Finite Group Databasebeta

← #368213

Subgroups — #368213

Order 512.

1982 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C4⋊C4C211yesmaximal, characteristic
2C2×#1870C211yesmaximal, characteristic
3C2×#1854C211yesmaximal, characteristic, complemented
4C2×#1736C211yesmaximal, characteristic, complemented
5#13871C211yesmaximal, characteristic
6#11267C211yesmaximal, characteristic, complemented
7#11267C211yesmaximal, characteristic, complemented
8#11096C211yesmaximal, characteristic, complemented
9#11095C211yesmaximal, characteristic, complemented
10#10908C211yesmaximal, characteristic, complemented
11#10907C211yesmaximal, characteristic, complemented
12#10730C211yesmaximal, characteristic, complemented
13#10730C211yesmaximal, characteristic, complemented
14#10730C211yesmaximal, characteristic, complemented
15#10722C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C22×C4×D4—21no—
18C22×C4×D4C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C22×#107C2211yescharacteristic
23C22×#106C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27D4×C4⋊C4—24no—
28D4×C4⋊C4—24no—
29C2×#389—21no—
30C2×#385—21no—
31C2×#385—21no—
32C2×#384C2211yescharacteristic
33C2×#380C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39#1870C418yescomplemented
40#1854—24no—
41#1736—24no—
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1440—21no—
59#1438—21no—
60#1437—21no—
61#1436—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C23×D4D411yescharacteristic
65C24×C4—21no—
66C24×C4—21no—
67C24×C4C2311yescharacteristic
68C24×C4C2311yescharacteristic
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—41no—
72C22×M16—41no—
73C22×M16—41no—
74C22×M16—41no—
75C22×M16C2×C414yescomplemented
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—28no—
85C2×C4×D4—44no—
86C2×C4×D4—44no—
87C2×C4×D4C2×C414yes—
88C2×C4×D4Q814yes—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—22no—
92C2×#117—22no—
93C2×#117—41no—
94C2×#117—41no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—22no—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—22no—
103C22×C4⋊C4—22no—
104C22×C4⋊C4—22no—
105C22×C4⋊C4—22no—
106C22×C4⋊C4—41no—
107C22×C4⋊C4—41no—
108C22×C4⋊C4—41no—
109C22×C4⋊C4—41no—
110C22×C4⋊C4D411yescharacteristic
111C22×C4⋊C4D414yes—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C22⋊C4D411yescharacteristic
127C22×C22⋊C4D411yescharacteristic
128C22×C42—21no—
129C22×C42—21no—
130C22×C42C2311yescharacteristic
131C2×#107—22no—
132C2×#107—22no—
133C2×#107—41no—
134C2×#106—22no—
135C2×#106—22no—
136C2×#106—41no—
137C2×C22⋊C8—22no—
138C2×C22⋊C8—22no—
139C2×C22⋊C8—41no—
140C2×C22⋊C8—41no—
141C2×C22⋊C8—41no—
142C2×C22⋊C8—41no—
143C2×C22⋊C8C2×C414yescomplemented
144C2×C22⋊C8C2×C414yescomplemented
145C2×C22⋊C8C2×C414yescomplemented
146#389—28no—
147#385—28no—
148#385—28no—
149#384—22no—
150#384—22no—
151#380—22no—
152#380—22no—
153#380—22no—
154#380—22no—
155#380—22no—
156#380—22no—
157#380—22no—
158#380—41no—
159#380—41no—
160#380D414yes—
161C4×C4⋊C4—22no—
162C4×C4⋊C4—22no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173#340—22no—
174#340—22no—
175#340—22no—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—22no—
180#340—22no—
181#340—41no—
182#340—41no—
183#340—41no—
184#340—41no—
185#340—41no—
186#340—41no—
187#336C2×C414yescomplemented
188#336C2×C414yescomplemented
189C25C2×D411yescharacteristic
190C25C2×D411yescharacteristic
191C22×D4—22no—
192C22×D4—22no—
193C22×D4—22no—
194C22×D4—22no—
195C22×D4—22no—
196C22×D4—22no—
197C22×D4C4⋊C414yes—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—81no—
237C23×C4—81no—
238C23×C4—81no—
239C23×C4—81no—
240C23×C4C22×C412yes—
241C23×C4C22×C412yes—
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D412yes—
247C23×C4C2×D412yes—
248C23×C4C2×Q812yes—
249C23×C4C2×Q812yes—
250C23×C4#4112yes—
251C23×C4#4112yes—
252C23×C4C2411yescharacteristic
253C2×M16—28no—
254C2×M16—44no—
255C2×M16—44no—
256C2×M16—44no—
257C2×M16—44no—
258C2×M16—44no—
259C2×M16—44no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
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×C8C22×C412yes—
285C22×C8C22×C412yes—
286C22×C8C22×C412yes—
287C22×C8C22×C412yes—
288C4×D4—28no—
289C4×D4—28no—
290C4×D4—28no—
291C4×D4—28no—
292C4×D4—432no—
293#117—28no—
294#117—44no—
295#117—44no—
296#117—44no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
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—28no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
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—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—24no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—81no—
358C2×C4⋊C4—81no—
359C2×C4⋊C4C4⋊C414yes—
360C2×C4⋊C4C2×D412yes—
361C2×C4⋊C4C2×D412yes—
362C2×C4⋊C4C2×D412yes—
363C2×C4⋊C4C2×D412yes—
364C2×C4⋊C4#4112yes—
365C2×C4⋊C4#4112yes—
366C2×C4⋊C4#4112yes—
367C2×C4⋊C4#4112yes—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
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—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—81no—
387C2×C22⋊C4—81no—
388C2×C22⋊C4—81no—
389C2×C22⋊C4—81no—
390C2×C22⋊C4C4⋊C414yes—
391C2×C22⋊C4C4⋊C414yes—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—24no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42C22×C412yes—
403C2×C42C2×Q812yes—
404#107—44no—
405#106—44no—
406C22⋊C8—28no—
407C22⋊C8—44no—
408C22⋊C8—44no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—81no—
418#95—81no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
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—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24C2×C4⋊C412yes—
444C24C2×C4⋊C412yes—
445C24#12012yes—
446C24#12312yes—
447C24AGL(1,ℤ/8)12yes—
448C24#13712yes—
449C24C22×D411yescharacteristic
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—28no—
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—28no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
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—48no—
522C22×C4—48no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
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—41no—
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—84no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4C2×C4⋊C412yes—
600C22×C4C2×C4⋊C412yes—
601C22×C4C2×C4⋊C412yes—
602C22×C4C2×C4⋊C412yes—
603C22×C4C4×D414yes—
604C22×C4C4×D414yes—
605C22×C4#12012yes—
606C22×C4C22⋊Q814yes—
607C22×C4C22⋊Q814yes—
608C22×C4#12312yes—
609C22×C4AGL(1,ℤ/8)12yes—
610C22×C4#13712yes—
611C22×C4C23×C411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×Q811yescharacteristic
615C22×C4C2×#4111yescharacteristic
616C22×C4C2×#4111yescharacteristic
617C22×C4C2×#4111yescharacteristic
618C22×C4C2×#4111yescharacteristic
619C22×C4C2×#4111yescharacteristic
620C22×C4C2×#4111yescharacteristic
621C22×C4H(5,𝔽2)11yescharacteristic
622C22×C4H(5,𝔽2)11yescharacteristic
623C22×C4H(5,𝔽2)11yescharacteristic
624C22×C4H(5,𝔽2)11yescharacteristic
625M16—416no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—28no—
658C4⋊C4—22no—
659C4⋊C4—22no—
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—48no—
669C4⋊C4—48no—
670C4⋊C4—48no—
671C4⋊C4—41no—
672C4⋊C4—41no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—41no—
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—41no—
687C4⋊C4—41no—
688C4⋊C4—41no—
689C4⋊C4—84no—
690C4⋊C4#12314yes—
691C22⋊C4—28no—
692C22⋊C4—28no—
693C22⋊C4—48no—
694C22⋊C4—48no—
695C22⋊C4—48no—
696C22⋊C4—84no—
697C22⋊C4—84no—
698C22⋊C4—84no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—48no—
704C42—48no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
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—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
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—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23#38514yes—
774C23#42814yes—
775C23C22×C4⋊C411yescharacteristic
776C23C2×#12011yescharacteristic
777C23C2×#12311yescharacteristic
778C23#54611yescharacteristic
779C23#54611yescharacteristic
780C23#54611yescharacteristic
781C23#54611yescharacteristic
782C23C2×AGL(1,ℤ/8)11yescharacteristic
783C23C2×AGL(1,ℤ/8)11yescharacteristic
784C23C2×#13711yescharacteristic
785C23C2×#13711yescharacteristic
786C23#57611yescharacteristic
787C23#57711yescharacteristic
788C23#57711yescharacteristic
789C23#57811yescharacteristic
790D4—232no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
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—816no—
856C2×C4—816no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—81no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
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#38514yes—
892C2×C4#42814yes—
893C2×C4C2×C4×D411yescharacteristic
894C2×C4C2×C4×D411yescharacteristic
895C2×C4C4×#4111yescharacteristic
896C2×C4C4×#4111yescharacteristic
897C2×C4#51811yescharacteristic
898C2×C4#51811yescharacteristic
899C2×C4C2×C22⋊Q811yescharacteristic
900C2×C4C2×C22⋊Q811yescharacteristic
901C2×C4C2×#12311yescharacteristic
902C2×C4#52511yescharacteristic
903C2×C4#52911yescharacteristic
904C2×C4#52911yescharacteristic
905C2×C4#53411yescharacteristic
906C2×C4#53511yescharacteristic
907C2×C4#53811yescharacteristic
908C2×C4#53811yescharacteristic
909C2×C4#54611yescharacteristic
910C2×C4#54611yescharacteristic
911C2×C4#54611yescharacteristic
912C2×C4#54611yescharacteristic
913C2×C4#55311yescharacteristic
914C2×C4#55311yescharacteristic
915C2×C4#55311yescharacteristic
916C2×C4#55311yescharacteristic
917C2×C4#55411yescharacteristic
918C2×C4#55411yescharacteristic
919C2×C4#55411yescharacteristic
920C2×C4#55411yescharacteristic
921C8—42no—
922C8—42no—
923C8—42no—
924C8—42no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—42no—
932C22—42no—
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—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22C2×#38511yescharacteristic
956C22#234911yescharacteristic
957C22#234911yescharacteristic
958C22#240411yescharacteristic
959C22#240511yescharacteristic
960C22#244411yescharacteristic
961C22#244411yescharacteristic
962C22C2×#42811yescharacteristic
963C22C2×#42811yescharacteristic
964C22#291211yescharacteristic
965C22#291311yescharacteristic
966C22#300311yescharacteristic
967C22#300411yescharacteristic
968C22#301211yescharacteristic
969C22#301311yescharacteristic
970C22#309211yescharacteristic
971C22#309211yescharacteristic
972C22#309611yescharacteristic
973C22#309711yescharacteristic
974C22#330611yescharacteristic
975C22#330811yescharacteristic
976C22#331011yescharacteristic
977C22#331211yescharacteristic
978C22#331411yescharacteristic
979C22#331611yescharacteristic
980C22#331811yescharacteristic
981C22#332011yescharacteristic
982C22#332411yescharacteristic
983C22#332511yescharacteristic
984C22#332811yescharacteristic
985C22#332911yescharacteristic
986C22#333011yescharacteristic
987C22#333111yescharacteristic
988C22#333211yescharacteristic
989C22#333311yescharacteristic
990C4—24no—
991C4—24no—
992C4—42no—
993C4—42no—
994C4—44no—
995C4—82no—
996C4—82no—
997C4—82no—
998C4—82no—
999C4—82no—
1000C4—161no—
1001C4—161no—
1002C4C4×#12311yescharacteristic
1003C4#232111yescharacteristic
1004C4#236411yescharacteristic
1005C4#236411yescharacteristic
1006C4#245011yescharacteristic
1007C4#245011yescharacteristic
1008C4#248711yescharacteristic
1009C4#257911yescharacteristic
1010C2—44no—
1011C2—44no—
1012C2#1401611yescharacteristic
1013C2#2084411yescharacteristic
1014C2#2084911yescharacteristic
1015C2#2270911yescharacteristic
1016C2#2271111yescharacteristic
1017C2#2271311yescharacteristic
1018C2#2271511yescharacteristic
1019C2#2397211yescharacteristic
1020C2#2398111yescharacteristic
1021C2#2404411yescharacteristic
1022C2#2405311yescharacteristic
1023C2#2621411yescharacteristic
1024C2#2621611yescharacteristic
1025C2#2621811yescharacteristic
1026C2#2622011yescharacteristic
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
3. C2×#1854C2semidirect
4. C2×#1736C2semidirect
6. #11267C2semidirect
7. #11267C2semidirect
8. #11096C2semidirect
9. #11095C2semidirect
10. #10908C2semidirect
11. #10907C2semidirect
12. #10730C2semidirect
13. #10730C2semidirect
14. #10730C2semidirect
15. #10722C2semidirect
39. #1870C4semidirect
75. C22×M16C2×C4semidirect
143. C2×C22⋊C8C2×C4semidirect
144. C2×C22⋊C8C2×C4semidirect
145. C2×C22⋊C8C2×C4semidirect
187. #336C2×C4semidirect
188. #336C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C4⋊C42
C2×#18702
C2×#18542
C2×#17362
#138712
#112672
#110962
#110952
#109082
#109072
#107302
#107222