Finite Group Databasebeta

← C2×#11214 #358071

Subgroups — C2×#11214 #358071

Order 512.

1850 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#428C211yesmaximal, characteristic
2C2×#2905C211yesmaximal, characteristic
3C22×#344C211yesmaximal, characteristic
4C22×#343C211yesmaximal, characteristic
5C2×#1736C211yesmaximal, characteristic
6C2×#1733C211yesmaximal, characteristic
7C22×#338C211yesmaximal, characteristic
8#11214C218yesmaximal, direct product factor
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C2×#428—22no—
17C2×#428—22no—
18C2×#428—22no—
19C2×#428—22no—
20C2×#428C414yescomplemented
21C2×#428C2214yes—
22C22×#107C412yescomplemented
23C22×#106C412yescomplemented
24#2905—22no—
25#2905—22no—
26#2905—22no—
27#2905C2214yes—
28C2×#424—22no—
29C2×#424—22no—
30C2×#423—22no—
31C2×#344—24no—
32C2×#344C2214yes—
33C2×#343—22no—
34C2×#343—22no—
35C2×#343C2214yes—
36#1736—22no—
37#1736C2214yes—
38C2×#340—22no—
39#1733—22no—
40#1733C2214yes—
41C2×#339—22no—
42C2×#338—24no—
43C2×#338C2214yes—
44C24×C4—21no—
45C24×C4C2311yescharacteristic
46C22×M16—21no—
47C22×M16—21no—
48C22×M16—21no—
49C22×M16—21no—
50C22×M16—22no—
51C22×M16—22no—
52C22×M16—21no—
53C22×M16—21no—
54C22×M16—21no—
55C22×M16—21no—
56C22×M16—21no—
57C22×M16—21no—
58C22×M16—21no—
59C22×M16—22no—
60C22×M16—22no—
61C22×M16—22no—
62C22×M16—22no—
63C22×M16—22no—
64C22×M16—21no—
65C22×M16—21no—
66C22×M16—21no—
67C22×M16—21no—
68C22×M16—21no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16C2×C412yes—
76C22×M16D412yes—
77C22×M16D412yes—
78C22×M16D414yes—
79C22×M16D412yes—
80C22×M16Q814yes—
81C22×M16Q814yes—
82C22×M16C2312yes—
83C22×M16C2312yes—
84C22×M16C2312yes—
85C22×M16C2312yes—
86C23×C8—21no—
87C23×C8—21no—
88C23×C8C2×C412yes—
89C23×C8D412yes—
90C2×#117—21no—
91C2×#117—21no—
92C2×#117—21no—
93C2×#117—21no—
94C2×#117—21no—
95C2×#117—21no—
96C2×#117—21no—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117—21no—
100C2×#117—21no—
101C2×#117—22no—
102C2×#117C2×C412yes—
103C2×#117D412yes—
104C2×#117D412yes—
105C2×#117D412yes—
106C2×#117D412yes—
107C2×#117Q814yes—
108C2×#117C2312yes—
109C2×#117C2312yes—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—21no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4—21no—
114C22×C4⋊C4—21no—
115C22×C4⋊C4—21no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4C2×C412yes—
123C22×C4⋊C4C2×C412yes—
124C22×C4⋊C4C2×C411yescharacteristic
125C22×C4⋊C4C2×C411yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C42—21no—
130C22×C42—21no—
131#428—28no—
132#428—28no—
133#428—28no—
134#428—28no—
135C2×#107—24no—
136C2×#107—24no—
137C2×#107C2×C418yescomplemented
138C2×#106—24no—
139C2×#106—24no—
140C2×#106C2×C418yescomplemented
141#424—28no—
142#424—28no—
143#424—28no—
144#424—28no—
145#423—28no—
146#423—28no—
147C2×C4⋊C8—28no—
148#344—28no—
149#343—28no—
150#340—28no—
151#339—28no—
152#338—28no—
153C25#4111yescharacteristic
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—41no—
160C23×C4—41no—
161C23×C4—41no—
162C23×C4—41no—
163C23×C4—41no—
164C23×C4—84no—
165C23×C4C22×C411yescharacteristic
166C23×C4C22×C411yescharacteristic
167C23×C4C2×D411yescharacteristic
168C23×C4C2×D411yescharacteristic
169C23×C4C2×D411yescharacteristic
170C23×C4C2×D411yescharacteristic
171C23×C4C2×D412yes—
172C23×C4C2×D411yescharacteristic
173C23×C4C2×D411yescharacteristic
174C23×C4C2×D411yescharacteristic
175C23×C4C2×D411yescharacteristic
176C23×C4C2×Q812yes—
177C23×C4C2×Q812yes—
178C23×C4C2×Q812yes—
179C23×C4#4112yes—
180C23×C4#4112yes—
181C23×C4#4111yescharacteristic
182C23×C4#4111yescharacteristic
183C23×C4#4111yescharacteristic
184C23×C4#4112yes—
185C23×C4#4112yes—
186C23×C4C2411yescharacteristic
187C2×M16—22no—
188C2×M16—22no—
189C2×M16—24no—
190C2×M16—24no—
191C2×M16—24no—
192C2×M16—24no—
193C2×M16—24no—
194C2×M16—24no—
195C2×M16—24no—
196C2×M16—24no—
197C2×M16—24no—
198C2×M16—22no—
199C2×M16—22no—
200C2×M16—22no—
201C2×M16—22no—
202C2×M16—22no—
203C2×M16—22no—
204C2×M16—22no—
205C2×M16—22no—
206C2×M16—24no—
207C2×M16—24no—
208C2×M16—24no—
209C2×M16—22no—
210C2×M16—22no—
211C2×M16—22no—
212C2×M16—22no—
213C2×M16—22no—
214C2×M16—22no—
215C2×M16—22no—
216C2×M16—22no—
217C2×M16—24no—
218C2×M16—24no—
219C2×M16—24no—
220C2×M16—24no—
221C2×M16—24no—
222C2×M16—24no—
223C2×M16—24no—
224C2×M16—24no—
225C2×M16—22no—
226C2×M16—22no—
227C2×M16—22no—
228C2×M16—22no—
229C2×M16—22no—
230C2×M16—22no—
231C2×M16—22no—
232C2×M16—22no—
233C2×M16—42no—
234C2×M16—41no—
235C2×M16—41no—
236C2×M16—42no—
237C2×M16—42no—
238C2×M16—42no—
239C2×M16—42no—
240C2×M16—42no—
241C2×M16—42no—
242C2×M16—42no—
243C2×M16—42no—
244C2×M16—42no—
245C2×M16—42no—
246C2×M16—42no—
247C2×M16—42no—
248C2×M16—42no—
249C2×M16—42no—
250C2×M16—42no—
251C2×M16—42no—
252C2×M16—42no—
253C2×M16—42no—
254C2×M16C4⋊C418yes—
255C2×M16C2×D414yes—
256C2×M16C2×D414yes—
257C2×M16C2×Q814yes—
258C2×M16C2×Q814yes—
259C22×C8—22no—
260C22×C8—22no—
261C22×C8—24no—
262C22×C8—22no—
263C22×C8—22no—
264C22×C8—22no—
265C22×C8—22no—
266C22×C8—24no—
267C22×C8—24no—
268C22×C8—24no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—42no—
272C22×C8—41no—
273C22×C8—41no—
274C22×C8—42no—
275C22×C8—42no—
276C22×C8C4⋊C418yes—
277C22×C8C22×C414yes—
278C22×C8C2×D414yes—
279#117—22no—
280#117—22no—
281#117—22no—
282#117—22no—
283#117—22no—
284#117—22no—
285#117—22no—
286#117—22no—
287#117—22no—
288#117—22no—
289#117—22no—
290#117—22no—
291#117—24no—
292#117—22no—
293#117—24no—
294#117—22no—
295#117—24no—
296#117—22no—
297#117—42no—
298#117—42no—
299#117—42no—
300#117C22⋊C414yes—
301#117C22⋊C414yes—
302#117C2×D414yes—
303#117C2×D414yes—
304#117C2×Q814yes—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—41no—
331C2×C4⋊C4—41no—
332C2×C4⋊C4—41no—
333C2×C4⋊C4—41no—
334C2×C4⋊C4—41no—
335C2×C4⋊C4—41no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4—41no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—41no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4C22⋊C412yes—
343C2×C4⋊C4C22⋊C412yes—
344C2×C4⋊C4C22⋊C412yes—
345C2×C4⋊C4C22⋊C412yes—
346C2×C4⋊C4C22×C414yes—
347C2×C4⋊C4C22×C412yes—
348C2×C4⋊C4C22×C412yes—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—42no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—22no—
367C2×C42—42no—
368C2×C42—41no—
369#107—216no—
370#106—216no—
371C4⋊C8—232no—
372C24—42no—
373C24—42no—
374C24C4×D411yescharacteristic
375C24C4×D411yescharacteristic
376C24#12111yescharacteristic
377C24#12111yescharacteristic
378C24C22⋊Q812yes—
379C24#12311yescharacteristic
380C24#12311yescharacteristic
381C24#12512yes—
382C24#12512yes—
383C24#12612yes—
384C24C2×#4111yescharacteristic
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—24no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—44no—
400C22×C4—82no—
401C22×C4—82no—
402C22×C4—82no—
403C22×C4—82no—
404C22×C4—84no—
405C22×C4—84no—
406C22×C4—84no—
407C22×C4—84no—
408C22×C4—84no—
409C22×C4—84no—
410C22×C4—84no—
411C22×C4C2×C22⋊C411yescharacteristic
412C22×C4C2×C22⋊C411yescharacteristic
413C22×C4C2×C22⋊C411yescharacteristic
414C22×C4C2×C22⋊C411yescharacteristic
415C22×C4C2×C4⋊C412yes—
416C22×C4C2×C4⋊C412yes—
417C22×C4#11712yes—
418C22×C4#11712yes—
419C22×C4C4×D411yescharacteristic
420C22×C4C4×D411yescharacteristic
421C22×C4C4×D411yescharacteristic
422C22×C4C4×D411yescharacteristic
423C22×C4C4×D411yescharacteristic
424C22×C4C4×D411yescharacteristic
425C22×C4C4×Q812yes—
426C22×C4C4×Q812yes—
427C22×C4C4×Q812yes—
428C22×C4C4×Q812yes—
429C22×C4#12011yescharacteristic
430C22×C4#12011yescharacteristic
431C22×C4#12011yescharacteristic
432C22×C4#12011yescharacteristic
433C22×C4#12112yes—
434C22×C4#12112yes—
435C22×C4#12112yes—
436C22×C4#12112yes—
437C22×C4#12111yescharacteristic
438C22×C4#12111yescharacteristic
439C22×C4#12111yescharacteristic
440C22×C4#12111yescharacteristic
441C22×C4#12112yes—
442C22×C4#12112yes—
443C22×C4#12112yes—
444C22×C4#12112yes—
445C22×C4#12111yescharacteristic
446C22×C4#12111yescharacteristic
447C22×C4C22⋊Q812yes—
448C22×C4C22⋊Q812yes—
449C22×C4C22⋊Q812yes—
450C22×C4C22⋊Q812yes—
451C22×C4C22⋊Q812yes—
452C22×C4C22⋊Q812yes—
453C22×C4C22⋊Q812yes—
454C22×C4C22⋊Q812yes—
455C22×C4C22⋊Q812yes—
456C22×C4C22⋊Q812yes—
457C22×C4C22⋊Q812yes—
458C22×C4C22⋊Q812yes—
459C22×C4C22⋊Q812yes—
460C22×C4C22⋊Q812yes—
461C22×C4C22⋊Q812yes—
462C22×C4#12312yes—
463C22×C4#12312yes—
464C22×C4#12312yes—
465C22×C4#12312yes—
466C22×C4#12311yescharacteristic
467C22×C4#12311yescharacteristic
468C22×C4#12412yes—
469C22×C4#12412yes—
470C22×C4#12512yes—
471C22×C4#12512yes—
472C22×C4#12512yes—
473C22×C4#12512yes—
474C22×C4#12512yes—
475C22×C4#12512yes—
476C22×C4#12612yes—
477C22×C4#12612yes—
478C22×C4#12612yes—
479C22×C4C4⋊Q812yes—
480C22×C4C4⋊Q812yes—
481C22×C4C4⋊Q812yes—
482C22×C4C4⋊Q812yes—
483C22×C4C4⋊Q812yes—
484C22×C4C4⋊Q812yes—
485C22×C4C23×C411yescharacteristic
486C22×C4C22×D411yescharacteristic
487C22×C4C22×D411yescharacteristic
488C22×C4C22×D411yescharacteristic
489C22×C4C22×D411yescharacteristic
490C22×C4C22×D411yescharacteristic
491C22×C4C22×Q811yescharacteristic
492C22×C4C22×Q811yescharacteristic
493C22×C4C22×Q811yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4C2×#4111yescharacteristic
498C22×C4C2×#4111yescharacteristic
499M16—24no—
500M16—24no—
501M16—24no—
502M16—24no—
503M16—28no—
504M16—28no—
505M16—24no—
506M16—24no—
507M16—24no—
508M16—24no—
509M16—42no—
510M16—42no—
511M16—42no—
512M16—42no—
513M16—42no—
514M16—42no—
515M16—42no—
516M16—42no—
517M16—44no—
518M16—44no—
519M16—44no—
520M16—44no—
521M16—44no—
522M16—44no—
523C2×C8—24no—
524C2×C8—24no—
525C2×C8—28no—
526C2×C8—28no—
527C2×C8—24no—
528C2×C8—24no—
529C2×C8—24no—
530C2×C8—24no—
531C2×C8—24no—
532C2×C8—42no—
533C2×C8—42no—
534C2×C8—42no—
535C2×C8—42no—
536C2×C8—44no—
537C2×C8—44no—
538C2×C8—44no—
539C2×C8—44no—
540C2×C8—44no—
541C2×C8—44no—
542C2×C8C2×C4⋊C418yes—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—44no—
560C4⋊C4C2×C22⋊C414yes—
561C4⋊C4C2×C22⋊C414yes—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—24no—
565C22⋊C4—24no—
566C22⋊C4—24no—
567C22⋊C4—42no—
568C22⋊C4—44no—
569C42—24no—
570C42—24no—
571C42—24no—
572C42—24no—
573C42—24no—
574C42—42no—
575C42—44no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—44no—
589C23—41no—
590C23—44no—
591C23—44no—
592C23—44no—
593C23—41no—
594C23#38611yescharacteristic
595C23#38611yescharacteristic
596C23#38611yescharacteristic
597C23#38611yescharacteristic
598C23#38712yes—
599C23#38712yes—
600C23#38912yes—
601C23#38912yes—
602C23#39612yes—
603C23#39612yes—
604C23#39812yes—
605C23#39812yes—
606C23#39812yes—
607C23#39812yes—
608C23#40012yes—
609C23#40012yes—
610C23C2×C4×D411yescharacteristic
611C23C2×#12111yescharacteristic
612C23C2×C22⋊Q811yescharacteristic
613C23C2×#12311yescharacteristic
614C23C2×#12511yescharacteristic
615C23C2×#12511yescharacteristic
616C23C2×#12611yescharacteristic
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—82no—
624C2×C4—82no—
625C2×C4—82no—
626C2×C4—82no—
627C2×C4—82no—
628C2×C4—82no—
629C2×C4—88no—
630C2×C4—84no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4—84no—
634C2×C4—84no—
635C2×C4—84no—
636C2×C4—84no—
637C2×C4#38012yes—
638C2×C4#38012yes—
639C2×C4#38012yes—
640C2×C4#38012yes—
641C2×C4#38611yescharacteristic
642C2×C4#38611yescharacteristic
643C2×C4#38611yescharacteristic
644C2×C4#38611yescharacteristic
645C2×C4#38712yes—
646C2×C4#38712yes—
647C2×C4#38712yes—
648C2×C4#38712yes—
649C2×C4#38712yes—
650C2×C4#38712yes—
651C2×C4#38912yes—
652C2×C4#38912yes—
653C2×C4#38912yes—
654C2×C4#38912yes—
655C2×C4#38912yes—
656C2×C4#38912yes—
657C2×C4#39112yes—
658C2×C4#39112yes—
659C2×C4#39112yes—
660C2×C4#39112yes—
661C2×C4#39412yes—
662C2×C4#39412yes—
663C2×C4#39412yes—
664C2×C4#39412yes—
665C2×C4#39512yes—
666C2×C4#39512yes—
667C2×C4#39512yes—
668C2×C4#39512yes—
669C2×C4#39612yes—
670C2×C4#39612yes—
671C2×C4#39612yes—
672C2×C4#39612yes—
673C2×C4#39612yes—
674C2×C4#39612yes—
675C2×C4#39812yes—
676C2×C4#39812yes—
677C2×C4#39812yes—
678C2×C4#39812yes—
679C2×C4#39812yes—
680C2×C4#39812yes—
681C2×C4#39812yes—
682C2×C4#39812yes—
683C2×C4#40012yes—
684C2×C4#40012yes—
685C2×C4C22×C22⋊C411yescharacteristic
686C2×C4C22×C4⋊C411yescharacteristic
687C2×C4C2×#11711yescharacteristic
688C2×C4C2×C4×D411yescharacteristic
689C2×C4C2×C4×Q811yescharacteristic
690C2×C4C2×C4×Q811yescharacteristic
691C2×C4C2×#12011yescharacteristic
692C2×C4C2×#12111yescharacteristic
693C2×C4C2×#12111yescharacteristic
694C2×C4C2×#12111yescharacteristic
695C2×C4C2×#12111yescharacteristic
696C2×C4C2×#12111yescharacteristic
697C2×C4C2×C22⋊Q811yescharacteristic
698C2×C4C2×C22⋊Q811yescharacteristic
699C2×C4C2×C22⋊Q811yescharacteristic
700C2×C4C2×C22⋊Q811yescharacteristic
701C2×C4C2×C22⋊Q811yescharacteristic
702C2×C4C2×C22⋊Q811yescharacteristic
703C2×C4C2×C22⋊Q811yescharacteristic
704C2×C4C2×#12311yescharacteristic
705C2×C4C2×#12311yescharacteristic
706C2×C4C2×#12411yescharacteristic
707C2×C4C2×#12511yescharacteristic
708C2×C4C2×#12511yescharacteristic
709C2×C4C2×#12611yescharacteristic
710C2×C4C2×C4⋊Q811yescharacteristic
711C2×C4C2×C4⋊Q811yescharacteristic
712C2×C4C2×C4⋊Q811yescharacteristic
713C8—28no—
714C8—44no—
715C8—44no—
716C8—44no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22#144112yes—
746C22#144112yes—
747C22#144112yes—
748C22#144112yes—
749C22#190212yes—
750C22#190312yes—
751C22C2×#38611yescharacteristic
752C22C2×#38711yescharacteristic
753C22C2×#38911yescharacteristic
754C22C2×#39611yescharacteristic
755C22C2×#39811yescharacteristic
756C22C2×#39811yescharacteristic
757C22C2×#40011yescharacteristic
758C4—44no—
759C4—44no—
760C4—84no—
761C4—84no—
762C4#144112yes—
763C4#144112yes—
764C4#144112yes—
765C4#144112yes—
766C4C2×#38011yescharacteristic
767C4C2×#38711yescharacteristic
768C4C2×#38911yescharacteristic
769C4C2×#39111yescharacteristic
770C4C2×#39411yescharacteristic
771C4C2×#39511yescharacteristic
772C4C2×#39611yescharacteristic
773C4C2×#39811yescharacteristic
774C2—21no—
775C2—21no—
776C2—21no—
777C2—21no—
778C2—22no—
779C2—22no—
780C2—22no—
781C2—21no—
782C2—21no—
783C2#1121414yesdirect product factor
784C2C2×#144111yescharacteristic
785C2C2×#190211yescharacteristic
786C2C2×#190311yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #11214C2direct (N × H)
20. C2×#428C4semidirect
22. C22×#107C4semidirect
23. C22×#106C4semidirect
137. C2×#107C2×C4semidirect
140. C2×#106C2×C4semidirect
783. C2#11214direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4282
C2×#29052
C22×#3442
C22×#3432
C2×#17362
C2×#17332
C22×#3382
#112142