Finite Group Databasebeta

← #11664115

Subgroups — #11664115

Order 768.

2134 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#520C211yesmaximal, characteristic, complemented
2#85747C211yesmaximal, characteristic, complemented
3#84082C211yesmaximal, characteristic, complemented
4#84080C211yesmaximal, characteristic, complemented
5#82576C214yesmaximal, complemented
6#82568C214yesmaximal, complemented
7#82565C212yesmaximal, complemented
8#82564C212yesmaximal, complemented
9#82560C212yesmaximal, complemented
10#82558C212yesmaximal, complemented
11#82445C212yesmaximal, complemented
12#82442C212yesmaximal, complemented
13#82310C212yesmaximal, complemented
14#82309C212yesmaximal, complemented
15#82210C211yesmaximal, characteristic, complemented
16#82139C211yesmaximal, characteristic, complemented
17C2×#4968C211yesmaximal, characteristic, complemented
18#60588—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic
20C3×#520—21no—
21C3×#520—21no—
22C3×#520—22no—
23C3×#520C2212yes—
24C3×#520C2212yes—
25C3×#520C2214yescomplemented
26C2×C3×C4×Q8C2212yescomplemented
27C2×C3×C4×D4—22no—
28C2×C3×C4×D4C2212yescomplemented
29C2×C3×#117—21no—
30C2×C3×#117C2211yescharacteristic
31C22×C3×C4⋊C4—21no—
32C22×C3×C4⋊C4C2211yescharacteristic
33C2×#950C2212yes—
34C2×#949C2212yes—
35#5791C2211yescharacteristic
36C2×#930C2211yescharacteristic
37#5535C2212yescomplemented
38#5534C2212yescomplemented
39#5532—21no—
40#5530—21no—
41#5527—22no—
42#5525C2211yescharacteristic, complemented
43#5523C2211yescharacteristic, complemented
44#5521C2211yescharacteristic, complemented
45#5519C2211yescharacteristic, complemented
46#5514—21no—
47#5507—21no—
48#5490—22no—
49#5479C2212yes—
50#5477C2212yes—
51#5239C2212yescomplemented
52#5238C2214yes—
53#5238C2212yescomplemented
54#5233C2212yes—
55#5232C2212yes—
56#5228C2211yescharacteristic, complemented
57#5227C2212yes—
58#5227C2211yescharacteristic, complemented
59#5218C2211yescharacteristic, complemented
60#5217C2212yes—
61#5217C2211yescharacteristic, complemented
62#5207C2211yescharacteristic
63C2×#830C2211yescharacteristic
64#5030C2214yescomplemented
65#5028C2214yescomplemented
66#5027C2214yescomplemented
67#5026C2214yescomplemented
68C4×#215C2214yescomplemented
69C4×#215C2214yescomplemented
70#5022C2214yescomplemented
71#5020C2214yescomplemented
72C4×#214C2214yescomplemented
73#5016C2214yescomplemented
74#5015C2214yescomplemented
75#5014C2214yescomplemented
76#5014C2214yescomplemented
77C4×#213C2214yescomplemented
78#5009C2214yescomplemented
79#5008C2214yescomplemented
80#5000C2214yescomplemented
81#4999C2212yescomplemented
82#4997C2212yescomplemented
83#4971C2212yescomplemented
84#4970C2212yescomplemented
85#4968C2212yes—
86#4968C2212yes—
87#4968C2212yescomplemented
88#4968C2214yescomplemented
89#4967C2212yescomplemented
90#4966C2212yescomplemented
91C2×#809C2212yescomplemented
92#4964C2212yescomplemented
93C2×#808C2212yescomplemented
94#4926C2212yescomplemented
95#4925C2212yescomplemented
96#3494—31no—
97C2×#520D311yescharacteristic, complemented
98#3125—34no—
99#3119—34no—
100#3117—32no—
101#3109—32no—
102#3105—32no—
103#3103—32no—
104#3092—31no—
105C2×#481—31no—
106#3084—32no—
107#3045—32no—
108#3006—31no—
109#3002—31no—
110#2952—32no—
111#2946—32no—
112#2924—31no—
113C2×C3×#41—28no—
114C2×C3×#41—21no—
115C2×C3×#41—21no—
116C2×C3×#41C2312yes—
117C2×C3×#41C2312yes—
118C22×C3×Q8C2311yescharacteristic
119C22×C3×D4—21no—
120C22×C3×D4C2311yescharacteristic
121C23×C3×C4—21no—
122C23×C3×C4—21no—
123C23×C3×C4—22no—
124C23×C3×C4C2311yescharacteristic
125C22×#67—21no—
126C2×#235—22no—
127C2×#235C2311yescharacteristic
128C22×D12C2311yescharacteristic
129C3×C4×Q8—22no—
130C3×C4×Q8—22no—
131C3×C4×Q8C2314yes—
132C3×C4×Q8C2314yes—
133C3×C4×D4—24no—
134C3×C4×D4—24no—
135C3×C4×D4—24no—
136C3×C4×D4—24no—
137C3×C4×D4—22no—
138C3×C4×D4—22no—
139C3×C4×D4C2314yes—
140C3×C4×D4C2314yes—
141C3×#117—22no—
142C3×#117—22no—
143C3×#117—24no—
144C3×#117D412yes—
145C3×#117D411yescharacteristic
146C3×#117D411yescharacteristic
147C3×#117C2311yescharacteristic
148C3×#117C2311yescharacteristic
149C3×#117C2312yes—
150C2×C3×C4⋊C4—21no—
151C2×C3×C4⋊C4—22no—
152C2×C3×C4⋊C4—21no—
153C2×C3×C4⋊C4—21no—
154C2×C3×C4⋊C4—22no—
155C2×C3×C4⋊C4—22no—
156C2×C3×C4⋊C4—24no—
157C2×C3×C4⋊C4D411yescharacteristic
158C2×C3×C4⋊C4D411yescharacteristic
159C2×C3×C4⋊C4C2312yes—
160C2×C3×C4⋊C4C2312yes—
161C2×C3×C4⋊C4C2312yes—
162C2×C3×C22⋊C4—22no—
163C2×C3×C22⋊C4D412yes—
164C2×C3×C42—22no—
165C2×C3×C42C2312yes—
166#953—21no—
167#950—28no—
168#949—28no—
169C2×#216C2312yes—
170C2×#215C2314yes—
171C2×#215C2312yes—
172C2×#214C2312yes—
173C2×#213C2314yes—
174C2×#213C2312yes—
175#930—22no—
176#930—21no—
177#930—21no—
178#930C2312yes—
179#930C2311yescharacteristic
180#930C2311yescharacteristic
181#930C2312yes—
182#929—22no—
183#929—21no—
184C4×#67—22no—
185C4×#67—21no—
186C4×#67—21no—
187C2×(C2×D3)⋊C4—21no—
188#926C2311yescharacteristic
189C2×C4⋊Dic3C2311yescharacteristic
190#924C2311yescharacteristic
191#924C2311yescharacteristic
192C2×#208C2312yes—
193C22×C3⋊C8C2312yes—
194#898—22no—
195#896—22no—
196#895—21no—
197#895—21no—
198#894—22no—
199#894—22no—
200#893—21no—
201#893—21no—
202#892—21no—
203D3×C4⋊C4—21no—
204#890—21no—
205#888—21no—
206#885—22no—
207#884—22no—
208#884—22no—
209#883—22no—
210#882—22no—
211#67⋊C4—22no—
212D3×C22⋊C4—22no—
213#878—22no—
214#876—22no—
215#875—22no—
216#875C2312yes—
217#874C2312yes—
218C4×D12—22no—
219C4×D12C2312yes—
220C4×D12C2312yes—
221C4×D12C2312yes—
222#872—22no—
223#870C2312yes—
224#869C2312yes—
225C4×Dic6C2312yes—
226#835C2314yes—
227#835C2312yes—
228#835C2312yes—
229#832C2314yes—
230#832C2312yes—
231#832C2312yes—
232#830C2311yescharacteristic
233#830C2312yes—
234#830C2311yescharacteristic
235#830C2312yes—
236#830C2312yes—
237#810C2314yes—
238#809C2314yes—
239#809C2314yes—
240#809C2314yes—
241#808C2314yes—
242#808C2314yes—
243#808C2314yes—
244#807C2314yes—
245C4⋊(C3⋊C8)C2314yes—
246C4⋊(C3⋊C8)C2314yes—
247#803C2314yes—
248C4×C3⋊C8C2314yes—
249C22×#41C2×D311yescharacteristic
250C2×AGL(1,ℤ/8)—32no—
251C2×#135—32no—
252#555—61no—
253#553—61no—
254#553—61no—
255#551—62no—
256#547—61no—
257#546—62no—
258#544—31no—
259#542—32no—
260#540—32no—
261#535—31no—
262#532—32no—
263#529—32no—
264#525—31no—
265C2×#121—31no—
266#520—21no—
267#520—21no—
268#520—22no—
269#520—31no—
270#520C2×D312yes—
271#520C2×D312yes—
272#520C2×D314yescomplemented
273#518—31no—
274C2×C4×Q8C2×D312yescomplemented
275C2×C4×D4—22no—
276C2×C4×D4C2×D312yescomplemented
277C2×#117—21no—
278C2×#117C2×D311yescharacteristic
279C22×C4⋊C4—21no—
280C22×C4⋊C4C2×D311yescharacteristic
281#484—32no—
282#483—32no—
283#481—32no—
284#481—32no—
285#481—34no—
286#481—32no—
287#480—32no—
288#479—34no—
289#478—34no—
290#476—34no—
291#475—34no—
292#464—34no—
293#463—34no—
294#460—34no—
295#459—34no—
296#452—32no—
297#451—31no—
298#450—31no—
299#449—32no—
300#449—34no—
301#448—31no—
302#448—32no—
303#447—32no—
304#447—31no—
305#442—34no—
306#442—34no—
307#441—34no—
308#440—34no—
309C4×SD16—34no—
310C4×SD16—34no—
311C4×SD16—34no—
312C4×D8—34no—
313#433—34no—
314#432—32no—
315#431—32no—
316#428—32no—
317C2×#106—32no—
318#424—32no—
319#417—32no—
320#417—32no—
321#416—32no—
322C2×#102—32no—
323#407—31no—
324C2×C22⋊C8—31no—
325#405—32no—
326C24×C3—21no—
327C24×C3C2×D411yescharacteristic
328C23×D3—21no—
329C3×#41—28no—
330C3×#41—28no—
331C3×#41—24no—
332C3×#41—24no—
333C3×#41—24no—
334C3×#41#4118yescomplemented
335C2×C3×Q8—24no—
336C2×C3×Q8—21no—
337C2×C3×Q8C2412yes—
338C2×C3×D4—28no—
339C2×C3×D4—22no—
340C2×C3×D4—22no—
341C2×C3×D4—24no—
342C2×C3×D4—21no—
343C2×C3×D4C2412yes—
344C22×C3×C4—28no—
345C22×C3×C4—21no—
346C22×C3×C4—22no—
347C22×C3×C4—22no—
348C22×C3×C4—24no—
349C22×C3×C4—22no—
350C22×C3×C4—22no—
351C22×C3×C4—22no—
352C22×C3×C4—24no—
353C22×C3×C4—24no—
354C22×C3×C4—84no—
355C22×C3×C4—82no—
356C22×C3×C4C2×D411yescharacteristic
357C22×C3×C4C2×D411yescharacteristic
358C22×C3×C4C2×D411yescharacteristic
359C22×C3×C4C2×D412yes—
360C22×C3×C4C2×D412yes—
361C22×C3×C4C2411yescharacteristic
362C22×C3×C4C2411yescharacteristic
363C22×C3×C4C2411yescharacteristic
364C2×#67—21no—
365C2×#67—22no—
366C2×#67—21no—
367C2×#67—22no—
368C2×#67—21no—
369C2×#67—82no—
370C22×Dic3—21no—
371#235—24no—
372#235—84no—
373C2×D12—24no—
374C2×D12—21no—
375C2×D12—22no—
376C2×D12—22no—
377C2×D12C2411yescharacteristic
378C2×D12C2412yes—
379C2×C4×D3—21no—
380C2×C4×D3—22no—
381C2×C4×D3—22no—
382C2×C4×D3—22no—
383C2×Dic6—22no—
384C2×Dic6C2411yescharacteristic
385C3×C4⋊C4—22no—
386C3×C4⋊C4—22no—
387C3×C4⋊C4—24no—
388C3×C4⋊C4—24no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4C2×D411yescharacteristic
391C3×C4⋊C4C2×D411yescharacteristic
392C3×C4⋊C4C2×D411yescharacteristic
393C3×C4⋊C4C2×D411yescharacteristic
394C3×C4⋊C4C2×D412yes—
395C3×C4⋊C4C2×D412yes—
396C3×C4⋊C4C2414yes—
397C3×C22⋊C4—24no—
398C3×C22⋊C4—24no—
399C3×C22⋊C4C2×D412yes—
400C3×C22⋊C4C2×D412yes—
401C3×C22⋊C4C2×D412yes—
402C3×C22⋊C4C2×D412yes—
403C3×C42—24no—
404C3×C42—24no—
405C3×C42C2×D412yes—
406C3×C42C2×D412yes—
407C3×C42C2412yes—
408C3×C42C2412yes—
409#217—21no—
410#217—21no—
411#217—21no—
412#216—24no—
413#215—28no—
414#215—24no—
415#214—24no—
416#213—28no—
417#213—24no—
418(C2×D3)⋊C4—22no—
419(C2×D3)⋊C4—22no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—22no—
422(C2×D3)⋊C4—22no—
423(C2×D3)⋊C4—22no—
424(C2×D3)⋊C4—22no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—22no—
427C4⋊Dic3—22no—
428C4⋊Dic3—21no—
429C4⋊Dic3C2411yescharacteristic
430C4⋊Dic3C2412yes—
431C4⋊Dic3C2411yescharacteristic
432Dic3⋊C4—22no—
433Dic3⋊C4—22no—
434Dic3⋊C4—22no—
435Dic3⋊C4—21no—
436Dic3⋊C4—21no—
437C4×Dic3—22no—
438C4×Dic3—21no—
439#208—24no—
440C2×C3⋊C8—24no—
441C2×C3⋊C8C2412yes—
442C2×C3⋊C8C2414yes—
443C2×C3⋊C8C2412yes—
444C2×#41—28no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—31no—
448C2×#41—62no—
449C2×#41C22×D312yes—
450C2×#41C22×D312yes—
451C22×Q8C22×D311yescharacteristic
452C22×D4—21no—
453C22×D4—31no—
454C22×D4—61no—
455C22×D4C22×D311yescharacteristic
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—22no—
459C23×C4C22×D311yescharacteristic
460AGL(1,ℤ/8)—68no—
461#135—68no—
462C2×Q16—32no—
463C2×SD16—32no—
464C2×SD16—34no—
465C2×SD16—32no—
466C2×D8—32no—
467C2×D8—34no—
468C2×M16—32no—
469C22×C8—32no—
470C4⋊Q8—32no—
471C4⋊Q8—61no—
472#127—32no—
473#126—62no—
474#126—62no—
475#125—32no—
476#125—61no—
477#124—32no—
478#124—62no—
479#124—62no—
480#123—61no—
481#123—62no—
482#123—62no—
483#123—62no—
484#123—62no—
485C22⋊Q8—31no—
486C22⋊Q8—31no—
487C22⋊Q8—62no—
488C22⋊Q8—62no—
489#121—32no—
490#121—32no—
491#121—31no—
492#121—31no—
493#121—61no—
494#121—61no—
495#121—62no—
496#121—61no—
497#121—61no—
498#121—62no—
499#121—62no—
500#120—61no—
501#120—62no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—32no—
505C4×Q8C22×D314yes—
506C4×Q8C22×D314yes—
507C4×D4—24no—
508C4×D4—24no—
509C4×D4—24no—
510C4×D4—24no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—32no—
514C4×D4—32no—
515C4×D4—32no—
516C4×D4—61no—
517C4×D4—61no—
518C4×D4—62no—
519C4×D4—61no—
520C4×D4—61no—
521C4×D4—62no—
522C4×D4—62no—
523C4×D4C22×D314yes—
524C4×D4C22×D314yes—
525#117—22no—
526#117—22no—
527#117—24no—
528#117—31no—
529#117—61no—
530#117—62no—
531#117#6712yes—
532#117#6711yescharacteristic
533#117#6711yescharacteristic
534#117C22×D311yescharacteristic
535#117C22×D311yescharacteristic
536#117C22×D312yes—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—24no—
544C2×C4⋊C4—31no—
545C2×C4⋊C4—61no—
546C2×C4⋊C4#6711yescharacteristic
547C2×C4⋊C4#6711yescharacteristic
548C2×C4⋊C4C22×D312yes—
549C2×C4⋊C4C22×D312yes—
550C2×C4⋊C4C22×D312yes—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—61no—
553C2×C22⋊C4—62no—
554C2×C22⋊C4#6712yes—
555C2×C42—22no—
556C2×C42C22×D312yes—
557#107—34no—
558#106—34no—
559#106—34no—
560#106—34no—
561C4⋊C8—34no—
562C4⋊C8—34no—
563#103—32no—
564#103—32no—
565#103—34no—
566#103—34no—
567#102—32no—
568#102—32no—
569#102—34no—
570#102—34no—
571#102—34no—
572#102—34no—
573C22⋊C8—31no—
574C22⋊C8—31no—
575C22⋊C8—32no—
576C22⋊C8—32no—
577C22⋊C8—32no—
578#97—34no—
579C4×C8—34no—
580C23×C3—24no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—41no—
585C23×C3—42no—
586C23×C3—42no—
587C23×C3C22×D411yescharacteristic
588C23×C3C22×D411yescharacteristic
589C23×C3C22×D411yescharacteristic
590C22×D3—22no—
591C22×D3—21no—
592C22×D3—42no—
593C22×D3—81no—
594C22×D3—81no—
595C3×Q8—24no—
596C3×Q8—22no—
597C3×Q8C2×#4114yes—
598C3×D4—28no—
599C3×D4—24no—
600C3×D4—28no—
601C3×D4—22no—
602C3×D4C2×#4114yes—
603C2×C3×C4—24no—
604C2×C3×C4—28no—
605C2×C3×C4—22no—
606C2×C3×C4—24no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—28no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—24no—
614C2×C3×C4—42no—
615C2×C3×C4—44no—
616C2×C3×C4—84no—
617C2×C3×C4—84no—
618C2×C3×C4—82no—
619C2×C3×C4—82no—
620C2×C3×C4C22×D412yes—
621C2×C3×C4C22×D412yes—
622C2×C3×C4C22×D411yescharacteristic
623C2×C3×C4C22×D411yescharacteristic
624C2×C3×C4C22×D412yes—
625C2×C3×C4C22×D412yes—
626C2×C3×C4C22×D411yescharacteristic
627C2×C3×C4C2×#4114yes—
628C2×C3×C4C2511yescharacteristic
629#67—42no—
630#67—42no—
631#67—44no—
632#67—81no—
633#67—82no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—22no—
637C2×Dic3—21no—
638C2×Dic3—81no—
639D12—24no—
640D12—22no—
641D12—42no—
642D12—82no—
643D12—82no—
644C4×D3—42no—
645C4×D3—82no—
646C4×D3—82no—
647C4×D3—82no—
648Dic6—22no—
649Dic6—82no—
650C3⋊C8—22no—
651C3⋊C8—22no—
652C3⋊C8—24no—
653C24—21no—
654C24—61no—
655C24C2×#6711yescharacteristic
656#41—28no—
657#41—28no—
658#41—24no—
659#41—24no—
660#41—24no—
661#41—64no—
662#41—244no—
663#41#23518yescomplemented
664C2×Q8—24no—
665C2×Q8—21no—
666C2×Q8—31no—
667C2×Q8—62no—
668C2×Q8C23×D312yes—
669C2×D4—28no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—24no—
673C2×D4—21no—
674C2×D4—32no—
675C2×D4—31no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—62no—
679C2×D4—61no—
680C2×D4—62no—
681C2×D4—64no—
682C2×D4—61no—
683C2×D4—62no—
684C2×D4—62no—
685C2×D4—242no—
686C2×D4C23×D312yes—
687C22×C4—28no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—62no—
700C22×C4—62no—
701C22×C4—62no—
702C22×C4—84no—
703C22×C4—82no—
704C22×C4C2×#6712yes—
705C22×C4C2×#6711yescharacteristic
706C22×C4C2×#6711yescharacteristic
707C22×C4C2×#6711yescharacteristic
708C22×C4C2×#6712yes—
709C22×C4C23×D311yescharacteristic
710C22×C4C23×D311yescharacteristic
711C22×C4C23×D311yescharacteristic
712Q16—64no—
713SD16—64no—
714SD16—68no—
715SD16—64no—
716D8—64no—
717D8—68no—
718M16—64no—
719C2×C8—32no—
720C2×C8—34no—
721C2×C8—32no—
722C2×C8—64no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—22no—
728C4⋊C4—32no—
729C4⋊C4—31no—
730C4⋊C4—31no—
731C4⋊C4—61no—
732C4⋊C4—62no—
733C4⋊C4—61no—
734C4⋊C4—62no—
735C4⋊C4—62no—
736C4⋊C4—62no—
737C4⋊C4—61no—
738C4⋊C4C2×#6711yescharacteristic
739C4⋊C4C2×#6711yescharacteristic
740C4⋊C4C2×#6712yes—
741C4⋊C4C2×#6711yescharacteristic
742C4⋊C4C2×#6711yescharacteristic
743C4⋊C4C2×#6712yes—
744C4⋊C4C23×D314yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—61no—
748C22⋊C4—61no—
749C22⋊C4—61no—
750C22⋊C4—62no—
751C22⋊C4—62no—
752C22⋊C4—62no—
753C22⋊C4—62no—
754C22⋊C4—62no—
755C22⋊C4—62no—
756C22⋊C4—61no—
757C22⋊C4—62no—
758C22⋊C4—61no—
759C22⋊C4C2×#6712yes—
760C22⋊C4C2×#6712yes—
761C22⋊C4C2×#6712yes—
762C22⋊C4C2×#6712yes—
763C42—24no—
764C42—24no—
765C42—61no—
766C42—62no—
767C42C2×#6712yes—
768C42C2×#6712yes—
769C42C23×D312yes—
770C42C23×D312yes—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—24no—
778C22×C3—21no—
779C22×C3—44no—
780C22×C3—48no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3#52512yes—
784C22×C3#57712yes—
785C22×C3C23×D411yescharacteristic
786C2×D3—42no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—42no—
790C2×D3—41no—
791C2×D3—42no—
792C2×D3—162no—
793C3×C4—22no—
794C3×C4—22no—
795C3×C4—21no—
796C3×C4—24no—
797C3×C4—21no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—44no—
801C3×C4#52512yes—
802C3×C4C22×#4112yes—
803Dic3—41no—
804Dic3—41no—
805Dic3—41no—
806Dic3—42no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—41no—
812C23—42no—
813C23—42no—
814C23—62no—
815C23—61no—
816C23—122no—
817C23—241no—
818C23—241no—
819C23C22×#6711yescharacteristic
820C23C22×#6711yescharacteristic
821C23C22×#6711yescharacteristic
822Q8—24no—
823Q8—22no—
824Q8—62no—
825Q8—242no—
826Q8C2×#23514yes—
827D4—28no—
828D4—24no—
829D4—28no—
830D4—22no—
831D4—64no—
832D4—62no—
833D4—122no—
834D4—124no—
835D4—122no—
836D4—122no—
837D4—242no—
838D4—242no—
839D4—242no—
840D4—241no—
841D4C2×#23514yes—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—28no—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—42no—
854C2×C4—44no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—62no—
859C2×C4—84no—
860C2×C4—84no—
861C2×C4—82no—
862C2×C4—82no—
863C2×C4—122no—
864C2×C4—242no—
865C2×C4—242no—
866C2×C4—242no—
867C2×C4—241no—
868C2×C4C2×#23514yes—
869C2×C4C22×#6712yes—
870C2×C4C22×#6712yes—
871C2×C4C22×#6712yes—
872C2×C4C22×#6711yescharacteristic
873C2×C4C22×#6712yes—
874C2×C4C22×#6711yescharacteristic
875C2×C4C22×#6711yescharacteristic
876C2×C4C24×D311yescharacteristic
877C8—62no—
878C8—62no—
879C8—64no—
880C2×C3—22no—
881C2×C3—22no—
882C2×C3—41no—
883C2×C3—44no—
884C2×C3C2×#52511yescharacteristic
885C2×C3C2×#57711yescharacteristic
886C2×C3#358511yescharacteristic
887D3—81no—
888D3—82no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—24no—
895C22—21no—
896C22—21no—
897C22—44no—
898C22—48no—
899C22—42no—
900C22—42no—
901C22—121no—
902C22—122no—
903C22—122no—
904C22—121no—
905C22—121no—
906C22—122no—
907C22—482no—
908C22#579112yes—
909C22#583712yes—
910C22C23×#6711yescharacteristic
911C4—21no—
912C4—24no—
913C4—21no—
914C4—22no—
915C4—22no—
916C4—22no—
917C4—22no—
918C4—44no—
919C4—121no—
920C4—121no—
921C4—122no—
922C4—121no—
923C4#579112yes—
924C4C22×#23512yes—
925C3#6058811yescharacteristic, complemented, Sylow
926C2—22no—
927C2—22no—
928C2—41no—
929C2—44no—
930C2—242no—
931C2—241no—
932C2C2×#579111yescharacteristic
933C2#8727711yescharacteristic
934C2C2×#583711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#520C2
socleC22×C3C23×D4
hypercenterC2×#520D3
hypocenterC3#60588
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×C3×#520C2semidirect
2. #85747C2semidirect
3. #84082C2semidirect
4. #84080C2semidirect
5. #82576C2semidirect
6. #82568C2semidirect
7. #82565C2semidirect
8. #82564C2semidirect
9. #82560C2semidirect
10. #82558C2semidirect
11. #82445C2semidirect
12. #82442C2semidirect
13. #82310C2semidirect
14. #82309C2semidirect
15. #82210C2semidirect
16. #82139C2semidirect
17. C2×#4968C2semidirect
25. C3×#520C22semidirect
26. C2×C3×C4×Q8C22semidirect
28. C2×C3×C4×D4C22semidirect
37. #5535C22semidirect
38. #5534C22semidirect
42. #5525C22semidirect
43. #5523C22semidirect
44. #5521C22semidirect
45. #5519C22semidirect
51. #5239C22semidirect
53. #5238C22semidirect
56. #5228C22semidirect
58. #5227C22semidirect
59. #5218C22semidirect
61. #5217C22semidirect
64. #5030C22semidirect
65. #5028C22semidirect
66. #5027C22semidirect
67. #5026C22semidirect
68. C4×#215C22semidirect
69. C4×#215C22semidirect
70. #5022C22semidirect
71. #5020C22semidirect
72. C4×#214C22semidirect
73. #5016C22semidirect
74. #5015C22semidirect
75. #5014C22semidirect
76. #5014C22semidirect
77. C4×#213C22semidirect
78. #5009C22semidirect
79. #5008C22semidirect
80. #5000C22semidirect
81. #4999C22semidirect
82. #4997C22semidirect
83. #4971C22semidirect
84. #4970C22semidirect
87. #4968C22semidirect
88. #4968C22semidirect
89. #4967C22semidirect
90. #4966C22semidirect
91. C2×#809C22semidirect
92. #4964C22semidirect
93. C2×#808C22semidirect
94. #4926C22semidirect
95. #4925C22semidirect
97. C2×#520D3semidirect
272. #520C2×D3semidirect
274. C2×C4×Q8C2×D3semidirect
276. C2×C4×D4C2×D3semidirect
334. C3×#41#41semidirect
663. #41#235semidirect
925. C3#60588semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5202
#857472
#840822
#840802
#825762
#825682
#825652
#825642
#825602
#825582
#824452
#824422
#823102
#823092
#822102
#821392
C2×#49682
#605883