Finite Group Databasebeta

← #11858079

Subgroups — #11858079

Order 1152.

1849 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64364C211yesmaximal, characteristic
2#10594990C211yesmaximal, characteristic, complemented
3C2×#63817C211yesmaximal, characteristic, complemented
4C3×#5225C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591562C212yesmaximal, complemented
7#10591560C212yesmaximal, complemented
8#10591554C212yesmaximal, complemented
9#10591552C212yesmaximal, complemented
10#10591106C211yesmaximal, characteristic, complemented
11#10591105C211yesmaximal, characteristic, complemented
12#78957—31nomaximal
13#78790—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15#64364—24no—
16#64364C418yescomplemented
17C2×#3832—21no—
18C2×#3832C2212yes—
19C2×Q8×C3⋊D3—21no—
20C2×Q8×C3⋊D3C2212yes—
21C2×#3828—22no—
22C2×#3828C2211yescharacteristic
23C2×#3828C2211yescharacteristic
24C3×#926C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28#63952—22no—
29#63900C2212yes—
30#63894—21no—
31#63849C2212yes—
32#63844—21no—
33C2×#3712C2212yes—
34#63817—24no—
35C2×#3710C2212yes—
36C3×#835C2212yes—
37C3×#835C2212yes—
38C3×#835C2212yes—
39C3×#835C2212yes—
40#63567C2211yescharacteristic
41#63567C2212yes—
42#63567C2211yescharacteristic
43#63564C2211yescharacteristic
44#63564C2212yes—
45#63564C2211yescharacteristic
46C2×#1007—31no—
47C2×#1007—31no—
48C2×#1007—61no—
49C2×#907—31no—
50C2×#901—31no—
51#5523—31no—
52#5504—31no—
53C3×#419—31no—
54C2×C3×#103—31no—
55#5225D311yescharacteristic, complemented
56C2×#835D311yescharacteristic, complemented
57#5133—31no—
58#5113—31no—
59#5002—31no—
60#4966—31no—
61#4804—32no—
62#4804—32no—
63#4803—32no—
64#4803—32no—
65#4802—32no—
66#4802—32no—
67D3×#103—32no—
68D3×#103—32no—
69C2×C32×Q8—21no—
70C2×C32×Q8—22no—
71C2×C32×Q8C2×C414yescomplemented
72C2×C32×Q8C2312yes—
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C2×#638—21no—
76C2×#638D412yes—
77#3832—28no—
78#3832—24no—
79#3832C2×C418yescomplemented
80Q8×C3⋊D3—24no—
81Q8×C3⋊D3—28no—
82Q8×C3⋊D3C2×C418yescomplemented
83#3828—22no—
84#3828—216no—
85#3828C2×C414yes—
86#3828C2×C414yescomplemented
87#3828D414yes—
88C2×C4⋊(C3⋊D3)—22no—
89C2×C4⋊(C3⋊D3)D411yescharacteristic
90C2×C4⋊(C3⋊D3)C2311yescharacteristic
91C2×C4×C3⋊D3—22no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3—22no—
94C2×C4×C3⋊D3C2312yes—
95C2×#634—22no—
96C2×#634D411yescharacteristic
97C2×#634C2311yescharacteristic
98C22×C3×Dic3—21no—
99C2×#624—22no—
100C3×#217—21no—
101C3×C4⋊Dic3—21no—
102C3×C4⋊Dic3C2312yes—
103C3×C4⋊Dic3C2311yescharacteristic
104C3×C4⋊Dic3C2311yescharacteristic
105C3×C4×Dic3—21no—
106C3×#208—22no—
107C2×C3×C3⋊C8—22no—
108C2×C3×C3⋊C8C2311yescharacteristic
109C2×C3×C3⋊C8C2311yescharacteristic
110C2×C3×C3⋊C8C2312yes—
111#3724—22no—
112#3722—22no—
113Dic32—22no—
114#3712—24no—
115#3710—24no—
116#2898—91noSylow
117C22×C3×Q8—21no—
118C22×C3×Q8C2×D311yescharacteristic
119C22×C3×Q8C2×D311yescharacteristic
120#1007—38no—
121#1007—38no—
122#1007—68no—
123#1007—64no—
124#1007—64no—
125#1007—68no—
126C2×#239—32no—
127C2×#239—32no—
128C2×#239—62no—
129C2×#239—61no—
130C2×#239—61no—
131C2×#239—62no—
132C2×D3×Q8—32no—
133C2×D3×Q8—32no—
134C2×D3×Q8—62no—
135C2×D3×Q8—61no—
136C2×D3×Q8—61no—
137C2×D3×Q8—62no—
138C2×#235—31no—
139C2×#235—31no—
140C2×#235—31no—
141C2×#235—31no—
142C2×#235—61no—
143C2×#235—61no—
144C2×#235—62no—
145C2×#235—62no—
146C2×#235—64no—
147C2×C3×M16—31no—
148C22×C3×C8—31no—
149C3×#117—31no—
150C2×C3×C4⋊C4—31no—
151C4×#67—62no—
152#926C2×D311yescharacteristic
153C2×C4⋊Dic3C2×D311yescharacteristic
154C2×#208C2×D311yescharacteristic
155C22×C3⋊C8C2×D311yescharacteristic
156#907—64no—
157#901—64no—
158C2×ΓL(1,𝔽25)—32no—
159C2×ΓL(1,𝔽25)—32no—
160C2×D3×C8—32no—
161C2×D3×C8—32no—
162#893—61no—
163#892—32no—
164#892—32no—
165D3×C4⋊C4—32no—
166D3×C4⋊C4—32no—
167#887—61no—
168#67⋊C4—62no—
169C4×D12—61no—
170C4×Dic6—61no—
171C3×#103—32no—
172C3×#103—32no—
173C3×#103—32no—
174C3×#103—32no—
175#835C2×D312yes—
176#835C2×D312yes—
177#835C2×D312yes—
178#835C2×D312yes—
179#821—32no—
180#821—31no—
181#821—31no—
182#816—32no—
183#816—31no—
184#816—31no—
185#810—32no—
186#810—31no—
187#810—31no—
188#809—32no—
189#809—31no—
190#809—31no—
191C23×C32C2×D411yescharacteristic
192C22×C3⋊D3—21no—
193C22×C3⋊D3C2×D412yes—
194C32×Q8—24no—
195C32×Q8—22no—
196C32×Q8C22×C414yes—
197C2×C32×C4—24no—
198C2×C32×C4—22no—
199C2×C32×C4C22×C412yes—
200C2×C32×C4C2×D411yescharacteristic
201C2×C32×C4C2×D412yes—
202C2×C32×C4C2411yescharacteristic
203#638—24no—
204#638C22⋊C418yes—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3C2×D412yes—
207C4⋊(C3⋊D3)—28no—
208C4⋊(C3⋊D3)—21no—
209C4⋊(C3⋊D3)C22⋊C414yes—
210C4⋊(C3⋊D3)C22×C412yes—
211C4×C3⋊D3—28no—
212C4×C3⋊D3—24no—
213C4×C3⋊D3—28no—
214C4×C3⋊D3C22×C414yes—
215C4×C3⋊D3C2×D414yes—
216#634—21no—
217#634—28no—
218#634C22⋊C414yes—
219#634C22×C412yes—
220C2×C3×Dic3—21no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—21no—
223C2×C3×Dic3—81no—
224#624—82no—
225C3×C3⋊C8—21no—
226C3×C3⋊C8—22no—
227C3×C3⋊C8—21no—
228C2×2−1+4—91no—
229C2×#131—91no—
230#520—91no—
231#419—31no—
232#419—92no—
233#417—92no—
234#417—91no—
235#416—92no—
236#416—91no—
237C2×#103—31no—
238C2×#103—92no—
239C2×C3×Q8—22no—
240C2×C3×Q8—24no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—22no—
244C2×C3×Q8—22no—
245C2×C3×Q8—24no—
246C2×C3×Q8—22no—
247C2×C3×Q8C4×D314yescomplemented
248C2×C3×Q8C4×D314yescomplemented
249C2×C3×Q8C22×D312yes—
250C2×C3×Q8C22×D312yes—
251C22×C3×C4—22no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—61no—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C2×#67—32no—
259C2×#67—32no—
260C2×#67—62no—
261C2×#67—62no—
262C2×#67—61no—
263C2×#67—61no—
264C22×Dic3—21no—
265#239—38no—
266#239—38no—
267#239—68no—
268#239—64no—
269#239—64no—
270#239—68no—
271#239—68no—
272#239—68no—
273#239—616no—
274D3×Q8—38no—
275D3×Q8—38no—
276D3×Q8—68no—
277D3×Q8—68no—
278D3×Q8—68no—
279D3×Q8—64no—
280D3×Q8—64no—
281D3×Q8—68no—
282D3×Q8—616no—
283#235—34no—
284#235—34no—
285#235—34no—
286#235—34no—
287#235—34no—
288#235—34no—
289#235—64no—
290#235—64no—
291#235—64no—
292#235—616no—
293#235—616no—
294#235—632no—
295#235—64no—
296#235—62no—
297#235—62no—
298C2×D12—31no—
299C2×D12—31no—
300C2×D12—31no—
301C2×D12—31no—
302C2×D12—61no—
303C2×D12—61no—
304C2×D12—62no—
305C2×D12—62no—
306C2×D12—64no—
307C2×C4×D3—32no—
308C2×C4×D3—32no—
309C2×C4×D3—62no—
310C2×C4×D3—62no—
311C2×C4×D3—62no—
312C2×C4×D3—62no—
313C2×C4×D3—62no—
314C2×C4×D3—64no—
315C2×C4×D3—64no—
316C2×C4×D3—62no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—62no—
320C2×C4×D3—62no—
321C2×Dic6—31no—
322C2×Dic6—31no—
323C2×Dic6—31no—
324C2×Dic6—31no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—62no—
328C2×Dic6—62no—
329C2×Dic6—64no—
330C3×M16—62no—
331C2×C3×C8—31no—
332C2×C3×C8—32no—
333C2×C3×C8—31no—
334C2×C3×C8—62no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—32no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C42—61no—
341#217—21no—
342(C2×D3)⋊C4—62no—
343(C2×D3)⋊C4—62no—
344C4⋊Dic3—21no—
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D312yes—
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—62no—
349Dic3⋊C4—62no—
350C4×Dic3—21no—
351C4×Dic3—62no—
352C4×Dic3—62no—
353#208—22no—
354C2×C3⋊C8—22no—
355C2×C3⋊C8C22×D311yescharacteristic
356C2×C3⋊C8C22×D312yes—
357C2×C3⋊C8C22×D311yescharacteristic
358ΓL(1,𝔽25)—64no—
359ΓL(1,𝔽25)—64no—
360D3×C8—64no—
361D3×C8—64no—
362C22×C32—21no—
363C22×C32—21no—
364C22×C32C2×C22⋊C412yes—
365C22×C32C22×D411yescharacteristic
366C2×C3⋊D3—22no—
367C2×C3⋊D3—22no—
368C2×C3⋊D3—22no—
369C2×C3⋊D3—41no—
370C2×C3⋊D3—41no—
371C2×C3⋊D3C2×C22⋊C414yes—
372C32×C4—24no—
373C32×C4C2×C22⋊C412yes—
374C32×C4C23×C411yescharacteristic
375C32×C4C22×D411yescharacteristic
376C3⋊Dic3—22no—
377C3⋊Dic3C2×C22⋊C414yes—
378C3×Dic3—41no—
379C3×Dic3—42no—
380C3×Dic3—41no—
3812−1+4—98no—
3822−1+4—184no—
383C2×#41—91no—
384C2×#41—92no—
385C2×#41—91no—
386C2×#41—182no—
387C2×#41—181no—
388C22×Q8—92no—
389C22×Q8—181no—
390C22×Q8D3211yescharacteristic
391#131—184no—
392C2×M16—31no—
393C2×M16—92no—
394C22×C8—31no—
395C22×C8—92no—
396C4×Q8—181no—
397C4×D4—181no—
398C4×D4—182no—
399#117—31no—
400#117—92no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—92no—
403#103—32no—
404#103—32no—
405#103—32no—
406#103—32no—
407#103—91no—
408#103—92no—
409#103—91no—
410#102—91no—
411#102—92no—
412#102—91no—
413C23×C3—21no—
414C23×C3D3×D411yescharacteristic
415C23×C3D3×D411yescharacteristic
416C22×D3—32no—
417C22×D3—32no—
418C22×D3—62no—
419C22×D3—62no—
420C22×D3—61no—
421C22×D3—61no—
422C3×Q8—24no—
423C3×Q8—28no—
424C3×Q8—24no—
425C3×Q8—24no—
426C3×Q8—22no—
427C3×Q8—22no—
428C3×Q8—24no—
429C3×Q8C2×C4×D314yes—
430C3×Q8C2×C4×D314yes—
431C2×C3×C4—24no—
432C2×C3×C4—28no—
433C2×C3×C4—24no—
434C2×C3×C4—24no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—22no—
441C2×C3×C4—61no—
442C2×C3×C4—62no—
443C2×C3×C4—61no—
444C2×C3×C4—241no—
445C2×C3×C4C2×C4×D312yes—
446C2×C3×C4C2×C4×D312yes—
447C2×C3×C4D3×D411yescharacteristic
448C2×C3×C4D3×D411yescharacteristic
449C2×C3×C4D3×D412yes—
450C2×C3×C4D3×D412yes—
451C2×C3×C4C23×D311yescharacteristic
452C2×C3×C4C23×D311yescharacteristic
453#67—38no—
454#67—38no—
455#67—68no—
456#67—68no—
457#67—64no—
458#67—64no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—22no—
462C2×Dic3—32no—
463C2×Dic3—32no—
464C2×Dic3—62no—
465C2×Dic3—62no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—81no—
469D12—34no—
470D12—34no—
471D12—32no—
472D12—32no—
473D12—64no—
474D12—62no—
475D12—68no—
476D12—68no—
477D12—616no—
478D12—62no—
479D12—61no—
480D12—61no—
481C4×D3—34no—
482C4×D3—34no—
483C4×D3—34no—
484C4×D3—34no—
485C4×D3—64no—
486C4×D3—64no—
487C4×D3—68no—
488C4×D3—68no—
489C4×D3—68no—
490C4×D3—68no—
491C4×D3—616no—
492C4×D3—616no—
493C4×D3—68no—
494C4×D3—64no—
495C4×D3—64no—
496C4×D3—242no—
497C4×D3—242no—
498Dic6—34no—
499Dic6—34no—
500Dic6—32no—
501Dic6—32no—
502Dic6—64no—
503Dic6—62no—
504Dic6—68no—
505Dic6—68no—
506Dic6—616no—
507Dic6—62no—
508Dic6—61no—
509Dic6—61no—
510C3×C8—61no—
511C3×C8—62no—
512C3×C8—61no—
513C3⋊C8—21no—
514C3⋊C8—22no—
515C3⋊C8—21no—
516C2×C32—22no—
517C2×C32C22×C22⋊C411yescharacteristic
518C2×C32#57711yescharacteristic
519C2×C32#57811yescharacteristic
520C3⋊D3—24no—
521C3⋊D3—42no—
522#41—94no—
523#41—94no—
524#41—98no—
525#41—94no—
526#41—1816no—
527#41—184no—
528#41—188no—
529#41—182no—
530C2×Q8—21no—
531C2×Q8—22no—
532C2×Q8—91no—
533C2×Q8—98no—
534C2×Q8—91no—
535C2×Q8—182no—
536C2×Q8—184no—
537C2×Q8—188no—
538C2×Q8#62414yescomplemented
539C2×Q8C2×D3212yes—
540C2×D4—92no—
541C2×D4—91no—
542C2×D4—91no—
543C2×D4—182no—
544C2×D4—181no—
545C22×C4—21no—
546C22×C4—61no—
547C22×C4—92no—
548C22×C4—182no—
549C22×C4—182no—
550C22×C4—182no—
551C22×C4—181no—
552C22×C4C2×D3211yescharacteristic
553M16—62no—
554M16—184no—
555C2×C8—31no—
556C2×C8—31no—
557C2×C8—32no—
558C2×C8—62no—
559C2×C8—184no—
560C4⋊C4—32no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—61no—
564C4⋊C4—182no—
565C22⋊C4—61no—
566C22⋊C4—182no—
567C42—61no—
568C42—182no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—22no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3D3×C22⋊C412yes—
578C22×C3D3×C22⋊C412yes—
579C22×C3C2×D3×D411yescharacteristic
580C22×C3C2×D3×D411yescharacteristic
581C2×D3—34no—
582C2×D3—34no—
583C2×D3—64no—
584C2×D3—62no—
585C2×D3—62no—
586C2×D3—62no—
587C2×D3—62no—
588C2×D3—64no—
589C2×D3—62no—
590C2×D3—62no—
591C2×D3—122no—
592C2×D3—122no—
593C2×D3—122no—
594C2×D3—122no—
595C2×D3—121no—
596C2×D3—121no—
597C2×D3—121no—
598C2×D3—121no—
599C3×C4—28no—
600C3×C4—24no—
601C3×C4—24no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—22no—
605C3×C4—121no—
606C3×C4—121no—
607C3×C4—122no—
608C3×C4D3×C22⋊C412yes—
609C3×C4D3×C22⋊C412yes—
610C3×C4C22×C4×D311yescharacteristic
611C3×C4C22×C4×D311yescharacteristic
612C3×C4C2×D3×D411yescharacteristic
613C3×C4C2×D3×D411yescharacteristic
614Dic3—34no—
615Dic3—34no—
616Dic3—42no—
617Dic3—41no—
618Dic3—41no—
619Dic3—64no—
620Dic3—64no—
621Dic3—62no—
622Dic3—62no—
623C32#289811yescharacteristic, complemented, Sylow
624C23—92no—
625C23—181no—
626C23#381111yescharacteristic
627Q8—22no—
628Q8—24no—
629Q8—94no—
630Q8—92no—
631Q8—188no—
632Q8—181no—
633Q8C2×#62414yes—
634D4—98no—
635D4—92no—
636D4—94no—
637D4—188no—
638D4—184no—
639D4—181no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—62no—
645C2×C4—92no—
646C2×C4—94no—
647C2×C4—94no—
648C2×C4—188no—
649C2×C4—188no—
650C2×C4—181no—
651C2×C4—184no—
652C2×C4—241no—
653C2×C4—722no—
654C2×C4C2×#62412yes—
655C2×C4#381112yes—
656C2×C4#381111yescharacteristic
657C2×C4C22×D3211yescharacteristic
658C8—61no—
659C8—61no—
660C8—62no—
661C2×C3—22no—
662C2×C3—22no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—42no—
667C2×C3C2×D3×C22⋊C411yescharacteristic
668C2×C3C2×D3×C22⋊C411yescharacteristic
669C2×C3#576211yescharacteristic
670C2×C3#576611yescharacteristic
671C2×C3#577811yescharacteristic
672C2×C3#577911yescharacteristic
673D3—64no—
674D3—64no—
675D3—124no—
676D3—124no—
677D3—122no—
678D3—122no—
679C22—21no—
680C22—21no—
681C22—94no—
682C22—182no—
683C22—182no—
684C22—182no—
685C22—361no—
686C22—361no—
687C22#6397412yes—
688C22C2×#381111yescharacteristic
689C4—24no—
690C4—94no—
691C4—121no—
692C4—122no—
693C4—121no—
694C4—182no—
695C4#6397412yes—
696C4C22×#62411yescharacteristic
697C4C2×#381111yescharacteristic
698C3—21no—
699C3#7879011yescharacteristic, complemented
700C3#7895711yescharacteristic, complemented
701C2—22no—
702C2—184no—
703C2—362no—
704C2#1059532411yescharacteristic
705C2#1059533711yescharacteristic
706C2C2×#6397411yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×#64364C2
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32#2898
LCSG ▷ 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. #10594990C2semidirect
3. C2×#63817C2semidirect
4. C3×#5225C2semidirect
5. C2×C3×#835C2semidirect
6. #10591562C2semidirect
7. #10591560C2semidirect
8. #10591554C2semidirect
9. #10591552C2semidirect
10. #10591106C2semidirect
11. #10591105C2semidirect
16. #64364C4semidirect
55. #5225D3semidirect
56. C2×#835D3semidirect
71. C2×C32×Q8C2×C4semidirect
79. #3832C2×C4semidirect
82. Q8×C3⋊D3C2×C4semidirect
86. #3828C2×C4semidirect
247. C2×C3×Q8C4×D3semidirect
248. C2×C3×Q8C4×D3semidirect
538. C2×Q8#624semidirect
623. C32#2898semidirect
699. C3#78790semidirect
700. C3#78957semidirect

Maximal subgroups

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

subgroupindex
C2×#643642
#105949902
C2×#638172
C3×#52252
C2×C3×#8352
#105915622
#105915602
#105915542
#105915522
#105911062
#105911052
#789573
#787903