Finite Group Databasebeta

← #11664132

Subgroups — #11664132

Order 768.

2074 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#520C211yesmaximal, characteristic, complemented
2#85727C211yesmaximal, characteristic, complemented
3#84084C211yesmaximal, characteristic, complemented
4#84080C211yesmaximal, characteristic
5#82575C214yesmaximal, complemented
6#82572C212yesmaximal, complemented
7#82571C212yesmaximal, complemented
8#82569C214yesmaximal, complemented
9#82559C212yesmaximal, complemented
10#82557C212yesmaximal, complemented
11#82447C212yesmaximal, complemented
12#82445C212yesmaximal, complemented
13#82315C212yesmaximal, complemented
14#82309C212yesmaximal, complemented
15#82210C211yesmaximal, characteristic, complemented
16C2×#4970C211yesmaximal, characteristic, complemented
17#82139C211yesmaximal, characteristic, complemented
18#60589—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic
20C3×#520—21no—
21C3×#520—22no—
22C3×#520—21no—
23C3×#520C2212yes—
24C3×#520C2212yes—
25C3×#520C2214yes—
26C2×C3×C4×Q8C2212yes—
27C2×C3×C4×D4—22no—
28C2×C3×C4×D4C2212yes—
29C2×C3×#117—21no—
30C2×C3×#117C2211yescharacteristic
31C22×C3×C4⋊C4—21no—
32C22×C3×C4⋊C4C2211yescharacteristic
33C2×#951C2212yes—
34C2×#950C2212yes—
35#5791C2211yescharacteristic
36C2×#924C2211yescharacteristic
37#5534C2212yescomplemented
38#5533—21no—
39#5531—22no—
40#5529—21no—
41#5526C2211yescharacteristic, complemented
42#5523C2211yescharacteristic, complemented
43#5519C2211yescharacteristic, complemented
44#5518C2212yescomplemented
45#5516C2211yescharacteristic, complemented
46#5513—21no—
47#5511—21no—
48#5495—22no—
49#5479C2212yes—
50#5470C2212yes—
51#5239C2212yes—
52#5239C2214yes—
53#5238C2212yes—
54#5233C2212yes—
55#5232C2212yes—
56#5228C2212yes—
57#5228C2211yescharacteristic
58#5227C2211yescharacteristic
59#5218C2211yescharacteristic
60#5218C2212yes—
61#5217C2211yescharacteristic
62#5207C2211yescharacteristic
63C2×#830C2211yescharacteristic
64#5031C2214yescomplemented
65#5030C2214yescomplemented
66C4×#216C2214yescomplemented
67C4×#216C2214yescomplemented
68#5028C2214yescomplemented
69#5026C2214yescomplemented
70#5022C2214yescomplemented
71#5021C2214yescomplemented
72#5019C2214yescomplemented
73#5018C2214yescomplemented
74#5018C2214yescomplemented
75C4×#214C2214yescomplemented
76#5016C2214yescomplemented
77C4×#213C2214yescomplemented
78#5009C2214yescomplemented
79#5007C2214yescomplemented
80#5000C2214yescomplemented
81#4999C2212yescomplemented
82#4997C2212yescomplemented
83#4971C2212yescomplemented
84#4970C2212yes—
85#4970C2212yes—
86#4970C2212yes—
87#4970C2214yescomplemented
88C2×#810C2212yescomplemented
89#4968C2212yes—
90#4967C2212yescomplemented
91#4966C2212yescomplemented
92#4964C2212yescomplemented
93C2×#807C2212yescomplemented
94#4926C2212yes—
95#4925C2212yes—
96#3495—31no—
97C2×#520D311yescharacteristic, complemented
98#3124—34no—
99#3120—34no—
100#3117—32no—
101#3110—32no—
102#3105—32no—
103#3104—32no—
104#3092—31no—
105C2×#484—31no—
106#3083—32no—
107#3046—32no—
108#3007—31no—
109#3002—31no—
110#2951—32no—
111#2947—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
125C2×#235C2311yescharacteristic
126C22×Dic6C2311yescharacteristic
127C3×C4×Q8—22no—
128C3×C4×Q8—22no—
129C3×C4×Q8C2314yes—
130C3×C4×Q8C2314yes—
131C3×C4×D4—24no—
132C3×C4×D4—24no—
133C3×C4×D4—24no—
134C3×C4×D4—24no—
135C3×C4×D4—22no—
136C3×C4×D4—22no—
137C3×C4×D4C2314yes—
138C3×C4×D4C2314yes—
139C3×#117—22no—
140C3×#117—24no—
141C3×#117—22no—
142C3×#117D411yescharacteristic
143C3×#117D412yes—
144C3×#117D411yescharacteristic
145C3×#117C2311yescharacteristic
146C3×#117C2311yescharacteristic
147C3×#117C2312yes—
148C2×C3×C4⋊C4—21no—
149C2×C3×C4⋊C4—22no—
150C2×C3×C4⋊C4—21no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4—22no—
153C2×C3×C4⋊C4—22no—
154C2×C3×C4⋊C4—24no—
155C2×C3×C4⋊C4D411yescharacteristic
156C2×C3×C4⋊C4D411yescharacteristic
157C2×C3×C4⋊C4C2312yes—
158C2×C3×C4⋊C4C2312yes—
159C2×C3×C4⋊C4C2312yes—
160C2×C3×C22⋊C4—22no—
161C2×C3×C22⋊C4D412yes—
162C2×C3×C42—22no—
163C2×C3×C42C2312yes—
164#953—21no—
165C2×#217—21no—
166#951—28no—
167#950—28no—
168C2×#216C2314yes—
169C2×#216C2312yes—
170C2×#215C2312yes—
171C2×#214C2314yes—
172C2×#214C2312yes—
173C2×#213C2312yes—
174#930C2311yescharacteristic
175#930C2311yescharacteristic
176#929—22no—
177#929—21no—
178C4×#67—22no—
179C4×#67—21no—
180C4×#67—21no—
181#926—22no—
182#926C2311yescharacteristic
183C2×C4⋊Dic3C2311yescharacteristic
184#924—22no—
185#924—21no—
186#924—21no—
187#924C2311yescharacteristic
188#924C2312yes—
189#924C2312yes—
190#924C2311yescharacteristic
191C2×Dic3⋊C4—21no—
192C2×#208C2312yes—
193C22×C3⋊C8C2312yes—
194#898—22no—
195#897—21no—
196#897—21no—
197#896—22no—
198#892—21no—
199D3×C4⋊C4—21no—
200#890—21no—
201#889—22no—
202#889—22no—
203#888—21no—
204#887—21no—
205#887—21no—
206#886—22no—
207#885—22no—
208#883—22no—
209#67⋊C4—22no—
210#879—22no—
211#879—22no—
212#878—22no—
213#877—22no—
214#876—22no—
215#875C2312yes—
216C4×D12C2312yes—
217#872—22no—
218#870—22no—
219#870C2312yes—
220#869C2312yes—
221#869C2312yes—
222C4×Dic6—22no—
223C4×Dic6C2312yes—
224C4×Dic6C2312yes—
225C4×Dic6C2312yes—
226#835C2312yes—
227#835C2314yes—
228#835C2312yes—
229#832C2312yes—
230#832C2314yes—
231#832C2312yes—
232#830C2311yescharacteristic
233#830C2312yes—
234#830C2311yescharacteristic
235#830C2312yes—
236#830C2312yes—
237#810C2314yes—
238#810C2314yes—
239#810C2314yes—
240#809C2314yes—
241#808C2314yes—
242#807C2314yes—
243#807C2314yes—
244#807C2314yes—
245C4⋊(C3⋊C8)C2314yes—
246C4⋊(C3⋊C8)C2314yes—
247#803C2314yes—
248C4×C3⋊C8C2314yes—
249C22×#41C2×D311yescharacteristic
250C2×#137—32no—
251C2×#135—32no—
252#556—61no—
253#554—61no—
254#552—61no—
255#552—62no—
256#552—61no—
257#551—62no—
258#544—31no—
259#542—32no—
260#541—32no—
261#536—31no—
262#533—32no—
263#529—32no—
264#525—31no—
265C2×C22⋊Q8—31no—
266#520—22no—
267#520—21no—
268#520—21no—
269#520—31no—
270#520C2×D312yes—
271#520C2×D314yes—
272#520C2×D312yes—
273#519—31no—
274C2×C4×Q8C2×D312yes—
275C2×C4×D4—22no—
276C2×C4×D4C2×D312yes—
277C2×#117—21no—
278C2×#117C2×D311yescharacteristic
279C22×C4⋊C4—21no—
280C22×C4⋊C4C2×D311yescharacteristic
281#484—32no—
282#484—32no—
283#484—34no—
284#484—32no—
285#483—32no—
286#481—32no—
287#480—32no—
288#479—34no—
289#478—34no—
290#477—34no—
291#474—34no—
292#464—34no—
293#463—34no—
294#462—34no—
295#461—34no—
296#452—32no—
297#452—34no—
298#451—31no—
299#451—32no—
300#450—32no—
301#450—31no—
302#449—32no—
303#448—31no—
304#447—31no—
305#441—34no—
306#440—34no—
307#440—34no—
308#440—34no—
309C4×Q16—34no—
310C4×Q16—34no—
311C4×SD16—34no—
312C4×D8—34no—
313#433—34no—
314#432—32no—
315#431—32no—
316#428—32no—
317C2×#107—32no—
318#424—32no—
319#417—32no—
320#417—32no—
321#416—32no—
322C2×#103—32no—
323#407—31no—
324C2×C22⋊C8—31no—
325#405—32no—
326C24×C3—21no—
327C24×C3C2×D411yescharacteristic
328C3×#41—28no—
329C3×#41—28no—
330C3×#41—24no—
331C3×#41—24no—
332C3×#41—24no—
333C3×#41#4118yes—
334C2×C3×Q8—24no—
335C2×C3×Q8—21no—
336C2×C3×Q8C2412yes—
337C2×C3×D4—28no—
338C2×C3×D4—22no—
339C2×C3×D4—22no—
340C2×C3×D4—24no—
341C2×C3×D4—21no—
342C2×C3×D4C2412yes—
343C22×C3×C4—28no—
344C22×C3×C4—21no—
345C22×C3×C4—22no—
346C22×C3×C4—22no—
347C22×C3×C4—24no—
348C22×C3×C4—22no—
349C22×C3×C4—22no—
350C22×C3×C4—22no—
351C22×C3×C4—24no—
352C22×C3×C4—24no—
353C22×C3×C4—84no—
354C22×C3×C4—82no—
355C22×C3×C4C2×D411yescharacteristic
356C22×C3×C4C2×D411yescharacteristic
357C22×C3×C4C2×D411yescharacteristic
358C22×C3×C4C2×D412yes—
359C22×C3×C4C2×D412yes—
360C22×C3×C4C2411yescharacteristic
361C22×C3×C4C2411yescharacteristic
362C22×C3×C4C2411yescharacteristic
363C2×#67—21no—
364C2×#67—21no—
365C2×#67—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368#235—24no—
369C2×D12C2411yescharacteristic
370C2×C4×D3—21no—
371C2×C4×D3—22no—
372C2×Dic6—24no—
373C2×Dic6—21no—
374C2×Dic6—22no—
375C2×Dic6C2411yescharacteristic
376C2×Dic6C2412yes—
377C3×C4⋊C4—22no—
378C3×C4⋊C4—22no—
379C3×C4⋊C4—24no—
380C3×C4⋊C4—24no—
381C3×C4⋊C4—22no—
382C3×C4⋊C4C2×D411yescharacteristic
383C3×C4⋊C4C2×D411yescharacteristic
384C3×C4⋊C4C2×D411yescharacteristic
385C3×C4⋊C4C2×D412yes—
386C3×C4⋊C4C2×D412yes—
387C3×C4⋊C4C2×D411yescharacteristic
388C3×C4⋊C4C2414yes—
389C3×C22⋊C4—24no—
390C3×C22⋊C4—24no—
391C3×C22⋊C4C2×D412yes—
392C3×C22⋊C4C2×D412yes—
393C3×C22⋊C4C2×D412yes—
394C3×C22⋊C4C2×D412yes—
395C3×C42—24no—
396C3×C42—24no—
397C3×C42C2×D412yes—
398C3×C42C2×D412yes—
399C3×C42C2412yes—
400C3×C42C2412yes—
401#217—21no—
402#217—21no—
403#217—22no—
404#217—21no—
405#217—22no—
406#216—24no—
407#216—28no—
408#215—24no—
409#214—24no—
410#214—28no—
411#213—24no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—22no—
415(C2×D3)⋊C4—22no—
416(C2×D3)⋊C4—21no—
417C4⋊Dic3—22no—
418C4⋊Dic3—22no—
419C4⋊Dic3—22no—
420C4⋊Dic3—21no—
421C4⋊Dic3C2411yescharacteristic
422C4⋊Dic3C2412yes—
423C4⋊Dic3C2411yescharacteristic
424Dic3⋊C4—21no—
425Dic3⋊C4—22no—
426Dic3⋊C4—22no—
427Dic3⋊C4—22no—
428Dic3⋊C4—22no—
429Dic3⋊C4—22no—
430Dic3⋊C4—22no—
431Dic3⋊C4—21no—
432Dic3⋊C4—22no—
433C4×Dic3—22no—
434C4×Dic3—22no—
435C4×Dic3—22no—
436C4×Dic3—21no—
437#208—24no—
438C2×C3⋊C8—24no—
439C2×C3⋊C8C2412yes—
440C2×C3⋊C8C2414yes—
441C2×C3⋊C8C2412yes—
442C2×#41—28no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—31no—
446C2×#41C22×D312yes—
447C2×#41C22×D312yes—
448C22×Q8—31no—
449C22×Q8C22×D311yescharacteristic
450C22×D4—21no—
451C22×D4C22×D311yescharacteristic
452C23×C4—21no—
453C23×C4—21no—
454C23×C4—22no—
455C23×C4C22×D311yescharacteristic
456#137—68no—
457#135—68no—
458C2×Q16—32no—
459C2×Q16—34no—
460C2×SD16—32no—
461C2×SD16—32no—
462C2×SD16—34no—
463C2×D8—32no—
464C2×M16—32no—
465C22×C8—32no—
466C4⋊Q8—32no—
467C4⋊Q8—32no—
468C4⋊Q8—61no—
469#126—62no—
470#126—62no—
471#126—62no—
472#126—62no—
473#125—32no—
474#125—62no—
475#125—62no—
476#125—61no—
477#125—62no—
478#124—32no—
479#124—62no—
480#123—61no—
481#123—62no—
482#123—62no—
483#123—62no—
484C22⋊Q8—32no—
485C22⋊Q8—32no—
486C22⋊Q8—31no—
487C22⋊Q8—31no—
488C22⋊Q8—61no—
489C22⋊Q8—61no—
490C22⋊Q8—62no—
491C22⋊Q8—61no—
492C22⋊Q8—61no—
493C22⋊Q8—62no—
494C22⋊Q8—62no—
495#121—31no—
496#121—31no—
497#120—61no—
498C4×Q8—22no—
499C4×Q8—22no—
500C4×Q8—32no—
501C4×Q8—32no—
502C4×Q8—32no—
503C4×Q8—61no—
504C4×Q8—61no—
505C4×Q8—62no—
506C4×Q8C22×D314yes—
507C4×Q8C22×D314yes—
508C4×D4—24no—
509C4×D4—24no—
510C4×D4—24no—
511C4×D4—24no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—32no—
515C4×D4—61no—
516C4×D4—61no—
517C4×D4—62no—
518C4×D4—62no—
519C4×D4C22×D314yes—
520C4×D4C22×D314yes—
521#117—22no—
522#117—22no—
523#117—24no—
524#117—31no—
525#117—62no—
526#117—61no—
527#117—62no—
528#117—62no—
529#117#6711yescharacteristic
530#117#6712yes—
531#117#6711yescharacteristic
532#117C22×D311yescharacteristic
533#117C22×D311yescharacteristic
534#117C22×D312yes—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—24no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—31no—
543C2×C4⋊C4—61no—
544C2×C4⋊C4—61no—
545C2×C4⋊C4#6711yescharacteristic
546C2×C4⋊C4#6711yescharacteristic
547C2×C4⋊C4C22×D312yes—
548C2×C4⋊C4C22×D312yes—
549C2×C4⋊C4C22×D312yes—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—61no—
552C2×C22⋊C4#6712yes—
553C2×C42—22no—
554C2×C42C22×D312yes—
555#107—34no—
556#107—34no—
557#107—34no—
558#106—34no—
559C4⋊C8—34no—
560C4⋊C8—34no—
561#103—32no—
562#103—32no—
563#103—34no—
564#103—34no—
565#103—34no—
566#103—34no—
567#102—32no—
568#102—32no—
569#102—34no—
570#102—34no—
571C22⋊C8—31no—
572C22⋊C8—31no—
573C22⋊C8—32no—
574C22⋊C8—32no—
575C22⋊C8—32no—
576#97—34no—
577C4×C8—34no—
578C23×C3—24no—
579C23×C3—22no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—41no—
583C23×C3—42no—
584C23×C3—42no—
585C23×C3C22×D411yescharacteristic
586C23×C3C22×D411yescharacteristic
587C23×C3C22×D411yescharacteristic
588C22×D3—21no—
589C3×Q8—24no—
590C3×Q8—22no—
591C3×Q8C2×#4114yes—
592C3×D4—28no—
593C3×D4—24no—
594C3×D4—28no—
595C3×D4—22no—
596C3×D4C2×#4114yes—
597C2×C3×C4—24no—
598C2×C3×C4—28no—
599C2×C3×C4—22no—
600C2×C3×C4—24no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—28no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—24no—
608C2×C3×C4—42no—
609C2×C3×C4—44no—
610C2×C3×C4—84no—
611C2×C3×C4—84no—
612C2×C3×C4—82no—
613C2×C3×C4—82no—
614C2×C3×C4C22×D412yes—
615C2×C3×C4C22×D412yes—
616C2×C3×C4C22×D411yescharacteristic
617C2×C3×C4C22×D411yescharacteristic
618C2×C3×C4C22×D412yes—
619C2×C3×C4C22×D412yes—
620C2×C3×C4C22×D411yescharacteristic
621C2×C3×C4C2×#4114yes—
622C2×C3×C4C2511yescharacteristic
623#67—42no—
624#67—42no—
625#67—81no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—42no—
632C2×Dic3—81no—
633D12—22no—
634C4×D3—42no—
635C4×D3—82no—
636Dic6—24no—
637Dic6—22no—
638Dic6—42no—
639Dic6—82no—
640C3⋊C8—22no—
641C3⋊C8—22no—
642C3⋊C8—24no—
643C24—21no—
644C24C2×#6711yescharacteristic
645#41—28no—
646#41—28no—
647#41—24no—
648#41—24no—
649#41—24no—
650#41—64no—
651#41#23518yes—
652C2×Q8—24no—
653C2×Q8—21no—
654C2×Q8—32no—
655C2×Q8—31no—
656C2×Q8—61no—
657C2×Q8—62no—
658C2×Q8—64no—
659C2×Q8C23×D312yes—
660C2×D4—28no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—31no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4C23×D312yes—
670C22×C4—28no—
671C22×C4—21no—
672C22×C4—24no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—62no—
684C22×C4—84no—
685C22×C4—82no—
686C22×C4C2×#6712yes—
687C22×C4C2×#6711yescharacteristic
688C22×C4C2×#6711yescharacteristic
689C22×C4C2×#6711yescharacteristic
690C22×C4C2×#6712yes—
691C22×C4C23×D311yescharacteristic
692C22×C4C23×D311yescharacteristic
693C22×C4C23×D311yescharacteristic
694Q16—64no—
695Q16—68no—
696SD16—64no—
697SD16—64no—
698SD16—68no—
699D8—64no—
700M16—64no—
701C2×C8—32no—
702C2×C8—34no—
703C2×C8—32no—
704C2×C8—64no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—22no—
710C4⋊C4—31no—
711C4⋊C4—32no—
712C4⋊C4—31no—
713C4⋊C4—61no—
714C4⋊C4—62no—
715C4⋊C4—62no—
716C4⋊C4—62no—
717C4⋊C4—62no—
718C4⋊C4—62no—
719C4⋊C4—62no—
720C4⋊C4—62no—
721C4⋊C4—62no—
722C4⋊C4—61no—
723C4⋊C4—61no—
724C4⋊C4—62no—
725C4⋊C4—62no—
726C4⋊C4C2×#6711yescharacteristic
727C4⋊C4C2×#6712yes—
728C4⋊C4C2×#6711yescharacteristic
729C4⋊C4C2×#6711yescharacteristic
730C4⋊C4C2×#6711yescharacteristic
731C4⋊C4C2×#6712yes—
732C4⋊C4C23×D314yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—62no—
736C22⋊C4—62no—
737C22⋊C4—61no—
738C22⋊C4—61no—
739C22⋊C4—61no—
740C22⋊C4—61no—
741C22⋊C4—62no—
742C22⋊C4—62no—
743C22⋊C4—61no—
744C22⋊C4—62no—
745C22⋊C4C2×#6712yes—
746C22⋊C4C2×#6712yes—
747C22⋊C4C2×#6712yes—
748C22⋊C4C2×#6712yes—
749C42—24no—
750C42—24no—
751C42—61no—
752C42—62no—
753C42—62no—
754C42—62no—
755C42C2×#6712yes—
756C42C2×#6712yes—
757C42C23×D312yes—
758C42C23×D312yes—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—24no—
766C22×C3—21no—
767C22×C3—44no—
768C22×C3—48no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3#52512yes—
772C22×C3#57812yes—
773C22×C3C23×D411yescharacteristic
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C3×C4—22no—
778C3×C4—22no—
779C3×C4—21no—
780C3×C4—24no—
781C3×C4—21no—
782C3×C4—22no—
783C3×C4—22no—
784C3×C4—44no—
785C3×C4#52512yes—
786C3×C4C22×#4112yes—
787Dic3—41no—
788Dic3—42no—
789Dic3—42no—
790Dic3—41no—
791Dic3—41no—
792C23—24no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—61no—
800C23C22×#6711yescharacteristic
801C23C22×#6711yescharacteristic
802C23C22×#6711yescharacteristic
803Q8—24no—
804Q8—22no—
805Q8—64no—
806Q8—62no—
807Q8—122no—
808Q8—242no—
809Q8C2×#23514yes—
810D4—28no—
811D4—24no—
812D4—28no—
813D4—22no—
814D4—62no—
815D4—122no—
816D4—122no—
817D4—241no—
818D4C2×#23514yes—
819C2×C4—24no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—28no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—42no—
831C2×C4—44no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—62no—
835C2×C4—61no—
836C2×C4—62no—
837C2×C4—84no—
838C2×C4—84no—
839C2×C4—82no—
840C2×C4—82no—
841C2×C4—122no—
842C2×C4—122no—
843C2×C4—242no—
844C2×C4—241no—
845C2×C4C2×#23514yes—
846C2×C4C22×#6712yes—
847C2×C4C22×#6712yes—
848C2×C4C22×#6712yes—
849C2×C4C22×#6711yescharacteristic
850C2×C4C22×#6712yes—
851C2×C4C22×#6711yescharacteristic
852C2×C4C22×#6711yescharacteristic
853C2×C4C24×D311yescharacteristic
854C8—62no—
855C8—62no—
856C8—64no—
857C2×C3—22no—
858C2×C3—22no—
859C2×C3—41no—
860C2×C3—44no—
861C2×C3C2×#52511yescharacteristic
862C2×C3C2×#57811yescharacteristic
863C2×C3#358511yescharacteristic
864D3—81no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—24no—
871C22—21no—
872C22—21no—
873C22—44no—
874C22—48no—
875C22—42no—
876C22—42no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22#579112yes—
881C22#583812yes—
882C22C23×#6711yescharacteristic
883C4—21no—
884C4—24no—
885C4—21no—
886C4—22no—
887C4—22no—
888C4—22no—
889C4—22no—
890C4—44no—
891C4—121no—
892C4—122no—
893C4—122no—
894C4—121no—
895C4—121no—
896C4#579112yes—
897C4C22×#23512yes—
898C3#6058911yescharacteristic, complemented, Sylow
899C2—22no—
900C2—22no—
901C2—41no—
902C2—44no—
903C2—241no—
904C2C2×#579111yescharacteristic
905C2#8727711yescharacteristic
906C2C2×#583811yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#520C2
socleC22×C3C23×D4
prime radical#84080C2
hypercenterC2×#520D3
hypocenterC3#60589
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. #85727C2semidirect
3. #84084C2semidirect
5. #82575C2semidirect
6. #82572C2semidirect
7. #82571C2semidirect
8. #82569C2semidirect
9. #82559C2semidirect
10. #82557C2semidirect
11. #82447C2semidirect
12. #82445C2semidirect
13. #82315C2semidirect
14. #82309C2semidirect
15. #82210C2semidirect
16. C2×#4970C2semidirect
17. #82139C2semidirect
37. #5534C22semidirect
41. #5526C22semidirect
42. #5523C22semidirect
43. #5519C22semidirect
44. #5518C22semidirect
45. #5516C22semidirect
64. #5031C22semidirect
65. #5030C22semidirect
66. C4×#216C22semidirect
67. C4×#216C22semidirect
68. #5028C22semidirect
69. #5026C22semidirect
70. #5022C22semidirect
71. #5021C22semidirect
72. #5019C22semidirect
73. #5018C22semidirect
74. #5018C22semidirect
75. C4×#214C22semidirect
76. #5016C22semidirect
77. C4×#213C22semidirect
78. #5009C22semidirect
79. #5007C22semidirect
80. #5000C22semidirect
81. #4999C22semidirect
82. #4997C22semidirect
83. #4971C22semidirect
87. #4970C22semidirect
88. C2×#810C22semidirect
90. #4967C22semidirect
91. #4966C22semidirect
92. #4964C22semidirect
93. C2×#807C22semidirect
97. C2×#520D3semidirect
898. C3#60589semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5202
#857272
#840842
#840802
#825752
#825722
#825712
#825692
#825592
#825572
#824472
#824452
#823152
#823092
#822102
C2×#49702
#821392
#605893