Finite Group Databasebeta

← #11858091

Subgroups — #11858091

Order 1152.

1585 conjugacy classes of subgroups.

The subgroup lattice has 669 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64297C211yesmaximal, characteristic
2C2×#64116C211yesmaximal, characteristic, complemented
3#10594990C211yesmaximal, characteristic, complemented
4C3×#5133C211yesmaximal, characteristic, complemented
5C3×#5120C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7#10591083C211yesmaximal, characteristic, complemented
8#10590957C212yesmaximal, complemented
9#10590956C212yesmaximal, complemented
10#10590691C212yesmaximal, complemented
11#10590672C212yesmaximal, complemented
12#78957—31nomaximal
13#78883—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17C2×#3804—22no—
18C2×#3799—21no—
19C2×#3797C2212yes—
20#64297—24no—
21#64297C418yescomplemented
22C2×#3796C2212yes—
23C2×D3×Dic6—21no—
24C2×C32×M16C2211yescharacteristic
25C22×C3⋊(C3⋊C8)C2211yescharacteristic
26#64116—24no—
27C2×#3743C2212yes—
28C2×C8×C3⋊D3C2212yes—
29C3×#926C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31#63952—22no—
32#63900C2212yes—
33#63894—21no—
34#63849C2212yes—
35#63844—21no—
36C3×#821C2212yes—
37C3×#816C2212yes—
38C3×#816C2212yes—
39C3×#816C2212yes—
40#63565C2211yescharacteristic
41#63565C2211yescharacteristic
42#63565C2212yes—
43#63565C2212yes—
44#63562C2211yescharacteristic
45#63562C2211yescharacteristic
46C2×#1010—31no—
47C2×#1007—31no—
48C2×#907—31no—
49C2×#907—31no—
50C2×#907—61no—
51#5523—31no—
52#5504—31no—
53C3×#419—31no—
54C3×#417—31no—
55#5233—31no—
56C2×#835—31no—
57#5133D311yescharacteristic, complemented
58#5120D311yescharacteristic, complemented
59#5002—31no—
60C2×#810—31no—
61#4804—32no—
62#4803—32no—
63#4802—32no—
64#4802—32no—
65D3×#103—32no—
66D3×#103—32no—
67#4772—32no—
68#4771—32no—
69C22×C32×C4C2311yescharacteristic
70C2×#638D412yes—
71#3828C2×C414yes—
72#3828D414yes—
73C2×C4⋊(C3⋊D3)D411yescharacteristic
74C2×C4×C3⋊D3C2312yes—
75C2×#634D411yescharacteristic
76C2×C3×#67—21no—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—21no—
79C3×#235—22no—
80C3×#235C2×C414yescomplemented
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×Dic6—21no—
84C2×C3×Dic6—22no—
85C2×C3×Dic6C2×C414yescomplemented
86C2×C3×Dic6C2312yes—
87C2×C3×Dic6C2311yescharacteristic
88C2×#627—22no—
89C2×#626—22no—
90C2×#624—22no—
91C2×#624—22no—
92#3804—216no—
93C2×D3×Dic3—22no—
94#3799—28no—
95#3797—24no—
96#3797C2×C418yescomplemented
97#3796—24no—
98#3796C2×C418yescomplemented
99D3×Dic6—28no—
100C32×M16—22no—
101C2×C32×C8C2312yes—
102C2×C3⋊(C3⋊C8)—22no—
103C2×C3⋊(C3⋊C8)C2311yescharacteristic
104C2×C3⋊(C3⋊C8)C2311yescharacteristic
105#3743—24no—
106C8×C3⋊D3—24no—
107C3×#217—21no—
108C3×C4⋊Dic3—21no—
109C3×C4⋊Dic3C2312yes—
110C3×C4⋊Dic3C2311yescharacteristic
111C3×C4⋊Dic3C2311yescharacteristic
112C3×C4×Dic3—21no—
113#3724—22no—
114#3722—22no—
115Dic32—22no—
116#2898—91noSylow
117C2×C3×#41—31no—
118C22×C3×Q8—31no—
119#1010—38no—
120#1010—64no—
121#1007—38no—
122#1007—64no—
123C2×#239—32no—
124C2×#239—61no—
125C2×D3×Q8—32no—
126C2×D3×Q8—32no—
127C2×D3×Q8—61no—
128C2×#237—32no—
129C2×#237—62no—
130C2×#235—31no—
131C2×#235—31no—
132C2×#235—61no—
133C2×#235—61no—
134C2×#235—62no—
135C2×#235C2×D311yescharacteristic
136C22×Dic6—61no—
137C22×Dic6C2×D311yescharacteristic
138C2×C3×M16—21no—
139C2×C3×M16C2×D311yescharacteristic
140C2×C3×M16C2×D311yescharacteristic
141C3×#117—31no—
142C2×C3×C4⋊C4—31no—
143C4×#67—62no—
144#926C2×D311yescharacteristic
145C2×C4⋊Dic3C2×D311yescharacteristic
146C22×C3⋊C8—31no—
147C22×C3⋊C8—31no—
148C22×C3⋊C8—61no—
149#907—64no—
150#907—64no—
151#907—68no—
152C2×ΓL(1,𝔽25)—32no—
153C2×ΓL(1,𝔽25)—32no—
154C2×ΓL(1,𝔽25)—62no—
155C2×D3×C8—32no—
156C2×D3×C8—32no—
157C2×D3×C8—62no—
158#893—61no—
159#892—32no—
160#892—32no—
161D3×C4⋊C4—32no—
162D3×C4⋊C4—32no—
163#887—61no—
164#67⋊C4—62no—
165C4×D12—61no—
166C4×Dic6—61no—
167C3×#103—32no—
168C3×#103—32no—
169C3×#103—32no—
170C3×#102—32no—
171#835—32no—
172#835—32no—
173#835—31no—
174#835—31no—
175#832—31no—
176#832—31no—
177#821C2×D312yes—
178#816C2×D312yes—
179#816C2×D312yes—
180#816C2×D312yes—
181#810—32no—
182#810—32no—
183#810—31no—
184#810—31no—
185#809—31no—
186#809—31no—
187C23×C32C2×D411yescharacteristic
188C22×C3⋊D3C2×D412yes—
189C22×C3×D3—21no—
190C2×C32×C4C22×C412yes—
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D412yes—
193C2×C32×C4C2411yescharacteristic
194#638C22⋊C418yes—
195C2×C3⋊Dic3C2×D412yes—
196C4⋊(C3⋊D3)C22⋊C414yes—
197C4×C3⋊D3C22×C414yes—
198C4×C3⋊D3C2×D414yes—
199#634C22⋊C414yes—
200C3×#67—24no—
201C2×C3×Dic3—24no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—81no—
208C3×D12—21no—
209C3×D12C22×C412yes—
210C3×C4×D3—24no—
211C3×Dic6—24no—
212C3×Dic6—22no—
213C3×Dic6—21no—
214C3×Dic6C22×C414yes—
215C3×Dic6C22×C412yes—
216#627—28no—
217#626—28no—
218#624—28no—
219#624—82no—
220D3×Dic3—28no—
221C32×C8—22no—
222C3⋊(C3⋊C8)—21no—
223C3⋊(C3⋊C8)—21no—
224C2×2−1+4—91no—
225C2×#131—91no—
226#520—91no—
227#419—31no—
228#419—92no—
229#417—31no—
230#417—92no—
231#416—92no—
232#416—91no—
233C2×#103—92no—
234C2×#103—91no—
235C3×#41—34no—
236C3×#41—62no—
237C2×C3×Q8—34no—
238C2×C3×Q8—31no—
239C2×C3×Q8—32no—
240C2×C3×Q8—61no—
241C2×C3×Q8—62no—
242C2×C3×D4—31no—
243C2×C3×D4—61no—
244C22×C3×C4—21no—
245C22×C3×C4—61no—
246C22×C3×C4—61no—
247C22×C3×C4—61no—
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C2×#67—21no—
251C2×#67—32no—
252C2×#67—32no—
253C2×#67—62no—
254C2×#67—62no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—62no—
258#239—38no—
259#239—68no—
260#239—64no—
261D3×Q8—38no—
262D3×Q8—38no—
263D3×Q8—64no—
264D3×Q8—64no—
265D3×Q8—68no—
266#237—38no—
267#237—64no—
268#237—616no—
269#235—22no—
270#235—34no—
271#235—34no—
272#235—34no—
273#235—34no—
274#235—64no—
275#235—64no—
276#235—68no—
277#235—616no—
278#235C4×D314yescomplemented
279C2×D12—31no—
280C2×D12—31no—
281C2×D12—61no—
282C2×D12—62no—
283C2×D12C22×D311yescharacteristic
284C2×C4×D3—21no—
285C2×C4×D3—32no—
286C2×C4×D3—32no—
287C2×C4×D3—62no—
288C2×C4×D3—62no—
289C2×C4×D3—62no—
290C2×C4×D3—62no—
291C2×C4×D3—62no—
292C2×C4×D3—62no—
293C2×Dic6—21no—
294C2×Dic6—22no—
295C2×Dic6—31no—
296C2×Dic6—31no—
297C2×Dic6—61no—
298C2×Dic6—68no—
299C2×Dic6—62no—
300C2×Dic6—62no—
301C2×Dic6C4×D314yescomplemented
302C2×Dic6C22×D312yes—
303C2×Dic6C22×D311yescharacteristic
304C3×M16—24no—
305C3×M16—22no—
306C3×M16—22no—
307C2×C3×C8—22no—
308C2×C3×C8C22×D312yes—
309C2×C3×C8C22×D312yes—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—32no—
313C3×C4⋊C4—61no—
314C3×C22⋊C4—61no—
315C3×C42—61no—
316#217—21no—
317(C2×D3)⋊C4—62no—
318(C2×D3)⋊C4—62no—
319C4⋊Dic3—21no—
320C4⋊Dic3C22×D311yescharacteristic
321C4⋊Dic3C22×D311yescharacteristic
322C4⋊Dic3C22×D312yes—
323Dic3⋊C4—62no—
324Dic3⋊C4—62no—
325C4×Dic3—21no—
326C4×Dic3—62no—
327C4×Dic3—62no—
328C2×C3⋊C8—31no—
329C2×C3⋊C8—31no—
330C2×C3⋊C8—31no—
331C2×C3⋊C8—31no—
332C2×C3⋊C8—61no—
333C2×C3⋊C8—61no—
334C2×C3⋊C8—64no—
335C2×C3⋊C8—62no—
336C2×C3⋊C8—62no—
337ΓL(1,𝔽25)—64no—
338ΓL(1,𝔽25)—64no—
339ΓL(1,𝔽25)—68no—
340D3×C8—64no—
341D3×C8—64no—
342D3×C8—68no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32C2×C22⋊C412yes—
346C22×C32C22×D411yescharacteristic
347C2×C3⋊D3—22no—
348C2×C3⋊D3—22no—
349C2×C3⋊D3C2×C22⋊C414yes—
350C2×C3×D3—22no—
351C2×C3×D3—41no—
352C2×C3×D3—41no—
353C32×C4C2×C22⋊C412yes—
354C32×C4C23×C411yescharacteristic
355C32×C4C22×D411yescharacteristic
356C3⋊Dic3C2×C22⋊C414yes—
357C3×Dic3—24no—
358C3×Dic3—22no—
359C3×Dic3—41no—
360C3×Dic3—42no—
361C3×Dic3—41no—
3622−1+4—98no—
3632−1+4—184no—
364C2×#41—31no—
365C2×#41—91no—
366C2×#41—92no—
367C2×#41—182no—
368C2×#41—181no—
369C22×Q8—31no—
370C22×Q8—92no—
371C22×Q8—181no—
372#131—184no—
373C2×M16—92no—
374C2×M16D3211yescharacteristic
375C22×C8—91no—
376C22×C8—92no—
377C4×Q8—181no—
378C4×D4—181no—
379C4×D4—182no—
380#117—31no—
381#117—92no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—92no—
384#103—32no—
385#103—32no—
386#103—32no—
387#103—92no—
388#103—91no—
389#103—92no—
390#103—91no—
391#102—32no—
392#102—91no—
393#102—91no—
394C23×C3—21no—
395C23×C3—61no—
396C23×C3D3×D411yescharacteristic
397C23×C3D3×D411yescharacteristic
398C22×D3—21no—
399C22×D3—32no—
400C22×D3—32no—
401C22×D3—62no—
402C3×Q8—32no—
403C3×Q8—34no—
404C3×Q8—64no—
405C3×Q8—61no—
406C3×Q8—62no—
407C3×D4—32no—
408C3×D4—64no—
409C3×D4—61no—
410C2×C3×C4—21no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—22no—
414C2×C3×C4—64no—
415C2×C3×C4—61no—
416C2×C3×C4—62no—
417C2×C3×C4—64no—
418C2×C3×C4—61no—
419C2×C3×C4—62no—
420C2×C3×C4—61no—
421C2×C3×C4—241no—
422C2×C3×C4C2×C4×D312yes—
423C2×C3×C4C2×C4×D312yes—
424C2×C3×C4D3×D411yescharacteristic
425C2×C3×C4D3×D411yescharacteristic
426C2×C3×C4D3×D412yes—
427C2×C3×C4D3×D412yes—
428C2×C3×C4C23×D311yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430#67—24no—
431#67—38no—
432#67—38no—
433#67—68no—
434#67—68no—
435C2×Dic3—24no—
436C2×Dic3—22no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—22no—
441C2×Dic3—32no—
442C2×Dic3—32no—
443C2×Dic3—62no—
444C2×Dic3—68no—
445C2×Dic3—81no—
446D12—21no—
447D12—34no—
448D12—34no—
449D12—64no—
450D12—68no—
451D12C2×C4×D312yes—
452C4×D3—24no—
453C4×D3—34no—
454C4×D3—34no—
455C4×D3—34no—
456C4×D3—34no—
457C4×D3—64no—
458C4×D3—64no—
459C4×D3—68no—
460C4×D3—68no—
461C4×D3—68no—
462C4×D3—242no—
463C4×D3—242no—
464Dic6—24no—
465Dic6—22no—
466Dic6—21no—
467Dic6—34no—
468Dic6—34no—
469Dic6—64no—
470Dic6—68no—
471Dic6—68no—
472Dic6C2×C4×D314yes—
473Dic6C2×C4×D312yes—
474C3×C8—24no—
475C3×C8—22no—
476C3×C8—22no—
477C3⋊C8—62no—
478C3⋊C8—62no—
479C3⋊C8—61no—
480C3⋊C8—61no—
481C3⋊C8—61no—
482C3⋊C8—61no—
483C2×C32—22no—
484C2×C32C22×C22⋊C411yescharacteristic
485C2×C32#57711yescharacteristic
486C2×C32#57811yescharacteristic
487C3⋊D3—24no—
488C3×D3—42no—
489#41—34no—
490#41—62no—
491#41—94no—
492#41—94no—
493#41—98no—
494#41—1816no—
495#41—188no—
496#41—184no—
497C2×Q8—32no—
498C2×Q8—31no—
499C2×Q8—34no—
500C2×Q8—61no—
501C2×Q8—62no—
502C2×Q8—91no—
503C2×Q8—98no—
504C2×Q8—182no—
505C2×Q8—188no—
506C2×Q8—184no—
507C2×D4—31no—
508C2×D4—61no—
509C2×D4—92no—
510C2×D4—91no—
511C2×D4—182no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—92no—
516C22×C4—182no—
517C22×C4—182no—
518C22×C4—182no—
519C22×C4C2×D3211yescharacteristic
520M16—22no—
521M16—184no—
522C2×C8—91no—
523C2×C8—91no—
524C2×C8—184no—
525C2×C8—182no—
526C2×C8C2×D3212yes—
527C4⋊C4—32no—
528C4⋊C4—31no—
529C4⋊C4—31no—
530C4⋊C4—61no—
531C4⋊C4—182no—
532C22⋊C4—61no—
533C22⋊C4—182no—
534C42—61no—
535C42—182no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—22no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—62no—
545C22×C3—121no—
546C22×C3—121no—
547C22×C3D3×C22⋊C412yes—
548C22×C3D3×C22⋊C412yes—
549C22×C3C2×D3×D411yescharacteristic
550C22×C3C2×D3×D411yescharacteristic
551C2×D3—22no—
552C2×D3—34no—
553C2×D3—34no—
554C2×D3—41no—
555C2×D3—41no—
556C2×D3—64no—
557C2×D3—62no—
558C2×D3—62no—
559C2×D3—62no—
560C2×D3—62no—
561C2×D3—122no—
562C2×D3—122no—
563C3×C4—21no—
564C3×C4—21no—
565C3×C4—22no—
566C3×C4—62no—
567C3×C4—64no—
568C3×C4—121no—
569C3×C4—122no—
570C3×C4—121no—
571C3×C4D3×C22⋊C412yes—
572C3×C4D3×C22⋊C412yes—
573C3×C4C22×C4×D311yescharacteristic
574C3×C4C22×C4×D311yescharacteristic
575C3×C4C2×D3×D411yescharacteristic
576C3×C4C2×D3×D411yescharacteristic
577Dic3—24no—
578Dic3—22no—
579Dic3—34no—
580Dic3—34no—
581Dic3—42no—
582Dic3—41no—
583Dic3—41no—
584Dic3—64no—
585C32#289811yescharacteristic, complemented, Sylow
586C23—61no—
587C23—92no—
588C23#380211yescharacteristic
589Q8—34no—
590Q8—32no—
591Q8—62no—
592Q8—61no—
593Q8—64no—
594Q8—94no—
595Q8—188no—
596D4—32no—
597D4—64no—
598D4—61no—
599D4—98no—
600D4—94no—
601D4—188no—
602C2×C4—61no—
603C2×C4—62no—
604C2×C4—64no—
605C2×C4—64no—
606C2×C4—61no—
607C2×C4—61no—
608C2×C4—62no—
609C2×C4—92no—
610C2×C4—94no—
611C2×C4—94no—
612C2×C4—188no—
613C2×C4—188no—
614C2×C4—241no—
615C2×C4—722no—
616C2×C4C4×D3212yes—
617C2×C4#380211yescharacteristic
618C2×C4#381112yes—
619C2×C4C22×D3211yescharacteristic
620C8—22no—
621C8—181no—
622C8—181no—
623C2×C3—22no—
624C2×C3—22no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—42no—
629C2×C3—122no—
630C2×C3C2×D3×C22⋊C411yescharacteristic
631C2×C3C2×D3×C22⋊C411yescharacteristic
632C2×C3#577511yescharacteristic
633C2×C3#577811yescharacteristic
634C2×C3#577911yescharacteristic
635C2×C3#577911yescharacteristic
636D3—42no—
637D3—64no—
638D3—64no—
639D3—124no—
640C22—21no—
641C22—21no—
642C22—62no—
643C22—94no—
644C22—121no—
645C22—121no—
646C22—182no—
647C22—182no—
648C22#6392112yes—
649C22C2×#380211yescharacteristic
650C4—62no—
651C4—64no—
652C4—94no—
653C4—122no—
654C4—121no—
655C4—121no—
656C4#6392112yes—
657C4C2×C4×D3211yescharacteristic
658C4C2×#381111yescharacteristic
659C3—21no—
660C3#7888311yescharacteristic, complemented
661C3#7895711yescharacteristic, complemented
662C2—22no—
663C2—122no—
664C2—184no—
665C2#1059471911yescharacteristic
666C2#1059472311yescharacteristic
667C2C2×#6392111yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#64297C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2898
LCSG ▷ 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
2. C2×#64116C2semidirect
3. #10594990C2semidirect
4. C3×#5133C2semidirect
5. C3×#5120C2semidirect
6. C2×#63565C2semidirect
7. #10591083C2semidirect
8. #10590957C2semidirect
9. #10590956C2semidirect
10. #10590691C2semidirect
11. #10590672C2semidirect
21. #64297C4semidirect
57. #5133D3semidirect
58. #5120D3semidirect
80. C3×#235C2×C4semidirect
85. C2×C3×Dic6C2×C4semidirect
96. #3797C2×C4semidirect
98. #3796C2×C4semidirect
278. #235C4×D3semidirect
301. C2×Dic6C4×D3semidirect
585. C32#2898semidirect
660. C3#78883semidirect
661. C3#78957semidirect

Maximal subgroups

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

subgroupindex
C2×#642972
C2×#641162
#105949902
C3×#51332
C3×#51202
C2×#635652
#105910832
#105909572
#105909562
#105906912
#105906722
#789573
#788833