Finite Group Databasebeta

← C2×#14393 #520695

Subgroups — C2×#14393 #520695

Order 512.

4842 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#388C211yesmaximal, characteristic
2C22×#385C211yesmaximal, characteristic
3C22×#382C211yesmaximal, characteristic, complemented
4#14393C2116yesmaximal, direct product factor
5C2×#1445C211yesmaximal, characteristic, complemented
6C2×#1443C211yesmaximal, characteristic, complemented
7C2×#1442C211yesmaximal, characteristic, complemented
8C2×#1441C211yesmaximal, characteristic, complemented
9C2×#1440C211yesmaximal, characteristic
10C2×#1439C211yesmaximal, characteristic
11C2×#1437C211yesmaximal, characteristic
12C2×#1436C211yesmaximal, characteristic, complemented
13C2×#1436C211yesmaximal, characteristic, complemented
14C2×#1434C211yesmaximal, characteristic, complemented
15C2×C22⋊#95C211yesmaximal, characteristic
16C2×C22⋊#95C211yesmaximal, characteristic
17C25×C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C42C2211yescharacteristic
29C23×C42C2211yescharacteristic
30C2×#388C4116yescomplemented
31C2×#388C2218yes—
32C2×#385—28no—
33C2×#385C2218yes—
34C2×#382—28no—
35C2×#382C2218yescomplemented
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38C22×#95C2211yescharacteristic
39C22×#95C2211yescharacteristic
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58#1445C2218yescomplemented
59#1443C2218yescomplemented
60#1442C2218yescomplemented
61#1441C2218yescomplemented
62#1440C2218yes—
63#1439C2218yes—
64#1437C2218yes—
65#1436C2218yescomplemented
66#1436C2218yescomplemented
67#1434C2218yescomplemented
68C22⋊#95C2218yes—
69C22⋊#95C2218yes—
70C26C2311yescharacteristic
71C24×C4—24no—
72C24×C4—24no—
73C24×C4—24no—
74C24×C4—42no—
75C24×C4—42no—
76C24×C4—42no—
77C24×C4—42no—
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2314yes—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—42no—
97C22×C4⋊C4—42no—
98C22×C4⋊C4—42no—
99C22×C4⋊C4—42no—
100C22×C4⋊C4—42no—
101C22×C4⋊C4—42no—
102C22×C4⋊C4—42no—
103C22×C4⋊C4C2×C418yescomplemented
104C22×C4⋊C4D418yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2314yes—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—42no—
119C22×C22⋊C4—42no—
120C22×C22⋊C4—42no—
121C22×C22⋊C4—42no—
122C22×C22⋊C4—42no—
123C22×C22⋊C4—42no—
124C22×C22⋊C4C2×C418yes—
125C22×C22⋊C4C2×C418yes—
126C22×C22⋊C4C2×C418yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C42—24no—
134C22×C42—24no—
135C22×C42—42no—
136C22×C42—42no—
137C22×C42—42no—
138C22×C42C2×C418yescomplemented
139C22×C42C2314yes—
140C22×C42C2314yes—
141#388C2×C4164yescomplemented
142#385—232no—
143#382—232no—
144C2×#95—24no—
145C2×#95—24no—
146C2×#95—24no—
147C2×#95—24no—
148C2×#95—24no—
149C2×#95—24no—
150C2×#95—24no—
151C2×#95—24no—
152C2×#95—24no—
153C2×#95—24no—
154C2×#95—42no—
155C2×#95—42no—
156C2×#95—42no—
157C2×#95—42no—
158C2×#95—42no—
159C2×#95—42no—
160C2×#95—42no—
161C2×#95—42no—
162C2×#95—42no—
163C2×#95—42no—
164C2×#95C2×C418yescomplemented
165C2×#95C2×C418yescomplemented
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C25—22no—
189C25—22no—
190C25—22no—
191C25—22no—
192C25—22no—
193C25—22no—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25C22×C414yes—
201C25#4114yes—
202C25#4114yes—
203C25C2412yes—
204C25C2411yescharacteristic
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—28no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—28no—
293C23×C4—28no—
294C23×C4—44no—
295C23×C4—44no—
296C23×C4—44no—
297C23×C4—44no—
298C23×C4—416no—
299C23×C4—416no—
300C23×C4—416no—
301C23×C4—416no—
302C23×C4—416no—
303C23×C4—416no—
304C23×C4—416no—
305C23×C4C22×C414yes—
306C23×C4C22×C414yes—
307C23×C4C22×C414yes—
308C23×C4C22×C414yes—
309C23×C4C22×C414yes—
310C23×C4C22×C414yes—
311C23×C4C2×D414yes—
312C23×C4C2×D414yes—
313C23×C4C2×D414yes—
314C23×C4#4114yes—
315C23×C4#4114yes—
316C23×C4#4114yes—
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C23×C4C2412yes—
326C23×C4C2412yes—
327C23×C4C2412yes—
328C23×C4C2412yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—416no—
335C2×C4⋊C4—416no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—416no—
344C2×C4⋊C4—416no—
345C2×C4⋊C4C22×C4116yescomplemented
346C2×C4⋊C4C2×D4116yes—
347C2×C22⋊C4—232no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—232no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—416no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—416no—
366C2×C22⋊C4—416no—
367C2×C22⋊C4—416no—
368C2×C22⋊C4C22×C4116yes—
369C2×C22⋊C4C22×C4116yes—
370C2×C22⋊C4C22×C4116yes—
371C2×C42—232no—
372C2×C42—28no—
373C2×C42—28no—
374C2×C42—44no—
375C2×C42—44no—
376C2×C42—44no—
377C2×C42—416no—
378C2×C42C22×C4116yescomplemented
379#95—28no—
380#95—28no—
381#95—28no—
382#95—28no—
383#95—28no—
384#95—28no—
385#95—28no—
386#95—28no—
387#95—28no—
388#95—28no—
389#95—44no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95C22×C4116yescomplemented
400#95C22×C4116yescomplemented
401C24—28no—
402C24—28no—
403C24—28no—
404C24—28no—
405C24—28no—
406C24—28no—
407C24—28no—
408C24—28no—
409C24—28no—
410C24—28no—
411C24—28no—
412C24—28no—
413C24—28no—
414C24—28no—
415C24—28no—
416C24—28no—
417C24—28no—
418C24—28no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—44no—
432C24—44no—
433C24—44no—
434C24—44no—
435C24—44no—
436C24—44no—
437C24—44no—
438C24—44no—
439C24—44no—
440C24—44no—
441C24—44no—
442C24—44no—
443C24—44no—
444C24—44no—
445C24—44no—
446C24—44no—
447C24#117116yes—
448C24C23×C414yes—
449C24C23×C412yes—
450C24C22×D412yes—
451C24C2×#4114yes—
452C24C2×#4114yes—
453C24C2×#4112yes—
454C24C2×#4112yes—
455C24C2×#4112yes—
456C24C2×#4112yes—
457C24C2×#4112yes—
458C24H(5,𝔽2)12yes—
459C24H(5,𝔽2)12yes—
460C24H(5,𝔽2)12yes—
461C24H(5,𝔽2)12yes—
462C24H(5,𝔽2)12yes—
463C242−1+412yes—
464C242−1+412yes—
465C242−1+412yes—
466C24C2511yescharacteristic
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—416no—
587C22×C4—416no—
588C22×C4—416no—
589C22×C4—416no—
590C22×C4—416no—
591C22×C4—416no—
592C22×C4—4128no—
593C22×C4—416no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4C4×D4116yes—
659C22×C4C23×C414yes—
660C22×C4C23×C414yes—
661C22×C4C23×C414yes—
662C22×C4C23×C414yes—
663C22×C4C23×C414yes—
664C22×C4C23×C414yes—
665C22×C4C22×D414yes—
666C22×C4C22×D414yes—
667C22×C4C22×D414yes—
668C22×C4C2×#4114yes—
669C22×C4C2×#4114yes—
670C22×C4C2×#4114yes—
671C4⋊C4—416no—
672C4⋊C4—416no—
673C4⋊C4—416no—
674C4⋊C4—416no—
675C22⋊C4—232no—
676C22⋊C4—232no—
677C22⋊C4—416no—
678C22⋊C4—416no—
679C22⋊C4—416no—
680C22⋊C4—416no—
681C42—232no—
682C42—416no—
683C23—232no—
684C23—232no—
685C23—232no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—416no—
705C23—416no—
706C23—416no—
707C23—416no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—416no—
715C23—42no—
716C23—42no—
717C23—416no—
718C23—416no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—416no—
724C23—416no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—416no—
730C23—416no—
731C23—416no—
732C23C2×#11718yes—
733C23C2×#11714yes—
734C23C2×C4×D414yes—
735C23C4×#4114yes—
736C23#51814yes—
737C23#52014yes—
738C23#52014yes—
739C23#52014yes—
740C23#53414yes—
741C23#53614yes—
742C23#53814yes—
743C23#53814yes—
744C23#53814yes—
745C23#53914yes—
746C23#53914yes—
747C23#53914yes—
748C23#53914yes—
749C23#53914yes—
750C23#54114yes—
751C23#54214yes—
752C23#54614yes—
753C23#54614yes—
754C23#54814yes—
755C23#55014yes—
756C23#55114yes—
757C23#55114yes—
758C23#55214yes—
759C23#55214yes—
760C23#55214yes—
761C23#55314yes—
762C23#55314yes—
763C23#55514yes—
764C23H(3,𝔽4)14yes—
765C23#56214yes—
766C23#56214yes—
767C23#56314yes—
768C23C24×C411yescharacteristic
769C23C23×D411yescharacteristic
770C23C22×#4111yescharacteristic
771C23C22×#4111yescharacteristic
772C23C22×#4111yescharacteristic
773C23C22×#4111yescharacteristic
774C23C22×#4111yescharacteristic
775C23C2×H(5,𝔽2)11yescharacteristic
776C23C2×H(5,𝔽2)11yescharacteristic
777C23C2×H(5,𝔽2)11yescharacteristic
778C23C2×H(5,𝔽2)11yescharacteristic
779C23C2×H(5,𝔽2)11yescharacteristic
780C23C2×2−1+411yescharacteristic
781C23C2×2−1+411yescharacteristic
782C23C2×2−1+411yescharacteristic
783C2×C4—232no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—464no—
818C2×C4—416no—
819C2×C4—416no—
820C2×C4—416no—
821C2×C4—416no—
822C2×C4—416no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—416no—
836C2×C4—416no—
837C2×C4—416no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—416no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—88no—
892C2×C4—88no—
893C2×C4—88no—
894C2×C4—88no—
895C2×C4C2×C4×D418yes—
896C22—28no—
897C22—28no—
898C22—28no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—464no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—44no—
907C22—44no—
908C22—44no—
909C22—44no—
910C22—44no—
911C22—44no—
912C22#231818yes—
913C22#232218yes—
914C22#233418yes—
915C22#234318yes—
916C22#235218yes—
917C22#236318yes—
918C22#237918yes—
919C22#268418yes—
920C22#269018yes—
921C22#269418yes—
922C22#273018yes—
923C22#274418yes—
924C22#276518yes—
925C22#278118yes—
926C22#278218yes—
927C22C22×#11711yescharacteristic
928C22C22×C4×D411yescharacteristic
929C22C2×C4×#4111yescharacteristic
930C22C2×#51811yescharacteristic
931C22C2×#52011yescharacteristic
932C22C2×#52011yescharacteristic
933C22C2×#52011yescharacteristic
934C22C2×#53411yescharacteristic
935C22C2×#53611yescharacteristic
936C22C2×#53811yescharacteristic
937C22C2×#53811yescharacteristic
938C22C2×#53811yescharacteristic
939C22C2×#53911yescharacteristic
940C22C2×#53911yescharacteristic
941C22C2×#53911yescharacteristic
942C22C2×#53911yescharacteristic
943C22C2×#53911yescharacteristic
944C22C2×#54111yescharacteristic
945C22C2×#54211yescharacteristic
946C22C2×#54611yescharacteristic
947C22C2×#54611yescharacteristic
948C22C2×#54811yescharacteristic
949C22C2×#55011yescharacteristic
950C22C2×#55111yescharacteristic
951C22C2×#55111yescharacteristic
952C22C2×#55211yescharacteristic
953C22C2×#55211yescharacteristic
954C22C2×#55211yescharacteristic
955C22C2×#55311yescharacteristic
956C22C2×#55311yescharacteristic
957C22C2×#55511yescharacteristic
958C22C2×H(3,𝔽4)11yescharacteristic
959C22C2×#56211yescharacteristic
960C22C2×#56211yescharacteristic
961C22C2×#56311yescharacteristic
962C4—28no—
963C4—44no—
964C4—44no—
965C4—44no—
966C4—44no—
967C4—44no—
968C4—44no—
969C4—44no—
970C4—44no—
971C4—44no—
972C4—82no—
973C4—82no—
974C4—82no—
975C4—82no—
976C2—48no—
977C2#14393116yesdirect product factor
978C2C2×#231811yescharacteristic
979C2C2×#232211yescharacteristic
980C2C2×#233411yescharacteristic
981C2C2×#234311yescharacteristic
982C2C2×#235211yescharacteristic
983C2C2×#236311yescharacteristic
984C2C2×#237911yescharacteristic
985C2C2×#268411yescharacteristic
986C2C2×#269011yescharacteristic
987C2C2×#269411yescharacteristic
988C2C2×#273011yescharacteristic
989C2C2×#274411yescharacteristic
990C2C2×#276511yescharacteristic
991C2C2×#278111yescharacteristic
992C2C2×#278211yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C22×#382C2semidirect
4. #14393C2direct (N × H)
5. C2×#1445C2semidirect
6. C2×#1443C2semidirect
7. C2×#1442C2semidirect
8. C2×#1441C2semidirect
12. C2×#1436C2semidirect
13. C2×#1436C2semidirect
14. C2×#1434C2semidirect
30. C2×#388C4semidirect
35. C2×#382C22semidirect
58. #1445C22semidirect
59. #1443C22semidirect
60. #1442C22semidirect
61. #1441C22semidirect
65. #1436C22semidirect
66. #1436C22semidirect
67. #1434C22semidirect
103. C22×C4⋊C4C2×C4semidirect
138. C22×C42C2×C4semidirect
141. #388C2×C4semidirect
164. C2×#95C2×C4semidirect
165. C2×#95C2×C4semidirect
345. C2×C4⋊C4C22×C4semidirect
378. C2×C42C22×C4semidirect
399. #95C22×C4semidirect
400. #95C22×C4semidirect
977. C2#14393direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3882
C22×#3852
C22×#3822
#143932
C2×#14452
C2×#14432
C2×#14422
C2×#14412
C2×#14402
C2×#14392
C2×#14372
C2×#14362
C2×#14342
C2×C22⋊#952