Finite Group Databasebeta

← #355731

Subgroups — #355731

Order 512.

1468 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1936C211yesmaximal, characteristic
2C2×#1925C211yesmaximal, characteristic
3C2×#1864C211yesmaximal, characteristic
4C4×#389C211yesmaximal, characteristic, complemented
5C4×#390C211yesmaximal, characteristic
6#10931C211yesmaximal, characteristic
7#10927C211yesmaximal, characteristic
8#10908C211yesmaximal, characteristic, complemented
9#10907C211yesmaximal, characteristic, complemented
10#10885C211yesmaximal, characteristic, complemented
11#10881C211yesmaximal, characteristic, complemented
12#10863C211yesmaximal, characteristic, complemented
13#10806C211yesmaximal, characteristic, complemented
14#10788C211yesmaximal, characteristic
15#10693C211yesmaximal, characteristic, complemented
16C22×C4×D4C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#102C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#97C2211yescharacteristic
24C22×#97C2211yescharacteristic
25C2×#390C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×C4×C4⋊C4—21no—
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C22⋊C4—21no—
34C2×C4×C22⋊C4—21no—
35C2×C43C2211yescharacteristic
36#1936C418yescomplemented
37#1925C418yescomplemented
38#1864C418yescomplemented
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53#1437—21no—
54#1437—21no—
55#1436—21no—
56#1436—21no—
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4×#95—21no—
62C23×D4C2311yescharacteristic
63C24×C4—21no—
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C2×C4×D4—22no—
69C2×C4×D4—41no—
70C2×C4×D4—41no—
71C2×C4×D4—41no—
72C2×C4×D4—41no—
73C2×C4×D4C2×C414yes—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4C2311yescharacteristic
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C22⋊C4—21no—
84C22×C22⋊C4—21no—
85C22×C22⋊C4—21no—
86C22×C22⋊C4—21no—
87C22×C22⋊C4—21no—
88C22×C42—21no—
89C22×C42—21no—
90C22×C42—21no—
91C22×C42D411yescharacteristic
92C22×C42D411yescharacteristic
93C22×C42D411yescharacteristic
94C22×C42D411yescharacteristic
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C2×#107—41no—
99C2×#107—41no—
100C2×#107C2×C414yescomplemented
101C2×#106—41no—
102C2×#106—41no—
103C2×#106C2×C414yes—
104C2×#102—41no—
105C2×#102—41no—
106C2×#102—41no—
107C2×#102—41no—
108C2×#102—41no—
109C2×#102—41no—
110C2×#102C2×C414yes—
111C2×#102C2×C414yes—
112C2×#102C2×C414yes—
113C2×#102C2×C414yes—
114C2×#102C2×C414yes—
115C2×#102C2×C414yes—
116C2×#97—22no—
117C2×#97—41no—
118C2×#97—41no—
119C2×#97—41no—
120C2×#97—41no—
121C2×#97C2×C414yescomplemented
122#390—22no—
123#390—22no—
124#390C2×C414yes—
125#390C2×C414yes—
126#389—22no—
127#389—22no—
128#389C2×C414yes—
129#389C2×C414yescomplemented
130C4×C4⋊C4—22no—
131C4×C4⋊C4—41no—
132C4×C4⋊C4—41no—
133C4×C4⋊C4—41no—
134C4×C4⋊C4—41no—
135C4×C4⋊C4—44no—
136C4×C4⋊C4C2×C414yescomplemented
137C4×C22⋊C4—44no—
138C4×C22⋊C4—44no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C43—41no—
153C43—41no—
154#340—41no—
155#340—41no—
156#340—41no—
157#340—41no—
158#340—41no—
159#340—41no—
160#340C2×C414yes—
161#340C2×C414yescomplemented
162#340C2×C414yescomplemented
163#340C2×C414yescomplemented
164#336—22no—
165#336—22no—
166#336C2×C414yes—
167#336C2×C414yescomplemented
168C25—21no—
169C22×D4—21no—
170C22×D4—21no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4—21no—
174C22×D4—21no—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4C22×C412yes—
181C22×D4C22×C412yes—
182C22×D4C22×C412yes—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—24no—
191C23×C4—42no—
192C23×C4—42no—
193C23×C4—42no—
194C23×C4—42no—
195C23×C4—42no—
196C23×C4—42no—
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D411yescharacteristic
200C23×C4C2×D411yescharacteristic
201C23×C4C2×D411yescharacteristic
202C23×C4C2×D411yescharacteristic
203C23×C4C2411yescharacteristic
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8C22×C412yes—
227C22×C8C22×C412yes—
228C22×C8C22×C412yes—
229C22×C8C22×C412yes—
230C22×C8C22×C412yes—
231C22×C8C22×C412yes—
232C4×D4—44no—
233C4×D4—44no—
234C4×D4—44no—
235C4×D4—44no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4C22×C412yes—
276C2×C4⋊C4C22×C412yes—
277C2×C4⋊C4C22×C412yes—
278C2×C4⋊C4C22×C412yes—
279C2×C4⋊C4C22×C412yes—
280C2×C4⋊C4C22×C412yes—
281C2×C4⋊C4C22×C412yes—
282C2×C4⋊C4C22×C412yes—
283C2×C4⋊C4C22×C412yes—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—42no—
297C2×C22⋊C4—42no—
298C2×C22⋊C4—42no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—24no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—41no—
317C2×C42—41no—
318C2×C42—41no—
319C2×C42—41no—
320C2×C42—41no—
321C2×C42—41no—
322C2×C42—41no—
323C2×C42—41no—
324C2×C42—42no—
325C2×C42—42no—
326C2×C42—42no—
327C2×C42—42no—
328C2×C42—42no—
329C2×C42—42no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42C22×C412yes—
333C2×C42C22×C412yes—
334C2×C42C22×C412yes—
335C2×C42#4112yes—
336C2×C42#4112yes—
337C2×C42#4112yes—
338#107—44no—
339#106—44no—
340#102—44no—
341#102—44no—
342#102—44no—
343#102C42116yescomplemented
344#97—44no—
345#97—44no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—42no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95—42no—
357#95—42no—
358#95—42no—
359C24—22no—
360C24—22no—
361C24—22no—
362C24—41no—
363C24—41no—
364C24—41no—
365C24—41no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24C22×D411yescharacteristic
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4C2×C4214yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—48no—
445C22×C4—48no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—48no—
487C22×C4—84no—
488C22×C4—84no—
489C22×C4—84no—
490C22×C4—84no—
491C22×C4C4×D412yes—
492C22×C4C4×D412yes—
493C22×C4C4×D412yes—
494C22×C4C4×D412yes—
495C22×C4C4×D412yes—
496C22×C4C4×D412yes—
497C22×C4AGL(1,ℤ/8)12yes—
498C22×C4AGL(1,ℤ/8)12yes—
499C22×C4AGL(1,ℤ/8)12yes—
500C22×C4#13712yes—
501C22×C4C23×C411yescharacteristic
502C22×C4C23×C411yescharacteristic
503C22×C4C23×C411yescharacteristic
504C22×C4C2×#4111yescharacteristic
505C22×C4C2×#4111yescharacteristic
506C22×C4C2×#4111yescharacteristic
507C22×C4H(5,𝔽2)11yescharacteristic
508C22×C4H(5,𝔽2)11yescharacteristic
509C22×C4H(5,𝔽2)11yescharacteristic
510C22×C4H(5,𝔽2)11yescharacteristic
511C22×C4H(5,𝔽2)11yescharacteristic
512C22×C42−1+411yescharacteristic
513C22×C42−1+411yescharacteristic
514C22×C42−1+411yescharacteristic
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8C2×C4214yes—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4C2×C4214yes—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—22no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—44no—
591C42—44no—
592C42—44no—
593C42—44no—
594C42—48no—
595C42—84no—
596C42—84no—
597C23—24no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—81no—
617C23—81no—
618C23—81no—
619C23—81no—
620C23—81no—
621C23—81no—
622C23—81no—
623C23—81no—
624C23—81no—
625C23—81no—
626C23—81no—
627C23—81no—
628C23—81no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23C2×C4×D411yescharacteristic
633C23C2×C4×D411yescharacteristic
634C23C2×C4×D411yescharacteristic
635C23#53411yescharacteristic
636C23#53511yescharacteristic
637C23#53611yescharacteristic
638C23#53711yescharacteristic
639C23C2×AGL(1,ℤ/8)11yescharacteristic
640C23C2×AGL(1,ℤ/8)11yescharacteristic
641C23C2×AGL(1,ℤ/8)11yescharacteristic
642C23C2×#13711yescharacteristic
643C23#57511yescharacteristic
644C23#57511yescharacteristic
645C23#57511yescharacteristic
646C23#57511yescharacteristic
647D4—24no—
648D4—24no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—42no—
654D4—42no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—816no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4#44014yes—
746C2×C4#44214yes—
747C2×C4C22×C4211yescharacteristic
748C2×C4C4×#4111yescharacteristic
749C2×C4C4×#4111yescharacteristic
750C2×C4C4×#4111yescharacteristic
751C2×C4#51811yescharacteristic
752C2×C4#51811yescharacteristic
753C2×C4#51811yescharacteristic
754C2×C4#51811yescharacteristic
755C2×C4#51911yescharacteristic
756C2×C4#52011yescharacteristic
757C2×C4#52011yescharacteristic
758C2×C4#52011yescharacteristic
759C2×C4#52011yescharacteristic
760C2×C4#52011yescharacteristic
761C2×C4#52011yescharacteristic
762C2×C4#52011yescharacteristic
763C2×C4#53811yescharacteristic
764C2×C4#53811yescharacteristic
765C2×C4#53811yescharacteristic
766C2×C4#53911yescharacteristic
767C2×C4#53911yescharacteristic
768C2×C4#53911yescharacteristic
769C2×C4#54011yescharacteristic
770C2×C4#54111yescharacteristic
771C2×C4#54211yescharacteristic
772C2×C4#54211yescharacteristic
773C2×C4#54211yescharacteristic
774C2×C4#54211yescharacteristic
775C8—24no—
776C8—42no—
777C8—42no—
778C8—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22C42×D411yescharacteristic
795C22#232111yescharacteristic
796C22#232211yescharacteristic
797C22#232311yescharacteristic
798C22#232411yescharacteristic
799C22#232511yescharacteristic
800C22#232611yescharacteristic
801C22C2×#44011yescharacteristic
802C22C2×#44211yescharacteristic
803C22#294311yescharacteristic
804C22#294311yescharacteristic
805C22C4×AGL(1,ℤ/8)11yescharacteristic
806C22C4×AGL(1,ℤ/8)11yescharacteristic
807C22C4×AGL(1,ℤ/8)11yescharacteristic
808C22C4×AGL(1,ℤ/8)11yescharacteristic
809C22C4×AGL(1,ℤ/8)11yescharacteristic
810C22C4×AGL(1,ℤ/8)11yescharacteristic
811C22C4×#13711yescharacteristic
812C22C4×#13711yescharacteristic
813C22#319311yescharacteristic
814C22#319411yescharacteristic
815C22#319411yescharacteristic
816C22#319711yescharacteristic
817C22#321411yescharacteristic
818C22#321511yescharacteristic
819C22#321711yescharacteristic
820C22#321911yescharacteristic
821C22#323411yescharacteristic
822C22#323511yescharacteristic
823C22#323811yescharacteristic
824C22#324011yescharacteristic
825C22#325111yescharacteristic
826C22#325211yescharacteristic
827C22#325311yescharacteristic
828C22#325611yescharacteristic
829C4—24no—
830C4—24no—
831C4—44no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4#227411yescharacteristic
843C4#227511yescharacteristic
844C4#233211yescharacteristic
845C4#233411yescharacteristic
846C4#233411yescharacteristic
847C4#233511yescharacteristic
848C4#233511yescharacteristic
849C4#233711yescharacteristic
850C2—84no—
851C2#1378911yescharacteristic
852C2C4×#44211yescharacteristic
853C2C4×#44011yescharacteristic
854C2#2204911yescharacteristic
855C2#2205111yescharacteristic
856C2#2208111yescharacteristic
857C2#2208611yescharacteristic
858C2#2211711yescharacteristic
859C2#2212011yescharacteristic
860C2#2215111yescharacteristic
861C2#2215611yescharacteristic
862C2#2218611yescharacteristic
863C2#2219011yescharacteristic
864C2#2222411yescharacteristic
865C2#2222611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C4×#389C2semidirect
8. #10908C2semidirect
9. #10907C2semidirect
10. #10885C2semidirect
11. #10881C2semidirect
12. #10863C2semidirect
13. #10806C2semidirect
15. #10693C2semidirect
36. #1936C4semidirect
37. #1925C4semidirect
38. #1864C4semidirect
100. C2×#107C2×C4semidirect
121. C2×#97C2×C4semidirect
129. #389C2×C4semidirect
136. C4×C4⋊C4C2×C4semidirect
161. #340C2×C4semidirect
162. #340C2×C4semidirect
163. #340C2×C4semidirect
167. #336C2×C4semidirect
343. #102C42semidirect

Maximal subgroups

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

subgroupindex
C2×#19362
C2×#19252
C2×#18642
C4×#3892
C4×#3902
#109312
#109272
#109082
#109072
#108852
#108812
#108632
#108062
#107882
#106932