Finite Group Databasebeta

← C2×#62543 #10579957

Subgroups — C2×#62543 #10579957

Order 512.

6468 conjugacy classes of subgroups.

The subgroup lattice has 1095 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3511C211yesmaximal, characteristic, complemented
3#62543C2132yesmaximal, direct product factor
4C2×#3376C214yesmaximal, complemented
5C2×#3326C214yesmaximal, complemented
6C2×#3321C214yesmaximal, complemented
7C2×#3307C214yesmaximal, complemented
8C2×#3231C211yesmaximal, characteristic, complemented
9C2×#3228C211yesmaximal, characteristic, complemented
10C2×#3229C211yesmaximal, characteristic, complemented
11C2×#3207C211yesmaximal, characteristic, complemented
12C2×#3207C211yesmaximal, characteristic, complemented
13C2×#3206C211yesmaximal, characteristic, complemented
14C2×#3184C211yesmaximal, characteristic, complemented
15C2×#3182C211yesmaximal, characteristic, complemented
16C2×#3167C211yesmaximal, characteristic, complemented
17C2×#3141C211yesmaximal, characteristic, complemented
18C2×#3139C211yesmaximal, characteristic, complemented
19C2×#3131C211yesmaximal, characteristic, complemented
20C2×#2965C211yesmaximal, characteristic, complemented
21#3511—28no—
22#3511—28no—
23#3511C22116yescomplemented
24#3511C22116yescomplemented
25C2×#556—21no—
26C2×#556C2212yes—
27C2×#555—21no—
28C2×#555C2212yes—
29C2×#554—21no—
30C2×#554C2212yes—
31C2×#553—21no—
32C2×#553—21no—
33C2×#553C2212yes—
34C2×#553C2212yes—
35C2×#548—21no—
36C2×#548—21no—
37C2×#548C2212yes—
38C2×#548C2212yes—
39C2×#547—21no—
40C2×#547C2212yes—
41C2×#542—21no—
42C2×#542—21no—
43C2×#542—21no—
44C2×#542—21no—
45C2×#537—21no—
46C2×#537—21no—
47C2×#533C2211yescharacteristic
48C2×#533C2211yescharacteristic
49C2×#533C2211yescharacteristic
50C2×#533C2211yescharacteristic
51C2×#532C2211yescharacteristic
52C2×#532C2211yescharacteristic
53C2×#532C2211yescharacteristic
54C2×#532C2211yescharacteristic
55C2×#532C2211yescharacteristic
56C2×#532C2211yescharacteristic
57C22×C4⋊Q8C2211yescharacteristic
58C22×C4⋊Q8C2211yescharacteristic
59C2×#520—21no—
60C2×#520—21no—
61C2×C4×#41C2211yescharacteristic
62#3376C22164yescomplemented
63#3326C22164yescomplemented
64#3321C22164yescomplemented
65#3307C22164yescomplemented
66#3231C22116yescomplemented
67#3229C22116yescomplemented
68#3228C22116yescomplemented
69#3207C22116yescomplemented
70#3207C22116yescomplemented
71#3206C22116yescomplemented
72#3184C22116yescomplemented
73#3182C22116yescomplemented
74#3167C22116yescomplemented
75C2×#500C2211yescharacteristic
76C2×#498C2211yescharacteristic
77C2×#498C2211yescharacteristic
78C2×#493C2211yescharacteristic
79C2×#492C2211yescharacteristic
80C2×#492C2211yescharacteristic
81#3141C22116yescomplemented
82#3139C22116yescomplemented
83C2×#491C2214yes—
84C2×#489C2214yes—
85#3131C22116yescomplemented
86C2×#488C2214yes—
87C2×#487C2211yescharacteristic
88C2×#487C2211yescharacteristic
89C2×#487C2211yescharacteristic
90C2×#487C2211yescharacteristic
91C2×#487C2211yescharacteristic
92C2×#487C2211yescharacteristic
93C2×#486C2211yescharacteristic
94C2×#486C2211yescharacteristic
95C2×#486C2211yescharacteristic
96C2×#486C2211yescharacteristic
97C2×#485C2214yes—
98C2×#482C2214yes—
99C2×#483C2214yes—
100C2×#479C2214yes—
101C2×#475C2214yes—
102C2×#478C2214yes—
103C2×#469C2214yes—
104C2×#468C2214yes—
105C2×#465C2214yes—
106C2×#463C2214yes—
107C2×#463C2214yes—
108C2×#461C2214yes—
109C2×#449C2214yes—
110C2×#449C2214yes—
111C2×#448C2214yes—
112#2965C22116yescomplemented
113C2×#446C2212yes—
114C2×#442C2214yes—
115C2×#440C2214yes—
116C2×C4×SD16C2214yes—
117C2×#436C2212yes—
118C2×#435C2212yes—
119C2×#435C2212yes—
120C2×#431C2211yescharacteristic
121C2×#431C2211yescharacteristic
122C2×#431C2211yescharacteristic
123C2×#417C2214yes—
124C2×#419C2214yes—
125C2×#416C2214yes—
126C2×C4×M16C2211yescharacteristic
127C2×C4×M16C2211yescharacteristic
128C22×C4×C8C2211yescharacteristic
129C22×#41—21no—
130C22×#41—21no—
131C22×#41—21no—
132C22×#41—21no—
133C22×#41D411yescharacteristic
134C22×#41C2312yes—
135C22×#41C2312yes—
136C23×Q8—21no—
137C23×Q8C2312yes—
138C22×SD16C2314yes—
139C22×SD16C2314yes—
140C22×D8C2314yes—
141C22×M16C2312yes—
142C22×M16C2312yes—
143C23×C8C2312yes—
144#556—216no—
145#556—28no—
146#556C23116yes—
147#555—216no—
148#555—28no—
149#555C23116yes—
150#554—216no—
151#554—28no—
152#554C23116yes—
153#553—216no—
154#553—216no—
155#553—28no—
156#553—28no—
157#553C23116yes—
158#553C23116yes—
159#548—216no—
160#548—216no—
161#548—28no—
162#548—28no—
163#548C23116yes—
164#548C23116yes—
165#547—216no—
166#547—28no—
167#547C23116yes—
168#542—216no—
169#542—216no—
170#542—216no—
171#542—216no—
172#537—216no—
173#537—216no—
174#533—24no—
175#533—24no—
176#533—24no—
177#533—24no—
178#533C2318yes—
179#533C2318yes—
180#533C2318yes—
181#533C2318yes—
182#532—24no—
183#532—24no—
184#532—24no—
185#532—24no—
186#532—24no—
187#532—24no—
188#532C2318yes—
189#532C2318yes—
190#532C2318yes—
191#532C2318yes—
192#532C2318yes—
193#532C2318yes—
194C2×C4⋊Q8—21no—
195C2×C4⋊Q8—21no—
196C2×C4⋊Q8—21no—
197C2×C4⋊Q8—21no—
198C2×C4⋊Q8—24no—
199C2×C4⋊Q8—24no—
200C2×C4⋊Q8C2311yescharacteristic
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2318yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2318yes—
210C2×#127C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#126—22no—
213C2×#126—22no—
214C2×#126—22no—
215C2×#126—22no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125C2312yes—
219C2×#125C2312yes—
220C2×#124—22no—
221C2×#124—22no—
222C2×#124—22no—
223C2×#124—22no—
224C2×#124—21no—
225C2×#124—21no—
226C2×#124—21no—
227C2×#124—21no—
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#123—22no—
231C2×#123—22no—
232C2×#123—22no—
233C2×#123—22no—
234C2×C22⋊Q8—22no—
235C2×C22⋊Q8—22no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—22no—
243C2×C22⋊Q8—22no—
244C2×C22⋊Q8—22no—
245C2×C22⋊Q8—22no—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2312yes—
248C2×#121—22no—
249C2×#121—22no—
250C2×#121—22no—
251C2×#121—22no—
252C2×#121—22no—
253C2×#121—22no—
254C2×#121—21no—
255C2×#121—21no—
256C2×#121—21no—
257C2×#121—21no—
258C2×#121—21no—
259C2×#121—21no—
260C2×#121—21no—
261C2×#121—21no—
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2312yes—
265C2×#121C2312yes—
266#520—216no—
267#520—216no—
268C4×#41D418yes—
269C4×#41C2318yes—
270C2×C4×Q8—21no—
271C2×C4×Q8—21no—
272C2×C4×Q8—21no—
273C2×C4×Q8—21no—
274C2×C4×Q8—21no—
275C2×C4×Q8—21no—
276C2×C4×Q8D411yescharacteristic
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×D4—22no—
281C2×C4×D4—22no—
282C2×C4×D4—22no—
283C2×C4×D4—22no—
284C2×C4×D4—21no—
285C2×C4×D4—21no—
286C2×C4×D4—21no—
287C2×C4×D4—21no—
288C2×C4×D4—21no—
289C2×C4×D4—21no—
290C2×C4×D4—21no—
291C2×C4×D4—21no—
292C2×C4×D4D411yescharacteristic
293C2×C4×D4D411yescharacteristic
294C2×C4×D4D411yescharacteristic
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2311yescharacteristic
302C2×#117—21no—
303C2×#117—21no—
304C2×#117—22no—
305C2×#117—22no—
306C2×#117D411yescharacteristic
307C2×#117D411yescharacteristic
308C2×#117D411yescharacteristic
309C2×#117C2312yes—
310C2×#117C2312yes—
311C22×C4⋊C4—21no—
312C22×C4⋊C4—21no—
313C22×C4⋊C4—21no—
314C22×C4⋊C4—22no—
315C22×C4⋊C4—22no—
316C22×C4⋊C4C2312yes—
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320#500C2318yes—
321#498C2318yes—
322#498C2318yes—
323#493C2318yes—
324#492C2318yes—
325#492C2318yes—
326#491C23132yes—
327#489C23132yes—
328#488C23132yes—
329#487C2318yes—
330#487C2318yes—
331#487C2318yes—
332#487C2318yes—
333#487C2318yes—
334#487C2318yes—
335#486C2318yes—
336#486C2318yes—
337#486C2318yes—
338#486C2318yes—
339#485C23132yes—
340#483C23132yes—
341#482C23132yes—
342#479C23132yes—
343#478C23132yes—
344#475C23132yes—
345#469C23132yes—
346#468C23132yes—
347#465C23132yes—
348#463C23132yes—
349#463C23132yes—
350#461C23132yes—
351#449C23132yes—
352#449C23132yes—
353#448C23132yes—
354#446C23116yes—
355#442C23132yes—
356#440C23132yes—
357C4×SD16C23132yes—
358#436C23116yes—
359#435C23116yes—
360#435C23116yes—
361#431C2318yes—
362#431C2318yes—
363#431C2318yes—
364C2×#107C2314yes—
365C2×#106C2314yes—
366C2×#106C2314yes—
367C2×C4⋊C8C2312yes—
368C2×C4⋊C8C2312yes—
369C2×C4⋊C8C2312yes—
370#419C23132yes—
371#417C23132yes—
372#416C23132yes—
373C2×#103C2314yes—
374C2×#103C2314yes—
375C2×#103C2314yes—
376C2×#103C2314yes—
377C2×#103C2314yes—
378C2×#103C2314yes—
379C2×#102C2314yes—
380C2×#102C2314yes—
381C2×#102C2314yes—
382C2×#102C2314yes—
383C2×C22⋊C8C2312yes—
384C2×C22⋊C8C2312yes—
385C2×C22⋊C8C2312yes—
386C4×M16C2318yes—
387C4×M16C2318yes—
388C2×#97C2312yes—
389C2×#97C2312yes—
390C2×C4×C8C2311yescharacteristic
391C2×C4×C8C2311yescharacteristic
392C2×C4×C8C2312yes—
393C2×C4×C8C2318yes—
394C2×C4×C8C2311yescharacteristic
395C2×C4×C8C2311yescharacteristic
396C2×#41—28no—
397C2×#41—28no—
398C2×#41—24no—
399C2×#41—24no—
400C2×#41—28no—
401C2×#41—28no—
402C2×#41—44no—
403C2×#41—48no—
404C2×#41—48no—
405C2×#41—48no—
406C2×#41—48no—
407C2×#41—84no—
408C2×#41—84no—
409C2×#41C2×D418yes—
410C2×#41C2418yes—
411C2×#41C2418yes—
412C22×Q8—21no—
413C22×Q8—21no—
414C22×Q8—21no—
415C22×Q8—21no—
416C22×Q8—22no—
417C22×Q8—22no—
418C22×Q8—24no—
419C22×Q8—28no—
420C22×Q8—48no—
421C22×Q8—84no—
422C22×Q8C2×D411yescharacteristic
423C22×Q8C2412yes—
424C22×Q8C2412yes—
425C22×Q8C2418yes—
426C22×D4—22no—
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4—22no—
432C22×D4—21no—
433C22×D4—21no—
434C22×D4—21no—
435C22×D4—21no—
436C22×D4C2×D411yescharacteristic
437C22×D4C2×D411yescharacteristic
438C22×D4C2×D411yescharacteristic
439C22×D4C2412yes—
440C22×D4C2412yes—
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—22no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4C2×D411yescharacteristic
450C23×C4C2×D411yescharacteristic
451C23×C4C2×D411yescharacteristic
452C23×C4C2×D411yescharacteristic
453C23×C4C2×D411yescharacteristic
454C23×C4C2×D411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C2×SD16—48no—
459C2×SD16—48no—
460C2×SD16C24116yes—
461C2×SD16C24116yes—
462C2×D8—48no—
463C2×D8C24116yes—
464C2×M16—44no—
465C2×M16—44no—
466C2×M16C2418yes—
467C2×M16C2418yes—
468C22×C8—44no—
469C22×C8C2412yes—
470C22×C8C2412yes—
471C22×C8C2412yes—
472C22×C8C2412yes—
473C22×C8C2418yes—
474C4⋊Q8—22no—
475C4⋊Q8—22no—
476C4⋊Q8—22no—
477C4⋊Q8—22no—
478C4⋊Q8—28no—
479C4⋊Q8—28no—
480C4⋊Q8—24no—
481C4⋊Q8—28no—
482C4⋊Q8—28no—
483C4⋊Q8—24no—
484C4⋊Q8—22no—
485C4⋊Q8—22no—
486C4⋊Q8C2414yes—
487C4⋊Q8C2414yes—
488C4⋊Q8C2418yes—
489C4⋊Q8C2414yes—
490C4⋊Q8C2414yes—
491C4⋊Q8C2418yes—
492C4⋊Q8C2414yes—
493C4⋊Q8C2414yes—
494#127—22no—
495#127—22no—
496#127C2414yes—
497#127C2414yes—
498#126—216no—
499#126—216no—
500#126—216no—
501#126—216no—
502#125—28no—
503#125—28no—
504#125—24no—
505#125—24no—
506#125C2418yes—
507#125C2418yes—
508#124—216no—
509#124—216no—
510#124—216no—
511#124—216no—
512#124—28no—
513#124—28no—
514#124—28no—
515#124—28no—
516#124—24no—
517#124—24no—
518#124C2418yes—
519#124C2418yes—
520#123—216no—
521#123—216no—
522#123—216no—
523#123—216no—
524C22⋊Q8—216no—
525C22⋊Q8—216no—
526C22⋊Q8—28no—
527C22⋊Q8—28no—
528C22⋊Q8—28no—
529C22⋊Q8—28no—
530C22⋊Q8—28no—
531C22⋊Q8—28no—
532C22⋊Q8—24no—
533C22⋊Q8—24no—
534C22⋊Q8—216no—
535C22⋊Q8—216no—
536C22⋊Q8—216no—
537C22⋊Q8—216no—
538C22⋊Q8C2418yes—
539C22⋊Q8C2418yes—
540#121—216no—
541#121—216no—
542#121—216no—
543#121—216no—
544#121—216no—
545#121—216no—
546#121—28no—
547#121—28no—
548#121—28no—
549#121—28no—
550#121—28no—
551#121—28no—
552#121—28no—
553#121—28no—
554#121—24no—
555#121—24no—
556#121—24no—
557#121—24no—
558#121C2418yes—
559#121C2418yes—
560#121C2418yes—
561#121C2418yes—
562C4×Q8—28no—
563C4×Q8—28no—
564C4×Q8—28no—
565C4×Q8—28no—
566C4×Q8—28no—
567C4×Q8—28no—
568C4×Q8—24no—
569C4×Q8—24no—
570C4×Q8C2×D418yes—
571C4×Q8C2×D414yes—
572C4×Q8C2418yes—
573C4×Q8C2418yes—
574C4×Q8C2414yes—
575C4×D4—216no—
576C4×D4—216no—
577C4×D4—216no—
578C4×D4—216no—
579C4×D4—28no—
580C4×D4—28no—
581C4×D4—28no—
582C4×D4—28no—
583C4×D4—28no—
584C4×D4—28no—
585C4×D4—28no—
586C4×D4—28no—
587C4×D4—24no—
588C4×D4—24no—
589C4×D4—24no—
590C4×D4—24no—
591C4×D4C2×D418yes—
592C4×D4C2×D418yes—
593C4×D4C2×D418yes—
594C4×D4C2×D414yes—
595C4×D4C2×D414yes—
596C4×D4C2×D414yes—
597C4×D4C2418yes—
598C4×D4C2418yes—
599C4×D4C2418yes—
600C4×D4C2418yes—
601C4×D4C2414yes—
602C4×D4C2414yes—
603C4×D4C2414yes—
604#117—28no—
605#117—28no—
606#117—24no—
607#117—24no—
608#117—216no—
609#117—216no—
610#117C2×D418yes—
611#117C2×D418yes—
612#117C2×D418yes—
613#117C2418yes—
614#117C2418yes—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—28no—
628C2×C4⋊C4—28no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—28no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—24no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—216no—
640C2×C4⋊C4—216no—
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C42—22no—
675C2×C42—22no—
676C2×C42—22no—
677C2×C42—22no—
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D414yes—
685C2×C42C2×D414yes—
686C2×C42C2×D414yes—
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2414yes—
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2411yescharacteristic
694#107C24116yes—
695#106C24116yes—
696#106C24116yes—
697C4⋊C8C2418yes—
698C4⋊C8C2418yes—
699C4⋊C8C2418yes—
700#103C24116yes—
701#103C24116yes—
702#103C24116yes—
703#103C24116yes—
704#103C24116yes—
705#103C24116yes—
706#102C24116yes—
707#102C24116yes—
708#102C24116yes—
709#102C24116yes—
710C22⋊C8C2418yes—
711C22⋊C8C2418yes—
712C22⋊C8C2418yes—
713#97C2418yes—
714#97C2418yes—
715C4×C8C2414yes—
716C4×C8C2414yes—
717C4×C8C2418yes—
718C4×C8C2414yes—
719C4×C8C2414yes—
720C24—22no—
721C24—22no—
722C24C22×D411yescharacteristic
723C24C22×D411yescharacteristic
724C24C22×D411yescharacteristic
725#41—416no—
726#41—432no—
727#41—432no—
728#41—416no—
729#41—416no—
730#41—88no—
731#41—88no—
732#41—816no—
733#41—816no—
734C2×Q8—24no—
735C2×Q8—24no—
736C2×Q8—22no—
737C2×Q8—22no—
738C2×Q8—24no—
739C2×Q8—24no—
740C2×Q8—28no—
741C2×Q8—28no—
742C2×Q8—28no—
743C2×Q8—28no—
744C2×Q8—42no—
745C2×Q8—416no—
746C2×Q8—44no—
747C2×Q8—44no—
748C2×Q8—44no—
749C2×Q8—44no—
750C2×Q8—84no—
751C2×Q8—84no—
752C2×Q8—88no—
753C2×Q8—816no—
754C2×Q8C22×D414yes—
755C2×Q8C2514yes—
756C2×Q8C2514yes—
757C2×D4—28no—
758C2×D4—28no—
759C2×D4—28no—
760C2×D4—28no—
761C2×D4—28no—
762C2×D4—28no—
763C2×D4—22no—
764C2×D4—24no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—22no—
768C2×D4—24no—
769C2×D4—28no—
770C2×D4—28no—
771C2×D4—42no—
772C2×D4—42no—
773C2×D4—42no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—84no—
781C2×D4—84no—
782C2×D4—84no—
783C2×D4—84no—
784C2×D4C22×D414yes—
785C2×D4C22×D414yes—
786C2×D4C22×D414yes—
787C2×D4C2514yes—
788C2×D4C2514yes—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—28no—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—28no—
809C22×C4—28no—
810C22×C4—28no—
811C22×C4—28no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—84no—
815C22×C4—84no—
816C22×C4—84no—
817C22×C4—84no—
818C22×C4—84no—
819C22×C4—84no—
820C22×C4C22×D412yes—
821C22×C4C22×D412yes—
822C22×C4C22×D412yes—
823C22×C4C22×D414yes—
824C22×C4C22×D414yes—
825C22×C4C22×D414yes—
826C22×C4C22×D414yes—
827C22×C4C22×D414yes—
828C22×C4C22×D414yes—
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2511yescharacteristic
844SD16—416no—
845SD16—416no—
846D8—416no—
847M16—48no—
848M16—48no—
849C2×C8—24no—
850C2×C8—24no—
851C2×C8—24no—
852C2×C8—24no—
853C2×C8—48no—
854C2×C8C2514yes—
855C2×C8C2514yes—
856C2×C8C2514yes—
857C2×C8C2514yes—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—28no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4C22×D414yes—
883C4⋊C4C22×D414yes—
884C4⋊C4C22×D414yes—
885C4⋊C4C22×D414yes—
886C4⋊C4C22×D414yes—
887C4⋊C4C22×D414yes—
888C4⋊C4C2514yes—
889C4⋊C4C2514yes—
890C4⋊C4C2514yes—
891C4⋊C4C2514yes—
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⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4C22×D414yes—
909C22⋊C4C22×D414yes—
910C22⋊C4C22×D414yes—
911C22⋊C4C22×D414yes—
912C22⋊C4C22×D414yes—
913C22⋊C4C22×D414yes—
914C42—28no—
915C42—28no—
916C42—28no—
917C42—28no—
918C42C22×D412yes—
919C42C22×D414yes—
920C42C22×D414yes—
921C42C22×D414yes—
922C42C22×D414yes—
923C42C22×D412yes—
924C42C22×D414yes—
925C42C22×D412yes—
926C42C22×D414yes—
927C42C22×D412yes—
928C42C2512yes—
929C42C2512yes—
930C42C2512yes—
931C42C2512yes—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—24no—
942C23—24no—
943C23—44no—
944C23—44no—
945C23—44no—
946C23—44no—
947C23—44no—
948C23—44no—
949C23C23×D412yes—
950C23C23×D412yes—
951C23C23×D412yes—
952C23C23×D411yescharacteristic
953Q8—28no—
954Q8—28no—
955Q8—44no—
956Q8—44no—
957Q8—44no—
958Q8—48no—
959Q8—48no—
960Q8—48no—
961Q8—48no—
962Q8—88no—
963Q8—88no—
964D4—28no—
965D4—28no—
966D4—44no—
967D4—44no—
968D4—44no—
969D4—416no—
970D4—416no—
971D4—44no—
972D4—44no—
973D4—48no—
974D4—48no—
975D4—48no—
976D4—48no—
977D4—88no—
978D4—88no—
979D4—88no—
980D4—88no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—28no—
999C2×C4—28no—
1000C2×C4—28no—
1001C2×C4—28no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—416no—
1009C2×C4—416no—
1010C2×C4—44no—
1011C2×C4—44no—
1012C2×C4—44no—
1013C2×C4—44no—
1014C2×C4—44no—
1015C2×C4—44no—
1016C2×C4—88no—
1017C2×C4—88no—
1018C2×C4—88no—
1019C2×C4—88no—
1020C2×C4—88no—
1021C2×C4—88no—
1022C2×C4#57514yes—
1023C2×C4#57714yes—
1024C2×C4C23×D412yes—
1025C2×C4C23×D412yes—
1026C2×C4C23×D412yes—
1027C2×C4C23×D412yes—
1028C2×C4C23×D412yes—
1029C2×C4C23×D412yes—
1030C2×C4C23×D412yes—
1031C2×C4C23×D412yes—
1032C2×C4C23×D412yes—
1033C2×C4C23×D411yescharacteristic
1034C2×C4C23×D412yes—
1035C2×C4C23×D412yes—
1036C2×C4#58514yes—
1037C2×C4C2611yescharacteristic
1038C8—24no—
1039C8—24no—
1040C8—24no—
1041C8—24no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—22no—
1049C22—22no—
1050C22—22no—
1051C22—44no—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22—44no—
1057C22—44no—
1058C22—44no—
1059C22—44no—
1060C22—88no—
1061C22—88no—
1062C22#350012yes—
1063C22C2×#57512yes—
1064C22C2×#57712yes—
1065C22C24×D411yescharacteristic
1066C4—22no—
1067C4—22no—
1068C4—22no—
1069C4—22no—
1070C4—22no—
1071C4—22no—
1072C4—22no—
1073C4—22no—
1074C4—22no—
1075C4—44no—
1076C4—44no—
1077C4—44no—
1078C4—44no—
1079C4—44no—
1080C4—44no—
1081C4#350012yes—
1082C4C2×#57514yes—
1083C4C2×#57714yes—
1084C4C2×#58512yes—
1085C2—42no—
1086C2—42no—
1087C2—42no—
1088C2—84no—
1089C2—84no—
1090C2#6254314yesdirect product factor
1091C2C2×#350011yescharacteristic
1092C2C22×#57511yescharacteristic
1093C2C22×#57711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3511C2semidirect
2. C2×#3511C2semidirect
3. #62543C2direct (N × H)
4. C2×#3376C2semidirect
5. C2×#3326C2semidirect
6. C2×#3321C2semidirect
7. C2×#3307C2semidirect
8. C2×#3231C2semidirect
9. C2×#3228C2semidirect
10. C2×#3229C2semidirect
11. C2×#3207C2semidirect
12. C2×#3207C2semidirect
13. C2×#3206C2semidirect
14. C2×#3184C2semidirect
15. C2×#3182C2semidirect
16. C2×#3167C2semidirect
17. C2×#3141C2semidirect
18. C2×#3139C2semidirect
19. C2×#3131C2semidirect
20. C2×#2965C2semidirect
23. #3511C22semidirect
24. #3511C22semidirect
62. #3376C22semidirect
63. #3326C22semidirect
64. #3321C22semidirect
65. #3307C22semidirect
66. #3231C22semidirect
67. #3229C22semidirect
68. #3228C22semidirect
69. #3207C22semidirect
70. #3207C22semidirect
71. #3206C22semidirect
72. #3184C22semidirect
73. #3182C22semidirect
74. #3167C22semidirect
81. #3141C22semidirect
82. #3139C22semidirect
85. #3131C22semidirect
112. #2965C22semidirect
1090. C2#62543direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35112
#625432
C2×#33762
C2×#33262
C2×#33212
C2×#33072
C2×#32312
C2×#32282
C2×#32292
C2×#32072
C2×#32062
C2×#31842
C2×#31822
C2×#31672
C2×#31412
C2×#31392
C2×#31312
C2×#29652