Finite Group Databasebeta

← #11895869

Subgroups — #11895869

Order 1152.

884 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#634C211yesmaximal, characteristic, complemented
2#10593863C211yesmaximal, characteristic, complemented
3C3×#5019C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic
5#10591476C212yesmaximal
6#10591446C212yesmaximal, complemented
7#10590541C212yesmaximal, complemented
8#10590496C212yesmaximal, complemented
9#10590296C211yesmaximal, characteristic, complemented
10#10590287C211yesmaximal, characteristic, complemented
11#10590272C211yesmaximal, characteristic, complemented
12#80416—31nomaximal
13#79571—31nomaximal
14C22×#634—21no—
15C32×C4×D4C2211yescharacteristic
16D4×C3⋊Dic3C2212yes—
17#64133—21no—
18#64097C2212yes—
19#64087—22no—
20#64078C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#214C2212yes—
23C2×C3×#213C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26#63863C2212yes—
27#63858—22no—
28#63857—21no—
29#63843C2212yes—
30#63841—21no—
31C3×#832C2211yescharacteristic
32C3×#810C2212yes—
33C3×#809C2211yescharacteristic
34C3×#807C2211yescharacteristic
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2212yes—
38#63572C2212yes—
39#63566C2212yes—
40#63566C2212yes—
41#63563C2212yes—
42#63555C2212yes—
43#5732—31no—
44#5542—31no—
45D4×Dic6—31no—
46D4×Dic6—31no—
47D4×Dic6—61no—
48C3×#461—31no—
49C3×C4×D8—31no—
50#5165—32no—
51#5164—32no—
52#5153—32no—
53#5079—31no—
54#5019D311yescharacteristic, complemented
55C4×#213D311yescharacteristic
56#5007—31no—
57#4875—32no—
58#4846—31no—
59#4831—31no—
60#4794—32no—
61#4793—32no—
62#4765—32no—
63#4757—32no—
64#4681—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C22×C3⋊Dic3—22no—
69C2×#634—21no—
70C2×#634—22no—
71C2×#634—44no—
72C2×#634D411yescharacteristic
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×Dic6C2312yes—
76C32×C4⋊C4C2311yescharacteristic
77C32×C22⋊C4—21no—
78C32×C42C2311yescharacteristic
79#3757—22no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)D411yescharacteristic
82C4⋊(C3⋊Dic3)C2312yes—
83#3750—22no—
84#3750D412yes—
85C4×C3⋊Dic3C2312yes—
86C3×#214—24no—
87C3×#213—22no—
88C3×(C2×D3)⋊C4—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98Dic32—22no—
99#3367—91noSylow
100C22×Dic6—61no—
101C22×Dic6—61no—
102C22×Dic6—62no—
103C2×C3×SD16—32no—
104C2×C3×D8—31no—
105C3×C4⋊Q8—31no—
106C3×C4×D4—21no—
107C3×C4×D4—31no—
108C3×C4×D4C2×D311yescharacteristic
109C3×C4×D4C2×D311yescharacteristic
110#947—32no—
111Q8×Dic3—32no—
112#936—32no—
113D4×Dic3—32no—
114D4×Dic3—32no—
115D4×Dic3—62no—
116C2×#214C2×D312yes—
117C2×#213C2×D311yescharacteristic
118#926—61no—
119#924—61no—
120#924—61no—
121#924—61no—
122#924—62no—
123#898—62no—
124#897—61no—
125#892—61no—
126#888—32no—
127#888—32no—
128#888—62no—
129#887—32no—
130#879—62no—
131#878—62no—
132#878—62no—
133#878—64no—
134C4×D12C2×D311yescharacteristic
135#869—31no—
136#869—31no—
137#869—61no—
138#869C2×D311yescharacteristic
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C3×#107—31no—
143C3×C4⋊C8—31no—
144C3×#103—32no—
145C3×#102—31no—
146C3×#102—31no—
147C3×C4×C8—31no—
148#835—32no—
149#835—32no—
150#832—32no—
151#832C2×D311yescharacteristic
152#821—32no—
153#818—32no—
154#816—32no—
155#816—32no—
156#815—32no—
157#815—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—32no—
160#810C2×D312yes—
161#809C2×D311yescharacteristic
162#807—32no—
163#807C2×D311yescharacteristic
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C23×C32—21no—
167C22×C3×D3—21no—
168C32×D4—21no—
169C32×D4#4112yes—
170C2×C32×C4—21no—
171C2×C32×C4—42no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—44no—
177C2×C3⋊Dic3C2×D412yes—
178C2×C3⋊Dic3C2×D412yes—
179#634—22no—
180#634—44no—
181#634—42no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—22no—
184C3×D12—21no—
185C3×D12—21no—
186C3×C4×D3—42no—
187C3×Dic6—22no—
188C3×Dic6—22no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—22no—
191C3×C3⋊C8—21no—
192#556—91no—
193D4×Q8—91no—
194#489—92no—
195#487—91no—
196#477—92no—
197#474—91no—
198#463—92no—
199#461—31no—
200#446—91no—
201#440—92no—
202C4×D8—31no—
203C2×C3×Q8—32no—
204C2×C3×D4—21no—
205C2×C3×D4—31no—
206C2×C3×D4C22×D311yescharacteristic
207C2×C3×D4C22×D311yescharacteristic
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—61no—
212C22×Dic3—62no—
213C22×Dic3—62no—
214C22×Dic3—64no—
215C2×D12C22×D311yescharacteristic
216C2×C4×D3—21no—
217C2×Dic6—31no—
218C2×Dic6—31no—
219C2×Dic6—61no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—62no—
223C2×Dic6—64no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—128no—
227C2×Dic6—124no—
228C2×Dic6—124no—
229C2×Dic6C22×D312yes—
230C3×SD16—64no—
231C3×D8—62no—
232C2×C3×C8—31no—
233C2×C3×C8—32no—
234C2×C3×C8—31no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4C22×D311yescharacteristic
240C3×C4⋊C4C22×D311yescharacteristic
241C3×C22⋊C4—22no—
242C3×C22⋊C4—21no—
243C3×C22⋊C4—21no—
244C3×C22⋊C4—61no—
245C3×C42—21no—
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D311yescharacteristic
248#217—62no—
249#217—62no—
250#217—62no—
251#217—62no—
252#217—64no—
253#214—24no—
254#213—22no—
255(C2×D3)⋊C4—21no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—32no—
263C4⋊Dic3—32no—
264C4⋊Dic3—61no—
265C4⋊Dic3—62no—
266C4⋊Dic3—62no—
267C4⋊Dic3—62no—
268C4⋊Dic3—61no—
269C4⋊Dic3—61no—
270C4⋊Dic3C22×D311yescharacteristic
271Dic3⋊C4—32no—
272Dic3⋊C4—32no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277Dic3⋊C4—64no—
278C4×Dic3—32no—
279C4×Dic3—32no—
280C4×Dic3—62no—
281C4×Dic3—62no—
282C4×Dic3—62no—
283C2×C3⋊C8C22×D311yescharacteristic
284C2×C3⋊C8C22×D311yescharacteristic
285C2×C3⋊C8C22×D312yes—
286C22×C32—22no—
287C22×C32—41no—
288C22×C32—41no—
289C22×C32C22×D411yescharacteristic
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C32×C4—21no—
294C32×C4—41no—
295C32×C4AGL(1,ℤ/8)12yes—
296C32×C4C2×#4111yescharacteristic
297C32×C42−1+411yescharacteristic
298C3⋊Dic3—22no—
299C3⋊Dic3—22no—
300C3⋊Dic3—42no—
301C3×Dic3—42no—
302C3×Dic3—41no—
303C22×Q8—181no—
304C2×SD16—32no—
305C2×D8—31no—
306C4⋊Q8—31no—
307C4⋊Q8—92no—
308C4⋊Q8—91no—
309#126—182no—
310#124—92no—
311C22⋊Q8—182no—
312C22⋊Q8—181no—
313C22⋊Q8—181no—
314C4×Q8—91no—
315C4×Q8—92no—
316C4×D4—31no—
317C4×D4—92no—
318C4×D4D3211yescharacteristic
319#117—181no—
320#107—31no—
321#107—92no—
322C4⋊C8—31no—
323C4⋊C8—92no—
324#103—32no—
325#103—92no—
326#103—92no—
327#102—31no—
328#102—31no—
329#102—92no—
330#97—92no—
331C4×C8—31no—
332C23×C3—22no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—61no—
336C22×D3—21no—
337C3×Q8—62no—
338C3×Q8—62no—
339C3×D4—22no—
340C3×D4—21no—
341C3×D4—21no—
342C3×D4—22no—
343C3×D4—61no—
344C3×D4—61no—
345C3×D4#23512yes—
346C3×D4#23712yes—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—44no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—61no—
357C2×C3×C4—62no—
358C2×C3×C4—122no—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365C2×Dic3—21no—
366C2×Dic3—22no—
367C2×Dic3—32no—
368C2×Dic3—32no—
369C2×Dic3—32no—
370C2×Dic3—32no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—64no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—128no—
377C2×Dic3—124no—
378C2×Dic3—124no—
379D12—21no—
380D12—21no—
381C4×D3—42no—
382Dic6—22no—
383Dic6—22no—
384Dic6—64no—
385Dic6—62no—
386Dic6—62no—
387Dic6—128no—
388Dic6—124no—
389Dic6—124no—
390Dic6—124no—
391Dic6—122no—
392Dic6—122no—
393C3×C8—62no—
394C3×C8—61no—
395C3×C8—61no—
396C3⋊C8—21no—
397C3⋊C8—22no—
398C3⋊C8—21no—
399C2×C32—42no—
400C2×C32#54811yescharacteristic
401C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
402C2×C32#57811yescharacteristic
403C3×D3—81no—
404C2×Q8—32no—
405C2×Q8—91no—
406C2×Q8—182no—
407C2×Q8—181no—
408C2×Q8—364no—
409C2×D4—31no—
410C2×D4C2×D3211yescharacteristic
411C22×C4—21no—
412C22×C4—61no—
413C22×C4—182no—
414SD16—64no—
415D8—62no—
416C2×C8—31no—
417C2×C8—31no—
418C2×C8—32no—
419C4⋊C4—31no—
420C4⋊C4—61no—
421C4⋊C4—61no—
422C4⋊C4—91no—
423C4⋊C4—92no—
424C4⋊C4—92no—
425C4⋊C4—182no—
426C4⋊C4—182no—
427C4⋊C4—181no—
428C4⋊C4C2×D3211yescharacteristic
429C22⋊C4—21no—
430C22⋊C4—61no—
431C22⋊C4—182no—
432C22⋊C4—182no—
433C22⋊C4—182no—
434C42—92no—
435C42—182no—
436C42C2×D3211yescharacteristic
437C22×C3—24no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—21no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—121no—
448C22×C3—121no—
449C22×C3—121no—
450C22×C3C2×D3×D411yescharacteristic
451C22×C3C2×D3×D411yescharacteristic
452C2×D3—41no—
453C2×D3—41no—
454C2×D3—41no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—22no—
460C3×C4—41no—
461C3×C4—42no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—121no—
465C3×C4—122no—
466C3×C4#91112yes—
467C3×C4#91412yes—
468C3×C4C2×#23511yescharacteristic
469C3×C4C2×#23711yescharacteristic
470C3×C4#101011yescharacteristic
471C3×C4#101011yescharacteristic
472Dic3—41no—
473Dic3—42no—
474Dic3—64no—
475Dic3—62no—
476Dic3—62no—
477Dic3—62no—
478Dic3—62no—
479Dic3—122no—
480Dic3—124no—
481Dic3—122no—
482Dic3—122no—
483C32#336711yescharacteristic, complemented, Sylow
484C23—21no—
485C23—61no—
486Q8—62no—
487Q8—62no—
488Q8—182no—
489Q8—364no—
490Q8—362no—
491D4—21no—
492D4—61no—
493D4—61no—
494D4#379512yes—
495C2×C4—21no—
496C2×C4—42no—
497C2×C4—61no—
498C2×C4—62no—
499C2×C4—92no—
500C2×C4—92no—
501C2×C4—122no—
502C2×C4—182no—
503C2×C4—364no—
504C2×C4#381111yescharacteristic
505C2×C4#381111yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—61no—
508C8—62no—
509C8—61no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—44no—
514C2×C3—42no—
515C2×C3—42no—
516C2×C3—241no—
517C2×C3#555211yescharacteristic
518C2×C3#559811yescharacteristic
519C2×C3C2×#91111yescharacteristic
520C2×C3C2×#91411yescharacteristic
521C2×C3#577111yescharacteristic
522C2×C3#577911yescharacteristic
523D3—81no—
524C22—22no—
525C22—41no—
526C22—41no—
527C22—121no—
528C22—121no—
529C22—121no—
530C22C2×#381111yescharacteristic
531C4—21no—
532C4—41no—
533C4—121no—
534C4—122no—
535C4—182no—
536C4—182no—
537C4—362no—
538C4#6393712yes—
539C4C2×#379511yescharacteristic
540C4#6429811yescharacteristic
541C3—21no—
542C3#7957111yescharacteristic, complemented
543C3#8041611yescharacteristic, complemented
544C2—42no—
545C2—241no—
546C2#1059491811yescharacteristic
547C2C2×#6393711yescharacteristic
548C2#1059547211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC4×D4D32
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×#634C2semidirect
2. #10593863C2semidirect
3. C3×#5019C2semidirect
6. #10591446C2semidirect
7. #10590541C2semidirect
8. #10590496C2semidirect
9. #10590296C2semidirect
10. #10590287C2semidirect
11. #10590272C2semidirect
54. #5019D3semidirect
483. C32#3367semidirect
542. C3#79571semidirect
543. C3#80416semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
#105938632
C3×#50192
C3×C4×#2132
#105914762
#105914462
#105905412
#105904962
#105902962
#105902872
#105902722
#804163
#795713