Finite Group Databasebeta

← #11886685

Subgroups — #11886685

Order 1152.

967 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5838C211yesmaximal, characteristic, complemented
2C3×#5837C211yesmaximal, characteristic, complemented
3#10595467C211yesmaximal, characteristic, complemented
4#10595466C211yesmaximal, characteristic, complemented
5#10592945C211yesmaximal, characteristic, complemented
6#10591684C211yesmaximal, characteristic, complemented
7#10591682C211yesmaximal, characteristic, complemented
8#10591679C211yesmaximal, characteristic, complemented
9#10591674C211yesmaximal, characteristic, complemented
10#10591674C211yesmaximal, characteristic, complemented
11#10591664C211yesmaximal, characteristic, complemented
12#10591660C211yesmaximal, characteristic, complemented
13#10591642C211yesmaximal, characteristic, complemented
14#10591641C211yesmaximal, characteristic, complemented
15#10591611C211yesmaximal, characteristic, complemented
16#84019—31nomaximal
17#84013—31nomaximal
18C32×2−1+4C2211yescharacteristic
19C3×#1010C2211yescharacteristic, complemented
20C3×#1009C2211yescharacteristic
21#64298C2211yescharacteristic
22#64160C2211yescharacteristic
23#64160C2211yescharacteristic, complemented
24#64153C2211yescharacteristic, complemented
25C3×#951—21no—
26C3×#951C2211yescharacteristic
27C3×#950—21no—
28C3×#950—21no—
29C3×#950C2211yescharacteristic
30C3×#950C2211yescharacteristic
31C3×#949—21no—
32C3×#949C2211yescharacteristic
33C3×#948C2211yescharacteristic
34C3×#948C2211yescharacteristic, complemented
35C2×C3×#216—21no—
36C2×C3×#216C2211yescharacteristic, complemented
37C3×#942—21no—
38C3×#942—21no—
39C3×#942C2211yescharacteristic
40C3×#942C2211yescharacteristic, complemented
41C2×C3×#215—21no—
42C2×C3×#215C2211yescharacteristic
43#63947—21no—
44#63946—21no—
45#63943—21no—
46D3×#216—21no—
47#63933—21no—
48#63932—21no—
49#63929—21no—
50D3×#214—21no—
51#63863C2211yescharacteristic
52C2×#3719C2211yescharacteristic, complemented
53C2×#3716C2211yescharacteristic
54#63827C2211yescharacteristic
55#63823C2211yescharacteristic
56#63814C2211yescharacteristic
57#63814C2211yescharacteristic, complemented
58#63664C2211yescharacteristic
59#63664C2211yescharacteristic, complemented
60#63663C2211yescharacteristic, complemented
61#63577C2211yescharacteristic, complemented
62#63577C2211yescharacteristic, complemented
63#63568C2211yescharacteristic
64#63568C2211yescharacteristic, complemented
65#63561C2211yescharacteristic, complemented
66#63560C2211yescharacteristic, complemented
67#63558C2211yescharacteristic
68#63555C2211yescharacteristic, complemented
69C3×#578—31no—
70C3×#577—31no—
71#5838—31no—
72#5838D311yescharacteristic, complemented
73#5837D311yescharacteristic, complemented
74#5836—31no—
75#5771—31no—
76#5770—31no—
77#5246—31no—
78#5246—31no—
79#5246—61no—
80#5245—31no—
81#5242—31no—
82#5205—31no—
83#5205—31no—
84#5204—31no—
85#5204—31no—
86#5203—31no—
87#5202—31no—
88#5201—31no—
89#5200—31no—
90#5197—31no—
91#5197—31no—
92#5192—31no—
93#5190—31no—
94#5177—31no—
95#5167—31no—
96#5145—31no—
97#5145—31no—
98#5143—31no—
99#5141—31no—
100C32×#41—21no—
101C32×#41—21no—
102C32×#41—41no—
103C32×#41C2311yescharacteristic
104C32×#41C2311yescharacteristic
105C2×C32×Q8—21no—
106C2×C32×Q8—21no—
107C2×C32×Q8C2311yescharacteristic
108C2×#634C2311yescharacteristic
109C3×#239—21no—
110C3×D3×Q8—21no—
111C3×#237—21no—
112C3×#237—41no—
113C3×D3×D4—21no—
114C3×D3×D4—41no—
115C3×#235—21no—
116C3×#235—21no—
117C3×#235C2311yescharacteristic
118C3×#235C2311yescharacteristic
119C2×C3×D12—21no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×Dic6—21no—
122C2×C3×Dic6C2311yescharacteristic
123#3805—41no—
124#3795—21no—
125#3795—21no—
126D3×Dic6—21no—
127D3×Dic6—21no—
128#3756—21no—
129#3756—21no—
130#3754—21no—
131#3754—21no—
132#3750—41no—
133C4×C3⋊Dic3C2311yescharacteristic
134#3748C2311yescharacteristic
135#3748C2311yescharacteristic
136C3×#216—21no—
137C3×#216—21no—
138C3×#216—21no—
139C3×#216—21no—
140C3×#216—21no—
141C3×#216D411yescharacteristic
142C3×#216D411yescharacteristic
143C3×#215—21no—
144C3×#215—21no—
145C3×#215—21no—
146C3×#215—21no—
147C3×#215—21no—
148C3×#215D411yescharacteristic
149C3×#215D411yescharacteristic
150C3×#214—21no—
151C3×#214D411yescharacteristic
152C3×#214D411yescharacteristic
153C3×#213—21no—
154C3×#213D411yescharacteristic
155C3×#213D411yescharacteristic
156C3×#208—21no—
157C3×#208—21no—
158C3×#208C2311yescharacteristic
159C3×#208C2311yescharacteristic
160C2×C3×C3⋊C8—21no—
161C2×C3×C3⋊C8—21no—
162C2×C3×C3⋊C8C2311yescharacteristic
163C2×C3×C3⋊C8C2311yescharacteristic
164(C2×D3)⋊Dic3—41no—
165#3719—21no—
166#3719—21no—
167#3718—21no—
168#3716—21no—
169#3716—21no—
170#3715—21no—
171#3715—21no—
172#3713—21no—
173#3711—21no—
174#3711—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3289—91noSylow
178C3×2−1+4—21no—
179C3×2−1+4—31no—
180C3×2−1+4C2×D311yescharacteristic
181C3×2−1+4C2×D311yescharacteristic
182C3×H(5,𝔽2)—31no—
183#1010—31no—
184#1010—31no—
185#1010C2×D311yescharacteristic, complemented
186#1009C2×D311yescharacteristic
187C3×#137—31no—
188C3×#137—31no—
189C3×#137—31no—
190C3×#137—61no—
191C3×#137—61no—
192C3×#137—61no—
193C3×AGL(1,ℤ/8)—31no—
194C3×AGL(1,ℤ/8)—61no—
195C3×#135—31no—
196C3×#135—31no—
197C3×#135—61no—
198C3×#135—61no—
199C2×C3×Q16—31no—
200C2×C3×Q16—61no—
201C2×C3×SD16—31no—
202C2×C3×SD16—61no—
203C3×#131—31no—
204C3×#131—31no—
205#951—21no—
206#951—31no—
207#951—31no—
208#951—31no—
209#951—31no—
210#951—31no—
211#951—61no—
212#951—61no—
213#951—61no—
214#951—61no—
215#951C2×D311yescharacteristic
216#950—21no—
217#950—21no—
218#950—61no—
219#950—61no—
220#950C2×D311yescharacteristic
221#950C2×D311yescharacteristic
222#949—21no—
223#949—31no—
224#949C2×D311yescharacteristic
225#948—31no—
226#948—31no—
227#948C2×D311yescharacteristic
228#948C2×D311yescharacteristic, complemented
229#947—31no—
230#944—31no—
231#944—31no—
232#944—61no—
233C2×#216—21no—
234C2×#216—31no—
235C2×#216—61no—
236C2×#216C2×D311yescharacteristic, complemented
237#942—21no—
238#942—21no—
239#942—31no—
240#942—61no—
241#942C2×D311yescharacteristic
242#942C2×D311yescharacteristic, complemented
243C2×#215—21no—
244C2×#215C2×D311yescharacteristic
245#936—31no—
246C2×#214—31no—
247C2×#214—61no—
248#932—31no—
249#932—61no—
250#918—61no—
251D3×Q16—61no—
252#916—61no—
253#915—61no—
254#915—61no—
255D3×SD16—61no—
256#912—61no—
257#911—61no—
258C2×Dic12—31no—
259C2×#204—31no—
260#901—31no—
261#901—31no—
262#837—31no—
263#837—31no—
264#837—31no—
265#837—31no—
266#837—31no—
267#837—31no—
268#837—61no—
269#837—61no—
270#836—31no—
271#836—31no—
272#836—31no—
273#836—61no—
274#833—31no—
275#825—31no—
276#825—31no—
277#824—31no—
278#824—31no—
279#824—31no—
280#823—31no—
281#822—31no—
282#822—31no—
283#819—31no—
284#819—31no—
285#815—31no—
286#815—31no—
287C22×C3×D3—21no—
288C22×C3×D3—41no—
289C32×Q8—21no—
290C32×Q8—21no—
291C32×Q8—41no—
292C32×Q8C2×D411yescharacteristic
293C32×Q8C2×D411yescharacteristic
294C32×D4—21no—
295C32×D4—21no—
296C32×D4—41no—
297C32×D4C2×D411yescharacteristic
298C32×D4C2×D411yescharacteristic
299C2×C32×C4—21no—
300C2×C32×C4—21no—
301C2×C32×C4—21no—
302C2×C32×C4—41no—
303C2×C32×C4—41no—
304C2×C32×C4C2411yescharacteristic
305C2×C3⋊Dic3—21no—
306C2×C3⋊Dic3—21no—
307#634—21no—
308#634—21no—
309C3×#67—21no—
310C3×#67—21no—
311C3×#67—41no—
312C3×#67—41no—
313C2×C3×Dic3—21no—
314C2×C3×Dic3—41no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12—41no—
318C3×D12C2×D411yescharacteristic
319C3×D12C2×D411yescharacteristic
320C3×C4×D3—21no—
321C3×C4×D3—21no—
322C3×C4×D3—41no—
323C3×C4×D3—41no—
324C3×Dic6—21no—
325C3×Dic6—21no—
326C3×Dic6—41no—
327C3×Dic6C2×D411yescharacteristic
328C3×Dic6C2×D411yescharacteristic
329#627—41no—
330#625—41no—
331D3×Dic3—41no—
332D3×Dic3—41no—
333C3⋊(C3⋊C8)—21no—
334C3⋊(C3⋊C8)—21no—
335C3×C3⋊C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8C2×D411yescharacteristic
338C3×C3⋊C8C2×D411yescharacteristic
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341#578—31no—
342#578—91no—
343#577—31no—
344#577—91no—
345#497—91no—
346#473—91no—
347#473—91no—
348#471—91no—
349#471—91no—
350#456—91no—
351#456—91no—
352#455—91no—
353#454—91no—
354#444—91no—
355#444—91no—
356C3×#41—21no—
357C3×#41—21no—
358C3×#41—21no—
359C3×#41—21no—
360C3×#41—21no—
361C3×#41—21no—
362C3×#41—31no—
363C3×#41—31no—
364C3×#41—41no—
365C3×#41—41no—
366C3×#41—41no—
367C3×#41—41no—
368C3×#41—42no—
369C3×#41—61no—
370C3×#41—61no—
371C3×#41—61no—
372C3×#41—61no—
373C3×#41—121no—
374C3×#41C22×D311yescharacteristic
375C3×#41C22×D311yescharacteristic
376C3×#41C22×D311yescharacteristic
377C3×#41C22×D311yescharacteristic
378C2×C3×Q8—21no—
379C2×C3×Q8—21no—
380C2×C3×Q8—21no—
381C2×C3×Q8—21no—
382C2×C3×Q8—21no—
383C2×C3×Q8—31no—
384C2×C3×Q8—41no—
385C2×C3×Q8—41no—
386C2×C3×Q8—61no—
387C2×C3×Q8—61no—
388C2×C3×Q8C22×D311yescharacteristic
389C2×C3×Q8C22×D311yescharacteristic
390C2×C3×D4—31no—
391C2×C3×D4—61no—
392C2×C3×D4—61no—
393C2×C3×D4—121no—
394#239—21no—
395D3×Q8—21no—
396D3×Q8—61no—
397D3×Q8—61no—
398#237—21no—
399#237—41no—
400#237—61no—
401#237—61no—
402#237—121no—
403#237—121no—
404D3×D4—21no—
405D3×D4—41no—
406#235—21no—
407#235—21no—
408#235—61no—
409#235—61no—
410#235C22×D311yescharacteristic
411#235C22×D311yescharacteristic
412C2×D12—21no—
413C2×D12C22×D311yescharacteristic
414C2×Dic6—21no—
415C2×Dic6—31no—
416C2×Dic6—31no—
417C2×Dic6—61no—
418C2×Dic6—61no—
419C2×Dic6—61no—
420C2×Dic6C22×D311yescharacteristic
421C3×Q16—31no—
422C3×Q16—31no—
423C3×Q16—61no—
424C3×Q16—61no—
425C3×Q16—61no—
426C3×Q16—61no—
427C3×Q16—61no—
428C3×SD16—31no—
429C3×SD16—31no—
430C3×SD16—31no—
431C3×SD16—31no—
432C3×SD16—61no—
433C3×SD16—61no—
434C3×SD16—61no—
435C3×SD16—61no—
436C3×SD16—61no—
437C3×SD16—61no—
438C3×D8—31no—
439C3×D8—31no—
440C3×D8—61no—
441C3×M16—31no—
442C3×M16—31no—
443C3×M16—61no—
444C3×M16—61no—
445C2×C3×C8—31no—
446C2×C3×C8—31no—
447C2×C3×C8—61no—
448C2×C3×C8—61no—
449#217—121no—
450#216—21no—
451#216—21no—
452#216—21no—
453#216—21no—
454#216—21no—
455#216—61no—
456#216—61no—
457#216—61no—
458#216—61no—
459#216—61no—
460#216—61no—
461#216—61no—
462#216—61no—
463#216—121no—
464#216—121no—
465#216#6711yescharacteristic
466#216#6711yescharacteristic
467#215—21no—
468#215—21no—
469#215—21no—
470#215—21no—
471#215—21no—
472#215—61no—
473#215—61no—
474#215#6711yescharacteristic
475#215#6711yescharacteristic
476#214—21no—
477#214—61no—
478#214—61no—
479#214—61no—
480#214—61no—
481#214—61no—
482#214—61no—
483#214—61no—
484#214—61no—
485#214—121no—
486#214—121no—
487#214#6711yescharacteristic
488#214#6711yescharacteristic
489#213—21no—
490#213—61no—
491#213—61no—
492#213#6711yescharacteristic
493#213#6711yescharacteristic
494(C2×D3)⋊C4—121no—
495Dic3⋊C4—121no—
496Dic3⋊C4—121no—
497Dic3⋊C4—122no—
498C4×Dic3—31no—
499C4×Dic3—31no—
500C4×Dic3—61no—
501#208—21no—
502#208—21no—
503#208—31no—
504#208—31no—
505#208—31no—
506#208—31no—
507#208—61no—
508#208—61no—
509#208—61no—
510#208—61no—
511#208C22×D311yescharacteristic
512#208C22×D311yescharacteristic
513C2×C3⋊C8—21no—
514C2×C3⋊C8—21no—
515C2×C3⋊C8—61no—
516C2×C3⋊C8—61no—
517C2×C3⋊C8C22×D311yescharacteristic
518C2×C3⋊C8C22×D311yescharacteristic
519Dic12—61no—
520Dic12—61no—
521#204—61no—
522#204—61no—
523ΓL(1,𝔽25)—61no—
524ΓL(1,𝔽25)—61no—
525D3×C8—61no—
526D3×C8—61no—
527C22×C32—21no—
528C22×C32—21no—
529C22×C32H(5,𝔽2)11yescharacteristic
530C2×C3×D3—21no—
531C2×C3×D3—21no—
532C2×C3×D3—41no—
533C2×C3×D3—81no—
534C2×C3×D3—161no—
535C32×C4—21no—
536C32×C4—21no—
537C32×C4—41no—
538C32×C4C22×D411yescharacteristic
539C32×C4C22×D411yescharacteristic
540C3⋊Dic3—41no—
541C3⋊Dic3—41no—
542C3×Dic3—21no—
543C3×Dic3—21no—
544C3×Dic3—41no—
5452−1+4—31no—
5462−1+4—91no—
5472−1+4D3211yescharacteristic
548H(5,𝔽2)—31no—
549#137—31no—
550#137—31no—
551#137—31no—
552#137—61no—
553#137—61no—
554#137—61no—
555#137—91no—
556#137—91no—
557#137—91no—
558#137—181no—
559#137—181no—
560#137—181no—
561AGL(1,ℤ/8)—31no—
562AGL(1,ℤ/8)—61no—
563AGL(1,ℤ/8)—91no—
564AGL(1,ℤ/8)—181no—
565#135—31no—
566#135—31no—
567#135—61no—
568#135—61no—
569#135—181no—
570#135—181no—
571C2×Q16—31no—
572C2×Q16—61no—
573C2×Q16—91no—
574C2×Q16—181no—
575C2×SD16—31no—
576C2×SD16—61no—
577C2×SD16—91no—
578C2×SD16—181no—
579#131—31no—
580#131—31no—
581#131—91no—
582#131—91no—
583C4⋊Q8—91no—
584#124—91no—
585#108—91no—
586#108—91no—
587#104—91no—
588#104—91no—
589#104—91no—
590#104—91no—
591#101—91no—
592#101—91no—
593#101—91no—
594#100—91no—
595#97—91no—
596C23×C3—61no—
597C23×C3—121no—
598C22×D3—21no—
599C22×D3—41no—
600C3×Q8—21no—
601C3×Q8—21no—
602C3×Q8—21no—
603C3×Q8—21no—
604C3×Q8—21no—
605C3×Q8—21no—
606C3×Q8—31no—
607C3×Q8—31no—
608C3×Q8—41no—
609C3×Q8—41no—
610C3×Q8—41no—
611C3×Q8—41no—
612C3×Q8—42no—
613C3×Q8—61no—
614C3×Q8—61no—
615C3×Q8—121no—
616C3×Q8D3×D411yescharacteristic
617C3×Q8D3×D411yescharacteristic
618C3×Q8C2×#6711yescharacteristic
619C3×Q8C2×#6711yescharacteristic
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—31no—
627C3×D4—31no—
628C3×D4—41no—
629C3×D4—41no—
630C3×D4—41no—
631C3×D4—41no—
632C3×D4—42no—
633C3×D4—61no—
634C3×D4—61no—
635C3×D4—61no—
636C3×D4—61no—
637C3×D4—121no—
638C3×D4—121no—
639C3×D4—121no—
640C3×D4D3×D411yescharacteristic
641C3×D4D3×D411yescharacteristic
642C3×D4C2×#6711yescharacteristic
643C3×D4C2×#6711yescharacteristic
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—22no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—42no—
659C2×C3×C4—42no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—121no—
664C2×C3×C4—121no—
665C2×C3×C4—121no—
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668#67—21no—
669#67—21no—
670#67—41no—
671#67—41no—
672#67—121no—
673#67—121no—
674C2×Dic3—21no—
675C2×Dic3—41no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—121no—
681C2×Dic3—121no—
682C2×Dic3—121no—
683C2×Dic3—121no—
684D12—21no—
685D12—21no—
686D12—41no—
687D12C2×#6711yescharacteristic
688D12C2×#6711yescharacteristic
689C4×D3—21no—
690C4×D3—21no—
691C4×D3—41no—
692C4×D3—41no—
693C4×D3—121no—
694C4×D3—121no—
695Dic6—21no—
696Dic6—21no—
697Dic6—41no—
698Dic6—61no—
699Dic6—61no—
700Dic6—61no—
701Dic6—61no—
702Dic6—121no—
703Dic6—121no—
704Dic6—121no—
705Dic6—121no—
706Dic6C2×#6711yescharacteristic
707Dic6C2×#6711yescharacteristic
708C3×C8—31no—
709C3×C8—31no—
710C3×C8—31no—
711C3×C8—31no—
712C3×C8—61no—
713C3×C8—61no—
714C3⋊C8—21no—
715C3⋊C8—21no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—61no—
719C3⋊C8—61no—
720C3⋊C8—121no—
721C3⋊C8—121no—
722C3⋊C8C2×#6711yescharacteristic
723C3⋊C8C2×#6711yescharacteristic
724C3⋊C8C2×#6711yescharacteristic
725C3⋊C8C2×#6711yescharacteristic
726C2×C32—21no—
727C2×C32—41no—
728C2×C32—41no—
729C2×C32D4211yescharacteristic
730C3×D3—41no—
731C3×D3—41no—
732C3×D3—81no—
733#41—21no—
734#41—21no—
735#41—31no—
736#41—31no—
737#41—41no—
738#41—61no—
739#41—61no—
740#41—61no—
741#41—61no—
742#41—121no—
743#41—181no—
744#41—181no—
745#41—361no—
746#41C2×D3211yescharacteristic
747#41C2×D3211yescharacteristic
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—31no—
751C2×Q8—61no—
752C2×Q8—61no—
753C2×Q8—91no—
754C2×Q8—181no—
755C2×Q8—181no—
756C2×Q8C2×D3211yescharacteristic
757C2×D4—31no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4—121no—
761Q16—31no—
762Q16—31no—
763Q16—61no—
764Q16—61no—
765Q16—61no—
766Q16—61no—
767Q16—61no—
768Q16—181no—
769Q16—181no—
770Q16—181no—
771Q16—181no—
772Q16—181no—
773SD16—31no—
774SD16—31no—
775SD16—31no—
776SD16—31no—
777SD16—61no—
778SD16—61no—
779SD16—61no—
780SD16—61no—
781SD16—61no—
782SD16—61no—
783SD16—181no—
784SD16—181no—
785SD16—181no—
786SD16—181no—
787SD16—181no—
788SD16—181no—
789D8—31no—
790D8—31no—
791D8—61no—
792D8—181no—
793M16—31no—
794M16—31no—
795M16—61no—
796M16—61no—
797M16—91no—
798M16—91no—
799M16—181no—
800M16—181no—
801C2×C8—31no—
802C2×C8—31no—
803C2×C8—61no—
804C2×C8—61no—
805C2×C8—181no—
806C2×C8—181no—
807C4⋊C4—361no—
808C22⋊C4—361no—
809C42—91no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—121no—
820C22×C3—241no—
821C22×C3—481no—
822C22×C3#100411yescharacteristic
823C22×C3#100411yescharacteristic
824C2×D3—21no—
825C2×D3—21no—
826C2×D3—41no—
827C2×D3—81no—
828C2×D3—161no—
829C3×C4—21no—
830C3×C4—21no—
831C3×C4—21no—
832C3×C4—21no—
833C3×C4—21no—
834C3×C4—21no—
835C3×C4—41no—
836C3×C4—41no—
837C3×C4—42no—
838C3×C4—41no—
839C3×C4—41no—
840C3×C4—61no—
841C3×C4—61no—
842C3×C4—121no—
843C3×C4C2×D3×D411yescharacteristic
844C3×C4C2×D3×D411yescharacteristic
845C3×C4C22×#6711yescharacteristic
846C3×C4C22×#6711yescharacteristic
847Dic3—21no—
848Dic3—21no—
849Dic3—41no—
850Dic3—121no—
851Dic3—121no—
852Dic3—122no—
853Dic3—121no—
854Dic3—121no—
855Dic3—241no—
856C32#328911yescharacteristic, complemented, Sylow
857C23—61no—
858C23—121no—
859Q8—21no—
860Q8—21no—
861Q8—31no—
862Q8—31no—
863Q8—41no—
864Q8—61no—
865Q8—61no—
866Q8—121no—
867Q8—181no—
868Q8—181no—
869Q8—361no—
870Q8D3×#6711yescharacteristic
871Q8D3×#6711yescharacteristic
872D4—21no—
873D4—21no—
874D4—31no—
875D4—31no—
876D4—41no—
877D4—61no—
878D4—61no—
879D4—61no—
880D4—61no—
881D4—121no—
882D4—121no—
883D4—121no—
884D4—361no—
885D4D3×#6711yescharacteristic
886D4D3×#6711yescharacteristic
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—121no—
896C2×C4—121no—
897C2×C4—121no—
898C2×C4—181no—
899C2×C4—181no—
900C2×C4—361no—
901C2×C4—361no—
902C2×C4C22×D3211yescharacteristic
903C8—31no—
904C8—31no—
905C8—31no—
906C8—31no—
907C8—61no—
908C8—61no—
909C8—181no—
910C8—181no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—41no—
915C2×C3—41no—
916C2×C3—41no—
917C2×C3—41no—
918C2×C3—41no—
919C2×C3—81no—
920C2×C3—81no—
921C2×C3—121no—
922C2×C3—121no—
923C2×C3—241no—
924C2×C3D4×#6711yescharacteristic
925C2×C3D4×#6711yescharacteristic
926D3—41no—
927D3—41no—
928D3—81no—
929C22—21no—
930C22—21no—
931C22—61no—
932C22—61no—
933C22—121no—
934C22—241no—
935C22—481no—
936C22#6433011yescharacteristic
937C4—21no—
938C4—21no—
939C4—41no—
940C4—61no—
941C4—61no—
942C4—121no—
943C4—361no—
944C4—361no—
945C4C2×D3×#6711yescharacteristic
946C4C2×D3×#6711yescharacteristic
947C3—21no—
948C3#8401311yescharacteristic, complemented
949C3#8401911yescharacteristic, complemented
950C2—21no—
951C2—41no—
952C2—41no—
953C2—121no—
954C2—121no—
955C2—241no—
956C2#67211yescharacteristic
subgroupG/H
centerC2#672
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×2−1+4C22
socleC2×C32D42
hypercenter2−1+4D32
hypocenterC32#3289
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. C3×#5838C2semidirect
2. C3×#5837C2semidirect
3. #10595467C2semidirect
4. #10595466C2semidirect
5. #10592945C2semidirect
6. #10591684C2semidirect
7. #10591682C2semidirect
8. #10591679C2semidirect
9. #10591674C2semidirect
10. #10591674C2semidirect
11. #10591664C2semidirect
12. #10591660C2semidirect
13. #10591642C2semidirect
14. #10591641C2semidirect
15. #10591611C2semidirect
19. C3×#1010C22semidirect
23. #64160C22semidirect
24. #64153C22semidirect
34. C3×#948C22semidirect
36. C2×C3×#216C22semidirect
40. C3×#942C22semidirect
52. C2×#3719C22semidirect
57. #63814C22semidirect
59. #63664C22semidirect
60. #63663C22semidirect
61. #63577C22semidirect
62. #63577C22semidirect
64. #63568C22semidirect
65. #63561C22semidirect
66. #63560C22semidirect
68. #63555C22semidirect
72. #5838D3semidirect
73. #5837D3semidirect
185. #1010C2×D3semidirect
228. #948C2×D3semidirect
236. C2×#216C2×D3semidirect
242. #942C2×D3semidirect
856. C32#3289semidirect
948. C3#84013semidirect
949. C3#84019semidirect

Maximal subgroups

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

subgroupindex
C3×#58382
C3×#58372
#105954672
#105954662
#105929452
#105916842
#105916822
#105916792
#105916742
#105916642
#105916602
#105916422
#105916412
#105916112
#840193
#840133