Finite Group Databasebeta

← #11886606

Subgroups — #11886606

Order 1152.

980 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5752C211yesmaximal, characteristic, complemented
2#10595466C211yesmaximal, characteristic, complemented
3#10595456C211yesmaximal, characteristic, complemented
4#10594679C211yesmaximal, characteristic, complemented
5#10592840C211yesmaximal, characteristic, complemented
6C3×#5145C211yesmaximal, characteristic, complemented
7#10591688C211yesmaximal, characteristic, complemented
8#10591666C211yesmaximal, characteristic, complemented
9#10591019C211yesmaximal, characteristic, complemented
10#10591013C211yesmaximal, characteristic, complemented
11#10590986C211yesmaximal, characteristic, complemented
12#10590984C211yesmaximal, characteristic, complemented
13#10590926C211yesmaximal, characteristic, complemented
14#10590916C211yesmaximal, characteristic, complemented
15#10590883C211yesmaximal, characteristic, complemented
16#84009—31nomaximal
17#79900—31nomaximal
18C3×#1009C2211yescharacteristic
19C3×#1009C2211yescharacteristic, complemented
20#64308C2211yescharacteristic, complemented
21#64298C2211yescharacteristic, complemented
22C32×#131C2211yescharacteristic, complemented
23#64160C2211yescharacteristic, complemented
24#64158C2211yescharacteristic
25C2×#3744C2211yescharacteristic, complemented
26C3×#950C2211yescharacteristic
27C3×#908—21no—
28C3×#908—21no—
29C3×#908C2211yescharacteristic
30C3×#908C2211yescharacteristic, complemented
31C3×#904—21no—
32C3×#904C2211yescharacteristic
33C2×C3×D24—21no—
34C2×C3×D24C2211yescharacteristic, complemented
35C3×#901C2211yescharacteristic, complemented
36#63949—21no—
37#63947—21no—
38#63943—21no—
39#63939—21no—
40#63934—21no—
41#63932—21no—
42D3×#214—21no—
43D3×#213—21no—
44#63911C2211yescharacteristic, complemented
45#63860C2211yescharacteristic, complemented
46#63831C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48#63825C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50#63823C2211yescharacteristic, complemented
51#63823C2211yescharacteristic, complemented
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×#815C2211yescharacteristic, complemented
65#63569C2211yescharacteristic, complemented
66#63569C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C3×#576—31no—
70#5836—31no—
71#5835—31no—
72#5770—31no—
73#5770—31no—
74#5769—31no—
75#5752D311yescharacteristic, complemented
76#5751—31no—
77C3×#444—31no—
78#5242—31no—
79#5241—31no—
80#5201—31no—
81#5200—31no—
82#5199—31no—
83#5198—31no—
84#5197—31no—
85#5160—31no—
86#5154—31no—
87#5145D311yescharacteristic, complemented
88#5142—31no—
89#5141—31no—
90#5141—31no—
91#5141—61no—
92#4898—31no—
93#4897—31no—
94#4827—31no—
95#4825—31no—
96#4822—31no—
97#4822—31no—
98#4717—31no—
99#4712—31no—
100C32×#41C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C3×#239—21no—
104C3×#239—21no—
105C3×D3×D4—21no—
106C3×D3×D4—21no—
107C3×D3×D4—41no—
108C3×D3×D4—41no—
109C3×#235—21no—
110C3×#235—21no—
111C3×#235C2311yescharacteristic
112C3×#235C2311yescharacteristic
113C3×#235C2311yescharacteristic
114C2×C3×D12—21no—
115C2×C3×D12—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
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×Dic12D411yescharacteristic, complemented
149C3×D24—21no—
150C3×D24—21no—
151C3×D24—21no—
152C3×D24—21no—
153C3×D24D411yescharacteristic, complemented
154C3×#204—21no—
155C3×#204—21no—
156C3×#204D411yescharacteristic, complemented
157C3×#204D411yescharacteristic, complemented
158C3×ΓL(1,𝔽25)—21no—
159C3×D3×C8—21no—
160(C2×D3)⋊Dic3—41no—
161#3719—21no—
162#3717—21no—
163#3716—21no—
164#3716—21no—
165#3716—21no—
166#3715—21no—
167#3715—21no—
168#3714—21no—
169#3714—21no—
170#3714—21no—
171#3713—21no—
172#3713—21no—
173#3711—21no—
174#3711—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3288—91noSylow
178C3×H(5,𝔽2)—31no—
179C3×H(5,𝔽2)—31no—
180#1010—31no—
181#1010—31no—
182#1009—31no—
183#1009—31no—
184#1009C2×D311yescharacteristic
185#1009C2×D311yescharacteristic, complemented
186C3×AGL(1,ℤ/8)—31no—
187C3×AGL(1,ℤ/8)—31no—
188C3×AGL(1,ℤ/8)—61no—
189C3×AGL(1,ℤ/8)—61no—
190C3×#135—31no—
191C3×#135—31no—
192C3×#135—61no—
193C2×C3×D8—31no—
194C2×C3×D8—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—61no—
203#951—61no—
204#950—61no—
205#950—61no—
206#950C2×D311yescharacteristic
207#949—31no—
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#940—31no—
217#936—31no—
218C2×#214—31no—
219C2×#214—61no—
220#932—31no—
221#932—31no—
222#932—61no—
223#932—61no—
224C2×#213—31no—
225C2×#213—61no—
226#919—61no—
227#918—61no—
228#918—61no—
229#916—61no—
230#916—61no—
231#914—61no—
232#914—61no—
233D3×SD16—61no—
234D3×SD16—61no—
235#911—61no—
236#911—61no—
237D3×D8—61no—
238#909—31no—
239#909—61no—
240#908—21no—
241#908—21no—
242#908—31no—
243#908—61no—
244#908C2×D311yescharacteristic
245#908C2×D311yescharacteristic, complemented
246#904—21no—
247#904—61no—
248#904C2×D311yescharacteristic
249C2×D24—21no—
250C2×D24—31no—
251C2×D24C2×D311yescharacteristic, complemented
252C2×#204—31no—
253C2×#204—31no—
254C2×#204—31no—
255C2×#204—61no—
256C2×#204—61no—
257#901—31no—
258#901—31no—
259#901C2×D311yescharacteristic, complemented
260#875—31no—
261#874—31no—
262C3×#108—31no—
263C3×#104—31no—
264C3×#104—31no—
265C3×#97—31no—
266#837—31no—
267#837—31no—
268#837C2×D311yescharacteristic, complemented
269#833—31no—
270#833—31no—
271#825C2×D311yescharacteristic, complemented
272#824—31no—
273#824—31no—
274#824—61no—
275#823—31no—
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—
284#815C2×D311yescharacteristic, complemented
285#805—31no—
286#805—31no—
287C22×C3⋊D3—21no—
288C22×C3×D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3—41no—
291C22×C3×D3—41no—
292C2×D32—41no—
293C32×Q8C2×D411yescharacteristic
294C32×D4—21no—
295C32×D4C2×D411yescharacteristic
296C2×C32×C4—21no—
297C2×C32×C4C2411yescharacteristic
298C2×C3⋊Dic3—21no—
299C4⋊(C3⋊D3)—21no—
300C4⋊(C3⋊D3)—21no—
301#634—21no—
302#634—21no—
303C3×#67—21no—
304C3×#67—21no—
305C3×#67—21no—
306C3×#67—41no—
307C3×#67—41no—
308C2×C3×Dic3—21no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—41no—
314C3×D12—41no—
315C3×D12C2×D411yescharacteristic
316C3×D12C2×D411yescharacteristic
317C3×D12C2×D411yescharacteristic
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×C4×D3—21no—
321C3×C4×D3—41no—
322C3×C4×D3—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—91no—
343#577—91no—
344#576—31no—
345#576—91no—
346#496—91no—
347#472—91no—
348#472—91no—
349#471—91no—
350#471—91no—
351#455—91no—
352#454—91no—
353#453—91no—
354#453—91no—
355#444—31no—
356#444—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×#41C22×D311yescharacteristic
366C3×#41C22×D311yescharacteristic
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—61no—
370C2×C3×D4—61no—
371C2×C3×D4—61no—
372C2×C3×D4—61no—
373C2×C3×D4—121no—
374C2×C3×D4—121no—
375C2×#67—121no—
376#239—21no—
377#239—21no—
378#239—61no—
379#239—61no—
380D3×Q8—61no—
381D3×Q8—61no—
382#237—61no—
383#237—61no—
384#237—121no—
385#237—121no—
386D3×D4—21no—
387D3×D4—21no—
388D3×D4—41no—
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—21no—
405C2×D12—31no—
406C2×D12—31no—
407C2×D12—61no—
408C2×D12—61no—
409C2×D12—61no—
410C2×D12—121no—
411C2×D12C22×D311yescharacteristic
412C2×D12C22×D311yescharacteristic
413C2×Dic6—31no—
414C2×Dic6—31no—
415C2×Dic6—61no—
416C2×Dic6—61no—
417C2×Dic6—61no—
418C3×Q16—31no—
419C3×Q16—31no—
420C3×SD16—31no—
421C3×SD16—31no—
422C3×SD16—31no—
423C3×SD16—31no—
424C3×SD16—61no—
425C3×SD16—61no—
426C3×D8—31no—
427C3×D8—31no—
428C3×D8—61no—
429C3×D8—61no—
430C3×D8—61no—
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#217—121no—
450#216—61no—
451#216—61no—
452#216—61no—
453#216—121no—
454#216D1211yescharacteristic, complemented
455#215—61no—
456#215—61no—
457#215—61no—
458#215—61no—
459#215—61no—
460#215—121no—
461#215D1211yescharacteristic, complemented
462#214—61no—
463#214—61no—
464#214—61no—
465#214—61no—
466#214—61no—
467#214—61no—
468#214—61no—
469#214—121no—
470#214D1211yescharacteristic, complemented
471#213—61no—
472#213—61no—
473#213—61no—
474#213—61no—
475#213—61no—
476#213—61no—
477#213—61no—
478#213—61no—
479#213—61no—
480#213—121no—
481#213D1211yescharacteristic, complemented
482(C2×D3)⋊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—61no—
497Dic12#6711yescharacteristic, complemented
498D24—21no—
499D24—21no—
500D24—21no—
501D24—21no—
502D24—61no—
503D24—61no—
504D24—61no—
505D24#6711yescharacteristic, complemented
506#204—21no—
507#204—21no—
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—41no—
535C2×C3×D3—81no—
536C2×C3×D3—81no—
537C2×C3×D3—161no—
538C2×C3×D3—161no—
539D32—161no—
540C32×C4—21no—
541C32×C4C22×D411yescharacteristic
542C32×C4C22×D411yescharacteristic
543C3⋊Dic3—41no—
544C3×Dic3—21no—
545C3×Dic3—21no—
546C3×Dic3—21no—
547C3×Dic3—41no—
5482−1+4—91no—
549H(5,𝔽2)—31no—
550H(5,𝔽2)—31no—
551H(5,𝔽2)—91no—
552#137—91no—
553#137—91no—
554#137—181no—
555#137—181no—
556AGL(1,ℤ/8)—31no—
557AGL(1,ℤ/8)—31no—
558AGL(1,ℤ/8)—61no—
559AGL(1,ℤ/8)—61no—
560AGL(1,ℤ/8)—91no—
561AGL(1,ℤ/8)—91no—
562AGL(1,ℤ/8)—91no—
563AGL(1,ℤ/8)—91no—
564AGL(1,ℤ/8)—181no—
565AGL(1,ℤ/8)—181no—
566AGL(1,ℤ/8)—181no—
567AGL(1,ℤ/8)—181no—
568#135—31no—
569#135—31no—
570#135—61no—
571#135—181no—
572#135—181no—
573#135—181no—
574C2×SD16—91no—
575C2×SD16—91no—
576C2×SD16—181no—
577C2×SD16—181no—
578C2×D8—31no—
579C2×D8—61no—
580C2×D8—91no—
581C2×D8—181no—
582#131—31no—
583#131—91no—
584#131—91no—
585#131D3211yescharacteristic, complemented
586#127—91no—
587#124—91no—
588#108—31no—
589#108—91no—
590#104—31no—
591#104—31no—
592#104—91no—
593#104—91no—
594#101—91no—
595#100—91no—
596#100—91no—
597#100—91no—
598#97—31no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—121no—
602C23×C3—121no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—41no—
606C22×D3—41no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—121no—
612C3×Q8—21no—
613C3×Q8—31no—
614C3×Q8—31no—
615C3×Q8—31no—
616C3×Q8C2×D1211yescharacteristic
617C3×Q8D3×D411yescharacteristic
618C3×D4—21no—
619C3×D4—21no—
620C3×D4—21no—
621C3×D4—31no—
622C3×D4—31no—
623C3×D4—31no—
624C3×D4—41no—
625C3×D4—61no—
626C3×D4—61no—
627C3×D4—61no—
628C3×D4—61no—
629C3×D4—61no—
630C3×D4—61no—
631C3×D4—61no—
632C3×D4—121no—
633C3×D4—121no—
634C3×D4—121no—
635C3×D4—121no—
636C3×D4C2×D1211yescharacteristic
637C3×D4D3×D411yescharacteristic
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—41no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—121no—
647C2×C3×C4—121no—
648C2×C3×C4C23×D311yescharacteristic
649C2×C3×C4C23×D311yescharacteristic
650#67—21no—
651#67—21no—
652#67—21no—
653#67—41no—
654#67—41no—
655#67—121no—
656#67—121no—
657#67—121no—
658#67—121no—
659#67—242no—
660C2×Dic3—21no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—121no—
664C2×Dic3—121no—
665C2×Dic3—121no—
666D12—21no—
667D12—21no—
668D12—21no—
669D12—21no—
670D12—41no—
671D12—41no—
672D12—61no—
673D12—61no—
674D12—61no—
675D12—61no—
676D12—121no—
677D12—121no—
678D12—121no—
679D12—121no—
680D12—242no—
681D12C2×D1211yescharacteristic
682D12C2×#6711yescharacteristic
683D12C2×#6711yescharacteristic
684C4×D3—21no—
685C4×D3—21no—
686C4×D3—21no—
687C4×D3—41no—
688C4×D3—41no—
689C4×D3—121no—
690C4×D3—121no—
691C4×D3—121no—
692C4×D3—121no—
693Dic6—61no—
694Dic6—61no—
695Dic6—61no—
696Dic6—61no—
697Dic6—121no—
698Dic6—121no—
699Dic6—121no—
700Dic6—121no—
701Dic6C2×D1211yescharacteristic
702Dic6C2×#6711yescharacteristic
703Dic6C2×#6711yescharacteristic
704C3×C8—21no—
705C3×C8—21no—
706C3×C8—21no—
707C3×C8—21no—
708C3×C8—31no—
709C3×C8—31no—
710C3×C8—41no—
711C3×C8—61no—
712C3×C8D3×D411yescharacteristic
713C3×C8D3×D411yescharacteristic
714C3×C8C2×#6711yescharacteristic
715C3×C8C2×#6711yescharacteristic
716C3⋊C8—21no—
717C3⋊C8—61no—
718C3⋊C8—61no—
719C3⋊C8—61no—
720C3⋊C8—61no—
721C3⋊C8—121no—
722C3⋊C8—121no—
723C3⋊C8C2×D1211yescharacteristic
724C3⋊C8C2×D1211yescharacteristic
725C2×C32—21no—
726C2×C32—41no—
727C2×C32D4211yescharacteristic
728C3⋊D3—81no—
729C3×D3—41no—
730C3×D3—41no—
731C3×D3—41no—
732C3×D3—81no—
733C3×D3—81no—
734#41—31no—
735#41—31no—
736#41—31no—
737#41—61no—
738#41—61no—
739#41—61no—
740#41—61no—
741#41—181no—
742#41—181no—
743#41—181no—
744#41—181no—
745#41—361no—
746#41C2×D3211yescharacteristic
747C2×Q8—91no—
748C2×Q8—181no—
749C2×Q8—181no—
750C2×D4—31no—
751C2×D4—31no—
752C2×D4—61no—
753C2×D4—61no—
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—91no—
757C2×D4—121no—
758C2×D4—121no—
759C2×D4—181no—
760C2×D4—181no—
761C2×D4—361no—
762C2×D4—361no—
763Q16—31no—
764Q16—31no—
765Q16—181no—
766Q16—181no—
767SD16—31no—
768SD16—31no—
769SD16—31no—
770SD16—31no—
771SD16—61no—
772SD16—61no—
773SD16—181no—
774SD16—181no—
775SD16—181no—
776SD16—181no—
777SD16—181no—
778SD16—181no—
779SD16—181no—
780SD16—181no—
781SD16—181no—
782SD16—181no—
783D8—31no—
784D8—31no—
785D8—61no—
786D8—61no—
787D8—61no—
788D8—61no—
789D8—181no—
790D8—181no—
791D8—181no—
792D8—181no—
793D8—181no—
794D8—181no—
795M16—21no—
796M16—31no—
797M16—61no—
798M16—91no—
799M16—91no—
800M16—181no—
801M16—181no—
802M16C2×D3211yescharacteristic
803C2×C8—21no—
804C2×C8—31no—
805C2×C8—61no—
806C2×C8—181no—
807C2×C8—181no—
808C2×C8C2×D3211yescharacteristic
809C22⋊C4—361no—
810C42—31no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—41no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—241no—
821C22×C3—241no—
822C22×C3—481no—
823C22×C3—481no—
824C22×C3#100411yescharacteristic
825C22×C3#100911yescharacteristic
826C2×D3—21no—
827C2×D3—21no—
828C2×D3—21no—
829C2×D3—41no—
830C2×D3—41no—
831C2×D3—81no—
832C2×D3—81no—
833C2×D3—121no—
834C2×D3—121no—
835C2×D3—161no—
836C2×D3—161no—
837C2×D3—241no—
838C2×D3—241no—
839C2×D3—241no—
840C2×D3—481no—
841C2×D3—481no—
842C2×D3—481no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—41no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—121no—
852C3×C4C22×D1211yescharacteristic
853C3×C4C2×D3×D411yescharacteristic
854C3×C4C2×D3×D411yescharacteristic
855C3×C4C22×#6711yescharacteristic
856Dic3—21no—
857Dic3—21no—
858Dic3—21no—
859Dic3—41no—
860Dic3—121no—
861Dic3—121no—
862Dic3—241no—
863C32#328811yescharacteristic, complemented, Sylow
864C23—61no—
865C23—61no—
866C23—121no—
867C23—121no—
868C23—181no—
869C23—361no—
870Q8—31no—
871Q8—31no—
872Q8—31no—
873Q8—181no—
874Q8—181no—
875Q8—361no—
876Q8D3×D1211yescharacteristic
877D4—21no—
878D4—31no—
879D4—31no—
880D4—31no—
881D4—61no—
882D4—61no—
883D4—61no—
884D4—61no—
885D4—61no—
886D4—61no—
887D4—61no—
888D4—121no—
889D4—121no—
890D4—121no—
891D4—121no—
892D4—181no—
893D4—181no—
894D4—361no—
895D4—361no—
896D4—361no—
897D4—722no—
898D4D3×D1211yescharacteristic
899C2×C4—21no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—121no—
905C2×C4—121no—
906C2×C4—181no—
907C2×C4—361no—
908C2×C4—361no—
909C2×C4—361no—
910C2×C4C22×D3211yescharacteristic
911C8—21no—
912C8—31no—
913C8—31no—
914C8—61no—
915C8—181no—
916C8—181no—
917C8D3×#6711yescharacteristic
918C8D3×#6711yescharacteristic
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—41no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—81no—
926C2×C3—121no—
927C2×C3—121no—
928C2×C3—121no—
929C2×C3—241no—
930C2×C3—241no—
931C2×C3D4×D1211yescharacteristic
932C2×C3D4×#6711yescharacteristic
933D3—41no—
934D3—41no—
935D3—41no—
936D3—81no—
937D3—81no—
938D3—241no—
939D3—241no—
940D3—481no—
941C22—21no—
942C22—61no—
943C22—61no—
944C22—61no—
945C22—121no—
946C22—121no—
947C22—241no—
948C22—241no—
949C22—361no—
950C22—481no—
951C22—481no—
952C22—721no—
953C22—1441no—
954C22#6430711yescharacteristic
955C4—21no—
956C4—61no—
957C4—61no—
958C4—61no—
959C4—121no—
960C4—361no—
961C4C2×D3×D1211yescharacteristic
962C4C2×D3×#6711yescharacteristic
963C3—21no—
964C3#7990011yescharacteristic, complemented
965C3#8400911yescharacteristic, complemented
966C2—21no—
967C2—41no—
968C2—121no—
969C2—121no—
970C2—121no—
971C2—241no—
972C2—241no—
973C2—721no—
974C2D12×#6711yescharacteristic
subgroupG/H
centerC2D12×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#131C22
socleC2×C32D42
hypercenter#131D32
hypocenterC32#3288
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×#5752C2semidirect
2. #10595466C2semidirect
3. #10595456C2semidirect
4. #10594679C2semidirect
5. #10592840C2semidirect
6. C3×#5145C2semidirect
7. #10591688C2semidirect
8. #10591666C2semidirect
9. #10591019C2semidirect
10. #10591013C2semidirect
11. #10590986C2semidirect
12. #10590984C2semidirect
13. #10590926C2semidirect
14. #10590916C2semidirect
15. #10590883C2semidirect
19. C3×#1009C22semidirect
20. #64308C22semidirect
21. #64298C22semidirect
22. C32×#131C22semidirect
23. #64160C22semidirect
25. C2×#3744C22semidirect
30. C3×#908C22semidirect
34. C2×C3×D24C22semidirect
35. C3×#901C22semidirect
44. #63911C22semidirect
45. #63860C22semidirect
46. #63831C22semidirect
47. C2×#3716C22semidirect
48. #63825C22semidirect
49. C2×#3714C22semidirect
50. #63823C22semidirect
51. #63823C22semidirect
52. #63814C22semidirect
53. #63814C22semidirect
58. #63651C22semidirect
59. #63650C22semidirect
60. #63646C22semidirect
61. C3×#837C22semidirect
62. C3×#825C22semidirect
63. C3×#822C22semidirect
64. C3×#815C22semidirect
65. #63569C22semidirect
66. #63569C22semidirect
67. #63558C22semidirect
68. #63558C22semidirect
75. #5752D3semidirect
87. #5145D3semidirect
141. C3×#216D4semidirect
142. C3×#215D4semidirect
143. C3×#214D4semidirect
144. C3×#213D4semidirect
148. C3×Dic12D4semidirect
153. C3×D24D4semidirect
156. C3×#204D4semidirect
157. C3×#204D4semidirect
185. #1009C2×D3semidirect
197. C3×#131C2×D3semidirect
198. C3×#131C2×D3semidirect
245. #908C2×D3semidirect
251. C2×D24C2×D3semidirect
259. #901C2×D3semidirect
268. #837C2×D3semidirect
271. #825C2×D3semidirect
280. #822C2×D3semidirect
284. #815C2×D3semidirect
454. #216D12semidirect
461. #215D12semidirect
470. #214D12semidirect
481. #213D12semidirect
497. Dic12#67semidirect
505. D24#67semidirect
518. #204#67semidirect
519. #204#67semidirect
585. #131D32semidirect
863. C32#3288semidirect
964. C3#79900semidirect
965. C3#84009semidirect

Maximal subgroups

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

subgroupindex
C3×#57522
#105954662
#105954562
#105946792
#105928402
C3×#51452
#105916882
#105916662
#105910192
#105910132
#105909862
#105909842
#105909262
#105909162
#105908832
#840093
#799003