Finite Group Databasebeta

← #364992

Subgroups — #364992

Order 512.

2028 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2536C211yesmaximal, characteristic
2C2×#2352C211yesmaximal, characteristic
3C2×#1954C211yesmaximal, characteristic
4C2×#1873C211yesmaximal, characteristic, complemented
5C2×#1872C211yesmaximal, characteristic, complemented
6C2×#1805C211yesmaximal, characteristic, complemented
7C2×C4×#103C211yesmaximal, characteristic, complemented
8#11200C211yesmaximal, characteristic, complemented
9#11199C211yesmaximal, characteristic, complemented
10#10970C211yesmaximal, characteristic, complemented
11#10970C211yesmaximal, characteristic, complemented
12#10850C211yesmaximal, characteristic, complemented
13#10842C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32#2536—24no—
33#2536C418yescomplemented
34C2×#398—21no—
35C2×#394—21no—
36#2352—24no—
37#2352—24no—
38C2×#388—21no—
39C2×#388—21no—
40C2×#388—21no—
41C2×#387—21no—
42C2×#386—21no—
43C2×#382C2211yescharacteristic
44C2×#382C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4—21no—
51#1954—24no—
52#1873—24no—
53#1872—24no—
54#1805—24no—
55C4×#103—24no—
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#340C2211yescharacteristic
60C2×#340C2211yescharacteristic
61C2×#340C2211yescharacteristic
62C2×#340C2211yescharacteristic
63C2×#340C2211yescharacteristic
64C2×#340C2211yescharacteristic
65C2×#340C2211yescharacteristic
66C2×#340C2211yescharacteristic
67C2×#340C2211yescharacteristic
68C23×Q8C2311yescharacteristic
69C23×D4D411yescharacteristic
70C24×C4—21no—
71C24×C4C2311yescharacteristic
72C24×C4C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C2×C22⋊Q8—22no—
78C2×C22⋊Q8—22no—
79C2×C22⋊Q8—22no—
80C2×C22⋊Q8—22no—
81C2×C22⋊Q8—22no—
82C2×C22⋊Q8—22no—
83C2×C22⋊Q8—41no—
84C2×C22⋊Q8—41no—
85C2×C22⋊Q8—41no—
86C2×C22⋊Q8—41no—
87C2×C22⋊Q8C2×C414yes—
88C2×C22⋊Q8C2×C414yescomplemented
89C2×C4×Q8—22no—
90C2×C4×Q8—22no—
91C2×C4×Q8—22no—
92C2×C4×Q8—22no—
93C2×C4×Q8—22no—
94C2×C4×Q8C2×C414yescomplemented
95C2×C4×D4—22no—
96C2×C4×D4—22no—
97C2×C4×D4—22no—
98C2×C4×D4—22no—
99C2×C4×D4C2×C414yes—
100C2×C4×D4D414yes—
101C2×#117—22no—
102C2×#117—22no—
103C2×#117—22no—
104C2×#117—22no—
105C2×#117—41no—
106C2×#117—41no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—22no—
112C22×C4⋊C4—22no—
113C22×C4⋊C4—22no—
114C22×C4⋊C4—22no—
115C22×C4⋊C4—41no—
116C22×C4⋊C4—41no—
117C22×C4⋊C4D411yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C22⋊C4—21no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4D411yescharacteristic
133C22×C22⋊C4D411yescharacteristic
134C22×C42—21no—
135C22×C42—21no—
136C22×C42—21no—
137C22×C42C2311yescharacteristic
138C2×C4⋊C8—22no—
139C2×C4⋊C8—22no—
140C2×C4⋊C8—22no—
141C2×#103—22no—
142C2×#103—22no—
143C2×#103—22no—
144C2×#103—22no—
145C2×#103—22no—
146C2×#103—22no—
147C2×#103—22no—
148C2×#103—22no—
149C2×#103—22no—
150C2×#103—41no—
151C2×#103—41no—
152C2×#103D414yescomplemented
153C2×C22⋊C8—22no—
154C2×C22⋊C8—22no—
155C2×C22⋊C8—22no—
156C2×C22⋊C8—22no—
157C2×C22⋊C8—22no—
158C2×C22⋊C8—22no—
159C2×C22⋊C8—22no—
160C2×C22⋊C8—22no—
161C2×C22⋊C8—41no—
162C2×C22⋊C8—41no—
163C2×C22⋊C8—41no—
164C2×C22⋊C8—41no—
165C2×C4×C8—22no—
166C2×C4×C8—22no—
167C2×C4×C8—22no—
168#398—28no—
169#394—28no—
170#388—28no—
171#388—28no—
172#388—28no—
173#387—28no—
174#386—28no—
175#382—22no—
176#382—22no—
177#382C2×C414yescomplemented
178#382D414yes—
179#380—22no—
180#380—22no—
181#380—22no—
182#380—22no—
183#380—22no—
184#380—22no—
185#380C2×C414yes—
186#380C2×C414yescomplemented
187C4×C4⋊C4—22no—
188C4×C4⋊C4D414yes—
189C4×C22⋊C4—28no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199#340—22no—
200#340—22no—
201#340—22no—
202#340—22no—
203#340—22no—
204#340—22no—
205#340—22no—
206#340—22no—
207#340—41no—
208#340—41no—
209#340—41no—
210#340—41no—
211C25C2×D411yescharacteristic
212C25C2×D411yescharacteristic
213C22×Q8—21no—
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8—21no—
217C22×Q8—21no—
218C22×Q8—21no—
219C22×Q8—21no—
220C22×Q8—21no—
221C22×Q8—21no—
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8C22×C412yes—
225C22×Q8C2×D412yes—
226C22×Q8#4112yes—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—41no—
232C22×D4—41no—
233C22×D4C22⋊C414yes—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—24no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—81no—
272C23×C4—81no—
273C23×C4C22×C412yes—
274C23×C4C22×C412yes—
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D412yes—
278C23×C4C2×D412yes—
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2411yescharacteristic
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8C2×D412yes—
309C22×C8#4112yes—
310C22⋊Q8—28no—
311C22⋊Q8—28no—
312C22⋊Q8—44no—
313C22⋊Q8—44no—
314C22⋊Q8—44no—
315C22⋊Q8—44no—
316C22⋊Q8—44no—
317C22⋊Q8—44no—
318C4×Q8—28no—
319C4×Q8—28no—
320C4×Q8—44no—
321C4×Q8—44no—
322C4×D4—28no—
323C4×D4—28no—
324C4×D4—28no—
325C4×D4—28no—
326#117—44no—
327#117—44no—
328#117—44no—
329#117—44no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4C22⋊C414yes—
382C2×C4⋊C4C22×C412yes—
383C2×C4⋊C4C22×C412yes—
384C2×C4⋊C4C22×C412yes—
385C2×C4⋊C4C2×D412yes—
386C2×C4⋊C4C2×D412yes—
387C2×C4⋊C4C2×D412yes—
388C2×C4⋊C4C2×D412yes—
389C2×C4⋊C4C2×D412yes—
390C2×C4⋊C4#4112yes—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—81no—
415C2×C22⋊C4—81no—
416C2×C22⋊C4C22⋊C414yes—
417C2×C22⋊C4C22⋊C414yes—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—42no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42—81no—
426C2×C42—81no—
427C2×C42C22×C412yes—
428C2×C42C2×D412yes—
429C2×C42C2×D412yes—
430C2×C42C2×D412yes—
431C2×C42#4112yes—
432C2×C42#4112yes—
433C4⋊C8—44no—
434#103—28no—
435#103—28no—
436#103—44no—
437#103—44no—
438C22⋊C8—44no—
439C22⋊C8—44no—
440C22⋊C8—44no—
441C22⋊C8—44no—
442C4×C8—44no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—24no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24C2×C22⋊C412yes—
479C24C2×C22⋊C412yes—
480C24#13512yes—
481C24#13512yes—
482C24C22×D411yescharacteristic
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8—41no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8—41no—
509C2×Q8—41no—
510C2×Q8C4×D414yes—
511C2×D4—28no—
512C2×D4—28no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—48no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—48no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—84no—
653C22×C4—84no—
654C22×C4—84no—
655C22×C4—84no—
656C22×C4—84no—
657C22×C4C2×C22⋊C412yes—
658C22×C4C2×C22⋊C412yes—
659C22×C4C2×C22⋊C412yes—
660C22×C4C2×C22⋊C412yes—
661C22×C4#12012yes—
662C22×C4#12012yes—
663C22×C4#12312yes—
664C22×C4#12312yes—
665C22×C4C23×C411yescharacteristic
666C22×C4C22×D411yescharacteristic
667C22×C4C22×D411yescharacteristic
668C22×C4C22×D411yescharacteristic
669C22×C4C22×D411yescharacteristic
670C22×C4C2×#4111yescharacteristic
671C22×C4C2×#4111yescharacteristic
672C22×C4C2×#4111yescharacteristic
673C22×C4C2×#4111yescharacteristic
674C22×C4C2×#4111yescharacteristic
675C22×C4H(5,𝔽2)11yescharacteristic
676C22×C4H(5,𝔽2)11yescharacteristic
677C22×C4H(5,𝔽2)11yescharacteristic
678C22×C42−1+411yescharacteristic
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—22no—
685C2×C8—41no—
686C2×C8—41no—
687C2×C8—41no—
688C2×C8—41no—
689C2×C8—41no—
690C2×C8—41no—
691C2×C8—41no—
692C2×C8—41no—
693C2×C8—41no—
694C2×C8—41no—
695C2×C8—41no—
696C2×C8—41no—
697C2×C8—41no—
698C2×C8—41no—
699C2×C8—41no—
700C2×C8—41no—
701C2×C8—41no—
702C2×C8—41no—
703C2×C8—41no—
704C2×C8—41no—
705C2×C8—41no—
706C2×C8—41no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—28no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—22no—
720C4⋊C4—22no—
721C4⋊C4—22no—
722C4⋊C4—22no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—48no—
726C4⋊C4—41no—
727C4⋊C4—41no—
728C4⋊C4—41no—
729C4⋊C4—41no—
730C4⋊C4—41no—
731C4⋊C4—41no—
732C4⋊C4—41no—
733C4⋊C4—41no—
734C4⋊C4—41no—
735C4⋊C4—41no—
736C4⋊C4—41no—
737C4⋊C4—41no—
738C4⋊C4—48no—
739C4⋊C4#12114yes—
740C22⋊C4—28no—
741C22⋊C4—28no—
742C22⋊C4—48no—
743C22⋊C4—48no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—48no—
747C22⋊C4—48no—
748C22⋊C4—84no—
749C42—48no—
750C42—48no—
751C42—84no—
752C42C4×D414yes—
753C42C4×D414yes—
754C42#12114yes—
755C42#12114yes—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#41614yes—
826C23C22×C22⋊C411yescharacteristic
827C23C2×#12011yescharacteristic
828C23C2×#12311yescharacteristic
829C23D4211yescharacteristic
830C23#54611yescharacteristic
831C23#54611yescharacteristic
832C23#54711yescharacteristic
833C23C2×#13511yescharacteristic
834C23C2×#13511yescharacteristic
835C23#57511yescharacteristic
836C23#57511yescharacteristic
837C23#57711yescharacteristic
838C23#57711yescharacteristic
839C23#57811yescharacteristic
840C23#57811yescharacteristic
841Q8—24no—
842Q8—24no—
843Q8—42no—
844Q8—42no—
845Q8—42no—
846Q8—42no—
847Q8—42no—
848Q8—42no—
849D4—416no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—42no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—42no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—42no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—816no—
925C2×C4—81no—
926C2×C4—81no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4—81no—
939C2×C4—81no—
940C2×C4—81no—
941C2×C4—81no—
942C2×C4—81no—
943C2×C4—81no—
944C2×C4—81no—
945C2×C4—81no—
946C2×C4—81no—
947C2×C4—81no—
948C2×C4—81no—
949C2×C4#38614yes—
950C2×C4#38614yes—
951C2×C4C2×C4×D411yescharacteristic
952C2×C4C2×C4×D411yescharacteristic
953C2×C4C2×C4×D411yescharacteristic
954C2×C4C4×#4111yescharacteristic
955C2×C4#51811yescharacteristic
956C2×C4#52011yescharacteristic
957C2×C4C2×#12111yescharacteristic
958C2×C4C2×#12111yescharacteristic
959C2×C4C2×#12111yescharacteristic
960C2×C4#52511yescharacteristic
961C2×C4#52911yescharacteristic
962C2×C4#53211yescharacteristic
963C2×C4#53511yescharacteristic
964C2×C4#53711yescharacteristic
965C2×C4#54011yescharacteristic
966C2×C4#54211yescharacteristic
967C2×C4D4211yescharacteristic
968C2×C4D4211yescharacteristic
969C2×C4#54611yescharacteristic
970C2×C4#54611yescharacteristic
971C2×C4#54611yescharacteristic
972C2×C4#54711yescharacteristic
973C2×C4#54711yescharacteristic
974C2×C4#54811yescharacteristic
975C2×C4#55011yescharacteristic
976C2×C4#55311yescharacteristic
977C2×C4#55311yescharacteristic
978C2×C4#55511yescharacteristic
979C8—42no—
980C8—42no—
981C8—81no—
982C8—81no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22—42no—
1001C22—42no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—81no—
1006C22—81no—
1007C22—81no—
1008C22—81no—
1009C22—81no—
1010C22—81no—
1011C22—81no—
1012C22—81no—
1013C22C2×#38611yescharacteristic
1014C22D4×C22⋊C411yescharacteristic
1015C22#233911yescharacteristic
1016C22#240711yescharacteristic
1017C22#240811yescharacteristic
1018C22#242011yescharacteristic
1019C22#242211yescharacteristic
1020C22C2×#41611yescharacteristic
1021C22#289611yescharacteristic
1022C22#289811yescharacteristic
1023C22#289811yescharacteristic
1024C22#300211yescharacteristic
1025C22#300211yescharacteristic
1026C22#300911yescharacteristic
1027C22#301111yescharacteristic
1028C22#309111yescharacteristic
1029C22#309111yescharacteristic
1030C22#309711yescharacteristic
1031C22#309711yescharacteristic
1032C22#327511yescharacteristic
1033C22#327711yescharacteristic
1034C22#328211yescharacteristic
1035C22#328511yescharacteristic
1036C22#329611yescharacteristic
1037C22#330011yescharacteristic
1038C22#330011yescharacteristic
1039C22#330111yescharacteristic
1040C22#332311yescharacteristic
1041C22#332611yescharacteristic
1042C22#332711yescharacteristic
1043C22#332711yescharacteristic
1044C22#333611yescharacteristic
1045C22#333711yescharacteristic
1046C22#335111yescharacteristic
1047C22#335211yescharacteristic
1048C4—24no—
1049C4—24no—
1050C4—42no—
1051C4—42no—
1052C4—44no—
1053C4—44no—
1054C4—82no—
1055C4—82no—
1056C4—82no—
1057C4—82no—
1058C4—82no—
1059C4—82no—
1060C4C4×#12111yescharacteristic
1061C4#232411yescharacteristic
1062C4#236111yescharacteristic
1063C4#236311yescharacteristic
1064C4#242711yescharacteristic
1065C4#242811yescharacteristic
1066C4#253511yescharacteristic
1067C4#253711yescharacteristic
1068C2—44no—
1069C2—82no—
1070C2#1397011yescharacteristic
1071C2#2090811yescharacteristic
1072C2#2091311yescharacteristic
1073C2#2241611yescharacteristic
1074C2#2242911yescharacteristic
1075C2#2248611yescharacteristic
1076C2#2249911yescharacteristic
1077C2#2412611yescharacteristic
1078C2#2412711yescharacteristic
1079C2#2424611yescharacteristic
1080C2#2424711yescharacteristic
1081C2#2497511yescharacteristic
1082C2#2497611yescharacteristic
1083C2#2502011yescharacteristic
1084C2#2502111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1873C2semidirect
5. C2×#1872C2semidirect
6. C2×#1805C2semidirect
7. C2×C4×#103C2semidirect
8. #11200C2semidirect
9. #11199C2semidirect
10. #10970C2semidirect
11. #10970C2semidirect
12. #10850C2semidirect
13. #10842C2semidirect
14. #10731C2semidirect
15. #10730C2semidirect
33. #2536C4semidirect
88. C2×C22⋊Q8C2×C4semidirect
94. C2×C4×Q8C2×C4semidirect
152. C2×#103D4semidirect
177. #382C2×C4semidirect
186. #380C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#25362
C2×#23522
C2×#19542
C2×#18732
C2×#18722
C2×#18052
C2×C4×#1032
#112002
#111992
#109702
#108502
#108422
#107312
#107302