Finite Group Databasebeta

← #6379505

Subgroups — #6379505

Order 512.

3671 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3481C211yesmaximal, characteristic
2#34126C212yesmaximal, complemented
3#22535C212yesmaximal, complemented
4#22513C212yesmaximal, complemented
5#22477C214yesmaximal, complemented
6#22476C212yesmaximal, complemented
7#22405C214yesmaximal, complemented
8D4×#99C212yesmaximal, complemented
9#21421C212yesmaximal, complemented
10#21420C214yesmaximal, complemented
11#20723C211yesmaximal, characteristic, complemented
12#20722C212yesmaximal, complemented
13C4×#410C211yesmaximal, characteristic, complemented
14C2×C4×#99C212yesmaximal, complemented
15#3481—22no—
16#3481—24no—
17#3481—22no—
18#3481—22no—
19#3481—24no—
20#3481—22no—
21C2×#559C411yescharacteristic, complemented
22C2×#554C411yescharacteristic, complemented
23C2×#554C2211yescharacteristic
24C2×#553C411yescharacteristic, complemented
25C2×#553C412yescomplemented
26C2×#553C2211yescharacteristic
27C2×#551C412yescomplemented
28C2×#551C2212yes—
29C2×#546C411yescharacteristic, complemented
30C2×#546C2212yes—
31C2×#546C2211yescharacteristic
32C2×D42C2211yescharacteristic
33C2×#532C411yescharacteristic, complemented
34C2×#529C412yescomplemented
35C2×#529C411yescharacteristic, complemented
36C2×#529C2211yescharacteristic
37C2×#525C412yescomplemented
38C2×#525C2212yes—
39C2×C4×#41C411yescharacteristic, complemented
40C2×C4×#41C2211yescharacteristic
41C22×C4×D4C411yescharacteristic, complemented
42C22×C4×D4C2212yes—
43C22×C4×D4C2211yescharacteristic
44C2×#410C2212yes—
45C22×#99C2214yes—
46#2357—22no—
47#2353—24no—
48#2349—22no—
49#2345C2214yescomplemented
50#2342C2218yescomplemented
51D4×C22⋊C4C2214yes—
52#2293—22no—
53#2290—24no—
54#2283C2212yescomplemented
55#2280C2214yescomplemented
56C42×D4—22no—
57C4×#117C2212yescomplemented
58C2×C4×C22⋊C4C2214yescomplemented
59#1996C2218yescomplemented
60#1996C2214yescomplemented
61#1964C2214yes—
62#1964C2218yescomplemented
63#1899C2218yescomplemented
64#1898C2218yes—
65#1898C2218yescomplemented
66#1820C2212yescomplemented
67#1819C2214yescomplemented
68#1799C2212yes—
69#1799C2214yes—
70#1799C2212yescomplemented
71#1799C2214yescomplemented
72#1782C2212yes—
73#1781C2214yes—
74C4×#99C2212yes—
75C4×#99C2214yes—
76C4×#99C2211yescharacteristic
77C4×#99C2212yes—
78C4×#99C2211yescharacteristic
79C4×#99C2214yescomplemented
80C4×#99C2212yescomplemented
81C4×#99C2214yescomplemented
82C4×#99C2212yescomplemented
83C4×#99C2212yescomplemented
84C4×#99C2214yescomplemented
85#1740C2212yescomplemented
86C2×#342C2214yescomplemented
87C22×#41C2×C411yescharacteristic
88C22×#41C2×C412yescomplemented
89C22×#41C2311yescharacteristic
90C23×D4C2×C411yescharacteristic
91C23×D4C2312yes—
92C23×D4C2311yescharacteristic
93C24×C4C2×C412yescomplemented
94C24×C4C2312yes—
95#559—22no—
96#559—22no—
97#559—24no—
98#554—24no—
99#554—22no—
100#554—22no—
101#554—22no—
102#554—24no—
103#554—22no—
104#553—24no—
105#553—24no—
106#553—24no—
107#553—24no—
108#553—22no—
109#553—22no—
110#553—24no—
111#553—22no—
112#553—24no—
113#553—22no—
114#551—24no—
115#551—24no—
116#551—24no—
117#551—24no—
118#551—24no—
119#551—24no—
120#551—24no—
121#551—24no—
122#546—22no—
123#546—24no—
124#546—22no—
125#546—24no—
126#546—22no—
127#546—22no—
128#546—24no—
129#546—24no—
130#546—24no—
131#546—24no—
132D42—22no—
133D42—24no—
134D42—22no—
135#532—22no—
136#532—22no—
137#532—22no—
138#532—22no—
139C2×C4⋊Q8C2×C411yescharacteristic, complemented
140C2×#127C2×C411yescharacteristic
141#529—24no—
142#529—24no—
143#529—24no—
144#529—24no—
145#529—22no—
146#529—22no—
147#529—22no—
148#529—22no—
149#529—22no—
150#529—22no—
151#529—22no—
152#529—22no—
153C2×#126C2×C412yescomplemented
154C2×#126C2×C412yescomplemented
155C2×#126C2×C412yescomplemented
156C2×#126C2×C412yescomplemented
157C2×#125C2×C412yescomplemented
158C2×#125C2×C411yescharacteristic, complemented
159C2×#125C2×C411yescharacteristic, complemented
160C2×#124C2×C411yescharacteristic
161C2×#124C2×C412yescomplemented
162C2×#124C2×C411yescharacteristic, complemented
163C2×#124C2×C412yescomplemented
164#525—24no—
165#525—24no—
166#525—24no—
167#525—24no—
168#525—24no—
169#525—24no—
170#525—24no—
171#525—24no—
172C2×#123C2×C412yes—
173C2×#123C2×C412yescomplemented
174C2×#123C2×C412yescomplemented
175C2×#123C2×C412yescomplemented
176C2×#123C2×C412yescomplemented
177C2×#123C2×C412yescomplemented
178C2×#123C2×C412yescomplemented
179C2×#123C2312yes—
180C2×C22⋊Q8C2×C412yescomplemented
181C2×C22⋊Q8C2×C412yescomplemented
182C2×C22⋊Q8C2×C412yescomplemented
183C2×C22⋊Q8C2×C411yescharacteristic, complemented
184C2×C22⋊Q8C2×C412yescomplemented
185C2×C22⋊Q8C2312yes—
186C2×C22⋊Q8C2311yescharacteristic
187C2×#121C2×C412yes—
188C2×#121C2×C412yes—
189C2×#121C2×C411yescharacteristic
190C2×#121C2×C411yescharacteristic
191C2×#121C2×C412yescomplemented
192C2×#121C2×C412yescomplemented
193C2×#121C2×C411yescharacteristic, complemented
194C2×#121C2×C412yescomplemented
195C2×#121C2312yes—
196C2×#121C2311yescharacteristic
197C2×#120C2×C412yes—
198C2×#120C2×C412yescomplemented
199C2×#120C2312yes—
200C2×#120C2312yes—
201C4×#41—22no—
202C4×#41—21no—
203C4×#41—21no—
204C4×#41—22no—
205C4×#41—21no—
206C4×#41—21no—
207C4×#41—22no—
208C4×#41—22no—
209C4×#41—22no—
210C4×#41—22no—
211C2×C4×Q8C2×C411yescharacteristic, complemented
212C2×C4×Q8C2×C411yescharacteristic, complemented
213C2×C4×Q8C2×C411yescharacteristic, complemented
214C2×C4×Q8C2×C411yescharacteristic, complemented
215C2×C4×D4—24no—
216C2×C4×D4—24no—
217C2×C4×D4—24no—
218C2×C4×D4—24no—
219C2×C4×D4—22no—
220C2×C4×D4—21no—
221C2×C4×D4—21no—
222C2×C4×D4—22no—
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4—24no—
226C2×C4×D4C2×C411yescharacteristic
227C2×C4×D4C2×C411yescharacteristic
228C2×C4×D4C2×C411yescharacteristic
229C2×C4×D4C2×C412yes—
230C2×C4×D4C2×C411yescharacteristic
231C2×C4×D4C2×C411yescharacteristic
232C2×C4×D4C2×C412yes—
233C2×C4×D4C2×C411yescharacteristic
234C2×C4×D4C2×C412yescomplemented
235C2×C4×D4C2×C411yescharacteristic, complemented
236C2×C4×D4C2×C412yescomplemented
237C2×C4×D4C2×C411yescharacteristic, complemented
238C2×C4×D4C2×C412yescomplemented
239C2×C4×D4C2×C412yescomplemented
240C2×C4×D4C2×C412yescomplemented
241C2×C4×D4C2×C412yescomplemented
242C2×C4×D4C2×C412yescomplemented
243C2×C4×D4C2×C412yescomplemented
244C2×C4×D4C2×C411yescharacteristic, complemented
245C2×C4×D4C2×C411yescharacteristic, complemented
246C2×C4×D4D412yes—
247C2×C4×D4D414yes—
248C2×C4×D4D412yes—
249C2×C4×D4D412yes—
250C2×C4×D4D414yes—
251C2×C4×D4D412yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2312yes—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2312yes—
258C2×C4×D4C2311yescharacteristic
259C2×#117—24no—
260C2×#117C2×C412yescomplemented
261C2×#117C2×C411yescharacteristic, complemented
262C2×#117C2×C411yescharacteristic, complemented
263C2×#117C2×C411yescharacteristic, complemented
264C2×#117C2×C412yescomplemented
265C2×#117C2×C412yescomplemented
266C2×#117C2314yes—
267C2×#117C2311yescharacteristic
268C22×C4⋊C4C2×C411yescharacteristic, complemented
269C22×C4⋊C4C2×C412yescomplemented
270C22×C4⋊C4C2311yescharacteristic
271C22×C22⋊C4C2×C412yescomplemented
272C22×C22⋊C4C2×C412yescomplemented
273C22×C22⋊C4C2312yes—
274C22×C22⋊C4C2318yes—
275C22×C22⋊C4C2312yes—
276C22×C42—24no—
277C22×C42C2×C411yescharacteristic, complemented
278C22×C42C2×C412yescomplemented
279C22×C42C2×C411yescharacteristic, complemented
280C22×C42C2311yescharacteristic
281#410—28no—
282C2×#99—216no—
283C2×#99C2314yes—
284C2×#99C2312yes—
285C2×#99C2318yes—
286C2×#99C2314yes—
287C2×#99C2318yes—
288C2×#99C2314yes—
289C2×#99C2312yes—
290#390—24no—
291#389—24no—
292#388—28no—
293#388—28no—
294#387—28no—
295#386—28no—
296#385—28no—
297#383—22no—
298#382—22no—
299#381—24no—
300#381C2314yes—
301#380—24no—
302#380C2314yes—
303#380C2318yes—
304#379C2318yes—
305C4×C4⋊C4—24no—
306C4×C4⋊C4—22no—
307C4×C4⋊C4—22no—
308C4×C4⋊C4—22no—
309C4×C22⋊C4—24no—
310C4×C22⋊C4—24no—
311C4×C22⋊C4—24no—
312C4×C22⋊C4—28no—
313C4×C22⋊C4C2314yes—
314C4×C22⋊C4C2318yes—
315C4×C22⋊C4C2312yes—
316C4×C22⋊C4C2314yes—
317C4×C22⋊C4C2312yes—
318#376—22no—
319#376—22no—
320C2×#95—24no—
321C43—22no—
322#342C2318yes—
323#342C2314yes—
324#342C2312yes—
325#342C2314yes—
326#342C2314yes—
327#342C2318yes—
328#342C2312yes—
329C25C22×C412yes—
330C25C2412yes—
331C2×#41—21no—
332C2×#41—22no—
333C2×#41—21no—
334C2×#41—24no—
335C2×#41—24no—
336C2×#41—24no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—42no—
340C2×#41—44no—
341C2×#41—84no—
342C22×Q8C22×C411yescharacteristic
343C22×Q8C22×C411yescharacteristic
344C22×Q8C22×C412yes—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—21no—
349C22×D4—21no—
350C22×D4—28no—
351C22×D4—44no—
352C22×D4—44no—
353C22×D4—44no—
354C22×D4C22×C412yes—
355C22×D4C22×C411yescharacteristic
356C22×D4C22×C412yes—
357C22×D4C22×C411yescharacteristic
358C22×D4C22×C412yes—
359C22×D4C22×C412yes—
360C22×D4C22×C411yescharacteristic
361C22×D4C22×C412yes—
362C22×D4C22×C412yes—
363C22×D4C22×C412yes—
364C22×D4C22×C412yes—
365C22×D4C22×C411yescharacteristic
366C22×D4C2×D412yes—
367C22×D4C2×D414yes—
368C22×D4C2×D412yes—
369C22×D4C2411yescharacteristic
370C22×D4C2412yes—
371C22×D4C2411yescharacteristic
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—28no—
377C23×C4—84no—
378C23×C4—84no—
379C23×C4C22×C411yescharacteristic
380C23×C4C22×C412yes—
381C23×C4C22×C411yescharacteristic
382C23×C4C22×C412yes—
383C23×C4C22×C411yescharacteristic
384C23×C4C22×C412yes—
385C23×C4C22×C411yescharacteristic
386C23×C4C22×C411yescharacteristic
387C23×C4C22×C411yescharacteristic
388C23×C4C22×C412yes—
389C23×C4C22×C412yes—
390C23×C4C22×C412yes—
391C23×C4C22×C412yes—
392C23×C4C22×C412yes—
393C23×C4C22×C412yes—
394C23×C4C22×C412yes—
395C23×C4C2×D414yes—
396C23×C4C2×D414yes—
397C23×C4C2×D414yes—
398C23×C4C2×D414yes—
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2412yes—
403C4⋊Q8—22no—
404C4⋊Q8—22no—
405#127—22no—
406#127—22no—
407#126—24no—
408#126—24no—
409#126—24no—
410#126—24no—
411#126—24no—
412#126—24no—
413#126—24no—
414#126—24no—
415#125—24no—
416#125—24no—
417#125—22no—
418#125—22no—
419#125—22no—
420#125—22no—
421#124—22no—
422#124—22no—
423#124—24no—
424#124—24no—
425#124—24no—
426#124—24no—
427#124—22no—
428#124—22no—
429#123—24no—
430#123—24no—
431#123—24no—
432#123—24no—
433#123—24no—
434#123—24no—
435#123—24no—
436#123—24no—
437#123—24no—
438#123—24no—
439#123—24no—
440#123—24no—
441#123—24no—
442#123—24no—
443#123—24no—
444#123—24no—
445C22⋊Q8—24no—
446C22⋊Q8—24no—
447C22⋊Q8—24no—
448C22⋊Q8—24no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—24no—
452C22⋊Q8—24no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—24no—
456C22⋊Q8—24no—
457C22⋊Q8—24no—
458C22⋊Q8—24no—
459#121—24no—
460#121—24no—
461#121—22no—
462#121—22no—
463#121—24no—
464#121—24no—
465#121—22no—
466#121—22no—
467#121—24no—
468#121—24no—
469#121—24no—
470#121—24no—
471#121—22no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—24no—
476#121—24no—
477#121—24no—
478#121—24no—
479#120—24no—
480#120—24no—
481#120—24no—
482#120—24no—
483#120—24no—
484#120—24no—
485#120—24no—
486#120—24no—
487C4×Q8—22no—
488C4×Q8—21no—
489C4×Q8—21no—
490C4×Q8—22no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×Q8—22no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—22no—
497C4×Q8—22no—
498C4×D4—22no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—22no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—24no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—24no—
510C4×D4—24no—
511C4×D4—24no—
512C4×D4—24no—
513C4×D4—24no—
514C4×D4—24no—
515C4×D4—24no—
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—24no—
523C4×D4—24no—
524C4×D4—24no—
525C4×D4—24no—
526C4×D4—24no—
527C4×D4—24no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4—21no—
549C4×D4—22no—
550C4×D4—22no—
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—416no—
554C4×D4C22⋊C412yes—
555C4×D4C22⋊C411yescharacteristic
556C4×D4C22⋊C411yescharacteristic
557C4×D4C22⋊C412yes—
558C4×D4C22⋊C411yescharacteristic
559C4×D4C22⋊C411yescharacteristic
560C4×D4C22⋊C414yes—
561C4×D4C22⋊C414yes—
562C4×D4C22⋊C414yes—
563C4×D4C22⋊C414yes—
564C4×D4C22⋊C412yes—
565C4×D4C22⋊C412yes—
566C4×D4C22⋊C412yes—
567C4×D4C22⋊C412yes—
568C4×D4C22⋊C414yes—
569C4×D4C22⋊C412yes—
570C4×D4C22⋊C412yes—
571C4×D4C22⋊C414yes—
572C4×D4C22⋊C414yes—
573C4×D4C22⋊C414yes—
574C4×D4C22⋊C414yes—
575C4×D4C22⋊C412yes—
576C4×D4C22⋊C412yes—
577C4×D4C22⋊C414yes—
578#117—24no—
579#117—24no—
580#117—22no—
581#117—22no—
582#117—22no—
583#117—21no—
584#117—21no—
585#117—22no—
586#117—22no—
587#117—22no—
588#117—22no—
589#117—22no—
590#117—22no—
591#117—22no—
592#117—22no—
593#117—24no—
594#117—24no—
595#117—28no—
596#117—44no—
597#117—88no—
598C2×C4⋊C4—24no—
599C2×C4⋊C4—24no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—28no—
606C2×C4⋊C4C22×C411yescharacteristic
607C2×C4⋊C4C22×C411yescharacteristic
608C2×C4⋊C4C22×C412yes—
609C2×C4⋊C4C22×C412yes—
610C2×C4⋊C4C22×C412yes—
611C2×C4⋊C4C22×C412yes—
612C2×C4⋊C4C22×C411yescharacteristic
613C2×C4⋊C4C22×C412yes—
614C2×C4⋊C4C22×C412yes—
615C2×C4⋊C4C22×C411yescharacteristic
616C2×C4⋊C4C22×C411yescharacteristic
617C2×C4⋊C4C22×C411yescharacteristic
618C2×C4⋊C4C22×C412yes—
619C2×C4⋊C4C22×C412yes—
620C2×C4⋊C4C22×C412yes—
621C2×C4⋊C4C22×C412yes—
622C2×C4⋊C4C22×C411yescharacteristic
623C2×C4⋊C4C22×C411yescharacteristic
624C2×C4⋊C4C22×C411yescharacteristic
625C2×C4⋊C4C22×C411yescharacteristic
626C2×C4⋊C4C22×C412yes—
627C2×C4⋊C4C2×D412yes—
628C2×C4⋊C4C2×D414yes—
629C2×C4⋊C4C2×D412yes—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—216no—
639C2×C22⋊C4—28no—
640C2×C22⋊C4—28no—
641C2×C22⋊C4—28no—
642C2×C22⋊C4—48no—
643C2×C22⋊C4C22×C411yescharacteristic
644C2×C22⋊C4C22×C412yes—
645C2×C22⋊C4C22×C412yes—
646C2×C22⋊C4C22×C412yes—
647C2×C22⋊C4C22×C412yes—
648C2×C22⋊C4C22×C412yes—
649C2×C22⋊C4C22×C412yes—
650C2×C22⋊C4C22×C412yes—
651C2×C22⋊C4C22×C412yes—
652C2×C22⋊C4C22×C412yes—
653C2×C22⋊C4C22×C412yes—
654C2×C22⋊C4C22×C411yescharacteristic
655C2×C22⋊C4C22×C411yescharacteristic
656C2×C22⋊C4C22×C411yescharacteristic
657C2×C22⋊C4C22×C412yes—
658C2×C22⋊C4C22×C412yes—
659C2×C22⋊C4C22×C412yes—
660C2×C22⋊C4C22×C412yes—
661C2×C22⋊C4C22×C412yes—
662C2×C22⋊C4C22×C412yes—
663C2×C22⋊C4C22×C412yes—
664C2×C22⋊C4C22×C412yes—
665C2×C22⋊C4C2×D414yes—
666C2×C22⋊C4C2×D414yes—
667C2×C22⋊C4C2×D414yes—
668C2×C22⋊C4C2×D414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2411yescharacteristic
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2411yescharacteristic
674C2×C22⋊C4C2414yes—
675C2×C42—22no—
676C2×C42—22no—
677C2×C42—22no—
678C2×C42—22no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—22no—
688C2×C42—24no—
689C2×C42—24no—
690C2×C42—24no—
691C2×C42—22no—
692C2×C42—28no—
693C2×C42—88no—
694C2×C42C22×C411yescharacteristic
695C2×C42C22×C411yescharacteristic
696C2×C42C22×C412yes—
697C2×C42C22×C412yes—
698C2×C42C22×C411yescharacteristic
699C2×C42C22×C411yescharacteristic
700C2×C42C22×C411yescharacteristic
701C2×C42C22×C412yes—
702C2×C42C22×C411yescharacteristic
703C2×C42C22×C411yescharacteristic
704C2×C42C22×C411yescharacteristic
705C2×C42C22×C411yescharacteristic
706C2×C42C22×C411yescharacteristic
707C2×C42C2×D412yes—
708C2×C42C2×D412yes—
709C2×C42C2×D412yes—
710C2×C42C2×D412yes—
711#99—28no—
712#99—24no—
713#99—216no—
714#99—28no—
715#99—44no—
716#99—48no—
717#99#4118yescomplemented
718#95—22no—
719#95—24no—
720#95—28no—
721#95—22no—
722#95—24no—
723#95—24no—
724#95—24no—
725#95—28no—
726#95—24no—
727C24—24no—
728C24—24no—
729C24—22no—
730C24—22no—
731C24—24no—
732C24—42no—
733C24—44no—
734C24—44no—
735C24—82no—
736C24—82no—
737C24C23×C412yes—
738C24C23×C412yes—
739C24C23×C411yescharacteristic
740C24C23×C412yes—
741C24C23×C411yescharacteristic
742C24C22×D414yes—
743C24C22×D414yes—
744C24C2511yescharacteristic
745#41—48no—
746#41—48no—
747#41—48no—
748#41—44no—
749#41—44no—
750#41—88no—
751#41—88no—
752C2×Q8—22no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—24no—
756C2×Q8—22no—
757C2×Q8—41no—
758C2×Q8—42no—
759C2×Q8—82no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—28no—
763C2×D4—24no—
764C2×D4—22no—
765C2×D4—22no—
766C2×D4—24no—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—22no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—42no—
786C2×D4—44no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—44no—
792C2×D4—48no—
793C2×D4—416no—
794C2×D4—416no—
795C2×D4—48no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—82no—
801C2×D4—82no—
802C2×D4—82no—
803C2×D4C2×C22⋊C412yes—
804C2×D4C2×C22⋊C411yescharacteristic
805C2×D4C2×C22⋊C414yes—
806C2×D4C2×C22⋊C412yes—
807C2×D4C2×C22⋊C414yes—
808C2×D4C2×C22⋊C412yes—
809C2×D4C2×C22⋊C411yescharacteristic
810C2×D4C2×#4114yes—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—24no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—24no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—28no—
842C22×C4—24no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—44no—
846C22×C4—42no—
847C22×C4—44no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—42no—
853C22×C4—44no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—416no—
858C22×C4—44no—
859C22×C4—416no—
860C22×C4—84no—
861C22×C4—84no—
862C22×C4—82no—
863C22×C4—82no—
864C22×C4—84no—
865C22×C4—84no—
866C22×C4—82no—
867C22×C4—84no—
868C22×C4—84no—
869C22×C4—88no—
870C22×C4—82no—
871C22×C4—82no—
872C22×C4—82no—
873C22×C4C2×C22⋊C412yes—
874C22×C4C2×C22⋊C412yes—
875C22×C4C2×C22⋊C414yes—
876C22×C4C2×C22⋊C412yes—
877C22×C4C2×C22⋊C412yes—
878C22×C4C2×C22⋊C414yes—
879C22×C4C2×C22⋊C414yes—
880C22×C4C2×C22⋊C414yes—
881C22×C4C2×C22⋊C414yes—
882C22×C4C2×C22⋊C414yes—
883C22×C4C23×C411yescharacteristic
884C22×C4C23×C412yes—
885C22×C4C23×C411yescharacteristic
886C22×C4C23×C411yescharacteristic
887C22×C4C23×C411yescharacteristic
888C22×C4C23×C411yescharacteristic
889C22×C4C23×C411yescharacteristic
890C22×C4C23×C411yescharacteristic
891C22×C4C23×C412yes—
892C22×C4C23×C411yescharacteristic
893C22×C4C23×C411yescharacteristic
894C22×C4C23×C411yescharacteristic
895C22×C4C23×C412yes—
896C22×C4C23×C411yescharacteristic
897C22×C4C23×C412yes—
898C22×C4C23×C411yescharacteristic
899C22×C4C23×C412yes—
900C22×C4C22×D412yes—
901C22×C4C22×D412yes—
902C22×C4C22×D412yes—
903C22×C4C22×D412yes—
904C22×C4C22×D412yes—
905C22×C4C22×D412yes—
906C22×C4C22×D414yes—
907C22×C4C22×D414yes—
908C4⋊C4—22no—
909C4⋊C4—24no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—24no—
913C4⋊C4—22no—
914C4⋊C4—22no—
915C4⋊C4—24no—
916C4⋊C4—22no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—22no—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—48no—
932C4⋊C4—48no—
933C4⋊C4—88no—
934C4⋊C4C2×C22⋊C412yes—
935C4⋊C4C2×C22⋊C411yescharacteristic
936C4⋊C4C2×C22⋊C411yescharacteristic
937C4⋊C4C2×C22⋊C412yes—
938C4⋊C4C2×C22⋊C412yes—
939C4⋊C4C2×C22⋊C414yes—
940C4⋊C4C2×C22⋊C414yes—
941C22⋊C4—22no—
942C22⋊C4—22no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—22no—
946C22⋊C4—22no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—22no—
950C22⋊C4—24no—
951C22⋊C4—22no—
952C22⋊C4—24no—
953C22⋊C4—22no—
954C22⋊C4—24no—
955C22⋊C4—24no—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—24no—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—24no—
967C22⋊C4—24no—
968C22⋊C4—28no—
969C22⋊C4—24no—
970C22⋊C4—28no—
971C22⋊C4—24no—
972C22⋊C4—416no—
973C22⋊C4—416no—
974C22⋊C4—88no—
975C22⋊C4C2×C22⋊C412yes—
976C22⋊C4C2×C22⋊C412yes—
977C22⋊C4C2×C22⋊C412yes—
978C22⋊C4C2×C22⋊C412yes—
979C22⋊C4C2×C22⋊C414yes—
980C22⋊C4C2×C22⋊C414yes—
981C22⋊C4C2×C22⋊C414yes—
982C22⋊C4C2×C22⋊C414yes—
983C22⋊C4C2×C22⋊C414yes—
984C22⋊C4C2×C22⋊C414yes—
985C22⋊C4C2×#4118yes—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—22no—
990C42—21no—
991C42—22no—
992C42—22no—
993C42—21no—
994C42—21no—
995C42—22no—
996C42—22no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—22no—
1003C42—21no—
1004C42—48no—
1005C42—44no—
1006C42—48no—
1007C42—44no—
1008C42—48no—
1009C42—88no—
1010C42C2×C22⋊C411yescharacteristic
1011C42C2×C22⋊C411yescharacteristic
1012C42C2×C22⋊C412yes—
1013C42C2×C22⋊C412yes—
1014C42C2×C22⋊C412yes—
1015C42C2×C22⋊C412yes—
1016C42C2×C22⋊C412yes—
1017C42C2×C22⋊C411yescharacteristic
1018C42C2×C22⋊C411yescharacteristic
1019C42C2×C22⋊C412yes—
1020C23—28no—
1021C23—24no—
1022C23—21no—
1023C23—22no—
1024C23—21no—
1025C23—22no—
1026C23—28no—
1027C23—22no—
1028C23—22no—
1029C23—28no—
1030C23—22no—
1031C23—21no—
1032C23—21no—
1033C23—22no—
1034C23—21no—
1035C23—22no—
1036C23—44no—
1037C23—42no—
1038C23—41no—
1039C23—41no—
1040C23—44no—
1041C23—42no—
1042C23—42no—
1043C23—44no—
1044C23—44no—
1045C23—44no—
1046C23—41no—
1047C23—41no—
1048C23—44no—
1049C23—42no—
1050C23—41no—
1051C23—41no—
1052C23—42no—
1053C23—44no—
1054C23—82no—
1055C23—82no—
1056C23—88no—
1057C23—88no—
1058C23—88no—
1059C23—88no—
1060C23C22×C22⋊C414yes—
1061C23C22×C22⋊C412yes—
1062C23C22×C22⋊C412yes—
1063C23C4×#4112yes—
1064C23C24×C411yescharacteristic
1065C23C23×D412yes—
1066C23C22×#4112yes—
1067C23#58512yes—
1068Q8—44no—
1069Q8—42no—
1070Q8—42no—
1071Q8—84no—
1072D4—24no—
1073D4—28no—
1074D4—28no—
1075D4—22no—
1076D4—24no—
1077D4—42no—
1078D4—44no—
1079D4—48no—
1080D4—44no—
1081D4—42no—
1082D4—48no—
1083D4—44no—
1084D4—44no—
1085D4—44no—
1086D4—44no—
1087D4—48no—
1088D4—44no—
1089D4—42no—
1090D4—84no—
1091D4—84no—
1092D4—84no—
1093D4#41014yescomplemented
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—28no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—28no—
1122C2×C4—44no—
1123C2×C4—44no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—41no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—44no—
1130C2×C4—44no—
1131C2×C4—44no—
1132C2×C4—44no—
1133C2×C4—44no—
1134C2×C4—42no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—44no—
1140C2×C4—44no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—44no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—44no—
1149C2×C4—44no—
1150C2×C4—44no—
1151C2×C4—44no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—44no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—48no—
1164C2×C4—44no—
1165C2×C4—44no—
1166C2×C4—48no—
1167C2×C4—44no—
1168C2×C4—48no—
1169C2×C4—82no—
1170C2×C4—82no—
1171C2×C4—82no—
1172C2×C4—82no—
1173C2×C4—82no—
1174C2×C4—82no—
1175C2×C4—832no—
1176C2×C4C22×C22⋊C411yescharacteristic
1177C2×C4C22×C22⋊C411yescharacteristic
1178C2×C4C22×C22⋊C411yescharacteristic
1179C2×C4C22×C22⋊C411yescharacteristic
1180C2×C4C22×C22⋊C412yes—
1181C2×C4C22×C22⋊C412yes—
1182C2×C4C22×C22⋊C412yes—
1183C2×C4C22×C22⋊C412yes—
1184C2×C4C22×C22⋊C412yes—
1185C2×C4C22×C22⋊C414yes—
1186C2×C4C22×C22⋊C411yescharacteristic
1187C2×C4C22×C22⋊C411yescharacteristic
1188C2×C4C4×#4112yes—
1189C22—22no—
1190C22—22no—
1191C22—21no—
1192C22—22no—
1193C22—21no—
1194C22—22no—
1195C22—22no—
1196C22—22no—
1197C22—24no—
1198C22—22no—
1199C22—24no—
1200C22—22no—
1201C22—24no—
1202C22—42no—
1203C22—42no—
1204C22—416no—
1205C22—44no—
1206C22—44no—
1207C22—42no—
1208C22—42no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—42no—
1213C22—41no—
1214C22—42no—
1215C22—42no—
1216C22—41no—
1217C22—88no—
1218C22—82no—
1219C22—82no—
1220C22—88no—
1221C22—81no—
1222C22—81no—
1223C22—82no—
1224C22—82no—
1225C22—88no—
1226C22C2×#41014yes—
1227C22C23×C22⋊C411yescharacteristic
1228C22C2×C4×#4111yescharacteristic
1229C22#342811yescharacteristic
1230C22D4×#4114yes—
1231C4—21no—
1232C4—21no—
1233C4—22no—
1234C4—22no—
1235C4—21no—
1236C4—22no—
1237C4—21no—
1238C4—22no—
1239C4—22no—
1240C4—22no—
1241C4—24no—
1242C4—48no—
1243C4—42no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—42no—
1248C4—41no—
1249C4—42no—
1250C4—41no—
1251C4—84no—
1252C4—88no—
1253C4C2×#41012yes—
1254C4#288312yes—
1255C2—24no—
1256C2—21no—
1257C2—21no—
1258C2—24no—
1259C2—44no—
1260C2—42no—
1261C2—42no—
1262C2—81no—
1263C2—82no—
1264C2C22⋊C4×#4111yescharacteristic
1265C2C22×#41011yescharacteristic
1266C2C2×#288311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC24C25
socleC22C23×C22⋊C4
prime radicalC2×#3481C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C24 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34126C2semidirect
3. #22535C2semidirect
4. #22513C2semidirect
5. #22477C2semidirect
6. #22476C2semidirect
7. #22405C2semidirect
8. D4×#99C2semidirect
9. #21421C2semidirect
10. #21420C2semidirect
11. #20723C2semidirect
12. #20722C2semidirect
13. C4×#410C2semidirect
14. C2×C4×#99C2semidirect
21. C2×#559C4semidirect
22. C2×#554C4semidirect
24. C2×#553C4semidirect
25. C2×#553C4semidirect
27. C2×#551C4semidirect
29. C2×#546C4semidirect
33. C2×#532C4semidirect
34. C2×#529C4semidirect
35. C2×#529C4semidirect
37. C2×#525C4semidirect
39. C2×C4×#41C4semidirect
41. C22×C4×D4C4semidirect
49. #2345C22semidirect
50. #2342C22semidirect
54. #2283C22semidirect
55. #2280C22semidirect
57. C4×#117C22semidirect
58. C2×C4×C22⋊C4C22semidirect
59. #1996C22semidirect
60. #1996C22semidirect
62. #1964C22semidirect
63. #1899C22semidirect
65. #1898C22semidirect
66. #1820C22semidirect
67. #1819C22semidirect
70. #1799C22semidirect
71. #1799C22semidirect
79. C4×#99C22semidirect
80. C4×#99C22semidirect
81. C4×#99C22semidirect
82. C4×#99C22semidirect
83. C4×#99C22semidirect
84. C4×#99C22semidirect
85. #1740C22semidirect
86. C2×#342C22semidirect
88. C22×#41C2×C4semidirect
93. C24×C4C2×C4semidirect
139. C2×C4⋊Q8C2×C4semidirect
153. C2×#126C2×C4semidirect
154. C2×#126C2×C4semidirect
155. C2×#126C2×C4semidirect
156. C2×#126C2×C4semidirect
157. C2×#125C2×C4semidirect
158. C2×#125C2×C4semidirect
159. C2×#125C2×C4semidirect
161. C2×#124C2×C4semidirect
162. C2×#124C2×C4semidirect
163. C2×#124C2×C4semidirect
173. C2×#123C2×C4semidirect
174. C2×#123C2×C4semidirect
175. C2×#123C2×C4semidirect
176. C2×#123C2×C4semidirect
177. C2×#123C2×C4semidirect
178. C2×#123C2×C4semidirect
180. C2×C22⋊Q8C2×C4semidirect
181. C2×C22⋊Q8C2×C4semidirect
182. C2×C22⋊Q8C2×C4semidirect
183. C2×C22⋊Q8C2×C4semidirect
184. C2×C22⋊Q8C2×C4semidirect
191. C2×#121C2×C4semidirect
192. C2×#121C2×C4semidirect
193. C2×#121C2×C4semidirect
194. C2×#121C2×C4semidirect
198. C2×#120C2×C4semidirect
211. C2×C4×Q8C2×C4semidirect
212. C2×C4×Q8C2×C4semidirect
213. C2×C4×Q8C2×C4semidirect
214. C2×C4×Q8C2×C4semidirect
234. C2×C4×D4C2×C4semidirect
235. C2×C4×D4C2×C4semidirect
236. C2×C4×D4C2×C4semidirect
237. C2×C4×D4C2×C4semidirect
238. C2×C4×D4C2×C4semidirect
239. C2×C4×D4C2×C4semidirect
240. C2×C4×D4C2×C4semidirect
241. C2×C4×D4C2×C4semidirect
242. C2×C4×D4C2×C4semidirect
243. C2×C4×D4C2×C4semidirect
244. C2×C4×D4C2×C4semidirect
245. C2×C4×D4C2×C4semidirect
260. C2×#117C2×C4semidirect
261. C2×#117C2×C4semidirect
262. C2×#117C2×C4semidirect
263. C2×#117C2×C4semidirect
264. C2×#117C2×C4semidirect
265. C2×#117C2×C4semidirect
268. C22×C4⋊C4C2×C4semidirect
269. C22×C4⋊C4C2×C4semidirect
271. C22×C22⋊C4C2×C4semidirect
272. C22×C22⋊C4C2×C4semidirect
277. C22×C42C2×C4semidirect
278. C22×C42C2×C4semidirect
279. C22×C42C2×C4semidirect
717. #99#41semidirect
1093. D4#410semidirect

Maximal subgroups

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

subgroupindex
C2×#34812
#341262
#225352
#225132
#224772
#224762
#224052
D4×#992
#214212
#214202
#207232
#207222
C4×#4102
C2×C4×#992