
66C2×C3×C3⋊C8C2312yes—
67C3×D24—24no—
68C3×ΓL(1,𝔽25)—24no—
69(C2×D3)⋊Dic3—24no—
70#3713—24no—
71#3711—24no—
72#3710—22no—
73C2×#469—91noSylow
74C2×D3×D4—34no—
75C2×D3×D4—64no—
76C22×C4×D3—32no—
77C2×C3×D8—32no—
78C2×C3×M16—32no—
79C3×#121—34no—
80#939—64no—
81#938—34no—
82C2×#213—34no—
83#930—34no—
84C2×#208—32no—
85D3×D8—68no—
86D3×M16—68no—
87C2×D24C2×D312yescomplemented
88C2×ΓL(1,𝔽25)—32no—
89C2×ΓL(1,𝔽25)C2×D312yescomplemented
90C2×D3×C8—32no—
91C2×D3×C8—32no—
92C2×D3×C8—61no—
93#895C2×D314yescomplemented
94D3×C4⋊C4—34no—
95D3×C4⋊C4—62no—
96#884—64no—
97D3×C22⋊C4—64no—
98C3×#106—21no—
99C3×#106C2×D312yescomplemented
100C3×#102—34no—
101#832—34no—
102#821—34no—
103#817—32no—
104#817—61no—
105#809C2×D314yescomplemented
106#808—34no—
107#808—62no—
108C22×C3⋊D3C2×D411yescharacteristic
109C22×C3×D3—24no—
110C22×C3×D3C2×D412yes—
111C2×D32—22no—
112C2×D32—24no—
113C2×D32—44no—
114C2×D32—44no—
115C2×D32—44no—
116C2×C32×C4—22no—
117C2×C32×C4C2411yescharacteristic
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3C2×D411yescharacteristic
120C4×C3⋊D3—44no—
121C4×C3⋊D3C2×D412yes—
122C4×C3⋊D3#4112yes—
123C2×C3×Dic3C2×D412yes—
124C3×D12—24no—
125C3×D12—24no—
126C3×D12—48no—
127C3×C4×D3—22no—
128C3×C4×D3—22no—
129#625—48no—
130#625—44no—
131#624—22no—
132D3×Dic3—24no—
133C32×C8C2×D412yescomplemented
134C3⋊(C3⋊C8)C2×D412yescomplemented
135C3×C3⋊C8—22no—
136C22×D8—91no—
137C22×M16—91no—
138C2×#121—92no—
139#469—32no—
140#469—94no—
141#469—92no—
142C2×#106—91no—
143C2×#102—92no—
144C23×D3—32no—
145C23×D3—64no—
146C2×C3×D4—34no—
147C2×C3×D4—64no—
148C22×C3×C4—32no—
149C2×#67—64no—
150C2×#67—64no—
151C2×#67—64no—
152C22×Dic3—32no—
153D3×D4—68no—
154D3×D4—68no—
155D3×D4—1216no—
156C2×D12—24no—
157C2×D12C22×D314yes—
158C2×C4×D3—32no—
159C2×C4×D3—32no—
160C2×C4×D3—32no—
161C2×C4×D3—61no—
162C2×C4×D3—64no—
163C2×C4×D3—64no—
164C2×C4×D3—64no—
165C2×C4×D3—122no—
166C2×C4×D3C22×D312yes—
167C3×D8—64no—
168C3×M16—64no—
169C2×C3×C8—21no—
170C2×C3×C8—32no—
171C2×C3×C8C22×D312yes—
172C3×C4⋊C4—22no—
173C3×C4⋊C4C22×D314yes—
174C3×C22⋊C4—64no—
175#217—64no—
176#213—68no—
177(C2×D3)⋊C4—24no—
178(C2×D3)⋊C4—64no—
179C4⋊Dic3—34no—
180C4⋊Dic3—62no—
181Dic3⋊C4—64no—
182Dic3⋊C4—122no—
183#208—64no—
184C2×C3⋊C8—32no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8C22×D312yes—
187D24—24no—
188ΓL(1,𝔽25)—24no—
189ΓL(1,𝔽25)—64no—
190D3×C8—38no—
191D3×C8—64no—
192D3×C8—64no—
193C22×C32C22×D411yescharacteristic
194C2×C3⋊D3#12112yes—
195C2×C3⋊D3AGL(1,ℤ/8)14yes—
196C2×C3×D3—22no—
197C2×C3×D3—24no—
198C2×C3×D3—44no—
199C2×C3×D3—44no—
200C2×C3×D3—44no—
201D32—44no—
202D32—88no—
203C32×C4—42no—
204C32×C4C22×D411yescharacteristic
205C32×C4C2×#4111yescharacteristic
206C3⋊Dic3—42no—
207C3⋊Dic3#12112yes—
208C3×Dic3—22no—
209C22×D4—92no—
210C22×D4—182no—
211C23×C4—91no—
212C2×D8—32no—
213C2×D8—92no—
214C2×D8—184no—
215C2×M16—32no—
216C2×M16—92no—
217C2×M16—184no—
218C22×C8—91no—
219C22×C8—91no—
220#121—34no—
221#121—94no—
222#121—184no—
223C2×C4⋊C4—92no—
224C2×C22⋊C4—182no—
225#106—91no—
226#106—92no—
227#106D3211yescharacteristic, complemented
228#102—34no—
229#102—94no—
230C23×C3—32no—
231C23×C3—64no—
232C22×D3—24no—
233C22×D3—32no—
234C22×D3—61no—
235C22×D3—64no—
236C22×D3—68no—
237C22×D3—128no—
238C22×D3—128no—
239C22×D3—128no—
240C22×D3D3×D412yes—
241C3×D4—64no—
242C3×D4—64no—
243C3×D4—128no—
244C2×C3×C4—24no—
245C2×C3×C4—21no—
246C2×C3×C4—32no—
247C2×C3×C4—42no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4C23×D312yes—
251#67—128no—
252#67—128no—
253#67—128no—
254C2×Dic3—32no—
255C2×Dic3—61no—
256C2×Dic3—64no—
257C2×Dic3—64no—
258C2×Dic3—122no—
259C2×Dic3D3×D412yes—
260D12—24no—
261D12—24no—
262D12—48no—
263C4×D3—22no—
264C4×D3—22no—
265C4×D3—34no—
266C4×D3—34no—
267C4×D3—62no—
268C4×D3—62no—
269C4×D3—64no—
270C4×D3—64no—
271C4×D3—128no—
272C4×D3—244no—
273C3×C8—22no—
274C3×C8—62no—
275C3×C8D3×D414yescomplemented
276C3⋊C8—22no—
277C3⋊C8—34no—
278C3⋊C8—62no—
279C2×C32C2×#12111yescharacteristic
280C2×C32C2×AGL(1,ℤ/8)12yes—
281C3⋊D3#46914yescomplemented
282C3×D3—42no—
283C3×D3—84no—
284C24—91no—
285C24—182no—
286C2×D4—34no—
287C2×D4—64no—
288C2×D4—184no—
289C2×D4—184no—
290C2×D4—182no—
291C2×D4—184no—
292C2×D4—368no—
293C22×C4—32no—
294C22×C4—91no—
295C22×C4—92no—
296C22×C4—91no—
297C22×C4—182no—
298C22×C4—182no—
299C22×C4—182no—
300D8—64no—
301D8—184no—
302M16—64no—
303M16—184no—
304C2×C8—32no—
305C2×C8—91no—
306C2×C8—94no—
307C2×C8—182no—
308C2×C8C2×D3211yescharacteristic
309C4⋊C4—92no—
310C4⋊C4—182no—
311C4⋊C4C2×D3212yes—
312C22⋊C4—64no—
313C22⋊C4—184no—
314C22×C3—21no—
315C22×C3—64no—
316C22×C3—62no—
317C22×C3—124no—
318C22×C3—124no—
319C22×C3—124no—
320C22×C3C2×D3×D412yes—
321C2×D3—24no—
322C2×D3—22no—
323C2×D3—38no—
324C2×D3—34no—
325C2×D3—44no—
326C2×D3—44no—
327C2×D3—44no—
328C2×D3—62no—
329C2×D3—64no—
330C2×D3—128no—
331C2×D3—2416no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—44no—
335C3×C4—62no—
336C3×C4—82no—
337C3×C4C2×D3×D412yes—
338C3×C4D3×#4112yes—
339Dic3—22no—
340Dic3—34no—
341Dic3—62no—
342Dic3—124no—
343Dic3—242no—
344C32C2×#46911yescharacteristic, complemented, Sylow
345C23—32no—
346C23—64no—
347C23—91no—
348C23—182no—
349C23—184no—
350C23—364no—
351C23—364no—
352C23—364no—
353D4—64no—
354D4—64no—
355D4—128no—
356D4—364no—
357D4—368no—
358C2×C4—22no—
359C2×C4—32no—
360C2×C4—62no—
361C2×C4—62no—
362C2×C4—91no—
363C2×C4—92no—
364C2×C4—92no—
365C2×C4—182no—
366C2×C4—184no—
367C2×C4—182no—
368C2×C4—364no—
369C2×C4C22×D3211yescharacteristic
370C8—62no—
371C8—92no—
372C8#380212yescomplemented
373C2×C3—21no—
374C2×C3—22no—
375C2×C3—122no—
376C2×C3—244no—
377C2×C3D3×#12112yes—
378C2×C3D3×AGL(1,ℤ/8)14yes—
379D3—38no—
380D3—42no—
381D3—64no—
382D3—84no—
383C22—62no—
384C22—64no—
385C22—92no—
386C22—94no—
387C22—124no—
388C22—124no—
389C22—124no—
390C22—364no—
391C22—728no—
392C22D32×D411yescharacteristic
393C4—42no—
394C4—62no—
395C4—92no—
396C4—362no—
397C4C2×#380211yescharacteristic
398C4#6431911yescharacteristic
399C3—21no—
400C3D3×#46912yescomplemented
401C2—94no—
402C2—122no—
403C2—244no—
404C2#1059461211yescharacteristic
405C2#1059474012yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
hypercenter#106D32
hypocenterC32C2×#469
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. C2×#63797C2semidirect
2. C2×#63791C2semidirect
3. #10594612C2semidirect
4. C3⋊D3×#106C2semidirect
5. C3×#4865C2semidirect
6. #10590836C2semidirect
7. #10590593C2semidirect
8. #10590504C2semidirect
15. C2×C3×D24C22semidirect
16. C2×C3×ΓL(1,𝔽25)C22semidirect
17. C3×#895C22semidirect
19. #63908C22semidirect
21. C2×#3713C22semidirect
22. C2×#3711C22semidirect
26. C32×#106C22semidirect
27. #63644C22semidirect
28. #63635C22semidirect
29. C3×#809C22semidirect
30. #63563C22semidirect
38. #4865D3semidirect
64. C8×C3⋊D3D4semidirect
87. C2×D24C2×D3semidirect
89. C2×ΓL(1,𝔽25)C2×D3semidirect
93. #895C2×D3semidirect
99. C3×#106C2×D3semidirect
105. #809C2×D3semidirect
133. C32×C8C2×D4semidirect
134. C3⋊(C3⋊C8)C2×D4semidirect
227. #106D32semidirect
275. C3×C8D3×D4semidirect
281. C3⋊D3#469semidirect
344. C32C2×#469semidirect
372. C8#3802semidirect
400. C3D3×#469semidirect

Maximal subgroups

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

subgroupindex
C2×#637972
C2×#637912
#105946122
C3⋊D3×#1062
C3×#48652
#105908362
#105905932
#105905042
D3×#4693