Finite Group Databasebeta

← #11901956

Subgroups — #11901956

Order 1152.

2157 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C3×#5470C212yesmaximal, complemented
3#10595050C212yesmaximal, complemented
4#10594981C214yesmaximal
5#10594969C212yesmaximal
6#10594813C214yesmaximal, complemented
7#10593935C218yesmaximal, complemented
8#10593855C218yesmaximal, complemented
9#86274—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3752C2212yes—
13C2×#3750C2212yes—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64081C2214yes—
16#64081C2214yes—
17C3×#926C2214yes—
18C3×#924C2218yes—
19C3×#870C2214yescomplemented
20C3×#869C2214yescomplemented
21C3×C4×Dic6C2218yescomplemented
22#63982C2218yes—
23#63974C2214yes—
24#63957C2214yes—
25#63919C2214yescomplemented
26C4×#627C2218yescomplemented
27#63900C2214yes—
28#63895C22116yes—
29#63888C22116yes—
30C4×#624C2214yes—
31#63874C2214yes—
32#63872C2214yescomplemented
33#63849C2214yes—
34#63847C22116yescomplemented
35#63839C22116yescomplemented
36C3×#533—32no—
37#5729—38no—
38#5689—38no—
39#5634—38no—
40#5623—38no—
41#5578—316no—
42D3×#117—34no—
43#5517—34no—
44C2×#872—32no—
45C2×#872—61no—
46#5470D312yescomplemented
47C23×C3⋊D3C2311yescharacteristic
48C22×C32×C4C2312yes—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2311yescharacteristic
52C2×C4×C3⋊D3Q818yescomplemented
53C2×C4×C3⋊D3C2312yes—
54C2×C4×C3⋊D3C2312yes—
55C2×C3×Dic6C2318yes—
56C2×#627C2318yes—
57C2×#624C2318yes—
58C32×C42C2312yes—
59C32×C42C2312yes—
60#3752C2318yes—
61#3750C2318yes—
62C4×C3⋊Dic3C2312yes—
63C4×C3⋊Dic3C2312yes—
64C3×#217C2318yes—
65C3×C4⋊Dic3C2318yes—
66C3×C4⋊Dic3C2318yes—
67C3×Dic3⋊C4C23116yes—
68C3×C4×Dic3C2318yes—
69#3724C2318yes—
70#3724C2318yes—
71Dic3⋊Dic3C23116yes—
72#3722C2318yes—
73Dic32C2318yes—
74#3458—91noSylow
75C22×C4×D3—32no—
76C22×C4×D3—61no—
77C3×C4⋊Q8—34no—
78C3×#125—34no—
79C3×C22⋊Q8—38no—
80C3×C4×Q8—38no—
81C3×#117—34no—
82C2×C3×C42—21no—
83C2×C3×C42C2×D312yes—
84#946—316no—
85#944—316no—
86C2×(C2×D3)⋊C4—34no—
87C2×(C2×D3)⋊C4—62no—
88#926C2×D314yes—
89#924C2×D318yes—
90C2×Dic3⋊C4—34no—
91C2×Dic3⋊C4—62no—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—61no—
94#897—316no—
95#896—316no—
96#896—316no—
97#892—38no—
98D3×C4⋊C4—38no—
99#890—38no—
100#889—316no—
101#889—316no—
102#888—316no—
103#888—38no—
104D3×C22⋊C4—38no—
105#878—316no—
106#877—38no—
107#872—34no—
108#872—34no—
109#872—38no—
110#872—38no—
111#872—64no—
112#872—64no—
113C42×D3—38no—
114#870C2×D314yescomplemented
115#869C2×D314yescomplemented
116C4×Dic6—316no—
117C4×Dic6C2×D318yescomplemented
118C23×C32C2411yescharacteristic
119C22×C3⋊D3—42no—
120C22×C3⋊D3C2×Q814yes—
121C22×C3⋊D3C2412yes—
122C2×C32×C4—42no—
123C2×C32×C4C2×Q814yes—
124C2×C32×C4C2414yes—
125C2×C32×C4C2411yescharacteristic
126C2×C32×C4C2411yescharacteristic
127C2×C3⋊Dic3—42no—
128C2×C3⋊Dic3C2×Q814yes—
129C2×C3⋊Dic3C2414yes—
130C2×C3⋊Dic3C2412yes—
131C4×C3⋊D3C2×Q818yes—
132C4×C3⋊D3C2×Q818yes—
133C2×C3×Dic3C24116yes—
134C3×Dic6—48no—
135#627—48no—
136#624—48no—
137#544—94no—
138#544—98no—
139#543—94no—
140#533—32no—
141#533—92no—
142#533—98no—
143C2×#117—92no—
144C2×#117—91no—
145C23×D3—32no—
146C23×D3—61no—
147C2×C3×Q8—38no—
148C22×C3×C4—21no—
149C22×C3×C4—22no—
150C22×C3×C4C22×D314yes—
151C22×C3×C4C22×D312yes—
152C22×Dic3—32no—
153C22×Dic3—34no—
154C22×Dic3—61no—
155C22×Dic3—62no—
156C2×C4×D3—316no—
157C2×C4×D3—34no—
158C2×C4×D3—34no—
159C2×C4×D3—316no—
160C2×C4×D3—62no—
161C2×C4×D3—62no—
162C2×C4×D3—68no—
163C2×Dic6—316no—
164C2×Dic6C22×D318yes—
165C3×C4⋊C4—316no—
166C3×C4⋊C4—38no—
167C3×C4⋊C4—38no—
168C3×C22⋊C4—38no—
169C3×C42—22no—
170C3×C42—22no—
171C3×C42—38no—
172C3×C42C22×D314yes—
173C3×C42C22×D312yes—
174C3×C42C22×D312yes—
175#217C22×D318yes—
176(C2×D3)⋊C4—38no—
177(C2×D3)⋊C4—38no—
178(C2×D3)⋊C4—316no—
179(C2×D3)⋊C4—68no—
180C4⋊Dic3—316no—
181C4⋊Dic3C22×D318yes—
182C4⋊Dic3C22×D318yes—
183Dic3⋊C4—38no—
184Dic3⋊C4—38no—
185Dic3⋊C4—316no—
186Dic3⋊C4—316no—
187Dic3⋊C4—316no—
188Dic3⋊C4—68no—
189Dic3⋊C4C22×D3116yes—
190C4×Dic3—34no—
191C4×Dic3—34no—
192C4×Dic3—316no—
193C4×Dic3—62no—
194C4×Dic3—62no—
195C4×Dic3C22×D318yes—
196C22×C32—22no—
197C22×C32C22×Q812yes—
198C22×C32C2511yescharacteristic
199C2×C3⋊D3—24no—
200C2×C3⋊D3—44no—
201C2×C3⋊D3C22×Q814yes—
202C32×C4—24no—
203C32×C4C22×Q812yes—
204C32×C4C22×Q812yes—
205C3⋊Dic3—24no—
206C3⋊Dic3C22×Q814yes—
207C3×Dic3—216no—
208C23×C4—91no—
209C4⋊Q8—34no—
210C4⋊Q8—94no—
211C4⋊Q8—916no—
212#125—34no—
213#125—916no—
214#125—94no—
215C22⋊Q8—38no—
216C22⋊Q8—98no—
217C22⋊Q8—916no—
218C22⋊Q8—916no—
219C4×Q8—38no—
220C4×Q8—98no—
221#117—34no—
222#117—94no—
223#117—94no—
224#117—94no—
225#117—94no—
226#117—94no—
227C2×C4⋊C4—94no—
228C2×C4⋊C4—92no—
229C2×C22⋊C4—94no—
230C2×C22⋊C4—92no—
231C2×C42—94no—
232C2×C42—91no—
233C2×C42D3211yescharacteristic
234C23×C3—21no—
235C23×C3C23×D312yes—
236C22×D3—34no—
237C22×D3—38no—
238C22×D3—64no—
239C22×D3—62no—
240C22×D3—124no—
241C22×D3—124no—
242C3×Q8—128no—
243C2×C3×C4—21no—
244C2×C3×C4—24no—
245C2×C3×C4—21no—
246C2×C3×C4—24no—
247C2×C3×C4—316no—
248C2×C3×C4—44no—
249C2×C3×C4—44no—
250C2×C3×C4D3×Q818yes—
251C2×C3×C4C23×D314yes—
252C2×C3×C4C23×D314yes—
253C2×C3×C4C23×D312yes—
254C2×C3×C4C23×D312yes—
255C2×Dic3—38no—
256C2×Dic3—34no—
257C2×Dic3—38no—
258C2×Dic3—64no—
259C2×Dic3—62no—
260C2×Dic3—64no—
261C2×Dic3—124no—
262C2×Dic3—124no—
263C2×Dic3C23×D3116yes—
264C4×D3—316no—
265C4×D3—316no—
266C4×D3—68no—
267C4×D3—68no—
268C4×D3—1216no—
269Dic6—48no—
270Dic6—1216no—
271C2×C32—22no—
272C2×C32C23×Q811yescharacteristic
273C2×C32#58512yes—
274C3⋊D3—24no—
275C24—91no—
276C2×Q8—38no—
277C2×Q8—98no—
278C22×C4—98no—
279C22×C4—91no—
280C22×C4—92no—
281C22×C4—92no—
282C22×C4—98no—
283C22×C4—92no—
284C22×C4C2×D3212yes—
285C22×C4C2×D3211yescharacteristic
286C4⋊C4—38no—
287C4⋊C4—316no—
288C4⋊C4—38no—
289C4⋊C4—98no—
290C4⋊C4—98no—
291C4⋊C4—916no—
292C4⋊C4—98no—
293C22⋊C4—38no—
294C22⋊C4—98no—
295C22⋊C4—98no—
296C42—38no—
297C42—98no—
298C42—92no—
299C42—92no—
300C42C2×D3212yes—
301C42C2×D3212yes—
302C22×C3—24no—
303C22×C3—24no—
304C22×C3—22no—
305C22×C3—21no—
306C22×C3C2×D3×Q814yes—
307C22×C3C24×D312yes—
308C2×D3—38no—
309C2×D3—64no—
310C2×D3—68no—
311C2×D3—124no—
312C2×D3—128no—
313C2×D3—128no—
314C3×C4—24no—
315C3×C4—24no—
316C3×C4—22no—
317C3×C4—22no—
318C3×C4—44no—
319C3×C4—616no—
320C3×C4C2×D3×Q814yes—
321C3×C4C2×D3×Q814yes—
322Dic3—216no—
323Dic3—38no—
324Dic3—64no—
325Dic3—68no—
326Dic3—124no—
327C32#345811yescharacteristic, complemented, Sylow
328C23—92no—
329C23—94no—
330C23—362no—
331C23C22×D3211yescharacteristic
332Q8—128no—
333Q8—368no—
334C2×C4—316no—
335C2×C4—42no—
336C2×C4—94no—
337C2×C4—92no—
338C2×C4—98no—
339C2×C4—98no—
340C2×C4—94no—
341C2×C4—368no—
342C2×C4—362no—
343C2×C4#379714yes—
344C2×C4C22×D3214yes—
345C2×C4C22×D3211yescharacteristic
346C2×C4C22×D3211yescharacteristic
347C2×C3—24no—
348C2×C3—24no—
349C2×C3—21no—
350C2×C3—22no—
351C2×C3C22×D3×Q812yes—
352C2×C3#596414yes—
353D3—68no—
354D3—124no—
355C22—22no—
356C22—94no—
357C22—184no—
358C22—364no—
359C22C2×#379712yes—
360C22C23×D3211yescharacteristic
361C4—24no—
362C4—616no—
363C4—94no—
364C4—184no—
365C4C2×#379712yes—
366C4C2×#379712yes—
367C3—21no—
368C3#8627412yescomplemented
369C2—22no—
370C2—184no—
371C2C22×#379711yescharacteristic
372C2#1059666912yes—
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#3458
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#5470C2semidirect
3. #10595050C2semidirect
6. #10594813C2semidirect
7. #10593935C2semidirect
8. #10593855C2semidirect
19. C3×#870C22semidirect
20. C3×#869C22semidirect
21. C3×C4×Dic6C22semidirect
25. #63919C22semidirect
26. C4×#627C22semidirect
32. #63872C22semidirect
34. #63847C22semidirect
35. #63839C22semidirect
46. #5470D3semidirect
52. C2×C4×C3⋊D3Q8semidirect
114. #870C2×D3semidirect
115. #869C2×D3semidirect
117. C4×Dic6C2×D3semidirect
327. C32#3458semidirect
368. C3#86274semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C3×#54702
#105950502
#105949812
#105949692
#105948132
#105939352
#105938552
#862743