Finite Group Databasebeta

← #10574305

Subgroups — #10574305

Order 512.

7865 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#41C211yesmaximal, characteristic
2#60241C218yesmaximal, complemented
3#60240C2116yesmaximal, complemented
4#60239C218yesmaximal, complemented
5#60232C214yesmaximal, complemented
6#60231C218yesmaximal, complemented
7#60230C214yesmaximal, complemented
8#60144C212yesmaximal, complemented
9#60141C214yesmaximal, complemented
10C2×D4×M16C212yesmaximal, complemented
11#60125C211yesmaximal, characteristic, complemented
12#60123C211yesmaximal, characteristic, complemented
13#60064C212yesmaximal, complemented
14C2×#2879C212yesmaximal, complemented
15C23×#41C2212yes—
16C2×#568C2214yescomplemented
17C23×M16C2214yescomplemented
18D4×#41C414yes—
19D4×#41C418yes—
20D4×#41C414yes—
21D4×#41C2214yes—
22D4×#41C2218yes—
23D4×#41C2214yes—
24C2×#550C411yescharacteristic
25C2×D4×Q8C411yescharacteristic
26C2×#548C412yes—
27C2×#547C412yes—
28C2×#547C411yescharacteristic
29C2×#546C414yes—
30C2×#546C412yes—
31C2×D42C411yescharacteristic
32C2×D42C412yes—
33C2×#532C2212yes—
34C2×#532C2211yescharacteristic
35C2×#525C2214yes—
36C2×#525C2212yes—
37C2×C4×#41C2211yescharacteristic
38C22×C4×D4C2212yes—
39C22×C4×D4C2211yescharacteristic
40#2981C22116yescomplemented
41#2981C22116yescomplemented
42#2980C22116yescomplemented
43#2979C22116yescomplemented
44#2978C22132yescomplemented
45#2977C22132yescomplemented
46#2976C22132yescomplemented
47#2976C22132yescomplemented
48#2975C2218yescomplemented
49#2974C2218yescomplemented
50#2974C22116yescomplemented
51#2974C2218yescomplemented
52#2973C22116yescomplemented
53#2972C2218yescomplemented
54#2935C2218yescomplemented
55#2935C2218yescomplemented
56D4×M16C2214yes—
57D4×M16C22116yescomplemented
58D4×M16C2218yescomplemented
59D4×M16C2218yescomplemented
60D4×M16C2218yescomplemented
61D4×M16C22116yescomplemented
62D4×M16C2214yescomplemented
63D4×M16C2214yescomplemented
64D4×M16C2218yescomplemented
65D4×M16C2214yescomplemented
66#2933C22116yescomplemented
67#2933C22116yescomplemented
68#2932C2218yescomplemented
69#2931C2218yescomplemented
70#2930C22116yescomplemented
71#2929C22116yescomplemented
72C2×#436C2214yescomplemented
73C2×#435C2218yescomplemented
74C2×C8×D4C2214yescomplemented
75#2925C2218yescomplemented
76#2925C2218yescomplemented
77#2923C2218yescomplemented
78#2922C2218yescomplemented
79#2921C2214yescomplemented
80#2921C2214yescomplemented
81#2920C2214yescomplemented
82#2920C2214yescomplemented
83#2905C2212yescomplemented
84C2×#423C2212yescomplemented
85#2880C22116yescomplemented
86#2880C22116yescomplemented
87#2879C2211yescharacteristic
88#2879C2212yes—
89#2879C2211yescharacteristic
90#2879C2218yescomplemented
91#2879C2218yescomplemented
92#2879C2214yescomplemented
93#2879C22116yescomplemented
94C2×#408C22116yescomplemented
95C2×#407C2218yescomplemented
96C2×#407C2218yescomplemented
97C2×#407C2214yescomplemented
98#2873C2212yescomplemented
99C2×C4×M16C2212yescomplemented
100C22×#41—416no—
101C22×#41C2×C414yes—
102C22×#41C2×C412yes—
103C22×#41C2×C412yes—
104C22×#41C2×C418yes—
105C22×#41C2×C418yes—
106C22×#41C2311yescharacteristic
107C22×#41C2312yes—
108C22×#41C2318yes—
109C22×#41C2314yes—
110C22×#41C2318yes—
111C23×Q8C2×C412yes—
112C23×D4C2×C412yes—
113C23×D4C2×C414yes—
114C23×D4C2×C411yescharacteristic
115C23×D4C2×C412yes—
116C24×C4C2312yes—
117C24×C4C2314yes—
118#568—416no—
119C2×#131C23116yescomplemented
120C2×#131C23116yescomplemented
121C22×M16—416no—
122C22×M16C2312yes—
123C22×M16C2312yes—
124C22×M16C2314yes—
125C22×M16C2318yes—
126C22×M16C23116yes—
127C22×M16C2318yes—
128C22×M16C2318yescomplemented
129C22×M16C2318yescomplemented
130C22×M16C2318yescomplemented
131C23×C8C2318yescomplemented
132#550C2×C414yes—
133#550C2×C418yes—
134#550C2×C414yes—
135D4×Q8C2×C414yes—
136D4×Q8C2×C418yes—
137D4×Q8C2×C414yes—
138#548C2×C418yes—
139#548C2×C418yes—
140#548C2×C418yes—
141#548C2×C418yes—
142#547C2×C418yes—
143#547C2×C414yes—
144#547C2×C4116yes—
145#547C2×C418yes—
146#547C2×C418yes—
147#547C2×C414yes—
148#546C2×C4116yes—
149#546C2×C418yes—
150#546C2×C4116yes—
151#546C2×C4116yes—
152#546C2×C418yes—
153#546C2×C418yes—
154#546C2×C4116yes—
155#546C2×C418yes—
156D42C2×C414yes—
157D42C2×C418yes—
158D42C2×C418yes—
159D42C2×C4116yes—
160D42C2×C414yes—
161D42C2×C418yes—
162#532C2×C414yes—
163#532C2×C414yes—
164#532C2×C418yes—
165#532C2×C418yes—
166#532C2314yes—
167#532C2314yes—
168#532C2318yes—
169#532C2318yes—
170C2×C4⋊Q8C2×C411yescharacteristic
171C2×C4⋊Q8C2×C412yes—
172C2×#127C2×C411yescharacteristic
173C2×#127C2×C412yes—
174C2×#124C2×C412yes—
175C2×#124C2×C414yes—
176#525C2×C418yes—
177#525C2×C418yes—
178#525C2×C4116yes—
179#525C2×C4116yes—
180#525C2318yes—
181#525C2318yes—
182#525C23116yes—
183#525C23116yes—
184C2×#123C2×C414yes—
185C2×#123C2×C414yes—
186C2×#123C2×C414yes—
187C2×C22⋊Q8C2×C412yes—
188C2×C22⋊Q8C2×C414yes—
189C2×C22⋊Q8C2×C412yes—
190C2×C22⋊Q8C2×C414yes—
191C2×#121C2×C412yes—
192C2×#121C2×C414yes—
193C2×#121C2×C412yes—
194C2×#121C2×C414yes—
195C2×#121C2×C412yes—
196C2×#121C2×C412yes—
197C2×#121C2×C412yes—
198C2×#121C2×C412yes—
199C2×#121C2×C414yes—
200C2×#120C2×C414yes—
201C2×#120C2×C414yes—
202C2×#120C2×C414yes—
203C4×#41C2×C414yes—
204C4×#41C2×C414yes—
205C4×#41C2314yes—
206C4×#41C2314yes—
207C2×C4×Q8C2×C411yescharacteristic
208C2×C4×Q8C2×C411yescharacteristic
209C2×C4×D4C2×C411yescharacteristic
210C2×C4×D4C2×C412yes—
211C2×C4×D4C2×C412yes—
212C2×C4×D4C2×C414yes—
213C2×C4×D4C2×C411yescharacteristic
214C2×C4×D4C2×C412yes—
215C2×C4×D4C2×C412yes—
216C2×C4×D4C2×C412yes—
217C2×C4×D4C2×C414yes—
218C2×C4×D4C2×C414yes—
219C2×C4×D4C2×C414yes—
220C2×C4×D4C2×C418yes—
221C2×C4×D4C2×C412yes—
222C2×C4×D4C2×C411yescharacteristic
223C2×C4×D4C2×C412yes—
224C2×C4×D4C2×C411yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2314yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2314yes—
234C2×C4×D4C2318yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2314yes—
238C2×#117C2311yescharacteristic
239C2×#117C2312yes—
240C22×C4⋊C4C2×C411yescharacteristic
241C22×C4⋊C4C2×C412yes—
242C22×C22⋊C4C2×C412yes—
243C22×C22⋊C4C2×C414yes—
244C22×C42C2311yescharacteristic
245C22×C42C2312yes—
246#436C2318yes—
247#436C23116yescomplemented
248#436C2318yescomplemented
249#436C23132yescomplemented
250#436C23132yescomplemented
251#436C23116yescomplemented
252#436C23116yescomplemented
253#435C23116yes—
254#435C23116yescomplemented
255#435C23116yescomplemented
256#435C23116yescomplemented
257#435C23132yescomplemented
258#435C23132yescomplemented
259#435C23132yescomplemented
260#435C23132yescomplemented
261#435C23132yescomplemented
262#435C23132yescomplemented
263C8×D4C2318yes—
264C8×D4C23116yescomplemented
265C8×D4C2318yescomplemented
266C8×D4C23132yescomplemented
267C8×D4C23132yescomplemented
268C8×D4C23116yescomplemented
269C8×D4C23116yescomplemented
270#433C23116yescomplemented
271#433C23116yescomplemented
272#433C23132yescomplemented
273#432C2318yescomplemented
274#432C2318yescomplemented
275#432C2318yescomplemented
276#432C2318yescomplemented
277#431C2318yescomplemented
278#431C2318yescomplemented
279#431C2318yescomplemented
280#431C2318yescomplemented
281#424C2318yescomplemented
282#424C2318yescomplemented
283#423C2314yes—
284#423C2314yes—
285#423C2318yes—
286#423C2314yescomplemented
287#423C2314yescomplemented
288C2×C4⋊C8C2314yescomplemented
289C2×C4⋊C8C2314yescomplemented
290#408C2318yes—
291#408C23116yes—
292#408C2318yes—
293#408C23116yescomplemented
294#408C23116yescomplemented
295#408C23132yescomplemented
296#408C23132yescomplemented
297#408C23132yescomplemented
298#408C23132yescomplemented
299#407C2318yes—
300#407C2314yes—
301#407C2318yes—
302#407C2314yes—
303#407C23116yes—
304#407C2318yes—
305#407C23116yescomplemented
306#407C23116yescomplemented
307#407C2318yescomplemented
308#407C2318yescomplemented
309#407C23116yescomplemented
310#407C23116yescomplemented
311C2×C22⋊C8C23116yescomplemented
312C2×C22⋊C8C23116yescomplemented
313C2×C22⋊C8C2318yescomplemented
314C2×C22⋊C8C2318yescomplemented
315C2×C22⋊C8C23116yescomplemented
316C2×C22⋊C8C23116yescomplemented
317#405C23116yescomplemented
318C4×M16C2314yes—
319C4×M16C2314yes—
320C4×M16C2318yes—
321C4×M16C2314yescomplemented
322C4×M16C2314yescomplemented
323C2×#97C2314yescomplemented
324C2×C4×C8C2314yescomplemented
325C25C22×C412yes—
326C25C22×C414yes—
327C2×#41—216no—
328C2×#41—28no—
329C2×#41—416no—
330C2×#41—416no—
331C2×#41—48no—
332C2×#41—48no—
333C2×#41—432no—
334C2×#41—432no—
335C2×#41—416no—
336C2×#41—416no—
337C2×#41—416no—
338C2×#41—416no—
339C2×#41C22×C414yes—
340C2×#41C22×C418yes—
341C2×#41C22×C4116yes—
342C2×#41C22×C4116yes—
343C2×#41C22×C4116yes—
344C2×#41C22×C418yes—
345C2×#41C22×C418yes—
346C2×#41C22×C418yes—
347C2×#41C22×C418yes—
348C2×#41C2414yes—
349C2×#41C2418yes—
350C2×#41C24116yes—
351C22×Q8—48no—
352C22×Q8C22×C411yescharacteristic
353C22×Q8C22×C412yes—
354C22×Q8C22×C414yes—
355C22×Q8C22×C418yes—
356C22×Q8C22×C418yes—
357C22×D4—48no—
358C22×D4—44no—
359C22×D4—48no—
360C22×D4—416no—
361C22×D4C22×C411yescharacteristic
362C22×D4C22×C412yes—
363C22×D4C22×C411yescharacteristic
364C22×D4C22×C412yes—
365C22×D4C22×C414yes—
366C22×D4C22×C414yes—
367C22×D4C22×C412yes—
368C22×D4C22×C412yes—
369C22×D4C22×C414yes—
370C22×D4C22×C411yescharacteristic
371C22×D4C22×C412yes—
372C22×D4C22×C412yes—
373C22×D4C22×C414yes—
374C22×D4C22×C414yes—
375C22×D4C22×C418yes—
376C22×D4C22×C414yes—
377C22×D4C22×C414yes—
378C22×D4C22×C414yes—
379C22×D4C22×C418yes—
380C22×D4C22×C418yes—
381C22×D4C22×C4116yes—
382C22×D4C22×C4116yes—
383C22×D4C22×C414yes—
384C22×D4C22×C412yes—
385C23×C4—216no—
386C23×C4—416no—
387C23×C4C22×C412yes—
388C23×C4C22×C412yes—
389C23×C4C22×C412yes—
390C23×C4C22×C414yes—
391C23×C4C22×C414yes—
392C23×C4C22×C414yes—
393C23×C4C22×C412yes—
394C23×C4C22×C411yescharacteristic
395C23×C4C22×C414yes—
396C23×C4C22×C414yes—
397C23×C4C22×C418yes—
398C23×C4C22×C418yes—
399C23×C4C22×C412yes—
400C23×C4C22×C411yescharacteristic
401C23×C4C2412yes—
402C23×C4C2412yes—
403C23×C4C2412yes—
404C23×C4C2414yes—
405C23×C4C2414yes—
406C23×C4C2414yes—
407C23×C4C2418yes—
408C23×C4C2418yes—
409C23×C4C2411yescharacteristic
410#131—432no—
411#131—432no—
412C2×M16—28no—
413C2×M16—216no—
414C2×M16—28no—
415C2×M16—416no—
416C2×M16—416no—
417C2×M16—416no—
418C2×M16—416no—
419C2×M16—416no—
420C2×M16—432no—
421C2×M16C2414yes—
422C2×M16C2414yes—
423C2×M16C2418yes—
424C2×M16C2414yes—
425C2×M16C2418yes—
426C2×M16C2414yes—
427C2×M16C24116yes—
428C2×M16C24116yes—
429C2×M16C24132yes—
430C22×C8—416no—
431C22×C8C2414yes—
432C22×C8C2418yes—
433C22×C8C2414yes—
434C22×C8C24116yes—
435C22×C8C24116yes—
436C22×C8C24132yes—
437C4⋊Q8C22×C414yes—
438C4⋊Q8C22×C414yes—
439C4⋊Q8C22×C418yes—
440C4⋊Q8C22×C418yes—
441#127C22×C414yes—
442#127C22×C418yes—
443#127C22×C414yes—
444#127C22×C418yes—
445#124C22×C418yes—
446#124C22×C418yes—
447#124C22×C4116yes—
448#124C22×C4116yes—
449#123C22×C4116yes—
450#123C22×C4116yes—
451#123C22×C4116yes—
452#123C22×C4116yes—
453#123C22×C4116yes—
454#123C22×C4116yes—
455C22⋊Q8C22×C418yes—
456C22⋊Q8C22×C418yes—
457C22⋊Q8C22×C4116yes—
458C22⋊Q8C22×C4116yes—
459C22⋊Q8C22×C418yes—
460C22⋊Q8C22×C418yes—
461C22⋊Q8C22×C4116yes—
462C22⋊Q8C22×C4116yes—
463#121C22×C418yes—
464#121C22×C418yes—
465#121C22×C4116yes—
466#121C22×C4116yes—
467#121C22×C418yes—
468#121C22×C418yes—
469#121C22×C4116yes—
470#121C22×C4116yes—
471#121C22×C418yes—
472#121C22×C418yes—
473#121C22×C418yes—
474#121C22×C418yes—
475#121C22×C418yes—
476#121C22×C418yes—
477#121C22×C418yes—
478#121C22×C418yes—
479#121C22×C4116yes—
480#121C22×C4116yes—
481#120C22×C4116yes—
482#120C22×C4116yes—
483#120C22×C4116yes—
484#120C22×C4116yes—
485#120C22×C4116yes—
486#120C22×C4116yes—
487C4×Q8C22×C414yes—
488C4×Q8C22×C414yes—
489C4×Q8C22×C414yes—
490C4×Q8C22×C414yes—
491C4×D4C22×C412yes—
492C4×D4C22×C411yescharacteristic
493C4×D4C22×C411yescharacteristic
494C4×D4C22×C414yes—
495C4×D4C22×C418yes—
496C4×D4C22×C414yes—
497C4×D4C22×C418yes—
498C4×D4C22×C412yes—
499C4×D4C22×C414yes—
500C4×D4C22×C412yes—
501C4×D4C22×C414yes—
502C4×D4C22×C414yes—
503C4×D4C22×C412yes—
504C4×D4C22×C412yes—
505C4×D4C22×C418yes—
506C4×D4C22×C414yes—
507C4×D4C22×C414yes—
508C4×D4C22×C414yes—
509C4×D4C22×C414yes—
510C4×D4C22×C414yes—
511C4×D4C22×C414yes—
512C4×D4C22×C418yes—
513C4×D4C22×C418yes—
514C4×D4C22×C418yes—
515C4×D4C22×C418yes—
516C4×D4C22×C412yes—
517C4×D4C22×C412yes—
518C4×D4C22×C414yes—
519C4×D4C22×C414yes—
520C4×D4C22×C414yes—
521C4×D4C22×C418yes—
522C4×D4C22×C418yes—
523C4×D4C22×C414yes—
524C4×D4C22×C418yes—
525C4×D4C22×C414yes—
526C4×D4C22×C418yes—
527C4×D4C22×C414yes—
528C4×D4C22×C418yes—
529C4×D4C22×C414yes—
530C4×D4C22×C4116yes—
531C4×D4C22×C418yes—
532C4×D4C2411yescharacteristic
533C4×D4C2412yes—
534C4×D4C2411yescharacteristic
535C4×D4C2414yes—
536C4×D4C2418yes—
537C4×D4C2414yes—
538C4×D4C2418yes—
539C4×D4C2412yes—
540C4×D4C2414yes—
541C4×D4C2412yes—
542C4×D4C2414yes—
543C4×D4C24116yes—
544C4×D4C2418yes—
545#117C22×C418yes—
546#117C22×C414yes—
547#117C2414yes—
548#117C2418yes—
549C2×C4⋊C4C22×C411yescharacteristic
550C2×C4⋊C4C22×C411yescharacteristic
551C2×C4⋊C4C22×C412yes—
552C2×C4⋊C4C22×C412yes—
553C2×C4⋊C4C22×C414yes—
554C2×C4⋊C4C22×C412yes—
555C2×C4⋊C4C22×C412yes—
556C2×C4⋊C4C22×C414yes—
557C2×C4⋊C4C22×C414yes—
558C2×C4⋊C4C22×C414yes—
559C2×C4⋊C4C22×C418yes—
560C2×C4⋊C4C22×C412yes—
561C2×C4⋊C4C22×C412yes—
562C2×C4⋊C4C22×C411yescharacteristic
563C2×C4⋊C4C22×C411yescharacteristic
564C2×C4⋊C4C22×C414yes—
565C2×C4⋊C4C22×C412yes—
566C2×C22⋊C4C22×C412yes—
567C2×C22⋊C4C22×C412yes—
568C2×C22⋊C4C22×C414yes—
569C2×C22⋊C4C22×C412yes—
570C2×C22⋊C4C22×C414yes—
571C2×C22⋊C4C22×C412yes—
572C2×C22⋊C4C22×C414yes—
573C2×C22⋊C4C22×C414yes—
574C2×C22⋊C4C22×C414yes—
575C2×C22⋊C4C22×C414yes—
576C2×C22⋊C4C22×C414yes—
577C2×C22⋊C4C22×C418yes—
578C2×C22⋊C4C22×C418yes—
579C2×C22⋊C4C22×C418yes—
580C2×C22⋊C4C22×C418yes—
581C2×C22⋊C4C22×C412yes—
582C2×C22⋊C4C22×C412yes—
583C2×C22⋊C4C22×C412yes—
584C2×C22⋊C4C22×C414yes—
585C2×C22⋊C4C22×C414yes—
586C2×C22⋊C4C22×C414yes—
587C2×C42C22×C412yes—
588C2×C42C22×C411yescharacteristic
589C2×C42C22×C412yes—
590C2×C42C22×C411yescharacteristic
591C2×C42C22×C414yes—
592C2×C42C22×C414yes—
593C2×C42C22×C412yes—
594C2×C42C22×C412yes—
595C2×C42C2412yes—
596C2×C42C2411yescharacteristic
597C2×C42C2411yescharacteristic
598C2×C42C2412yes—
599C2×C42C2412yes—
600C2×C42C2414yes—
601C2×C42C2414yes—
602C4⋊C8C2418yes—
603C4⋊C8C2418yes—
604C4⋊C8C2418yes—
605C4⋊C8C2418yes—
606C4⋊C8C24116yes—
607C4⋊C8C24116yes—
608C22⋊C8C24116yes—
609C22⋊C8C24116yes—
610C22⋊C8C2418yes—
611C22⋊C8C24116yes—
612C22⋊C8C2418yes—
613C22⋊C8C24116yes—
614C22⋊C8C2418yes—
615C22⋊C8C2418yes—
616C22⋊C8C24132yes—
617C22⋊C8C24132yes—
618C22⋊C8C24116yes—
619C22⋊C8C24116yes—
620#97C2418yes—
621#97C2418yes—
622#97C24116yes—
623C4×C8C2418yes—
624C4×C8C2418yes—
625C4×C8C24116yes—
626C24—28no—
627C24—48no—
628C24—44no—
629C24—48no—
630C24—82no—
631C24—84no—
632C24C23×C412yes—
633C24C23×C414yes—
634C24C23×C412yes—
635C24C23×C414yes—
636C24C23×C414yes—
637C24C23×C418yes—
638C24C23×C412yes—
639C24C23×C418yes—
640C24C23×C411yescharacteristic
641#41—216no—
642#41—232no—
643#41—216no—
644#41—216no—
645#41—28no—
646#41—28no—
647#41—432no—
648#41—416no—
649#41—416no—
650#41—432no—
651#41—432no—
652#41—416no—
653#41—416no—
654#41—416no—
655#41—416no—
656C2×Q8—24no—
657C2×Q8—28no—
658C2×Q8—48no—
659C2×Q8—416no—
660C2×Q8—416no—
661C2×Q8C23×C414yes—
662C2×Q8C23×C418yes—
663C2×Q8C23×C4116yes—
664C2×D4—28no—
665C2×D4—216no—
666C2×D4—24no—
667C2×D4—28no—
668C2×D4—216no—
669C2×D4—24no—
670C2×D4—28no—
671C2×D4—42no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—48no—
675C2×D4—416no—
676C2×D4—416no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—416no—
682C2×D4—44no—
683C2×D4—48no—
684C2×D4—432no—
685C2×D4—432no—
686C2×D4—84no—
687C2×D4—82no—
688C2×D4C23×C412yes—
689C2×D4C23×C411yescharacteristic
690C2×D4C23×C418yes—
691C2×D4C23×C414yes—
692C2×D4C23×C414yes—
693C2×D4C23×C418yes—
694C2×D4C23×C412yes—
695C2×D4C23×C414yes—
696C2×D4C23×C4116yes—
697C2×D4C23×C418yes—
698C2×D4C23×C414yes—
699C2×D4C23×C418yes—
700C2×D4C23×C412yes—
701C2×D4C23×C414yes—
702C2×D4C23×C4116yes—
703C2×D4C23×C418yes—
704C2×D4C23×C4116yes—
705C2×D4C23×C4116yes—
706C2×D4C23×C4116yes—
707C2×D4C23×C411yescharacteristic
708C22×C4—28no—
709C22×C4—28no—
710C22×C4—28no—
711C22×C4—216no—
712C22×C4—216no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—28no—
716C22×C4—28no—
717C22×C4—28no—
718C22×C4—28no—
719C22×C4—216no—
720C22×C4—28no—
721C22×C4—416no—
722C22×C4—416no—
723C22×C4—416no—
724C22×C4—416no—
725C22×C4—42no—
726C22×C4—44no—
727C22×C4—48no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—81no—
731C22×C4—82no—
732C22×C4C23×C411yescharacteristic
733C22×C4C23×C412yes—
734C22×C4C23×C414yes—
735C22×C4C23×C414yes—
736C22×C4C23×C412yes—
737C22×C4C23×C412yes—
738C22×C4C23×C412yes—
739C22×C4C23×C414yes—
740C22×C4C23×C414yes—
741C22×C4C23×C414yes—
742C22×C4C23×C412yes—
743C22×C4C23×C412yes—
744C22×C4C23×C414yes—
745C22×C4C23×C418yes—
746C22×C4C23×C414yes—
747C22×C4C23×C414yes—
748C22×C4C23×C414yes—
749C22×C4C23×C414yes—
750C22×C4C23×C411yescharacteristic
751C22×C4C23×C412yes—
752C22×C4C23×C411yescharacteristic
753C22×C4C23×C412yes—
754C22×C4C23×C411yescharacteristic
755C22×C4C23×C414yes—
756C22×C4C23×C414yes—
757C22×C4C23×C412yes—
758C22×C4C23×C412yes—
759C22×C4C23×C414yes—
760C22×C4C23×C412yes—
761C22×C4C23×C418yes—
762C22×C4C23×C418yes—
763C22×C4C23×C418yes—
764C22×C4C23×C418yes—
765C22×C4C23×C418yes—
766C22×C4C23×C418yes—
767C22×C4C23×C411yescharacteristic
768C22×C4C23×C412yes—
769C22×C4H(5,𝔽2)18yes—
770C22×C4C2514yes—
771C22×C4C2512yes—
772C22×C4C2514yes—
773C22×C4C2518yes—
774C22×C4C2512yes—
775C22×C4C2511yescharacteristic
776C22×C4C2512yes—
777M16—28no—
778M16—28no—
779M16—216no—
780M16—28no—
781M16—216no—
782M16—28no—
783M16—416no—
784M16—416no—
785M16—432no—
786C2×C8—28no—
787C2×C8—216no—
788C2×C8—28no—
789C2×C8—416no—
790C2×C8—416no—
791C2×C8—432no—
792C2×C8C2518yes—
793C2×C8C2518yes—
794C2×C8C25116yes—
795C4⋊C4C23×C412yes—
796C4⋊C4C23×C411yescharacteristic
797C4⋊C4C23×C411yescharacteristic
798C4⋊C4C23×C412yes—
799C4⋊C4C23×C414yes—
800C4⋊C4C23×C412yes—
801C4⋊C4C23×C414yes—
802C4⋊C4C23×C414yes—
803C4⋊C4C23×C418yes—
804C4⋊C4C23×C414yes—
805C4⋊C4C23×C418yes—
806C4⋊C4C23×C418yes—
807C4⋊C4C23×C418yes—
808C4⋊C4C23×C414yes—
809C4⋊C4C23×C414yes—
810C4⋊C4C23×C4116yes—
811C4⋊C4C23×C418yes—
812C22⋊C4C23×C412yes—
813C22⋊C4C23×C412yes—
814C22⋊C4C23×C412yes—
815C22⋊C4C23×C412yes—
816C22⋊C4C23×C414yes—
817C22⋊C4C23×C418yes—
818C22⋊C4C23×C414yes—
819C22⋊C4C23×C418yes—
820C22⋊C4C23×C414yes—
821C22⋊C4C23×C418yes—
822C22⋊C4C23×C414yes—
823C22⋊C4C23×C418yes—
824C22⋊C4C23×C414yes—
825C22⋊C4C23×C418yes—
826C22⋊C4C23×C414yes—
827C22⋊C4C23×C418yes—
828C22⋊C4C23×C418yes—
829C22⋊C4C23×C418yes—
830C22⋊C4C23×C418yes—
831C22⋊C4C23×C4116yes—
832C22⋊C4C23×C4116yes—
833C22⋊C4C23×C4116yes—
834C42C23×C411yescharacteristic
835C42C23×C411yescharacteristic
836C42C23×C414yes—
837C42C23×C412yes—
838C42C23×C414yes—
839C42C23×C414yes—
840C42C23×C412yes—
841C42C23×C412yes—
842C42C23×C414yes—
843C42C23×C412yes—
844C42C23×C414yes—
845C42C23×C412yes—
846C42C2511yescharacteristic
847C42C2512yes—
848C42C2514yes—
849C42C2511yescharacteristic
850C23—24no—
851C23—28no—
852C23—24no—
853C23—24no—
854C23—28no—
855C23—28no—
856C23—24no—
857C23—28no—
858C23—216no—
859C23—41no—
860C23—42no—
861C23—41no—
862C23—42no—
863C23—42no—
864C23—44no—
865C23—48no—
866C23—48no—
867C23—42no—
868C23—44no—
869C23—44no—
870C23—48no—
871C23—42no—
872C23—44no—
873C23—44no—
874C23—48no—
875C23—48no—
876C23—816no—
877C23—832no—
878C23#51814yes—
879C23C24×C412yes—
880C23C24×C414yes—
881C23C24×C418yes—
882C23C24×C414yes—
883C23C24×C412yes—
884C23C24×C411yescharacteristic
885C23C24×C412yes—
886Q8—28no—
887Q8—216no—
888Q8—416no—
889D4—216no—
890D4—232no—
891D4—24no—
892D4—28no—
893D4—216no—
894D4—28no—
895D4—216no—
896D4—22no—
897D4—24no—
898D4—28no—
899D4—42no—
900D4—44no—
901D4—44no—
902D4—48no—
903D4—416no—
904D4—416no—
905D4—416no—
906D4—416no—
907D4—48no—
908D4#56814yescomplemented
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—28no—
912C2×C4—28no—
913C2×C4—24no—
914C2×C4—28no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—216no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—28no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—28no—
924C2×C4—28no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—28no—
928C2×C4—28no—
929C2×C4—216no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—28no—
933C2×C4—48no—
934C2×C4—48no—
935C2×C4—48no—
936C2×C4—48no—
937C2×C4—48no—
938C2×C4—48no—
939C2×C4—42no—
940C2×C4—44no—
941C2×C4—41no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—44no—
947C2×C4—44no—
948C2×C4—41no—
949C2×C4—42no—
950C2×C4#51814yes—
951C2×C4#51818yes—
952C2×C4C24×C411yescharacteristic
953C2×C4C24×C411yescharacteristic
954C2×C4C24×C411yescharacteristic
955C2×C4C24×C414yes—
956C2×C4C24×C414yes—
957C2×C4C24×C412yes—
958C2×C4C24×C414yes—
959C2×C4C24×C412yes—
960C2×C4C24×C412yes—
961C2×C4C24×C412yes—
962C2×C4C24×C414yes—
963C2×C4C24×C418yes—
964C2×C4C24×C411yescharacteristic
965C2×C4C24×C412yes—
966C2×C4C24×C411yescharacteristic
967C2×C4C2×H(5,𝔽2)14yes—
968C2×C4C2×H(5,𝔽2)14yes—
969C2×C4C2×H(5,𝔽2)14yes—
970C2×C4C2611yescharacteristic
971C8—28no—
972C8—216no—
973C8—28no—
974C22—21no—
975C22—22no—
976C22—21no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—24no—
981C22—22no—
982C22—24no—
983C22—28no—
984C22—24no—
985C22—24no—
986C22—28no—
987C22—22no—
988C22—22no—
989C22—24no—
990C22—24no—
991C22—28no—
992C22—44no—
993C22—416no—
994C22—48no—
995C22—48no—
996C22—84no—
997C22—88no—
998C22—816no—
999C22—88no—
1000C22—816no—
1001C22C2×#51812yes—
1002C22C2×#51814yes—
1003C22C2×#56814yes—
1004C22C25×C411yescharacteristic
1005C4—21no—
1006C4—22no—
1007C4—24no—
1008C4—21no—
1009C4—21no—
1010C4—22no—
1011C4—24no—
1012C4—22no—
1013C4—22no—
1014C4—24no—
1015C4—24no—
1016C4—28no—
1017C4C2×#51812yes—
1018C4C2×#51814yes—
1019C4C2×#56812yes—
1020C4C22×H(5,𝔽2)12yes—
1021C2—22no—
1022C2—24no—
1023C2—24no—
1024C2—44no—
1025C2—44no—
1026C2—42no—
1027C2—48no—
1028C2C22×#51811yescharacteristic
1029C2C22×#56811yescharacteristic
1030C2#6307611yescharacteristic
subgroupG/H
center, Frattini, cosocleC2×C4C26
commutator, socleC22C25×C4
prime radicalC2×D4×#41C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60241C2semidirect
3. #60240C2semidirect
4. #60239C2semidirect
5. #60232C2semidirect
6. #60231C2semidirect
7. #60230C2semidirect
8. #60144C2semidirect
9. #60141C2semidirect
10. C2×D4×M16C2semidirect
11. #60125C2semidirect
12. #60123C2semidirect
13. #60064C2semidirect
14. C2×#2879C2semidirect
16. C2×#568C22semidirect
17. C23×M16C22semidirect
40. #2981C22semidirect
41. #2981C22semidirect
42. #2980C22semidirect
43. #2979C22semidirect
44. #2978C22semidirect
45. #2977C22semidirect
46. #2976C22semidirect
47. #2976C22semidirect
48. #2975C22semidirect
49. #2974C22semidirect
50. #2974C22semidirect
51. #2974C22semidirect
52. #2973C22semidirect
53. #2972C22semidirect
54. #2935C22semidirect
55. #2935C22semidirect
57. D4×M16C22semidirect
58. D4×M16C22semidirect
59. D4×M16C22semidirect
60. D4×M16C22semidirect
61. D4×M16C22semidirect
62. D4×M16C22semidirect
63. D4×M16C22semidirect
64. D4×M16C22semidirect
65. D4×M16C22semidirect
66. #2933C22semidirect
67. #2933C22semidirect
68. #2932C22semidirect
69. #2931C22semidirect
70. #2930C22semidirect
71. #2929C22semidirect
72. C2×#436C22semidirect
73. C2×#435C22semidirect
74. C2×C8×D4C22semidirect
75. #2925C22semidirect
76. #2925C22semidirect
77. #2923C22semidirect
78. #2922C22semidirect
79. #2921C22semidirect
80. #2921C22semidirect
81. #2920C22semidirect
82. #2920C22semidirect
83. #2905C22semidirect
84. C2×#423C22semidirect
85. #2880C22semidirect
86. #2880C22semidirect
90. #2879C22semidirect
91. #2879C22semidirect
92. #2879C22semidirect
93. #2879C22semidirect
94. C2×#408C22semidirect
95. C2×#407C22semidirect
96. C2×#407C22semidirect
97. C2×#407C22semidirect
98. #2873C22semidirect
99. C2×C4×M16C22semidirect
119. C2×#131C23semidirect
120. C2×#131C23semidirect
128. C22×M16C23semidirect
129. C22×M16C23semidirect
130. C22×M16C23semidirect
131. C23×C8C23semidirect
247. #436C23semidirect
248. #436C23semidirect
249. #436C23semidirect
250. #436C23semidirect
251. #436C23semidirect
252. #436C23semidirect
254. #435C23semidirect
255. #435C23semidirect
256. #435C23semidirect
257. #435C23semidirect
258. #435C23semidirect
259. #435C23semidirect
260. #435C23semidirect
261. #435C23semidirect
262. #435C23semidirect
264. C8×D4C23semidirect
265. C8×D4C23semidirect
266. C8×D4C23semidirect
267. C8×D4C23semidirect
268. C8×D4C23semidirect
269. C8×D4C23semidirect
270. #433C23semidirect
271. #433C23semidirect
272. #433C23semidirect
273. #432C23semidirect
274. #432C23semidirect
275. #432C23semidirect
276. #432C23semidirect
277. #431C23semidirect
278. #431C23semidirect
279. #431C23semidirect
280. #431C23semidirect
281. #424C23semidirect
282. #424C23semidirect
286. #423C23semidirect
287. #423C23semidirect
288. C2×C4⋊C8C23semidirect
289. C2×C4⋊C8C23semidirect
293. #408C23semidirect
294. #408C23semidirect
295. #408C23semidirect
296. #408C23semidirect
297. #408C23semidirect
298. #408C23semidirect
305. #407C23semidirect
306. #407C23semidirect
307. #407C23semidirect
308. #407C23semidirect
309. #407C23semidirect
310. #407C23semidirect
311. C2×C22⋊C8C23semidirect
312. C2×C22⋊C8C23semidirect
313. C2×C22⋊C8C23semidirect
314. C2×C22⋊C8C23semidirect
315. C2×C22⋊C8C23semidirect
316. C2×C22⋊C8C23semidirect
317. #405C23semidirect
321. C4×M16C23semidirect
322. C4×M16C23semidirect
323. C2×#97C23semidirect
324. C2×C4×C8C23semidirect
908. D4#568semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#412
#602412
#602402
#602392
#602322
#602312
#602302
#601442
#601412
C2×D4×M162
#601252
#601232
#600642
C2×#28792