Finite Group Databasebeta

← #11680630

Subgroups — #11680630

Order 768.

2232 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3519C211yesmaximal, characteristic, complemented
2C2×#5553C211yesmaximal, characteristic, complemented
3#83655C212yesmaximal, complemented
4#83642C212yesmaximal, complemented
5#83619C214yesmaximal, complemented
6#83585C212yesmaximal, complemented
7#83507C214yesmaximal, complemented
8#83492C212yesmaximal, complemented
9#83316C211yesmaximal, characteristic, complemented
10#83302C211yesmaximal, characteristic, complemented
11#83152C211yesmaximal, characteristic, complemented
12#83146C211yesmaximal, characteristic, complemented
13#82931C212yesmaximal, complemented
14#82926C212yesmaximal, complemented
15#82625C212yesmaximal, complemented
16#82624C212yesmaximal, complemented
17#82303C211yesmaximal, characteristic, complemented
18#61605—31nomaximal, Sylow
19C22×#235C2212yescomplemented
20C3×#555C2211yescharacteristic, complemented
21C3×#554C2211yescharacteristic, complemented
22C3×#553—21no—
23C3×#553C2212yescomplemented
24C3×#550C2211yescharacteristic, complemented
25C3×#546—22no—
26C3×#546C2212yescomplemented
27C3×D42—21no—
28C3×D42C2211yescharacteristic, complemented
29C3×#540—21no—
30C3×#538—22no—
31C3×#532C2211yescharacteristic
32C3×#529C2211yescharacteristic
33C3×#525C2212yes—
34C2×C3×#121C2212yes—
35C3×#518—21no—
36C2×C3×C4×D4C2211yescharacteristic
37C2×#950C2214yescomplemented
38C2×#940—21no—
39C2×#932C2214yescomplemented
40C2×#930C2212yescomplemented
41#5553—22no—
42#5553—21no—
43#5553—21no—
44#5553C2212yes—
45#5553C2214yescomplemented
46#5553C2212yescomplemented
47C2×#893—21no—
48C2×#884—22no—
49C2×#874C2211yescharacteristic, complemented
50C2×C4×Dic6C2211yescharacteristic, complemented
51#5238C2214yescomplemented
52#5217C2214yescomplemented
53#5207C2212yescomplemented
54C2×#830C2212yescomplemented
55#5091C2212yescomplemented
56#5088C2212yescomplemented
57#5075C2212yescomplemented
58#5073C2212yescomplemented
59#5067C2212yescomplemented
60#5063C2212yescomplemented
61#5058C2212yescomplemented
62#5054C2212yescomplemented
63#5050C2211yescharacteristic, complemented
64#5049C2214yescomplemented
65#5047C2214yescomplemented
66#5046C2212yescomplemented
67#5043C2211yescharacteristic, complemented
68#5040C2211yescharacteristic
69#5040C2212yescomplemented
70#5039C2214yescomplemented
71#5038C2214yescomplemented
72#5038C2214yescomplemented
73#5037C2214yescomplemented
74#5037C2214yescomplemented
75#5037C2214yescomplemented
76#5036C2212yes—
77#5036C2212yescomplemented
78#5036C2212yescomplemented
79#5033C2211yescharacteristic
80#5033C2212yescomplemented
81C4×#216C2212yescomplemented
82#5027C2212yescomplemented
83#5018C2214yescomplemented
84C4×#214C2212yescomplemented
85#5015C2212yescomplemented
86#5015C2214yescomplemented
87#5012C2212yescomplemented
88#5011C2214yescomplemented
89D4×C3⋊C8C2212yescomplemented
90#5003C2214yescomplemented
91#5002C2214yescomplemented
92#4967C2214yescomplemented
93#4966C2214yescomplemented
94#4926C2211yescharacteristic, complemented
95#4925C2211yescharacteristic, complemented
96#3519D311yescharacteristic, complemented
97C2×#550—31no—
98#3333—32no—
99#3309—34no—
100#3305—32no—
101#3287—32no—
102#3274—32no—
103#3268—34no—
104#3217—31no—
105#3205—31no—
106#3194—32no—
107#3186—32no—
108#3112—31no—
109#3108—31no—
110#3006—32no—
111#3002—32no—
112#2974—31no—
113C2×C3×#41—21no—
114C2×C3×#41C2312yes—
115C22×C3×D4—22no—
116C22×C3×D4—21no—
117C22×C3×D4D411yescharacteristic
118C22×C3×D4C2312yes—
119C23×C3×C4C2312yes—
120C22×#67—22no—
121C22×#67—22no—
122C2×#235—22no—
123C2×#235—22no—
124C2×#235—48no—
125C2×#235C2314yes—
126C2×#235C2314yes—
127C22×D12—21no—
128C22×D12—21no—
129C22×D12C2312yes—
130C22×C4×D3—22no—
131C22×Dic6C2311yescharacteristic
132C3×C4⋊Q8C2311yescharacteristic
133C3×#127—21no—
134C3×#127C2311yescharacteristic
135C3×#126—22no—
136C3×#126—21no—
137C3×#125—21no—
138C3×#125C2311yescharacteristic
139C3×#124—22no—
140C3×#124—21no—
141C3×#124C2311yescharacteristic
142C3×#123—22no—
143C3×#123—21no—
144C3×#123—22no—
145C3×#123—22no—
146C3×C22⋊Q8—22no—
147C3×C22⋊Q8C2311yescharacteristic
148C3×C22⋊Q8C2312yes—
149C3×#121—22no—
150C3×#121—21no—
151C3×#121—22no—
152C3×#121—22no—
153C3×#121—21no—
154C3×#121—21no—
155C3×#121—22no—
156C3×#121—22no—
157C3×#121C2311yescharacteristic
158C3×#121C2312yes—
159C3×#121C2312yes—
160C3×#121C2312yes—
161C3×#121C2312yes—
162C3×#120—22no—
163C3×#120—22no—
164C3×#120—22no—
165C3×C4×Q8C2311yescharacteristic
166C3×C4×D4—21no—
167C3×C4×D4—22no—
168C3×C4×D4—22no—
169C3×C4×D4—21no—
170C3×C4×D4—21no—
171C3×C4×D4—22no—
172C3×C4×D4—21no—
173C3×C4×D4D411yescharacteristic
174C3×C4×D4D412yes—
175C3×C4×D4D411yescharacteristic
176C3×C4×D4C2311yescharacteristic
177C3×C4×D4C2312yes—
178C3×C4×D4C2311yescharacteristic
179C3×C4×D4C2312yes—
180C3×C4×D4C2311yescharacteristic
181C3×#117—21no—
182C3×#117—21no—
183C3×#117C2312yes—
184C2×C3×C4⋊C4D411yescharacteristic
185C2×C3×C4⋊C4C2312yes—
186C2×C3×C22⋊C4—22no—
187C2×C3×C22⋊C4—22no—
188C2×C3×C22⋊C4D412yes—
189C2×C3×C42C2311yescharacteristic
190#950—48no—
191C2×#216C2312yes—
192C2×#215C2314yes—
193#940—22no—
194#940—22no—
195#940—24no—
196C2×#214C2312yes—
197C2×#214C2314yes—
198#932—48no—
199C2×#213C2314yes—
200C2×#213C2314yes—
201C2×#213C2314yes—
202#930—22no—
203#930—22no—
204#930C2314yes—
205#930C2314yes—
206C2×(C2×D3)⋊C4—22no—
207C2×C4⋊Dic3C2311yescharacteristic
208C2×Dic3⋊C4—21no—
209C2×C4×Dic3—21no—
210C2×#208C2314yes—
211C22×C3⋊C8C2314yes—
212#893—22no—
213#893—22no—
214#893—24no—
215#884—24no—
216#884—24no—
217#884—24no—
218#884—24no—
219#874—21no—
220#874—21no—
221#874C2312yes—
222#874C2312yes—
223C4×Dic6—21no—
224C4×Dic6—21no—
225C4×Dic6C2312yes—
226C4×Dic6C2312yes—
227#835C2312yes—
228#832C2312yes—
229#832C2314yes—
230#830C2311yescharacteristic
231#830C2311yescharacteristic
232#830C2312yes—
233#830C2314yes—
234#830C2314yes—
235#810C2312yes—
236#810C2314yes—
237#810C2312yes—
238#809C2314yes—
239#809C2314yes—
240#809C2314yes—
241#809C2314yes—
242#808C2312yes—
243#807C2312yes—
244#807C2314yes—
245C4⋊(C3⋊C8)C2312yes—
246C4⋊(C3⋊C8)C2312yes—
247#803C2312yes—
248C4×C3⋊C8C2312yes—
249C22×#41—32no—
250C2×AGL(1,ℤ/8)—34no—
251C2×#135—34no—
252#555C2×D311yescharacteristic, complemented
253#554C2×D311yescharacteristic, complemented
254#553—21no—
255#553C2×D312yescomplemented
256#550—32no—
257#550—34no—
258#550—32no—
259#550—61no—
260#550—62no—
261#550—61no—
262#550C2×D311yescharacteristic, complemented
263#546—22no—
264#546C2×D312yescomplemented
265D42—21no—
266D42C2×D311yescharacteristic, complemented
267#540—21no—
268#538—22no—
269#532C2×D311yescharacteristic
270C2×#127—31no—
271C2×#127—61no—
272#529C2×D311yescharacteristic
273#525C2×D312yes—
274C2×#121—32no—
275C2×#121—62no—
276C2×#121C2×D312yes—
277#518—21no—
278C2×C4×Q8—31no—
279C2×C4×D4—61no—
280C2×C4×D4C2×D311yescharacteristic
281#496—32no—
282#493—32no—
283#490—32no—
284#486—32no—
285#483—31no—
286#482—34no—
287#480—31no—
288#480—32no—
289#480—34no—
290#479—32no—
291#477—32no—
292#469—34no—
293#468—34no—
294#466—34no—
295#466—34no—
296#464—32no—
297#460—32no—
298#460—32no—
299#459—34no—
300#459—32no—
301#452—34no—
302#451—31no—
303#450—32no—
304#449—34no—
305#449—34no—
306#449—34no—
307#449—34no—
308#448—31no—
309#448—32no—
310#447—34no—
311#447—32no—
312#447—32no—
313#447—32no—
314#440—34no—
315C4×Q16—32no—
316C4×SD16—32no—
317#436—32no—
318#435—34no—
319C8×D4—32no—
320#432—31no—
321#431—31no—
322#417—34no—
323#416—34no—
324#407—32no—
325C2×C22⋊C8—32no—
326C24×C3—22no—
327C24×C3C2×D412yes—
328C23×D3—22no—
329C3×#41—44no—
330C3×#41—82no—
331C2×C3×Q8—21no—
332C2×C3×Q8C2411yescharacteristic
333C2×C3×D4—22no—
334C2×C3×D4—22no—
335C2×C3×D4—21no—
336C2×C3×D4—22no—
337C2×C3×D4—22no—
338C2×C3×D4—22no—
339C2×C3×D4—21no—
340C2×C3×D4—21no—
341C2×C3×D4—22no—
342C2×C3×D4—42no—
343C2×C3×D4—44no—
344C2×C3×D4—44no—
345C2×C3×D4—84no—
346C2×C3×D4C2×D411yescharacteristic
347C2×C3×D4C2×D411yescharacteristic
348C2×C3×D4C2×D412yes—
349C2×C3×D4C2411yescharacteristic
350C2×C3×D4C2412yes—
351C22×C3×C4—22no—
352C22×C3×C4—21no—
353C22×C3×C4—22no—
354C22×C3×C4—22no—
355C22×C3×C4—44no—
356C22×C3×C4C2×D411yescharacteristic
357C22×C3×C4C2×D411yescharacteristic
358C22×C3×C4C2×D412yes—
359C22×C3×C4C2×D412yes—
360C22×C3×C4C2×D412yes—
361C22×C3×C4C2411yescharacteristic
362C22×C3×C4C2412yes—
363C22×C3×C4C2412yes—
364C2×#67—24no—
365C2×#67—24no—
366C2×#67—24no—
367C2×#67—24no—
368C2×#67—48no—
369C2×#67—84no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372#235—28no—
373#235—28no—
374#235—44no—
375#235—44no—
376#235—48no—
377#235—48no—
378C2×D12—22no—
379C2×D12—22no—
380C2×D12—22no—
381C2×D12—22no—
382C2×D12—22no—
383C2×D12—44no—
384C2×D12—44no—
385C2×D12—82no—
386C2×D12C2414yes—
387C2×C4×D3—24no—
388C2×C4×D3—24no—
389C2×C4×D3—48no—
390C2×Dic6—21no—
391C2×Dic6—24no—
392C2×Dic6C2412yes—
393C3×C4⋊C4—22no—
394C3×C4⋊C4—21no—
395C3×C4⋊C4—21no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—21no—
398C3×C4⋊C4—22no—
399C3×C4⋊C4—21no—
400C3×C4⋊C4C2×D411yescharacteristic
401C3×C4⋊C4C2×D411yescharacteristic
402C3×C4⋊C4C2×D412yes—
403C3×C4⋊C4C2411yescharacteristic
404C3×C4⋊C4C2412yes—
405C3×C4⋊C4C2411yescharacteristic
406C3×C22⋊C4—22no—
407C3×C22⋊C4—22no—
408C3×C22⋊C4—21no—
409C3×C22⋊C4—21no—
410C3×C22⋊C4—21no—
411C3×C22⋊C4—22no—
412C3×C22⋊C4—22no—
413C3×C22⋊C4—22no—
414C3×C22⋊C4—21no—
415C3×C22⋊C4—22no—
416C3×C22⋊C4—21no—
417C3×C22⋊C4—22no—
418C3×C22⋊C4C2×D412yes—
419C3×C22⋊C4C2×D412yes—
420C3×C22⋊C4C2×D412yes—
421C3×C22⋊C4C2×D412yes—
422C3×C42—22no—
423C3×C42—21no—
424C3×C42C2×D411yescharacteristic
425C3×C42C2×D411yescharacteristic
426C3×C42C2411yescharacteristic
427C3×C42C2411yescharacteristic
428#216—24no—
429#215—44no—
430#214—24no—
431#214—28no—
432#213—44no—
433#213—44no—
434#213—44no—
435(C2×D3)⋊C4—24no—
436(C2×D3)⋊C4—24no—
437C4⋊Dic3—21no—
438C4⋊Dic3C2412yes—
439Dic3⋊C4—22no—
440Dic3⋊C4—22no—
441C4×Dic3—22no—
442C4×Dic3—22no—
443#208—44no—
444C2×C3⋊C8—44no—
445C2×C3⋊C8C2412yes—
446C2×C3⋊C8C2412yes—
447C2×C3⋊C8C2414yes—
448C2×#41—21no—
449C2×#41—34no—
450C2×#41—34no—
451C2×#41—62no—
452C2×#41—62no—
453C2×#41—128no—
454C2×#41C22×D312yes—
455C22×Q8—31no—
456C22×D4—22no—
457C22×D4—21no—
458C22×D4—32no—
459C22×D4—62no—
460C22×D4—62no—
461C22×D4—61no—
462C22×D4—61no—
463C22×D4#6711yescharacteristic
464C22×D4C22×D312yes—
465C23×C4—62no—
466C23×C4C22×D312yes—
467AGL(1,ℤ/8)—128no—
468#135—128no—
469C2×Q16—32no—
470C2×SD16—34no—
471C2×SD16—32no—
472C2×SD16—34no—
473C2×D8—34no—
474C2×D8—34no—
475C2×D8—34no—
476C2×M16—34no—
477C22×C8—34no—
478C4⋊Q8C22×D311yescharacteristic
479#127—21no—
480#127—32no—
481#127—32no—
482#127—62no—
483#127—62no—
484#127—64no—
485#127—61no—
486#127—61no—
487#127C22×D311yescharacteristic
488#126—22no—
489#126—21no—
490#125—21no—
491#125C22×D311yescharacteristic
492#124—22no—
493#124—21no—
494#124C22×D311yescharacteristic
495#123—22no—
496#123—21no—
497#123—22no—
498#123—22no—
499C22⋊Q8—22no—
500C22⋊Q8C22×D311yescharacteristic
501C22⋊Q8C22×D312yes—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—21no—
508#121—22no—
509#121—22no—
510#121—34no—
511#121—34no—
512#121—62no—
513#121—62no—
514#121—64no—
515#121—64no—
516#121—64no—
517#121—64no—
518#121C22×D311yescharacteristic
519#121C22×D312yes—
520#121C22×D312yes—
521#121C22×D312yes—
522#121C22×D312yes—
523#120—22no—
524#120—22no—
525#120—22no—
526C4×Q8—32no—
527C4×Q8—32no—
528C4×Q8—61no—
529C4×Q8—61no—
530C4×Q8C22×D311yescharacteristic
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—22no—
537C4×D4—21no—
538C4×D4—62no—
539C4×D4—62no—
540C4×D4—64no—
541C4×D4#6711yescharacteristic
542C4×D4#6712yes—
543C4×D4#6711yescharacteristic
544C4×D4C22×D311yescharacteristic
545C4×D4C22×D312yes—
546C4×D4C22×D311yescharacteristic
547C4×D4C22×D312yes—
548C4×D4C22×D311yescharacteristic
549#117—21no—
550#117—21no—
551#117C22×D312yes—
552C2×C4⋊C4—31no—
553C2×C4⋊C4—61no—
554C2×C4⋊C4#6711yescharacteristic
555C2×C4⋊C4C22×D312yes—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—62no—
559C2×C22⋊C4#6712yes—
560C2×C42—61no—
561C2×C42C22×D311yescharacteristic
562#107—32no—
563#107—34no—
564#106—32no—
565C4⋊C8—32no—
566C4⋊C8—32no—
567#103—32no—
568#103—32no—
569#103—34no—
570#103—32no—
571#102—32no—
572#102—34no—
573#102—34no—
574#102—34no—
575#102—34no—
576#102—34no—
577C22⋊C8—31no—
578C22⋊C8—32no—
579C22⋊C8—34no—
580C22⋊C8—31no—
581C22⋊C8—34no—
582#97—32no—
583C4×C8—32no—
584C23×C3—24no—
585C23×C3—21no—
586C23×C3—22no—
587C23×C3—42no—
588C23×C3—42no—
589C23×C3—44no—
590C23×C3—82no—
591C23×C3—82no—
592C23×C3C22×D412yes—
593C23×C3C22×D412yes—
594C23×C3C22×D411yescharacteristic
595C22×D3—24no—
596C22×D3—44no—
597C22×D3—44no—
598C22×D3—44no—
599C3×Q8—22no—
600C3×Q8—81no—
601C3×D4—22no—
602C3×D4—22no—
603C3×D4—22no—
604C3×D4—24no—
605C3×D4—42no—
606C3×D4—44no—
607C3×D4—42no—
608C3×D4—44no—
609C3×D4—42no—
610C3×D4—82no—
611C3×D4—81no—
612C3×D4—82no—
613C3×D4—82no—
614C3×D4—82no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—24no—
618C2×C3×C4—24no—
619C2×C3×C4—22no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—22no—
623C2×C3×C4—21no—
624C2×C3×C4—42no—
625C2×C3×C4—42no—
626C2×C3×C4—42no—
627C2×C3×C4—42no—
628C2×C3×C4—82no—
629C2×C3×C4—82no—
630C2×C3×C4—82no—
631C2×C3×C4C22×D411yescharacteristic
632C2×C3×C4C22×D411yescharacteristic
633C2×C3×C4C22×D411yescharacteristic
634C2×C3×C4C22×D411yescharacteristic
635C2×C3×C4C22×D412yes—
636C2×C3×C4C22×D412yes—
637C2×C3×C4C22×D411yescharacteristic
638C2×C3×C4C2511yescharacteristic
639#67—48no—
640#67—48no—
641#67—84no—
642#67—84no—
643C2×Dic3—24no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—42no—
647D12—24no—
648D12—24no—
649D12—44no—
650D12—44no—
651D12—44no—
652D12—82no—
653D12—82no—
654C4×D3—48no—
655C4×D3—48no—
656Dic6—24no—
657Dic6—22no—
658Dic6H(5,𝔽2)14yes—
659C3⋊C8—22no—
660C3⋊C8—24no—
661C3⋊C8—22no—
662C24—22no—
663C24—62no—
664C24C2×#6712yes—
665#41—44no—
666#41—68no—
667#41—68no—
668#41—82no—
669#41—124no—
670#41—124no—
671#41—128no—
672#41—128no—
673C2×Q8—21no—
674C2×Q8—32no—
675C2×Q8—64no—
676C2×Q8—61no—
677C2×Q8C23×D311yescharacteristic
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—22no—
687C2×D4—34no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—64no—
692C2×D4—64no—
693C2×D4—64no—
694C2×D4—64no—
695C2×D4—62no—
696C2×D4—62no—
697C2×D4—62no—
698C2×D4—62no—
699C2×D4—62no—
700C2×D4—84no—
701C2×D4—124no—
702C2×D4—124no—
703C2×D4—128no—
704C2×D4—242no—
705C2×D4—244no—
706C2×D4C2×#6711yescharacteristic
707C2×D4C2×#6711yescharacteristic
708C2×D4C2×#6712yes—
709C2×D4C23×D311yescharacteristic
710C2×D4C23×D312yes—
711C22×C4—22no—
712C22×C4—21no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—44no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—64no—
719C22×C4—64no—
720C22×C4—128no—
721C22×C4C2×#6711yescharacteristic
722C22×C4C2×#6711yescharacteristic
723C22×C4C2×#6712yes—
724C22×C4C2×#6712yes—
725C22×C4C2×#6712yes—
726C22×C4C23×D311yescharacteristic
727C22×C4C23×D312yes—
728C22×C4C23×D312yes—
729Q16—64no—
730SD16—68no—
731SD16—64no—
732SD16—124no—
733D8—124no—
734D8—124no—
735D8—124no—
736M16—124no—
737C2×C8—32no—
738C2×C8—32no—
739C2×C8—34no—
740C2×C8—124no—
741C4⋊C4—22no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—22no—
747C4⋊C4—21no—
748C4⋊C4—32no—
749C4⋊C4—61no—
750C4⋊C4—62no—
751C4⋊C4—62no—
752C4⋊C4C2×#6711yescharacteristic
753C4⋊C4C2×#6711yescharacteristic
754C4⋊C4C2×#6712yes—
755C4⋊C4C23×D311yescharacteristic
756C4⋊C4C23×D311yescharacteristic
757C4⋊C4C23×D312yes—
758C22⋊C4—22no—
759C22⋊C4—22no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—22no—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—21no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—22no—
770C22⋊C4—64no—
771C22⋊C4—64no—
772C22⋊C4C2×#6712yes—
773C22⋊C4C2×#6712yes—
774C22⋊C4C2×#6712yes—
775C22⋊C4C2×#6712yes—
776C42—22no—
777C42—21no—
778C42—62no—
779C42—62no—
780C42C2×#6711yescharacteristic
781C42C2×#6711yescharacteristic
782C42C23×D311yescharacteristic
783C42C23×D311yescharacteristic
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—42no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—41no—
798C22×C3—84no—
799C22×C3—164no—
800C22×C3#57612yes—
801C22×C3C23×D411yescharacteristic
802C2×D3—44no—
803C2×D3—44no—
804C2×D3—44no—
805C2×D3—88no—
806C3×C4—21no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—21no—
810C3×C4—21no—
811C3×C4—21no—
812C3×C4—41no—
813C3×C4—41no—
814C3×C4—41no—
815C3×C4—42no—
816C3×C4#57512yes—
817C3×C4C2×H(5,𝔽2)12yes—
818Dic3—24no—
819Dic3—42no—
820C23—24no—
821C23—21no—
822C23—22no—
823C23—42no—
824C23—42no—
825C23—44no—
826C23—64no—
827C23—82no—
828C23—82no—
829C23—124no—
830C23—124no—
831C23—124no—
832C23C22×#6712yes—
833C23C22×#6712yes—
834C23C22×#6711yescharacteristic
835Q8—22no—
836Q8—34no—
837Q8—64no—
838Q8—62no—
839Q8—81no—
840D4—22no—
841D4—24no—
842D4—22no—
843D4—22no—
844D4—42no—
845D4—44no—
846D4—42no—
847D4—44no—
848D4—42no—
849D4—64no—
850D4—64no—
851D4—82no—
852D4—81no—
853D4—82no—
854D4—82no—
855D4—82no—
856D4—124no—
857D4—124no—
858D4—128no—
859D4—128no—
860D4—124no—
861D4—242no—
862D4—242no—
863D4—244no—
864D4—244no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—22no—
873C2×C4—21no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—64no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—82no—
882C2×C4—82no—
883C2×C4—82no—
884C2×C4—128no—
885C2×C4—128no—
886C2×C4—122no—
887C2×C4C22×#6712yes—
888C2×C4C22×#6711yescharacteristic
889C2×C4C22×#6711yescharacteristic
890C2×C4C22×#6711yescharacteristic
891C2×C4C22×#6711yescharacteristic
892C2×C4C22×#6712yes—
893C2×C4C22×#6711yescharacteristic
894C2×C4C24×D311yescharacteristic
895C8—62no—
896C8—64no—
897C8—62no—
898C2×C3—22no—
899C2×C3—42no—
900C2×C3—42no—
901C2×C3—82no—
902C2×C3—81no—
903C2×C3#348411yescharacteristic
904C2×C3C2×#57511yescharacteristic
905C2×C3C2×#57611yescharacteristic
906D3—84no—
907C22—21no—
908C22—21no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—41no—
916C22—42no—
917C22—42no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—84no—
922C22—124no—
923C22—124no—
924C22—124no—
925C22—164no—
926C22—248no—
927C22#583512yes—
928C22C23×#6711yescharacteristic
929C4—21no—
930C4—21no—
931C4—21no—
932C4—21no—
933C4—22no—
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—41no—
939C4—64no—
940C4—122no—
941C4#582212yes—
942C4D3×H(5,𝔽2)12yes—
943C3#6160511yescharacteristic, complemented, Sylow
944C2—22no—
945C2—42no—
946C2—42no—
947C2—81no—
948C2—82no—
949C2—244no—
950C2C2×#582211yescharacteristic
951C2C2×#583511yescharacteristic
952C2#8728411yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3519C2
socleC22×C3C23×D4
hypercenter#3519D3
hypocenterC3#61605
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3519

Complements

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

NH ≅ G/Ntype
1. C3×#3519C2semidirect
2. C2×#5553C2semidirect
3. #83655C2semidirect
4. #83642C2semidirect
5. #83619C2semidirect
6. #83585C2semidirect
7. #83507C2semidirect
8. #83492C2semidirect
9. #83316C2semidirect
10. #83302C2semidirect
11. #83152C2semidirect
12. #83146C2semidirect
13. #82931C2semidirect
14. #82926C2semidirect
15. #82625C2semidirect
16. #82624C2semidirect
17. #82303C2semidirect
19. C22×#235C22semidirect
20. C3×#555C22semidirect
21. C3×#554C22semidirect
23. C3×#553C22semidirect
24. C3×#550C22semidirect
26. C3×#546C22semidirect
28. C3×D42C22semidirect
37. C2×#950C22semidirect
39. C2×#932C22semidirect
40. C2×#930C22semidirect
45. #5553C22semidirect
46. #5553C22semidirect
49. C2×#874C22semidirect
50. C2×C4×Dic6C22semidirect
51. #5238C22semidirect
52. #5217C22semidirect
53. #5207C22semidirect
54. C2×#830C22semidirect
55. #5091C22semidirect
56. #5088C22semidirect
57. #5075C22semidirect
58. #5073C22semidirect
59. #5067C22semidirect
60. #5063C22semidirect
61. #5058C22semidirect
62. #5054C22semidirect
63. #5050C22semidirect
64. #5049C22semidirect
65. #5047C22semidirect
66. #5046C22semidirect
67. #5043C22semidirect
69. #5040C22semidirect
70. #5039C22semidirect
71. #5038C22semidirect
72. #5038C22semidirect
73. #5037C22semidirect
74. #5037C22semidirect
75. #5037C22semidirect
77. #5036C22semidirect
78. #5036C22semidirect
80. #5033C22semidirect
81. C4×#216C22semidirect
82. #5027C22semidirect
83. #5018C22semidirect
84. C4×#214C22semidirect
85. #5015C22semidirect
86. #5015C22semidirect
87. #5012C22semidirect
88. #5011C22semidirect
89. D4×C3⋊C8C22semidirect
90. #5003C22semidirect
91. #5002C22semidirect
92. #4967C22semidirect
93. #4966C22semidirect
94. #4926C22semidirect
95. #4925C22semidirect
96. #3519D3semidirect
252. #555C2×D3semidirect
253. #554C2×D3semidirect
255. #553C2×D3semidirect
262. #550C2×D3semidirect
264. #546C2×D3semidirect
266. D42C2×D3semidirect
943. C3#61605semidirect

Maximal subgroups

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

subgroupindex
C3×#35192
C2×#55532
#836552
#836422
#836192
#835852
#835072
#834922
#833162
#833022
#831522
#831462
#829312
#829262
#826252
#826242
#823032
#616053