Finite Group Databasebeta

← #11870521

Subgroups — #11870521

Order 1152.

1007 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 1007 conjugacy classes of subgroups — too many to draw. Only its 172 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#10596199C211yesmaximal, characteristic, complemented
2C4×#3802C211yesmaximal, characteristic
3C3×#5083C212yesmaximal, complemented
4#10591652C212yesmaximal
5#10591571C214yesmaximal, complemented
6#10591553C212yesmaximal, complemented
7#10590268C212yesmaximal, complemented
8#10590256C211yesmaximal, characteristic, complemented
9#80408—32nomaximal
10C2×#3802C2211yescharacteristic
11C2×C4×D32—21no—
12C32×C4⋊Q8C2211yescharacteristic, complemented
13#64155C2212yes—
14Q8×C3⋊Dic3C2212yescomplemented
15#64106—21no—
16#64101—21no—
17#64099—21no—
18#64096—21no—
19C42×C3⋊D3C2211yescharacteristic
20#64078C2211yescharacteristic, complemented
21C2×C3×#215C2214yes—
22C3×C4×D12C2212yes—
23#63921—21no—
24#63902—21no—
25C4×#625—21no—
26#63900C2211yescharacteristic
27#63898C2212yes—
28C3×#835C2214yescomplemented
29C3×C4⋊(C3⋊C8)C2212yescomplemented
30#63573C2214yescomplemented
31#63563C2214yes—
32#63557C2212yes—
33#63553C2212yescomplemented
34#5728—32no—
35#5728—61no—
36C4×D3×D4—32no—
37C3×#461—32no—
38#5169—34no—
39Dic3×SD16—34no—
40#5083D312yescomplemented
41#5008—32no—
42#4842—32no—
43#4833—32no—
44#4805—34no—
45#4788—34no—
46C22×D32—21no—
47C2×C32×Q8C2312yes—
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3D411yescharacteristic
50C2×C4×C3⋊D3C2311yescharacteristic
51C2×#634—21no—
52C2×C3×D12C2312yes—
53C2×C3×C4×D3—22no—
54C2×#625—21no—
55C2×#624—21no—
56C2×D3×Dic3—22no—
57#3802—24no—
58C4×D32—44no—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C42C2311yescharacteristic
62#3752—22no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—22no—
65C4⋊(C3⋊Dic3)C2312yes—
66#3750—22no—
67C4×C3⋊Dic3—22no—
68C4×C3⋊Dic3D411yescharacteristic
69C4×C3⋊Dic3D411yescharacteristic
70C4×C3⋊Dic3C2311yescharacteristic
71C3×#215—28no—
72C3×(C2×D3)⋊C4—22no—
73C3×C4⋊Dic3C2312yes—
74C2×C3×C3⋊C8C2314yes—
75#3724—21no—
76(C2×D3)⋊Dic3—22no—
77#3101—91noSylow
78C2×D3×D4—32no—
79C22×C4×D3—62no—
80C2×C3×SD16—34no—
81C3×C4⋊Q8—21no—
82C3×C4⋊Q8C2×D312yescomplemented
83C3×C4×D4—32no—
84#946—34no—
85#946—62no—
86Q8×Dic3—34no—
87Q8×Dic3—62no—
88C2×#215C2×D314yes—
89D4×Dic3—32no—
90C4×#67—62no—
91#897—62no—
92#897—62no—
93#893—32no—
94#892—62no—
95#892—62no—
96D3×C4⋊C4—32no—
97#890—62no—
98#890—62no—
99#887—62no—
100#887—62no—
101#67⋊C4—62no—
102D3×C22⋊C4—62no—
103C4×D12C2×D312yes—
104C42×D3—32no—
105C42×D3—61no—
106#869—32no—
107#869—61no—
108C3×C4⋊C8—32no—
109C3×#103—34no—
110#835C2×D314yescomplemented
111#832—34no—
112#821—34no—
113(C2×D3)⋊C8—34no—
114#817—34no—
115C8×Dic3—34no—
116#808—34no—
117C4⋊(C3⋊C8)C2×D312yescomplemented
118C22×C3⋊D3C2×D411yescharacteristic
119C22×C3×D3—22no—
120C2×D32—24no—
121C2×D32—42no—
122C2×D32—42no—
123C32×Q8—24no—
124C2×C32×C4—22no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2411yescharacteristic
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3C2×D411yescharacteristic
130C2×C3⋊Dic3C2×D411yescharacteristic
131C2×C3⋊Dic3C2×D411yescharacteristic
132C4×C3⋊D3—22no—
133C4×C3⋊D3—41no—
134C4×C3⋊D3SD1614yescomplemented
135#634—42no—
136C2×C3×Dic3—22no—
137C3×D12—22no—
138C3×D12#4114yes—
139C3×C4×D3—44no—
140#625—24no—
141#624—42no—
142D3×Dic3—44no—
143C3×C3⋊C8—24no—
144#533—91no—
145C2×C4×D4—91no—
146#483—92no—
147#476—92no—
148#461—32no—
149#450—92no—
150C4×SD16—94no—
151#431—91no—
152C23×D3—62no—
153C2×C3×Q8—22no—
154C2×C3×Q8C22×D314yes—
155C2×C3×D4—32no—
156C22×C3×C4—62no—
157C2×#67—62no—
158C22×Dic3—62no—
159D3×D4—64no—
160D3×D4—64no—
161C2×D12C22×D312yes—
162C2×C4×D3—22no—
163C2×C4×D3—32no—
164C2×C4×D3—32no—
165C2×C4×D3—32no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×C4×D3—62no—
170C2×C4×D3—62no—
171C2×C4×D3—128no—
172C2×Dic6—62no—
173C2×Dic6—62no—
174C3×SD16—68no—
175C2×C3×C8—34no—
176C3×C4⋊C4—22no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—32no—
181C3×C22⋊C4—62no—
182C3×C42—21no—
183C3×C42C22×D312yes—
184#217—62no—
185#215—28no—
186(C2×D3)⋊C4—22no—
187(C2×D3)⋊C4—62no—
188(C2×D3)⋊C4—64no—
189(C2×D3)⋊C4—64no—
190C4⋊Dic3—34no—
191C4⋊Dic3—62no—
192C4⋊Dic3—64no—
193C4⋊Dic3—62no—
194C4⋊Dic3—64no—
195C4⋊Dic3—62no—
196C4⋊Dic3C22×D312yes—
197Dic3⋊C4—62no—
198Dic3⋊C4—64no—
199Dic3⋊C4—64no—
200C4×Dic3—32no—
201C4×Dic3—32no—
202C4×Dic3—32no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—64no—
207C4×Dic3—64no—
208C2×C3⋊C8C22×D314yes—
209C22×C32C22×D411yescharacteristic
210C2×C3⋊D3—21no—
211C2×C3⋊D3—21no—
212C2×C3⋊D3C2×SD1612yes—
213C2×C3×D3—24no—
214C2×C3×D3—42no—
215C2×C3×D3—42no—
216D32—48no—
217C32×C4—21no—
218C32×C4—42no—
219C32×C4C2×SD1612yes—
220C32×C4C2×#4112yes—
221C3⋊Dic3—21no—
222C3⋊Dic3—21no—
223C3⋊Dic3—42no—
224C3⋊Dic3C2×SD1612yes—
225C3×Dic3—42no—
226C22×D4—91no—
227C23×C4—181no—
228C2×SD16—34no—
229C4⋊Q8—91no—
230C4⋊Q8D3211yescharacteristic, complemented
231#125—181no—
232C22⋊Q8—92no—
233C22⋊Q8—181no—
234C4×Q8—92no—
235C4×Q8—181no—
236C4×D4—32no—
237C4×D4—92no—
238C4×D4—181no—
239C4×D4—181no—
240#117—181no—
241C2×C4⋊C4—91no—
242C2×C22⋊C4—181no—
243C2×C42—91no—
244#106—94no—
245C4⋊C8—32no—
246#103—34no—
247#102—94no—
248C22⋊C8—92no—
249C4×C8—92no—
250C23×C3—62no—
251C22×D3—22no—
252C22×D3—32no—
253C22×D3—61no—
254C22×D3—68no—
255C22×D3—124no—
256C22×D3—124no—
257C3×Q8—24no—
258C3×Q8—24no—
259C3×Q8—44no—
260C3×D4—34no—
261C3×D4—62no—
262C2×C3×C4—24no—
263C2×C3×C4—24no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—62no—
268C2×C3×C4—124no—
269C2×C3×C4D3×D412yes—
270C2×C3×C4D3×D412yes—
271C2×C3×C4C23×D312yes—
272#67—68no—
273C2×Dic3—22no—
274C2×Dic3—32no—
275C2×Dic3—32no—
276C2×Dic3—32no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282C2×Dic3—124no—
283D12—22no—
284D12#23714yes—
285C4×D3—38no—
286C4×D3—44no—
287C4×D3—64no—
288C4×D3—62no—
289C4×D3—62no—
290C4×D3—122no—
291C4×D3—124no—
292C4×D3—124no—
293C4×D3—122no—
294C4×D3—122no—
295Dic6—124no—
296Dic6—124no—
297C3×C8—64no—
298C3⋊C8—24no—
299C2×C32#52511yescharacteristic
300C2×C32C22×SD1611yescharacteristic
301C2×C32#57511yescharacteristic
302C3⋊D3—22no—
303C3×D3—44no—
304C24—181no—
305C2×Q8—181no—
306C2×Q8C2×D3212yes—
307C2×D4—32no—
308C2×D4—181no—
309C2×D4—184no—
310C22×C4—62no—
311C22×C4—91no—
312C22×C4—91no—
313C22×C4—91no—
314C22×C4—181no—
315C22×C4—182no—
316C22×C4—364no—
317SD16—68no—
318C2×C8—34no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—32no—
322C4⋊C4—92no—
323C4⋊C4—182no—
324C4⋊C4—182no—
325C4⋊C4—181no—
326C4⋊C4—181no—
327C22⋊C4—62no—
328C22⋊C4—182no—
329C22⋊C4—182no—
330C42—91no—
331C42—91no—
332C42—91no—
333C42—182no—
334C42C2×D3211yescharacteristic
335C22×C3—21no—
336C22×C3—64no—
337C22×C3—122no—
338C22×C3—122no—
339C22×C3C2×D3×D412yes—
340C2×D3—24no—
341C2×D3—34no—
342C2×D3—42no—
343C2×D3—42no—
344C2×D3—62no—
345C2×D3—62no—
346C2×D3—62no—
347C2×D3—121no—
348C2×D3—121no—
349C2×D3—1216no—
350C3×C4—22no—
351C3×C4—22no—
352C3×C4—22no—
353C3×C4—22no—
354C3×C4—44no—
355C3×C4—44no—
356C3×C4—122no—
357C3×C4D3×SD1614yes—
358C3×C4C2×#23712yes—
359C3×C4D3×#4112yes—
360Dic3—34no—
361Dic3—42no—
362Dic3—62no—
363Dic3—62no—
364Dic3—62no—
365Dic3—121no—
366Dic3—121no—
367Dic3—124no—
368Dic3—124no—
369C32#310111yescharacteristic, complemented, Sylow
370C23—62no—
371C23—91no—
372C23—184no—
373C23—362no—
374C23—362no—
375Q8—24no—
376Q8—362no—
377D4—34no—
378D4—62no—
379D4—184no—
380C2×C4—22no—
381C2×C4—62no—
382C2×C4—91no—
383C2×C4—94no—
384C2×C4—91no—
385C2×C4—91no—
386C2×C4—124no—
387C2×C4—182no—
388C2×C4—182no—
389C2×C4—361no—
390C2×C4—364no—
391C2×C4—362no—
392C2×C4#381111yescharacteristic
393C2×C4#381111yescharacteristic
394C2×C4C22×D3211yescharacteristic
395C8—64no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—124no—
400C2×C3#560612yes—
401C2×C3C2×D3×SD1612yes—
402C2×C3#577712yes—
403D3—44no—
404D3—64no—
405D3—122no—
406C22—64no—
407C22—92no—
408C22—122no—
409C22—122no—
410C22—181no—
411C22—181no—
412C22—368no—
413C22C2×#381111yescharacteristic
414C4—21no—
415C4—42no—
416C4—92no—
417C4—122no—
418C4—181no—
419C4—181no—
420C4—362no—
421C4#6394012yes—
422C4D3×#23712yes—
423C3—21no—
424C3#8040812yescomplemented
425C2—124no—
426C2—182no—
427C2#1059530611yescharacteristic
428C2C2×#6394011yescharacteristic
429C2#1059532311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC4⋊Q8D32
hypocenterC32#3101
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
3. C3×#5083C2semidirect
5. #10591571C2semidirect
6. #10591553C2semidirect
7. #10590268C2semidirect
8. #10590256C2semidirect
12. C32×C4⋊Q8C22semidirect
14. Q8×C3⋊Dic3C22semidirect
20. #64078C22semidirect
28. C3×#835C22semidirect
29. C3×C4⋊(C3⋊C8)C22semidirect
30. #63573C22semidirect
33. #63553C22semidirect
40. #5083D3semidirect
82. C3×C4⋊Q8C2×D3semidirect
110. #835C2×D3semidirect
117. C4⋊(C3⋊C8)C2×D3semidirect
134. C4×C3⋊D3SD16semidirect
230. C4⋊Q8D32semidirect
369. C32#3101semidirect
424. C3#80408semidirect

Maximal subgroups

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

subgroupindex
#105961992
C4×#38022
C3×#50832
#105916522
#105915712
#105915532
#105902682
#105902562
#804083