Finite Group Databasebeta

← #11878863

Subgroups — #11878863

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
1C2×#63914C211yesmaximal, characteristic
2#10594810C211yesmaximal, characteristic, complemented
3#10592417C211yesmaximal, characteristic, complemented
4C3×#4731C212yesmaximal, complemented
5#10591169C212yesmaximal, complemented
6#10590885C212yesmaximal, complemented
7#10590884C212yesmaximal, complemented
8#10590876C214yesmaximal, complemented
9#80138—32nomaximal
10C22×C3×D12C2212yes—
11C22×#625—21no—
12C22×#625—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C3×#924C2212yes—
15C2×C3×#204C2214yescomplemented
16#63982—21no—
17#63957—21no—
18#63919C2211yescharacteristic, complemented
19#63914—21no—
20#63914—21no—
21#63914C2212yes—
22#63914C2212yes—
23#63873C2211yescharacteristic, complemented
24#63870—21no—
25#63843C2212yescomplemented
26#63838—21no—
27C2×#3715C2214yescomplemented
28C32×C22⋊C8C2211yescharacteristic
29#63657C2211yescharacteristic
30#63641C2212yescomplemented
31C8×C3⋊Dic3C2212yescomplemented
32C3×#821C2214yescomplemented
33#63562C2214yescomplemented
34C2×#940—32no—
35#5622—32no—
36C3×#450—32no—
37#5218—32no—
38#5175—34no—
39#5163—34no—
40#5046—32no—
41#4762—34no—
42#4760—34no—
43#4731D312yescomplemented
44#4718—32no—
45#4718—61no—
46C23×C3×D3—22no—
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C22×C3⋊Dic3D411yescharacteristic
50C2×C3×D12—22no—
51C2×C3×D12—44no—
52C2×C3×D12C2314yes—
53C2×C3×Dic6C2312yes—
54C2×#627—21no—
55C2×#625—22no—
56C2×#625—22no—
57C2×#625—22no—
58C2×#625—22no—
59C2×#625—44no—
60C2×#625—44no—
61C2×C32×C8C2312yes—
62C4×C3⋊Dic3D411yescharacteristic
63C4×C3⋊Dic3D411yescharacteristic
64C4×C3⋊Dic3C2311yescharacteristic
65C4×C3⋊Dic3C2311yescharacteristic
66C2×C3⋊(C3⋊C8)C2312yes—
67C3×#217—22no—
68C3×C4⋊Dic3C2312yes—
69C3×Dic3⋊C4—22no—
70C3×#204—44no—
71#3724—21no—
72#3724—21no—
73#3724—21no—
74Dic3⋊Dic3—22no—
75Dic32—22no—
76#3715—44no—
77#3208—91noSylow
78C22×C3×D4—32no—
79C22×#67—62no—
80C22×#67—62no—
81C22×D12C2×D312yes—
82C2×C3×SD16—34no—
83C3×C22⋊Q8—32no—
84Q8×Dic3—32no—
85#944—32no—
86C2×#215—34no—
87#940—34no—
88#940—34no—
89#940—62no—
90#940—62no—
91C2×#214—34no—
92#924C2×D312yes—
93C2×C4×Dic3—32no—
94C2×C4×Dic3—61no—
95C2×#204C2×D314yescomplemented
96#889—62no—
97#888—32no—
98#887—32no—
99#887—62no—
100#878—62no—
101#877—62no—
102C3×#102—34no—
103C3×C22⋊C8—21no—
104C3×C22⋊C8C2×D312yes—
105#832—34no—
106#830—32no—
107#830—61no—
108#821C2×D314yescomplemented
109Dic3⋊C8—34no—
110Dic3⋊C8—62no—
111C8×Dic3—34no—
112C8×Dic3—62no—
113#809—34no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—24no—
116C22×C3×D3—44no—
117C22×C3×D3—44no—
118C22×C3×D3—44no—
119C2×C32×C4—22no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2411yescharacteristic
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3SD1614yescomplemented
124C2×C3⋊Dic3C2×D411yescharacteristic
125C2×C3⋊Dic3C2×D411yescharacteristic
126C2×C3⋊Dic3C2×D411yescharacteristic
127C2×C3⋊Dic3C2×D411yescharacteristic
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C3×D12—24no—
131C3×D12—24no—
132C3×D12—44no—
133C3×Dic6—24no—
134#627—42no—
135#625—44no—
136#625—44no—
137#625—44no—
138#625—44no—
139C32×C8—22no—
140C3⋊(C3⋊C8)—22no—
141#533—91no—
142C2×#127—91no—
143#492—92no—
144#486—92no—
145#460—94no—
146#450—32no—
147#450—92no—
148#431—91no—
149C24×C3—62no—
150C23×D3—22no—
151C2×C3×Q8—32no—
152C2×C3×D4—34no—
153C2×C3×D4—62no—
154C2×C3×D4—124no—
155C22×C3×C4—21no—
156C22×C3×C4C22×D312yes—
157C2×#67—64no—
158C2×#67—64no—
159C2×#67—64no—
160C2×#67—64no—
161C2×#67—128no—
162C2×#67—128no—
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C2×D12—22no—
168C2×D12—44no—
169C2×D12C22×D314yes—
170C2×Dic6—62no—
171C2×Dic6C22×D312yes—
172C3×SD16—124no—
173C2×C3×C8—22no—
174C2×C3×C8C22×D314yes—
175C3×C4⋊C4—32no—
176C3×C4⋊C4—62no—
177C3×C22⋊C4—62no—
178#217—22no—
179#215—124no—
180#214—124no—
181C4⋊Dic3—62no—
182C4⋊Dic3C22×D312yes—
183Dic3⋊C4—22no—
184Dic3⋊C4—62no—
185Dic3⋊C4—62no—
186Dic3⋊C4—62no—
187Dic3⋊C4—62no—
188C4×Dic3—32no—
189C4×Dic3—32no—
190C4×Dic3—32no—
191C4×Dic3—32no—
192C4×Dic3—61no—
193C4×Dic3—61no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C4×Dic3—62no—
197C4×Dic3—62no—
198C2×C3⋊C8—34no—
199C2×C3⋊C8—62no—
200#204—44no—
201C22×C32—21no—
202C22×C32—21no—
203C22×C32C2×SD1612yes—
204C22×C32C22×D411yescharacteristic
205C2×C3×D3—44no—
206C2×C3×D3—44no—
207C2×C3×D3—44no—
208C2×C3×D3—88no—
209C32×C4—21no—
210C32×C4H(5,𝔽2)12yes—
211C3⋊Dic3—21no—
212C3⋊Dic3C2×SD1612yes—
213C3⋊Dic3C2×SD1612yes—
214C3⋊Dic3AGL(1,ℤ/8)12yes—
215C3×Dic3—42no—
216C3×Dic3—42no—
217C22×D4—32no—
218C22×D4—181no—
219C22×D4—181no—
220C2×SD16—34no—
221C2×SD16—94no—
222C4⋊Q8—91no—
223C4⋊Q8—91no—
224#127—92no—
225#127—92no—
226#127—181no—
227#127—181no—
228#125—181no—
229C22⋊Q8—32no—
230C22⋊Q8—181no—
231C4×Q8—92no—
232C4×Q8—181no—
233#117—181no—
234C2×C42—91no—
235C4⋊C8—92no—
236#102—34no—
237#102—94no—
238C22⋊C8—91no—
239C22⋊C8D3211yescharacteristic
240C4×C8—92no—
241C23×C3—21no—
242C23×C3—64no—
243C23×C3—124no—
244C23×C3—124no—
245C23×C3—124no—
246C23×C3D3×D412yes—
247C22×D3—24no—
248C22×D3—44no—
249C22×D3—44no—
250C22×D3—44no—
251C3×Q8—64no—
252C3×D4—64no—
253C3×D4—64no—
254C3×D4—124no—
255C2×C3×C4—24no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—42no—
259C2×C3×C4—62no—
260C2×C3×C4—62no—
261C2×C3×C4D3×D412yes—
262C2×C3×C4C23×D312yes—
263#67—128no—
264#67—128no—
265#67—128no—
266#67—128no—
267C2×Dic3—22no—
268C2×Dic3—22no—
269C2×Dic3—38no—
270C2×Dic3—32no—
271C2×Dic3—32no—
272C2×Dic3—32no—
273C2×Dic3—32no—
274C2×Dic3—64no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—64no—
280C2×Dic3—122no—
281D12—24no—
282D12—24no—
283D12—44no—
284Dic6—24no—
285Dic6—124no—
286C3×C8—24no—
287C3×C8—42no—
288C3⋊C8—64no—
289C3⋊C8—122no—
290C2×C32—22no—
291C2×C32#53511yescharacteristic
292C2×C32C22×SD1611yescharacteristic
293C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
294C3×D3—84no—
295C24—62no—
296C2×Q8—32no—
297C2×Q8—181no—
298C2×D4—34no—
299C2×D4—62no—
300C2×D4—124no—
301C2×D4—182no—
302C2×D4—182no—
303C2×D4—182no—
304C2×D4—182no—
305C2×D4—364no—
306C2×D4—364no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4C2×D3211yescharacteristic
310SD16—124no—
311SD16—364no—
312C2×C8—92no—
313C2×C8C2×D3212yes—
314C4⋊C4—32no—
315C4⋊C4—62no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C4⋊C4—182no—
319C4⋊C4—181no—
320C22⋊C4—62no—
321C42—91no—
322C42—91no—
323C42—91no—
324C42—91no—
325C42—182no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—21no—
329C22×C3—22no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—124no—
333C22×C3—124no—
334C22×C3—124no—
335C22×C3—248no—
336C22×C3D3×SD1614yes—
337C22×C3C2×D3×D412yes—
338C2×D3—44no—
339C2×D3—44no—
340C2×D3—44no—
341C2×D3—88no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—41no—
345C3×C4—122no—
346C3×C4—122no—
347C3×C4#100414yes—
348Dic3—34no—
349Dic3—34no—
350Dic3—34no—
351Dic3—42no—
352Dic3—42no—
353Dic3—62no—
354Dic3—62no—
355Dic3—62no—
356Dic3—62no—
357Dic3—121no—
358C32#320811yescharacteristic, complemented, Sylow
359C23—64no—
360C23—124no—
361C23—124no—
362C23—124no—
363C23#380211yescharacteristic
364Q8—64no—
365Q8—362no—
366D4—64no—
367D4—64no—
368D4—124no—
369D4—364no—
370D4—364no—
371D4—364no—
372D4—364no—
373C2×C4—22no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—91no—
377C2×C4—91no—
378C2×C4—91no—
379C2×C4—94no—
380C2×C4—91no—
381C2×C4—182no—
382C2×C4#380211yescharacteristic
383C2×C4C22×D3211yescharacteristic
384C8—22no—
385C8—182no—
386C2×C3—24no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—42no—
391C2×C3—244no—
392C2×C3#559212yes—
393C2×C3C2×D3×SD1612yes—
394C2×C3D3×AGL(1,ℤ/8)12yes—
395D3—84no—
396C22—21no—
397C22—21no—
398C22—124no—
399C22—124no—
400C22—124no—
401C22—248no—
402C22#6379612yes—
403C22C2×#380211yescharacteristic
404C4—21no—
405C4—92no—
406C4—92no—
407C4—92no—
408C4—122no—
409C4—122no—
410C4—181no—
411C4#6431312yes—
412C3—21no—
413C3#8013812yescomplemented
414C2—22no—
415C2—244no—
416C2#1059419211yescharacteristic
417C2C2×#6379611yescharacteristic
418C2#1059471611yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#63914C2
hypercenterC22⋊C8D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594810C2semidirect
3. #10592417C2semidirect
4. C3×#4731C2semidirect
5. #10591169C2semidirect
6. #10590885C2semidirect
7. #10590884C2semidirect
8. #10590876C2semidirect
15. C2×C3×#204C22semidirect
18. #63919C22semidirect
23. #63873C22semidirect
25. #63843C22semidirect
27. C2×#3715C22semidirect
30. #63641C22semidirect
31. C8×C3⋊Dic3C22semidirect
32. C3×#821C22semidirect
33. #63562C22semidirect
43. #4731D3semidirect
95. C2×#204C2×D3semidirect
108. #821C2×D3semidirect
123. C2×C3⋊Dic3SD16semidirect
358. C32#3208semidirect
413. C3#80138semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
#105948102
#105924172
C3×#47312
#105911692
#105908852
#105908842
#105908762
#801383