Finite Group Databasebeta

← C2×#13997 #514288

Subgroups — C2×#13997 #514288

Order 512.

7258 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Q8C211yesmaximal, characteristic
2C22×#391C211yesmaximal, characteristic, complemented
3C22×#391C211yesmaximal, characteristic, complemented
4C22×#389C211yesmaximal, characteristic, complemented
5C22×#380C211yesmaximal, characteristic
6C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
7C22×C4×C22⋊C4C211yesmaximal, characteristic
8#13997C2116yesmaximal, direct product factor
9C2×#1445C212yesmaximal, complemented
10C2×#1439C212yesmaximal
11C2×#1437C212yesmaximal
12C2×C4⋊#95C212yesmaximal, complemented
13C24×Q8C2211yescharacteristic
14C25×C4C2211yescharacteristic
15C22×C22⋊Q8—28no—
16C22×C22⋊Q8—28no—
17C22×C22⋊Q8C4116yescomplemented
18C22×C22⋊Q8C2218yes—
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2212yes—
21C23×C4⋊C4C2212yes—
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2212yes—
26C23×C22⋊C4C2212yes—
27C23×C22⋊C4C2211yescharacteristic
28C23×C42C2211yescharacteristic
29C23×C42C2212yes—
30C23×C42C2211yescharacteristic
31C2×#391—28no—
32C2×#391—28no—
33C2×#391C2218yescomplemented
34C2×#391C2218yescomplemented
35C2×#389—28no—
36C2×#389C2218yescomplemented
37C2×#380—28no—
38C2×#380C2218yes—
39C2×C4×C4⋊C4—28no—
40C2×C4×C4⋊C4C2218yescomplemented
41C2×C4×C22⋊C4—28no—
42C2×C4×C22⋊C4C2218yes—
43C22×#95C2212yes—
44C22×#95C2212yes—
45C22×#95C2212yes—
46C22×#95C2211yescharacteristic
47C22×#95C2212yes—
48C22×#95C2212yes—
49C22×#95C2212yes—
50C22×#95C2211yescharacteristic
51C22×#95C2212yes—
52#1445C22116yescomplemented
53#1439C22116yes—
54#1437C22116yes—
55C4⋊#95C22116yescomplemented
56C26C2311yescharacteristic
57C23×Q8—24no—
58C23×Q8—24no—
59C23×Q8—24no—
60C23×Q8—24no—
61C23×Q8—24no—
62C23×Q8—24no—
63C23×Q8C2×C418yes—
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×C4C2312yes—
77C24×C4C2311yescharacteristic
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
87C22×C4⋊C4—28no—
88C22×C4⋊C4—28no—
89C22×C4⋊C4—24no—
90C22×C4⋊C4—24no—
91C22×C4⋊C4—24no—
92C22×C4⋊C4—28no—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—28no—
96C22×C4⋊C4—44no—
97C22×C4⋊C4C2×C4116yes—
98C22×C4⋊C4C2×C418yes—
99C22×C4⋊C4D418yes—
100C22×C4⋊C4D418yes—
101C22×C4⋊C4D418yes—
102C22×C4⋊C4C2314yes—
103C22×C4⋊C4C2318yes—
104C22×C4⋊C4C2318yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2314yes—
107C22×C22⋊C4—24no—
108C22×C22⋊C4—28no—
109C22×C22⋊C4—28no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—28no—
115C22×C22⋊C4—28no—
116C22×C22⋊C4—44no—
117C22×C22⋊C4C2×C4116yes—
118C22×C22⋊C4Q818yescomplemented
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2318yes—
121C22×C22⋊C4C2318yes—
122C22×C22⋊C4C2314yes—
123C22×C42—24no—
124C22×C42—24no—
125C22×C42—24no—
126C22×C42—28no—
127C22×C42—24no—
128C22×C42—24no—
129C22×C42—28no—
130C22×C42—44no—
131C22×C42D418yes—
132C22×C42C2314yes—
133C22×C42C2318yes—
134C22×C42C2314yes—
135#391—232no—
136#391—232no—
137#389—232no—
138#380—232no—
139C4×C4⋊C4—232no—
140C4×C22⋊C4—232no—
141C2×#95—24no—
142C2×#95—24no—
143C2×#95—28no—
144C2×#95—28no—
145C2×#95—28no—
146C2×#95—28no—
147C2×#95—28no—
148C2×#95—28no—
149C2×#95—28no—
150C2×#95C2314yes—
151C2×#95C2318yes—
152C2×#95C2318yes—
153C2×#95C2318yes—
154C2×#95C2318yes—
155C2×#95C2318yes—
156C2×#95C2318yes—
157C2×#95C2318yes—
158C2×#95C2314yes—
159C25—22no—
160C25—22no—
161C25—22no—
162C25—22no—
163C25—22no—
164C25—22no—
165C25—22no—
166C25—22no—
167C25—22no—
168C25—22no—
169C25—22no—
170C25—22no—
171C25C22×C414yes—
172C25C2×Q814yes—
173C25#4114yes—
174C25C2412yes—
175C25C2411yescharacteristic
176C22×Q8—232no—
177C22×Q8—232no—
178C22×Q8—232no—
179C22×Q8—28no—
180C22×Q8—28no—
181C22×Q8—28no—
182C22×Q8—28no—
183C22×Q8—28no—
184C22×Q8—28no—
185C22×Q8—416no—
186C22×Q8—416no—
187C22×Q8—416no—
188C22×Q8—416no—
189C22×Q8C22×C4116yes—
190C23×C4—22no—
191C23×C4—24no—
192C23×C4—24no—
193C23×C4—22no—
194C23×C4—24no—
195C23×C4—22no—
196C23×C4—24no—
197C23×C4—22no—
198C23×C4—24no—
199C23×C4—24no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—24no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—22no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—232no—
235C23×C4—232no—
236C23×C4—232no—
237C23×C4—28no—
238C23×C4—28no—
239C23×C4—28no—
240C23×C4—28no—
241C23×C4—28no—
242C23×C4—28no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—416no—
251C23×C4—416no—
252C23×C4—416no—
253C23×C4—416no—
254C23×C4C22×C418yes—
255C23×C4C22×C414yes—
256C23×C4C22×C4116yes—
257C23×C4C22×C418yes—
258C23×C4C22×C414yes—
259C23×C4C2×D418yes—
260C23×C4C2×D414yes—
261C23×C4C2×D418yes—
262C23×C4C2×D418yes—
263C23×C4C2×D414yes—
264C23×C4C2×D414yes—
265C23×C4C2×D414yes—
266C23×C4C2×D414yes—
267C23×C4C2×D414yes—
268C23×C4C2×Q814yes—
269C23×C4C2×Q814yes—
270C23×C4#4114yes—
271C23×C4#4114yes—
272C23×C4#4114yes—
273C23×C4#4114yes—
274C23×C4C2414yes—
275C23×C4C2414yes—
276C23×C4C2412yes—
277C23×C4C2414yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2414yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C22⋊Q8—2256no—
285C2×C4⋊C4—264no—
286C2×C4⋊C4—232no—
287C2×C4⋊C4—216no—
288C2×C4⋊C4—216no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—216no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—216no—
296C2×C4⋊C4—48no—
297C2×C4⋊C4—432no—
298C2×C4⋊C4—416no—
299C2×C4⋊C4C22⋊C4164yescomplemented
300C2×C4⋊C4C22×C4132yes—
301C2×C4⋊C4C22×C4116yes—
302C2×C4⋊C4C2×D4116yes—
303C2×C4⋊C4C2×D4116yes—
304C2×C4⋊C4C2×D4116yes—
305C2×C22⋊C4—232no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—264no—
308C2×C22⋊C4—232no—
309C2×C22⋊C4—216no—
310C2×C22⋊C4—216no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—216no—
316C2×C22⋊C4—216no—
317C2×C22⋊C4—48no—
318C2×C22⋊C4—432no—
319C2×C22⋊C4C22×C4132yes—
320C2×C22⋊C4C2×Q8116yescomplemented
321C2×C42—232no—
322C2×C42—28no—
323C2×C42—28no—
324C2×C42—28no—
325C2×C42—216no—
326C2×C42—28no—
327C2×C42—28no—
328C2×C42—216no—
329C2×C42—48no—
330C2×C42—432no—
331C2×C42—416no—
332C2×C42C2×D4116yes—
333#95—28no—
334#95—28no—
335#95—216no—
336#95—216no—
337#95—216no—
338#95—216no—
339#95—216no—
340#95—216no—
341#95—216no—
342C24—28no—
343C24—28no—
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—22no—
361C24—22no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—44no—
373C24—44no—
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—
388C24C4×Q8116yes—
389C24C23×C414yes—
390C24C23×C412yes—
391C24C22×D412yes—
392C24C22×D412yes—
393C24C22×D412yes—
394C24C22×D412yes—
395C24C22×Q814yes—
396C24C22×Q812yes—
397C24C2×#4114yes—
398C24C2×#4112yes—
399C24C2×#4112yes—
400C24C2×#4112yes—
401C24C2×#4112yes—
402C24C2×#4112yes—
403C24H(5,𝔽2)12yes—
404C242−1+412yes—
405C242−1+412yes—
406C242−1+412yes—
407C24C2511yescharacteristic
408C2×Q8—232no—
409C2×Q8—232no—
410C2×Q8—232no—
411C2×Q8—416no—
412C2×Q8—416no—
413C2×Q8—416no—
414C2×Q8—416no—
415C2×Q8—4128no—
416C22×C4—216no—
417C22×C4—216no—
418C22×C4—28no—
419C22×C4—28no—
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—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—216no—
437C22×C4—28no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—216no—
441C22×C4—216no—
442C22×C4—28no—
443C22×C4—216no—
444C22×C4—28no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—216no—
449C22×C4—28no—
450C22×C4—216no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—232no—
491C22×C4—232no—
492C22×C4—232no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—44no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—48no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—48no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—416no—
525C22×C4—416no—
526C22×C4—416no—
527C22×C4—416no—
528C22×C4—4128no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4C2×C22⋊C4132yes—
537C22×C4C2×C22⋊C4116yes—
538C22×C4C4×D4116yes—
539C22×C4C4×D4116yes—
540C22×C4#121116yes—
541C22×C4#121116yes—
542C22×C4C22⋊Q8116yescomplemented
543C22×C4#124116yes—
544C22×C4#127116yes—
545C22×C4C23×C418yes—
546C22×C4C23×C414yes—
547C22×C4C23×C418yes—
548C22×C4C23×C414yes—
549C22×C4C22×D414yes—
550C22×C4C22×D418yes—
551C22×C4C22×D418yes—
552C22×C4C22×D418yes—
553C22×C4C22×D414yes—
554C22×C4C22×D414yes—
555C22×C4C22×D414yes—
556C22×C4C22×D414yes—
557C22×C4C22×D414yes—
558C22×C4C22×Q814yes—
559C22×C4C22×Q814yes—
560C22×C4C2×#4114yes—
561C22×C4C2×#4114yes—
562C22×C4C2×#4114yes—
563C22×C4C2×#4114yes—
564C4⋊C4—264no—
565C4⋊C4—232no—
566C4⋊C4—432no—
567C4⋊C4—416no—
568C4⋊C4C2×C22⋊C4164yescomplemented
569C22⋊C4—232no—
570C22⋊C4—264no—
571C22⋊C4—232no—
572C22⋊C4—432no—
573C42—232no—
574C42—432no—
575C42—416no—
576C23—232no—
577C23—232no—
578C23—24no—
579C23—24no—
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—232no—
597C23—416no—
598C23—416no—
599C23—416no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—416no—
604C23—42no—
605C23—416no—
606C23—42no—
607C23—42no—
608C23—416no—
609C23—416no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—416no—
621C23—416no—
622C23—416no—
623C23—416no—
624C23—416no—
625C23C22×C22⋊C414yes—
626C23C2×C4×D414yes—
627C23C2×C4×D414yes—
628C23C2×C4×Q818yes—
629C23C2×C4×Q814yes—
630C23C4×#4114yes—
631C23#51914yes—
632C23#52014yes—
633C23C2×#12114yes—
634C23C2×#12114yes—
635C23C2×C22⋊Q814yes—
636C23#52514yes—
637C23C2×#12414yes—
638C23#52914yes—
639C23C2×#12714yes—
640C23#53314yes—
641C23#53614yes—
642C23#53714yes—
643C23#54114yes—
644C23#54214yes—
645C23#54614yes—
646C23#54614yes—
647C23#54614yes—
648C23#54714yes—
649C23#54714yes—
650C23#54714yes—
651C23#54814yes—
652C23#54814yes—
653C23#54814yes—
654C23D4×Q814yes—
655C23D4×Q814yes—
656C23D4×Q814yes—
657C23#55214yes—
658C23#55214yes—
659C23#55414yes—
660C23#55614yes—
661C23C24×C411yescharacteristic
662C23C23×D411yescharacteristic
663C23C23×D411yescharacteristic
664C23C23×D411yescharacteristic
665C23C23×D411yescharacteristic
666C23C23×Q811yescharacteristic
667C23C22×#4111yescharacteristic
668C23C22×#4111yescharacteristic
669C23C22×#4111yescharacteristic
670C23C22×#4111yescharacteristic
671C23C22×#4111yescharacteristic
672C23C2×H(5,𝔽2)11yescharacteristic
673C23C2×2−1+411yescharacteristic
674C23C2×2−1+411yescharacteristic
675C23C2×2−1+411yescharacteristic
676Q8—464no—
677C2×C4—264no—
678C2×C4—28no—
679C2×C4—28no—
680C2×C4—24no—
681C2×C4—232no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—28no—
685C2×C4—28no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—28no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—24no—
698C2×C4—28no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—24no—
705C2×C4—28no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—416no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—432no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—416no—
736C2×C4—416no—
737C2×C4—416no—
738C2×C4—432no—
739C2×C4—464no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—816no—
748C2×C4#390164yes—
749C2×C4C22×C22⋊C4116yes—
750C2×C4C22×C22⋊C418yes—
751C2×C4C2×C4×D418yes—
752C2×C4C2×C4×D418yes—
753C2×C4C2×#12118yes—
754C2×C4C2×#12118yes—
755C2×C4C2×C22⋊Q818yescomplemented
756C2×C4C2×#12418yes—
757C2×C4C2×#12718yes—
758C22—28no—
759C22—28no—
760C22—28no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—464no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22C2×#39018yes—
775C22C4×C22⋊Q818yes—
776C22#232318yes—
777C22#233918yes—
778C22Q8×C22⋊C418yes—
779C22#236018yes—
780C22#236218yes—
781C22#241518yes—
782C22#241718yes—
783C22#242718yes—
784C22#242918yes—
785C22#248918yes—
786C22#249218yes—
787C22#254018yes—
788C22#254218yes—
789C22C23×C22⋊C411yescharacteristic
790C22C22×C4×D411yescharacteristic
791C22C22×C4×D411yescharacteristic
792C22C22×C4×Q811yescharacteristic
793C22C2×C4×#4111yescharacteristic
794C22C2×#51911yescharacteristic
795C22C2×#52011yescharacteristic
796C22C22×#12111yescharacteristic
797C22C22×#12111yescharacteristic
798C22C22×C22⋊Q811yescharacteristic
799C22C2×#52511yescharacteristic
800C22C22×#12411yescharacteristic
801C22C2×#52911yescharacteristic
802C22C22×#12711yescharacteristic
803C22C2×#53311yescharacteristic
804C22C2×#53611yescharacteristic
805C22C2×#53711yescharacteristic
806C22C2×#54111yescharacteristic
807C22C2×#54211yescharacteristic
808C22C2×#54611yescharacteristic
809C22C2×#54611yescharacteristic
810C22C2×#54611yescharacteristic
811C22C2×#54711yescharacteristic
812C22C2×#54711yescharacteristic
813C22C2×#54711yescharacteristic
814C22C2×#54811yescharacteristic
815C22C2×#54811yescharacteristic
816C22C2×#54811yescharacteristic
817C22C2×D4×Q811yescharacteristic
818C22C2×D4×Q811yescharacteristic
819C22C2×D4×Q811yescharacteristic
820C22C2×#55211yescharacteristic
821C22C2×#55211yescharacteristic
822C22C2×#55411yescharacteristic
823C22C2×#55611yescharacteristic
824C4—216no—
825C4—28no—
826C4—44no—
827C4—44no—
828C4—48no—
829C4—44no—
830C4—44no—
831C4—48no—
832C4—84no—
833C4C2×#390116yes—
834C2—48no—
835C2#13997116yesdirect product factor
836C2C22×#39011yescharacteristic
837C2C2×C4×C22⋊Q811yescharacteristic
838C2C2×#232311yescharacteristic
839C2C2×#233911yescharacteristic
840C2C2×Q8×C22⋊C411yescharacteristic
841C2C2×#236011yescharacteristic
842C2C2×#236211yescharacteristic
843C2C2×#241711yescharacteristic
844C2C2×#242911yescharacteristic
845C2C2×#242711yescharacteristic
846C2C2×#241511yescharacteristic
847C2C2×#249211yescharacteristic
848C2C2×#248911yescharacteristic
849C2C2×#254011yescharacteristic
850C2C2×#254211yescharacteristic
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. C22×#391C2semidirect
3. C22×#391C2semidirect
4. C22×#389C2semidirect
6. C22×C4×C4⋊C4C2semidirect
8. #13997C2direct (N × H)
9. C2×#1445C2semidirect
12. C2×C4⋊#95C2semidirect
17. C22×C22⋊Q8C4semidirect
33. C2×#391C22semidirect
34. C2×#391C22semidirect
36. C2×#389C22semidirect
40. C2×C4×C4⋊C4C22semidirect
52. #1445C22semidirect
55. C4⋊#95C22semidirect
86. C2×C22⋊Q8C2×C4semidirect
118. C22×C22⋊C4Q8semidirect
299. C2×C4⋊C4C22⋊C4semidirect
320. C2×C22⋊C4C2×Q8semidirect
542. C22×C4C22⋊Q8semidirect
568. C4⋊C4C2×C22⋊C4semidirect
755. C2×C4C2×C22⋊Q8semidirect
835. C2#13997direct (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
C22×#3912
C22×#3892
C22×#3802
C22×C4×C4⋊C42
C22×C4×C22⋊C42
#139972
C2×#14452
C2×#14392
C2×#14372
C2×C4⋊#952