Finite Group Databasebeta

← #10833378

Subgroups — #10833378

Order 768.

1418 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3489C211yesmaximal, characteristic
2C2×#5246C211yesmaximal, characteristic, complemented
3#84084C211yesmaximal, characteristic, complemented
4C22×#837C211yesmaximal, characteristic, complemented
5#82925C211yesmaximal, characteristic, complemented
6#82811C211yesmaximal, characteristic, complemented
7#72143C211yesmaximal, characteristic, complemented
8#71881C211yesmaximal, characteristic, complemented
9#71876C211yesmaximal, characteristic, complemented
10#71868C211yesmaximal, characteristic, complemented
11#71863C211yesmaximal, characteristic, complemented
12#71711C211yesmaximal, characteristic, complemented
13#71698C211yesmaximal, characteristic, complemented
14#71666C211yesmaximal, characteristic, complemented
15#71664C211yesmaximal, characteristic, complemented
16#24466—31nomaximal, Sylow
17C2×C3×2−1+4C2211yescharacteristic
18C22×C3×#41C2211yescharacteristic
19C3×D4×Q8—21no—
20C3×#548—21no—
21C3×#547—21no—
22C3×#547—22no—
23C3×#546—21no—
24C3×#546—22no—
25C3×#537—21no—
26C3×#537C2211yescharacteristic
27C3×#536—21no—
28C3×#536C2211yescharacteristic
29C3×#525—21no—
30C3×#525C2211yescharacteristic
31C2×C3×C22⋊Q8—21no—
32C2×C3×C22⋊Q8C2211yescharacteristic
33C3×#520C2211yescharacteristic
34C2×#951C2211yescharacteristic
35C2×#951C2211yescharacteristic
36C2×#951C2211yescharacteristic, complemented
37C2×#944C2211yescharacteristic, complemented
38C2×#924C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C22×#208C2211yescharacteristic
41#5246—24no—
42#5239—21no—
43#5239—21no—
44C2×#837—24no—
45C2×#837C2211yescharacteristic
46C2×#837C2211yescharacteristic
47C2×#837C2211yescharacteristic
48C2×#837C2211yescharacteristic
49C2×#837C2211yescharacteristic, complemented
50C2×#837C2211yescharacteristic, complemented
51#5232C2211yescharacteristic
52#5232C2211yescharacteristic
53#5232C2211yescharacteristic, complemented
54#5229C2211yescharacteristic, complemented
55#5228—21no—
56C2×#836C2211yescharacteristic, complemented
57C2×#836C2211yescharacteristic, complemented
58#5218—21no—
59#5207C2211yescharacteristic
60#5052—21no—
61#5051—21no—
62#5042—21no—
63#5041—21no—
64#5004C2211yescharacteristic, complemented
65#4995C2211yescharacteristic, complemented
66#4976—22no—
67#4975C2211yescharacteristic, complemented
68#4973C2211yescharacteristic, complemented
69#4942—22no—
70#4532C2211yescharacteristic, complemented
71#4532C2211yescharacteristic, complemented
72#4530C2211yescharacteristic, complemented
73#4530C2211yescharacteristic, complemented
74#3489D311yescharacteristic
75#3056—31no—
76C2×#456—31no—
77#3007—31no—
78C22×#104—31no—
79#2857—31no—
80#2039—31no—
81#2038—31no—
82#2007—31no—
83#2005—31no—
84#1901—31no—
85#1896—31no—
86#1882—31no—
87#1859—31no—
88#1793—31no—
89C3×2−1+4—22no—
90C3×2−1+4—22no—
91C3×2−1+4—41no—
92C3×2−1+4—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—22no—
100C2×C3×#41—41no—
101C2×C3×#41—41no—
102C2×C3×#41D411yescharacteristic
103C2×C3×#41D411yescharacteristic
104C2×C3×#41C2311yescharacteristic
105C2×C3×#41C2311yescharacteristic
106C2×C3×#41C2311yescharacteristic
107C22×C3×Q8—21no—
108C22×C3×Q8—21no—
109C22×C3×Q8D411yescharacteristic
110C22×C3×Q8C2311yescharacteristic
111C22×C3×D4—21no—
112C22×C3×D4D411yescharacteristic
113C23×C3×C4—21no—
114C23×C3×C4C2311yescharacteristic
115C23×Dic3—21no—
116C22×Dic6C2311yescharacteristic
117C3×C4⋊Q8—22no—
118C3×C4⋊Q8—21no—
119C3×#124—22no—
120C3×#124—21no—
121C3×#123—22no—
122C3×#123—22no—
123C3×#123—22no—
124C3×#123—21no—
125C3×#123—22no—
126C3×C22⋊Q8—22no—
127C3×C22⋊Q8—22no—
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8—21no—
130C3×C22⋊Q8—21no—
131C3×C22⋊Q8—21no—
132C3×C22⋊Q8—21no—
133C3×C22⋊Q8—21no—
134C3×C22⋊Q8—21no—
135C3×C22⋊Q8—21no—
136C3×C22⋊Q8—21no—
137C3×C22⋊Q8D411yescharacteristic
138C3×C22⋊Q8D411yescharacteristic
139C3×#121—22no—
140C3×#121—22no—
141C3×#121—22no—
142C3×#121—21no—
143C3×#121—21no—
144C3×#121—22no—
145C3×#121D411yescharacteristic
146C3×#121D411yescharacteristic
147C3×#120—22no—
148C3×#120—21no—
149C3×C4×Q8—21no—
150C3×C4×D4—22no—
151C3×C4×D4—22no—
152C3×C4×D4—21no—
153C3×C4×D4—22no—
154C3×C4×D4—21no—
155C3×C4×D4—21no—
156C3×#117—21no—
157C3×#117C2311yescharacteristic
158C2×C3×C4⋊C4—22no—
159C2×C3×C4⋊C4—21no—
160C2×C3×C4⋊C4D412yes—
161C2×C3×C4⋊C4C2311yescharacteristic
162C2×C3×C22⋊C4—22no—
163C2×C3×C22⋊C4D412yes—
164C2×#217—21no—
165#951—22no—
166#951—22no—
167#951—22no—
168#951—41no—
169#951—41no—
170#951—41no—
171#944—22no—
172#944—41no—
173C2×#216—21no—
174C2×#216—21no—
175C2×#216—21no—
176C2×#214—21no—
177C2×#214—21no—
178C2×#214—21no—
179C2×C4⋊Dic3C2311yescharacteristic
180#924—21no—
181#924—21no—
182#924—21no—
183#924—21no—
184C2×Dic3⋊C4—22no—
185C2×Dic3⋊C4—22no—
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#836—22no—
207#836—41no—
208#835—21no—
209#835—21no—
210#835—21no—
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—
222C2×2−1+4C2×D311yescharacteristic
223C22×#41C2×D311yescharacteristic
224C2×#137—31no—
225C2×#137—31no—
226C2×#137—31no—
227C22×M16—31no—
228D4×Q8—21no—
229#548—21no—
230#547—21no—
231#547—22no—
232#546—21no—
233#546—22no—
234#537—21no—
235#537C2×D311yescharacteristic
236#536—21no—
237#536C2×D311yescharacteristic
238C2×C4⋊Q8—31no—
239#525—21no—
240#525C2×D311yescharacteristic
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—31no—
243C2×C22⋊Q8C2×D311yescharacteristic
244#520C2×D311yescharacteristic
245C22×C42—31no—
246#470—61no—
247#468—61no—
248#467—61no—
249#465—61no—
250#456—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×#101—31no—
268C2×#101—31no—
269#407—31no—
270#391—31no—
271#391—31no—
272#389—62no—
273#384—31no—
274#380—62no—
275#343—31no—
276#343—31no—
277#339—31no—
278#339—31no—
279C24×C3—21no—
280C24×C3C2×D411yescharacteristic
281C3×#41—21no—
282C3×#41—21no—
283C3×#41—22no—
284C3×#41—22no—
285C3×#41—21no—
286C3×#41—21no—
287C3×#41—21no—
288C3×#41—21no—
289C3×#41—21no—
290C3×#41—21no—
291C3×#41—21no—
292C3×#41—21no—
293C3×#41—42no—
294C3×#41—42no—
295C3×#41—41no—
296C3×#41—41no—
297C3×#41—42no—
298C3×#41—42no—
299C3×#41—42no—
300C3×#41—42no—
301C3×#41—44no—
302C3×#41—44no—
303C3×#41—42no—
304C3×#41—42no—
305C3×#41C2×D412yes—
306C3×#41#4112yes—
307C2×C3×Q8—22no—
308C2×C3×Q8—21no—
309C2×C3×Q8—21no—
310C2×C3×Q8—21no—
311C2×C3×Q8—21no—
312C2×C3×Q8—21no—
313C2×C3×Q8—21no—
314C2×C3×Q8—21no—
315C2×C3×Q8—22no—
316C2×C3×Q8—41no—
317C2×C3×Q8—42no—
318C2×C3×Q8—42no—
319C2×C3×Q8—42no—
320C2×C3×Q8—42no—
321C2×C3×Q8C2×D411yescharacteristic
322C2×C3×Q8C2×D411yescharacteristic
323C2×C3×Q8C2×D411yescharacteristic
324C2×C3×D4—21no—
325C2×C3×D4—22no—
326C2×C3×D4—22no—
327C2×C3×D4—21no—
328C2×C3×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—22no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—41no—
336C2×C3×D4—42no—
337C2×C3×D4—42no—
338C2×C3×D4C2×D411yescharacteristic
339C2×C3×D4C2×D411yescharacteristic
340C2×C3×D4C2×D411yescharacteristic
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—22no—
347C22×C3×C4—22no—
348C22×C3×C4—21no—
349C22×C3×C4—22no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—42no—
355C22×C3×C4—42no—
356C22×C3×C4C2×D412yes—
357C22×C3×C4C2×D411yescharacteristic
358C22×C3×C4C2×D411yescharacteristic
359C22×C3×C4C2×D411yescharacteristic
360C22×C3×C4C2×D411yescharacteristic
361C22×C3×C4C2×D411yescharacteristic
362C22×C3×C4C2×D412yes—
363C22×C3×C4C2411yescharacteristic
364C22×Dic3—21no—
365C22×Dic3—24no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—42no—
370C22×Dic3—42no—
371C2×Dic6—21no—
372C2×Dic6—21no—
373C2×Dic6—21no—
374C2×Dic6—21no—
375C2×Dic6—21no—
376C2×Dic6—21no—
377C3×C4⋊C4—22no—
378C3×C4⋊C4—22no—
379C3×C4⋊C4—22no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—22no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4C2×D411yescharacteristic
388C3×C4⋊C4C2×D411yescharacteristic
389C3×C22⋊C4—22no—
390C3×C22⋊C4—22no—
391C3×C22⋊C4—22no—
392C3×C22⋊C4—22no—
393C3×C22⋊C4—22no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4—22no—
396C3×C22⋊C4—22no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—21no—
400C3×C22⋊C4—21no—
401C3×C42—22no—
402C3×C42—21no—
403#217—41no—
404#217—41no—
405#216—42no—
406#216—42no—
407#216—42no—
408#214—42no—
409#214—42no—
410#214—42no—
411C4⋊Dic3—21no—
412C4⋊Dic3—21no—
413Dic3⋊C4—44no—
414Dic3⋊C4—44no—
415Dic3⋊C4—41no—
416Dic3⋊C4—41no—
417C4×Dic3—21no—
418C4×Dic3—21no—
419C4×Dic3—21no—
420C4×Dic3—42no—
421C4×Dic3C2×D412yes—
422#208—21no—
423#208—21no—
424#208—21no—
425#208—21no—
426#208—21no—
427#208—21no—
428#208—21no—
429#208—42no—
430#208C2×D412yes—
431C2×C3⋊C8—21no—
432C2×C3⋊C8—21no—
433C2×C3⋊C8—21no—
434C2×C3⋊C8—21no—
435C2×C3⋊C8—42no—
4362−1+4—22no—
4372−1+4—22no—
4382−1+4—41no—
4392−1+4—41no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—22no—
444C2×#41—21no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C2×#41#6711yescharacteristic
450C2×#41#6711yescharacteristic
451C2×#41C22×D311yescharacteristic
452C2×#41C22×D311yescharacteristic
453C2×#41C22×D311yescharacteristic
454C22×Q8—21no—
455C22×Q8—21no—
456C22×Q8—31no—
457C22×Q8#6711yescharacteristic
458C22×Q8C22×D311yescharacteristic
459C22×D4—21no—
460C22×D4#6711yescharacteristic
461C23×C4—21no—
462C23×C4—61no—
463C23×C4C22×D311yescharacteristic
464#137—62no—
465#137—62no—
466#137—62no—
467#137—121no—
468#137—121no—
469#137—121no—
470C2×Q16—61no—
471C2×Q16—61no—
472C2×Q16—61no—
473C2×SD16—61no—
474C2×SD16—61no—
475C2×SD16—61no—
476C2×M16—31no—
477C2×M16—31no—
478C2×M16—31no—
479C2×M16—31no—
480C2×M16—61no—
481C2×M16—62no—
482C2×M16—121no—
483C22×C8—61no—
484C4⋊Q8—22no—
485C4⋊Q8—21no—
486C4⋊Q8—62no—
487C4⋊Q8—121no—
488#124—22no—
489#124—21no—
490#123—22no—
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8—21no—
505C22⋊Q8—21no—
506C22⋊Q8—61no—
507C22⋊Q8—61no—
508C22⋊Q8—61no—
509C22⋊Q8—61no—
510C22⋊Q8#6711yescharacteristic
511C22⋊Q8#6711yescharacteristic
512#121—22no—
513#121—22no—
514#121—22no—
515#121—21no—
516#121—21no—
517#121—22no—
518#121#6711yescharacteristic
519#121#6711yescharacteristic
520#120—22no—
521#120—21no—
522C4×Q8—21no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529#117—21no—
530#117C22×D311yescharacteristic
531C2×C4⋊C4—22no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—31no—
534C2×C4⋊C4—61no—
535C2×C4⋊C4—62no—
536C2×C4⋊C4—62no—
537C2×C4⋊C4#6712yes—
538C2×C4⋊C4C22×D311yescharacteristic
539C2×C22⋊C4—22no—
540C2×C22⋊C4—61no—
541C2×C22⋊C4#6712yes—
542C2×C42—31no—
543C2×C42—31no—
544C2×C42—62no—
545C2×C42—61no—
546C2×C42—121no—
547#107—61no—
548#106—61no—
549#104—34no—
550#104—62no—
551#104—62no—
552#104—62no—
553#104—62no—
554#104—121no—
555#103—61no—
556#103—61no—
557#103—61no—
558#103—61no—
559#103—61no—
560#102—61no—
561#102—61no—
562#102—61no—
563#101—62no—
564#101—121no—
565C22⋊C8—61no—
566C22⋊C8—61no—
567#95—62no—
568#95—62no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—22no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—41no—
576C23×C3—42no—
577C23×C3—42no—
578C23×C3—81no—
579C23×C3#12011yescharacteristic
580C23×C3#12011yescharacteristic
581C23×C3C22×D411yescharacteristic
582C3×Q8—21no—
583C3×Q8—21no—
584C3×Q8—21no—
585C3×Q8—21no—
586C3×Q8—21no—
587C3×Q8—42no—
588C3×Q8—44no—
589C3×Q8—41no—
590C3×Q8—41no—
591C3×Q8—41no—
592C3×Q8—41no—
593C3×Q8#12112yes—
594C3×D4—22no—
595C3×D4—22no—
596C3×D4—21no—
597C3×D4—21no—
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—42no—
602C3×D4—42no—
603C3×D4—42no—
604C3×D4—44no—
605C3×D4—41no—
606C3×D4—41no—
607C3×D4—41no—
608C3×D4—41no—
609C3×D4—42no—
610C3×D4—81no—
611C3×D4—82no—
612C3×D4#12112yes—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—22no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—22no—
626C2×C3×C4—21no—
627C2×C3×C4—22no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—22no—
631C2×C3×C4—21no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—42no—
635C2×C3×C4—42no—
636C2×C3×C4—42no—
637C2×C3×C4—44no—
638C2×C3×C4—44no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—42no—
644C2×C3×C4—82no—
645C2×C3×C4#12011yescharacteristic
646C2×C3×C4#12011yescharacteristic
647C2×C3×C4C22×D411yescharacteristic
648C2×C3×C4C22×D411yescharacteristic
649C2×C3×C4C22×D411yescharacteristic
650C2×C3×C4C2×#4111yescharacteristic
651C2×C3×C4H(5,𝔽2)11yescharacteristic
652C2×C3×C4H(5,𝔽2)11yescharacteristic
653C2×Dic3—22no—
654C2×Dic3—22no—
655C2×Dic3—22no—
656C2×Dic3—22no—
657C2×Dic3—48no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—42no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665Dic6—41no—
666Dic6—41no—
667Dic6—41no—
668Dic6—41no—
669C3⋊C8—22no—
670C3⋊C8—41no—
671C3⋊C8—41no—
672C3⋊C8—41no—
673C24—21no—
674C24C2×#6711yescharacteristic
675#41—21no—
676#41—21no—
677#41—22no—
678#41—22no—
679#41—21no—
680#41—21no—
681#41—21no—
682#41—21no—
683#41—21no—
684#41—21no—
685#41—21no—
686#41—21no—
687#41—42no—
688#41—42no—
689#41—41no—
690#41—41no—
691#41—42no—
692#41—42no—
693#41—42no—
694#41—42no—
695#41—44no—
696#41—44no—
697#41—42no—
698#41—42no—
699#41D3×D412yes—
700#41#23712yes—
701C2×Q8—22no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—22no—
710C2×Q8—41no—
711C2×Q8—42no—
712C2×Q8—42no—
713C2×Q8—42no—
714C2×Q8—42no—
715C2×Q8—61no—
716C2×Q8—61no—
717C2×Q8—61no—
718C2×Q8—61no—
719C2×Q8—61no—
720C2×Q8—61no—
721C2×Q8C2×#6711yescharacteristic
722C2×Q8C2×#6711yescharacteristic
723C2×Q8C2×#6711yescharacteristic
724C2×D4—21no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—41no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4C2×#6711yescharacteristic
739C2×D4C2×#6711yescharacteristic
740C2×D4C2×#6711yescharacteristic
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—61no—
757C22×C4—64no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—122no—
762C22×C4—122no—
763C22×C4C2×#6712yes—
764C22×C4C2×#6711yescharacteristic
765C22×C4C2×#6711yescharacteristic
766C22×C4C2×#6711yescharacteristic
767C22×C4C2×#6711yescharacteristic
768C22×C4C2×#6711yescharacteristic
769C22×C4C2×#6712yes—
770C22×C4C23×D311yescharacteristic
771Q16—122no—
772Q16—122no—
773Q16—122no—
774SD16—122no—
775SD16—122no—
776SD16—122no—
777M16—32no—
778M16—61no—
779M16—61no—
780M16—61no—
781M16—61no—
782M16—61no—
783M16—61no—
784M16—61no—
785M16—122no—
786C2×C8—61no—
787C2×C8—61no—
788C2×C8—61no—
789C2×C8—61no—
790C2×C8—122no—
791C4⋊C4—22no—
792C4⋊C4—22no—
793C4⋊C4—22no—
794C4⋊C4—22no—
795C4⋊C4—21no—
796C4⋊C4—22no—
797C4⋊C4—22no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—61no—
802C4⋊C4—61no—
803C4⋊C4—124no—
804C4⋊C4—124no—
805C4⋊C4—121no—
806C4⋊C4—121no—
807C4⋊C4C2×#6711yescharacteristic
808C4⋊C4C2×#6711yescharacteristic
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—22no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—121no—
822C22⋊C4—121no—
823C42—22no—
824C42—21no—
825C42—32no—
826C42—61no—
827C42—61no—
828C42—61no—
829C42—122no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—22no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—84no—
849C22×C3#45612yescomplemented
850C22×C3C2×#12011yescharacteristic
851C22×C3D4211yescharacteristic
852C22×C3#54611yescharacteristic
853C3×C4—21no—
854C3×C4—21no—
855C3×C4—22no—
856C3×C4—42no—
857C3×C4—41no—
858C3×C4—41no—
859C3×C4—41no—
860C3×C4—42no—
861C3×C4—41no—
862C3×C4C2×#12111yescharacteristic
863C3×C4#53411yescharacteristic
864C3×C4D4211yescharacteristic
865C3×C4#54611yescharacteristic
866Dic3—24no—
867Dic3—42no—
868Dic3—81no—
869Dic3—81no—
870C23—22no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—41no—
877C23—42no—
878C23—42no—
879C23—81no—
880C23#95311yescharacteristic
881C23#95311yescharacteristic
882C23C22×#6711yescharacteristic
883Q8—21no—
884Q8—21no—
885Q8—21no—
886Q8—21no—
887Q8—21no—
888Q8—42no—
889Q8—44no—
890Q8—41no—
891Q8—41no—
892Q8—41no—
893Q8—41no—
894Q8—121no—
895Q8—121no—
896Q8—121no—
897Q8—121no—
898Q8#93912yes—
899D4—22no—
900D4—22no—
901D4—21no—
902D4—21no—
903D4—21no—
904D4—21no—
905D4—21no—
906D4—42no—
907D4—42no—
908D4—42no—
909D4—44no—
910D4—42no—
911D4—41no—
912D4—41no—
913D4—41no—
914D4—41no—
915D4—81no—
916D4—82no—
917D4#93912yes—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—21no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—44no—
943C2×C4—44no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—62no—
950C2×C4—62no—
951C2×C4—62no—
952C2×C4—62no—
953C2×C4—82no—
954C2×C4—128no—
955C2×C4—121no—
956C2×C4—121no—
957C2×C4—122no—
958C2×C4—121no—
959C2×C4—121no—
960C2×C4—121no—
961C2×C4—121no—
962C2×C4#95311yescharacteristic
963C2×C4#95311yescharacteristic
964C2×C4C2×D3×D411yescharacteristic
965C2×C4C2×#23711yescharacteristic
966C2×C4#100411yescharacteristic
967C2×C4#100411yescharacteristic
968C2×C4C22×#6711yescharacteristic
969C2×C4C22×#6711yescharacteristic
970C8—62no—
971C8—121no—
972C8—121no—
973C8—121no—
974C2×C3—21no—
975C2×C3—22no—
976C2×C3—21no—
977C2×C3—41no—
978C2×C3—42no—
979C2×C3—81no—
980C2×C3—81no—
981C2×C3#241011yescharacteristic
982C2×C3C2×#45611yescharacteristic
983C2×C3#301811yescharacteristic
984C22—21no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—22no—
990C22—21no—
991C22—21no—
992C22—42no—
993C22—42no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—84no—
1003C22#524612yescomplemented
1004C22D4×#6711yescharacteristic
1005C22#580611yescharacteristic
1006C22C2×#95311yescharacteristic
1007C4—21no—
1008C4—21no—
1009C4—22no—
1010C4—42no—
1011C4—41no—
1012C4—41no—
1013C4—41no—
1014C4—42no—
1015C4—41no—
1016C4—64no—
1017C4—122no—
1018C4—241no—
1019C4—241no—
1020C4D4×#6711yescharacteristic
1021C4C2×#93911yescharacteristic
1022C4#580411yescharacteristic
1023C4#580611yescharacteristic
1024C3#2446611yescharacteristic, complemented, Sylow
1025C2—21no—
1026C2—22no—
1027C2—21no—
1028C2—41no—
1029C2—42no—
1030C2—81no—
1031C2—81no—
1032C2#8404811yescharacteristic
1033C2C2×#524611yescharacteristic
1034C2#8412111yescharacteristic
subgroupG/H
centerC22C2×#953
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#3489C2
socleC22×C3C2×#120
hypercenter#3489D3
hypocenterC3#24466
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3489

Complements

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

NH ≅ G/Ntype
2. C2×#5246C2semidirect
3. #84084C2semidirect
4. C22×#837C2semidirect
5. #82925C2semidirect
6. #82811C2semidirect
7. #72143C2semidirect
8. #71881C2semidirect
9. #71876C2semidirect
10. #71868C2semidirect
11. #71863C2semidirect
12. #71711C2semidirect
13. #71698C2semidirect
14. #71666C2semidirect
15. #71664C2semidirect
36. C2×#951C22semidirect
37. C2×#944C22semidirect
49. C2×#837C22semidirect
50. C2×#837C22semidirect
53. #5232C22semidirect
54. #5229C22semidirect
56. C2×#836C22semidirect
57. C2×#836C22semidirect
64. #5004C22semidirect
65. #4995C22semidirect
67. #4975C22semidirect
68. #4973C22semidirect
70. #4532C22semidirect
71. #4532C22semidirect
72. #4530C22semidirect
73. #4530C22semidirect
205. #837D4semidirect
849. C22×C3#456semidirect
1003. C22#5246semidirect
1024. C3#24466semidirect

Maximal subgroups

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

subgroupindex
C3×#34892
C2×#52462
#840842
C22×#8372
#829252
#828112
#721432
#718812
#718762
#718682
#718632
#717112
#716982
#716662
#716642
#244663