Finite Group Databasebeta

← C2×#61878 #10578276

Subgroups — C2×#61878 #10578276

Order 512.

6076 conjugacy classes of subgroups.

The subgroup lattice has 1059 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3504C211yesmaximal, characteristic, complemented
2C2×#3550C211yesmaximal, characteristic, complemented
3#61878C2132yesmaximal, direct product factor
4C2×#3387C212yesmaximal, complemented
5C2×#3386C212yesmaximal, complemented
6C2×#3385C212yesmaximal, complemented
7C2×#3384C212yesmaximal, complemented
8C2×#3377C212yesmaximal, complemented
9C2×#3371C212yesmaximal, complemented
10C2×#3376C212yesmaximal, complemented
11C2×#3370C212yesmaximal, complemented
12C2×#3244C212yesmaximal, complemented
13C2×#3243C212yesmaximal, complemented
14C2×#3236C211yesmaximal, characteristic, complemented
15C2×#3234C211yesmaximal, characteristic, complemented
16C2×#3125C212yesmaximal, complemented
17C2×#3124C212yesmaximal, complemented
18C2×#3116C211yesmaximal, characteristic, complemented
19C2×#3115C211yesmaximal, characteristic
20C2×#2987C211yesmaximal, characteristic, complemented
21#3550—28no—
22#3550C22116yescomplemented
23C2×#563—21no—
24C2×#563—21no—
25#3504—28no—
26#3504C22116yescomplemented
27C2×#559C2212yes—
28C2×Q82C2212yes—
29C2×#557C2212yes—
30C2×#557C2212yes—
31C2×#556—21no—
32C2×#556C2212yes—
33C2×#554—22no—
34C2×#554—22no—
35C2×#554C2212yes—
36C2×#554C2212yes—
37C2×D4×Q8—21no—
38C2×D4×Q8C2212yes—
39C2×#544—21no—
40C2×#544—21no—
41C2×#544C2211yescharacteristic
42C2×#544C2211yescharacteristic
43C2×#542—22no—
44C2×#542C2212yes—
45C2×#542C2212yes—
46C2×#536—22no—
47C2×#533—21no—
48C2×#533C2211yescharacteristic
49C2×#533C2211yescharacteristic
50C2×#532C2211yescharacteristic
51C22×#125—21no—
52C22×#125C2211yescharacteristic
53C2×#520C2211yescharacteristic
54C2×#520C2211yescharacteristic
55C2×C4×#41C2211yescharacteristic
56#3387C22132yescomplemented
57#3386C22132yescomplemented
58#3385C22132yescomplemented
59#3384C22132yescomplemented
60#3377C22132yescomplemented
61#3376C22132yescomplemented
62#3371C22132yescomplemented
63#3370C22132yescomplemented
64#3244C22132yescomplemented
65#3243C22132yescomplemented
66#3236C22116yescomplemented
67#3234C22116yescomplemented
68C2×#501C2212yes—
69C2×#501C2212yes—
70C2×#501C2212yes—
71C2×#501C2212yes—
72C2×#500C2212yes—
73C2×#498C2212yes—
74C2×#491C2212yes—
75C2×#490C2212yes—
76C2×#489C2212yes—
77C2×#489C2212yes—
78C2×#488C2212yes—
79C2×#488C2212yes—
80#3125C22132yescomplemented
81#3124C22132yescomplemented
82#3116C22116yescomplemented
83#3115C22116yes—
84C2×#484C2212yes—
85C2×#481C2212yes—
86C2×#485C2212yes—
87C2×#482C2212yes—
88C2×#483C2212yes—
89C2×#480C2212yes—
90C2×#479C2212yes—
91C2×#479C2212yes—
92C2×#479C2212yes—
93C2×#479C2212yes—
94C2×#477C2211yescharacteristic
95C2×#477C2212yes—
96C2×#477C2212yes—
97C2×#475C2211yescharacteristic
98C2×#475C2212yes—
99C2×#475C2212yes—
100C2×#478C2212yes—
101C2×#478C2212yes—
102C2×#478C2212yes—
103C2×#478C2212yes—
104C2×#476C2211yescharacteristic
105C2×#476C2212yes—
106C2×#476C2212yes—
107C2×#474C2211yescharacteristic
108C2×#474C2212yes—
109C2×#474C2212yes—
110C2×#464C2212yes—
111C2×#464C2212yes—
112C2×#462C2211yescharacteristic
113C2×#460C2211yescharacteristic
114C2×#463C2212yes—
115C2×#463C2212yes—
116C2×#461C2211yescharacteristic
117C2×#459C2211yescharacteristic
118C2×#452C2212yes—
119C2×#449C2212yes—
120#2987C22116yescomplemented
121C2×#446C2212yes—
122C2×#446C2212yes—
123C2×#446C2212yes—
124C2×#446C2212yes—
125C2×#442C2212yes—
126C2×#442C2212yes—
127C2×#441C2212yes—
128C2×#441C2212yes—
129C2×#440C2212yes—
130C2×#440C2212yes—
131C2×#440C2212yes—
132C2×#440C2212yes—
133C2×C4×Q16C2212yes—
134C2×C4×SD16C2212yes—
135C2×C4×SD16C2212yes—
136C2×C4×D8C2212yes—
137C2×#433C2212yes—
138C2×#433C2212yes—
139C2×#432C2211yescharacteristic
140C2×#432C2211yescharacteristic
141C22×#41—21no—
142C22×#41C2311yescharacteristic
143C23×Q8—22no—
144C22×Q16C2312yes—
145C22×SD16C2312yes—
146C22×SD16C2312yes—
147C22×D8C2312yes—
148#563—216no—
149#563—216no—
150#559—28no—
151#559C23116yes—
152Q82—28no—
153Q82C23116yes—
154#557—28no—
155#557—28no—
156#557C23116yes—
157#557C23116yes—
158#556—216no—
159#556—28no—
160#556C23116yes—
161#554—232no—
162#554—232no—
163#554—28no—
164#554—28no—
165#554C23116yes—
166#554C23116yes—
167D4×Q8—216no—
168D4×Q8—28no—
169D4×Q8C23116yes—
170#544—216no—
171#544—216no—
172#544—24no—
173#544—24no—
174#544C2318yes—
175#544C2318yes—
176#542—232no—
177#542—28no—
178#542—28no—
179#542C23116yes—
180#542C23116yes—
181#536—232no—
182#533—216no—
183#533—24no—
184#533D418yes—
185#533C2318yes—
186#533C2318yes—
187#532—24no—
188#532C2318yes—
189C2×C4⋊Q8—22no—
190C2×C4⋊Q8—22no—
191C2×C4⋊Q8—21no—
192C2×C4⋊Q8—21no—
193C2×C4⋊Q8—22no—
194C2×C4⋊Q8—22no—
195C2×C4⋊Q8—22no—
196C2×C4⋊Q8D411yescharacteristic
197C2×C4⋊Q8D411yescharacteristic
198C2×C4⋊Q8C2311yescharacteristic
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×#127C2311yescharacteristic
206C2×#126—22no—
207C2×#126—22no—
208C2×#126—22no—
209C2×#126—22no—
210C2×#125—216no—
211C2×#125—21no—
212C2×#125—21no—
213C2×#125—22no—
214C2×#125—22no—
215C2×#125—22no—
216C2×#125—22no—
217C2×#125—21no—
218C2×#125—21no—
219C2×#125—24no—
220C2×#125—21no—
221C2×#125D411yescharacteristic
222C2×#125D411yescharacteristic
223C2×#125C2312yes—
224C2×#125C2312yes—
225C2×#125C2312yes—
226C2×#125C2312yes—
227C2×#125C2318yes—
228C2×#124—22no—
229C2×#124—22no—
230C2×#124—22no—
231C2×#124—21no—
232C2×#124C2312yes—
233C2×#124C2312yes—
234C2×#123—22no—
235C2×#123—22no—
236C2×#123—22no—
237C2×#123—22no—
238C2×C22⋊Q8—22no—
239C2×C22⋊Q8—22no—
240C2×C22⋊Q8—22no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—22no—
243C2×C22⋊Q8—22no—
244C2×C22⋊Q8—22no—
245C2×C22⋊Q8—22no—
246C2×C22⋊Q8—22no—
247C2×C22⋊Q8—22no—
248C2×C22⋊Q8—22no—
249C2×C22⋊Q8—22no—
250C2×C22⋊Q8—22no—
251C2×C22⋊Q8—22no—
252C2×C22⋊Q8—22no—
253C2×C22⋊Q8D412yes—
254C2×C22⋊Q8D412yes—
255C2×C22⋊Q8C2312yes—
256C2×#121—21no—
257C2×#121C2312yes—
258#520—24no—
259#520—24no—
260#520C2318yes—
261#520C2318yes—
262C4×#41—24no—
263C4×#41C2318yes—
264C2×C4×Q8—22no—
265C2×C4×Q8—22no—
266C2×C4×Q8—22no—
267C2×C4×Q8—21no—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×D4—21no—
278C2×C4×D4—21no—
279C2×C4×D4—22no—
280C2×C4×D4—22no—
281C2×C4×D4—22no—
282C2×C4×D4—21no—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×#117—21no—
291C2×#117—21no—
292C2×#117—21no—
293C2×#117—22no—
294C2×#117—21no—
295C2×#117C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2311yescharacteristic
298C22×C4⋊C4—21no—
299C22×C4⋊C4—21no—
300C22×C4⋊C4—21no—
301C22×C4⋊C4—21no—
302C22×C4⋊C4—22no—
303C22×C4⋊C4—22no—
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2311yescharacteristic
306C22×C42—21no—
307C22×C42C2311yescharacteristic
308#501C23116yes—
309#501C23116yes—
310#501C23116yes—
311#501C23116yes—
312#500C23116yes—
313#498C23116yes—
314#491C23116yes—
315#490C23116yes—
316#489C23116yes—
317#489C23116yes—
318#488C23116yes—
319#488C23116yes—
320#485C23116yes—
321#484C23116yes—
322#483C23116yes—
323#482C23116yes—
324#481C23116yes—
325#480C23116yes—
326#479C23116yes—
327#479C23116yes—
328#479C23116yes—
329#479C23116yes—
330#478C23116yes—
331#478C23116yes—
332#478C23116yes—
333#478C23116yes—
334#477C2318yes—
335#477C23116yes—
336#477C23116yes—
337#476C23116yes—
338#476C2318yes—
339#476C23116yes—
340#475C2318yes—
341#475C23116yes—
342#475C23116yes—
343#474C23116yes—
344#474C2318yes—
345#474C23116yes—
346#464C23116yes—
347#464C23116yes—
348#463C23116yes—
349#463C23116yes—
350#462C2318yes—
351#461C2318yes—
352#460C2318yes—
353#459C2318yes—
354#452C23116yes—
355#449C23116yes—
356#446C23116yes—
357#446C23116yes—
358#446C23116yes—
359#446C23116yes—
360#442C23116yes—
361#442C23116yes—
362#441C23116yes—
363#441C23116yes—
364#440C23116yes—
365#440C23116yes—
366#440C23116yes—
367#440C23116yes—
368C4×Q16C23116yes—
369C4×SD16C23116yes—
370C4×SD16C23116yes—
371C4×D8C23116yes—
372#433C23116yes—
373#433C23116yes—
374#432C2318yes—
375#432C2318yes—
376C2×#107C2312yes—
377C2×#107C2312yes—
378C2×#107C2312yes—
379C2×#107C2312yes—
380C2×#107C2312yes—
381C2×#107C2312yes—
382C2×#106C2312yes—
383C2×#106C2312yes—
384C2×#106C2312yes—
385C2×#106C2312yes—
386C2×#106C2312yes—
387C2×#106C2312yes—
388C2×C4⋊C8C2311yescharacteristic
389C2×C4⋊C8C2311yescharacteristic
390C2×C4⋊C8C2312yes—
391C2×C4⋊C8C2312yes—
392C2×C4⋊C8C2311yescharacteristic
393C2×C4⋊C8C2312yes—
394C2×C4⋊C8C2311yescharacteristic
395C2×C4⋊C8C2312yes—
396C2×#103C2312yes—
397C2×#103C2312yes—
398C2×#103C2312yes—
399C2×#103C2312yes—
400C2×#103C2312yes—
401C2×#103C2312yes—
402C2×#103C2312yes—
403C2×#103C2312yes—
404C2×#102C2312yes—
405C2×#102C2312yes—
406C2×#102C2312yes—
407C2×#102C2312yes—
408C2×#102C2312yes—
409C2×#102C2312yes—
410C2×#102C2312yes—
411C2×#102C2312yes—
412C2×C22⋊C8C2312yes—
413C2×C22⋊C8C2312yes—
414C2×#97C2312yes—
415C2×#97C2312yes—
416C2×#97C2312yes—
417C2×#97C2312yes—
418C2×C4×C8C2312yes—
419C2×C4×C8C2312yes—
420C2×#41—24no—
421C2×#41—24no—
422C2×#41—22no—
423C2×#41—28no—
424C2×#41—84no—
425C2×#41C2414yes—
426C22×Q8—216no—
427C22×Q8—21no—
428C22×Q8—22no—
429C22×Q8—22no—
430C22×Q8—22no—
431C22×Q8—22no—
432C22×Q8—21no—
433C22×Q8—88no—
434C22×Q8C2×D412yes—
435C22×Q8C2×D412yes—
436C22×Q8C2412yes—
437C22×Q8C2411yescharacteristic
438C22×D4—21no—
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4C2412yes—
443C22×D4C2411yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—21no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4C2×D411yescharacteristic
455C23×C4C2×D411yescharacteristic
456C23×C4C2411yescharacteristic
457C2×Q16—28no—
458C2×Q16C2418yes—
459C2×SD16—28no—
460C2×SD16—28no—
461C2×SD16C2418yes—
462C2×SD16C2418yes—
463C2×D8—28no—
464C2×D8C2418yes—
465C22×C8C2412yes—
466C22×C8C2412yes—
467C22×C8C2412yes—
468C22×C8C2412yes—
469C4⋊Q8—216no—
470C4⋊Q8—216no—
471C4⋊Q8—28no—
472C4⋊Q8—28no—
473C4⋊Q8—216no—
474C4⋊Q8—216no—
475C4⋊Q8—216no—
476C4⋊Q8—22no—
477C4⋊Q8—22no—
478C4⋊Q8—22no—
479C4⋊Q8—24no—
480C4⋊Q8—24no—
481C4⋊Q8—24no—
482C4⋊Q8—24no—
483C4⋊Q8C2×D418yes—
484C4⋊Q8C2×D418yes—
485C4⋊Q8C2414yes—
486C4⋊Q8C2414yes—
487C4⋊Q8C2414yes—
488C4⋊Q8C2418yes—
489C4⋊Q8C2418yes—
490C4⋊Q8C2418yes—
491C4⋊Q8C2418yes—
492#127—22no—
493#127C2414yes—
494#126—216no—
495#126—216no—
496#126—216no—
497#126—216no—
498#125—28no—
499#125—28no—
500#125—216no—
501#125—216no—
502#125—216no—
503#125—216no—
504#125—28no—
505#125—28no—
506#125—24no—
507#125—24no—
508#125—28no—
509#125—24no—
510#125—24no—
511#125C2×D418yes—
512#125C2×D418yes—
513#125C2418yes—
514#125C2418yes—
515#125C2418yes—
516#125C2418yes—
517#124—216no—
518#124—216no—
519#124—216no—
520#124—28no—
521#124—24no—
522#124—24no—
523#124C2418yes—
524#124C2418yes—
525#123—216no—
526#123—216no—
527#123—216no—
528#123—216no—
529C22⋊Q8—216no—
530C22⋊Q8—216no—
531C22⋊Q8—216no—
532C22⋊Q8—28no—
533C22⋊Q8—24no—
534C22⋊Q8—216no—
535C22⋊Q8—216no—
536C22⋊Q8—216no—
537C22⋊Q8—216no—
538C22⋊Q8—216no—
539C22⋊Q8—216no—
540C22⋊Q8—216no—
541C22⋊Q8—216no—
542C22⋊Q8—216no—
543C22⋊Q8—216no—
544C22⋊Q8—216no—
545C22⋊Q8C2×D4116yes—
546C22⋊Q8C2×D4116yes—
547C22⋊Q8C2418yes—
548#121—28no—
549#121—24no—
550#121C2418yes—
551C4×Q8—216no—
552C4×Q8—216no—
553C4×Q8—216no—
554C4×Q8—28no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—24no—
558C4×Q8—24no—
559C4×Q8—24no—
560C4×Q8—24no—
561C4×Q8—24no—
562C4×Q8C2×D418yes—
563C4×Q8C2×D418yes—
564C4×Q8C2414yes—
565C4×Q8C2414yes—
566C4×Q8C2418yes—
567C4×Q8C2418yes—
568C4×Q8C2418yes—
569C4×Q8C2418yes—
570C4×Q8C2418yes—
571C4×Q8C2418yes—
572C4×Q8C2418yes—
573C4×D4—28no—
574C4×D4—28no—
575C4×D4—216no—
576C4×D4—216no—
577C4×D4—216no—
578C4×D4—28no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—24no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4C2414yes—
587C4×D4C2414yes—
588C4×D4C2418yes—
589C4×D4C2418yes—
590C4×D4C2418yes—
591C4×D4C2418yes—
592C4×D4C2418yes—
593#117—28no—
594#117—22no—
595#117—28no—
596#117—28no—
597#117—216no—
598#117—28no—
599#117C2×D414yes—
600#117C2×D414yes—
601#117C2414yes—
602#117C2414yes—
603#117C2414yes—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—28no—
617C2×C4⋊C4—28no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—28no—
635C2×C4⋊C4—28no—
636C2×C4⋊C4—216no—
637C2×C4⋊C4—216no—
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D412yes—
641C2×C4⋊C4C2×D412yes—
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D412yes—
645C2×C4⋊C4C2×D412yes—
646C2×C4⋊C4C2×D412yes—
647C2×C4⋊C4C2×D412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4C2×D412yes—
671C2×C22⋊C4C2×D412yes—
672C2×C42—21no—
673C2×C42—22no—
674C2×C42—22no—
675C2×C42—22no—
676C2×C42—22no—
677C2×C42—22no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—28no—
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D414yes—
683C2×C42C2×D411yescharacteristic
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2414yes—
689#107C2418yes—
690#107C2418yes—
691#107C2418yes—
692#107C2418yes—
693#107C2418yes—
694#107C2418yes—
695#106C2418yes—
696#106C2418yes—
697#106C2418yes—
698#106C2418yes—
699#106C2418yes—
700#106C2418yes—
701C4⋊C8C2414yes—
702C4⋊C8C2414yes—
703C4⋊C8C2414yes—
704C4⋊C8C2414yes—
705C4⋊C8C2418yes—
706C4⋊C8C2418yes—
707C4⋊C8C2418yes—
708C4⋊C8C2418yes—
709#103C2418yes—
710#103C2418yes—
711#103C2418yes—
712#103C2418yes—
713#103C2418yes—
714#103C2418yes—
715#103C2418yes—
716#103C2418yes—
717#102C2418yes—
718#102C2418yes—
719#102C2418yes—
720#102C2418yes—
721#102C2418yes—
722#102C2418yes—
723#102C2418yes—
724#102C2418yes—
725C22⋊C8C2418yes—
726C22⋊C8C2418yes—
727#97C2418yes—
728#97C2418yes—
729#97C2418yes—
730#97C2418yes—
731C4×C8C2418yes—
732C4×C8C2418yes—
733C24—21no—
734C24—22no—
735C24C22×D411yescharacteristic
736#41—216no—
737#41—28no—
738#41—28no—
739#41—816no—
740C2×Q8—21no—
741C2×Q8—22no—
742C2×Q8—24no—
743C2×Q8—28no—
744C2×Q8—28no—
745C2×Q8—28no—
746C2×Q8—28no—
747C2×Q8—24no—
748C2×Q8—22no—
749C2×Q8—24no—
750C2×Q8—24no—
751C2×Q8—44no—
752C2×Q8—44no—
753C2×Q8—44no—
754C2×Q8—84no—
755C2×Q8—84no—
756C2×Q8—84no—
757C2×Q8—84no—
758C2×Q8—82no—
759C2×Q8—832no—
760C2×Q8C22×D418yes—
761C2×Q8C22×D418yes—
762C2×Q82−1+414yes—
763C2×Q8C2514yes—
764C2×Q8C2512yes—
765C2×D4—28no—
766C2×D4—24no—
767C2×D4—28no—
768C2×D4—21no—
769C2×D4—22no—
770C2×D4—24no—
771C2×D4—24no—
772C2×D4—22no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—44no—
776C2×D4—82no—
777C2×D4—84no—
778C2×D42−1+414yes—
779C2×D4C2514yes—
780C2×D4C2512yes—
781C22×C4—28no—
782C22×C4—21no—
783C22×C4—24no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—28no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—28no—
799C22×C4—28no—
800C22×C4—28no—
801C22×C4—28no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—48no—
805C22×C4—82no—
806C22×C4—84no—
807C22×C4—82no—
808C22×C4—84no—
809C22×C4—84no—
810C22×C4—84no—
811C22×C4—82no—
812C22×C4—82no—
813C22×C4C22×D412yes—
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D412yes—
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D412yes—
820C22×C4C22×D412yes—
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D412yes—
823C22×C4C22×D414yes—
824C22×C4C22×D414yes—
825C22×C4C2512yes—
826C22×C4C2511yescharacteristic
827Q16—216no—
828SD16—216no—
829SD16—216no—
830D8—216no—
831C2×C8—24no—
832C2×C8—24no—
833C2×C8—24no—
834C2×C8—24no—
835C2×C8C2514yes—
836C2×C8C2514yes—
837C2×C8C2514yes—
838C2×C8C2514yes—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4C22×D414yes—
872C4⋊C4C22×D414yes—
873C4⋊C4C22×D418yes—
874C4⋊C4C22×D418yes—
875C4⋊C4C22×D414yes—
876C4⋊C4C22×D414yes—
877C4⋊C4C22×D418yes—
878C4⋊C4C22×D418yes—
879C4⋊C4C22×D418yes—
880C4⋊C4C22×D418yes—
881C4⋊C4C2514yes—
882C4⋊C4C2512yes—
883C4⋊C4C2514yes—
884C4⋊C4C2512yes—
885C4⋊C4C2514yes—
886C4⋊C4C2514yes—
887C22⋊C4—28no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4C22×D418yes—
902C22⋊C4C22×D418yes—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—28no—
907C42—28no—
908C42—28no—
909C42—28no—
910C42—28no—
911C42C22×D414yes—
912C42C22×D414yes—
913C42C22×D412yes—
914C42C22×D412yes—
915C42C22×D414yes—
916C42C22×D414yes—
917C42C2514yes—
918C42C2514yes—
919C42C2512yes—
920C42C2512yes—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—24no—
926C23—24no—
927C23—42no—
928C23—42no—
929C23—44no—
930C23—44no—
931C23—44no—
932C23C23×D412yes—
933C23C23×D411yescharacteristic
934Q8—22no—
935Q8—24no—
936Q8—24no—
937Q8—24no—
938Q8—48no—
939Q8—48no—
940Q8—48no—
941Q8—44no—
942Q8—88no—
943Q8—88no—
944Q8—88no—
945Q8—88no—
946Q8—84no—
947Q8C2×2−1+414yes—
948D4—216no—
949D4—22no—
950D4—24no—
951D4—24no—
952D4—24no—
953D4—48no—
954D4—44no—
955D4—84no—
956D4—88no—
957D4C2×2−1+414yes—
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—22no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—44no—
981C2×C4—44no—
982C2×C4—416no—
983C2×C4—44no—
984C2×C4—44no—
985C2×C4—44no—
986C2×C4—42no—
987C2×C4—44no—
988C2×C4—42no—
989C2×C4—44no—
990C2×C4—84no—
991C2×C4—88no—
992C2×C4—84no—
993C2×C4—88no—
994C2×C4—88no—
995C2×C4—88no—
996C2×C4—84no—
997C2×C4—84no—
998C2×C4C23×D412yes—
999C2×C4C23×D414yes—
1000C2×C4C23×D412yes—
1001C2×C4C23×D412yes—
1002C2×C4C23×D412yes—
1003C2×C4C23×D414yes—
1004C2×C4C23×D414yes—
1005C2×C4C23×D412yes—
1006C2×C4C23×D414yes—
1007C2×C4C23×D411yescharacteristic
1008C2×C4C2×2−1+412yes—
1009C2×C4C2×2−1+412yes—
1010C2×C4C2611yescharacteristic
1011C8—24no—
1012C8—24no—
1013C8—24no—
1014C8—24no—
1015C22—22no—
1016C22—24no—
1017C22—22no—
1018C22—22no—
1019C22—42no—
1020C22—42no—
1021C22—44no—
1022C22—48no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—88no—
1027C22#348612yes—
1028C22#358512yes—
1029C22#358612yes—
1030C22C24×D411yescharacteristic
1031C4—22no—
1032C4—24no—
1033C4—22no—
1034C4—22no—
1035C4—24no—
1036C4—24no—
1037C4—22no—
1038C4—22no—
1039C4—24no—
1040C4—24no—
1041C4—44no—
1042C4—44no—
1043C4—44no—
1044C4—44no—
1045C4—42no—
1046C4—44no—
1047C4—42no—
1048C4#348612yes—
1049C4C22×2−1+411yescharacteristic
1050C4C22×2−1+411yescharacteristic
1051C2—42no—
1052C2—44no—
1053C2—84no—
1054C2#6187814yesdirect product factor
1055C2C2×#348611yescharacteristic
1056C2C2×#358511yescharacteristic
1057C2C2×#358611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
prime radicalC2×#3115C2
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×#3504C2semidirect
2. C2×#3550C2semidirect
3. #61878C2direct (N × H)
4. C2×#3387C2semidirect
5. C2×#3386C2semidirect
6. C2×#3385C2semidirect
7. C2×#3384C2semidirect
8. C2×#3377C2semidirect
9. C2×#3371C2semidirect
10. C2×#3376C2semidirect
11. C2×#3370C2semidirect
12. C2×#3244C2semidirect
13. C2×#3243C2semidirect
14. C2×#3236C2semidirect
15. C2×#3234C2semidirect
16. C2×#3125C2semidirect
17. C2×#3124C2semidirect
18. C2×#3116C2semidirect
20. C2×#2987C2semidirect
22. #3550C22semidirect
26. #3504C22semidirect
56. #3387C22semidirect
57. #3386C22semidirect
58. #3385C22semidirect
59. #3384C22semidirect
60. #3377C22semidirect
61. #3376C22semidirect
62. #3371C22semidirect
63. #3370C22semidirect
64. #3244C22semidirect
65. #3243C22semidirect
66. #3236C22semidirect
67. #3234C22semidirect
80. #3125C22semidirect
81. #3124C22semidirect
82. #3116C22semidirect
120. #2987C22semidirect
1054. C2#61878direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35042
C2×#35502
#618782
C2×#33872
C2×#33862
C2×#33852
C2×#33842
C2×#33772
C2×#33712
C2×#33762
C2×#33702
C2×#32442
C2×#32432
C2×#32362
C2×#32342
C2×#31252
C2×#31242
C2×#31162
C2×#31152
C2×#29872