Finite Group Databasebeta

← #11868110

Subgroups — #11868110

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
1C3×#5777C211yesmaximal, characteristic, complemented
2D3×#949C211yesmaximal, characteristic, complemented
3#10595441C211yesmaximal, characteristic, complemented
4C2×#63939C211yesmaximal, characteristic, complemented
5#10592902C211yesmaximal, characteristic, complemented
6C3×#5203C211yesmaximal, characteristic, complemented
7#10591678C211yesmaximal, characteristic, complemented
8#10591677C211yesmaximal, characteristic, complemented
9#10591643C211yesmaximal, characteristic, complemented
10#10591642C211yesmaximal, characteristic, complemented
11#10591637C211yesmaximal, characteristic, complemented
12D3×#823C211yesmaximal, characteristic, complemented
13#10590984C211yesmaximal, characteristic, complemented
14#10590982C211yesmaximal, characteristic, complemented
15#10590973C211yesmaximal, characteristic, complemented
16#84002—31nomaximal
17#80930—31nomaximal
18C3×D3×#41C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C32×#137C2211yescharacteristic, complemented
22#64158C2211yescharacteristic
23#64157C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25C3×#949C2211yescharacteristic
26C3×#949C2211yescharacteristic, complemented
27C3×#948C2211yescharacteristic, complemented
28C3×#942C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#919—21no—
31C3×#918—21no—
32C3×#916—21no—
33C3×#914—21no—
34C3×#908C2211yescharacteristic, complemented
35C3×D3×M16C2211yescharacteristic
36#63939—21no—
37#63939—21no—
38#63939—21no—
39#63939—21no—
40#63939—21no—
41D3×#215—21no—
42#63925—21no—
43D3×#213—21no—
44#63825C2211yescharacteristic
45C2×#3714C2211yescharacteristic, complemented
46#63823C2211yescharacteristic
47C2×#3713C2211yescharacteristic, complemented
48C2×#3711—21no—
49C2×#3711C2211yescharacteristic
50#63815—21no—
51#63815C2211yescharacteristic, complemented
52#63814—21no—
53#63814C2211yescharacteristic, complemented
54D3×#208—21no—
55D3×#208C2211yescharacteristic
56D3×#208C2211yescharacteristic
57#63663C2211yescharacteristic, complemented
58#63650C2211yescharacteristic, complemented
59#63649C2211yescharacteristic, complemented
60C3×#836C2211yescharacteristic, complemented
61C3×#823C2211yescharacteristic, complemented
62C3×#822C2211yescharacteristic, complemented
63#63578C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63559C2211yescharacteristic, complemented
66#63558C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C3×#575—31no—
70C2×#949—31no—
71C2×#949—31no—
72#5819—31no—
73#5777D311yescharacteristic, complemented
74D3×AGL(1,ℤ/8)—31no—
75C2×#914—31no—
76#5750—31no—
77C3×#471—31no—
78#5237—31no—
79#5203—31no—
80#5203—31no—
81#5203—31no—
82#5203—31no—
83#5203—61no—
84#5203D311yescharacteristic, complemented
85#5199—31no—
86#5199—31no—
87#5199—31no—
88#5199—31no—
89#5199—31no—
90#5177—31no—
91#5142—31no—
92C2×#823—31no—
93#5124—31no—
94#4897—31no—
95#4893—31no—
96#4754—31no—
97#4751—31no—
98#4749—31no—
99D3×#100—31no—
100C22×D32—21no—
101C32×#41C2311yescharacteristic
102C2×C32×Q8C2311yescharacteristic
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C3×#239—21no—
105C3×#239—21no—
106C3×#239—21no—
107C3×#239—21no—
108C3×#239D411yescharacteristic
109C3×D3×Q8D411yescharacteristic
110C3×#237—21no—
111C3×#237D411yescharacteristic
112C3×D3×D4—21no—
113C3×D3×D4D411yescharacteristic
114C3×#235—21no—
115C3×#235C2311yescharacteristic
116C2×C3×D12—21no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3C2311yescharacteristic
122C2×#626—21no—
123D3×D12—21no—
124D3×D12—21no—
125D3×D12—21no—
126D3×D12—21no—
127C32×Q16—21no—
128C32×SD16—21no—
129C32×M16C2311yescharacteristic
130#3755—21no—
131#3755—21no—
132#3755—21no—
133#3753—21no—
134#3748—21no—
135#3748C2311yescharacteristic
136#3748C2311yescharacteristic
137C2×C3⋊(C3⋊C8)—21no—
138C2×C3⋊(C3⋊C8)C2311yescharacteristic
139C3×#216—21no—
140C3×#215—21no—
141C3×#215—21no—
142C3×#215—21no—
143C3×#215—21no—
144C3×#215—21no—
145C3×#213—21no—
146C3×#213—21no—
147C3×#208—21no—
148C3×#208C2311yescharacteristic
149C3×#208C2311yescharacteristic
150C3×#208C2311yescharacteristic
151C2×C3×C3⋊C8—21no—
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×D24—21no—
154C3×#204—21no—
155C3×ΓL(1,𝔽25)—21no—
156C3×D3×C8—21no—
157#3717—21no—
158#3715—21no—
159#3714—21no—
160#3714—21no—
161#3714—21no—
162#3713—21no—
163#3713—21no—
164#3713—21no—
165#3711—21no—
166#3711—21no—
167#3711—21no—
168#3711—21no—
169#3711D411yescharacteristic
170#3711D411yescharacteristic
171#3711D411yescharacteristic
172#3711D411yescharacteristic
173D3×C3⋊C8—21no—
174D3×C3⋊C8—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3068—91noSylow
178C2×C3×#41—31no—
179C2×C3×#41—31no—
180D3×#41C2×D311yescharacteristic
181C2×#239C2×D311yescharacteristic
182C2×D3×D4—31no—
183C22×D12—31no—
184C3×#137—21no—
185C3×#137—31no—
186C3×#137—61no—
187C3×#137C2×D311yescharacteristic, complemented
188C3×#137C2×D311yescharacteristic, complemented
189C3×AGL(1,ℤ/8)—31no—
190C3×AGL(1,ℤ/8)—31no—
191C3×AGL(1,ℤ/8)—31no—
192C3×AGL(1,ℤ/8)—61no—
193C3×#135—61no—
194C3×#135—61no—
195C2×C3×SD16—31no—
196C3×#131—31no—
197C2×C3×M16—31no—
198#949—31no—
199#949—31no—
200#949—31no—
201#949—31no—
202#949—61no—
203#949—61no—
204#949—61no—
205#949—61no—
206#949—61no—
207#949—61no—
208#949—61no—
209#949C2×D311yescharacteristic
210#949C2×D311yescharacteristic, complemented
211#948—31no—
212#948—31no—
213#948—31no—
214#948—31no—
215#948—61no—
216#948—61no—
217#948—61no—
218#948C2×D311yescharacteristic, complemented
219#942C2×D311yescharacteristic, complemented
220C2×#215—31no—
221C2×#215—31no—
222C2×#215—61no—
223C2×#215—61no—
224C2×#215C2×D311yescharacteristic, complemented
225#932—31no—
226C2×#213—31no—
227C2×#213—31no—
228C2×#213—31no—
229C2×#213—61no—
230C2×#208—31no—
231C2×#208—31no—
232C2×#208—31no—
233C2×#208—61no—
234C2×#208—61no—
235#919—21no—
236#918—21no—
237#916—21no—
238#914—21no—
239#914—61no—
240#914—61no—
241#914—61no—
242#914—61no—
243#914—61no—
244D3×SD16—61no—
245#911—61no—
246D3×D8—61no—
247#908—31no—
248#908C2×D311yescharacteristic, complemented
249#907—31no—
250#907—61no—
251D3×M16—31no—
252D3×M16—31no—
253D3×M16—61no—
254D3×M16C2×D311yescharacteristic
255C2×D24—31no—
256#901—31no—
257#901—61no—
258C2×ΓL(1,𝔽25)—31no—
259C2×ΓL(1,𝔽25)—61no—
260C3×#108—31no—
261C3×#101—31no—
262C3×#100—31no—
263#836—31no—
264#836—31no—
265#836—61no—
266#836C2×D311yescharacteristic, complemented
267#833—31no—
268#833—31no—
269#833—31no—
270#823—31no—
271#823—31no—
272#823—31no—
273#823—31no—
274#823—31no—
275#823—31no—
276#823—31no—
277#823—61no—
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—21no—
291C22×C3×D3#4111yescharacteristic
292C2×D32—41no—
293C2×D32—41no—
294C2×D32—82no—
295C32×Q8—21no—
296C32×Q8—21no—
297C32×Q8C2×D411yescharacteristic
298C32×D4—21no—
299C32×D4C2×D411yescharacteristic
300C2×C32×C4—21no—
301C2×C32×C4—21no—
302C2×C32×C4C2411yescharacteristic
303C4⋊(C3⋊D3)—21no—
304C4⋊(C3⋊D3)—21no—
305C3×#67—21no—
306C3×#67—21no—
307C3×#67—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3#4111yescharacteristic
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12—41no—
316C3×D12—41no—
317C3×D12C2×D411yescharacteristic
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×C4×D3—21no—
321C3×C4×D3—41no—
322C3×C4×D3—41no—
323C3×C4×D3C2×D411yescharacteristic
324C3×C4×D3C2×D411yescharacteristic
325C3×C4×D3C2×D411yescharacteristic
326C3×C4×D3C2×D411yescharacteristic
327C3×Dic6—21no—
328C3×Dic6C2×D411yescharacteristic
329#626—41no—
330#626—41no—
331C32×C8—21no—
332C3⋊(C3⋊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—31no—
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—91no—
355C2×#100—91no—
356C23×D3—61no—
357C23×D3—61no—
358C3×#41—21no—
359C3×#41—31no—
360C3×#41—31no—
361C3×#41—31no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41—61no—
365C3×#41—61no—
366C3×#41—61no—
367C3×#41—61no—
368C3×#41C22×D311yescharacteristic
369C3×#41C22×D311yescharacteristic
370C2×C3×Q8—21no—
371C2×C3×Q8—31no—
372C2×C3×Q8C22×D311yescharacteristic
373C2×C3×Q8C22×D311yescharacteristic
374C2×C3×D4—31no—
375C2×C3×D4—31no—
376C2×C3×D4—31no—
377C2×C3×D4—61no—
378C2×C3×D4—61no—
379C22×C3×C4—31no—
380C22×C3×C4—61no—
381C22×C3×C4—61no—
382C2×#67—61no—
383#239—21no—
384#239—21no—
385#239—21no—
386#239—21no—
387#239#6711yescharacteristic
388D3×Q8#6711yescharacteristic
389#237—21no—
390#237#6711yescharacteristic
391D3×D4—21no—
392D3×D4—61no—
393D3×D4—61no—
394D3×D4—61no—
395D3×D4—61no—
396D3×D4#6711yescharacteristic
397#235—21no—
398#235C22×D311yescharacteristic
399C2×D12—21no—
400C2×D12—31no—
401C2×D12—31no—
402C2×D12—61no—
403C2×D12—61no—
404C2×D12—61no—
405C2×D12—61no—
406C2×D12—61no—
407C2×D12—61no—
408C2×D12C22×D311yescharacteristic
409C2×D12C22×D311yescharacteristic
410C2×C4×D3—21no—
411C2×C4×D3—21no—
412C2×C4×D3C22×D311yescharacteristic
413C3×Q16—21no—
414C3×Q16—21no—
415C3×Q16—41no—
416C3×Q16—61no—
417C3×SD16—21no—
418C3×SD16—21no—
419C3×SD16—41no—
420C3×SD16—61no—
421C3×SD16—61no—
422C3×SD16—61no—
423C3×SD16—61no—
424C3×SD16—61no—
425C3×SD16—61no—
426C3×D8—61no—
427C3×D8—61no—
428C3×D8—61no—
429C3×M16—21no—
430C3×M16—31no—
431C3×M16—31no—
432C3×M16—31no—
433C3×M16—61no—
434C3×M16—61no—
435C3×M16C22×D311yescharacteristic
436C3×M16C22×D311yescharacteristic
437C2×C3×C8—31no—
438C2×C3×C8—61no—
439C2×C3×C8—61no—
440#216—21no—
441#215—21no—
442#215—21no—
443#215—21no—
444#215—21no—
445#215—21no—
446#215—61no—
447#215—61no—
448#215—61no—
449#215—61no—
450#215—61no—
451#215—61no—
452#215—61no—
453#215—61no—
454#215—121no—
455#215—121no—
456#215—121no—
457#214—61no—
458#213—21no—
459#213—21no—
460#213—61no—
461#213—61no—
462#213—61no—
463#213—61no—
464#213—61no—
465#213—61no—
466#213—61no—
467#213—61no—
468#213—61no—
469#213—61no—
470#213—61no—
471#213—121no—
472#208—21no—
473#208—31no—
474#208—31no—
475#208—31no—
476#208—31no—
477#208—31no—
478#208—31no—
479#208—31no—
480#208—31no—
481#208—61no—
482#208—61no—
483#208—61no—
484#208—61no—
485#208—61no—
486#208—61no—
487#208—61no—
488#208—61no—
489#208—121no—
490#208C22×D311yescharacteristic
491#208C22×D311yescharacteristic
492#208C22×D311yescharacteristic
493C2×C3⋊C8—21no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—61no—
497C2×C3⋊C8—61no—
498C2×C3⋊C8—61no—
499C2×C3⋊C8—61no—
500C2×C3⋊C8—61no—
501C2×C3⋊C8—61no—
502C2×C3⋊C8—61no—
503C2×C3⋊C8—121no—
504C2×C3⋊C8C22×D311yescharacteristic
505D24—21no—
506D24—61no—
507D24—61no—
508D24—61no—
509#204—21no—
510#204—61no—
511ΓL(1,𝔽25)—21no—
512ΓL(1,𝔽25)—31no—
513ΓL(1,𝔽25)—31no—
514ΓL(1,𝔽25)—31no—
515ΓL(1,𝔽25)—31no—
516ΓL(1,𝔽25)—61no—
517ΓL(1,𝔽25)—61no—
518ΓL(1,𝔽25)—61no—
519ΓL(1,𝔽25)—61no—
520D3×C8—21no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—61no—
524D3×C8—61no—
525C22×C32—21no—
526C22×C32C2×#4111yescharacteristic
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—81no—
536C2×C3×D3#12111yescharacteristic
537C2×C3×D3#12111yescharacteristic
538D32—82no—
539D32—82no—
540C32×C4—21no—
541C32×C4—41no—
542C32×C4C22×D411yescharacteristic
543C32×C4C22×D411yescharacteristic
544C3×Dic3—21no—
545C3×Dic3#12111yescharacteristic
546C3×Dic3#12111yescharacteristic
547C2×#41—31no—
548C2×#41—31no—
549C22×D4—91no—
550#137—31no—
551#137—61no—
552#137D3211yescharacteristic, complemented
553AGL(1,ℤ/8)—31no—
554AGL(1,ℤ/8)—31no—
555AGL(1,ℤ/8)—31no—
556AGL(1,ℤ/8)—61no—
557AGL(1,ℤ/8)—91no—
558AGL(1,ℤ/8)—91no—
559AGL(1,ℤ/8)—91no—
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—61no—
567#135—61no—
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—91no—
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#101—91no—
592#100—31no—
593#100—91no—
594#100—91no—
595#100—91no—
596#100—91no—
597#100—91no—
598C23×C3—31no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
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#23711yescharacteristic
615C3×Q8—21no—
616C3×Q8—21no—
617C3×Q8—21no—
618C3×Q8—21no—
619C3×Q8—21no—
620C3×Q8—31no—
621C3×Q8—41no—
622C3×Q8—41no—
623C3×Q8—61no—
624C3×Q8D3×D411yescharacteristic
625C3×Q8C2×#6711yescharacteristic
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—31no—
630C3×D4—41no—
631C3×D4—61no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—61no—
635C3×D4—61no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4—121no—
640C3×D4—121no—
641C3×D4D3×D411yescharacteristic
642C3×D4C2×#6711yescharacteristic
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—31no—
649C2×C3×C4—31no—
650C2×C3×C4—31no—
651C2×C3×C4—31no—
652C2×C3×C4—31no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—121no—
660C2×C3×C4—121no—
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663#67—21no—
664#67—21no—
665#67—21no—
666#67—121no—
667#67—121no—
668C2×Dic3—21no—
669C2×Dic3#23711yescharacteristic
670D12—21no—
671D12—21no—
672D12—21no—
673D12—21no—
674D12—21no—
675D12—41no—
676D12—41no—
677D12—61no—
678D12—61no—
679D12—61no—
680D12—61no—
681D12—121no—
682D12—121no—
683D12—121no—
684D12—121no—
685D12C2×#6711yescharacteristic
686C4×D3—21no—
687C4×D3—21no—
688C4×D3—21no—
689C4×D3—41no—
690C4×D3—41no—
691C4×D3D3×D411yescharacteristic
692C4×D3D3×D411yescharacteristic
693C4×D3C2×#6711yescharacteristic
694C4×D3C2×#6711yescharacteristic
695Dic6—21no—
696Dic6C2×#6711yescharacteristic
697C3×C8—21no—
698C3×C8—21no—
699C3×C8—31no—
700C3×C8—31no—
701C3×C8—41no—
702C3×C8—61no—
703C3×C8—61no—
704C3×C8—61no—
705C3⋊C8—21no—
706C3⋊C8—21no—
707C3⋊C8—21no—
708C3⋊C8—31no—
709C3⋊C8—31no—
710C3⋊C8—31no—
711C3⋊C8—31no—
712C3⋊C8—61no—
713C3⋊C8—61no—
714C3⋊C8—61no—
715C3⋊C8—61no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—121no—
719C3⋊C8—121no—
720C3⋊C8D3×D411yescharacteristic
721C3⋊C8D3×D411yescharacteristic
722C2×C32—21no—
723C2×C32—41no—
724C2×C32C2×#12111yescharacteristic
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—31no—
734#41—31no—
735#41—61no—
736#41—61no—
737#41—61no—
738#41—61no—
739#41—61no—
740#41—61no—
741#41C2×D3211yescharacteristic
742C2×Q8—31no—
743C2×Q8C2×D3211yescharacteristic
744C2×D4—31no—
745C2×D4—31no—
746C2×D4—31no—
747C2×D4—61no—
748C2×D4—61no—
749C2×D4—91no—
750C2×D4—181no—
751C2×D4—181no—
752C2×D4—181no—
753C2×D4—181no—
754C2×D4—181no—
755C22×C4—31no—
756C22×C4—61no—
757C22×C4—61no—
758Q16—21no—
759Q16—61no—
760SD16—21no—
761SD16—61no—
762SD16—61no—
763SD16—61no—
764SD16—61no—
765SD16—61no—
766SD16—61no—
767SD16—181no—
768SD16—181no—
769SD16—181no—
770SD16—181no—
771SD16—181no—
772D8—61no—
773D8—61no—
774D8—61no—
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—91no—
788M16—91no—
789M16—91no—
790M16—91no—
791M16—91no—
792M16—91no—
793M16—181no—
794M16—181no—
795M16—181no—
796M16—181no—
797M16—181no—
798M16C2×D3211yescharacteristic
799C2×C8—31no—
800C2×C8—61no—
801C2×C8—61no—
802C2×C8—91no—
803C2×C8—181no—
804C2×C8—181no—
805C2×C8—181no—
806C2×C8—181no—
807C2×C8—181no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—31no—
812C22×C3—31no—
813C22×C3—41no—
814C22×C3—61no—
815C22×C3—121no—
816C22×C3—121no—
817C22×C3—121no—
818C22×C3—241no—
819C22×C3—241no—
820C22×C3—241no—
821C22×C3C2×#23711yescharacteristic
822C22×C3D3×#4111yescharacteristic
823C2×D3—21no—
824C2×D3—41no—
825C2×D3—41no—
826C2×D3—41no—
827C2×D3—81no—
828C2×D3—81no—
829C2×D3—81no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—241no—
833C2×D3—242no—
834C2×D3—242no—
835C2×D3—242no—
836C2×D3—242no—
837C2×D3—241no—
838C2×D3—241no—
839C2×D3—481no—
840C2×D3#93911yescharacteristic
841C2×D3#93911yescharacteristic
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—31no—
847C3×C4—31no—
848C3×C4—41no—
849C3×C4—41no—
850C3×C4—41no—
851C3×C4—61no—
852C3×C4—81no—
853C3×C4C2×D3×D411yescharacteristic
854C3×C4C2×D3×D411yescharacteristic
855C3×C4C2×D3×D411yescharacteristic
856C3×C4C22×#6711yescharacteristic
857Dic3—21no—
858Dic3#93911yescharacteristic
859Dic3#93911yescharacteristic
860C32#306811yescharacteristic, complemented, Sylow
861C23—31no—
862C23—61no—
863C23—61no—
864C23—61no—
865C23—181no—
866C23—361no—
867C23—361no—
868C23—722no—
869Q8—21no—
870Q8—21no—
871Q8—31no—
872Q8—61no—
873Q8D3×#6711yescharacteristic
874D4—21no—
875D4—31no—
876D4—61no—
877D4—61no—
878D4—61no—
879D4—61no—
880D4—61no—
881D4—61no—
882D4—61no—
883D4—61no—
884D4—121no—
885D4—121no—
886D4—181no—
887D4—181no—
888D4—361no—
889D4—361no—
890D4D3×#6711yescharacteristic
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—31no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—31no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—121no—
903C2×C4—121no—
904C2×C4C22×D3211yescharacteristic
905C8—21no—
906C8—31no—
907C8—31no—
908C8—61no—
909C8—61no—
910C8—61no—
911C8—91no—
912C8—91no—
913C8—181no—
914C8—181no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—41no—
919C2×C3—41no—
920C2×C3—41no—
921C2×C3—61no—
922C2×C3—61no—
923C2×C3—81no—
924C2×C3—121no—
925C2×C3—241no—
926C2×C3—241no—
927C2×C3D3×#12111yescharacteristic
928C2×C3C2×#93911yescharacteristic
929D3—21no—
930D3—21no—
931D3—41no—
932D3—81no—
933D3—81no—
934D3—241no—
935D3—241no—
936D3—481no—
937C22—21no—
938C22—31no—
939C22—31no—
940C22—61no—
941C22—121no—
942C22—121no—
943C22—121no—
944C22—241no—
945C22—241no—
946C22—241no—
947C22—361no—
948C22—721no—
949C22—722no—
950C22—722no—
951C22D3×#23711yescharacteristic
952C4—21no—
953C4—31no—
954C4—31no—
955C4—41no—
956C4—61no—
957C4D32×D411yescharacteristic
958C4C2×D3×#6711yescharacteristic
959C3—21no—
960C3#8093011yescharacteristic, complemented
961C3#8400211yescharacteristic, complemented
962C2—21no—
963C2—41no—
964C2—61no—
965C2—61no—
966C2—121no—
967C2—241no—
968C2—241no—
969C2—721no—
970C2D3×#93911yescharacteristic
subgroupG/H
centerC2D3×#939
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#137C22
socleC2×C32C2×#121
hypercenter#137D32
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C3×#5777C2semidirect
2. D3×#949C2semidirect
3. #10595441C2semidirect
4. C2×#63939C2semidirect
5. #10592902C2semidirect
6. C3×#5203C2semidirect
7. #10591678C2semidirect
8. #10591677C2semidirect
9. #10591643C2semidirect
10. #10591642C2semidirect
11. #10591637C2semidirect
12. D3×#823C2semidirect
13. #10590984C2semidirect
14. #10590982C2semidirect
15. #10590973C2semidirect
21. C32×#137C22semidirect
23. #64157C22semidirect
24. C2×#3755C22semidirect
26. C3×#949C22semidirect
27. C3×#948C22semidirect
28. C3×#942C22semidirect
29. C2×C3×#215C22semidirect
34. C3×#908C22semidirect
45. C2×#3714C22semidirect
47. C2×#3713C22semidirect
51. #63815C22semidirect
53. #63814C22semidirect
57. #63663C22semidirect
58. #63650C22semidirect
59. #63649C22semidirect
60. C3×#836C22semidirect
61. C3×#823C22semidirect
62. C3×#822C22semidirect
63. #63578C22semidirect
64. #63577C22semidirect
65. #63559C22semidirect
66. #63558C22semidirect
67. #63558C22semidirect
68. #63558C22semidirect
73. #5777D3semidirect
84. #5203D3semidirect
187. C3×#137C2×D3semidirect
188. C3×#137C2×D3semidirect
210. #949C2×D3semidirect
218. #948C2×D3semidirect
219. #942C2×D3semidirect
224. C2×#215C2×D3semidirect
248. #908C2×D3semidirect
266. #836C2×D3semidirect
278. #823C2×D3semidirect
285. #822C2×D3semidirect
552. #137D32semidirect
860. C32#3068semidirect
960. C3#80930semidirect
961. C3#84002semidirect

Maximal subgroups

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

subgroupindex
C3×#57772
D3×#9492
#105954412
C2×#639392
#105929022
C3×#52032
#105916782
#105916772
#105916432
#105916422
#105916372
D3×#8232
#105909842
#105909822
#105909732
#840023
#809303