Finite Group Databasebeta

← C2×#15131 #608363

Subgroups — C2×#15131 #608363

Order 512.

5950 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#396C212yesmaximal
2C22×#389C211yesmaximal, characteristic, complemented
3C22×#389C211yesmaximal, characteristic, complemented
4C22×#384C211yesmaximal, characteristic, complemented
5C22×#380C211yesmaximal, characteristic
6C22×#380C211yesmaximal, characteristic
7C22×C4×C22⋊C4C211yesmaximal, characteristic
8#15131C2116yesmaximal, direct product factor
9C2×#1441C212yesmaximal, complemented
10C2×#1441C212yesmaximal, complemented
11C2×#1439C212yesmaximal
12C2×C4⋊#95C211yesmaximal, characteristic, complemented
13C25×C4C2211yescharacteristic
14C23×C4⋊C4C2212yes—
15C23×C4⋊C4C2211yescharacteristic
16C23×C4⋊C4C2211yescharacteristic
17C23×C4⋊C4C2212yes—
18C23×C4⋊C4C2212yes—
19C23×C4⋊C4C2212yes—
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23C23×C22⋊C4C2212yes—
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27C23×C42C2211yescharacteristic
28C2×#396—216no—
29C2×#396C22116yes—
30C2×#389—28no—
31C2×#389—28no—
32C2×#389C2218yescomplemented
33C2×#389C2218yescomplemented
34C2×#384—28no—
35C2×#384C2218yescomplemented
36C2×#380—28no—
37C2×#380—28no—
38C2×#380C2218yes—
39C2×#380C2218yes—
40C2×C4×C22⋊C4—28no—
41C2×C4×C22⋊C4C2218yes—
42C22×#95C2212yes—
43C22×#95C2212yes—
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2212yes—
47C22×#95C2212yes—
48C22×#95C2212yes—
49C22×#95C2212yes—
50#1441C22116yescomplemented
51#1441C22116yescomplemented
52#1439C22116yes—
53C4⋊#95C2218yescomplemented
54C26C2311yescharacteristic
55C24×C4—24no—
56C24×C4—24no—
57C24×C4—24no—
58C24×C4—24no—
59C24×C4—24no—
60C24×C4—24no—
61C24×C4Q818yes—
62C24×C4C2312yes—
63C24×C4C2312yes—
64C24×C4C2311yescharacteristic
65C24×C4C2312yes—
66C24×C4C2312yes—
67C24×C4C2314yes—
68C24×C4C2311yescharacteristic
69C24×C4C2311yescharacteristic
70C24×C4C2311yescharacteristic
71C24×C4C2311yescharacteristic
72C24×C4C2311yescharacteristic
73C22×C4⋊C4—24no—
74C22×C4⋊C4—24no—
75C22×C4⋊C4—24no—
76C22×C4⋊C4—24no—
77C22×C4⋊C4—28no—
78C22×C4⋊C4—28no—
79C22×C4⋊C4—28no—
80C22×C4⋊C4—24no—
81C22×C4⋊C4—24no—
82C22×C4⋊C4—28no—
83C22×C4⋊C4—28no—
84C22×C4⋊C4—24no—
85C22×C4⋊C4—28no—
86C22×C4⋊C4—28no—
87C22×C4⋊C4—24no—
88C22×C4⋊C4—28no—
89C22×C4⋊C4—28no—
90C22×C4⋊C4—24no—
91C22×C4⋊C4—24no—
92C22×C4⋊C4—44no—
93C22×C4⋊C4—44no—
94C22×C4⋊C4—44no—
95C22×C4⋊C4D418yes—
96C22×C4⋊C4D418yes—
97C22×C4⋊C4C2318yes—
98C22×C4⋊C4C2314yes—
99C22×C4⋊C4C2314yes—
100C22×C4⋊C4C2318yes—
101C22×C4⋊C4C2318yes—
102C22×C4⋊C4C2318yes—
103C22×C4⋊C4C2314yes—
104C22×C4⋊C4C2314yes—
105C22×C22⋊C4—24no—
106C22×C22⋊C4—24no—
107C22×C22⋊C4—24no—
108C22×C22⋊C4—24no—
109C22×C22⋊C4—28no—
110C22×C22⋊C4—28no—
111C22×C22⋊C4—28no—
112C22×C22⋊C4—28no—
113C22×C22⋊C4—44no—
114C22×C22⋊C4—44no—
115C22×C22⋊C4D418yes—
116C22×C22⋊C4Q818yes—
117C22×C22⋊C4C2318yes—
118C22×C22⋊C4C2318yes—
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2314yes—
121C22×C42—24no—
122C22×C42—24no—
123C22×C42—24no—
124C22×C42—24no—
125C22×C42—24no—
126C22×C42D418yes—
127C22×C42C2314yes—
128C22×C42C2314yes—
129#396—264no—
130#389—232no—
131#389—232no—
132#384—232no—
133#380—232no—
134#380—232no—
135C4×C22⋊C4—232no—
136C2×#95—28no—
137C2×#95—24no—
138C2×#95—24no—
139C2×#95—28no—
140C2×#95—28no—
141C2×#95—28no—
142C2×#95—28no—
143C2×#95—44no—
144C2×#95C2318yes—
145C2×#95C2318yes—
146C2×#95C2318yes—
147C2×#95C2314yes—
148C2×#95C2314yes—
149C2×#95C2318yes—
150C2×#95C2318yes—
151C2×#95C2318yes—
152C25—22no—
153C25—22no—
154C25—22no—
155C25—22no—
156C25—22no—
157C25—22no—
158C25—22no—
159C25—22no—
160C25—22no—
161C25—22no—
162C25—22no—
163C25—22no—
164C25C2×D414yes—
165C25C2×Q814yes—
166C25C2×Q814yes—
167C25C2412yes—
168C25C2411yescharacteristic
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—24no—
178C23×C4—24no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—24no—
182C23×C4—24no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—24no—
191C23×C4—24no—
192C23×C4—24no—
193C23×C4—24no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—24no—
200C23×C4—24no—
201C23×C4—22no—
202C23×C4—24no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—24no—
206C23×C4—22no—
207C23×C4—232no—
208C23×C4—232no—
209C23×C4—232no—
210C23×C4—28no—
211C23×C4—28no—
212C23×C4—28no—
213C23×C4—28no—
214C23×C4—28no—
215C23×C4—28no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—416no—
231C23×C4—416no—
232C23×C4—416no—
233C23×C4—416no—
234C23×C4C2×D418yes—
235C23×C4C2×D418yes—
236C23×C4C2×D414yes—
237C23×C4C2×D414yes—
238C23×C4C2×D414yes—
239C23×C4C2×D414yes—
240C23×C4C2×D414yes—
241C23×C4C2×D414yes—
242C23×C4C2×D414yes—
243C23×C4C2×Q814yes—
244C23×C4C2×Q814yes—
245C23×C4C2×Q8116yes—
246C23×C4C2×Q814yes—
247C23×C4C2×Q814yes—
248C23×C4#4114yes—
249C23×C4#4114yes—
250C23×C4#4114yes—
251C23×C4#4114yes—
252C23×C4#4114yes—
253C23×C4C2414yes—
254C23×C4C2414yes—
255C23×C4C2414yes—
256C23×C4C2414yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C2×C4⋊C4—232no—
264C2×C4⋊C4—232no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4—28no—
268C2×C4⋊C4—28no—
269C2×C4⋊C4—28no—
270C2×C4⋊C4—28no—
271C2×C4⋊C4—216no—
272C2×C4⋊C4—216no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—216no—
275C2×C4⋊C4—216no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—216no—
278C2×C4⋊C4—216no—
279C2×C4⋊C4—216no—
280C2×C4⋊C4—216no—
281C2×C4⋊C4—216no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—48no—
285C2×C4⋊C4—48no—
286C2×C4⋊C4—48no—
287C2×C4⋊C4—432no—
288C2×C4⋊C4—432no—
289C2×C4⋊C4—432no—
290C2×C4⋊C4—432no—
291C2×C4⋊C4—416no—
292C2×C4⋊C4—416no—
293C2×C4⋊C4C2×D4116yes—
294C2×C4⋊C4C2×D4116yes—
295C2×C22⋊C4—232no—
296C2×C22⋊C4—232no—
297C2×C22⋊C4—28no—
298C2×C22⋊C4—28no—
299C2×C22⋊C4—28no—
300C2×C22⋊C4—28no—
301C2×C22⋊C4—216no—
302C2×C22⋊C4—216no—
303C2×C22⋊C4—216no—
304C2×C22⋊C4—216no—
305C2×C22⋊C4—48no—
306C2×C22⋊C4—48no—
307C2×C22⋊C4—432no—
308C2×C22⋊C4—432no—
309C2×C22⋊C4C2×D4116yes—
310C2×C22⋊C4C2×Q8116yes—
311C2×C42—232no—
312C2×C42—28no—
313C2×C42—28no—
314C2×C42—28no—
315C2×C42—28no—
316C2×C42—28no—
317C2×C42—416no—
318C2×C42C2×D4116yes—
319#95—28no—
320#95—28no—
321#95—216no—
322#95—216no—
323#95—216no—
324#95—216no—
325#95—216no—
326#95—48no—
327C24—28no—
328C24—28no—
329C24—28no—
330C24—28no—
331C24—28no—
332C24—28no—
333C24—28no—
334C24—28no—
335C24—28no—
336C24—28no—
337C24—28no—
338C24—28no—
339C24—28no—
340C24—28no—
341C24—28no—
342C24—28no—
343C24—28no—
344C24—28no—
345C24—22no—
346C24—22no—
347C24—22no—
348C24—22no—
349C24—22no—
350C24—22no—
351C24—22no—
352C24—22no—
353C24—22no—
354C24—22no—
355C24—22no—
356C24—22no—
357C24—44no—
358C24—44no—
359C24—44no—
360C24—44no—
361C24—44no—
362C24—44no—
363C24—44no—
364C24—44no—
365C24—44no—
366C24—44no—
367C24—44no—
368C24—44no—
369C24—44no—
370C24—44no—
371C24—44no—
372C24—44no—
373C24C4⋊Q8116yes—
374C24C22×D414yes—
375C24C22×D412yes—
376C24C22×D412yes—
377C24C22×D412yes—
378C24C22×D412yes—
379C24C22×Q814yes—
380C24C22×Q814yes—
381C24C22×Q812yes—
382C24C22×Q812yes—
383C24C2×#4112yes—
384C24C2×#4112yes—
385C24C2×#4112yes—
386C24C2×#4112yes—
387C24C2×#4112yes—
388C24H(5,𝔽2)12yes—
389C24H(5,𝔽2)12yes—
390C242−1+412yes—
391C242−1+412yes—
392C24C2511yescharacteristic
393C22×C4—28no—
394C22×C4—28no—
395C22×C4—28no—
396C22×C4—28no—
397C22×C4—28no—
398C22×C4—28no—
399C22×C4—28no—
400C22×C4—28no—
401C22×C4—28no—
402C22×C4—28no—
403C22×C4—28no—
404C22×C4—28no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—28no—
414C22×C4—216no—
415C22×C4—216no—
416C22×C4—28no—
417C22×C4—28no—
418C22×C4—28no—
419C22×C4—28no—
420C22×C4—216no—
421C22×C4—216no—
422C22×C4—28no—
423C22×C4—216no—
424C22×C4—216no—
425C22×C4—28no—
426C22×C4—28no—
427C22×C4—28no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—232no—
459C22×C4—232no—
460C22×C4—232no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—44no—
476C22×C4—44no—
477C22×C4—48no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—48no—
483C22×C4—44no—
484C22×C4—48no—
485C22×C4—44no—
486C22×C4—48no—
487C22×C4—48no—
488C22×C4—44no—
489C22×C4—48no—
490C22×C4—48no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—48no—
494C22×C4—44no—
495C22×C4—416no—
496C22×C4—416no—
497C22×C4—416no—
498C22×C4—416no—
499C22×C4—4128no—
500C22×C4—48no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4#121116yes—
515C22×C4#121116yes—
516C22×C4#121116yes—
517C22×C4#121116yes—
518C22×C4C22⋊Q8116yes—
519C22×C4C22⋊Q8116yes—
520C22×C4C22⋊Q8116yes—
521C22×C4C22⋊Q8116yes—
522C22×C4#126116yes—
523C22×C4C22×D418yes—
524C22×C4C22×D414yes—
525C22×C4C22×D418yes—
526C22×C4C22×D414yes—
527C22×C4C22×D414yes—
528C22×C4C22×D414yes—
529C22×C4C22×D414yes—
530C22×C4C22×D414yes—
531C22×C4C22×D414yes—
532C22×C4C22×Q814yes—
533C22×C4C22×Q814yes—
534C22×C4C22×Q814yes—
535C22×C4C22×Q814yes—
536C22×C4C2×#4114yes—
537C22×C4C2×#4114yes—
538C22×C4C2×#4114yes—
539C22×C4C2×#4114yes—
540C22×C4C2×#4114yes—
541C4⋊C4—232no—
542C4⋊C4—232no—
543C4⋊C4—432no—
544C4⋊C4—432no—
545C4⋊C4—432no—
546C4⋊C4—432no—
547C4⋊C4—416no—
548C4⋊C4—416no—
549C22⋊C4—232no—
550C22⋊C4—232no—
551C22⋊C4—432no—
552C22⋊C4—432no—
553C42—232no—
554C42—416no—
555C23—232no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—232no—
569C23—232no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—416no—
577C23—416no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—416no—
583C23—416no—
584C23—42no—
585C23—42no—
586C23—416no—
587C23—42no—
588C23—416no—
589C23—42no—
590C23—416no—
591C23—42no—
592C23—42no—
593C23—416no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—416no—
601C23—416no—
602C23—416no—
603C23—416no—
604C23C2×#12114yes—
605C23C2×#12114yes—
606C23C2×#12114yes—
607C23C2×#12114yes—
608C23C2×C22⋊Q814yes—
609C23C2×C22⋊Q814yes—
610C23C2×C22⋊Q814yes—
611C23C2×C22⋊Q814yes—
612C23C2×#12614yes—
613C23C2×C4⋊Q818yes—
614C23C2×C4⋊Q814yes—
615C23#53214yes—
616C23#53314yes—
617C23#53314yes—
618C23#53714yes—
619C23#53714yes—
620C23#54014yes—
621C23#54114yes—
622C23#54414yes—
623C23#54414yes—
624C23D4214yes—
625C23D4214yes—
626C23#54614yes—
627C23#54714yes—
628C23#54714yes—
629C23#54714yes—
630C23#54814yes—
631C23D4×Q814yes—
632C23D4×Q814yes—
633C23#55014yes—
634C23#55214yes—
635C23#55314yes—
636C23#55414yes—
637C23#55414yes—
638C23#55514yes—
639C23#55614yes—
640C23C23×D411yescharacteristic
641C23C23×D411yescharacteristic
642C23C23×D411yescharacteristic
643C23C23×D411yescharacteristic
644C23C23×Q811yescharacteristic
645C23C23×Q811yescharacteristic
646C23C22×#4111yescharacteristic
647C23C22×#4111yescharacteristic
648C23C22×#4111yescharacteristic
649C23C22×#4111yescharacteristic
650C23C22×#4111yescharacteristic
651C23C2×H(5,𝔽2)11yescharacteristic
652C23C2×H(5,𝔽2)11yescharacteristic
653C23C2×2−1+411yescharacteristic
654C23C2×2−1+411yescharacteristic
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—232no—
658C2×C4—232no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—28no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—28no—
677C2×C4—28no—
678C2×C4—24no—
679C2×C4—28no—
680C2×C4—24no—
681C2×C4—28no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—416no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—432no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—416no—
707C2×C4—432no—
708C2×C4—416no—
709C2×C4—464no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—816no—
725C2×C4—816no—
726C2×C4#396164yescomplemented
727C2×C4C2×#12118yes—
728C2×C4C2×#12118yes—
729C2×C4C2×#12118yes—
730C2×C4C2×#12118yes—
731C2×C4C2×C22⋊Q818yes—
732C2×C4C2×C22⋊Q818yes—
733C2×C4C2×C22⋊Q818yes—
734C2×C4C2×C22⋊Q818yes—
735C2×C4C2×#12618yes—
736C22—28no—
737C22—28no—
738C22—28no—
739C22—464no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22C2×#39618yes—
753C22#241618yes—
754C22#241718yes—
755C22#242818yes—
756C22#242918yes—
757C22#243918yes—
758C22#244018yes—
759C22#244018yes—
760C22#244118yes—
761C22#249618yes—
762C22#249718yes—
763C22#253718yes—
764C22#253818yes—
765C22#262918yes—
766C22#285718yes—
767C22C22×#12111yescharacteristic
768C22C22×#12111yescharacteristic
769C22C22×#12111yescharacteristic
770C22C22×#12111yescharacteristic
771C22C22×C22⋊Q811yescharacteristic
772C22C22×C22⋊Q811yescharacteristic
773C22C22×C22⋊Q811yescharacteristic
774C22C22×C22⋊Q811yescharacteristic
775C22C22×#12611yescharacteristic
776C22C22×C4⋊Q811yescharacteristic
777C22C2×#53211yescharacteristic
778C22C2×#53311yescharacteristic
779C22C2×#53311yescharacteristic
780C22C2×#53711yescharacteristic
781C22C2×#53711yescharacteristic
782C22C2×#54011yescharacteristic
783C22C2×#54111yescharacteristic
784C22C2×#54411yescharacteristic
785C22C2×#54411yescharacteristic
786C22C2×D4211yescharacteristic
787C22C2×D4211yescharacteristic
788C22C2×#54611yescharacteristic
789C22C2×#54711yescharacteristic
790C22C2×#54711yescharacteristic
791C22C2×#54711yescharacteristic
792C22C2×#54811yescharacteristic
793C22C2×D4×Q811yescharacteristic
794C22C2×D4×Q811yescharacteristic
795C22C2×#55011yescharacteristic
796C22C2×#55211yescharacteristic
797C22C2×#55311yescharacteristic
798C22C2×#55411yescharacteristic
799C22C2×#55411yescharacteristic
800C22C2×#55511yescharacteristic
801C22C2×#55611yescharacteristic
802C4—28no—
803C4—28no—
804C4—44no—
805C4—48no—
806C4—44no—
807C4—48no—
808C4—44no—
809C4—84no—
810C4—84no—
811C4C2×#396116yescomplemented
812C2—48no—
813C2#15131116yesdirect product factor
814C2C22×#39611yescharacteristic
815C2C2×#262911yescharacteristic
816C2C2×#241611yescharacteristic
817C2C2×#244011yescharacteristic
818C2C2×#244011yescharacteristic
819C2C2×#242811yescharacteristic
820C2C2×#241711yescharacteristic
821C2C2×#242911yescharacteristic
822C2C2×#243911yescharacteristic
823C2C2×#244111yescharacteristic
824C2C2×#249611yescharacteristic
825C2C2×#249711yescharacteristic
826C2C2×#253711yescharacteristic
827C2C2×#253811yescharacteristic
828C2C2×#285711yescharacteristic
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×#389C2semidirect
3. C22×#389C2semidirect
4. C22×#384C2semidirect
8. #15131C2direct (N × H)
9. C2×#1441C2semidirect
10. C2×#1441C2semidirect
12. C2×C4⋊#95C2semidirect
32. C2×#389C22semidirect
33. C2×#389C22semidirect
35. C2×#384C22semidirect
50. #1441C22semidirect
51. #1441C22semidirect
53. C4⋊#95C22semidirect
726. C2×C4#396semidirect
811. C4C2×#396semidirect
813. C2#15131direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3962
C22×#3892
C22×#3842
C22×#3802
C22×C4×C22⋊C42
#151312
C2×#14412
C2×#14392
C2×C4⋊#952