Finite Group Databasebeta

← C2×#61874 #10578272

Subgroups — C2×#61874 #10578272

Order 512.

6070 conjugacy classes of subgroups.

The subgroup lattice has 1053 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3502C211yesmaximal, characteristic, complemented
2C2×#3554C211yesmaximal, characteristic
3#61874C2132yesmaximal, direct product factor
4C2×#3390C212yesmaximal, complemented
5C2×#3388C212yesmaximal, complemented
6C2×#3386C212yesmaximal, complemented
7C2×#3385C212yesmaximal, complemented
8C2×#3371C212yesmaximal, complemented
9C2×#3371C212yesmaximal, complemented
10C2×#3375C212yesmaximal, complemented
11C2×#3368C212yesmaximal, complemented
12C2×#3243C212yesmaximal, complemented
13C2×#3241C212yesmaximal, complemented
14C2×#3240C211yesmaximal, characteristic, complemented
15C2×#3235C211yesmaximal, characteristic, complemented
16C2×#3126C212yesmaximal, complemented
17C2×#3121C212yesmaximal, complemented
18C2×#3112C211yesmaximal, characteristic, complemented
19C2×#3117C211yesmaximal, characteristic, complemented
20C2×#2987C211yesmaximal, characteristic, complemented
21#3554—28no—
22#3554C22116yes—
23C2×#562—22no—
24#3502—28no—
25#3502C22116yescomplemented
26C2×#559C2212yes—
27C2×#559C2211yescharacteristic
28C2×Q82—21no—
29C2×Q82C2212yes—
30C2×#557—21no—
31C2×#557—22no—
32C2×#557C2211yescharacteristic
33C2×#557C2212yes—
34C2×#557C2212yes—
35C2×#557C2212yes—
36C2×#554C2212yes—
37C2×#550C2211yescharacteristic
38C2×D4×Q8C2211yescharacteristic
39C2×#548—21no—
40C2×#547—21no—
41C2×#544—21no—
42C2×#544—21no—
43C2×#544C2212yes—
44C2×#542—21no—
45C2×#542C2212yes—
46C2×#540C2212yes—
47C2×#539—22no—
48C2×#536—21no—
49C2×#533—22no—
50C2×#533C2211yescharacteristic
51C2×#533C2211yescharacteristic
52C2×#532C2211yescharacteristic
53C2×#529C2211yescharacteristic
54C2×#519C2212yes—
55C22×C4×Q8C2211yescharacteristic
56#3390C22132yescomplemented
57#3388C22132yescomplemented
58#3386C22132yescomplemented
59#3385C22132yescomplemented
60#3375C22132yescomplemented
61#3371C22132yescomplemented
62#3371C22132yescomplemented
63#3368C22132yescomplemented
64#3243C22132yescomplemented
65#3241C22132yescomplemented
66#3240C22116yescomplemented
67#3235C22116yescomplemented
68C2×#501C2211yescharacteristic
69C2×#501C2212yes—
70C2×#501C2212yes—
71C2×#501C2212yes—
72C2×#501C2211yescharacteristic
73C2×#500C2212yes—
74C2×#499C2212yes—
75C2×#490C2212yes—
76C2×#490C2212yes—
77C2×#489C2211yescharacteristic
78C2×#489C2212yes—
79C2×#489C2211yescharacteristic
80C2×#488C2212yes—
81C2×#486C2212yes—
82#3126C22132yescomplemented
83#3121C22132yescomplemented
84#3117C22116yescomplemented
85#3112C22116yescomplemented
86C2×#484C2211yescharacteristic
87C2×#481C2211yescharacteristic
88C2×#485C2212yes—
89C2×#482C2212yes—
90C2×#482C2212yes—
91C2×#482C2212yes—
92C2×#480C2212yes—
93C2×#479C2212yes—
94C2×#479C2212yes—
95C2×#479C2212yes—
96C2×#479C2212yes—
97C2×#479C2212yes—
98C2×#477C2212yes—
99C2×#477C2212yes—
100C2×#477C2212yes—
101C2×#475C2212yes—
102C2×#478C2212yes—
103C2×#478C2212yes—
104C2×#478C2212yes—
105C2×#478C2212yes—
106C2×#476C2212yes—
107C2×#476C2212yes—
108C2×#474C2212yes—
109C2×#474C2212yes—
110C2×#474C2212yes—
111C2×#464C2212yes—
112C2×#464C2212yes—
113C2×#464C2212yes—
114C2×#460C2212yes—
115C2×#460C2212yes—
116C2×#460C2212yes—
117C2×#451C2211yescharacteristic
118C2×#448C2211yescharacteristic
119C2×#448C2212yes—
120#2987C22116yescomplemented
121C2×#446C2212yes—
122C2×#446C2212yes—
123C2×#446C2212yes—
124C2×#446C2212yes—
125C2×#441C2212yes—
126C2×#441C2212yes—
127C2×#440C2212yes—
128C2×#440C2212yes—
129C2×#440C2212yes—
130C2×#440C2212yes—
131C2×#440C2212yes—
132C2×#440C2212yes—
133C2×C4×Q16C2212yes—
134C2×C4×SD16C2212yes—
135C2×C4×SD16C2212yes—
136C2×C4×SD16C2212yes—
137C2×#433C2212yes—
138C2×#433C2212yes—
139C2×#432C2211yescharacteristic
140C2×#432C2211yescharacteristic
141C22×#41—21no—
142C22×#41—21no—
143C23×Q8—21no—
144C23×Q8C2311yescharacteristic
145C22×Q16C2312yes—
146C22×SD16C2312yes—
147C22×SD16C2312yes—
148C22×SD16C2312yes—
149#562—232no—
150#559—28no—
151#559—24no—
152#559C2318yes—
153#559C23116yes—
154Q82—216no—
155Q82—28no—
156Q82C23116yes—
157#557—216no—
158#557—232no—
159#557—28no—
160#557—28no—
161#557—28no—
162#557—24no—
163#557C23116yes—
164#557C23116yes—
165#557C23116yes—
166#557C2318yes—
167#554—28no—
168#554C23116yes—
169#550—24no—
170#550C2318yes—
171D4×Q8—24no—
172D4×Q8C2318yes—
173#548—216no—
174#547—216no—
175#544—216no—
176#544—216no—
177#544—28no—
178#544C23116yes—
179#542—216no—
180#542—28no—
181#542C23116yes—
182#540—28no—
183#540C23116yes—
184#539—232no—
185#536—216no—
186#533—232no—
187#533—24no—
188#533D418yes—
189#533C2318yes—
190#533C2318yes—
191#532—24no—
192#532C2318yes—
193C2×C4⋊Q8—22no—
194C2×C4⋊Q8—21no—
195C2×C4⋊Q8—22no—
196C2×C4⋊Q8—22no—
197C2×C4⋊Q8—22no—
198C2×C4⋊Q8—22no—
199C2×C4⋊Q8—22no—
200C2×C4⋊Q8—22no—
201C2×C4⋊Q8D411yescharacteristic
202C2×C4⋊Q8D411yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#127C2312yes—
210C2×#127C2311yescharacteristic
211#529—24no—
212#529C2318yes—
213C2×#126—22no—
214C2×#126—21no—
215C2×#125—22no—
216C2×#125—22no—
217C2×#125—22no—
218C2×#125—22no—
219C2×#125—22no—
220C2×#125—22no—
221C2×#125—22no—
222C2×#125—22no—
223C2×#125D412yes—
224C2×#125C2312yes—
225C2×#125C2312yes—
226C2×#125C2312yes—
227C2×#125C2312yes—
228C2×#125C2311yescharacteristic
229C2×#124—21no—
230C2×#124—22no—
231C2×#124—22no—
232C2×#124—21no—
233C2×#124C2312yes—
234C2×#124C2311yescharacteristic
235C2×#123—21no—
236C2×#123—22no—
237C2×#123—22no—
238C2×#123—22no—
239C2×#123—22no—
240C2×#123—22no—
241C2×#123—22no—
242C2×C22⋊Q8—22no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—22no—
246C2×C22⋊Q8—22no—
247C2×C22⋊Q8—22no—
248C2×C22⋊Q8—22no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8—22no—
251C2×C22⋊Q8—22no—
252C2×C22⋊Q8D412yes—
253C2×C22⋊Q8D411yescharacteristic
254C2×C22⋊Q8D411yescharacteristic
255C2×C22⋊Q8C2311yescharacteristic
256C2×#121—21no—
257C2×#121—22no—
258C2×#121—21no—
259C2×#121—22no—
260C2×#121—22no—
261C2×#121C2312yes—
262C2×#121C2311yescharacteristic
263#519—28no—
264#519C23116yes—
265C2×C4×Q8—22no—
266C2×C4×Q8—22no—
267C2×C4×Q8—22no—
268C2×C4×Q8—22no—
269C2×C4×Q8—22no—
270C2×C4×Q8—22no—
271C2×C4×Q8—21no—
272C2×C4×Q8—21no—
273C2×C4×Q8—21no—
274C2×C4×Q8—24no—
275C2×C4×Q8—21no—
276C2×C4×Q8—21no—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2318yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2312yes—
289C2×C4×D4—21no—
290C2×C4×D4—22no—
291C2×C4×D4—21no—
292C2×C4×D4—21no—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×#117—22no—
299C2×#117—22no—
300C2×#117—21no—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C22×C4⋊C4—21no—
304C22×C4⋊C4—22no—
305C22×C4⋊C4C2311yescharacteristic
306C22×C42—21no—
307C22×C42C2311yescharacteristic
308#501C2318yes—
309#501C23116yes—
310#501C23116yes—
311#501C23116yes—
312#501C2318yes—
313#500C23116yes—
314#499C23116yes—
315#490C23116yes—
316#490C23116yes—
317#489C2318yes—
318#489C23116yes—
319#489C2318yes—
320#488C23116yes—
321#486C23116yes—
322#485C23116yes—
323#484C2318yes—
324#482C23116yes—
325#482C23116yes—
326#482C23116yes—
327#481C2318yes—
328#480C23116yes—
329#479C23116yes—
330#479C23116yes—
331#479C23116yes—
332#479C23116yes—
333#479C23116yes—
334#478C23116yes—
335#478C23116yes—
336#478C23116yes—
337#478C23116yes—
338#477C23116yes—
339#477C23116yes—
340#477C23116yes—
341#476C23116yes—
342#476C23116yes—
343#475C23116yes—
344#474C23116yes—
345#474C23116yes—
346#474C23116yes—
347#464C23116yes—
348#464C23116yes—
349#464C23116yes—
350#460C23116yes—
351#460C23116yes—
352#460C23116yes—
353#451C2318yes—
354#448C23116yes—
355#448C2318yes—
356#446C23116yes—
357#446C23116yes—
358#446C23116yes—
359#446C23116yes—
360#441C23116yes—
361#441C23116yes—
362#440C23116yes—
363#440C23116yes—
364#440C23116yes—
365#440C23116yes—
366#440C23116yes—
367#440C23116yes—
368C4×Q16C23116yes—
369C4×SD16C23116yes—
370C4×SD16C23116yes—
371C4×SD16C23116yes—
372#433C23116yes—
373#433C23116yes—
374#432C2318yes—
375#432C2318yes—
376C2×#107C2312yes—
377C2×#107C2312yes—
378C2×#107C2312yes—
379C2×#107C2312yes—
380C2×#107C2312yes—
381C2×#107C2312yes—
382C2×#107C2312yes—
383C2×#106C2312yes—
384C2×#106C2312yes—
385C2×#106C2312yes—
386C2×#106C2312yes—
387C2×#106C2312yes—
388C2×C4⋊C8C2312yes—
389C2×C4⋊C8C2312yes—
390C2×C4⋊C8C2312yes—
391C2×C4⋊C8C2312yes—
392C2×C4⋊C8C2312yes—
393C2×C4⋊C8C2312yes—
394C2×#103C2312yes—
395C2×#103C2312yes—
396C2×#103C2312yes—
397C2×#103C2312yes—
398C2×#103C2312yes—
399C2×#103C2312yes—
400C2×#103C2312yes—
401C2×#102C2312yes—
402C2×#102C2312yes—
403C2×#102C2312yes—
404C2×#102C2312yes—
405C2×#102C2312yes—
406C2×#102C2312yes—
407C2×#102C2312yes—
408C2×#102C2312yes—
409C2×#102C2312yes—
410C2×C22⋊C8C2312yes—
411C2×C22⋊C8C2311yescharacteristic
412C2×C22⋊C8C2311yescharacteristic
413C2×#97C2311yescharacteristic
414C2×#97C2311yescharacteristic
415C2×#97C2312yes—
416C2×#97C2312yes—
417C2×#97C2312yes—
418C2×C4×C8C2312yes—
419C2×C4×C8C2312yes—
420C2×#41—28no—
421C2×#41—28no—
422C2×#41—84no—
423C2×#41—84no—
424C22×Q8—28no—
425C22×Q8—28no—
426C22×Q8—21no—
427C22×Q8—22no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—22no—
432C22×Q8—22no—
433C22×Q8—22no—
434C22×Q8—84no—
435C22×Q8C2×D412yes—
436C22×Q8C2×D411yescharacteristic
437C22×Q8C2×D411yescharacteristic
438C22×Q8C2411yescharacteristic
439C22×Q8C2414yes—
440C22×Q8C2412yes—
441C22×D4—21no—
442C22×D4—22no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4C2411yescharacteristic
448C22×D4C2412yes—
449C23×C4—21no—
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4C2×D411yescharacteristic
457C23×C4C2×D411yescharacteristic
458C23×C4C2411yescharacteristic
459C2×Q16—28no—
460C2×Q16C2418yes—
461C2×SD16—28no—
462C2×SD16—28no—
463C2×SD16—28no—
464C2×SD16C2418yes—
465C2×SD16C2418yes—
466C2×SD16C2418yes—
467C22×C8C2412yes—
468C22×C8C2412yes—
469C22×C8C2412yes—
470C22×C8C2412yes—
471C4⋊Q8—216no—
472C4⋊Q8—28no—
473C4⋊Q8—216no—
474C4⋊Q8—216no—
475C4⋊Q8—216no—
476C4⋊Q8—216no—
477C4⋊Q8—216no—
478C4⋊Q8—216no—
479C4⋊Q8—22no—
480C4⋊Q8—22no—
481C4⋊Q8—22no—
482C4⋊Q8—24no—
483C4⋊Q8—24no—
484C4⋊Q8—24no—
485C4⋊Q8C2×D418yes—
486C4⋊Q8C2×D418yes—
487C4⋊Q8C2414yes—
488C4⋊Q8C2414yes—
489C4⋊Q8C2414yes—
490C4⋊Q8C2418yes—
491C4⋊Q8C2418yes—
492C4⋊Q8C2418yes—
493#127—22no—
494#127—24no—
495#127C2414yes—
496#127C2418yes—
497#126—216no—
498#126—28no—
499#125—216no—
500#125—216no—
501#125—216no—
502#125—216no—
503#125—216no—
504#125—216no—
505#125—216no—
506#125—216no—
507#125—22no—
508#125—24no—
509#125—24no—
510#125—24no—
511#125—24no—
512#125C2×D4116yes—
513#125C2414yes—
514#125C2418yes—
515#125C2418yes—
516#125C2418yes—
517#125C2418yes—
518#124—28no—
519#124—216no—
520#124—216no—
521#124—28no—
522#124—22no—
523#124—24no—
524#124C2414yes—
525#124C2418yes—
526#123—28no—
527#123—216no—
528#123—216no—
529#123—216no—
530#123—216no—
531#123—216no—
532#123—216no—
533C22⋊Q8—216no—
534C22⋊Q8—28no—
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—216no—
538C22⋊Q8—216no—
539C22⋊Q8—216no—
540C22⋊Q8—216no—
541C22⋊Q8—28no—
542C22⋊Q8—216no—
543C22⋊Q8—216no—
544C22⋊Q8C2×D4116yes—
545C22⋊Q8C2×D418yes—
546C22⋊Q8C2×D418yes—
547C22⋊Q8C2414yes—
548#121—28no—
549#121—22no—
550#121—24no—
551#121—216no—
552#121—28no—
553#121—216no—
554#121—216no—
555#121C2414yes—
556#121C2418yes—
557C4×Q8—216no—
558C4×Q8—216no—
559C4×Q8—216no—
560C4×Q8—216no—
561C4×Q8—216no—
562C4×Q8—216no—
563C4×Q8—28no—
564C4×Q8—28no—
565C4×Q8—24no—
566C4×Q8—28no—
567C4×Q8—24no—
568C4×Q8—28no—
569C4×Q8—28no—
570C4×Q8—24no—
571C4×Q8—24no—
572C4×Q8—24no—
573C4×Q8—24no—
574C4×Q8—22no—
575C4×Q8—24no—
576C4×Q8C2×D414yes—
577C4×Q8C2×D414yes—
578C4×Q8C2×D418yes—
579C4×Q8C2418yes—
580C4×Q8C2418yes—
581C4×Q8C2418yes—
582C4×Q8C2418yes—
583C4×Q8C2418yes—
584C4×Q8C2418yes—
585C4×Q8C2414yes—
586C4×Q8C2418yes—
587C4×Q8C2414yes—
588C4×Q8C2414yes—
589C4×Q8C2418yes—
590C4×D4—28no—
591C4×D4—216no—
592C4×D4—28no—
593C4×D4—28no—
594C4×D4—22no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4C2414yes—
600C4×D4C2418yes—
601C4×D4C2418yes—
602C4×D4C2418yes—
603C4×D4C2418yes—
604#117—24no—
605#117—216no—
606#117—216no—
607#117—28no—
608#117C2×D418yes—
609#117C2418yes—
610#117C2418yes—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—28no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—216no—
640C2×C4⋊C4C2×D412yes—
641C2×C4⋊C4C2×D412yes—
642C2×C4⋊C4C2×D412yes—
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D412yes—
645C2×C4⋊C4C2×D412yes—
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D412yes—
648C2×C4⋊C4C2×D412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2412yes—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4C2×D412yes—
670C2×C22⋊C4C2×D412yes—
671C2×C42—21no—
672C2×C42—22no—
673C2×C42—22no—
674C2×C42—22no—
675C2×C42—22no—
676C2×C42—22no—
677C2×C42—22no—
678C2×C42—22no—
679C2×C42—22no—
680C2×C42—28no—
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D414yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2414yes—
689#107C2418yes—
690#107C2418yes—
691#107C2418yes—
692#107C2418yes—
693#107C2418yes—
694#107C2418yes—
695#107C2418yes—
696#106C2418yes—
697#106C2418yes—
698#106C2418yes—
699#106C2418yes—
700#106C2418yes—
701C4⋊C8C2418yes—
702C4⋊C8C2418yes—
703C4⋊C8C2418yes—
704C4⋊C8C2418yes—
705C4⋊C8C2418yes—
706C4⋊C8C2418yes—
707#103C2418yes—
708#103C2418yes—
709#103C2418yes—
710#103C2418yes—
711#103C2418yes—
712#103C2418yes—
713#103C2418yes—
714#102C2418yes—
715#102C2418yes—
716#102C2418yes—
717#102C2418yes—
718#102C2418yes—
719#102C2418yes—
720#102C2418yes—
721#102C2418yes—
722#102C2418yes—
723C22⋊C8C2418yes—
724C22⋊C8C2414yes—
725C22⋊C8C2414yes—
726#97C2414yes—
727#97C2414yes—
728#97C2418yes—
729#97C2418yes—
730#97C2418yes—
731C4×C8C2418yes—
732C4×C8C2418yes—
733C24—21no—
734C24—22no—
735C24C22×D411yescharacteristic
736#41—816no—
737#41—816no—
738C2×Q8—216no—
739C2×Q8—28no—
740C2×Q8—216no—
741C2×Q8—24no—
742C2×Q8—22no—
743C2×Q8—21no—
744C2×Q8—24no—
745C2×Q8—24no—
746C2×Q8—24no—
747C2×Q8—28no—
748C2×Q8—28no—
749C2×Q8—28no—
750C2×Q8—24no—
751C2×Q8—24no—
752C2×Q8—42no—
753C2×Q8—44no—
754C2×Q8—42no—
755C2×Q8—44no—
756C2×Q8—44no—
757C2×Q8—82no—
758C2×Q8—84no—
759C2×Q8—84no—
760C2×Q8—84no—
761C2×Q8—816no—
762C2×Q8C22×D418yes—
763C2×Q8C22×D414yes—
764C2×Q8C22×D414yes—
765C2×Q82−1+418yes—
766C2×Q8C2512yes—
767C2×Q8C2514yes—
768C2×D4—24no—
769C2×D4—28no—
770C2×D4—21no—
771C2×D4—22no—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—44no—
780C2×D4—82no—
781C2×D4—84no—
782C2×D4—84no—
783C2×D4—82no—
784C2×D4—84no—
785C2×D4C2514yes—
786C2×D4C2512yes—
787C22×C4—28no—
788C22×C4—24no—
789C22×C4—22no—
790C22×C4—24no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—28no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—44no—
807C22×C4—84no—
808C22×C4—84no—
809C22×C4—84no—
810C22×C4—84no—
811C22×C4—82no—
812C22×C4C22×D412yes—
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D412yes—
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D412yes—
819C22×C4C22×D412yes—
820C22×C4C22×D412yes—
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D414yes—
823C22×C4C22×D414yes—
824C22×C4C2512yes—
825C22×C4C2511yescharacteristic
826Q16—216no—
827SD16—216no—
828SD16—216no—
829SD16—216no—
830C2×C8—24no—
831C2×C8—24no—
832C2×C8—24no—
833C2×C8—24no—
834C2×C8C2514yes—
835C2×C8C2514yes—
836C2×C8C2514yes—
837C2×C8C2514yes—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—24no—
844C4⋊C4—22no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—24no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—24no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—22no—
870C4⋊C4C22×D418yes—
871C4⋊C4C22×D418yes—
872C4⋊C4C22×D418yes—
873C4⋊C4C22×D414yes—
874C4⋊C4C22×D418yes—
875C4⋊C4C22×D418yes—
876C4⋊C4C22×D414yes—
877C4⋊C4C22×D418yes—
878C4⋊C4C22×D418yes—
879C4⋊C4C2514yes—
880C4⋊C4C2514yes—
881C4⋊C4C2514yes—
882C4⋊C4C2512yes—
883C4⋊C4C2512yes—
884C4⋊C4C2514yes—
885C22⋊C4—28no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—24no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4C22×D418yes—
899C22⋊C4C22×D418yes—
900C42—28no—
901C42—28no—
902C42—24no—
903C42—28no—
904C42—28no—
905C42—28no—
906C42—28no—
907C42—28no—
908C42—28no—
909C42C22×D414yes—
910C42C22×D414yes—
911C42C22×D412yes—
912C42C22×D412yes—
913C42C22×D414yes—
914C42C22×D414yes—
915C42C2514yes—
916C42C2514yes—
917C42C2512yes—
918C42C2512yes—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—24no—
924C23—42no—
925C23—44no—
926C23—44no—
927C23—42no—
928C23—42no—
929C23—44no—
930C23C23×D412yes—
931C23C23×D411yescharacteristic
932Q8—216no—
933Q8—24no—
934Q8—28no—
935Q8—24no—
936Q8—44no—
937Q8—48no—
938Q8—44no—
939Q8—48no—
940Q8—48no—
941Q8—42no—
942Q8—84no—
943Q8—88no—
944Q8—88no—
945Q8—88no—
946Q8C2×2−1+418yes—
947D4—24no—
948D4—24no—
949D4—24no—
950D4—48no—
951D4—42no—
952D4—44no—
953D4—84no—
954D4—88no—
955D4—88no—
956D4—84no—
957D4—88no—
958C2×C4—216no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—28no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—44no—
980C2×C4—44no—
981C2×C4—48no—
982C2×C4—42no—
983C2×C4—44no—
984C2×C4—44no—
985C2×C4—44no—
986C2×C4—42no—
987C2×C4—44no—
988C2×C4—42no—
989C2×C4—88no—
990C2×C4—88no—
991C2×C4—88no—
992C2×C4—88no—
993C2×C4—84no—
994C2×C4C23×D412yes—
995C2×C4C23×D412yes—
996C2×C4C23×D412yes—
997C2×C4C23×D414yes—
998C2×C4C23×D412yes—
999C2×C4C23×D414yes—
1000C2×C4C23×D414yes—
1001C2×C4C23×D414yes—
1002C2×C4C23×D412yes—
1003C2×C4C23×D411yescharacteristic
1004C2×C4C2×2−1+414yes—
1005C2×C4C2611yescharacteristic
1006C8—24no—
1007C8—24no—
1008C8—24no—
1009C8—24no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—44no—
1014C22—42no—
1015C22—44no—
1016C22—42no—
1017C22—44no—
1018C22—44no—
1019C22—42no—
1020C22—84no—
1021C22—88no—
1022C22#348612yes—
1023C22#358512yes—
1024C22#358612yes—
1025C22C24×D411yescharacteristic
1026C4—28no—
1027C4—22no—
1028C4—22no—
1029C4—22no—
1030C4—24no—
1031C4—24no—
1032C4—22no—
1033C4—22no—
1034C4—24no—
1035C4—24no—
1036C4—42no—
1037C4—42no—
1038C4—44no—
1039C4—44no—
1040C4—44no—
1041C4—42no—
1042C4—44no—
1043C4#348612yes—
1044C4C22×2−1+412yes—
1045C2—42no—
1046C2—82no—
1047C2—84no—
1048C2#6187414yesdirect product factor
1049C2C2×#348611yescharacteristic
1050C2C2×#358511yescharacteristic
1051C2C2×#358611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
prime radicalC2×#3554C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#533 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3502C2semidirect
3. #61874C2direct (N × H)
4. C2×#3390C2semidirect
5. C2×#3388C2semidirect
6. C2×#3386C2semidirect
7. C2×#3385C2semidirect
8. C2×#3371C2semidirect
9. C2×#3371C2semidirect
10. C2×#3375C2semidirect
11. C2×#3368C2semidirect
12. C2×#3243C2semidirect
13. C2×#3241C2semidirect
14. C2×#3240C2semidirect
15. C2×#3235C2semidirect
16. C2×#3126C2semidirect
17. C2×#3121C2semidirect
18. C2×#3112C2semidirect
19. C2×#3117C2semidirect
20. C2×#2987C2semidirect
25. #3502C22semidirect
56. #3390C22semidirect
57. #3388C22semidirect
58. #3386C22semidirect
59. #3385C22semidirect
60. #3375C22semidirect
61. #3371C22semidirect
62. #3371C22semidirect
63. #3368C22semidirect
64. #3243C22semidirect
65. #3241C22semidirect
66. #3240C22semidirect
67. #3235C22semidirect
82. #3126C22semidirect
83. #3121C22semidirect
84. #3117C22semidirect
85. #3112C22semidirect
120. #2987C22semidirect
1048. C2#61874direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35022
C2×#35542
#618742
C2×#33902
C2×#33882
C2×#33862
C2×#33852
C2×#33712
C2×#33752
C2×#33682
C2×#32432
C2×#32412
C2×#32402
C2×#32352
C2×#31262
C2×#31212
C2×#31122
C2×#31172
C2×#29872