Finite Group Databasebeta

← C2×#14079 #514404

Subgroups — C2×#14079 #514404

Order 512.

5014 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#388C211yesmaximal, characteristic
2C22×#388C211yesmaximal, characteristic
3C22×#388C211yesmaximal, characteristic
4C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
5C22×#376C211yesmaximal, characteristic, complemented
6#14079C2116yesmaximal, direct product factor
7C2×#1444C211yesmaximal, characteristic, complemented
8C2×#1442C211yesmaximal, characteristic, complemented
9C2×#1439C211yesmaximal, characteristic
10C2×#1439C211yesmaximal, characteristic
11C2×#1437C211yesmaximal, characteristic
12C2×#1437C211yesmaximal, characteristic
13C2×#1436C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×C4⋊#95C211yesmaximal, characteristic, complemented
16C2×#1434C211yesmaximal, characteristic, complemented
17C23×C4⋊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×C22⋊C4C2211yescharacteristic
29C23×C42C2211yescharacteristic
30C23×C42C2211yescharacteristic
31C23×C42C2211yescharacteristic
32C23×C42C2211yescharacteristic
33C23×C42C2211yescharacteristic
34C2×#388—28no—
35C2×#388—28no—
36C2×#388C4116yescomplemented
37C2×#388C2218yes—
38C2×#388C2218yes—
39C2×#388C2218yes—
40C2×C4×C4⋊C4—28no—
41C2×C4×C4⋊C4C2218yescomplemented
42C2×#376—28no—
43C2×#376C2218yescomplemented
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
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62#1444C2218yescomplemented
63#1442C2218yescomplemented
64#1439C2218yes—
65#1439C2218yes—
66#1437C2218yes—
67#1437C2218yes—
68#1436C2218yescomplemented
69#1436C2218yescomplemented
70C4⋊#95C2218yescomplemented
71#1434C2218yescomplemented
72C26C2311yescharacteristic
73C24×C4C2311yescharacteristic
74C24×C4C2311yescharacteristic
75C24×C4C2311yescharacteristic
76C24×C4C2311yescharacteristic
77C24×C4C2311yescharacteristic
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C22×C4⋊C4—24no—
88C22×C4⋊C4—24no—
89C22×C4⋊C4—24no—
90C22×C4⋊C4—24no—
91C22×C4⋊C4—24no—
92C22×C4⋊C4—24no—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—42no—
98C22×C4⋊C4—42no—
99C22×C4⋊C4—42no—
100C22×C4⋊C4—42no—
101C22×C4⋊C4C2×C418yes—
102C22×C4⋊C4C2314yes—
103C22×C4⋊C4C2314yes—
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2314yes—
107C22×C22⋊C4—24no—
108C22×C22⋊C4—24no—
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—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—42no—
122C22×C22⋊C4—42no—
123C22×C22⋊C4—42no—
124C22×C22⋊C4—42no—
125C22×C22⋊C4C2×C418yes—
126C22×C22⋊C4C2×C418yes—
127C22×C22⋊C4C2×C418yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C42—24no—
136C22×C42—24no—
137C22×C42—24no—
138C22×C42—24no—
139C22×C42—24no—
140C22×C42—24no—
141C22×C42—24no—
142C22×C42—24no—
143C22×C42—24no—
144C22×C42—24no—
145C22×C42—24no—
146C22×C42—24no—
147C22×C42—24no—
148C22×C42C2×C418yes—
149C22×C42D418yes—
150C22×C42C2314yes—
151C22×C42C2314yes—
152C22×C42C2314yes—
153C22×C42C2314yes—
154C22×C42C2314yes—
155#388—232no—
156#388—232no—
157#388C2×C4164yescomplemented
158C4×C4⋊C4—232no—
159#376—232no—
160C2×#95—24no—
161C2×#95—24no—
162C2×#95—24no—
163C2×#95—24no—
164C2×#95—24no—
165C2×#95—24no—
166C2×#95—24no—
167C2×#95—24no—
168C2×#95—24no—
169C2×#95—24no—
170C2×#95—24no—
171C2×#95—42no—
172C2×#95—42no—
173C2×#95—42no—
174C2×#95—42no—
175C2×#95C2×C418yes—
176C2×#95C2×C418yes—
177C2×#95D418yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—22no—
209C25—22no—
210C25C22×C414yes—
211C25C2412yes—
212C25C2411yescharacteristic
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—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×C4C22×C414yes—
292C23×C4C22×C414yes—
293C23×C4C22×C414yes—
294C23×C4C22×C414yes—
295C23×C4C22×C414yes—
296C23×C4C22×C414yes—
297C23×C4C2×D414yes—
298C23×C4C2×D414yes—
299C23×C4C2×D414yes—
300C23×C4C2×D414yes—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4#4114yes—
304C23×C4#4114yes—
305C23×C4#4114yes—
306C23×C4#4114yes—
307C23×C4#4114yes—
308C23×C4#4114yes—
309C23×C4#4114yes—
310C23×C4#4114yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C2×C4⋊C4—232no—
326C2×C4⋊C4—232no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—416no—
342C2×C4⋊C4—416no—
343C2×C4⋊C4—416no—
344C2×C4⋊C4C22×C4116yes—
345C2×C22⋊C4—232no—
346C2×C22⋊C4—232no—
347C2×C22⋊C4—232no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
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—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—416no—
367C2×C22⋊C4—416no—
368C2×C22⋊C4—416no—
369C2×C22⋊C4—416no—
370C2×C22⋊C4C22×C4116yes—
371C2×C22⋊C4C22×C4116yes—
372C2×C22⋊C4C22×C4116yes—
373C2×C42—232no—
374C2×C42—232no—
375C2×C42—232no—
376C2×C42—232no—
377C2×C42—28no—
378C2×C42—28no—
379C2×C42—28no—
380C2×C42—28no—
381C2×C42—28no—
382C2×C42—28no—
383C2×C42—28no—
384C2×C42—28no—
385C2×C42—28no—
386C2×C42—28no—
387C2×C42—28no—
388C2×C42—28no—
389C2×C42—28no—
390C2×C42—416no—
391C2×C42C22×C4116yes—
392C2×C42C2×D4116yes—
393#95—28no—
394#95—28no—
395#95—28no—
396#95—28no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95C22×C4116yes—
409#95C22×C4116yes—
410#95C2×D4116yes—
411C24—28no—
412C24—28no—
413C24—28no—
414C24—28no—
415C24—28no—
416C24—28no—
417C24—28no—
418C24—22no—
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—22no—
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—44no—
448C24—44no—
449C24—44no—
450C24—44no—
451C24—44no—
452C24—44no—
453C24—44no—
454C24—44no—
455C24—44no—
456C24—44no—
457C24—44no—
458C24—44no—
459C24—44no—
460C24C23×C414yes—
461C24C23×C412yes—
462C24C22×D412yes—
463C24C22×D412yes—
464C24C2×#4112yes—
465C24C2×#4112yes—
466C24C2×#4112yes—
467C24C2×#4112yes—
468C24C2×#4112yes—
469C24C2×#4112yes—
470C24C2×#4112yes—
471C24C2×#4112yes—
472C24H(5,𝔽2)12yes—
473C24H(5,𝔽2)12yes—
474C242−1+412yes—
475C242−1+412yes—
476C24C2511yescharacteristic
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—22no—
502C22×C4—22no—
503C22×C4—22no—
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—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
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—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
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#117116yes—
650C22×C4C4×D4116yes—
651C22×C4C4×D4116yes—
652C22×C4#121116yes—
653C22×C4C23×C414yes—
654C22×C4C23×C414yes—
655C22×C4C23×C414yes—
656C22×C4C23×C414yes—
657C22×C4C23×C414yes—
658C22×C4C23×C414yes—
659C22×C4C22×D414yes—
660C22×C4C22×D414yes—
661C22×C4C22×D414yes—
662C22×C4C22×D414yes—
663C22×C4C22×D414yes—
664C22×C4C22×D414yes—
665C22×C4C2×#4114yes—
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—232no—
675C4⋊C4—416no—
676C4⋊C4—416no—
677C4⋊C4—416no—
678C22⋊C4—232no—
679C22⋊C4—232no—
680C22⋊C4—232no—
681C22⋊C4—416no—
682C22⋊C4—416no—
683C22⋊C4—416no—
684C22⋊C4—416no—
685C42—232no—
686C42—232no—
687C42—232no—
688C42—232no—
689C42—416no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—416no—
698C23—416no—
699C23—416no—
700C23—416no—
701C23—416no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
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—42no—
729C23—42no—
730C23—416no—
731C23—416no—
732C23—88no—
733C23—88no—
734C23—88no—
735C23—88no—
736C23—88no—
737C23—88no—
738C23—88no—
739C23—88no—
740C23C2×#11714yes—
741C23C2×C4×D414yes—
742C23C2×C4×D414yes—
743C23C4×#4114yes—
744C23C4×#4114yes—
745C23#52014yes—
746C23#52014yes—
747C23C2×#12114yes—
748C23#52514yes—
749C23#52514yes—
750C23#52514yes—
751C23#52914yes—
752C23#52914yes—
753C23#52914yes—
754C23#53214yes—
755C23#53514yes—
756C23#53614yes—
757C23#54214yes—
758C23#54214yes—
759C23#54614yes—
760C23#54714yes—
761C23#54714yes—
762C23#55014yes—
763C23#55114yes—
764C23#55114yes—
765C23#55214yes—
766C23#55214yes—
767C23#55214yes—
768C23#55214yes—
769C23#55314yes—
770C23#55514yes—
771C23#55514yes—
772C23#55514yes—
773C23#55614yes—
774C23#55614yes—
775C23C24×C411yescharacteristic
776C23C23×D411yescharacteristic
777C23C23×D411yescharacteristic
778C23C22×#4111yescharacteristic
779C23C22×#4111yescharacteristic
780C23C22×#4111yescharacteristic
781C23C22×#4111yescharacteristic
782C23C22×#4111yescharacteristic
783C23C22×#4111yescharacteristic
784C23C22×#4111yescharacteristic
785C23C22×#4111yescharacteristic
786C23C2×H(5,𝔽2)11yescharacteristic
787C23C2×H(5,𝔽2)11yescharacteristic
788C23C2×2−1+411yescharacteristic
789C23C2×2−1+411yescharacteristic
790C2×C4—232no—
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—232no—
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—232no—
817C2×C4—232no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—416no—
843C2×C4—416no—
844C2×C4—416no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—416no—
849C2×C4—416no—
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—42no—
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—416no—
880C2×C4—416no—
881C2×C4—416no—
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—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—88no—
897C2×C4—88no—
898C2×C4C2×#11718yes—
899C2×C4C2×C4×D418yes—
900C2×C4C2×C4×D418yes—
901C2×C4C2×#12118yes—
902C22—44no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—44no—
907C22—44no—
908C22—44no—
909C22—82no—
910C22—82no—
911C22—82no—
912C22—82no—
913C22—82no—
914C22—82no—
915C22—82no—
916C22—82no—
917C22—832no—
918C22#229018yes—
919C22C4×#12118yes—
920C22#232618yes—
921C22#234618yes—
922C22#235418yes—
923C22#235918yes—
924C22#237318yes—
925C22#241318yes—
926C22#241418yes—
927C22#247418yes—
928C22#247918yes—
929C22#252918yes—
930C22#253218yes—
931C22#260418yes—
932C22#261018yes—
933C22C22×#11711yescharacteristic
934C22C22×C4×D411yescharacteristic
935C22C22×C4×D411yescharacteristic
936C22C2×C4×#4111yescharacteristic
937C22C2×C4×#4111yescharacteristic
938C22C2×#52011yescharacteristic
939C22C2×#52011yescharacteristic
940C22C22×#12111yescharacteristic
941C22C2×#52511yescharacteristic
942C22C2×#52511yescharacteristic
943C22C2×#52511yescharacteristic
944C22C2×#52911yescharacteristic
945C22C2×#52911yescharacteristic
946C22C2×#52911yescharacteristic
947C22C2×#53211yescharacteristic
948C22C2×#53511yescharacteristic
949C22C2×#53611yescharacteristic
950C22C2×#54211yescharacteristic
951C22C2×#54211yescharacteristic
952C22C2×#54611yescharacteristic
953C22C2×#54711yescharacteristic
954C22C2×#54711yescharacteristic
955C22C2×#55011yescharacteristic
956C22C2×#55111yescharacteristic
957C22C2×#55111yescharacteristic
958C22C2×#55211yescharacteristic
959C22C2×#55211yescharacteristic
960C22C2×#55211yescharacteristic
961C22C2×#55211yescharacteristic
962C22C2×#55311yescharacteristic
963C22C2×#55511yescharacteristic
964C22C2×#55511yescharacteristic
965C22C2×#55511yescharacteristic
966C22C2×#55611yescharacteristic
967C22C2×#55611yescharacteristic
968C4—28no—
969C4—28no—
970C4—28no—
971C4—28no—
972C4—44no—
973C4—44no—
974C4—44no—
975C4—44no—
976C4—44no—
977C4—44no—
978C4—44no—
979C4—44no—
980C4—82no—
981C4—82no—
982C2—84no—
983C2#14079116yesdirect product factor
984C2C2×#229011yescharacteristic
985C2C2×C4×#12111yescharacteristic
986C2C2×#232611yescharacteristic
987C2C2×#234611yescharacteristic
988C2C2×#235411yescharacteristic
989C2C2×#235911yescharacteristic
990C2C2×#237311yescharacteristic
991C2C2×#241411yescharacteristic
992C2C2×#247411yescharacteristic
993C2C2×#247911yescharacteristic
994C2C2×#241311yescharacteristic
995C2C2×#252911yescharacteristic
996C2C2×#253211yescharacteristic
997C2C2×#260411yescharacteristic
998C2C2×#261011yescharacteristic
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
4. C22×C4×C4⋊C4C2semidirect
5. C22×#376C2semidirect
6. #14079C2direct (N × H)
7. C2×#1444C2semidirect
8. C2×#1442C2semidirect
13. C2×#1436C2semidirect
14. C2×#1436C2semidirect
15. C2×C4⋊#95C2semidirect
16. C2×#1434C2semidirect
36. C2×#388C4semidirect
41. C2×C4×C4⋊C4C22semidirect
43. C2×#376C22semidirect
62. #1444C22semidirect
63. #1442C22semidirect
68. #1436C22semidirect
69. #1436C22semidirect
70. C4⋊#95C22semidirect
71. #1434C22semidirect
157. #388C2×C4semidirect
983. C2#14079direct (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×C4×C4⋊C42
C22×#3762
#140792
C2×#14442
C2×#14422
C2×#14392
C2×#14372
C2×#14362
C2×C4⋊#952
C2×#14342