Finite Group Databasebeta

← #11868138

Subgroups — #11868138

Order 1152.

984 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595317C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3D3×#908C211yesmaximal, characteristic, complemented
4#10594706C211yesmaximal, characteristic, complemented
5#10592453C211yesmaximal, characteristic, complemented
6C3×#4754C211yesmaximal, characteristic, complemented
7C3×#4751C211yesmaximal, characteristic, complemented
8#10591643C211yesmaximal, characteristic, complemented
9#10591542C211yesmaximal, characteristic, complemented
10D3×#823C211yesmaximal, characteristic, complemented
11#10590997C211yesmaximal, characteristic, complemented
12#10590988C211yesmaximal, characteristic, complemented
13#10590987C211yesmaximal, characteristic, complemented
14#10590982C211yesmaximal, characteristic, complemented
15#10590973C211yesmaximal, characteristic, complemented
16#80930—31nomaximal
17#78720—31nomaximal
18C2×C3×#239C2211yescharacteristic
19D3×#235C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21#64151C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic, complemented
23#64117C2211yescharacteristic
24#64116C2211yescharacteristic, complemented
25C3×#942C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic, complemented
27C3×#908C2211yescharacteristic
28C3×#907C2211yescharacteristic, complemented
29C3×D3×M16C2211yescharacteristic
30C3×D3×M16C2211yescharacteristic
31#63949—21no—
32#63947—21no—
33#63943—21no—
34#63939—21no—
35#63939—21no—
36#63939—21no—
37#63939—21no—
38#63939—21no—
39#63830C2211yescharacteristic
40#63830C2211yescharacteristic, complemented
41#63825C2211yescharacteristic
42C2×#3714C2211yescharacteristic, complemented
43#63823C2211yescharacteristic, complemented
44C2×#3713C2211yescharacteristic, complemented
45C2×#3711C2211yescharacteristic
46#63817C2211yescharacteristic, complemented
47#63815C2211yescharacteristic, complemented
48D3×#208C2211yescharacteristic
49#63804—21no—
50#63803—21no—
51#63795—21no—
52#63794—21no—
53D3×D24—21no—
54D3×#204—21no—
55#63791—21no—
56D3×ΓL(1,𝔽25)—21no—
57C32×#101C2211yescharacteristic, complemented
58#63650C2211yescharacteristic, complemented
59#63649C2211yescharacteristic, complemented
60C3×#836C2211yescharacteristic, complemented
61C3×#823C2211yescharacteristic, complemented
62C3×#823C2211yescharacteristic, complemented
63C3×#823C2211yescharacteristic, complemented
64C3×#822C2211yescharacteristic, complemented
65#63578C2211yescharacteristic, complemented
66#63577C2211yescharacteristic, complemented
67#63559C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69#5822—31no—
70C2×#949—31no—
71#5777—31no—
72D3×AGL(1,ℤ/8)—31no—
73C2×#914—31no—
74#5750—31no—
75C2×#908—31no—
76#5745—31no—
77C3×#471—31no—
78C3×#413—31no—
79#5203—31no—
80#5199—31no—
81#5177—31no—
82#5142—31no—
83C2×#823—31no—
84#5124—31no—
85#4897—31no—
86#4893—31no—
87#4754—31no—
88#4754—31no—
89#4754—31no—
90#4754—31no—
91#4754—61no—
92#4754D311yescharacteristic, complemented
93#4751D311yescharacteristic, complemented
94#4749—31no—
95#4749—31no—
96#4749—31no—
97#4749—31no—
98#4749—31no—
99D3×#100—31no—
100C22×D32—21no—
101C2×C32×Q8C2311yescharacteristic
102#3828C2311yescharacteristic
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C3×#239—21no—
105C3×#239—21no—
106C3×#239—21no—
107C3×#239—21no—
108C3×#235C2311yescharacteristic
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114D3×#67—21no—
115C2×#626—21no—
116#3804—21no—
117D3×D12—21no—
118D3×D12—21no—
119D3×D12—21no—
120D3×D12—21no—
121D3×D12D411yescharacteristic
122C4×D32—21no—
123#3799D411yescharacteristic
124#3798—21no—
125#3795D411yescharacteristic
126D3×Dic6D411yescharacteristic
127C32×M16C2311yescharacteristic
128C32×M16C2311yescharacteristic
129#3756—21no—
130#3755—21no—
131#3755—21no—
132#3755—21no—
133#3748C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135#3745—21no—
136#3744—21no—
137#3743—21no—
138C8×C3⋊D3—21no—
139C3×#216—21no—
140C3×#215—21no—
141C3×#215—21no—
142C3×#215—21no—
143C3×#208C2311yescharacteristic
144C3×#208C2311yescharacteristic
145C3×#208C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C3×D24—21no—
148C3×#204—21no—
149C3×ΓL(1,𝔽25)—21no—
150C3×ΓL(1,𝔽25)—21no—
151C3×ΓL(1,𝔽25)—21no—
152C3×D3×C8—21no—
153C3×D3×C8—21no—
154C3×D3×C8—21no—
155#3717—21no—
156#3716—21no—
157#3716—21no—
158#3715—21no—
159#3714—21no—
160#3714—21no—
161#3714—21no—
162#3714—21no—
163#3714—21no—
164#3713—21no—
165#3713—21no—
166#3713—21no—
167#3712—21no—
168#3711—21no—
169#3711—21no—
170#3711D411yescharacteristic
171#3711D411yescharacteristic
172#3711D411yescharacteristic
173#3711D411yescharacteristic
174#3710—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3068—91noSylow
178C2×C3×#41—31no—
179D3×#41—31no—
180C2×#239C2×D311yescharacteristic
181C2×D3×D4—31no—
182C2×#235—31no—
183C22×D12—31no—
184C3×#137—31no—
185C3×AGL(1,ℤ/8)—31no—
186C2×C3×SD16—31no—
187C3×#131—31no—
188C2×C3×M16—31no—
189C2×C3×M16—31no—
190#951—61no—
191#950—61no—
192#950—61no—
193#949—31no—
194#949—31no—
195#949—61no—
196#949—61no—
197#949—61no—
198#949—61no—
199#949—61no—
200#948—31no—
201#942—31no—
202#942—31no—
203#942—61no—
204#942C2×D311yescharacteristic, complemented
205C2×#215—31no—
206C2×#215—31no—
207C2×#215—61no—
208C2×#215C2×D311yescharacteristic, complemented
209#932—31no—
210#932—31no—
211#932—31no—
212C2×#213—31no—
213C2×#213—31no—
214C2×#213—31no—
215C2×#208—31no—
216C2×#208—31no—
217#919—61no—
218#918—61no—
219#916—61no—
220#914—61no—
221#914—61no—
222#914—61no—
223#914—61no—
224#914—61no—
225#914—61no—
226D3×SD16—61no—
227#911—61no—
228D3×D8—61no—
229#908—31no—
230#908—31no—
231#908—31no—
232#908—31no—
233#908—31no—
234#908—61no—
235#908—61no—
236#908—61no—
237#908C2×D311yescharacteristic
238#907—31no—
239#907—31no—
240#907—31no—
241#907—31no—
242#907—61no—
243#907—61no—
244#907C2×D311yescharacteristic, complemented
245D3×M16—31no—
246D3×M16—61no—
247D3×M16—61no—
248D3×M16—61no—
249D3×M16C2×D311yescharacteristic
250D3×M16C2×D311yescharacteristic
251C2×D24—31no—
252C2×D24—61no—
253C2×#204—61no—
254#901—31no—
255#901—61no—
256#901—61no—
257#901—61no—
258C2×ΓL(1,𝔽25)—31no—
259C2×ΓL(1,𝔽25)—61no—
260C3×#108—31no—
261C3×#101—21no—
262C3×#101—31no—
263C3×#101C2×D311yescharacteristic, complemented
264C3×#101C2×D311yescharacteristic, complemented
265C3×#100—31no—
266C3×#100—31no—
267C3×#100—31no—
268#836C2×D311yescharacteristic, complemented
269#833—31no—
270#823—31no—
271#823—31no—
272#823—31no—
273#823—31no—
274#823—31no—
275#823—61no—
276#823C2×D311yescharacteristic, complemented
277#823C2×D311yescharacteristic, complemented
278#823C2×D311yescharacteristic, complemented
279#822—31no—
280#822—31no—
281#822—31no—
282#822—31no—
283#822—31no—
284#822—61no—
285#822C2×D311yescharacteristic, complemented
286#819—31no—
287C22×C3⋊D3—21no—
288C22×C3×D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3#4111yescharacteristic
291C2×D32—21no—
292C2×D32—41no—
293C2×D32—41no—
294C2×D32—82no—
295C32×Q8—21no—
296C32×Q8—21no—
297C2×C32×C4—21no—
298C2×C32×C4C2411yescharacteristic
299#638—21no—
300C4⋊(C3⋊D3)—21no—
301C4⋊(C3⋊D3)—21no—
302C4⋊(C3⋊D3)C2×D411yescharacteristic
303C4×C3⋊D3—21no—
304#634C2×D411yescharacteristic
305C3×#67—21no—
306C2×C3×Dic3#4111yescharacteristic
307C3×D12—21no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—41no—
312C3×D12—41no—
313C3×D12C2×D411yescharacteristic
314C3×C4×D3—21no—
315C3×C4×D3—41no—
316C3×C4×D3—41no—
317C3×C4×D3C2×D411yescharacteristic
318C3×C4×D3C2×D411yescharacteristic
319C3×C4×D3C2×D411yescharacteristic
320C3×C4×D3C2×D411yescharacteristic
321C3×Dic6C2×D411yescharacteristic
322#627—21no—
323#626—21no—
324#626—21no—
325#626—41no—
326#626—41no—
327#625—21no—
328#624—21no—
329D3×Dic3—21no—
330D3×Dic3—21no—
331C32×C8—21no—
332C32×C8—21no—
333C3⋊(C3⋊C8)—21no—
334C3⋊(C3⋊C8)C2×D411yescharacteristic
335C3⋊(C3⋊C8)C2×D411yescharacteristic
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8—21no—
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341#575—91no—
342C2×AGL(1,ℤ/8)—91no—
343C2×AGL(1,ℤ/8)—91no—
344#568—91no—
345#472—91no—
346#472—91no—
347#472—91no—
348#472—91no—
349#471—31no—
350#471—91no—
351#471—91no—
352#471—91no—
353#430—91no—
354#413—31no—
355C2×#100—91no—
356C23×D3—61no—
357C23×D3—61no—
358C3×#41—31no—
359C3×#41—61no—
360C3×#41—61no—
361C3×#41—61no—
362C3×#41—61no—
363C2×C3×Q8—21no—
364C2×C3×Q8C22×D311yescharacteristic
365C2×C3×Q8C22×D311yescharacteristic
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—61no—
369C22×C3×C4—31no—
370C22×C3×C4—61no—
371C2×#67—61no—
372C2×#67—61no—
373#239—21no—
374#239—21no—
375#239—21no—
376#239—21no—
377#239—31no—
378D3×Q8—31no—
379#237—31no—
380#237—61no—
381D3×D4—31no—
382D3×D4—61no—
383D3×D4—61no—
384D3×D4—61no—
385D3×D4—61no—
386D3×D4—61no—
387#235—31no—
388#235—31no—
389#235—31no—
390#235—31no—
391#235—61no—
392#235—61no—
393#235—61no—
394#235—61no—
395#235C22×D311yescharacteristic
396C2×D12—21no—
397C2×D12—31no—
398C2×D12—31no—
399C2×D12—31no—
400C2×D12—61no—
401C2×D12—61no—
402C2×D12—61no—
403C2×D12—61no—
404C2×D12—61no—
405C2×D12—61no—
406C2×D12C22×D311yescharacteristic
407C2×D12C22×D311yescharacteristic
408C2×C4×D3—21no—
409C2×C4×D3—61no—
410C2×C4×D3—61no—
411C2×C4×D3C22×D311yescharacteristic
412C2×Dic6—31no—
413C3×Q16—61no—
414C3×SD16—61no—
415C3×SD16—61no—
416C3×SD16—61no—
417C3×SD16—61no—
418C3×D8—61no—
419C3×M16—21no—
420C3×M16—21no—
421C3×M16—31no—
422C3×M16—31no—
423C3×M16—31no—
424C3×M16—61no—
425C3×M16—61no—
426C3×M16—61no—
427C3×M16C22×D311yescharacteristic
428C3×M16C22×D311yescharacteristic
429C3×M16C22×D311yescharacteristic
430C3×M16C22×D311yescharacteristic
431C2×C3×C8—31no—
432C2×C3×C8—61no—
433C2×C3×C8—61no—
434C2×C3×C8—61no—
435#216—21no—
436#216—61no—
437#216—61no—
438#216—121no—
439#215—21no—
440#215—21no—
441#215—21no—
442#215—61no—
443#215—61no—
444#215—61no—
445#215—61no—
446#215—61no—
447#215—61no—
448#215—61no—
449#215—61no—
450#215—121no—
451#215—121no—
452#215—121no—
453#214—61no—
454#214—61no—
455#214—61no—
456#213—61no—
457#213—61no—
458#213—61no—
459#213—61no—
460#213—61no—
461#213—61no—
462#213—61no—
463#213—61no—
464#213—61no—
465#213—61no—
466#213—61no—
467#208—31no—
468#208—31no—
469#208—31no—
470#208—31no—
471#208—31no—
472#208—31no—
473#208—61no—
474#208—61no—
475#208—61no—
476#208C22×D311yescharacteristic
477#208C22×D311yescharacteristic
478#208C22×D311yescharacteristic
479C2×C3⋊C8—31no—
480C2×C3⋊C8—31no—
481C2×C3⋊C8—61no—
482C2×C3⋊C8—61no—
483C2×C3⋊C8—61no—
484C2×C3⋊C8C22×D311yescharacteristic
485D24—21no—
486D24—61no—
487D24—61no—
488D24—61no—
489D24—61no—
490D24—61no—
491D24—61no—
492D24—61no—
493D24—121no—
494#204—21no—
495#204—61no—
496#204—61no—
497#204—61no—
498#204—61no—
499#204—61no—
500#204—121no—
501ΓL(1,𝔽25)—21no—
502ΓL(1,𝔽25)—21no—
503ΓL(1,𝔽25)—21no—
504ΓL(1,𝔽25)—31no—
505ΓL(1,𝔽25)—31no—
506ΓL(1,𝔽25)—31no—
507ΓL(1,𝔽25)—31no—
508ΓL(1,𝔽25)—61no—
509ΓL(1,𝔽25)—61no—
510ΓL(1,𝔽25)—61no—
511ΓL(1,𝔽25)—61no—
512ΓL(1,𝔽25)—61no—
513ΓL(1,𝔽25)—61no—
514ΓL(1,𝔽25)—121no—
515D3×C8—21no—
516D3×C8—21no—
517D3×C8—21no—
518D3×C8—61no—
519D3×C8—61no—
520D3×C8—61no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—61no—
524D3×C8—121no—
525C22×C32C2×#4111yescharacteristic
526C2×C3⋊D3—21no—
527C2×C3⋊D3—41no—
528C2×C3⋊D3—81no—
529C2×C3×D3—21no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—81no—
534C2×C3×D3—81no—
535C2×C3×D3#12111yescharacteristic
536C2×C3×D3#12111yescharacteristic
537D32—81no—
538D32—82no—
539D32—82no—
540C32×C4—41no—
541C32×C4C22×D411yescharacteristic
542C32×C4C22×D411yescharacteristic
543C3⋊Dic3—21no—
544C3×Dic3—21no—
545C3×Dic3#12111yescharacteristic
546C3×Dic3#12111yescharacteristic
547C2×#41—31no—
548C2×#41—91no—
549C22×D4—91no—
550#137—31no—
551#137—91no—
552#137—181no—
553AGL(1,ℤ/8)—31no—
554AGL(1,ℤ/8)—91no—
555AGL(1,ℤ/8)—91no—
556AGL(1,ℤ/8)—91no—
557AGL(1,ℤ/8)—91no—
558AGL(1,ℤ/8)—91no—
559AGL(1,ℤ/8)—181no—
560AGL(1,ℤ/8)—181no—
561AGL(1,ℤ/8)—181no—
562AGL(1,ℤ/8)—181no—
563AGL(1,ℤ/8)—181no—
564AGL(1,ℤ/8)—181no—
565AGL(1,ℤ/8)—181no—
566#135—181no—
567#135—181no—
568C2×SD16—31no—
569C2×SD16—91no—
570C2×SD16—181no—
571C2×D8—91no—
572C2×D8—91no—
573C2×D8—181no—
574#131—31no—
575#131—91no—
576#131—91no—
577#131—91no—
578#131—181no—
579#131—181no—
580C2×M16—31no—
581C2×M16—31no—
582C2×M16—91no—
583C2×M16—91no—
584C2×M16—181no—
585C2×M16—181no—
586#108—31no—
587#108—91no—
588#108—91no—
589#108—91no—
590#101—31no—
591#101D3211yescharacteristic, complemented
592#100—31no—
593#100—31no—
594#100—31no—
595#100—91no—
596#100—91no—
597#100—91no—
598C23×C3—31no—
599C23×C3—61no—
600C23×C3—61no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—242no—
613C22×D3—242no—
614C22×D3#23511yescharacteristic
615C3×Q8—21no—
616C3×Q8—21no—
617C3×Q8—21no—
618C3×Q8—21no—
619C3×Q8—31no—
620C3×Q8—41no—
621C3×Q8—41no—
622C3×D4—31no—
623C3×D4—61no—
624C3×D4—61no—
625C3×D4—61no—
626C3×D4—61no—
627C3×D4—61no—
628C3×D4—121no—
629C3×D4—121no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—31no—
634C2×C3×C4—31no—
635C2×C3×C4—31no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—41no—
639C2×C3×C4—61no—
640C2×C3×C4—121no—
641C2×C3×C4—121no—
642C2×C3×C4C23×D311yescharacteristic
643C2×C3×C4C23×D311yescharacteristic
644#67—21no—
645#67—61no—
646#67—61no—
647#67—61no—
648#67—61no—
649#67—61no—
650#67—61no—
651#67—121no—
652#67—121no—
653#67—121no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3#23511yescharacteristic
657D12—21no—
658D12—21no—
659D12—21no—
660D12—21no—
661D12—31no—
662D12—31no—
663D12—41no—
664D12—41no—
665D12—61no—
666D12—61no—
667D12—61no—
668D12—61no—
669D12—61no—
670D12—61no—
671D12—61no—
672D12—121no—
673D12—121no—
674D12—121no—
675D12—121no—
676D12D3×D411yescharacteristic
677C4×D3—21no—
678C4×D3—41no—
679C4×D3—41no—
680C4×D3—61no—
681C4×D3—61no—
682C4×D3—61no—
683C4×D3—61no—
684C4×D3—61no—
685C4×D3—61no—
686C4×D3—121no—
687C4×D3D3×D411yescharacteristic
688C4×D3D3×D411yescharacteristic
689C4×D3D3×D411yescharacteristic
690C4×D3D3×D411yescharacteristic
691Dic6—31no—
692Dic6—31no—
693Dic6—61no—
694Dic6—61no—
695Dic6—61no—
696Dic6D3×D411yescharacteristic
697C3×C8—21no—
698C3×C8—21no—
699C3×C8—21no—
700C3×C8—21no—
701C3×C8—31no—
702C3×C8—31no—
703C3×C8—41no—
704C3×C8—41no—
705C3×C8—61no—
706C3×C8—61no—
707C3×C8—61no—
708C3⋊C8—21no—
709C3⋊C8—21no—
710C3⋊C8—21no—
711C3⋊C8—31no—
712C3⋊C8—31no—
713C3⋊C8—31no—
714C3⋊C8—31no—
715C3⋊C8—61no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—61no—
719C3⋊C8—121no—
720C3⋊C8D3×D411yescharacteristic
721C3⋊C8D3×D411yescharacteristic
722C2×C32—21no—
723C2×C32C2×#12111yescharacteristic
724C3⋊D3—41no—
725C3⋊D3—81no—
726C3×D3—21no—
727C3×D3—21no—
728C3×D3—41no—
729C3×D3—81no—
730C3×D3—81no—
731C24—181no—
732#41—31no—
733#41—61no—
734#41—61no—
735#41—61no—
736#41—61no—
737#41—91no—
738#41—91no—
739#41—91no—
740#41—181no—
741#41—181no—
742C2×Q8—91no—
743C2×Q8C2×D3211yescharacteristic
744C2×D4—31no—
745C2×D4—31no—
746C2×D4—61no—
747C2×D4—91no—
748C2×D4—91no—
749C2×D4—181no—
750C2×D4—181no—
751C2×D4—181no—
752C2×D4—181no—
753C2×D4—181no—
754C2×D4—181no—
755C22×C4—31no—
756C22×C4—61no—
757C22×C4—181no—
758Q16—61no—
759Q16—181no—
760SD16—61no—
761SD16—61no—
762SD16—61no—
763SD16—61no—
764SD16—181no—
765SD16—181no—
766SD16—181no—
767SD16—181no—
768SD16—181no—
769SD16—181no—
770SD16—181no—
771SD16—181no—
772D8—61no—
773D8—181no—
774D8—181no—
775D8—181no—
776D8—181no—
777D8—181no—
778D8—181no—
779D8—181no—
780D8—181no—
781D8—181no—
782M16—31no—
783M16—31no—
784M16—31no—
785M16—61no—
786M16—61no—
787M16—61no—
788M16—91no—
789M16—91no—
790M16—91no—
791M16—91no—
792M16—91no—
793M16—181no—
794M16—181no—
795M16—181no—
796M16—181no—
797M16C2×D3211yescharacteristic
798M16C2×D3211yescharacteristic
799C2×C8—31no—
800C2×C8—61no—
801C2×C8—61no—
802C2×C8—61no—
803C2×C8—91no—
804C2×C8—181no—
805C2×C8—181no—
806C2×C8—181no—
807C2×C8—181no—
808C22×C3—21no—
809C22×C3—31no—
810C22×C3—31no—
811C22×C3—61no—
812C22×C3—121no—
813C22×C3—121no—
814C22×C3—121no—
815C22×C3—241no—
816C22×C3—241no—
817C22×C3C2×#23511yescharacteristic
818C22×C3D3×#4111yescharacteristic
819C2×D3—21no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—41no—
823C2×D3—61no—
824C2×D3—61no—
825C2×D3—81no—
826C2×D3—81no—
827C2×D3—121no—
828C2×D3—121no—
829C2×D3—121no—
830C2×D3—241no—
831C2×D3—241no—
832C2×D3—242no—
833C2×D3—242no—
834C2×D3—241no—
835C2×D3—242no—
836C2×D3—242no—
837C2×D3—241no—
838C2×D3—241no—
839C2×D3—481no—
840C2×D3#88411yescharacteristic
841C2×D3#88411yescharacteristic
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—31no—
845C3×C4—31no—
846C3×C4—41no—
847C3×C4—41no—
848C3×C4—61no—
849C3×C4—81no—
850C3×C4C2×D3×D411yescharacteristic
851C3×C4C2×D3×D411yescharacteristic
852C3×C4C2×D3×D411yescharacteristic
853C3×C4C2×D3×D411yescharacteristic
854Dic3—21no—
855Dic3—61no—
856Dic3—61no—
857Dic3—121no—
858Dic3#88411yescharacteristic
859Dic3#88411yescharacteristic
860C32#306811yescharacteristic, complemented, Sylow
861C23—31no—
862C23—61no—
863C23—61no—
864C23—181no—
865C23—181no—
866C23—361no—
867C23—361no—
868C23—722no—
869Q8—21no—
870Q8—21no—
871Q8—31no—
872Q8—91no—
873Q8—181no—
874D4—31no—
875D4—61no—
876D4—61no—
877D4—61no—
878D4—61no—
879D4—61no—
880D4—91no—
881D4—121no—
882D4—121no—
883D4—181no—
884D4—181no—
885D4—181no—
886D4—181no—
887D4—181no—
888D4—181no—
889D4—361no—
890D4—361no—
891C2×C4—21no—
892C2×C4—31no—
893C2×C4—31no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—61no—
898C2×C4—121no—
899C2×C4—121no—
900C2×C4—181no—
901C2×C4—181no—
902C2×C4—181no—
903C2×C4—181no—
904C2×C4C22×D3211yescharacteristic
905C8—21no—
906C8—21no—
907C8—31no—
908C8—31no—
909C8—61no—
910C8—61no—
911C8—61no—
912C8—91no—
913C8—91no—
914C8—181no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—41no—
919C2×C3—61no—
920C2×C3—61no—
921C2×C3—121no—
922C2×C3—241no—
923C2×C3—241no—
924C2×C3C2×#88411yescharacteristic
925C2×C3D3×#12111yescharacteristic
926D3—21no—
927D3—21no—
928D3—41no—
929D3—81no—
930D3—81no—
931D3—121no—
932D3—121no—
933D3—241no—
934D3—241no—
935D3—241no—
936D3—481no—
937C22—31no—
938C22—31no—
939C22—61no—
940C22—121no—
941C22—121no—
942C22—121no—
943C22—181no—
944C22—241no—
945C22—241no—
946C22—361no—
947C22—721no—
948C22—721no—
949C22—722no—
950C22—722no—
951C22D3×#23511yescharacteristic
952C4—31no—
953C4—31no—
954C4—41no—
955C4—61no—
956C4—181no—
957C4D32×D411yescharacteristic
958C4D32×D411yescharacteristic
959C3—21no—
960C3#7872011yescharacteristic, complemented
961C3#8093011yescharacteristic, complemented
962C2—21no—
963C2—61no—
964C2—61no—
965C2—121no—
966C2—241no—
967C2—241no—
968C2—361no—
969C2—721no—
970C2D3×#88411yescharacteristic
subgroupG/H
centerC2D3×#884
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#101C22
socleC2×C32C2×#121
hypercenter#101D32
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
1. #10595317C2semidirect
2. C2×#63939C2semidirect
3. D3×#908C2semidirect
4. #10594706C2semidirect
5. #10592453C2semidirect
6. C3×#4754C2semidirect
7. C3×#4751C2semidirect
8. #10591643C2semidirect
9. #10591542C2semidirect
10. D3×#823C2semidirect
11. #10590997C2semidirect
12. #10590988C2semidirect
13. #10590987C2semidirect
14. #10590982C2semidirect
15. #10590973C2semidirect
21. #64151C22semidirect
22. C2×#3755C22semidirect
24. #64116C22semidirect
25. C3×#942C22semidirect
26. C2×C3×#215C22semidirect
28. C3×#907C22semidirect
40. #63830C22semidirect
42. C2×#3714C22semidirect
43. #63823C22semidirect
44. C2×#3713C22semidirect
46. #63817C22semidirect
47. #63815C22semidirect
57. C32×#101C22semidirect
58. #63650C22semidirect
59. #63649C22semidirect
60. C3×#836C22semidirect
61. C3×#823C22semidirect
62. C3×#823C22semidirect
63. C3×#823C22semidirect
64. C3×#822C22semidirect
65. #63578C22semidirect
66. #63577C22semidirect
67. #63559C22semidirect
68. #63558C22semidirect
92. #4754D3semidirect
93. #4751D3semidirect
204. #942C2×D3semidirect
208. C2×#215C2×D3semidirect
244. #907C2×D3semidirect
263. C3×#101C2×D3semidirect
264. C3×#101C2×D3semidirect
268. #836C2×D3semidirect
276. #823C2×D3semidirect
277. #823C2×D3semidirect
278. #823C2×D3semidirect
285. #822C2×D3semidirect
591. #101D32semidirect
860. C32#3068semidirect
960. C3#78720semidirect
961. C3#80930semidirect

Maximal subgroups

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

subgroupindex
#105953172
C2×#639392
D3×#9082
#105947062
#105924532
C3×#47542
C3×#47512
#105916432
#105915422
D3×#8232
#105909972
#105909882
#105909872
#105909822
#105909732
#809303
#787203