Finite Group Databasebeta

← #356650

Subgroups — #356650

Order 512.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1033 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2361C211yesmaximal, characteristic
2C2×#1895C211yesmaximal, characteristic
3C2×#1875C211yesmaximal, characteristic
4C2×C4×#102C211yesmaximal, characteristic, complemented
5C2×#1753C211yesmaximal, characteristic, complemented
6C2×#1736C211yesmaximal, characteristic, complemented
7#13801C211yesmaximal, characteristic, complemented
8#10931C211yesmaximal, characteristic, complemented
9#10927C211yesmaximal, characteristic, complemented
10#10884C211yesmaximal, characteristic, complemented
11#10880C211yesmaximal, characteristic, complemented
12#10807C211yesmaximal, characteristic, complemented
13#10788C211yesmaximal, characteristic, complemented
14#10730C211yesmaximal, characteristic, complemented
15#10703C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C22×#121C2211yescharacteristic
18C22×C4×D4—21no—
19C22×C4×D4C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×#97C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29#2361—24no—
30#2361C418yescomplemented
31C2×#390C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#388—21no—
34C2×#386—21no—
35C2×#385—21no—
36C2×#380C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41#1895C418yescomplemented
42#1875C418yescomplemented
43C4×#102—24no—
44#1753—24no—
45#1736—24no—
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
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×D4—21no—
67C23×D4C2311yescharacteristic
68C24×C4—21no—
69C24×C4—21no—
70C24×C4C2311yescharacteristic
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—41no—
76C22×M16—41no—
77C22×M16C2×C414yescomplemented
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C2×#121—22no—
83C2×#121—22no—
84C2×#121—22no—
85C2×#121C2×C414yes—
86C2×#121C2×C414yes—
87C2×#121C2×C414yes—
88C2×C4×D4—28no—
89C2×C4×D4—22no—
90C2×C4×D4—22no—
91C2×C4×D4—22no—
92C2×C4×D4—41no—
93C2×C4×D4—41no—
94C2×C4×D4—44no—
95C2×C4×D4—44no—
96C2×C4×D4C2×C414yes—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117—22no—
100C2×#117—41no—
101C2×#117—41no—
102C2×#117C2×C414yescomplemented
103C22×C4⋊C4—22no—
104C22×C4⋊C4—22no—
105C22×C4⋊C4—22no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—41no—
109C22×C4⋊C4—41no—
110C22×C4⋊C4C2×C414yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4D411yescharacteristic
125C22×C22⋊C4D411yescharacteristic
126C22×C42—21no—
127C22×C42—21no—
128C22×C42—21no—
129C22×C42—21no—
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C2×#102—22no—
133C2×#102—22no—
134C2×#102—22no—
135C2×#102—22no—
136C2×#102—41no—
137C2×#102—41no—
138C2×#102—41no—
139C2×#102—41no—
140C2×#102C2×C414yescomplemented
141C2×#102C2×C414yescomplemented
142C2×#102C2×C414yescomplemented
143C2×#102C2×C414yescomplemented
144C2×C22⋊C8—22no—
145C2×C22⋊C8—22no—
146C2×C22⋊C8C2×C414yescomplemented
147C2×#97—22no—
148C2×#97—22no—
149C2×#97—41no—
150C2×C4×C8—22no—
151C2×C4×C8—22no—
152C2×C4×C8—41no—
153#390—22no—
154#390C2×C414yes—
155#389—22no—
156#389C2×C414yes—
157#388—28no—
158#386—28no—
159#385—28no—
160#380—22no—
161#380C2×C414yescomplemented
162C4×C4⋊C4—22no—
163C4×C4⋊C4—22no—
164C4×C4⋊C4—22no—
165C4×C4⋊C4—41no—
166C4×C4⋊C4—41no—
167C4×C4⋊C4C2×C414yes—
168C4×C22⋊C4C2×C414yes—
169C4×C22⋊C4D414yes—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177C2×#95—21no—
178C2×#95—21no—
179C2×#95D411yescharacteristic
180C2×#95D411yescharacteristic
181#340—22no—
182#340—22no—
183#340—22no—
184#340—22no—
185#340—22no—
186#340—41no—
187#340—41no—
188#340C2×C414yescomplemented
189#340C2×C414yescomplemented
190#340C2×C414yescomplemented
191#340C2×C414yescomplemented
192#340D414yescomplemented
193#336—22no—
194#336—22no—
195C25—21no—
196C25C2×D411yescharacteristic
197C22×D4—24no—
198C22×D4—24no—
199C22×D4—24no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—42no—
212C22×D4—42no—
213C22×D4—42no—
214C22×D4—42no—
215C22×D4C22×C412yes—
216C22×D4C22×C412yes—
217C22×D4C22×C412yes—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—81no—
244C23×C4—81no—
245C23×C4—81no—
246C23×C4—81no—
247C23×C4C22×C412yes—
248C23×C4C22×C412yes—
249C23×C4C22×C412yes—
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D412yes—
256C23×C4#4112yes—
257C23×C4#4112yes—
258C23×C4C2411yescharacteristic
259C2×M16—28no—
260C2×M16—28no—
261C2×M16—44no—
262C2×M16—44no—
263C2×M16—44no—
264C2×M16—44no—
265C2×M16—44no—
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×C8C22×C412yes—
289C22×C8C22×C412yes—
290C22×C8C22×C412yes—
291C22×C8C22×C412yes—
292C22×C8C2×D412yes—
293C22×C8#4112yes—
294#121—28no—
295#121—28no—
296#121—28no—
297#121C42116yescomplemented
298C4×D4—28no—
299C4×D4—44no—
300C4×D4—44no—
301C4×D4—44no—
302C4×D4—432no—
303#117—28no—
304#117—44no—
305#117—44no—
306#117—44no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
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—28no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4C22×C412yes—
347C2×C4⋊C4C22×C412yes—
348C2×C4⋊C4C22×C412yes—
349C2×C4⋊C4C22×C412yes—
350C2×C4⋊C4C22×C412yes—
351C2×C4⋊C4C22×C412yes—
352C2×C4⋊C4C22×C412yes—
353C2×C4⋊C4C22×C412yes—
354C2×C4⋊C4C22×C412yes—
355C2×C4⋊C4C2×D412yes—
356C2×C4⋊C4C2×D412yes—
357C2×C4⋊C4#4112yes—
358C2×C4⋊C4#4112yes—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—41no—
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—81no—
378C2×C22⋊C4—81no—
379C2×C22⋊C4—81no—
380C2×C22⋊C4—81no—
381C2×C22⋊C4C22⋊C414yes—
382C2×C22⋊C4C22⋊C414yes—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—81no—
402C2×C42—81no—
403C2×C42C22×C412yes—
404C2×C42C22×C412yes—
405C2×C42C2×D412yes—
406C2×C42C2×D412yes—
407#102—28no—
408#102—28no—
409#102—44no—
410#102—44no—
411C22⋊C8—28no—
412#97—44no—
413C4×C8—44no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—81no—
422#95—81no—
423#95C22⋊C414yes—
424#95C22⋊C414yes—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—41no—
441C24—41no—
442C24—41no—
443C24—41no—
444C24—41no—
445C24—41no—
446C24—41no—
447C24—41no—
448C24—41no—
449C24—41no—
450C24—41no—
451C24—41no—
452C24C2×C22⋊C412yes—
453C24C4×D412yes—
454C24C4×D412yes—
455C24C22×D411yescharacteristic
456C2×D4—216no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4C2×C4214yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—48no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
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—48no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4—84no—
600C22×C4—84no—
601C22×C4—84no—
602C22×C4—84no—
603C22×C4—84no—
604C22×C4C2×C4214yes—
605C22×C4C2×C22⋊C412yes—
606C22×C4C2×C22⋊C412yes—
607C22×C4C2×C22⋊C412yes—
608C22×C4C2×C22⋊C412yes—
609C22×C4C2×C22⋊C412yes—
610C22×C4#11714yes—
611C22×C4C4×D414yes—
612C22×C4C4×D414yes—
613C22×C4C4×D412yes—
614C22×C4C4×D412yes—
615C22×C4AGL(1,ℤ/8)12yes—
616C22×C4AGL(1,ℤ/8)12yes—
617C22×C4C23×C411yescharacteristic
618C22×C4C23×C411yescharacteristic
619C22×C4C23×C411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C2×#4111yescharacteristic
623C22×C4C2×#4111yescharacteristic
624C22×C4C2×#4111yescharacteristic
625C22×C4C2×#4111yescharacteristic
626C22×C4C2×#4111yescharacteristic
627C22×C4H(5,𝔽2)11yescharacteristic
628C22×C4H(5,𝔽2)11yescharacteristic
629C22×C4H(5,𝔽2)11yescharacteristic
630C22×C42−1+411yescharacteristic
631M16—416no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8C4×D414yescomplemented
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—48no—
678C4⋊C4—41no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—41no—
683C4⋊C4—41no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4—48no—
687C4⋊C4C2×C4214yes—
688C4⋊C4C4×D414yes—
689C4⋊C4C4×D414yescomplemented
690C22⋊C4—216no—
691C22⋊C4—28no—
692C22⋊C4—44no—
693C22⋊C4—48no—
694C22⋊C4—48no—
695C22⋊C4—48no—
696C22⋊C4—84no—
697C22⋊C4—84no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—48no—
707C42—48no—
708C42—84no—
709C42—84no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—24no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—81no—
764C23—81no—
765C23—81no—
766C23—81no—
767C23—81no—
768C23—81no—
769C23—81no—
770C23—81no—
771C23—81no—
772C23—81no—
773C23—81no—
774C23—81no—
775C23—81no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23C4×C22⋊C414yes—
780C23C22×C22⋊C411yescharacteristic
781C23C2×C4×D411yescharacteristic
782C23C2×C4×D411yescharacteristic
783C23D4211yescharacteristic
784C23#54611yescharacteristic
785C23#54611yescharacteristic
786C23#54711yescharacteristic
787C23C2×AGL(1,ℤ/8)11yescharacteristic
788C23C2×AGL(1,ℤ/8)11yescharacteristic
789C23#57511yescharacteristic
790C23#57511yescharacteristic
791C23#57611yescharacteristic
792C23#57711yescharacteristic
793C23#57711yescharacteristic
794C23#57811yescharacteristic
795D4—24no—
796D4—24no—
797D4—432no—
798D4—42no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—42no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—41no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—42no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—816no—
879C2×C4—816no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—81no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4C4×C22⋊C414yes—
897C2×C4#41814yes—
898C2×C4C22×C4211yescharacteristic
899C2×C4C2×#11711yescharacteristic
900C2×C4C2×C4×D411yescharacteristic
901C2×C4C2×C4×D411yescharacteristic
902C2×C4C2×C4×D411yescharacteristic
903C2×C4C2×C4×D411yescharacteristic
904C2×C4C2×C4×D411yescharacteristic
905C2×C4C4×#4111yescharacteristic
906C2×C4C4×#4111yescharacteristic
907C2×C4C4×#4111yescharacteristic
908C2×C4#51811yescharacteristic
909C2×C4#51811yescharacteristic
910C2×C4#51811yescharacteristic
911C2×C4#52011yescharacteristic
912C2×C4#52011yescharacteristic
913C2×C4#52011yescharacteristic
914C2×C4D4211yescharacteristic
915C2×C4#54611yescharacteristic
916C2×C4#54611yescharacteristic
917C2×C4#54611yescharacteristic
918C2×C4#54711yescharacteristic
919C2×C4#54811yescharacteristic
920C2×C4#55111yescharacteristic
921C2×C4#55111yescharacteristic
922C2×C4#55211yescharacteristic
923C2×C4#55311yescharacteristic
924C2×C4#55311yescharacteristic
925C2×C4#55311yescharacteristic
926C8—24no—
927C8—42no—
928C8—42no—
929C8—42no—
930C22—24no—
931C22—24no—
932C22—24no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—44no—
946C22—44no—
947C22—44no—
948C22—82no—
949C22—82no—
950C22—82no—
951C22—82no—
952C22—82no—
953C22—82no—
954C22—82no—
955C22—82no—
956C22—82no—
957C22—82no—
958C22—82no—
959C22—82no—
960C22C2×C4×C22⋊C411yescharacteristic
961C22D4×C22⋊C411yescharacteristic
962C22#233911yescharacteristic
963C22#235811yescharacteristic
964C22#235911yescharacteristic
965C22#236111yescharacteristic
966C22#236411yescharacteristic
967C22C2×#41811yescharacteristic
968C22#289611yescharacteristic
969C22#289711yescharacteristic
970C22#289811yescharacteristic
971C22C4×AGL(1,ℤ/8)11yescharacteristic
972C22C4×AGL(1,ℤ/8)11yescharacteristic
973C22C4×AGL(1,ℤ/8)11yescharacteristic
974C22C4×AGL(1,ℤ/8)11yescharacteristic
975C22#294611yescharacteristic
976C22#294711yescharacteristic
977C22#295111yescharacteristic
978C22#295211yescharacteristic
979C22#326411yescharacteristic
980C22#326511yescharacteristic
981C22#326911yescharacteristic
982C22#327111yescharacteristic
983C22#331011yescharacteristic
984C22#331311yescharacteristic
985C22#331811yescharacteristic
986C22#332111yescharacteristic
987C22#332211yescharacteristic
988C22#332611yescharacteristic
989C22#333011yescharacteristic
990C22#333211yescharacteristic
991C22#335111yescharacteristic
992C22#335311yescharacteristic
993C22#335411yescharacteristic
994C22#335511yescharacteristic
995C4—24no—
996C4—24no—
997C4—44no—
998C4—44no—
999C4—42no—
1000C4—44no—
1001C4—42no—
1002C4—42no—
1003C4—82no—
1004C4—82no—
1005C4—82no—
1006C4—82no—
1007C4C42×D411yescharacteristic
1008C4#227511yescharacteristic
1009C4#235211yescharacteristic
1010C4#235311yescharacteristic
1011C4#235811yescharacteristic
1012C4#235911yescharacteristic
1013C4#236111yescharacteristic
1014C4#236411yescharacteristic
1015C2—44no—
1016C2—84no—
1017C2#1381311yescharacteristic
1018C2C4×#41811yescharacteristic
1019C2#2041511yescharacteristic
1020C2#2242311yescharacteristic
1021C2#2242611yescharacteristic
1022C2#2250011yescharacteristic
1023C2#2250111yescharacteristic
1024C2#2287811yescharacteristic
1025C2#2288311yescharacteristic
1026C2#2292411yescharacteristic
1027C2#2292611yescharacteristic
1028C2#2303411yescharacteristic
1029C2#2303711yescharacteristic
1030C2#2313811yescharacteristic
1031C2#2314011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C2×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
4. C2×C4×#102C2semidirect
5. C2×#1753C2semidirect
6. C2×#1736C2semidirect
7. #13801C2semidirect
8. #10931C2semidirect
9. #10927C2semidirect
10. #10884C2semidirect
11. #10880C2semidirect
12. #10807C2semidirect
13. #10788C2semidirect
14. #10730C2semidirect
15. #10703C2semidirect
30. #2361C4semidirect
41. #1895C4semidirect
42. #1875C4semidirect
77. C22×M16C2×C4semidirect
102. C2×#117C2×C4semidirect
140. C2×#102C2×C4semidirect
141. C2×#102C2×C4semidirect
142. C2×#102C2×C4semidirect
143. C2×#102C2×C4semidirect
146. C2×C22⋊C8C2×C4semidirect
161. #380C2×C4semidirect
188. #340C2×C4semidirect
189. #340C2×C4semidirect
190. #340C2×C4semidirect
191. #340C2×C4semidirect
192. #340D4semidirect
297. #121C42semidirect
659. C2×C8C4×D4semidirect
689. C4⋊C4C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#23612
C2×#18952
C2×#18752
C2×C4×#1022
C2×#17532
C2×#17362
#138012
#109312
#109272
#108842
#108802
#108072
#107882
#107302
#107032