Finite Group Databasebeta

← #11885773

Subgroups — #11885773

Order 1152.

1307 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 1307 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×D3×D24C212yesmaximal, complemented
2#10594618C212yesmaximal, complemented
3#10592571C211yesmaximal, characteristic, complemented
4C3×#4883C212yesmaximal, complemented
5#10590886C211yesmaximal, characteristic, complemented
6C8×#625C211yesmaximal, characteristic, complemented
7#10590595C214yesmaximal, complemented
8#10590551C212yesmaximal, complemented
9#80729—32nomaximal
10C2×#3802—22no—
11C2×D3×D12C2214yescomplemented
12C2×#3745C2211yescharacteristic
13#64102C2212yescomplemented
14C2×C3×D24C2212yescomplemented
15C2×C3×D3×C8C2212yescomplemented
16C3×#895C2214yescomplemented
17#63922—24no—
18#63914C2212yescomplemented
19#63912—22no—
20C4×#625C2211yescharacteristic
21C2×#3714C2214yescomplemented
22C2×#3713C2212yescomplemented
23D3×D24—28no—
24C32×#107C2211yescharacteristic, complemented
25C8×C3⋊Dic3C2211yescharacteristic, complemented
26#63636C2212yescomplemented
27C3×#809C2214yescomplemented
28#63572C2211yescharacteristic, complemented
29(C2×D3)⋊(C3⋊C8)C2212yescomplemented
30C2×D3×D8—32no—
31C22×D24—32no—
32#5609—34no—
33C3×#466—32no—
34#5151—32no—
35C8×#67—32no—
36#5036—34no—
37#4883D312yescomplemented
38#4872—32no—
39#4872—61no—
40#4786—34no—
41#4773—34no—
42C22×D32—24no—
43C2×C4⋊(C3⋊D3)C2312yes—
44C2×C4×C3⋊D3—22no—
45C2×C3×D12—24no—
46C2×C3×D12C2314yes—
47C2×C3×C4×D3C2312yes—
48C2×#626—24no—
49C2×#625—22no—
50C2×#625—22no—
51C2×#625D411yescharacteristic
52#3802—48no—
53D3×D12—28no—
54D3×D12—44no—
55C2×C32×C8C2311yescharacteristic
56C32×C4⋊C4C2312yes—
57#3752—22no—
58C4×C3⋊Dic3C2311yescharacteristic
59C2×C3⋊(C3⋊C8)C2311yescharacteristic
60#3745D414yescomplemented
61C3×(C2×D3)⋊C4—24no—
62C2×C3×C3⋊C8C2312yes—
63C3×D24—24no—
64C3×D3×C8—24no—
65#3724D411yescharacteristic
66(C2×D3)⋊Dic3D412yes—
67#3714—28no—
68#3713—42no—
69D4×D8—91noSylow
70C2×D3×D4—34no—
71C2×D3×D4—64no—
72C22×D12—34no—
73C2×C3×D8—32no—
74C22×C3×C8—32no—
75C3×#121—34no—
76#940—34no—
77#937—64no—
78C2×#213—34no—
79C2×#213—34no—
80C4×#67—32no—
81D3×D8—68no—
82C2×D24—32no—
83C2×D24—34no—
84C2×D24—61no—
85C2×D24—68no—
86C2×D24C2×D312yescomplemented
87C2×D3×C8C2×D312yescomplemented
88#895C2×D314yescomplemented
89#893—34no—
90#893—62no—
91#884—64no—
92#882—64no—
93C3×#107—21no—
94C3×#107C2×D312yescomplemented
95C3×#102—34no—
96#830—32no—
97(C2×D3)⋊C8—32no—
98Dic3⋊C8—32no—
99C8×Dic3—32no—
100C8×Dic3—61no—
101#809—34no—
102#809—62no—
103#809C2×D314yescomplemented
104C22×C3⋊D3—22no—
105C22×C3×D3—24no—
106C22×C3×D3C2×D412yes—
107C2×D32—48no—
108C2×D32—48no—
109C2×D32—84no—
110C2×C32×C4—22no—
111C2×C32×C4C2411yescharacteristic
112C2×C3⋊Dic3C2×D411yescharacteristic
113C2×C3⋊Dic3C2×D411yescharacteristic
114C4⋊(C3⋊D3)—22no—
115C4⋊(C3⋊D3)C2×D414yescomplemented
116C4×C3⋊D3—44no—
117C2×C3×Dic3C2×D412yes—
118C3×D12—24no—
119C3×D12—24no—
120C3×D12—48no—
121C3×C4×D3—22no—
122C3×C4×D3—22no—
123#626—48no—
124#625—44no—
125#625—82no—
126#625D814yescomplemented
127C32×C8C2×D412yescomplemented
128C3⋊(C3⋊C8)—21no—
129C3×C3⋊C8—22no—
130C22×D8—92no—
131D42—92no—
132#493—91no—
133#466—32no—
134#459—92no—
135#447—94no—
136C4×D8—91no—
137C8×D4—91no—
138C23×D3—64no—
139C23×D3—64no—
140C2×C3×D4—34no—
141C2×C3×D4—64no—
142C22×C3×C4—32no—
143C2×#67—32no—
144C2×#67—64no—
145C2×#67—64no—
146C2×#67—64no—
147D3×D4—68no—
148D3×D4—124no—
149D3×D4—1216no—
150C2×D12—24no—
151C2×D12—34no—
152C2×D12—62no—
153C2×D12—68no—
154C2×D12—64no—
155C2×D12—124no—
156C2×D12C22×D314yes—
157C2×C4×D3—64no—
158C2×C4×D3—122no—
159C2×C4×D3C22×D312yes—
160C3×D8—64no—
161C2×C3×C8—21no—
162C2×C3×C8—32no—
163C2×C3×C8—64no—
164C2×C3×C8C22×D312yes—
165C3×C4⋊C4—22no—
166C3×C4⋊C4C22×D314yes—
167C3×C22⋊C4—64no—
168#217—32no—
169#213—68no—
170#213—124no—
171(C2×D3)⋊C4—24no—
172(C2×D3)⋊C4—32no—
173(C2×D3)⋊C4—64no—
174(C2×D3)⋊C4—122no—
175Dic3⋊C4—32no—
176C4×Dic3—32no—
177C4×Dic3—61no—
178C2×C3⋊C8—32no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8C22×D312yes—
181D24—24no—
182D24—38no—
183D24—64no—
184D24—68no—
185D3×C8—24no—
186C22×C32C22×D411yescharacteristic
187C2×C3⋊D3—24no—
188C2×C3⋊D3—42no—
189C2×C3⋊D3—42no—
190C2×C3×D3—22no—
191C2×C3×D3—22no—
192C2×C3×D3—44no—
193C2×C3×D3—44no—
194C2×C3×D3—44no—
195C2×C3×D3C2×D814yescomplemented
196D32—816no—
197C32×C4—42no—
198C32×C4C22×D411yescharacteristic
199C32×C4H(5,𝔽2)11yescharacteristic
200C3⋊Dic3—21no—
201C3⋊Dic3C2×D812yescomplemented
202C3×Dic3—22no—
203C22×D4—94no—
204C22×D4—182no—
205C2×D8—32no—
206C2×D8—94no—
207C2×D8—92no—
208C2×D8—91no—
209C2×D8—188no—
210C22×C8—32no—
211#127—92no—
212#121—34no—
213#121—182no—
214#120—184no—
215C4×D4—91no—
216C4×D4—92no—
217#107D3211yescharacteristic, complemented
218C4⋊C8—91no—
219#102—34no—
220#102—92no—
221C22⋊C8—92no—
222C4×C8—91no—
223C23×C3—32no—
224C23×C3—64no—
225C22×D3—24no—
226C22×D3—64no—
227C22×D3—122no—
228C22×D3—128no—
229C22×D3—128no—
230C22×D3—128no—
231C22×D3—128no—
232C22×D3—244no—
233C22×D3—244no—
234C22×D3D3×D412yes—
235C3×D4—64no—
236C3×D4—64no—
237C3×D4—128no—
238C2×C3×C4—24no—
239C2×C3×C4—21no—
240C2×C3×C4—32no—
241C2×C3×C4—42no—
242C2×C3×C4—62no—
243C2×C3×C4—62no—
244C2×C3×C4C23×D312yes—
245#67—38no—
246#67—128no—
247#67—128no—
248#67—244no—
249C2×Dic3—32no—
250C2×Dic3—32no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3D3×D412yes—
254D12—24no—
255D12—24no—
256D12—38no—
257D12—48no—
258D12—64no—
259D12—64no—
260D12—122no—
261D12—128no—
262C4×D3—22no—
263C4×D3—22no—
264C4×D3—128no—
265C4×D3—244no—
266C3×C8—22no—
267C3×C8—62no—
268C3×C8D3×D414yescomplemented
269C3⋊C8—22no—
270C3⋊C8—62no—
271C3⋊C8—121no—
272C2×C32D4211yescharacteristic
273C2×C32C22×D811yescharacteristic
274C2×C32#57611yescharacteristic
275C3⋊D3—44no—
276C3×D3—24no—
277C3×D3—84no—
278C24—184no—
279C2×D4—34no—
280C2×D4—64no—
281C2×D4—91no—
282C2×D4—92no—
283C2×D4—184no—
284C2×D4—188no—
285C2×D4—182no—
286C2×D4—182no—
287C2×D4—364no—
288C2×D4—368no—
289C22×C4—32no—
290C22×C4—182no—
291D8—64no—
292D8—94no—
293D8—188no—
294D8—362no—
295C2×C8—32no—
296C2×C8—64no—
297C2×C8—91no—
298C2×C8C2×D3211yescharacteristic
299C4⋊C4—91no—
300C4⋊C4C2×D3212yes—
301C22⋊C4—64no—
302C22⋊C4—92no—
303C22⋊C4—182no—
304C42—91no—
305C22×C3—21no—
306C22×C3—34no—
307C22×C3—62no—
308C22×C3—62no—
309C22×C3—124no—
310C22×C3—124no—
311C22×C3—124no—
312C22×C3C2×D3×D412yes—
313C2×D3—22no—
314C2×D3—22no—
315C2×D3—44no—
316C2×D3—44no—
317C2×D3—44no—
318C2×D3—68no—
319C2×D3—124no—
320C2×D3—124no—
321C2×D3—124no—
322C2×D3—242no—
323C2×D3—242no—
324C2×D3—2416no—
325C2×D3—2416no—
326C2×D3D3×D814yescomplemented
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—44no—
330C3×C4—62no—
331C3×C4—82no—
332C3×C4C2×D3×D412yes—
333C3×C4#100912yes—
334Dic3—22no—
335Dic3—34no—
336Dic3—62no—
337Dic3—62no—
338Dic3—121no—
339C32D4×D811yescharacteristic, complemented, Sylow
340C23—32no—
341C23—64no—
342C23—182no—
343C23—368no—
344C23—368no—
345C23—724no—
346D4—64no—
347D4—64no—
348D4—94no—
349D4—94no—
350D4—128no—
351D4—182no—
352D4—368no—
353D4—364no—
354D4—722no—
355C2×C4—22no—
356C2×C4—32no—
357C2×C4—62no—
358C2×C4—62no—
359C2×C4—91no—
360C2×C4—91no—
361C2×C4—364no—
362C2×C4C22×D3211yescharacteristic
363C8—62no—
364C8—181no—
365C8#380212yescomplemented
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—64no—
370C2×C3—244no—
371C2×C3#560912yes—
372C2×C3C2×D3×D812yes—
373C2×C3#576912yes—
374D3—24no—
375D3—84no—
376D3—128no—
377D3—244no—
378C22—34no—
379C22—62no—
380C22—62no—
381C22—124no—
382C22—124no—
383C22—124no—
384C22—184no—
385C22—362no—
386C22—362no—
387C22—7216no—
388C22D32×D411yescharacteristic
389C4—42no—
390C4—62no—
391C4—92no—
392C4—181no—
393C4C2×#380211yescharacteristic
394C4#6432011yescharacteristic
395C3—21no—
396C3#8072912yescomplemented
397C2—64no—
398C2—244no—
399C2—364no—
400C2#1059461811yescharacteristic
401C2D32×D811yescharacteristic
402C2#1059477111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×D3×D24C2semidirect
2. #10594618C2semidirect
3. #10592571C2semidirect
4. C3×#4883C2semidirect
5. #10590886C2semidirect
6. C8×#625C2semidirect
7. #10590595C2semidirect
8. #10590551C2semidirect
11. C2×D3×D12C22semidirect
13. #64102C22semidirect
14. C2×C3×D24C22semidirect
15. C2×C3×D3×C8C22semidirect
16. C3×#895C22semidirect
18. #63914C22semidirect
21. C2×#3714C22semidirect
22. C2×#3713C22semidirect
24. C32×#107C22semidirect
25. C8×C3⋊Dic3C22semidirect
26. #63636C22semidirect
27. C3×#809C22semidirect
28. #63572C22semidirect
29. (C2×D3)⋊(C3⋊C8)C22semidirect
37. #4883D3semidirect
60. #3745D4semidirect
86. C2×D24C2×D3semidirect
87. C2×D3×C8C2×D3semidirect
88. #895C2×D3semidirect
94. C3×#107C2×D3semidirect
103. #809C2×D3semidirect
115. C4⋊(C3⋊D3)C2×D4semidirect
126. #625D8semidirect
127. C32×C8C2×D4semidirect
195. C2×C3×D3C2×D8semidirect
201. C3⋊Dic3C2×D8semidirect
217. #107D32semidirect
268. C3×C8D3×D4semidirect
326. C2×D3D3×D8semidirect
339. C32D4×D8semidirect
365. C8#3802semidirect
396. C3#80729semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D242
#105946182
#105925712
C3×#48832
#105908862
C8×#6252
#105905952
#105905512
#807293