Finite Group Databasebeta

← #11661705

Subgroups — #11661705

Order 768.

4810 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5964C211yesmaximal, characteristic, complemented
2C2×C3×#575C211yesmaximal, characteristic, complemented
3C2×#5833C211yesmaximal, characteristic, complemented
4C2×#5822C211yesmaximal, characteristic, complemented
5C2×#5232C211yesmaximal, characteristic, complemented
6#83984C214yesmaximal, complemented
7#83981C214yesmaximal, complemented
8#83949C214yesmaximal, complemented
9#83946C214yesmaximal, complemented
10#83913C214yesmaximal, complemented
11#83912C214yesmaximal, complemented
12C2×#5133C211yesmaximal, characteristic, complemented
13#83762C211yesmaximal, characteristic, complemented
14#60371—31nomaximal, Sylow
15C22×C3×#41C2211yescharacteristic
16C22×C3×#41C2211yescharacteristic, complemented
17#5964—28no—
18#5964—28no—
19C2×#1010—21no—
20C2×#1010C2212yescomplemented
21C2×#1009—21no—
22C2×#1009C2212yescomplemented
23C2×D3×#41—22no—
24C2×D3×#41C2214yes—
25C2×#1007C2212yescomplemented
26C2×#1004—22no—
27C2×#1004C2212yescomplemented
28C22×#235—22no—
29C22×#235C2211yescharacteristic
30C22×#235C2211yescharacteristic
31C3×#575—28no—
32C2×C3×#137C2212yescomplemented
33C2×C3×#137C2212yescomplemented
34C2×C3×AGL(1,ℤ/8)C2212yescomplemented
35C2×C3×AGL(1,ℤ/8)C2212yescomplemented
36C2×C3×#135C2214yescomplemented
37C22×C3×M16C2211yescharacteristic, complemented
38#5833—22no—
39#5833—22no—
40#5833C2214yescomplemented
41#5833C2214yescomplemented
42C2×#951C2212yescomplemented
43#5822—28no—
44C2×#950C2214yescomplemented
45C2×#949C2212yescomplemented
46C2×#946C2212yescomplemented
47C2×#942C2212yescomplemented
48C2×#939—22no—
49C2×#938C2212yescomplemented
50C2×#932C2212yescomplemented
51C2×#930—21no—
52C22×C4⋊Dic3C2211yescharacteristic, complemented
53C2×#924—21no—
54C22×#208C2211yescharacteristic, complemented
55#5232C2214yescomplemented
56#5232C2214yescomplemented
57C2×#835C2212yescomplemented
58C2×#832C2212yescomplemented
59#5187C2218yescomplemented
60#5186C2218yescomplemented
61#5173C2218yescomplemented
62#5172C2218yescomplemented
63#5170C2218yescomplemented
64#5169C2218yescomplemented
65#5158C2218yescomplemented
66#5156C2218yescomplemented
67#5133C2214yescomplemented
68#5133C2214yescomplemented
69#5129C2214yescomplemented
70#5126C2214yescomplemented
71C2×#821C2212yescomplemented
72#5110C2214yescomplemented
73C2×#816C2212yescomplemented
74C2×#585—31no—
75C2×#575—31no—
76C2×#575D311yescharacteristic, complemented
77C2×#537—31no—
78#3013—34no—
79#3013—34no—
80#3012—34no—
81#3012—34no—
82#3007—34no—
83#3006—34no—
84C2×#417—31no—
85C2×#417—31no—
86#2879—31no—
87C2×C3×#41—21no—
88C2×C3×#41—21no—
89C2×C3×#41—24no—
90C2×C3×#41—21no—
91C2×C3×#41—21no—
92C2×C3×#41—24no—
93C2×C3×#41—24no—
94C2×C3×#41D418yescomplemented
95C2×C3×#41C2312yes—
96C2×C3×#41C2312yes—
97C2×C3×#41C2312yes—
98C2×C3×#41C2312yes—
99C22×C3×Q8C2311yescharacteristic
100C22×C3×Q8C2311yescharacteristic
101C22×C3×D4—21no—
102C22×C3×D4—21no—
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4—21no—
106C23×C3×C4—21no—
107C23×C3×C4C2311yescharacteristic
108C22×#67—21no—
109C22×#67—24no—
110C22×#67—22no—
111C22×#67D412yes—
112C23×Dic3—21no—
113#1010—216no—
114#1010—28no—
115#1010—28no—
116#1009—216no—
117#1009—28no—
118#1009—28no—
119D3×#41—232no—
120D3×#41—216no—
121D3×#41—216no—
122#1007—28no—
123#1007—28no—
124C2×#239—22no—
125C2×#239C2314yes—
126C2×D3×Q8—22no—
127C2×D3×Q8C2314yes—
128#1004—232no—
129#1004—28no—
130#1004—28no—
131C2×#237—24no—
132C2×#237—24no—
133C2×#237—22no—
134C2×#237C2314yes—
135C2×D3×D4—24no—
136C2×D3×D4—24no—
137C2×D3×D4—22no—
138C2×D3×D4C2314yes—
139C2×#235—232no—
140C2×#235—21no—
141C2×#235—21no—
142C2×#235—24no—
143C2×#235—24no—
144C2×#235—24no—
145C2×#235—24no—
146C2×#235—22no—
147C2×#235—24no—
148C2×#235—22no—
149C2×#235D412yes—
150C2×#235D412yes—
151C2×#235D418yescomplemented
152C2×#235C2312yes—
153C2×#235C2312yes—
154C2×#235C2312yes—
155C2×#235C2312yes—
156C22×D12—22no—
157C22×D12D411yescharacteristic
158C22×D12C2311yescharacteristic
159C22×C4×D3—21no—
160C22×C4×D3—24no—
161C22×C4×D3C2312yes—
162C22×Dic6—22no—
163C22×Dic6D411yescharacteristic
164C22×Dic6C2311yescharacteristic
165C3×#137—28no—
166C3×#137—28no—
167C3×AGL(1,ℤ/8)—28no—
168C3×AGL(1,ℤ/8)—28no—
169C3×#135—216no—
170C2×C3×Q16C2314yes—
171C2×C3×SD16C2314yes—
172C2×C3×SD16C2314yes—
173C2×C3×D8C2314yes—
174C2×C3×M16—24no—
175C2×C3×M16C2312yes—
176C2×C3×M16C2312yes—
177C22×C3×C8C2312yes—
178C2×#217—22no—
179#951—28no—
180#950—216no—
181#949—28no—
182#946—24no—
183#946C2318yes—
184C2×#216C2314yes—
185#942—28no—
186C2×#215C2314yes—
187#939—28no—
188#939—28no—
189#938—24no—
190#938C2318yes—
191C2×#214C2314yes—
192#932—28no—
193C2×#213C2314yes—
194#930—24no—
195#930—24no—
196C2×(C2×D3)⋊C4—22no—
197C2×C4⋊Dic3—21no—
198C2×C4⋊Dic3—21no—
199C2×C4⋊Dic3—21no—
200C2×C4⋊Dic3C2312yes—
201C2×C4⋊Dic3C2312yes—
202C2×C4⋊Dic3C2312yes—
203#924—24no—
204#924—24no—
205C2×Dic3⋊C4—22no—
206C2×#208—24no—
207C2×#208C2312yes—
208C2×#208C2312yes—
209C22×C3⋊C8C2312yes—
210#835C2318yes—
211#832C2318yes—
212#821C2318yes—
213(C2×D3)⋊C8C2318yes—
214(C2×D3)⋊C8C2318yes—
215#816C2318yes—
216#585—68no—
217#585—68no—
218C2×2−1+4—32no—
219C2×2−1+4—32no—
220C2×2−1+4—61no—
221C2×H(5,𝔽2)—32no—
222C2×H(5,𝔽2)—32no—
223C2×H(5,𝔽2)—62no—
224C2×H(5,𝔽2)—61no—
225C22×#41—31no—
226C22×#41—34no—
227C22×#41—31no—
228C22×#41—62no—
229C22×#41—62no—
230C22×#41C2×D311yescharacteristic
231C22×#41C2×D311yescharacteristic, complemented
232#575—28no—
233#575—68no—
234C2×#137—32no—
235C2×#137—32no—
236C2×#137C2×D312yescomplemented
237C2×#137C2×D312yescomplemented
238C2×AGL(1,ℤ/8)—32no—
239C2×AGL(1,ℤ/8)—32no—
240C2×AGL(1,ℤ/8)C2×D312yescomplemented
241C2×AGL(1,ℤ/8)C2×D312yescomplemented
242C2×#135—34no—
243C2×#135C2×D314yescomplemented
244C22×M16—31no—
245C22×M16C2×D311yescharacteristic, complemented
246#537—34no—
247#537—34no—
248#537—62no—
249#537—62no—
250C2×C22⋊Q8—32no—
251C2×C22⋊Q8—61no—
252C2×#121—32no—
253C2×#121—61no—
254C2×#121—62no—
255C22×C4⋊C4—31no—
256#452—38no—
257#452—38no—
258#451—38no—
259#450—38no—
260#449—38no—
261#449—38no—
262#448—38no—
263#447—38no—
264#417—34no—
265#417—34no—
266#417—34no—
267#417—34no—
268C2×#103—32no—
269C2×#103—32no—
270C2×#102—32no—
271C2×#102—32no—
272#408—34no—
273#408—34no—
274#407—34no—
275C24×C3—21no—
276C24×C3—21no—
277C24×C3C2×D411yescharacteristic
278C23×D3—21no—
279C23×D3—24no—
280C23×D3C2×D412yes—
281C3×#41—28no—
282C3×#41—28no—
283C3×#41—24no—
284C3×#41—24no—
285C3×#41—24no—
286C3×#41—24no—
287C3×#41—24no—
288C3×#41—24no—
289C3×#41—44no—
290C3×#41—44no—
291C3×#41C2×D418yes—
292C3×#41C2×D418yescomplemented
293C2×C3×Q8—21no—
294C2×C3×Q8—22no—
295C2×C3×Q8—21no—
296C2×C3×Q8—22no—
297C2×C3×Q8—22no—
298C2×C3×Q8C2×D414yescomplemented
299C2×C3×Q8C2412yes—
300C2×C3×Q8C2412yes—
301C2×C3×D4—28no—
302C2×C3×D4—22no—
303C2×C3×D4—22no—
304C2×C3×D4—22no—
305C2×C3×D4—22no—
306C2×C3×D4—21no—
307C2×C3×D4—22no—
308C2×C3×D4—22no—
309C2×C3×D4—22no—
310C2×C3×D4—21no—
311C2×C3×D4—44no—
312C2×C3×D4C2×D414yescomplemented
313C2×C3×D4C2412yes—
314C2×C3×D4C2412yes—
315C22×C3×C4—21no—
316C22×C3×C4—28no—
317C22×C3×C4—22no—
318C22×C3×C4—22no—
319C22×C3×C4—21no—
320C22×C3×C4—22no—
321C22×C3×C4—22no—
322C22×C3×C4—44no—
323C22×C3×C4C2×D411yescharacteristic
324C22×C3×C4C2×D411yescharacteristic
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2×D414yes—
327C22×C3×C4C2×D414yes—
328C22×C3×C4C2411yescharacteristic
329C22×C3×C4C2411yescharacteristic
330C22×C3×C4C2411yescharacteristic
331C2×#67—232no—
332C2×#67—28no—
333C2×#67—28no—
334C2×#67—22no—
335C2×#67—22no—
336C2×#67—24no—
337C2×#67—28no—
338C2×#67—24no—
339C2×#67—84no—
340C2×#67C2×D414yes—
341C2×#67C2×D414yes—
342C22×Dic3—21no—
343C22×Dic3—24no—
344C22×Dic3—22no—
345C22×Dic3—22no—
346C22×Dic3—22no—
347C22×Dic3—82no—
348C22×Dic3C2×D412yes—
349#239—216no—
350#239—28no—
351#239—28no—
352D3×Q8—216no—
353D3×Q8—28no—
354D3×Q8—28no—
355#237—232no—
356#237—232no—
357#237—216no—
358#237—28no—
359#237—28no—
360D3×D4—232no—
361D3×D4—232no—
362D3×D4—216no—
363D3×D4—28no—
364D3×D4—28no—
365#235—232no—
366#235—232no—
367#235—216no—
368#235—216no—
369#235—28no—
370#235—28no—
371#235—28no—
372#235—28no—
373#235—24no—
374#235—24no—
375#235—24no—
376#235—24no—
377#235—24no—
378#235—24no—
379#235C2×D418yes—
380#235C2×D418yescomplemented
381C2×D12—216no—
382C2×D12—24no—
383C2×D12—24no—
384C2×D12—21no—
385C2×D12—22no—
386C2×D12C2×D412yes—
387C2×D12C2×D412yes—
388C2×D12C2×D414yescomplemented
389C2×D12C2412yes—
390C2×C4×D3—232no—
391C2×C4×D3—24no—
392C2×C4×D3—28no—
393C2×C4×D3—22no—
394C2×C4×D3—22no—
395C2×C4×D3—24no—
396C2×C4×D3—24no—
397C2×C4×D3—24no—
398C2×C4×D3C2×D414yes—
399C2×C4×D3C2414yes—
400C2×Dic6—216no—
401C2×Dic6—24no—
402C2×Dic6—21no—
403C2×Dic6—22no—
404C2×Dic6—24no—
405C2×Dic6C2×D412yes—
406C2×Dic6C2×D412yes—
407C2×Dic6C2×D414yescomplemented
408C2×Dic6C2412yes—
409C3×Q16—28no—
410C3×SD16—28no—
411C3×SD16—28no—
412C3×D8—28no—
413C3×M16—24no—
414C3×M16—24no—
415C2×C3×C8—24no—
416C2×C3×C8C2414yes—
417#217—28no—
418#216—28no—
419#215—28no—
420#214—28no—
421#213—28no—
422(C2×D3)⋊C4—28no—
423C4⋊Dic3—22no—
424C4⋊Dic3—22no—
425C4⋊Dic3—22no—
426C4⋊Dic3C2414yes—
427Dic3⋊C4—28no—
428#208—24no—
429#208—24no—
430C2×C3⋊C8—24no—
431C2×C3⋊C8C2414yes—
4322−1+4—68no—
4332−1+4—68no—
4342−1+4—616no—
4352−1+4—68no—
4362−1+4—68no—
437H(5,𝔽2)—68no—
438H(5,𝔽2)—632no—
439H(5,𝔽2)—68no—
440H(5,𝔽2)—616no—
441H(5,𝔽2)—68no—
442H(5,𝔽2)—68no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—24no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—24no—
449C2×#41—24no—
450C2×#41—32no—
451C2×#41—32no—
452C2×#41—32no—
453C2×#41—32no—
454C2×#41—34no—
455C2×#41—34no—
456C2×#41—38no—
457C2×#41—32no—
458C2×#41—32no—
459C2×#41—64no—
460C2×#41—64no—
461C2×#41—62no—
462C2×#41—62no—
463C2×#41—632no—
464C2×#41—64no—
465C2×#41—64no—
466C2×#41—62no—
467C2×#41—62no—
468C2×#41—616no—
469C2×#41—632no—
470C2×#41—616no—
471C2×#41—61no—
472C2×#41—61no—
473C2×#41—64no—
474C2×#41—64no—
475C2×#41—64no—
476C2×#41#6718yescomplemented
477C2×#41C22×D312yes—
478C2×#41C22×D312yes—
479C2×#41C22×D312yes—
480C2×#41C22×D312yes—
481C22×Q8—31no—
482C22×Q8—34no—
483C22×Q8—31no—
484C22×Q8—62no—
485C22×Q8—62no—
486C22×Q8C22×D311yescharacteristic
487C22×Q8C22×D311yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—32no—
491C22×D4—34no—
492C22×D4—31no—
493C22×D4—31no—
494C22×D4—62no—
495C22×D4—64no—
496C22×D4—62no—
497C22×D4—64no—
498C22×D4—64no—
499C22×D4—61no—
500C22×D4—62no—
501C22×D4C22×D311yescharacteristic
502C22×D4C22×D311yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—32no—
506C23×C4—64no—
507C23×C4—61no—
508C23×C4—61no—
509C23×C4C22×D311yescharacteristic
510#137—28no—
511#137—28no—
512#137—68no—
513#137—68no—
514AGL(1,ℤ/8)—28no—
515AGL(1,ℤ/8)—28no—
516AGL(1,ℤ/8)—68no—
517AGL(1,ℤ/8)—68no—
518#135—216no—
519#135—616no—
520C2×Q16—34no—
521C2×Q16C22×D314yes—
522C2×SD16—34no—
523C2×SD16—34no—
524C2×SD16C22×D314yes—
525C2×SD16C22×D314yes—
526C2×D8—34no—
527C2×D8C22×D314yes—
528C2×M16—24no—
529C2×M16—32no—
530C2×M16—32no—
531C2×M16—64no—
532C2×M16C22×D312yes—
533C2×M16C22×D312yes—
534C22×C8—32no—
535C22×C8C22×D312yes—
536C22⋊Q8—38no—
537C22⋊Q8—64no—
538C22⋊Q8—64no—
539C22⋊Q8—64no—
540#121—38no—
541#121—64no—
542#121—64no—
543#121—64no—
544#121—68no—
545#121—68no—
546C2×C4⋊C4—32no—
547C2×C4⋊C4—32no—
548C2×C4⋊C4—32no—
549C2×C4⋊C4—62no—
550C2×C4⋊C4—61no—
551C2×C4⋊C4—61no—
552C2×C4⋊C4—61no—
553C2×C22⋊C4—62no—
554C2×C22⋊C4—62no—
555#103—38no—
556#103—38no—
557#102—38no—
558#102—38no—
559C22⋊C8—38no—
560C22⋊C8—38no—
561C23×C3—22no—
562C23×C3—24no—
563C23×C3—22no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—42no—
567C23×C3—42no—
568C23×C3—42no—
569C23×C3—81no—
570C23×C3—81no—
571C23×C3#12014yes—
572C23×C3C22×D411yescharacteristic
573C23×C3C22×D411yescharacteristic
574C23×C3C22×D411yescharacteristic
575C22×D3—22no—
576C22×D3—216no—
577C22×D3—24no—
578C22×D3—24no—
579C22×D3—42no—
580C22×D3—42no—
581C22×D3—84no—
582C22×D3—84no—
583C22×D3—81no—
584C22×D3—81no—
585C22×D3C22×D414yes—
586C3×Q8—24no—
587C3×Q8—22no—
588C3×Q8—22no—
589C3×Q8—22no—
590C3×Q8—42no—
591C3×Q8C22×D414yes—
592C3×D4—28no—
593C3×D4—28no—
594C3×D4—24no—
595C3×D4—22no—
596C3×D4—22no—
597C3×D4—22no—
598C3×D4—44no—
599C3×D4—44no—
600C3×D4—42no—
601C3×D4C22×D414yes—
602C2×C3×C4—24no—
603C2×C3×C4—22no—
604C2×C3×C4—28no—
605C2×C3×C4—28no—
606C2×C3×C4—22no—
607C2×C3×C4—42no—
608C2×C3×C4—44no—
609C2×C3×C4—44no—
610C2×C3×C4#12014yes—
611C2×C3×C4#12014yes—
612C2×C3×C4#12014yes—
613C2×C3×C4C22×D411yescharacteristic
614C2×C3×C4C22×D411yescharacteristic
615C2×C3×C4C22×D411yescharacteristic
616C2×C3×C4C22×D412yes—
617C2×C3×C4C22×D412yes—
618C2×C3×C4C22×D412yes—
619C2×C3×C4C22×D412yes—
620C2×C3×C4C22×D412yes—
621C2×C3×C4C22×D412yes—
622C2×C3×C4C2511yescharacteristic
623#67—216no—
624#67—216no—
625#67—28no—
626#67—28no—
627#67—28no—
628#67—28no—
629#67—88no—
630C2×Dic3—216no—
631C2×Dic3—24no—
632C2×Dic3—24no—
633C2×Dic3—22no—
634C2×Dic3—24no—
635C2×Dic3—44no—
636C2×Dic3—82no—
637C2×Dic3—82no—
638C2×Dic3C22×D414yes—
639D12—216no—
640D12—24no—
641D12—24no—
642D12—24no—
643D12—22no—
644D12C22×D414yes—
645C4×D3—216no—
646C4×D3—216no—
647C4×D3—28no—
648C4×D3—28no—
649C4×D3—28no—
650C4×D3—24no—
651C4×D3—24no—
652Dic6—216no—
653Dic6—24no—
654Dic6—24no—
655Dic6—24no—
656Dic6—22no—
657Dic6C22×D414yes—
658C3×C8—24no—
659C3⋊C8—24no—
660C24—21no—
661C24—21no—
662C24—32no—
663C24—64no—
664C24—61no—
665C24D3×D411yescharacteristic
666#41—28no—
667#41—28no—
668#41—24no—
669#41—24no—
670#41—24no—
671#41—24no—
672#41—24no—
673#41—24no—
674#41—38no—
675#41—38no—
676#41—44no—
677#41—44no—
678#41—632no—
679#41—632no—
680#41—616no—
681#41—616no—
682#41—68no—
683#41—632no—
684#41—632no—
685#41—616no—
686#41—68no—
687#41—616no—
688#41—68no—
689#41—68no—
690#41—68no—
691#41—68no—
692#41—68no—
693#41—68no—
694#41—64no—
695#41—64no—
696#41—64no—
697#41—64no—
698#41—64no—
699#41—64no—
700#41C2×#6718yes—
701#41C2×#6718yescomplemented
702C2×Q8—21no—
703C2×Q8—22no—
704C2×Q8—21no—
705C2×Q8—22no—
706C2×Q8—22no—
707C2×Q8—32no—
708C2×Q8—32no—
709C2×Q8—34no—
710C2×Q8—32no—
711C2×Q8—64no—
712C2×Q8—616no—
713C2×Q8—68no—
714C2×Q8—616no—
715C2×Q8—68no—
716C2×Q8—64no—
717C2×Q8—61no—
718C2×Q8—62no—
719C2×Q8C2×#6714yescomplemented
720C2×Q8C23×D312yes—
721C2×Q8C23×D312yes—
722C2×D4—28no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—21no—
728C2×D4—22no—
729C2×D4—22no—
730C2×D4—21no—
731C2×D4—22no—
732C2×D4—34no—
733C2×D4—34no—
734C2×D4—34no—
735C2×D4—32no—
736C2×D4—32no—
737C2×D4—32no—
738C2×D4—44no—
739C2×D4—64no—
740C2×D4—616no—
741C2×D4—64no—
742C2×D4—68no—
743C2×D4—632no—
744C2×D4—632no—
745C2×D4—616no—
746C2×D4—64no—
747C2×D4—632no—
748C2×D4—68no—
749C2×D4—68no—
750C2×D4—62no—
751C2×D4—62no—
752C2×D4—68no—
753C2×D4—68no—
754C2×D4—64no—
755C2×D4—61no—
756C2×D4—62no—
757C2×D4—244no—
758C2×D4C2×#6714yescomplemented
759C2×D4C23×D312yes—
760C2×D4C23×D312yes—
761C22×C4—21no—
762C22×C4—28no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—32no—
769C22×C4—34no—
770C22×C4—34no—
771C22×C4—44no—
772C22×C4—64no—
773C22×C4—64no—
774C22×C4—632no—
775C22×C4—64no—
776C22×C4—61no—
777C22×C4—68no—
778C22×C4—64no—
779C22×C4—62no—
780C22×C4—62no—
781C22×C4—64no—
782C22×C4—62no—
783C22×C4—62no—
784C22×C4—62no—
785C22×C4—242no—
786C22×C4D3×D411yescharacteristic
787C22×C4D3×D411yescharacteristic
788C22×C4D3×D411yescharacteristic
789C22×C4D3×D414yes—
790C22×C4C2×#6714yes—
791C22×C4C23×D311yescharacteristic
792C22×C4C23×D311yescharacteristic
793C22×C4C23×D311yescharacteristic
794Q16—28no—
795Q16—68no—
796SD16—28no—
797SD16—28no—
798SD16—68no—
799SD16—68no—
800D8—28no—
801D8—68no—
802M16—24no—
803M16—24no—
804M16—64no—
805M16—64no—
806C2×C8—24no—
807C2×C8—34no—
808C2×C8—64no—
809C2×C8C23×D314yes—
810C4⋊C4—34no—
811C4⋊C4—68no—
812C4⋊C4—62no—
813C4⋊C4—62no—
814C4⋊C4—62no—
815C22⋊C4—68no—
816C22⋊C4—68no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—24no—
824C22×C3—44no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—84no—
831C22×C3—84no—
832C22×C3C2×#12012yes—
833C22×C3C2×#12012yes—
834C22×C3C2×#12012yes—
835C22×C3C23×D411yescharacteristic
836C2×D3—24no—
837C2×D3—24no—
838C2×D3—24no—
839C2×D3—24no—
840C2×D3—42no—
841C2×D3—42no—
842C2×D3—84no—
843C2×D3—84no—
844C2×D3—816no—
845C3×C4—24no—
846C3×C4—42no—
847C3×C4C2×#12012yes—
848C3×C4C2×#12012yes—
849C3×C4C2×#12012yes—
850C3×C4C23×D411yescharacteristic
851C3×C4C23×D411yescharacteristic
852Dic3—24no—
853Dic3—24no—
854Dic3—44no—
855C23—22no—
856C23—24no—
857C23—22no—
858C23—34no—
859C23—41no—
860C23—41no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—616no—
865C23—62no—
866C23—64no—
867C23—64no—
868C23—81no—
869C23—81no—
870C23—122no—
871C23—122no—
872C23—241no—
873C23—241no—
874C23—244no—
875C23—244no—
876C23#93714yes—
877C23C2×D3×D411yescharacteristic
878C23C2×D3×D411yescharacteristic
879C23C2×D3×D411yescharacteristic
880Q8—22no—
881Q8—24no—
882Q8—22no—
883Q8—22no—
884Q8—34no—
885Q8—42no—
886Q8—616no—
887Q8—62no—
888Q8—64no—
889Q8—64no—
890Q8—64no—
891Q8C22×#6714yes—
892D4—28no—
893D4—28no—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—24no—
898D4—34no—
899D4—44no—
900D4—44no—
901D4—42no—
902D4—616no—
903D4—616no—
904D4—616no—
905D4—68no—
906D4—68no—
907D4—68no—
908D4—68no—
909D4—62no—
910D4—64no—
911D4—64no—
912D4—64no—
913D4—248no—
914D4C22×#6714yes—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—28no—
918C2×C4—28no—
919C2×C4—22no—
920C2×C4—34no—
921C2×C4—42no—
922C2×C4—44no—
923C2×C4—44no—
924C2×C4—616no—
925C2×C4—616no—
926C2×C4—616no—
927C2×C4—62no—
928C2×C4—64no—
929C2×C4—64no—
930C2×C4—64no—
931C2×C4—64no—
932C2×C4—68no—
933C2×C4—68no—
934C2×C4—68no—
935C2×C4—64no—
936C2×C4—124no—
937C2×C4—242no—
938C2×C4—242no—
939C2×C4#93714yes—
940C2×C4#93714yes—
941C2×C4#93714yes—
942C2×C4C2×D3×D412yes—
943C2×C4C2×D3×D412yes—
944C2×C4C2×D3×D412yes—
945C2×C4C2×D3×D411yescharacteristic
946C2×C4C2×D3×D411yescharacteristic
947C2×C4C2×D3×D411yescharacteristic
948C2×C4C22×#6712yes—
949C2×C4C22×#6712yes—
950C2×C4C22×#6712yes—
951C2×C4C24×D311yescharacteristic
952C8—24no—
953C8—64no—
954C2×C3—22no—
955C2×C3—22no—
956C2×C3—22no—
957C2×C3—44no—
958C2×C3—82no—
959C2×C3C22×#12011yescharacteristic
960C2×C3#358511yescharacteristic
961C2×C3#358611yescharacteristic
962D3—44no—
963D3—44no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—24no—
971C22—44no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—64no—
978C22—64no—
979C22—64no—
980C22—64no—
981C22—84no—
982C22—84no—
983C22—122no—
984C22—122no—
985C22—244no—
986C22—244no—
987C22—2416no—
988C22C2×#93712yes—
989C22C2×#93712yes—
990C22C2×#93712yes—
991C22C22×D3×D411yescharacteristic
992C4—24no—
993C4—42no—
994C4—64no—
995C4—64no—
996C4—124no—
997C4C2×#93712yes—
998C4C2×#93712yes—
999C4C2×#93712yes—
1000C4C22×D3×D411yescharacteristic
1001C4C23×#6711yescharacteristic
1002C3#6037111yescharacteristic, complemented, Sylow
1003C2—22no—
1004C2—22no—
1005C2—22no—
1006C2—44no—
1007C2—82no—
1008C2—124no—
1009C2—124no—
1010C2#8720011yescharacteristic
1011C2#8720111yescharacteristic
1012C2C22×#93711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#575C2
socleC22×C3C23×D4
hypercenterC2×#575D3
hypocenterC3#60371
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#5964C2semidirect
2. C2×C3×#575C2semidirect
3. C2×#5833C2semidirect
4. C2×#5822C2semidirect
5. C2×#5232C2semidirect
6. #83984C2semidirect
7. #83981C2semidirect
8. #83949C2semidirect
9. #83946C2semidirect
10. #83913C2semidirect
11. #83912C2semidirect
12. C2×#5133C2semidirect
13. #83762C2semidirect
16. C22×C3×#41C22semidirect
20. C2×#1010C22semidirect
22. C2×#1009C22semidirect
25. C2×#1007C22semidirect
27. C2×#1004C22semidirect
32. C2×C3×#137C22semidirect
33. C2×C3×#137C22semidirect
34. C2×C3×AGL(1,ℤ/8)C22semidirect
35. C2×C3×AGL(1,ℤ/8)C22semidirect
36. C2×C3×#135C22semidirect
37. C22×C3×M16C22semidirect
40. #5833C22semidirect
41. #5833C22semidirect
42. C2×#951C22semidirect
44. C2×#950C22semidirect
45. C2×#949C22semidirect
46. C2×#946C22semidirect
47. C2×#942C22semidirect
49. C2×#938C22semidirect
50. C2×#932C22semidirect
52. C22×C4⋊Dic3C22semidirect
54. C22×#208C22semidirect
55. #5232C22semidirect
56. #5232C22semidirect
57. C2×#835C22semidirect
58. C2×#832C22semidirect
59. #5187C22semidirect
60. #5186C22semidirect
61. #5173C22semidirect
62. #5172C22semidirect
63. #5170C22semidirect
64. #5169C22semidirect
65. #5158C22semidirect
66. #5156C22semidirect
67. #5133C22semidirect
68. #5133C22semidirect
69. #5129C22semidirect
70. #5126C22semidirect
71. C2×#821C22semidirect
72. #5110C22semidirect
73. C2×#816C22semidirect
76. C2×#575D3semidirect
94. C2×C3×#41D4semidirect
151. C2×#235D4semidirect
231. C22×#41C2×D3semidirect
236. C2×#137C2×D3semidirect
237. C2×#137C2×D3semidirect
240. C2×AGL(1,ℤ/8)C2×D3semidirect
241. C2×AGL(1,ℤ/8)C2×D3semidirect
243. C2×#135C2×D3semidirect
245. C22×M16C2×D3semidirect
292. C3×#41C2×D4semidirect
298. C2×C3×Q8C2×D4semidirect
312. C2×C3×D4C2×D4semidirect
380. #235C2×D4semidirect
388. C2×D12C2×D4semidirect
407. C2×Dic6C2×D4semidirect
476. C2×#41#67semidirect
701. #41C2×#67semidirect
719. C2×Q8C2×#67semidirect
758. C2×D4C2×#67semidirect
1002. C3#60371semidirect

Maximal subgroups

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

subgroupindex
C2×#59642
C2×C3×#5752
C2×#58332
C2×#58222
C2×#52322
#839842
#839812
#839492
#839462
#839132
#839122
C2×#51332
#837622
#603713