Finite Group Databasebeta

← #11662474

Subgroups — #11662474

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#537C211yesmaximal, characteristic, complemented
2#87268C211yesmaximal, characteristic, complemented
3C2×#5822C211yesmaximal, characteristic, complemented
4C2×#5819C211yesmaximal, characteristic, complemented
5#84072C211yesmaximal, characteristic, complemented
6#83423C214yesmaximal, complemented
7#83422C214yesmaximal, complemented
8#83421C214yesmaximal, complemented
9#83420C214yesmaximal, complemented
10#82732C214yesmaximal, complemented
11#82621C214yesmaximal, complemented
12C2×#4966C211yesmaximal, characteristic, complemented
13C2×#4964C211yesmaximal, characteristic, complemented
14#60456—31nomaximal, Sylow
15C22×C3×#41C2211yescharacteristic
16C22×C3×#41C2211yescharacteristic
17C22×#235C2211yescharacteristic
18C3×#537—22no—
19C3×#537—22no—
20C3×#537C2214yes—
21C3×#537C2214yescomplemented
22C2×C3×C22⋊Q8—21no—
23C2×C3×C22⋊Q8C2212yescomplemented
24C2×C3×#121—21no—
25C2×C3×#121—22no—
26C2×C3×#121C2212yescomplemented
27C22×C3×C4⋊C4C2211yescharacteristic
28#5833C2212yescomplemented
29#5833C2212yescomplemented
30#5832—22no—
31#5830C2212yescomplemented
32#5828—22no—
33#5825C2212yescomplemented
34C2×#951C2212yescomplemented
35#5822—28no—
36C2×#950C2214yescomplemented
37C2×#949C2212yescomplemented
38#5819—28no—
39C2×#948C2214yescomplemented
40C2×#948C2214yescomplemented
41#5816—21no—
42C2×#942C2212yes—
43#5805—21no—
44#5804—22no—
45C2×#932C2212yes—
46#5791C2214yes—
47C2×#926C2211yescharacteristic
48C22×#208C2211yescharacteristic
49C22×#208C2211yescharacteristic
50C22×#208C2214yescomplemented
51#5233C2214yescomplemented
52#5232C2212yescomplemented
53#5232C2212yescomplemented
54#5225C2212yescomplemented
55#5215C2212yescomplemented
56#5052C2218yescomplemented
57#5051C2218yescomplemented
58#5049C2218yescomplemented
59#5048C2218yescomplemented
60#5042C2218yescomplemented
61#5041C2218yescomplemented
62#5039C2218yescomplemented
63#5038C2218yescomplemented
64C2×#810C2212yescomplemented
65#4966C2214yes—
66#4966C2214yescomplemented
67C2×#809C2212yescomplemented
68#4964C2214yescomplemented
69#4964C2214yescomplemented
70C2×#808C2212yescomplemented
71C2×#807C2212yescomplemented
72C2×#575—31no—
73C2×#568—31no—
74#3449—31no—
75C2×#537D311yescharacteristic, complemented
76#3063—34no—
77#3062—34no—
78#3061—34no—
79#3060—34no—
80#3056—34no—
81#3055—34no—
82C2×#428—31no—
83#2896—31no—
84C2×#417—31no—
85C2×C3×#41—24no—
86C2×C3×#41—21no—
87C2×C3×#41—21no—
88C2×C3×#41—24no—
89C2×C3×#41—24no—
90C2×C3×#41—24no—
91C2×C3×#41D412yes—
92C2×C3×#41D412yes—
93C2×C3×#41C2312yes—
94C2×C3×#41C2312yes—
95C2×C3×#41C2312yes—
96C2×C3×#41C2312yes—
97C22×C3×Q8D411yescharacteristic
98C22×C3×Q8C2311yescharacteristic
99C22×C3×D4—21no—
100C22×C3×D4—22no—
101C22×C3×D4D412yes—
102C22×C3×D4D411yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4—21no—
105C23×C3×C4—21no—
106C23×C3×C4C2312yes—
107C23×C3×C4C2311yescharacteristic
108C22×#67—21no—
109C2×#235—21no—
110C2×#235—21no—
111C2×#235—24no—
112C2×#235—24no—
113C2×#235C2312yes—
114C2×#235C2312yes—
115C22×D12C2311yescharacteristic
116C22×C4×D3—21no—
117C22×Dic6C2311yescharacteristic
118C3×C22⋊Q8—24no—
119C3×C22⋊Q8—24no—
120C3×C22⋊Q8—24no—
121C3×C22⋊Q8C2318yes—
122C3×#121—24no—
123C3×#121—28no—
124C3×#121—24no—
125C3×#121—28no—
126C3×#121—24no—
127C3×#121C2318yes—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—22no—
132C2×C3×C4⋊C4C2312yes—
133C2×C3×C4⋊C4C2312yes—
134C2×C3×C4⋊C4C2312yes—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137#953—24no—
138C2×#217—21no—
139#951—28no—
140#950—216no—
141#949—28no—
142#948—216no—
143#948—216no—
144#947—22no—
145#946—22no—
146#946—22no—
147#944—22no—
148C2×#216C2314yes—
149#942—28no—
150C2×#215C2314yes—
151#940—22no—
152#939—24no—
153#939—24no—
154#938—22no—
155#938—22no—
156#937—24no—
157#936—22no—
158#935—24no—
159C2×#214C2314yes—
160#932—28no—
161C2×#213C2314yes—
162#930C2314yes—
163#930C2314yes—
164#929—24no—
165C4×#67—24no—
166C4×#67—24no—
167#926—21no—
168#926—21no—
169#926C2312yes—
170#926C2312yes—
171C2×C4⋊Dic3C2311yescharacteristic
172C2×C4⋊Dic3C2311yescharacteristic
173#924C2314yes—
174#924C2314yes—
175C2×C4×Dic3—21no—
176C2×#208—24no—
177C2×#208—216no—
178C2×#208D418yescomplemented
179C2×#208C2312yes—
180C2×#208C2312yes—
181C2×#208C2318yes—
182C2×#208C2312yes—
183C2×#208C2312yes—
184C22×C3⋊C8C2312yes—
185C22×C3⋊C8C2318yes—
186C22×C3⋊C8C2312yes—
187#835C2314yes—
188#835C2314yes—
189#832C2314yes—
190#832C2314yes—
191#810C2318yes—
192#809C2318yes—
193#808C2318yes—
194#807C2318yes—
195C22×#41—31no—
196C22×#41C2×D311yescharacteristic
197C22×#41C2×D311yescharacteristic
198#575—68no—
199C2×#137—32no—
200C2×#137—32no—
201C2×AGL(1,ℤ/8)—32no—
202C2×AGL(1,ℤ/8)—32no—
203C2×#135—34no—
204#568—68no—
205C2×#131—34no—
206C2×#131—34no—
207C22×M16—31no—
208C22×M16—31no—
209C22×M16—34no—
210#537—22no—
211#537—22no—
212#537—32no—
213#537—32no—
214#537C2×D314yes—
215#537C2×D314yescomplemented
216#536—32no—
217#536—61no—
218#535—32no—
219#535—61no—
220#534—62no—
221#532—62no—
222#525—34no—
223#525—62no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2×D312yescomplemented
226C2×#121—21no—
227C2×#121—22no—
228C2×#121C2×D312yescomplemented
229C2×#117—31no—
230C22×C4⋊C4C2×D311yescharacteristic
231#470—38no—
232#469—38no—
233#468—38no—
234#468—38no—
235#467—38no—
236#466—38no—
237#465—38no—
238#465—38no—
239#428—34no—
240#428—34no—
241C2×#107—32no—
242C2×#106—32no—
243#419—32no—
244#418—32no—
245#417—32no—
246#417—32no—
247#417—34no—
248#417—34no—
249#416—34no—
250C2×#103—32no—
251C2×#102—32no—
252C24×C3—21no—
253C24×C3C2×D412yes—
254C24×C3C2×D411yescharacteristic
255C23×D3—21no—
256C3×#41—28no—
257C3×#41—28no—
258C3×#41—24no—
259C3×#41—24no—
260C3×#41—24no—
261C3×#41—24no—
262C3×#41—24no—
263C3×#41—24no—
264C3×#41—24no—
265C3×#41—24no—
266C3×#41—44no—
267C3×#41—44no—
268C2×C3×Q8—24no—
269C2×C3×Q8—21no—
270C2×C3×Q8—22no—
271C2×C3×Q8—22no—
272C2×C3×Q8C2×D412yes—
273C2×C3×Q8C2×D412yes—
274C2×C3×Q8C2412yes—
275C2×C3×D4—28no—
276C2×C3×D4—22no—
277C2×C3×D4—22no—
278C2×C3×D4—28no—
279C2×C3×D4—24no—
280C2×C3×D4—22no—
281C2×C3×D4—21no—
282C2×C3×D4—22no—
283C2×C3×D4—44no—
284C2×C3×D4—84no—
285C2×C3×D4C2×D414yes—
286C2×C3×D4C2×D412yes—
287C2×C3×D4C2×D412yes—
288C2×C3×D4C2×D414yes—
289C2×C3×D4C2412yes—
290C22×C3×C4—24no—
291C22×C3×C4—24no—
292C22×C3×C4—22no—
293C22×C3×C4—21no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—44no—
299C22×C3×C4—82no—
300C22×C3×C4C2×D414yes—
301C22×C3×C4C2×D414yes—
302C22×C3×C4C2×D412yes—
303C22×C3×C4C2×D411yescharacteristic
304C22×C3×C4C2×D411yescharacteristic
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4#4114yes—
307C22×C3×C4C2414yes—
308C22×C3×C4C2411yescharacteristic
309C22×C3×C4C2411yescharacteristic
310C22×C3×C4C2411yescharacteristic
311C2×#67—22no—
312C2×#67—22no—
313C2×#67—24no—
314C2×#67—24no—
315C2×#67—44no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319#235—24no—
320#235—24no—
321#235—24no—
322#235—24no—
323#235—44no—
324#235—44no—
325C2×D12—22no—
326C2×D12—22no—
327C2×D12—21no—
328C2×D12C2412yes—
329C2×C4×D3—22no—
330C2×C4×D3—22no—
331C2×C4×D3—44no—
332C2×Dic6—22no—
333C2×Dic6—22no—
334C2×Dic6—21no—
335C2×Dic6C2412yes—
336C3×C4⋊C4—22no—
337C3×C4⋊C4—22no—
338C3×C4⋊C4—22no—
339C3×C4⋊C4—28no—
340C3×C4⋊C4C2414yes—
341C3×C22⋊C4—28no—
342C3×C22⋊C4—28no—
343#217—24no—
344#217—24no—
345#217—22no—
346#217—22no—
347#216—28no—
348#215—28no—
349#214—28no—
350#213—28no—
351(C2×D3)⋊C4—24no—
352(C2×D3)⋊C4—24no—
353C4⋊Dic3—21no—
354C4⋊Dic3—21no—
355C4⋊Dic3C2412yes—
356C4⋊Dic3C2412yes—
357Dic3⋊C4—24no—
358Dic3⋊C4—24no—
359C4×Dic3—22no—
360C4×Dic3—22no—
361#208—24no—
362#208—24no—
363#208—216no—
364#208C2×D418yes—
365#208C2×D418yescomplemented
366C2×C3⋊C8—24no—
367C2×C3⋊C8—216no—
368C2×C3⋊C8C2×D418yescomplemented
369C2×C3⋊C8C2414yes—
370C2×C3⋊C8C2414yes—
371C2×#41—24no—
372C2×#41—24no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—24no—
376C2×#41—24no—
377C2×#41—32no—
378C2×#41—32no—
379C2×#41—61no—
380C2×#41—61no—
381C2×#41—64no—
382C2×#41—64no—
383C2×#41#6712yes—
384C2×#41#6712yes—
385C2×#41C22×D312yes—
386C2×#41C22×D312yes—
387C2×#41C22×D312yes—
388C2×#41C22×D312yes—
389C22×Q8—31no—
390C22×Q8#6711yescharacteristic
391C22×Q8C22×D311yescharacteristic
392C22×D4—21no—
393C22×D4—22no—
394C22×D4—31no—
395C22×D4—61no—
396C22×D4#6712yes—
397C22×D4#6711yescharacteristic
398C22×D4C22×D311yescharacteristic
399C23×C4—21no—
400C23×C4—21no—
401C23×C4—61no—
402C23×C4C22×D312yes—
403C23×C4C22×D311yescharacteristic
404#137—68no—
405#137—68no—
406AGL(1,ℤ/8)—68no—
407AGL(1,ℤ/8)—68no—
408#135—616no—
409C2×Q16—34no—
410C2×SD16—34no—
411C2×SD16—34no—
412C2×D8—34no—
413#131—616no—
414#131—616no—
415C2×M16—38no—
416C2×M16—32no—
417C2×M16—32no—
418C2×M16—32no—
419C2×M16—32no—
420C2×M16—38no—
421C2×M16—616no—
422C2×M16—64no—
423C22×C8—32no—
424C22×C8—32no—
425C22×C8—38no—
426C4⋊Q8—62no—
427#127—62no—
428#124—62no—
429#124—62no—
430#123—64no—
431#123—64no—
432C22⋊Q8—24no—
433C22⋊Q8—24no—
434C22⋊Q8—24no—
435C22⋊Q8—34no—
436C22⋊Q8—34no—
437C22⋊Q8—62no—
438C22⋊Q8—62no—
439C22⋊Q8C22×D318yes—
440#121—24no—
441#121—28no—
442#121—24no—
443#121—28no—
444#121—24no—
445#121—34no—
446#121—34no—
447#121—62no—
448#121—62no—
449#121—64no—
450#121—64no—
451#121C22×D318yes—
452#120—64no—
453#120—64no—
454C4×D4—64no—
455C4×D4—64no—
456#117—32no—
457#117—32no—
458#117—61no—
459#117—61no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4C22×D312yes—
467C2×C4⋊C4C22×D312yes—
468C2×C4⋊C4C22×D312yes—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—61no—
472C2×C42—61no—
473#107—38no—
474#106—38no—
475#103—34no—
476#103—34no—
477#103—38no—
478#102—34no—
479#102—34no—
480#102—38no—
481C23×C3—24no—
482C23×C3—22no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—42no—
486C23×C3—42no—
487C23×C3—42no—
488C23×C3—42no—
489C23×C3—42no—
490C23×C3#12114yes—
491C23×C3C22×D414yes—
492C23×C3C22×D411yescharacteristic
493C23×C3C22×D411yescharacteristic
494C23×C3C22×D411yescharacteristic
495C22×D3—22no—
496C22×D3—42no—
497C22×D3—81no—
498C22×D3—81no—
499C3×Q8—24no—
500C3×Q8—24no—
501C3×Q8—22no—
502C3×Q8—22no—
503C3×Q8—42no—
504C3×D4—28no—
505C3×D4—28no—
506C3×D4—24no—
507C3×D4—24no—
508C3×D4—22no—
509C3×D4—22no—
510C3×D4—44no—
511C3×D4—44no—
512C3×D4—42no—
513C3×D4—88no—
514C2×C3×C4—24no—
515C2×C3×C4—28no—
516C2×C3×C4—24no—
517C2×C3×C4—24no—
518C2×C3×C4—24no—
519C2×C3×C4—22no—
520C2×C3×C4—44no—
521C2×C3×C4—42no—
522C2×C3×C4—44no—
523C2×C3×C4—44no—
524C2×C3×C4—82no—
525C2×C3×C4—82no—
526C2×C3×C4#12114yes—
527C2×C3×C4#12114yes—
528C2×C3×C4#12114yes—
529C2×C3×C4C22×D412yes—
530C2×C3×C4C22×D412yes—
531C2×C3×C4C22×D412yes—
532C2×C3×C4C22×D414yes—
533C2×C3×C4C22×D411yescharacteristic
534C2×C3×C4C22×D411yescharacteristic
535C2×C3×C4C22×D411yescharacteristic
536C2×C3×C4C2×#4112yes—
537C2×C3×C4C2×#4112yes—
538C2×C3×C4C2×#4112yes—
539C2×C3×C4C2511yescharacteristic
540#67—44no—
541#67—44no—
542#67—84no—
543#67—84no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—42no—
548C2×Dic3—81no—
549C2×Dic3—81no—
550D12—22no—
551D12—22no—
552D12—42no—
553C4×D3—44no—
554C4×D3—44no—
555Dic6—22no—
556Dic6—22no—
557Dic6—42no—
558C3⋊C8—24no—
559C3⋊C8C22×D418yes—
560C24—21no—
561C24—61no—
562C24C2×#6712yes—
563C24C2×#6711yescharacteristic
564#41—28no—
565#41—28no—
566#41—24no—
567#41—24no—
568#41—24no—
569#41—24no—
570#41—24no—
571#41—24no—
572#41—24no—
573#41—24no—
574#41—44no—
575#41—44no—
576#41—64no—
577#41—64no—
578#41—64no—
579#41—64no—
580#41—124no—
581#41—124no—
582C2×Q8—24no—
583C2×Q8—21no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—32no—
587C2×Q8—61no—
588C2×Q8—62no—
589C2×Q8—62no—
590C2×Q8C2×#6712yes—
591C2×Q8C2×#6712yes—
592C2×Q8C23×D312yes—
593C2×D4—28no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—28no—
597C2×D4—24no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—21no—
601C2×D4—32no—
602C2×D4—44no—
603C2×D4—62no—
604C2×D4—62no—
605C2×D4—64no—
606C2×D4—64no—
607C2×D4—62no—
608C2×D4—62no—
609C2×D4—61no—
610C2×D4—84no—
611C2×D4—124no—
612C2×D4C2×#6714yes—
613C2×D4C2×#6714yes—
614C2×D4C2×#6712yes—
615C2×D4C2×#6712yes—
616C2×D4C23×D312yes—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—44no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—82no—
632C22×C4—124no—
633C22×C4D3×D414yes—
634C22×C4#23714yes—
635C22×C4C2×#6712yes—
636C22×C4C2×#6714yes—
637C22×C4C2×#6711yescharacteristic
638C22×C4C2×#6711yescharacteristic
639C22×C4C2×#6711yescharacteristic
640C22×C4C23×D314yes—
641C22×C4C23×D311yescharacteristic
642C22×C4C23×D311yescharacteristic
643C22×C4C23×D311yescharacteristic
644Q16—68no—
645SD16—68no—
646SD16—68no—
647D8—68no—
648M16—38no—
649M16—38no—
650M16—616no—
651M16—64no—
652M16—64no—
653C2×C8—38no—
654C2×C8—34no—
655C2×C8—34no—
656C2×C8—616no—
657C2×C8—64no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—28no—
662C4⋊C4—32no—
663C4⋊C4—32no—
664C4⋊C4—61no—
665C4⋊C4—61no—
666C4⋊C4—64no—
667C4⋊C4—64no—
668C4⋊C4C23×D314yes—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—62no—
672C22⋊C4—62no—
673C22⋊C4—64no—
674C22⋊C4—64no—
675C22⋊C4—64no—
676C22⋊C4—64no—
677C42—62no—
678C42—62no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—24no—
686C22×C3—24no—
687C22×C3—24no—
688C22×C3—44no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—84no—
693C22×C3—84no—
694C22×C3C2×#12112yes—
695C22×C3C2×#12112yes—
696C22×C3C2×#12112yes—
697C22×C3C23×D411yescharacteristic
698C2×D3—42no—
699C2×D3—42no—
700C2×D3—42no—
701C2×D3—84no—
702C3×C4—24no—
703C3×C4—44no—
704C3×C4—42no—
705C3×C4C2×#12112yes—
706C3×C4C2×#12112yes—
707C3×C4C2×#12112yes—
708C3×C4C23×D411yescharacteristic
709C3×C4C22×#4111yescharacteristic
710Dic3—42no—
711Dic3—42no—
712Dic3—42no—
713C23—24no—
714C23—22no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—62no—
723C23—122no—
724C23—241no—
725C23—241no—
726C23#93914yes—
727C23C22×#6714yes—
728C23C22×#6711yescharacteristic
729C23C22×#6711yescharacteristic
730C23C22×#6711yescharacteristic
731Q8—24no—
732Q8—24no—
733Q8—22no—
734Q8—22no—
735Q8—42no—
736Q8—62no—
737Q8—62no—
738Q8—122no—
739D4—28no—
740D4—28no—
741D4—22no—
742D4—22no—
743D4—24no—
744D4—24no—
745D4—44no—
746D4—44no—
747D4—42no—
748D4—62no—
749D4—62no—
750D4—88no—
751D4—124no—
752D4—124no—
753D4—122no—
754D4—244no—
755D4—244no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—28no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—82no—
770C2×C4—82no—
771C2×C4—122no—
772C2×C4—124no—
773C2×C4—124no—
774C2×C4—241no—
775C2×C4—241no—
776C2×C4#93914yes—
777C2×C4#93914yes—
778C2×C4#93914yes—
779C2×C4C2×D3×D412yes—
780C2×C4C2×D3×D412yes—
781C2×C4C2×D3×D412yes—
782C2×C4C2×#23712yes—
783C2×C4C2×#23712yes—
784C2×C4C2×#23712yes—
785C2×C4C22×#6714yes—
786C2×C4C22×#6711yescharacteristic
787C2×C4C22×#6711yescharacteristic
788C2×C4C22×#6711yescharacteristic
789C2×C4C24×D311yescharacteristic
790C8—38no—
791C8—64no—
792C2×C3—22no—
793C2×C3—22no—
794C2×C3—22no—
795C2×C3—44no—
796C2×C3—82no—
797C2×C3C22×#12111yescharacteristic
798C2×C3#358511yescharacteristic
799C2×C3#358611yescharacteristic
800D3—82no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—24no—
808C22—24no—
809C22—24no—
810C22—44no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—84no—
815C22—84no—
816C22—122no—
817C22—122no—
818C22—122no—
819C22—244no—
820C22C2×#93912yes—
821C22C2×#93912yes—
822C22C2×#93912yes—
823C22C23×#6711yescharacteristic
824C4—24no—
825C4—42no—
826C4—44no—
827C4—122no—
828C4—122no—
829C4—122no—
830C4C2×#93912yes—
831C4C2×#93912yes—
832C4C2×#93912yes—
833C4C22×D3×D411yescharacteristic
834C4C22×#23711yescharacteristic
835C3#6045611yescharacteristic, complemented, Sylow
836C2—22no—
837C2—22no—
838C2—22no—
839C2—44no—
840C2—82no—
841C2—242no—
842C2C22×#93911yescharacteristic
843C2#8727711yescharacteristic
844C2#8728711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#537C2
socleC22×C3C23×D4
hypercenterC2×#537D3
hypocenterC3#60456
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×C3×#537C2semidirect
2. #87268C2semidirect
3. C2×#5822C2semidirect
4. C2×#5819C2semidirect
5. #84072C2semidirect
6. #83423C2semidirect
7. #83422C2semidirect
8. #83421C2semidirect
9. #83420C2semidirect
10. #82732C2semidirect
11. #82621C2semidirect
12. C2×#4966C2semidirect
13. C2×#4964C2semidirect
21. C3×#537C22semidirect
23. C2×C3×C22⋊Q8C22semidirect
26. C2×C3×#121C22semidirect
28. #5833C22semidirect
29. #5833C22semidirect
31. #5830C22semidirect
33. #5825C22semidirect
34. C2×#951C22semidirect
36. C2×#950C22semidirect
37. C2×#949C22semidirect
39. C2×#948C22semidirect
40. C2×#948C22semidirect
50. C22×#208C22semidirect
51. #5233C22semidirect
52. #5232C22semidirect
53. #5232C22semidirect
54. #5225C22semidirect
55. #5215C22semidirect
56. #5052C22semidirect
57. #5051C22semidirect
58. #5049C22semidirect
59. #5048C22semidirect
60. #5042C22semidirect
61. #5041C22semidirect
62. #5039C22semidirect
63. #5038C22semidirect
64. C2×#810C22semidirect
66. #4966C22semidirect
67. C2×#809C22semidirect
68. #4964C22semidirect
69. #4964C22semidirect
70. C2×#808C22semidirect
71. C2×#807C22semidirect
75. C2×#537D3semidirect
178. C2×#208D4semidirect
215. #537C2×D3semidirect
225. C2×C22⋊Q8C2×D3semidirect
228. C2×#121C2×D3semidirect
365. #208C2×D4semidirect
368. C2×C3⋊C8C2×D4semidirect
835. C3#60456semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5372
#872682
C2×#58222
C2×#58192
#840722
#834232
#834222
#834212
#834202
#827322
#826212
C2×#49662
C2×#49642
#604563