Finite Group Databasebeta

← #11873539

Subgroups — #11873539

Order 1152.

945 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 945 conjugacy classes of subgroups — too many to draw. Only its 164 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
1#10594009C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic, complemented
3C3⋊D3×#97C211yesmaximal, characteristic, complemented
4C3×#4714C212yesmaximal, complemented
5#10590940C212yesmaximal
6#10590866C214yesmaximal, complemented
7#10590672C212yesmaximal, complemented
8#10590280C212yesmaximal, complemented
9D3×#489—32nomaximal
10C2×#3802C2211yescharacteristic
11C2×#3797—21no—
12C2×#3797C2211yescharacteristic
13C2×C8×C3⋊D3C2212yes—
14C42×C3⋊D3C2211yescharacteristic
15C3×#875C2212yes—
16C3×#869C2212yescomplemented
17#63921—21no—
18#63921—21no—
19#63919—21no—
20#63919C2212yescomplemented
21#63915—21no—
22#63915—21no—
23#63900—21no—
24#63900C2212yes—
25#63873—21no—
26#63863C2212yes—
27C32×#97C2211yescharacteristic, complemented
28#63642C2212yescomplemented
29#63630C2211yescharacteristic, complemented
30C3×#821C2214yes—
31C3×#816C2214yescomplemented
32#63565C2214yescomplemented
33#63562C2214yes—
34D3×C4⋊Q8—32no—
35D3×#124—32no—
36C3×#489—32no—
37#5089—32no—
38#5055—32no—
39D3×#103—34no—
40#4794—34no—
41D3×#102—34no—
42#4765—34no—
43#4714D312yescomplemented
44D3×#97—32no—
45D3×#97—61no—
46C22×D32—21no—
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3C2311yescharacteristic
50C2×C3×D12C2312yes—
51C2×C3×Dic6—22no—
52C2×C3×Dic6C2312yes—
53C2×#627—22no—
54C2×#627—21no—
55C2×#625—21no—
56C2×#624—22no—
57C2×#624—21no—
58#3802—24no—
59#3797—24no—
60#3797—44no—
61C2×C32×C8C2312yes—
62C32×C42C2311yescharacteristic
63C4×C3⋊Dic3D411yescharacteristic
64C4×C3⋊Dic3D411yescharacteristic
65C4×C3⋊Dic3C2311yescharacteristic
66C2×C3⋊(C3⋊C8)C2312yes—
67C8×C3⋊D3—24no—
68C3×(C2×D3)⋊C4—22no—
69C3×(C2×D3)⋊C4—22no—
70C3×C4⋊Dic3—22no—
71C3×C4⋊Dic3C2314yes—
72#3724—22no—
73#3724—22no—
74(C2×D3)⋊Dic3—22no—
75(C2×D3)⋊Dic3—22no—
76C2×#489—91noSylow
77C2×D3×Q8—32no—
78C2×D3×Q8—62no—
79C2×D3×D4—32no—
80C3×C4⋊Q8—32no—
81C3×#124—32no—
82#947—32no—
83#944—62no—
84#936—32no—
85C2×D3×C8—34no—
86C2×D3×C8—62no—
87D3×C4⋊C4—34no—
88D3×C4⋊C4—62no—
89#888—34no—
90#888—62no—
91#885—62no—
92#885—62no—
93D3×C22⋊C4—62no—
94D3×C22⋊C4—62no—
95#875C2×D312yes—
96C42×D3—32no—
97C42×D3—61no—
98#869C2×D312yescomplemented
99C3×#103—34no—
100C3×#102—34no—
101C3×#97—21no—
102C3×#97C2×D312yescomplemented
103#835—34no—
104#832—34no—
105#821C2×D314yes—
106#816C2×D314yescomplemented
107#815—34no—
108#815—62no—
109#810—34no—
110#809—34no—
111#803—32no—
112#803—61no—
113C22×C3⋊D3C2×D411yescharacteristic
114C22×C3×D3—22no—
115C2×D32—42no—
116C2×D32—42no—
117C2×D32—42no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2411yescharacteristic
121C2×C3⋊Dic3C2×D411yescharacteristic
122C2×C3⋊Dic3C2×D411yescharacteristic
123C2×C3⋊Dic3C2×D411yescharacteristic
124C4×C3⋊D3—22no—
125C4×C3⋊D3—22no—
126C4×C3⋊D3#4114yes—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—24no—
129C3×D12—24no—
130C3×Dic6—24no—
131C3×Dic6—44no—
132#627—44no—
133#627—42no—
134#625—42no—
135#624—42no—
136#624—44no—
137C32×C8—22no—
138C3⋊(C3⋊C8)—22no—
139C2×C4⋊Q8—91no—
140C2×#124—91no—
141#489—32no—
142#489—94no—
143#489—92no—
144C2×#103—92no—
145C2×#102—92no—
146C2×#97—91no—
147C23×D3—62no—
148C2×C3×Q8—32no—
149C2×C3×Q8—62no—
150C2×C3×D4—32no—
151C2×#67—62no—
152D3×Q8—68no—
153D3×Q8—128no—
154D3×D4—68no—
155C2×D12C22×D312yes—
156C2×C4×D3—32no—
157C2×C4×D3—32no—
158C2×C4×D3—32no—
159C2×C4×D3—61no—
160C2×C4×D3—61no—
161C2×C4×D3—61no—
162C2×C4×D3—62no—
163C2×C4×D3—64no—
164C2×Dic6—22no—
165C2×Dic6—62no—
166C2×Dic6—64no—
167C2×Dic6C22×D312yes—
168C2×C3×C8—22no—
169C2×C3×C8C22×D314yes—
170C3×C4⋊C4—34no—
171C3×C4⋊C4—62no—
172C3×C22⋊C4—62no—
173C3×C22⋊C4—62no—
174C3×C42—21no—
175C3×C42C22×D312yes—
176#217—62no—
177#217—62no—
178(C2×D3)⋊C4—22no—
179(C2×D3)⋊C4—22no—
180(C2×D3)⋊C4—62no—
181(C2×D3)⋊C4—62no—
182C4⋊Dic3—22no—
183C4⋊Dic3C22×D314yes—
184Dic3⋊C4—64no—
185Dic3⋊C4—64no—
186C4×Dic3—32no—
187C4×Dic3—32no—
188C4×Dic3—32no—
189C4×Dic3—61no—
190C4×Dic3—61no—
191C4×Dic3—61no—
192C2×C3⋊C8—34no—
193C2×C3⋊C8—62no—
194D3×C8—68no—
195D3×C8—68no—
196C22×C32C22×D411yescharacteristic
197C2×C3⋊D3#12412yes—
198C2×C3⋊D3AGL(1,ℤ/8)12yes—
199C2×C3⋊D3#13712yes—
200C2×C3×D3—42no—
201C2×C3×D3—42no—
202C2×C3×D3—42no—
203D32—84no—
204C32×C4—21no—
205C32×C4—21no—
206C32×C4C2×#4112yes—
207C3⋊Dic3—21no—
208C3⋊Dic3—21no—
209C3⋊Dic3#12412yes—
210C3×Dic3—42no—
211C3×Dic3—44no—
212C22×Q8—91no—
213C22×Q8—181no—
214C22×D4—91no—
215C22×C8—92no—
216C4⋊Q8—32no—
217C4⋊Q8—92no—
218C4⋊Q8—181no—
219C4⋊Q8—181no—
220#124—32no—
221#124—92no—
222#124—181no—
223#124—181no—
224C2×C4⋊C4—92no—
225C2×C4⋊C4—181no—
226C2×C22⋊C4—181no—
227C2×C22⋊C4—181no—
228C2×C42—91no—
229#103—34no—
230#103—94no—
231#102—34no—
232#102—94no—
233#97—92no—
234#97—91no—
235#97D3211yescharacteristic, complemented
236C23×C3—62no—
237C22×D3—22no—
238C22×D3—32no—
239C22×D3—61no—
240C22×D3—124no—
241C22×D3—124no—
242C22×D3—124no—
243C3×Q8—64no—
244C3×Q8—124no—
245C3×D4—64no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—64no—
250C2×C3×C4—62no—
251C2×C3×C4D3×D412yes—
252C2×C3×C4D3×D412yes—
253C2×C3×C4C23×D312yes—
254#67—124no—
255C2×Dic3—24no—
256C2×Dic3—22no—
257C2×Dic3—32no—
258C2×Dic3—32no—
259C2×Dic3—32no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263D12—24no—
264C4×D3—38no—
265C4×D3—64no—
266C4×D3—64no—
267C4×D3—64no—
268C4×D3—122no—
269C4×D3—122no—
270C4×D3—124no—
271C4×D3—128no—
272Dic6—24no—
273Dic6—44no—
274Dic6—124no—
275Dic6—128no—
276C3×C8—24no—
277C3×C8—24no—
278C3⋊C8—64no—
279C3⋊C8—64no—
280C2×C32C2×#12411yescharacteristic
281C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
282C2×C32C2×#13711yescharacteristic
283C3⋊D3#48914yescomplemented
284C3×D3—82no—
285C24—181no—
286C2×Q8—32no—
287C2×Q8—62no—
288C2×Q8—181no—
289C2×Q8—182no—
290C2×Q8—184no—
291C2×Q8—364no—
292C2×D4—32no—
293C2×D4—184no—
294C2×D4—181no—
295C22×C4—91no—
296C22×C4—91no—
297C22×C4—91no—
298C22×C4—181no—
299C22×C4—182no—
300C2×C8—92no—
301C2×C8—184no—
302C2×C8C2×D3212yes—
303C4⋊C4—34no—
304C4⋊C4—62no—
305C4⋊C4—182no—
306C4⋊C4—182no—
307C22⋊C4—62no—
308C22⋊C4—62no—
309C22⋊C4—182no—
310C22⋊C4—182no—
311C42—91no—
312C42—91no—
313C42—91no—
314C42C2×D3211yescharacteristic
315C22×C3—21no—
316C22×C3—122no—
317C22×C3—122no—
318C22×C3—122no—
319C22×C3C2×D3×D412yes—
320C2×D3—34no—
321C2×D3—34no—
322C2×D3—34no—
323C2×D3—42no—
324C2×D3—42no—
325C2×D3—42no—
326C2×D3—62no—
327C2×D3—62no—
328C2×D3—62no—
329C2×D3—248no—
330C3×C4—22no—
331C3×C4—22no—
332C3×C4—22no—
333C3×C4—41no—
334C3×C4—41no—
335C3×C4—122no—
336C3×C4—124no—
337C3×C4D3×#4114yes—
338Dic3—34no—
339Dic3—42no—
340Dic3—44no—
341Dic3—62no—
342Dic3—62no—
343Dic3—62no—
344Dic3—121no—
345Dic3—121no—
346C32C2×#48911yescharacteristic, complemented, Sylow
347C23—62no—
348C23—91no—
349C23—362no—
350C23—362no—
351C23—362no—
352Q8—64no—
353Q8—124no—
354Q8—362no—
355Q8—364no—
356D4—64no—
357D4—362no—
358C2×C4—62no—
359C2×C4—64no—
360C2×C4—91no—
361C2×C4—94no—
362C2×C4—91no—
363C2×C4—91no—
364C2×C4—182no—
365C2×C4—182no—
366C2×C4—362no—
367C2×C4—364no—
368C2×C4#380211yescharacteristic
369C2×C4#380211yescharacteristic
370C2×C4C22×D3211yescharacteristic
371C8—22no—
372C8—182no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—242no—
377C2×C3D3×#12412yes—
378C2×C3D3×AGL(1,ℤ/8)12yes—
379C2×C3D3×#13712yes—
380D3—38no—
381D3—64no—
382D3—82no—
383C22—92no—
384C22—92no—
385C22—92no—
386C22—122no—
387C22—122no—
388C22—122no—
389C22—724no—
390C22C2×#380211yescharacteristic
391C4—21no—
392C4—21no—
393C4—92no—
394C4—124no—
395C4—122no—
396C4—181no—
397C4—181no—
398C4#6430612yes—
399C3—21no—
400C3D3×#48912yescomplemented
401C2—94no—
402C2—242no—
403C2#1059400911yescharacteristic
404C2#1059471611yescharacteristic
405C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenter#97D32
hypocenterC32C2×#489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10593909C2semidirect
3. C3⋊D3×#97C2semidirect
4. C3×#4714C2semidirect
6. #10590866C2semidirect
7. #10590672C2semidirect
8. #10590280C2semidirect
16. C3×#869C22semidirect
20. #63919C22semidirect
27. C32×#97C22semidirect
28. #63642C22semidirect
29. #63630C22semidirect
31. C3×#816C22semidirect
32. #63565C22semidirect
43. #4714D3semidirect
98. #869C2×D3semidirect
102. C3×#97C2×D3semidirect
106. #816C2×D3semidirect
235. #97D32semidirect
283. C3⋊D3#489semidirect
346. C32C2×#489semidirect
400. C3D3×#489semidirect

Maximal subgroups

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

subgroupindex
#105940092
#105939092
C3⋊D3×#972
C3×#47142
#105909402
#105908662
#105906722
#105902802
D3×#4893