Finite Group Databasebeta

← #520619

Subgroups — #520619

Order 512.

4326 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2283C211yesmaximal, characteristic, complemented
2C2×#2280C211yesmaximal, characteristic
3C22×C4×C22⋊C4C211yesmaximal, characteristic
4#14685C211yesmaximal, characteristic, complemented
5#14684C211yesmaximal, characteristic, complemented
6#14681C211yesmaximal, characteristic
7#13919C212yesmaximal, complemented
8#13915C212yesmaximal, complemented
9#13898C212yesmaximal, complemented
10#13892C212yesmaximal, complemented
11#13891C212yesmaximal, complemented
12#13888C212yesmaximal, complemented
13#13878C212yesmaximal, complemented
14#13873C212yesmaximal
15#13873C212yesmaximal
16#13822C212yesmaximal, complemented
17#13816C212yesmaximal, complemented
18#13799C212yesmaximal, complemented
19C4×#381C211yesmaximal, characteristic, complemented
20C25×C4C2211yescharacteristic
21C22×#117C2212yes—
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C42C2211yescharacteristic
25C23×C42C2211yescharacteristic
26C2×#388C2214yes—
27C2×#388C2214yes—
28#2283—28no—
29C2×#383C2212yescomplemented
30C2×#382C2212yescomplemented
31#2280—28no—
32C2×#381C2212yes—
33C2×#381C2211yescharacteristic
34C2×#381C2211yescharacteristic
35C2×#381C2211yescharacteristic
36C2×#381C2211yescharacteristic
37C2×#380C2212yes—
38C2×#380C2212yes—
39C2×#380C2212yes—
40C2×#380C2212yes—
41C2×#379C2212yes—
42C2×#379C2212yes—
43C2×C4×C4⋊C4C2212yescomplemented
44C2×C4×C22⋊C4C4116yescomplemented
45C2×C4×C22⋊C4C2212yes—
46C2×C4×C22⋊C4C2212yes—
47C2×C4×C22⋊C4C2212yes—
48C2×C4×C22⋊C4C2212yes—
49C2×C4×C22⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×#376C2212yescomplemented
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60#1444C2214yescomplemented
61#1442C2214yescomplemented
62#1440C2214yes—
63#1440C2214yes—
64#1439C2214yes—
65#1439C2214yes—
66#1437C2214yes—
67#1437C2214yes—
68#1436C2214yescomplemented
69#1436C2214yescomplemented
70#1436C2214yescomplemented
71#1436C2214yescomplemented
72C4⋊#95C2212yescomplemented
73C4⋊#95C2212yescomplemented
74#1434C2214yescomplemented
75#1434C2212yescomplemented
76#1434C2212yescomplemented
77#1434C2212yescomplemented
78#1434C2212yescomplemented
79#1434C2212yescomplemented
80#1434C2212yescomplemented
81#1434C2212yescomplemented
82#1434C2212yescomplemented
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C22⋊#95C2212yes—
88C22⋊#95C2212yes—
89C22⋊#95C2212yes—
90C22⋊#95C2212yes—
91C4×#95C2212yescomplemented
92C4×#95C2212yescomplemented
93C4×#95C2214yescomplemented
94C26C2311yescharacteristic
95C24×C4—24no—
96C24×C4—28no—
97C24×C4—24no—
98C24×C4—44no—
99C24×C4C2×C418yes—
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C2×#117—28no—
111C2×#117—28no—
112C2×#117—44no—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C22⋊C4—28no—
117C22×C22⋊C4—28no—
118C22×C22⋊C4C2×C418yes—
119C22×C22⋊C4C2×C418yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2311yescharacteristic
126C22×C22⋊C4C2311yescharacteristic
127C22×C22⋊C4C2311yescharacteristic
128C22×C22⋊C4C2311yescharacteristic
129C22×C22⋊C4C2311yescharacteristic
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2311yescharacteristic
136C22×C42—24no—
137C22×C42—24no—
138C22×C42—44no—
139C22×C42C2×C418yes—
140C22×C42C2×C418yes—
141C22×C42C2314yes—
142C22×C42C2314yes—
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2314yes—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#388—216no—
153#388—216no—
154#383—28no—
155#382—28no—
156#381—24no—
157#381—24no—
158#381—28no—
159#381—24no—
160#381D418yes—
161#380—28no—
162#380—28no—
163#380—28no—
164#380—44no—
165#379—28no—
166#379—44no—
167C4×C4⋊C4—28no—
168C4×C22⋊C4—28no—
169C4×C22⋊C4—28no—
170C4×C22⋊C4—28no—
171C4×C22⋊C4—44no—
172C4×C22⋊C4C2×C418yes—
173C4×C22⋊C4C2×C418yes—
174C4×C22⋊C4C2×C418yes—
175C4×C22⋊C4C2×C418yes—
176C4×C22⋊C4C2×C418yes—
177C4×C22⋊C4C2×C418yes—
178C4×C22⋊C4C2×C418yes—
179C4×C22⋊C4C2×C418yes—
180#376—28no—
181C2×#95C2×C418yes—
182C2×#95C2×C418yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2312yes—
212C2×#95C2312yes—
213C25—24no—
214C25—24no—
215C25—24no—
216C25—22no—
217C25—22no—
218C25—24no—
219C25—42no—
220C25—42no—
221C25C22×C414yes—
222C25C2411yescharacteristic
223C25C2411yescharacteristic
224C25C2411yescharacteristic
225C23×C4—22no—
226C23×C4—24no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—232no—
237C23×C4—232no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—416no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—432no—
264C23×C4—432no—
265C23×C4C22×C414yes—
266C23×C4C22×C414yes—
267C23×C4C22×C414yes—
268C23×C4C22×C414yes—
269C23×C4C22×C414yes—
270C23×C4C22×C414yes—
271C23×C4C22×C414yes—
272C23×C4C22×C414yes—
273C23×C4C22×C414yes—
274C23×C4C22×C414yes—
275C23×C4C2×D414yes—
276C23×C4#4118yes—
277C23×C4#4114yes—
278C23×C4C2414yes—
279C23×C4C2414yes—
280C23×C4C2414yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2414yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294#117—432no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—232no—
313C2×C22⋊C4—232no—
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—28no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4C22×C414yes—
336C2×C22⋊C4C22×C414yes—
337C2×C22⋊C4C22×C414yes—
338C2×C22⋊C4C22×C414yes—
339C2×C22⋊C4C22×C414yes—
340C2×C22⋊C4C22×C414yes—
341C2×C22⋊C4C22×C414yes—
342C2×C22⋊C4C22×C414yes—
343C2×C22⋊C4C2×D418yes—
344C2×C22⋊C4#4118yes—
345C2×C22⋊C4#4118yes—
346C2×C42—232no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—28no—
356C2×C42—28no—
357C2×C42—28no—
358C2×C42—28no—
359C2×C42—28no—
360C2×C42—44no—
361C2×C42—416no—
362C2×C42—42no—
363C2×C42—42no—
364C2×C42—42no—
365C2×C42—42no—
366C2×C42—44no—
367C2×C42—44no—
368C2×C42—44no—
369C2×C42C22×C414yes—
370C2×C42C22×C414yes—
371C2×C42C22×C414yes—
372C2×C42C22×C414yes—
373C2×C42C22×C414yes—
374C2×C42C22×C414yes—
375C2×C42C22×C414yes—
376C2×C42C22×C414yes—
377#95—28no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—28no—
382#95—24no—
383#95—28no—
384#95—28no—
385#95—24no—
386#95—24no—
387#95—28no—
388#95—28no—
389#95—28no—
390#95—28no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95C22×C414yes—
398#95C22×C414yes—
399#95C22×C414yes—
400#95C22×C414yes—
401#95C22×C414yes—
402#95C22×C414yes—
403#95C22×C414yes—
404#95C22×C414yes—
405#95C2×D418yes—
406#95C2×D418yes—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—232no—
412C24—28no—
413C24—28no—
414C24—28no—
415C24—21no—
416C24—21no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—21no—
422C24—21no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—28no—
430C24—28no—
431C24—44no—
432C24—44no—
433C24—48no—
434C24—48no—
435C24—48no—
436C24—48no—
437C24—416no—
438C24—416no—
439C24—416no—
440C24—48no—
441C24—48no—
442C24C23×C412yes—
443C24C23×C412yes—
444C24C23×C412yes—
445C24C22×D412yes—
446C24C2×#4114yes—
447C24C2×#4114yes—
448C24C2×#4114yes—
449C24C2×#4112yes—
450C24H(5,𝔽2)14yes—
451C24C2511yescharacteristic
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—216no—
457C22×C4—216no—
458C22×C4—216no—
459C22×C4—216no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
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—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—24no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—4128no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—416no—
559C22×C4—416no—
560C22×C4#117116yes—
561C22×C4C4×D4116yes—
562C22×C4C23×C412yes—
563C22×C4C23×C412yes—
564C22×C4C23×C412yes—
565C22×C4C23×C412yes—
566C22×C4C23×C412yes—
567C22×C4C23×C412yes—
568C22×C4C23×C412yes—
569C22×C4C23×C412yes—
570C22×C4C23×C412yes—
571C22×C4C23×C412yes—
572C22×C4C23×C412yes—
573C22×C4C23×C412yes—
574C22×C4C22×D418yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C2×#4114yes—
578C22×C4C2×#4114yes—
579C22×C4C2×#4114yes—
580C22×C4C2×#4114yes—
581C22×C4C2×#4114yes—
582C22×C4C2×#4114yes—
583C22×C4C2×#4112yes—
584C22×C4C2×#4112yes—
585C4⋊C4—416no—
586C4⋊C4—416no—
587C4⋊C4—88no—
588C22⋊C4—28no—
589C22⋊C4—28no—
590C22⋊C4—216no—
591C22⋊C4—28no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—416no—
596C22⋊C4—416no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—88no—
601C22⋊C4—88no—
602C22⋊C4#117116yescomplemented
603C22⋊C4#117116yescomplemented
604C42—28no—
605C42—28no—
606C42—28no—
607C42—28no—
608C42—44no—
609C42—44no—
610C42—44no—
611C42—44no—
612C42—416no—
613C42—416no—
614C42—88no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—28no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—28no—
625C23—28no—
626C23—28no—
627C23—232no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—28no—
641C23—28no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—28no—
647C23—28no—
648C23—416no—
649C23—416no—
650C23—416no—
651C23—416no—
652C23—464no—
653C23—464no—
654C23—416no—
655C23—416no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23C2×#11714yes—
669C23C2×#11714yes—
670C23C2×#11714yes—
671C23C2×C4×D414yes—
672C23#51814yes—
673C23#54618yes—
674C23#55118yes—
675C23C24×C411yescharacteristic
676C23C23×D411yescharacteristic
677C23C22×#4112yes—
678C23C22×#4112yes—
679C23C22×#4112yes—
680C23C22×#4111yescharacteristic
681C23C2×H(5,𝔽2)12yes—
682C23#58512yes—
683C23#58512yes—
684C2×C4—232no—
685C2×C4—232no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—416no—
732C2×C4—416no—
733C2×C4—416no—
734C2×C4—416no—
735C2×C4—416no—
736C2×C4—416no—
737C2×C4—416no—
738C2×C4—416no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4C2×#11714yes—
771C2×C4C2×#11714yes—
772C2×C4C2×#11714yes—
773C2×C4C2×#11714yes—
774C2×C4C2×#11714yes—
775C2×C4C2×#11714yes—
776C2×C4C2×C4×D414yes—
777C2×C4C2×C4×D414yes—
778C22—216no—
779C22—24no—
780C22—24no—
781C22—216no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—464no—
793C22—48no—
794C22—48no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—48no—
800C22—48no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22#234218yes—
806C22C22×#11711yescharacteristic
807C22C22×#11711yescharacteristic
808C22C22×#11711yescharacteristic
809C22C22×C4×D411yescharacteristic
810C22C2×#51811yescharacteristic
811C22#342811yescharacteristic
812C22#342811yescharacteristic
813C22#344414yes—
814C22C2×#54612yes—
815C22D4×#4112yes—
816C22D4×#4112yes—
817C22C2×#55112yes—
818C22#347512yes—
819C22#347512yes—
820C22#349314yes—
821C22#351314yes—
822C22#351314yes—
823C4—24no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—24no—
828C4—24no—
829C4—24no—
830C4—24no—
831C4—48no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—84no—
837C4—84no—
838C4—84no—
839C2—28no—
840C2—44no—
841C2—44no—
842C2#3401211yescharacteristic
843C2C2×#234211yescharacteristic
844C2D4×#11711yescharacteristic
845C2D4×#11711yescharacteristic
846C2#3417911yescharacteristic
847C2#3419011yescharacteristic
848C2#3419011yescharacteristic
849C2#3613814yes—
850C2#3619814yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2283C2semidirect
4. #14685C2semidirect
5. #14684C2semidirect
7. #13919C2semidirect
8. #13915C2semidirect
9. #13898C2semidirect
10. #13892C2semidirect
11. #13891C2semidirect
12. #13888C2semidirect
13. #13878C2semidirect
16. #13822C2semidirect
17. #13816C2semidirect
18. #13799C2semidirect
19. C4×#381C2semidirect
29. C2×#383C22semidirect
30. C2×#382C22semidirect
43. C2×C4×C4⋊C4C22semidirect
44. C2×C4×C22⋊C4C4semidirect
57. C2×#376C22semidirect
60. #1444C22semidirect
61. #1442C22semidirect
68. #1436C22semidirect
69. #1436C22semidirect
70. #1436C22semidirect
71. #1436C22semidirect
72. C4⋊#95C22semidirect
73. C4⋊#95C22semidirect
74. #1434C22semidirect
75. #1434C22semidirect
76. #1434C22semidirect
77. #1434C22semidirect
78. #1434C22semidirect
79. #1434C22semidirect
80. #1434C22semidirect
81. #1434C22semidirect
82. #1434C22semidirect
91. C4×#95C22semidirect
92. C4×#95C22semidirect
93. C4×#95C22semidirect
602. C22⋊C4#117semidirect
603. C22⋊C4#117semidirect

Maximal subgroups

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

subgroupindex
C2×#22832
C2×#22802
C22×C4×C22⋊C42
#146852
#146842
#146812
#139192
#139152
#138982
#138922
#138912
#138882
#138782
#138732
#138222
#138162
#137992
C4×#3812