Finite Group Databasebeta

← #11868174

Subgroups — #11868174

Order 1152.

944 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#915C211yesmaximal, characteristic, complemented
2D3×#942C211yesmaximal, characteristic, complemented
3#10595095C211yesmaximal, characteristic
4#10594668C211yesmaximal, characteristic, complemented
5#10592876C211yesmaximal, characteristic, complemented
6C3×#5177C211yesmaximal, characteristic, complemented
7#10591641C211yesmaximal, characteristic, complemented
8D3×#836C211yesmaximal, characteristic, complemented
9#10591543C211yesmaximal, characteristic, complemented
10#10591506C211yesmaximal, characteristic, complemented
11#10591501C211yesmaximal, characteristic, complemented
12#10591407C211yesmaximal, characteristic, complemented
13#10590933C211yesmaximal, characteristic, complemented
14#10590930C211yesmaximal, characteristic, complemented
15#10590912C211yesmaximal, characteristic, complemented
16#83998—31nomaximal
17#80931—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20D3×#235C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22#64151C2211yescharacteristic
23#64141C2211yescharacteristic
24#64110C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic, complemented
26C3×#942C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic, complemented
28C3×#932C2211yescharacteristic
29C3×#915—21no—
30C3×#915—21no—
31C3×#915—21no—
32C3×#915—21no—
33C2×C3×Dic12C2211yescharacteristic, complemented
34C3×#901C2211yescharacteristic
35C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
36#63948—21no—
37#63946—21no—
38D3×#216—21no—
39D3×#215—21no—
40#63935—21no—
41#63933—21no—
42#63929—21no—
43#63925—21no—
44#63833C2211yescharacteristic
45#63833C2211yescharacteristic
46#63827C2211yescharacteristic
47#63827C2211yescharacteristic
48#63817C2211yescharacteristic
49#63814C2211yescharacteristic
50D3×#208C2211yescharacteristic
51D3×#208C2211yescharacteristic
52D3×#208C2211yescharacteristic
53#63805—21no—
54#63804—21no—
55#63791—21no—
56D3×ΓL(1,𝔽25)—21no—
57#63663C2211yescharacteristic, complemented
58#63660C2211yescharacteristic, complemented
59#63646C2211yescharacteristic, complemented
60C3×#836C2211yescharacteristic, complemented
61C3×#833C2211yescharacteristic, complemented
62C3×#819C2211yescharacteristic, complemented
63#63577C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63560C2211yescharacteristic, complemented
66#63560C2211yescharacteristic, complemented
67#63560C2211yescharacteristic, complemented
68#63560C2211yescharacteristic, complemented
69C2×C3×#137—31no—
70#5822—31no—
71C2×#942—31no—
72D3×#137—31no—
73#5773—31no—
74C2×#915D311yescharacteristic, complemented
75#5750—31no—
76#5745—31no—
77C3×#471—31no—
78#5237—31no—
79C2×#836—31no—
80#5204—31no—
81#5200—31no—
82#5192—31no—
83#5192—31no—
84#5192—31no—
85#5192—31no—
86#5177—31no—
87#5177—31no—
88#5177—31no—
89#5177—31no—
90#5177—61no—
91#5177D311yescharacteristic, complemented
92#5143—31no—
93#5125—31no—
94#4896—31no—
95#4893—31no—
96#4755—31no—
97D3×#101—31no—
98#4748—31no—
99#4745—31no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102#3828C2311yescharacteristic
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C3×D3×Q8—21no—
106C3×D3×Q8—21no—
107C3×D3×Q8—21no—
108C3×D3×Q8—21no—
109C3×#237—21no—
110C3×#237—21no—
111C3×#237—21no—
112C3×#237—21no—
113C3×#235C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6—21no—
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119D3×#67—21no—
120#3804—21no—
121D3×D12D411yescharacteristic
122C4×D32—21no—
123#3799D411yescharacteristic
124#3798—21no—
125#3795D411yescharacteristic
126D3×Dic6D411yescharacteristic
127C32×SD16—21no—
128C32×SD16—21no—
129C2×C32×C8C2311yescharacteristic
130#3756—21no—
131#3755—21no—
132#3754—21no—
133#3753—21no—
134#3748C2311yescharacteristic
135#3748C2311yescharacteristic
136#3748C2311yescharacteristic
137#3743—21no—
138C8×C3⋊D3—21no—
139C3×#216—21no—
140C3×#216—21no—
141C3×#216—21no—
142C3×#215—21no—
143C3×#214—21no—
144C3×#214—21no—
145C3×#214—21no—
146C3×#213—21no—
147C3×#208C2311yescharacteristic
148C3×#208C2311yescharacteristic
149C3×#208C2311yescharacteristic
150C2×C3×C3⋊C8C2311yescharacteristic
151C3×Dic12—21no—
152C3×Dic12—21no—
153C3×ΓL(1,𝔽25)—21no—
154C3×ΓL(1,𝔽25)D411yescharacteristic
155C3×ΓL(1,𝔽25)D411yescharacteristic
156C3×ΓL(1,𝔽25)D411yescharacteristic
157C3×ΓL(1,𝔽25)D411yescharacteristic
158C3×D3×C8—21no—
159#3719—21no—
160#3719—21no—
161#3718—21no—
162#3718—21no—
163#3717—21no—
164#3717—21no—
165#3715—21no—
166#3715—21no—
167#3712—21no—
168#3711—21no—
169#3711—21no—
170#3711—21no—
171#3711—21no—
172#3710—21no—
173D3×C3⋊C8—21no—
174D3×C3⋊C8—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3069—91noSylow
178C2×C3×#41—31no—
179C22×C3×Q8—31no—
180D3×#41—31no—
181C2×D3×Q8C2×D311yescharacteristic
182C2×#237C2×D311yescharacteristic
183C2×#235—31no—
184C3×#137—31no—
185C3×#137—61no—
186C3×#137—61no—
187C3×#137—61no—
188C3×#137—61no—
189C3×AGL(1,ℤ/8)—31no—
190C2×C3×Q16—31no—
191C2×C3×Q16—31no—
192C2×C3×SD16—21no—
193C2×C3×SD16—31no—
194C2×C3×SD16C2×D311yescharacteristic, complemented
195C2×C3×SD16C2×D311yescharacteristic, complemented
196C3×#131—31no—
197C2×C3×M16—31no—
198#951—31no—
199#951—31no—
200#951—61no—
201#950—61no—
202#950—61no—
203#949—61no—
204#948—31no—
205C2×#216—61no—
206C2×#216C2×D311yescharacteristic, complemented
207#942—31no—
208#942—31no—
209#942—31no—
210#942—31no—
211#942—31no—
212#942—31no—
213#942—61no—
214#942—61no—
215#942—61no—
216#942C2×D311yescharacteristic
217C2×#215—61no—
218C2×#214C2×D311yescharacteristic, complemented
219#932—31no—
220#932—31no—
221#932—61no—
222#932C2×D311yescharacteristic
223C2×#208—31no—
224C2×#208—31no—
225C2×#208—31no—
226#918—61no—
227D3×Q16—61no—
228#916—61no—
229#915—21no—
230#915—21no—
231#915—21no—
232#915—21no—
233#915—61no—
234#915—61no—
235D3×SD16—61no—
236#912—61no—
237#911—61no—
238#909—31no—
239#909—31no—
240#907—31no—
241#907—61no—
242#907—61no—
243#907—61no—
244D3×M16—31no—
245D3×M16—31no—
246D3×M16—31no—
247D3×M16—61no—
248D3×M16—61no—
249D3×M16—61no—
250C2×Dic12C2×D311yescharacteristic, complemented
251#901—31no—
252#901—31no—
253#901—31no—
254#901—31no—
255#901—61no—
256#901—61no—
257#901C2×D311yescharacteristic
258C2×ΓL(1,𝔽25)—61no—
259C2×ΓL(1,𝔽25)C2×D311yescharacteristic
260C3×#108—31no—
261C3×#101—31no—
262C3×#100—31no—
263#836—31no—
264#836—31no—
265#836—31no—
266#836—31no—
267#836—31no—
268#836—31no—
269#836—61no—
270#836C2×D311yescharacteristic, complemented
271#833—31no—
272#833—31no—
273#833—61no—
274#833C2×D311yescharacteristic, complemented
275#824—31no—
276#824—31no—
277#824—31no—
278#824—31no—
279#822—31no—
280#822—31no—
281#819—31no—
282#819—31no—
283#819—31no—
284#819—31no—
285#819—61no—
286#819C2×D311yescharacteristic, complemented
287C23×C32—21no—
288C22×C3×D3#4111yescharacteristic
289C2×D32—21no—
290C32×Q8—21no—
291C32×Q8—21no—
292C32×D4—21no—
293C32×D4—21no—
294C2×C32×C4—21no—
295C2×C32×C4C2411yescharacteristic
296#638—21no—
297C4⋊(C3⋊D3)C2×D411yescharacteristic
298C4×C3⋊D3—21no—
299#634C2×D411yescharacteristic
300C3×#67—21no—
301C3×#67—41no—
302C3×#67—41no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—41no—
306C2×C3×Dic3—41no—
307C2×C3×Dic3#4111yescharacteristic
308C3×D12C2×D411yescharacteristic
309C3×C4×D3—21no—
310C3×C4×D3—41no—
311C3×C4×D3—41no—
312C3×C4×D3C2×D411yescharacteristic
313C3×C4×D3C2×D411yescharacteristic
314C3×C4×D3C2×D411yescharacteristic
315C3×C4×D3C2×D411yescharacteristic
316C3×Dic6—21no—
317C3×Dic6—21no—
318C3×Dic6—21no—
319C3×Dic6—21no—
320C3×Dic6—41no—
321C3×Dic6—41no—
322C3×Dic6C2×D411yescharacteristic
323#627—21no—
324#626—21no—
325#626—21no—
326#625—21no—
327#624—21no—
328D3×Dic3—21no—
329D3×Dic3—21no—
330C32×C8C2×D411yescharacteristic
331C32×C8C2×D411yescharacteristic
332C3⋊(C3⋊C8)—21no—
333C3⋊(C3⋊C8)—21no—
334C3⋊(C3⋊C8)—21no—
335C3×C3⋊C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8C2×D411yescharacteristic
339C3×C3⋊C8C2×D411yescharacteristic
340#575—91no—
341C2×#137—31no—
342C2×#137—91no—
343#568—91no—
344#473—91no—
345#473—91no—
346#473—91no—
347#473—91no—
348#471—31no—
349#471—91no—
350#471—91no—
351#471—91no—
352#430—91no—
353#413—91no—
354C2×#101—91no—
355C3×#41—31no—
356C3×#41—61no—
357C3×#41—61no—
358C3×#41—61no—
359C3×#41—61no—
360C2×C3×Q8—21no—
361C2×C3×Q8—31no—
362C2×C3×Q8—31no—
363C2×C3×Q8—61no—
364C2×C3×Q8—61no—
365C2×C3×Q8—61no—
366C2×C3×Q8—61no—
367C2×C3×Q8—61no—
368C2×C3×Q8C22×D311yescharacteristic
369C2×C3×Q8C22×D311yescharacteristic
370C2×C3×D4—21no—
371C2×C3×D4—61no—
372C2×C3×D4C22×D311yescharacteristic
373C2×C3×D4C22×D311yescharacteristic
374C22×C3×C4—31no—
375C22×C3×C4—61no—
376C22×C3×C4—61no—
377C2×#67—21no—
378C2×#67—61no—
379C22×Dic3—21no—
380#239—31no—
381D3×Q8—21no—
382D3×Q8—21no—
383D3×Q8—21no—
384D3×Q8—21no—
385D3×Q8—31no—
386#237—21no—
387#237—21no—
388#237—21no—
389#237—21no—
390#237—31no—
391#237—61no—
392D3×D4—31no—
393D3×D4—61no—
394#235—31no—
395#235—31no—
396#235—31no—
397#235—31no—
398#235—61no—
399#235—61no—
400#235—61no—
401#235—61no—
402#235C22×D311yescharacteristic
403C2×D12—31no—
404C2×C4×D3—21no—
405C2×C4×D3—61no—
406C2×C4×D3—61no—
407C2×C4×D3C22×D311yescharacteristic
408C2×Dic6—21no—
409C2×Dic6—31no—
410C2×Dic6C22×D311yescharacteristic
411C2×Dic6C22×D311yescharacteristic
412C3×Q16—61no—
413C3×Q16—61no—
414C3×Q16—61no—
415C3×Q16—61no—
416C3×Q16—61no—
417C3×SD16—21no—
418C3×SD16—21no—
419C3×SD16—21no—
420C3×SD16—21no—
421C3×SD16—41no—
422C3×SD16—41no—
423C3×SD16—61no—
424C3×SD16—61no—
425C3×SD16—61no—
426C3×SD16—61no—
427C3×D8—61no—
428C3×M16—31no—
429C3×M16—31no—
430C3×M16—31no—
431C3×M16—31no—
432C3×M16—31no—
433C3×M16—31no—
434C3×M16—31no—
435C3×M16—61no—
436C2×C3×C8—21no—
437C2×C3×C8—31no—
438C2×C3×C8—61no—
439C2×C3×C8C22×D311yescharacteristic
440C2×C3×C8C22×D311yescharacteristic
441#216—21no—
442#216—21no—
443#216—21no—
444#216—61no—
445#216—61no—
446#216—61no—
447#216—61no—
448#216—61no—
449#216—61no—
450#216—61no—
451#216—61no—
452#216—121no—
453#215—21no—
454#215—61no—
455#215—61no—
456#215—61no—
457#215—61no—
458#215—61no—
459#215—61no—
460#215—121no—
461#214—21no—
462#214—21no—
463#214—21no—
464#214—61no—
465#214—61no—
466#214—61no—
467#214—61no—
468#214—121no—
469#213—21no—
470#213—61no—
471#213—61no—
472#213—121no—
473#208—31no—
474#208—31no—
475#208—31no—
476#208—31no—
477#208—31no—
478#208—31no—
479#208—61no—
480#208—61no—
481#208—61no—
482#208—61no—
483#208—61no—
484#208—61no—
485#208—61no—
486#208C22×D311yescharacteristic
487#208C22×D311yescharacteristic
488#208C22×D311yescharacteristic
489C2×C3⋊C8—61no—
490C2×C3⋊C8—61no—
491C2×C3⋊C8—61no—
492C2×C3⋊C8—61no—
493C2×C3⋊C8C22×D311yescharacteristic
494Dic12—21no—
495Dic12—21no—
496Dic12—61no—
497Dic12—61no—
498#204—61no—
499#204—61no—
500ΓL(1,𝔽25)—21no—
501ΓL(1,𝔽25)—61no—
502ΓL(1,𝔽25)—61no—
503ΓL(1,𝔽25)—61no—
504ΓL(1,𝔽25)—61no—
505ΓL(1,𝔽25)—61no—
506ΓL(1,𝔽25)—61no—
507ΓL(1,𝔽25)—61no—
508ΓL(1,𝔽25)—61no—
509ΓL(1,𝔽25)—121no—
510ΓL(1,𝔽25)#6711yescharacteristic
511ΓL(1,𝔽25)#6711yescharacteristic
512ΓL(1,𝔽25)#6711yescharacteristic
513ΓL(1,𝔽25)#6711yescharacteristic
514D3×C8—21no—
515D3×C8—61no—
516D3×C8—61no—
517D3×C8—61no—
518D3×C8—61no—
519D3×C8—61no—
520D3×C8—61no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—121no—
524C22×C32—41no—
525C22×C32—81no—
526C22×C32C2×#4111yescharacteristic
527C2×C3⋊D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—41no—
530C2×C3×D3#12111yescharacteristic
531C2×C3×D3#12111yescharacteristic
532D32—81no—
533C32×C4—41no—
534C32×C4C22×D411yescharacteristic
535C32×C4C22×D411yescharacteristic
536C3⋊Dic3—21no—
537C3×Dic3—21no—
538C3×Dic3—41no—
539C3×Dic3—41no—
540C3×Dic3#12111yescharacteristic
541C3×Dic3#12111yescharacteristic
542C2×#41—31no—
543C2×#41—91no—
544C22×Q8—31no—
545#137—31no—
546#137—61no—
547#137—61no—
548#137—61no—
549#137—61no—
550#137—91no—
551#137—91no—
552#137—91no—
553#137—91no—
554#137—91no—
555#137—181no—
556#137—181no—
557#137—181no—
558AGL(1,ℤ/8)—31no—
559AGL(1,ℤ/8)—91no—
560AGL(1,ℤ/8)—181no—
561#135—181no—
562#135—181no—
563C2×Q16—31no—
564C2×Q16—31no—
565C2×Q16—181no—
566C2×SD16—31no—
567C2×SD16—181no—
568C2×SD16D3211yescharacteristic, complemented
569#131—31no—
570#131—91no—
571#131—91no—
572#131—91no—
573#131—181no—
574#131—181no—
575C2×M16—31no—
576C2×M16—91no—
577C2×M16—91no—
578C2×M16—91no—
579C2×M16—181no—
580C2×M16—181no—
581#108—31no—
582#108—91no—
583#108—91no—
584#108—91no—
585#101—31no—
586#101—91no—
587#101—91no—
588#101—91no—
589#101—91no—
590#101—91no—
591#100—31no—
592#100—91no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—31no—
596C23×C3—41no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3#23711yescharacteristic
600C3×Q8—21no—
601C3×Q8—21no—
602C3×Q8—21no—
603C3×Q8—21no—
604C3×Q8—31no—
605C3×Q8—41no—
606C3×Q8—41no—
607C3×Q8—61no—
608C3×Q8—61no—
609C3×Q8—61no—
610C3×Q8—61no—
611C3×Q8—121no—
612C3×Q8—121no—
613C3×D4—21no—
614C3×D4—21no—
615C3×D4—21no—
616C3×D4—21no—
617C3×D4—31no—
618C3×D4—41no—
619C3×D4—41no—
620C3×D4—61no—
621C3×D4—121no—
622C3×D4—121no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—31no—
627C2×C3×C4—31no—
628C2×C3×C4—31no—
629C2×C3×C4—31no—
630C2×C3×C4—31no—
631C2×C3×C4—41no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—121no—
636C2×C3×C4—121no—
637C2×C3×C4—121no—
638C2×C3×C4—121no—
639C2×C3×C4C23×D311yescharacteristic
640C2×C3×C4C23×D311yescharacteristic
641#67—21no—
642#67—41no—
643#67—41no—
644#67—61no—
645#67—61no—
646#67—61no—
647#67—61no—
648#67—61no—
649#67—61no—
650#67—121no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3#23711yescharacteristic
658D12—31no—
659D12—31no—
660D12—61no—
661D12—61no—
662D12—61no—
663D12D3×D411yescharacteristic
664C4×D3—21no—
665C4×D3—41no—
666C4×D3—41no—
667C4×D3—61no—
668C4×D3—61no—
669C4×D3—61no—
670C4×D3—61no—
671C4×D3—61no—
672C4×D3—61no—
673C4×D3—121no—
674C4×D3D3×D411yescharacteristic
675C4×D3D3×D411yescharacteristic
676C4×D3C2×#6711yescharacteristic
677C4×D3C2×#6711yescharacteristic
678Dic6—21no—
679Dic6—21no—
680Dic6—21no—
681Dic6—21no—
682Dic6—31no—
683Dic6—31no—
684Dic6—41no—
685Dic6—41no—
686Dic6—61no—
687Dic6—61no—
688Dic6—61no—
689Dic6D3×D411yescharacteristic
690C3×C8—21no—
691C3×C8—21no—
692C3×C8—31no—
693C3×C8—31no—
694C3×C8—61no—
695C3×C8—61no—
696C3×C8—61no—
697C3×C8D3×D411yescharacteristic
698C3×C8D3×D411yescharacteristic
699C3×C8C2×#6711yescharacteristic
700C3×C8C2×#6711yescharacteristic
701C3⋊C8—21no—
702C3⋊C8—21no—
703C3⋊C8—21no—
704C3⋊C8—61no—
705C3⋊C8—61no—
706C3⋊C8—61no—
707C3⋊C8—61no—
708C3⋊C8—61no—
709C3⋊C8—61no—
710C3⋊C8—121no—
711C3⋊C8—121no—
712C3⋊C8—121no—
713C3⋊C8C2×#6711yescharacteristic
714C3⋊C8C2×#6711yescharacteristic
715C2×C32—21no—
716C2×C32—81no—
717C2×C32C2×#12111yescharacteristic
718C3⋊D3—41no—
719C3×D3—21no—
720C3×D3—21no—
721C3×D3—41no—
722#41—31no—
723#41—61no—
724#41—61no—
725#41—61no—
726#41—61no—
727#41—91no—
728#41—91no—
729#41—91no—
730#41—181no—
731#41—181no—
732C2×Q8—31no—
733C2×Q8—31no—
734C2×Q8—61no—
735C2×Q8—61no—
736C2×Q8—61no—
737C2×Q8—61no—
738C2×Q8—61no—
739C2×Q8—91no—
740C2×Q8C2×D3211yescharacteristic
741C2×D4—61no—
742C2×D4—91no—
743C2×D4—181no—
744C2×D4C2×D3211yescharacteristic
745C22×C4—31no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—181no—
749Q16—61no—
750Q16—61no—
751Q16—61no—
752Q16—61no—
753Q16—61no—
754Q16—181no—
755Q16—181no—
756Q16—181no—
757Q16—181no—
758Q16—181no—
759SD16—21no—
760SD16—21no—
761SD16—61no—
762SD16—61no—
763SD16—61no—
764SD16—61no—
765SD16—181no—
766SD16—181no—
767SD16—181no—
768SD16—181no—
769SD16—181no—
770SD16—181no—
771D8—61no—
772D8—181no—
773M16—31no—
774M16—31no—
775M16—31no—
776M16—31no—
777M16—31no—
778M16—31no—
779M16—31no—
780M16—61no—
781M16—91no—
782M16—91no—
783M16—91no—
784M16—181no—
785M16—181no—
786M16—181no—
787M16—181no—
788M16—181no—
789M16—181no—
790C2×C8—31no—
791C2×C8—61no—
792C2×C8—181no—
793C2×C8—181no—
794C2×C8—181no—
795C2×C8—181no—
796C2×C8—181no—
797C2×C8—181no—
798C2×C8C2×D3211yescharacteristic
799C22×C3—21no—
800C22×C3—31no—
801C22×C3—31no—
802C22×C3—41no—
803C22×C3—41no—
804C22×C3—61no—
805C22×C3—81no—
806C22×C3—81no—
807C22×C3—81no—
808C22×C3—121no—
809C22×C3—161no—
810C22×C3C2×#23711yescharacteristic
811C22×C3D3×#4111yescharacteristic
812C2×D3—21no—
813C2×D3—41no—
814C2×D3—61no—
815C2×D3—61no—
816C2×D3—121no—
817C2×D3—241no—
818C2×D3—241no—
819C2×D3#93811yescharacteristic
820C2×D3#93811yescharacteristic
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—31no—
824C3×C4—31no—
825C3×C4—41no—
826C3×C4—41no—
827C3×C4—61no—
828C3×C4—81no—
829C3×C4—121no—
830C3×C4—121no—
831C3×C4C2×D3×D411yescharacteristic
832C3×C4C2×D3×D411yescharacteristic
833C3×C4C2×D3×D411yescharacteristic
834C3×C4C22×#6711yescharacteristic
835Dic3—21no—
836Dic3—41no—
837Dic3—41no—
838Dic3—61no—
839Dic3—61no—
840Dic3—121no—
841Dic3#93811yescharacteristic
842Dic3#93811yescharacteristic
843C32#306911yescharacteristic, complemented, Sylow
844C23—21no—
845C23—31no—
846C23—181no—
847Q8—21no—
848Q8—21no—
849Q8—31no—
850Q8—61no—
851Q8—61no—
852Q8—61no—
853Q8—61no—
854Q8—91no—
855Q8—121no—
856Q8—121no—
857Q8—181no—
858D4—21no—
859D4—21no—
860D4—31no—
861D4—61no—
862D4—91no—
863D4—121no—
864D4—121no—
865D4—181no—
866D4—181no—
867D4—181no—
868D4—181no—
869C2×C4—21no—
870C2×C4—31no—
871C2×C4—31no—
872C2×C4—31no—
873C2×C4—31no—
874C2×C4—31no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—121no—
879C2×C4—121no—
880C2×C4—121no—
881C2×C4—121no—
882C2×C4—181no—
883C2×C4—181no—
884C2×C4—181no—
885C2×C4—181no—
886C2×C4C22×D3211yescharacteristic
887C8—31no—
888C8—31no—
889C8—61no—
890C8—61no—
891C8—61no—
892C8—181no—
893C8—181no—
894C8—181no—
895C8D3×#6711yescharacteristic
896C8D3×#6711yescharacteristic
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—41no—
901C2×C3—61no—
902C2×C3—61no—
903C2×C3—81no—
904C2×C3—81no—
905C2×C3—121no—
906C2×C3—161no—
907C2×C3D3×#12111yescharacteristic
908C2×C3C2×#93811yescharacteristic
909D3—21no—
910D3—21no—
911D3—41no—
912D3—121no—
913D3—121no—
914D3—241no—
915C22—31no—
916C22—31no—
917C22—41no—
918C22—61no—
919C22—81no—
920C22—121no—
921C22—181no—
922C22—721no—
923C22D3×#23711yescharacteristic
924C4—31no—
925C4—31no—
926C4—41no—
927C4—61no—
928C4—121no—
929C4—121no—
930C4—181no—
931C4D32×D411yescharacteristic
932C4C2×D3×#6711yescharacteristic
933C3—21no—
934C3#8093111yescharacteristic, complemented
935C3#8399811yescharacteristic, complemented
936C2—21no—
937C2—61no—
938C2—61no—
939C2—81no—
940C2—121no—
941C2—361no—
942C2D3×#93811yescharacteristic
subgroupG/H
centerC2D3×#938
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC2×C32C2×#121
prime radical#10595095C2
hypercenterC2×SD16D32
hypocenterC32#3069
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#915C2semidirect
2. D3×#942C2semidirect
4. #10594668C2semidirect
5. #10592876C2semidirect
6. C3×#5177C2semidirect
7. #10591641C2semidirect
8. D3×#836C2semidirect
9. #10591543C2semidirect
10. #10591506C2semidirect
11. #10591501C2semidirect
12. #10591407C2semidirect
13. #10590933C2semidirect
14. #10590930C2semidirect
15. #10590912C2semidirect
21. C2×C32×SD16C22semidirect
25. C2×C3×#216C22semidirect
27. C2×C3×#214C22semidirect
33. C2×C3×Dic12C22semidirect
57. #63663C22semidirect
58. #63660C22semidirect
59. #63646C22semidirect
60. C3×#836C22semidirect
61. C3×#833C22semidirect
62. C3×#819C22semidirect
63. #63577C22semidirect
64. #63577C22semidirect
65. #63560C22semidirect
66. #63560C22semidirect
67. #63560C22semidirect
68. #63560C22semidirect
74. C2×#915D3semidirect
91. #5177D3semidirect
194. C2×C3×SD16C2×D3semidirect
195. C2×C3×SD16C2×D3semidirect
206. C2×#216C2×D3semidirect
218. C2×#214C2×D3semidirect
250. C2×Dic12C2×D3semidirect
270. #836C2×D3semidirect
274. #833C2×D3semidirect
286. #819C2×D3semidirect
568. C2×SD16D32semidirect
843. C32#3069semidirect
934. C3#80931semidirect
935. C3#83998semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9152
D3×#9422
#105950952
#105946682
#105928762
C3×#51772
#105916412
D3×#8362
#105915432
#105915062
#105915012
#105914072
#105909332
#105909302
#105909122
#839983
#809313