Finite Group Databasebeta

← C4×#2535 #514896

Subgroups — C4×#2535 #514896

Order 512.

4726 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2535C211yesmaximal, characteristic
2C2×C4×#121C212yesmaximal, complemented
3C2×C42×D4C211yesmaximal, characteristic, complemented
4C2×C42×D4C211yesmaximal, characteristic, complemented
5#14225C212yesmaximal, complemented
6#14175C212yesmaximal, complemented
7#14150C211yesmaximal, characteristic, complemented
8#14068C214yesmaximal, complemented
9#13993C212yesmaximal, complemented
10#13970C212yesmaximal, complemented
11#13941C211yesmaximal, characteristic, complemented
12#13905C211yesmaximal, characteristic, complemented
13C4×#397C212yesmaximal, complemented
14C4×#392C212yesmaximal, complemented
15C4×#382C211yesmaximal, characteristic, complemented
16C4×#380C212yesmaximal, complemented
17C4×#386C214yesmaximal, complemented
18C22×#121C2212yes—
19C22×C4×D4C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2214yes—
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C23×C42C2212yes—
27C23×C42C2212yes—
28#2535C4116yesdirect product factor
29C2×#397C2212yes—
30C2×#392C2212yes—
31C4×#121—216no—
32C2×#390C2212yes—
33C2×#389C2212yes—
34C2×#388C2214yes—
35C2×#386C2214yes—
36C2×#386C2214yes—
37C2×#386C2214yes—
38C2×#382C2211yescharacteristic
39C2×#382C2211yescharacteristic
40C2×#380C2212yes—
41C2×#380C2212yes—
42C2×#380C2212yes—
43C42×D4—28no—
44C42×D4—28no—
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C22⋊C4C2212yes—
53C2×C4×C22⋊C4C2214yes—
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2214yes—
60C2×C43C2211yescharacteristic
61#1445C2212yes—
62#1444C2212yes—
63#1443C2214yes—
64#1442C2212yes—
65#1440C2214yes—
66#1439C2212yes—
67#1439C2214yes—
68#1439C2212yes—
69#1438C2212yes—
70#1438C2214yes—
71#1437C2214yes—
72#1437C2214yes—
73#1436C2214yes—
74#1436C2214yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78#1434C2212yes—
79#1434C2214yes—
80#1434C2212yes—
81C22⋊#95C2214yes—
82C22⋊#95C2214yes—
83C22⋊#95C2214yes—
84C4×#95C2212yes—
85C4×#95C2214yes—
86C4×#95C2212yes—
87C23×D4C2311yescharacteristic
88C23×D4C2314yes—
89C23×D4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2312yes—
92C24×C4C2312yes—
93C24×C4C2312yes—
94C24×C4C2312yes—
95C24×C4C2312yes—
96C2×#121—28no—
97C2×#121—28no—
98C2×#121C2×C4116yescomplemented
99C2×C4×D4—24no—
100C2×C4×D4—28no—
101C2×C4×D4—216no—
102C2×C4×D4—216no—
103C2×C4×D4—24no—
104C2×C4×D4—28no—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4—24no—
111C2×C4×D4—24no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—48no—
115C2×C4×D4C2×C418yescomplemented
116C2×C4×D4C2×C418yescomplemented
117C2×C4×D4D418yescomplemented
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C42—28no—
140C22×C42—28no—
141C22×C42—28no—
142C22×C42—28no—
143C22×C42—48no—
144C22×C42C2312yes—
145C22×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2312yes—
148C22×C42C2314yes—
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#397C2×C4116yescomplemented
159#392C2×C4116yescomplemented
160#390—28no—
161#389—28no—
162#388—216no—
163#386—216no—
164#386—216no—
165#386C2×C4132yescomplemented
166#382—24no—
167#382C2×C418yescomplemented
168#380—28no—
169#380—28no—
170#380C2×C4116yescomplemented
171C4×C4⋊C4—24no—
172C4×C4⋊C4—24no—
173C4×C4⋊C4—24no—
174C4×C4⋊C4—24no—
175C4×C4⋊C4—24no—
176C4×C4⋊C4—24no—
177C4×C4⋊C4—28no—
178C4×C22⋊C4—216no—
179C4×C22⋊C4—28no—
180C4×C22⋊C4—28no—
181C4×C22⋊C4—28no—
182C4×C22⋊C4—28no—
183C4×C22⋊C4—28no—
184C4×C22⋊C4—28no—
185C4×C22⋊C4—48no—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C43D418yescomplemented
208C25C2412yes—
209C25C2412yes—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—28no—
213C22×D4—28no—
214C22×D4—28no—
215C22×D4—28no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—44no—
223C22×D4—44no—
224C22×D4C22×C414yes—
225C22×D4C22×C4116yes—
226C22×D4C22×C414yes—
227C22×D4C2×D414yes—
228C22×D4#4114yes—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—28no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—28no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—28no—
255C23×C4—24no—
256C23×C4—42no—
257C23×C4—44no—
258C23×C4—42no—
259C23×C4—44no—
260C23×C4—44no—
261C23×C4C22×C418yes—
262C23×C4C22×C418yes—
263C23×C4C2×D418yes—
264C23×C4#4118yes—
265C23×C4C2414yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2414yes—
269C23×C4C2411yescharacteristic
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280#121—264no—
281C4×D4—232no—
282C4×D4—232no—
283C4×D4—232no—
284C4×D4—232no—
285C4×D4—232no—
286C4×D4—232no—
287C4×D4—464no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4C22×C414yes—
309C2×C4⋊C4C22×C414yes—
310C2×C4⋊C4C22×C418yes—
311C2×C4⋊C4C2×D414yes—
312C2×C4⋊C4#4114yes—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4C22×C418yes—
344C2×C22⋊C4C22×C418yes—
345C2×C22⋊C4C22×C4116yes—
346C2×C22⋊C4C22×C4116yes—
347C2×C22⋊C4C2×D418yes—
348C2×C22⋊C4#4118yes—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—24no—
354C2×C42—28no—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—28no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—28no—
369C2×C42—28no—
370C2×C42—432no—
371C2×C42—44no—
372C2×C42—44no—
373C2×C42—42no—
374C2×C42—432no—
375C2×C42C22×C414yes—
376C2×C42C2×D414yes—
377C2×C42C2×D414yes—
378C2×C42C2×D414yes—
379C2×C42C2×D414yes—
380C2×C42C2×D414yes—
381C2×C42C2×D414yes—
382C2×C42C2×D414yes—
383C2×C42C2×D414yes—
384C2×C42#4114yes—
385C2×C42#4114yes—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—28no—
393#95—28no—
394#95—28no—
395#95—28no—
396#95—24no—
397#95—24no—
398#95—28no—
399#95—28no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95C22×C4116yes—
405#95C22×C418yes—
406#95C22×C418yes—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—24no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—24no—
424C24—22no—
425C24—24no—
426C24—22no—
427C24C23×C414yes—
428C24C23×C414yes—
429C24C22×D414yes—
430C24C2×#4114yes—
431C24C2×#4114yes—
432C24C2×#4114yes—
433C24C2511yescharacteristic
434C2×D4—28no—
435C2×D4—28no—
436C2×D4—216no—
437C2×D4—216no—
438C2×D4—232no—
439C2×D4—232no—
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—28no—
443C2×D4—28no—
444C2×D4—28no—
445C2×D4—28no—
446C2×D4—28no—
447C2×D4—416no—
448C2×D4—416no—
449C2×D4—416no—
450C2×D4—416no—
451C2×D4—416no—
452C2×D4C4×D4116yescomplemented
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—216no—
463C22×C4—216no—
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—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—216no—
505C22×C4—216no—
506C22×C4—216no—
507C22×C4—216no—
508C22×C4—216no—
509C22×C4—216no—
510C22×C4—216no—
511C22×C4—232no—
512C22×C4—216no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—416no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—416no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—416no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—416no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—416no—
544C22×C4—48no—
545C22×C4C23×C418yes—
546C22×C4C23×C414yes—
547C22×C4C23×C414yes—
548C22×C4C23×C412yes—
549C22×C4C23×C412yes—
550C22×C4C23×C412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D414yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C2×#4114yes—
563C22×C4C2×#4114yes—
564C22×C4C2×#4114yes—
565C22×C4C2×#4112yes—
566C22×C4C2×#4112yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4114yes—
569C22×C4C2×#4112yes—
570C22×C4C2×#4112yes—
571C22×C4C2×#4112yes—
572C22×C4C2×#4112yes—
573C22×C4C2×#4112yes—
574C22×C4C2×#4114yes—
575C22×C4H(5,𝔽2)14yes—
576C4⋊C4—28no—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—28no—
580C4⋊C4—216no—
581C4⋊C4—28no—
582C4⋊C4—28no—
583C4⋊C4—416no—
584C4⋊C4—48no—
585C22⋊C4—216no—
586C22⋊C4—216no—
587C22⋊C4—232no—
588C22⋊C4—216no—
589C22⋊C4—216no—
590C22⋊C4—216no—
591C22⋊C4—216no—
592C22⋊C4—416no—
593C22⋊C4—416no—
594C22⋊C4—416no—
595C22⋊C4—416no—
596C22⋊C4—416no—
597C42—28no—
598C42—28no—
599C42—28no—
600C42—28no—
601C42—44no—
602C42—48no—
603C42—48no—
604C42—48no—
605C42—48no—
606C42—48no—
607C42—48no—
608C42—416no—
609C42C4×D4116yescomplemented
610C42#121116yes—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—28no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—28no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—28no—
631C23—28no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—28no—
637C23—24no—
638C23—24no—
639C23—28no—
640C23—24no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—44no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—44no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—44no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—44no—
664C23—44no—
665C23—42no—
666C23—42no—
667C23C2×C4×D418yes—
668C23C4×#4118yes—
669C23C24×C411yescharacteristic
670C23C23×D411yescharacteristic
671C23C23×D411yescharacteristic
672C23C22×#4111yescharacteristic
673C23C22×#4111yescharacteristic
674C23C22×#4111yescharacteristic
675C23C22×#4111yescharacteristic
676C23C22×#4112yes—
677C23C22×#4112yes—
678C23C2×H(5,𝔽2)12yes—
679C23#58512yes—
680D4—232no—
681D4—232no—
682D4—464no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—24no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—28no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—28no—
720C2×C4—432no—
721C2×C4—432no—
722C2×C4—432no—
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×C4—42no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—432no—
751C2×C4—432no—
752C2×C4—432no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4C2×C4×D414yes—
761C2×C4C2×C4×D414yes—
762C2×C4C2×C4×D414yes—
763C2×C4C2×C4×D414yes—
764C2×C4C4×#4114yes—
765C2×C4C2×#12114yes—
766C2×C4C2×#12114yes—
767C2×C4C2×#12114yes—
768C2×C4#52514yes—
769C2×C4#52514yes—
770C2×C4#52514yes—
771C2×C4#52914yes—
772C2×C4#53214yes—
773C2×C4#53514yes—
774C2×C4#54618yes—
775C2×C4#55318yes—
776C22—28no—
777C22—216no—
778C22—28no—
779C22—28no—
780C22—28no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—48no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—48no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—48no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22C22×C4×D411yescharacteristic
803C22C22×C4×D411yescharacteristic
804C22C2×C4×#4112yes—
805C22C2×C4×#4111yescharacteristic
806C22C4×H(5,𝔽2)12yes—
807C22C22×#12111yescharacteristic
808C22C2×#52511yescharacteristic
809C22C2×#52511yescharacteristic
810C22C2×#52511yescharacteristic
811C22C2×#52911yescharacteristic
812C22C2×#53211yescharacteristic
813C22#344412yes—
814C22C2×#53511yescharacteristic
815C22#344911yescharacteristic
816C22#346012yes—
817C22C2×#54612yes—
818C22D4×#4112yes—
819C22C2×#55312yes—
820C22#347512yes—
821C22#347512yes—
822C22#348012yes—
823C22#348112yes—
824C22#348112yes—
825C4—24no—
826C4—24no—
827C4—24no—
828C4—24no—
829C4—44no—
830C4—44no—
831C4—44no—
832C4—42no—
833C4—48no—
834C4—44no—
835C4—44no—
836C4—44no—
837C4—84no—
838C4C4×#12118yes—
839C4#253518yesdirect product factor
840C2—48no—
841C2—48no—
842C2C2×C4×#12111yescharacteristic
843C2C4×#52511yescharacteristic
844C2C4×#53511yescharacteristic
845C2C4×#54612yes—
846C2C4×#55312yes—
847C2C2×#253511yescharacteristic
848C2#3488912yes—
849C2#3490911yescharacteristic
850C2#3491712yes—
851C2#3493511yescharacteristic
852C2#3496311yescharacteristic
subgroupG/H
centerC23×C4C24
commutatorC23C24×C4
Frattini, socle, cosocleC24C25
prime radicalC2×#2535C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×#121C2semidirect
3. C2×C42×D4C2semidirect
4. C2×C42×D4C2semidirect
5. #14225C2semidirect
6. #14175C2semidirect
7. #14150C2semidirect
8. #14068C2semidirect
9. #13993C2semidirect
10. #13970C2semidirect
11. #13941C2semidirect
12. #13905C2semidirect
13. C4×#397C2semidirect
14. C4×#392C2semidirect
15. C4×#382C2semidirect
16. C4×#380C2semidirect
17. C4×#386C2semidirect
28. #2535C4direct (N × H)
98. C2×#121C2×C4semidirect
115. C2×C4×D4C2×C4semidirect
116. C2×C4×D4C2×C4semidirect
117. C2×C4×D4D4semidirect
158. #397C2×C4semidirect
159. #392C2×C4semidirect
165. #386C2×C4semidirect
167. #382C2×C4semidirect
170. #380C2×C4semidirect
207. C43D4semidirect
452. C2×D4C4×D4semidirect
609. C42C4×D4semidirect
839. C4#2535direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25352
C2×C4×#1212
C2×C42×D42
#142252
#141752
#141502
#140682
#139932
#139702
#139412
#139052
C4×#3972
C4×#3922
C4×#3822
C4×#3802
C4×#3862