Finite Group Databasebeta

← #355423

Subgroups — #355423

Order 512.

1802 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#435C211yesmaximal, characteristic
2C2×#1869C211yesmaximal, characteristic
3C2×#1753C211yesmaximal, characteristic, complemented
4C2×#1729C211yesmaximal, characteristic, complemented
5#13839C211yesmaximal, characteristic
6#10922C211yesmaximal, characteristic, complemented
7#10921C211yesmaximal, characteristic, complemented
8#10877C211yesmaximal, characteristic, complemented
9#10876C211yesmaximal, characteristic, complemented
10#10798C211yesmaximal, characteristic, complemented
11#10798C211yesmaximal, characteristic, complemented
12#10714C211yesmaximal, characteristic, complemented
13#10714C211yesmaximal, characteristic, complemented
14#10714C211yesmaximal, characteristic, complemented
15#10713C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C2×#435—24no—
22C2×#435—24no—
23C2×#435C418yescomplemented
24C22×C4⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×#97C2211yescharacteristic
31C22×#97C2211yescharacteristic
32C22×C4×C8C2211yescharacteristic
33C2×C4×C22⋊C4C2211yescharacteristic
34C2×C4×C22⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36#1869C418yescomplemented
37#1753—24no—
38#1729—24no—
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
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55#1441C412yes—
56#1440C412yes—
57#1439C412yes—
58#1438C412yes—
59C4×#95C2211yescharacteristic
60C4×#95C2211yescharacteristic
61C23×D4C2×C411yescharacteristic
62C24×C4C2311yescharacteristic
63C24×C4C2311yescharacteristic
64C22×M16—41no—
65C22×M16—41no—
66C22×M16—41no—
67C22×M16—41no—
68C22×M16C2×C414yes—
69C22×M16D414yes—
70C22×M16D414yes—
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—22no—
75C23×C8—41no—
76C23×C8—41no—
77C23×C8—41no—
78C23×C8—41no—
79C23×C8—41no—
80C23×C8—41no—
81C23×C8—41no—
82C23×C8—41no—
83C23×C8C2×C414yes—
84C23×C8C2×C414yes—
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C23×C8C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C2×C4×D4—22no—
94C2×C4×D4—22no—
95C2×C4×D4—22no—
96C2×C4×D4—22no—
97C2×C4×D4C2×C414yes—
98C2×C4×D4C2×C414yes—
99C2×#117—22no—
100C2×#117—22no—
101C2×#117—41no—
102C2×#117—41no—
103C2×#117—41no—
104C2×#117—41no—
105C22×C4⋊C4C2×C411yescharacteristic
106C22×C4⋊C4C2×C412yes—
107C22×C22⋊C4C2×C412yes—
108C22×C22⋊C4C2×C412yes—
109C22×C22⋊C4C2×C411yescharacteristic
110C22×C22⋊C4C2×C411yescharacteristic
111C22×C22⋊C4C2×C412yes—
112C22×C22⋊C4C2×C412yes—
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118#435—232no—
119C2×C4⋊C8—22no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8C2×C414yes—
122C2×C22⋊C8—22no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—22no—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—41no—
129C2×C22⋊C8—41no—
130C2×C22⋊C8—41no—
131C2×C22⋊C8—41no—
132C2×C22⋊C8C2×C414yes—
133C2×C22⋊C8C2×C414yes—
134C2×C22⋊C8C2×C414yes—
135C2×C22⋊C8C2×C414yes—
136C2×C22⋊C8C2×C414yes—
137C2×#97—22no—
138C2×#97—22no—
139C2×#97—22no—
140C2×#97—41no—
141C2×#97—41no—
142C2×#97C2×C414yes—
143C2×C4×C8—22no—
144C2×C4×C8—41no—
145C2×C4×C8—41no—
146C4×C22⋊C4—22no—
147C4×C22⋊C4—22no—
148C4×C22⋊C4—41no—
149C4×C22⋊C4—41no—
150C4×C22⋊C4—41no—
151C4×C22⋊C4—41no—
152C2×#95C2×C412yes—
153C2×#95C2×C412yes—
154C2×#95C2×C412yes—
155C2×#95C2×C412yes—
156C2×#95C2×C412yes—
157C2×#95C2×C412yes—
158C2×#95C2×C412yes—
159#336—22no—
160#336—22no—
161#336—22no—
162#336—22no—
163#336—22no—
164#336—22no—
165#336—41no—
166#336—41no—
167#336—41no—
168#336—41no—
169#336—41no—
170#336—41no—
171#336—41no—
172#336—41no—
173#336C2×C414yes—
174#336C2×C414yes—
175C25C22×C411yescharacteristic
176C25C22×C411yescharacteristic
177C22×D4—22no—
178C22×D4—22no—
179C22×D4—24no—
180C22×D4—42no—
181C22×D4C4214yes—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
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×C4C22×C412yes—
203C23×C4C22×C412yes—
204C23×C4C22×C412yes—
205C23×C4C22×C411yescharacteristic
206C23×C4C22×C411yescharacteristic
207C23×C4C22×C411yescharacteristic
208C23×C4C22×C412yes—
209C23×C4C22×C412yes—
210C23×C4C22×C412yes—
211C23×C4C22×C411yescharacteristic
212C23×C4C22×C412yes—
213C23×C4C22×C412yes—
214C23×C4C2×D412yes—
215C23×C4C2×D412yes—
216C23×C4#4112yes—
217C23×C4#4112yes—
218C23×C4C2411yescharacteristic
219C2×M16—44no—
220C2×M16—44no—
221C2×M16—44no—
222C2×M16—44no—
223C2×M16—44no—
224C2×M16—44no—
225C2×M16C22⋊C4116yescomplemented
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—28no—
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×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—28no—
272C22×C8—44no—
273C22×C8—44no—
274C22×C8—44no—
275C22×C8—44no—
276C22×C8—44no—
277C22×C8—44no—
278C22×C8—44no—
279C22×C8—44no—
280C22×C8—44no—
281C22×C8—44no—
282C22×C8—44no—
283C22×C8—44no—
284C22×C8C22×C412yes—
285C22×C8C22×C412yes—
286C22×C8C22×C412yes—
287C22×C8C22×C412yes—
288C22×C8C22×C412yes—
289C22×C8C22×C412yes—
290C22×C8C22×C412yes—
291C22×C8C22×C412yes—
292C22×C8C2×D412yes—
293C22×C8C2×D412yes—
294C22×C8C2×D412yes—
295C22×C8C2×D412yes—
296C4×D4—28no—
297C4×D4—28no—
298C4×D4—28no—
299C4×D4—28no—
300#117—44no—
301#117—44no—
302#117—44no—
303#117—44no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4C4214yes—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
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⋊C4C4214yes—
327C2×C22⋊C4C4214yes—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
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—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42C22×C412yes—
357C2×C42C22×C412yes—
358C4⋊C8—28no—
359C22⋊C8—28no—
360C22⋊C8—28no—
361C22⋊C8—28no—
362C22⋊C8—44no—
363C22⋊C8—44no—
364#97—28no—
365#97—44no—
366C4×C8—44no—
367#95—24no—
368#95—24no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—42no—
373#95—42no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24C2×C4212yes—
392C24C2×C4212yes—
393C24C4×D412yes—
394C24C4×D412yes—
395C24#13114yes—
396C24C23×C411yescharacteristic
397C2×D4—28no—
398C2×D4—28no—
399C2×D4—44no—
400C2×D4—48no—
401C2×D4—48no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
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—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
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—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
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—22no—
481C22×C4—22no—
482C22×C4—22no—
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×C4C2×C4212yes—
500C22×C4C2×C4212yes—
501C22×C4C2×C4212yes—
502C22×C4C2×C4212yes—
503C22×C4C2×C22⋊C414yes—
504C22×C4#11714yes—
505C22×C4C4×D414yes—
506C22×C4C4×D414yes—
507C22×C4C4×D412yes—
508C22×C4C4×D412yes—
509C22×C4#13114yes—
510C22×C4C23×C411yescharacteristic
511C22×C4C23×C411yescharacteristic
512C22×C4C22×D411yescharacteristic
513C22×C4C22×D411yescharacteristic
514C22×C4C2×#4111yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4H(5,𝔽2)11yescharacteristic
517C22×C4H(5,𝔽2)11yescharacteristic
518C22×C4H(5,𝔽2)11yescharacteristic
519C22×C4H(5,𝔽2)11yescharacteristic
520C22×C4H(5,𝔽2)11yescharacteristic
521C22×C4H(5,𝔽2)11yescharacteristic
522C22×C42−1+411yescharacteristic
523C22×C42−1+411yescharacteristic
524M16—416no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—416no—
556C2×C8—416no—
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—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8C2×C22⋊C414yes—
582C2×C8C2×C22⋊C414yes—
583C4⋊C4—28no—
584C4⋊C4—48no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
604C42—41no—
605C42—41no—
606C42—41no—
607C42—41no—
608C42—41no—
609C42—41no—
610C42—41no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23C4×C22⋊C414yes—
656C23#40514yes—
657C23C22×C4211yescharacteristic
658C23C2×C4×D411yescharacteristic
659C23C2×C4×D411yescharacteristic
660C23#51811yescharacteristic
661C23#51811yescharacteristic
662C23#52011yescharacteristic
663C23#52011yescharacteristic
664C23C2×#13112yes—
665C23C2×#13112yes—
666C23#56812yes—
667C23#56812yes—
668D4—416no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
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—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4C4×C22⋊C414yes—
737C2×C4C22×C22⋊C411yescharacteristic
738C2×C4C2×#11711yescharacteristic
739C2×C4C2×C4×D411yescharacteristic
740C2×C4C2×C4×D411yescharacteristic
741C2×C4#51811yescharacteristic
742C2×C4#51811yescharacteristic
743C2×C4#51811yescharacteristic
744C2×C4#51811yescharacteristic
745C2×C4#52011yescharacteristic
746C2×C4#52011yescharacteristic
747C2×C4#52011yescharacteristic
748C2×C4#52011yescharacteristic
749C2×C4#53411yescharacteristic
750C2×C4#53411yescharacteristic
751C2×C4#53411yescharacteristic
752C2×C4#53411yescharacteristic
753C2×C4#53511yescharacteristic
754C2×C4#53611yescharacteristic
755C2×C4#53711yescharacteristic
756C2×C4#53711yescharacteristic
757C2×C4#53811yescharacteristic
758C2×C4#53811yescharacteristic
759C2×C4#53811yescharacteristic
760C2×C4#53811yescharacteristic
761C2×C4#53911yescharacteristic
762C2×C4#53911yescharacteristic
763C2×C4#53911yescharacteristic
764C2×C4#53911yescharacteristic
765C8—24no—
766C8—24no—
767C8—42no—
768C8—42no—
769C8—42no—
770C8—42no—
771C8—42no—
772C8—42no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22C2×C4×C22⋊C411yescharacteristic
796C22#227511yescharacteristic
797C22#227511yescharacteristic
798C22#232111yescharacteristic
799C22#232211yescharacteristic
800C22#232511yescharacteristic
801C22#232511yescharacteristic
802C22C2×#40511yescharacteristic
803C22#287311yescharacteristic
804C22C4×#13111yescharacteristic
805C22#287511yescharacteristic
806C22#293312yes—
807C22#293312yes—
808C22#293312yes—
809C22#293512yes—
810C22#297612yes—
811C22#297712yes—
812C22#298012yes—
813C22#298112yes—
814C22#299212yes—
815C22#299212yes—
816C22#299412yes—
817C22#299512yes—
818C4—24no—
819C4—44no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4#230811yescharacteristic
827C4#231111yescharacteristic
828C4#231811yescharacteristic
829C4#231811yescharacteristic
830C4#232111yescharacteristic
831C4#232211yescharacteristic
832C4#232511yescharacteristic
833C4#232511yescharacteristic
834C2—44no—
835C2—44no—
836C2#1378411yescharacteristic
837C2#2038711yescharacteristic
838C2#2038911yescharacteristic
839C2#2055711yescharacteristic
840C2#2056011yescharacteristic
841C2#2056311yescharacteristic
842C2#2056611yescharacteristic
843C2#2203712yes—
844C2#2207212yes—
845C2#2217112yes—
846C2#2217512yes—
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C22×C42
socleC24C23×C4
prime radicalC23×D4C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1753C2semidirect
4. C2×#1729C2semidirect
6. #10922C2semidirect
7. #10921C2semidirect
8. #10877C2semidirect
9. #10876C2semidirect
10. #10798C2semidirect
11. #10798C2semidirect
12. #10714C2semidirect
13. #10714C2semidirect
14. #10714C2semidirect
15. #10713C2semidirect
23. C2×#435C4semidirect
36. #1869C4semidirect
225. C2×M16C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4352
C2×#18692
C2×#17532
C2×#17292
#138392
#109222
#109212
#108772
#108762
#107982
#107142
#107132