Finite Group Databasebeta

← C2×#14740 #607672

Subgroups — C2×#14740 #607672

Order 512.

4942 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#397C211yesmaximal, characteristic
2C22×#387C211yesmaximal, characteristic, complemented
3C22×#385C211yesmaximal, characteristic
4C22×C4×C22⋊C4C211yesmaximal, characteristic
5#14740C2116yesmaximal, direct product factor
6C2×#1445C211yesmaximal, characteristic, complemented
7C2×#1443C211yesmaximal, characteristic, complemented
8C2×#1442C211yesmaximal, characteristic, complemented
9C2×#1441C211yesmaximal, characteristic, complemented
10C2×#1440C211yesmaximal, characteristic
11C2×#1440C211yesmaximal, characteristic
12C2×#1439C211yesmaximal, characteristic
13C2×#1436C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×#1434C211yesmaximal, characteristic, complemented
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×#397—28no—
31C2×#397C2218yes—
32C2×#387—28no—
33C2×#387C2218yescomplemented
34C2×#385—28no—
35C2×#385C2218yes—
36C2×C4×C22⋊C4—28no—
37C2×C4×C22⋊C4C2218yes—
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
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60#1445C2218yescomplemented
61#1443C2218yescomplemented
62#1442C2218yescomplemented
63#1441C2218yescomplemented
64#1440C2218yes—
65#1440C2218yes—
66#1439C2218yes—
67#1436C2218yescomplemented
68#1436C2218yescomplemented
69#1434C2218yescomplemented
70C22⋊#95C2218yes—
71C26C2311yescharacteristic
72C24×C4—24no—
73C24×C4—24no—
74C24×C4—24no—
75C24×C4—24no—
76C24×C4—24no—
77C24×C4—42no—
78C24×C4—42no—
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—
93C24×C4C2311yescharacteristic
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—24no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—42no—
103C22×C4⋊C4—42no—
104C22×C4⋊C4—42no—
105C22×C4⋊C4D418yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2314yes—
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—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—42no—
126C22×C22⋊C4—42no—
127C22×C22⋊C4D418yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C42—24no—
135C22×C42—24no—
136C22×C42—24no—
137C22×C42—24no—
138C22×C42—42no—
139C22×C42—42no—
140C22×C42C2314yes—
141C22×C42C2314yes—
142#397—232no—
143#387—232no—
144#385—232no—
145C4×C22⋊C4—232no—
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—24no—
155C2×#95—24no—
156C2×#95—24no—
157C2×#95—24no—
158C2×#95—24no—
159C2×#95—24no—
160C2×#95—24no—
161C2×#95—24no—
162C2×#95—24no—
163C2×#95—24no—
164C2×#95—24no—
165C2×#95—42no—
166C2×#95—42no—
167C2×#95—42no—
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—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C25—22no—
191C25—22no—
192C25—22no—
193C25—22no—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25C2×D414yes—
203C25#4114yes—
204C25#4114yes—
205C25C2412yes—
206C25C2411yescharacteristic
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—232no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—28no—
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—28no—
268C23×C4—28no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
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—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—28no—
298C23×C4—28no—
299C23×C4—44no—
300C23×C4—44no—
301C23×C4—416no—
302C23×C4—416no—
303C23×C4—416no—
304C23×C4—416no—
305C23×C4—416no—
306C23×C4—416no—
307C23×C4C2×D414yes—
308C23×C4C2×D414yes—
309C23×C4C2×D414yes—
310C23×C4C2×D414yes—
311C23×C4C2×D414yes—
312C23×C4#4114yes—
313C23×C4#4114yes—
314C23×C4#4114yes—
315C23×C4#4114yes—
316C23×C4#4114yes—
317C23×C4#4114yes—
318C23×C4#4114yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C23×C4C2412yes—
326C23×C4C2412yes—
327C23×C4C2412yes—
328C23×C4C2412yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C23×C4C2412yes—
332C23×C4C2412yes—
333C2×C4⋊C4—232no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—416no—
346C2×C4⋊C4—416no—
347C2×C4⋊C4—416no—
348C2×C4⋊C4C2×D4116yes—
349C2×C22⋊C4—232no—
350C2×C22⋊C4—232no—
351C2×C22⋊C4—232no—
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—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—416no—
370C2×C22⋊C4—416no—
371C2×C22⋊C4—416no—
372C2×C22⋊C4C2×D4116yes—
373C2×C42—28no—
374C2×C42—28no—
375C2×C42—28no—
376C2×C42—28no—
377C2×C42—44no—
378C2×C42—44no—
379C2×C42—416no—
380C2×C42—416no—
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—28no—
390#95—28no—
391#95—28no—
392#95—28no—
393#95—28no—
394#95—28no—
395#95—28no—
396#95—28no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—44no—
401#95—44no—
402#95—44no—
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—28no—
420C24—28no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
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—44no—
448C24—44no—
449C24#123116yes—
450C24C22×D414yes—
451C24C22×D412yes—
452C24C22×D412yes—
453C24C2×#4114yes—
454C24C2×#4114yes—
455C24C2×#4112yes—
456C24C2×#4112yes—
457C24C2×#4112yes—
458C24C2×#4112yes—
459C24C2×#4112yes—
460C24C2×#4112yes—
461C24C2×#4112yes—
462C24C2×#4112yes—
463C24C2×#4112yes—
464C24H(5,𝔽2)12yes—
465C24H(5,𝔽2)12yes—
466C242−1+412yes—
467C242−1+412yes—
468C24C2511yescharacteristic
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—232no—
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—28no—
505C22×C4—28no—
506C22×C4—28no—
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—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—416no—
590C22×C4—416no—
591C22×C4—416no—
592C22×C4—416no—
593C22×C4—4128no—
594C22×C4—416no—
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—416no—
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×C4—44no—
659C22×C4—44no—
660C22×C4#123116yes—
661C22×C4C22×D414yes—
662C22×C4C22×D414yes—
663C22×C4C22×D414yes—
664C22×C4C22×D414yes—
665C22×C4C22×D414yes—
666C22×C4C2×#4114yes—
667C22×C4C2×#4114yes—
668C22×C4C2×#4114yes—
669C22×C4C2×#4114yes—
670C22×C4C2×#4114yes—
671C22×C4C2×#4114yes—
672C22×C4C2×#4114yes—
673C4⋊C4—232no—
674C4⋊C4—416no—
675C4⋊C4—416no—
676C4⋊C4—416no—
677C22⋊C4—232no—
678C22⋊C4—232no—
679C22⋊C4—232no—
680C22⋊C4—416no—
681C22⋊C4—416no—
682C22⋊C4—416no—
683C42—416no—
684C42—416no—
685C23—232no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—232no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—232no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—416no—
707C23—416no—
708C23—416no—
709C23—416no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—416no—
714C23—42no—
715C23—416no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—416no—
729C23—416no—
730C23—416no—
731C23—416no—
732C23—416no—
733C23—416no—
734C23C2×#12318yes—
735C23C2×#12314yes—
736C23C2×#12314yes—
737C23#52514yes—
738C23#52514yes—
739C23#52514yes—
740C23#52914yes—
741C23#52914yes—
742C23#52914yes—
743C23#52914yes—
744C23#52914yes—
745C23#52914yes—
746C23#52914yes—
747C23#53214yes—
748C23#53814yes—
749C23#53914yes—
750C23#53914yes—
751C23#53914yes—
752C23#54114yes—
753C23#54214yes—
754C23D4214yes—
755C23#54614yes—
756C23#54614yes—
757C23#54714yes—
758C23#54714yes—
759C23#54814yes—
760C23#54814yes—
761C23#55114yes—
762C23#55114yes—
763C23#55114yes—
764C23#55214yes—
765C23#55214yes—
766C23#55314yes—
767C23#55314yes—
768C23#55614yes—
769C23#55614yes—
770C23C23×D411yescharacteristic
771C23C23×D411yescharacteristic
772C23C22×#4111yescharacteristic
773C23C22×#4111yescharacteristic
774C23C22×#4111yescharacteristic
775C23C22×#4111yescharacteristic
776C23C22×#4111yescharacteristic
777C23C22×#4111yescharacteristic
778C23C22×#4111yescharacteristic
779C23C22×#4111yescharacteristic
780C23C22×#4111yescharacteristic
781C23C2×H(5,𝔽2)11yescharacteristic
782C23C2×H(5,𝔽2)11yescharacteristic
783C23C2×2−1+411yescharacteristic
784C23C2×2−1+411yescharacteristic
785C2×C4—24no—
786C2×C4—232no—
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—24no—
818C2×C4—24no—
819C2×C4—464no—
820C2×C4—416no—
821C2×C4—416no—
822C2×C4—42no—
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—416no—
833C2×C4—416no—
834C2×C4—42no—
835C2×C4—416no—
836C2×C4—42no—
837C2×C4—42no—
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—416no—
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—416no—
864C2×C4—416no—
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—42no—
892C2×C4—42no—
893C2×C4—88no—
894C2×C4—88no—
895C2×C4—88no—
896C2×C4—88no—
897C2×C4C2×#12318yes—
898C22—28no—
899C22—28no—
900C22—28no—
901C22—44no—
902C22—44no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—44no—
907C22—44no—
908C22—44no—
909C22—464no—
910C22—44no—
911C22—44no—
912C22—44no—
913C22—44no—
914C22#239518yes—
915C22#241818yes—
916C22#241918yes—
917C22#242118yes—
918C22#244318yes—
919C22#246018yes—
920C22#246118yes—
921C22#246618yes—
922C22#247818yes—
923C22#252318yes—
924C22#253018yes—
925C22#256018yes—
926C22#257618yes—
927C22#265218yes—
928C22#285318yes—
929C22C22×#12311yescharacteristic
930C22C22×#12311yescharacteristic
931C22C2×#52511yescharacteristic
932C22C2×#52511yescharacteristic
933C22C2×#52511yescharacteristic
934C22C2×#52911yescharacteristic
935C22C2×#52911yescharacteristic
936C22C2×#52911yescharacteristic
937C22C2×#52911yescharacteristic
938C22C2×#52911yescharacteristic
939C22C2×#52911yescharacteristic
940C22C2×#52911yescharacteristic
941C22C2×#53211yescharacteristic
942C22C2×#53811yescharacteristic
943C22C2×#53911yescharacteristic
944C22C2×#53911yescharacteristic
945C22C2×#53911yescharacteristic
946C22C2×#54111yescharacteristic
947C22C2×#54211yescharacteristic
948C22C2×D4211yescharacteristic
949C22C2×#54611yescharacteristic
950C22C2×#54611yescharacteristic
951C22C2×#54711yescharacteristic
952C22C2×#54711yescharacteristic
953C22C2×#54811yescharacteristic
954C22C2×#54811yescharacteristic
955C22C2×#55111yescharacteristic
956C22C2×#55111yescharacteristic
957C22C2×#55111yescharacteristic
958C22C2×#55211yescharacteristic
959C22C2×#55211yescharacteristic
960C22C2×#55311yescharacteristic
961C22C2×#55311yescharacteristic
962C22C2×#55611yescharacteristic
963C22C2×#55611yescharacteristic
964C4—28no—
965C4—44no—
966C4—44no—
967C4—44no—
968C4—44no—
969C4—44no—
970C4—44no—
971C4—44no—
972C4—44no—
973C4—44no—
974C4—82no—
975C4—82no—
976C4—82no—
977C4—82no—
978C2—48no—
979C2#14740116yesdirect product factor
980C2C2×#239511yescharacteristic
981C2C2×#265211yescharacteristic
982C2C2×#241811yescharacteristic
983C2C2×#244311yescharacteristic
984C2C2×#246011yescharacteristic
985C2C2×#246611yescharacteristic
986C2C2×#241911yescharacteristic
987C2C2×#246111yescharacteristic
988C2C2×#242111yescharacteristic
989C2C2×#247811yescharacteristic
990C2C2×#252311yescharacteristic
991C2C2×#253011yescharacteristic
992C2C2×#256011yescharacteristic
993C2C2×#257611yescharacteristic
994C2C2×#285311yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#387C2semidirect
5. #14740C2direct (N × H)
6. C2×#1445C2semidirect
7. C2×#1443C2semidirect
8. C2×#1442C2semidirect
9. C2×#1441C2semidirect
13. C2×#1436C2semidirect
14. C2×#1436C2semidirect
15. C2×#1434C2semidirect
33. C2×#387C22semidirect
60. #1445C22semidirect
61. #1443C22semidirect
62. #1442C22semidirect
63. #1441C22semidirect
67. #1436C22semidirect
68. #1436C22semidirect
69. #1434C22semidirect
979. C2#14740direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3972
C22×#3872
C22×#3852
C22×C4×C22⋊C42
#147402
C2×#14452
C2×#14432
C2×#14422
C2×#14412
C2×#14402
C2×#14392
C2×#14362
C2×#14342
C2×C22⋊#952