Finite Group Databasebeta

← #357009

Subgroups — #357009

Order 512.

1836 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#435C211yesmaximal, characteristic
2C2×#1954C211yesmaximal, characteristic
3C2×C8×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×#1768C211yesmaximal, characteristic, complemented
5C2×#1753C211yesmaximal, characteristic, complemented
6C2×C8×C22⋊C4C211yesmaximal, characteristic, complemented
7#13847C211yesmaximal, characteristic
8#10922C211yesmaximal, characteristic, complemented
9#10921C211yesmaximal, characteristic, complemented
10#10921C211yesmaximal, characteristic, complemented
11#10921C211yesmaximal, characteristic, complemented
12#10835C211yesmaximal, characteristic, complemented
13#10715C211yesmaximal, characteristic, complemented
14#10714C211yesmaximal, characteristic, complemented
15#10694C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C2×#435—24no—
20C2×#435—24no—
21C2×#435C418yescomplemented
22C22×C4⋊C8C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×#97C2211yescharacteristic
31C22×#97C2211yescharacteristic
32C22×C4×C8C2211yescharacteristic
33C22×C4×C8C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35C22×C4×C8C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C22⋊C4C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39C2×C4×C22⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41C2×#376C2211yescharacteristic
42#1954C418yescomplemented
43C8×C4⋊C4—24no—
44#1768—24no—
45#1753—24no—
46C8×C22⋊C4—24no—
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1445C412yes—
60#1439C412yes—
61#1439C412yes—
62#1438C412yes—
63C23×D4C2×C411yescharacteristic
64C24×C4C2311yescharacteristic
65C24×C4C2311yescharacteristic
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—41no—
71C22×M16—41no—
72C22×M16C2×C414yes—
73C23×C8—22no—
74C23×C8—22no—
75C23×C8—22no—
76C23×C8—22no—
77C23×C8—41no—
78C23×C8—41no—
79C23×C8C2×C414yes—
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C2×C4×D4—22no—
89C2×C4×D4—22no—
90C2×C4×D4—22no—
91C2×C4×D4—22no—
92C2×C4×D4C2×C414yes—
93C2×C4×D4C2×C414yes—
94C22×C4⋊C4C2×C412yes—
95C22×C4⋊C4C2×C411yescharacteristic
96C22×C22⋊C4C2×C412yes—
97C22×C22⋊C4C2×C412yes—
98C22×C22⋊C4C2×C412yes—
99C22×C22⋊C4C2×C411yescharacteristic
100C22×C22⋊C4C2×C411yescharacteristic
101C22×C22⋊C4C2×C412yes—
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107#435—232no—
108C2×C4⋊C8—22no—
109C2×C4⋊C8—22no—
110C2×C4⋊C8C2×C414yes—
111C2×C4⋊C8C2×C414yes—
112C2×C4⋊C8D414yes—
113C2×C4⋊C8D414yes—
114C2×C22⋊C8—22no—
115C2×C22⋊C8—22no—
116C2×C22⋊C8—22no—
117C2×C22⋊C8—22no—
118C2×C22⋊C8—22no—
119C2×C22⋊C8—22no—
120C2×C22⋊C8—22no—
121C2×C22⋊C8—22no—
122C2×C22⋊C8—41no—
123C2×C22⋊C8—41no—
124C2×C22⋊C8—41no—
125C2×C22⋊C8—41no—
126C2×C22⋊C8C2×C414yes—
127C2×C22⋊C8C2×C414yes—
128C2×C22⋊C8C2×C414yes—
129C2×C22⋊C8C2×C414yes—
130C2×C22⋊C8C2×C414yes—
131C2×C22⋊C8C2×C414yes—
132C2×#97—22no—
133C2×#97—22no—
134C2×#97—22no—
135C2×#97—22no—
136C2×#97—41no—
137C2×#97C2×C414yes—
138C2×C4×C8—22no—
139C2×C4×C8—22no—
140C2×C4×C8—22no—
141C2×C4×C8—22no—
142C2×C4×C8—22no—
143C2×C4×C8—22no—
144C2×C4×C8—22no—
145C2×C4×C8—22no—
146C2×C4×C8—41no—
147C2×C4×C8—41no—
148C2×C4×C8—41no—
149C2×C4×C8C2×C414yes—
150C4×C4⋊C4—22no—
151C4×C4⋊C4—22no—
152C4×C22⋊C4—22no—
153C4×C22⋊C4—22no—
154C4×C22⋊C4—22no—
155C4×C22⋊C4—22no—
156C4×C22⋊C4—41no—
157C4×C22⋊C4—41no—
158C4×C22⋊C4—41no—
159C4×C22⋊C4—41no—
160#376—22no—
161#376—22no—
162C2×#95C2×C412yes—
163C2×#95C2×C412yes—
164C2×#95C2×C412yes—
165C2×#95C2×C412yes—
166C2×#95C2×C412yes—
167C2×#95C2×C412yes—
168C2×#95C2×C412yes—
169#336—22no—
170#336—22no—
171#336—22no—
172#336—22no—
173#336—22no—
174#336—22no—
175#336—22no—
176#336—22no—
177#336—22no—
178#336—41no—
179#336—41no—
180#336D414yescomplemented
181C25C22×C411yescharacteristic
182C25C22×C411yescharacteristic
183C22×D4—24no—
184C22×D4—22no—
185C22×D4—22no—
186C22×D4—42no—
187C22×D4C4214yes—
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×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4C22×C412yes—
213C23×C4C22×C411yescharacteristic
214C23×C4C22×C411yescharacteristic
215C23×C4C22×C412yes—
216C23×C4C22×C412yes—
217C23×C4C22×C412yes—
218C23×C4C22×C412yes—
219C23×C4C22×C412yes—
220C23×C4C22×C412yes—
221C23×C4C22×C412yes—
222C23×C4C22×C411yescharacteristic
223C23×C4C22×C411yescharacteristic
224C23×C4C2411yescharacteristic
225C2×M16—28no—
226C2×M16—28no—
227C2×M16—44no—
228C2×M16—44no—
229C2×M16—44no—
230C2×M16—44no—
231C2×M16—44no—
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—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—28no—
273C22×C8—28no—
274C22×C8—44no—
275C22×C8—44no—
276C22×C8—44no—
277C22×C8—44no—
278C22×C8—44no—
279C22×C8C22×C412yes—
280C22×C8C22×C412yes—
281C22×C8C22×C412yes—
282C22×C8C22×C412yes—
283C22×C8C22×C412yes—
284C22×C8C22×C412yes—
285C22×C8C22×C412yes—
286C22×C8C22×C412yes—
287C22×C8C2×D412yes—
288C22×C8C2×D412yes—
289C22×C8C2×D412yes—
290C22×C8C2×D412yes—
291C22×C8C2×D412yes—
292C22×C8C2×D412yes—
293C22×C8#4112yes—
294C22×C8#4112yes—
295C4×D4—28no—
296C4×D4—28no—
297C4×D4—28no—
298C4×D4—28no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4C4214yes—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4C4214yes—
322C2×C22⋊C4C4214yes—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
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×C42C22×C412yes—
346C2×C42C22×C412yes—
347C2×C42C2×D412yes—
348C2×C42C2×D412yes—
349C2×C42C2×D412yes—
350C2×C42#4112yes—
351C2×C42#4112yes—
352C2×C42#4112yes—
353C4⋊C8—28no—
354C4⋊C8C22⋊C4116yescomplemented
355C22⋊C8—28no—
356C22⋊C8—28no—
357C22⋊C8—28no—
358C22⋊C8—28no—
359C22⋊C8—44no—
360C22⋊C8—44no—
361#97—28no—
362#97—44no—
363C4×C8—28no—
364C4×C8—44no—
365C4×C8—44no—
366C4×C8—44no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—42no—
373#95—42no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24C2×C4212yes—
394C24C2×C4212yes—
395C24#13114yes—
396C24C23×C411yescharacteristic
397C2×D4—28no—
398C2×D4—28no—
399C2×D4—44no—
400C2×D4—48no—
401C2×D4—48no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
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—22no—
465C22×C4—22no—
466C22×C4—22no—
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×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4C2×C4212yes—
500C22×C4C2×C4212yes—
501C22×C4C2×C4212yes—
502C22×C4C2×C4212yes—
503C22×C4C4×D414yes—
504C22×C4C4×D412yes—
505C22×C4C4×D412yes—
506C22×C4C4×D412yes—
507C22×C4C4×D412yes—
508C22×C4#13114yes—
509C22×C4#13114yes—
510C22×C4C23×C411yescharacteristic
511C22×C4C23×C411yescharacteristic
512C22×C4C22×D411yescharacteristic
513C22×C4C22×D411yescharacteristic
514C22×C4C22×D411yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4C2×#4111yescharacteristic
519C22×C4C2×#4111yescharacteristic
520C22×C4H(5,𝔽2)11yescharacteristic
521C22×C4H(5,𝔽2)11yescharacteristic
522C22×C4H(5,𝔽2)11yescharacteristic
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—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—416no—
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×C8C2×C22⋊C414yes—
579C2×C8C2×C22⋊C414yes—
580C2×C8C4×D414yes—
581C2×C8C4×D414yes—
582C4⋊C4—216no—
583C4⋊C4—28no—
584C22⋊C4—216no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
604C42—41no—
605C42—41no—
606C42C2×C22⋊C414yes—
607C42#11714yes—
608C42C4×D414yes—
609C42C4×D414yes—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23#40514yes—
656C23C22×C4211yescharacteristic
657C23C2×C4×D411yescharacteristic
658C23C2×C4×D411yescharacteristic
659C23C2×C4×D411yescharacteristic
660C23C4×#4111yescharacteristic
661C23#51811yescharacteristic
662C23#52011yescharacteristic
663C23C2×#13112yes—
664C23C2×#13112yes—
665C23C2×#13112yes—
666C23#56812yes—
667D4—416no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
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—24no—
684C2×C4—24no—
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—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
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×C4C4×C22⋊C414yes—
735C2×C4C4×C22⋊C414yes—
736C2×C4C22×C22⋊C411yescharacteristic
737C2×C4C2×#11711yescharacteristic
738C2×C4C2×C4×D411yescharacteristic
739C2×C4C2×C4×D411yescharacteristic
740C2×C4C2×C4×D411yescharacteristic
741C2×C4C2×C4×D411yescharacteristic
742C2×C4C4×#4111yescharacteristic
743C2×C4C4×#4111yescharacteristic
744C2×C4#51811yescharacteristic
745C2×C4#51811yescharacteristic
746C2×C4#52011yescharacteristic
747C2×C4#52011yescharacteristic
748C2×C4D4211yescharacteristic
749C2×C4D4211yescharacteristic
750C2×C4#54611yescharacteristic
751C2×C4#54611yescharacteristic
752C2×C4#54711yescharacteristic
753C2×C4#54811yescharacteristic
754C2×C4#54811yescharacteristic
755C2×C4#55011yescharacteristic
756C2×C4#55011yescharacteristic
757C2×C4#55011yescharacteristic
758C2×C4#55311yescharacteristic
759C2×C4#55311yescharacteristic
760C2×C4#55511yescharacteristic
761C2×C4#55611yescharacteristic
762C2×C4#55911yescharacteristic
763C2×C4#55911yescharacteristic
764C8—24no—
765C8—24no—
766C8—24no—
767C8—24no—
768C8—42no—
769C8—42no—
770C8—42no—
771C8—42no—
772C22—24no—
773C22—24no—
774C22—24no—
775C22—42no—
776C22—44no—
777C22—42no—
778C22—44no—
779C22—42no—
780C22—44no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22C2×C4×C22⋊C411yescharacteristic
795C22C42×D411yescharacteristic
796C22#227511yescharacteristic
797C22#236111yescharacteristic
798C22#236311yescharacteristic
799C22#236611yescharacteristic
800C22#236711yescharacteristic
801C22C2×#40511yescharacteristic
802C22#287311yescharacteristic
803C22C4×#13111yescharacteristic
804C22C4×#13111yescharacteristic
805C22#292912yes—
806C22#292912yes—
807C22#293112yes—
808C22#293312yes—
809C22#293312yes—
810C22#293312yes—
811C22#296612yes—
812C22#296912yes—
813C22#297612yes—
814C22#297712yes—
815C22#299312yes—
816C22#299412yes—
817C4—24no—
818C4—24no—
819C4—44no—
820C4—44no—
821C4—44no—
822C4—42no—
823C4—42no—
824C4—82no—
825C4D4×C22⋊C411yescharacteristic
826C4#234111yescharacteristic
827C4#235411yescharacteristic
828C4#235711yescharacteristic
829C4#236111yescharacteristic
830C4#236311yescharacteristic
831C4#236611yescharacteristic
832C4#236711yescharacteristic
833C2—44no—
834C2—82no—
835C2#1382011yescharacteristic
836C2#2038311yescharacteristic
837C2#2038911yescharacteristic
838C2#2048411yescharacteristic
839C2#2049011yescharacteristic
840C2#2055711yescharacteristic
841C2#2056111yescharacteristic
842C2#2299212yes—
843C2#2309012yes—
844C2#2317712yes—
845C2#2321012yes—
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×C8×C4⋊C4C2semidirect
4. C2×#1768C2semidirect
5. C2×#1753C2semidirect
6. C2×C8×C22⋊C4C2semidirect
8. #10922C2semidirect
9. #10921C2semidirect
10. #10921C2semidirect
11. #10921C2semidirect
12. #10835C2semidirect
13. #10715C2semidirect
14. #10714C2semidirect
15. #10694C2semidirect
21. C2×#435C4semidirect
42. #1954C4semidirect
180. #336D4semidirect
354. C4⋊C8C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4352
C2×#19542
C2×C8×C4⋊C42
C2×#17682
C2×#17532
C2×C8×C22⋊C42
#138472
#109222
#109212
#108352
#107152
#107142
#106942