Finite Group Databasebeta

← C2×#61061 #10576071

Subgroups — C2×#61061 #10576071

Order 512.

10390 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#578C211yesmaximal, characteristic, complemented
2C23×#137C211yesmaximal, characteristic, complemented
3C2×#3487C211yesmaximal, characteristic, complemented
4C2×#3486C211yesmaximal, characteristic, complemented
5#61061C2132yesmaximal, direct product factor
6C2×#3278C214yesmaximal, complemented
7C2×#3277C214yesmaximal, complemented
8C2×#3271C214yesmaximal, complemented
9C2×#3270C214yesmaximal, complemented
10C2×#3154C211yesmaximal, characteristic, complemented
11C2×#3057C211yesmaximal, characteristic, complemented
12C2×#3054C211yesmaximal, characteristic, complemented
13C2×#3044C211yesmaximal, characteristic, complemented
14C2×#3043C211yesmaximal, characteristic, complemented
15C2×#3011C211yesmaximal, characteristic, complemented
16C2×#3010C211yesmaximal, characteristic, complemented
17C2×#3005C211yesmaximal, characteristic, complemented
18C2×#3004C211yesmaximal, characteristic, complemented
19C2×#2950C211yesmaximal, characteristic, complemented
20C2×#2930C211yesmaximal, characteristic, complemented
21C22×2−1+4C2211yescharacteristic
22C22×2−1+4C2211yescharacteristic
23C23×#41C2211yescharacteristic
24C24×Q8C2211yescharacteristic
25C2×#578—216no—
26C2×#578C22116yescomplemented
27C22×#137—216no—
28C22×#137C2211yescharacteristic
29C22×#137C2211yescharacteristic
30C22×#137C2214yes—
31C22×#137C2214yes—
32C22×#137C2211yescharacteristic
33C22×#137C22116yescomplemented
34C22×#137C2212yescomplemented
35C22×#137C2212yescomplemented
36C22×AGL(1,ℤ/8)C2211yescharacteristic
37C22×#135C2211yescharacteristic
38C22×#135C2212yescomplemented
39C23×Q16C2211yescharacteristic
40C23×Q16C2211yescharacteristic
41C23×Q16C2212yescomplemented
42C23×SD16C2211yescharacteristic
43C23×SD16C2211yescharacteristic
44C22×#131C2211yescharacteristic
45C23×M16C2211yescharacteristic
46#3487—28no—
47#3487C22116yescomplemented
48#3486—28no—
49#3486C22116yescomplemented
50C2×#550—22no—
51C2×#550C2214yes—
52C2×D4×Q8—22no—
53C2×D4×Q8C2214yescomplemented
54C2×#548—22no—
55C2×#548—22no—
56C2×#548C2214yes—
57C2×#548C2214yescomplemented
58C2×#536—22no—
59C2×#536C2211yescharacteristic
60C2×#536C2211yescharacteristic
61C2×#535—22no—
62C2×#535C2211yescharacteristic
63C2×#535C2211yescharacteristic
64C2×#525—22no—
65C2×#525—22no—
66C2×#525C2211yescharacteristic
67C2×#525C2211yescharacteristic
68C2×#525C2211yescharacteristic
69C2×#519C2211yescharacteristic
70C2×#519C2211yescharacteristic
71#3278C22164yescomplemented
72#3277C22164yescomplemented
73#3271C22164yescomplemented
74#3270C22164yescomplemented
75#3154C22116yescomplemented
76C2×#497C2212yescomplemented
77C2×#496C2212yescomplemented
78C2×#495C2212yescomplemented
79C2×#492C2212yescomplemented
80#3057C22116yescomplemented
81#3054C22116yescomplemented
82C2×#470C2212yescomplemented
83C2×#469C2212yescomplemented
84C2×#468C2212yescomplemented
85C2×#468C2212yescomplemented
86C2×#468C2214yescomplemented
87C2×#465C2214yescomplemented
88#3044C22116yescomplemented
89#3043C22116yescomplemented
90C2×#464C2214yescomplemented
91C2×#464C2214yescomplemented
92C2×#462C2214yescomplemented
93C2×#460C2214yescomplemented
94#3011C22116yescomplemented
95#3010C22116yescomplemented
96#3005C22116yescomplemented
97#3004C22116yescomplemented
98C2×#452C2214yes—
99C2×#452C2214yescomplemented
100C2×#449C2214yes—
101C2×#449C2214yescomplemented
102C2×#451C2214yescomplemented
103C2×#451C2214yescomplemented
104C2×#448C2214yescomplemented
105C2×#448C2214yescomplemented
106#2950C22116yescomplemented
107C2×#441C2214yescomplemented
108C2×C4×Q16C2214yescomplemented
109#2930C22116yescomplemented
110C2×#436C2214yescomplemented
111C2×#435C2214yescomplemented
112C2×#427C2211yescharacteristic
113C2×#424C2211yescharacteristic
114C2×#419C2211yescharacteristic
115C2×#419C2211yescharacteristic
116C2×#419C2211yescharacteristic
117C2×#418C2211yescharacteristic
118C2×#416C2211yescharacteristic
119C2×#416C2211yescharacteristic
120C2×#408C2211yescharacteristic
121C2×#407C2211yescharacteristic
122C2×#405C2211yescharacteristic
123C2×2−1+4—24no—
124C2×2−1+4—24no—
125C2×2−1+4—28no—
126C2×2−1+4—28no—
127C2×2−1+4—44no—
128C2×2−1+4—44no—
129C2×2−1+4C2318yes—
130C2×2−1+4C2318yes—
131C22×#41—22no—
132C22×#41—22no—
133C22×#41—21no—
134C22×#41—21no—
135C22×#41—22no—
136C22×#41—24no—
137C22×#41—28no—
138C22×#41—44no—
139C22×#41C2311yescharacteristic
140C22×#41C2311yescharacteristic
141C22×#41C2314yes—
142C22×#41C2318yes—
143C22×#41C2312yes—
144C22×#41C2312yes—
145C22×#41C2311yescharacteristic
146C23×Q8—21no—
147C23×Q8—21no—
148C23×Q8—21no—
149C23×Q8—22no—
150C23×Q8—24no—
151C23×Q8—28no—
152C23×Q8—44no—
153C23×Q8C2311yescharacteristic
154C23×Q8C2314yes—
155C23×Q8C2318yes—
156C23×Q8C2312yes—
157C23×Q8C2312yes—
158C23×Q8C2311yescharacteristic
159C23×Q8C2311yescharacteristic
160C23×D4—21no—
161C23×D4C2311yescharacteristic
162C24×C4—21no—
163C24×C4—21no—
164C24×C4C2311yescharacteristic
165#578—2128no—
166C2×#137—28no—
167C2×#137—28no—
168C2×#137—232no—
169C2×#137—232no—
170C2×#137—216no—
171C2×#137—216no—
172C2×#137—2128no—
173C2×#137—44no—
174C2×#137C2318yes—
175C2×#137C2318yes—
176C2×#137C23132yes—
177C2×#137C23132yes—
178C2×#137C2318yes—
179C2×#137C23116yescomplemented
180C2×#137C23116yescomplemented
181C2×AGL(1,ℤ/8)—44no—
182C2×AGL(1,ℤ/8)C2318yes—
183C2×#135—216no—
184C2×#135—28no—
185C2×#135C2318yes—
186C2×#135C23116yescomplemented
187C22×Q16—28no—
188C22×Q16—216no—
189C22×Q16D4116yescomplemented
190C22×Q16C2311yescharacteristic
191C22×Q16C2312yes—
192C22×Q16C2314yes—
193C22×Q16C2312yes—
194C22×Q16C2318yes—
195C22×Q16C2312yes—
196C22×Q16C2312yes—
197C22×Q16C2312yes—
198C22×Q16C2318yes—
199C22×Q16C23116yescomplemented
200C22×SD16—28no—
201C22×SD16—28no—
202C22×SD16C2311yescharacteristic
203C22×SD16C2312yes—
204C22×SD16C2311yescharacteristic
205C22×SD16C2312yes—
206C22×SD16C2318yes—
207C22×SD16C2312yes—
208C22×SD16C2314yes—
209C22×SD16C2312yes—
210C22×SD16C2318yes—
211C22×SD16C2312yes—
212C22×SD16C2312yes—
213C22×D8C2311yescharacteristic
214C22×D8C2312yes—
215C2×#131—28no—
216C2×#131C2318yes—
217C22×M16—28no—
218C22×M16C2311yescharacteristic
219C22×M16C2311yescharacteristic
220C22×M16C2312yes—
221C22×M16C2312yes—
222C22×M16C2312yes—
223C22×M16C2318yes—
224C23×C8C2311yescharacteristic
225C23×C8C2312yes—
226C23×C8C2311yescharacteristic
227#550—232no—
228#550—216no—
229#550C23132yes—
230D4×Q8—232no—
231D4×Q8—216no—
232D4×Q8C23132yescomplemented
233#548—232no—
234#548—232no—
235#548—216no—
236#548—216no—
237#548C23132yes—
238#548C23132yescomplemented
239#536—24no—
240#536—232no—
241#536—24no—
242#536C2318yes—
243#536C2318yes—
244#535—24no—
245#535—232no—
246#535—24no—
247#535C2318yes—
248#535C2318yes—
249C2×C4⋊Q8—21no—
250C2×C4⋊Q8—24no—
251C2×C4⋊Q8C2312yes—
252C2×#127—24no—
253C2×#127—21no—
254C2×#127C2312yes—
255C2×#124—21no—
256C2×#124—21no—
257C2×#124—24no—
258C2×#124—24no—
259C2×#124C2312yes—
260C2×#124C2312yes—
261#525—24no—
262#525—24no—
263#525—232no—
264#525—232no—
265#525D418yes—
266#525C2318yes—
267#525C2318yes—
268#525C2318yes—
269C2×#123—22no—
270C2×#123—21no—
271C2×#123—21no—
272C2×#123—22no—
273C2×#123D412yes—
274C2×C22⋊Q8—24no—
275C2×C22⋊Q8—24no—
276C2×C22⋊Q8—22no—
277C2×C22⋊Q8—24no—
278C2×C22⋊Q8—24no—
279C2×C22⋊Q8D412yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×#121—24no—
284C2×#121—24no—
285C2×#121—22no—
286C2×#121—24no—
287C2×#121—24no—
288C2×#121D412yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2314yes—
292C2×#120—21no—
293C2×#120—21no—
294C2×#120—22no—
295C2×#120—22no—
296C2×#120D412yes—
297#519—24no—
298#519—24no—
299#519C2318yes—
300#519C2318yes—
301C2×C4×Q8—22no—
302C2×C4×Q8—22no—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2314yes—
305C2×C4×D4—24no—
306C2×C4×D4—22no—
307C2×C4×D4—22no—
308C2×C4×D4—24no—
309C2×C4×D4—24no—
310C2×C4×D4—24no—
311C2×C4×D4C2314yes—
312C2×#117—22no—
313C2×#117—22no—
314C2×#117C2311yescharacteristic
315C2×#117C2311yescharacteristic
316C2×#117C2311yescharacteristic
317#497C23116yescomplemented
318#496C23116yescomplemented
319#495C23116yescomplemented
320#492C23116yescomplemented
321#470C23116yescomplemented
322#469C23116yescomplemented
323#468C23116yescomplemented
324#468C23132yescomplemented
325#468C23116yescomplemented
326#465C23132yescomplemented
327#464C23132yescomplemented
328#464C23132yescomplemented
329#462C23132yescomplemented
330#460C23132yescomplemented
331#452C23132yes—
332#452C23132yescomplemented
333#451C23132yescomplemented
334#451C23132yescomplemented
335#449C23132yes—
336#449C23132yescomplemented
337#448C23132yescomplemented
338#448C23132yescomplemented
339#441C23132yescomplemented
340C4×Q16C23132yescomplemented
341#436C23132yescomplemented
342#435C23132yescomplemented
343#427C2318yes—
344C2×#107C2312yes—
345C2×#106C2312yes—
346#424C2318yes—
347C2×C4⋊C8C2314yes—
348#419C2318yes—
349#419C2318yes—
350#419C2318yes—
351#418C2318yes—
352#416C2318yes—
353#416C2318yes—
354C2×#103C2312yes—
355C2×#103C2312yes—
356C2×#103C2314yes—
357C2×#103C2314yes—
358C2×#103C2314yes—
359C2×#102C2312yes—
360C2×#102C2312yes—
361C2×#102C2314yes—
362#408C2318yes—
363#407C2318yes—
364C2×C22⋊C8C2314yes—
365C2×C22⋊C8C2314yes—
366#405C2318yes—
367C2×#97C2312yes—
368C2×C4×C8C2312yes—
369C25—21no—
370C25C2×D411yescharacteristic
3712−1+4—232no—
3722−1+4—232no—
3732−1+4—416no—
3742−1+4—416no—
3752−1+4—432no—
3762−1+4—432no—
377C2×#41—216no—
378C2×#41—216no—
379C2×#41—28no—
380C2×#41—28no—
381C2×#41—24no—
382C2×#41—22no—
383C2×#41—22no—
384C2×#41—24no—
385C2×#41—216no—
386C2×#41—28no—
387C2×#41—24no—
388C2×#41—24no—
389C2×#41—28no—
390C2×#41—28no—
391C2×#41—216no—
392C2×#41—232no—
393C2×#41—24no—
394C2×#41—24no—
395C2×#41—24no—
396C2×#41—24no—
397C2×#41—48no—
398C2×#41—416no—
399C2×#41—44no—
400C2×#41—44no—
401C2×#41—416no—
402C2×#41—416no—
403C2×#41—416no—
404C2×#41—432no—
405C2×#41—48no—
406C2×#41—48no—
407C2×#41C2×D414yes—
408C2×#41C2414yes—
409C2×#41C2414yes—
410C2×#41C24116yes—
411C2×#41C2418yes—
412C2×#41C2418yes—
413C2×#41C2414yes—
414C22×Q8—28no—
415C22×Q8—28no—
416C22×Q8—21no—
417C22×Q8—21no—
418C22×Q8—22no—
419C22×Q8—22no—
420C22×Q8—22no—
421C22×Q8—24no—
422C22×Q8—21no—
423C22×Q8—22no—
424C22×Q8—28no—
425C22×Q8—22no—
426C22×Q8—24no—
427C22×Q8—216no—
428C22×Q8—28no—
429C22×Q8—24no—
430C22×Q8—24no—
431C22×Q8—24no—
432C22×Q8—28no—
433C22×Q8—28no—
434C22×Q8—216no—
435C22×Q8—232no—
436C22×Q8—24no—
437C22×Q8—24no—
438C22×Q8—48no—
439C22×Q8—48no—
440C22×Q8—416no—
441C22×Q8—44no—
442C22×Q8—44no—
443C22×Q8—416no—
444C22×Q8—432no—
445C22×Q8—48no—
446C22×Q8—48no—
447C22×Q8C2×D418yes—
448C22×Q8C2×D418yes—
449C22×Q8C2×D411yescharacteristic
450C22×Q8C2411yescharacteristic
451C22×Q8C2412yes—
452C22×Q8C2411yescharacteristic
453C22×Q8C2414yes—
454C22×Q8C2418yes—
455C22×Q8C24116yes—
456C22×Q8C2418yes—
457C22×Q8C2412yes—
458C22×Q8C2412yes—
459C22×Q8C2414yes—
460C22×Q8C2414yes—
461C22×D4—22no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—22no—
465C22×D4—24no—
466C22×D4—22no—
467C22×D4—28no—
468C22×D4—24no—
469C22×D4—22no—
470C22×D4—24no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—24no—
474C22×D4—24no—
475C22×D4—48no—
476C22×D4C2×D412yes—
477C22×D4C2×D411yescharacteristic
478C22×D4C2×D414yes—
479C22×D4C2411yescharacteristic
480C22×D4C2412yes—
481C22×D4C2411yescharacteristic
482C22×D4C2414yes—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4—24no—
486C23×C4—24no—
487C23×C4—22no—
488C23×C4—24no—
489C23×C4—22no—
490C23×C4—21no—
491C23×C4—28no—
492C23×C4—22no—
493C23×C4—21no—
494C23×C4—24no—
495C23×C4—22no—
496C23×C4—21no—
497C23×C4—28no—
498C23×C4—48no—
499C23×C4—48no—
500C23×C4C2×D412yes—
501C23×C4C2×D411yescharacteristic
502C23×C4C2×D414yes—
503C23×C4C2412yes—
504C23×C4C2412yes—
505C23×C4C2414yes—
506C23×C4C2411yescharacteristic
507#137—232no—
508#137—232no—
509#137—2128no—
510#137—2128no—
511#137—264no—
512#137—264no—
513#137—416no—
514AGL(1,ℤ/8)—416no—
515#135—264no—
516#135—232no—
517C2×Q16—216no—
518C2×Q16—232no—
519C2×Q16—28no—
520C2×Q16—28no—
521C2×Q16—264no—
522C2×Q16—24no—
523C2×Q16—44no—
524C2×Q16C2×D4116yes—
525C2×Q16C2×D4116yes—
526C2×Q16C2×D4164yescomplemented
527C2×Q16C24116yes—
528C2×Q16C2414yes—
529C2×Q16C2418yes—
530C2×Q16C2418yes—
531C2×Q16C2418yes—
532C2×Q16C2418yes—
533C2×Q16C2418yes—
534C2×SD16—216no—
535C2×SD16—232no—
536C2×SD16—28no—
537C2×SD16—28no—
538C2×SD16—28no—
539C2×SD16—28no—
540C2×SD16—232no—
541C2×SD16—24no—
542C2×SD16—24no—
543C2×SD16—44no—
544C2×SD16—44no—
545C2×SD16C24116yes—
546C2×SD16C2418yes—
547C2×SD16C2418yes—
548C2×SD16C2414yes—
549C2×SD16C2414yes—
550C2×SD16C2418yes—
551C2×SD16C2418yes—
552C2×SD16C2418yes—
553C2×SD16C2418yes—
554C2×D8—24no—
555C2×D8—44no—
556C2×D8C2414yes—
557C2×D8C2418yes—
558#131—232no—
559C2×M16—24no—
560C2×M16—24no—
561C2×M16—28no—
562C2×M16—28no—
563C2×M16—232no—
564C2×M16—28no—
565C2×M16C2418yes—
566C2×M16C2418yes—
567C2×M16C2414yes—
568C2×M16C2418yes—
569C2×M16C2414yes—
570C22×C8—24no—
571C22×C8—28no—
572C22×C8C2×D418yes—
573C22×C8C2412yes—
574C22×C8C2412yes—
575C22×C8C2414yes—
576C22×C8C2418yes—
577C22×C8C2412yes—
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2414yes—
581C4⋊Q8—28no—
582C4⋊Q8—232no—
583C4⋊Q8—24no—
584C4⋊Q8C2418yes—
585#127—232no—
586#127—28no—
587#127—24no—
588#127C2418yes—
589#124—28no—
590#124—28no—
591#124—232no—
592#124—232no—
593#124—24no—
594#124—24no—
595#124C2418yes—
596#124C2418yes—
597#123—216no—
598#123—28no—
599#123—28no—
600#123—216no—
601#123C2×D4116yes—
602C22⋊Q8—24no—
603C22⋊Q8—24no—
604C22⋊Q8—28no—
605C22⋊Q8—232no—
606C22⋊Q8—232no—
607C22⋊Q8—216no—
608C22⋊Q8—232no—
609C22⋊Q8—232no—
610C22⋊Q8C2×D4116yes—
611C22⋊Q8C2418yes—
612C22⋊Q8C2418yes—
613C22⋊Q8C24116yes—
614#121—232no—
615#121—232no—
616#121—24no—
617#121—24no—
618#121—28no—
619#121—216no—
620#121—232no—
621#121—232no—
622#121C2×D4116yes—
623#121C2418yes—
624#121C2418yes—
625#121C24116yes—
626#120—28no—
627#120—28no—
628#120—216no—
629#120—216no—
630#120C2×D4116yes—
631C4×Q8—216no—
632C4×Q8—216no—
633C4×Q8—28no—
634C4×Q8—28no—
635C4×Q8C24116yes—
636C4×Q8C24116yes—
637C4×D4—232no—
638C4×D4—216no—
639C4×D4—216no—
640C4×D4—232no—
641C4×D4—232no—
642C4×D4—232no—
643C4×D4C2×D4116yes—
644C4×D4C24116yes—
645#117—22no—
646#117—22no—
647#117—216no—
648#117—216no—
649#117C2×D414yes—
650#117C2414yes—
651#117C2414yes—
652#117C2414yes—
653C2×C4⋊C4—24no—
654C2×C4⋊C4—24no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—24no—
657C2×C4⋊C4—24no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4C2×D412yes—
660C2×C4⋊C4C2×D414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—24no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—24no—
670C2×C22⋊C4—24no—
671C2×C22⋊C4—24no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4C2×D412yes—
674C2×C22⋊C4C2×D414yes—
675C2×C22⋊C4C2×D414yes—
676C2×C42—24no—
677C2×C42—24no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42C2412yes—
681#107C2418yes—
682#106C2418yes—
683C4⋊C8C24116yes—
684#103C2418yes—
685#103C2418yes—
686#103C24116yes—
687#103C24116yes—
688#103C24116yes—
689#102C2418yes—
690#102C2418yes—
691#102C24116yes—
692C22⋊C8C24116yes—
693C22⋊C8C24116yes—
694#97C2418yes—
695C4×C8C2418yes—
696C24—24no—
697C24—21no—
698C24—22no—
699C24—21no—
700C24—24no—
701C24—44no—
702C24—44no—
703C24—84no—
704C24C22×D412yes—
705C24C22×D412yes—
706C24C22×D411yescharacteristic
707C24C22×D414yes—
708#41—216no—
709#41—28no—
710#41—28no—
711#41—216no—
712#41—216no—
713#41—232no—
714#41—28no—
715#41—28no—
716#41—28no—
717#41—28no—
718#41—416no—
719#41—48no—
720#41—48no—
721#41—464no—
722#41—464no—
723#41—432no—
724#41—464no—
725#41—416no—
726#41—416no—
727#41—432no—
728#41—432no—
729#41—48no—
730#41—48no—
731C2×Q8—28no—
732C2×Q8—216no—
733C2×Q8—28no—
734C2×Q8—216no—
735C2×Q8—24no—
736C2×Q8—24no—
737C2×Q8—22no—
738C2×Q8—24no—
739C2×Q8—22no—
740C2×Q8—28no—
741C2×Q8—21no—
742C2×Q8—216no—
743C2×Q8—24no—
744C2×Q8—22no—
745C2×Q8—28no—
746C2×Q8—21no—
747C2×Q8—24no—
748C2×Q8—28no—
749C2×Q8—24no—
750C2×Q8—28no—
751C2×Q8—216no—
752C2×Q8—216no—
753C2×Q8—232no—
754C2×Q8—24no—
755C2×Q8—28no—
756C2×Q8—22no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—24no—
760C2×Q8—22no—
761C2×Q8—28no—
762C2×Q8—416no—
763C2×Q8—432no—
764C2×Q8—48no—
765C2×Q8—48no—
766C2×Q8—416no—
767C2×Q8—48no—
768C2×Q8—48no—
769C2×Q8—432no—
770C2×Q8—464no—
771C2×Q8—416no—
772C2×Q8—416no—
773C2×Q8—432no—
774C2×Q8—432no—
775C2×Q8—44no—
776C2×Q8—48no—
777C2×Q8C22×D418yes—
778C2×Q8C22×D4116yes—
779C2×Q8C22×D418yes—
780C2×Q8C22×D4116yes—
781C2×Q8C22×D414yes—
782C2×Q8C2512yes—
783C2×Q8C2514yes—
784C2×Q8C2512yes—
785C2×Q8C2514yes—
786C2×Q8C2514yes—
787C2×D4—28no—
788C2×D4—28no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—28no—
792C2×D4—216no—
793C2×D4—28no—
794C2×D4—216no—
795C2×D4—28no—
796C2×D4—24no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—24no—
800C2×D4—28no—
801C2×D4—21no—
802C2×D4—24no—
803C2×D4—22no—
804C2×D4—21no—
805C2×D4—216no—
806C2×D4—22no—
807C2×D4—24no—
808C2×D4—22no—
809C2×D4—28no—
810C2×D4—48no—
811C2×D4—416no—
812C2×D4—432no—
813C2×D4—48no—
814C2×D4—48no—
815C2×D4—48no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—44no—
819C2×D4—48no—
820C2×D4—88no—
821C2×D4—88no—
822C2×D4—84no—
823C2×D4C22×D418yes—
824C2×D4C22×D414yes—
825C2×D4C22×D4116yes—
826C2×D4C2512yes—
827C2×D4C2514yes—
828C2×D4C2512yes—
829C22×C4—24no—
830C22×C4—28no—
831C22×C4—28no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—28no—
837C22×C4—216no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—28no—
841C22×C4—24no—
842C22×C4—28no—
843C22×C4—24no—
844C22×C4—28no—
845C22×C4—216no—
846C22×C4—28no—
847C22×C4—24no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—21no—
853C22×C4—28no—
854C22×C4—24no—
855C22×C4—216no—
856C22×C4—28no—
857C22×C4—24no—
858C22×C4—416no—
859C22×C4—432no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—416no—
863C22×C4—432no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4C22×D418yes—
870C22×C4C22×D414yes—
871C22×C4C22×D414yes—
872C22×C4C22×D414yes—
873C22×C4C22×D414yes—
874C22×C4C22×D412yes—
875C22×C4C22×D412yes—
876C22×C4C22×D412yes—
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D414yes—
879C22×C4H(5,𝔽2)14yes—
880C22×C4C2514yes—
881C22×C4C2514yes—
882C22×C4C2512yes—
883C22×C4C2511yescharacteristic
884Q16—232no—
885Q16—216no—
886Q16—216no—
887Q16—28no—
888Q16—48no—
889Q16C22×D4132yes—
890Q16C22×D4132yes—
891SD16—232no—
892SD16—216no—
893SD16—216no—
894SD16—216no—
895SD16—216no—
896SD16—28no—
897SD16—28no—
898SD16—48no—
899SD16—48no—
900D8—28no—
901D8—48no—
902M16—28no—
903M16—28no—
904M16—216no—
905M16—216no—
906M16—216no—
907C2×C8—24no—
908C2×C8—24no—
909C2×C8—28no—
910C2×C8—24no—
911C2×C8—216no—
912C2×C8C22×D414yes—
913C2×C8C22×D414yes—
914C2×C8C22×D4116yes—
915C2×C8C2514yes—
916C2×C8C2514yes—
917C2×C8C2514yes—
918C2×C8C2512yes—
919C2×C8C2512yes—
920C4⋊C4—216no—
921C4⋊C4—216no—
922C4⋊C4—28no—
923C4⋊C4—216no—
924C4⋊C4—216no—
925C4⋊C4—28no—
926C4⋊C4—22no—
927C4⋊C4—22no—
928C4⋊C4C22×D418yes—
929C4⋊C4C22×D4116yes—
930C4⋊C4C2514yes—
931C4⋊C4C2514yes—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—216no—
937C22⋊C4—28no—
938C22⋊C4—216no—
939C22⋊C4—216no—
940C22⋊C4—216no—
941C22⋊C4—28no—
942C22⋊C4C22×D418yes—
943C22⋊C4C22×D4116yes—
944C22⋊C4C22×D4116yes—
945C42—216no—
946C42—216no—
947C42—24no—
948C42—24no—
949C42C22×D414yes—
950C42C2514yes—
951C23—24no—
952C23—24no—
953C23—28no—
954C23—24no—
955C23—28no—
956C23—24no—
957C23—24no—
958C23—22no—
959C23—24no—
960C23—22no—
961C23—48no—
962C23—416no—
963C23—44no—
964C23—44no—
965C23—48no—
966C23—42no—
967C23—42no—
968C23—48no—
969C23—44no—
970C23—88no—
971C23—816no—
972C23D4214yes—
973C23C23×D414yes—
974C23C23×D414yes—
975C23C23×D412yes—
976C23C23×D411yescharacteristic
977Q8—24no—
978Q8—24no—
979Q8—28no—
980Q8—216no—
981Q8—28no—
982Q8—216no—
983Q8—28no—
984Q8—24no—
985Q8—22no—
986Q8—22no—
987Q8—22no—
988Q8—24no—
989Q8—22no—
990Q8—432no—
991Q8—416no—
992Q8—416no—
993Q8—44no—
994Q8—48no—
995Q8—42no—
996Q8—42no—
997Q8C23×D418yes—
998Q8C23×D418yes—
999D4—216no—
1000D4—22no—
1001D4—22no—
1002D4—24no—
1003D4—22no—
1004D4—24no—
1005D4—22no—
1006D4—28no—
1007D4—416no—
1008D4—432no—
1009D4—416no—
1010D4—416no—
1011D4—416no—
1012D4—48no—
1013D4—48no—
1014D4—44no—
1015D4—48no—
1016D4—42no—
1017D4—42no—
1018D4—816no—
1019D4—816no—
1020D4—88no—
1021C2×C4—28no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—28no—
1028C2×C4—216no—
1029C2×C4—216no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—28no—
1036C2×C4—216no—
1037C2×C4—28no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—432no—
1044C2×C4—416no—
1045C2×C4—416no—
1046C2×C4—432no—
1047C2×C4—416no—
1048C2×C4—416no—
1049C2×C4—44no—
1050C2×C4—44no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—48no—
1054C2×C4—44no—
1055C2×C4—48no—
1056C2×C4—48no—
1057C2×C4D4214yes—
1058C2×C4D4218yes—
1059C2×C4C23×D418yes—
1060C2×C4C23×D414yes—
1061C2×C4C23×D414yes—
1062C2×C4C23×D412yes—
1063C2×C4C23×D414yes—
1064C2×C4C23×D412yes—
1065C2×C4C23×D411yescharacteristic
1066C2×C4C2×H(5,𝔽2)12yes—
1067C2×C4C2×H(5,𝔽2)14yes—
1068C2×C4C2611yescharacteristic
1069C8—24no—
1070C8—24no—
1071C8—24no—
1072C8C23×D414yes—
1073C8C23×D414yes—
1074C22—24no—
1075C22—28no—
1076C22—24no—
1077C22—28no—
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—416no—
1082C22—48no—
1083C22—48no—
1084C22—44no—
1085C22—44no—
1086C22—48no—
1087C22—42no—
1088C22—42no—
1089C22—44no—
1090C22—816no—
1091C22—84no—
1092C22—84no—
1093C22—88no—
1094C22C2×D4214yes—
1095C22C2×D4212yes—
1096C22#358614yes—
1097C22C24×D411yescharacteristic
1098C4—28no—
1099C4—24no—
1100C4—28no—
1101C4—28no—
1102C4—24no—
1103C4—44no—
1104C4—44no—
1105C4—42no—
1106C4—42no—
1107C4—44no—
1108C4C2×D4212yes—
1109C4C2×D4214yes—
1110C4C24×D411yescharacteristic
1111C4C22×H(5,𝔽2)11yescharacteristic
1112C2—24no—
1113C2—44no—
1114C2—44no—
1115C2—82no—
1116C2—82no—
1117C2—84no—
1118C2#6106114yesdirect product factor
1119C2C22×D4211yescharacteristic
1120C2C2×#358612yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#578C2semidirect
2. C23×#137C2semidirect
3. C2×#3487C2semidirect
4. C2×#3486C2semidirect
5. #61061C2direct (N × H)
6. C2×#3278C2semidirect
7. C2×#3277C2semidirect
8. C2×#3271C2semidirect
9. C2×#3270C2semidirect
10. C2×#3154C2semidirect
11. C2×#3057C2semidirect
12. C2×#3054C2semidirect
13. C2×#3044C2semidirect
14. C2×#3043C2semidirect
15. C2×#3011C2semidirect
16. C2×#3010C2semidirect
17. C2×#3005C2semidirect
18. C2×#3004C2semidirect
19. C2×#2950C2semidirect
20. C2×#2930C2semidirect
26. C2×#578C22semidirect
33. C22×#137C22semidirect
34. C22×#137C22semidirect
35. C22×#137C22semidirect
38. C22×#135C22semidirect
41. C23×Q16C22semidirect
47. #3487C22semidirect
49. #3486C22semidirect
53. C2×D4×Q8C22semidirect
57. C2×#548C22semidirect
71. #3278C22semidirect
72. #3277C22semidirect
73. #3271C22semidirect
74. #3270C22semidirect
75. #3154C22semidirect
76. C2×#497C22semidirect
77. C2×#496C22semidirect
78. C2×#495C22semidirect
79. C2×#492C22semidirect
80. #3057C22semidirect
81. #3054C22semidirect
82. C2×#470C22semidirect
83. C2×#469C22semidirect
84. C2×#468C22semidirect
85. C2×#468C22semidirect
86. C2×#468C22semidirect
87. C2×#465C22semidirect
88. #3044C22semidirect
89. #3043C22semidirect
90. C2×#464C22semidirect
91. C2×#464C22semidirect
92. C2×#462C22semidirect
93. C2×#460C22semidirect
94. #3011C22semidirect
95. #3010C22semidirect
96. #3005C22semidirect
97. #3004C22semidirect
99. C2×#452C22semidirect
101. C2×#449C22semidirect
102. C2×#451C22semidirect
103. C2×#451C22semidirect
104. C2×#448C22semidirect
105. C2×#448C22semidirect
106. #2950C22semidirect
107. C2×#441C22semidirect
108. C2×C4×Q16C22semidirect
109. #2930C22semidirect
110. C2×#436C22semidirect
111. C2×#435C22semidirect
179. C2×#137C23semidirect
180. C2×#137C23semidirect
186. C2×#135C23semidirect
189. C22×Q16D4semidirect
199. C22×Q16C23semidirect
232. D4×Q8C23semidirect
238. #548C23semidirect
317. #497C23semidirect
318. #496C23semidirect
319. #495C23semidirect
320. #492C23semidirect
321. #470C23semidirect
322. #469C23semidirect
323. #468C23semidirect
324. #468C23semidirect
325. #468C23semidirect
326. #465C23semidirect
327. #464C23semidirect
328. #464C23semidirect
329. #462C23semidirect
330. #460C23semidirect
332. #452C23semidirect
333. #451C23semidirect
334. #451C23semidirect
336. #449C23semidirect
337. #448C23semidirect
338. #448C23semidirect
339. #441C23semidirect
340. C4×Q16C23semidirect
341. #436C23semidirect
342. #435C23semidirect
526. C2×Q16C2×D4semidirect
1118. C2#61061direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5782
C23×#1372
C2×#34872
C2×#34862
#610612
C2×#32782
C2×#32772
C2×#32712
C2×#32702
C2×#31542
C2×#30572
C2×#30542
C2×#30442
C2×#30432
C2×#30112
C2×#30102
C2×#30052
C2×#30042
C2×#29502
C2×#29302