Finite Group Databasebeta

← #11886693

Subgroups — #11886693

Order 1152.

948 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5771C211yesmaximal, characteristic, complemented
2C3×#5770C211yesmaximal, characteristic, complemented
3#10595446C211yesmaximal, characteristic, complemented
4#10595445C211yesmaximal, characteristic, complemented
5#10592896C211yesmaximal, characteristic, complemented
6#10591687C211yesmaximal, characteristic, complemented
7#10591687C211yesmaximal, characteristic, complemented
8#10591684C211yesmaximal, characteristic, complemented
9#10591683C211yesmaximal, characteristic, complemented
10#10591681C211yesmaximal, characteristic, complemented
11#10591664C211yesmaximal, characteristic, complemented
12#10590930C211yesmaximal, characteristic, complemented
13#10590925C211yesmaximal, characteristic, complemented
14#10590922C211yesmaximal, characteristic, complemented
15#10590870C211yesmaximal, characteristic, complemented
16#84019—31nomaximal
17#84013—31nomaximal
18C3×#1010C2211yescharacteristic
19C3×#1010C2211yescharacteristic
20C3×#1010C2211yescharacteristic, complemented
21C3×#1009C2211yescharacteristic
22C32×#135C2211yescharacteristic
23#64157C2211yescharacteristic
24#64157C2211yescharacteristic, complemented
25C3×#951C2211yescharacteristic
26C3×#951C2211yescharacteristic
27C3×#951C2211yescharacteristic, complemented
28C3×#949C2211yescharacteristic
29C3×#918—21no—
30C3×D3×Q16—21no—
31C3×#916—21no—
32C3×#915—21no—
33C3×#915—21no—
34C3×D3×SD16—21no—
35C3×#912—21no—
36C3×#911—21no—
37C2×C3×Dic12C2211yescharacteristic, complemented
38C2×C3×#204C2211yescharacteristic
39C3×#901C2211yescharacteristic
40C3×#901C2211yescharacteristic, complemented
41#63873C2211yescharacteristic, complemented
42#63863C2211yescharacteristic
43C2×#3718—21no—
44C2×#3718C2211yescharacteristic, complemented
45#63827—21no—
46#63827—21no—
47#63827—21no—
48#63827C2211yescharacteristic
49#63827C2211yescharacteristic
50#63827C2211yescharacteristic, complemented
51C2×#3715—21no—
52C2×#3715C2211yescharacteristic
53#63823—21no—
54#63823C2211yescharacteristic
55#63822—21no—
56#63822—21no—
57#63822C2211yescharacteristic
58#63664C2211yescharacteristic
59#63664C2211yescharacteristic, complemented
60#63646C2211yescharacteristic, complemented
61#63642C2211yescharacteristic, complemented
62#63578C2211yescharacteristic, complemented
63#63568C2211yescharacteristic
64#63568C2211yescharacteristic, complemented
65#63560C2211yescharacteristic, complemented
66#63560C2211yescharacteristic, complemented
67#63560C2211yescharacteristic, complemented
68#63558C2211yescharacteristic
69C3×#578—31no—
70C3×#577—31no—
71#5838—31no—
72#5838—31no—
73#5837—31no—
74#5836—31no—
75#5771D311yescharacteristic, complemented
76#5770D311yescharacteristic, complemented
77#5246—31no—
78#5246—31no—
79#5245—31no—
80#5242—31no—
81#5205—31no—
82#5205—31no—
83#5204—31no—
84#5204—31no—
85#5203—31no—
86#5202—31no—
87#5201—31no—
88#5200—31no—
89#5197—31no—
90#5197—31no—
91#5197—61no—
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×#41C2311yescharacteristic
101C32×#41C2311yescharacteristic
102C3×#239—21no—
103C3×D3×Q8—21no—
104C3×D3×Q8—21no—
105C3×D3×Q8—21no—
106C3×#237—21no—
107C3×#237—21no—
108C3×#237—21no—
109C3×#237—41no—
110C3×#237—41no—
111C3×#237—41no—
112C3×D3×D4—21no—
113C3×D3×D4—41no—
114C3×#235—21no—
115C3×#235—21no—
116C3×#235—21no—
117C3×#235—21no—
118C3×#235C2311yescharacteristic
119C3×#235C2311yescharacteristic
120C2×C3×D12—21no—
121C2×C3×D12C2311yescharacteristic
122C2×C3×Dic6—21no—
123C2×C3×Dic6—21no—
124C2×C3×Dic6—21no—
125C2×C3×Dic6C2311yescharacteristic
126C2×C3×Dic6C2311yescharacteristic
127C2×C3×Dic6C2311yescharacteristic
128C32×Q16D411yescharacteristic
129C32×SD16D411yescharacteristic
130C32×SD16D411yescharacteristic
131C32×D8D411yescharacteristic
132C2×C32×C8C2311yescharacteristic
133C4×C3⋊Dic3C2311yescharacteristic
134#3748—21no—
135#3748—21no—
136#3748C2311yescharacteristic
137#3748C2311yescharacteristic
138C2×C3⋊(C3⋊C8)—21no—
139C2×C3⋊(C3⋊C8)—21no—
140C2×C3⋊(C3⋊C8)C2311yescharacteristic
141C3×#216—21no—
142C3×#216—21no—
143C3×#216—21no—
144C3×#215—21no—
145C3×#214—21no—
146C3×#214—21no—
147C3×#214—21no—
148C3×#213—21no—
149C3×#208C2311yescharacteristic
150C3×#208C2311yescharacteristic
151C3×Dic12—21no—
152C3×Dic12—21no—
153C3×#204—21no—
154C3×#204—21no—
155C3×ΓL(1,𝔽25)—21no—
156C3×ΓL(1,𝔽25)—21no—
157C3×D3×C8—21no—
158C3×D3×C8—21no—
159#3724—41no—
160(C2×D3)⋊Dic3—41no—
161#3718—21no—
162#3718—21no—
163#3718—21no—
164#3718—21no—
165#3718—21no—
166#3718D411yescharacteristic
167#3715—21no—
168#3715—21no—
169#3715—21no—
170#3715—21no—
171#3715—21no—
172#3715—21no—
173#3715D411yescharacteristic
174#3715D411yescharacteristic
175#3713—21no—
176#3713D411yescharacteristic
177#3289—91noSylow
178C3×2−1+4—31no—
179C3×2−1+4—31no—
180C3×2−1+4—31no—
181C3×H(5,𝔽2)—31no—
182#1010C2×D311yescharacteristic
183#1010C2×D311yescharacteristic
184#1010C2×D311yescharacteristic, complemented
185#1009C2×D311yescharacteristic
186C3×#137—31no—
187C3×#137—31no—
188C3×#137—31no—
189C3×#137—61no—
190C3×#137—61no—
191C3×#137—61no—
192C3×AGL(1,ℤ/8)—31no—
193C3×AGL(1,ℤ/8)—61no—
194C3×#135—21no—
195C3×#135—61no—
196C3×#135—61no—
197C3×#135C2×D311yescharacteristic
198C3×#135C2×D311yescharacteristic
199C2×C3×Q16—31no—
200C2×C3×Q16—61no—
201C2×C3×SD16—31no—
202C2×C3×SD16—61no—
203C3×#131—31no—
204C3×#131—31no—
205#951—31no—
206#951—31no—
207#951—31no—
208#951—61no—
209#951—61no—
210#951—61no—
211#951C2×D311yescharacteristic
212#951C2×D311yescharacteristic
213#951C2×D311yescharacteristic, complemented
214#950—31no—
215#950—31no—
216#950—61no—
217#950—61no—
218#950—61no—
219#950—61no—
220#949—31no—
221#949—61no—
222#949C2×D311yescharacteristic
223#948—31no—
224#948—31no—
225#948—31no—
226#948—31no—
227#948—61no—
228#948—61no—
229#947—31no—
230#944—31no—
231#944—31no—
232C2×#216—31no—
233C2×#216—31no—
234C2×#216—61no—
235C2×#216—61no—
236#942—31no—
237#942—31no—
238#942—31no—
239#942—61no—
240#942—61no—
241#942—61no—
242C2×#215—31no—
243C2×#215—61no—
244#936—31no—
245C2×#214—31no—
246C2×#214—61no—
247#932—31no—
248#932—61no—
249#918—21no—
250D3×Q16—21no—
251#916—21no—
252#915—21no—
253#915—21no—
254D3×SD16—21no—
255#912—21no—
256#911—21no—
257C2×Dic12C2×D311yescharacteristic, complemented
258C2×#204C2×D311yescharacteristic
259#901C2×D311yescharacteristic
260#901C2×D311yescharacteristic, complemented
261#837—31no—
262#837—31no—
263#837—31no—
264#837—31no—
265#837—31no—
266#837—31no—
267#837—61no—
268#837—61no—
269#836—31no—
270#836—31no—
271#836—31no—
272#833—31no—
273#825—31no—
274#825—31no—
275#824—31no—
276#824—31no—
277#824—31no—
278#823—31no—
279#822—31no—
280#822—31no—
281#819—31no—
282#819—31no—
283#819—61no—
284#815—31no—
285#815—31no—
286#815—61no—
287C22×C3×D3—21no—
288C22×C3×D3—41no—
289C32×Q8C2×D411yescharacteristic
290C32×Q8C2×D411yescharacteristic
291C32×D4—21no—
292C32×D4—21no—
293C32×D4C2×D411yescharacteristic
294C32×D4C2×D411yescharacteristic
295C2×C32×C4—21no—
296C2×C32×C4—21no—
297C2×C32×C4C2411yescharacteristic
298C2×C3⋊Dic3—21no—
299C3×#67—21no—
300C3×#67—21no—
301C3×#67—41no—
302C3×#67—41no—
303C3×#67—41no—
304C3×#67—41no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—41no—
309C2×C3×Dic3—41no—
310C2×C3×Dic3—41no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—41no—
314C3×D12C2×D411yescharacteristic
315C3×D12C2×D411yescharacteristic
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—41no—
319C3×C4×D3—41no—
320C3×C4×D3—41no—
321C3×C4×D3—41no—
322C3×Dic6—21no—
323C3×Dic6—21no—
324C3×Dic6—21no—
325C3×Dic6—21no—
326C3×Dic6—21no—
327C3×Dic6—21no—
328C3×Dic6—41no—
329C3×Dic6—41no—
330C3×Dic6—41no—
331C3×Dic6C2×D411yescharacteristic
332C3×Dic6C2×D411yescharacteristic
333C32×C8C2×D411yescharacteristic
334C32×C8C2×D411yescharacteristic
335C3⋊(C3⋊C8)—21no—
336C3⋊(C3⋊C8)—21no—
337C3⋊(C3⋊C8)C2×D411yescharacteristic
338C3⋊(C3⋊C8)C2×D411yescharacteristic
339C3×C3⋊C8—21no—
340C3×C3⋊C8—21no—
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—31no—
359C3×#41—31no—
360C3×#41—61no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41—61no—
365C3×#41—61no—
366C3×#41—61no—
367C3×#41—61no—
368C3×#41—121no—
369C3×#41—121no—
370C3×#41—121no—
371C3×#41C22×D311yescharacteristic
372C3×#41C22×D311yescharacteristic
373C3×#41C22×D311yescharacteristic
374C3×#41C22×D311yescharacteristic
375C2×C3×Q8—31no—
376C2×C3×Q8—31no—
377C2×C3×Q8—31no—
378C2×C3×Q8—61no—
379C2×C3×Q8—61no—
380C2×C3×Q8—61no—
381C2×C3×Q8—61no—
382C2×C3×Q8—61no—
383C2×C3×Q8—61no—
384C2×C3×D4—31no—
385C2×C3×D4—61no—
386C2×C3×D4—61no—
387C2×C3×D4—121no—
388#239—21no—
389D3×Q8—21no—
390D3×Q8—21no—
391D3×Q8—21no—
392#237—21no—
393#237—21no—
394#237—21no—
395#237—41no—
396#237—41no—
397#237—41no—
398D3×D4—21no—
399D3×D4—41no—
400#235—21no—
401#235—21no—
402#235—21no—
403#235—21no—
404#235C22×D311yescharacteristic
405#235C22×D311yescharacteristic
406C2×D12—21no—
407C2×D12C22×D311yescharacteristic
408C2×Dic6—21no—
409C2×Dic6—21no—
410C2×Dic6—21no—
411C2×Dic6C22×D311yescharacteristic
412C2×Dic6C22×D311yescharacteristic
413C2×Dic6C22×D311yescharacteristic
414C3×Q16—21no—
415C3×Q16—61no—
416C3×Q16—61no—
417C3×Q16—61no—
418C3×Q16—61no—
419C3×Q16—61no—
420C3×Q16#6711yescharacteristic
421C3×Q16#6711yescharacteristic
422C3×SD16—21no—
423C3×SD16—21no—
424C3×SD16—61no—
425C3×SD16—61no—
426C3×SD16—61no—
427C3×SD16—61no—
428C3×SD16—61no—
429C3×SD16—61no—
430C3×SD16#6711yescharacteristic
431C3×SD16#6711yescharacteristic
432C3×SD16#6711yescharacteristic
433C3×SD16#6711yescharacteristic
434C3×D8—21no—
435C3×D8—61no—
436C3×D8#6711yescharacteristic
437C3×D8#6711yescharacteristic
438C3×M16—31no—
439C3×M16—31no—
440C3×M16—61no—
441C3×M16—61no—
442C2×C3×C8—21no—
443C2×C3×C8—61no—
444C2×C3×C8—61no—
445C2×C3×C8C22×D311yescharacteristic
446C2×C3×C8C22×D311yescharacteristic
447#217—121no—
448#216—21no—
449#216—21no—
450#216—21no—
451#216—31no—
452#216—31no—
453#216—61no—
454#216—61no—
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#215—21no—
464#215—31no—
465#215—31no—
466#215—61no—
467#215—61no—
468#215—61no—
469#215—61no—
470#215—61no—
471#215—61no—
472#214—21no—
473#214—21no—
474#214—21no—
475#214—31no—
476#214—31no—
477#214—61no—
478#214—61no—
479#214—61no—
480#214—61no—
481#214—61no—
482#214—61no—
483#213—21no—
484#213—31no—
485#213—31no—
486#213—61no—
487#213—61no—
488(C2×D3)⋊C4—121no—
489Dic3⋊C4—121no—
490Dic3⋊C4—121no—
491C4×Dic3—31no—
492C4×Dic3—31no—
493C4×Dic3—61no—
494#208—31no—
495#208—31no—
496#208—31no—
497#208—31no—
498#208—61no—
499#208—61no—
500#208—61no—
501#208—61no—
502#208—61no—
503#208—61no—
504#208—121no—
505#208—121no—
506#208C22×D311yescharacteristic
507#208C22×D311yescharacteristic
508C2×C3⋊C8—31no—
509C2×C3⋊C8—31no—
510C2×C3⋊C8—61no—
511C2×C3⋊C8—61no—
512C2×C3⋊C8—61no—
513C2×C3⋊C8—61no—
514C2×C3⋊C8—61no—
515C2×C3⋊C8—121no—
516C2×C3⋊C8—121no—
517Dic12—21no—
518Dic12—21no—
519#204—21no—
520#204—21no—
521ΓL(1,𝔽25)—21no—
522ΓL(1,𝔽25)—21no—
523D3×C8—21no—
524D3×C8—21no—
525C22×C32—21no—
526C22×C32—21no—
527C22×C32H(5,𝔽2)11yescharacteristic
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—41no—
531C2×C3×D3—81no—
532C2×C3×D3—161no—
533C32×C4—21no—
534C32×C4—21no—
535C32×C4C22×D411yescharacteristic
536C32×C4C22×D411yescharacteristic
537C3⋊Dic3—41no—
538C3×Dic3—21no—
539C3×Dic3—21no—
540C3×Dic3—41no—
541C3×Dic3—41no—
542C3×Dic3—41no—
5432−1+4—31no—
5442−1+4—31no—
5452−1+4—31no—
546H(5,𝔽2)—31no—
547#137—31no—
548#137—31no—
549#137—31no—
550#137—61no—
551#137—61no—
552#137—61no—
553#137—91no—
554#137—91no—
555#137—91no—
556#137—181no—
557#137—181no—
558#137—181no—
559AGL(1,ℤ/8)—31no—
560AGL(1,ℤ/8)—61no—
561AGL(1,ℤ/8)—91no—
562AGL(1,ℤ/8)—181no—
563#135—61no—
564#135—61no—
565#135—91no—
566#135—181no—
567#135—181no—
568#135D3211yescharacteristic
569C2×Q16—31no—
570C2×Q16—61no—
571C2×Q16—91no—
572C2×Q16—181no—
573C2×SD16—31no—
574C2×SD16—61no—
575C2×SD16—91no—
576C2×SD16—181no—
577#131—31no—
578#131—31no—
579#131—91no—
580#131—91no—
581C4⋊Q8—91no—
582#124—91no—
583#108—91no—
584#108—91no—
585#104—91no—
586#104—91no—
587#104—91no—
588#104—91no—
589#101—91no—
590#101—91no—
591#101—91no—
592#100—91no—
593#97—91no—
594C23×C3—61no—
595C23×C3—121no—
596C22×D3—21no—
597C22×D3—41no—
598C3×Q8—21no—
599C3×Q8—21no—
600C3×Q8—31no—
601C3×Q8—31no—
602C3×Q8—61no—
603C3×Q8—61no—
604C3×Q8—61no—
605C3×Q8—61no—
606C3×Q8—61no—
607C3×Q8—61no—
608C3×Q8—121no—
609C3×Q8—121no—
610C3×Q8—121no—
611C3×Q8C2×#6711yescharacteristic
612C3×Q8C2×#6711yescharacteristic
613C3×Q8C2×#6711yescharacteristic
614C3×Q8C2×#6711yescharacteristic
615C3×D4—21no—
616C3×D4—21no—
617C3×D4—21no—
618C3×D4—21no—
619C3×D4—21no—
620C3×D4—21no—
621C3×D4—31no—
622C3×D4—31no—
623C3×D4—41no—
624C3×D4—41no—
625C3×D4—61no—
626C3×D4—61no—
627C3×D4—61no—
628C3×D4—61no—
629C3×D4—121no—
630C3×D4—121no—
631C3×D4—121no—
632C3×D4—121no—
633C3×D4—121no—
634C3×D4C2×#6711yescharacteristic
635C3×D4C2×#6711yescharacteristic
636C3×D4C2×#6711yescharacteristic
637C3×D4C2×#6711yescharacteristic
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—121no—
651C2×C3×C4—121no—
652C2×C3×C4—121no—
653C2×C3×C4—121no—
654C2×C3×C4—121no—
655C2×C3×C4—121no—
656C2×C3×C4—121no—
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659#67—21no—
660#67—21no—
661#67—41no—
662#67—41no—
663#67—41no—
664#67—41no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—41no—
669C2×Dic3—41no—
670C2×Dic3—41no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—121no—
674D12—21no—
675D12—21no—
676D12—41no—
677D12D3×D411yescharacteristic
678D12D3×D411yescharacteristic
679C4×D3—21no—
680C4×D3—21no—
681C4×D3—41no—
682C4×D3—41no—
683C4×D3—41no—
684C4×D3—41no—
685Dic6—21no—
686Dic6—21no—
687Dic6—21no—
688Dic6—21no—
689Dic6—21no—
690Dic6—21no—
691Dic6—41no—
692Dic6—41no—
693Dic6—41no—
694Dic6D3×D411yescharacteristic
695Dic6D3×D411yescharacteristic
696C3×C8—21no—
697C3×C8—21no—
698C3×C8—61no—
699C3×C8—61no—
700C3×C8C2×#6711yescharacteristic
701C3×C8C2×#6711yescharacteristic
702C3×C8C2×#6711yescharacteristic
703C3×C8C2×#6711yescharacteristic
704C3⋊C8—21no—
705C3⋊C8—21no—
706C3⋊C8—31no—
707C3⋊C8—31no—
708C3⋊C8—31no—
709C3⋊C8—31no—
710C3⋊C8—61no—
711C3⋊C8—61no—
712C3⋊C8—61no—
713C3⋊C8—61no—
714C3⋊C8—61no—
715C3⋊C8—61no—
716C3⋊C8—121no—
717C3⋊C8—121no—
718C2×C32—21no—
719C2×C32—41no—
720C2×C32—41no—
721C2×C32D4211yescharacteristic
722C3×D3—41no—
723C3×D3—41no—
724C3×D3—81no—
725#41—31no—
726#41—31no—
727#41—61no—
728#41—61no—
729#41—61no—
730#41—61no—
731#41—61no—
732#41—61no—
733#41—61no—
734#41—61no—
735#41—121no—
736#41—121no—
737#41—121no—
738#41C2×D3211yescharacteristic
739#41C2×D3211yescharacteristic
740C2×Q8—31no—
741C2×Q8—31no—
742C2×Q8—31no—
743C2×Q8—61no—
744C2×Q8—61no—
745C2×Q8—61no—
746C2×Q8—61no—
747C2×Q8—61no—
748C2×Q8—61no—
749C2×D4—31no—
750C2×D4—61no—
751C2×D4—61no—
752C2×D4—121no—
753Q16—61no—
754Q16—61no—
755Q16—61no—
756Q16—61no—
757Q16—61no—
758Q16—91no—
759Q16—181no—
760Q16—181no—
761Q16—181no—
762Q16—181no—
763Q16—181no—
764Q16#62511yescharacteristic
765SD16—61no—
766SD16—61no—
767SD16—61no—
768SD16—61no—
769SD16—61no—
770SD16—61no—
771SD16—91no—
772SD16—91no—
773SD16—181no—
774SD16—181no—
775SD16—181no—
776SD16—181no—
777SD16—181no—
778SD16—181no—
779SD16#62511yescharacteristic
780SD16#62511yescharacteristic
781D8—61no—
782D8—91no—
783D8—181no—
784D8#62511yescharacteristic
785M16—31no—
786M16—31no—
787M16—61no—
788M16—61no—
789M16—91no—
790M16—91no—
791M16—181no—
792M16—181no—
793C2×C8—61no—
794C2×C8—61no—
795C2×C8—91no—
796C2×C8—181no—
797C2×C8—181no—
798C2×C8C2×D3211yescharacteristic
799C4⋊C4—361no—
800C22⋊C4—361no—
801C42—91no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—61no—
810C22×C3—61no—
811C22×C3—121no—
812C22×C3—241no—
813C22×C3—481no—
814C22×C3#100411yescharacteristic
815C22×C3#100411yescharacteristic
816C2×D3—21no—
817C2×D3—21no—
818C2×D3—41no—
819C2×D3—81no—
820C2×D3—161no—
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—41no—
828C3×C4—41no—
829C3×C4—61no—
830C3×C4—61no—
831C3×C4—121no—
832C3×C4—121no—
833C3×C4—121no—
834C3×C4C2×D3×D411yescharacteristic
835C3×C4C2×D3×D411yescharacteristic
836C3×C4C22×#6711yescharacteristic
837C3×C4C22×#6711yescharacteristic
838Dic3—21no—
839Dic3—21no—
840Dic3—41no—
841Dic3—41no—
842Dic3—41no—
843Dic3—121no—
844Dic3—121no—
845Dic3—241no—
846C32#328911yescharacteristic, complemented, Sylow
847C23—61no—
848C23—121no—
849Q8—31no—
850Q8—31no—
851Q8—61no—
852Q8—61no—
853Q8—61no—
854Q8—61no—
855Q8—61no—
856Q8—61no—
857Q8—121no—
858Q8—121no—
859Q8—121no—
860Q8C2×#62511yescharacteristic
861Q8C2×#62511yescharacteristic
862D4—21no—
863D4—21no—
864D4—31no—
865D4—31no—
866D4—61no—
867D4—61no—
868D4—61no—
869D4—61no—
870D4—121no—
871D4—121no—
872D4—121no—
873D4—121no—
874D4—121no—
875D4C2×#62511yescharacteristic
876D4C2×#62511yescharacteristic
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—121no—
885C2×C4—121no—
886C2×C4—121no—
887C2×C4—121no—
888C2×C4—121no—
889C2×C4—121no—
890C2×C4—121no—
891C2×C4—181no—
892C2×C4C22×D3211yescharacteristic
893C8—61no—
894C8—61no—
895C8—91no—
896C8—91no—
897C8—181no—
898C8—181no—
899C8C2×#62511yescharacteristic
900C8C2×#62511yescharacteristic
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—41no—
905C2×C3—41no—
906C2×C3—41no—
907C2×C3—41no—
908C2×C3—41no—
909C2×C3—81no—
910C2×C3—81no—
911C2×C3—121no—
912C2×C3—121no—
913C2×C3—241no—
914C2×C3D4×#6711yescharacteristic
915C2×C3D4×#6711yescharacteristic
916D3—41no—
917D3—41no—
918D3—81no—
919C22—21no—
920C22—21no—
921C22—61no—
922C22—61no—
923C22—121no—
924C22—241no—
925C22—481no—
926C22#6431311yescharacteristic
927C4—21no—
928C4—21no—
929C4—61no—
930C4—61no—
931C4—121no—
932C4—121no—
933C4—121no—
934C4—361no—
935C4D32×D411yescharacteristic
936C4C22×#62511yescharacteristic
937C3—21no—
938C3#8401311yescharacteristic, complemented
939C3#8401911yescharacteristic, complemented
940C2—21no—
941C2—41no—
942C2—41no—
943C2—121no—
944C2—121no—
945C2—241no—
946C2D4×#62511yescharacteristic
subgroupG/H
centerC2D4×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#135C22
socleC2×C32D42
hypercenter#135D32
hypocenterC32#3289
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. C3×#5771C2semidirect
2. C3×#5770C2semidirect
3. #10595446C2semidirect
4. #10595445C2semidirect
5. #10592896C2semidirect
6. #10591687C2semidirect
7. #10591687C2semidirect
8. #10591684C2semidirect
9. #10591683C2semidirect
10. #10591681C2semidirect
11. #10591664C2semidirect
12. #10590930C2semidirect
13. #10590925C2semidirect
14. #10590922C2semidirect
15. #10590870C2semidirect
20. C3×#1010C22semidirect
24. #64157C22semidirect
27. C3×#951C22semidirect
37. C2×C3×Dic12C22semidirect
40. C3×#901C22semidirect
41. #63873C22semidirect
44. C2×#3718C22semidirect
50. #63827C22semidirect
59. #63664C22semidirect
60. #63646C22semidirect
61. #63642C22semidirect
62. #63578C22semidirect
64. #63568C22semidirect
65. #63560C22semidirect
66. #63560C22semidirect
67. #63560C22semidirect
75. #5771D3semidirect
76. #5770D3semidirect
184. #1010C2×D3semidirect
213. #951C2×D3semidirect
257. C2×Dic12C2×D3semidirect
260. #901C2×D3semidirect
846. C32#3289semidirect
938. C3#84013semidirect
939. C3#84019semidirect

Maximal subgroups

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

subgroupindex
C3×#57712
C3×#57702
#105954462
#105954452
#105928962
#105916872
#105916842
#105916832
#105916812
#105916642
#105909302
#105909252
#105909222
#105908702
#840193
#840133