Finite Group Databasebeta

← #372602

Subgroups — #372602

Order 512.

1652 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2452C211yesmaximal, characteristic
2C2×#1988C211yesmaximal, characteristic, complemented
3C2×#1916C211yesmaximal, characteristic, complemented
4C2×C4×#102C211yesmaximal, characteristic
5C4⋊C42C211yesmaximal, characteristic, complemented
6#11384C211yesmaximal, characteristic, complemented
7#11207C211yesmaximal, characteristic, complemented
8#11076C211yesmaximal, characteristic
9#11049C211yesmaximal, characteristic
10#10931C211yesmaximal, characteristic
11#10931C211yesmaximal, characteristic
12#10884C211yesmaximal, characteristic, complemented
13#10884C211yesmaximal, characteristic, complemented
14#10880C211yesmaximal, characteristic, complemented
15#10788C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×C22⋊Q8—21no—
18C22×C4×D4C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×C4×C8C2211yescharacteristic
25#2452—24no—
26#2452C418yescomplemented
27C2×#396—21no—
28C2×#393—21no—
29C2×#390C2211yescharacteristic
30C2×#390C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#385—21no—
34C2×#384C2211yescharacteristic
35C2×C4×C4⋊C4—21no—
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40#1988—24no—
41#1916—24no—
42C4×#102—24no—
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×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1436—21no—
60#1436—21no—
61C4⋊#95—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C23×Q8—21no—
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C2×C4⋊Q8—22no—
72C2×C4⋊Q8—22no—
73C2×C4⋊Q8—22no—
74C2×C4⋊Q8—41no—
75C2×C4⋊Q8—41no—
76C2×C4⋊Q8C2×C414yes—
77C2×C22⋊Q8—28no—
78C2×C22⋊Q8—44no—
79C2×C22⋊Q8—44no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—41no—
84C2×C4×D4—41no—
85C2×C4×D4C2×C414yes—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4D411yescharacteristic
92C22×C4⋊C4D411yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C42—21no—
106C22×C42—21no—
107C22×C42—21no—
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C2×C4⋊C8—22no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8—41no—
114C2×#102—22no—
115C2×#102—22no—
116C2×#102—22no—
117C2×#102—22no—
118C2×#102—22no—
119C2×#102—22no—
120C2×#102—22no—
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—41no—
124C2×#102—41no—
125C2×#102Q814yescomplemented
126C2×C4×C8—22no—
127C2×C4×C8—22no—
128C2×C4×C8—41no—
129#396—28no—
130#393—28no—
131#390—22no—
132#390—22no—
133#390C2×C414yes—
134#390C2×C414yes—
135#389—22no—
136#389—22no—
137#389C2×C414yes—
138#389C2×C414yes—
139#385—28no—
140#384—22no—
141#384—22no—
142C4×C4⋊C4—22no—
143C4×C4⋊C4—22no—
144C4×C4⋊C4—22no—
145C4×C4⋊C4—22no—
146C4×C4⋊C4—41no—
147C4×C4⋊C4—41no—
148C4×C4⋊C4—44no—
149C4×C4⋊C4C2×C414yes—
150C4×C4⋊C4D414yes—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95D411yescharacteristic
161C2×#95D411yescharacteristic
162#340—22no—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#340—41no—
172#340—41no—
173#340D414yes—
174#336—22no—
175#336—22no—
176#336—22no—
177#336—22no—
178C25—21no—
179C22×Q8—24no—
180C22×Q8—42no—
181C22×Q8—42no—
182C22×Q8—42no—
183C22×Q8—42no—
184C22×Q8—81no—
185C22×Q8—81no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4C22×C412yes—
198C22×D4C2×Q812yes—
199C22×D4#4112yes—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—24no—
208C23×C4—42no—
209C23×C4—42no—
210C23×C4—42no—
211C23×C4—42no—
212C23×C4—81no—
213C23×C4—81no—
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D411yescharacteristic
218C23×C4C2×D411yescharacteristic
219C23×C4C2×D411yescharacteristic
220C23×C4C2411yescharacteristic
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
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×C8C2×D412yes—
248C22×C8C2×Q812yes—
249C4⋊Q8—28no—
250C4⋊Q8—44no—
251C4⋊Q8—44no—
252C4⋊Q8—44no—
253C22⋊Q8—432no—
254C4×D4—28no—
255C4×D4—44no—
256C4×D4—44no—
257C4×D4—44no—
258C2×C4⋊C4—21no—
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—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—81no—
305C2×C4⋊C4—81no—
306C2×C4⋊C4C22⋊C414yes—
307C2×C4⋊C4C22⋊C414yes—
308C2×C4⋊C4D814yes—
309C2×C4⋊C4SD1614yes—
310C2×C4⋊C4C22×C412yes—
311C2×C4⋊C4C22×C412yes—
312C2×C4⋊C4C22×C412yes—
313C2×C4⋊C4C2×D412yes—
314C2×C4⋊C4C2×D412yes—
315C2×C4⋊C4C2×Q812yes—
316C2×C4⋊C4#4112yes—
317C2×C4⋊C4#4112yes—
318C2×C4⋊C4#4112yes—
319C2×C4⋊C4#4112yes—
320C2×C4⋊C4#4112yes—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
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—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—81no—
335C2×C22⋊C4—81no—
336C2×C42—21no—
337C2×C42—21no—
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—24no—
349C2×C42—42no—
350C2×C42—42no—
351C2×C42—42no—
352C2×C42—42no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42—81no—
356C2×C42—81no—
357C2×C42C22×C412yes—
358C2×C42C22×C412yes—
359C2×C42C22×C412yes—
360C2×C42C2×D412yes—
361C2×C42C2×D412yes—
362C2×C42C2×D412yes—
363C4⋊C8—44no—
364#102—28no—
365#102—28no—
366#102—44no—
367#102—44no—
368C4×C8—44no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—42no—
373#95—42no—
374#95—42no—
375#95—42no—
376#95—81no—
377#95—81no—
378#95C22⋊C414yes—
379#95C22⋊C414yes—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—41no—
384C24—41no—
385C24—41no—
386C24—41no—
387C24—41no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24—41no—
395C24C22×D411yescharacteristic
396C2×Q8—48no—
397C2×Q8—48no—
398C2×Q8—84no—
399C2×Q8—84no—
400C2×Q8—84no—
401C2×Q8—84no—
402C2×Q8—84no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
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×D4C4×Q814yes—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
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—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—48no—
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—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
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—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—48no—
512C22×C4—84no—
513C22×C4—84no—
514C22×C4—84no—
515C22×C4—84no—
516C22×C4—84no—
517C22×C4C2×C22⋊C412yes—
518C22×C4C2×C22⋊C412yes—
519C22×C4C2×C22⋊C412yes—
520C22×C4C2×C22⋊C412yes—
521C22×C4C2×C22⋊C412yes—
522C22×C4C2×C22⋊C412yes—
523C22×C4C2×D812yes—
524C22×C4C2×D812yes—
525C22×C4C2×D812yes—
526C22×C4C2×SD1612yes—
527C22×C4C2×SD1612yes—
528C22×C4C2×SD1612yes—
529C22×C4C23×C411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C22×Q811yescharacteristic
533C22×C4C2×#4111yescharacteristic
534C22×C4C2×#4111yescharacteristic
535C22×C4C2×#4111yescharacteristic
536C22×C4C2×#4111yescharacteristic
537C22×C4C2×#4111yescharacteristic
538C22×C4C2×#4111yescharacteristic
539C22×C4H(5,𝔽2)11yescharacteristic
540C22×C4H(5,𝔽2)11yescharacteristic
541C22×C42−1+411yescharacteristic
542C22×C42−1+411yescharacteristic
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—44no—
588C4⋊C4—48no—
589C4⋊C4—48no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—41no—
599C4⋊C4—41no—
600C4⋊C4—48no—
601C4⋊C4—48no—
602C4⋊C4—84no—
603C4⋊C4#102116yescomplemented
604C4⋊C4C4×D414yes—
605C4⋊C4C22⋊Q814yescomplemented
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—84no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—48no—
624C42—84no—
625C42—84no—
626C23—24no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—81no—
646C23—81no—
647C23—81no—
648C23—81no—
649C23—81no—
650C23—81no—
651C23—81no—
652C23—81no—
653C23—81no—
654C23—81no—
655C23—81no—
656C23—81no—
657C23—81no—
658C23—81no—
659C23—81no—
660C23—81no—
661C23C22×C22⋊C411yescharacteristic
662C23#52511yescharacteristic
663C23#52511yescharacteristic
664C23D4211yescharacteristic
665C23#54611yescharacteristic
666C23#54811yescharacteristic
667C23D4×Q811yescharacteristic
668C23C22×D811yescharacteristic
669C23C22×SD1611yescharacteristic
670C23#57511yescharacteristic
671C23#57511yescharacteristic
672C23#57611yescharacteristic
673C23#57711yescharacteristic
674C23#57711yescharacteristic
675C23#57811yescharacteristic
676Q8—816no—
677D4—24no—
678D4—24no—
679D4—42no—
680D4—42no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—816no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4C2×#10214yes—
775C2×C4C2×#10214yes—
776C2×C4C2×#10214yes—
777C2×C4C2×C4×D411yescharacteristic
778C2×C4C2×C4×Q811yescharacteristic
779C2×C4C4×#4111yescharacteristic
780C2×C4C4×#4111yescharacteristic
781C2×C4#51811yescharacteristic
782C2×C4#51911yescharacteristic
783C2×C4C2×C22⋊Q811yescharacteristic
784C2×C4#52511yescharacteristic
785C2×C4#52911yescharacteristic
786C2×C4#53211yescharacteristic
787C2×C4#53211yescharacteristic
788C2×C4#53311yescharacteristic
789C2×C4#53911yescharacteristic
790C2×C4#53911yescharacteristic
791C2×C4#54211yescharacteristic
792C2×C4#54211yescharacteristic
793C2×C4D4211yescharacteristic
794C2×C4#54611yescharacteristic
795C2×C4#54711yescharacteristic
796C2×C4#54811yescharacteristic
797C2×C4#54811yescharacteristic
798C2×C4D4×Q811yescharacteristic
799C2×C4#55111yescharacteristic
800C2×C4#55111yescharacteristic
801C2×C4#55211yescharacteristic
802C2×C4#55411yescharacteristic
803C2×C4#55411yescharacteristic
804C2×C4#55611yescharacteristic
805C8—42no—
806C8—42no—
807C8—81no—
808C8—81no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22#229711yescharacteristic
825C22D4×C22⋊C411yescharacteristic
826C22Q8×C22⋊C411yescharacteristic
827C22#244911yescharacteristic
828C22#246311yescharacteristic
829C22#246511yescharacteristic
830C22#247711yescharacteristic
831C22C22×#10211yescharacteristic
832C22#289611yescharacteristic
833C22#289711yescharacteristic
834C22#289811yescharacteristic
835C22#310011yescharacteristic
836C22#310011yescharacteristic
837C22#310311yescharacteristic
838C22#310311yescharacteristic
839C22#311811yescharacteristic
840C22#312111yescharacteristic
841C22#312411yescharacteristic
842C22#312511yescharacteristic
843C22#326911yescharacteristic
844C22#327111yescharacteristic
845C22D4×D811yescharacteristic
846C22D4×SD1611yescharacteristic
847C22#329411yescharacteristic
848C22#329511yescharacteristic
849C22#331311yescharacteristic
850C22#332111yescharacteristic
851C22#335811yescharacteristic
852C22#335911yescharacteristic
853C22#337011yescharacteristic
854C22#337611yescharacteristic
855C22Q8×D811yescharacteristic
856C22Q8×SD1611yescharacteristic
857C22#338811yescharacteristic
858C22#338911yescharacteristic
859C4—24no—
860C4—24no—
861C4—24no—
862C4—44no—
863C4—44no—
864C4—42no—
865C4—42no—
866C4—42no—
867C4—82no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4C4×C22⋊Q811yescharacteristic
873C4#233211yescharacteristic
874C4#236211yescharacteristic
875C4#236811yescharacteristic
876C4#245211yescharacteristic
877C4#246111yescharacteristic
878C4#255611yescharacteristic
879C4#256011yescharacteristic
880C2—84no—
881C2#1409911yescharacteristic
882C2#2138611yescharacteristic
883C2#2139711yescharacteristic
884C2D4×#10211yescharacteristic
885C2#2242611yescharacteristic
886C2Q8×#10211yescharacteristic
887C2#2252611yescharacteristic
888C2#2636811yescharacteristic
889C2#2637311yescharacteristic
890C2#2688911yescharacteristic
891C2#2690211yescharacteristic
892C2#2699811yescharacteristic
893C2#2700211yescharacteristic
894C2#2742211yescharacteristic
895C2#2742611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1988C2semidirect
3. C2×#1916C2semidirect
5. C4⋊C42C2semidirect
6. #11384C2semidirect
7. #11207C2semidirect
12. #10884C2semidirect
13. #10884C2semidirect
14. #10880C2semidirect
26. #2452C4semidirect
125. C2×#102Q8semidirect
603. C4⋊C4#102semidirect
605. C4⋊C4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#24522
C2×#19882
C2×#19162
C2×C4×#1022
C4⋊C422
#113842
#112072
#110762
#110492
#109312
#108842
#108802
#107882