Finite Group Databasebeta

← #11863662

Subgroups — #11863662

Order 1152.

1905 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 1905 conjugacy classes of subgroups — too many to draw. Only its 206 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×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×#63944C212yesmaximal, complemented
3#10594925C211yesmaximal, characteristic
4C3×#5228C212yesmaximal, complemented
5#10591603C214yesmaximal, complemented
6#10591552C212yesmaximal, complemented
7#10591190C212yesmaximal, complemented
8#10591152C211yesmaximal, characteristic
9D3×#451—32nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×Q8×C3⋊D3—28no—
12C2×Q8×C3⋊D3—21no—
13C2×Q8×C3⋊D3—21no—
14C2×Q8×C3⋊D3C2212yes—
15C2×Q8×C3⋊D3C2212yes—
16C22×C4×C3⋊D3—21no—
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×#634—21no—
19C22×#634C2211yescharacteristic
20C2×#3797C2211yescharacteristic
21C2×C3×#216C2214yescomplemented
22C3×#924C2212yes—
23#63982—21no—
24#63974—21no—
25#63944—28no—
26#63900C2211yescharacteristic
27#63883—21no—
28#63871C2212yes—
29#63865—21no—
30C2×#3719C2214yescomplemented
31C2×#3710C2212yes—
32C3×#835C2214yescomplemented
33C3×#830C2212yes—
34#63567C2214yescomplemented
35#63557C2212yes—
36C22×D3×Q8—32no—
37C22×D3×Q8—61no—
38C2×D3×Q16—34no—
39D3×C22⋊Q8—32no—
40C3×#451—32no—
41#5228D312yescomplemented
42#5186—34no—
43#5050—32no—
44#4809—34no—
45D3×#103—34no—
46#4739—32no—
47D3×C22⋊C8—32no—
48C23×C3⋊D3D411yescharacteristic
49C2×C32×Q8—24no—
50C2×C32×Q8—21no—
51C2×C32×Q8C2312yes—
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3D411yescharacteristic
56Q8×C3⋊D3—28no—
57Q8×C3⋊D3—28no—
58Q8×C3⋊D3—24no—
59Q8×C3⋊D3—24no—
60Q8×C3⋊D3—24no—
61Q8×C3⋊D3D418yes—
62C2×C4×C3⋊D3—28no—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—24no—
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3D411yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C4×C3⋊D3C2311yescharacteristic
70C2×#634—28no—
71C2×#634—21no—
72C2×#634—22no—
73C2×#634—22no—
74C2×#634—24no—
75C2×#634C2312yes—
76C2×C3×Dic6C2312yes—
77C2×#627—21no—
78C2×#624—21no—
79C2×#624—21no—
80#3797—24no—
81C3×#217—22no—
82C3×#216—28no—
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—22no—
85C2×C3×C3⋊C8C2314yes—
86#3724—21no—
87Dic3⋊Dic3—22no—
88#3722—22no—
89#3719—28no—
90#3710—24no—
91C2×#451—91noSylow
92C22×C3×Q8—21no—
93C22×C3×Q8C2×D312yes—
94C2×D3×Q8—34no—
95C2×D3×Q8—34no—
96C2×D3×Q8—32no—
97C2×D3×Q8—62no—
98C2×D3×Q8—62no—
99C2×D3×Q8—62no—
100C2×D3×Q8—62no—
101C2×D3×Q8—616no—
102C2×D3×Q8—62no—
103C2×D3×Q8—62no—
104C2×D3×Q8—616no—
105C22×C4×D3—32no—
106C22×C4×D3—61no—
107C22×C4×D3—62no—
108C22×C4×D3—62no—
109C22×Dic6—32no—
110C22×Dic6—61no—
111C22×Dic6—62no—
112C22×Dic6—62no—
113C2×C3×Q16—34no—
114C3×C22⋊Q8—32no—
115#946—32no—
116C2×#216—34no—
117C2×#216C2×D314yescomplemented
118#924C2×D312yes—
119D3×Q16—616no—
120C2×Dic12—34no—
121C2×D3×C8—34no—
122#897—32no—
123#896—62no—
124D3×C4⋊C4—32no—
125D3×C4⋊C4—62no—
126D3×C22⋊C4—62no—
127#878—62no—
128C3×#103—34no—
129C3×C22⋊C8—32no—
130#835C2×D314yescomplemented
131#830C2×D312yes—
132(C2×D3)⋊C8—34no—
133#816—34no—
134#810—34no—
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3Q1614yescomplemented
139C22×C3⋊D3C2×D411yescharacteristic
140C22×C3⋊D3C2×D411yescharacteristic
141C32×Q8—24no—
142C32×Q8—22no—
143C32×Q8C2×D414yes—
144C2×C32×C4—24no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—24no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3C2×D411yescharacteristic
153C2×C3⋊Dic3C2×D411yescharacteristic
154C4×C3⋊D3—28no—
155C4×C3⋊D3—28no—
156C4×C3⋊D3—22no—
157C4×C3⋊D3—22no—
158C4×C3⋊D3—22no—
159C4×C3⋊D3C2×D414yes—
160#634—28no—
161#634—24no—
162#634—22no—
163#634—28no—
164#634C2×D414yes—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C3×Dic6—24no—
168#627—42no—
169#624—42no—
170#624—42no—
171C3×C3⋊C8—24no—
172C23×Q8—91no—
173C22×Q16—92no—
174C2×C22⋊Q8—91no—
175#451—32no—
176#451—92no—
177#451—94no—
178C2×#103—92no—
179C2×C22⋊C8—91no—
180C23×D3—32no—
181C23×D3—61no—
182C2×C3×Q8—28no—
183C2×C3×Q8—22no—
184C2×C3×Q8—28no—
185C2×C3×Q8—22no—
186C2×C3×Q8—22no—
187C2×C3×Q8—32no—
188C2×C3×Q8C22×D314yes—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4C22×D312yes—
193C22×Dic3—32no—
194C22×Dic3—61no—
195C22×Dic3—62no—
196C22×Dic3—62no—
197D3×Q8—316no—
198D3×Q8—68no—
199D3×Q8—68no—
200D3×Q8—68no—
201D3×Q8—68no—
202D3×Q8—68no—
203D3×Q8—68no—
204D3×Q8—616no—
205D3×Q8—616no—
206D3×Q8—616no—
207D3×Q8—616no—
208D3×Q8—68no—
209D3×Q8—68no—
210C2×C4×D3—32no—
211C2×C4×D3—32no—
212C2×C4×D3—32no—
213C2×C4×D3—32no—
214C2×C4×D3—61no—
215C2×C4×D3—61no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×C4×D3—68no—
219C2×C4×D3—64no—
220C2×C4×D3—64no—
221C2×C4×D3—68no—
222C2×C4×D3—64no—
223C2×C4×D3—64no—
224C2×C4×D3—616no—
225C2×C4×D3—616no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×Dic6—34no—
229C2×Dic6—62no—
230C2×Dic6—68no—
231C2×Dic6—64no—
232C2×Dic6—64no—
233C2×Dic6—64no—
234C2×Dic6—64no—
235C2×Dic6—68no—
236C2×Dic6—616no—
237C2×Dic6—616no—
238C2×Dic6—62no—
239C2×Dic6—62no—
240C2×Dic6—62no—
241C2×Dic6C22×D312yes—
242C3×Q16—68no—
243C2×C3×C8—34no—
244C3×C4⋊C4—32no—
245C3×C4⋊C4—62no—
246C3×C22⋊C4—62no—
247#217—22no—
248#216—28no—
249#216—68no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252C4⋊Dic3—62no—
253C4⋊Dic3C22×D312yes—
254Dic3⋊C4—22no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257C2×C3⋊C8C22×D314yes—
258Dic12—68no—
259D3×C8—68no—
260C22×C32—21no—
261C22×C32—21no—
262C22×C32C2×Q1612yescomplemented
263C22×C32C22×D411yescharacteristic
264C2×C3⋊D3—21no—
265C2×C3⋊D3—21no—
266C2×C3⋊D3—28no—
267C2×C3⋊D3#12012yes—
268C2×C3⋊D3C2×Q1612yes—
269C2×C3⋊D3C2×Q1612yescomplemented
270C2×C3⋊D3#13712yes—
271C32×C4—24no—
272C32×C4—21no—
273C32×C4C22×D412yes—
274C3⋊Dic3—21no—
275C3⋊Dic3—24no—
276C3⋊Dic3#12012yes—
277C3×Dic3—42no—
278C3×Dic3—42no—
279C22×Q8—91no—
280C22×Q8—92no—
281C22×Q8—92no—
282C22×Q8—91no—
283C22×Q8—181no—
284C22×Q8—181no—
285C22×Q8—181no—
286C22×Q8—188no—
287C22×Q8D3211yescharacteristic
288C23×C4—91no—
289C23×C4—181no—
290C2×Q16—34no—
291C2×Q16—94no—
292C2×Q16—188no—
293C22×C8—92no—
294C22⋊Q8—32no—
295C22⋊Q8—92no—
296C22⋊Q8—181no—
297C22⋊Q8—181no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—181no—
300C2×C22⋊C4—181no—
301#103—34no—
302#103—94no—
303C22⋊C8—32no—
304C22⋊C8—92no—
305C23×C3—21no—
306C23×C3D3×D412yes—
307C22×D3—32no—
308C22×D3—38no—
309C22×D3—32no—
310C22×D3—64no—
311C22×D3—61no—
312C22×D3—61no—
313C22×D3—64no—
314C22×D3—64no—
315C22×D3—64no—
316C22×D3—64no—
317C3×Q8—28no—
318C3×Q8—28no—
319C3×Q8—24no—
320C3×Q8—24no—
321C3×Q8—24no—
322C3×Q8—64no—
323C3×Q8D3×D418yes—
324C2×C3×C4—28no—
325C2×C3×C4—28no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—24no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4D3×D412yes—
335C2×C3×C4C23×D312yes—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—32no—
339C2×Dic3—32no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C2×Dic3—68no—
345C2×Dic3—68no—
346C2×Dic3—64no—
347C2×Dic3—64no—
348C4×D3—38no—
349C4×D3—64no—
350C4×D3—64no—
351C4×D3—64no—
352C4×D3—616no—
353C4×D3—64no—
354C4×D3—64no—
355C4×D3—616no—
356C4×D3—616no—
357C4×D3—616no—
358C4×D3—64no—
359C4×D3—64no—
360C4×D3—124no—
361C4×D3—124no—
362Dic6—24no—
363Dic6—38no—
364Dic6—64no—
365Dic6—616no—
366Dic6—616no—
367Dic6—616no—
368Dic6—68no—
369Dic6—68no—
370Dic6—616no—
371Dic6—64no—
372Dic6—64no—
373Dic6—124no—
374C3×C8—64no—
375C3⋊C8—24no—
376C2×C32—22no—
377C2×C32C2×#12011yescharacteristic
378C2×C32C22×Q1611yescharacteristic
379C2×C32C2×#13711yescharacteristic
380C3⋊D3—22no—
381C3⋊D3#45114yescomplemented
382C24—91no—
383C2×Q8—24no—
384C2×Q8—21no—
385C2×Q8—32no—
386C2×Q8—98no—
387C2×Q8—92no—
388C2×Q8—182no—
389C2×Q8—182no—
390C2×Q8—184no—
391C2×Q8—188no—
392C2×Q8—181no—
393C2×Q8—184no—
394C2×Q8—184no—
395C2×Q8—184no—
396C2×Q8—188no—
397C2×Q8—188no—
398C2×Q8—184no—
399C2×Q8—181no—
400C2×Q8C2×D3212yes—
401C22×C4—21no—
402C22×C4—91no—
403C22×C4—91no—
404C22×C4—91no—
405C22×C4—91no—
406C22×C4—91no—
407C22×C4—184no—
408C22×C4—182no—
409C22×C4—182no—
410C22×C4—188no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4C2×D3211yescharacteristic
415Q16—68no—
416Q16—188no—
417C2×C8—34no—
418C2×C8—184no—
419C4⋊C4—32no—
420C4⋊C4—62no—
421C4⋊C4—181no—
422C4⋊C4—182no—
423C22⋊C4—62no—
424C22⋊C4—182no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3D3×Q1614yescomplemented
432C22×C3C2×D3×D412yes—
433C2×D3—34no—
434C2×D3—34no—
435C2×D3—34no—
436C2×D3—34no—
437C2×D3—62no—
438C2×D3—62no—
439C2×D3—62no—
440C2×D3—62no—
441C2×D3—616no—
442C2×D3—62no—
443C2×D3—616no—
444C2×D3—62no—
445C2×D3—62no—
446C2×D3—62no—
447C3×C4—28no—
448C3×C4—22no—
449C3×C4—28no—
450C3×C4—22no—
451C3×C4—22no—
452C3×C4—122no—
453C3×C4—122no—
454C3×C4C2×D3×D414yes—
455Dic3—34no—
456Dic3—42no—
457Dic3—42no—
458Dic3—62no—
459Dic3—62no—
460Dic3—68no—
461Dic3—68no—
462Dic3—62no—
463C32C2×#45111yescharacteristic, complemented, Sylow
464C23—91no—
465C23—91no—
466C23—94no—
467C23—182no—
468C23—182no—
469C23#381111yescharacteristic
470Q8—24no—
471Q8—22no—
472Q8—64no—
473Q8—94no—
474Q8—188no—
475Q8—188no—
476Q8—184no—
477Q8—182no—
478Q8—362no—
479Q8#381114yes—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—91no—
486C2×C4—94no—
487C2×C4—91no—
488C2×C4—182no—
489C2×C4—182no—
490C2×C4—188no—
491C2×C4—188no—
492C2×C4—182no—
493C2×C4—184no—
494C2×C4—182no—
495C2×C4—182no—
496C2×C4—362no—
497C2×C4—362no—
498C2×C4#381111yescharacteristic
499C2×C4C22×D3211yescharacteristic
500C8—64no—
501C2×C3—24no—
502C2×C3—24no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3D3×#12012yes—
507C2×C3C2×D3×Q1612yes—
508C2×C3D3×#13712yes—
509D3—38no—
510D3—64no—
511D3—64no—
512D3—64no—
513C22—21no—
514C22—21no—
515C22—92no—
516C22—92no—
517C22—92no—
518C22—92no—
519C22—188no—
520C22—181no—
521C22—181no—
522C22#6394412yescomplemented
523C22C2×#381111yescharacteristic
524C4—24no—
525C4—21no—
526C4—92no—
527C4—122no—
528C4—122no—
529C4—181no—
530C4—184no—
531C4C2×#381112yes—
532C3—21no—
533C3D3×#45112yescomplemented
534C2—22no—
535C2—94no—
536C2—182no—
537C2#1059532211yescharacteristic
538C2C2×#6394411yescharacteristic
539C2#1059552711yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×Q8D32
hypocenterC32C2×#451
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63944C2semidirect
4. C3×#5228C2semidirect
5. #10591603C2semidirect
6. #10591552C2semidirect
7. #10591190C2semidirect
21. C2×C3×#216C22semidirect
30. C2×#3719C22semidirect
32. C3×#835C22semidirect
34. #63567C22semidirect
41. #5228D3semidirect
117. C2×#216C2×D3semidirect
130. #835C2×D3semidirect
138. C22×C3⋊D3Q16semidirect
262. C22×C32C2×Q16semidirect
269. C2×C3⋊D3C2×Q16semidirect
381. C3⋊D3#451semidirect
431. C22×C3D3×Q16semidirect
463. C32C2×#451semidirect
522. C22#63944semidirect
533. C3D3×#451semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C2×#639442
#105949252
C3×#52282
#105916032
#105915522
#105911902
#105911522
D3×#4513