Finite Group Databasebeta

← #945666

Subgroups — #945666

Order 512.

2990 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2545C211yesmaximal, characteristic, complemented
2C2×#2545C211yesmaximal, characteristic, complemented
3C2×#2448C211yesmaximal, characteristic, complemented
4C2×#2658C211yesmaximal, characteristic, complemented
5#17136C214yesmaximal, complemented
6#16548C214yesmaximal, complemented
7#16355C214yesmaximal, complemented
8#15446C214yesmaximal, complemented
9#15243C211yesmaximal, characteristic, complemented
10#15227C211yesmaximal, characteristic
11#15227C211yesmaximal, characteristic
12#15227C211yesmaximal, characteristic
13#15217C211yesmaximal, characteristic, complemented
14#15188C211yesmaximal, characteristic, complemented
15#14260C211yesmaximal, characteristic, complemented
16#14026C211yesmaximal, characteristic, complemented
17#14024C211yesmaximal, characteristic, complemented
18#14024C211yesmaximal, characteristic, complemented
19#13846C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×#127C2211yescharacteristic
24C22×#124C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×#124C2211yescharacteristic
28C22×#124C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32#2658—28no—
33#2545—28no—
34#2545—28no—
35#2448—28no—
36C2×#399C2214yes—
37C2×#399C2214yes—
38C2×#399C2212yes—
39C2×#397C2212yes—
40C2×#396C2214yes—
41C2×#396C2212yes—
42C2×#396C2212yes—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#388C2212yes—
58C2×#388C2214yes—
59C2×#388C2212yes—
60C2×#388C2212yes—
61C2×#388C2212yes—
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×#376C2211yescharacteristic
65#1445C2212yes—
66#1443C2212yes—
67#1442C2212yes—
68#1442C2214yes—
69#1441C2212yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2214yes—
81#1438C2214yes—
82#1438C2214yes—
83#1438C2214yes—
84#1438C2214yes—
85#1438C2214yes—
86#1437C2214yes—
87#1436C2214yes—
88#1436C2214yes—
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C23×D4C2311yescharacteristic
100C23×D4C2314yes—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—42no—
106C2×C4⋊Q8—42no—
107C2×C4⋊Q8—42no—
108C2×C4⋊Q8—42no—
109C2×C4⋊Q8D418yescomplemented
110C2×#127—42no—
111C2×#127—42no—
112C2×#127—42no—
113C2×#124—24no—
114C2×#124—24no—
115C2×#124—24no—
116C2×#124—24no—
117C2×#124—24no—
118C2×#124—24no—
119C2×#124—24no—
120C2×#124—24no—
121C2×#124—24no—
122C2×#124—42no—
123C2×#124—42no—
124C2×#124—42no—
125C2×#124—42no—
126C2×#124—42no—
127C2×#124—42no—
128C2×#124—42no—
129C2×#124—42no—
130C2×#124—42no—
131C2×C4×Q8—24no—
132C2×C4×Q8—24no—
133C2×C4×Q8—24no—
134C2×C4×Q8—42no—
135C2×C4×Q8—42no—
136C2×C4×Q8—42no—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2314yes—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2312yes—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2312yes—
177#399—216no—
178#399—216no—
179#399—28no—
180#397—28no—
181#396—28no—
182#396—28no—
183#396—216no—
184#391—24no—
185#391—24no—
186#391—24no—
187#391—42no—
188#391—42no—
189#391—42no—
190#391—42no—
191#390—24no—
192#390—24no—
193#390—24no—
194#390—24no—
195#390—24no—
196#390—42no—
197#389—24no—
198#388—28no—
199#388—216no—
200#388—28no—
201#388—28no—
202#388—28no—
203C4×C4⋊C4—24no—
204C4×C4⋊C4D418yescomplemented
205#376—24no—
206C2×#95C2312yes—
207C2×#95C2314yes—
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×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2311yescharacteristic
230C2×#95C2311yescharacteristic
231C25C2412yes—
232C25C2412yes—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8C2×D414yes—
253C22×Q8C2×D414yes—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—28no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4—44no—
274C22×D4—44no—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C4⋊Q8—416no—
293C4⋊Q8—416no—
294C4⋊Q8—416no—
295#127—416no—
296#124—416no—
297#124—416no—
298#124—416no—
299#124—416no—
300#124—416no—
301#124—416no—
302C4×Q8—416no—
303C4×Q8—416no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4C2×D4116yes—
338C2×C4⋊C4C2×D414yes—
339C2×C4⋊C4C2×D414yes—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42C2×D414yes—
411C2×C42C2×D414yes—
412C2×C42C2×D414yes—
413C2×C42C2×D414yes—
414C2×C42#4114yes—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—28no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—42no—
428#95—42no—
429#95—44no—
430#95—44no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95—44no—
438#95C2×D414yes—
439#95C2×D414yes—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—24no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24—24no—
459C24—24no—
460C24—24no—
461C24—24no—
462C24C2511yescharacteristic
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×D4—416no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—88no—
500C2×D4—88no—
501C2×D4—88no—
502C2×D4—88no—
503C2×D4—88no—
504C2×D4—88no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
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—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
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—22no—
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—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4C22×D414yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D414yes—
595C22×C4C22×D412yes—
596C22×C4C22×D414yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C2×#4114yes—
600C22×C4C2×#4112yes—
601C22×C4H(5,𝔽2)12yes—
602C22×C4H(5,𝔽2)12yes—
603C22×C4H(5,𝔽2)12yes—
604C22×C4H(5,𝔽2)12yes—
605C22×C42−1+414yes—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—416no—
609C4⋊C4—48no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—416no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—84no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—416no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—416no—
629C22⋊C4—416no—
630C22⋊C4—416no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—84no—
634C22⋊C4—84no—
635C22⋊C4—88no—
636C22⋊C4—88no—
637C42—28no—
638C42—28no—
639C42—28no—
640C42—28no—
641C42—28no—
642C42—48no—
643C42—48no—
644C42—44no—
645C42—44no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—42no—
675C23—42no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23C23×D411yescharacteristic
693C23C23×D411yescharacteristic
694C23C22×#4111yescharacteristic
695C23C2×H(5,𝔽2)11yescharacteristic
696C23C2×H(5,𝔽2)11yescharacteristic
697C23C2×H(5,𝔽2)11yescharacteristic
698C23C2×H(5,𝔽2)11yescharacteristic
699C23C2×2−1+412yes—
700C23#58512yes—
701C23#58512yes—
702C23#58512yes—
703Q8—416no—
704Q8—416no—
705Q8—88no—
706D4—832no—
707D4—88no—
708D4—88no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
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—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
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—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
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—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4#53414yes—
804C2×C4#53514yes—
805C2×C4#54014yes—
806C2×C4D4214yes—
807C2×C4#54614yes—
808C2×C4#55014yes—
809C2×C4#56014yes—
810C22—82no—
811C22—82no—
812C22—84no—
813C22—84no—
814C22—82no—
815C22—82no—
816C22—84no—
817C22—84no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—84no—
827C22—84no—
828C22—82no—
829C22—82no—
830C22—84no—
831C22—84no—
832C22C2×#53411yescharacteristic
833C22C2×#53511yescharacteristic
834C22#344911yescharacteristic
835C22#344911yescharacteristic
836C22C2×#54011yescharacteristic
837C22C2×D4211yescharacteristic
838C22C2×#54611yescharacteristic
839C22C2×#55011yescharacteristic
840C22#348712yes—
841C22#349712yes—
842C22#349911yescharacteristic
843C22#350011yescharacteristic
844C22#350712yes—
845C22#351012yes—
846C22C2×#56011yescharacteristic
847C22#355412yes—
848C22#356112yes—
849C22#356112yes—
850C22#356112yes—
851C22#356212yes—
852C22#356212yes—
853C22#356212yes—
854C22#356212yes—
855C4—42no—
856C4—44no—
857C4—42no—
858C4—42no—
859C4—44no—
860C4—44no—
861C4—44no—
862C4—42no—
863C4—44no—
864C4—42no—
865C4—42no—
866C4—82no—
867C4—82no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4#267318yes—
872C2—162no—
873C2—162no—
874C2#3739111yescharacteristic
875C2#3754411yescharacteristic
876C2#3768311yescharacteristic
877C2#3935611yescharacteristic
878C2#3974011yescharacteristic
879C2#3974111yescharacteristic
880C2#4270512yes—
881C2#4279712yes—
882C2#4524012yes—
883C2C2×#267311yescharacteristic
884C2#5304312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2545C2semidirect
2. C2×#2545C2semidirect
3. C2×#2448C2semidirect
4. C2×#2658C2semidirect
5. #17136C2semidirect
6. #16548C2semidirect
7. #16355C2semidirect
8. #15446C2semidirect
9. #15243C2semidirect
13. #15217C2semidirect
14. #15188C2semidirect
15. #14260C2semidirect
16. #14026C2semidirect
17. #14024C2semidirect
18. #14024C2semidirect
19. #13846C2semidirect
109. C2×C4⋊Q8D4semidirect
204. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25452
C2×#24482
C2×#26582
#171362
#165482
#163552
#154462
#152432
#152272
#152172
#151882
#142602
#140262
#140242
#138462