Finite Group Databasebeta

← #11868823

Subgroups — #11868823

Order 1152.

895 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63919C211yesmaximal, characteristic, complemented
2#10594958C211yesmaximal, characteristic
3#10592817C211yesmaximal, characteristic, complemented
4C3×#5133C211yesmaximal, characteristic
5C3×#5121C211yesmaximal, characteristic, complemented
6#10591139C211yesmaximal, characteristic, complemented
7#10591087C211yesmaximal, characteristic
8#10590817C212yesmaximal, complemented
9#10590816C212yesmaximal, complemented
10#10590778C212yesmaximal, complemented
11#10590776C212yesmaximal, complemented
12#79240—31nomaximal
13#78870—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×#627—21no—
16C2×C32×M16C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22#67⋊Dic3—21no—
23#67⋊Dic3—21no—
24C2×#3724—21no—
25#63919—21no—
26#63919—21no—
27#63919C2212yes—
28#63919C2212yes—
29#63898C2211yescharacteristic
30#63898C2211yescharacteristic
31C4×D3×Dic3—21no—
32#63855—21no—
33#63843C2211yescharacteristic
34#63843C2211yescharacteristic
35#63641C2212yes—
36#63641C2212yes—
37C3×#821C2212yes—
38C3×#818C2212yes—
39C3×#817C2212yes—
40C3×#816C2212yes—
41#63576C2212yes—
42#63574C2212yes—
43#63565C2212yes—
44#63562C2212yes—
45Dic3×#41—31no—
46#5522—31no—
47C2×#888—31no—
48C2×#888—31no—
49C3×#428—31no—
50C3×#417—31no—
51#5232—31no—
52#5133D311yescharacteristic
53#5121D311yescharacteristic, complemented
54#5118—31no—
55#5118—31no—
56#5118—61no—
57#4995—31no—
58#4966—31no—
59#4964—31no—
60#4890—32no—
61#4875—32no—
62#4870—32no—
63#4854—32no—
64#4793—32no—
65#4791—32no—
66#4761—32no—
67#4759—32no—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3D411yescharacteristic
70C22×C3⋊Dic3D411yescharacteristic
71C2×C3×#67—21no—
72C22×C3×Dic3—21no—
73C22×C3×Dic3—21no—
74C3×#235—22no—
75C3×#235Q814yescomplemented
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×Dic6C2311yescharacteristic
79C2×#627—22no—
80C2×#627—22no—
81C2×#627—44no—
82C2×D3×Dic3—21no—
83C2×D3×Dic3—21no—
84C32×M16—22no—
85C2×C32×C8C2312yes—
86C4×C3⋊Dic3D411yescharacteristic
87C4×C3⋊Dic3D411yescharacteristic
88C4×C3⋊Dic3C2311yescharacteristic
89C4×C3⋊Dic3C2311yescharacteristic
90#3748—22no—
91C2×C3⋊(C3⋊C8)C2312yes—
92C3×#217—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×C4⋊Dic3C2312yes—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4×Dic3—21no—
100#3724—22no—
101#3724—22no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106Dic32—21no—
107Dic32—21no—
108#3079—91noSylow
109C2×C3×#41—31no—
110C2×#235C2×D311yescharacteristic
111C22×Dic6—61no—
112C22×Dic6—61no—
113C2×C3×M16—21no—
114C2×C3×M16C2×D311yescharacteristic
115C2×C3×M16C2×D311yescharacteristic
116C3×#117—31no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C4⋊C4—31no—
119Q8×Dic3—31no—
120Q8×Dic3—31no—
121D4×Dic3—31no—
122D4×Dic3—31no—
123D4×Dic3—61no—
124D4×Dic3—61no—
125#926—61no—
126#926C2×D311yescharacteristic
127C2×C4⋊Dic3C2×D311yescharacteristic
128C2×C4⋊Dic3C2×D311yescharacteristic
129C2×Dic3⋊C4—61no—
130C2×Dic3⋊C4—61no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—61no—
134C2×C4×Dic3—61no—
135C2×#208—31no—
136C2×#208—31no—
137C2×#208—61no—
138#893—31no—
139#893—31no—
140#888—32no—
141#888—32no—
142#888—32no—
143#888—32no—
144#888—61no—
145#888—61no—
146#888—61no—
147#888—61no—
148#887—31no—
149#887—31no—
150#67⋊C4—61no—
151#67⋊C4—61no—
152#872—61no—
153C42×D3—61no—
154C3×#107—32no—
155C3×#106—32no—
156C3×#103—32no—
157C3×#102—32no—
158#835—32no—
159#832—32no—
160#821C2×D312yes—
161#818C2×D312yes—
162#817C2×D312yes—
163#816C2×D312yes—
164Dic3⋊C8—32no—
165Dic3⋊C8—32no—
166Dic3⋊C8—32no—
167Dic3⋊C8—32no—
168Dic3⋊C8—62no—
169Dic3⋊C8—62no—
170#810—32no—
171#809—32no—
172#808—32no—
173#808—32no—
174#807—32no—
175#807—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3×D3—21no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×Q812yes—
180C2×C32×C4#4112yes—
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3C2×D411yescharacteristic
185C2×C3⋊Dic3C2×D411yescharacteristic
186C2×C3⋊Dic3C2×D411yescharacteristic
187C2×C3⋊Dic3C2×D411yescharacteristic
188C3×#67—24no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—42no—
195C2×C3×Dic3—42no—
196C3×D12—21no—
197C3×D12C2×Q812yescomplemented
198C3×C4×D3—24no—
199C3×Dic6—21no—
200C3×Dic6C2×Q812yescomplemented
201#627—44no—
202#627—44no—
203D3×Dic3—42no—
204D3×Dic3—42no—
205C32×C8—22no—
206C3⋊(C3⋊C8)—22no—
207C2×C4⋊Q8—91no—
208C4×#41—91no—
209#477—92no—
210#476—92no—
211#475—92no—
212#474—92no—
213#428—31no—
214#428—91no—
215#423—91no—
216#417—31no—
217#417—91no—
218C3×#41—34no—
219C3×#41—62no—
220C2×C3×Q8—31no—
221C2×C3×D4—31no—
222C2×C3×D4—61no—
223C22×C3×C4—21no—
224C22×C3×C4—61no—
225C22×C3×C4—61no—
226C22×C3×C4—61no—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C2×#67—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—31no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—31no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240#235—22no—
241#235Dic614yescomplemented
242C2×D12C22×D311yescharacteristic
243C2×C4×D3—21no—
244C2×C4×D3—61no—
245C2×C4×D3—61no—
246C2×Dic6—62no—
247C2×Dic6—62no—
248C2×Dic6—62no—
249C2×Dic6—62no—
250C2×Dic6—124no—
251C2×Dic6—124no—
252C2×Dic6C22×D311yescharacteristic
253C3×M16—22no—
254C3×M16—22no—
255C3×M16—42no—
256C2×C3×C8—22no—
257C2×C3×C8C22×D312yes—
258C2×C3×C8C22×D312yes—
259C3×C4⋊C4—31no—
260C3×C4⋊C4—32no—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—32no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4—61no—
265C3×C22⋊C4—61no—
266C3×C42—61no—
267#217—21no—
268#217—61no—
269#217—61no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—61no—
272C4⋊Dic3—21no—
273C4⋊Dic3—21no—
274C4⋊Dic3—61no—
275C4⋊Dic3—61no—
276C4⋊Dic3C22×D311yescharacteristic
277C4⋊Dic3C22×D312yes—
278C4⋊Dic3C22×D311yescharacteristic
279C4⋊Dic3C22×D312yes—
280Dic3⋊C4—61no—
281Dic3⋊C4—61no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286C4×Dic3—21no—
287C4×Dic3—31no—
288C4×Dic3—31no—
289C4×Dic3—31no—
290C4×Dic3—31no—
291C4×Dic3—31no—
292C4×Dic3—31no—
293C4×Dic3—31no—
294C4×Dic3—31no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3—61no—
299C4×Dic3—61no—
300C4×Dic3—61no—
301C4×Dic3—61no—
302C4×Dic3—61no—
303#208—62no—
304#208—62no—
305#208—122no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—32no—
308C2×C3⋊C8—62no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32C22⋊Q812yes—
312C22×C32C22×D411yescharacteristic
313C2×C3×D3—22no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C32×C4C22⋊Q812yes—
317C32×C4C22×Q811yescharacteristic
318C32×C4C2×#4111yescharacteristic
319C3⋊Dic3—21no—
320C3⋊Dic3—21no—
321C3⋊Dic3AGL(1,ℤ/8)12yes—
322C3⋊Dic3#13712yes—
323C3×Dic3—22no—
324C3×Dic3—41no—
325C3×Dic3—42no—
326C3×Dic3—42no—
327C3×Dic3—41no—
328C2×#41—31no—
329C22×Q8—181no—
330C2×M16—91no—
331C2×M16D3211yescharacteristic
332C4⋊Q8—92no—
333C4⋊Q8—92no—
334C4⋊Q8—181no—
335C4⋊Q8—181no—
336C4×Q8—91no—
337C4×Q8—91no—
338C4×D4—91no—
339C4×D4—91no—
340C4×D4—181no—
341C4×D4—181no—
342#117—31no—
343#117—181no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—181no—
347C2×C42—91no—
348C2×C42—181no—
349#107—32no—
350#107—92no—
351#106—32no—
352#106—92no—
353C4⋊C8—92no—
354C4⋊C8—92no—
355#103—32no—
356#103—92no—
357#102—32no—
358#102—92no—
359C23×C3—21no—
360C23×C3—61no—
361C23×C3D3×D411yescharacteristic
362C23×C3D3×D411yescharacteristic
363C22×D3—21no—
364C3×Q8—32no—
365C3×Q8—61no—
366C3×D4—32no—
367C3×D4—64no—
368C3×D4—61no—
369C2×C3×C4—21no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—61no—
374C2×C3×C4—64no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—122no—
380C2×C3×C4—122no—
381C2×C3×C4C2×Dic612yes—
382C2×C3×C4#23512yes—
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4#23712yes—
386C2×C3×C4D3×Q812yes—
387C2×C3×C4C23×D311yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389#67—24no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—31no—
396C2×Dic3—31no—
397C2×Dic3—31no—
398C2×Dic3—31no—
399C2×Dic3—31no—
400C2×Dic3—31no—
401C2×Dic3—31no—
402C2×Dic3—31no—
403C2×Dic3—42no—
404C2×Dic3—42no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—122no—
414C2×Dic3—122no—
415C2×Dic3—122no—
416C2×Dic3—122no—
417D12—21no—
418D12C2×Dic612yescomplemented
419C4×D3—24no—
420C4×D3—122no—
421C4×D3—122no—
422Dic6—21no—
423Dic6—124no—
424Dic6—124no—
425Dic6—124no—
426Dic6—124no—
427Dic6C2×Dic612yescomplemented
428C3×C8—22no—
429C3×C8—22no—
430C3×C8—42no—
431C3⋊C8—62no—
432C3⋊C8—62no—
433C3⋊C8—122no—
434C2×C32—22no—
435C2×C32C2×C22⋊Q811yescharacteristic
436C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
437C2×C32C2×#13711yescharacteristic
438C3×D3—42no—
439#41—34no—
440#41—62no—
441C2×Q8—31no—
442C2×Q8—182no—
443C2×Q8—182no—
444C2×Q8—364no—
445C2×D4—31no—
446C2×D4—61no—
447C22×C4—61no—
448C22×C4—61no—
449C22×C4—61no—
450C22×C4—91no—
451C22×C4—91no—
452C22×C4—181no—
453C22×C4—181no—
454C22×C4C2×D3211yescharacteristic
455M16—22no—
456M16—182no—
457C2×C8—92no—
458C2×C8C2×D3212yes—
459C4⋊C4—32no—
460C4⋊C4—32no—
461C4⋊C4—31no—
462C4⋊C4—31no—
463C4⋊C4—61no—
464C4⋊C4—61no—
465C4⋊C4—182no—
466C4⋊C4—182no—
467C4⋊C4—181no—
468C4⋊C4—181no—
469C22⋊C4—61no—
470C22⋊C4—181no—
471C22⋊C4—181no—
472C42—61no—
473C42—91no—
474C42—91no—
475C42—91no—
476C42—91no—
477C42—181no—
478C42—181no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—22no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—62no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3#87812yes—
491C22×C3#89612yes—
492C22×C3C2×D3×D411yescharacteristic
493C22×C3C2×D3×D411yescharacteristic
494C2×D3—22no—
495C2×D3—41no—
496C2×D3—41no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—22no—
500C3×C4—62no—
501C3×C4—122no—
502C3×C4—122no—
503C3×C4—121no—
504C3×C4—121no—
505C3×C4#87812yes—
506C3×C4#89612yes—
507C3×C4C22×Dic611yescharacteristic
508C3×C4C2×#23511yescharacteristic
509C3×C4C2×#23711yescharacteristic
510C3×C4C2×D3×Q811yescharacteristic
511Dic3—22no—
512Dic3—32no—
513Dic3—32no—
514Dic3—32no—
515Dic3—32no—
516Dic3—42no—
517Dic3—42no—
518Dic3—41no—
519Dic3—41no—
520Dic3—62no—
521Dic3—62no—
522Dic3—61no—
523Dic3—61no—
524Dic3—61no—
525Dic3—61no—
526Dic3—121no—
527Dic3—121no—
528C32#307911yescharacteristic, complemented, Sylow
529C23—61no—
530C23#380211yescharacteristic
531Q8—32no—
532Q8—61no—
533Q8—364no—
534Q8—364no—
535D4—32no—
536D4—64no—
537D4—61no—
538C2×C4—61no—
539C2×C4—64no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—91no—
545C2×C4—91no—
546C2×C4—91no—
547C2×C4—91no—
548C2×C4—122no—
549C2×C4—122no—
550C2×C4—182no—
551C2×C4—182no—
552C2×C4—362no—
553C2×C4—362no—
554C2×C4D3×Dic612yes—
555C2×C4#380211yescharacteristic
556C2×C4#380412yes—
557C2×C4C22×D3211yescharacteristic
558C8—22no—
559C8—182no—
560C2×C3—22no—
561C2×C3—22no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—42no—
566C2×C3—122no—
567C2×C3C2×#87811yescharacteristic
568C2×C3C2×#89611yescharacteristic
569C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
570C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
571C2×C3D3×#13711yescharacteristic
572C2×C3D3×#13711yescharacteristic
573D3—42no—
574C22—21no—
575C22—21no—
576C22—62no—
577C22—121no—
578C22—121no—
579C22#6389912yes—
580C22C2×#380211yescharacteristic
581C4—62no—
582C4—92no—
583C4—92no—
584C4—122no—
585C4—122no—
586C4—121no—
587C4—121no—
588C4—181no—
589C4—181no—
590C4#6389912yes—
591C4C2×D3×Dic611yescharacteristic
592C4C2×#380411yescharacteristic
593C3—21no—
594C3#7887011yescharacteristic, complemented
595C3#7924011yescharacteristic, complemented
596C2—22no—
597C2—122no—
598C2#1059471611yescharacteristic
599C2#1059471711yescharacteristic
600C2C2×#6389911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC2×M16D32
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#63919C2semidirect
3. #10592817C2semidirect
5. C3×#5121C2semidirect
6. #10591139C2semidirect
8. #10590817C2semidirect
9. #10590816C2semidirect
10. #10590778C2semidirect
11. #10590776C2semidirect
53. #5121D3semidirect
75. C3×#235Q8semidirect
197. C3×D12C2×Q8semidirect
200. C3×Dic6C2×Q8semidirect
241. #235Dic6semidirect
418. D12C2×Dic6semidirect
427. Dic6C2×Dic6semidirect
528. C32#3079semidirect
594. C3#78870semidirect
595. C3#79240semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
#105949582
#105928172
C3×#51332
C3×#51212
#105911392
#105910872
#105908172
#105908162
#105907782
#105907762
#792403
#788703