Finite Group Databasebeta

← C2×#10743 #353423

Subgroups — C2×#10743 #353423

Order 512.

4134 conjugacy classes of subgroups.

The subgroup lattice has 955 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3428C211yesmaximal, characteristic
2C22×#410C211yesmaximal, characteristic
3C2×#2879C211yesmaximal, characteristic
4C2×#1733C212yesmaximal, complemented
5C22×H(3,ℤ/4)C212yesmaximal, complemented
6#10743C218yesmaximal, direct product factor
7C23×#41C2211yescharacteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10#3428—22no—
11#3428—22no—
12#3428—24no—
13#3428—24no—
14#3428C414yescomplemented
15#3428C2214yes—
16C2×#520—24no—
17C2×#519C412yescomplemented
18C2×#518—22no—
19C2×#518C412yescomplemented
20C2×C4×#41—24no—
21C22×#117—22no—
22C22×#117C2212yes—
23C22×#117C2212yes—
24C2×#410—22no—
25C2×#410—22no—
26C2×#410—22no—
27C2×#410C414yescomplemented
28C2×#410C414yescomplemented
29C2×#410C2214yes—
30C22×#99—22no—
31#2879—22no—
32#2879—22no—
33#2879C414yescomplemented
34#2879C2214yes—
35C2×#408—22no—
36C2×#408C414yescomplemented
37C2×#407—22no—
38#1733—24no—
39#1733C2218yescomplemented
40C2×#339—24no—
41C2×H(3,ℤ/4)—24no—
42C2×H(3,ℤ/4)—24no—
43C2×H(3,ℤ/4)C2218yescomplemented
44C22×#41—22no—
45C22×#41—22no—
46C22×#41—22no—
47C22×#41—22no—
48C22×#41—22no—
49C22×#41—22no—
50C22×#41—22no—
51C22×#41—22no—
52C22×#41C2×C412yes—
53C22×#41C2×C412yes—
54C22×#41C2×C412yes—
55C22×#41C2×C412yes—
56C22×#41C2×C412yes—
57C22×#41D412yes—
58C22×#41D412yes—
59C22×#41D412yes—
60C22×#41D412yes—
61C22×#41Q812yes—
62C22×#41Q812yes—
63C22×#41C2312yes—
64C23×Q8C2×C411yescharacteristic
65C23×D4C2×C411yescharacteristic
66C23×D4D412yes—
67C24×C4D412yes—
68C24×C4C2311yescharacteristic
69C22×M16—21no—
70C22×M16—21no—
71C22×M16—21no—
72C22×M16—21no—
73C22×M16—21no—
74C22×M16—21no—
75C22×M16—21no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—22no—
79C22×M16—22no—
80C22×M16—22no—
81C22×M16—22no—
82C22×M16—22no—
83C22×M16—22no—
84C22×M16C2×C412yescomplemented
85C22×M16C2×C412yescomplemented
86C22×M16C2×C412yescomplemented
87C22×M16C2312yes—
88C22×M16C2312yes—
89C23×C8—21no—
90C23×C8C2×C412yescomplemented
91#520—216no—
92#520—216no—
93#520—216no—
94#520—216no—
95#519—24no—
96#519—28no—
97#519C2×C418yescomplemented
98#518—216no—
99#518—28no—
100#518—24no—
101#518—28no—
102#518—28no—
103#518C2×C418yescomplemented
104C4×#41—216no—
105C4×#41—216no—
106C4×#41—216no—
107C4×#41—216no—
108C2×C4×Q8—28no—
109C2×C4×D4—216no—
110C2×C4×D4—28no—
111C2×#117—24no—
112C2×#117—24no—
113C2×#117—28no—
114C2×#117—28no—
115C2×#117—24no—
116C2×#117—28no—
117C2×#117—22no—
118C2×#117—28no—
119C2×#117—22no—
120C2×#117—22no—
121C2×#117—22no—
122C2×#117—22no—
123C2×#117—22no—
124C2×#117—22no—
125C2×#117—22no—
126C2×#117—22no—
127C2×#117—22no—
128C2×#117—22no—
129C2×#117—22no—
130C2×#117—22no—
131C2×#117—22no—
132C2×#117—22no—
133C2×#117C2×C414yes—
134C2×#117C2×C414yes—
135C2×#117C2×C414yescomplemented
136C2×#117C2×C414yescomplemented
137C2×#117D414yes—
138C2×#117D414yes—
139C2×#117D414yes—
140C2×#117C2314yes—
141C2×#117C2314yes—
142C22×C4⋊C4—24no—
143C22×C4⋊C4—22no—
144C22×C4⋊C4—22no—
145C22×C22⋊C4—24no—
146C22×C22⋊C4—22no—
147C22×C22⋊C4—22no—
148C22×C42—24no—
149C22×C42—22no—
150C22×C42D414yes—
151#410—28no—
152#410—28no—
153#410—28no—
154#410C2×C4116yescomplemented
155C2×#99—28no—
156C2×#99—28no—
157C2×#99—28no—
158#408—28no—
159#408—28no—
160#408—28no—
161#408C2×C4116yescomplemented
162#407—28no—
163#407—28no—
164C2×C22⋊C8—28no—
165#339—216no—
166H(3,ℤ/4)—216no—
167C25C22⋊C412yes—
168C25C2×D411yescharacteristic
169C2×#41—24no—
170C2×#41—24no—
171C2×#41—24no—
172C2×#41—24no—
173C2×#41—24no—
174C2×#41—24no—
175C2×#41—24no—
176C2×#41—24no—
177C2×#41—24no—
178C2×#41—24no—
179C2×#41—24no—
180C2×#41—24no—
181C2×#41—24no—
182C2×#41—24no—
183C2×#41—24no—
184C2×#41—24no—
185C2×#41—24no—
186C2×#41—24no—
187C2×#41—24no—
188C2×#41—24no—
189C2×#41—24no—
190C2×#41—24no—
191C2×#41—24no—
192C2×#41—24no—
193C2×#41—24no—
194C2×#41—24no—
195C2×#41—24no—
196C2×#41—24no—
197C2×#41—24no—
198C2×#41—24no—
199C2×#41—24no—
200C2×#41—24no—
201C2×#41—24no—
202C2×#41—24no—
203C2×#41—24no—
204C2×#41—24no—
205C2×#41—24no—
206C2×#41—24no—
207C2×#41—24no—
208C2×#41—24no—
209C2×#41—24no—
210C2×#41—24no—
211C2×#41—24no—
212C2×#41—24no—
213C2×#41—24no—
214C2×#41—24no—
215C2×#41—24no—
216C2×#41—24no—
217C2×#41C4214yes—
218C2×#41C4214yes—
219C2×#41C22⋊C414yes—
220C2×#41C22⋊C414yes—
221C2×#41C22⋊C414yes—
222C2×#41C22⋊C414yes—
223C2×#41C4⋊C414yes—
224C2×#41C4⋊C414yes—
225C2×#41C4⋊C414yes—
226C2×#41C4⋊C414yes—
227C2×#41C4⋊C414yes—
228C2×#41C4⋊C414yes—
229C2×#41C22×C414yes—
230C2×#41C22×C414yes—
231C2×#41C2×D414yes—
232C2×#41C2×Q814yes—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8C4212yes—
238C22×Q8C4212yes—
239C22×Q8C22⋊C412yes—
240C22×Q8C4⋊C412yes—
241C22×Q8C4⋊C412yes—
242C22×Q8C22×C412yes—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4C4212yes—
252C22×D4C4212yes—
253C22×D4C22⋊C414yes—
254C22×D4C22⋊C414yes—
255C22×D4C22⋊C412yes—
256C22×D4C22⋊C414yes—
257C22×D4C4⋊C414yes—
258C22×D4C4⋊C414yes—
259C22×D4C4⋊C412yes—
260C22×D4C4⋊C412yes—
261C22×D4C22×C412yes—
262C22×D4C2×D414yes—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—28no—
272C23×C4—24no—
273C23×C4—42no—
274C23×C4C22⋊C412yes—
275C23×C4C22⋊C414yes—
276C23×C4C22⋊C414yes—
277C23×C4C22⋊C414yes—
278C23×C4C4⋊C414yes—
279C23×C4C4⋊C414yes—
280C23×C4C22×C411yescharacteristic
281C23×C4C22×C411yescharacteristic
282C23×C4C22×C411yescharacteristic
283C23×C4C22×C411yescharacteristic
284C23×C4C22×C411yescharacteristic
285C23×C4C22×C411yescharacteristic
286C23×C4C2×D414yes—
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D412yes—
293C23×C4C2×D412yes—
294C23×C4C2×D412yes—
295C23×C4C2×D412yes—
296C23×C4C2×Q811yescharacteristic
297C23×C4C2×Q811yescharacteristic
298C23×C4#4112yes—
299C23×C4#4112yes—
300C23×C4#4112yes—
301C23×C4#4112yes—
302C23×C4C2411yescharacteristic
303C2×M16—22no—
304C2×M16—22no—
305C2×M16—22no—
306C2×M16—22no—
307C2×M16—24no—
308C2×M16—24no—
309C2×M16—24no—
310C2×M16—22no—
311C2×M16—22no—
312C2×M16—22no—
313C2×M16—24no—
314C2×M16—24no—
315C2×M16—24no—
316C2×M16—24no—
317C2×M16—24no—
318C2×M16—24no—
319C2×M16—24no—
320C2×M16—41no—
321C2×M16—42no—
322C2×M16—41no—
323C2×M16—42no—
324C2×M16—41no—
325C2×M16—41no—
326C2×M16—42no—
327C2×M16—42no—
328C2×M16—42no—
329C2×M16—42no—
330C2×M16—42no—
331C2×M16—42no—
332C2×M16—41no—
333C2×M16—41no—
334C2×M16—42no—
335C2×M16—41no—
336C2×M16—42no—
337C2×M16—41no—
338C2×M16C22×C414yescomplemented
339C22×C8—22no—
340C22×C8—22no—
341C22×C8—22no—
342C22×C8—22no—
343C22×C8—24no—
344C22×C8—24no—
345C22×C8—22no—
346C22×C8—42no—
347C22×C8—42no—
348C22×C8C22×C414yescomplemented
349C4×Q8—232no—
350C4×Q8—232no—
351C4×D4—264no—
352C4×D4—264no—
353C4×D4—232no—
354C4×D4—232no—
355#117—216no—
356#117—216no—
357#117—216no—
358#117—216no—
359#117—216no—
360#117—24no—
361#117—216no—
362#117—24no—
363#117—24no—
364#117—24no—
365#117—24no—
366#117—24no—
367#117—24no—
368#117—24no—
369#117—24no—
370#117—24no—
371#117—24no—
372#117—24no—
373#117—24no—
374#117—24no—
375#117—24no—
376#117—24no—
377#117—24no—
378#117—24no—
379#117—24no—
380#117—24no—
381#117—24no—
382#117—42no—
383#117—42no—
384#117—42no—
385#117—42no—
386#117—42no—
387#117—42no—
388#117C22⋊C418yes—
389#117C22⋊C418yes—
390#117C22×C418yes—
391#117C22×C418yescomplemented
392#117C2×D418yes—
393C2×C4⋊C4—28no—
394C2×C4⋊C4—216no—
395C2×C4⋊C4—216no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C22⋊C4—28no—
409C2×C22⋊C4—216no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—216no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—42no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—42no—
423C2×C42—28no—
424C2×C42—216no—
425C2×C42—216no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—24no—
430C2×C42—24no—
431C2×C42—24no—
432C2×C42—42no—
433C2×C42—42no—
434C2×C42—42no—
435C2×C42C22⋊C418yes—
436C2×C42C22⋊C418yes—
437C2×C42C2×D418yes—
438#99—232no—
439C22⋊C8—232no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—82no—
445C24—84no—
446C24#9514yes—
447C24#9514yes—
448C24C2×C22⋊C414yes—
449C24C2×C22⋊C411yescharacteristic
450C24C2×C22⋊C411yescharacteristic
451C24C2×C22⋊C411yescharacteristic
452C24C2×C22⋊C411yescharacteristic
453C24C2×C4⋊C411yescharacteristic
454C24C2×C4⋊C411yescharacteristic
455C24#12012yes—
456C24#12012yes—
457C24#12312yes—
458C24#12312yes—
459C24C22×D411yescharacteristic
460#41—28no—
461#41—28no—
462#41—28no—
463#41—28no—
464#41—28no—
465#41—28no—
466#41—28no—
467#41—28no—
468#41—28no—
469#41—28no—
470#41—28no—
471#41—28no—
472#41—28no—
473#41—28no—
474#41—28no—
475#41—28no—
476#41—28no—
477#41—28no—
478#41—28no—
479#41—28no—
480#41—28no—
481#41—28no—
482#41—28no—
483#41—28no—
484#41—28no—
485#41—28no—
486#41—28no—
487#41—28no—
488#41—28no—
489#41—28no—
490#41—28no—
491#41—28no—
492C2×Q8—24no—
493C2×Q8—24no—
494C2×Q8—24no—
495C2×Q8—24no—
496C2×Q8—24no—
497C2×Q8—24no—
498C2×Q8—24no—
499C2×Q8—24no—
500C2×Q8—24no—
501C2×Q8—24no—
502C2×Q8—24no—
503C2×Q8—24no—
504C2×Q8#9514yes—
505C2×Q8#9514yes—
506C2×Q8C2×C4214yes—
507C2×Q8C2×C4⋊C414yes—
508C2×D4—28no—
509C2×D4—28no—
510C2×D4—28no—
511C2×D4—28no—
512C2×D4—28no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C2×D4—28no—
517C2×D4—28no—
518C2×D4—28no—
519C2×D4—28no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—24no—
526C2×D4—24no—
527C2×D4—24no—
528C2×D4—24no—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—24no—
532C2×D4#9514yes—
533C2×D4#9514yes—
534C2×D4#9518yes—
535C2×D4#9518yes—
536C2×D4C2×C4214yes—
537C2×D4C2×C22⋊C418yes—
538C2×D4C2×C4⋊C414yes—
539C2×D4C2×C4⋊C418yes—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—28no—
569C22×C4—232no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—88no—
576C22×C4—816no—
577C22×C4—88no—
578C22×C4#9514yes—
579C22×C4#9514yes—
580C22×C4#9518yes—
581C22×C4#9518yes—
582C22×C4C2×C4211yescharacteristic
583C22×C4C2×C4211yescharacteristic
584C22×C4C2×C4211yescharacteristic
585C22×C4C2×C4211yescharacteristic
586C22×C4C2×C22⋊C418yes—
587C22×C4C2×C22⋊C414yes—
588C22×C4C2×C22⋊C411yescharacteristic
589C22×C4C2×C22⋊C411yescharacteristic
590C22×C4C2×C22⋊C411yescharacteristic
591C22×C4C2×C22⋊C411yescharacteristic
592C22×C4C2×C22⋊C412yes—
593C22×C4C2×C22⋊C412yes—
594C22×C4C2×C22⋊C412yes—
595C22×C4C2×C22⋊C412yes—
596C22×C4C2×C22⋊C411yescharacteristic
597C22×C4C2×C22⋊C411yescharacteristic
598C22×C4C2×C22⋊C411yescharacteristic
599C22×C4C2×C22⋊C411yescharacteristic
600C22×C4C2×C4⋊C418yes—
601C22×C4C2×C4⋊C411yescharacteristic
602C22×C4C2×C4⋊C411yescharacteristic
603C22×C4C2×C4⋊C411yescharacteristic
604C22×C4C2×C4⋊C411yescharacteristic
605C22×C4C2×C4⋊C411yescharacteristic
606C22×C4C2×C4⋊C411yescharacteristic
607C22×C4C2×C4⋊C411yescharacteristic
608C22×C4C2×C4⋊C411yescharacteristic
609C22×C4C2×C4⋊C411yescharacteristic
610C22×C4C2×C4⋊C411yescharacteristic
611C22×C4#11712yes—
612C22×C4#11712yes—
613C22×C4#11712yes—
614C22×C4#11712yes—
615C22×C4C4×D412yes—
616C22×C4C4×D412yes—
617C22×C4C4×D412yes—
618C22×C4C4×D412yes—
619C22×C4C4×D412yes—
620C22×C4C4×D412yes—
621C22×C4C4×D412yes—
622C22×C4C4×D412yes—
623C22×C4C4×D412yes—
624C22×C4C4×D412yes—
625C22×C4C4×D412yes—
626C22×C4C4×D412yes—
627C22×C4C4×D412yes—
628C22×C4C4×D412yes—
629C22×C4C4×D412yes—
630C22×C4C4×D412yes—
631C22×C4#12012yes—
632C22×C4#12011yescharacteristic
633C22×C4#12012yes—
634C22×C4#12011yescharacteristic
635C22×C4#12011yescharacteristic
636C22×C4#12011yescharacteristic
637C22×C4#12012yes—
638C22×C4#12012yes—
639C22×C4#12112yes—
640C22×C4#12112yes—
641C22×C4#12112yes—
642C22×C4#12112yes—
643C22×C4#12112yes—
644C22×C4#12112yes—
645C22×C4#12112yes—
646C22×C4#12112yes—
647C22×C4C22⋊Q812yes—
648C22×C4C22⋊Q812yes—
649C22×C4C22⋊Q812yes—
650C22×C4C22⋊Q812yes—
651C22×C4C22⋊Q812yes—
652C22×C4C22⋊Q812yes—
653C22×C4C22⋊Q812yes—
654C22×C4C22⋊Q812yes—
655C22×C4#12311yescharacteristic
656C22×C4#12311yescharacteristic
657C22×C4#12311yescharacteristic
658C22×C4#12312yes—
659C22×C4#12312yes—
660C22×C4#12311yescharacteristic
661C22×C4#12312yes—
662C22×C4#12312yes—
663C22×C4C23×C411yescharacteristic
664C22×C4C23×C411yescharacteristic
665C22×C4C23×C411yescharacteristic
666C22×C4C22×D411yescharacteristic
667C22×C4C22×D411yescharacteristic
668C22×C4C22×D412yes—
669C22×C4C22×D412yes—
670C22×C4C22×Q811yescharacteristic
671C22×C4C2×#4112yes—
672C22×C4C2×#4112yes—
673M16—28no—
674M16—42no—
675M16—42no—
676M16—44no—
677M16—42no—
678M16—42no—
679M16—42no—
680M16—42no—
681M16—44no—
682M16—42no—
683M16—42no—
684M16—44no—
685C2×C8—24no—
686C2×C8—24no—
687C2×C8—28no—
688C2×C8—44no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—44no—
692C2×C8—42no—
693C2×C8—44no—
694C2×C8—42no—
695C4⋊C4—232no—
696C4⋊C4—28no—
697C4⋊C4—28no—
698C4⋊C4—28no—
699C4⋊C4—28no—
700C4⋊C4—28no—
701C4⋊C4—44no—
702C4⋊C4—44no—
703C4⋊C4—44no—
704C22⋊C4—232no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—28no—
710C22⋊C4—44no—
711C22⋊C4—44no—
712C22⋊C4—44no—
713C42—232no—
714C42—28no—
715C42—28no—
716C42—28no—
717C42—28no—
718C42—44no—
719C42—44no—
720C42—44no—
721C42C2×C22⋊C4116yes—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—44no—
729C23—44no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—48no—
734C23—48no—
735C23—84no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—82no—
740C23—82no—
741C23—81no—
742C23—84no—
743C23—84no—
744C23—84no—
745C23—84no—
746C23C2×#9511yescharacteristic
747C23C2×#9518yes—
748C23C2×#9511yescharacteristic
749C23C2×#9511yescharacteristic
750C23C2×#9511yescharacteristic
751C23#37911yescharacteristic
752C23#37911yescharacteristic
753C23#37912yes—
754C23#38111yescharacteristic
755C23#38111yescharacteristic
756C23#38112yes—
757C23#38512yes—
758C23#38512yes—
759C23#38512yes—
760C23#38512yes—
761C23#38612yes—
762C23#38612yes—
763C23#38612yes—
764C23#38612yes—
765C23C22×C22⋊C411yescharacteristic
766C23C22×C22⋊C411yescharacteristic
767C23C22×C4⋊C411yescharacteristic
768C23C2×#12012yes—
769C23C2×#12312yes—
770Q8—28no—
771Q8—28no—
772Q8—28no—
773Q8—28no—
774D4—216no—
775D4—216no—
776D4—216no—
777D4—216no—
778D4—28no—
779D4—28no—
780D4—28no—
781D4—28no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—216no—
797C2×C4—416no—
798C2×C4—48no—
799C2×C4—88no—
800C2×C4—88no—
801C2×C4—832no—
802C2×C4—88no—
803C2×C4—88no—
804C2×C4—88no—
805C2×C4C2×#9518yes—
806C2×C4C2×#9511yescharacteristic
807C2×C4C2×#9511yescharacteristic
808C2×C4C2×#9511yescharacteristic
809C2×C4C2×#9511yescharacteristic
810C2×C4C4×C22⋊C412yes—
811C2×C4C4×C22⋊C412yes—
812C2×C4C4×C22⋊C412yes—
813C2×C4C4×C22⋊C412yes—
814C2×C4C4×C22⋊C412yes—
815C2×C4C4×C22⋊C412yes—
816C2×C4C4×C22⋊C412yes—
817C2×C4C4×C22⋊C412yes—
818C2×C4#37911yescharacteristic
819C2×C4#37912yes—
820C2×C4#37911yescharacteristic
821C2×C4#38012yes—
822C2×C4#38012yes—
823C2×C4#38012yes—
824C2×C4#38012yes—
825C2×C4#38012yes—
826C2×C4#38012yes—
827C2×C4#38012yes—
828C2×C4#38012yes—
829C2×C4#38111yescharacteristic
830C2×C4#38111yescharacteristic
831C2×C4#38112yes—
832C2×C4#38512yes—
833C2×C4#38512yes—
834C2×C4#38512yes—
835C2×C4#38512yes—
836C2×C4#38511yescharacteristic
837C2×C4#38511yescharacteristic
838C2×C4#38511yescharacteristic
839C2×C4#38511yescharacteristic
840C2×C4#38511yescharacteristic
841C2×C4#38511yescharacteristic
842C2×C4#38511yescharacteristic
843C2×C4#38511yescharacteristic
844C2×C4#38512yes—
845C2×C4#38512yes—
846C2×C4#38512yes—
847C2×C4#38512yes—
848C2×C4#38612yes—
849C2×C4#38612yes—
850C2×C4#38612yes—
851C2×C4#38612yes—
852C2×C4#38611yescharacteristic
853C2×C4#38611yescharacteristic
854C2×C4#38611yescharacteristic
855C2×C4#38612yes—
856C2×C4#38612yes—
857C2×C4#38611yescharacteristic
858C2×C4#38611yescharacteristic
859C2×C4#38611yescharacteristic
860C2×C4#38611yescharacteristic
861C2×C4#38612yes—
862C2×C4#38612yes—
863C2×C4#38611yescharacteristic
864C2×C4C22×C4211yescharacteristic
865C2×C4C22×C22⋊C412yes—
866C2×C4C22×C22⋊C411yescharacteristic
867C2×C4C22×C4⋊C411yescharacteristic
868C2×C4C22×C4⋊C411yescharacteristic
869C2×C4C2×#11712yes—
870C2×C4C2×C4×D412yes—
871C2×C4C2×C4×D412yes—
872C2×C4C2×C4×D412yes—
873C2×C4C2×C4×D412yes—
874C2×C4C2×#12011yescharacteristic
875C2×C4C2×#12011yescharacteristic
876C2×C4C2×#12112yes—
877C2×C4C2×#12112yes—
878C2×C4C2×C22⋊Q812yes—
879C2×C4C2×C22⋊Q812yes—
880C2×C4C2×#12311yescharacteristic
881C2×C4C2×#12311yescharacteristic
882C8—44no—
883C8—44no—
884C22—22no—
885C22—24no—
886C22—22no—
887C22—22no—
888C22—24no—
889C22—28no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—48no—
909C22—48no—
910C22—48no—
911C22—48no—
912C22—84no—
913C22—84no—
914C22—84no—
915C22C22⋊#9511yescharacteristic
916C22C22⋊#9511yescharacteristic
917C22C22⋊#9511yescharacteristic
918C22C22⋊#9512yes—
919C22C22⋊#9512yes—
920C22C22⋊#9511yescharacteristic
921C22C22×#9511yescharacteristic
922C22C2×#37911yescharacteristic
923C22C2×#38111yescharacteristic
924C22C2×#38512yes—
925C22C2×#38612yes—
926C4—28no—
927C4—416no—
928C4—88no—
929C4C22⋊#9511yescharacteristic
930C4C22⋊#9511yescharacteristic
931C4C22⋊#9511yescharacteristic
932C4C22⋊#9511yescharacteristic
933C4C22⋊#9512yes—
934C4C22⋊#9512yes—
935C4C2×C4×C22⋊C412yes—
936C4C2×#38012yes—
937C4C2×#38511yescharacteristic
938C4C2×#38511yescharacteristic
939C4C2×#38611yescharacteristic
940C4C2×#38611yescharacteristic
941C2—21no—
942C2—22no—
943C2—21no—
944C2—21no—
945C2—21no—
946C2—21no—
947C2—21no—
948C2—22no—
949C2—22no—
950C2—22no—
951C2—48no—
952C2#1074312yesdirect product factor
953C2C2×C22⋊#9511yescharacteristic
subgroupG/H
centerC2×C4#386
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC22C22⋊#95
prime radicalC23×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1733C2semidirect
5. C22×H(3,ℤ/4)C2semidirect
6. #10743C2direct (N × H)
14. #3428C4semidirect
17. C2×#519C4semidirect
19. C2×#518C4semidirect
27. C2×#410C4semidirect
28. C2×#410C4semidirect
33. #2879C4semidirect
36. C2×#408C4semidirect
39. #1733C22semidirect
43. C2×H(3,ℤ/4)C22semidirect
84. C22×M16C2×C4semidirect
85. C22×M16C2×C4semidirect
86. C22×M16C2×C4semidirect
90. C23×C8C2×C4semidirect
97. #519C2×C4semidirect
103. #518C2×C4semidirect
135. C2×#117C2×C4semidirect
136. C2×#117C2×C4semidirect
154. #410C2×C4semidirect
161. #408C2×C4semidirect
338. C2×M16C22×C4semidirect
348. C22×C8C22×C4semidirect
391. #117C22×C4semidirect
952. C2#10743direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#34282
C22×#4102
C2×#28792
C2×#17332
C22×H(3,ℤ/4)2
#107432