Finite Group Databasebeta

← #11878864

Subgroups — #11878864

Order 1152.

1070 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63911C211yesmaximal, characteristic
2#10594808C211yesmaximal, characteristic, complemented
3#10592430C211yesmaximal, characteristic, complemented
4C3×#4731C211yesmaximal, characteristic, complemented
5C3×#4718C211yesmaximal, characteristic, complemented
6#10591183C211yesmaximal, characteristic, complemented
7#10591172C211yesmaximal, characteristic, complemented
8#10590879C212yesmaximal, complemented
9#10590878C212yesmaximal, complemented
10#10590877C212yesmaximal, complemented
11#10590799C212yesmaximal, complemented
12#80138—31nomaximal
13#79305—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×#626—21no—
17C22×#626—21no—
18#64133C2211yescharacteristic
19C2×#3744C2212yescomplemented
20C3×#924C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#204C2212yescomplemented
23#63964—21no—
24#63955—21no—
25#63918C2211yescharacteristic, complemented
26#63911—21no—
27#63911—21no—
28#63911C2212yes—
29#63911C2212yes—
30#63867—21no—
31#63866C2211yescharacteristic, complemented
32#63844C2211yescharacteristic, complemented
33Dic3×Dic6C2211yescharacteristic, complemented
34#63837—21no—
35C2×#3717C2212yescomplemented
36C2×#3716C2212yescomplemented
37C32×C22⋊C8C2211yescharacteristic
38#63648C2212yescomplemented
39C3×#830C2211yescharacteristic
40C3×#821C2212yescomplemented
41C3×Dic3⋊C8C2212yescomplemented
42C3×C8×Dic3C2212yescomplemented
43#63564C2212yescomplemented
44#63563C2212yescomplemented
45C2×#940—31no—
46#5622—31no—
47C2×#874—31no—
48#5470—31no—
49C3×#450—31no—
50C3×#431—31no—
51#5218—31no—
52#5175—32no—
53#5163—32no—
54#5046—31no—
55#4848—32no—
56#4848—32no—
57#4762—32no—
58#4760—32no—
59#4731—31no—
60#4731—31no—
61#4731—31no—
62#4731—31no—
63#4731—61no—
64#4731D311yescharacteristic, complemented
65#4718D311yescharacteristic, complemented
66#4694—32no—
67#4693—32no—
68C23×C3⋊D3—21no—
69C23×C3×D3—21no—
70C22×C32×C4C2311yescharacteristic
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)—42no—
73C2×C4⋊(C3⋊D3)C2312yes—
74C2×#634C2311yescharacteristic
75C22×C3×Dic3D411yescharacteristic
76C22×C3×Dic3D411yescharacteristic
77C2×C3×D12—21no—
78C2×C3×D12—42no—
79C2×C3×D12C2312yes—
80C2×C3×Dic6C2311yescharacteristic
81C2×#627—21no—
82C2×#626—22no—
83C2×#626—22no—
84C2×#626—22no—
85C2×#626—22no—
86C2×#626—44no—
87C2×#626—44no—
88C2×C32×C8C2312yes—
89#3757—21no—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91#3750—21no—
92#3744—42no—
93C3×#217—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—21no—
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3C2311yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C2×C3×C3⋊C8C2312yes—
101C3×#204—42no—
102#3724—21no—
103Dic3⋊Dic3—21no—
104Dic3⋊Dic3—21no—
105Dic3⋊Dic3—21no—
106Dic3⋊Dic3—21no—
107Dic32—21no—
108Dic32—21no—
109#3717—42no—
110#3716—42no—
111#3208—91noSylow
112C22×C3×D4—31no—
113C22×#67—61no—
114C22×#67—61no—
115C22×D12—31no—
116C22×D12—31no—
117C22×D12—61no—
118C22×D12—61no—
119C22×D12—61no—
120C22×D12C2×D311yescharacteristic
121C2×C3×SD16—32no—
122C3×C22⋊Q8—31no—
123C2×C3×C42—31no—
124Q8×Dic3—31no—
125#944—31no—
126C2×#215—32no—
127#940—32no—
128#940—32no—
129#940—61no—
130#940—61no—
131C2×#214—32no—
132#926—61no—
133#924—31no—
134#924—31no—
135#924—61no—
136#924—61no—
137#924C2×D311yescharacteristic
138C2×C4×Dic3C2×D311yescharacteristic
139C2×#204—32no—
140C2×#204—32no—
141C2×#204—32no—
142C2×#204—32no—
143C2×#204—62no—
144C2×#204C2×D312yescomplemented
145#889—61no—
146#888—31no—
147#887—31no—
148#887—61no—
149#878—61no—
150#877—61no—
151#874—32no—
152#874—32no—
153#874—61no—
154#874—61no—
155#870—61no—
156#869—31no—
157#869—31no—
158C4×Dic6—31no—
159C4×Dic6—31no—
160C4×Dic6—61no—
161C3×C4⋊C8—32no—
162C3×#102—32no—
163C3×C22⋊C8—21no—
164C3×C22⋊C8—31no—
165C3×C22⋊C8C2×D311yescharacteristic
166C3×C22⋊C8C2×D311yescharacteristic
167C3×C4×C8—32no—
168#832—32no—
169#830C2×D311yescharacteristic
170#821—32no—
171#821—32no—
172#821—32no—
173#821—32no—
174#821—62no—
175#821C2×D312yescomplemented
176Dic3⋊C8C2×D312yescomplemented
177C8×Dic3C2×D312yescomplemented
178#809—32no—
179C23×C32C2×D411yescharacteristic
180C22×C3⋊D3—22no—
181C22×C3⋊D3—42no—
182C22×C3⋊D3—42no—
183C22×C3⋊D3—42no—
184C22×C3×D3—22no—
185C22×C3×D3—42no—
186C22×C3×D3—42no—
187C22×C3×D3—42no—
188C2×C32×C4—22no—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2411yescharacteristic
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C4⋊(C3⋊D3)—22no—
194C4⋊(C3⋊D3)—22no—
195C4⋊(C3⋊D3)—42no—
196#634—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3SD1614yescomplemented
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C3×D12—22no—
206C3×D12—22no—
207C3×D12—42no—
208C3×Dic6—22no—
209#627—42no—
210#626—44no—
211#626—44no—
212#626—44no—
213#626—44no—
214C32×C8—22no—
215C3×C3⋊C8—22no—
216#533—91no—
217C2×#127—91no—
218#492—92no—
219#486—92no—
220#460—92no—
221#460—92no—
222#450—31no—
223#450—91no—
224#450—91no—
225#450—91no—
226#431—31no—
227C24×C3—61no—
228C23×D3—21no—
229C23×D3—61no—
230C23×D3—61no—
231C23×D3—121no—
232C2×C3×Q8—31no—
233C2×C3×D4—32no—
234C2×C3×D4—61no—
235C2×C3×D4—122no—
236C22×C3×C4—21no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—62no—
242C2×#67—62no—
243C2×#67—62no—
244C2×#67—62no—
245C2×#67—124no—
246C2×#67—124no—
247C22×Dic3D1211yescharacteristic
248C22×Dic3D1211yescharacteristic
249C2×D12—21no—
250C2×D12—32no—
251C2×D12—32no—
252C2×D12—42no—
253C2×D12—62no—
254C2×D12—62no—
255C2×D12—62no—
256C2×D12—62no—
257C2×D12—62no—
258C2×D12—61no—
259C2×D12—61no—
260C2×D12—121no—
261C2×D12—122no—
262C2×D12—122no—
263C2×D12—124no—
264C2×D12—124no—
265C2×D12—124no—
266C2×D12C22×D312yes—
267C2×Dic6—31no—
268C2×Dic6—31no—
269C2×Dic6—61no—
270C2×Dic6—61no—
271C2×Dic6—61no—
272C2×Dic6C22×D311yescharacteristic
273C3×SD16—122no—
274C2×C3×C8—22no—
275C2×C3×C8—32no—
276C2×C3×C8C22×D312yes—
277C2×C3×C8C22×D312yes—
278C3×C4⋊C4—31no—
279C3×C4⋊C4—61no—
280C3×C22⋊C4—61no—
281C3×C42—31no—
282C3×C42—31no—
283C3×C42—31no—
284C3×C42—31no—
285#217—21no—
286#217—61no—
287#217—61no—
288#217—121no—
289#215—122no—
290#214—122no—
291C4⋊Dic3—31no—
292C4⋊Dic3—31no—
293C4⋊Dic3—61no—
294C4⋊Dic3—61no—
295C4⋊Dic3—61no—
296C4⋊Dic3—61no—
297C4⋊Dic3—61no—
298C4⋊Dic3C22×D311yescharacteristic
299Dic3⋊C4—21no—
300Dic3⋊C4—61no—
301Dic3⋊C4—61no—
302Dic3⋊C4—61no—
303Dic3⋊C4—61no—
304Dic3⋊C4—61no—
305Dic3⋊C4—61no—
306Dic3⋊C4—61no—
307Dic3⋊C4—61no—
308Dic3⋊C4—121no—
309C4×Dic3—61no—
310C4×Dic3—61no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C4×Dic3D1211yescharacteristic
314C4×Dic3D1211yescharacteristic
315C4×Dic3C22×D311yescharacteristic
316C4×Dic3C22×D311yescharacteristic
317C2×C3⋊C8C22×D312yes—
318#204—42no—
319#204—122no—
320#204—122no—
321#204—124no—
322#204—122no—
323#204—122no—
324C22×C32—21no—
325C22×C32—21no—
326C22×C32C2×SD1612yes—
327C22×C32C22×D411yescharacteristic
328C2×C3⋊D3—42no—
329C2×C3⋊D3—42no—
330C2×C3⋊D3—42no—
331C2×C3⋊D3—84no—
332C2×C3×D3—42no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C2×C3×D3—84no—
336C32×C4—21no—
337C32×C4H(5,𝔽2)12yes—
338C3⋊Dic3—41no—
339C3⋊Dic3—41no—
340C3×Dic3—21no—
341C3×Dic3—41no—
342C3×Dic3—41no—
343C3×Dic3C2×SD1612yes—
344C3×Dic3C2×SD1612yes—
345C3×Dic3AGL(1,ℤ/8)12yes—
346C22×D4—31no—
347C22×D4—91no—
348C22×D4—181no—
349C22×D4—181no—
350C2×SD16—32no—
351C2×SD16—92no—
352C2×SD16—92no—
353C2×SD16—92no—
354C4⋊Q8—91no—
355C4⋊Q8—91no—
356#127—92no—
357#127—92no—
358#127—181no—
359#127—181no—
360#125—181no—
361C22⋊Q8—31no—
362C22⋊Q8—91no—
363C22⋊Q8—181no—
364C4×Q8—91no—
365C4×Q8—91no—
366C4×Q8—181no—
367#117—181no—
368C2×C42—31no—
369C4⋊C8—32no—
370#102—32no—
371#102—92no—
372#102—92no—
373#102—92no—
374C22⋊C8—31no—
375C22⋊C8D3211yescharacteristic
376C4×C8—32no—
377C23×C3—21no—
378C23×C3—62no—
379C23×C3—122no—
380C23×C3—122no—
381C23×C3—122no—
382C23×C3C2×D1211yescharacteristic
383C23×C3D3×D411yescharacteristic
384C22×D3—22no—
385C22×D3—42no—
386C22×D3—42no—
387C22×D3—42no—
388C22×D3—62no—
389C22×D3—62no—
390C22×D3—122no—
391C22×D3—122no—
392C22×D3—122no—
393C22×D3—122no—
394C22×D3—122no—
395C22×D3—124no—
396C22×D3—122no—
397C22×D3—122no—
398C22×D3—242no—
399C22×D3—242no—
400C3×Q8—62no—
401C3×D4—62no—
402C3×D4—62no—
403C3×D4—122no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—34no—
409C2×C3×C4—31no—
410C2×C3×C4—31no—
411C2×C3×C4—31no—
412C2×C3×C4—31no—
413C2×C3×C4—42no—
414C2×C3×C4—62no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4C2×D1211yescharacteristic
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4C23×D311yescharacteristic
420C2×C3×C4C23×D311yescharacteristic
421#67—124no—
422#67—124no—
423#67—124no—
424#67—124no—
425C2×Dic3—22no—
426C2×Dic3—21no—
427C2×Dic3—21no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—61no—
431C2×Dic3—61no—
432C2×Dic3—121no—
433C2×Dic3—121no—
434C2×Dic3#20414yescomplemented
435C2×Dic3C2×D1211yescharacteristic
436C2×Dic3C2×D1211yescharacteristic
437C2×Dic3C2×D1211yescharacteristic
438C2×Dic3C2×D1211yescharacteristic
439D12—22no—
440D12—22no—
441D12—42no—
442D12—64no—
443D12—62no—
444D12—62no—
445D12—62no—
446D12—62no—
447D12—122no—
448D12—122no—
449D12—122no—
450D12—124no—
451D12—124no—
452D12—124no—
453D12—124no—
454D12—124no—
455Dic6—22no—
456Dic6—62no—
457Dic6—62no—
458Dic6—122no—
459Dic6—122no—
460Dic6—122no—
461C3×C8—22no—
462C3×C8—22no—
463C3×C8—42no—
464C3×C8—62no—
465C3⋊C8—22no—
466C2×C32—22no—
467C2×C32#53511yescharacteristic
468C2×C32C22×SD1611yescharacteristic
469C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
470C3⋊D3—82no—
471C3×D3—82no—
472C24—61no—
473C24—181no—
474C2×Q8—31no—
475C2×Q8—91no—
476C2×Q8—181no—
477C2×D4—32no—
478C2×D4—61no—
479C2×D4—92no—
480C2×D4—122no—
481C2×D4—182no—
482C2×D4—182no—
483C2×D4—182no—
484C2×D4—182no—
485C2×D4—181no—
486C2×D4—362no—
487C2×D4—364no—
488C2×D4—364no—
489C22×C4—31no—
490C22×C4—31no—
491C22×C4C2×D3211yescharacteristic
492SD16—122no—
493SD16—362no—
494SD16—362no—
495SD16—362no—
496C2×C8—32no—
497C2×C8C2×D3212yes—
498C4⋊C4—31no—
499C4⋊C4—61no—
500C4⋊C4—91no—
501C4⋊C4—181no—
502C4⋊C4—181no—
503C4⋊C4—181no—
504C4⋊C4—181no—
505C4⋊C4—181no—
506C4⋊C4—181no—
507C22⋊C4—61no—
508C22⋊C4—181no—
509C42—31no—
510C42—31no—
511C42—31no—
512C42—31no—
513C42—181no—
514C42—181no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—22no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—122no—
524C22×C3—122no—
525C22×C3—122no—
526C22×C3—244no—
527C22×C3C2×#20412yes—
528C22×C3D3×SD1612yes—
529C22×C3C22×D1211yescharacteristic
530C22×C3C2×D3×D411yescharacteristic
531C2×D3—42no—
532C2×D3—42no—
533C2×D3—42no—
534C2×D3—84no—
535C2×D3—124no—
536C2×D3—122no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—122no—
540C2×D3—122no—
541C2×D3—122no—
542C2×D3—242no—
543C2×D3—242no—
544C2×D3—244no—
545C2×D3—244no—
546C2×D3—248no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—22no—
550C3×C4—32no—
551C3×C4—32no—
552C3×C4—32no—
553C3×C4—41no—
554C3×C4—61no—
555C3×C4—121no—
556C3×C4—121no—
557C3×C4#100412yes—
558C3×C4#100912yes—
559Dic3—21no—
560Dic3—41no—
561Dic3—41no—
562Dic3—121no—
563Dic3—121no—
564Dic3—121no—
565Dic3—121no—
566Dic3—241no—
567Dic3—241no—
568Dic3C2×#20412yes—
569Dic3C2×#20412yes—
570Dic3#90812yes—
571C32#320811yescharacteristic, complemented, Sylow
572C23—62no—
573C23—122no—
574C23—122no—
575C23—122no—
576C23—182no—
577C23—362no—
578C23—362no—
579C23—362no—
580C23D3×D1211yescharacteristic
581Q8—62no—
582Q8—182no—
583Q8—362no—
584D4—62no—
585D4—62no—
586D4—122no—
587D4—182no—
588D4—182no—
589D4—362no—
590D4—364no—
591D4—364no—
592D4—364no—
593D4—364no—
594C2×C4—22no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—31no—
598C2×C4—34no—
599C2×C4—31no—
600C2×C4—62no—
601C2×C4—61no—
602C2×C4—61no—
603C2×C4—181no—
604C2×C4—181no—
605C2×C4D3×D1211yescharacteristic
606C2×C4C22×D3211yescharacteristic
607C8—22no—
608C8—62no—
609C2×C3—22no—
610C2×C3—22no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—42no—
615C2×C3—242no—
616C2×C3#552511yescharacteristic
617C2×C3#559211yescharacteristic
618C2×C3C22×#20411yescharacteristic
619C2×C3C2×#90811yescharacteristic
620C2×C3C2×D3×SD1611yescharacteristic
621C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
622D3—82no—
623D3—244no—
624D3—242no—
625D3—242no—
626C22—21no—
627C22—21no—
628C22—122no—
629C22—122no—
630C22—122no—
631C22—244no—
632C22—362no—
633C22—362no—
634C22—362no—
635C22—724no—
636C22D3×#20412yes—
637C22C2×D3×D1211yescharacteristic
638C4—21no—
639C4—32no—
640C4—32no—
641C4—32no—
642C4—61no—
643C4—121no—
644C4—121no—
645C4—361no—
646C4—361no—
647C4#6431412yes—
648C3—21no—
649C3#7930511yescharacteristic, complemented
650C3#8013811yescharacteristic, complemented
651C2—22no—
652C2—242no—
653C2—722no—
654C2#1059408011yescharacteristic
655C2C2×D3×#20411yescharacteristic
656C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#63911C2
hypercenterC22⋊C8D32
hypocenterC32#3208
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. #10594808C2semidirect
3. #10592430C2semidirect
4. C3×#4731C2semidirect
5. C3×#4718C2semidirect
6. #10591183C2semidirect
7. #10591172C2semidirect
8. #10590879C2semidirect
9. #10590878C2semidirect
10. #10590877C2semidirect
11. #10590799C2semidirect
19. C2×#3744C22semidirect
22. C2×C3×#204C22semidirect
25. #63918C22semidirect
31. #63866C22semidirect
32. #63844C22semidirect
33. Dic3×Dic6C22semidirect
35. C2×#3717C22semidirect
36. C2×#3716C22semidirect
38. #63648C22semidirect
40. C3×#821C22semidirect
41. C3×Dic3⋊C8C22semidirect
42. C3×C8×Dic3C22semidirect
43. #63564C22semidirect
44. #63563C22semidirect
64. #4731D3semidirect
65. #4718D3semidirect
144. C2×#204C2×D3semidirect
175. #821C2×D3semidirect
176. Dic3⋊C8C2×D3semidirect
177. C8×Dic3C2×D3semidirect
200. C2×C3×Dic3SD16semidirect
434. C2×Dic3#204semidirect
571. C32#3208semidirect
649. C3#79305semidirect
650. C3#80138semidirect

Maximal subgroups

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

subgroupindex
C2×#639112
#105948082
#105924302
C3×#47312
C3×#47182
#105911832
#105911722
#105908792
#105908782
#105908772
#105907992
#801383
#793053