Finite Group Databasebeta

← C2×#61672 #10577277

Subgroups — C2×#61672 #10577277

Order 512.

7514 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3497C211yesmaximal, characteristic, complemented
2C2×#3547C211yesmaximal, characteristic, complemented
3#61672C2132yesmaximal, direct product factor
4C2×#3321C212yesmaximal, complemented
5C2×#3317C212yesmaximal, complemented
6C2×#3312C212yesmaximal, complemented
7C2×#3316C212yesmaximal, complemented
8C2×#3271C212yesmaximal, complemented
9C2×#3270C212yesmaximal, complemented
10C2×#3270C212yesmaximal, complemented
11C2×#3269C212yesmaximal, complemented
12C2×#3219C211yesmaximal, characteristic, complemented
13C2×#3216C211yesmaximal, characteristic, complemented
14C2×#3204C212yesmaximal, complemented
15C2×#3201C212yesmaximal, complemented
16C2×#3113C211yesmaximal, characteristic, complemented
17C2×#3117C211yesmaximal, characteristic, complemented
18C2×#3013C212yesmaximal, complemented
19C2×#3011C212yesmaximal, complemented
20C2×#2980C211yesmaximal, characteristic, complemented
21C22×2−1+4C2212yes—
22C22×#137C2212yes—
23C22×#137C2212yes—
24C22×#135C2212yes—
25C23×Q16C2212yes—
26#3547—28no—
27#3547C22116yescomplemented
28C2×#562—22no—
29#3497—28no—
30#3497C22116yescomplemented
31C2×#555—21no—
32C2×#555C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#553—21no—
35C2×#552C2212yes—
36C2×#550—21no—
37C2×#550C2212yes—
38C2×D4×Q8—21no—
39C2×D4×Q8C2211yescharacteristic
40C2×D4×Q8C2212yes—
41C2×#548—22no—
42C2×#548C2212yes—
43C2×#548C2212yes—
44C2×#548C2212yes—
45C2×#547C2211yescharacteristic
46C2×#544—21no—
47C2×#542—22no—
48C2×#540—21no—
49C2×#537—21no—
50C2×#537—21no—
51C2×#537C2212yes—
52C2×#537C2212yes—
53C2×#536C2212yes—
54C2×#533C2211yescharacteristic
55C2×#532—22no—
56C2×#532C2211yescharacteristic
57C2×#532C2211yescharacteristic
58C2×#529C2211yescharacteristic
59C22×C4×Q8C2211yescharacteristic
60#3321C22132yescomplemented
61#3317C22132yescomplemented
62#3316C22132yescomplemented
63#3312C22132yescomplemented
64#3271C22132yescomplemented
65#3270C22132yescomplemented
66#3270C22132yescomplemented
67#3269C22132yescomplemented
68#3219C22116yescomplemented
69#3216C22116yescomplemented
70#3204C22132yescomplemented
71#3201C22132yescomplemented
72C2×#497C2212yes—
73C2×#497C2211yescharacteristic
74C2×#496C2211yescharacteristic
75C2×#491C2211yescharacteristic
76C2×#490C2211yescharacteristic
77C2×#489C2212yes—
78#3117C22116yescomplemented
79#3113C22116yescomplemented
80C2×#484C2211yescharacteristic
81C2×#481C2211yescharacteristic
82C2×#481C2212yes—
83C2×#485C2212yes—
84C2×#482C2212yes—
85C2×#483C2212yes—
86C2×#483C2212yes—
87C2×#479C2212yes—
88C2×#475C2212yes—
89C2×#470C2212yes—
90C2×#470C2212yes—
91C2×#469C2212yes—
92C2×#468C2212yes—
93C2×#467C2212yes—
94C2×#465C2212yes—
95C2×#465C2212yes—
96C2×#465C2212yes—
97C2×#464C2212yes—
98C2×#464C2212yes—
99C2×#462C2212yes—
100C2×#462C2212yes—
101C2×#460C2212yes—
102C2×#463C2212yes—
103#3013C22132yescomplemented
104#3011C22132yescomplemented
105C2×#452C2212yes—
106C2×#452C2212yes—
107C2×#452C2212yes—
108C2×#452C2212yes—
109C2×#452C2212yes—
110C2×#452C2212yes—
111C2×#452C2212yes—
112C2×#449C2212yes—
113C2×#449C2212yes—
114C2×#449C2212yes—
115C2×#451C2212yes—
116C2×#451C2212yes—
117C2×#451C2212yes—
118C2×#451C2212yes—
119C2×#451C2211yescharacteristic
120C2×#451C2212yes—
121C2×#448C2212yes—
122C2×#448C2212yes—
123C2×#448C2211yescharacteristic
124#2980C22116yescomplemented
125C2×#441C2212yes—
126C2×#441C2212yes—
127C2×#441C2212yes—
128C2×#440C2212yes—
129C2×#435C2212yes—
130C2×#435C2212yes—
131C2×#435C2212yes—
132C2×#435C2212yes—
133C2×#432C2211yescharacteristic
134C2×#432C2211yescharacteristic
135C2×#417C2212yes—
136C2×#419C2212yes—
137C2×#416C2212yes—
138C22×#103C2212yes—
139C2×#408C2212yes—
140C2×#408C2212yes—
141C2×2−1+4—28no—
142C2×2−1+4—48no—
143C2×2−1+4—48no—
144C2×2−1+4C23116yes—
145C22×#41—22no—
146C22×#41—22no—
147C22×#41—22no—
148C22×#41C2312yes—
149C22×#41C2312yes—
150C22×#41C2312yes—
151C22×#41C2312yes—
152C22×#41C2312yes—
153C23×Q8—22no—
154C23×Q8C2311yescharacteristic
155C23×Q8C2312yes—
156C23×Q8C2312yes—
157C23×Q8C2312yes—
158C2×#137—48no—
159C2×#137—48no—
160C2×#137C23116yes—
161C2×#137C23116yes—
162C2×#135—48no—
163C2×#135C23116yes—
164C22×Q16—48no—
165C22×Q16C2312yes—
166C22×Q16C2312yes—
167C22×Q16C2312yes—
168C22×Q16C2312yes—
169C22×Q16C2312yes—
170C22×Q16C2312yes—
171C22×Q16C23116yes—
172C22×SD16C2312yes—
173C22×SD16C2312yes—
174C22×SD16C2312yes—
175C22×SD16C2312yes—
176C22×SD16C2312yes—
177C22×D8C2312yes—
178C22×M16C2312yes—
179C22×M16C2312yes—
180C23×C8C2312yes—
181C23×C8C2312yes—
182#562—232no—
183#555—216no—
184#555—24no—
185#555C2318yes—
186#554—24no—
187#554C2318yes—
188#553—216no—
189#552—28no—
190#552C23116yes—
191#550—216no—
192#550—28no—
193#550C23116yes—
194D4×Q8—216no—
195D4×Q8—28no—
196D4×Q8—24no—
197D4×Q8C23116yes—
198D4×Q8C2318yes—
199#548—232no—
200#548—28no—
201#548—28no—
202#548—28no—
203#548C23116yes—
204#548C23116yes—
205#548C23116yes—
206#547—24no—
207#547C2318yes—
208#544—216no—
209#542—232no—
210#540—216no—
211#537—28no—
212#537—28no—
213#537—216no—
214#537—216no—
215#537C23116yes—
216#537C23116yes—
217#536—28no—
218#536C23116yes—
219#533—24no—
220#533C2318yes—
221#532—232no—
222#532—24no—
223#532D418yes—
224#532C2318yes—
225#532C2318yes—
226C2×C4⋊Q8—22no—
227C2×C4⋊Q8—22no—
228C2×C4⋊Q8—21no—
229C2×C4⋊Q8D411yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×#127—22no—
234C2×#127D411yescharacteristic
235C2×#127C2311yescharacteristic
236#529—24no—
237#529C2318yes—
238C2×#126—22no—
239C2×#126—21no—
240C2×#125—22no—
241C2×#125—21no—
242C2×#125—21no—
243C2×#125C2311yescharacteristic
244C2×#124—22no—
245C2×#124—22no—
246C2×#124—22no—
247C2×#124—22no—
248C2×#124—22no—
249C2×#124D412yes—
250C2×#124C2312yes—
251C2×#124C2311yescharacteristic
252C2×#123—22no—
253C2×#123—22no—
254C2×#123—22no—
255C2×#123—21no—
256C2×#123—22no—
257C2×C22⋊Q8—22no—
258C2×C22⋊Q8—22no—
259C2×C22⋊Q8—21no—
260C2×C22⋊Q8—22no—
261C2×C22⋊Q8—22no—
262C2×C22⋊Q8—22no—
263C2×C22⋊Q8—22no—
264C2×C22⋊Q8—22no—
265C2×C22⋊Q8—22no—
266C2×C22⋊Q8—22no—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2311yescharacteristic
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×#121—22no—
275C2×#121—22no—
276C2×#121—22no—
277C2×#121—22no—
278C2×#121—22no—
279C2×#121—22no—
280C2×#121—22no—
281C2×#121—22no—
282C2×#121—21no—
283C2×#121—22no—
284C2×#121—21no—
285C2×#121—21no—
286C2×#121—21no—
287C2×#121—22no—
288C2×#121—22no—
289C2×#121D412yes—
290C2×#121D411yescharacteristic
291C2×#121D411yescharacteristic
292C2×#121C2312yes—
293C2×#121C2311yescharacteristic
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×C4×Q8—21no—
297C2×C4×Q8—21no—
298C2×C4×Q8—24no—
299C2×C4×Q8—21no—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2318yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×D4—22no—
306C2×C4×D4—21no—
307C2×C4×D4—21no—
308C2×C4×D4—21no—
309C2×C4×D4—22no—
310C2×C4×D4—22no—
311C2×C4×D4—22no—
312C2×C4×D4—22no—
313C2×C4×D4—21no—
314C2×C4×D4—21no—
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×#117—21no—
320C2×#117—21no—
321C2×#117—22no—
322C2×#117—21no—
323C2×#117C2312yes—
324C22×C4⋊C4—21no—
325C22×C4⋊C4—21no—
326C22×C4⋊C4C2311yescharacteristic
327C22×C4⋊C4C2312yes—
328C22×C42—21no—
329C22×C42C2311yescharacteristic
330#497C23116yes—
331#497C2318yes—
332#496C2318yes—
333#491C2318yes—
334#490C2318yes—
335#489C23116yes—
336#485C23116yes—
337#484C2318yes—
338#483C23116yes—
339#483C23116yes—
340#482C23116yes—
341#481C2318yes—
342#481C23116yes—
343#479C23116yes—
344#475C23116yes—
345#470C23116yes—
346#470C23116yes—
347#469C23116yes—
348#468C23116yes—
349#467C23116yes—
350#465C23116yes—
351#465C23116yes—
352#465C23116yes—
353#464C23116yes—
354#464C23116yes—
355#463C23116yes—
356#462C23116yes—
357#462C23116yes—
358#460C23116yes—
359#452C23116yes—
360#452C23116yes—
361#452C23116yes—
362#452C23116yes—
363#452C23116yes—
364#452C23116yes—
365#452C23116yes—
366#451C23116yes—
367#451C2318yes—
368#451C23116yes—
369#451C23116yes—
370#451C23116yes—
371#451C23116yes—
372#449C23116yes—
373#449C23116yes—
374#449C23116yes—
375#448C2318yes—
376#448C23116yes—
377#448C23116yes—
378#441C23116yes—
379#441C23116yes—
380#441C23116yes—
381#440C23116yes—
382#435C23116yes—
383#435C23116yes—
384#435C23116yes—
385#435C23116yes—
386#432C2318yes—
387#432C2318yes—
388C2×#107C2312yes—
389C2×#106C2312yes—
390C2×#106C2312yes—
391C2×#106C2312yes—
392C2×C4⋊C8C2312yes—
393C2×C4⋊C8C2312yes—
394#419C23116yes—
395#417C23116yes—
396#416C23116yes—
397C2×#103C2312yes—
398C2×#103C2312yes—
399C2×#103C2312yes—
400C2×#103C2312yes—
401C2×#103C2312yes—
402C2×#103C2312yes—
403C2×#103C2312yes—
404C2×#103C2312yes—
405C2×#103C2312yes—
406C2×#103C2312yes—
407C2×#103C2312yes—
408C2×#103C23116yes—
409C2×#102C2312yes—
410C2×#102C2312yes—
411C2×#102C2312yes—
412C2×#102C2312yes—
413C2×#102C2312yes—
414#408C23116yes—
415#408C23116yes—
416C2×C22⋊C8C2312yes—
417C2×C22⋊C8C2312yes—
418C2×C22⋊C8C2312yes—
419C2×C22⋊C8C2312yes—
420C2×C22⋊C8C2311yescharacteristic
421C2×C22⋊C8C2312yes—
422C2×C22⋊C8C2311yescharacteristic
423C2×#97C2312yes—
424C2×#97C2311yescharacteristic
425C2×#97C2311yescharacteristic
4262−1+4—432no—
4272−1+4—432no—
4282−1+4—464no—
429C2×#41—216no—
430C2×#41—216no—
431C2×#41—216no—
432C2×#41—24no—
433C2×#41—24no—
434C2×#41—24no—
435C2×#41—24no—
436C2×#41—28no—
437C2×#41—28no—
438C2×#41—44no—
439C2×#41—44no—
440C2×#41—44no—
441C2×#41—44no—
442C2×#41—44no—
443C2×#41—44no—
444C2×#41—416no—
445C2×#41—416no—
446C2×#41—44no—
447C2×#41—44no—
448C2×#41—416no—
449C2×#41C2×D418yes—
450C2×#41C2418yes—
451C2×#41C2418yes—
452C2×#41C2418yes—
453C2×#41C2418yes—
454C2×#41C2418yes—
455C22×Q8—28no—
456C22×Q8—216no—
457C22×Q8—21no—
458C22×Q8—22no—
459C22×Q8—22no—
460C22×Q8—22no—
461C22×Q8—24no—
462C22×Q8—24no—
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8—24no—
466C22×Q8—28no—
467C22×Q8—28no—
468C22×Q8—44no—
469C22×Q8—44no—
470C22×Q8—44no—
471C22×Q8—44no—
472C22×Q8—416no—
473C22×Q8C2×D412yes—
474C22×Q8C2414yes—
475C22×Q8C2411yescharacteristic
476C22×Q8C2412yes—
477C22×Q8C2412yes—
478C22×Q8C2418yes—
479C22×Q8C2418yes—
480C22×Q8C2412yes—
481C22×Q8C2418yes—
482C22×D4—22no—
483C22×D4—22no—
484C22×D4—22no—
485C22×D4—21no—
486C22×D4—22no—
487C22×D4—22no—
488C22×D4—22no—
489C22×D4—22no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2×D411yescharacteristic
493C22×D4C2×D411yescharacteristic
494C22×D4C2×D412yes—
495C22×D4C2×D412yes—
496C22×D4C2×D412yes—
497C22×D4C2×D412yes—
498C22×D4C2411yescharacteristic
499C22×D4C2412yes—
500C23×C4—21no—
501C23×C4—22no—
502C23×C4—22no—
503C23×C4—21no—
504C23×C4—22no—
505C23×C4—22no—
506C23×C4—21no—
507C23×C4—22no—
508C23×C4—22no—
509C23×C4—22no—
510C23×C4—22no—
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2412yes—
514C23×C4C2411yescharacteristic
515C23×C4C2412yes—
516#137—432no—
517#137—432no—
518#135—432no—
519C2×Q16—28no—
520C2×Q16—28no—
521C2×Q16—28no—
522C2×Q16—44no—
523C2×Q16—44no—
524C2×Q16—44no—
525C2×Q16—432no—
526C2×Q16C2418yes—
527C2×Q16C2418yes—
528C2×Q16C2418yes—
529C2×Q16C2418yes—
530C2×Q16C2418yes—
531C2×Q16C2418yes—
532C2×SD16—28no—
533C2×SD16—44no—
534C2×SD16—44no—
535C2×SD16—44no—
536C2×SD16—44no—
537C2×SD16C2418yes—
538C2×SD16C2418yes—
539C2×SD16C2418yes—
540C2×SD16C2418yes—
541C2×SD16C2418yes—
542C2×D8—44no—
543C2×D8C2418yes—
544C2×M16—44no—
545C2×M16—44no—
546C2×M16C2418yes—
547C2×M16C2418yes—
548C22×C8—44no—
549C22×C8—44no—
550C22×C8C2412yes—
551C22×C8C2412yes—
552C22×C8C2412yes—
553C22×C8C2412yes—
554C22×C8C2418yes—
555C22×C8C2418yes—
556C4⋊Q8—216no—
557C4⋊Q8—216no—
558C4⋊Q8—28no—
559C4⋊Q8—22no—
560C4⋊Q8—22no—
561C4⋊Q8—22no—
562C4⋊Q8C2×D418yes—
563C4⋊Q8C2414yes—
564C4⋊Q8C2414yes—
565C4⋊Q8C2414yes—
566#127—216no—
567#127—22no—
568#127C2×D418yes—
569#127C2414yes—
570#126—216no—
571#126—28no—
572#125—216no—
573#125—28no—
574#125—28no—
575#125—22no—
576#125C2414yes—
577#124—216no—
578#124—216no—
579#124—216no—
580#124—216no—
581#124—216no—
582#124—22no—
583#124—24no—
584#124C2×D4116yes—
585#124C2414yes—
586#124C2418yes—
587#123—216no—
588#123—216no—
589#123—216no—
590#123—28no—
591#123—216no—
592C22⋊Q8—216no—
593C22⋊Q8—216no—
594C22⋊Q8—28no—
595C22⋊Q8—22no—
596C22⋊Q8—24no—
597C22⋊Q8—24no—
598C22⋊Q8—24no—
599C22⋊Q8—24no—
600C22⋊Q8—24no—
601C22⋊Q8—24no—
602C22⋊Q8—216no—
603C22⋊Q8—216no—
604C22⋊Q8—216no—
605C22⋊Q8—216no—
606C22⋊Q8—216no—
607C22⋊Q8—216no—
608C22⋊Q8—216no—
609C22⋊Q8C2414yes—
610C22⋊Q8C2418yes—
611C22⋊Q8C2418yes—
612C22⋊Q8C2418yes—
613C22⋊Q8C2418yes—
614C22⋊Q8C2418yes—
615C22⋊Q8C2418yes—
616#121—216no—
617#121—216no—
618#121—216no—
619#121—216no—
620#121—216no—
621#121—216no—
622#121—216no—
623#121—216no—
624#121—28no—
625#121—216no—
626#121—28no—
627#121—28no—
628#121—28no—
629#121—22no—
630#121—24no—
631#121—24no—
632#121—24no—
633#121—216no—
634#121—216no—
635#121C2×D4116yes—
636#121C2×D418yes—
637#121C2×D418yes—
638#121C2414yes—
639#121C2418yes—
640#121C2418yes—
641#121C2418yes—
642C4×Q8—28no—
643C4×Q8—24no—
644C4×Q8—28no—
645C4×Q8—24no—
646C4×Q8—28no—
647C4×Q8—22no—
648C4×Q8—24no—
649C4×Q8C2418yes—
650C4×Q8C2418yes—
651C4×Q8C2414yes—
652C4×Q8C2418yes—
653C4×D4—216no—
654C4×D4—28no—
655C4×D4—28no—
656C4×D4—28no—
657C4×D4—216no—
658C4×D4—216no—
659C4×D4—216no—
660C4×D4—216no—
661C4×D4—28no—
662C4×D4—28no—
663C4×D4—22no—
664C4×D4C2×D414yes—
665C4×D4C2×D414yes—
666C4×D4C2×D418yes—
667C4×D4C2414yes—
668C4×D4C2414yes—
669C4×D4C2414yes—
670C4×D4C2418yes—
671#117—28no—
672#117—24no—
673#117—28no—
674#117—216no—
675#117—28no—
676#117C2418yes—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—28no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—24no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—28no—
701C2×C4⋊C4C2×D411yescharacteristic
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C4⋊C4C2×D412yes—
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2418yes—
709C2×C4⋊C4C2411yescharacteristic
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4C2×D412yes—
728C2×C22⋊C4C2×D412yes—
729C2×C22⋊C4C2×D412yes—
730C2×C22⋊C4C2×D412yes—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—21no—
734C2×C42—22no—
735C2×C42—22no—
736C2×C42—28no—
737C2×C42C2×D411yescharacteristic
738C2×C42C2×D411yescharacteristic
739C2×C42C2×D414yes—
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2414yes—
743#107C2418yes—
744#106C2418yes—
745#106C2418yes—
746#106C2418yes—
747C4⋊C8C2418yes—
748C4⋊C8C2418yes—
749#103C2418yes—
750#103C2418yes—
751#103C2418yes—
752#103C2418yes—
753#103C2418yes—
754#103C2418yes—
755#103C2418yes—
756#103C2418yes—
757#103C2418yes—
758#103C2418yes—
759#103C2418yes—
760#102C2418yes—
761#102C2418yes—
762#102C2418yes—
763#102C2418yes—
764#102C2418yes—
765C22⋊C8C2414yes—
766C22⋊C8C2418yes—
767C22⋊C8C2414yes—
768C22⋊C8C2418yes—
769C22⋊C8C2418yes—
770C22⋊C8C2418yes—
771C22⋊C8C2418yes—
772#97C2418yes—
773#97C2414yes—
774#97C2414yes—
775C24—21no—
776C24—22no—
777C24C22×D412yes—
778C24C22×D412yes—
779C24C22×D411yescharacteristic
780#41—216no—
781#41—216no—
782#41—416no—
783#41—48no—
784#41—48no—
785#41—48no—
786#41—48no—
787#41—48no—
788#41—48no—
789#41—416no—
790#41—416no—
791#41—464no—
792#41—464no—
793#41—416no—
794#41—48no—
795#41—48no—
796#41—464no—
797#41—88no—
798C2×Q8—28no—
799C2×Q8—216no—
800C2×Q8—216no—
801C2×Q8—24no—
802C2×Q8—22no—
803C2×Q8—21no—
804C2×Q8—22no—
805C2×Q8—28no—
806C2×Q8—28no—
807C2×Q8—22no—
808C2×Q8—24no—
809C2×Q8—28no—
810C2×Q8—24no—
811C2×Q8—216no—
812C2×Q8—216no—
813C2×Q8—24no—
814C2×Q8—24no—
815C2×Q8—24no—
816C2×Q8—24no—
817C2×Q8—24no—
818C2×Q8—44no—
819C2×Q8—48no—
820C2×Q8—48no—
821C2×Q8—48no—
822C2×Q8—48no—
823C2×Q8—416no—
824C2×Q8—416no—
825C2×Q8—48no—
826C2×Q8—48no—
827C2×Q8—464no—
828C2×Q8—82no—
829C2×Q8—84no—
830C2×Q8—88no—
831C2×Q8C22×D418yes—
832C2×Q8H(5,𝔽2)18yes—
833C2×Q8C2514yes—
834C2×Q8C2512yes—
835C2×Q8C2514yes—
836C2×Q8C2514yes—
837C2×D4—28no—
838C2×D4—28no—
839C2×D4—28no—
840C2×D4—24no—
841C2×D4—28no—
842C2×D4—28no—
843C2×D4—28no—
844C2×D4—28no—
845C2×D4—24no—
846C2×D4—21no—
847C2×D4—22no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—24no—
851C2×D4—24no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—48no—
859C2×D4—48no—
860C2×D4—44no—
861C2×D4—48no—
862C2×D4—82no—
863C2×D4—82no—
864C2×D4—84no—
865C2×D4—84no—
866C2×D4—84no—
867C2×D4—84no—
868C2×D4C22×D414yes—
869C2×D4C22×D414yes—
870C2×D4C22×D418yes—
871C2×D4C22×D418yes—
872C2×D4C22×D418yes—
873C2×D4C22×D418yes—
874C2×D4C2514yes—
875C2×D4C2512yes—
876C22×C4—28no—
877C22×C4—24no—
878C22×C4—22no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—28no—
885C22×C4—28no—
886C22×C4—21no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—24no—
894C22×C4—28no—
895C22×C4—28no—
896C22×C4—24no—
897C22×C4—28no—
898C22×C4—28no—
899C22×C4—28no—
900C22×C4—28no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—48no—
904C22×C4—48no—
905C22×C4—48no—
906C22×C4—48no—
907C22×C4—44no—
908C22×C4—48no—
909C22×C4—84no—
910C22×C4—84no—
911C22×C4—82no—
912C22×C4—84no—
913C22×C4C22×D412yes—
914C22×C4C22×D414yes—
915C22×C4C22×D414yes—
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D412yes—
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D412yes—
923C22×C4C22×D414yes—
924C22×C4C22×D414yes—
925C22×C4C2512yes—
926C22×C4C2514yes—
927C22×C4C2514yes—
928C22×C4C2511yescharacteristic
929Q16—216no—
930Q16—216no—
931Q16—216no—
932Q16—48no—
933Q16—48no—
934Q16—48no—
935SD16—216no—
936SD16—48no—
937SD16—48no—
938SD16—48no—
939SD16—48no—
940D8—48no—
941M16—48no—
942M16—48no—
943C2×C8—24no—
944C2×C8—24no—
945C2×C8—24no—
946C2×C8—24no—
947C2×C8—48no—
948C2×C8—48no—
949C2×C8C2514yes—
950C2×C8C2514yes—
951C2×C8C2514yes—
952C2×C8C2514yes—
953C4⋊C4—21no—
954C4⋊C4—24no—
955C4⋊C4—28no—
956C4⋊C4—28no—
957C4⋊C4—28no—
958C4⋊C4—22no—
959C4⋊C4—24no—
960C4⋊C4—22no—
961C4⋊C4—28no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—28no—
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—24no—
968C4⋊C4—24no—
969C4⋊C4—28no—
970C4⋊C4—28no—
971C4⋊C4—28no—
972C4⋊C4—28no—
973C4⋊C4—24no—
974C4⋊C4—28no—
975C4⋊C4—24no—
976C4⋊C4—21no—
977C4⋊C4C22×D414yes—
978C4⋊C4C22×D414yes—
979C4⋊C4C22×D418yes—
980C4⋊C4C2512yes—
981C4⋊C4C2514yes—
982C4⋊C4C2512yes—
983C4⋊C4C2514yes—
984C22⋊C4—28no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—28no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—28no—
995C22⋊C4—28no—
996C22⋊C4—24no—
997C22⋊C4—28no—
998C22⋊C4—28no—
999C22⋊C4—28no—
1000C22⋊C4—24no—
1001C22⋊C4C22×D418yes—
1002C22⋊C4C22×D418yes—
1003C22⋊C4C22×D418yes—
1004C22⋊C4C22×D418yes—
1005C42—28no—
1006C42—28no—
1007C42—28no—
1008C42—28no—
1009C42—24no—
1010C42C22×D414yes—
1011C42C22×D414yes—
1012C42C22×D412yes—
1013C42C22×D412yes—
1014C42C2512yes—
1015C42C2512yes—
1016C23—22no—
1017C23—22no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—22no—
1023C23—24no—
1024C23—24no—
1025C23—22no—
1026C23—24no—
1027C23—42no—
1028C23—44no—
1029C23—44no—
1030C23—42no—
1031C23—44no—
1032C23—42no—
1033C23C23×D414yes—
1034C23C23×D414yes—
1035C23C23×D412yes—
1036C23C23×D411yescharacteristic
1037Q8—216no—
1038Q8—24no—
1039Q8—28no—
1040Q8—24no—
1041Q8—24no—
1042Q8—24no—
1043Q8—24no—
1044Q8—24no—
1045Q8—48no—
1046Q8—416no—
1047Q8—416no—
1048Q8—44no—
1049Q8—42no—
1050Q8—44no—
1051Q8—88no—
1052Q8—84no—
1053Q8C2×H(5,𝔽2)18yes—
1054D4—24no—
1055D4—24no—
1056D4—24no—
1057D4—44no—
1058D4—44no—
1059D4—48no—
1060D4—48no—
1061D4—48no—
1062D4—48no—
1063D4—416no—
1064D4—416no—
1065D4—48no—
1066D4—416no—
1067D4—44no—
1068D4—42no—
1069D4—84no—
1070D4—84no—
1071D4—88no—
1072D4—88no—
1073D4—88no—
1074D4—88no—
1075C2×C4—216no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—28no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—28no—
1092C2×C4—28no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—44no—
1101C2×C4—44no—
1102C2×C4—416no—
1103C2×C4—416no—
1104C2×C4—416no—
1105C2×C4—416no—
1106C2×C4—48no—
1107C2×C4—416no—
1108C2×C4—42no—
1109C2×C4—42no—
1110C2×C4—44no—
1111C2×C4—44no—
1112C2×C4—44no—
1113C2×C4—44no—
1114C2×C4—42no—
1115C2×C4—88no—
1116C2×C4—88no—
1117C2×C4—84no—
1118C2×C4—88no—
1119C2×C4C23×D412yes—
1120C2×C4C23×D412yes—
1121C2×C4C23×D412yes—
1122C2×C4C23×D412yes—
1123C2×C4C23×D414yes—
1124C2×C4C23×D412yes—
1125C2×C4C23×D414yes—
1126C2×C4C23×D411yescharacteristic
1127C2×C4C2×H(5,𝔽2)14yes—
1128C2×C4C2611yescharacteristic
1129C8—24no—
1130C8—24no—
1131C8—24no—
1132C8—24no—
1133C22—22no—
1134C22—24no—
1135C22—24no—
1136C22—22no—
1137C22—22no—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—44no—
1143C22—48no—
1144C22—48no—
1145C22—44no—
1146C22—42no—
1147C22—42no—
1148C22—44no—
1149C22—44no—
1150C22—42no—
1151C22—84no—
1152C22—88no—
1153C22#348412yes—
1154C22#358612yes—
1155C22#358612yes—
1156C22C24×D411yescharacteristic
1157C4—28no—
1158C4—22no—
1159C4—24no—
1160C4—24no—
1161C4—22no—
1162C4—22no—
1163C4—22no—
1164C4—22no—
1165C4—44no—
1166C4—44no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—44no—
1171C4—44no—
1172C4#348412yes—
1173C4C22×H(5,𝔽2)12yes—
1174C2—42no—
1175C2—44no—
1176C2—44no—
1177C2—84no—
1178C2—82no—
1179C2#6167214yesdirect product factor
1180C2C2×#348411yescharacteristic
1181C2C2×#358611yescharacteristic
1182C2C2×#358611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#532 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3497C2semidirect
2. C2×#3547C2semidirect
3. #61672C2direct (N × H)
4. C2×#3321C2semidirect
5. C2×#3317C2semidirect
6. C2×#3312C2semidirect
7. C2×#3316C2semidirect
8. C2×#3271C2semidirect
9. C2×#3270C2semidirect
10. C2×#3270C2semidirect
11. C2×#3269C2semidirect
12. C2×#3219C2semidirect
13. C2×#3216C2semidirect
14. C2×#3204C2semidirect
15. C2×#3201C2semidirect
16. C2×#3113C2semidirect
17. C2×#3117C2semidirect
18. C2×#3013C2semidirect
19. C2×#3011C2semidirect
20. C2×#2980C2semidirect
27. #3547C22semidirect
30. #3497C22semidirect
60. #3321C22semidirect
61. #3317C22semidirect
62. #3316C22semidirect
63. #3312C22semidirect
64. #3271C22semidirect
65. #3270C22semidirect
66. #3270C22semidirect
67. #3269C22semidirect
68. #3219C22semidirect
69. #3216C22semidirect
70. #3204C22semidirect
71. #3201C22semidirect
78. #3117C22semidirect
79. #3113C22semidirect
103. #3013C22semidirect
104. #3011C22semidirect
124. #2980C22semidirect
1179. C2#61672direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#34972
C2×#35472
#616722
C2×#33212
C2×#33172
C2×#33122
C2×#33162
C2×#32712
C2×#32702
C2×#32692
C2×#32192
C2×#32162
C2×#32042
C2×#32012
C2×#31132
C2×#31172
C2×#30132
C2×#30112
C2×#29802