Finite Group Databasebeta

← C2×#14197 #514683

Subgroups — C2×#14197 #514683

Order 512.

5074 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×#397C211yesmaximal, characteristic
2C22×#388C211yesmaximal, characteristic
3C22×C4×C22⋊C4C211yesmaximal, characteristic
4#14197C2116yesmaximal, direct product factor
5C2×#1443C211yesmaximal, characteristic, complemented
6C2×#1443C211yesmaximal, characteristic, complemented
7C2×#1440C211yesmaximal, characteristic
8C2×#1437C211yesmaximal, characteristic
9C2×#1436C211yesmaximal, characteristic, complemented
10C2×#1436C211yesmaximal, characteristic, complemented
11C2×#1436C211yesmaximal, characteristic, complemented
12C2×#1436C211yesmaximal, characteristic, complemented
13C2×#1434C211yesmaximal, characteristic, complemented
14C2×C22⋊#95C211yesmaximal, characteristic
15C2×C22⋊#95C211yesmaximal, characteristic
16C2×C4×#95C211yesmaximal, characteristic, complemented
17C25×C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27C23×C42C2211yescharacteristic
28C23×C42C2211yescharacteristic
29C23×C42C2211yescharacteristic
30C2×#397C4116yescomplemented
31C2×#397C2218yes—
32C2×#388—28no—
33C2×#388C2218yes—
34C2×C4×C22⋊C4—28no—
35C2×C4×C22⋊C4C2218yes—
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#1443C2218yescomplemented
59#1443C2218yescomplemented
60#1440C2218yes—
61#1437C2218yes—
62#1436C2218yescomplemented
63#1436C2218yescomplemented
64#1436C2218yescomplemented
65#1436C2218yescomplemented
66#1434C2218yescomplemented
67C22⋊#95C2218yes—
68C22⋊#95C2218yes—
69C4×#95C2218yescomplemented
70C26C2311yescharacteristic
71C24×C4—24no—
72C24×C4—24no—
73C24×C4—24no—
74C24×C4—24no—
75C24×C4—24no—
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×C4C2314yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—42no—
97C22×C4⋊C4—42no—
98C22×C4⋊C4C2×C418yescomplemented
99C22×C4⋊C4C2314yes—
100C22×C4⋊C4C2314yes—
101C22×C22⋊C4—24no—
102C22×C22⋊C4—24no—
103C22×C22⋊C4—24no—
104C22×C22⋊C4—24no—
105C22×C22⋊C4—24no—
106C22×C22⋊C4—24no—
107C22×C22⋊C4—24no—
108C22×C22⋊C4—24no—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—42no—
112C22×C22⋊C4—42no—
113C22×C22⋊C4—42no—
114C22×C22⋊C4—42no—
115C22×C22⋊C4C2×C418yes—
116C22×C22⋊C4C2×C418yes—
117C22×C22⋊C4C2×C418yes—
118C22×C22⋊C4D418yes—
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2314yes—
125C22×C42—24no—
126C22×C42—24no—
127C22×C42—24no—
128C22×C42—24no—
129C22×C42—24no—
130C22×C42—24no—
131C22×C42—24no—
132C22×C42—42no—
133C22×C42—42no—
134C22×C42—42no—
135C22×C42—42no—
136C22×C42—42no—
137C22×C42C2314yes—
138C22×C42C2314yes—
139C22×C42C2314yes—
140C22×C42C2314yes—
141#397C2×C4164yescomplemented
142#388—232no—
143C4×C22⋊C4—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—24no—
155C2×#95—24no—
156C2×#95—24no—
157C2×#95—24no—
158C2×#95—42no—
159C2×#95—42no—
160C2×#95—42no—
161C2×#95—42no—
162C2×#95—42no—
163C2×#95C2×C418yescomplemented
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—
201C25C2×D414yes—
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—232no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—28no—
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—28no—
276C23×C4—28no—
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—28no—
292C23×C4—28no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4—416no—
296C23×C4—416no—
297C23×C4—416no—
298C23×C4—416no—
299C23×C4—416no—
300C23×C4—416no—
301C23×C4C22×C414yes—
302C23×C4C22×C414yes—
303C23×C4C22×C414yes—
304C23×C4C22×C414yes—
305C23×C4C22×C414yes—
306C23×C4C22×C414yes—
307C23×C4C2×D414yes—
308C23×C4C2×D414yes—
309C23×C4#4114yes—
310C23×C4#4114yes—
311C23×C4#4114yes—
312C23×C4#4114yes—
313C23×C4#4114yes—
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—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—416no—
338C2×C4⋊C4C22×C4116yescomplemented
339C2×C22⋊C4—232no—
340C2×C22⋊C4—232no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—232no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—416no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—416no—
358C2×C22⋊C4—416no—
359C2×C22⋊C4C22×C4116yes—
360C2×C22⋊C4C22×C4116yes—
361C2×C22⋊C4C22×C4116yes—
362C2×C22⋊C4C2×D4116yes—
363C2×C42—28no—
364C2×C42—28no—
365C2×C42—28no—
366C2×C42—28no—
367C2×C42—28no—
368C2×C42—28no—
369C2×C42—28no—
370C2×C42—44no—
371C2×C42—44no—
372C2×C42—44no—
373C2×C42—44no—
374C2×C42—44no—
375C2×C42—416no—
376C2×C42—416no—
377C2×C42—416no—
378C2×C42—416no—
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—28no—
390#95—28no—
391#95—28no—
392#95—28no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95—44no—
398#95C22×C4116yescomplemented
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—
447C24C4×D4116yes—
448C24C23×C414yes—
449C24C23×C412yes—
450C24C22×D414yes—
451C24C22×D412yes—
452C24C2×#4114yes—
453C24C2×#4112yes—
454C24C2×#4112yes—
455C24C2×#4112yes—
456C24C2×#4112yes—
457C24C2×#4112yes—
458C24C2×#4112yes—
459C24C2×#4112yes—
460C24C2×#4112yes—
461C24C2×#4112yes—
462C24H(5,𝔽2)12yes—
463C24H(5,𝔽2)12yes—
464C24H(5,𝔽2)12yes—
465C242−1+412yes—
466C24C2511yescharacteristic
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—232no—
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—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—28no—
517C22×C4—28no—
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—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—416no—
593C22×C4—416no—
594C22×C4—416no—
595C22×C4—416no—
596C22×C4—416no—
597C22×C4—4128no—
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—416no—
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#123116yes—
654C22×C4#126116yes—
655C22×C4C23×C414yes—
656C22×C4C23×C414yes—
657C22×C4C23×C414yes—
658C22×C4C23×C414yes—
659C22×C4C23×C414yes—
660C22×C4C23×C414yes—
661C22×C4C22×D414yes—
662C22×C4C22×D414yes—
663C22×C4C2×#4114yes—
664C22×C4C2×#4114yes—
665C22×C4C2×#4114yes—
666C22×C4C2×#4114yes—
667C22×C4C2×#4114yes—
668C22×C4C2×#4114yes—
669C22×C4C2×#4114yes—
670C22×C4C2×#4114yes—
671C4⋊C4—416no—
672C4⋊C4—416no—
673C22⋊C4—232no—
674C22⋊C4—232no—
675C22⋊C4—232no—
676C22⋊C4—416no—
677C22⋊C4—416no—
678C22⋊C4—416no—
679C42—416no—
680C42—416no—
681C42—416no—
682C42—416no—
683C23—232no—
684C23—232no—
685C23—24no—
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—232no—
704C23—416no—
705C23—416no—
706C23—416no—
707C23—416no—
708C23—416no—
709C23—416no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—416no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—416no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—416no—
729C23—416no—
730C23—416no—
731C23—416no—
732C23C2×C4×D418yes—
733C23C2×C4×D414yes—
734C23C4×#4114yes—
735C23C4×#4114yes—
736C23C4×#4114yes—
737C23C4×#4114yes—
738C23#51814yes—
739C23#52014yes—
740C23C2×#12314yes—
741C23#52514yes—
742C23C2×#12614yes—
743C23#52914yes—
744C23#52914yes—
745C23#52914yes—
746C23#52914yes—
747C23#52914yes—
748C23#53814yes—
749C23#53814yes—
750C23#54214yes—
751C23#54214yes—
752C23#54614yes—
753C23#54614yes—
754C23#54614yes—
755C23#54714yes—
756C23#55114yes—
757C23#55114yes—
758C23#55114yes—
759C23#55214yes—
760C23#55214yes—
761C23#55314yes—
762C23#55314yes—
763C23#55314yes—
764C23#55314yes—
765C23#55314yes—
766C23#55614yes—
767C23#55914yes—
768C23C24×C411yescharacteristic
769C23C23×D411yescharacteristic
770C23C22×#4111yescharacteristic
771C23C22×#4111yescharacteristic
772C23C22×#4111yescharacteristic
773C23C22×#4111yescharacteristic
774C23C22×#4111yescharacteristic
775C23C22×#4111yescharacteristic
776C23C22×#4111yescharacteristic
777C23C22×#4111yescharacteristic
778C23C22×#4111yescharacteristic
779C23C2×H(5,𝔽2)11yescharacteristic
780C23C2×H(5,𝔽2)11yescharacteristic
781C23C2×H(5,𝔽2)11yescharacteristic
782C23C2×2−1+411yescharacteristic
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—232no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—232no—
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—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—464no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—416no—
831C2×C4—416no—
832C2×C4—416no—
833C2×C4—416no—
834C2×C4—42no—
835C2×C4—42no—
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—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—416no—
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—416no—
876C2×C4—416no—
877C2×C4—416no—
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—88no—
893C2×C4—88no—
894C2×C4C2×#12318yes—
895C2×C4C2×#12618yes—
896C22—28no—
897C22—28no—
898C22—28no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—464no—
907C22—44no—
908C22—44no—
909C22—44no—
910C22—44no—
911C22—44no—
912C22C4×#12318yes—
913C22C4×#12618yes—
914C22#233718yes—
915C22#235918yes—
916C22#236418yes—
917C22#237318yes—
918C22#237418yes—
919C22#244418yes—
920C22#244718yes—
921C22#247018yes—
922C22#248018yes—
923C22#249418yes—
924C22#253018yes—
925C22#257818yes—
926C22#259518yes—
927C22C22×C4×D411yescharacteristic
928C22C2×C4×#4111yescharacteristic
929C22C2×C4×#4111yescharacteristic
930C22C2×C4×#4111yescharacteristic
931C22C2×C4×#4111yescharacteristic
932C22C2×#51811yescharacteristic
933C22C2×#52011yescharacteristic
934C22C22×#12311yescharacteristic
935C22C2×#52511yescharacteristic
936C22C22×#12611yescharacteristic
937C22C2×#52911yescharacteristic
938C22C2×#52911yescharacteristic
939C22C2×#52911yescharacteristic
940C22C2×#52911yescharacteristic
941C22C2×#52911yescharacteristic
942C22C2×#53811yescharacteristic
943C22C2×#53811yescharacteristic
944C22C2×#54211yescharacteristic
945C22C2×#54211yescharacteristic
946C22C2×#54611yescharacteristic
947C22C2×#54611yescharacteristic
948C22C2×#54611yescharacteristic
949C22C2×#54711yescharacteristic
950C22C2×#55111yescharacteristic
951C22C2×#55111yescharacteristic
952C22C2×#55111yescharacteristic
953C22C2×#55211yescharacteristic
954C22C2×#55211yescharacteristic
955C22C2×#55311yescharacteristic
956C22C2×#55311yescharacteristic
957C22C2×#55311yescharacteristic
958C22C2×#55311yescharacteristic
959C22C2×#55311yescharacteristic
960C22C2×#55611yescharacteristic
961C22C2×#55911yescharacteristic
962C4—28no—
963C4—28no—
964C4—44no—
965C4—44no—
966C4—44no—
967C4—44no—
968C4—44no—
969C4—44no—
970C4—44no—
971C4—44no—
972C4—44no—
973C4—44no—
974C4—82no—
975C4—82no—
976C2—48no—
977C2#14197116yesdirect product factor
978C2C2×C4×#12311yescharacteristic
979C2C2×C4×#12611yescharacteristic
980C2C2×#233711yescharacteristic
981C2C2×#235911yescharacteristic
982C2C2×#236411yescharacteristic
983C2C2×#237311yescharacteristic
984C2C2×#237411yescharacteristic
985C2C2×#248011yescharacteristic
986C2C2×#244411yescharacteristic
987C2C2×#244711yescharacteristic
988C2C2×#247011yescharacteristic
989C2C2×#249411yescharacteristic
990C2C2×#253011yescharacteristic
991C2C2×#257811yescharacteristic
992C2C2×#259511yescharacteristic
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. #14197C2direct (N × H)
5. C2×#1443C2semidirect
6. C2×#1443C2semidirect
9. C2×#1436C2semidirect
10. C2×#1436C2semidirect
11. C2×#1436C2semidirect
12. C2×#1436C2semidirect
13. C2×#1434C2semidirect
16. C2×C4×#95C2semidirect
30. C2×#397C4semidirect
58. #1443C22semidirect
59. #1443C22semidirect
62. #1436C22semidirect
63. #1436C22semidirect
64. #1436C22semidirect
65. #1436C22semidirect
66. #1434C22semidirect
69. C4×#95C22semidirect
98. C22×C4⋊C4C2×C4semidirect
141. #397C2×C4semidirect
163. C2×#95C2×C4semidirect
164. C2×#95C2×C4semidirect
165. C2×#95C2×C4semidirect
338. C2×C4⋊C4C22×C4semidirect
398. #95C22×C4semidirect
399. #95C22×C4semidirect
400. #95C22×C4semidirect
977. C2#14197direct (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×#3882
C22×C4×C22⋊C42
#141972
C2×#14432
C2×#14402
C2×#14372
C2×#14362
C2×#14342
C2×C22⋊#952
C2×C4×#952