Finite Group Databasebeta

← #372693

Subgroups — #372693

Order 512.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2426C211yesmaximal, characteristic
2C2×#1983C211yesmaximal, characteristic, complemented
3C2×#1923C211yesmaximal, characteristic, complemented
4C2×#1875C211yesmaximal, characteristic
5C2×#1873C211yesmaximal, characteristic, complemented
6C2×C4×#103C211yesmaximal, characteristic, complemented
7#13801C211yesmaximal, characteristic, complemented
8#11227C211yesmaximal, characteristic, complemented
9#11009C211yesmaximal, characteristic, complemented
10#10970C211yesmaximal, characteristic, complemented
11#10969C211yesmaximal, characteristic
12#10931C211yesmaximal, characteristic, complemented
13#10925C211yesmaximal, characteristic, complemented
14#10885C211yesmaximal, characteristic, complemented
15#10789C211yesmaximal, characteristic, complemented
16C22×#124C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×#121C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32C22×C4×C8C2211yescharacteristic
33#2426—24no—
34#2426C418yescomplemented
35C2×#396—21no—
36C2×#394—21no—
37C2×#390—21no—
38C2×#390C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#388—21no—
41C2×#380C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C22⋊C4C2211yescharacteristic
45#1983—24no—
46#1923—24no—
47#1875—24no—
48#1873—24no—
49C4×#103—24no—
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1437—21no—
61#1437—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64#1434—21no—
65C4×#95—21no—
66C23×Q8C2311yescharacteristic
67C23×D4—21no—
68C23×D4C2311yescharacteristic
69C24×C4C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C2×#124—22no—
75C2×#124—22no—
76C2×#124—22no—
77C2×#124—41no—
78C2×#124—41no—
79C2×#124C2×C414yes—
80C2×C22⋊Q8—22no—
81C2×C22⋊Q8—22no—
82C2×C22⋊Q8—22no—
83C2×C22⋊Q8—41no—
84C2×C22⋊Q8—41no—
85C2×C22⋊Q8C2×C414yes—
86C2×#121—22no—
87C2×#121—22no—
88C2×#121—22no—
89C2×#121—41no—
90C2×#121—41no—
91C2×#121C2×C414yes—
92C2×C4×Q8—22no—
93C2×C4×Q8—22no—
94C2×C4×Q8—22no—
95C2×C4×Q8—41no—
96C2×C4×Q8—41no—
97C2×C4×Q8C2×C414yes—
98C2×#117—22no—
99C2×#117—22no—
100C2×#117—22no—
101C2×#117—22no—
102C2×#117—41no—
103C2×#117—41no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C22⋊C4—21no—
114C22×C22⋊C4—21no—
115C22×C22⋊C4—21no—
116C22×C22⋊C4—21no—
117C22×C22⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4D411yescharacteristic
122C22×C22⋊C4D411yescharacteristic
123C22×C42—21no—
124C22×C42—21no—
125C22×C42—21no—
126C22×C42—21no—
127C22×C42C2311yescharacteristic
128C22×C42C2311yescharacteristic
129C2×C4⋊C8—22no—
130C2×C4⋊C8—22no—
131C2×C4⋊C8—41no—
132C2×#103—22no—
133C2×#103—22no—
134C2×#103—22no—
135C2×#103—22no—
136C2×#103—22no—
137C2×#103—22no—
138C2×#103—22no—
139C2×#103—22no—
140C2×#103—22no—
141C2×#103—41no—
142C2×#103—41no—
143C2×#103D414yescomplemented
144C2×#102—22no—
145C2×#102—22no—
146C2×#102—22no—
147C2×#102—22no—
148C2×#102—22no—
149C2×#102—22no—
150C2×#102—22no—
151C2×#102—22no—
152C2×#102—41no—
153C2×#102—41no—
154C2×#102—41no—
155C2×#102—41no—
156C2×C22⋊C8—22no—
157C2×C22⋊C8—22no—
158C2×C22⋊C8—22no—
159C2×C22⋊C8—22no—
160C2×C22⋊C8—41no—
161C2×C22⋊C8—41no—
162C2×C4×C8—22no—
163C2×C4×C8—22no—
164C2×C4×C8—41no—
165#396—28no—
166#394—28no—
167#390—28no—
168#390—22no—
169#390C2×C414yes—
170#389—22no—
171#389C2×C414yes—
172#388—28no—
173#380—22no—
174#380—22no—
175C4×C4⋊C4—22no—
176C4×C4⋊C4—22no—
177C4×C4⋊C4—41no—
178C4×C4⋊C4—41no—
179C4×C22⋊C4C2×C414yes—
180C4×C22⋊C4D414yes—
181C2×#95—21no—
182C2×#95—21no—
183C2×#95—21no—
184C2×#95—21no—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95D411yescharacteristic
190C2×#95D411yescharacteristic
191#340—22no—
192#340—22no—
193#340—22no—
194#340—22no—
195#340—22no—
196#340—41no—
197#340—41no—
198#340D414yes—
199#336—22no—
200#336—22no—
201C25—21no—
202C25C2×D411yescharacteristic
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8—21no—
213C22×Q8—21no—
214C22×Q8C22×C412yes—
215C22×Q8C2×D412yes—
216C22×Q8#4112yes—
217C22×D4—24no—
218C22×D4—21no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—21no—
230C22×D4—21no—
231C22×D4—42no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4—42no—
235C22×D4—81no—
236C22×D4—81no—
237C22×D4C22×C412yes—
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×C4C22×C412yes—
258C23×C4C2×D411yescharacteristic
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D411yescharacteristic
261C23×C4C2×D411yescharacteristic
262C23×C4C2×D412yes—
263C23×C4C2×D411yescharacteristic
264C23×C4C2411yescharacteristic
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
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×C8C2×D412yes—
292C22×C8C2×D412yes—
293#124—28no—
294#124—44no—
295#124—44no—
296#124—44no—
297C22⋊Q8—28no—
298C22⋊Q8—44no—
299C22⋊Q8—44no—
300C22⋊Q8—44no—
301#121—28no—
302#121—44no—
303#121—44no—
304#121—44no—
305C4×Q8—28no—
306C4×Q8—44no—
307C4×Q8—44no—
308C4×Q8—44no—
309#117—44no—
310#117—44no—
311#117—44no—
312#117—44no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—81no—
347C2×C4⋊C4—81no—
348C2×C4⋊C4C22×C412yes—
349C2×C4⋊C4C22×C412yes—
350C2×C4⋊C4C2×D412yes—
351C2×C4⋊C4C2×D412yes—
352C2×C4⋊C4C2×D412yes—
353C2×C4⋊C4#4112yes—
354C2×C4⋊C4#4112yes—
355C2×C4⋊C4#4112yes—
356C2×C4⋊C4#4112yes—
357C2×C4⋊C4#4112yes—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—81no—
383C2×C22⋊C4—81no—
384C2×C22⋊C4—81no—
385C2×C22⋊C4—81no—
386C2×C22⋊C4C22⋊C414yes—
387C2×C22⋊C4C22⋊C414yes—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—81no—
407C2×C42—81no—
408C2×C42C22×C412yes—
409C2×C42C22×C412yes—
410C2×C42C2×D412yes—
411C2×C42C2×D412yes—
412C4⋊C8—44no—
413#103—28no—
414#103—28no—
415#103—44no—
416#103—44no—
417#102—44no—
418#102—44no—
419#102—44no—
420#102—44no—
421C22⋊C8—44no—
422C22⋊C8—44no—
423C4×C8—44no—
424#95—24no—
425#95—24no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—81no—
431#95—81no—
432#95C22⋊C414yes—
433#95C22⋊C414yes—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—22no—
449C24—41no—
450C24—41no—
451C24—41no—
452C24—41no—
453C24—41no—
454C24—41no—
455C24—41no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24—41no—
460C24—41no—
461C24—41no—
462C24—41no—
463C24C2×C22⋊C412yes—
464C24C22×D411yescharacteristic
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—41no—
481C2×Q8—41no—
482C2×Q8—41no—
483C2×Q8—41no—
484C2×Q8—41no—
485C2×Q8—41no—
486C2×Q8—41no—
487C2×Q8—41no—
488C2×Q8—41no—
489C2×Q8—41no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8C4×D414yes—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—41no—
502C2×D4—41no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C2×D4—84no—
524C2×D4—84no—
525C2×D4—84no—
526C2×D4—84no—
527C2×D4—84no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
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—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
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—41no—
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×C4C2×C22⋊C412yes—
634C22×C4C2×C22⋊C412yes—
635C22×C4C2×C22⋊C412yes—
636C22×C4C2×C22⋊C412yes—
637C22×C4C2×C22⋊C412yes—
638C22×C4#13512yes—
639C22×C4#13512yes—
640C22×C4C23×C411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C22×D411yescharacteristic
644C22×C4C2×#4111yescharacteristic
645C22×C4C2×#4111yescharacteristic
646C22×C4C2×#4111yescharacteristic
647C22×C4C2×#4111yescharacteristic
648C22×C4C2×#4111yescharacteristic
649C22×C4C2×#4111yescharacteristic
650C22×C4H(5,𝔽2)11yescharacteristic
651C22×C4H(5,𝔽2)11yescharacteristic
652C22×C4H(5,𝔽2)11yescharacteristic
653C22×C4H(5,𝔽2)11yescharacteristic
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8—41no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—41no—
667C2×C8—41no—
668C2×C8—41no—
669C2×C8—41no—
670C2×C8—41no—
671C2×C8—41no—
672C2×C8—41no—
673C2×C8—41no—
674C2×C8—41no—
675C2×C8—41no—
676C2×C8—41no—
677C2×C8—41no—
678C2×C8—41no—
679C2×C8—41no—
680C2×C8—41no—
681C2×C8—41no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—48no—
697C4⋊C4—48no—
698C4⋊C4—41no—
699C4⋊C4—41no—
700C4⋊C4—41no—
701C4⋊C4—41no—
702C4⋊C4—41no—
703C4⋊C4—41no—
704C4⋊C4—41no—
705C4⋊C4—41no—
706C4⋊C4—84no—
707C4⋊C4C4×D414yes—
708C4⋊C4#12114yes—
709C22⋊C4—28no—
710C22⋊C4—44no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—48no—
714C22⋊C4—48no—
715C22⋊C4—48no—
716C22⋊C4—48no—
717C22⋊C4—84no—
718C22⋊C4—84no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—48no—
728C42—48no—
729C42—84no—
730C42—84no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—81no—
774C23—81no—
775C23—81no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23—81no—
784C23—81no—
785C23—81no—
786C23—81no—
787C23—81no—
788C23—81no—
789C23—81no—
790C23—81no—
791C23—81no—
792C23—81no—
793C23—81no—
794C23—81no—
795C23—81no—
796C23—81no—
797C23—81no—
798C23—81no—
799C23—81no—
800C23—81no—
801C23C22×C22⋊C411yescharacteristic
802C23#52511yescharacteristic
803C23#52511yescharacteristic
804C23D4211yescharacteristic
805C23D4211yescharacteristic
806C23#54611yescharacteristic
807C23#54611yescharacteristic
808C23C2×#13511yescharacteristic
809C23C2×#13511yescharacteristic
810C23#57511yescharacteristic
811C23#57511yescharacteristic
812C23#57611yescharacteristic
813C23#57711yescharacteristic
814C23#57711yescharacteristic
815C23#57811yescharacteristic
816Q8—24no—
817Q8—24no—
818Q8—42no—
819Q8—42no—
820Q8—42no—
821Q8—42no—
822Q8—42no—
823Q8—42no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—816no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—22no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—42no—
861C2×C4—41no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—42no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—41no—
871C2×C4—42no—
872C2×C4—41no—
873C2×C4—42no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—41no—
877C2×C4—42no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—41no—
887C2×C4—41no—
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—81no—
909C2×C4—81no—
910C2×C4—81no—
911C2×C4—81no—
912C2×C4—81no—
913C2×C4—81no—
914C2×C4—81no—
915C2×C4—81no—
916C2×C4—81no—
917C2×C4—81no—
918C2×C4—81no—
919C2×C4—81no—
920C2×C4—81no—
921C2×C4—81no—
922C2×C4—81no—
923C2×C4—81no—
924C2×C4#41614yes—
925C2×C4C2×C4×D411yescharacteristic
926C2×C4C2×C4×D411yescharacteristic
927C2×C4C4×#4111yescharacteristic
928C2×C4C4×#4111yescharacteristic
929C2×C4#51811yescharacteristic
930C2×C4#51811yescharacteristic
931C2×C4C2×#12111yescharacteristic
932C2×C4#52511yescharacteristic
933C2×C4#52911yescharacteristic
934C2×C4#53211yescharacteristic
935C2×C4#53211yescharacteristic
936C2×C4#53211yescharacteristic
937C2×C4#53811yescharacteristic
938C2×C4#53811yescharacteristic
939C2×C4#54011yescharacteristic
940C2×C4#54011yescharacteristic
941C2×C4D4211yescharacteristic
942C2×C4D4211yescharacteristic
943C2×C4#54611yescharacteristic
944C2×C4#54611yescharacteristic
945C2×C4#54611yescharacteristic
946C2×C4#54611yescharacteristic
947C2×C4#54611yescharacteristic
948C2×C4#55011yescharacteristic
949C2×C4#55311yescharacteristic
950C2×C4#55311yescharacteristic
951C2×C4#55311yescharacteristic
952C2×C4#55511yescharacteristic
953C8—42no—
954C8—42no—
955C8—81no—
956C8—81no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—82no—
973C22—82no—
974C22—82no—
975C22—82no—
976C22—82no—
977C22—82no—
978C22—82no—
979C22—161no—
980C22—161no—
981C22—161no—
982C22—161no—
983C22—161no—
984C22—161no—
985C22—161no—
986C22—161no—
987C22#229711yescharacteristic
988C22D4×C22⋊C411yescharacteristic
989C22D4×C22⋊C411yescharacteristic
990C22#242411yescharacteristic
991C22#245611yescharacteristic
992C22#246411yescharacteristic
993C22#247611yescharacteristic
994C22C2×#41611yescharacteristic
995C22#289611yescharacteristic
996C22#289711yescharacteristic
997C22#289811yescharacteristic
998C22#310211yescharacteristic
999C22#310211yescharacteristic
1000C22#310211yescharacteristic
1001C22#310211yescharacteristic
1002C22#311811yescharacteristic
1003C22#312111yescharacteristic
1004C22#312411yescharacteristic
1005C22#312511yescharacteristic
1006C22#326711yescharacteristic
1007C22#326811yescharacteristic
1008C22#327511yescharacteristic
1009C22#327711yescharacteristic
1010C22#328211yescharacteristic
1011C22#328411yescharacteristic
1012C22#328511yescharacteristic
1013C22#328711yescharacteristic
1014C22#330011yescharacteristic
1015C22#330111yescharacteristic
1016C22#330411yescharacteristic
1017C22#330511yescharacteristic
1018C22#331111yescharacteristic
1019C22#331911yescharacteristic
1020C22#332611yescharacteristic
1021C22#332711yescharacteristic
1022C4—24no—
1023C4—42no—
1024C4—44no—
1025C4—44no—
1026C4—42no—
1027C4—42no—
1028C4—44no—
1029C4—42no—
1030C4—82no—
1031C4—82no—
1032C4—82no—
1033C4—82no—
1034C4C4×#12111yescharacteristic
1035C4#233311yescharacteristic
1036C4#236311yescharacteristic
1037C4#236411yescharacteristic
1038C4#242811yescharacteristic
1039C4#246411yescharacteristic
1040C4#255511yescharacteristic
1041C4#255911yescharacteristic
1042C2—82no—
1043C2—162no—
1044C2#1410011yescharacteristic
1045C2#2138711yescharacteristic
1046C2#2139711yescharacteristic
1047C2#2241611yescharacteristic
1048C2#2241811yescharacteristic
1049C2#2242411yescharacteristic
1050C2#2242911yescharacteristic
1051C2#2515811yescharacteristic
1052C2#2516311yescharacteristic
1053C2#2662311yescharacteristic
1054C2#2662611yescharacteristic
1055C2#2693611yescharacteristic
1056C2#2694011yescharacteristic
1057C2#2740011yescharacteristic
1058C2#2740411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1983C2semidirect
3. C2×#1923C2semidirect
5. C2×#1873C2semidirect
6. C2×C4×#103C2semidirect
7. #13801C2semidirect
8. #11227C2semidirect
9. #11009C2semidirect
10. #10970C2semidirect
12. #10931C2semidirect
13. #10925C2semidirect
14. #10885C2semidirect
15. #10789C2semidirect
34. #2426C4semidirect
143. C2×#103D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24262
C2×#19832
C2×#19232
C2×#18752
C2×#18732
C2×C4×#1032
#138012
#112272
#110092
#109702
#109692
#109312
#109252
#108852
#107892