Finite Group Databasebeta

← #4928838

Subgroups — #4928838

Order 512.

2687 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2662C211yesmaximal, characteristic
2C2×#2399C211yesmaximal, characteristic, complemented
3#15093C212yesmaximal, complemented
4#15070C212yesmaximal, complemented
5#15011C212yesmaximal, complemented
6#14999C212yesmaximal, complemented
7#14956C212yesmaximal, complemented
8#14928C212yesmaximal
9#14789C212yesmaximal, complemented
10#14780C212yesmaximal, complemented
11#14227C212yesmaximal, complemented
12#14188C212yesmaximal, complemented
13#14169C211yesmaximal, characteristic, complemented
14#14166C211yesmaximal, characteristic, complemented
15#14166C211yesmaximal, characteristic, complemented
16#14153C211yesmaximal, characteristic, complemented
17#14085C212yesmaximal, complemented
18#14026C212yesmaximal, complemented
19#13750C211yesmaximal, characteristic, complemented
20C22×#126C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×#124C2212yes—
23C22×C4×Q8C2212yes—
24#2662—28no—
25#2399—28no—
26C2×#398C2212yes—
27C2×#398C2212yes—
28C2×#396C2212yes—
29C2×#395C2211yescharacteristic
30C2×#395C2212yes—
31C2×#395C2212yes—
32C2×#394C2211yescharacteristic
33C2×#394C2212yes—
34C2×#394C2212yes—
35C2×#393C2211yescharacteristic
36C2×#393C2212yes—
37C2×#392C2211yescharacteristic
38C2×#391C2212yes—
39C2×#391C2212yes—
40C2×#390C2212yes—
41C2×#390C2212yes—
42C2×#390C2212yes—
43C2×#388C2212yes—
44C2×#388C2212yes—
45C2×#388C2212yes—
46C2×#388C2212yes—
47C2×#388C2212yes—
48C2×#388C2212yes—
49C2×C4×C4⋊C4C2212yes—
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×#376C2211yescharacteristic
56C2×#376C2211yescharacteristic
57#1446C2212yes—
58#1446C2212yes—
59#1443C2212yes—
60#1442C2212yes—
61#1442C2212yes—
62#1442C2212yes—
63#1441C2212yes—
64#1441C2212yes—
65#1441C2212yes—
66#1440C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1438C2212yes—
78#1438C2212yes—
79#1437C2212yes—
80#1437C2212yes—
81#1437C2212yes—
82#1437C2212yes—
83#1437C2212yes—
84#1437C2211yescharacteristic
85#1437C2212yes—
86#1437C2211yescharacteristic
87#1437C2211yescharacteristic
88#1437C2211yescharacteristic
89#1437C2212yes—
90#1437C2212yes—
91#1437C2212yes—
92#1437C2212yes—
93#1437C2212yes—
94#1436C2211yescharacteristic
95#1436C2212yes—
96#1436C2212yes—
97#1436C2211yescharacteristic
98#1436C2212yes—
99#1436C2211yescharacteristic
100#1436C2211yescharacteristic
101#1436C2212yes—
102#1436C2212yes—
103C4⋊#95C2212yes—
104#1434C2212yes—
105C4×#95C2212yes—
106C4×#95C2212yes—
107C4×#95C2212yes—
108C4×#95C2212yes—
109C23×Q8C2312yes—
110C23×Q8C2311yescharacteristic
111C23×D4C2312yes—
112C23×D4C2311yescharacteristic
113C2×#126—24no—
114C2×#126—24no—
115C2×#126—24no—
116C2×#124—24no—
117C2×#124—28no—
118C2×#124—24no—
119C2×#124—24no—
120C2×#124—44no—
121C2×#124—44no—
122C2×C4×Q8—28no—
123C2×C4×Q8—44no—
124C2×C4×Q8—44no—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2312yes—
167C22×C42C2312yes—
168C22×C42C2312yes—
169C22×C42C2311yescharacteristic
170#398—28no—
171#398—28no—
172#396—28no—
173#395—28no—
174#395—28no—
175#395—24no—
176#394—28no—
177#394—24no—
178#394—28no—
179#393—24no—
180#393—28no—
181#392—24no—
182#391—44no—
183#391—44no—
184#390—28no—
185#390—44no—
186#390—44no—
187#388—28no—
188#388—28no—
189#388—44no—
190#388—44no—
191#388—44no—
192#388—44no—
193C4×C4⋊C4—28no—
194C4×C4⋊C4—24no—
195C4×C4⋊C4—28no—
196C4×C4⋊C4—24no—
197C4×C4⋊C4—28no—
198C4×C4⋊C4D418yes—
199#376—24no—
200#376—24no—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2311yescharacteristic
213C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
237C2×#95C2311yescharacteristic
238C2×#95C2312yes—
239C25C2412yes—
240C25C2411yescharacteristic
241C22×Q8—24no—
242C22×Q8—22no—
243C22×Q8—24no—
244C22×Q8—22no—
245C22×Q8—24no—
246C22×Q8—22no—
247C22×Q8—24no—
248C22×Q8—24no—
249C22×Q8—42no—
250C22×Q8—42no—
251C22×Q8—42no—
252C22×Q8—42no—
253C22×D4—22no—
254C22×D4—24no—
255C22×D4—22no—
256C22×D4—24no—
257C22×D4—22no—
258C22×D4—24no—
259C22×D4—42no—
260C22×D4—42no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4—42no—
265C23×C4C2411yescharacteristic
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282#126—416no—
283#124—432no—
284#124—416no—
285C4×Q8—432no—
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—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
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—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4C2×D418yes—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42C2×D418yes—
413C2×C42C2×D414yes—
414C2×C42#4118yes—
415C2×C42#4114yes—
416C2×C42#4114yes—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—22no—
421#95—24no—
422#95—22no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—22no—
431#95—22no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95C2×D414yes—
453#95C2×D414yes—
454#95#4118yes—
455C24—21no—
456C24—22no—
457C24—21no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24C2511yescharacteristic
480C2×Q8—216no—
481C2×Q8—48no—
482C2×Q8—48no—
483C2×Q8—48no—
484C2×Q8—48no—
485C2×Q8—48no—
486C2×Q8—48no—
487C2×Q8—44no—
488C2×Q8—48no—
489C2×Q8—84no—
490C2×Q8—82no—
491C2×Q8—82no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—44no—
496C2×D4—48no—
497C2×D4—84no—
498C2×D4—84no—
499C2×D4—84no—
500C2×D4—82no—
501C2×D4—82no—
502C2×D4—84no—
503C2×D4—84no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
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—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
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—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—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4C22×D414yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D414yes—
596C22×C4C2×#4114yes—
597C22×C4C2×#4114yes—
598C22×C4C2×#4114yes—
599C22×C4C2×#4114yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4114yes—
607C22×C4C2×#4114yes—
608C22×C4H(5,𝔽2)14yes—
609C22×C4H(5,𝔽2)14yes—
610C22×C42−1+414yes—
611C4⋊C4—216no—
612C4⋊C4—216no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—48no—
622C4⋊C4—84no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—48no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C42—28no—
645C42—28no—
646C42—28no—
647C42—28no—
648C42—48no—
649C42—48no—
650C42—48no—
651C42—84no—
652C42—84no—
653C42—84no—
654C42—84no—
655C42#124116yescomplemented
656C23—41no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—41no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—41no—
689C23—42no—
690C23—41no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23C23×D411yescharacteristic
713C23C22×#4111yescharacteristic
714C23C22×#4111yescharacteristic
715C23C22×#4112yes—
716C23C22×#4112yes—
717C23C2×H(5,𝔽2)12yes—
718C23C2×H(5,𝔽2)12yes—
719C23C2×2−1+412yes—
720C23#58512yes—
721Q8—432no—
722Q8—88no—
723D4—816no—
724D4—88no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
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—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—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4C2×#12414yes—
829C2×C4C2×#12414yes—
830C2×C4C2×#12414yes—
831C2×C4#53218yes—
832C22—81no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—81no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22C22×#12411yescharacteristic
857C22C2×#53212yes—
858C22#344411yescharacteristic
859C22#344411yescharacteristic
860C22#344412yes—
861C22#348411yescharacteristic
862C22#348611yescharacteristic
863C22#348812yes—
864C22#349012yes—
865C22#349512yes—
866C22#350612yes—
867C22#350612yes—
868C22#350811yescharacteristic
869C22#351011yescharacteristic
870C22#351112yes—
871C22#351112yes—
872C22#351112yes—
873C22#351312yes—
874C22#351812yes—
875C22#351912yes—
876C22#352012yes—
877C4—24no—
878C4—24no—
879C4—28no—
880C4—24no—
881C4—44no—
882C4—44no—
883C4—44no—
884C4—44no—
885C4—44no—
886C4—44no—
887C4—44no—
888C4—44no—
889C4—81no—
890C4—81no—
891C4—82no—
892C4—81no—
893C4—82no—
894C2—161no—
895C2—162no—
896C2#3539212yes—
897C2#3555611yescharacteristic
898C2#3557312yes—
899C2#3559211yescharacteristic
900C2#3574412yes—
901C2#3581412yes—
902C2#3586612yes—
903C2#3593312yes—
904C2#3663911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2399C2semidirect
3. #15093C2semidirect
4. #15070C2semidirect
5. #15011C2semidirect
6. #14999C2semidirect
7. #14956C2semidirect
9. #14789C2semidirect
10. #14780C2semidirect
11. #14227C2semidirect
12. #14188C2semidirect
13. #14169C2semidirect
14. #14166C2semidirect
15. #14166C2semidirect
16. #14153C2semidirect
17. #14085C2semidirect
18. #14026C2semidirect
19. #13750C2semidirect
655. C42#124semidirect

Maximal subgroups

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

subgroupindex
C2×#26622
C2×#23992
#150932
#150702
#150112
#149992
#149562
#149282
#147892
#147802
#142272
#141882
#141692
#141662
#141532
#140852
#140262
#137502