Finite Group Databasebeta

← C2×#11059 #357706

Subgroups — C2×#11059 #357706

Order 512.

2626 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2905C211yesmaximal, characteristic
2C22×#419C211yesmaximal, characteristic
3C22×#419C211yesmaximal, characteristic
4C23×#101C211yesmaximal, characteristic
5C22×#344C211yesmaximal, characteristic
6C2×#1733C211yesmaximal, characteristic
7C22×#338C211yesmaximal, characteristic
8#11059C218yesmaximal, direct product factor
9C24×Q8C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C22×#117C2211yescharacteristic
16#2905—22no—
17#2905—22no—
18#2905—22no—
19#2905C2214yes—
20C2×#424—22no—
21C2×#424—22no—
22C2×#423—22no—
23C2×#419—24no—
24C2×#419—22no—
25C2×#419—24no—
26C2×#419—22no—
27C2×#419—22no—
28C2×#419—22no—
29C2×#419—22no—
30C2×#419C414yescomplemented
31C2×#419C2214yes—
32C2×#419C2214yes—
33C22×#103—22no—
34C22×#103C414yescomplemented
35C22×#101—24no—
36C22×#101—22no—
37C22×#101—22no—
38C22×#101—24no—
39C22×#101C2214yes—
40C2×#344—24no—
41C2×#344C2214yes—
42#1733—22no—
43#1733C2214yes—
44C2×#339—22no—
45C2×#338—24no—
46C2×#338C2214yes—
47C23×Q8—21no—
48C23×Q8—21no—
49C23×Q8—22no—
50C23×Q8—22no—
51C23×Q8—21no—
52C23×Q8—21no—
53C23×Q8—21no—
54C23×Q8—21no—
55C23×Q8—21no—
56C23×Q8—21no—
57C23×Q8—21no—
58C23×Q8—22no—
59C23×Q8—22no—
60C23×Q8—21no—
61C23×Q8—21no—
62C23×Q8—22no—
63C23×Q8—22no—
64C23×Q8C2×C412yes—
65C23×Q8C2×C412yes—
66C23×Q8D414yes—
67C23×Q8Q814yes—
68C23×Q8C2312yes—
69C24×C4—21no—
70C24×C4C2311yescharacteristic
71C22×M16—21no—
72C22×M16—21no—
73C22×M16—21no—
74C22×M16—21no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—21no—
83C22×M16—21no—
84C22×M16—22no—
85C22×M16—22no—
86C22×M16—22no—
87C22×M16—22no—
88C22×M16—22no—
89C22×M16—22no—
90C22×M16—22no—
91C22×M16—21no—
92C22×M16—22no—
93C22×M16—21no—
94C22×M16—21no—
95C22×M16—22no—
96C22×M16—22no—
97C22×M16—21no—
98C22×M16—21no—
99C22×M16—22no—
100C22×M16—22no—
101C22×M16—22no—
102C22×M16C2×C412yes—
103C22×M16D412yes—
104C22×M16D412yes—
105C22×M16D414yes—
106C22×M16D412yes—
107C22×M16C2312yes—
108C22×M16C2312yes—
109C22×M16C2312yes—
110C22×M16C2312yes—
111C23×C8—21no—
112C23×C8—21no—
113C23×C8C2×C412yes—
114C23×C8D412yes—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117—21no—
120C2×#117—21no—
121C2×#117—21no—
122C2×#117—22no—
123C2×#117—22no—
124C2×#117—21no—
125C2×#117—21no—
126C2×#117—22no—
127C2×#117C2×C412yes—
128C2×#117D414yes—
129C2×#117D412yes—
130C2×#117D412yes—
131C2×#117D412yes—
132C2×#117D412yes—
133C2×#117C2312yes—
134C2×#117C2312yes—
135C22×C4⋊C4—21no—
136C22×C4⋊C4C2×C412yes—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C42—21no—
140C22×C42—21no—
141#424—28no—
142#424—28no—
143#424—28no—
144#424—28no—
145#423—28no—
146#423—28no—
147C2×C4⋊C8—28no—
148#419—216no—
149#419—28no—
150#419—28no—
151#419—28no—
152#419—28no—
153#419—28no—
154#419—28no—
155C2×#103—216no—
156C2×#103—28no—
157C2×#103—28no—
158C2×#103—28no—
159C2×#103C2×C4116yescomplemented
160C2×#101—216no—
161C2×#101—216no—
162C2×#101—28no—
163C2×#101—28no—
164C2×#101—28no—
165#344—28no—
166#339—28no—
167#338—28no—
168C25#4111yescharacteristic
169C22×Q8—22no—
170C22×Q8—22no—
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—22no—
184C22×Q8—22no—
185C22×Q8—22no—
186C22×Q8—24no—
187C22×Q8—24no—
188C22×Q8—22no—
189C22×Q8—22no—
190C22×Q8—22no—
191C22×Q8—22no—
192C22×Q8—24no—
193C22×Q8—24no—
194C22×Q8—24no—
195C22×Q8—24no—
196C22×Q8—24no—
197C22×Q8—24no—
198C22×Q8—24no—
199C22×Q8—24no—
200C22×Q8—24no—
201C22×Q8—24no—
202C22×Q8—24no—
203C22×Q8—24no—
204C22×Q8—24no—
205C22×Q8—24no—
206C22×Q8—24no—
207C22×Q8—24no—
208C22×Q8—24no—
209C22×Q8—24no—
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—41no—
219C22×Q8—41no—
220C22×Q8—41no—
221C22×Q8—41no—
222C22×Q8—41no—
223C22×Q8—41no—
224C22×Q8—41no—
225C22×Q8—41no—
226C22×Q8—41no—
227C22×Q8—41no—
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—42no—
239C22×Q8—42no—
240C22×Q8—42no—
241C22×Q8—42no—
242C22×Q8—42no—
243C22×Q8—42no—
244C22×Q8—42no—
245C22×Q8—42no—
246C22×Q8—42no—
247C22×Q8—42no—
248C22×Q8—42no—
249C22×Q8—42no—
250C22×Q8—42no—
251C22×Q8—42no—
252C22×Q8C4⋊C418yes—
253C22×Q8C4⋊C418yes—
254C22×Q8C22×C414yes—
255C22×Q8C2×D414yes—
256C22×Q8C2×Q814yes—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—41no—
264C23×C4—41no—
265C23×C4—41no—
266C23×C4—41no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—41no—
270C23×C4C22×C411yescharacteristic
271C23×C4C22×C411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D412yes—
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D412yes—
280C23×C4C2×D412yes—
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×Q812yes—
284C23×C4#4112yes—
285C23×C4#4112yes—
286C23×C4#4111yescharacteristic
287C23×C4#4111yescharacteristic
288C23×C4#4111yescharacteristic
289C23×C4#4112yes—
290C23×C4#4112yes—
291C23×C4C2411yescharacteristic
292C2×M16—22no—
293C2×M16—22no—
294C2×M16—24no—
295C2×M16—24no—
296C2×M16—24no—
297C2×M16—22no—
298C2×M16—22no—
299C2×M16—22no—
300C2×M16—22no—
301C2×M16—24no—
302C2×M16—24no—
303C2×M16—22no—
304C2×M16—22no—
305C2×M16—22no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—22no—
311C2×M16—22no—
312C2×M16—22no—
313C2×M16—22no—
314C2×M16—22no—
315C2×M16—22no—
316C2×M16—22no—
317C2×M16—24no—
318C2×M16—24no—
319C2×M16—24no—
320C2×M16—24no—
321C2×M16—24no—
322C2×M16—24no—
323C2×M16—24no—
324C2×M16—24no—
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—42no—
334C2×M16—42no—
335C2×M16—42no—
336C2×M16—42no—
337C2×M16—42no—
338C2×M16—41no—
339C2×M16—41no—
340C2×M16—42no—
341C2×M16—42no—
342C2×M16—42no—
343C2×M16—42no—
344C2×M16—42no—
345C2×M16—42no—
346C2×M16—42no—
347C2×M16—42no—
348C2×M16—42no—
349C2×M16—42no—
350C2×M16—42no—
351C2×M16—42no—
352C2×M16—42no—
353C2×M16—42no—
354C2×M16—42no—
355C2×M16—42no—
356C2×M16—42no—
357C2×M16—42no—
358C2×M16—42no—
359C2×M16—42no—
360C2×M16—42no—
361C2×M16—42no—
362C2×M16C2×D414yes—
363C2×M16C2×D414yes—
364C22×C8—22no—
365C22×C8—22no—
366C22×C8—24no—
367C22×C8—24no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—24no—
371C22×C8—22no—
372C22×C8—22no—
373C22×C8—24no—
374C22×C8—24no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—42no—
378C22×C8—41no—
379C22×C8—41no—
380C22×C8—42no—
381C22×C8—42no—
382C22×C8C22×C414yes—
383C22×C8C2×D414yes—
384#117—22no—
385#117—22no—
386#117—22no—
387#117—22no—
388#117—22no—
389#117—22no—
390#117—22no—
391#117—22no—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—22no—
396#117—24no—
397#117—22no—
398#117—24no—
399#117—22no—
400#117—24no—
401#117—22no—
402#117—42no—
403#117—42no—
404#117—42no—
405#117C22⋊C414yes—
406#117C22⋊C414yes—
407#117C2×D414yes—
408#117C2×D414yes—
409#117C2×D414yes—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4C22⋊C414yes—
418C2×C4⋊C4C22⋊C414yes—
419C2×C4⋊C4C22×C414yes—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—41no—
429C2×C22⋊C4—42no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—24no—
437C2×C42—22no—
438C2×C42—42no—
439C2×C42—41no—
440C4⋊C8—232no—
441#103—232no—
442#103—232no—
443#101—232no—
444C24—44no—
445C24C4×D411yescharacteristic
446C24C4×D411yescharacteristic
447C24#12111yescharacteristic
448C24#12111yescharacteristic
449C24C22⋊Q812yes—
450C24#12311yescharacteristic
451C24#12312yes—
452C24#12311yescharacteristic
453C24#12312yes—
454C24#12612yes—
455C24C2×#4111yescharacteristic
456C2×Q8—24no—
457C2×Q8—24no—
458C2×Q8—24no—
459C2×Q8—28no—
460C2×Q8—28no—
461C2×Q8—24no—
462C2×Q8—24no—
463C2×Q8—24no—
464C2×Q8—24no—
465C2×Q8—24no—
466C2×Q8—24no—
467C2×Q8—24no—
468C2×Q8—24no—
469C2×Q8—24no—
470C2×Q8—24no—
471C2×Q8—24no—
472C2×Q8—24no—
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—28no—
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—28no—
479C2×Q8—28no—
480C2×Q8—28no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8—44no—
522C2×Q8—44no—
523C2×Q8—44no—
524C2×Q8—44no—
525C2×Q8—44no—
526C2×Q8—44no—
527C2×Q8—44no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×Q8—44no—
531C2×Q8C2×C4⋊C418yes—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—42no—
559C22×C4—44no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4C2×C22⋊C411yescharacteristic
563C22×C4C2×C22⋊C411yescharacteristic
564C22×C4C2×C22⋊C411yescharacteristic
565C22×C4C2×C22⋊C411yescharacteristic
566C22×C4C2×C4⋊C412yes—
567C22×C4C2×C4⋊C412yes—
568C22×C4#11712yes—
569C22×C4#11712yes—
570C22×C4C4×D411yescharacteristic
571C22×C4C4×D411yescharacteristic
572C22×C4C4×D411yescharacteristic
573C22×C4C4×D411yescharacteristic
574C22×C4C4×D412yes—
575C22×C4C4×D412yes—
576C22×C4C4×D412yes—
577C22×C4C4×D412yes—
578C22×C4C4×D411yescharacteristic
579C22×C4C4×D411yescharacteristic
580C22×C4#12012yes—
581C22×C4#12012yes—
582C22×C4#12012yes—
583C22×C4#12012yes—
584C22×C4#12011yescharacteristic
585C22×C4#12011yescharacteristic
586C22×C4#12011yescharacteristic
587C22×C4#12011yescharacteristic
588C22×C4#12112yes—
589C22×C4#12112yes—
590C22×C4#12112yes—
591C22×C4#12112yes—
592C22×C4#12111yescharacteristic
593C22×C4#12111yescharacteristic
594C22×C4#12111yescharacteristic
595C22×C4#12111yescharacteristic
596C22×C4#12112yes—
597C22×C4#12112yes—
598C22×C4#12112yes—
599C22×C4#12112yes—
600C22×C4#12112yes—
601C22×C4#12112yes—
602C22×C4#12112yes—
603C22×C4#12112yes—
604C22×C4#12111yescharacteristic
605C22×C4#12111yescharacteristic
606C22×C4C22⋊Q812yes—
607C22×C4C22⋊Q812yes—
608C22×C4C22⋊Q812yes—
609C22×C4C22⋊Q812yes—
610C22×C4C22⋊Q812yes—
611C22×C4C22⋊Q812yes—
612C22×C4C22⋊Q812yes—
613C22×C4C22⋊Q812yes—
614C22×C4C22⋊Q812yes—
615C22×C4C22⋊Q812yes—
616C22×C4C22⋊Q812yes—
617C22×C4#12312yes—
618C22×C4#12312yes—
619C22×C4#12312yes—
620C22×C4#12312yes—
621C22×C4#12312yes—
622C22×C4#12311yescharacteristic
623C22×C4#12311yescharacteristic
624C22×C4#12312yes—
625C22×C4#12412yes—
626C22×C4#12412yes—
627C22×C4#12412yes—
628C22×C4#12412yes—
629C22×C4#12412yes—
630C22×C4#12412yes—
631C22×C4#12612yes—
632C22×C4#12612yes—
633C22×C4#12612yes—
634C22×C4#12712yes—
635C22×C4#12712yes—
636C22×C4C23×C411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C22×D411yescharacteristic
644C22×C4C22×Q811yescharacteristic
645C22×C4C2×#4111yescharacteristic
646C22×C4C2×#4111yescharacteristic
647C22×C4C2×#4111yescharacteristic
648C22×C4C2×#4111yescharacteristic
649C22×C4C2×#4111yescharacteristic
650M16—24no—
651M16—24no—
652M16—24no—
653M16—24no—
654M16—42no—
655M16—42no—
656M16—42no—
657M16—42no—
658M16—42no—
659M16—42no—
660M16—42no—
661M16—42no—
662M16—42no—
663M16—42no—
664M16—42no—
665M16—42no—
666M16—44no—
667M16—44no—
668M16—44no—
669M16—44no—
670M16—44no—
671M16—44no—
672M16—44no—
673M16—44no—
674C2×C8—24no—
675C2×C8—24no—
676C2×C8—24no—
677C2×C8—24no—
678C2×C8—24no—
679C2×C8—24no—
680C2×C8—24no—
681C2×C8—24no—
682C2×C8—42no—
683C2×C8—42no—
684C2×C8—42no—
685C2×C8—42no—
686C2×C8—44no—
687C2×C8—44no—
688C2×C8—44no—
689C2×C8—44no—
690C2×C8—44no—
691C2×C8—44no—
692C2×C8—44no—
693C2×C8—44no—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—42no—
699C4⋊C4—44no—
700C4⋊C4C2×C22⋊C418yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—44no—
708C42—24no—
709C42—24no—
710C42—24no—
711C42—24no—
712C42—24no—
713C42—42no—
714C42—44no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—42no—
719C23—42no—
720C23—44no—
721C23—42no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—42no—
726C23#38512yes—
727C23#38512yes—
728C23#38611yescharacteristic
729C23#38611yescharacteristic
730C23#38611yescharacteristic
731C23#38611yescharacteristic
732C23#38812yes—
733C23#38812yes—
734C23#39412yes—
735C23#39412yes—
736C23#39612yes—
737C23#39612yes—
738C23#39712yes—
739C23#39712yes—
740C23#39912yes—
741C23#39912yes—
742C23C2×C4×D411yescharacteristic
743C23C2×#12111yescharacteristic
744C23C2×C22⋊Q811yescharacteristic
745C23C2×#12311yescharacteristic
746C23C2×#12311yescharacteristic
747C23C2×#12311yescharacteristic
748C23C2×#12611yescharacteristic
749Q8—28no—
750Q8—28no—
751Q8—44no—
752Q8—44no—
753Q8—44no—
754Q8—44no—
755Q8—48no—
756Q8—48no—
757Q8—48no—
758Q8—48no—
759Q8—44no—
760Q8—44no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—48no—
770C2×C4—48no—
771C2×C4—48no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4—88no—
779C2×C4#38012yes—
780C2×C4#38012yes—
781C2×C4#38012yes—
782C2×C4#38012yes—
783C2×C4#38512yes—
784C2×C4#38512yes—
785C2×C4#38512yes—
786C2×C4#38512yes—
787C2×C4#38512yes—
788C2×C4#38512yes—
789C2×C4#38611yescharacteristic
790C2×C4#38611yescharacteristic
791C2×C4#38611yescharacteristic
792C2×C4#38611yescharacteristic
793C2×C4#38812yes—
794C2×C4#38812yes—
795C2×C4#38812yes—
796C2×C4#38812yes—
797C2×C4#38812yes—
798C2×C4#38812yes—
799C2×C4#39012yes—
800C2×C4#39012yes—
801C2×C4#39012yes—
802C2×C4#39012yes—
803C2×C4#39212yes—
804C2×C4#39212yes—
805C2×C4#39212yes—
806C2×C4#39212yes—
807C2×C4#39312yes—
808C2×C4#39312yes—
809C2×C4#39312yes—
810C2×C4#39312yes—
811C2×C4#39412yes—
812C2×C4#39412yes—
813C2×C4#39412yes—
814C2×C4#39412yes—
815C2×C4#39412yes—
816C2×C4#39412yes—
817C2×C4#39612yes—
818C2×C4#39612yes—
819C2×C4#39612yes—
820C2×C4#39612yes—
821C2×C4#39612yes—
822C2×C4#39612yes—
823C2×C4#39712yes—
824C2×C4#39712yes—
825C2×C4#39912yes—
826C2×C4#39912yes—
827C2×C4C22×C22⋊C411yescharacteristic
828C2×C4C22×C4⋊C411yescharacteristic
829C2×C4C2×#11711yescharacteristic
830C2×C4C2×C4×D411yescharacteristic
831C2×C4C2×C4×D411yescharacteristic
832C2×C4C2×C4×D411yescharacteristic
833C2×C4C2×#12011yescharacteristic
834C2×C4C2×#12011yescharacteristic
835C2×C4C2×#12011yescharacteristic
836C2×C4C2×#12111yescharacteristic
837C2×C4C2×#12111yescharacteristic
838C2×C4C2×#12111yescharacteristic
839C2×C4C2×#12111yescharacteristic
840C2×C4C2×#12111yescharacteristic
841C2×C4C2×#12111yescharacteristic
842C2×C4C2×#12111yescharacteristic
843C2×C4C2×C22⋊Q811yescharacteristic
844C2×C4C2×C22⋊Q811yescharacteristic
845C2×C4C2×C22⋊Q811yescharacteristic
846C2×C4C2×C22⋊Q811yescharacteristic
847C2×C4C2×C22⋊Q811yescharacteristic
848C2×C4C2×#12311yescharacteristic
849C2×C4C2×#12311yescharacteristic
850C2×C4C2×#12411yescharacteristic
851C2×C4C2×#12411yescharacteristic
852C2×C4C2×#12411yescharacteristic
853C2×C4C2×#12611yescharacteristic
854C2×C4C2×#12711yescharacteristic
855C8—44no—
856C8—44no—
857C8—44no—
858C8—44no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22#143912yes—
882C22#143912yes—
883C22#143912yes—
884C22#143912yes—
885C22#190214yes—
886C22C2×#38511yescharacteristic
887C22C2×#38611yescharacteristic
888C22C2×#38811yescharacteristic
889C22C2×#39411yescharacteristic
890C22C2×#39611yescharacteristic
891C22C2×#39711yescharacteristic
892C22C2×#39911yescharacteristic
893C4—48no—
894C4—48no—
895C4—84no—
896C4#143912yes—
897C4#143912yes—
898C4#143912yes—
899C4#143912yes—
900C4C2×#38011yescharacteristic
901C4C2×#38511yescharacteristic
902C4C2×#38811yescharacteristic
903C4C2×#39011yescharacteristic
904C4C2×#39211yescharacteristic
905C4C2×#39311yescharacteristic
906C4C2×#39411yescharacteristic
907C4C2×#39611yescharacteristic
908C2—21no—
909C2—21no—
910C2—21no—
911C2—21no—
912C2—22no—
913C2—22no—
914C2—22no—
915C2—21no—
916C2—21no—
917C2#1105914yesdirect product factor
918C2C2×#143911yescharacteristic
919C2C2×#190212yes—
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. #11059C2direct (N × H)
30. C2×#419C4semidirect
34. C22×#103C4semidirect
159. C2×#103C2×C4semidirect
917. C2#11059direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29052
C22×#4192
C23×#1012
C22×#3442
C2×#17332
C22×#3382
#110592