Finite Group Databasebeta

← #6343419

Subgroups — #6343419

Order 512.

3172 conjugacy classes of subgroups.

The subgroup lattice has 1281 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic
2C2×#2974C211yesmaximal, characteristic, complemented
3#34194C211yesmaximal, characteristic, complemented
4#17600C214yesmaximal, complemented
5#17598C218yesmaximal, complemented
6#17596C211yesmaximal, characteristic, complemented
7#17592C212yesmaximal, complemented
8#17581C211yesmaximal, characteristic, complemented
9#17578C212yesmaximal, complemented
10#17575C211yesmaximal, characteristic, complemented
11#17572C212yesmaximal, complemented
12#17567C211yesmaximal, characteristic, complemented
13C2×#1520C212yesmaximal, complemented
14#17548C214yesmaximal, complemented
15#3520—21no—
16#3520—22no—
17#3520—21no—
18#3520—21no—
19#3520—22no—
20#3520—21no—
21#3520C412yescomplemented
22#3520C412yescomplemented
23#3520C414yescomplemented
24#3520C2212yes—
25#3520C2214yes—
26#3520C2212yes—
27C2×#556C411yescharacteristic, complemented
28C2×#554—21no—
29C2×#552C412yescomplemented
30C2×#551—22no—
31C2×D4×Q8C411yescharacteristic, complemented
32C2×#548C412yescomplemented
33C2×#547C411yescharacteristic, complemented
34C2×#547C411yescharacteristic, complemented
35C2×#546—21no—
36C2×#542—21no—
37C2×#539—22no—
38C2×#533C2211yescharacteristic
39C2×#529C2211yescharacteristic
40C2×#525C2212yes—
41C22×C22⋊Q8C2212yes—
42C2×#520—21no—
43C22×C4×D4C2211yescharacteristic
44#2974—21no—
45#2974—22no—
46#2974—21no—
47#2974C2212yescomplemented
48#2974C2214yescomplemented
49#2974C2212yescomplemented
50C2×#436—21no—
51C2×#435—22no—
52C2×C8×D4—21no—
53C2×#432C2211yescharacteristic
54C2×#431C2211yescharacteristic
55C2×#407C2212yes—
56C22×C22⋊C8C2212yes—
57#2354—21no—
58#2352—22no—
59D4×C4⋊C4—21no—
60#2345—21no—
61#2342—22no—
62D4×C22⋊C4—21no—
63#2319C2212yescomplemented
64#2318C2214yescomplemented
65#2285C2211yescharacteristic
66#2283C2211yescharacteristic
67#2280C2212yes—
68C2×#380C2212yes—
69#2275C2212yescomplemented
70#1521C2214yescomplemented
71#1520C2211yescharacteristic
72#1520C2212yes—
73#1520C2212yes—
74#1520C2212yes—
75#1520C2211yescharacteristic
76#1520C2212yes—
77#1520C2212yes—
78#1520C2218yescomplemented
79#1519C2211yescharacteristic
80#1519C2211yescharacteristic
81#1519C2212yes—
82#1518C2214yescomplemented
83#1516C2218yescomplemented
84#1515C2214yescomplemented
85#1513C2218yescomplemented
86#1512C2214yescomplemented
87#1511C2218yescomplemented
88#1509C2214yescomplemented
89#1508C2218yescomplemented
90#1506C2214yescomplemented
91#1504C2218yescomplemented
92#1503C2214yescomplemented
93#1501C2218yescomplemented
94#1500C2214yescomplemented
95C2×#328C2218yescomplemented
96C22×#41—21no—
97C22×#41C2×C412yescomplemented
98C23×Q8C2×C412yescomplemented
99C23×D4D411yescharacteristic
100C24×C4C2312yes—
101C22×M16—22no—
102C23×C8—22no—
103#556—21no—
104#556—21no—
105#556—22no—
106#556C2×C412yes—
107#556C2×C414yescomplemented
108#556C2×C412yescomplemented
109#554—22no—
110#554—24no—
111#554—22no—
112#554—22no—
113#554—24no—
114#554—22no—
115#552—22no—
116#552—22no—
117#552—22no—
118#552—22no—
119#552C2×C414yes—
120#552C2×C414yescomplemented
121#552C2×C414yescomplemented
122#552C2×C414yescomplemented
123#551—24no—
124#551—24no—
125#551—24no—
126#551—24no—
127#551—24no—
128#551—24no—
129#551—24no—
130#551—24no—
131D4×Q8—21no—
132D4×Q8—22no—
133D4×Q8—21no—
134D4×Q8C2×C412yes—
135D4×Q8C2×C412yescomplemented
136D4×Q8C2×C414yescomplemented
137#548—22no—
138#548—22no—
139#548—22no—
140#548—22no—
141#548C2×C414yes—
142#548C2×C414yescomplemented
143#548C2×C414yescomplemented
144#548C2×C414yescomplemented
145#547—21no—
146#547—22no—
147#547—21no—
148#547—21no—
149#547—21no—
150#547—22no—
151#547C2×C412yes—
152#547C2×C412yes—
153#547C2×C412yescomplemented
154#547C2×C414yescomplemented
155#547C2×C414yescomplemented
156#547C2×C412yescomplemented
157#546—22no—
158#546—24no—
159#546—22no—
160#546—22no—
161#546—24no—
162#546—22no—
163#542—22no—
164#542—22no—
165#542—24no—
166#542—22no—
167#542—24no—
168#542—22no—
169#539—24no—
170#539—24no—
171#539—24no—
172#539—24no—
173#539—24no—
174#539—24no—
175#539—24no—
176#539—24no—
177#533—21no—
178#533—21no—
179#533—21no—
180#533—21no—
181#533C2×C412yescomplemented
182#533C2×C412yescomplemented
183#533C2312yes—
184#533C2312yes—
185C2×C4⋊Q8—21no—
186C2×C4⋊Q8C2×C411yescharacteristic, complemented
187C2×C4⋊Q8C2×C411yescharacteristic, complemented
188#529—21no—
189#529—21no—
190#529—21no—
191#529—21no—
192#529C2×C412yescomplemented
193#529C2×C412yescomplemented
194#529C2312yes—
195#529C2312yes—
196C2×#126—22no—
197C2×#126—22no—
198C2×#126—21no—
199C2×#125—22no—
200C2×#125—21no—
201C2×#125C2×C411yescharacteristic, complemented
202C2×#124—21no—
203C2×#124—22no—
204C2×#124C2×C411yescharacteristic, complemented
205#525—22no—
206#525—22no—
207#525—22no—
208#525—22no—
209#525C2×C414yescomplemented
210#525C2×C414yescomplemented
211#525C2314yes—
212#525C2314yes—
213C2×#123—22no—
214C2×#123—22no—
215C2×#123—21no—
216C2×#123—22no—
217C2×#123—22no—
218C2×C22⋊Q8—22no—
219C2×C22⋊Q8—22no—
220C2×C22⋊Q8—22no—
221C2×C22⋊Q8—22no—
222C2×C22⋊Q8—22no—
223C2×C22⋊Q8—22no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—22no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—22no—
228C2×C22⋊Q8C2×C412yescomplemented
229C2×C22⋊Q8C2×C412yescomplemented
230C2×C22⋊Q8C2×C414yescomplemented
231C2×C22⋊Q8C2×C414yescomplemented
232C2×C22⋊Q8C2×C412yescomplemented
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×#121—22no—
238C2×#121—21no—
239C2×#121C2×C412yescomplemented
240C2×#121C2311yescharacteristic
241C2×#120—22no—
242#520—22no—
243#520—24no—
244#520—22no—
245#520—22no—
246#520—24no—
247#520—22no—
248C2×C4×Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8C2×C411yescharacteristic, complemented
251C2×C4×Q8C2×C412yescomplemented
252C2×C4×D4—21no—
253C2×C4×D4—22no—
254C2×C4×D4—22no—
255C2×C4×D4—21no—
256C2×C4×D4—22no—
257C2×C4×D4—22no—
258C2×C4×D4C2×C411yescharacteristic
259C2×C4×D4C2×C411yescharacteristic
260C2×C4×D4C2×C412yes—
261C2×C4×D4C2×C411yescharacteristic
262C2×C4×D4C2×C411yescharacteristic
263C2×C4×D4C2×C412yes—
264C2×C4×D4C2×C411yescharacteristic, complemented
265C2×C4×D4D411yescharacteristic
266C2×C4×D4D411yescharacteristic
267C2×C4×D4D412yes—
268C2×C4×D4D411yescharacteristic
269C2×C4×D4D412yes—
270C2×C4×D4D411yescharacteristic
271C2×C4×D4D411yescharacteristic
272C2×C4×D4D412yes—
273C2×C4×D4D411yescharacteristic
274C2×C4×D4C2312yes—
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2311yescharacteristic
277C2×#117—21no—
278C2×#117—21no—
279C2×#117—22no—
280C2×#117—22no—
281C2×#117—21no—
282C2×#117C2×C412yescomplemented
283C22×C4⋊C4—22no—
284C22×C4⋊C4—21no—
285C22×C4⋊C4—22no—
286C22×C4⋊C4C2×C412yescomplemented
287C22×C4⋊C4D411yescharacteristic
288C22×C22⋊C4—22no—
289C22×C22⋊C4—22no—
290C22×C22⋊C4D412yes—
291C22×C42C2311yescharacteristic
292#436—22no—
293#436—24no—
294#436—22no—
295#435—24no—
296#435—24no—
297#435—24no—
298#435—24no—
299C8×D4—22no—
300C8×D4—24no—
301C8×D4—22no—
302#432—21no—
303#432—21no—
304#432C2312yes—
305#432C2312yes—
306#431—21no—
307#431—21no—
308#431C2312yes—
309#431C2312yes—
310C2×C4⋊C8—21no—
311C2×C4⋊C8—21no—
312#407—22no—
313#407—22no—
314#407C2314yes—
315#407C2314yes—
316C2×C22⋊C8—22no—
317C2×C22⋊C8—22no—
318C2×C22⋊C8—22no—
319C2×C22⋊C8—22no—
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2312yes—
322C2×C22⋊C8C2314yes—
323C2×C22⋊C8C2314yes—
324C2×C22⋊C8C2311yescharacteristic
325C2×#97—21no—
326C2×C4×C8—21no—
327#390—22no—
328#389—22no—
329#388—24no—
330#388—24no—
331#387—24no—
332#386—24no—
333#385—24no—
334#384—21no—
335#383C2312yes—
336#382—21no—
337#382C2312yes—
338#381—21no—
339#381C2314yes—
340#380—21no—
341#380—22no—
342#380—22no—
343#380—22no—
344#380C2314yes—
345#380C2311yescharacteristic
346#380C2312yes—
347#380C2311yescharacteristic
348#379—22no—
349C4×C4⋊C4—22no—
350C4×C4⋊C4—21no—
351C4×C4⋊C4—21no—
352C4×C4⋊C4C2312yes—
353C4×C22⋊C4—21no—
354C4×C22⋊C4—22no—
355C4×C22⋊C4—24no—
356C4×C22⋊C4C2314yes—
357#376C2312yes—
358C2×#95C2314yes—
359#328C2314yes—
360#328C2318yes—
361#328C2318yes—
362#328C2318yes—
363#328C2314yes—
364#328C2318yes—
365#328C2318yes—
366#327C2314yes—
367#327C2314yes—
368#327C2318yes—
369C25C2×D412yes—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41—24no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—48no—
376C2×#41—84no—
377C2×#41C22×C414yes—
378C2×#41C22×C414yes—
379C22×Q8—21no—
380C22×Q8—22no—
381C22×Q8—22no—
382C22×Q8—22no—
383C22×Q8—84no—
384C22×Q8C22×C411yescharacteristic
385C22×Q8C22×C412yes—
386C22×Q8C22×C414yes—
387C22×Q8C22×C414yes—
388C22×D4—22no—
389C22×D4—21no—
390C22×D4—22no—
391C22×D4—44no—
392C22×D4C22⋊C411yescharacteristic
393C22×D4C22⋊C411yescharacteristic
394C22×D4C22⋊C412yes—
395C22×D4C22⋊C411yescharacteristic
396C22×D4C22⋊C411yescharacteristic
397C22×D4C22⋊C412yes—
398C22×D4C22×C411yescharacteristic
399C22×D4C2×D411yescharacteristic
400C22×D4C2×D412yes—
401C22×D4C2×D411yescharacteristic
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—21no—
405C23×C4—22no—
406C23×C4—24no—
407C23×C4—84no—
408C23×C4C22×C412yes—
409C23×C4C22×C412yes—
410C23×C4C22×C412yes—
411C23×C4C22×C412yes—
412C23×C4C2×D411yescharacteristic
413C23×C4C2×D412yes—
414C23×C4C2×D411yescharacteristic
415C23×C4C2×D412yes—
416C23×C4C2×D412yes—
417C23×C4C2×D412yes—
418C23×C4C2×D412yes—
419C23×C4C2×D412yes—
420C23×C4C2×D412yes—
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2412yes—
424C2×M16—24no—
425C2×M16—24no—
426C2×M16—84no—
427C22×C8—21no—
428C22×C8—22no—
429C22×C8—21no—
430C22×C8—24no—
431C22×C8—24no—
432C22×C8—84no—
433C4⋊Q8—22no—
434C4⋊Q8—24no—
435C4⋊Q8—22no—
436C4⋊Q8—21no—
437C4⋊Q8—21no—
438C4⋊Q8—21no—
439C4⋊Q8—21no—
440C4⋊Q8C22×C412yes—
441C4⋊Q8C22×C412yes—
442C4⋊Q8C22×C412yes—
443C4⋊Q8C22×C412yes—
444#126—24no—
445#126—24no—
446#126—24no—
447#126—24no—
448#126—24no—
449#126—24no—
450#126—24no—
451#126—24no—
452#126—22no—
453#126—22no—
454#126—22no—
455#126—22no—
456#125—24no—
457#125—24no—
458#125—24no—
459#125—24no—
460#125—22no—
461#125—22no—
462#125—21no—
463#125—21no—
464#125—22no—
465#125—22no—
466#125C22×C412yes—
467#125C22×C412yes—
468#124—22no—
469#124—22no—
470#124—24no—
471#124—24no—
472#124—24no—
473#124—24no—
474#124—24no—
475#124—21no—
476#124—21no—
477#124C22×C412yes—
478#124C22×C412yes—
479#123—24no—
480#123—24no—
481#123—24no—
482#123—24no—
483#123—24no—
484#123—24no—
485#123—22no—
486#123—22no—
487#123—24no—
488#123—24no—
489#123—22no—
490#123—22no—
491#123—24no—
492#123—24no—
493#123—24no—
494#123—24no—
495#123—24no—
496#123—24no—
497#123—24no—
498#123—24no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8—22no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—21no—
512C22⋊Q8—21no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—24no—
516C22⋊Q8—24no—
517C22⋊Q8—24no—
518C22⋊Q8—24no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521C22⋊Q8—24no—
522C22⋊Q8—24no—
523C22⋊Q8—24no—
524C22⋊Q8—24no—
525C22⋊Q8—22no—
526C22⋊Q8—24no—
527C22⋊Q8—22no—
528C22⋊Q8—24no—
529C22⋊Q8—24no—
530C22⋊Q8—24no—
531C22⋊Q8—24no—
532C22⋊Q8C22×C412yes—
533C22⋊Q8C22×C414yes—
534C22⋊Q8C22×C414yes—
535C22⋊Q8C22×C414yes—
536C22⋊Q8C22×C414yes—
537C22⋊Q8C22×C414yes—
538C22⋊Q8C22×C414yes—
539C22⋊Q8C22×C414yes—
540C22⋊Q8C2412yes—
541C22⋊Q8C2414yes—
542#121—24no—
543#121—24no—
544#121—24no—
545#121—24no—
546#121—22no—
547#121—22no—
548#121—24no—
549#121—22no—
550#121—22no—
551#121—21no—
552#121—21no—
553#121C22×C414yes—
554#121C22×C414yes—
555#121C22×C412yes—
556#121C2412yes—
557#120—24no—
558#120—24no—
559#120—24no—
560#120—24no—
561C4×Q8—22no—
562C4×Q8—24no—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—22no—
566C4×Q8—21no—
567C4×Q8—21no—
568C4×Q8—22no—
569C4×Q8—22no—
570C4×Q8—22no—
571C4×Q8—22no—
572C4×Q8C22×C412yes—
573C4×Q8C22×C412yes—
574C4×Q8C22×C414yes—
575C4×Q8C22×C414yes—
576C4×D4—22no—
577C4×D4—24no—
578C4×D4—22no—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—24no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—24no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—48no—
598C4×D4C22⋊C412yes—
599C4×D4C22⋊C411yescharacteristic
600C4×D4C22⋊C411yescharacteristic
601C4×D4C22⋊C412yes—
602C4×D4C22⋊C412yes—
603C4×D4C22⋊C412yes—
604C4×D4C22⋊C412yes—
605C4×D4C22⋊C411yescharacteristic
606C4×D4C22⋊C411yescharacteristic
607C4×D4C22⋊C412yes—
608C4×D4C22⋊C412yes—
609C4×D4C22⋊C411yescharacteristic
610C4×D4C22⋊C411yescharacteristic
611C4×D4C22⋊C411yescharacteristic
612C4×D4C22⋊C411yescharacteristic
613C4×D4C22⋊C412yes—
614C4×D4C22⋊C412yes—
615C4×D4C22⋊C412yes—
616C4×D4C22⋊C412yes—
617C4×D4C22⋊C412yes—
618C4×D4C22×C412yes—
619C4×D4C22×C412yes—
620C4×D4C22×C411yescharacteristic
621C4×D4C22×C411yescharacteristic
622C4×D4C22×C412yes—
623C4×D4C22×C411yescharacteristic
624C4×D4C22×C411yescharacteristic
625C4×D4C22×C412yes—
626C4×D4C22×C412yes—
627C4×D4C22×C412yes—
628C4×D4C22×C412yes—
629C4×D4C22×C412yes—
630C4×D4C2×D411yescharacteristic
631C4×D4C2×D412yes—
632C4×D4C2×D411yescharacteristic
633C4×D4C2×D412yes—
634C4×D4C2×D412yes—
635C4×D4C2×D412yes—
636C4×D4C2×D412yes—
637C4×D4C2×D411yescharacteristic
638C4×D4C2×D412yes—
639C4×D4C2×D411yescharacteristic
640#117—22no—
641#117—22no—
642#117—22no—
643#117—22no—
644#117—22no—
645#117—22no—
646#117—24no—
647#117—24no—
648#117—24no—
649#117—24no—
650#117—22no—
651#117—22no—
652#117—22no—
653#117—22no—
654#117—82no—
655#117—84no—
656#117C22×C414yes—
657#117C22×C414yes—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—24no—
662C2×C4⋊C4—24no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—24no—
676C2×C4⋊C4—24no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—24no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—24no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—84no—
687C2×C4⋊C4C22⋊C411yescharacteristic
688C2×C4⋊C4C22⋊C412yes—
689C2×C4⋊C4C22⋊C411yescharacteristic
690C2×C4⋊C4C22⋊C411yescharacteristic
691C2×C4⋊C4C22⋊C411yescharacteristic
692C2×C4⋊C4C22⋊C412yes—
693C2×C4⋊C4C22×C411yescharacteristic
694C2×C4⋊C4C22×C412yes—
695C2×C4⋊C4C22×C414yes—
696C2×C4⋊C4C22×C414yes—
697C2×C4⋊C4C22×C411yescharacteristic
698C2×C4⋊C4C2×D411yescharacteristic
699C2×C4⋊C4C2×D412yes—
700C2×C4⋊C4C2×D411yescharacteristic
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—24no—
704C2×C22⋊C4—24no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—24no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—24no—
721C2×C22⋊C4—24no—
722C2×C22⋊C4—84no—
723C2×C22⋊C4C22⋊C412yes—
724C2×C22⋊C4C22⋊C412yes—
725C2×C22⋊C4C22⋊C412yes—
726C2×C22⋊C4C22⋊C412yes—
727C2×C22⋊C4C22⋊C412yes—
728C2×C22⋊C4C22⋊C412yes—
729C2×C22⋊C4C22⋊C412yes—
730C2×C22⋊C4C22⋊C412yes—
731C2×C22⋊C4C2×D412yes—
732C2×C22⋊C4C2×D412yes—
733C2×C22⋊C4C2×D412yes—
734C2×C22⋊C4C2×D412yes—
735C2×C42—22no—
736C2×C42—22no—
737C2×C42—21no—
738C2×C42—22no—
739C2×C42—24no—
740C2×C42—22no—
741C2×C42C22×C411yescharacteristic
742C2×C42C22×C411yescharacteristic
743C2×C42C22×C411yescharacteristic
744C2×C42C22×C411yescharacteristic
745C2×C42C2×D411yescharacteristic
746C2×C42C2×D411yescharacteristic
747C2×C42C2×D411yescharacteristic
748C2×C42C2×D411yescharacteristic
749C2×C42C2×D411yescharacteristic
750C2×C42C2×D411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C4⋊C8—22no—
754C4⋊C8—22no—
755C4⋊C8—22no—
756C4⋊C8—22no—
757C22⋊C8—21no—
758C22⋊C8—22no—
759C22⋊C8—24no—
760C22⋊C8—24no—
761C22⋊C8—24no—
762C22⋊C8—24no—
763C22⋊C8—21no—
764C22⋊C8C2412yes—
765C22⋊C8C2414yes—
766C22⋊C8C2412yes—
767#97—22no—
768#97—22no—
769C4×C8—22no—
770C4×C8—22no—
771#95—24no—
772#95—22no—
773#95—24no—
774#95—22no—
775#95—22no—
776#95—22no—
777#95C2412yes—
778#95C2414yes—
779#95C2412yes—
780C24—24no—
781C24—24no—
782C24—21no—
783C24—44no—
784C24—82no—
785C24C2×C22⋊C412yes—
786C24C2×C22⋊C412yes—
787C24C2×C22⋊C412yes—
788C24C2×C22⋊C412yes—
789C24C22×D412yes—
790C24C22×D412yes—
791C24C22×D411yescharacteristic
792#41—416no—
793#41—48no—
794#41—48no—
795#41—84no—
796#41—84no—
797#41—84no—
798#41—84no—
799C2×Q8—22no—
800C2×Q8—22no—
801C2×Q8—21no—
802C2×Q8—22no—
803C2×Q8—24no—
804C2×Q8—24no—
805C2×Q8—42no—
806C2×Q8—44no—
807C2×Q8—44no—
808C2×Q8—84no—
809C2×Q8—84no—
810C2×Q8—84no—
811C2×Q8—84no—
812C2×Q8—84no—
813C2×Q8C23×C412yes—
814C2×Q8C23×C414yes—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—22no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—22no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—21no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—48no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—84no—
836C2×D4C2×C22⋊C412yes—
837C2×D4C2×C22⋊C411yescharacteristic
838C2×D4C2×C22⋊C412yes—
839C2×D4C2×C22⋊C412yes—
840C2×D4C2×C22⋊C411yescharacteristic
841C2×D4C2×C22⋊C411yescharacteristic
842C2×D4C2×C22⋊C412yes—
843C2×D4C2×C22⋊C412yes—
844C2×D4C2×C22⋊C412yes—
845C2×D4C2×C22⋊C411yescharacteristic
846C2×D4C23×C412yes—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—24no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—42no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—42no—
873C22×C4—44no—
874C22×C4—48no—
875C22×C4—48no—
876C22×C4—82no—
877C22×C4—82no—
878C22×C4—82no—
879C22×C4—82no—
880C22×C4—82no—
881C22×C4—82no—
882C22×C4—82no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4C2×C22⋊C411yescharacteristic
888C22×C4C2×C22⋊C411yescharacteristic
889C22×C4C2×C22⋊C411yescharacteristic
890C22×C4C2×C22⋊C411yescharacteristic
891C22×C4C2×C22⋊C411yescharacteristic
892C22×C4C2×C22⋊C411yescharacteristic
893C22×C4C2×C22⋊C412yes—
894C22×C4C2×C22⋊C412yes—
895C22×C4C2×C22⋊C412yes—
896C22×C4C2×C22⋊C412yes—
897C22×C4C2×C22⋊C412yes—
898C22×C4C2×C22⋊C411yescharacteristic
899C22×C4C2×C22⋊C411yescharacteristic
900C22×C4C2×C22⋊C412yes—
901C22×C4C2×C22⋊C412yes—
902C22×C4C2×C22⋊C412yes—
903C22×C4C2×C22⋊C412yes—
904C22×C4C2×C22⋊C412yes—
905C22×C4C2×C22⋊C412yes—
906C22×C4C2×C22⋊C412yes—
907C22×C4C23×C411yescharacteristic
908C22×C4C23×C411yescharacteristic
909C22×C4C23×C412yes—
910C22×C4C23×C412yes—
911C22×C4C23×C412yes—
912C22×C4C23×C412yes—
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D412yes—
920C22×C4C22×D412yes—
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D412yes—
923C22×C4C22×D412yes—
924C22×C4C22×D412yes—
925C22×C4C22×D412yes—
926C22×C4C2511yescharacteristic
927M16—84no—
928M16—84no—
929C2×C8—22no—
930C2×C8—22no—
931C2×C8—24no—
932C2×C8—42no—
933C2×C8—44no—
934C2×C8—42no—
935C2×C8—84no—
936C2×C8—84no—
937C4⋊C4—22no—
938C4⋊C4—24no—
939C4⋊C4—24no—
940C4⋊C4—21no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—24no—
946C4⋊C4—22no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—24no—
960C4⋊C4—24no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—21no—
964C4⋊C4—22no—
965C4⋊C4—24no—
966C4⋊C4—42no—
967C4⋊C4—44no—
968C4⋊C4—42no—
969C4⋊C4—44no—
970C4⋊C4—82no—
971C4⋊C4—84no—
972C4⋊C4C2×C22⋊C412yes—
973C4⋊C4C2×C22⋊C411yescharacteristic
974C4⋊C4C2×C22⋊C411yescharacteristic
975C4⋊C4C2×C22⋊C412yes—
976C4⋊C4C2×C22⋊C412yes—
977C4⋊C4C2×C22⋊C412yes—
978C4⋊C4C2×C22⋊C412yes—
979C4⋊C4C2×C22⋊C412yes—
980C4⋊C4C2×C22⋊C411yescharacteristic
981C4⋊C4C2×C22⋊C411yescharacteristic
982C4⋊C4C23×C412yes—
983C4⋊C4C23×C414yes—
984C4⋊C4C23×C412yes—
985C22⋊C4—22no—
986C22⋊C4—24no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—22no—
996C22⋊C4—24no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—24no—
1003C22⋊C4—24no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—48no—
1008C22⋊C4—42no—
1009C22⋊C4—44no—
1010C22⋊C4—42no—
1011C22⋊C4—84no—
1012C22⋊C4—84no—
1013C22⋊C4C2×C22⋊C412yes—
1014C22⋊C4C2×C22⋊C412yes—
1015C22⋊C4C2×C22⋊C412yes—
1016C22⋊C4C2×C22⋊C412yes—
1017C22⋊C4C2×C22⋊C412yes—
1018C22⋊C4C2×C22⋊C412yes—
1019C22⋊C4C2×C22⋊C412yes—
1020C22⋊C4C2×C22⋊C412yes—
1021C22⋊C4C2×C22⋊C412yes—
1022C22⋊C4C2×C22⋊C412yes—
1023C22⋊C4C2×C22⋊C412yes—
1024C22⋊C4C2×C22⋊C412yes—
1025C22⋊C4C2×C22⋊C412yes—
1026C22⋊C4C2×C22⋊C412yes—
1027C22⋊C4C2×C22⋊C412yes—
1028C22⋊C4C2×C22⋊C412yes—
1029C42—24no—
1030C42—24no—
1031C42—24no—
1032C42—24no—
1033C42—22no—
1034C42—22no—
1035C42—44no—
1036C42—82no—
1037C42—84no—
1038C42C2×C22⋊C411yescharacteristic
1039C42C2×C22⋊C411yescharacteristic
1040C42C2×C22⋊C411yescharacteristic
1041C42C2×C22⋊C411yescharacteristic
1042C42C2×C22⋊C411yescharacteristic
1043C42C2×C22⋊C411yescharacteristic
1044C42C2×C22⋊C411yescharacteristic
1045C42C2×C22⋊C411yescharacteristic
1046C42C23×C411yescharacteristic
1047C42C23×C411yescharacteristic
1048C42C23×C411yescharacteristic
1049C42C23×C411yescharacteristic
1050C42C22×D411yescharacteristic
1051C42C22×D411yescharacteristic
1052C42C22×D411yescharacteristic
1053C42C22×D411yescharacteristic
1054C23—24no—
1055C23—24no—
1056C23—24no—
1057C23—24no—
1058C23—24no—
1059C23—22no—
1060C23—22no—
1061C23—24no—
1062C23—24no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—42no—
1067C23—42no—
1068C23—41no—
1069C23—42no—
1070C23—41no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—88no—
1081C23—88no—
1082C23C22×C22⋊C412yes—
1083C23C22×C22⋊C412yes—
1084C23C22×C22⋊C412yes—
1085C23C22×C22⋊C411yescharacteristic
1086C23C22×C22⋊C411yescharacteristic
1087C23C22×C22⋊C412yes—
1088C23#57712yes—
1089C23#57812yes—
1090C23C23×D411yescharacteristic
1091Q8—42no—
1092Q8—44no—
1093Q8—44no—
1094Q8—42no—
1095Q8—44no—
1096Q8—44no—
1097Q8—84no—
1098Q8—84no—
1099D4—24no—
1100D4—24no—
1101D4—24no—
1102D4—22no—
1103D4—22no—
1104D4—22no—
1105D4—42no—
1106D4—42no—
1107D4—42no—
1108D4—42no—
1109D4—48no—
1110D4—44no—
1111D4—48no—
1112D4—42no—
1113D4—42no—
1114D4—42no—
1115D4—84no—
1116D4—84no—
1117D4#42114yes—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—44no—
1166C2×C4—42no—
1167C2×C4—44no—
1168C2×C4—48no—
1169C2×C4—44no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—48no—
1173C2×C4—44no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—44no—
1178C2×C4—44no—
1179C2×C4—42no—
1180C2×C4—44no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—84no—
1184C2×C4—84no—
1185C2×C4—84no—
1186C2×C4—84no—
1187C2×C4—168no—
1188C2×C4C22×C22⋊C411yescharacteristic
1189C2×C4C22×C22⋊C411yescharacteristic
1190C2×C4C22×C22⋊C411yescharacteristic
1191C2×C4C22×C22⋊C412yes—
1192C2×C4C22×C22⋊C412yes—
1193C2×C4C22×C22⋊C411yescharacteristic
1194C2×C4C22×C22⋊C411yescharacteristic
1195C2×C4C22×C22⋊C411yescharacteristic
1196C2×C4C22×C22⋊C411yescharacteristic
1197C2×C4C22×C22⋊C411yescharacteristic
1198C2×C4C22×C22⋊C412yes—
1199C2×C4C22×C22⋊C412yes—
1200C2×C4C22×C22⋊C411yescharacteristic
1201C2×C4C22×C22⋊C411yescharacteristic
1202C2×C4C24×C411yescharacteristic
1203C2×C4C23×D411yescharacteristic
1204C8—42no—
1205C8—44no—
1206C8—42no—
1207C22—21no—
1208C22—21no—
1209C22—21no—
1210C22—22no—
1211C22—22no—
1212C22—21no—
1213C22—21no—
1214C22—21no—
1215C22—22no—
1216C22—22no—
1217C22—22no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—42no—
1225C22—42no—
1226C22—44no—
1227C22—44no—
1228C22—48no—
1229C22—48no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—82no—
1234C22—82no—
1235C22—84no—
1236C22—84no—
1237C22—84no—
1238C22#289812yes—
1239C22#289812yes—
1240C22C2×#42114yes—
1241C22C23×C22⋊C411yescharacteristic
1242C22C2×#57711yescharacteristic
1243C22C2×#57811yescharacteristic
1244C4—21no—
1245C4—21no—
1246C4—21no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—22no—
1251C4—21no—
1252C4—21no—
1253C4—21no—
1254C4—21no—
1255C4—21no—
1256C4—21no—
1257C4—21no—
1258C4—44no—
1259C4—42no—
1260C4—42no—
1261C4—42no—
1262C4—44no—
1263C4—82no—
1264C4—84no—
1265C4—82no—
1266C4#288312yes—
1267C4C2×#42112yes—
1268C2—21no—
1269C2—21no—
1270C2—22no—
1271C2—22no—
1272C2—24no—
1273C2—42no—
1274C2—42no—
1275C2—42no—
1276C2—82no—
1277C2C2×#288311yescharacteristic
1278C2C2×#289811yescharacteristic
1279C2C22×#42111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3520C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2974C2semidirect
3. #34194C2semidirect
4. #17600C2semidirect
5. #17598C2semidirect
6. #17596C2semidirect
7. #17592C2semidirect
8. #17581C2semidirect
9. #17578C2semidirect
10. #17575C2semidirect
11. #17572C2semidirect
12. #17567C2semidirect
13. C2×#1520C2semidirect
14. #17548C2semidirect
21. #3520C4semidirect
22. #3520C4semidirect
23. #3520C4semidirect
27. C2×#556C4semidirect
29. C2×#552C4semidirect
31. C2×D4×Q8C4semidirect
32. C2×#548C4semidirect
33. C2×#547C4semidirect
34. C2×#547C4semidirect
47. #2974C22semidirect
48. #2974C22semidirect
49. #2974C22semidirect
63. #2319C22semidirect
64. #2318C22semidirect
69. #2275C22semidirect
70. #1521C22semidirect
78. #1520C22semidirect
82. #1518C22semidirect
83. #1516C22semidirect
84. #1515C22semidirect
85. #1513C22semidirect
86. #1512C22semidirect
87. #1511C22semidirect
88. #1509C22semidirect
89. #1508C22semidirect
90. #1506C22semidirect
91. #1504C22semidirect
92. #1503C22semidirect
93. #1501C22semidirect
94. #1500C22semidirect
95. C2×#328C22semidirect
97. C22×#41C2×C4semidirect
98. C23×Q8C2×C4semidirect
107. #556C2×C4semidirect
108. #556C2×C4semidirect
120. #552C2×C4semidirect
121. #552C2×C4semidirect
122. #552C2×C4semidirect
135. D4×Q8C2×C4semidirect
136. D4×Q8C2×C4semidirect
142. #548C2×C4semidirect
143. #548C2×C4semidirect
144. #548C2×C4semidirect
153. #547C2×C4semidirect
154. #547C2×C4semidirect
155. #547C2×C4semidirect
156. #547C2×C4semidirect
181. #533C2×C4semidirect
182. #533C2×C4semidirect
186. C2×C4⋊Q8C2×C4semidirect
187. C2×C4⋊Q8C2×C4semidirect
192. #529C2×C4semidirect
193. #529C2×C4semidirect
201. C2×#125C2×C4semidirect
204. C2×#124C2×C4semidirect
209. #525C2×C4semidirect
210. #525C2×C4semidirect
228. C2×C22⋊Q8C2×C4semidirect
229. C2×C22⋊Q8C2×C4semidirect
230. C2×C22⋊Q8C2×C4semidirect
231. C2×C22⋊Q8C2×C4semidirect
232. C2×C22⋊Q8C2×C4semidirect
239. C2×#121C2×C4semidirect
250. C2×C4×Q8C2×C4semidirect
251. C2×C4×Q8C2×C4semidirect
264. C2×C4×D4C2×C4semidirect
282. C2×#117C2×C4semidirect
286. C22×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35202
C2×#29742
#341942
#176002
#175982
#175962
#175922
#175812
#175782
#175752
#175722
#175672
C2×#15202
#175482