Finite Group Databasebeta

← #11878868

Subgroups — #11878868

Order 1152.

1035 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 1035 conjugacy classes of subgroups — too many to draw. Only its 166 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#10594008C211yesmaximal, characteristic
2#10593882C211yesmaximal, characteristic, complemented
3#10592532C211yesmaximal, characteristic, complemented
4C3×#4848C212yesmaximal, complemented
5#10590943C214yesmaximal, complemented
6#10590885C212yesmaximal, complemented
7#10590884C212yesmaximal, complemented
8#10590364C212yesmaximal, complemented
9#80387—32nomaximal
10C2×#3802—21no—
11C2×#3802—21no—
12C2×#3802C2212yes—
13C42×C3⋊D3C2211yescharacteristic
14C2×C3×#204C2214yescomplemented
15C3×#874C2212yes—
16C3×C4×Dic6C2212yescomplemented
17#63919C2211yescharacteristic, complemented
18C4×#627—21no—
19#63914—21no—
20#63914—21no—
21#63914C2212yes—
22#63874—21no—
23#63873C2211yescharacteristic, complemented
24#63871C2212yes—
25#63870—21no—
26#63865—21no—
27C2×#3715C2214yescomplemented
28C32×C4⋊C8C2211yescharacteristic, complemented
29#63647C2212yes—
30C8×C3⋊Dic3C2212yescomplemented
31C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
32C3×#821C2214yescomplemented
33#63562C2214yescomplemented
34D3×#127—32no—
35#5578—32no—
36C3×#460—32no—
37#5175—34no—
38#5169—34no—
39#5075—32no—
40#5027—32no—
41#4848D312yescomplemented
42#4833—32no—
43#4833—61no—
44#4776—34no—
45#4760—34no—
46C22×D32—22no—
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3C2311yescharacteristic
50C2×C3×D12—22no—
51C2×C3×D12—22no—
52C2×C3×D12C2314yes—
53C2×C3×Dic6C2312yes—
54C2×#627—21no—
55C2×#625—22no—
56C2×#625—22no—
57C2×#625—22no—
58#3802—42no—
59#3802—42no—
60#3802—44no—
61#3802—44no—
62C2×C32×C8C2312yes—
63C32×C42C2311yescharacteristic
64C4×C3⋊Dic3D411yescharacteristic
65C4×C3⋊Dic3D411yescharacteristic
66C4×C3⋊Dic3C2311yescharacteristic
67C2×C3⋊(C3⋊C8)C2312yes—
68C3×C4⋊Dic3C2312yes—
69C3×Dic3⋊C4—22no—
70C3×C4×Dic3—22no—
71C3×#204—44no—
72#3724—21no—
73#3724—21no—
74#3724—21no—
75Dic3⋊Dic3—22no—
76#3722—22no—
77#3715—44no—
78#3208—91noSylow
79C2×D3×D4—34no—
80C2×D3×D4—62no—
81C2×D3×D4—62no—
82C2×C3×SD16—34no—
83C3×#127—32no—
84C3×C4×Q8—32no—
85#946—32no—
86#944—32no—
87C2×#215—34no—
88#940—34no—
89#940—62no—
90#940—62no—
91C2×#214—34no—
92C2×#204C2×D314yescomplemented
93#897—32no—
94#896—62no—
95#889—62no—
96#888—32no—
97#874C2×D312yes—
98#872—62no—
99C42×D3—32no—
100C42×D3—61no—
101C4×Dic6—62no—
102C4×Dic6C2×D312yescomplemented
103C3×C4⋊C8—21no—
104C3×C4⋊C8C2×D312yescomplemented
105C3×#102—34no—
106#832—34no—
107#821C2×D314yescomplemented
108(C2×D3)⋊C8—34no—
109(C2×D3)⋊C8—62no—
110C8×Dic3—34no—
111C8×Dic3—62no—
112#809—34no—
113C4⋊(C3⋊C8)—32no—
114C4⋊(C3⋊C8)—61no—
115C22×C3⋊D3C2×D411yescharacteristic
116C22×C3×D3—24no—
117C2×D32—44no—
118C2×D32—44no—
119C2×D32—44no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2411yescharacteristic
123C2×C3⋊Dic3C2×D411yescharacteristic
124C2×C3⋊Dic3C2×D411yescharacteristic
125C2×C3⋊Dic3C2×D411yescharacteristic
126C4×C3⋊D3—21no—
127C4×C3⋊D3—21no—
128C4×C3⋊D3—22no—
129C4×C3⋊D3SD1614yescomplemented
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C3×D12—24no—
133C3×D12—24no—
134C3×D12—44no—
135C3×D12—44no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138#627—42no—
139#625—44no—
140#625—44no—
141#625—44no—
142C32×C8—22no—
143C3⋊(C3⋊C8)—22no—
144#533—91no—
145C2×#127—91no—
146#492—92no—
147#486—92no—
148#460—32no—
149#460—92no—
150#450—94no—
151#431—91no—
152C23×D3—64no—
153C2×C3×Q8—32no—
154C2×C3×D4—34no—
155C2×C3×D4—62no—
156C2×C3×D4—62no—
157C2×#67—64no—
158C2×#67—64no—
159C2×#67—64no—
160D3×D4—128no—
161D3×D4—124no—
162D3×D4—124no—
163D3×D4—128no—
164C2×D12—22no—
165C2×D12—22no—
166C2×D12C22×D314yes—
167C2×C4×D3—32no—
168C2×C4×D3—32no—
169C2×C4×D3—32no—
170C2×C4×D3—61no—
171C2×C4×D3—61no—
172C2×C4×D3—61no—
173C2×Dic6—62no—
174C2×Dic6C22×D312yes—
175C3×SD16—124no—
176C2×C3×C8—22no—
177C2×C3×C8C22×D314yes—
178C3×C4⋊C4—32no—
179C3×C4⋊C4—62no—
180C3×C42—21no—
181C3×C42—62no—
182C3×C42C22×D312yes—
183#215—124no—
184#214—124no—
185(C2×D3)⋊C4—62no—
186(C2×D3)⋊C4—62no—
187C4⋊Dic3—62no—
188C4⋊Dic3C22×D312yes—
189Dic3⋊C4—22no—
190Dic3⋊C4—62no—
191Dic3⋊C4—62no—
192Dic3⋊C4—62no—
193Dic3⋊C4—62no—
194C4×Dic3—22no—
195C4×Dic3—32no—
196C4×Dic3—32no—
197C4×Dic3—32no—
198C4×Dic3—61no—
199C4×Dic3—61no—
200C4×Dic3—61no—
201C2×C3⋊C8—34no—
202C2×C3⋊C8—62no—
203#204—44no—
204C22×C32C22×D411yescharacteristic
205C2×C3⋊D3—21no—
206C2×C3⋊D3—21no—
207C2×C3⋊D3C2×SD1612yes—
208C2×C3×D3—44no—
209C2×C3×D3—44no—
210C2×C3×D3—44no—
211D32—88no—
212C32×C4—21no—
213C32×C4C2×SD1612yes—
214C32×C4H(5,𝔽2)11yescharacteristic
215C32×C4H(5,𝔽2)11yescharacteristic
216C3⋊Dic3—21no—
217C3⋊Dic3C2×SD1612yes—
218C3⋊Dic3AGL(1,ℤ/8)12yes—
219C3×Dic3—42no—
220C3×Dic3—42no—
221C22×D4—92no—
222C22×D4—181no—
223C22×D4—181no—
224C2×SD16—34no—
225C2×SD16—94no—
226C4⋊Q8—91no—
227C4⋊Q8—91no—
228#127—32no—
229#127—92no—
230#127—181no—
231#127—181no—
232#125—181no—
233C22⋊Q8—92no—
234C22⋊Q8—181no—
235C4×Q8—32no—
236C4×Q8—181no—
237#117—181no—
238C2×C42—91no—
239C4⋊C8—91no—
240C4⋊C8D3211yescharacteristic, complemented
241#102—34no—
242#102—94no—
243C22⋊C8—92no—
244C4×C8—92no—
245C23×C3—64no—
246C22×D3—24no—
247C22×D3—32no—
248C22×D3—61no—
249C22×D3—128no—
250C22×D3—128no—
251C22×D3—128no—
252C3×Q8—62no—
253C3×Q8—62no—
254C3×D4—64no—
255C3×D4—64no—
256C3×D4—124no—
257C3×D4—124no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—62no—
262C2×C3×C4—62no—
263C2×C3×C4D3×D412yes—
264C2×C3×C4D3×D412yes—
265C2×C3×C4C23×D312yes—
266#67—128no—
267#67—128no—
268#67—128no—
269C2×Dic3—22no—
270C2×Dic3—22no—
271C2×Dic3—32no—
272C2×Dic3—32no—
273C2×Dic3—32no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277D12—24no—
278D12—24no—
279D12—44no—
280D12—44no—
281C4×D3—38no—
282C4×D3—64no—
283C4×D3—64no—
284C4×D3—62no—
285C4×D3—62no—
286C4×D3—122no—
287C4×D3—121no—
288C4×D3—121no—
289Dic6—22no—
290Dic6—22no—
291Dic6—124no—
292C3×C8—24no—
293C3×C8—42no—
294C3⋊C8—64no—
295C3⋊C8—122no—
296C2×C32#53511yescharacteristic
297C2×C32C22×SD1611yescharacteristic
298C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
299C3⋊D3—22no—
300C3×D3—84no—
301C24—182no—
302C2×Q8—32no—
303C2×Q8—181no—
304C2×D4—34no—
305C2×D4—62no—
306C2×D4—62no—
307C2×D4—182no—
308C2×D4—182no—
309C2×D4—182no—
310C2×D4—364no—
311C2×D4—362no—
312C2×D4—362no—
313C2×D4—364no—
314C22×C4—91no—
315C22×C4—91no—
316C22×C4—91no—
317SD16—124no—
318SD16—364no—
319C2×C8—92no—
320C2×C8C2×D3212yes—
321C4⋊C4—32no—
322C4⋊C4—62no—
323C4⋊C4—181no—
324C4⋊C4—181no—
325C4⋊C4—182no—
326C4⋊C4—181no—
327C22⋊C4—182no—
328C42—62no—
329C42—91no—
330C42—91no—
331C42—91no—
332C42C2×D3211yescharacteristic
333C22×C3—21no—
334C22×C3—124no—
335C22×C3—124no—
336C22×C3—124no—
337C22×C3C2×D3×D412yes—
338C2×D3—34no—
339C2×D3—44no—
340C2×D3—44no—
341C2×D3—44no—
342C2×D3—62no—
343C2×D3—62no—
344C2×D3—62no—
345C2×D3—121no—
346C2×D3—121no—
347C2×D3—2416no—
348C3×C4—22no—
349C3×C4—22no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—122no—
354C3×C4—122no—
355C3×C4D3×SD1614yes—
356C3×C4#100412yes—
357C3×C4#100912yes—
358Dic3—34no—
359Dic3—34no—
360Dic3—42no—
361Dic3—42no—
362Dic3—62no—
363Dic3—62no—
364Dic3—62no—
365Dic3—121no—
366C32#320811yescharacteristic, complemented, Sylow
367C23—64no—
368C23—91no—
369C23—364no—
370C23—364no—
371C23—364no—
372Q8—62no—
373Q8—62no—
374Q8—362no—
375D4—64no—
376D4—64no—
377D4—124no—
378D4—124no—
379D4—364no—
380D4—364no—
381D4—364no—
382C2×C4—62no—
383C2×C4—62no—
384C2×C4—91no—
385C2×C4—91no—
386C2×C4—94no—
387C2×C4—91no—
388C2×C4—182no—
389C2×C4—181no—
390C2×C4—181no—
391C2×C4#380211yescharacteristic
392C2×C4#380211yescharacteristic
393C2×C4C22×D3211yescharacteristic
394C8—22no—
395C8—182no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—244no—
400C2×C3#560712yes—
401C2×C3C2×D3×SD1612yes—
402C2×C3D3×AGL(1,ℤ/8)12yes—
403D3—64no—
404D3—84no—
405D3—122no—
406C22—92no—
407C22—124no—
408C22—124no—
409C22—124no—
410C22—181no—
411C22—181no—
412C22—728no—
413C22C2×#380211yescharacteristic
414C4—21no—
415C4—92no—
416C4—92no—
417C4—122no—
418C4—122no—
419C4—181no—
420C4#6379612yes—
421C4#6431311yescharacteristic
422C4#6432011yescharacteristic
423C3—21no—
424C3#8038712yescomplemented
425C2—182no—
426C2—244no—
427C2#1059463411yescharacteristic
428C2C2×#6379611yescharacteristic
429C2#1059471611yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10594008C2
hypercenterC4⋊C8D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593882C2semidirect
3. #10592532C2semidirect
4. C3×#4848C2semidirect
5. #10590943C2semidirect
6. #10590885C2semidirect
7. #10590884C2semidirect
8. #10590364C2semidirect
14. C2×C3×#204C22semidirect
16. C3×C4×Dic6C22semidirect
17. #63919C22semidirect
23. #63873C22semidirect
27. C2×#3715C22semidirect
28. C32×C4⋊C8C22semidirect
30. C8×C3⋊Dic3C22semidirect
31. C4⋊(C3⋊(C3⋊C8))C22semidirect
32. C3×#821C22semidirect
33. #63562C22semidirect
41. #4848D3semidirect
92. C2×#204C2×D3semidirect
102. C4×Dic6C2×D3semidirect
104. C3×C4⋊C8C2×D3semidirect
107. #821C2×D3semidirect
129. C4×C3⋊D3SD16semidirect
240. C4⋊C8D32semidirect
366. C32#3208semidirect
424. C3#80387semidirect

Maximal subgroups

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

subgroupindex
#105940082
#105938822
#105925322
C3×#48482
#105909432
#105908852
#105908842
#105903642
#803873