Finite Group Databasebeta

← #10833393

Subgroups — #10833393

Order 768.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3488C211yesmaximal, characteristic
2C2×#5242C211yesmaximal, characteristic, complemented
3#84084C211yesmaximal, characteristic, complemented
4C22×#837C211yesmaximal, characteristic, complemented
5#82925C211yesmaximal, characteristic, complemented
6#82698C211yesmaximal, characteristic, complemented
7#72140C211yesmaximal, characteristic, complemented
8#71881C211yesmaximal, characteristic, complemented
9#71877C211yesmaximal, characteristic, complemented
10#71857C211yesmaximal, characteristic, complemented
11#71852C211yesmaximal, characteristic, complemented
12#71711C211yesmaximal, characteristic, complemented
13#71683C211yesmaximal, characteristic, complemented
14#71666C211yesmaximal, characteristic, complemented
15#71665C211yesmaximal, characteristic, complemented
16#24467—31nomaximal, Sylow
17C2×C3×H(5,𝔽2)C2211yescharacteristic
18C22×C3×#41C2211yescharacteristic
19C3×#550—21no—
20C3×#548—21no—
21C3×#546—21no—
22C3×#546—22no—
23C3×D42—22no—
24C3×D42—21no—
25C3×#537—21no—
26C3×#537C2211yescharacteristic
27C3×#535—21no—
28C3×#535C2211yescharacteristic
29C3×#525—21no—
30C3×#525C2211yescharacteristic
31C2×C3×#121—21no—
32C2×C3×#121C2211yescharacteristic
33C3×#520C2211yescharacteristic
34C2×#951C2211yescharacteristic
35C2×#951C2211yescharacteristic, complemented
36C2×#951C2211yescharacteristic, complemented
37C2×#936C2211yescharacteristic, complemented
38C2×#924C2211yescharacteristic, complemented
39C22×C4×Dic3C2211yescharacteristic, complemented
40C22×#208C2211yescharacteristic, complemented
41#5242—24no—
42#5239—21no—
43#5239—21no—
44C2×#837—24no—
45C2×#837C2211yescharacteristic
46C2×#837C2211yescharacteristic
47C2×#837C2211yescharacteristic, complemented
48C2×#837C2211yescharacteristic, complemented
49C2×#837C2211yescharacteristic, complemented
50C2×#837C2211yescharacteristic, complemented
51#5232C2211yescharacteristic
52#5232C2211yescharacteristic, complemented
53#5232C2211yescharacteristic, complemented
54#5228—21no—
55#5221C2211yescharacteristic, complemented
56#5220—22no—
57#5218—21no—
58C2×#833C2211yescharacteristic, complemented
59C2×#833C2211yescharacteristic, complemented
60#5207C2211yescharacteristic, complemented
61#5052—21no—
62#5051—21no—
63#5042—21no—
64#5041—21no—
65#5004C2211yescharacteristic, complemented
66#4995C2211yescharacteristic, complemented
67#4977C2211yescharacteristic, complemented
68#4973C2211yescharacteristic, complemented
69#4945—22no—
70#4532C2211yescharacteristic, complemented
71#4532C2211yescharacteristic, complemented
72#4530C2211yescharacteristic, complemented
73#4530C2211yescharacteristic, complemented
74#3488D311yescharacteristic
75#3056—31no—
76C2×#455—31no—
77#3007—31no—
78C22×#104—31no—
79#2850—31no—
80#2040—31no—
81#2037—31no—
82#2007—31no—
83#2004—31no—
84#1900—31no—
85#1896—31no—
86#1882—31no—
87#1860—31no—
88#1792—31no—
89C3×H(5,𝔽2)—22no—
90C3×H(5,𝔽2)—22no—
91C3×H(5,𝔽2)—41no—
92C3×H(5,𝔽2)—41no—
93C2×C3×#41—21no—
94C2×C3×#41—21no—
95C2×C3×#41—21no—
96C2×C3×#41—21no—
97C2×C3×#41—22no—
98C2×C3×#41—22no—
99C2×C3×#41—41no—
100C2×C3×#41—41no—
101C2×C3×#41D411yescharacteristic
102C2×C3×#41D411yescharacteristic
103C2×C3×#41C2311yescharacteristic
104C2×C3×#41C2311yescharacteristic
105C2×C3×#41C2311yescharacteristic
106C22×C3×Q8D411yescharacteristic
107C22×C3×D4—21no—
108C22×C3×D4—22no—
109C22×C3×D4—22no—
110C22×C3×D4—21no—
111C22×C3×D4—21no—
112C22×C3×D4D411yescharacteristic
113C22×C3×D4D412yes—
114C22×C3×D4C2311yescharacteristic
115C23×C3×C4—21no—
116C23×C3×C4C2311yescharacteristic
117C23×Dic3—21no—
118C22×Dic6C2311yescharacteristic
119C3×#127—22no—
120C3×#127—21no—
121C3×#124—22no—
122C3×#124—21no—
123C3×#123—22no—
124C3×#123—21no—
125C3×C22⋊Q8—22no—
126C3×C22⋊Q8—21no—
127C3×C22⋊Q8—21no—
128C3×C22⋊Q8D411yescharacteristic
129C3×C22⋊Q8D411yescharacteristic
130C3×#121—22no—
131C3×#121—22no—
132C3×#121—22no—
133C3×#121—22no—
134C3×#121—22no—
135C3×#121—21no—
136C3×#121—21no—
137C3×#121—21no—
138C3×#121—21no—
139C3×#121—21no—
140C3×#121—21no—
141C3×#121—22no—
142C3×#121—21no—
143C3×#121—21no—
144C3×#121D411yescharacteristic
145C3×#121D411yescharacteristic
146C3×#120—22no—
147C3×#120—22no—
148C3×#120—22no—
149C3×#120—21no—
150C3×#120—22no—
151C3×C4×Q8—21no—
152C3×C4×D4—22no—
153C3×C4×D4—22no—
154C3×C4×D4—21no—
155C3×C4×D4—22no—
156C3×C4×D4—21no—
157C3×C4×D4—21no—
158C3×#117—21no—
159C3×#117C2311yescharacteristic
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4C2311yescharacteristic
162C2×C3×C22⋊C4—22no—
163C2×C3×C22⋊C4D412yes—
164C2×#217—22no—
165C2×#217—22no—
166C2×#217—21no—
167#951—22no—
168#951—22no—
169#951—22no—
170#951—41no—
171#951—41no—
172#951—41no—
173C2×#216—21no—
174C2×#216—21no—
175C2×#216—21no—
176#936—22no—
177#936—41no—
178C2×#214—21no—
179C2×#214—21no—
180C2×#214—21no—
181C2×C4⋊Dic3C2311yescharacteristic
182#924—21no—
183#924—21no—
184#924—21no—
185#924—21no—
186C2×Dic3⋊C4—21no—
187C2×C4×Dic3—22no—
188C2×C4×Dic3—21no—
189C2×C4×Dic3—41no—
190C2×C4×Dic3C2311yescharacteristic
191C2×C4×Dic3C2311yescharacteristic
192C2×#208—21no—
193C2×#208—22no—
194C2×#208—41no—
195C2×#208C2311yescharacteristic
196C2×#208C2311yescharacteristic
197C2×#208C2311yescharacteristic
198C2×#208C2311yescharacteristic
199C22×C3⋊C8—21no—
200#837—22no—
201#837—22no—
202#837—22no—
203#837—22no—
204#837—41no—
205#837D414yescomplemented
206#835—21no—
207#835—21no—
208#835—21no—
209#833—22no—
210#833—41no—
211#832—21no—
212#832—21no—
213#832—21no—
214C3⋊#95—22no—
215C3⋊#95—22no—
216#830—21no—
217#830—21no—
218#810—21no—
219#810—21no—
220#808—21no—
221#807—21no—
222C2×H(5,𝔽2)C2×D311yescharacteristic
223C22×#41C2×D311yescharacteristic
224C2×#137—31no—
225C2×#137—31no—
226C2×#137—31no—
227C22×M16—31no—
228#550—21no—
229#548—21no—
230#546—21no—
231#546—22no—
232D42—22no—
233D42—21no—
234#537—21no—
235#537C2×D311yescharacteristic
236#535—21no—
237#535C2×D311yescharacteristic
238C2×#124—31no—
239#525—21no—
240#525C2×D311yescharacteristic
241C2×C22⋊Q8—31no—
242C2×#121—21no—
243C2×#121C2×D311yescharacteristic
244#520C2×D311yescharacteristic
245C22×C42—31no—
246#470—61no—
247#468—61no—
248#467—61no—
249#465—61no—
250#455—64no—
251#452—61no—
252#452—61no—
253#451—61no—
254#450—61no—
255#428—31no—
256C2×#104—31no—
257C2×#104—31no—
258C2×#104—31no—
259C2×#104—31no—
260C2×#104—31no—
261C2×#104—31no—
262C2×#104—64no—
263#419—31no—
264#417—31no—
265#417—31no—
266#417—31no—
267C2×#100—31no—
268C2×#100—31no—
269#407—31no—
270#391—31no—
271#390—31no—
272#388—62no—
273#386—62no—
274#382—31no—
275#343—31no—
276#343—31no—
277#339—31no—
278#339—31no—
279C24×C3—22no—
280C24×C3—21no—
281C24×C3C2×D411yescharacteristic
282C24×C3C2×D412yes—
283C3×#41—21no—
284C3×#41—21no—
285C3×#41—22no—
286C3×#41—22no—
287C3×#41—21no—
288C3×#41—21no—
289C3×#41—21no—
290C3×#41—21no—
291C3×#41—21no—
292C3×#41—21no—
293C3×#41—21no—
294C3×#41—21no—
295C3×#41—42no—
296C3×#41—42no—
297C3×#41—41no—
298C3×#41—41no—
299C3×#41—42no—
300C3×#41—42no—
301C3×#41—42no—
302C3×#41—42no—
303C3×#41—42no—
304C3×#41—42no—
305C3×#41C2×D412yes—
306C3×#41#4112yes—
307C2×C3×Q8—21no—
308C2×C3×Q8—22no—
309C2×C3×Q8—41no—
310C2×C3×Q8C2×D411yescharacteristic
311C2×C3×Q8C2×D411yescharacteristic
312C2×C3×Q8C2×D411yescharacteristic
313C2×C3×D4—21no—
314C2×C3×D4—22no—
315C2×C3×D4—22no—
316C2×C3×D4—22no—
317C2×C3×D4—22no—
318C2×C3×D4—21no—
319C2×C3×D4—21no—
320C2×C3×D4—21no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—22no—
324C2×C3×D4—22no—
325C2×C3×D4—22no—
326C2×C3×D4—21no—
327C2×C3×D4—22no—
328C2×C3×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—41no—
336C2×C3×D4—42no—
337C2×C3×D4—42no—
338C2×C3×D4—42no—
339C2×C3×D4—42no—
340C2×C3×D4—44no—
341C2×C3×D4—44no—
342C2×C3×D4—42no—
343C2×C3×D4—42no—
344C2×C3×D4—44no—
345C2×C3×D4—84no—
346C2×C3×D4C2×D411yescharacteristic
347C2×C3×D4C2×D411yescharacteristic
348C2×C3×D4C2×D411yescharacteristic
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—22no—
355C22×C3×C4—21no—
356C22×C3×C4—22no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—42no—
362C22×C3×C4—42no—
363C22×C3×C4C2×D411yescharacteristic
364C22×C3×C4C2×D411yescharacteristic
365C22×C3×C4C2×D411yescharacteristic
366C22×C3×C4C2×D411yescharacteristic
367C22×C3×C4C2×D411yescharacteristic
368C22×C3×C4C2×D412yes—
369C22×C3×C4C2411yescharacteristic
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3—42no—
375C22×Dic3—42no—
376C22×Dic3—42no—
377C2×Dic6—21no—
378C2×Dic6—21no—
379C2×Dic6—21no—
380C2×Dic6—21no—
381C2×Dic6—21no—
382C2×Dic6—21no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—22no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4C2×D411yescharacteristic
390C3×C4⋊C4C2×D411yescharacteristic
391C3×C22⋊C4—22no—
392C3×C22⋊C4—22no—
393C3×C22⋊C4—22no—
394C3×C22⋊C4—22no—
395C3×C22⋊C4—22no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—21no—
400C3×C22⋊C4—22no—
401C3×C22⋊C4—22no—
402C3×C22⋊C4—21no—
403C3×C42—22no—
404C3×C42—21no—
405#217—44no—
406#217—44no—
407#217—41no—
408#217—41no—
409#216—42no—
410#216—42no—
411#216—42no—
412#214—42no—
413#214—42no—
414#214—42no—
415C4⋊Dic3—21no—
416C4⋊Dic3—21no—
417Dic3⋊C4—41no—
418Dic3⋊C4—41no—
419C4×Dic3—21no—
420C4×Dic3—21no—
421C4×Dic3—21no—
422C4×Dic3—42no—
423C4×Dic3C2×D412yescomplemented
424#208—21no—
425#208—21no—
426#208—21no—
427#208—21no—
428#208—21no—
429#208—21no—
430#208—21no—
431#208—42no—
432#208C2×D412yescomplemented
433C2×C3⋊C8—21no—
434C2×C3⋊C8—21no—
435C2×C3⋊C8—21no—
436C2×C3⋊C8—21no—
437C2×C3⋊C8—42no—
438H(5,𝔽2)—22no—
439H(5,𝔽2)—22no—
440H(5,𝔽2)—41no—
441H(5,𝔽2)—41no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—41no—
449C2×#41—41no—
450C2×#41#6711yescharacteristic
451C2×#41#6711yescharacteristic
452C2×#41C22×D311yescharacteristic
453C2×#41C22×D311yescharacteristic
454C2×#41C22×D311yescharacteristic
455C22×Q8—31no—
456C22×Q8#6711yescharacteristic
457C22×D4—21no—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4#6711yescharacteristic
463C22×D4#6712yes—
464C22×D4C22×D311yescharacteristic
465C23×C4—21no—
466C23×C4—61no—
467C23×C4C22×D311yescharacteristic
468#137—62no—
469#137—62no—
470#137—62no—
471#137—121no—
472#137—121no—
473#137—121no—
474C2×Q16—61no—
475C2×Q16—61no—
476C2×Q16—61no—
477C2×SD16—61no—
478C2×SD16—61no—
479C2×SD16—61no—
480C2×M16—31no—
481C2×M16—31no—
482C2×M16—31no—
483C2×M16—31no—
484C2×M16—61no—
485C2×M16—62no—
486C2×M16—121no—
487C22×C8—61no—
488#127—22no—
489#127—21no—
490#124—22no—
491#124—21no—
492#124—62no—
493#124—121no—
494#123—22no—
495#123—21no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—61no—
500C22⋊Q8—61no—
501C22⋊Q8—61no—
502C22⋊Q8—61no—
503C22⋊Q8#6711yescharacteristic
504C22⋊Q8#6711yescharacteristic
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—22no—
517#121—21no—
518#121—21no—
519#121#6711yescharacteristic
520#121#6711yescharacteristic
521#120—22no—
522#120—22no—
523#120—22no—
524#120—21no—
525#120—22no—
526C4×Q8—21no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—21no—
530C4×D4—22no—
531C4×D4—21no—
532C4×D4—21no—
533#117—21no—
534#117C22×D311yescharacteristic
535C2×C4⋊C4—21no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—61no—
538C2×C4⋊C4C22×D311yescharacteristic
539C2×C22⋊C4—22no—
540C2×C22⋊C4—61no—
541C2×C22⋊C4—62no—
542C2×C22⋊C4—62no—
543C2×C22⋊C4#6712yes—
544C2×C42—31no—
545C2×C42—31no—
546C2×C42—62no—
547C2×C42—61no—
548C2×C42—121no—
549#107—61no—
550#106—61no—
551#104—34no—
552#104—62no—
553#104—62no—
554#104—62no—
555#104—62no—
556#104—121no—
557#103—61no—
558#103—61no—
559#103—61no—
560#103—61no—
561#103—61no—
562#102—61no—
563#102—61no—
564#102—61no—
565#100—62no—
566#100—121no—
567C22⋊C8—61no—
568C22⋊C8—61no—
569#95—62no—
570#95—62no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—41no—
581C23×C3—42no—
582C23×C3—44no—
583C23×C3—42no—
584C23×C3—42no—
585C23×C3—42no—
586C23×C3—81no—
587C23×C3—82no—
588C23×C3—82no—
589C23×C3#12011yescharacteristic
590C23×C3#12011yescharacteristic
591C23×C3C22×D411yescharacteristic
592C3×Q8—21no—
593C3×Q8—21no—
594C3×Q8—21no—
595C3×Q8—21no—
596C3×Q8—21no—
597C3×Q8—42no—
598C3×Q8#12112yes—
599C3×D4—22no—
600C3×D4—22no—
601C3×D4—21no—
602C3×D4—21no—
603C3×D4—21no—
604C3×D4—21no—
605C3×D4—21no—
606C3×D4—42no—
607C3×D4—42no—
608C3×D4—44no—
609C3×D4—42no—
610C3×D4—44no—
611C3×D4—41no—
612C3×D4—41no—
613C3×D4—41no—
614C3×D4—41no—
615C3×D4—44no—
616C3×D4—42no—
617C3×D4—41no—
618C3×D4—41no—
619C3×D4—41no—
620C3×D4—41no—
621C3×D4—81no—
622C3×D4—82no—
623C3×D4—82no—
624C3×D4—82no—
625C3×D4—82no—
626C3×D4#12112yes—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—22no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—22no—
640C2×C3×C4—21no—
641C2×C3×C4—22no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—42no—
646C2×C3×C4—42no—
647C2×C3×C4—42no—
648C2×C3×C4—44no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—42no—
654C2×C3×C4—82no—
655C2×C3×C4#12011yescharacteristic
656C2×C3×C4#12011yescharacteristic
657C2×C3×C4C22×D411yescharacteristic
658C2×C3×C4C22×D411yescharacteristic
659C2×C3×C4C22×D411yescharacteristic
660C2×C3×C4C2×#4111yescharacteristic
661C2×C3×C4H(5,𝔽2)11yescharacteristic
662C2×C3×C4H(5,𝔽2)11yescharacteristic
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3—48no—
669C2×Dic3—41no—
670C2×Dic3—42no—
671C2×Dic3—41no—
672C2×Dic3—41no—
673C2×Dic3—41no—
674C2×Dic3—41no—
675Dic6—41no—
676Dic6—41no—
677Dic6—41no—
678Dic6—41no—
679C3⋊C8—22no—
680C3⋊C8—41no—
681C3⋊C8—41no—
682C3⋊C8—41no—
683C24—22no—
684C24—21no—
685C24C2×#6711yescharacteristic
686C24C2×#6712yes—
687#41—21no—
688#41—21no—
689#41—22no—
690#41—22no—
691#41—21no—
692#41—21no—
693#41—21no—
694#41—21no—
695#41—21no—
696#41—21no—
697#41—21no—
698#41—21no—
699#41—42no—
700#41—42no—
701#41—41no—
702#41—41no—
703#41—42no—
704#41—42no—
705#41—42no—
706#41—42no—
707#41—42no—
708#41—42no—
709#41D3×D412yes—
710#41#23712yes—
711C2×Q8—21no—
712C2×Q8—22no—
713C2×Q8—41no—
714C2×Q8—61no—
715C2×Q8—61no—
716C2×Q8—61no—
717C2×Q8—61no—
718C2×Q8—61no—
719C2×Q8—61no—
720C2×Q8C2×#6711yescharacteristic
721C2×Q8C2×#6711yescharacteristic
722C2×Q8C2×#6711yescharacteristic
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—21no—
737C2×D4—22no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—41no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—42no—
753C2×D4—42no—
754C2×D4—44no—
755C2×D4—84no—
756C2×D4C2×#6711yescharacteristic
757C2×D4C2×#6711yescharacteristic
758C2×D4C2×#6711yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—122no—
778C22×C4—122no—
779C22×C4—122no—
780C22×C4C2×#6711yescharacteristic
781C22×C4C2×#6711yescharacteristic
782C22×C4C2×#6711yescharacteristic
783C22×C4C2×#6711yescharacteristic
784C22×C4C2×#6711yescharacteristic
785C22×C4C2×#6712yes—
786C22×C4C23×D311yescharacteristic
787Q16—122no—
788Q16—122no—
789Q16—122no—
790SD16—122no—
791SD16—122no—
792SD16—122no—
793M16—32no—
794M16—61no—
795M16—61no—
796M16—61no—
797M16—61no—
798M16—61no—
799M16—61no—
800M16—61no—
801M16—122no—
802C2×C8—61no—
803C2×C8—61no—
804C2×C8—61no—
805C2×C8—61no—
806C2×C8—122no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—61no—
814C4⋊C4—61no—
815C4⋊C4—121no—
816C4⋊C4—121no—
817C4⋊C4C2×#6711yescharacteristic
818C4⋊C4C2×#6711yescharacteristic
819C22⋊C4—22no—
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—21no—
831C22⋊C4—124no—
832C22⋊C4—124no—
833C22⋊C4—121no—
834C22⋊C4—121no—
835C42—22no—
836C42—21no—
837C42—32no—
838C42—61no—
839C42—61no—
840C42—61no—
841C42—122no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—22no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—41no—
853C22×C3—41no—
854C22×C3—41no—
855C22×C3—41no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—41no—
859C22×C3—41no—
860C22×C3—41no—
861C22×C3—42no—
862C22×C3—41no—
863C22×C3—84no—
864C22×C3—82no—
865C22×C3—82no—
866C22×C3—164no—
867C22×C3#45512yescomplemented
868C22×C3C2×#12011yescharacteristic
869C22×C3D4211yescharacteristic
870C22×C3#54611yescharacteristic
871C3×C4—21no—
872C3×C4—21no—
873C3×C4—22no—
874C3×C4—41no—
875C3×C4—41no—
876C3×C4—42no—
877C3×C4—41no—
878C3×C4—41no—
879C3×C4C2×#12111yescharacteristic
880C3×C4#53411yescharacteristic
881C3×C4D4211yescharacteristic
882C3×C4#54611yescharacteristic
883Dic3—42no—
884Dic3—42no—
885Dic3—81no—
886Dic3—81no—
887C23—22no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—22no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—22no—
896C23—41no—
897C23—42no—
898C23—44no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—81no—
903C23—82no—
904C23—82no—
905C23#95311yescharacteristic
906C23#95311yescharacteristic
907C23C22×#6711yescharacteristic
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—21no—
913Q8—42no—
914Q8—121no—
915Q8—121no—
916Q8—121no—
917Q8—121no—
918Q8#93912yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—44no—
929D4—42no—
930D4—44no—
931D4—44no—
932D4—42no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—82no—
942D4—81no—
943D4—82no—
944D4—82no—
945D4—82no—
946D4#93912yes—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—44no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—42no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—82no—
977C2×C4—121no—
978C2×C4—121no—
979C2×C4—121no—
980C2×C4—128no—
981C2×C4—121no—
982C2×C4—122no—
983C2×C4—121no—
984C2×C4—121no—
985C2×C4—121no—
986C2×C4—121no—
987C2×C4#95311yescharacteristic
988C2×C4#95311yescharacteristic
989C2×C4C2×D3×D411yescharacteristic
990C2×C4C2×#23711yescharacteristic
991C2×C4#100411yescharacteristic
992C2×C4#100411yescharacteristic
993C2×C4C22×#6711yescharacteristic
994C2×C4C22×#6711yescharacteristic
995C8—62no—
996C8—121no—
997C8—121no—
998C8—121no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—22no—
1002C2×C3—41no—
1003C2×C3—42no—
1004C2×C3—81no—
1005C2×C3—82no—
1006C2×C3—81no—
1007C2×C3#241011yescharacteristic
1008C2×C3C2×#45511yescharacteristic
1009C2×C3#301811yescharacteristic
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—22no—
1016C22—21no—
1017C22—21no—
1018C22—42no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—42no—
1025C22—42no—
1026C22—41no—
1027C22—41no—
1028C22—41no—
1029C22—42no—
1030C22—41no—
1031C22—84no—
1032C22—82no—
1033C22—82no—
1034C22—164no—
1035C22#524212yescomplemented
1036C22D4×#6711yescharacteristic
1037C22#580611yescharacteristic
1038C22C2×#95311yescharacteristic
1039C4—21no—
1040C4—21no—
1041C4—22no—
1042C4—41no—
1043C4—41no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—122no—
1048C4—122no—
1049C4—241no—
1050C4—241no—
1051C4D4×#6711yescharacteristic
1052C4C2×#93911yescharacteristic
1053C4#580411yescharacteristic
1054C4#580611yescharacteristic
1055C3#2446711yescharacteristic, complemented, Sylow
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2#8404811yescharacteristic
1065C2C2×#524211yescharacteristic
1066C2#8412111yescharacteristic
subgroupG/H
centerC22C2×#953
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#3488C2
socleC22×C3C2×#120
hypercenter#3488D3
hypocenterC3#24467
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3488

Complements

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

NH ≅ G/Ntype
2. C2×#5242C2semidirect
3. #84084C2semidirect
4. C22×#837C2semidirect
5. #82925C2semidirect
6. #82698C2semidirect
7. #72140C2semidirect
8. #71881C2semidirect
9. #71877C2semidirect
10. #71857C2semidirect
11. #71852C2semidirect
12. #71711C2semidirect
13. #71683C2semidirect
14. #71666C2semidirect
15. #71665C2semidirect
35. C2×#951C22semidirect
36. C2×#951C22semidirect
37. C2×#936C22semidirect
38. C2×#924C22semidirect
39. C22×C4×Dic3C22semidirect
40. C22×#208C22semidirect
47. C2×#837C22semidirect
48. C2×#837C22semidirect
49. C2×#837C22semidirect
50. C2×#837C22semidirect
52. #5232C22semidirect
53. #5232C22semidirect
55. #5221C22semidirect
58. C2×#833C22semidirect
59. C2×#833C22semidirect
60. #5207C22semidirect
65. #5004C22semidirect
66. #4995C22semidirect
67. #4977C22semidirect
68. #4973C22semidirect
70. #4532C22semidirect
71. #4532C22semidirect
72. #4530C22semidirect
73. #4530C22semidirect
205. #837D4semidirect
423. C4×Dic3C2×D4semidirect
432. #208C2×D4semidirect
867. C22×C3#455semidirect
1035. C22#5242semidirect
1055. C3#24467semidirect

Maximal subgroups

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

subgroupindex
C3×#34882
C2×#52422
#840842
C22×#8372
#829252
#826982
#721402
#718812
#718772
#718572
#718522
#717112
#716832
#716662
#716652
#244673