Finite Group Databasebeta

← #389303

Subgroups — #389303

Order 512.

1448 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2033C211yesmaximal, characteristic
2#14137C211yesmaximal, characteristic
3#13974C211yesmaximal, characteristic, complemented
4#11379C211yesmaximal, characteristic, complemented
5#11219C211yesmaximal, characteristic, complemented
6#11189C211yesmaximal, characteristic, complemented
7#11066C211yesmaximal, characteristic, complemented
8#10969C211yesmaximal, characteristic
9#10931C211yesmaximal, characteristic, complemented
10#10925C211yesmaximal, characteristic, complemented
11#10921C211yesmaximal, characteristic, complemented
12#10820C211yesmaximal, characteristic, complemented
13#10806C211yesmaximal, characteristic, complemented
14#10730C211yesmaximal, characteristic, complemented
15#10730C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C23×C4⋊C4C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#102C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#390C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#388—21no—
30C2×#386—21no—
31C2×#386—21no—
32C2×#380C2211yescharacteristic
33C2×#380C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36#2033C418yescomplemented
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51#1443—21no—
52#1440—21no—
53#1439—21no—
54#1439—21no—
55#1436—21no—
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C23×D4—21no—
61C23×D4C2311yescharacteristic
62C24×C4—21no—
63C24×C4C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C2×#121—22no—
69C2×#121—41no—
70C2×#121—41no—
71C2×#121—41no—
72C2×#121—41no—
73C2×#121C2×C414yes—
74C22×C4⋊C4—22no—
75C22×C4⋊C4—22no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—41no—
79C22×C4⋊C4—41no—
80C22×C4⋊C4—41no—
81C22×C4⋊C4—41no—
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C22⋊C4—21no—
90C22×C22⋊C4—21no—
91C22×C22⋊C4—21no—
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C22⋊C4—21no—
96C22×C22⋊C4D411yescharacteristic
97C22×C22⋊C4D411yescharacteristic
98C22×C42—21no—
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C2×#107—41no—
102C2×#107—41no—
103C2×#107C2×C414yescomplemented
104C2×#102—22no—
105C2×#102—22no—
106C2×#102—41no—
107C2×#102—41no—
108C2×#102—41no—
109C2×#102—41no—
110C2×#102—41no—
111C2×#102—41no—
112C2×#102—41no—
113C2×#102—41no—
114C2×#102C2×C414yescomplemented
115C2×#102C2×C414yescomplemented
116C2×C22⋊C8—22no—
117C2×C22⋊C8—22no—
118C2×C22⋊C8—41no—
119C2×C22⋊C8—41no—
120C2×C22⋊C8—41no—
121C2×C22⋊C8C2×C414yes—
122C2×C4×C8—22no—
123C2×C4×C8—41no—
124C2×C4×C8—41no—
125#390—22no—
126#390—22no—
127#390—41no—
128#390—41no—
129#389—41no—
130#389—41no—
131#388—44no—
132#386—44no—
133#386—44no—
134#380—22no—
135#380—22no—
136#380—41no—
137#380C2×C414yes—
138C4×C4⋊C4—22no—
139C4×C4⋊C4—41no—
140C4×C22⋊C4—41no—
141C4×C22⋊C4—41no—
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—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95D411yescharacteristic
155C2×#95D411yescharacteristic
156#340—22no—
157#340—22no—
158#340—41no—
159#340—41no—
160#340—41no—
161#340—41no—
162#340—41no—
163#340—41no—
164#340—41no—
165#340—41no—
166#340C2×C414yescomplemented
167#336—41no—
168#336—41no—
169#336—41no—
170C25—21no—
171C25C2×D411yescharacteristic
172C22×D4—24no—
173C22×D4—21no—
174C22×D4—21no—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—42no—
187C22×D4—42no—
188C22×D4—42no—
189C22×D4—42no—
190C22×D4—42no—
191C22×D4—42no—
192C22×D4C22×C412yes—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
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—42no—
213C23×C4—42no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4—42no—
217C23×C4—81no—
218C23×C4—81no—
219C23×C4C22×C412yes—
220C23×C4C2×D411yescharacteristic
221C23×C4C2×D411yescharacteristic
222C23×C4C2×D411yescharacteristic
223C23×C4C2×D411yescharacteristic
224C23×C4C2×D411yescharacteristic
225C23×C4#4112yes—
226C23×C4C2411yescharacteristic
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8C22×C412yes—
253C22×C8C22×C412yes—
254C22×C8#4112yes—
255#121—44no—
256#121—44no—
257#121—44no—
258#121—44no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
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—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4C22×C412yes—
306C2×C4⋊C4C22×C412yes—
307C2×C4⋊C4C22×C412yes—
308C2×C4⋊C4#4112yes—
309C2×C4⋊C4#4112yes—
310C2×C4⋊C4#4112yes—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—41no—
316C2×C22⋊C4—41no—
317C2×C22⋊C4—41no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—81no—
333C2×C22⋊C4—81no—
334C2×C22⋊C4—81no—
335C2×C22⋊C4—81no—
336C2×C22⋊C4—81no—
337C2×C22⋊C4D814yes—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—42no—
351C2×C42—42no—
352C2×C42—81no—
353#107—44no—
354#102—44no—
355#102—44no—
356#102—44no—
357#102—44no—
358C22⋊C8—44no—
359C22⋊C8—44no—
360C4×C8—44no—
361#95—24no—
362#95—41no—
363#95—41no—
364#95—42no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—42no—
373#95—42no—
374#95—81no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—22no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24—41no—
395C24—41no—
396C24—41no—
397C24—41no—
398C24—41no—
399C24—41no—
400C24—41no—
401C24—41no—
402C24C4×D412yes—
403C24C2×D812yes—
404C24#13512yes—
405C24C22×D411yescharacteristic
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—48no—
413C2×D4—48no—
414C2×D4—48no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—84no—
438C2×D4—84no—
439C2×D4—84no—
440C2×D4—84no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
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—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—48no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
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—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—84no—
551C22×C4—84no—
552C22×C4—84no—
553C22×C4—84no—
554C22×C4—84no—
555C22×C4—84no—
556C22×C4C4×D412yes—
557C22×C4C2×D812yes—
558C22×C4C2×D812yes—
559C22×C4AGL(1,ℤ/8)12yes—
560C22×C4C23×C411yescharacteristic
561C22×C4C2×#4111yescharacteristic
562C22×C4C2×#4111yescharacteristic
563C22×C4C2×#4111yescharacteristic
564C22×C4C2×#4111yescharacteristic
565C22×C4C2×#4111yescharacteristic
566C22×C4H(5,𝔽2)11yescharacteristic
567C22×C4H(5,𝔽2)11yescharacteristic
568C22×C4H(5,𝔽2)11yescharacteristic
569C22×C4H(5,𝔽2)11yescharacteristic
570C22×C4H(5,𝔽2)11yescharacteristic
571C22×C4H(5,𝔽2)11yescharacteristic
572C22×C4H(5,𝔽2)11yescharacteristic
573C22×C42−1+411yescharacteristic
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—48no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—41no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—84no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—41no—
647C42—41no—
648C42—41no—
649C42—84no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—81no—
692C23—81no—
693C23—81no—
694C23—81no—
695C23—81no—
696C23—81no—
697C23—81no—
698C23—81no—
699C23—81no—
700C23—81no—
701C23—81no—
702C23—81no—
703C23—81no—
704C23—81no—
705C23—81no—
706C23—81no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23C4×D814yes—
720C23C2×C4×D411yescharacteristic
721C23#53411yescharacteristic
722C23#53511yescharacteristic
723C23#54611yescharacteristic
724C23#54611yescharacteristic
725C23#54611yescharacteristic
726C23#54711yescharacteristic
727C23C22×D811yescharacteristic
728C23C2×#13511yescharacteristic
729C23C2×AGL(1,ℤ/8)11yescharacteristic
730C23#57511yescharacteristic
731C23#57711yescharacteristic
732C23#57711yescharacteristic
733C23#57711yescharacteristic
734C23#57811yescharacteristic
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—816no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—816no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4C4×#4111yescharacteristic
838C2×C4C4×#4111yescharacteristic
839C2×C4#51811yescharacteristic
840C2×C4#51811yescharacteristic
841C2×C4#51811yescharacteristic
842C2×C4#52011yescharacteristic
843C2×C4#53811yescharacteristic
844C2×C4#53811yescharacteristic
845C2×C4#53811yescharacteristic
846C2×C4#53811yescharacteristic
847C2×C4#53811yescharacteristic
848C2×C4#53911yescharacteristic
849C2×C4#54011yescharacteristic
850C2×C4#54011yescharacteristic
851C2×C4#54011yescharacteristic
852C2×C4#54211yescharacteristic
853C2×C4#55111yescharacteristic
854C2×C4#55111yescharacteristic
855C2×C4#55111yescharacteristic
856C2×C4#55211yescharacteristic
857C2×C4#55311yescharacteristic
858C2×C4#55311yescharacteristic
859C2×C4#55511yescharacteristic
860C2×C4#55511yescharacteristic
861C2×C4#56011yescharacteristic
862C2×C4#56011yescharacteristic
863C2×C4#56211yescharacteristic
864C2×C4#56211yescharacteristic
865C8—42no—
866C8—42no—
867C8—42no—
868C8—81no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—82no—
885C22—82no—
886C22—82no—
887C22—82no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—161no—
892C22—161no—
893C22—161no—
894C22—161no—
895C22—161no—
896C22—161no—
897C22—161no—
898C22—161no—
899C22#232111yescharacteristic
900C22#235911yescharacteristic
901C22#236411yescharacteristic
902C22#268511yescharacteristic
903C22#268611yescharacteristic
904C22#269911yescharacteristic
905C22#270611yescharacteristic
906C22C2×C4×D811yescharacteristic
907C22C4×AGL(1,ℤ/8)11yescharacteristic
908C22#294711yescharacteristic
909C22#295211yescharacteristic
910C22#318611yescharacteristic
911C22#318811yescharacteristic
912C22#320111yescharacteristic
913C22#320411yescharacteristic
914C22#320511yescharacteristic
915C22#321111yescharacteristic
916C22#322211yescharacteristic
917C22#322511yescharacteristic
918C22#329411yescharacteristic
919C22#329411yescharacteristic
920C22#329411yescharacteristic
921C22#330011yescharacteristic
922C22#330111yescharacteristic
923C22#330111yescharacteristic
924C22#331011yescharacteristic
925C22#331311yescharacteristic
926C22#332411yescharacteristic
927C22#332611yescharacteristic
928C22#332611yescharacteristic
929C22#333011yescharacteristic
930C22#333411yescharacteristic
931C22#333711yescharacteristic
932C22#334511yescharacteristic
933C22#335011yescharacteristic
934C4—42no—
935C4—42no—
936C4—42no—
937C4—42no—
938C4—82no—
939C4—82no—
940C4—82no—
941C4—82no—
942C4—82no—
943C4—82no—
944C4—81no—
945C4—161no—
946C4#233311yescharacteristic
947C4#233511yescharacteristic
948C4#237211yescharacteristic
949C4#237711yescharacteristic
950C4#274111yescharacteristic
951C4#274911yescharacteristic
952C4#275611yescharacteristic
953C4#278111yescharacteristic
954C2—44no—
955C2—162no—
956C2#1453911yescharacteristic
957C2#2204011yescharacteristic
958C2#2205911yescharacteristic
959C2#2291611yescharacteristic
960C2#2294411yescharacteristic
961C2#2312711yescharacteristic
962C2#2313811yescharacteristic
963C2#3128611yescharacteristic
964C2#3130011yescharacteristic
965C2#3131811yescharacteristic
966C2#3133211yescharacteristic
967C2#3171811yescharacteristic
968C2#3172611yescharacteristic
969C2#3193011yescharacteristic
970C2#3194311yescharacteristic
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
3. #13974C2semidirect
4. #11379C2semidirect
5. #11219C2semidirect
6. #11189C2semidirect
7. #11066C2semidirect
9. #10931C2semidirect
10. #10925C2semidirect
11. #10921C2semidirect
12. #10820C2semidirect
13. #10806C2semidirect
14. #10730C2semidirect
15. #10730C2semidirect
36. #2033C4semidirect
103. C2×#107C2×C4semidirect
114. C2×#102C2×C4semidirect
115. C2×#102C2×C4semidirect
166. #340C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#20332
#141372
#139742
#113792
#112192
#111892
#110662
#109692
#109312
#109252
#109212
#108202
#108062
#107302