Finite Group Databasebeta

← #11886865

Subgroups — #11886865

Order 1152.

972 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5751C211yesmaximal, characteristic, complemented
2#10595466C211yesmaximal, characteristic, complemented
3#10595457C211yesmaximal, characteristic, complemented
4#10594679C211yesmaximal, characteristic, complemented
5#10592840C211yesmaximal, characteristic, complemented
6C3×#5144C211yesmaximal, characteristic, complemented
7#10591689C211yesmaximal, characteristic, complemented
8#10591666C211yesmaximal, characteristic, complemented
9#10591017C211yesmaximal, characteristic, complemented
10#10591013C211yesmaximal, characteristic, complemented
11#10590986C211yesmaximal, characteristic, complemented
12#10590985C211yesmaximal, characteristic, complemented
13#10590925C211yesmaximal, characteristic, complemented
14#10590915C211yesmaximal, characteristic, complemented
15#10590877C211yesmaximal, characteristic, complemented
16#84014—31nomaximal
17#79893—31nomaximal
18C3×#1010C2211yescharacteristic
19C3×#1009C2211yescharacteristic, complemented
20#64308C2211yescharacteristic, complemented
21#64298C2211yescharacteristic
22C32×#131C2211yescharacteristic, complemented
23#64160C2211yescharacteristic, complemented
24#64158C2211yescharacteristic
25C2×#3744C2211yescharacteristic, complemented
26C3×#950C2211yescharacteristic
27C3×#909—21no—
28C3×#909C2211yescharacteristic, complemented
29C3×#908—21no—
30C3×#908C2211yescharacteristic
31C3×#904—21no—
32C3×#904C2211yescharacteristic
33C2×C3×#204—21no—
34C2×C3×#204C2211yescharacteristic, complemented
35C3×#901C2211yescharacteristic, complemented
36#63948—21no—
37#63947—21no—
38#63943—21no—
39D3×#215—21no—
40#63935—21no—
41#63932—21no—
42D3×#214—21no—
43#63925—21no—
44#63911C2211yescharacteristic
45#63866C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic, complemented
47#63831C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49#63827C2211yescharacteristic, complemented
50#63825C2211yescharacteristic
51#63823C2211yescharacteristic
52#63814C2211yescharacteristic, complemented
53#63814C2211yescharacteristic, complemented
54#63806—21no—
55#63801—21no—
56#63795—21no—
57D3×#204—21no—
58#63651C2211yescharacteristic, complemented
59#63650C2211yescharacteristic, complemented
60#63646C2211yescharacteristic, complemented
61C3×#837C2211yescharacteristic, complemented
62C3×#825C2211yescharacteristic, complemented
63C3×#822C2211yescharacteristic, complemented
64C3×C8×Dic3C2211yescharacteristic, complemented
65#63569C2211yescharacteristic, complemented
66#63569C2211yescharacteristic, complemented
67#63560C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C3×#577—31no—
70#5837—31no—
71#5836—31no—
72#5770—31no—
73#5770—31no—
74#5770—31no—
75#5751—31no—
76#5751D311yescharacteristic, complemented
77C3×#443—31no—
78#5246—31no—
79#5241—31no—
80#5205—31no—
81#5203—31no—
82#5200—31no—
83#5198—31no—
84#5196—31no—
85#5177—31no—
86#5175—31no—
87#5144D311yescharacteristic, complemented
88#5141—31no—
89#5141—31no—
90#5141—31no—
91#5141—61no—
92#4898—31no—
93#4898—31no—
94#4826—31no—
95#4826—31no—
96#4822—31no—
97#4822—31no—
98#4700—31no—
99#4693—31no—
100C32×#41C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C3×#239—21no—
104C3×D3×Q8—21no—
105C3×#237—21no—
106C3×#237—41no—
107C3×D3×D4—21no—
108C3×D3×D4—41no—
109C3×#235—21no—
110C3×#235—21no—
111C3×#235C2311yescharacteristic
112C3×#235C2311yescharacteristic
113C3×#235C2311yescharacteristic
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×Dic6—21no—
117C2×C3×Dic6C2311yescharacteristic
118#3811—41no—
119C2×#626—41no—
120#3805—41no—
121D3×D12—21no—
122D3×D12—21no—
123#3799—21no—
124#3799—21no—
125#3795—21no—
126#3795—21no—
127D3×Dic6—21no—
128D3×Dic6—21no—
129C32×M16—21no—
130C32×M16C2311yescharacteristic
131C2×C32×C8—21no—
132C2×C32×C8C2311yescharacteristic
133#3756—21no—
134#3755—21no—
135#3754—21no—
136#3753—21no—
137#3748C2311yescharacteristic
138#3748C2311yescharacteristic
139#3744—21no—
140#3744—21no—
141C3×#216D411yescharacteristic, complemented
142C3×#215D411yescharacteristic, complemented
143C3×#214D411yescharacteristic, complemented
144C3×#213D411yescharacteristic, complemented
145C3×C4×Dic3C2311yescharacteristic
146C3×#208C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148C3×Dic12—21no—
149C3×Dic12D411yescharacteristic, complemented
150C3×D24—21no—
151C3×D24D411yescharacteristic, complemented
152C3×#204—21no—
153C3×#204—21no—
154C3×#204—21no—
155C3×#204—21no—
156C3×#204D411yescharacteristic, complemented
157C3×#204D411yescharacteristic, complemented
158C3×ΓL(1,𝔽25)—21no—
159C3×D3×C8—21no—
160Dic3⋊Dic3—41no—
161#3719—21no—
162#3718—21no—
163#3717—21no—
164#3717—21no—
165#3717—21no—
166#3716—21no—
167#3716—21no—
168#3716—21no—
169#3715—21no—
170#3715—21no—
171#3714—21no—
172#3713—21no—
173#3711—21no—
174#3711—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3291—91noSylow
178C3×2−1+4—31no—
179C3×H(5,𝔽2)—31no—
180#1010—31no—
181#1010—31no—
182#1010C2×D311yescharacteristic
183#1009—31no—
184#1009—31no—
185#1009C2×D311yescharacteristic, complemented
186C3×#137—31no—
187C3×#137—61no—
188C3×AGL(1,ℤ/8)—31no—
189C3×AGL(1,ℤ/8)—61no—
190C3×#135—31no—
191C3×#135—31no—
192C3×#135—61no—
193C2×C3×SD16—31no—
194C2×C3×SD16—61no—
195C3×#131—21no—
196C3×#131—31no—
197C3×#131C2×D311yescharacteristic, complemented
198C3×#131C2×D311yescharacteristic, complemented
199#951—31no—
200#951—31no—
201#951—31no—
202#951—31no—
203#951—61no—
204#951—61no—
205#950—61no—
206#950—61no—
207#950C2×D311yescharacteristic
208#949—31no—
209#949—31no—
210#949—31no—
211#949—31no—
212#949—61no—
213#949—61no—
214#948—31no—
215#948—31no—
216#944—31no—
217#942—31no—
218#942—61no—
219C2×#215—31no—
220C2×#215—61no—
221#940—31no—
222C2×#214—31no—
223C2×#214—61no—
224#932—31no—
225#932—61no—
226#918—61no—
227#918—61no—
228#918—61no—
229#916—61no—
230#916—61no—
231#916—61no—
232D3×SD16—61no—
233D3×SD16—61no—
234D3×SD16—61no—
235#911—61no—
236#911—61no—
237#911—61no—
238#909—21no—
239#909—31no—
240#909—61no—
241#909C2×D311yescharacteristic, complemented
242#908—21no—
243#908—31no—
244#908—61no—
245#908C2×D311yescharacteristic
246#904—21no—
247#904—61no—
248#904C2×D311yescharacteristic
249C2×#204—21no—
250C2×#204—31no—
251C2×#204—31no—
252C2×#204—31no—
253C2×#204—31no—
254C2×#204—61no—
255C2×#204—61no—
256C2×#204C2×D311yescharacteristic, complemented
257#901—31no—
258#901—31no—
259#901C2×D311yescharacteristic, complemented
260#874—31no—
261#869—31no—
262C3×#108—31no—
263C3×#104—31no—
264C3×#104—31no—
265C3×C4×C8—31no—
266#837—31no—
267#837—31no—
268#837C2×D311yescharacteristic, complemented
269#836—31no—
270#833—31no—
271#825C2×D311yescharacteristic, complemented
272#824—31no—
273#824—31no—
274#824—31no—
275#824—61no—
276#823—31no—
277#823—31no—
278#823—31no—
279#823—61no—
280#822C2×D311yescharacteristic, complemented
281#819—31no—
282#819—31no—
283#819—61no—
284C8×Dic3C2×D311yescharacteristic, complemented
285#805—31no—
286#805—31no—
287C22×C3⋊D3—21no—
288C22×C3×D3—21no—
289C22×C3×D3—41no—
290C2×D32—41no—
291C32×Q8C2×D411yescharacteristic
292C32×D4—21no—
293C32×D4C2×D411yescharacteristic
294C2×C32×C4—21no—
295C2×C32×C4C2411yescharacteristic
296C2×C3⋊Dic3—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)—21no—
299#634—21no—
300#634—21no—
301C3×#67—21no—
302C3×#67—21no—
303C3×#67—21no—
304C3×#67—41no—
305C3×#67—41no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—41no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—41no—
312C3×D12C2×D411yescharacteristic
313C3×D12C2×D411yescharacteristic
314C3×D12C2×D411yescharacteristic
315C3×C4×D3—21no—
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—41no—
319C3×C4×D3—41no—
320C3×Dic6—21no—
321C3×Dic6—21no—
322C3×Dic6—41no—
323C3×Dic6C2×D411yescharacteristic
324C3×Dic6C2×D411yescharacteristic
325C3×Dic6C2×D411yescharacteristic
326#627—41no—
327#626—41no—
328#626—41no—
329#626—82no—
330#625—41no—
331#624—41no—
332D3×Dic3—41no—
333D3×Dic3—41no—
334C32×C8—21no—
335C32×C8C2×D411yescharacteristic
336C32×C8C2×D411yescharacteristic
337C3⋊(C3⋊C8)—21no—
338C3⋊(C3⋊C8)—21no—
339C3×C3⋊C8—21no—
340C3×C3⋊C8C2×D411yescharacteristic
341C3×C3⋊C8C2×D411yescharacteristic
342#577—31no—
343#577—91no—
344#577—91no—
345#577—91no—
346#492—91no—
347#471—91no—
348#471—91no—
349#471—91no—
350#471—91no—
351#456—91no—
352#456—91no—
353#453—91no—
354#453—91no—
355#443—31no—
356#443—91no—
357C3×#41—21no—
358C3×#41—31no—
359C3×#41—31no—
360C3×#41—31no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41—61no—
365C3×#41—121no—
366C3×#41C22×D311yescharacteristic
367C3×#41C22×D311yescharacteristic
368C2×C3×Q8—31no—
369C2×C3×Q8—61no—
370C2×C3×Q8—61no—
371C2×C3×D4—31no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4—121no—
375C2×#67—121no—
376#239—21no—
377#239—61no—
378#239—61no—
379D3×Q8—21no—
380D3×Q8—61no—
381D3×Q8—61no—
382#237—21no—
383#237—41no—
384#237—61no—
385#237—61no—
386#237—121no—
387#237—121no—
388D3×D4—21no—
389D3×D4—41no—
390D3×D4—61no—
391D3×D4—61no—
392D3×D4—121no—
393D3×D4—121no—
394#235—21no—
395#235—21no—
396#235—61no—
397#235—61no—
398#235—61no—
399#235—61no—
400#235C22×D311yescharacteristic
401#235C22×D311yescharacteristic
402#235C22×D311yescharacteristic
403C2×D12—21no—
404C2×D12—31no—
405C2×D12—31no—
406C2×D12—61no—
407C2×D12—61no—
408C2×D12—61no—
409C2×D12—121no—
410C2×D12C22×D311yescharacteristic
411C2×Dic6—21no—
412C2×Dic6—31no—
413C2×Dic6—31no—
414C2×Dic6—61no—
415C2×Dic6—61no—
416C2×Dic6—61no—
417C2×Dic6C22×D311yescharacteristic
418C3×Q16—31no—
419C3×Q16—31no—
420C3×Q16—61no—
421C3×SD16—31no—
422C3×SD16—31no—
423C3×SD16—31no—
424C3×SD16—31no—
425C3×SD16—61no—
426C3×SD16—61no—
427C3×SD16—61no—
428C3×SD16—61no—
429C3×D8—31no—
430C3×D8—31no—
431C3×D8—61no—
432C3×M16—21no—
433C3×M16—21no—
434C3×M16—21no—
435C3×M16—31no—
436C3×M16—41no—
437C3×M16—61no—
438C3×M16C22×D311yescharacteristic
439C3×M16C22×D311yescharacteristic
440C2×C3×C8—21no—
441C2×C3×C8—21no—
442C2×C3×C8—21no—
443C2×C3×C8—31no—
444C2×C3×C8—41no—
445C2×C3×C8—61no—
446C2×C3×C8C22×D311yescharacteristic
447C2×C3×C8C22×D311yescharacteristic
448C3×C42—31no—
449#216—61no—
450#216—61no—
451#216—61no—
452#216—61no—
453#216—61no—
454#216—121no—
455#216D1211yescharacteristic, complemented
456#215—61no—
457#215—61no—
458#215—61no—
459#215—61no—
460#215—61no—
461#215—61no—
462#215—61no—
463#215—121no—
464#215D1211yescharacteristic, complemented
465#214—61no—
466#214—61no—
467#214—61no—
468#214—61no—
469#214—61no—
470#214—61no—
471#214—61no—
472#214—121no—
473#214D1211yescharacteristic, complemented
474#213—61no—
475#213—61no—
476#213—61no—
477#213—61no—
478#213—61no—
479#213—121no—
480#213D1211yescharacteristic, complemented
481C4⋊Dic3—121no—
482Dic3⋊C4—121no—
483C4×Dic3C22×D311yescharacteristic
484#208—31no—
485#208—31no—
486#208—31no—
487#208—31no—
488#208—61no—
489#208—61no—
490#208—61no—
491#208—61no—
492#208C22×D311yescharacteristic
493C2×C3⋊C8—61no—
494C2×C3⋊C8—61no—
495C2×C3⋊C8C22×D311yescharacteristic
496Dic12—21no—
497Dic12—61no—
498Dic12#6711yescharacteristic, complemented
499D24—21no—
500D24—61no—
501D24#6711yescharacteristic, complemented
502#204—21no—
503#204—21no—
504#204—21no—
505#204—21no—
506#204—61no—
507#204—61no—
508#204—61no—
509#204—61no—
510#204—61no—
511#204—61no—
512#204—61no—
513#204—61no—
514#204—61no—
515#204—61no—
516#204—121no—
517#204—121no—
518#204#6711yescharacteristic, complemented
519#204#6711yescharacteristic, complemented
520ΓL(1,𝔽25)—21no—
521ΓL(1,𝔽25)—61no—
522ΓL(1,𝔽25)—61no—
523D3×C8—21no—
524D3×C8—61no—
525D3×C8—61no—
526C22×C32—21no—
527C22×C32H(5,𝔽2)11yescharacteristic
528C2×C3⋊D3—41no—
529C2×C3⋊D3—81no—
530C2×C3×D3—21no—
531C2×C3×D3—21no—
532C2×C3×D3—21no—
533C2×C3×D3—41no—
534C2×C3×D3—81no—
535C2×C3×D3—161no—
536D32—161no—
537C32×C4—21no—
538C32×C4C22×D411yescharacteristic
539C32×C4C22×D411yescharacteristic
540C3⋊Dic3—41no—
541C3×Dic3—22no—
542C3×Dic3—21no—
543C3×Dic3—21no—
544C3×Dic3—21no—
545C3×Dic3—41no—
5462−1+4—31no—
5472−1+4—91no—
548H(5,𝔽2)—31no—
549H(5,𝔽2)—91no—
550#137—31no—
551#137—61no—
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)—61no—
560AGL(1,ℤ/8)—91no—
561AGL(1,ℤ/8)—91no—
562AGL(1,ℤ/8)—91no—
563AGL(1,ℤ/8)—181no—
564AGL(1,ℤ/8)—181no—
565AGL(1,ℤ/8)—181no—
566#135—31no—
567#135—31no—
568#135—61no—
569#135—181no—
570#135—181no—
571#135—181no—
572C2×SD16—31no—
573C2×SD16—61no—
574C2×SD16—91no—
575C2×SD16—91no—
576C2×SD16—91no—
577C2×SD16—181no—
578C2×SD16—181no—
579C2×SD16—181no—
580#131—31no—
581#131—91no—
582#131—91no—
583#131D3211yescharacteristic, complemented
584C4⋊Q8—91no—
585#127—91no—
586#108—31no—
587#108—91no—
588#104—31no—
589#104—31no—
590#104—91no—
591#104—91no—
592#101—91no—
593#101—91no—
594#100—91no—
595#100—91no—
596C4×C8—31no—
597C23×C3—61no—
598C23×C3—121no—
599C22×D3—21no—
600C22×D3—41no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—121no—
606C3×Q8—21no—
607C3×Q8—31no—
608C3×Q8—31no—
609C3×Q8—31no—
610C3×Q8—61no—
611C3×Q8—61no—
612C3×Q8—121no—
613C3×Q8C2×D1211yescharacteristic
614C3×Q8D3×D411yescharacteristic
615C3×D4—21no—
616C3×D4—21no—
617C3×D4—21no—
618C3×D4—31no—
619C3×D4—31no—
620C3×D4—31no—
621C3×D4—41no—
622C3×D4—61no—
623C3×D4—61no—
624C3×D4—61no—
625C3×D4—61no—
626C3×D4—61no—
627C3×D4—121no—
628C3×D4—121no—
629C3×D4—121no—
630C3×D4C2×D1211yescharacteristic
631C3×D4D3×D411yescharacteristic
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—41no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—121no—
642C2×C3×C4—121no—
643C2×C3×C4—121no—
644C2×C3×C4C23×D311yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646#67—21no—
647#67—21no—
648#67—21no—
649#67—41no—
650#67—41no—
651#67—121no—
652#67—121no—
653#67—121no—
654#67—121no—
655#67—242no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—41no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—121no—
662C2×Dic3—121no—
663C2×Dic3—121no—
664D12—21no—
665D12—21no—
666D12—41no—
667D12—61no—
668D12—61no—
669D12—61no—
670D12—61no—
671D12—121no—
672D12—121no—
673D12—121no—
674D12—121no—
675D12—242no—
676D12C2×D1211yescharacteristic
677D12C2×#6711yescharacteristic
678D12C2×#6711yescharacteristic
679C4×D3—21no—
680C4×D3—21no—
681C4×D3—21no—
682C4×D3—41no—
683C4×D3—41no—
684C4×D3—121no—
685C4×D3—121no—
686C4×D3—121no—
687C4×D3—121no—
688Dic6—21no—
689Dic6—21no—
690Dic6—41no—
691Dic6—61no—
692Dic6—61no—
693Dic6—61no—
694Dic6—61no—
695Dic6—121no—
696Dic6—121no—
697Dic6—121no—
698Dic6—121no—
699Dic6C2×D1211yescharacteristic
700Dic6C2×#6711yescharacteristic
701Dic6C2×#6711yescharacteristic
702C3×C8—21no—
703C3×C8—21no—
704C3×C8—21no—
705C3×C8—21no—
706C3×C8—31no—
707C3×C8—31no—
708C3×C8—41no—
709C3×C8—61no—
710C3×C8D3×D411yescharacteristic
711C3×C8D3×D411yescharacteristic
712C3×C8C2×#6711yescharacteristic
713C3×C8C2×#6711yescharacteristic
714C3⋊C8—21no—
715C3⋊C8—61no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—61no—
719C3⋊C8—121no—
720C3⋊C8—121no—
721C3⋊C8C2×D1211yescharacteristic
722C3⋊C8C2×D1211yescharacteristic
723C2×C32—21no—
724C2×C32—41no—
725C2×C32D4211yescharacteristic
726C3⋊D3—81no—
727C3×D3—41no—
728C3×D3—41no—
729C3×D3—41no—
730C3×D3—81no—
731#41—31no—
732#41—31no—
733#41—31no—
734#41—61no—
735#41—61no—
736#41—61no—
737#41—61no—
738#41—121no—
739#41—181no—
740#41—181no—
741#41—181no—
742#41—181no—
743#41—361no—
744#41C2×D3211yescharacteristic
745C2×Q8—31no—
746C2×Q8—61no—
747C2×Q8—61no—
748C2×Q8—91no—
749C2×Q8—181no—
750C2×Q8—181no—
751C2×D4—31no—
752C2×D4—61no—
753C2×D4—61no—
754C2×D4—91no—
755C2×D4—121no—
756C2×D4—181no—
757C2×D4—181no—
758C2×D4—361no—
759C2×D4—361no—
760Q16—31no—
761Q16—31no—
762Q16—61no—
763Q16—181no—
764Q16—181no—
765Q16—181no—
766SD16—31no—
767SD16—31no—
768SD16—31no—
769SD16—31no—
770SD16—61no—
771SD16—61no—
772SD16—61no—
773SD16—61no—
774SD16—181no—
775SD16—181no—
776SD16—181no—
777SD16—181no—
778SD16—181no—
779SD16—181no—
780SD16—181no—
781SD16—181no—
782SD16—181no—
783SD16—181no—
784SD16—181no—
785SD16—181no—
786D8—31no—
787D8—31no—
788D8—61no—
789D8—181no—
790D8—181no—
791D8—181no—
792M16—21no—
793M16—31no—
794M16—61no—
795M16—91no—
796M16—91no—
797M16—181no—
798M16—181no—
799M16C2×D3211yescharacteristic
800C2×C8—21no—
801C2×C8—31no—
802C2×C8—61no—
803C2×C8—181no—
804C2×C8—181no—
805C2×C8C2×D3211yescharacteristic
806C4⋊C4—361no—
807C42—31no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—41no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—121no—
816C22×C3—241no—
817C22×C3—481no—
818C22×C3#100411yescharacteristic
819C22×C3#100911yescharacteristic
820C2×D3—21no—
821C2×D3—21no—
822C2×D3—21no—
823C2×D3—41no—
824C2×D3—81no—
825C2×D3—121no—
826C2×D3—121no—
827C2×D3—161no—
828C2×D3—241no—
829C2×D3—241no—
830C2×D3—241no—
831C2×D3—481no—
832C2×D3—481no—
833C2×D3—481no—
834C3×C4—21no—
835C3×C4—21no—
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—41no—
839C3×C4—62no—
840C3×C4—61no—
841C3×C4—61no—
842C3×C4—61no—
843C3×C4—121no—
844C3×C4C22×D1211yescharacteristic
845C3×C4C2×D3×D411yescharacteristic
846C3×C4C2×D3×D411yescharacteristic
847C3×C4C22×#6711yescharacteristic
848Dic3—22no—
849Dic3—21no—
850Dic3—21no—
851Dic3—21no—
852Dic3—41no—
853Dic3—121no—
854Dic3—121no—
855Dic3—241no—
856C32#329111yescharacteristic, complemented, Sylow
857C23—61no—
858C23—121no—
859C23—181no—
860C23—361no—
861Q8—31no—
862Q8—31no—
863Q8—31no—
864Q8—61no—
865Q8—61no—
866Q8—121no—
867Q8—181no—
868Q8—181no—
869Q8—361no—
870Q8D3×D1211yescharacteristic
871D4—21no—
872D4—31no—
873D4—31no—
874D4—31no—
875D4—61no—
876D4—61no—
877D4—61no—
878D4—61no—
879D4—61no—
880D4—121no—
881D4—121no—
882D4—121no—
883D4—181no—
884D4—181no—
885D4—361no—
886D4—361no—
887D4—361no—
888D4—722no—
889D4D3×D1211yescharacteristic
890C2×C4—21no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—121no—
897C2×C4—121no—
898C2×C4—121no—
899C2×C4—181no—
900C2×C4—361no—
901C2×C4—361no—
902C2×C4—361no—
903C2×C4C22×D3211yescharacteristic
904C8—21no—
905C8—31no—
906C8—31no—
907C8—61no—
908C8—181no—
909C8—181no—
910C8D3×#6711yescharacteristic
911C8D3×#6711yescharacteristic
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—41no—
916C2×C3—41no—
917C2×C3—41no—
918C2×C3—81no—
919C2×C3—121no—
920C2×C3—121no—
921C2×C3—121no—
922C2×C3—241no—
923C2×C3D4×D1211yescharacteristic
924C2×C3D4×#6711yescharacteristic
925D3—41no—
926D3—41no—
927D3—41no—
928D3—81no—
929D3—241no—
930D3—241no—
931D3—481no—
932C22—21no—
933C22—61no—
934C22—61no—
935C22—61no—
936C22—121no—
937C22—241no—
938C22—361no—
939C22—481no—
940C22—721no—
941C22—1441no—
942C22#6430711yescharacteristic
943C4—21no—
944C4—62no—
945C4—61no—
946C4—61no—
947C4—61no—
948C4—121no—
949C4—361no—
950C4C2×D3×D1211yescharacteristic
951C4C2×D3×#6711yescharacteristic
952C3—21no—
953C3#7989311yescharacteristic, complemented
954C3#8401411yescharacteristic, complemented
955C2—21no—
956C2—41no—
957C2—121no—
958C2—121no—
959C2—121no—
960C2—241no—
961C2—721no—
962C2D12×#6711yescharacteristic
subgroupG/H
centerC2D12×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#131C22
socleC2×C32D42
hypercenter#131D32
hypocenterC32#3291
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131

Complements

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

NH ≅ G/Ntype
1. C3×#5751C2semidirect
2. #10595466C2semidirect
3. #10595457C2semidirect
4. #10594679C2semidirect
5. #10592840C2semidirect
6. C3×#5144C2semidirect
7. #10591689C2semidirect
8. #10591666C2semidirect
9. #10591017C2semidirect
10. #10591013C2semidirect
11. #10590986C2semidirect
12. #10590985C2semidirect
13. #10590925C2semidirect
14. #10590915C2semidirect
15. #10590877C2semidirect
19. C3×#1009C22semidirect
20. #64308C22semidirect
22. C32×#131C22semidirect
23. #64160C22semidirect
25. C2×#3744C22semidirect
28. C3×#909C22semidirect
34. C2×C3×#204C22semidirect
35. C3×#901C22semidirect
45. #63866C22semidirect
46. C2×#3717C22semidirect
47. #63831C22semidirect
48. C2×#3716C22semidirect
49. #63827C22semidirect
52. #63814C22semidirect
53. #63814C22semidirect
58. #63651C22semidirect
59. #63650C22semidirect
60. #63646C22semidirect
61. C3×#837C22semidirect
62. C3×#825C22semidirect
63. C3×#822C22semidirect
64. C3×C8×Dic3C22semidirect
65. #63569C22semidirect
66. #63569C22semidirect
67. #63560C22semidirect
68. #63558C22semidirect
76. #5751D3semidirect
87. #5144D3semidirect
141. C3×#216D4semidirect
142. C3×#215D4semidirect
143. C3×#214D4semidirect
144. C3×#213D4semidirect
149. C3×Dic12D4semidirect
151. C3×D24D4semidirect
156. C3×#204D4semidirect
157. C3×#204D4semidirect
185. #1009C2×D3semidirect
197. C3×#131C2×D3semidirect
198. C3×#131C2×D3semidirect
241. #909C2×D3semidirect
256. C2×#204C2×D3semidirect
259. #901C2×D3semidirect
268. #837C2×D3semidirect
271. #825C2×D3semidirect
280. #822C2×D3semidirect
284. C8×Dic3C2×D3semidirect
455. #216D12semidirect
464. #215D12semidirect
473. #214D12semidirect
480. #213D12semidirect
498. Dic12#67semidirect
501. D24#67semidirect
518. #204#67semidirect
519. #204#67semidirect
583. #131D32semidirect
856. C32#3291semidirect
953. C3#79893semidirect
954. C3#84014semidirect

Maximal subgroups

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

subgroupindex
C3×#57512
#105954662
#105954572
#105946792
#105928402
C3×#51442
#105916892
#105916662
#105910172
#105910132
#105909862
#105909852
#105909252
#105909152
#105908772
#840143
#798933