Finite Group Databasebeta

← #360377

Subgroups — #360377

Order 512.

1302 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1832C211yesmaximal, characteristic, complemented
2C2×#1797C211yesmaximal, characteristic
3C2×#1797C211yesmaximal, characteristic
4C2×#1768C211yesmaximal, characteristic, complemented
5#13753C211yesmaximal, characteristic
6#11298C211yesmaximal, characteristic, complemented
7#11298C211yesmaximal, characteristic, complemented
8#11147C211yesmaximal, characteristic
9#11147C211yesmaximal, characteristic
10#10922C211yesmaximal, characteristic
11#10921C211yesmaximal, characteristic
12#10833C211yesmaximal, characteristic, complemented
13#10833C211yesmaximal, characteristic, complemented
14#10798C211yesmaximal, characteristic, complemented
15#10797C211yesmaximal, characteristic, complemented
16C23×C42C2211yescharacteristic
17C22×C4⋊C8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×#97C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27C2×C4×C22⋊C4C2211yescharacteristic
28C2×C4×C22⋊C4C2211yescharacteristic
29C2×#376C2211yescharacteristic
30C2×#376C2211yescharacteristic
31#1832—24no—
32#1797—24no—
33#1797—24no—
34#1768—24no—
35C2×#336C2211yescharacteristic
36C2×#336C2211yescharacteristic
37C2×#336C2211yescharacteristic
38C2×#336C2211yescharacteristic
39C2×#336C2211yescharacteristic
40C2×#336C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53#1434C411yescharacteristic
54#1434C411yescharacteristic
55#1434C411yescharacteristic
56#1434C411yescharacteristic
57C22⋊#95C411yescharacteristic
58C22⋊#95C411yescharacteristic
59C22⋊#95C411yescharacteristic
60C22⋊#95C411yescharacteristic
61C4×#95C2211yescharacteristic
62C4×#95C2211yescharacteristic
63C24×C4C2×C411yescharacteristic
64C24×C4C2×C411yescharacteristic
65C24×C4C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C22×C22⋊C4C2×C411yescharacteristic
75C22×C22⋊C4C2×C411yescharacteristic
76C22×C22⋊C4C2×C411yescharacteristic
77C22×C22⋊C4C2×C411yescharacteristic
78C22×C42—22no—
79C22×C42—22no—
80C22×C42—22no—
81C22×C42—22no—
82C22×C42—22no—
83C22×C42—22no—
84C22×C42C2×C411yescharacteristic
85C22×C42C2×C411yescharacteristic
86C22×C42C2311yescharacteristic
87C22×C42C2311yescharacteristic
88C22×C42C2311yescharacteristic
89C22×C42C2311yescharacteristic
90C22×C42C2311yescharacteristic
91C22×C42C2311yescharacteristic
92C2×C4⋊C8—22no—
93C2×C4⋊C8—22no—
94C2×C4⋊C8—22no—
95C2×C4⋊C8—22no—
96C2×C4⋊C8—22no—
97C2×C4⋊C8—22no—
98C2×C4⋊C8—22no—
99C2×C4⋊C8—22no—
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8D414yes—
103C2×C4⋊C8D414yes—
104C2×C22⋊C8—22no—
105C2×C22⋊C8—22no—
106C2×C22⋊C8—22no—
107C2×C22⋊C8—22no—
108C2×C22⋊C8—22no—
109C2×C22⋊C8—22no—
110C2×C22⋊C8—22no—
111C2×C22⋊C8—22no—
112C2×C22⋊C8—41no—
113C2×C22⋊C8—41no—
114C2×C22⋊C8—41no—
115C2×C22⋊C8—41no—
116C2×#97—22no—
117C2×#97—22no—
118C2×#97—41no—
119C2×C4×C8—22no—
120C2×C4×C8—22no—
121C2×C4×C8—41no—
122C4×C22⋊C4—22no—
123C4×C22⋊C4—22no—
124C4×C22⋊C4—22no—
125C4×C22⋊C4—22no—
126#376—22no—
127#376—22no—
128#376—22no—
129#376—22no—
130C2×#95C2×C411yescharacteristic
131C2×#95C2×C411yescharacteristic
132C2×#95C2×C411yescharacteristic
133C2×#95C2×C411yescharacteristic
134C2×#95C2×C411yescharacteristic
135C2×#95C2×C411yescharacteristic
136C2×#95C2×C411yescharacteristic
137C2×#95C2×C411yescharacteristic
138C2×#95C2×C411yescharacteristic
139C2×#95C2×C411yescharacteristic
140C2×#95C2×C411yescharacteristic
141C2×#95C2×C411yescharacteristic
142C2×#95C2×C411yescharacteristic
143C2×#95C2×C411yescharacteristic
144C2×#95C2×C411yescharacteristic
145C2×#95C2×C411yescharacteristic
146C2×#95C2×C411yescharacteristic
147C2×#95C2×C411yescharacteristic
148C2×#95C2×C411yescharacteristic
149C2×#95C2×C411yescharacteristic
150#336—22no—
151#336—22no—
152#336—22no—
153#336—22no—
154#336—22no—
155#336—22no—
156#336—22no—
157#336—22no—
158#336—22no—
159#336—22no—
160#336—22no—
161#336—22no—
162#336—41no—
163#336—41no—
164#336—41no—
165#336—41no—
166#336—41no—
167#336—41no—
168C25C22×C411yescharacteristic
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—41no—
192C23×C4—41no—
193C23×C4—41no—
194C23×C4—41no—
195C23×C4C22×C411yescharacteristic
196C23×C4C22×C411yescharacteristic
197C23×C4C22×C411yescharacteristic
198C23×C4C22×C411yescharacteristic
199C23×C4C22×C411yescharacteristic
200C23×C4C22×C411yescharacteristic
201C23×C4C22×C411yescharacteristic
202C23×C4C22×C411yescharacteristic
203C23×C4C22×C411yescharacteristic
204C23×C4C22×C411yescharacteristic
205C23×C4C22×C411yescharacteristic
206C23×C4C22×C411yescharacteristic
207C23×C4C22×C411yescharacteristic
208C23×C4#4112yes—
209C23×C4#4112yes—
210C23×C4C2411yescharacteristic
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×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×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8C2×D412yes—
264C22×C8C2×D412yes—
265C22×C8C2×D412yes—
266C22×C8C2×D412yes—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—41no—
276C2×C22⋊C4—41no—
277C2×C22⋊C4—41no—
278C2×C22⋊C4—41no—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—22no—
284C2×C42—22no—
285C2×C42—22no—
286C2×C42—22no—
287C2×C42—22no—
288C2×C42—22no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42—21no—
298C2×C42—21no—
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—21no—
312C2×C42—21no—
313C2×C42—44no—
314C2×C42—44no—
315C2×C42—44no—
316C2×C42—44no—
317C2×C42C2×D412yes—
318C2×C42C2×D412yes—
319C2×C42#4112yes—
320C2×C42#4112yes—
321C2×C42#4112yes—
322C2×C42#4112yes—
323C2×C42#4112yes—
324C2×C42#4112yes—
325C4⋊C8—28no—
326C4⋊C8—28no—
327C4⋊C8—44no—
328C4⋊C8—44no—
329C22⋊C8—44no—
330C22⋊C8—44no—
331C22⋊C8—44no—
332C22⋊C8—44no—
333#97—44no—
334C4×C8—44no—
335#95—22no—
336#95—22no—
337#95—22no—
338#95—22no—
339#95—22no—
340#95—22no—
341#95—22no—
342#95—22no—
343#95—22no—
344#95—22no—
345#95—22no—
346#95—22no—
347#95—22no—
348#95—22no—
349#95—22no—
350#95—22no—
351#95—41no—
352#95—41no—
353#95—41no—
354#95—41no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—21no—
359C24—21no—
360C24—21no—
361C24—21no—
362C24—21no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—21no—
367C24#11712yes—
368C24#13112yes—
369C24#13112yes—
370C24C23×C411yescharacteristic
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—28no—
380C22×C4—28no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
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—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
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—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—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—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4—44no—
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—44no—
492C22×C4—44no—
493C22×C4#11712yes—
494C22×C4#11712yes—
495C22×C4#11712yes—
496C22×C4#11712yes—
497C22×C4#11712yes—
498C22×C4C4×D412yes—
499C22×C4C4×D412yes—
500C22×C4C4×D412yes—
501C22×C4C4×D412yes—
502C22×C4#13112yes—
503C22×C4#13112yes—
504C22×C4C22×D411yescharacteristic
505C22×C4C22×D411yescharacteristic
506C22×C4C2×#4111yescharacteristic
507C22×C4C2×#4111yescharacteristic
508C22×C4C2×#4111yescharacteristic
509C22×C4C2×#4111yescharacteristic
510C22×C4C2×#4111yescharacteristic
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4C2×#4111yescharacteristic
514C22×C4H(5,𝔽2)11yescharacteristic
515C22×C4H(5,𝔽2)11yescharacteristic
516C22×C42−1+411yescharacteristic
517C22×C42−1+411yescharacteristic
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×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
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—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C22⋊C4—44no—
575C22⋊C4—44no—
576C22⋊C4—44no—
577C22⋊C4—44no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—41no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—41no—
591C42—41no—
592C42—41no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—44no—
599C42—44no—
600C42#12114yes—
601C42#12314yes—
602C42#12414yes—
603C42#12614yes—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23#43314yes—
639C23C2×#11711yescharacteristic
640C23C2×#11711yescharacteristic
641C23C2×#11711yescharacteristic
642C23C2×C4×D411yescharacteristic
643C23C2×C4×D411yescharacteristic
644C23#52011yescharacteristic
645C23#52011yescharacteristic
646C23C2×#13111yescharacteristic
647C23C2×#13111yescharacteristic
648C23C2×#13111yescharacteristic
649C23C2×#13111yescharacteristic
650C23#56811yescharacteristic
651C23#56811yescharacteristic
652C23#56811yescharacteristic
653C23#56811yescharacteristic
654C2×C4—22no—
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—22no—
680C2×C4—22no—
681C2×C4—416no—
682C2×C4—416no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
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—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—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4#38814yes—
754C2×C4#38814yes—
755C2×C4C2×#12111yescharacteristic
756C2×C4C2×#12311yescharacteristic
757C2×C4C2×#12411yescharacteristic
758C2×C4C2×#12611yescharacteristic
759C2×C4#52911yescharacteristic
760C2×C4#52911yescharacteristic
761C2×C4#52911yescharacteristic
762C2×C4#52911yescharacteristic
763C2×C4#54011yescharacteristic
764C2×C4#54111yescharacteristic
765C2×C4#54211yescharacteristic
766C2×C4#54211yescharacteristic
767C2×C4#54611yescharacteristic
768C2×C4#54611yescharacteristic
769C2×C4#54611yescharacteristic
770C2×C4#54711yescharacteristic
771C2×C4#54811yescharacteristic
772C2×C4#54811yescharacteristic
773C2×C4#54811yescharacteristic
774C2×C4#55011yescharacteristic
775C2×C4#55211yescharacteristic
776C2×C4#55211yescharacteristic
777C2×C4#55211yescharacteristic
778C2×C4#55311yescharacteristic
779C2×C4#55311yescharacteristic
780C2×C4#55311yescharacteristic
781C2×C4#55511yescharacteristic
782C2×C4#55611yescharacteristic
783C8—42no—
784C8—42no—
785C8—42no—
786C8—42no—
787C8—81no—
788C8—81no—
789C8—81no—
790C8—81no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22#228311yescharacteristic
807C22C2×#38811yescharacteristic
808C22#231411yescharacteristic
809C22#235211yescharacteristic
810C22#235211yescharacteristic
811C22#235211yescharacteristic
812C22#235411yescharacteristic
813C22C2×#43311yescharacteristic
814C22#292111yescharacteristic
815C22#292211yescharacteristic
816C22#292311yescharacteristic
817C22#292411yescharacteristic
818C22#292411yescharacteristic
819C22#292411yescharacteristic
820C22#292411yescharacteristic
821C22#292411yescharacteristic
822C22#292411yescharacteristic
823C22#292511yescharacteristic
824C22#292511yescharacteristic
825C22#292911yescharacteristic
826C22#292911yescharacteristic
827C22#293011yescharacteristic
828C22#293011yescharacteristic
829C22#293311yescharacteristic
830C22#293311yescharacteristic
831C22#293311yescharacteristic
832C22#293311yescharacteristic
833C22#299211yescharacteristic
834C22#299211yescharacteristic
835C22#299311yescharacteristic
836C22#299311yescharacteristic
837C22#299411yescharacteristic
838C22#299411yescharacteristic
839C22#299511yescharacteristic
840C22#299511yescharacteristic
841C4—24no—
842C4—24no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—81no—
849C4—81no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4#242011yescharacteristic
855C4#242111yescharacteristic
856C4#242611yescharacteristic
857C4#242711yescharacteristic
858C4#248911yescharacteristic
859C4#249011yescharacteristic
860C4#249411yescharacteristic
861C4#249511yescharacteristic
862C2—44no—
863C2#1387511yescharacteristic
864C2#2077911yescharacteristic
865C2#2078511yescharacteristic
866C2#2105011yescharacteristic
867C2#2105311yescharacteristic
868C2#2192811yescharacteristic
869C2#2192811yescharacteristic
870C2#2275211yescharacteristic
871C2#2275311yescharacteristic
872C2#2275411yescharacteristic
873C2#2275411yescharacteristic
874C2#2275511yescharacteristic
875C2#2275511yescharacteristic
876C2#2280011yescharacteristic
877C2#2280111yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC25C22×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#1832C2semidirect
4. C2×#1768C2semidirect
6. #11298C2semidirect
7. #11298C2semidirect
12. #10833C2semidirect
13. #10833C2semidirect
14. #10798C2semidirect
15. #10797C2semidirect

Maximal subgroups

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

subgroupindex
C2×#18322
C2×#17972
C2×#17682
#137532
#112982
#111472
#109222
#109212
#108332
#107982
#107972