Finite Group Databasebeta

← C2×#11318 #358365

Subgroups — C2×#11318 #358365

Order 512.

2342 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#342C211yesmaximal, characteristic
2C22×#342C211yesmaximal, characteristic
3C22×#342C211yesmaximal, characteristic
4C22×#342C211yesmaximal, characteristic
5C22×#342C211yesmaximal, characteristic
6C22×#342C211yesmaximal, characteristic
7C22×#342C211yesmaximal, characteristic
8#11318C218yesmaximal, direct product factor
9C23×C22⋊C4C2211yescharacteristic
10C23×C22⋊C4C2211yescharacteristic
11C23×C22⋊C4C2211yescharacteristic
12C23×C22⋊C4C2211yescharacteristic
13C23×C22⋊C4C2211yescharacteristic
14C23×C22⋊C4C2211yescharacteristic
15C23×C22⋊C4C2211yescharacteristic
16C2×#342—24no—
17C2×#342—24no—
18C2×#342—24no—
19C2×#342—24no—
20C2×#342—24no—
21C2×#342—24no—
22C2×#342C418yescomplemented
23C2×#342C2214yes—
24C2×#342C2214yes—
25C2×#342C2214yes—
26C2×#342C2214yes—
27C2×#342C2214yes—
28C2×#342C2214yes—
29C2×#342C2214yes—
30C26C2311yescharacteristic
31C24×C4—21no—
32C24×C4—21no—
33C24×C4—21no—
34C24×C4—21no—
35C24×C4—21no—
36C24×C4—21no—
37C24×C4—21no—
38C22×C22⋊C4—22no—
39C22×C22⋊C4—22no—
40C22×C22⋊C4—22no—
41C22×C22⋊C4—22no—
42C22×C22⋊C4—22no—
43C22×C22⋊C4—22no—
44C22×C22⋊C4—22no—
45C22×C22⋊C4—22no—
46C22×C22⋊C4—21no—
47C22×C22⋊C4—21no—
48C22×C22⋊C4—21no—
49C22×C22⋊C4—21no—
50C22×C22⋊C4—22no—
51C22×C22⋊C4—22no—
52C22×C22⋊C4—21no—
53C22×C22⋊C4—21no—
54C22×C22⋊C4—21no—
55C22×C22⋊C4—21no—
56C22×C22⋊C4—21no—
57C22×C22⋊C4—21no—
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C22⋊C4—21no—
62C22×C22⋊C4—21no—
63C22×C22⋊C4—21no—
64C22×C22⋊C4—21no—
65C22×C22⋊C4—21no—
66C22×C22⋊C4—21no—
67C22×C22⋊C4—21no—
68C22×C22⋊C4—21no—
69C22×C22⋊C4—21no—
70C22×C22⋊C4—22no—
71C22×C22⋊C4—21no—
72C22×C22⋊C4—21no—
73C22×C22⋊C4—22no—
74C22×C22⋊C4—21no—
75C22×C22⋊C4—21no—
76C22×C22⋊C4—22no—
77C22×C22⋊C4—21no—
78C22×C22⋊C4—21no—
79C22×C22⋊C4—22no—
80C22×C22⋊C4—22no—
81C22×C22⋊C4—22no—
82C22×C22⋊C4—22no—
83C22×C22⋊C4—22no—
84C22×C22⋊C4—21no—
85C22×C22⋊C4—22no—
86C22×C22⋊C4—21no—
87C22×C22⋊C4—21no—
88C22×C22⋊C4—21no—
89C22×C22⋊C4—21no—
90C22×C22⋊C4—21no—
91C22×C22⋊C4—21no—
92C22×C22⋊C4—22no—
93C22×C22⋊C4—22no—
94C22×C22⋊C4C2×C414yes—
95C22×C22⋊C4C2×C414yes—
96C22×C22⋊C4C2×C414yes—
97C22×C22⋊C4D414yes—
98C22×C22⋊C4D414yes—
99C22×C22⋊C4D414yes—
100C22×C22⋊C4Q814yes—
101C22×C22⋊C4C2312yes—
102C22×C22⋊C4C2312yes—
103C22×C22⋊C4C2312yes—
104C22×C22⋊C4C2312yes—
105C22×C22⋊C4C2312yes—
106C22×C22⋊C4C2312yes—
107C22×C22⋊C4C2312yes—
108#342—28no—
109#342—28no—
110#342—28no—
111#342—28no—
112#342—28no—
113#342—28no—
114#342C2×C4116yescomplemented
115C25—84no—
116C25C22×C412yes—
117C25C2×D412yes—
118C25C2×D412yes—
119C25C2×D412yes—
120C25C2×Q812yes—
121C25#4111yescharacteristic
122C25#4111yescharacteristic
123C25#4111yescharacteristic
124C25#4111yescharacteristic
125C25#4111yescharacteristic
126C25#4111yescharacteristic
127C25#4111yescharacteristic
128C25#4111yescharacteristic
129C25#4111yescharacteristic
130C25#4111yescharacteristic
131C25#4112yes—
132C25#4112yes—
133C25#4112yes—
134C25#4111yescharacteristic
135C25#4111yescharacteristic
136C25#4111yescharacteristic
137C25#4111yescharacteristic
138C25C2411yescharacteristic
139C23×C4—24no—
140C23×C4—24no—
141C23×C4—24no—
142C23×C4—24no—
143C23×C4—24no—
144C23×C4—24no—
145C23×C4—24no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—42no—
154C23×C4—42no—
155C23×C4—42no—
156C23×C4—42no—
157C23×C4—42no—
158C23×C4—42no—
159C23×C4—41no—
160C23×C4—41no—
161C23×C4—41no—
162C23×C4—41no—
163C23×C4—41no—
164C23×C4—41no—
165C23×C4—41no—
166C23×C4—41no—
167C23×C4—41no—
168C23×C4—41no—
169C23×C4—41no—
170C23×C4—42no—
171C23×C4—41no—
172C23×C4—41no—
173C23×C4—41no—
174C23×C4—84no—
175C23×C4—84no—
176C23×C4—84no—
177C23×C4—84no—
178C23×C4—84no—
179C23×C4—84no—
180C23×C4—84no—
181C2×C22⋊C4—24no—
182C2×C22⋊C4—24no—
183C2×C22⋊C4—24no—
184C2×C22⋊C4—24no—
185C2×C22⋊C4—24no—
186C2×C22⋊C4—24no—
187C2×C22⋊C4—24no—
188C2×C22⋊C4—24no—
189C2×C22⋊C4—24no—
190C2×C22⋊C4—24no—
191C2×C22⋊C4—24no—
192C2×C22⋊C4—24no—
193C2×C22⋊C4—24no—
194C2×C22⋊C4—24no—
195C2×C22⋊C4—24no—
196C2×C22⋊C4—24no—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—24no—
199C2×C22⋊C4—24no—
200C2×C22⋊C4—24no—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—24no—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—24no—
206C2×C22⋊C4—24no—
207C2×C22⋊C4—24no—
208C2×C22⋊C4—24no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—22no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—24no—
238C2×C22⋊C4—24no—
239C2×C22⋊C4—24no—
240C2×C22⋊C4—24no—
241C2×C22⋊C4—24no—
242C2×C22⋊C4—24no—
243C2×C22⋊C4—24no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—42no—
252C2×C22⋊C4—42no—
253C2×C22⋊C4—42no—
254C2×C22⋊C4—42no—
255C2×C22⋊C4—42no—
256C2×C22⋊C4—42no—
257C2×C22⋊C4—42no—
258C2×C22⋊C4—42no—
259C2×C22⋊C4—42no—
260C2×C22⋊C4—42no—
261C2×C22⋊C4—42no—
262C2×C22⋊C4—42no—
263C2×C22⋊C4—42no—
264C2×C22⋊C4—42no—
265C2×C22⋊C4—42no—
266C2×C22⋊C4—42no—
267C2×C22⋊C4—42no—
268C2×C22⋊C4—42no—
269C2×C22⋊C4—42no—
270C2×C22⋊C4—42no—
271C2×C22⋊C4—42no—
272C2×C22⋊C4—42no—
273C2×C22⋊C4—42no—
274C2×C22⋊C4—42no—
275C2×C22⋊C4—42no—
276C2×C22⋊C4—42no—
277C2×C22⋊C4—42no—
278C2×C22⋊C4—42no—
279C2×C22⋊C4—42no—
280C2×C22⋊C4—42no—
281C2×C22⋊C4—42no—
282C2×C22⋊C4—42no—
283C2×C22⋊C4—42no—
284C2×C22⋊C4—42no—
285C2×C22⋊C4—41no—
286C2×C22⋊C4—41no—
287C2×C22⋊C4—41no—
288C2×C22⋊C4—41no—
289C2×C22⋊C4—41no—
290C2×C22⋊C4—41no—
291C2×C22⋊C4—41no—
292C2×C22⋊C4—41no—
293C2×C22⋊C4—41no—
294C2×C22⋊C4—41no—
295C2×C22⋊C4—41no—
296C2×C22⋊C4—41no—
297C2×C22⋊C4—41no—
298C2×C22⋊C4—41no—
299C2×C22⋊C4—42no—
300C2×C22⋊C4C22×C414yes—
301C2×C22⋊C4C22×C414yes—
302C2×C22⋊C4C22×C414yes—
303C2×C22⋊C4C2×D414yes—
304C2×C22⋊C4C2×D414yes—
305C2×C22⋊C4C2×D414yes—
306C2×C22⋊C4C2×Q814yes—
307C24—44no—
308C24—44no—
309C24—44no—
310C24—44no—
311C24—44no—
312C24—44no—
313C24—44no—
314C24—84no—
315C24—84no—
316C24—84no—
317C24—84no—
318C24—84no—
319C24—84no—
320C24—84no—
321C24—84no—
322C24—82no—
323C24—82no—
324C24—82no—
325C24—82no—
326C24—82no—
327C24—82no—
328C24—82no—
329C24—82no—
330C24#11712yes—
331C24#11712yes—
332C24#11712yes—
333C24#11712yes—
334C24#11712yes—
335C24#11712yes—
336C24C4×D412yes—
337C24C4×D412yes—
338C24C4×D412yes—
339C24C4×D412yes—
340C24C4×D412yes—
341C24C4×D412yes—
342C24C4×Q812yes—
343C24C4×Q812yes—
344C24#12112yes—
345C24#12112yes—
346C24#12112yes—
347C24#12112yes—
348C24#12112yes—
349C24#12112yes—
350C24C22⋊Q812yes—
351C24C22⋊Q812yes—
352C24C22⋊Q812yes—
353C24C22⋊Q812yes—
354C24C22⋊Q812yes—
355C24C22⋊Q812yes—
356C24#12312yes—
357C24#12312yes—
358C24#12312yes—
359C24#12312yes—
360C24#12312yes—
361C24#12312yes—
362C24#12312yes—
363C24#12312yes—
364C24#12312yes—
365C24#12312yes—
366C24#12312yes—
367C24#12312yes—
368C24#12412yes—
369C24#12412yes—
370C24#12412yes—
371C24#12412yes—
372C24#12412yes—
373C24#12412yes—
374C24#12512yes—
375C24#12512yes—
376C24#12512yes—
377C24#12512yes—
378C24#12512yes—
379C24#12512yes—
380C24#12611yescharacteristic
381C24#12611yescharacteristic
382C24#12611yescharacteristic
383C24#12611yescharacteristic
384C24#12611yescharacteristic
385C24#12611yescharacteristic
386C24#12611yescharacteristic
387C24#12611yescharacteristic
388C24#12611yescharacteristic
389C24#12611yescharacteristic
390C24#12612yes—
391C24#12612yes—
392C24#12612yes—
393C24#12611yescharacteristic
394C24#12611yescharacteristic
395C24#12611yescharacteristic
396C24#12611yescharacteristic
397C24#12611yescharacteristic
398C24#12611yescharacteristic
399C24#12611yescharacteristic
400C24#12611yescharacteristic
401C24#12611yescharacteristic
402C24#12611yescharacteristic
403C24#12611yescharacteristic
404C24#12611yescharacteristic
405C24#12611yescharacteristic
406C24#12611yescharacteristic
407C24#12611yescharacteristic
408C24#12611yescharacteristic
409C24#12611yescharacteristic
410C24#12611yescharacteristic
411C24#12612yes—
412C24#12612yes—
413C24#12612yes—
414C24C23×C411yescharacteristic
415C24C22×D411yescharacteristic
416C24C22×D411yescharacteristic
417C24C22×D411yescharacteristic
418C24C22×Q811yescharacteristic
419C24C2×#4111yescharacteristic
420C24C2×#4111yescharacteristic
421C24C2×#4111yescharacteristic
422C24C2×#4111yescharacteristic
423C24C2×#4111yescharacteristic
424C24C2×#4111yescharacteristic
425C24C2×#4111yescharacteristic
426C24C2×#4111yescharacteristic
427C24C2×#4111yescharacteristic
428C24C2×#4111yescharacteristic
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—84no—
465C22×C4—84no—
466C22×C4—84no—
467C22×C4—84no—
468C22×C4—84no—
469C22×C4—84no—
470C22×C4—84no—
471C22×C4—88no—
472C22×C4—88no—
473C22×C4—88no—
474C22×C4—88no—
475C22×C4—88no—
476C22×C4—88no—
477C22×C4—84no—
478C22×C4—84no—
479C22×C4—84no—
480C22×C4—84no—
481C22×C4—84no—
482C22×C4—84no—
483C22×C4—84no—
484C22×C4—88no—
485C22×C4—88no—
486C22×C4—88no—
487C22×C4—88no—
488C22×C4—88no—
489C22×C4—88no—
490C22×C4—88no—
491C22×C4—88no—
492C22×C4—84no—
493C22×C4—84no—
494C22×C4—84no—
495C22×C4—84no—
496C22×C4—84no—
497C22×C4—84no—
498C22×C4—84no—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—24no—
505C22⋊C4—24no—
506C22⋊C4—24no—
507C22⋊C4—24no—
508C22⋊C4—24no—
509C22⋊C4—24no—
510C22⋊C4—24no—
511C22⋊C4—24no—
512C22⋊C4—24no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C22⋊C4—44no—
528C22⋊C4—44no—
529C22⋊C4—44no—
530C22⋊C4—44no—
531C22⋊C4—44no—
532C22⋊C4—44no—
533C22⋊C4—44no—
534C22⋊C4—44no—
535C22⋊C4—44no—
536C22⋊C4—44no—
537C22⋊C4—44no—
538C22⋊C4—44no—
539C22⋊C4—44no—
540C22⋊C4—44no—
541C23—24no—
542C23—24no—
543C23—24no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—44no—
549C23—44no—
550C23—44no—
551C23—44no—
552C23—44no—
553C23—44no—
554C23—44no—
555C23—44no—
556C23—44no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23—44no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—44no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—44no—
577C23—44no—
578C23—44no—
579C23—44no—
580C23—44no—
581C23—44no—
582C23—44no—
583C23—44no—
584C23—44no—
585C23—44no—
586C23—44no—
587C23—44no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—44no—
603C23—44no—
604C23—82no—
605C23—82no—
606C23—82no—
607C23—82no—
608C23—82no—
609C23—82no—
610C23—82no—
611C23—82no—
612C23—82no—
613C23—82no—
614C23—82no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23—82no—
619C23—82no—
620C23—82no—
621C23—82no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23—82no—
626C23—82no—
627C23—82no—
628C23—82no—
629C23—82no—
630C23—82no—
631C23—82no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23—81no—
638C23—81no—
639C23—81no—
640C23#38312yes—
641C23#38312yes—
642C23#38312yes—
643C23#38312yes—
644C23#38712yes—
645C23#38712yes—
646C23#38712yes—
647C23#38712yes—
648C23#38712yes—
649C23#38712yes—
650C23#38712yes—
651C23#38712yes—
652C23#38712yes—
653C23#38712yes—
654C23#38712yes—
655C23#38712yes—
656C23#38812yes—
657C23#38812yes—
658C23#38812yes—
659C23#38812yes—
660C23#38812yes—
661C23#38812yes—
662C23#38812yes—
663C23#38812yes—
664C23#38812yes—
665C23#38812yes—
666C23#38812yes—
667C23#38812yes—
668C23#39612yes—
669C23#39612yes—
670C23#39612yes—
671C23#39612yes—
672C23#39712yes—
673C23#39712yes—
674C23#39712yes—
675C23#39712yes—
676C23#39712yes—
677C23#39712yes—
678C23#39712yes—
679C23#39712yes—
680C23#39712yes—
681C23#39712yes—
682C23#39712yes—
683C23#39712yes—
684C23#40012yes—
685C23#40012yes—
686C23#40012yes—
687C23#40012yes—
688C23#40012yes—
689C23#40012yes—
690C23#40012yes—
691C23#40012yes—
692C23#40012yes—
693C23#40012yes—
694C23#40012yes—
695C23#40012yes—
696C23#40111yescharacteristic
697C23#40111yescharacteristic
698C23#40111yescharacteristic
699C23#40111yescharacteristic
700C23#40111yescharacteristic
701C23#40111yescharacteristic
702C23#40111yescharacteristic
703C23#40111yescharacteristic
704C23C2×#11711yescharacteristic
705C23C2×#11711yescharacteristic
706C23C2×#11711yescharacteristic
707C23C2×C4×D411yescharacteristic
708C23C2×C4×D411yescharacteristic
709C23C2×C4×D411yescharacteristic
710C23C2×C4×Q811yescharacteristic
711C23C2×#12111yescharacteristic
712C23C2×#12111yescharacteristic
713C23C2×#12111yescharacteristic
714C23C2×C22⋊Q811yescharacteristic
715C23C2×C22⋊Q811yescharacteristic
716C23C2×C22⋊Q811yescharacteristic
717C23C2×#12311yescharacteristic
718C23C2×#12311yescharacteristic
719C23C2×#12311yescharacteristic
720C23C2×#12311yescharacteristic
721C23C2×#12311yescharacteristic
722C23C2×#12311yescharacteristic
723C23C2×#12411yescharacteristic
724C23C2×#12411yescharacteristic
725C23C2×#12411yescharacteristic
726C23C2×#12511yescharacteristic
727C23C2×#12511yescharacteristic
728C23C2×#12511yescharacteristic
729C23C2×#12611yescharacteristic
730C23C2×#12611yescharacteristic
731C23C2×#12611yescharacteristic
732C23C2×#12611yescharacteristic
733C23C2×#12611yescharacteristic
734C23C2×#12611yescharacteristic
735C23C2×#12611yescharacteristic
736C23C2×#12611yescharacteristic
737C23C2×#12611yescharacteristic
738C23C2×#12611yescharacteristic
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—88no—
754C2×C4—88no—
755C2×C4—88no—
756C2×C4—88no—
757C2×C4—88no—
758C2×C4—88no—
759C2×C4—88no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4—84no—
766C2×C4—84no—
767C2×C4—88no—
768C2×C4—88no—
769C2×C4—88no—
770C2×C4—88no—
771C2×C4—88no—
772C2×C4—88no—
773C2×C4—88no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4—84no—
779C2×C4—84no—
780C2×C4—84no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—24no—
796C22—24no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—24no—
806C22—24no—
807C22—24no—
808C22—24no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22#144312yes—
880C22#144312yes—
881C22#144312yes—
882C22#144312yes—
883C22#144312yes—
884C22#144312yes—
885C22#144312yes—
886C22#144312yes—
887C22#210414yes—
888C22C2×#38311yescharacteristic
889C22C2×#38711yescharacteristic
890C22C2×#38711yescharacteristic
891C22C2×#38711yescharacteristic
892C22C2×#38811yescharacteristic
893C22C2×#38811yescharacteristic
894C22C2×#38811yescharacteristic
895C22C2×#39611yescharacteristic
896C22C2×#39711yescharacteristic
897C22C2×#39711yescharacteristic
898C22C2×#39711yescharacteristic
899C22C2×#40011yescharacteristic
900C22C2×#40011yescharacteristic
901C22C2×#40011yescharacteristic
902C22C2×#40111yescharacteristic
903C4—84no—
904C4—84no—
905C4—84no—
906C4—84no—
907C4—84no—
908C4—84no—
909C4—84no—
910C2—21no—
911C2—21no—
912C2—21no—
913C2—21no—
914C2—21no—
915C2—21no—
916C2—21no—
917C2—21no—
918C2—21no—
919C2—21no—
920C2—22no—
921C2—22no—
922C2—22no—
923C2—22no—
924C2—22no—
925C2—22no—
926C2—22no—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2#1131814yesdirect product factor
932C2C2×#144311yescharacteristic
933C2C2×#210412yes—
subgroupG/H
center, socleC23#401
commutatorC24C23×C4
Frattini, cosocleC25C24
prime radicalC26C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C26 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
8. #11318C2direct (N × H)
22. C2×#342C4semidirect
114. #342C2×C4semidirect
931. C2#11318direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3422
#113182