Finite Group Databasebeta

← #1409738

Subgroups — #1409738

Order 512.

3092 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2416C211yesmaximal, characteristic
2C2×#2450C211yesmaximal, characteristic, complemented
3#17079C211yesmaximal, characteristic, complemented
4#17058C211yesmaximal, characteristic, complemented
5#16956C212yesmaximal, complemented
6#16934C212yesmaximal, complemented
7#16802C211yesmaximal, characteristic, complemented
8#16557C211yesmaximal, characteristic, complemented
9#16368C212yesmaximal, complemented
10#16367C212yesmaximal, complemented
11#15167C211yesmaximal, characteristic, complemented
12#14913C211yesmaximal, characteristic, complemented
13#14843C211yesmaximal, characteristic, complemented
14#14826C211yesmaximal, characteristic, complemented
15#14759C212yesmaximal, complemented
16#14747C211yesmaximal, characteristic, complemented
17#14737C212yesmaximal, complemented
18#14326C211yesmaximal, characteristic, complemented
19#14271C211yesmaximal, characteristic, complemented
20#14023C212yesmaximal, complemented
21#14023C212yesmaximal, complemented
22C2×#1445C211yesmaximal, characteristic, complemented
23D4×#95C211yesmaximal, characteristic, complemented
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2212yes—
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×C4×D4C2212yes—
29C22×C4×D4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31#2450—28no—
32#2416—28no—
33C2×#400C2211yescharacteristic
34C2×#400C2211yescharacteristic
35C2×#400C2211yescharacteristic
36C2×#398C2211yescharacteristic
37C2×#397C2212yes—
38C2×#396C2212yes—
39C2×#396C2211yescharacteristic
40C2×#394C2212yes—
41C2×#394C2211yescharacteristic
42C2×#393C2211yescharacteristic
43C2×#393C2212yes—
44C2×#391C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#387C2211yescharacteristic
48C2×#386C2211yescharacteristic
49C2×#386C2211yescharacteristic
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#385C2211yescharacteristic
58C2×#385C2211yescharacteristic
59C2×#385C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2212yes—
64C22×#95C2211yescharacteristic
65C22×#95C2212yes—
66C22×#95C2211yescharacteristic
67#1446C2212yes—
68#1445C2212yes—
69#1445C2212yes—
70#1445C2211yescharacteristic
71#1445C2211yescharacteristic
72#1445C2211yescharacteristic
73#1445C2211yescharacteristic
74#1445C2212yes—
75#1445C2211yescharacteristic
76#1445C2211yescharacteristic
77#1443C2212yes—
78#1443C2212yes—
79#1442C2212yes—
80#1442C2212yes—
81#1442C2212yes—
82#1442C2211yescharacteristic
83#1442C2211yescharacteristic
84#1442C2212yes—
85#1442C2211yescharacteristic
86#1442C2212yes—
87#1441C2212yes—
88#1441C2212yes—
89#1441C2212yes—
90#1441C2211yescharacteristic
91#1440C2212yes—
92#1440C2212yes—
93#1440C2212yes—
94#1440C2212yes—
95#1440C2212yes—
96#1440C2212yes—
97#1440C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1438C2211yescharacteristic
106#1438C2211yescharacteristic
107#1438C2211yescharacteristic
108#1438C2212yes—
109#1438C2212yes—
110#1437C2212yes—
111#1437C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114C4⋊#95C2212yes—
115C4⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2212yes—
118C22⋊#95C2212yes—
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C4×#95C2211yescharacteristic
125C23×Q8C2311yescharacteristic
126C23×D4C2312yes—
127C23×D4C2312yes—
128C23×D4C2311yescharacteristic
129C23×D4C2311yescharacteristic
130C24×C4C2312yes—
131C24×C4C2312yes—
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2312yes—
136C24×C4C2311yescharacteristic
137C2×C22⋊Q8—24no—
138C2×C22⋊Q8—44no—
139C2×#121—28no—
140C2×#121—28no—
141C2×#121—28no—
142C2×#121—24no—
143C2×#121—24no—
144C2×#121—24no—
145C2×#121—42no—
146C2×#121—44no—
147C2×C4×D4—28no—
148C2×C4×D4—44no—
149C2×C4×D4—44no—
150C2×C4×D4—44no—
151C2×C4×D4D418yes—
152C22×C4⋊C4—24no—
153C22×C4⋊C4—24no—
154C22×C4⋊C4—42no—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2311yescharacteristic
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2311yescharacteristic
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C42C2312yes—
193C22×C42C2311yescharacteristic
194#400—24no—
195#400—24no—
196#400—42no—
197#398—24no—
198#397—44no—
199#396—28no—
200#396—24no—
201#394—28no—
202#394—42no—
203#393—24no—
204#393—44no—
205#391—24no—
206#390—24no—
207#389—24no—
208#387—24no—
209#386—24no—
210#386—24no—
211#386—28no—
212#386—44no—
213#386—44no—
214#386—44no—
215#386—44no—
216#386—44no—
217#386—44no—
218#385—24no—
219#385—24no—
220#385—24no—
221#380—24no—
222#380—24no—
223C2×#95—24no—
224C2×#95—42no—
225C2×#95—42no—
226C2×#95—44no—
227C2×#95—44no—
228C2×#95C2312yes—
229C2×#95C2311yescharacteristic
230C2×#95C2311yescharacteristic
231C2×#95C2312yes—
232C2×#95C2311yescharacteristic
233C2×#95C2311yescharacteristic
234C2×#95C2312yes—
235C2×#95C2311yescharacteristic
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2311yescharacteristic
239C2×#95C2311yescharacteristic
240C2×#95C2311yescharacteristic
241C2×#95C2311yescharacteristic
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2311yescharacteristic
245C2×#95C2311yescharacteristic
246C2×#95C2311yescharacteristic
247C2×#95C2311yescharacteristic
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2311yescharacteristic
251C2×#95C2311yescharacteristic
252C2×#95C2311yescharacteristic
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C25C2412yes—
277C25C2411yescharacteristic
278C25C2411yescharacteristic
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8—42no—
282C22×Q8—41no—
283C22×Q8—42no—
284C22×D4—24no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—24no—
288C22×D4—24no—
289C22×D4—24no—
290C22×D4—24no—
291C22×D4—24no—
292C22×D4—24no—
293C22×D4—24no—
294C22×D4—24no—
295C22×D4—24no—
296C22×D4—24no—
297C22×D4—22no—
298C22×D4—24no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—42no—
302C22×D4—42no—
303C22×D4—42no—
304C22×D4—42no—
305C22×D4—42no—
306C22×D4C2×D414yes—
307C22×D4#4118yes—
308C23×C4—24no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—24no—
315C23×C4—22no—
316C23×C4—24no—
317C23×C4—24no—
318C23×C4—24no—
319C23×C4—24no—
320C23×C4—24no—
321C23×C4—24no—
322C23×C4—24no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—24no—
326C23×C4—24no—
327C23×C4—22no—
328C23×C4—24no—
329C23×C4—42no—
330C23×C4—42no—
331C23×C4—42no—
332C23×C4—42no—
333C23×C4—42no—
334C23×C4—42no—
335C23×C4—42no—
336C23×C4—42no—
337C23×C4—41no—
338C23×C4—42no—
339C23×C4—42no—
340C23×C4—42no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4—42no—
344C23×C4—42no—
345C23×C4—42no—
346C23×C4—42no—
347C23×C4C2×D414yes—
348C23×C4C2×D414yes—
349C23×C4C2411yescharacteristic
350C23×C4C2411yescharacteristic
351C23×C4C2411yescharacteristic
352C23×C4C2411yescharacteristic
353C23×C4C2412yes—
354C23×C4C2411yescharacteristic
355C23×C4C2412yes—
356C23×C4C2411yescharacteristic
357C23×C4C2411yescharacteristic
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2411yescharacteristic
362C23×C4C2411yescharacteristic
363C23×C4C2411yescharacteristic
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2411yescharacteristic
367C23×C4C2411yescharacteristic
368C23×C4C2411yescharacteristic
369C22⋊Q8—416no—
370#121—416no—
371#121—416no—
372#121—432no—
373C4×D4—416no—
374C4×D4—432no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—416no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4—42no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4C2×D414yes—
409C2×C4⋊C4#4114yes—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—41no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4—42no—
441C2×C22⋊C4—42no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—42no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—42no—
471C2×C22⋊C4C2×D414yes—
472C2×C22⋊C4C2×D414yes—
473C2×C42—24no—
474C2×C42—42no—
475C2×C42—42no—
476C2×C42—42no—
477C2×C42C2×D414yes—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—24no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—24no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—24no—
494#95—24no—
495#95—22no—
496#95—24no—
497#95—24no—
498#95—24no—
499#95—22no—
500#95—24no—
501#95—22no—
502#95—24no—
503#95—42no—
504#95—42no—
505#95—42no—
506#95—42no—
507#95—42no—
508#95—42no—
509#95—42no—
510#95—42no—
511#95—42no—
512#95—42no—
513#95—42no—
514#95—42no—
515#95—42no—
516#95—42no—
517#95—42no—
518#95—42no—
519#95—42no—
520#95—42no—
521#95—42no—
522#95—42no—
523#95—42no—
524#95—42no—
525#95—42no—
526C24—21no—
527C24—21no—
528C24—22no—
529C24—21no—
530C24—22no—
531C24—21no—
532C24—21no—
533C24—22no—
534C24—22no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—21no—
539C24—22no—
540C24—21no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24C22×D412yes—
557C24C22×D412yes—
558C24C2×#4114yes—
559C24C2×#4114yes—
560C24H(5,𝔽2)14yes—
561C24H(5,𝔽2)12yes—
562C242−1+412yes—
563C24C2511yescharacteristic
564C2×Q8—44no—
565C2×Q8—44no—
566C2×Q8—82no—
567C2×Q8—84no—
568C2×Q8—84no—
569C2×D4—28no—
570C2×D4—28no—
571C2×D4—216no—
572C2×D4—216no—
573C2×D4—48no—
574C2×D4—48no—
575C2×D4—48no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—48no—
579C2×D4—48no—
580C2×D4—48no—
581C2×D4—48no—
582C2×D4—48no—
583C2×D4—48no—
584C2×D4—48no—
585C2×D4—48no—
586C2×D4—44no—
587C2×D4—84no—
588C2×D4—84no—
589C2×D4—84no—
590C2×D4—84no—
591C2×D4—84no—
592C2×D4#124116yes—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—28no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—28no—
628C22×C4—28no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—21no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—48no—
705C22×C4—48no—
706C22×C4—48no—
707C22×C4—48no—
708C22×C4—48no—
709C22×C4—44no—
710C22×C4—48no—
711C22×C4—48no—
712C22×C4—48no—
713C22×C4—48no—
714C22×C4—48no—
715C22×C4—48no—
716C22×C4—48no—
717C22×C4—48no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—48no—
721C22×C4—84no—
722C22×C4—84no—
723C22×C4—84no—
724C22×C4—84no—
725C22×C4—84no—
726C22×C4—82no—
727C22×C4—84no—
728C22×C4—84no—
729C22×C4—84no—
730C22×C4—84no—
731C22×C4—84no—
732C22×C4—84no—
733C22×C4—84no—
734C22×C4—82no—
735C22×C4—82no—
736C22×C4—84no—
737C22×C4—84no—
738C22×C4—84no—
739C22×C4C22×D412yes—
740C22×C4C22×D412yes—
741C22×C4C22×D412yes—
742C22×C4C22×D412yes—
743C22×C4C22×D412yes—
744C22×C4C2×#4114yes—
745C22×C4C2×#4114yes—
746C22×C4C2×#4112yes—
747C22×C4H(5,𝔽2)14yes—
748C22×C4H(5,𝔽2)12yes—
749C22×C42−1+412yes—
750C4⋊C4—28no—
751C4⋊C4—44no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—44no—
757C4⋊C4—44no—
758C4⋊C4—48no—
759C4⋊C4—44no—
760C4⋊C4—44no—
761C4⋊C4—82no—
762C4⋊C4—82no—
763C4⋊C4—82no—
764C22⋊C4—28no—
765C22⋊C4—44no—
766C22⋊C4—48no—
767C22⋊C4—44no—
768C22⋊C4—48no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4—48no—
774C22⋊C4—48no—
775C22⋊C4—84no—
776C22⋊C4—84no—
777C22⋊C4—84no—
778C22⋊C4—84no—
779C22⋊C4—82no—
780C22⋊C4—82no—
781C22⋊C4—82no—
782C22⋊C4—84no—
783C22⋊C4—84no—
784C22⋊C4—84no—
785C22⋊C4—84no—
786C22⋊C4—84no—
787C42—44no—
788C42—48no—
789C23—22no—
790C23—24no—
791C23—22no—
792C23—22no—
793C23—24no—
794C23—22no—
795C23—24no—
796C23—22no—
797C23—24no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—24no—
810C23—24no—
811C23—22no—
812C23—24no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—42no—
820C23—41no—
821C23—41no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—41no—
828C23—41no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23C2×#12414yes—
865C23C2×#12414yes—
866C23#53414yes—
867C23#53714yes—
868C23#53818yes—
869C23#53918yes—
870C23C23×D411yescharacteristic
871C23C22×#4112yes—
872C23C22×#4111yescharacteristic
873C23C2×H(5,𝔽2)12yes—
874C23C2×H(5,𝔽2)11yescharacteristic
875C23C2×H(5,𝔽2)11yescharacteristic
876C23C2×H(5,𝔽2)12yes—
877C23C2×2−1+411yescharacteristic
878C23C2×2−1+411yescharacteristic
879C23#58512yes—
880C23#58511yescharacteristic
881Q8—88no—
882D4—232no—
883D4—88no—
884D4—816no—
885D4—816no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—24no—
899C2×C4—22no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—416no—
912C2×C4—42no—
913C2×C4—41no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—41no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—42no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—42no—
969C2×C4—41no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—41no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—88no—
1002C2×C4—816no—
1003C2×C4—816no—
1004C2×C4—88no—
1005C2×C4—816no—
1006C2×C4—88no—
1007C2×C4C2×#12414yes—
1008C2×C4#54614yes—
1009C22—28no—
1010C22—28no—
1011C22—28no—
1012C22—28no—
1013C22—24no—
1014C22—24no—
1015C22—24no—
1016C22—24no—
1017C22—24no—
1018C22—24no—
1019C22—24no—
1020C22—24no—
1021C22—24no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—82no—
1031C22—82no—
1032C22—82no—
1033C22—82no—
1034C22—82no—
1035C22—82no—
1036C22—82no—
1037C22—82no—
1038C22—82no—
1039C22—82no—
1040C22—82no—
1041C22—82no—
1042C22—82no—
1043C22—82no—
1044C22—82no—
1045C22#263918yes—
1046C22C22×#12411yescharacteristic
1047C22C2×#53411yescharacteristic
1048C22C2×#53711yescharacteristic
1049C22C2×#53812yes—
1050C22C2×#53912yes—
1051C22C2×#54611yescharacteristic
1052C22#348112yes—
1053C22#348511yescharacteristic
1054C22#348911yescharacteristic
1055C22#349412yes—
1056C22#349811yescharacteristic
1057C22#351512yes—
1058C22#351611yescharacteristic
1059C22#351912yes—
1060C22#352112yes—
1061C22#352211yescharacteristic
1062C22#353412yes—
1063C22#353412yes—
1064C22#353412yes—
1065C22#353612yes—
1066C22#354112yes—
1067C22#355211yescharacteristic
1068C22#355811yescharacteristic
1069C4—24no—
1070C4—24no—
1071C4—44no—
1072C4—44no—
1073C4—42no—
1074C4—42no—
1075C4—42no—
1076C4—42no—
1077C4—82no—
1078C4—82no—
1079C4—82no—
1080C4—82no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—82no—
1086C4—81no—
1087C4—81no—
1088C4—81no—
1089C2—28no—
1090C2—44no—
1091C2—162no—
1092C2C2×#263911yescharacteristic
1093C2#3604211yescharacteristic
1094C2#3628911yescharacteristic
1095C2#3783411yescharacteristic
1096C2#3802511yescharacteristic
1097C2#3850512yes—
1098C2#3851312yes—
1099C2#4078212yes—
1100C2#4079012yes—
1101C2#4136811yescharacteristic
1102C2#4195211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2416C2
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×#2450C2semidirect
3. #17079C2semidirect
4. #17058C2semidirect
5. #16956C2semidirect
6. #16934C2semidirect
7. #16802C2semidirect
8. #16557C2semidirect
9. #16368C2semidirect
10. #16367C2semidirect
11. #15167C2semidirect
12. #14913C2semidirect
13. #14843C2semidirect
14. #14826C2semidirect
15. #14759C2semidirect
16. #14747C2semidirect
17. #14737C2semidirect
18. #14326C2semidirect
19. #14271C2semidirect
20. #14023C2semidirect
21. #14023C2semidirect
22. C2×#1445C2semidirect
23. D4×#95C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24162
C2×#24502
#170792
#170582
#169562
#169342
#168022
#165572
#163682
#163672
#151672
#149132
#148432
#148262
#147592
#147472
#147372
#143262
#142712
#140232
C2×#14452
D4×#952