Finite Group Databasebeta

← #357181

Subgroups — #357181

Order 512.

1752 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1870C211yesmaximal, characteristic
2C2×#1869C211yesmaximal, characteristic
3C2×#1752C211yesmaximal, characteristic, complemented
4C2×#1753C211yesmaximal, characteristic, complemented
5C2×#1753C211yesmaximal, characteristic, complemented
6C2×C8×C22⋊C4C211yesmaximal, characteristic, complemented
7C4×#390C211yesmaximal, characteristic
8#10922C211yesmaximal, characteristic, complemented
9#10922C211yesmaximal, characteristic, complemented
10#10921C211yesmaximal, characteristic, complemented
11#10921C211yesmaximal, characteristic, complemented
12#10875C211yesmaximal, characteristic, complemented
13#10874C211yesmaximal, characteristic, complemented
14#10693C211yesmaximal, characteristic, complemented
15C4×#336C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×#97C2211yescharacteristic
26C22×#97C2211yescharacteristic
27C22×#97C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29C22×C4×C8C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31C2×#390C412yes—
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C22⋊C4C2211yescharacteristic
34C2×C4×C22⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36C2×C4×C22⋊C4C2211yescharacteristic
37C2×C43C2211yescharacteristic
38#1870C418yescomplemented
39#1869C418yescomplemented
40#1753—24no—
41#1753—24no—
42#1752—24no—
43C8×C22⋊C4—24no—
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1437C412yes—
59#1437C412yes—
60C4⋊#95C412yes—
61C23×D4C2×C411yescharacteristic
62C24×C4C2311yescharacteristic
63C24×C4C2311yescharacteristic
64C22×M16—22no—
65C22×M16—22no—
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—41no—
69C22×M16—41no—
70C22×M16C2×C414yes—
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—22no—
75C23×C8—41no—
76C23×C8—41no—
77C23×C8C2×C414yes—
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C2×C4×D4—41no—
87C2×C4×D4—41no—
88C2×C4×D4—41no—
89C2×C4×D4—41no—
90C2×C4×D4C2×C414yes—
91C2×C4×D4C2×C414yes—
92C22×C4⋊C4C2×C412yes—
93C22×C4⋊C4C2×C411yescharacteristic
94C22×C22⋊C4C2×C412yes—
95C22×C22⋊C4C2×C412yes—
96C22×C22⋊C4C2×C412yes—
97C22×C22⋊C4C2×C412yes—
98C22×C22⋊C4C2×C411yescharacteristic
99C22×C22⋊C4C2×C411yescharacteristic
100C22×C42C2×C412yes—
101C22×C42C2×C412yes—
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107C2×C22⋊C8—22no—
108C2×C22⋊C8—22no—
109C2×C22⋊C8—22no—
110C2×C22⋊C8—22no—
111C2×C22⋊C8—22no—
112C2×C22⋊C8—22no—
113C2×C22⋊C8—22no—
114C2×C22⋊C8—22no—
115C2×C22⋊C8—41no—
116C2×C22⋊C8—41no—
117C2×C22⋊C8—41no—
118C2×C22⋊C8—41no—
119C2×C22⋊C8C2×C414yes—
120C2×C22⋊C8C2×C414yes—
121C2×C22⋊C8C2×C414yes—
122C2×C22⋊C8C2×C414yes—
123C2×C22⋊C8C2×C414yes—
124C2×C22⋊C8C2×C414yes—
125C2×#97—22no—
126C2×#97—22no—
127C2×#97—22no—
128C2×#97—22no—
129C2×#97—22no—
130C2×#97—22no—
131C2×#97—41no—
132C2×#97—41no—
133C2×#97—41no—
134C2×C4×C8—22no—
135C2×C4×C8—22no—
136C2×C4×C8—22no—
137C2×C4×C8—22no—
138C2×C4×C8—22no—
139C2×C4×C8—22no—
140C2×C4×C8—41no—
141C2×C4×C8—41no—
142C2×C4×C8—41no—
143#390—28no—
144C4×C4⋊C4—41no—
145C4×C4⋊C4—41no—
146C4×C22⋊C4—22no—
147C4×C22⋊C4—22no—
148C4×C22⋊C4—22no—
149C4×C22⋊C4—22no—
150C4×C22⋊C4—22no—
151C4×C22⋊C4—22no—
152C4×C22⋊C4—22no—
153C4×C22⋊C4—22no—
154C2×#95C2×C412yes—
155C2×#95C2×C412yes—
156C2×#95C2×C412yes—
157C2×#95C2×C412yes—
158C2×#95C2×C412yes—
159C43—41no—
160C43—41no—
161#336—22no—
162#336—22no—
163#336—22no—
164#336—22no—
165#336—22no—
166#336—22no—
167#336—41no—
168#336—41no—
169#336C2×C414yes—
170#336C2×C414yes—
171#336C2×C414yes—
172#336C2×C414yes—
173#336D414yescomplemented
174#336D414yescomplemented
175C25C22×C411yescharacteristic
176C25C22×C411yescharacteristic
177C22×D4—24no—
178C22×D4—24no—
179C22×D4—41no—
180C22×D4—41no—
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×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4C22×C412yes—
207C23×C4C22×C411yescharacteristic
208C23×C4C22×C411yescharacteristic
209C23×C4C22×C411yescharacteristic
210C23×C4C22×C412yes—
211C23×C4C22×C412yes—
212C23×C4C22×C412yes—
213C23×C4C22×C412yes—
214C23×C4C22×C412yes—
215C23×C4C22×C412yes—
216C23×C4C22×C411yescharacteristic
217C23×C4C22×C412yes—
218C23×C4C2411yescharacteristic
219C2×M16—28no—
220C2×M16—28no—
221C2×M16—44no—
222C2×M16—44no—
223C2×M16—44no—
224C2×M16—44no—
225C2×M16—44no—
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×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—28no—
267C22×C8—28no—
268C22×C8—44no—
269C22×C8—44no—
270C22×C8—44no—
271C22×C8—44no—
272C22×C8—44no—
273C22×C8C22×C412yes—
274C22×C8C22×C412yes—
275C22×C8C22×C412yes—
276C22×C8C22×C412yes—
277C22×C8C22×C412yes—
278C22×C8C22×C412yes—
279C22×C8C22×C412yes—
280C22×C8C22×C412yes—
281C22×C8C2×D412yes—
282C22×C8C2×D412yes—
283C22×C8C2×D412yes—
284C22×C8C2×D412yes—
285C22×C8#4112yes—
286C22×C8#4112yes—
287C22×C8#4112yes—
288C22×C8#4112yes—
289C4×D4—44no—
290C4×D4—44no—
291C4×D4—44no—
292C4×D4—44no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4C4214yes—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—41no—
311C2×C22⋊C4—41no—
312C2×C22⋊C4—41no—
313C2×C22⋊C4—41no—
314C2×C22⋊C4C4214yes—
315C2×C22⋊C4C4214yes—
316C2×C22⋊C4M1618yescomplemented
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—21no—
328C2×C42—21no—
329C2×C42—24no—
330C2×C42—24no—
331C2×C42—24no—
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—42no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42C22×C412yes—
348C2×C42C22×C412yes—
349C2×C42C2×D412yes—
350C2×C42C2×D412yes—
351C2×C42#4112yes—
352C2×C42#4112yes—
353C22⋊C8—28no—
354C22⋊C8—28no—
355C22⋊C8—28no—
356C22⋊C8—28no—
357C22⋊C8—44no—
358C22⋊C8—44no—
359#97—44no—
360#97—44no—
361#97—44no—
362C4×C8—44no—
363C4×C8—44no—
364C4×C8—44no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—42no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24C2×C4212yes—
390C24C2×C4212yes—
391C24C2×M1614yes—
392C24C23×C411yescharacteristic
393C2×D4—28no—
394C2×D4—28no—
395C2×D4—44no—
396C2×D4—48no—
397C2×D4—48no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
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—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—41no—
496C22×C4C2×C4212yes—
497C22×C4C2×C4212yes—
498C22×C4C2×C4212yes—
499C22×C4C2×C4212yes—
500C22×C4C4×D414yes—
501C22×C4C4×D414yes—
502C22×C4C2×M1614yes—
503C22×C4C2×M1614yes—
504C22×C4#13114yes—
505C22×C4#13114yes—
506C22×C4C23×C411yescharacteristic
507C22×C4C23×C411yescharacteristic
508C22×C4C22×D411yescharacteristic
509C22×C4C22×D411yescharacteristic
510C22×C4C2×#4111yescharacteristic
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4C2×#4111yescharacteristic
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
520M16—416no—
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—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—22no—
556C2×C8—22no—
557C2×C8—416no—
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×C8C4×D414yes—
575C2×C8C4×D414yes—
576C2×C8C4×D414yes—
577C2×C8C4×D414yes—
578C4⋊C4—44no—
579C4⋊C4—48no—
580C22⋊C4—216no—
581C22⋊C4—44no—
582C22⋊C4—44no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C42—22no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—48no—
599C42—48no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
604C42—41no—
605C42—41no—
606C42—41no—
607C42—41no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
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—
653C23C4×M1614yes—
654C23C22×C4211yescharacteristic
655C23C2×C4×D411yescharacteristic
656C23C2×C4×D411yescharacteristic
657C23C4×#4111yescharacteristic
658C23C4×#4111yescharacteristic
659C23#51811yescharacteristic
660C23#51811yescharacteristic
661C23C22×M1612yes—
662C23C2×#13112yes—
663C23C2×#13112yes—
664C23#56812yes—
665D4—416no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
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#40514yes—
733C2×C4#43518yes—
734C2×C4C2×C4×D411yescharacteristic
735C2×C4C2×C4×D411yescharacteristic
736C2×C4C2×C4×D411yescharacteristic
737C2×C4C2×C4×D411yescharacteristic
738C2×C4C4×#4111yescharacteristic
739C2×C4C4×#4111yescharacteristic
740C2×C4C4×#4111yescharacteristic
741C2×C4C4×#4111yescharacteristic
742C2×C4#51811yescharacteristic
743C2×C4#51811yescharacteristic
744C2×C4#51811yescharacteristic
745C2×C4#51811yescharacteristic
746C2×C4D4211yescharacteristic
747C2×C4#54611yescharacteristic
748C2×C4#54611yescharacteristic
749C2×C4#54611yescharacteristic
750C2×C4#54611yescharacteristic
751C2×C4#55011yescharacteristic
752C2×C4#55011yescharacteristic
753C2×C4#55111yescharacteristic
754C2×C4#55111yescharacteristic
755C2×C4#55311yescharacteristic
756C2×C4#55311yescharacteristic
757C2×C4#55311yescharacteristic
758C2×C4#55311yescharacteristic
759C2×C4#55511yescharacteristic
760C2×C4#55511yescharacteristic
761C2×C4#55911yescharacteristic
762C8—24no—
763C8—24no—
764C8—24no—
765C8—24no—
766C8—42no—
767C8—42no—
768C8—42no—
769C8—42no—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22C42×D411yescharacteristic
793C22C42×D411yescharacteristic
794C22#227311yescharacteristic
795C22#236411yescharacteristic
796C22#236411yescharacteristic
797C22#236611yescharacteristic
798C22#237211yescharacteristic
799C22C2×C4×M1611yescharacteristic
800C22C2×#40511yescharacteristic
801C22C4×#13111yescharacteristic
802C22#287511yescharacteristic
803C22C2×#43512yes—
804C22#293112yes—
805C22D4×M1612yes—
806C22#293512yes—
807C22#296512yes—
808C22#296612yes—
809C22#296912yes—
810C22#297012yes—
811C22#297412yes—
812C22#297412yes—
813C22#297612yes—
814C22#298112yes—
815C4—24no—
816C4—28no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—44no—
821C4—44no—
822C4—82no—
823C4#235811yescharacteristic
824C4#235811yescharacteristic
825C4#236311yescharacteristic
826C4#236311yescharacteristic
827C4#236311yescharacteristic
828C4#236311yescharacteristic
829C4#237411yescharacteristic
830C4#237411yescharacteristic
831C2—44no—
832C2—82no—
833C2#1382411yescharacteristic
834C2#2048511yescharacteristic
835C2C4×#43511yescharacteristic
836C2#2049111yescharacteristic
837C2#2049511yescharacteristic
838C2#2052511yescharacteristic
839C2#2053111yescharacteristic
840C2#2311712yes—
841C2#2311812yes—
842C2#2317412yes—
843C2#2327012yes—
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×#1752C2semidirect
4. C2×#1753C2semidirect
5. C2×#1753C2semidirect
6. C2×C8×C22⋊C4C2semidirect
8. #10922C2semidirect
9. #10922C2semidirect
10. #10921C2semidirect
11. #10921C2semidirect
12. #10875C2semidirect
13. #10874C2semidirect
14. #10693C2semidirect
15. C4×#336C2semidirect
38. #1870C4semidirect
39. #1869C4semidirect
173. #336D4semidirect
174. #336D4semidirect
316. C2×C22⋊C4M16semidirect

Maximal subgroups

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

subgroupindex
C2×#18702
C2×#18692
C2×#17522
C2×#17532
C2×C8×C22⋊C42
C4×#3902
#109222
#109212
#108752
#108742
#106932
C4×#3362