Finite Group Databasebeta

← C2×#13969 #514248

Subgroups — C2×#13969 #514248

Order 512.

8090 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Q8C211yesmaximal, characteristic
2C23×C4×Q8C211yesmaximal, characteristic, complemented
3C22×#391C211yesmaximal, characteristic, complemented
4C22×#380C211yesmaximal, characteristic
5C22×C4×C22⋊C4C211yesmaximal, characteristic
6#13969C2116yesmaximal, direct product factor
7C2×#1441C212yesmaximal, complemented
8C2×#1439C212yesmaximal
9C2×#1437C212yesmaximal
10C2×#1436C212yesmaximal, complemented
11C2×C4⋊#95C211yesmaximal, characteristic, complemented
12C2×C4⋊#95C211yesmaximal, characteristic, complemented
13C24×Q8C2211yescharacteristic
14C25×C4C2211yescharacteristic
15C22×C22⋊Q8—28no—
16C22×C22⋊Q8—28no—
17C22×C22⋊Q8C4116yescomplemented
18C22×C22⋊Q8C2218yes—
19C22×C4×Q8—28no—
20C22×C4×Q8—28no—
21C22×C4×Q8—28no—
22C22×C4×Q8C2218yescomplemented
23C23×C4⋊C4C2212yes—
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2212yes—
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2212yes—
30C23×C22⋊C4C2212yes—
31C23×C22⋊C4C2211yescharacteristic
32C23×C42C2212yes—
33C23×C42C2211yescharacteristic
34C23×C42C2211yescharacteristic
35C2×#391—28no—
36C2×#391C2218yescomplemented
37C2×#380—28no—
38C2×#380C2218yes—
39C2×C4×C22⋊C4—28no—
40C2×C4×C22⋊C4C2218yes—
41C22×#95C2212yes—
42C22×#95C2212yes—
43C22×#95C2211yescharacteristic
44C22×#95C2212yes—
45C22×#95C2212yes—
46C22×#95C2212yes—
47C22×#95C2211yescharacteristic
48C22×#95C2212yes—
49C22×#95C2212yes—
50#1441C22116yescomplemented
51#1439C22116yes—
52#1437C22116yes—
53#1436C22116yescomplemented
54C4⋊#95C2218yescomplemented
55C4⋊#95C2218yescomplemented
56C26C2311yescharacteristic
57C23×Q8—24no—
58C23×Q8—24no—
59C23×Q8—24no—
60C23×Q8—24no—
61C23×Q8C2×C418yes—
62C23×Q8D418yes—
63C23×Q8D418yes—
64C23×Q8C2314yes—
65C24×C4—24no—
66C24×C4—24no—
67C24×C4—24no—
68C24×C4—24no—
69C24×C4—24no—
70C24×C4—24no—
71C24×C4C2×C418yes—
72C24×C4C2312yes—
73C24×C4C2314yes—
74C24×C4C2311yescharacteristic
75C24×C4C2312yes—
76C24×C4C2311yescharacteristic
77C24×C4C2312yes—
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C24×C4C2312yes—
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C2×C22⋊Q8—2128no—
84C2×C22⋊Q8—232no—
85C2×C22⋊Q8—232no—
86C2×C22⋊Q8C2×C4164yescomplemented
87C2×C4×Q8—2128no—
88C2×C4×Q8—232no—
89C2×C4×Q8—232no—
90C2×C4×Q8—232no—
91C22×C4⋊C4—28no—
92C22×C4⋊C4—28no—
93C22×C4⋊C4—28no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—28no—
99C22×C4⋊C4—28no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4C2×C418yes—
104C22×C4⋊C4C2×C4116yes—
105C22×C4⋊C4D418yes—
106C22×C4⋊C4C2318yes—
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2318yes—
110C22×C4⋊C4C2314yes—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—28no—
113C22×C22⋊C4—28no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—28no—
119C22×C22⋊C4—28no—
120C22×C22⋊C4—44no—
121C22×C22⋊C4C2×C4116yes—
122C22×C22⋊C4Q818yescomplemented
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2318yes—
125C22×C22⋊C4C2318yes—
126C22×C22⋊C4C2314yes—
127C22×C42—28no—
128C22×C42—28no—
129C22×C42—28no—
130C22×C42—24no—
131C22×C42—24no—
132C22×C42—24no—
133C22×C42—24no—
134C22×C42—24no—
135C22×C42D418yes—
136C22×C42C2318yes—
137C22×C42C2314yes—
138C22×C42C2314yes—
139#391—232no—
140#380—232no—
141C4×C22⋊C4—232no—
142C2×#95—24no—
143C2×#95—24no—
144C2×#95—28no—
145C2×#95—28no—
146C2×#95—28no—
147C2×#95—28no—
148C2×#95—28no—
149C2×#95—44no—
150C2×#95—44no—
151C2×#95C2318yes—
152C2×#95C2318yes—
153C2×#95C2314yes—
154C2×#95C2318yes—
155C2×#95C2318yes—
156C2×#95C2318yes—
157C2×#95C2314yes—
158C2×#95C2318yes—
159C2×#95C2318yes—
160C25—22no—
161C25—22no—
162C25—22no—
163C25—22no—
164C25—22no—
165C25—22no—
166C25—22no—
167C25—22no—
168C25—22no—
169C25—22no—
170C25—22no—
171C25—22no—
172C25C22×C414yes—
173C25C2×Q814yes—
174C25#4114yes—
175C25C2412yes—
176C25C2411yescharacteristic
177C22×Q8—232no—
178C22×Q8—232no—
179C22×Q8—232no—
180C22×Q8—232no—
181C22×Q8—232no—
182C22×Q8—232no—
183C22×Q8—28no—
184C22×Q8—28no—
185C22×Q8—28no—
186C22×Q8—28no—
187C22×Q8C22⋊C4164yescomplemented
188C22×Q8C22×C4116yes—
189C22×Q8C2×D4116yes—
190C22×Q8C2×D4116yes—
191C23×C4—24no—
192C23×C4—24no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—24no—
196C23×C4—24no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—24no—
200C23×C4—24no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—24no—
206C23×C4—22no—
207C23×C4—24no—
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—24no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—24no—
230C23×C4—22no—
231C23×C4—24no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—232no—
236C23×C4—232no—
237C23×C4—232no—
238C23×C4—28no—
239C23×C4—28no—
240C23×C4—28no—
241C23×C4—28no—
242C23×C4—28no—
243C23×C4—28no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—416no—
252C23×C4—416no—
253C23×C4—416no—
254C23×C4—416no—
255C23×C4C22×C418yes—
256C23×C4C22×C414yes—
257C23×C4C22×C4116yes—
258C23×C4C22×C418yes—
259C23×C4C22×C414yes—
260C23×C4C2×D414yes—
261C23×C4C2×D418yes—
262C23×C4C2×D418yes—
263C23×C4C2×D418yes—
264C23×C4C2×D414yes—
265C23×C4C2×D414yes—
266C23×C4C2×D414yes—
267C23×C4C2×D414yes—
268C23×C4C2×D414yes—
269C23×C4C2×Q814yes—
270C23×C4C2×Q814yes—
271C23×C4#4114yes—
272C23×C4#4114yes—
273C23×C4#4114yes—
274C23×C4#4114yes—
275C23×C4C2414yes—
276C23×C4C2414yes—
277C23×C4C2412yes—
278C23×C4C2414yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2414yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C22⋊Q8—2256no—
286C4×Q8—2256no—
287C2×C4⋊C4—264no—
288C2×C4⋊C4—232no—
289C2×C4⋊C4—264no—
290C2×C4⋊C4—232no—
291C2×C4⋊C4—216no—
292C2×C4⋊C4—216no—
293C2×C4⋊C4—216no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—216no—
299C2×C4⋊C4—216no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—416no—
304C2×C4⋊C4C22×C4116yes—
305C2×C4⋊C4C22×C4132yes—
306C2×C4⋊C4C2×D4116yes—
307C2×C22⋊C4—232no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—264no—
310C2×C22⋊C4—232no—
311C2×C22⋊C4—216no—
312C2×C22⋊C4—216no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—216no—
318C2×C22⋊C4—216no—
319C2×C22⋊C4—48no—
320C2×C22⋊C4—432no—
321C2×C22⋊C4C22×C4132yes—
322C2×C22⋊C4C2×Q8116yescomplemented
323C2×C42—264no—
324C2×C42—232no—
325C2×C42—216no—
326C2×C42—216no—
327C2×C42—216no—
328C2×C42—28no—
329C2×C42—28no—
330C2×C42—28no—
331C2×C42—28no—
332C2×C42—28no—
333C2×C42—416no—
334C2×C42C2×D4116yes—
335#95—28no—
336#95—28no—
337#95—216no—
338#95—216no—
339#95—216no—
340#95—216no—
341#95—216no—
342#95—48no—
343#95—48no—
344C24—28no—
345C24—28no—
346C24—28no—
347C24—28no—
348C24—28no—
349C24—28no—
350C24—28no—
351C24—28no—
352C24—28no—
353C24—28no—
354C24—28no—
355C24—28no—
356C24—28no—
357C24—28no—
358C24—28no—
359C24—28no—
360C24—28no—
361C24—28no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—44no—
375C24—44no—
376C24—44no—
377C24—44no—
378C24—44no—
379C24—44no—
380C24—44no—
381C24—44no—
382C24—44no—
383C24—44no—
384C24—44no—
385C24—44no—
386C24—44no—
387C24—44no—
388C24—44no—
389C24—44no—
390C24C4×Q8116yescomplemented
391C24C23×C414yes—
392C24C23×C412yes—
393C24C22×D412yes—
394C24C22×D412yes—
395C24C22×D412yes—
396C24C22×D412yes—
397C24C22×Q814yes—
398C24C22×Q812yes—
399C24C2×#4114yes—
400C24C2×#4112yes—
401C24C2×#4112yes—
402C24C2×#4112yes—
403C24C2×#4112yes—
404C24C2×#4112yes—
405C24H(5,𝔽2)12yes—
406C242−1+412yes—
407C242−1+412yes—
408C242−1+412yes—
409C24C2511yescharacteristic
410C2×Q8—232no—
411C2×Q8—232no—
412C2×Q8—232no—
413C2×Q8—232no—
414C2×Q8—232no—
415C2×Q8—232no—
416C2×Q8—2256no—
417C2×Q8C2×C22⋊C4164yescomplemented
418C22×C4—216no—
419C22×C4—216no—
420C22×C4—28no—
421C22×C4—216no—
422C22×C4—216no—
423C22×C4—216no—
424C22×C4—216no—
425C22×C4—28no—
426C22×C4—28no—
427C22×C4—28no—
428C22×C4—28no—
429C22×C4—28no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—216no—
439C22×C4—28no—
440C22×C4—28no—
441C22×C4—28no—
442C22×C4—216no—
443C22×C4—216no—
444C22×C4—216no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—216no—
451C22×C4—216no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—232no—
493C22×C4—232no—
494C22×C4—232no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—48no—
509C22×C4—44no—
510C22×C4—48no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—44no—
517C22×C4—48no—
518C22×C4—44no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—44no—
522C22×C4—48no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—416no—
527C22×C4—416no—
528C22×C4—416no—
529C22×C4—416no—
530C22×C4—4128no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4C2×C22⋊C4132yes—
539C22×C4C2×C22⋊C4116yes—
540C22×C4C4×D4116yes—
541C22×C4C4×D4116yes—
542C22×C4#120116yes—
543C22×C4#121116yes—
544C22×C4#121116yes—
545C22×C4C22⋊Q8116yescomplemented
546C22×C4#123116yes—
547C22×C4C23×C418yes—
548C22×C4C23×C414yes—
549C22×C4C23×C418yes—
550C22×C4C23×C414yes—
551C22×C4C22×D418yes—
552C22×C4C22×D414yes—
553C22×C4C22×D418yes—
554C22×C4C22×D418yes—
555C22×C4C22×D414yes—
556C22×C4C22×D414yes—
557C22×C4C22×D414yes—
558C22×C4C22×D414yes—
559C22×C4C22×D414yes—
560C22×C4C22×Q814yes—
561C22×C4C22×Q814yes—
562C22×C4C2×#4114yes—
563C22×C4C2×#4114yes—
564C22×C4C2×#4114yes—
565C22×C4C2×#4114yes—
566C4⋊C4—264no—
567C4⋊C4—232no—
568C4⋊C4—264no—
569C4⋊C4—232no—
570C4⋊C4—416no—
571C22⋊C4—232no—
572C22⋊C4—264no—
573C22⋊C4—232no—
574C22⋊C4—432no—
575C42—264no—
576C42—232no—
577C42—416no—
578C23—232no—
579C23—232no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—232no—
599C23—416no—
600C23—416no—
601C23—416no—
602C23—416no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—416no—
607C23—42no—
608C23—416no—
609C23—416no—
610C23—42no—
611C23—42no—
612C23—416no—
613C23—416no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—416no—
625C23—416no—
626C23—416no—
627C23C22×C22⋊C414yes—
628C23C2×C4×D414yes—
629C23C2×C4×D414yes—
630C23C2×C4×Q814yes—
631C23C2×C4×Q818yescomplemented
632C23C4×#4114yes—
633C23#51914yes—
634C23#52014yes—
635C23C2×#12014yes—
636C23C2×#12114yes—
637C23C2×#12114yes—
638C23C2×C22⋊Q814yes—
639C23C2×#12314yes—
640C23#52514yes—
641C23#52914yes—
642C23#53314yes—
643C23#53614yes—
644C23#53714yes—
645C23#54114yes—
646C23#54214yes—
647C23#54614yes—
648C23#54714yes—
649C23#54814yes—
650C23#54814yes—
651C23#54814yes—
652C23#54814yes—
653C23#54814yes—
654C23D4×Q814yes—
655C23D4×Q814yes—
656C23D4×Q814yes—
657C23#55014yes—
658C23#55014yes—
659C23#55214yes—
660C23#55214yes—
661C23#55414yes—
662C23#55614yes—
663C23C24×C411yescharacteristic
664C23C23×D411yescharacteristic
665C23C23×D411yescharacteristic
666C23C23×D411yescharacteristic
667C23C23×D411yescharacteristic
668C23C23×Q811yescharacteristic
669C23C22×#4111yescharacteristic
670C23C22×#4111yescharacteristic
671C23C22×#4111yescharacteristic
672C23C22×#4111yescharacteristic
673C23C22×#4111yescharacteristic
674C23C2×H(5,𝔽2)11yescharacteristic
675C23C2×2−1+411yescharacteristic
676C23C2×2−1+411yescharacteristic
677C23C2×2−1+411yescharacteristic
678Q8—2128no—
679C2×C4—28no—
680C2×C4—28no—
681C2×C4—24no—
682C2×C4—28no—
683C2×C4—28no—
684C2×C4—28no—
685C2×C4—232no—
686C2×C4—28no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—264no—
693C2×C4—28no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—432no—
712C2×C4—416no—
713C2×C4—432no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—416no—
739C2×C4—416no—
740C2×C4—416no—
741C2×C4—464no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—816no—
750C2×C4#386164yes—
751C2×C4C22×C22⋊C4116yes—
752C2×C4C22×C22⋊C418yes—
753C2×C4C2×C4×D418yes—
754C2×C4C2×C4×D418yes—
755C2×C4C2×#12018yes—
756C2×C4C2×#12118yes—
757C2×C4C2×#12118yes—
758C2×C4C2×C22⋊Q818yescomplemented
759C2×C4C2×#12318yes—
760C22—28no—
761C22—28no—
762C22—28no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—464no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22C2×#38618yes—
777C22C4×C22⋊Q818yes—
778C22#232318yes—
779C22Q8×C22⋊C418yes—
780C22#234118yes—
781C22#236018yes—
782C22#236218yes—
783C22#240718yes—
784C22#240918yes—
785C22#242118yes—
786C22#242318yes—
787C22#242618yes—
788C22#242918yes—
789C22#253618yes—
790C22#253818yes—
791C22C23×C22⋊C411yescharacteristic
792C22C22×C4×D411yescharacteristic
793C22C22×C4×D411yescharacteristic
794C22C22×C4×Q811yescharacteristic
795C22C2×C4×#4111yescharacteristic
796C22C2×#51911yescharacteristic
797C22C2×#52011yescharacteristic
798C22C22×#12011yescharacteristic
799C22C22×#12111yescharacteristic
800C22C22×#12111yescharacteristic
801C22C22×C22⋊Q811yescharacteristic
802C22C22×#12311yescharacteristic
803C22C2×#52511yescharacteristic
804C22C2×#52911yescharacteristic
805C22C2×#53311yescharacteristic
806C22C2×#53611yescharacteristic
807C22C2×#53711yescharacteristic
808C22C2×#54111yescharacteristic
809C22C2×#54211yescharacteristic
810C22C2×#54611yescharacteristic
811C22C2×#54711yescharacteristic
812C22C2×#54811yescharacteristic
813C22C2×#54811yescharacteristic
814C22C2×#54811yescharacteristic
815C22C2×#54811yescharacteristic
816C22C2×#54811yescharacteristic
817C22C2×D4×Q811yescharacteristic
818C22C2×D4×Q811yescharacteristic
819C22C2×D4×Q811yescharacteristic
820C22C2×#55011yescharacteristic
821C22C2×#55011yescharacteristic
822C22C2×#55211yescharacteristic
823C22C2×#55211yescharacteristic
824C22C2×#55411yescharacteristic
825C22C2×#55611yescharacteristic
826C4—28no—
827C4—216no—
828C4—48no—
829C4—44no—
830C4—44no—
831C4—44no—
832C4—48no—
833C4—44no—
834C4—84no—
835C4C2×#386116yes—
836C2—48no—
837C2#13969116yesdirect product factor
838C2C22×#38611yescharacteristic
839C2C2×C4×C22⋊Q811yescharacteristic
840C2C2×#232311yescharacteristic
841C2C2×Q8×C22⋊C411yescharacteristic
842C2C2×#234111yescharacteristic
843C2C2×#236011yescharacteristic
844C2C2×#236211yescharacteristic
845C2C2×#240911yescharacteristic
846C2C2×#242311yescharacteristic
847C2C2×#242911yescharacteristic
848C2C2×#242111yescharacteristic
849C2C2×#242611yescharacteristic
850C2C2×#240711yescharacteristic
851C2C2×#253611yescharacteristic
852C2C2×#253811yescharacteristic
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
2. C23×C4×Q8C2semidirect
3. C22×#391C2semidirect
6. #13969C2direct (N × H)
7. C2×#1441C2semidirect
10. C2×#1436C2semidirect
11. C2×C4⋊#95C2semidirect
12. C2×C4⋊#95C2semidirect
17. C22×C22⋊Q8C4semidirect
22. C22×C4×Q8C22semidirect
36. C2×#391C22semidirect
50. #1441C22semidirect
53. #1436C22semidirect
54. C4⋊#95C22semidirect
55. C4⋊#95C22semidirect
86. C2×C22⋊Q8C2×C4semidirect
122. C22×C22⋊C4Q8semidirect
187. C22×Q8C22⋊C4semidirect
322. C2×C22⋊C4C2×Q8semidirect
390. C24C4×Q8semidirect
417. C2×Q8C2×C22⋊C4semidirect
545. C22×C4C22⋊Q8semidirect
631. C23C2×C4×Q8semidirect
758. C2×C4C2×C22⋊Q8semidirect
837. C2#13969direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊Q82
C23×C4×Q82
C22×#3912
C22×#3802
C22×C4×C22⋊C42
#139692
C2×#14412
C2×#14392
C2×#14372
C2×#14362
C2×C4⋊#952