Finite Group Databasebeta

← #11661860

Subgroups — #11661860

Order 768.

4764 conjugacy classes of subgroups.

The subgroup lattice has 1468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5964C211yesmaximal, characteristic, complemented
2C2×#5822C211yesmaximal, characteristic, complemented
3C2×#5748C211yesmaximal, characteristic, complemented
4#85735C211yesmaximal, characteristic, complemented
5C2×C3×#421C211yesmaximal, characteristic, complemented
6C2×#5132C211yesmaximal, characteristic, complemented
7C2×#5005C211yesmaximal, characteristic, complemented
8#78996C214yesmaximal, complemented
9#78995C214yesmaximal, complemented
10#78994C214yesmaximal, complemented
11#78993C214yesmaximal, complemented
12#78986C218yesmaximal, complemented
13#60387—31nomaximal, Sylow
14C22×C3×#41C2211yescharacteristic
15#5964—22no—
16#5964—22no—
17#5964—22no—
18#5964—22no—
19#5964—22no—
20#5964—22no—
21#5964C2214yes—
22#5964C2214yescomplemented
23C2×#1010—21no—
24C2×#1010C2212yescomplemented
25C2×#1009—21no—
26C2×#1009C2212yescomplemented
27C2×D3×#41—22no—
28C2×D3×#41—22no—
29C2×#1007—21no—
30C2×#1004—21no—
31C2×#1004—22no—
32C22×#235—22no—
33C22×#235C2211yescharacteristic
34C22×#235C2211yescharacteristic
35C22×#235C2211yescharacteristic, complemented
36C22×C3×M16C2211yescharacteristic, complemented
37C2×C3×#117C2211yescharacteristic, complemented
38C2×#951C2212yescomplemented
39#5822—22no—
40#5822—22no—
41#5822C2214yescomplemented
42#5822C2214yescomplemented
43C2×#950—22no—
44C2×#949C2212yescomplemented
45C2×#942—21no—
46C2×#932—21no—
47C22×#208C2211yescharacteristic, complemented
48#5748—22no—
49#5748—22no—
50#5748C2214yescomplemented
51#5748C2214yescomplemented
52C2×#909—21no—
53C2×#909C2212yescomplemented
54C2×#908—21no—
55C2×#908C2212yescomplemented
56C2×#904—22no—
57#5526C2212yescomplemented
58#5526C2212yescomplemented
59#5525C2212yescomplemented
60#5525C2212yescomplemented
61#5524—22no—
62#5524—22no—
63#5510—22no—
64#5493—22no—
65#5477C2214yescomplemented
66C3×#421C2214yescomplemented
67C3×#421C2214yescomplemented
68C2×C3×#104C2214yescomplemented
69C2×#824C2212yescomplemented
70#5132C2214yescomplemented
71#5132C2214yescomplemented
72C2×#823C2212yescomplemented
73#5005C2214yescomplemented
74#5005C2214yescomplemented
75C2×#805C2214yescomplemented
76#4827C22116yescomplemented
77#4826C22116yescomplemented
78#4825C22116yescomplemented
79#4822C22116yescomplemented
80C2×#585—31no—
81C2×#575—31no—
82C2×#575—31no—
83#3449—31no—
84#3022—34no—
85#3021—34no—
86#3020—34no—
87#3019—34no—
88#3018—38no—
89C2×#421—31no—
90C2×#421D311yescharacteristic, complemented
91C2×#413—31no—
92C2×C3×#41—21no—
93C2×C3×#41—21no—
94C2×C3×#41—21no—
95C2×C3×#41—21no—
96C2×C3×#41—21no—
97C2×C3×#41—21no—
98C2×C3×#41D412yescomplemented
99C2×C3×#41D412yescomplemented
100C2×C3×#41D412yescomplemented
101C2×C3×#41C2312yes—
102C2×C3×#41C2312yes—
103C2×C3×#41C2312yes—
104C22×C3×Q8D411yescharacteristic, complemented
105C22×C3×D4—21no—
106C22×C3×D4D411yescharacteristic, complemented
107C23×C3×C4—21no—
108C23×C3×C4C2311yescharacteristic
109C22×#67—24no—
110C22×#67—21no—
111C22×#67—21no—
112C22×#67D412yes—
113#1010—24no—
114#1010—24no—
115#1010—24no—
116#1010—24no—
117#1010—24no—
118#1010—24no—
119#1010—24no—
120#1010C2318yes—
121#1009—24no—
122#1009—24no—
123#1009—24no—
124#1009—24no—
125#1009—24no—
126#1009—24no—
127#1009—24no—
128#1009C2318yes—
129D3×#41—28no—
130D3×#41—28no—
131D3×#41—28no—
132D3×#41—28no—
133D3×#41—28no—
134D3×#41—28no—
135D3×#41—28no—
136D3×#41—28no—
137#1007—24no—
138#1007—24no—
139#1007—24no—
140#1007—24no—
141C2×#239—22no—
142C2×#239—22no—
143C2×D3×Q8—22no—
144C2×D3×Q8—22no—
145#1004—28no—
146#1004—28no—
147#1004—24no—
148#1004—24no—
149#1004—24no—
150#1004—24no—
151#1004—28no—
152#1004—28no—
153C2×#237—24no—
154C2×#237—22no—
155C2×#237—22no—
156C2×#237—24no—
157C2×D3×D4—24no—
158C2×D3×D4—22no—
159C2×D3×D4—24no—
160C2×D3×D4—22no—
161C2×#235—24no—
162C2×#235—24no—
163C2×#235—28no—
164C2×#235—28no—
165C2×#235—21no—
166C2×#235—21no—
167C2×#235—21no—
168C2×#235—21no—
169C2×#235—21no—
170C2×#235—21no—
171C2×#235—21no—
172C2×#235—21no—
173C2×#235—21no—
174C2×#235—21no—
175C2×#235—21no—
176C2×#235—21no—
177C2×#235—21no—
178C2×#235—21no—
179C2×#235—28no—
180C2×#235—28no—
181C2×#235—21no—
182C2×#235—21no—
183C2×#235—22no—
184C2×#235—21no—
185C2×#235—21no—
186C2×#235—21no—
187C2×#235—21no—
188C2×#235—21no—
189C2×#235—21no—
190C2×#235—21no—
191C2×#235—21no—
192C2×#235—22no—
193C2×#235D412yes—
194C2×#235D412yes—
195C2×#235D412yescomplemented
196C2×#235D412yescomplemented
197C2×#235D412yescomplemented
198C2×#235C2312yes—
199C2×#235C2312yes—
200C2×#235C2312yes—
201C2×#235C2312yes—
202C2×#235C2312yes—
203C2×#235C2312yes—
204C2×#235C2312yescomplemented
205C22×D12—22no—
206C22×D12D411yescharacteristic, complemented
207C22×D12C2311yescharacteristic
208C22×D12C2311yescharacteristic, complemented
209C22×C4×D3—24no—
210C22×C4×D3—21no—
211C22×C4×D3—21no—
212C22×C4×D3D412yes—
213C22×Dic6—22no—
214C22×Dic6D411yescharacteristic, complemented
215C22×Dic6C2311yescharacteristic
216C22×Dic6C2311yescharacteristic, complemented
217C2×C3×M16—21no—
218C2×C3×M16—21no—
219C2×C3×M16—21no—
220C2×C3×M16C2312yes—
221C2×C3×M16C2312yescomplemented
222C2×C3×M16C2312yescomplemented
223C22×C3×C8—21no—
224C3×#117—21no—
225C3×#117—21no—
226C3×#117C2312yes—
227C3×#117C2312yescomplemented
228C2×C3×C4⋊C4—21no—
229C2×C3×C22⋊C4—21no—
230C2×C3×C42C2312yescomplemented
231#951—24no—
232#951C2318yescomplemented
233#950—28no—
234#950—28no—
235#949—24no—
236#949C2318yescomplemented
237C2×#216—22no—
238#942—24no—
239#942—24no—
240C2×#215—22no—
241C2×#214—22no—
242#932—24no—
243#932—24no—
244C2×#213—22no—
245#930—28no—
246C2×#208—21no—
247C2×#208—21no—
248C2×#208—21no—
249C2×#208C2312yes—
250C2×#208C2312yescomplemented
251C2×#208C2312yescomplemented
252C22×C3⋊C8—21no—
253#909—24no—
254#909—24no—
255#909—24no—
256#909C2318yescomplemented
257#908—24no—
258#908—24no—
259#908—24no—
260#908C2318yescomplemented
261C2×Dic12—22no—
262#904—28no—
263#904—28no—
264C2×D24—22no—
265C2×#204—22no—
266C2×#204—22no—
267#897—24no—
268#897—24no—
269#895—24no—
270#895—24no—
271#886—24no—
272#886—24no—
273#882—24no—
274#882—24no—
275#875C2314yescomplemented
276#875C2314yescomplemented
277#874C2314yescomplemented
278C4×D12—28no—
279#869C2314yescomplemented
280C3×#104C23116yescomplemented
281#824C2318yescomplemented
282#823C2318yescomplemented
283#805C23116yescomplemented
284#585—34no—
285#585—34no—
286#585—62no—
287#585—62no—
288#585—62no—
289#585—62no—
290#585—62no—
291#585—62no—
292C2×2−1+4—32no—
293C2×2−1+4—61no—
294C2×2−1+4—61no—
295C2×H(5,𝔽2)—32no—
296C2×H(5,𝔽2)—62no—
297C2×H(5,𝔽2)—61no—
298C2×H(5,𝔽2)—61no—
299C22×#41—31no—
300C22×#41—31no—
301C22×#41—31no—
302C22×#41—62no—
303C22×#41—62no—
304C22×#41—62no—
305C22×#41C2×D311yescharacteristic
306#575—34no—
307#575—34no—
308#575—34no—
309#575—34no—
310#575—62no—
311#575—62no—
312#575—62no—
313#575—62no—
314C2×#137—32no—
315C2×#137—32no—
316C2×#137—61no—
317C2×#137—61no—
318C2×AGL(1,ℤ/8)—32no—
319C2×AGL(1,ℤ/8)—32no—
320C2×AGL(1,ℤ/8)—61no—
321C2×AGL(1,ℤ/8)—61no—
322C2×#135—62no—
323C2×#135—62no—
324C22×M16—31no—
325C22×M16C2×D311yescharacteristic, complemented
326#537—62no—
327#536—32no—
328#536—32no—
329#535—32no—
330#535—32no—
331#534—62no—
332#532—34no—
333#525—62no—
334#525—62no—
335C2×#117C2×D311yescharacteristic, complemented
336#456—316no—
337#455—316no—
338#454—316no—
339#453—316no—
340#421—34no—
341#421—34no—
342#421C2×D314yescomplemented
343#421C2×D314yescomplemented
344C2×#104—34no—
345C2×#104C2×D314yescomplemented
346#413—34no—
347#413—34no—
348C2×#101—32no—
349C2×#100—32no—
350C24×C3—21no—
351C24×C3C2×D411yescharacteristic
352C23×D3—24no—
353C23×D3—21no—
354C23×D3—21no—
355C23×D3C2×D412yes—
356C3×#41—22no—
357C3×#41—22no—
358C3×#41—22no—
359C3×#41—22no—
360C3×#41—22no—
361C3×#41—22no—
362C3×#41—22no—
363C3×#41—22no—
364C3×#41—22no—
365C3×#41—22no—
366C3×#41—22no—
367C3×#41—22no—
368C3×#41C2×D414yes—
369C3×#41C2×D414yes—
370C3×#41C2×D414yes—
371C3×#41C2414yes—
372C2×C3×Q8—21no—
373C2×C3×Q8—21no—
374C2×C3×Q8—21no—
375C2×C3×Q8C2×D412yes—
376C2×C3×Q8C2×D412yes—
377C2×C3×Q8C2×D412yes—
378C2×C3×D4—22no—
379C2×C3×D4—22no—
380C2×C3×D4—22no—
381C2×C3×D4—22no—
382C2×C3×D4—22no—
383C2×C3×D4—22no—
384C2×C3×D4—21no—
385C2×C3×D4—21no—
386C2×C3×D4—21no—
387C2×C3×D4C2×D412yes—
388C2×C3×D4C2×D412yes—
389C2×C3×D4C2×D412yes—
390C22×C3×C4—21no—
391C22×C3×C4—22no—
392C22×C3×C4—22no—
393C22×C3×C4—22no—
394C22×C3×C4—22no—
395C22×C3×C4—22no—
396C22×C3×C4—22no—
397C22×C3×C4—22no—
398C22×C3×C4C2×D411yescharacteristic
399C22×C3×C4C2×D411yescharacteristic
400C22×C3×C4C2×D411yescharacteristic
401C22×C3×C4C2×D411yescharacteristic
402C22×C3×C4C2×D411yescharacteristic
403C22×C3×C4C2×D411yescharacteristic
404C22×C3×C4C2×D411yescharacteristic
405C22×C3×C4C2×D411yescharacteristic
406C22×C3×C4C2×D411yescharacteristic
407C22×C3×C4C2×D411yescharacteristic
408C22×C3×C4C2×D411yescharacteristic
409C22×C3×C4C2411yescharacteristic
410C22×C3×C4C2411yescharacteristic
411C22×C3×C4C2411yescharacteristic
412C2×#67—24no—
413C2×#67—24no—
414C2×#67—216no—
415C2×#67—216no—
416C2×#67—22no—
417C2×#67—22no—
418C2×#67—22no—
419C2×#67—22no—
420C2×#67—22no—
421C2×#67—22no—
422C2×#67—22no—
423C2×#67—22no—
424C2×#67—22no—
425C2×#67—22no—
426C2×#67—22no—
427C2×#67—22no—
428C2×#67—41no—
429C2×#67—41no—
430C2×#67—41no—
431C2×#67—41no—
432C2×#67C2×D414yes—
433C2×#67C2×D414yes—
434C22×Dic3—24no—
435C22×Dic3—21no—
436C22×Dic3—21no—
437C22×Dic3C2×D412yes—
438#239—28no—
439#239—28no—
440#239—28no—
441#239—28no—
442D3×Q8—28no—
443D3×Q8—28no—
444D3×Q8—28no—
445D3×Q8—28no—
446#237—216no—
447#237—216no—
448#237—216no—
449#237—28no—
450#237—28no—
451#237—28no—
452#237—28no—
453#237—216no—
454D3×D4—216no—
455D3×D4—216no—
456D3×D4—216no—
457D3×D4—28no—
458D3×D4—28no—
459D3×D4—28no—
460D3×D4—216no—
461D3×D4—28no—
462#235—216no—
463#235—216no—
464#235—216no—
465#235—216no—
466#235—28no—
467#235—28no—
468#235—22no—
469#235—22no—
470#235—22no—
471#235—22no—
472#235—22no—
473#235—22no—
474#235—22no—
475#235—22no—
476#235—22no—
477#235—22no—
478#235—22no—
479#235—22no—
480#235—22no—
481#235—22no—
482#235—22no—
483#235—22no—
484#235—22no—
485#235—22no—
486#235—22no—
487#235—22no—
488#235—22no—
489#235—22no—
490#235—22no—
491#235—22no—
492#235—22no—
493#235—22no—
494#235—22no—
495#235—22no—
496#235—28no—
497#235—22no—
498#235—22no—
499#235—22no—
500#235—22no—
501#235—22no—
502#235—22no—
503#235—22no—
504#235—22no—
505#235—28no—
506#235—41no—
507#235—41no—
508#235—41no—
509#235—41no—
510#235—41no—
511#235—41no—
512#235—41no—
513#235—41no—
514#235C2×D414yes—
515#235C2×D414yes—
516#235C2×D414yes—
517#235C2414yes—
518C2×D12—24no—
519C2×D12—28no—
520C2×D12—21no—
521C2×D12—21no—
522C2×D12—21no—
523C2×D12—21no—
524C2×D12—21no—
525C2×D12—21no—
526C2×D12—21no—
527C2×D12—28no—
528C2×D12—21no—
529C2×D12—21no—
530C2×D12—21no—
531C2×D12—21no—
532C2×D12—21no—
533C2×D12—28no—
534C2×D12C2×D412yes—
535C2×D12C2×D412yes—
536C2×D12C2×D412yes—
537C2×D12C2×D412yes—
538C2×D12C2412yes—
539C2×D12C2412yes—
540C2×C4×D3—24no—
541C2×C4×D3—24no—
542C2×C4×D3—216no—
543C2×C4×D3—216no—
544C2×C4×D3—22no—
545C2×C4×D3—22no—
546C2×C4×D3—22no—
547C2×C4×D3—22no—
548C2×C4×D3—22no—
549C2×C4×D3—22no—
550C2×C4×D3—22no—
551C2×C4×D3—22no—
552C2×C4×D3—22no—
553C2×C4×D3—22no—
554C2×C4×D3—22no—
555C2×C4×D3—22no—
556C2×C4×D3—41no—
557C2×C4×D3—41no—
558C2×C4×D3—41no—
559C2×C4×D3—41no—
560C2×C4×D3C2×D414yes—
561C2×C4×D3C2×D414yes—
562C2×Dic6—24no—
563C2×Dic6—28no—
564C2×Dic6—21no—
565C2×Dic6—21no—
566C2×Dic6—21no—
567C2×Dic6—21no—
568C2×Dic6—21no—
569C2×Dic6—21no—
570C2×Dic6—21no—
571C2×Dic6—28no—
572C2×Dic6—21no—
573C2×Dic6—21no—
574C2×Dic6—21no—
575C2×Dic6—21no—
576C2×Dic6—21no—
577C2×Dic6C2×D412yes—
578C2×Dic6C2×D412yes—
579C2×Dic6C2×D412yes—
580C2×Dic6C2×D412yes—
581C2×Dic6C2412yes—
582C2×Dic6C2412yes—
583C3×M16—22no—
584C3×M16—22no—
585C3×M16—22no—
586C3×M16C2414yes—
587C2×C3×C8—22no—
588C2×C3×C8—22no—
589C2×C3×C8—22no—
590C3×C4⋊C4—22no—
591C3×C4⋊C4—22no—
592C3×C22⋊C4—22no—
593C3×C22⋊C4—22no—
594C3×C42—22no—
595C3×C42C2414yes—
596#216—28no—
597#215—28no—
598#214—28no—
599#213—28no—
600(C2×D3)⋊C4—28no—
601(C2×D3)⋊C4—28no—
602C4⋊Dic3—28no—
603#208—22no—
604#208—22no—
605#208—22no—
606#208C2414yes—
607C2×C3⋊C8—22no—
608C2×C3⋊C8—22no—
609C2×C3⋊C8—22no—
610Dic12—28no—
611D24—28no—
612#204—28no—
613#204—28no—
6142−1+4—38no—
6152−1+4—64no—
6162−1+4—64no—
6172−1+4—64no—
6182−1+4—64no—
6192−1+4—64no—
6202−1+4—64no—
6212−1+4—64no—
6222−1+4—64no—
6232−1+4—64no—
6242−1+4—64no—
6252−1+4—64no—
626H(5,𝔽2)—38no—
627H(5,𝔽2)—68no—
628H(5,𝔽2)—68no—
629H(5,𝔽2)—68no—
630H(5,𝔽2)—68no—
631H(5,𝔽2)—64no—
632H(5,𝔽2)—64no—
633H(5,𝔽2)—64no—
634H(5,𝔽2)—64no—
635H(5,𝔽2)—64no—
636H(5,𝔽2)—64no—
637H(5,𝔽2)—64no—
638H(5,𝔽2)—64no—
639H(5,𝔽2)—64no—
640H(5,𝔽2)—64no—
641H(5,𝔽2)—64no—
642C2×#41—21no—
643C2×#41—21no—
644C2×#41—21no—
645C2×#41—21no—
646C2×#41—21no—
647C2×#41—21no—
648C2×#41—32no—
649C2×#41—32no—
650C2×#41—32no—
651C2×#41—32no—
652C2×#41—32no—
653C2×#41—32no—
654C2×#41—32no—
655C2×#41—32no—
656C2×#41—32no—
657C2×#41—32no—
658C2×#41—32no—
659C2×#41—32no—
660C2×#41—62no—
661C2×#41—62no—
662C2×#41—68no—
663C2×#41—68no—
664C2×#41—64no—
665C2×#41—64no—
666C2×#41—68no—
667C2×#41—68no—
668C2×#41—64no—
669C2×#41—68no—
670C2×#41—68no—
671C2×#41—64no—
672C2×#41—62no—
673C2×#41—62no—
674C2×#41—68no—
675C2×#41—68no—
676C2×#41—68no—
677C2×#41—68no—
678C2×#41—68no—
679C2×#41—68no—
680C2×#41—62no—
681C2×#41—62no—
682C2×#41—61no—
683C2×#41—61no—
684C2×#41—61no—
685C2×#41—61no—
686C2×#41—61no—
687C2×#41—61no—
688C2×#41—61no—
689C2×#41—61no—
690C2×#41—61no—
691C2×#41—61no—
692C2×#41—61no—
693C2×#41—61no—
694C2×#41—61no—
695C2×#41—61no—
696C2×#41—61no—
697C2×#41—61no—
698C2×#41—61no—
699C2×#41—61no—
700C2×#41—61no—
701C2×#41—61no—
702C2×#41—61no—
703C2×#41—61no—
704C2×#41—61no—
705C2×#41—61no—
706C2×#41D1212yescomplemented
707C2×#41D1212yescomplemented
708C2×#41D1212yescomplemented
709C2×#41C22×D312yes—
710C2×#41C22×D312yes—
711C2×#41C22×D312yes—
712C22×Q8—31no—
713C22×Q8—31no—
714C22×Q8—31no—
715C22×Q8—62no—
716C22×Q8—62no—
717C22×Q8—62no—
718C22×Q8D1211yescharacteristic, complemented
719C22×D4—21no—
720C22×D4—32no—
721C22×D4—31no—
722C22×D4—31no—
723C22×D4—31no—
724C22×D4—62no—
725C22×D4—64no—
726C22×D4—64no—
727C22×D4—62no—
728C22×D4—64no—
729C22×D4—61no—
730C22×D4—62no—
731C22×D4—61no—
732C22×D4D1211yescharacteristic, complemented
733C23×C4—21no—
734C23×C4—32no—
735C23×C4—64no—
736C23×C4—61no—
737C23×C4—61no—
738C23×C4C22×D311yescharacteristic
739#137—38no—
740#137—38no—
741#137—64no—
742#137—64no—
743#137—64no—
744#137—64no—
745#137—64no—
746#137—64no—
747AGL(1,ℤ/8)—38no—
748AGL(1,ℤ/8)—38no—
749AGL(1,ℤ/8)—64no—
750AGL(1,ℤ/8)—64no—
751AGL(1,ℤ/8)—64no—
752AGL(1,ℤ/8)—64no—
753AGL(1,ℤ/8)—64no—
754AGL(1,ℤ/8)—64no—
755#135—68no—
756#135—68no—
757#135—68no—
758#135—68no—
759C2×Q16—62no—
760C2×Q16—62no—
761C2×SD16—62no—
762C2×SD16—62no—
763C2×SD16—62no—
764C2×SD16—62no—
765C2×D8—62no—
766C2×D8—62no—
767C2×M16—21no—
768C2×M16—21no—
769C2×M16—21no—
770C2×M16—32no—
771C2×M16—32no—
772C2×M16—32no—
773C2×M16—61no—
774C2×M16—61no—
775C2×M16—61no—
776C2×M16C22×D312yes—
777C2×M16C22×D312yescomplemented
778C2×M16C22×D312yescomplemented
779C22×C8—21no—
780C22×C8—61no—
781C4⋊Q8—34no—
782#127—34no—
783#124—34no—
784#124—34no—
785#123—64no—
786#123—64no—
787C22⋊Q8—64no—
788C22⋊Q8—64no—
789#121—64no—
790#121—64no—
791#121—68no—
792#120—64no—
793#120—64no—
794C4×D4—68no—
795#117—21no—
796#117—21no—
797#117C22×D312yes—
798#117C22×D312yescomplemented
799C2×C4⋊C4—21no—
800C2×C22⋊C4—21no—
801C2×C42C22×D312yescomplemented
802#104—316no—
803#104C22×D3116yescomplemented
804#101—38no—
805#100—38no—
806C23×C3—22no—
807C23×C3—22no—
808C23×C3—22no—
809C23×C3—81no—
810C23×C3—82no—
811C23×C3#12011yescharacteristic
812C23×C3#12011yescharacteristic
813C23×C3#12011yescharacteristic
814C23×C3#12011yescharacteristic
815C23×C3C22×D411yescharacteristic
816C23×C3C22×D411yescharacteristic
817C23×C3C22×D411yescharacteristic
818C22×D3—22no—
819C22×D3—22no—
820C22×D3—216no—
821C22×D3—22no—
822C22×D3—22no—
823C22×D3—22no—
824C22×D3—22no—
825C22×D3—41no—
826C22×D3—41no—
827C22×D3—82no—
828C22×D3—82no—
829C22×D3—88no—
830C22×D3—82no—
831C22×D3C22×D414yes—
832C3×Q8—22no—
833C3×Q8—22no—
834C3×Q8—22no—
835C3×Q8C22×D414yes—
836C3×D4—24no—
837C3×D4—24no—
838C3×D4—24no—
839C3×D4—24no—
840C3×D4—22no—
841C3×D4—22no—
842C3×D4—22no—
843C3×D4C22×D414yes—
844C2×C3×C4—22no—
845C2×C3×C4—22no—
846C2×C3×C4—22no—
847C2×C3×C4—24no—
848C2×C3×C4—24no—
849C2×C3×C4—24no—
850C2×C3×C4—24no—
851C2×C3×C4—24no—
852C2×C3×C4—82no—
853C2×C3×C4#12011yescharacteristic
854C2×C3×C4#12011yescharacteristic
855C2×C3×C4#12011yescharacteristic
856C2×C3×C4#12011yescharacteristic
857C2×C3×C4#12011yescharacteristic
858C2×C3×C4#12011yescharacteristic
859C2×C3×C4#12011yescharacteristic
860C2×C3×C4#12011yescharacteristic
861C2×C3×C4#12011yescharacteristic
862C2×C3×C4#12011yescharacteristic
863C2×C3×C4#12011yescharacteristic
864C2×C3×C4#12011yescharacteristic
865C2×C3×C4C22×D411yescharacteristic
866C2×C3×C4C22×D411yescharacteristic
867C2×C3×C4C22×D411yescharacteristic
868C2×C3×C4C22×D411yescharacteristic
869C2×C3×C4C22×D411yescharacteristic
870C2×C3×C4C22×D411yescharacteristic
871C2×C3×C4C22×D411yescharacteristic
872C2×C3×C4C22×D411yescharacteristic
873C2×C3×C4C22×D411yescharacteristic
874C2×C3×C4C22×D411yescharacteristic
875C2×C3×C4C22×D411yescharacteristic
876C2×C3×C4C22×D411yescharacteristic
877C2×C3×C4C22×D411yescharacteristic
878C2×C3×C4C22×D411yescharacteristic
879C2×C3×C4C22×D411yescharacteristic
880C2×C3×C4C2511yescharacteristic
881#67—216no—
882#67—216no—
883#67—24no—
884#67—24no—
885#67—24no—
886#67—24no—
887#67—24no—
888#67—24no—
889#67—24no—
890#67—24no—
891#67—42no—
892#67—42no—
893#67—42no—
894#67—42no—
895C2×Dic3—216no—
896C2×Dic3—22no—
897C2×Dic3—22no—
898C2×Dic3—22no—
899C2×Dic3—22no—
900C2×Dic3—22no—
901C2×Dic3—22no—
902C2×Dic3—41no—
903C2×Dic3—41no—
904C2×Dic3C22×D414yes—
905D12—216no—
906D12—22no—
907D12—22no—
908D12—22no—
909D12—22no—
910D12—22no—
911D12—22no—
912D12—22no—
913D12—22no—
914D12—22no—
915D12—41no—
916D12—41no—
917D12—88no—
918D12C22×D414yes—
919C4×D3—216no—
920C4×D3—216no—
921C4×D3—24no—
922C4×D3—24no—
923C4×D3—24no—
924C4×D3—24no—
925C4×D3—24no—
926C4×D3—24no—
927C4×D3—24no—
928C4×D3—24no—
929C4×D3—42no—
930C4×D3—42no—
931C4×D3—42no—
932C4×D3—42no—
933Dic6—216no—
934Dic6—22no—
935Dic6—22no—
936Dic6—22no—
937Dic6—22no—
938Dic6—22no—
939Dic6—22no—
940Dic6—22no—
941Dic6—22no—
942Dic6—22no—
943Dic6—41no—
944Dic6—41no—
945Dic6C22×D414yes—
946C3×C8—24no—
947C3⋊C8—24no—
948C24—21no—
949C24—32no—
950C24—64no—
951C24—61no—
952C24—61no—
953C24D3×D411yescharacteristic
954#41—22no—
955#41—22no—
956#41—22no—
957#41—22no—
958#41—22no—
959#41—22no—
960#41—22no—
961#41—22no—
962#41—22no—
963#41—22no—
964#41—22no—
965#41—22no—
966#41—34no—
967#41—34no—
968#41—34no—
969#41—34no—
970#41—68no—
971#41—68no—
972#41—616no—
973#41—616no—
974#41—616no—
975#41—616no—
976#41—68no—
977#41—68no—
978#41—616no—
979#41—616no—
980#41—616no—
981#41—616no—
982#41—68no—
983#41—68no—
984#41—68no—
985#41—68no—
986#41—68no—
987#41—68no—
988#41—68no—
989#41—68no—
990#41—62no—
991#41—62no—
992#41—62no—
993#41—62no—
994#41—62no—
995#41—62no—
996#41—62no—
997#41—62no—
998#41—62no—
999#41—62no—
1000#41—62no—
1001#41—62no—
1002#41—62no—
1003#41—62no—
1004#41—62no—
1005#41—62no—
1006#41—62no—
1007#41—62no—
1008#41—62no—
1009#41—62no—
1010#41—62no—
1011#41—62no—
1012#41—62no—
1013#41—62no—
1014#41—62no—
1015#41—62no—
1016#41—62no—
1017#41—62no—
1018#41—62no—
1019#41—62no—
1020#41—62no—
1021#41—62no—
1022#41—62no—
1023#41—62no—
1024#41—62no—
1025#41—62no—
1026#41—121no—
1027#41—121no—
1028#41—121no—
1029#41—121no—
1030#41—121no—
1031#41—121no—
1032#41—121no—
1033#41—121no—
1034#41C2×D1214yes—
1035#41C2×D1214yes—
1036#41C2×D1214yes—
1037#41C23×D314yes—
1038C2×Q8—21no—
1039C2×Q8—21no—
1040C2×Q8—21no—
1041C2×Q8—32no—
1042C2×Q8—32no—
1043C2×Q8—32no—
1044C2×Q8—32no—
1045C2×Q8—32no—
1046C2×Q8—32no—
1047C2×Q8—68no—
1048C2×Q8—64no—
1049C2×Q8—68no—
1050C2×Q8—68no—
1051C2×Q8—68no—
1052C2×Q8—68no—
1053C2×Q8—68no—
1054C2×Q8—61no—
1055C2×Q8—61no—
1056C2×Q8—61no—
1057C2×Q8—61no—
1058C2×Q8—61no—
1059C2×Q8—61no—
1060C2×Q8—61no—
1061C2×Q8—61no—
1062C2×Q8—61no—
1063C2×Q8—61no—
1064C2×Q8—61no—
1065C2×Q8—61no—
1066C2×Q8C2×D1212yes—
1067C2×Q8C2×D1212yes—
1068C2×Q8C2×D1212yes—
1069C2×D4—22no—
1070C2×D4—22no—
1071C2×D4—22no—
1072C2×D4—22no—
1073C2×D4—22no—
1074C2×D4—22no—
1075C2×D4—21no—
1076C2×D4—21no—
1077C2×D4—21no—
1078C2×D4—34no—
1079C2×D4—34no—
1080C2×D4—32no—
1081C2×D4—32no—
1082C2×D4—32no—
1083C2×D4—32no—
1084C2×D4—32no—
1085C2×D4—32no—
1086C2×D4—68no—
1087C2×D4—64no—
1088C2×D4—68no—
1089C2×D4—68no—
1090C2×D4—616no—
1091C2×D4—616no—
1092C2×D4—616no—
1093C2×D4—616no—
1094C2×D4—68no—
1095C2×D4—68no—
1096C2×D4—68no—
1097C2×D4—64no—
1098C2×D4—64no—
1099C2×D4—616no—
1100C2×D4—616no—
1101C2×D4—62no—
1102C2×D4—62no—
1103C2×D4—62no—
1104C2×D4—62no—
1105C2×D4—62no—
1106C2×D4—62no—
1107C2×D4—62no—
1108C2×D4—62no—
1109C2×D4—62no—
1110C2×D4—62no—
1111C2×D4—68no—
1112C2×D4—62no—
1113C2×D4—62no—
1114C2×D4—61no—
1115C2×D4—61no—
1116C2×D4—61no—
1117C2×D4—61no—
1118C2×D4—61no—
1119C2×D4—61no—
1120C2×D4—61no—
1121C2×D4—61no—
1122C2×D4—61no—
1123C2×D4—61no—
1124C2×D4—61no—
1125C2×D4—61no—
1126C2×D4—121no—
1127C2×D4—121no—
1128C2×D4—121no—
1129C2×D4—121no—
1130C2×D4C2×D1212yes—
1131C2×D4C2×D1212yes—
1132C2×D4C2×D1212yes—
1133C22×C4—21no—
1134C22×C4—22no—
1135C22×C4—22no—
1136C22×C4—22no—
1137C22×C4—22no—
1138C22×C4—22no—
1139C22×C4—22no—
1140C22×C4—22no—
1141C22×C4—32no—
1142C22×C4—34no—
1143C22×C4—34no—
1144C22×C4—64no—
1145C22×C4—64no—
1146C22×C4—616no—
1147C22×C4—616no—
1148C22×C4—64no—
1149C22×C4—61no—
1150C22×C4—62no—
1151C22×C4—62no—
1152C22×C4—62no—
1153C22×C4—62no—
1154C22×C4—62no—
1155C22×C4—62no—
1156C22×C4—62no—
1157C22×C4—62no—
1158C22×C4—62no—
1159C22×C4—62no—
1160C22×C4—61no—
1161C22×C4—62no—
1162C22×C4—62no—
1163C22×C4—121no—
1164C22×C4—121no—
1165C22×C4—121no—
1166C22×C4—121no—
1167C22×C4C2×D1211yescharacteristic
1168C22×C4C2×D1211yescharacteristic
1169C22×C4C2×D1211yescharacteristic
1170C22×C4C2×D1211yescharacteristic
1171C22×C4D3×D411yescharacteristic
1172C22×C4D3×D411yescharacteristic
1173C22×C4D3×D411yescharacteristic
1174C22×C4D3×D411yescharacteristic
1175C22×C4D3×D411yescharacteristic
1176C22×C4D3×D411yescharacteristic
1177C22×C4D3×D411yescharacteristic
1178C22×C4C23×D311yescharacteristic
1179C22×C4C23×D311yescharacteristic
1180C22×C4C23×D311yescharacteristic
1181Q16—68no—
1182Q16—68no—
1183SD16—68no—
1184SD16—68no—
1185SD16—68no—
1186SD16—68no—
1187D8—68no—
1188D8—68no—
1189M16—22no—
1190M16—22no—
1191M16—22no—
1192M16—34no—
1193M16—62no—
1194M16—62no—
1195M16—62no—
1196M16C23×D314yes—
1197C2×C8—22no—
1198C2×C8—22no—
1199C2×C8—22no—
1200C2×C8—62no—
1201C2×C8—62no—
1202C2×C8—62no—
1203C4⋊C4—22no—
1204C4⋊C4—22no—
1205C4⋊C4—68no—
1206C22⋊C4—22no—
1207C22⋊C4—22no—
1208C22⋊C4—68no—
1209C22⋊C4—68no—
1210C42—22no—
1211C42C23×D314yes—
1212C22×C3—24no—
1213C22×C3—41no—
1214C22×C3—41no—
1215C22×C3—41no—
1216C22×C3—41no—
1217C22×C3—41no—
1218C22×C3—41no—
1219C22×C3—41no—
1220C22×C3—44no—
1221C22×C3—82no—
1222C22×C3—82no—
1223C22×C3C2×#12011yescharacteristic
1224C22×C3C2×#12011yescharacteristic
1225C22×C3C2×#12011yescharacteristic
1226C22×C3C2×#12011yescharacteristic
1227C22×C3C2×#12011yescharacteristic
1228C22×C3C2×#12011yescharacteristic
1229C22×C3C23×D411yescharacteristic
1230C2×D3—24no—
1231C2×D3—24no—
1232C2×D3—44no—
1233C2×D3—44no—
1234C2×D3—44no—
1235C2×D3—44no—
1236C2×D3—42no—
1237C2×D3—82no—
1238C2×D3—82no—
1239C2×D3—82no—
1240C2×D3—816no—
1241C2×D3—82no—
1242C2×D3—82no—
1243C3×C4—24no—
1244C3×C4—44no—
1245C3×C4C2×#12011yescharacteristic
1246C3×C4C2×#12011yescharacteristic
1247C3×C4C2×#12011yescharacteristic
1248C3×C4C2×#12011yescharacteristic
1249C3×C4C2×#12011yescharacteristic
1250C3×C4C2×#12011yescharacteristic
1251C3×C4C23×D411yescharacteristic
1252C3×C4C23×D411yescharacteristic
1253Dic3—24no—
1254Dic3—24no—
1255Dic3—42no—
1256C23—22no—
1257C23—22no—
1258C23—22no—
1259C23—34no—
1260C23—616no—
1261C23—62no—
1262C23—62no—
1263C23—62no—
1264C23—62no—
1265C23—62no—
1266C23—62no—
1267C23—81no—
1268C23—82no—
1269C23—121no—
1270C23—121no—
1271C23—242no—
1272C23—242no—
1273C23—242no—
1274C23—248no—
1275C23#88211yescharacteristic
1276C23#88211yescharacteristic
1277C23#88211yescharacteristic
1278C23#88211yescharacteristic
1279C23C2×D3×D411yescharacteristic
1280C23C2×D3×D411yescharacteristic
1281C23C2×D3×D411yescharacteristic
1282Q8—22no—
1283Q8—22no—
1284Q8—22no—
1285Q8—34no—
1286Q8—616no—
1287Q8—62no—
1288Q8—62no—
1289Q8—62no—
1290Q8—62no—
1291Q8—62no—
1292Q8—62no—
1293Q8—62no—
1294Q8—62no—
1295Q8—62no—
1296Q8—121no—
1297Q8—121no—
1298Q8C22×D1214yes—
1299D4—24no—
1300D4—24no—
1301D4—24no—
1302D4—24no—
1303D4—22no—
1304D4—22no—
1305D4—22no—
1306D4—34no—
1307D4—616no—
1308D4—616no—
1309D4—616no—
1310D4—64no—
1311D4—64no—
1312D4—64no—
1313D4—64no—
1314D4—64no—
1315D4—64no—
1316D4—64no—
1317D4—64no—
1318D4—62no—
1319D4—62no—
1320D4—62no—
1321D4—62no—
1322D4—62no—
1323D4—62no—
1324D4—62no—
1325D4—62no—
1326D4—62no—
1327D4—122no—
1328D4—122no—
1329D4—122no—
1330D4—122no—
1331D4—121no—
1332D4—121no—
1333D4—248no—
1334D4C22×D1214yes—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—34no—
1344C2×C4—616no—
1345C2×C4—616no—
1346C2×C4—616no—
1347C2×C4—62no—
1348C2×C4—62no—
1349C2×C4—62no—
1350C2×C4—62no—
1351C2×C4—62no—
1352C2×C4—64no—
1353C2×C4—64no—
1354C2×C4—64no—
1355C2×C4—64no—
1356C2×C4—64no—
1357C2×C4—64no—
1358C2×C4—64no—
1359C2×C4—64no—
1360C2×C4—62no—
1361C2×C4—82no—
1362C2×C4—121no—
1363C2×C4—121no—
1364C2×C4—122no—
1365C2×C4—122no—
1366C2×C4—122no—
1367C2×C4—122no—
1368C2×C4#88211yescharacteristic
1369C2×C4#88211yescharacteristic
1370C2×C4#88211yescharacteristic
1371C2×C4#88211yescharacteristic
1372C2×C4#88211yescharacteristic
1373C2×C4#88211yescharacteristic
1374C2×C4#88211yescharacteristic
1375C2×C4#88211yescharacteristic
1376C2×C4#88211yescharacteristic
1377C2×C4#88211yescharacteristic
1378C2×C4#88211yescharacteristic
1379C2×C4#88211yescharacteristic
1380C2×C4C22×D1211yescharacteristic
1381C2×C4C22×D1211yescharacteristic
1382C2×C4C22×D1211yescharacteristic
1383C2×C4C22×D1211yescharacteristic
1384C2×C4C22×D1211yescharacteristic
1385C2×C4C22×D1211yescharacteristic
1386C2×C4C2×D3×D411yescharacteristic
1387C2×C4C2×D3×D411yescharacteristic
1388C2×C4C2×D3×D411yescharacteristic
1389C2×C4C2×D3×D411yescharacteristic
1390C2×C4C2×D3×D411yescharacteristic
1391C2×C4C2×D3×D411yescharacteristic
1392C2×C4C2×D3×D411yescharacteristic
1393C2×C4C2×D3×D411yescharacteristic
1394C2×C4C2×D3×D411yescharacteristic
1395C2×C4C24×D311yescharacteristic
1396C8—24no—
1397C8—64no—
1398C2×C3—21no—
1399C2×C3—21no—
1400C2×C3—21no—
1401C2×C3—21no—
1402C2×C3—21no—
1403C2×C3—21no—
1404C2×C3—21no—
1405C2×C3—44no—
1406C2×C3C22×#12011yescharacteristic
1407D3—44no—
1408D3—44no—
1409D3—82no—
1410C22—24no—
1411C22—41no—
1412C22—41no—
1413C22—41no—
1414C22—41no—
1415C22—41no—
1416C22—41no—
1417C22—41no—
1418C22—44no—
1419C22—64no—
1420C22—64no—
1421C22—82no—
1422C22—82no—
1423C22—124no—
1424C22—124no—
1425C22—124no—
1426C22—124no—
1427C22—122no—
1428C22—242no—
1429C22—242no—
1430C22—242no—
1431C22—242no—
1432C22—242no—
1433C22—2416no—
1434C22C2×#88211yescharacteristic
1435C22C2×#88211yescharacteristic
1436C22C2×#88211yescharacteristic
1437C22C2×#88211yescharacteristic
1438C22C2×#88211yescharacteristic
1439C22C2×#88211yescharacteristic
1440C22C22×D3×D411yescharacteristic
1441C4—24no—
1442C4—44no—
1443C4—64no—
1444C4—64no—
1445C4—122no—
1446C4C2×#88211yescharacteristic
1447C4C2×#88211yescharacteristic
1448C4C2×#88211yescharacteristic
1449C4C2×#88211yescharacteristic
1450C4C2×#88211yescharacteristic
1451C4C2×#88211yescharacteristic
1452C4C23×D1211yescharacteristic
1453C4C22×D3×D411yescharacteristic
1454C3#6038711yescharacteristic, complemented, Sylow
1455C2—21no—
1456C2—21no—
1457C2—21no—
1458C2—21no—
1459C2—21no—
1460C2—21no—
1461C2—21no—
1462C2—44no—
1463C2—124no—
1464C2—124no—
1465C2—242no—
1466C2C22×#88211yescharacteristic
subgroupG/H
centerC4C2×#882
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#421C2
socleC2×C3C22×#120
hypercenterC2×#421D3
hypocenterC3#60387
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×#5964C2semidirect
2. C2×#5822C2semidirect
3. C2×#5748C2semidirect
4. #85735C2semidirect
5. C2×C3×#421C2semidirect
6. C2×#5132C2semidirect
7. C2×#5005C2semidirect
8. #78996C2semidirect
9. #78995C2semidirect
10. #78994C2semidirect
11. #78993C2semidirect
12. #78986C2semidirect
22. #5964C22semidirect
24. C2×#1010C22semidirect
26. C2×#1009C22semidirect
35. C22×#235C22semidirect
36. C22×C3×M16C22semidirect
37. C2×C3×#117C22semidirect
38. C2×#951C22semidirect
41. #5822C22semidirect
42. #5822C22semidirect
44. C2×#949C22semidirect
47. C22×#208C22semidirect
50. #5748C22semidirect
51. #5748C22semidirect
53. C2×#909C22semidirect
55. C2×#908C22semidirect
57. #5526C22semidirect
58. #5526C22semidirect
59. #5525C22semidirect
60. #5525C22semidirect
65. #5477C22semidirect
66. C3×#421C22semidirect
67. C3×#421C22semidirect
68. C2×C3×#104C22semidirect
69. C2×#824C22semidirect
70. #5132C22semidirect
71. #5132C22semidirect
72. C2×#823C22semidirect
73. #5005C22semidirect
74. #5005C22semidirect
75. C2×#805C22semidirect
76. #4827C22semidirect
77. #4826C22semidirect
78. #4825C22semidirect
79. #4822C22semidirect
90. C2×#421D3semidirect
98. C2×C3×#41D4semidirect
99. C2×C3×#41D4semidirect
100. C2×C3×#41D4semidirect
104. C22×C3×Q8D4semidirect
106. C22×C3×D4D4semidirect
195. C2×#235D4semidirect
196. C2×#235D4semidirect
197. C2×#235D4semidirect
204. C2×#235C23semidirect
206. C22×D12D4semidirect
208. C22×D12C23semidirect
214. C22×Dic6D4semidirect
216. C22×Dic6C23semidirect
221. C2×C3×M16C23semidirect
222. C2×C3×M16C23semidirect
227. C3×#117C23semidirect
230. C2×C3×C42C23semidirect
232. #951C23semidirect
236. #949C23semidirect
250. C2×#208C23semidirect
251. C2×#208C23semidirect
256. #909C23semidirect
260. #908C23semidirect
275. #875C23semidirect
276. #875C23semidirect
277. #874C23semidirect
279. #869C23semidirect
280. C3×#104C23semidirect
281. #824C23semidirect
282. #823C23semidirect
283. #805C23semidirect
325. C22×M16C2×D3semidirect
335. C2×#117C2×D3semidirect
342. #421C2×D3semidirect
343. #421C2×D3semidirect
345. C2×#104C2×D3semidirect
706. C2×#41D12semidirect
707. C2×#41D12semidirect
708. C2×#41D12semidirect
718. C22×Q8D12semidirect
732. C22×D4D12semidirect
777. C2×M16C22×D3semidirect
778. C2×M16C22×D3semidirect
798. #117C22×D3semidirect
801. C2×C42C22×D3semidirect
803. #104C22×D3semidirect
1454. C3#60387semidirect

Maximal subgroups

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

subgroupindex
C2×#59642
C2×#58222
C2×#57482
#857352
C2×C3×#4212
C2×#51322
C2×#50052
#789962
#789952
#789942
#789932
#789862
#603873