Finite Group Databasebeta

← C2×#11140 #357834

Subgroups — C2×#11140 #357834

Order 512.

2578 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#430C211yesmaximal, characteristic
2C23×#101C211yesmaximal, characteristic
3C23×#101C211yesmaximal, characteristic
4C23×#101C211yesmaximal, characteristic
5C2×#1738C211yesmaximal, characteristic
6C2×#1738C211yesmaximal, characteristic
7C22×#338C211yesmaximal, characteristic
8#11140C218yesmaximal, direct product factor
9C24×Q8C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C23×M16C2211yescharacteristic
15C23×M16C2211yescharacteristic
16C2×#430—24no—
17C2×#430—22no—
18C2×#430—24no—
19C2×#430C2214yes—
20C22×#108—22no—
21C22×#101—24no—
22C22×#101—24no—
23C22×#101—22no—
24C22×#101—22no—
25C22×#101—24no—
26C22×#101—24no—
27C22×#101—22no—
28C22×#101—22no—
29C22×#101—24no—
30C22×#101—22no—
31C22×#101—22no—
32C22×#101C418yes—
33C22×#101C2214yes—
34C22×#101C2214yes—
35C22×#101C2214yes—
36#1738—22no—
37#1738—22no—
38#1738C2214yes—
39#1738C2214yes—
40C2×#341—22no—
41C2×#341—22no—
42C2×#338—24no—
43C2×#338C2214yes—
44C23×Q8—22no—
45C23×Q8—21no—
46C23×Q8—21no—
47C23×Q8—21no—
48C23×Q8—22no—
49C23×Q8—21no—
50C23×Q8—21no—
51C23×Q8—22no—
52C23×Q8—21no—
53C23×Q8—21no—
54C23×Q8—21no—
55C23×Q8—22no—
56C23×Q8—21no—
57C23×Q8—22no—
58C23×Q8—21no—
59C23×Q8—21no—
60C23×Q8—21no—
61C23×Q8—22no—
62C23×Q8C2×C414yes—
63C23×Q8D414yes—
64C23×Q8Q812yes—
65C23×Q8C2312yes—
66C24×C4Q812yes—
67C24×C4C2311yescharacteristic
68C22×M16—22no—
69C22×M16—21no—
70C22×M16—22no—
71C22×M16—21no—
72C22×M16—21no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—21no—
76C22×M16—21no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—22no—
82C22×M16—21no—
83C22×M16—21no—
84C22×M16—21no—
85C22×M16—22no—
86C22×M16—21no—
87C22×M16—21no—
88C22×M16—22no—
89C22×M16—22no—
90C22×M16—21no—
91C22×M16—21no—
92C22×M16—22no—
93C22×M16—21no—
94C22×M16—21no—
95C22×M16—22no—
96C22×M16—22no—
97C22×M16—22no—
98C22×M16—21no—
99C22×M16—22no—
100C22×M16—22no—
101C22×M16—21no—
102C22×M16—22no—
103C22×M16—21no—
104C22×M16—21no—
105C22×M16—21no—
106C22×M16—21no—
107C22×M16—22no—
108C22×M16—22no—
109C22×M16—22no—
110C22×M16—22no—
111C22×M16C2×C414yes—
112C22×M16C2×C414yes—
113C22×M16D412yes—
114C22×M16D414yes—
115C22×M16D412yes—
116C22×M16D414yes—
117C22×M16D412yes—
118C22×M16D412yes—
119C22×M16D414yes—
120C22×M16D412yes—
121C22×M16D412yes—
122C22×M16C2312yes—
123C22×M16C2312yes—
124C22×M16C2312yes—
125C22×M16C2312yes—
126C22×M16C2312yes—
127C22×M16C2312yes—
128C23×C8—21no—
129C23×C8—21no—
130C23×C8—21no—
131C23×C8—21no—
132C23×C8—21no—
133C23×C8—21no—
134#430—216no—
135#430—28no—
136#430—28no—
137C2×#108—216no—
138C2×#108—28no—
139C2×#101—216no—
140C2×#101—216no—
141C2×#101—216no—
142C2×#101—216no—
143C2×#101—28no—
144C2×#101—28no—
145C2×#101—216no—
146C2×#101—216no—
147C2×#101—28no—
148C2×#101—28no—
149C2×#101—28no—
150C2×#101—28no—
151C2×#101—28no—
152C2×#101—28no—
153C2×#101C2×C4116yes—
154#341—28no—
155#341—28no—
156#338—28no—
157C25C2×Q811yescharacteristic
158C22×Q8—24no—
159C22×Q8—24no—
160C22×Q8—24no—
161C22×Q8—24no—
162C22×Q8—24no—
163C22×Q8—24no—
164C22×Q8—24no—
165C22×Q8—24no—
166C22×Q8—24no—
167C22×Q8—24no—
168C22×Q8—24no—
169C22×Q8—24no—
170C22×Q8—24no—
171C22×Q8—24no—
172C22×Q8—24no—
173C22×Q8—24no—
174C22×Q8—24no—
175C22×Q8—24no—
176C22×Q8—24no—
177C22×Q8—24no—
178C22×Q8—24no—
179C22×Q8—22no—
180C22×Q8—22no—
181C22×Q8—22no—
182C22×Q8—22no—
183C22×Q8—24no—
184C22×Q8—22no—
185C22×Q8—22no—
186C22×Q8—24no—
187C22×Q8—24no—
188C22×Q8—24no—
189C22×Q8—24no—
190C22×Q8—24no—
191C22×Q8—22no—
192C22×Q8—22no—
193C22×Q8—22no—
194C22×Q8—22no—
195C22×Q8—22no—
196C22×Q8—22no—
197C22×Q8—22no—
198C22×Q8—22no—
199C22×Q8—22no—
200C22×Q8—22no—
201C22×Q8—22no—
202C22×Q8—22no—
203C22×Q8—42no—
204C22×Q8—42no—
205C22×Q8—41no—
206C22×Q8—41no—
207C22×Q8—42no—
208C22×Q8—41no—
209C22×Q8—42no—
210C22×Q8—41no—
211C22×Q8—42no—
212C22×Q8—41no—
213C22×Q8—41no—
214C22×Q8—42no—
215C22×Q8—41no—
216C22×Q8—41no—
217C22×Q8—41no—
218C22×Q8—42no—
219C22×Q8—42no—
220C22×Q8—41no—
221C22×Q8—41no—
222C22×Q8—41no—
223C22×Q8—42no—
224C22×Q8—42no—
225C22×Q8—42no—
226C22×Q8—42no—
227C22×Q8—42no—
228C22×Q8—42no—
229C22×Q8—42no—
230C22×Q8—42no—
231C22×Q8—42no—
232C22×Q8—42no—
233C22×Q8—42no—
234C22×Q8—42no—
235C22×Q8—42no—
236C22×Q8—41no—
237C22×Q8—41no—
238C22×Q8—41no—
239C22×Q8—42no—
240C22×Q8—41no—
241C22×Q8—42no—
242C22×Q8—42no—
243C22×Q8C4⋊C418yes—
244C22×Q8C22×C414yes—
245C22×Q8C2×D414yes—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4C4⋊C418yes—
256C23×C4C22×C412yes—
257C23×C4C2×D412yes—
258C23×C4C2×D411yescharacteristic
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D412yes—
261C23×C4C2×D411yescharacteristic
262C23×C4C2×D412yes—
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D412yes—
266C23×C4C2×D411yescharacteristic
267C23×C4C2×Q814yes—
268C23×C4C2×Q811yescharacteristic
269C23×C4#4111yescharacteristic
270C23×C4#4111yescharacteristic
271C23×C4#4112yes—
272C23×C4#4111yescharacteristic
273C23×C4#4112yes—
274C23×C4#4111yescharacteristic
275C23×C4#4111yescharacteristic
276C23×C4#4111yescharacteristic
277C23×C4#4112yes—
278C23×C4C2411yescharacteristic
279C2×M16—24no—
280C2×M16—24no—
281C2×M16—24no—
282C2×M16—24no—
283C2×M16—22no—
284C2×M16—22no—
285C2×M16—24no—
286C2×M16—24no—
287C2×M16—24no—
288C2×M16—24no—
289C2×M16—22no—
290C2×M16—22no—
291C2×M16—22no—
292C2×M16—24no—
293C2×M16—22no—
294C2×M16—24no—
295C2×M16—22no—
296C2×M16—22no—
297C2×M16—22no—
298C2×M16—24no—
299C2×M16—22no—
300C2×M16—22no—
301C2×M16—22no—
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—24no—
305C2×M16—24no—
306C2×M16—24no—
307C2×M16—24no—
308C2×M16—24no—
309C2×M16—24no—
310C2×M16—24no—
311C2×M16—24no—
312C2×M16—24no—
313C2×M16—24no—
314C2×M16—24no—
315C2×M16—24no—
316C2×M16—24no—
317C2×M16—24no—
318C2×M16—24no—
319C2×M16—24no—
320C2×M16—24no—
321C2×M16—24no—
322C2×M16—24no—
323C2×M16—24no—
324C2×M16—22no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16—22no—
330C2×M16—22no—
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—22no—
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—22no—
344C2×M16—42no—
345C2×M16—42no—
346C2×M16—42no—
347C2×M16—41no—
348C2×M16—41no—
349C2×M16—42no—
350C2×M16—41no—
351C2×M16—41no—
352C2×M16—42no—
353C2×M16—41no—
354C2×M16—42no—
355C2×M16—41no—
356C2×M16—42no—
357C2×M16—42no—
358C2×M16—42no—
359C2×M16—42no—
360C2×M16—42no—
361C2×M16—42no—
362C2×M16—42no—
363C2×M16—42no—
364C2×M16—42no—
365C2×M16—42no—
366C2×M16—42no—
367C2×M16—42no—
368C2×M16—42no—
369C2×M16—42no—
370C2×M16—42no—
371C2×M16—42no—
372C2×M16—42no—
373C2×M16—42no—
374C2×M16—42no—
375C2×M16—42no—
376C2×M16—42no—
377C2×M16C22⋊C418yes—
378C2×M16C22⋊C418yes—
379C2×M16C22×C414yes—
380C2×M16C22×C414yes—
381C2×M16C2×D414yes—
382C2×M16C2×D414yes—
383C2×M16C2×D414yes—
384C2×M16C2×D414yes—
385C2×M16C2×D414yes—
386C2×M16C2×D414yes—
387C22×C8—24no—
388C22×C8—24no—
389C22×C8—22no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—24no—
393C22×C8—22no—
394C22×C8—24no—
395C22×C8—22no—
396C22×C8—22no—
397C22×C8—22no—
398C22×C8—24no—
399C22×C8—22no—
400C22×C8—22no—
401C22×C8—22no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—42no—
405C22×C8—41no—
406C22×C8—41no—
407C22×C8—42no—
408C22×C8—41no—
409C22×C8—41no—
410C22×C8—42no—
411C22×C8—42no—
412C22×C8—41no—
413C22×C8—41no—
414C22×C8—42no—
415C22×C8—42no—
416C22×C8—42no—
417#108—232no—
418#101—232no—
419#101—232no—
420#101—232no—
421C24—44no—
422C24C2×C4⋊C412yes—
423C24C22⋊Q811yescharacteristic
424C24C22⋊Q811yescharacteristic
425C24C22⋊Q811yescharacteristic
426C24C22⋊Q812yes—
427C24C22⋊Q811yescharacteristic
428C24C22⋊Q811yescharacteristic
429C24C22⋊Q812yes—
430C24C22⋊Q811yescharacteristic
431C24C22⋊Q812yes—
432C24C22×Q811yescharacteristic
433C2×Q8—24no—
434C2×Q8—24no—
435C2×Q8—24no—
436C2×Q8—24no—
437C2×Q8—24no—
438C2×Q8—24no—
439C2×Q8—24no—
440C2×Q8—24no—
441C2×Q8—24no—
442C2×Q8—24no—
443C2×Q8—24no—
444C2×Q8—24no—
445C2×Q8—28no—
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—28no—
450C2×Q8—28no—
451C2×Q8—42no—
452C2×Q8—42no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—42no—
456C2×Q8—42no—
457C2×Q8—42no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—44no—
528C22×C4—42no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4C2×C22⋊C412yes—
532C22×C4C2×C22⋊C412yes—
533C22×C4C2×C4⋊C418yes—
534C22×C4C2×C4⋊C412yes—
535C22×C4#11712yes—
536C22×C4#11712yes—
537C22×C4C4×D412yes—
538C22×C4C4×D412yes—
539C22×C4C4×D412yes—
540C22×C4C4×D412yes—
541C22×C4C4×D412yes—
542C22×C4C4×D412yes—
543C22×C4C4×D412yes—
544C22×C4C4×D412yes—
545C22×C4#12012yes—
546C22×C4#12012yes—
547C22×C4#12012yes—
548C22×C4#12012yes—
549C22×C4#12012yes—
550C22×C4#12012yes—
551C22×C4#12112yes—
552C22×C4#12112yes—
553C22×C4#12112yes—
554C22×C4#12112yes—
555C22×C4#12111yescharacteristic
556C22×C4#12111yescharacteristic
557C22×C4#12112yes—
558C22×C4#12111yescharacteristic
559C22×C4#12112yes—
560C22×C4#12111yescharacteristic
561C22×C4#12111yescharacteristic
562C22×C4#12112yes—
563C22×C4#12111yescharacteristic
564C22×C4#12111yescharacteristic
565C22×C4#12112yes—
566C22×C4#12111yescharacteristic
567C22×C4#12111yescharacteristic
568C22×C4#12111yescharacteristic
569C22×C4#12111yescharacteristic
570C22×C4#12112yes—
571C22×C4#12112yes—
572C22×C4#12111yescharacteristic
573C22×C4C22⋊Q812yes—
574C22×C4C22⋊Q811yescharacteristic
575C22×C4C22⋊Q811yescharacteristic
576C22×C4C22⋊Q811yescharacteristic
577C22×C4C22⋊Q811yescharacteristic
578C22×C4C22⋊Q812yes—
579C22×C4C22⋊Q811yescharacteristic
580C22×C4C22⋊Q811yescharacteristic
581C22×C4C22⋊Q812yes—
582C22×C4#12312yes—
583C22×C4#12312yes—
584C22×C4#12312yes—
585C22×C4#12312yes—
586C22×C4#12312yes—
587C22×C4#12312yes—
588C22×C4#12312yes—
589C22×C4#12312yes—
590C22×C4#12312yes—
591C22×C4#12312yes—
592C22×C4#12412yes—
593C22×C4#12412yes—
594C22×C4#12412yes—
595C22×C4#12412yes—
596C22×C4#12412yes—
597C22×C4#12412yes—
598C22×C4#12612yes—
599C22×C4#12611yescharacteristic
600C22×C4#12611yescharacteristic
601C22×C4#12611yescharacteristic
602C22×C4#12612yes—
603C22×C4#12611yescharacteristic
604C22×C4#12712yes—
605C22×C4#12712yes—
606C22×C4C23×C411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C2×#4111yescharacteristic
615C22×C4C2×#4111yescharacteristic
616C22×C4C2×#4111yescharacteristic
617C22×C4C2×#4111yescharacteristic
618C22×C4C2×#4111yescharacteristic
619C22×C4C2×#4111yescharacteristic
620M16—24no—
621M16—24no—
622M16—24no—
623M16—28no—
624M16—28no—
625M16—24no—
626M16—24no—
627M16—24no—
628M16—24no—
629M16—24no—
630M16—24no—
631M16—24no—
632M16—24no—
633M16—24no—
634M16—24no—
635M16—42no—
636M16—42no—
637M16—42no—
638M16—42no—
639M16—42no—
640M16—42no—
641M16—42no—
642M16—42no—
643M16—42no—
644M16—42no—
645M16—44no—
646M16—44no—
647M16—44no—
648M16—44no—
649M16—44no—
650M16—44no—
651M16—44no—
652M16—44no—
653M16—44no—
654M16—44no—
655M16C2×C22⋊C418yes—
656C2×C8—24no—
657C2×C8—24no—
658C2×C8—24no—
659C2×C8—28no—
660C2×C8—28no—
661C2×C8—24no—
662C2×C8—24no—
663C2×C8—24no—
664C2×C8—24no—
665C2×C8—24no—
666C2×C8—42no—
667C2×C8—42no—
668C2×C8—42no—
669C2×C8—42no—
670C2×C8—42no—
671C2×C8—42no—
672C2×C8—42no—
673C2×C8—42no—
674C2×C8—42no—
675C2×C8—42no—
676C2×C8—44no—
677C2×C8—44no—
678C2×C8—44no—
679C2×C8—44no—
680C2×C8—44no—
681C2×C8—44no—
682C2×C8—44no—
683C2×C8—44no—
684C2×C8—44no—
685C2×C8—44no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—44no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—42no—
697C23#38012yes—
698C23#38012yes—
699C23#38512yes—
700C23#38512yes—
701C23#38512yes—
702C23#38512yes—
703C23#39312yes—
704C23#39312yes—
705C23#39611yescharacteristic
706C23#39611yescharacteristic
707C23#39611yescharacteristic
708C23#39612yes—
709C23#39612yes—
710C23#39611yescharacteristic
711C23#39912yes—
712C23#39912yes—
713C23C22×C4⋊C411yescharacteristic
714C23C2×C22⋊Q811yescharacteristic
715C23C2×C22⋊Q811yescharacteristic
716C23C2×C22⋊Q811yescharacteristic
717C23C2×C22⋊Q811yescharacteristic
718C23C2×C22⋊Q811yescharacteristic
719C23C2×C22⋊Q811yescharacteristic
720Q8—44no—
721Q8—44no—
722Q8—44no—
723Q8—44no—
724Q8—48no—
725Q8—48no—
726Q8—48no—
727Q8—48no—
728Q8—44no—
729Q8—44no—
730Q8—44no—
731Q8—44no—
732C2×C4—28no—
733C2×C4—28no—
734C2×C4—28no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—48no—
740C2×C4—48no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4#38012yes—
744C2×C4#38012yes—
745C2×C4#38512yes—
746C2×C4#38512yes—
747C2×C4#38512yes—
748C2×C4#38512yes—
749C2×C4#38612yes—
750C2×C4#38612yes—
751C2×C4#38612yes—
752C2×C4#38612yes—
753C2×C4#38812yes—
754C2×C4#38812yes—
755C2×C4#38812yes—
756C2×C4#38812yes—
757C2×C4#38812yes—
758C2×C4#38812yes—
759C2×C4#38812yes—
760C2×C4#38812yes—
761C2×C4#39012yes—
762C2×C4#39012yes—
763C2×C4#39012yes—
764C2×C4#39012yes—
765C2×C4#39212yes—
766C2×C4#39212yes—
767C2×C4#39212yes—
768C2×C4#39212yes—
769C2×C4#39312yes—
770C2×C4#39312yes—
771C2×C4#39412yes—
772C2×C4#39412yes—
773C2×C4#39412yes—
774C2×C4#39412yes—
775C2×C4#39412yes—
776C2×C4#39412yes—
777C2×C4#39412yes—
778C2×C4#39412yes—
779C2×C4#39612yes—
780C2×C4#39612yes—
781C2×C4#39611yescharacteristic
782C2×C4#39611yescharacteristic
783C2×C4#39611yescharacteristic
784C2×C4#39611yescharacteristic
785C2×C4#39712yes—
786C2×C4#39712yes—
787C2×C4#39712yes—
788C2×C4#39712yes—
789C2×C4#39912yes—
790C2×C4#39912yes—
791C2×C4C22×C22⋊C411yescharacteristic
792C2×C4C2×#11711yescharacteristic
793C2×C4C2×C4×D411yescharacteristic
794C2×C4C2×C4×D411yescharacteristic
795C2×C4C2×C4×D411yescharacteristic
796C2×C4C2×C4×D411yescharacteristic
797C2×C4C2×#12011yescharacteristic
798C2×C4C2×#12011yescharacteristic
799C2×C4C2×#12011yescharacteristic
800C2×C4C2×#12111yescharacteristic
801C2×C4C2×#12111yescharacteristic
802C2×C4C2×#12111yescharacteristic
803C2×C4C2×#12111yescharacteristic
804C2×C4C2×#12111yescharacteristic
805C2×C4C2×#12111yescharacteristic
806C2×C4C2×#12111yescharacteristic
807C2×C4C2×#12111yescharacteristic
808C2×C4C2×#12311yescharacteristic
809C2×C4C2×#12311yescharacteristic
810C2×C4C2×#12311yescharacteristic
811C2×C4C2×#12311yescharacteristic
812C2×C4C2×#12311yescharacteristic
813C2×C4C2×#12411yescharacteristic
814C2×C4C2×#12411yescharacteristic
815C2×C4C2×#12411yescharacteristic
816C2×C4C2×#12611yescharacteristic
817C2×C4C2×#12611yescharacteristic
818C2×C4C2×#12711yescharacteristic
819C8—28no—
820C8—44no—
821C8—44no—
822C8—44no—
823C8—44no—
824C8—44no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22#143912yes—
848C22#143912yes—
849C22#143912yes—
850C22#143912yes—
851C22#207014yes—
852C22C2×#38011yescharacteristic
853C22C2×#38511yescharacteristic
854C22C2×#38511yescharacteristic
855C22C2×#39311yescharacteristic
856C22C2×#39611yescharacteristic
857C22C2×#39611yescharacteristic
858C22C2×#39911yescharacteristic
859C4—48no—
860C4#143912yes—
861C4#143912yes—
862C4#143912yes—
863C4#143912yes—
864C4C2×#38611yescharacteristic
865C4C2×#38811yescharacteristic
866C4C2×#38811yescharacteristic
867C4C2×#39011yescharacteristic
868C4C2×#39211yescharacteristic
869C4C2×#39411yescharacteristic
870C4C2×#39411yescharacteristic
871C4C2×#39711yescharacteristic
872C2—21no—
873C2—21no—
874C2—21no—
875C2—22no—
876C2—22no—
877C2—22no—
878C2—21no—
879C2—21no—
880C2—21no—
881C2#1114014yesdirect product factor
882C2C2×#143911yescharacteristic
883C2C2×#207012yes—
subgroupG/H
center, socleC23#396
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×Q8
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. #11140C2direct (N × H)
881. C2#11140direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4302
C23×#1012
C2×#17382
C22×#3382
#111402