Finite Group Databasebeta

← #516503

Subgroups — #516503

Order 512.

2296 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#126C211yesmaximal, characteristic
2#14704C212yesmaximal, complemented
3#14701C212yesmaximal
4#14298C212yesmaximal, complemented
5#14291C212yesmaximal
6#14146C212yesmaximal
7#14146C212yesmaximal
8#14144C212yesmaximal, complemented
9#14144C212yesmaximal, complemented
10#13930C211yesmaximal, characteristic, complemented
11#13928C211yesmaximal, characteristic, complemented
12#13915C211yesmaximal, characteristic
13#13913C211yesmaximal, characteristic
14#13893C211yesmaximal, characteristic, complemented
15#13891C211yesmaximal, characteristic
16#13889C211yesmaximal, characteristic, complemented
17#13887C211yesmaximal, characteristic
18#13788C211yesmaximal, characteristic
19#13787C211yesmaximal, characteristic, complemented
20#13781C211yesmaximal, characteristic, complemented
21#13780C211yesmaximal, characteristic
22C4×#382C211yesmaximal, characteristic, complemented
23C42×C4⋊C4C211yesmaximal, characteristic, complemented
24C22×#126C2211yescharacteristic
25C4×#126C4116yescomplemented
26C2×#388C2212yes—
27C2×#388C2212yes—
28C2×#388C2212yes—
29C2×#388C2211yescharacteristic
30C2×#388C2211yescharacteristic
31C2×#388C2211yescharacteristic
32C2×#387C2212yes—
33C2×#387C2212yes—
34C2×#387C2212yes—
35C2×#387C2211yescharacteristic
36C2×#387C2211yescharacteristic
37C2×#387C2211yescharacteristic
38C2×#383C2211yescharacteristic
39C2×#383C2211yescharacteristic
40C2×#382C2211yescharacteristic
41C2×#382C2212yes—
42C2×#381C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2212yes—
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2212yes—
48C2×C4×C4⋊C4C2212yes—
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C43C2212yes—
56C2×C43C2211yescharacteristic
57#1444C2212yes—
58#1444C2212yes—
59#1444C2212yes—
60#1444C2212yes—
61#1442C2212yes—
62#1442C2212yes—
63#1442C2212yes—
64#1442C2212yes—
65#1441C2212yes—
66#1441C2212yes—
67#1441C2212yes—
68#1441C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1437C2212yes—
74#1437C2212yes—
75#1437C2212yes—
76#1437C2212yes—
77#1437C2212yes—
78#1436C2212yes—
79#1436C2212yes—
80#1436C2212yes—
81#1436C2212yes—
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4⋊#95C2211yescharacteristic
96C4⋊#95C2211yescharacteristic
97#1434C2212yes—
98#1434C2211yescharacteristic
99#1434C2211yescharacteristic
100#1434C2211yescharacteristic
101#1434C2212yes—
102#1434C2212yes—
103#1434C2212yes—
104#1434C2212yes—
105#1434C2211yescharacteristic
106#1434C2211yescharacteristic
107#1434C2212yes—
108#1434C2211yescharacteristic
109#1434C2211yescharacteristic
110#1434C2211yescharacteristic
111#1434C2211yescharacteristic
112#1434C2211yescharacteristic
113#1434C2212yes—
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2211yescharacteristic
116C4×#95C2212yes—
117C4×#95C2212yes—
118C4×#95C2211yescharacteristic
119C4×#95C2211yescharacteristic
120C4×#95C2211yescharacteristic
121C4×#95C2211yescharacteristic
122C4×#95C2211yescharacteristic
123C4×#95C2211yescharacteristic
124C24×C4C2311yescharacteristic
125C2×#126—28no—
126C2×#126C2×C418yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169#388—28no—
170#388—44no—
171#388—44no—
172#388C2×C418yes—
173#388C2×C418yes—
174#388C2×C418yes—
175#387—28no—
176#387—44no—
177#387—44no—
178#387C2×C418yes—
179#387C2×C418yes—
180#387C2×C418yes—
181#383—24no—
182#383C2×C418yes—
183#382—28no—
184#382—24no—
185#381—24no—
186#380—24no—
187C4×C4⋊C4—28no—
188C4×C4⋊C4—24no—
189C4×C4⋊C4—24no—
190C4×C4⋊C4—28no—
191C4×C4⋊C4—44no—
192C4×C4⋊C4C2×C418yes—
193C4×C4⋊C4C2×C418yes—
194C4×C4⋊C4C2×C418yes—
195C4×C22⋊C4C2×C418yes—
196C4×C22⋊C4C2×C418yes—
197C4×C22⋊C4C2×C418yes—
198C2×#95C2311yescharacteristic
199C2×#95C2311yescharacteristic
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206C2×#95C2311yescharacteristic
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2311yescharacteristic
240C2×#95C2311yescharacteristic
241C2×#95C2311yescharacteristic
242C2×#95C2311yescharacteristic
243C2×#95C2311yescharacteristic
244C2×#95C2311yescharacteristic
245C2×#95C2311yescharacteristic
246C2×#95C2311yescharacteristic
247C2×#95C2311yescharacteristic
248C2×#95C2311yescharacteristic
249C2×#95C2311yescharacteristic
250C2×#95C2311yescharacteristic
251C2×#95C2311yescharacteristic
252C2×#95C2311yescharacteristic
253C2×#95C2312yes—
254C43—44no—
255C43C2×C418yes—
256C25C2411yescharacteristic
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4C22×C414yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284#126—232no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4C22×C414yes—
318C2×C4⋊C4C22×C414yes—
319C2×C4⋊C4C22×C414yes—
320C2×C4⋊C4C22×C414yes—
321C2×C4⋊C4C22×C414yes—
322C2×C4⋊C4C22×C414yes—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4C22×C414yes—
344C2×C22⋊C4C22×C414yes—
345C2×C22⋊C4C22×C414yes—
346C2×C22⋊C4C22×C414yes—
347C2×C22⋊C4C22×C414yes—
348C2×C22⋊C4C22×C414yes—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—24no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42C22×C414yes—
387C2×C42C22×C414yes—
388C2×C42C22×C414yes—
389C2×C42C22×C414yes—
390C2×C42C22×C414yes—
391C2×C42C22×C414yes—
392C2×C42C22×C414yes—
393C2×C42C22×C414yes—
394C2×C42C22×C414yes—
395C2×C42C22×C414yes—
396C2×C42#4118yes—
397#95—24no—
398#95—24no—
399#95—22no—
400#95—22no—
401#95—24no—
402#95—22no—
403#95—24no—
404#95—22no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—22no—
411#95—24no—
412#95—24no—
413#95—22no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95C22×C414yes—
439#95C22×C414yes—
440#95C22×C414yes—
441#95C22×C414yes—
442#95C22×C414yes—
443#95C22×C414yes—
444#95C22×C414yes—
445#95C22×C414yes—
446#95C22×C414yes—
447#95C22×C414yes—
448#95C22×C414yes—
449#95C22×C414yes—
450#95#4114yes—
451#95#4114yes—
452#95#4118yes—
453C24—22no—
454C24—22no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—22no—
462C24—22no—
463C24C23×C412yes—
464C24C2511yescharacteristic
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—28no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—84no—
571C22×C4—84no—
572C22×C4C23×C412yes—
573C22×C4C23×C412yes—
574C22×C4C23×C412yes—
575C22×C4C23×C412yes—
576C22×C4C23×C412yes—
577C22×C4C23×C412yes—
578C22×C4C23×C412yes—
579C22×C4C23×C412yes—
580C22×C4C23×C412yes—
581C22×C4C23×C412yes—
582C22×C4C23×C412yes—
583C22×C4C23×C412yes—
584C22×C4C23×C412yes—
585C22×C4C23×C412yes—
586C22×C4C2×#4114yes—
587C22×C4C2×#4114yes—
588C22×C4C2×#4114yes—
589C22×C4C2×#4114yes—
590C22×C4C2×#4114yes—
591C22×C4C2×#4114yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4114yes—
596C22×C4H(5,𝔽2)12yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C42−1+412yes—
599C22×C42−1+412yes—
600C4⋊C4—216no—
601C4⋊C4—216no—
602C4⋊C4—28no—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—84no—
611C4⋊C4—84no—
612C4⋊C4—84no—
613C4⋊C4—84no—
614C22⋊C4—28no—
615C22⋊C4—28no—
616C22⋊C4—28no—
617C22⋊C4—28no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—84no—
621C22⋊C4—84no—
622C22⋊C4—84no—
623C22⋊C4—84no—
624C42—28no—
625C42—28no—
626C42—28no—
627C42—28no—
628C42—28no—
629C42—44no—
630C42—44no—
631C42—44no—
632C42—44no—
633C42—48no—
634C42—48no—
635C42—48no—
636C42—48no—
637C42—48no—
638C42—48no—
639C42—84no—
640C42—84no—
641C42#117116yes—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—41no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—41no—
664C23—41no—
665C23C24×C411yescharacteristic
666C23C22×#4112yes—
667C23C22×#4112yes—
668C23C22×#4111yescharacteristic
669C23C22×#4111yescharacteristic
670C23C2×H(5,𝔽2)11yescharacteristic
671C23C2×H(5,𝔽2)11yescharacteristic
672C23C2×2−1+411yescharacteristic
673C23C2×2−1+411yescharacteristic
674C23#58512yes—
675C23#58512yes—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—88no—
800C2×C4C2×#11714yes—
801C2×C4C2×#11714yes—
802C2×C4C2×#11714yes—
803C2×C4C4×#4114yes—
804C2×C4C4×#4114yes—
805C2×C4#52014yes—
806C2×C4#52014yes—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22C22×#11711yescharacteristic
819C22C2×C4×#4111yescharacteristic
820C22C2×C4×#4111yescharacteristic
821C22C2×#52011yescharacteristic
822C22C2×#52011yescharacteristic
823C22#342811yescharacteristic
824C22#342811yescharacteristic
825C22#344412yes—
826C22#344412yes—
827C22#346012yes—
828C22#346012yes—
829C22#346112yes—
830C22#346112yes—
831C22#351312yes—
832C22#351412yes—
833C22#351512yes—
834C22#351612yes—
835C22#351911yescharacteristic
836C22#352011yescharacteristic
837C22#352112yes—
838C22#352112yes—
839C22#352211yescharacteristic
840C22#352311yescharacteristic
841C4—24no—
842C4—24no—
843C4—24no—
844C4—24no—
845C4—24no—
846C4—24no—
847C4—24no—
848C4—42no—
849C4—42no—
850C4—44no—
851C4—44no—
852C4—44no—
853C4—44no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4—82no—
863C2—82no—
864C2#3402611yescharacteristic
865C2#3406011yescharacteristic
866C2#3406011yescharacteristic
867C2#3422911yescharacteristic
868C2#3423011yescharacteristic
869C2#3424311yescharacteristic
870C2#3424711yescharacteristic
871C2#3513312yes—
872C2#3513412yes—
873C2#3514012yes—
874C2#3514112yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14704C2semidirect
4. #14298C2semidirect
8. #14144C2semidirect
9. #14144C2semidirect
10. #13930C2semidirect
11. #13928C2semidirect
14. #13893C2semidirect
16. #13889C2semidirect
19. #13787C2semidirect
20. #13781C2semidirect
22. C4×#382C2semidirect
23. C42×C4⋊C4C2semidirect
25. C4×#126C4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1262
#147042
#147012
#142982
#142912
#141462
#141442
#139302
#139282
#139152
#139132
#138932
#138912
#138892
#138872
#137882
#137872
#137812
#137802
C4×#3822
C42×C4⋊C42