Finite Group Databasebeta

← #11863572

Subgroups — #11863572

Order 1152.

2093 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 2093 conjugacy classes of subgroups — too many to draw. Only its 202 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
1C22×#3802C211yesmaximal, characteristic
2#10594925C211yesmaximal, characteristic, complemented
3C2×#63796C212yesmaximal, complemented
4C3⋊D3×C22⋊C8C211yesmaximal, characteristic, complemented
5C3×#4731C212yesmaximal, complemented
6#10591169C212yesmaximal, complemented
7#10590943C214yesmaximal, complemented
8#10590940C212yesmaximal, complemented
9D3×#450—32nomaximal
10C23×D32—21no—
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×D12C2212yes—
13C22×#625—21no—
14C2×#3802—21no—
15C2×#3802—21no—
16C2×#3802—28no—
17C2×#3802C2212yes—
18C2×#3802C2212yes—
19C2×#3797C2211yescharacteristic, complemented
20C2×C8×C3⋊D3C2212yescomplemented
21C3×#924C2212yescomplemented
22C2×C3×#204C2214yescomplemented
23#63982—21no—
24#63974—21no—
25#63900C2211yescharacteristic, complemented
26#63883—21no—
27#63871C2212yescomplemented
28#63865—21no—
29C2×#3715C2214yescomplemented
30#63796—28no—
31C32×C22⋊C8C2211yescharacteristic, complemented
32#63657C2211yescharacteristic, complemented
33#63647C2212yescomplemented
34C3×#821C2214yescomplemented
35#63562C2214yescomplemented
36C22×D3×D4—32no—
37C2×D3×SD16—34no—
38D3×C22⋊Q8—32no—
39C3×#450—32no—
40#5218—32no—
41#5169—34no—
42#5046—32no—
43#4776—34no—
44D3×#102—34no—
45#4731D312yescomplemented
46D3×C22⋊C8—32no—
47D3×C22⋊C8—61no—
48C23×C3⋊D3D411yescharacteristic
49C23×C3×D3—22no—
50C22×D32—28no—
51C22×D32—22no—
52C22×D32—22no—
53C22×D32—44no—
54C22×D32—44no—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3D411yescharacteristic
57C2×C4×C3⋊D3—24no—
58C2×C4×C3⋊D3D411yescharacteristic
59C2×C4×C3⋊D3D411yescharacteristic
60C2×C4×C3⋊D3C2311yescharacteristic
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×C3×D12—22no—
63C2×C3×D12—28no—
64C2×C3×D12C2314yes—
65C2×C3×Dic6C2312yescomplemented
66C2×#627—21no—
67C2×#625—28no—
68C2×#625—22no—
69C2×#625—22no—
70C2×#624—21no—
71C2×#624—21no—
72#3802—28no—
73#3802—28no—
74#3802—24no—
75#3802—28no—
76#3802D418yes—
77#3797—24no—
78C2×C32×C8C2312yescomplemented
79C2×C3⋊(C3⋊C8)C2312yescomplemented
80C8×C3⋊D3—24no—
81C3×#217—22no—
82C3×C4⋊Dic3C2312yescomplemented
83C3×Dic3⋊C4—22no—
84C3×#204—28no—
85#3724—21no—
86Dic3⋊Dic3—22no—
87#3722—22no—
88#3715—28no—
89C2×#450—91noSylow
90C24×D3—62no—
91C22×C3×D4—32no—
92C22×#67—62no—
93C2×D3×Q8—32no—
94C2×D3×D4—34no—
95C2×D3×D4—34no—
96C2×D3×D4—62no—
97C2×D3×D4—62no—
98C2×D3×D4—616no—
99C22×D12C2×D312yes—
100C22×C4×D3—32no—
101C22×C4×D3—61no—
102C2×C3×SD16—34no—
103C3×C22⋊Q8—32no—
104#946—32no—
105C2×#215—34no—
106C2×#214—34no—
107#924C2×D312yescomplemented
108D3×SD16—616no—
109C2×#204C2×D314yescomplemented
110C2×D3×C8—34no—
111C2×D3×C8—62no—
112#897—32no—
113#896—62no—
114D3×C4⋊C4—32no—
115D3×C4⋊C4—62no—
116D3×C22⋊C4—62no—
117#878—62no—
118C3×#102—34no—
119C3×C22⋊C8—21no—
120C3×C22⋊C8C2×D312yescomplemented
121#832—34no—
122#830—32no—
123#830—61no—
124#821C2×D314yescomplemented
125(C2×D3)⋊C8—34no—
126(C2×D3)⋊C8—62no—
127#809—34no—
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3—22no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3SD1614yescomplemented
132C22×C3⋊D3C2×D411yescharacteristic
133C22×C3⋊D3C2×D411yescharacteristic
134C22×C3×D3—28no—
135C22×C3×D3—24no—
136C22×C3×D3—44no—
137C22×C3×D3—44no—
138C2×D32—28no—
139C2×D32—28no—
140C2×D32—44no—
141C2×D32—432no—
142C2×D32—44no—
143C2×D32—44no—
144C2×D32—44no—
145C2×C32×C4—22no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3C2×D411yescharacteristic
150C2×C3⋊Dic3C2×D411yescharacteristic
151C4×C3⋊D3—22no—
152C4×C3⋊D3—22no—
153C4×C3⋊D3—22no—
154C4×C3⋊D3C2×D414yes—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C3×D12—28no—
158C3×D12—24no—
159C3×D12C2×D418yes—
160C3×Dic6—24no—
161#627—42no—
162#625—28no—
163#625—28no—
164#624—42no—
165#624—42no—
166C32×C8—22no—
167C3⋊(C3⋊C8)—22no—
168C23×D4—91no—
169C22×SD16—92no—
170C2×C22⋊Q8—91no—
171#450—32no—
172#450—94no—
173#450—92no—
174C2×#102—92no—
175C2×C22⋊C8—91no—
176C24×C3—62no—
177C23×D3—22no—
178C23×D3—32no—
179C23×D3—61no—
180C23×D3—64no—
181C23×D3—64no—
182C23×D3—616no—
183C23×D3—128no—
184C23×D3—128no—
185C2×C3×Q8—32no—
186C2×C3×D4—34no—
187C2×C3×D4—68no—
188C2×C3×D4—62no—
189C22×C3×C4—21no—
190C22×C3×C4C22×D312yes—
191C2×#67—64no—
192C2×#67—64no—
193C2×#67—616no—
194C22×Dic3—32no—
195C22×Dic3—61no—
196D3×Q8—68no—
197D3×D4—316no—
198D3×D4—68no—
199D3×D4—68no—
200D3×D4—616no—
201D3×D4—616no—
202D3×D4—68no—
203C2×D12—22no—
204C2×D12—28no—
205C2×D12C22×D314yes—
206C2×C4×D3—32no—
207C2×C4×D3—32no—
208C2×C4×D3—32no—
209C2×C4×D3—32no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×C4×D3—68no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—124no—
218C2×Dic6—62no—
219C2×Dic6C22×D312yescomplemented
220C3×SD16—68no—
221C2×C3×C8—22no—
222C2×C3×C8C22×D314yescomplemented
223C3×C4⋊C4—32no—
224C3×C4⋊C4—62no—
225C3×C22⋊C4—62no—
226#217—22no—
227#215—68no—
228#214—68no—
229(C2×D3)⋊C4—62no—
230(C2×D3)⋊C4—62no—
231C4⋊Dic3—62no—
232C4⋊Dic3C22×D312yescomplemented
233Dic3⋊C4—22no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236C2×C3⋊C8—34no—
237C2×C3⋊C8—62no—
238#204—28no—
239D3×C8—68no—
240D3×C8—124no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32C2×SD1612yescomplemented
244C22×C32C22×D411yescharacteristic
245C2×C3⋊D3—21no—
246C2×C3⋊D3—21no—
247C2×C3⋊D3—28no—
248C2×C3⋊D3#12012yes—
249C2×C3⋊D3C2×SD1612yes—
250C2×C3⋊D3C2×SD1612yescomplemented
251C2×C3⋊D3AGL(1,ℤ/8)12yes—
252C2×C3×D3—28no—
253C2×C3×D3—416no—
254C2×C3×D3—44no—
255C2×C3×D3—44no—
256D32—416no—
257D32—416no—
258C32×C4—21no—
259C32×C4C22×D412yes—
260C3⋊Dic3—21no—
261C3⋊Dic3#12012yes—
262C3×Dic3—42no—
263C3×Dic3—42no—
264C25—181no—
265C22×Q8—91no—
266C22×D4—32no—
267C22×D4—92no—
268C22×D4—92no—
269C22×D4—181no—
270C22×D4—181no—
271C22×D4—181no—
272C22×D4—188no—
273C23×C4—91no—
274C2×SD16—34no—
275C2×SD16—94no—
276C2×SD16—188no—
277C22×C8—92no—
278C22⋊Q8—32no—
279C22⋊Q8—92no—
280C22⋊Q8—181no—
281C22⋊Q8—181no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—181no—
284C2×C22⋊C4—181no—
285#102—34no—
286#102—94no—
287C22⋊C8—91no—
288C22⋊C8—92no—
289C22⋊C8D3211yescharacteristic, complemented
290C23×C3—21no—
291C23×C3—68no—
292C23×C3—64no—
293C23×C3—124no—
294C23×C3—124no—
295C23×C3D3×D412yes—
296C22×D3—28no—
297C22×D3—24no—
298C22×D3—32no—
299C22×D3—38no—
300C22×D3—32no—
301C22×D3—44no—
302C22×D3—44no—
303C22×D3—61no—
304C22×D3—64no—
305C22×D3—61no—
306C22×D3—616no—
307C22×D3—616no—
308C22×D3—64no—
309C22×D3—64no—
310C22×D3—122no—
311C22×D3—122no—
312C22×D3—128no—
313C22×D3—128no—
314C22×D3—128no—
315C22×D3—1264no—
316C22×D3—128no—
317C3×Q8—64no—
318C3×D4—38no—
319C3×D4—68no—
320C3×D4—64no—
321C2×C3×C4—24no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—42no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4D3×D412yes—
328C2×C3×C4C23×D312yes—
329#67—616no—
330#67—616no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—32no—
334C2×Dic3—32no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—64no—
338C2×Dic3—122no—
339D12—28no—
340D12—24no—
341D12D3×D418yes—
342C4×D3—38no—
343C4×D3—64no—
344C4×D3—64no—
345C4×D3—64no—
346C4×D3—64no—
347C4×D3—122no—
348C4×D3—122no—
349C4×D3—122no—
350C4×D3—124no—
351C4×D3—124no—
352Dic6—24no—
353Dic6—124no—
354C3×C8—24no—
355C3×C8—42no—
356C3⋊C8—64no—
357C3⋊C8—122no—
358C2×C32—22no—
359C2×C32C2×#12011yescharacteristic
360C2×C32C22×SD1611yescharacteristic
361C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
362C3⋊D3—22no—
363C3⋊D3#45014yescomplemented
364C3×D3—48no—
365C24—62no—
366C24—91no—
367C24—182no—
368C24—182no—
369C24—188no—
370C24—364no—
371C24—364no—
372C2×Q8—32no—
373C2×Q8—181no—
374C2×Q8—184no—
375C2×D4—34no—
376C2×D4—68no—
377C2×D4—62no—
378C2×D4—98no—
379C2×D4—184no—
380C2×D4—182no—
381C2×D4—182no—
382C2×D4—188no—
383C2×D4—188no—
384C2×D4—188no—
385C2×D4—188no—
386C22×C4—91no—
387C22×C4—91no—
388C22×C4—91no—
389C22×C4—91no—
390C22×C4—91no—
391C22×C4—184no—
392C22×C4—181no—
393C22×C4—181no—
394C22×C4C2×D3211yescharacteristic
395SD16—68no—
396SD16—188no—
397C2×C8—92no—
398C2×C8—184no—
399C2×C8C2×D3212yescomplemented
400C4⋊C4—32no—
401C4⋊C4—62no—
402C4⋊C4—181no—
403C4⋊C4—182no—
404C22⋊C4—62no—
405C22⋊C4—182no—
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—21no—
409C22×C3—22no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—68no—
413C22×C3—1216no—
414C22×C3—124no—
415C22×C3—124no—
416C22×C3D3×SD1614yescomplemented
417C22×C3C2×D3×D412yes—
418C2×D3—28no—
419C2×D3—34no—
420C2×D3—34no—
421C2×D3—34no—
422C2×D3—34no—
423C2×D3—416no—
424C2×D3—44no—
425C2×D3—44no—
426C2×D3—62no—
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—616no—
431C2×D3—62no—
432C2×D3—62no—
433C2×D3—128no—
434C2×D3—121no—
435C2×D3—121no—
436C2×D3—1232no—
437C2×D3—1232no—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—41no—
441C3×C4—122no—
442C3×C4—122no—
443C3×C4C2×D3×D414yes—
444Dic3—34no—
445Dic3—42no—
446Dic3—42no—
447Dic3—62no—
448Dic3—62no—
449Dic3—121no—
450C32C2×#45011yescharacteristic, complemented, Sylow
451C23—68no—
452C23—64no—
453C23—91no—
454C23—91no—
455C23—94no—
456C23—124no—
457C23—124no—
458C23—182no—
459C23—182no—
460C23—188no—
461C23—188no—
462C23—364no—
463C23—364no—
464C23—364no—
465C23—3632no—
466C23—364no—
467C23#380211yescharacteristic
468Q8—64no—
469Q8—362no—
470D4—38no—
471D4—68no—
472D4—64no—
473D4—188no—
474D4—188no—
475C2×C4—22no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—91no—
479C2×C4—94no—
480C2×C4—91no—
481C2×C4—182no—
482C2×C4—182no—
483C2×C4—182no—
484C2×C4—182no—
485C2×C4—362no—
486C2×C4—362no—
487C2×C4#380211yescharacteristic
488C2×C4C22×D3211yescharacteristic
489C8—22no—
490C8—182no—
491C2×C3—24no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—42no—
496C2×C3—128no—
497C2×C3D3×#12012yes—
498C2×C3C2×D3×SD1612yes—
499C2×C3D3×AGL(1,ℤ/8)12yes—
500D3—38no—
501D3—48no—
502D3—64no—
503D3—64no—
504D3—122no—
505C22—21no—
506C22—21no—
507C22—68no—
508C22—92no—
509C22—92no—
510C22—92no—
511C22—92no—
512C22—1216no—
513C22—124no—
514C22—124no—
515C22—188no—
516C22—181no—
517C22—181no—
518C22—3616no—
519C22—3616no—
520C22#6379612yescomplemented
521C22C2×#380211yescharacteristic
522C4—21no—
523C4—92no—
524C4—122no—
525C4—122no—
526C4—181no—
527C4D32×D412yes—
528C3—21no—
529C3D3×#45012yescomplemented
530C2—22no—
531C2—94no—
532C2—128no—
533C2—182no—
534C2#1059425811yescharacteristic
535C2C2×#6379611yescharacteristic
536C2#1059471611yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC22×#3802C2
hypercenterC22⋊C8D32
hypocenterC32C2×#450
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. #10594925C2semidirect
3. C2×#63796C2semidirect
4. C3⋊D3×C22⋊C8C2semidirect
5. C3×#4731C2semidirect
6. #10591169C2semidirect
7. #10590943C2semidirect
8. #10590940C2semidirect
19. C2×#3797C22semidirect
20. C2×C8×C3⋊D3C22semidirect
21. C3×#924C22semidirect
22. C2×C3×#204C22semidirect
25. #63900C22semidirect
27. #63871C22semidirect
29. C2×#3715C22semidirect
31. C32×C22⋊C8C22semidirect
32. #63657C22semidirect
33. #63647C22semidirect
34. C3×#821C22semidirect
35. #63562C22semidirect
45. #4731D3semidirect
65. C2×C3×Dic6C23semidirect
78. C2×C32×C8C23semidirect
79. C2×C3⋊(C3⋊C8)C23semidirect
82. C3×C4⋊Dic3C23semidirect
107. #924C2×D3semidirect
109. C2×#204C2×D3semidirect
120. C3×C22⋊C8C2×D3semidirect
124. #821C2×D3semidirect
131. C22×C3⋊D3SD16semidirect
219. C2×Dic6C22×D3semidirect
222. C2×C3×C8C22×D3semidirect
232. C4⋊Dic3C22×D3semidirect
243. C22×C32C2×SD16semidirect
250. C2×C3⋊D3C2×SD16semidirect
289. C22⋊C8D32semidirect
363. C3⋊D3#450semidirect
399. C2×C8C2×D32semidirect
416. C22×C3D3×SD16semidirect
450. C32C2×#450semidirect
520. C22#63796semidirect
529. C3D3×#450semidirect

Maximal subgroups

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

subgroupindex
C22×#38022
#105949252
C2×#637962
C3⋊D3×C22⋊C82
C3×#47312
#105911692
#105909432
#105909402
D3×#4503