Finite Group Databasebeta

← #25968080

Subgroups — #25968080

Order 11008.

2444 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583449C211yesmaximal, characteristic, complemented
2C2×#14583449C211yesmaximal, characteristic, complemented
3#19145592C214yesmaximal, complemented
4#19145584C214yesmaximal, complemented
5#19145530C214yesmaximal, complemented
6#19145522C212yesmaximal, complemented
7#19145515C212yesmaximal, complemented
8#19145047C212yesmaximal, complemented
9#19144989C212yesmaximal, complemented
10#19144061C214yesmaximal, complemented
11#19143849C214yesmaximal, complemented
12C43×#2920C211yesmaximal, characteristic, complemented
13C22×#10621898—21no—
14C22×#10621898C2212yes—
15C2×#13063353C2218yescomplemented
16#14583449—21no—
17#14583449—21no—
18#14583449—21no—
19#14583449—21no—
20#14583449—21no—
21#14583449—21no—
22#14583449—21no—
23#14583449—21no—
24#14583449C2212yes—
25#14583449C2212yes—
26#14583449C2212yes—
27#14583449C2212yes—
28#14583449C2212yescomplemented
29#14583449C2212yescomplemented
30#14583449C2212yescomplemented
31#14583449C2212yescomplemented
32C2×#13063325C2211yescharacteristic, complemented
33C2×#13063325C2211yescharacteristic, complemented
34C2×#13063322C2211yescharacteristic, complemented
35C2×#13063322C2211yescharacteristic, complemented
36C2×#13063313—21no—
37C2×#13063313C2212yescomplemented
38C2×#13063299—21no—
39C2×#13063299—21no—
40C2×#13063299—21no—
41C2×#13063299C2212yes—
42C2×C4×D172—21no—
43C2×C4×D172—21no—
44C2×C4×D172—21no—
45C2×C4×D172C2212yescomplemented
46#14583288C2218yescomplemented
47#14583276C2214yescomplemented
48#14583272C2214yescomplemented
49#14583259C2218yescomplemented
50#14583250C2214yescomplemented
51#14583246C2214yescomplemented
52#14583115C22116yescomplemented
53#14583105C2218yescomplemented
54#14583095C2218yescomplemented
55#14583046C22116yescomplemented
56#14583040C2218yescomplemented
57#14583035C2218yescomplemented
58#14582901C2218yescomplemented
59C22×C42×C43C2211yescharacteristic
60C43×#432C2212yescomplemented
61C43×#432C2212yescomplemented
62C43×#431C2212yescomplemented
63C43×#431C2212yescomplemented
64C43×#423C2212yescomplemented
65C43×#407C2212yes—
66C4×M16×C43C2212yescomplemented
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898—22no—
70C2×#10621898—22no—
71C2×#10621898—22no—
72C2×#10621898—22no—
73C2×#10621898—48no—
74C2×#10621898—48no—
75C2×#10621898C2314yes—
76C2×#10621898C2314yes—
77C22×Dic86—21no—
78C22×Dic86C2312yes—
79C22×D172—21no—
80C22×D172—21no—
81C22×D172—21no—
82C22×D172—21no—
83C22×D172C2312yes—
84C22×D172C2312yes—
85C22×C22⋊D43—22no—
86C22×C22⋊D43—22no—
87C22×C4×D43—22no—
88C22×C4×D43—22no—
89#13063353—416no—
90C2×#10621873C23116yes—
91C2×D344C23116yes—
92#13063325—21no—
93#13063325—21no—
94#13063325—21no—
95#13063325—21no—
96#13063325C2312yes—
97#13063325C2312yes—
98#13063325C2312yes—
99#13063325C2312yes—
100#13063322—21no—
101#13063322—21no—
102#13063322—21no—
103#13063322—21no—
104#13063322C2312yes—
105#13063322C2312yes—
106#13063322C2312yes—
107#13063322C2312yes—
108#13063313—22no—
109#13063313—22no—
110#13063313—22no—
111#13063313—22no—
112#13063313—22no—
113#13063313—22no—
114#13063313C2314yes—
115#13063313C2314yes—
116#13063299—22no—
117#13063299—22no—
118#13063299—22no—
119#13063299—22no—
120#13063299—22no—
121#13063299—22no—
122#13063299—22no—
123#13063299—22no—
124#13063299—22no—
125#13063299—22no—
126#13063299—22no—
127#13063299—22no—
128#13063299—22no—
129#13063299—22no—
130#13063299C2314yes—
131#13063299C2314yes—
132C4×D172—22no—
133C4×D172—22no—
134C4×D172—22no—
135C4×D172—22no—
136C4×D172—22no—
137C4×D172—22no—
138C4×D172—22no—
139C4×D172—22no—
140C4×D172—22no—
141C4×D172—22no—
142C4×D172—22no—
143C4×D172—22no—
144C4×D172—22no—
145C4×D172—22no—
146C4×D172C2314yes—
147C4×D172C2314yes—
148C2×C4⋊Dic43—21no—
149C2×C4⋊Dic43—21no—
150C2×C4⋊Dic43—21no—
151C2×C4⋊Dic43C2312yes—
152C2×(C2×D43)⋊C4—22no—
153C2×(C2×D43)⋊C4—22no—
154C2×(C2×D43)⋊C4—22no—
155C2×(C2×D43)⋊C4—22no—
156#13063250C23116yes—
157#13063247C23116yes—
158C23×C4×C43D411yescharacteristic
159C23×C4×C43D411yescharacteristic
160C23×C4×C43C2311yescharacteristic
161C2×M16×C43C2314yes—
162C2×C42×C43D411yescharacteristic
163C2×C42×C43D411yescharacteristic
164C2×C42×C43D411yescharacteristic
165C2×C42×C43D411yescharacteristic
166C2×C42×C43D411yescharacteristic
167C2×C42×C43D411yescharacteristic
168C2×C42×C43C2311yescharacteristic
169C2×C42×C43C2311yescharacteristic
170C2×C42×C43C2311yescharacteristic
171C2×C42×C43C2311yescharacteristic
172C2×C42×C43C2311yescharacteristic
173C2×C42×C43C2311yescharacteristic
174C4⋊C8×C43C2314yes—
175C4⋊C8×C43C2314yes—
176C22⋊C8×C43C2314yes—
177C22⋊C8×C43C2314yes—
178#97×C43C2314yes—
179C4×C8×C43C2314yes—
180C24×C43C2×D411yescharacteristic
181C23×D43—22no—
182C23×D43—22no—
183C22×C4×C43—24no—
184C22×C4×C43—24no—
185C22×C4×C43—42no—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C22×C4×C43C2411yescharacteristic
203C22×C4×C43C2411yescharacteristic
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—48no—
209C2×C22⋊D43—48no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212#10621898—216no—
213#10621898—48no—
214#10621898—48no—
215#10621898—48no—
216#10621898—48no—
217#10621898—48no—
218#10621898—48no—
219#10621898—48no—
220C2×D172—22no—
221C2×D172—22no—
222C2×D172—22no—
223C2×D172—22no—
224C2×D172—22no—
225C2×D172—22no—
226C2×D172—22no—
227C2×D172—22no—
228C2×D172—22no—
229C2×D172—22no—
230C2×D172—28no—
231C2×D172—44no—
232C2×D172—44no—
233C2×D172—44no—
234C2×D172—44no—
235C2×D172—44no—
236C2×D172C2414yes—
237C2×D172C2414yes—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—24no—
241C2×C4×D43—24no—
242C2×C4×D43—48no—
243C2×C4×D43—48no—
244C2×Dic86—22no—
245C2×Dic86—22no—
246C2×Dic86—22no—
247C2×Dic86—44no—
248C2×Dic86—44no—
249C2×Dic86C2414yes—
250M16×C43—28no—
251C2×C8×C43C2418yes—
252C42×C43C2×D411yescharacteristic
253C42×C43C2×D411yescharacteristic
254C42×C43C2×D411yescharacteristic
255C42×C43C2×D411yescharacteristic
256C42×C43C2×D411yescharacteristic
257C42×C43C2×D411yescharacteristic
258C42×C43C2×D411yescharacteristic
259C42×C43C2×D411yescharacteristic
260C42×C43C2×D411yescharacteristic
261C42×C43C2×D411yescharacteristic
262C42×C43C2×D411yescharacteristic
263C42×C43C2×D411yescharacteristic
264C42×C43C2411yescharacteristic
265C42×C43C2411yescharacteristic
266C42×C43C2411yescharacteristic
267C42×C43C2411yescharacteristic
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276C4⋊Dic43—22no—
277C4⋊Dic43—22no—
278C4⋊Dic43—22no—
279C4⋊Dic43—22no—
280C4⋊Dic43—22no—
281C4⋊Dic43—22no—
282C4⋊Dic43—22no—
283C4⋊Dic43C2414yes—
284D344—416no—
285#10621873—416no—
286C23×C43—22no—
287C23×C43—22no—
288C23×C43—41no—
289C23×C43C22×D411yescharacteristic
290C23×C43C22×D411yescharacteristic
291C23×C43C22×D411yescharacteristic
292C22×D43—24no—
293C22×D43—24no—
294C22×D43—44no—
295C22×D43—44no—
296C22×D43—44no—
297C22×D43—44no—
298C22×D43—44no—
299C22×D43—44no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43AGL(1,ℤ/8)14yescomplemented
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C22×D411yescharacteristic
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43H(5,𝔽2)14yes—
329C2×C4×C43C2511yescharacteristic
330C22⋊D43—48no—
331C22⋊D43—48no—
332C22⋊D43—48no—
333C22⋊D43—48no—
334C2×Dic43—24no—
335C2×Dic43—24no—
336C2×Dic43—44no—
337C2×Dic43—44no—
338D172—28no—
339D172—28no—
340D172—44no—
341D172—44no—
342D172—44no—
343D172—44no—
344D172—44no—
345D172—44no—
346D172—44no—
347D172—44no—
348D172—44no—
349D172—44no—
350C4×D43—48no—
351C4×D43—48no—
352C4×D43—48no—
353C4×D43—48no—
354Dic86—28no—
355Dic86—44no—
356Dic86—44no—
357Dic86—44no—
358C8×C43—28no—
359#60803—431nomaximal, Sylow
360C22×C43—21no—
361C22×C43—21no—
362C22×C43—21no—
363C22×C43—21no—
364C22×C43—21no—
365C22×C43—21no—
366C22×C43—21no—
367C22×C43—44no—
368C22×C43#53512yes—
369C22×C43C2×AGL(1,ℤ/8)12yes—
370C22×C43C23×D411yescharacteristic
371C2×D43—44no—
372C2×D43—44no—
373C2×D43—44no—
374C2×D43—44no—
375C2×D43—44no—
376C2×D43—44no—
377C2×D43—88no—
378C2×D43—88no—
379C4×C43—21no—
380C4×C43—21no—
381C4×C43—21no—
382C4×C43—21no—
383C4×C43—21no—
384C4×C43—21no—
385C4×C43—21no—
386C4×C43#53512yes—
387C4×C43C2×AGL(1,ℤ/8)12yes—
388C4×C43C2×AGL(1,ℤ/8)12yes—
389C4×C43#57512yes—
390C4×C43C2×H(5,𝔽2)12yes—
391Dic43—44no—
392Dic43—44no—
393C2×#532—431no—
394C2×#532—431no—
395#3214—434no—
396#3213—434no—
397#3207—434no—
398#3206—432no—
399#3205—432no—
400#3151—432no—
401#3141—432no—
402#3036—434no—
403#3006—434no—
404#2920D4311yescharacteristic, complemented
405C2×C43—22no—
406C2×C43—22no—
407C2×C43—41no—
408C2×C43C2×#53511yescharacteristic
409C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
410C2×C43C2×#57511yescharacteristic
411D43—84no—
412D43—84no—
413C22×#41—432no—
414C22×#41—861no—
415C2×AGL(1,ℤ/8)—438no—
416#532—432no—
417#532—432no—
418#532—432no—
419#532—432no—
420#532—432no—
421#532—432no—
422#532—432no—
423#532—432no—
424#532—861no—
425#532—861no—
426#532—861no—
427#532—861no—
428#532—861no—
429#532—861no—
430#532—861no—
431#532—861no—
432C2×C4⋊Q8—431no—
433C2×C4⋊Q8—431no—
434C2×#127—431no—
435C2×#127—431no—
436C2×#124—432no—
437C2×#124—861no—
438C2×#121—432no—
439C2×#121—861no—
440C2×#121—861no—
441C2×#121—861no—
442C2×C4×D4—432no—
443C2×C4×D4—861no—
444C2×C4×D4—861no—
445C2×C4×D4—861no—
446C22×C42C2×D4311yescharacteristic
447#496—438no—
448#493—434no—
449#492—434no—
450#489—438no—
451#487—434no—
452#486—434no—
453#463—4316no—
454#461—438no—
455#459—438no—
456#449—4316no—
457#448—438no—
458#447—438no—
459#432C2×D4312yescomplemented
460#432C2×D4312yescomplemented
461#431C2×D4312yescomplemented
462#431C2×D4312yescomplemented
463#423C2×D4312yescomplemented
464#417—438no—
465#407C2×D4312yes—
466C4×M16C2×D4312yescomplemented
467C43#6080311yescharacteristic, complemented, Sylow
468C2×#41—434no—
469C2×#41—434no—
470C2×#41—862no—
471C2×#41—862no—
472C2×#41—862no—
473C2×#41—862no—
474C2×#41—862no—
475C2×#41—862no—
476C2×#41—1728no—
477C2×#41—1728no—
478C22×Q8—432no—
479C22×Q8—861no—
480C22×D4—432no—
481C22×D4—432no—
482C22×D4—862no—
483C22×D4—862no—
484C22×D4—861no—
485C22×D4—861no—
486C22×D4—861no—
487C22×D4—861no—
488C23×C4—862no—
489C23×C4—862no—
490C23×C4D17211yescharacteristic
491C23×C4D17211yescharacteristic
492C23×C4C22×D4311yescharacteristic
493AGL(1,ℤ/8)—17216no—
494C2×SD16—4316no—
495C2×D8—4316no—
496C2×M16C22×D4314yes—
497C4⋊Q8—432no—
498C4⋊Q8—432no—
499C4⋊Q8—432no—
500C4⋊Q8—432no—
501C4⋊Q8—861no—
502C4⋊Q8—861no—
503C4⋊Q8—861no—
504C4⋊Q8—861no—
505#127—432no—
506#127—432no—
507#127—432no—
508#127—432no—
509#127—861no—
510#127—861no—
511#127—861no—
512#127—861no—
513#124—434no—
514#124—434no—
515#124—862no—
516#124—862no—
517#124—862no—
518#124—862no—
519#124—862no—
520#124—862no—
521#121—434no—
522#121—434no—
523#121—862no—
524#121—862no—
525#121—862no—
526#121—862no—
527#121—862no—
528#121—862no—
529#121—862no—
530#121—862no—
531#121—862no—
532#121—862no—
533#121—862no—
534#121—862no—
535#121—862no—
536#121—862no—
537C4×D4—434no—
538C4×D4—434no—
539C4×D4—862no—
540C4×D4—862no—
541C4×D4—862no—
542C4×D4—862no—
543C4×D4—862no—
544C4×D4—862no—
545C4×D4—862no—
546C4×D4—862no—
547C4×D4—862no—
548C4×D4—862no—
549C4×D4—862no—
550C4×D4—862no—
551C4×D4—862no—
552C4×D4—862no—
553C2×C4⋊C4—432no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C22⋊C4—862no—
558C2×C22⋊C4—862no—
559C2×C22⋊C4—862no—
560C2×C22⋊C4—862no—
561C2×C42D17211yescharacteristic
562C2×C42D17211yescharacteristic
563C2×C42D17211yescharacteristic
564C2×C42D17211yescharacteristic
565C2×C42D17211yescharacteristic
566C2×C42D17211yescharacteristic
567C2×C42C22×D4311yescharacteristic
568C2×C42C22×D4311yescharacteristic
569C2×C42C22×D4311yescharacteristic
570C2×C42C22×D4311yescharacteristic
571C2×C42C22×D4311yescharacteristic
572C2×C42C22×D4311yescharacteristic
573C4⋊C8C22×D4314yes—
574C4⋊C8C22×D4314yes—
575#103—4316no—
576#102—4316no—
577C22⋊C8C22×D4314yes—
578C22⋊C8C22×D4314yes—
579#97C22×D4314yes—
580C4×C8C22×D4314yes—
581C24—862no—
582C24—862no—
583C24C2×D17211yescharacteristic
584#41—8616no—
585#41—1728no—
586#41—1728no—
587#41—1728no—
588#41—1728no—
589#41—1728no—
590#41—1728no—
591#41—1728no—
592C2×Q8—434no—
593C2×Q8—862no—
594C2×Q8—862no—
595C2×Q8—862no—
596C2×Q8—1724no—
597C2×Q8—1724no—
598C2×D4—434no—
599C2×D4—434no—
600C2×D4—864no—
601C2×D4—864no—
602C2×D4—864no—
603C2×D4—864no—
604C2×D4—862no—
605C2×D4—862no—
606C2×D4—862no—
607C2×D4—862no—
608C2×D4—862no—
609C2×D4—862no—
610C2×D4—862no—
611C2×D4—862no—
612C2×D4—862no—
613C2×D4—862no—
614C2×D4—868no—
615C2×D4—1724no—
616C2×D4—1724no—
617C2×D4—1724no—
618C2×D4—1724no—
619C2×D4—1728no—
620C2×D4—1728no—
621C2×D4—1724no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—42no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—864no—
628C22×C4—864no—
629C22×C4—864no—
630C22×C4—864no—
631C22×C4—1728no—
632C22×C4—1728no—
633C22×C4C2×D17211yescharacteristic
634C22×C4C2×D17211yescharacteristic
635C22×C4C2×D17211yescharacteristic
636C22×C4C2×D17211yescharacteristic
637C22×C4C2×D17211yescharacteristic
638C22×C4C2×D17211yescharacteristic
639C22×C4C2×D17211yescharacteristic
640C22×C4C2×D17211yescharacteristic
641C22×C4C2×D17211yescharacteristic
642C22×C4C2×D17211yescharacteristic
643C22×C4C2×D17211yescharacteristic
644C22×C4C2×D17211yescharacteristic
645C22×C4C2×D17211yescharacteristic
646C22×C4C2×D17211yescharacteristic
647C22×C4C2×D17211yescharacteristic
648C22×C4C23×D4311yescharacteristic
649C22×C4C23×D4311yescharacteristic
650C22×C4C23×D4311yescharacteristic
651SD16—17216no—
652D8—17216no—
653M16—28no—
654C2×C8C23×D4318yes—
655C4⋊C4—434no—
656C4⋊C4—862no—
657C4⋊C4—862no—
658C4⋊C4—862no—
659C4⋊C4—862no—
660C4⋊C4—862no—
661C4⋊C4—862no—
662C4⋊C4—862no—
663C22⋊C4—864no—
664C22⋊C4—864no—
665C22⋊C4—864no—
666C22⋊C4—864no—
667C22⋊C4—864no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C22⋊C4—864no—
671C42C2×D17211yescharacteristic
672C42C2×D17211yescharacteristic
673C42C2×D17211yescharacteristic
674C42C2×D17211yescharacteristic
675C42C2×D17211yescharacteristic
676C42C2×D17211yescharacteristic
677C42C2×D17211yescharacteristic
678C42C2×D17211yescharacteristic
679C42C2×D17211yescharacteristic
680C42C2×D17211yescharacteristic
681C42C2×D17211yescharacteristic
682C42C2×D17211yescharacteristic
683C42C23×D4311yescharacteristic
684C42C23×D4311yescharacteristic
685C42C23×D4311yescharacteristic
686C42C23×D4311yescharacteristic
687C23—22no—
688C23—22no—
689C23—41no—
690C23—864no—
691C23—864no—
692C23—1724no—
693C23—1724no—
694C23—1724no—
695C23—1724no—
696C23—1724no—
697C23—1724no—
698C23C22×D17211yescharacteristic
699C23C22×D17211yescharacteristic
700C23C22×D17211yescharacteristic
701Q8—868no—
702Q8—1724no—
703Q8—1724no—
704Q8—1724no—
705D4—868no—
706D4—868no—
707D4—1724no—
708D4—1724no—
709D4—1724no—
710D4—1724no—
711D4—1728no—
712D4—1728no—
713D4—1728no—
714D4—1728no—
715D4—1724no—
716D4—1724no—
717D4—1724no—
718D4—1724no—
719D4—1724no—
720D4—1724no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—864no—
738C2×C4—864no—
739C2×C4—1728no—
740C2×C4—1728no—
741C2×C4—1724no—
742C2×C4—1724no—
743C2×C4—1728no—
744C2×C4—1728no—
745C2×C4#1306335314yescomplemented
746C2×C4C22×D17211yescharacteristic
747C2×C4C22×D17211yescharacteristic
748C2×C4C22×D17211yescharacteristic
749C2×C4C22×D17211yescharacteristic
750C2×C4C22×D17211yescharacteristic
751C2×C4C22×D17211yescharacteristic
752C2×C4C22×D17211yescharacteristic
753C2×C4C22×D17211yescharacteristic
754C2×C4C22×D17211yescharacteristic
755C2×C4C22×D17211yescharacteristic
756C2×C4C22×D17211yescharacteristic
757C2×C4#1306337114yes—
758C2×C4C24×D4311yescharacteristic
759C8—28no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—44no—
768C22—3448no—
769C22—3448no—
770C22—1724no—
771C22—1724no—
772C22—1724no—
773C22—1724no—
774C22—1724no—
775C22—1724no—
776C22#1458346812yes—
777C22C2×#1306335312yes—
778C22C23×D17211yescharacteristic
779C4—21no—
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—1724no—
787C4—1724no—
788C4#1458346812yes—
789C4C2×#1306335312yes—
790C4C2×#1306335312yes—
791C4#1458369912yes—
792C4C2×#1306337112yes—
793C2—22no—
794C2—22no—
795C2—41no—
796C2—3444no—
797C2—3444no—
798C2C2×#1458346811yescharacteristic
799C2C22×#1306335311yescharacteristic
800C2C2×#1458369911yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2920C2
socleC22×C43C23×D4
hypercenter#2920D43
hypocenterC43#60803
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. C2×#14583449C2semidirect
2. C2×#14583449C2semidirect
3. #19145592C2semidirect
4. #19145584C2semidirect
5. #19145530C2semidirect
6. #19145522C2semidirect
7. #19145515C2semidirect
8. #19145047C2semidirect
9. #19144989C2semidirect
10. #19144061C2semidirect
11. #19143849C2semidirect
12. C43×#2920C2semidirect
15. C2×#13063353C22semidirect
28. #14583449C22semidirect
29. #14583449C22semidirect
30. #14583449C22semidirect
31. #14583449C22semidirect
32. C2×#13063325C22semidirect
33. C2×#13063325C22semidirect
34. C2×#13063322C22semidirect
35. C2×#13063322C22semidirect
37. C2×#13063313C22semidirect
45. C2×C4×D172C22semidirect
46. #14583288C22semidirect
47. #14583276C22semidirect
48. #14583272C22semidirect
49. #14583259C22semidirect
50. #14583250C22semidirect
51. #14583246C22semidirect
52. #14583115C22semidirect
53. #14583105C22semidirect
54. #14583095C22semidirect
55. #14583046C22semidirect
56. #14583040C22semidirect
57. #14583035C22semidirect
58. #14582901C22semidirect
60. C43×#432C22semidirect
61. C43×#432C22semidirect
62. C43×#431C22semidirect
63. C43×#431C22semidirect
64. C43×#423C22semidirect
66. C4×M16×C43C22semidirect
316. C2×C4×C43AGL(1,ℤ/8)semidirect
404. #2920D43semidirect
459. #432C2×D43semidirect
460. #432C2×D43semidirect
461. #431C2×D43semidirect
462. #431C2×D43semidirect
463. #423C2×D43semidirect
466. C4×M16C2×D43semidirect
467. C43#60803semidirect
745. C2×C4#13063353semidirect

Maximal subgroups

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

subgroupindex
C2×#145834492
#191455922
#191455842
#191455302
#191455222
#191455152
#191450472
#191449892
#191440612
#191438492
C43×#29202
#6080343