Finite Group Databasebeta

← #11661710

Subgroups — #11661710

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×#5822C211yesmaximal, characteristic, complemented
3C2×#5748C211yesmaximal, characteristic, complemented
4C2×#5510C211yesmaximal, characteristic, complemented
5C2×C3×#417C211yesmaximal, characteristic, complemented
6#83762C211yesmaximal, characteristic, complemented
7C2×#4966C211yesmaximal, characteristic, complemented
8#78887C214yesmaximal, complemented
9#78886C214yesmaximal, complemented
10#78885C214yesmaximal, complemented
11#78884C214yesmaximal, complemented
12#78795C214yesmaximal, complemented
13#78747C214yesmaximal, complemented
14#60371—31nomaximal, Sylow
15C22×C3×#41C2211yescharacteristic
16#5964—28no—
17#5964—28no—
18C2×#1010—21no—
19C2×#1010C2212yescomplemented
20C2×#1009—21no—
21C2×#1009C2212yescomplemented
22C2×D3×#41—22no—
23C2×D3×#41C2214yes—
24C2×#1007C2212yescomplemented
25C2×#1004—22no—
26C2×#1004C2212yescomplemented
27C22×#235—22no—
28C22×#235C2211yescharacteristic
29C22×#235C2211yescharacteristic
30C22×#235C2211yescharacteristic, complemented
31C22×C3×M16C2211yescharacteristic, complemented
32C22×C3×C4⋊C4C2211yescharacteristic, complemented
33C2×#951C2212yescomplemented
34#5822—28no—
35C2×#950C2214yescomplemented
36C2×#949C2212yescomplemented
37C2×#942C2212yescomplemented
38C2×#932C2212yescomplemented
39C2×#930—22no—
40C22×#208C2211yescharacteristic, complemented
41#5748—28no—
42C2×#909C2212yescomplemented
43C2×#909C2212yescomplemented
44C2×#908C2212yescomplemented
45C2×#908C2212yescomplemented
46C2×#904C2214yescomplemented
47#5510—22no—
48#5510—22no—
49#5510C2214yescomplemented
50#5510C2214yescomplemented
51C2×#897—21no—
52C2×#897C2212yescomplemented
53C2×#895—21no—
54C2×#895C2212yescomplemented
55C3×#417C2214yescomplemented
56C3×#417C2214yescomplemented
57C2×C3×#103C2212yescomplemented
58C2×C3×#102C2212yescomplemented
59#5129C2214yescomplemented
60#5126C2214yescomplemented
61#5110C2214yescomplemented
62C2×#810C2212yescomplemented
63#4966C2214yescomplemented
64#4966C2214yescomplemented
65C2×#809C2212yescomplemented
66#4810C2218yescomplemented
67#4809C2218yescomplemented
68#4808C2218yescomplemented
69#4806C2218yescomplemented
70#4783C2218yescomplemented
71#4781C2218yescomplemented
72#4776C2218yescomplemented
73#4773C2218yescomplemented
74C2×#585—31no—
75C2×#575—31no—
76C2×#575—31no—
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×#417D311yescharacteristic, complemented
86#2879—31no—
87C2×C3×#41—21no—
88C2×C3×#41—21no—
89C2×C3×#41—24no—
90C2×C3×#41D418yescomplemented
91C2×C3×#41C2312yes—
92C2×C3×#41C2312yes—
93C22×C3×Q8C2311yescharacteristic
94C22×C3×D4—21no—
95C22×C3×D4C2311yescharacteristic
96C23×C3×C4—21no—
97C23×C3×C4—21no—
98C23×C3×C4C2311yescharacteristic
99C22×#67—21no—
100C22×#67—24no—
101C22×#67—21no—
102C22×#67D412yes—
103#1010—216no—
104#1010—28no—
105#1010—28no—
106#1009—216no—
107#1009—28no—
108#1009—28no—
109D3×#41—232no—
110D3×#41—216no—
111D3×#41—216no—
112#1007—28no—
113#1007—28no—
114C2×#239—22no—
115C2×#239C2314yes—
116C2×D3×Q8—22no—
117C2×D3×Q8C2314yes—
118#1004—232no—
119#1004—28no—
120#1004—28no—
121C2×#237—24no—
122C2×#237—24no—
123C2×#237—22no—
124C2×#237C2314yes—
125C2×D3×D4—24no—
126C2×D3×D4—24no—
127C2×D3×D4—22no—
128C2×D3×D4C2314yes—
129C2×#235—232no—
130C2×#235—21no—
131C2×#235—21no—
132C2×#235—24no—
133C2×#235—24no—
134C2×#235—24no—
135C2×#235—24no—
136C2×#235—21no—
137C2×#235—21no—
138C2×#235—22no—
139C2×#235—24no—
140C2×#235—24no—
141C2×#235—24no—
142C2×#235—22no—
143C2×#235D412yes—
144C2×#235D412yes—
145C2×#235D418yescomplemented
146C2×#235C2312yes—
147C2×#235C2312yes—
148C2×#235C2312yes—
149C2×#235C2312yes—
150C2×#235C2312yes—
151C2×#235C2312yes—
152C22×D12—22no—
153C22×D12—22no—
154C22×D12D411yescharacteristic
155C22×D12C2311yescharacteristic
156C22×D12C2311yescharacteristic
157C22×C4×D3—21no—
158C22×C4×D3—24no—
159C22×C4×D3—21no—
160C22×C4×D3C2312yes—
161C22×Dic6—22no—
162C22×Dic6D411yescharacteristic
163C22×Dic6C2311yescharacteristic
164C22×Dic6C2311yescharacteristic
165C2×C3×M16—24no—
166C2×C3×M16C2312yes—
167C2×C3×M16C2312yes—
168C22×C3×C8C2312yes—
169C2×C3×C4⋊C4—21no—
170C2×C3×C4⋊C4—21no—
171C2×C3×C4⋊C4—21no—
172C2×C3×C4⋊C4C2312yes—
173C2×C3×C4⋊C4C2312yes—
174C2×C3×C4⋊C4C2312yes—
175#951—28no—
176#950—216no—
177#949—28no—
178C2×#216C2314yes—
179#942—28no—
180C2×#215C2314yes—
181C2×#214C2314yes—
182#932—28no—
183C2×#213C2314yes—
184#930—28no—
185#930—28no—
186C2×(C2×D3)⋊C4—22no—
187C2×(C2×D3)⋊C4—22no—
188C2×C4⋊Dic3—22no—
189C2×#208—24no—
190C2×#208C2312yes—
191C2×#208C2312yes—
192C22×C3⋊C8C2312yes—
193#909—28no—
194#909—28no—
195#908—28no—
196#908—28no—
197C2×Dic12C2314yes—
198#904—216no—
199C2×D24C2314yes—
200C2×#204C2314yes—
201C2×#204C2314yes—
202#897—24no—
203#897—24no—
204#897—24no—
205#897C2318yes—
206#895—24no—
207#895—24no—
208#895—24no—
209#895C2318yes—
210C3×#103C2318yes—
211C3×#102C2318yes—
212(C2×D3)⋊C8C2318yes—
213(C2×D3)⋊C8C2318yes—
214#810C2318yes—
215#809C2318yes—
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—31no—
229C22×#41—62no—
230C22×#41—62no—
231C22×#41C2×D311yescharacteristic
232#575—68no—
233#575—68no—
234C2×#137—32no—
235C2×#137—32no—
236C2×#137—32no—
237C2×#137—32no—
238C2×AGL(1,ℤ/8)—32no—
239C2×AGL(1,ℤ/8)—32no—
240C2×AGL(1,ℤ/8)—32no—
241C2×AGL(1,ℤ/8)—32no—
242C2×#135—34no—
243C2×#135—34no—
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⋊C4C2×D311yescharacteristic, complemented
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#417C2×D314yescomplemented
267#417C2×D314yescomplemented
268C2×#103—32no—
269C2×#103C2×D312yescomplemented
270C2×#102—32no—
271C2×#102C2×D312yescomplemented
272#408—34no—
273#408—34no—
274#407—34no—
275C24×C3—21no—
276C24×C3C2×D411yescharacteristic
277C23×D3—21no—
278C23×D3—24no—
279C23×D3—21no—
280C23×D3C2×D412yes—
281C3×#41—28no—
282C3×#41—28no—
283C3×#41—24no—
284C3×#41—24no—
285C3×#41C2×D418yes—
286C3×#41C2×D418yescomplemented
287C2×C3×Q8—21no—
288C2×C3×Q8—22no—
289C2×C3×Q8C2×D414yescomplemented
290C2×C3×Q8C2412yes—
291C2×C3×D4—28no—
292C2×C3×D4—22no—
293C2×C3×D4—22no—
294C2×C3×D4—21no—
295C2×C3×D4—22no—
296C2×C3×D4C2×D414yescomplemented
297C2×C3×D4C2412yes—
298C22×C3×C4—21no—
299C22×C3×C4—28no—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4—22no—
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—82no—
306C22×C3×C4C2×D414yes—
307C22×C3×C4C2×D411yescharacteristic
308C22×C3×C4C2×D411yescharacteristic
309C22×C3×C4C2×D411yescharacteristic
310C22×C3×C4C2×D414yes—
311C22×C3×C4C2411yescharacteristic
312C22×C3×C4C2411yescharacteristic
313C22×C3×C4C2411yescharacteristic
314C2×#67—232no—
315C2×#67—28no—
316C2×#67—28no—
317C2×#67—22no—
318C2×#67—22no—
319C2×#67—24no—
320C2×#67—22no—
321C2×#67—22no—
322C2×#67—24no—
323C2×#67—44no—
324C2×#67C2×D414yes—
325C2×#67C2×D414yes—
326C22×Dic3—21no—
327C22×Dic3—24no—
328C22×Dic3—21no—
329C22×Dic3C2×D412yes—
330#239—216no—
331#239—28no—
332#239—28no—
333D3×Q8—216no—
334D3×Q8—28no—
335D3×Q8—28no—
336#237—232no—
337#237—232no—
338#237—216no—
339#237—28no—
340#237—28no—
341D3×D4—232no—
342D3×D4—232no—
343D3×D4—216no—
344D3×D4—28no—
345D3×D4—28no—
346#235—232no—
347#235—232no—
348#235—216no—
349#235—216no—
350#235—28no—
351#235—28no—
352#235—28no—
353#235—28no—
354#235—24no—
355#235—24no—
356#235—24no—
357#235—24no—
358#235—24no—
359#235—24no—
360#235—24no—
361#235—24no—
362#235—24no—
363#235—24no—
364#235—44no—
365#235—44no—
366#235C2×D418yes—
367#235C2×D418yescomplemented
368C2×D12—216no—
369C2×D12—24no—
370C2×D12—24no—
371C2×D12—21no—
372C2×D12—22no—
373C2×D12—22no—
374C2×D12—22no—
375C2×D12—21no—
376C2×D12—28no—
377C2×D12—84no—
378C2×D12C2×D412yes—
379C2×D12C2×D412yes—
380C2×D12C2×D414yescomplemented
381C2×D12C2412yes—
382C2×D12C2412yes—
383C2×C4×D3—232no—
384C2×C4×D3—24no—
385C2×C4×D3—28no—
386C2×C4×D3—22no—
387C2×C4×D3—22no—
388C2×C4×D3—24no—
389C2×C4×D3—24no—
390C2×C4×D3—24no—
391C2×C4×D3—22no—
392C2×C4×D3—22no—
393C2×C4×D3—44no—
394C2×C4×D3C2×D414yes—
395C2×C4×D3C2414yes—
396C2×Dic6—216no—
397C2×Dic6—24no—
398C2×Dic6—21no—
399C2×Dic6—22no—
400C2×Dic6—24no—
401C2×Dic6—22no—
402C2×Dic6—22no—
403C2×Dic6—21no—
404C2×Dic6C2×D412yes—
405C2×Dic6C2×D412yes—
406C2×Dic6C2×D414yescomplemented
407C2×Dic6C2412yes—
408C2×Dic6C2412yes—
409C3×M16—24no—
410C3×M16—24no—
411C2×C3×C8—24no—
412C2×C3×C8C2414yes—
413C3×C4⋊C4—22no—
414C3×C4⋊C4—22no—
415C3×C4⋊C4—22no—
416C3×C4⋊C4C2414yes—
417#216—28no—
418#215—28no—
419#214—28no—
420#213—28no—
421(C2×D3)⋊C4—28no—
422(C2×D3)⋊C4—28no—
423C4⋊Dic3—28no—
424#208—24no—
425#208—24no—
426C2×C3⋊C8—24no—
427C2×C3⋊C8C2414yes—
428Dic12—28no—
429D24—28no—
430#204—28no—
431#204—28no—
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—32no—
447C2×#41—32no—
448C2×#41—32no—
449C2×#41—32no—
450C2×#41—34no—
451C2×#41—34no—
452C2×#41—38no—
453C2×#41—32no—
454C2×#41—32no—
455C2×#41—32no—
456C2×#41—32no—
457C2×#41—64no—
458C2×#41—64no—
459C2×#41—62no—
460C2×#41—62no—
461C2×#41—632no—
462C2×#41—64no—
463C2×#41—64no—
464C2×#41—62no—
465C2×#41—62no—
466C2×#41—616no—
467C2×#41—632no—
468C2×#41—616no—
469C2×#41—64no—
470C2×#41—64no—
471C2×#41—61no—
472C2×#41—61no—
473C2×#41—64no—
474C2×#41—61no—
475C2×#41—61no—
476C2×#41—64no—
477C2×#41—64no—
478C2×#41D1218yescomplemented
479C2×#41C22×D312yes—
480C2×#41C22×D312yes—
481C22×Q8—31no—
482C22×Q8—34no—
483C22×Q8—31no—
484C22×Q8—31no—
485C22×Q8—62no—
486C22×Q8—62no—
487C22×Q8C22×D311yescharacteristic
488C22×D4—21no—
489C22×D4—32no—
490C22×D4—34no—
491C22×D4—31no—
492C22×D4—31no—
493C22×D4—31no—
494C22×D4—62no—
495C22×D4—62no—
496C22×D4—64no—
497C22×D4—62no—
498C22×D4—64no—
499C22×D4—64no—
500C22×D4—61no—
501C22×D4—61no—
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—68no—
511#137—68no—
512#137—68no—
513#137—68no—
514AGL(1,ℤ/8)—68no—
515AGL(1,ℤ/8)—68no—
516AGL(1,ℤ/8)—68no—
517AGL(1,ℤ/8)—68no—
518#135—616no—
519#135—616no—
520C2×Q16—34no—
521C2×Q16—34no—
522C2×SD16—34no—
523C2×SD16—34no—
524C2×SD16—34no—
525C2×SD16—34no—
526C2×D8—34no—
527C2×D8—34no—
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—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—62no—
550C2×C4⋊C4C22×D312yes—
551C2×C4⋊C4C22×D312yes—
552C2×C4⋊C4C22×D312yes—
553C2×C22⋊C4—62no—
554C2×C22⋊C4—62no—
555#103—38no—
556#103C22×D318yes—
557#102—38no—
558#102C22×D318yes—
559C22⋊C8—38no—
560C22⋊C8—38no—
561C23×C3—22no—
562C23×C3—24no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—81no—
566C23×C3—81no—
567C23×C3#12014yes—
568C23×C3C22×D411yescharacteristic
569C23×C3C22×D411yescharacteristic
570C23×C3C22×D411yescharacteristic
571C22×D3—22no—
572C22×D3—216no—
573C22×D3—24no—
574C22×D3—24no—
575C22×D3—22no—
576C22×D3—42no—
577C22×D3—42no—
578C22×D3—42no—
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×Q8C22×D414yes—
589C3×D4—28no—
590C3×D4—28no—
591C3×D4—24no—
592C3×D4—22no—
593C3×D4C22×D414yes—
594C2×C3×C4—24no—
595C2×C3×C4—22no—
596C2×C3×C4—28no—
597C2×C3×C4—28no—
598C2×C3×C4—24no—
599C2×C3×C4—44no—
600C2×C3×C4—82no—
601C2×C3×C4—82no—
602C2×C3×C4#12014yes—
603C2×C3×C4#12014yes—
604C2×C3×C4#12014yes—
605C2×C3×C4C22×D412yes—
606C2×C3×C4C22×D412yes—
607C2×C3×C4C22×D412yes—
608C2×C3×C4C22×D411yescharacteristic
609C2×C3×C4C22×D411yescharacteristic
610C2×C3×C4C22×D411yescharacteristic
611C2×C3×C4C22×D412yes—
612C2×C3×C4C22×D412yes—
613C2×C3×C4C22×D412yes—
614C2×C3×C4C2511yescharacteristic
615#67—216no—
616#67—216no—
617#67—28no—
618#67—28no—
619#67—28no—
620#67—28no—
621#67—44no—
622#67—44no—
623C2×Dic3—216no—
624C2×Dic3—24no—
625C2×Dic3—24no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—42no—
629C2×Dic3C22×D414yes—
630D12—216no—
631D12—24no—
632D12—24no—
633D12—24no—
634D12—22no—
635D12—22no—
636D12—22no—
637D12—42no—
638D12—88no—
639D12C22×D414yes—
640C4×D3—216no—
641C4×D3—216no—
642C4×D3—28no—
643C4×D3—28no—
644C4×D3—28no—
645C4×D3—24no—
646C4×D3—24no—
647C4×D3—44no—
648C4×D3—44no—
649Dic6—216no—
650Dic6—24no—
651Dic6—24no—
652Dic6—24no—
653Dic6—22no—
654Dic6—22no—
655Dic6—22no—
656Dic6—42no—
657Dic6C22×D414yes—
658C3×C8—24no—
659C3⋊C8—24no—
660C24—21no—
661C24—32no—
662C24—64no—
663C24—61no—
664C24—61no—
665C24D3×D411yescharacteristic
666#41—28no—
667#41—28no—
668#41—24no—
669#41—24no—
670#41—38no—
671#41—38no—
672#41—632no—
673#41—632no—
674#41—616no—
675#41—616no—
676#41—68no—
677#41—632no—
678#41—632no—
679#41—616no—
680#41—68no—
681#41—616no—
682#41—68no—
683#41—68no—
684#41—68no—
685#41—68no—
686#41—68no—
687#41—68no—
688#41—64no—
689#41—64no—
690#41—64no—
691#41—64no—
692#41—64no—
693#41—64no—
694#41—64no—
695#41—64no—
696#41—64no—
697#41—64no—
698#41—124no—
699#41—124no—
700#41C2×D1218yes—
701#41C2×D1218yescomplemented
702C2×Q8—21no—
703C2×Q8—22no—
704C2×Q8—32no—
705C2×Q8—32no—
706C2×Q8—34no—
707C2×Q8—32no—
708C2×Q8—32no—
709C2×Q8—64no—
710C2×Q8—616no—
711C2×Q8—68no—
712C2×Q8—616no—
713C2×Q8—68no—
714C2×Q8—64no—
715C2×Q8—62no—
716C2×Q8—61no—
717C2×Q8—61no—
718C2×Q8—62no—
719C2×Q8—62no—
720C2×Q8C2×D1214yescomplemented
721C2×Q8C23×D312yes—
722C2×D4—28no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—21no—
726C2×D4—22no—
727C2×D4—34no—
728C2×D4—34no—
729C2×D4—34no—
730C2×D4—32no—
731C2×D4—32no—
732C2×D4—32no—
733C2×D4—32no—
734C2×D4—64no—
735C2×D4—616no—
736C2×D4—68no—
737C2×D4—64no—
738C2×D4—68no—
739C2×D4—632no—
740C2×D4—632no—
741C2×D4—616no—
742C2×D4—64no—
743C2×D4—632no—
744C2×D4—68no—
745C2×D4—68no—
746C2×D4—62no—
747C2×D4—62no—
748C2×D4—68no—
749C2×D4—62no—
750C2×D4—62no—
751C2×D4—64no—
752C2×D4—62no—
753C2×D4—62no—
754C2×D4—61no—
755C2×D4—62no—
756C2×D4—61no—
757C2×D4—124no—
758C2×D4—244no—
759C2×D4C2×D1214yescomplemented
760C2×D4C23×D312yes—
761C22×C4—21no—
762C22×C4—28no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—32no—
769C22×C4—34no—
770C22×C4—34no—
771C22×C4—64no—
772C22×C4—64no—
773C22×C4—632no—
774C22×C4—64no—
775C22×C4—61no—
776C22×C4—68no—
777C22×C4—64no—
778C22×C4—64no—
779C22×C4—62no—
780C22×C4—62no—
781C22×C4—61no—
782C22×C4—62no—
783C22×C4—62no—
784C22×C4—82no—
785C22×C4—124no—
786C22×C4C2×D1214yes—
787C22×C4D3×D411yescharacteristic
788C22×C4D3×D411yescharacteristic
789C22×C4D3×D411yescharacteristic
790C22×C4D3×D414yes—
791C22×C4C23×D311yescharacteristic
792C22×C4C23×D311yescharacteristic
793C22×C4C23×D311yescharacteristic
794Q16—68no—
795Q16—68no—
796SD16—68no—
797SD16—68no—
798SD16—68no—
799SD16—68no—
800D8—68no—
801D8—68no—
802M16—24no—
803M16—24no—
804M16—64no—
805M16—64no—
806C2×C8—24no—
807C2×C8—34no—
808C2×C8—64no—
809C2×C8C23×D314yes—
810C4⋊C4—22no—
811C4⋊C4—22no—
812C4⋊C4—22no—
813C4⋊C4—68no—
814C4⋊C4C23×D314yes—
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—84no—
828C22×C3C2×#12012yes—
829C22×C3C2×#12012yes—
830C22×C3C2×#12012yes—
831C22×C3C23×D411yescharacteristic
832C2×D3—24no—
833C2×D3—24no—
834C2×D3—24no—
835C2×D3—24no—
836C2×D3—42no—
837C2×D3—42no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3—84no—
842C2×D3—84no—
843C2×D3—816no—
844C2×D3—84no—
845C3×C4—24no—
846C3×C4—44no—
847C3×C4C2×#12012yes—
848C3×C4C2×#12012yes—
849C3×C4C2×#12012yes—
850C3×C4C23×D411yescharacteristic
851C3×C4C23×D411yescharacteristic
852Dic3—24no—
853Dic3—24no—
854Dic3—42no—
855C23—22no—
856C23—24no—
857C23—34no—
858C23—41no—
859C23—41no—
860C23—616no—
861C23—62no—
862C23—64no—
863C23—64no—
864C23—62no—
865C23—81no—
866C23—81no—
867C23—122no—
868C23—122no—
869C23—122no—
870C23—122no—
871C23—122no—
872C23—241no—
873C23—241no—
874C23—244no—
875C23—244no—
876C23#88214yes—
877C23C2×D3×D411yescharacteristic
878C23C2×D3×D411yescharacteristic
879C23C2×D3×D411yescharacteristic
880Q8—22no—
881Q8—24no—
882Q8—34no—
883Q8—616no—
884Q8—62no—
885Q8—64no—
886Q8—64no—
887Q8—64no—
888Q8—62no—
889Q8—62no—
890Q8—122no—
891Q8C22×D1214yes—
892D4—28no—
893D4—28no—
894D4—22no—
895D4—24no—
896D4—34no—
897D4—616no—
898D4—616no—
899D4—616no—
900D4—68no—
901D4—68no—
902D4—68no—
903D4—68no—
904D4—62no—
905D4—62no—
906D4—62no—
907D4—64no—
908D4—64no—
909D4—64no—
910D4—124no—
911D4—124no—
912D4—122no—
913D4—248no—
914D4C22×D1214yes—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—28no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—34no—
921C2×C4—44no—
922C2×C4—616no—
923C2×C4—616no—
924C2×C4—616no—
925C2×C4—62no—
926C2×C4—64no—
927C2×C4—64no—
928C2×C4—64no—
929C2×C4—64no—
930C2×C4—68no—
931C2×C4—68no—
932C2×C4—68no—
933C2×C4—62no—
934C2×C4—82no—
935C2×C4—82no—
936C2×C4—122no—
937C2×C4—124no—
938C2×C4—124no—
939C2×C4#88214yes—
940C2×C4#88214yes—
941C2×C4#88214yes—
942C2×C4C22×D1212yes—
943C2×C4C22×D1212yes—
944C2×C4C22×D1212yes—
945C2×C4C2×D3×D412yes—
946C2×C4C2×D3×D412yes—
947C2×C4C2×D3×D412yes—
948C2×C4C2×D3×D411yescharacteristic
949C2×C4C2×D3×D411yescharacteristic
950C2×C4C2×D3×D411yescharacteristic
951C2×C4C24×D311yescharacteristic
952C8—24no—
953C8—64no—
954C2×C3—22no—
955C2×C3—22no—
956C2×C3—22no—
957C2×C3—44no—
958C2×C3C22×#12011yescharacteristic
959C2×C3#358511yescharacteristic
960C2×C3#358611yescharacteristic
961D3—44no—
962D3—44no—
963D3—82no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—24no—
971C22—44no—
972C22—42no—
973C22—42no—
974C22—64no—
975C22—64no—
976C22—64no—
977C22—64no—
978C22—84no—
979C22—122no—
980C22—122no—
981C22—122no—
982C22—122no—
983C22—122no—
984C22—244no—
985C22—244no—
986C22—244no—
987C22—2416no—
988C22C2×#88212yes—
989C22C2×#88212yes—
990C22C2×#88212yes—
991C22C22×D3×D411yescharacteristic
992C4—24no—
993C4—44no—
994C4—64no—
995C4—64no—
996C4—122no—
997C4C2×#88212yes—
998C4C2×#88212yes—
999C4C2×#88212yes—
1000C4C23×D1211yescharacteristic
1001C4C22×D3×D411yescharacteristic
1002C3#6037111yescharacteristic, complemented, Sylow
1003C2—22no—
1004C2—22no—
1005C2—22no—
1006C2—44no—
1007C2—124no—
1008C2—124no—
1009C2—242no—
1010C2C22×#88211yescharacteristic
1011C2#8719211yescharacteristic
1012C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#417C2
socleC22×C3C23×D4
hypercenterC2×#417D3
hypocenterC3#60371
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#5964C2semidirect
2. C2×#5822C2semidirect
3. C2×#5748C2semidirect
4. C2×#5510C2semidirect
5. C2×C3×#417C2semidirect
6. #83762C2semidirect
7. C2×#4966C2semidirect
8. #78887C2semidirect
9. #78886C2semidirect
10. #78885C2semidirect
11. #78884C2semidirect
12. #78795C2semidirect
13. #78747C2semidirect
19. C2×#1010C22semidirect
21. C2×#1009C22semidirect
24. C2×#1007C22semidirect
26. C2×#1004C22semidirect
30. C22×#235C22semidirect
31. C22×C3×M16C22semidirect
32. C22×C3×C4⋊C4C22semidirect
33. C2×#951C22semidirect
35. C2×#950C22semidirect
36. C2×#949C22semidirect
37. C2×#942C22semidirect
38. C2×#932C22semidirect
40. C22×#208C22semidirect
42. C2×#909C22semidirect
43. C2×#909C22semidirect
44. C2×#908C22semidirect
45. C2×#908C22semidirect
46. C2×#904C22semidirect
49. #5510C22semidirect
50. #5510C22semidirect
52. C2×#897C22semidirect
54. C2×#895C22semidirect
55. C3×#417C22semidirect
56. C3×#417C22semidirect
57. C2×C3×#103C22semidirect
58. C2×C3×#102C22semidirect
59. #5129C22semidirect
60. #5126C22semidirect
61. #5110C22semidirect
62. C2×#810C22semidirect
63. #4966C22semidirect
64. #4966C22semidirect
65. C2×#809C22semidirect
66. #4810C22semidirect
67. #4809C22semidirect
68. #4808C22semidirect
69. #4806C22semidirect
70. #4783C22semidirect
71. #4781C22semidirect
72. #4776C22semidirect
73. #4773C22semidirect
85. C2×#417D3semidirect
90. C2×C3×#41D4semidirect
145. C2×#235D4semidirect
245. C22×M16C2×D3semidirect
255. C22×C4⋊C4C2×D3semidirect
266. #417C2×D3semidirect
267. #417C2×D3semidirect
269. C2×#103C2×D3semidirect
271. C2×#102C2×D3semidirect
286. C3×#41C2×D4semidirect
289. C2×C3×Q8C2×D4semidirect
296. C2×C3×D4C2×D4semidirect
367. #235C2×D4semidirect
380. C2×D12C2×D4semidirect
406. C2×Dic6C2×D4semidirect
478. C2×#41D12semidirect
701. #41C2×D12semidirect
720. C2×Q8C2×D12semidirect
759. C2×D4C2×D12semidirect
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×#58222
C2×#57482
C2×#55102
C2×C3×#4172
#837622
C2×#49662
#788872
#788862
#788852
#788842
#787952
#787472
#603713