Finite Group Databasebeta

← #439381

Subgroups — #439381

Order 512.

1278 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2023C211yesmaximal, characteristic
2C2×#1988C211yesmaximal, characteristic, complemented
3#15144C211yesmaximal, characteristic
4#14053C211yesmaximal, characteristic, complemented
5#11384C211yesmaximal, characteristic, complemented
6#11384C211yesmaximal, characteristic, complemented
7#11315C211yesmaximal, characteristic, complemented
8#11315C211yesmaximal, characteristic, complemented
9#11189C211yesmaximal, characteristic
10#11076C211yesmaximal, characteristic
11#11066C211yesmaximal, characteristic
12#10931C211yesmaximal, characteristic
13#10925C211yesmaximal, characteristic
14#10880C211yesmaximal, characteristic, complemented
15#10876C211yesmaximal, characteristic, complemented
16C22×C4⋊Q8C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×#102C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×C4×C8C2211yescharacteristic
24C2×#393—21no—
25C2×#393—21no—
26C2×#391—21no—
27C2×#390C2211yescharacteristic
28C2×#390C2211yescharacteristic
29C2×#390C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32#2023—24no—
33#1988—24no—
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50#1446—21no—
51#1441—21no—
52#1439—21no—
53#1439—21no—
54#1436—21no—
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4×#95C2211yescharacteristic
61C23×Q8—21no—
62C23×Q8—21no—
63C23×D4C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C2×C4⋊Q8—22no—
69C2×C4⋊Q8—22no—
70C2×C4⋊Q8—22no—
71C2×C4⋊Q8—22no—
72C2×C4⋊Q8—22no—
73C2×C4⋊Q8—22no—
74C2×C4⋊Q8—22no—
75C2×C4⋊Q8—22no—
76C2×C4⋊Q8—41no—
77C2×C4⋊Q8—41no—
78C2×C4⋊Q8—41no—
79C2×C4⋊Q8—41no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
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×C42—21no—
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8—41no—
103C2×#102—22no—
104C2×#102—22no—
105C2×#102—22no—
106C2×#102—22no—
107C2×#102—22no—
108C2×#102—41no—
109C2×#102—41no—
110C2×#102—41no—
111C2×#102—41no—
112C2×#102—41no—
113C2×#102—41no—
114C2×#102Q814yescomplemented
115C2×C4×C8—41no—
116C2×C4×C8—41no—
117C2×C4×C8—41no—
118#393—44no—
119#393—44no—
120#391—44no—
121#390—22no—
122#390—22no—
123#390—22no—
124#390—22no—
125#390—41no—
126#390—41no—
127#389—22no—
128#389—41no—
129C4×C4⋊C4—22no—
130C4×C4⋊C4—41no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95D411yescharacteristic
144C2×#95D411yescharacteristic
145C2×#95D411yescharacteristic
146C2×#95D411yescharacteristic
147#340—22no—
148#340—22no—
149#340—22no—
150#340—22no—
151#340—22no—
152#340—22no—
153#340—22no—
154#340—41no—
155#340—41no—
156#340—41no—
157#340—41no—
158#340D414yes—
159#336—22no—
160#336—22no—
161#336—41no—
162#336—41no—
163C25—21no—
164C22×Q8—24no—
165C22×Q8—42no—
166C22×Q8—42no—
167C22×Q8—42no—
168C22×Q8—42no—
169C22×Q8—42no—
170C22×Q8—42no—
171C22×Q8—42no—
172C22×Q8—42no—
173C22×Q8—42no—
174C22×Q8—81no—
175C22×Q8—81no—
176C22×Q8—81no—
177C22×Q8—81no—
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—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4C2×Q812yes—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4C2×D411yescharacteristic
200C23×C4C2×D411yescharacteristic
201C23×C4C2×D411yescharacteristic
202C23×C4C2×D411yescharacteristic
203C23×C4C2×D411yescharacteristic
204C23×C4C2×D411yescharacteristic
205C23×C4C2411yescharacteristic
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×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8C2×D412yes—
233C22×C8C2×Q812yes—
234C4⋊Q8—28no—
235C4⋊Q8—44no—
236C4⋊Q8—44no—
237C4⋊Q8—44no—
238C4⋊Q8—44no—
239C4⋊Q8—44no—
240C4⋊Q8—44no—
241C4⋊Q8—44no—
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—24no—
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—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—81no—
286C2×C4⋊C4C2×D412yes—
287C2×C4⋊C4C2×D412yes—
288C2×C4⋊C4C2×Q812yes—
289C2×C4⋊C4#4112yes—
290C2×C4⋊C4#4112yes—
291C2×C4⋊C4#4112yes—
292C2×C4⋊C4#4112yes—
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×C22⋊C4—42no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—81no—
308C2×C22⋊C4—81no—
309C2×C22⋊C4—81no—
310C2×C22⋊C4—81no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—42no—
328C2×C42—42no—
329C2×C42—81no—
330C2×C42#4112yes—
331C2×C42#4112yes—
332C4⋊C8—44no—
333#102—44no—
334#102—44no—
335#102—44no—
336#102—44no—
337C4×C8—44no—
338#95—41no—
339#95—41no—
340#95—42no—
341#95—42no—
342#95—42no—
343#95—42no—
344#95—42no—
345#95—42no—
346#95—42no—
347#95—42no—
348#95—42no—
349#95—42no—
350#95—81no—
351#95—81no—
352#95D814yes—
353#95SD1614yes—
354C24—22no—
355C24—41no—
356C24—41no—
357C24—41no—
358C24—41no—
359C24—41no—
360C24—41no—
361C24—41no—
362C24—41no—
363C24—41no—
364C24—41no—
365C24—41no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24C22×D411yescharacteristic
370C2×Q8—48no—
371C2×Q8—48no—
372C2×Q8—48no—
373C2×Q8—84no—
374C2×Q8—84no—
375C2×Q8—84no—
376C2×Q8—84no—
377C2×Q8—84no—
378C2×Q8—84no—
379C2×Q8—84no—
380C2×Q8—84no—
381C2×Q8—84no—
382C2×Q8—84no—
383C2×Q8—84no—
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×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
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—21no—
439C22×C4—21no—
440C22×C4—21no—
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—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
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—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#12412yes—
496C22×C4#12412yes—
497C22×C4C2×D812yes—
498C22×C4C2×D812yes—
499C22×C4C2×D812yes—
500C22×C4C2×SD1612yes—
501C22×C4C2×SD1612yes—
502C22×C4C2×SD1612yes—
503C22×C4C22×D411yescharacteristic
504C22×C4C22×Q811yescharacteristic
505C22×C4C2×#4111yescharacteristic
506C22×C4C2×#4111yescharacteristic
507C22×C4C2×#4111yescharacteristic
508C22×C4C2×#4111yescharacteristic
509C22×C4C2×#4111yescharacteristic
510C22×C4C2×#4111yescharacteristic
511C22×C4H(5,𝔽2)11yescharacteristic
512C22×C4H(5,𝔽2)11yescharacteristic
513C22×C4H(5,𝔽2)11yescharacteristic
514C22×C4H(5,𝔽2)11yescharacteristic
515C22×C42−1+411yescharacteristic
516C22×C42−1+411yescharacteristic
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
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×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
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—48no—
557C4⋊C4—48no—
558C4⋊C4—41no—
559C4⋊C4—41no—
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⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—84no—
575C4⋊C4#12414yes—
576C22⋊C4—84no—
577C22⋊C4—84no—
578C22⋊C4—84no—
579C22⋊C4—84no—
580C22⋊C4—84no—
581C22⋊C4—84no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—41no—
591C42—41no—
592C42—41no—
593C42—41no—
594C42—84no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—81no—
603C23—81no—
604C23—81no—
605C23—81no—
606C23—81no—
607C23—81no—
608C23—81no—
609C23—81no—
610C23—81no—
611C23—81no—
612C23—81no—
613C23—81no—
614C23—81no—
615C23—81no—
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#52511yescharacteristic
631C23C2×#12411yescharacteristic
632C23#53711yescharacteristic
633C23D4211yescharacteristic
634C23#54611yescharacteristic
635C23#54611yescharacteristic
636C23D4×Q811yescharacteristic
637C23C22×D811yescharacteristic
638C23C22×SD1611yescharacteristic
639C23#57511yescharacteristic
640C23#57511yescharacteristic
641C23#57611yescharacteristic
642C23#57711yescharacteristic
643C23#57711yescharacteristic
644C23#57811yescharacteristic
645Q8—816no—
646Q8—816no—
647D4—42no—
648D4—42no—
649D4—42no—
650D4—42no—
651D4—81no—
652D4—81no—
653D4—81no—
654D4—81no—
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—24no—
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—42no—
678C2×C4—41no—
679C2×C4—42no—
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—41no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
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—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
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#48614yes—
746C2×C4#52511yescharacteristic
747C2×C4C2×#12411yescharacteristic
748C2×C4#53311yescharacteristic
749C2×C4#53311yescharacteristic
750C2×C4#53711yescharacteristic
751C2×C4#53811yescharacteristic
752C2×C4#53811yescharacteristic
753C2×C4#54211yescharacteristic
754C2×C4#54211yescharacteristic
755C2×C4#54211yescharacteristic
756C2×C4#54211yescharacteristic
757C2×C4#54311yescharacteristic
758C2×C4#54611yescharacteristic
759C2×C4#54611yescharacteristic
760C2×C4D4×Q811yescharacteristic
761C2×C4#55111yescharacteristic
762C2×C4#55111yescharacteristic
763C2×C4#55411yescharacteristic
764C2×C4#55411yescharacteristic
765C2×C4#55611yescharacteristic
766C2×C4#55611yescharacteristic
767C2×C4#55611yescharacteristic
768C2×C4#55611yescharacteristic
769C2×C4#55911yescharacteristic
770C2×C4#55911yescharacteristic
771C2×C4#55911yescharacteristic
772C2×C4H(3,𝔽4)11yescharacteristic
773C2×C4#56311yescharacteristic
774C8—42no—
775C8—42no—
776C8—81no—
777C8—81no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—161no—
786C22—161no—
787C22—161no—
788C22—161no—
789C22—161no—
790C22—161no—
791C22—161no—
792C22—161no—
793C22#246511yescharacteristic
794C22#247211yescharacteristic
795C22#247211yescharacteristic
796C22#249211yescharacteristic
797C22#259211yescharacteristic
798C22#268311yescharacteristic
799C22#271211yescharacteristic
800C22#310011yescharacteristic
801C22#310311yescharacteristic
802C22#311811yescharacteristic
803C22#312111yescharacteristic
804C22C2×#48611yescharacteristic
805C22#313611yescharacteristic
806C22#313711yescharacteristic
807C22#314011yescharacteristic
808C22#324511yescharacteristic
809C22#324611yescharacteristic
810C22#326211yescharacteristic
811C22#326311yescharacteristic
812C22#327511yescharacteristic
813C22#327711yescharacteristic
814C22D4×D811yescharacteristic
815C22D4×SD1611yescharacteristic
816C22#329411yescharacteristic
817C22#329411yescharacteristic
818C22#329511yescharacteristic
819C22#329811yescharacteristic
820C22#331311yescharacteristic
821C22#331911yescharacteristic
822C22#332111yescharacteristic
823C22#332111yescharacteristic
824C22Q8×D811yescharacteristic
825C22Q8×SD1611yescharacteristic
826C22#338811yescharacteristic
827C22#338911yescharacteristic
828C4—24no—
829C4—42no—
830C4—44no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—161no—
840C4—161no—
841C4#246511yescharacteristic
842C4#249211yescharacteristic
843C4#259211yescharacteristic
844C4#260711yescharacteristic
845C4#271211yescharacteristic
846C4#275911yescharacteristic
847C4#275911yescharacteristic
848C4#280411yescharacteristic
849C2—162no—
850C2#1563611yescharacteristic
851C2#2699811yescharacteristic
852C2#2700211yescharacteristic
853C2#2722211yescharacteristic
854C2#2722611yescharacteristic
855C2#2725411yescharacteristic
856C2#2728511yescharacteristic
857C2#2781311yescharacteristic
858C2#2782611yescharacteristic
859C2#2934611yescharacteristic
860C2#2936211yescharacteristic
861C2#3123411yescharacteristic
862C2#3124011yescharacteristic
863C2#3211011yescharacteristic
864C2#3211211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1988C2semidirect
4. #14053C2semidirect
5. #11384C2semidirect
6. #11384C2semidirect
7. #11315C2semidirect
8. #11315C2semidirect
14. #10880C2semidirect
15. #10876C2semidirect
114. C2×#102Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#20232
C2×#19882
#151442
#140532
#113842
#113152
#111892
#110762
#110662
#109312
#109252
#108802
#108762