Finite Group Databasebeta

← #25967342

Subgroups — #25967342

Order 11008.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic, complemented
2C22×#13063299C211yesmaximal, characteristic, complemented
3#19145411C214yesmaximal, complemented
4#19145402C212yesmaximal, complemented
5#19145395C212yesmaximal, complemented
6#19145362C214yesmaximal, complemented
7#19145353C212yesmaximal, complemented
8#19145346C212yesmaximal, complemented
9#19144536C212yesmaximal, complemented
10#19144520C212yesmaximal, complemented
11#19144214C214yesmaximal, complemented
12#19143849C212yesmaximal, complemented
13#19143825C212yesmaximal, complemented
14C2×C43×#407C211yesmaximal, characteristic, complemented
15C22×#10621898C2211yescharacteristic, complemented
16C23×D172C2211yescharacteristic, complemented
17C23×C22⋊D43—21no—
18C2×#13063353C2214yescomplemented
19#14583410—21no—
20#14583410—21no—
21#14583410—21no—
22#14583410—21no—
23#14583410C2212yes—
24#14583410C2212yescomplemented
25#14583410C2212yescomplemented
26#14583410C2212yescomplemented
27C2×#13063308—21no—
28C2×#13063304C2211yescharacteristic, complemented
29C2×#13063304C2211yescharacteristic, complemented
30C2×#13063299—21no—
31C2×#13063299—21no—
32C2×#13063299—21no—
33C2×#13063299—21no—
34C2×#13063299—21no—
35C2×#13063299—21no—
36C2×#13063299C2212yes—
37C2×#13063299C2212yes—
38C2×#13063299C2212yes—
39C2×#13063299C2212yescomplemented
40C2×#13063299C2212yescomplemented
41C2×#13063299C2212yescomplemented
42C2×#13063299C2211yescharacteristic, complemented
43C2×#13063299C2211yescharacteristic, complemented
44C2×#13063294—21no—
45C2×C4×C22⋊D43—21no—
46C2×C4×C22⋊D43—21no—
47C2×#13063284C2211yescharacteristic, complemented
48C22×C4⋊Dic43C2211yescharacteristic, complemented
49C22×(C2×D43)⋊C4—21no—
50#14583235C2214yescomplemented
51#14583230C2214yescomplemented
52#14583224C2218yescomplemented
53#14583218C2214yescomplemented
54#14583218C2214yescomplemented
55#14583213C2214yescomplemented
56#14583213C2214yescomplemented
57#14583152C2218yescomplemented
58#14583145C2218yescomplemented
59#14583135C2218yescomplemented
60#14583128C2218yescomplemented
61#14583052C2214yescomplemented
62#14583052C2214yescomplemented
63#14583046C2218yescomplemented
64#14583040C2214yescomplemented
65#14583035C2214yescomplemented
66#14583035C2214yescomplemented
67#14583035C2214yescomplemented
68#14582941C2214yescomplemented
69#14582905C2214yescomplemented
70#14582901C2214yescomplemented
71C24×C4×C43C2211yescharacteristic
72C22×M16×C43C2212yescomplemented
73C43×#407C2212yescomplemented
74C43×#407C2212yescomplemented
75C43×#407C2212yescomplemented
76C43×#407C2212yescomplemented
77C2×C22⋊C8×C43C2212yescomplemented
78C2×C22⋊C8×C43C2212yescomplemented
79C24×D43—21no—
80C2×#10621898—21no—
81C2×#10621898—21no—
82C2×#10621898—44no—
83C2×#10621898C2312yes—
84C2×#10621898C2312yescomplemented
85C22×Dic86C2311yescharacteristic, complemented
86C22×D172—21no—
87C22×D172—21no—
88C22×D172—21no—
89C22×D172—44no—
90C22×D172C2312yes—
91C22×D172C2312yes—
92C22×D172C2312yes—
93C22×D172C2311yescharacteristic, complemented
94C22×C22⋊D43—21no—
95C22×C22⋊D43—21no—
96C22×C22⋊D43—21no—
97C22×C22⋊D43—22no—
98C22×C22⋊D43—22no—
99C22×C22⋊D43—22no—
100C22×C22⋊D43—22no—
101C22×C22⋊D43—22no—
102C22×C22⋊D43—22no—
103C22×C22⋊D43—48no—
104C23×Dic43—21no—
105C22×C4×D43—21no—
106#13063353—48no—
107C2×#10621873C2318yescomplemented
108C2×D344C2318yescomplemented
109#13063308—22no—
110#13063308—22no—
111#13063308—22no—
112#13063308—22no—
113#13063304—21no—
114#13063304—21no—
115#13063304—21no—
116#13063304—21no—
117#13063304C2312yes—
118#13063304C2312yes—
119#13063304C2312yescomplemented
120#13063304C2312yescomplemented
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#13063299—22no—
131#13063299—22no—
132#13063299—22no—
133#13063299—21no—
134#13063299—21no—
135#13063299—21no—
136#13063299—21no—
137#13063299C2314yes—
138#13063299C2314yes—
139#13063299C2314yes—
140#13063299C2314yes—
141#13063299C2312yes—
142#13063299C2312yes—
143#13063299C2312yescomplemented
144#13063299C2312yescomplemented
145#13063294—22no—
146#13063294—22no—
147#13063294—22no—
148#13063294—22no—
149C4×C22⋊D43—22no—
150C4×C22⋊D43—22no—
151C4×C22⋊D43—22no—
152C4×C22⋊D43—22no—
153C4×C22⋊D43—22no—
154C4×C22⋊D43—22no—
155C4×C22⋊D43—22no—
156C4×C22⋊D43—22no—
157#13063284—21no—
158#13063284—21no—
159#13063284C2312yes—
160#13063284C2312yescomplemented
161C2×C4⋊Dic43—21no—
162C2×C4⋊Dic43—21no—
163C2×C4⋊Dic43—21no—
164C2×C4⋊Dic43C2312yes—
165C2×C4⋊Dic43C2312yes—
166C2×C4⋊Dic43C2312yes—
167C2×C4⋊Dic43C2311yescharacteristic, complemented
168C2×C4⋊Dic43C2311yescharacteristic, complemented
169C2×Dic43⋊C4—21no—
170C2×Dic43⋊C4—21no—
171C2×C22⋊Dic43—21no—
172C2×C22⋊Dic43—21no—
173C2×C22⋊Dic43—21no—
174C2×(C2×D43)⋊C4—22no—
175C2×(C2×D43)⋊C4—22no—
176C2×(C2×D43)⋊C4—22no—
177C2×(C2×D43)⋊C4—22no—
178C2×(C2×D43)⋊C4—22no—
179C2×(C2×D43)⋊C4—22no—
180C2×(C2×D43)⋊C4—21no—
181C2×(C2×D43)⋊C4—21no—
182C2×C4×Dic43—21no—
183#13063259C2318yescomplemented
184#13063257C2318yescomplemented
185#13063250C2318yescomplemented
186#13063247C2318yescomplemented
187#13063247C2318yescomplemented
188#13063247C2318yescomplemented
189C25×C43D411yescharacteristic
190C23×C4×C43—44no—
191C23×C4×C43D411yescharacteristic
192C23×C4×C43D411yescharacteristic
193C23×C4×C43D411yescharacteristic
194C23×C4×C43D411yescharacteristic
195C23×C4×C43D411yescharacteristic
196C23×C4×C43D411yescharacteristic
197C23×C4×C43D411yescharacteristic
198C23×C4×C43C2311yescharacteristic
199C23×C4×C43C2311yescharacteristic
200C23×C4×C43C2311yescharacteristic
201C23×C4×C43C2311yescharacteristic
202C23×C4×C43C2311yescharacteristic
203C23×C4×C43C2311yescharacteristic
204C23×C4×C43C2311yescharacteristic
205C2×M16×C43—44no—
206C2×M16×C43C2314yes—
207C2×M16×C43C2314yescomplemented
208C22×C8×C43C2314yescomplemented
209C22⋊C8×C43C2314yes—
210C22⋊C8×C43C2314yes—
211C22⋊C8×C43C2314yescomplemented
212C22⋊C8×C43C2314yescomplemented
213C24×C43—24no—
214C24×C43—42no—
215C24×C43—42no—
216C24×C43C2×D411yescharacteristic
217C24×C43C2×D411yescharacteristic
218C24×C43C2×D411yescharacteristic
219C24×C43C2×D411yescharacteristic
220C24×C43C2×D411yescharacteristic
221C24×C43C2×D411yescharacteristic
222C24×C43C2×D411yescharacteristic
223C23×D43—21no—
224C23×D43—22no—
225C23×D43—22no—
226C23×D43—22no—
227C23×D43—44no—
228C23×D43—44no—
229C23×D43—44no—
230C22×C4×C43—24no—
231C22×C4×C43—24no—
232C22×C4×C43—24no—
233C22×C4×C43—42no—
234C22×C4×C43—42no—
235C22×C4×C43—42no—
236C22×C4×C43—42no—
237C22×C4×C43—42no—
238C22×C4×C43—42no—
239C22×C4×C43—42no—
240C22×C4×C43—42no—
241C22×C4×C43—42no—
242C22×C4×C43—42no—
243C22×C4×C43—42no—
244C22×C4×C43C2×D411yescharacteristic
245C22×C4×C43C2×D411yescharacteristic
246C22×C4×C43C2×D411yescharacteristic
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2×D411yescharacteristic
251C22×C4×C43C2×D411yescharacteristic
252C22×C4×C43C2×D411yescharacteristic
253C22×C4×C43C2×D411yescharacteristic
254C22×C4×C43C2×D411yescharacteristic
255C22×C4×C43C2×D411yescharacteristic
256C22×C4×C43C2×D411yescharacteristic
257C22×C4×C43C2×D411yescharacteristic
258C22×C4×C43C2×D411yescharacteristic
259C22×C4×C43C2×D411yescharacteristic
260C22×C4×C43C2×D411yescharacteristic
261C22×C4×C43C2×D411yescharacteristic
262C22×C4×C43C2×D411yescharacteristic
263C22×C4×C43C2×D411yescharacteristic
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2411yescharacteristic
266C22×C4×C43C2411yescharacteristic
267C22×C4×C43C2411yescharacteristic
268C22×C4×C43C2411yescharacteristic
269C22×C4×C43C2411yescharacteristic
270C22×C4×C43C2411yescharacteristic
271C22×C4×C43C2411yescharacteristic
272C2×C22⋊D43—22no—
273C2×C22⋊D43—22no—
274C2×C22⋊D43—22no—
275C2×C22⋊D43—22no—
276C2×C22⋊D43—22no—
277C2×C22⋊D43—22no—
278C2×C22⋊D43—24no—
279C2×C22⋊D43—24no—
280C2×C22⋊D43—24no—
281C2×C22⋊D43—24no—
282C2×C22⋊D43—44no—
283C2×C22⋊D43—48no—
284C2×C22⋊D43—48no—
285C2×C22⋊D43—48no—
286C2×C22⋊D43—48no—
287C2×C22⋊D43—48no—
288C2×C22⋊D43—44no—
289C2×C22⋊D43—44no—
290C2×C22⋊D43—48no—
291C22×Dic43—21no—
292C22×Dic43—21no—
293C22×Dic43—22no—
294C22×Dic43—22no—
295C22×Dic43—22no—
296C22×Dic43—21no—
297C22×Dic43—44no—
298#10621898—28no—
299#10621898—44no—
300#10621898—44no—
301#10621898—44no—
302C2×D172—22no—
303C2×D172—22no—
304C2×D172—22no—
305C2×D172—21no—
306C2×D172—28no—
307C2×D172—44no—
308C2×D172—44no—
309C2×D172—42no—
310C2×D172—44no—
311C2×D172—44no—
312C2×D172—44no—
313C2×D172C2414yes—
314C2×D172C2412yes—
315C2×C4×D43—22no—
316C2×C4×D43—22no—
317C2×C4×D43—44no—
318C2×Dic86—21no—
319C2×Dic86—42no—
320C2×Dic86C2412yes—
321M16×C43—28no—
322M16×C43—44no—
323C2×C8×C43—44no—
324C2×C8×C43C2418yes—
325C22⋊Dic43—22no—
326C22⋊Dic43—22no—
327C22⋊Dic43—22no—
328C22⋊Dic43—22no—
329C22⋊Dic43—22no—
330C22⋊Dic43—22no—
331(C2×D43)⋊C4—24no—
332(C2×D43)⋊C4—24no—
333(C2×D43)⋊C4—24no—
334(C2×D43)⋊C4—24no—
335(C2×D43)⋊C4—22no—
336(C2×D43)⋊C4—22no—
337(C2×D43)⋊C4—22no—
338(C2×D43)⋊C4—22no—
339C4⋊Dic43—22no—
340C4⋊Dic43—22no—
341C4⋊Dic43—22no—
342C4⋊Dic43—21no—
343C4⋊Dic43—21no—
344C4⋊Dic43C2412yes—
345C4⋊Dic43C2412yes—
346C4⋊Dic43C2414yes—
347Dic43⋊C4—22no—
348Dic43⋊C4—22no—
349Dic43⋊C4—22no—
350Dic43⋊C4—22no—
351C4×Dic43—22no—
352C4×Dic43—22no—
353D344—48no—
354#10621873—48no—
355C23×C43—22no—
356C23×C43—22no—
357C23×C43—22no—
358C23×C43—22no—
359C23×C43—22no—
360C23×C43—22no—
361C23×C43—22no—
362C23×C43—22no—
363C23×C43—22no—
364C23×C43—22no—
365C23×C43—22no—
366C23×C43—22no—
367C23×C43—41no—
368C23×C43—41no—
369C23×C43—41no—
370C23×C43—41no—
371C23×C43—41no—
372C23×C43—41no—
373C23×C43—41no—
374C23×C43—41no—
375C23×C43—416no—
376C23×C43AGL(1,ℤ/8)14yescomplemented
377C23×C43C22×D411yescharacteristic
378C23×C43C22×D411yescharacteristic
379C23×C43C22×D411yescharacteristic
380C23×C43C22×D411yescharacteristic
381C23×C43C22×D411yescharacteristic
382C23×C43C22×D411yescharacteristic
383C23×C43C22×D411yescharacteristic
384C22×D43—22no—
385C22×D43—24no—
386C22×D43—42no—
387C22×D43—44no—
388C22×D43—44no—
389C22×D43—44no—
390C22×D43—44no—
391C22×D43—42no—
392C22×D43—44no—
393C22×D43—44no—
394C22×D43—44no—
395C22×D43—44no—
396C22×D43—42no—
397C22×D43—44no—
398C22×D43—816no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—41no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43C22×D411yescharacteristic
427C2×C4×C43C22×D411yescharacteristic
428C2×C4×C43C22×D411yescharacteristic
429C2×C4×C43C22×D411yescharacteristic
430C2×C4×C43C22×D411yescharacteristic
431C2×C4×C43C22×D411yescharacteristic
432C2×C4×C43C22×D411yescharacteristic
433C2×C4×C43H(5,𝔽2)14yes—
434C2×C4×C43C2511yescharacteristic
435C22⋊D43—44no—
436C22⋊D43—44no—
437C22⋊D43—48no—
438C22⋊D43—48no—
439C22⋊D43—44no—
440C22⋊D43—44no—
441C22⋊D43—44no—
442C22⋊D43—48no—
443C22⋊D43—48no—
444C22⋊D43—44no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—24no—
449C2×Dic43—42no—
450C2×Dic43—44no—
451C2×Dic43—44no—
452C2×Dic43—42no—
453C2×Dic43—44no—
454C2×Dic43—42no—
455D172—28no—
456D172—24no—
457D172—44no—
458D172—44no—
459D172—42no—
460D172—44no—
461C4×D43—44no—
462C4×D43—44no—
463Dic86—24no—
464Dic86—42no—
465C8×C43—28no—
466#60750—431nomaximal, Sylow
467C22×C43—28no—
468C22×C43—21no—
469C22×C43—21no—
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—21no—
474C22×C43—21no—
475C22×C43—21no—
476C22×C43—21no—
477C22×C43—21no—
478C22×C43—21no—
479C22×C43—21no—
480C22×C43—21no—
481C22×C43—21no—
482C22×C43—21no—
483C22×C43—21no—
484C22×C43—44no—
485C22×C43—44no—
486C22×C43—44no—
487C22×C43—44no—
488C22×C43—44no—
489C22×C43—44no—
490C22×C43#53412yes—
491C22×C43C2×AGL(1,ℤ/8)12yes—
492C22×C43C2×AGL(1,ℤ/8)12yes—
493C22×C43C2×AGL(1,ℤ/8)12yes—
494C22×C43#57512yes—
495C22×C43C23×D411yescharacteristic
496C2×D43—44no—
497C2×D43—42no—
498C2×D43—44no—
499C2×D43—42no—
500C2×D43—44no—
501C2×D43—42no—
502C2×D43—84no—
503C2×D43—88no—
504C2×D43—88no—
505C2×D43—88no—
506C4×C43—21no—
507C4×C43—21no—
508C4×C43—21no—
509C4×C43—21no—
510C4×C43—21no—
511C4×C43—21no—
512C4×C43#53412yes—
513C4×C43C2×H(5,𝔽2)12yes—
514Dic43—42no—
515Dic43—44no—
516Dic43—42no—
517Dic43—42no—
518C2×#525—431no—
519C22×#121—431no—
520#3194—434no—
521#3193—432no—
522#3192—432no—
523#3188—434no—
524#3187—432no—
525#3186—432no—
526#3094—432no—
527#3092—432no—
528#3055—434no—
529#3006—432no—
530#3003—432no—
531C2×#407D4311yescharacteristic, complemented
532C2×C43—22no—
533C2×C43—22no—
534C2×C43—22no—
535C2×C43—22no—
536C2×C43—22no—
537C2×C43—41no—
538C2×C43—41no—
539C2×C43C2×#53411yescharacteristic
540C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
541C2×C43C2×#57511yescharacteristic
542D43—82no—
543D43—84no—
544C22×#41—431no—
545C23×D4—431no—
546C23×D4—861no—
547C24×C4C2×D4311yescharacteristic
548C2×AGL(1,ℤ/8)—434no—
549C22×M16C2×D4312yescomplemented
550#525—432no—
551#525—432no—
552#525—432no—
553#525—432no—
554#525—861no—
555#525—861no—
556#525—861no—
557#525—861no—
558C2×#123—861no—
559C2×C22⋊Q8—431no—
560C2×C22⋊Q8—431no—
561C2×#121—432no—
562C2×#121—432no—
563C2×#121—432no—
564C2×#121—432no—
565C2×#121—432no—
566C2×#121—432no—
567C2×#121—431no—
568C2×#121—431no—
569C2×#121—861no—
570C2×#121—861no—
571C2×#121—861no—
572C2×#121—861no—
573C2×#121—861no—
574C2×#121—861no—
575C2×#120—861no—
576C2×C4×D4—861no—
577C2×C4×D4—861no—
578C2×#117—431no—
579C22×C4⋊C4—431no—
580C22×C22⋊C4—861no—
581#484—434no—
582#483—434no—
583#482—438no—
584#481—434no—
585#481—434no—
586#480—434no—
587#480—434no—
588#469—438no—
589#468—438no—
590#466—438no—
591#465—438no—
592#450—434no—
593#450—434no—
594#449—438no—
595#448—434no—
596#447—434no—
597#447—434no—
598#447—434no—
599#428—434no—
600#418—434no—
601#417—434no—
602#407C2×D4312yescomplemented
603#407C2×D4312yescomplemented
604#407C2×D4312yescomplemented
605#407C2×D4312yescomplemented
606C2×C22⋊C8C2×D4312yescomplemented
607C2×C22⋊C8C2×D4312yescomplemented
608C43#6075011yescharacteristic, complemented, Sylow
609C25—861no—
610C25D17211yescharacteristic
611C2×#41—432no—
612C2×#41—432no—
613C2×#41—861no—
614C2×#41—861no—
615C2×#41—1724no—
616C22×Q8—431no—
617C22×D4—432no—
618C22×D4—432no—
619C22×D4—432no—
620C22×D4—431no—
621C22×D4—861no—
622C22×D4—861no—
623C22×D4—861no—
624C22×D4—862no—
625C22×D4—862no—
626C22×D4—862no—
627C22×D4—862no—
628C22×D4—862no—
629C22×D4—862no—
630C22×D4—861no—
631C22×D4—861no—
632C22×D4—861no—
633C22×D4—1724no—
634C22×D4—1728no—
635C23×C4—44no—
636C23×C4—861no—
637C23×C4—861no—
638C23×C4D17211yescharacteristic
639C23×C4D17211yescharacteristic
640C23×C4D17211yescharacteristic
641C23×C4D17211yescharacteristic
642C23×C4D17211yescharacteristic
643C23×C4D17211yescharacteristic
644C23×C4D17211yescharacteristic
645C23×C4C22×D4311yescharacteristic
646C23×C4C22×D4311yescharacteristic
647C23×C4C22×D4311yescharacteristic
648C23×C4C22×D4311yescharacteristic
649C23×C4C22×D4311yescharacteristic
650C23×C4C22×D4311yescharacteristic
651C23×C4C22×D4311yescharacteristic
652AGL(1,ℤ/8)—1728no—
653C2×SD16—438no—
654C2×D8—438no—
655C2×M16—44no—
656C2×M16C22×D4314yes—
657C2×M16C22×D4314yescomplemented
658C22×C8C22×D4314yescomplemented
659#123—862no—
660#123—862no—
661#123—862no—
662#123—862no—
663C22⋊Q8—432no—
664C22⋊Q8—432no—
665C22⋊Q8—432no—
666C22⋊Q8—432no—
667C22⋊Q8—861no—
668C22⋊Q8—861no—
669C22⋊Q8—861no—
670C22⋊Q8—861no—
671#121—434no—
672#121—434no—
673#121—434no—
674#121—434no—
675#121—432no—
676#121—432no—
677#121—432no—
678#121—432no—
679#121—862no—
680#121—862no—
681#121—862no—
682#121—862no—
683#121—862no—
684#121—862no—
685#121—862no—
686#121—862no—
687#121—862no—
688#121—862no—
689#121—862no—
690#121—862no—
691#121—861no—
692#121—861no—
693#121—861no—
694#121—861no—
695#120—862no—
696#120—862no—
697#120—862no—
698#120—862no—
699C4×D4—862no—
700C4×D4—862no—
701C4×D4—862no—
702C4×D4—862no—
703C4×D4—862no—
704C4×D4—862no—
705C4×D4—862no—
706C4×D4—862no—
707#117—432no—
708#117—432no—
709#117—861no—
710#117—861no—
711C2×C4⋊C4—432no—
712C2×C4⋊C4—432no—
713C2×C4⋊C4—432no—
714C2×C4⋊C4—431no—
715C2×C4⋊C4—431no—
716C2×C4⋊C4—861no—
717C2×C4⋊C4—861no—
718C2×C4⋊C4—861no—
719C2×C4⋊C4—861no—
720C2×C4⋊C4—861no—
721C2×C22⋊C4—861no—
722C2×C22⋊C4—861no—
723C2×C22⋊C4—861no—
724C2×C22⋊C4—862no—
725C2×C22⋊C4—862no—
726C2×C22⋊C4—862no—
727C2×C22⋊C4—862no—
728C2×C22⋊C4—862no—
729C2×C22⋊C4—862no—
730C2×C22⋊C4—861no—
731C2×C22⋊C4—861no—
732C2×C42—861no—
733#107—438no—
734#106—438no—
735#103—438no—
736#102—438no—
737#102—438no—
738#102—438no—
739C22⋊C8C22×D4314yes—
740C22⋊C8C22×D4314yes—
741C22⋊C8C22×D4314yescomplemented
742C22⋊C8C22×D4314yescomplemented
743C24—24no—
744C24—42no—
745C24—42no—
746C24—861no—
747C24—862no—
748C24—862no—
749C24—862no—
750C24—1724no—
751C24—1724no—
752C24—1724no—
753C24C2×D17211yescharacteristic
754C24C2×D17211yescharacteristic
755C24C2×D17211yescharacteristic
756C24C2×D17211yescharacteristic
757C24C2×D17211yescharacteristic
758C24C2×D17211yescharacteristic
759C24C2×D17211yescharacteristic
760#41—868no—
761#41—1724no—
762#41—1724no—
763#41—1724no—
764C2×Q8—432no—
765C2×Q8—861no—
766C2×Q8—1722no—
767C2×D4—432no—
768C2×D4—434no—
769C2×D4—862no—
770C2×D4—862no—
771C2×D4—862no—
772C2×D4—862no—
773C2×D4—862no—
774C2×D4—862no—
775C2×D4—864no—
776C2×D4—864no—
777C2×D4—864no—
778C2×D4—864no—
779C2×D4—862no—
780C2×D4—862no—
781C2×D4—862no—
782C2×D4—861no—
783C2×D4—868no—
784C2×D4—1724no—
785C2×D4—1724no—
786C2×D4—1722no—
787C2×D4—1724no—
788C2×D4—1724no—
789C2×D4—1724no—
790C2×D4—1728no—
791C2×D4—1728no—
792C2×D4—1728no—
793C2×D4—1728no—
794C2×D4—1728no—
795C2×D4—1724no—
796C2×D4—1724no—
797C2×D4—1728no—
798C2×D4—1724no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—862no—
816C22×C4—862no—
817C22×C4—862no—
818C22×C4—861no—
819C22×C4—862no—
820C22×C4—862no—
821C22×C4—1724no—
822C22×C4—1724no—
823C22×C4C2×D17211yescharacteristic
824C22×C4C2×D17211yescharacteristic
825C22×C4C2×D17211yescharacteristic
826C22×C4C2×D17211yescharacteristic
827C22×C4C2×D17211yescharacteristic
828C22×C4C2×D17211yescharacteristic
829C22×C4C2×D17211yescharacteristic
830C22×C4C2×D17211yescharacteristic
831C22×C4C2×D17211yescharacteristic
832C22×C4C2×D17211yescharacteristic
833C22×C4C2×D17211yescharacteristic
834C22×C4C2×D17211yescharacteristic
835C22×C4C2×D17211yescharacteristic
836C22×C4C2×D17211yescharacteristic
837C22×C4C2×D17211yescharacteristic
838C22×C4C2×D17211yescharacteristic
839C22×C4C2×D17211yescharacteristic
840C22×C4C2×D17211yescharacteristic
841C22×C4C2×D17211yescharacteristic
842C22×C4C2×D17211yescharacteristic
843C22×C4C2×D17211yescharacteristic
844C22×C4C23×D4311yescharacteristic
845C22×C4C23×D4311yescharacteristic
846C22×C4C23×D4311yescharacteristic
847C22×C4C23×D4311yescharacteristic
848C22×C4C23×D4311yescharacteristic
849C22×C4C23×D4311yescharacteristic
850C22×C4C23×D4311yescharacteristic
851SD16—1728no—
852D8—1728no—
853M16—28no—
854M16—44no—
855C2×C8—44no—
856C2×C8C23×D4318yes—
857C4⋊C4—432no—
858C4⋊C4—432no—
859C4⋊C4—434no—
860C4⋊C4—862no—
861C4⋊C4—862no—
862C4⋊C4—862no—
863C4⋊C4—861no—
864C4⋊C4—861no—
865C4⋊C4—862no—
866C4⋊C4—862no—
867C4⋊C4—862no—
868C4⋊C4—862no—
869C22⋊C4—862no—
870C22⋊C4—862no—
871C22⋊C4—862no—
872C22⋊C4—862no—
873C22⋊C4—862no—
874C22⋊C4—862no—
875C22⋊C4—864no—
876C22⋊C4—864no—
877C22⋊C4—864no—
878C22⋊C4—864no—
879C22⋊C4—862no—
880C22⋊C4—862no—
881C22⋊C4—862no—
882C22⋊C4—862no—
883C42—862no—
884C42—862no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—416no—
906C23—862no—
907C23—864no—
908C23—34416no—
909C23—1722no—
910C23—1724no—
911C23—1724no—
912C23—1724no—
913C23—1724no—
914C23—1722no—
915C23—1724no—
916C23—1724no—
917C23—1724no—
918C23—1722no—
919C23—1724no—
920C23—1724no—
921C23#1306335314yescomplemented
922C23C22×D17211yescharacteristic
923C23C22×D17211yescharacteristic
924C23C22×D17211yescharacteristic
925C23C22×D17211yescharacteristic
926C23C22×D17211yescharacteristic
927C23C22×D17211yescharacteristic
928C23C22×D17211yescharacteristic
929Q8—864no—
930Q8—1722no—
931D4—864no—
932D4—868no—
933D4—1724no—
934D4—1724no—
935D4—1722no—
936D4—1728no—
937D4—1728no—
938D4—1724no—
939D4—1724no—
940D4—1728no—
941D4—1728no—
942D4—1724no—
943D4—1724no—
944D4—1724no—
945D4—1724no—
946D4—1724no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—862no—
975C2×C4—862no—
976C2×C4—864no—
977C2×C4—862no—
978C2×C4—1724no—
979C2×C4—1724no—
980C2×C4—1724no—
981C2×C4—1722no—
982C2×C4—1722no—
983C2×C4—1724no—
984C2×C4—1722no—
985C2×C4—1724no—
986C2×C4C22×D17211yescharacteristic
987C2×C4C22×D17211yescharacteristic
988C2×C4C22×D17211yescharacteristic
989C2×C4C22×D17211yescharacteristic
990C2×C4C22×D17211yescharacteristic
991C2×C4C22×D17211yescharacteristic
992C2×C4C22×D17211yescharacteristic
993C2×C4#1306337014yes—
994C2×C4C24×D4311yescharacteristic
995C8—28no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—3448no—
1020C22—3448no—
1021C22—3448no—
1022C22—3444no—
1023C22—1724no—
1024C22—1722no—
1025C22—1722no—
1026C22—1724no—
1027C22—1722no—
1028C22—1724no—
1029C22#1458346112yes—
1030C22C2×#1306335312yes—
1031C22C2×#1306335312yes—
1032C22C2×#1306335312yes—
1033C22#1458369912yes—
1034C22C23×D17211yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—1724no—
1042C4—1722no—
1043C4—1722no—
1044C4—1722no—
1045C4#1458346112yes—
1046C4C2×#1306337012yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—3444no—
1055C2—3442no—
1056C2C2×#1458346111yescharacteristic
1057C2C22×#1306335311yescharacteristic
1058C2C2×#1458369911yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#407C2
socleC22×C43C23×D4
hypercenterC2×#407D43
hypocenterC43#60750
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#14583410C2semidirect
2. C22×#13063299C2semidirect
3. #19145411C2semidirect
4. #19145402C2semidirect
5. #19145395C2semidirect
6. #19145362C2semidirect
7. #19145353C2semidirect
8. #19145346C2semidirect
9. #19144536C2semidirect
10. #19144520C2semidirect
11. #19144214C2semidirect
12. #19143849C2semidirect
13. #19143825C2semidirect
14. C2×C43×#407C2semidirect
15. C22×#10621898C22semidirect
16. C23×D172C22semidirect
18. C2×#13063353C22semidirect
24. #14583410C22semidirect
25. #14583410C22semidirect
26. #14583410C22semidirect
28. C2×#13063304C22semidirect
29. C2×#13063304C22semidirect
39. C2×#13063299C22semidirect
40. C2×#13063299C22semidirect
41. C2×#13063299C22semidirect
42. C2×#13063299C22semidirect
43. C2×#13063299C22semidirect
47. C2×#13063284C22semidirect
48. C22×C4⋊Dic43C22semidirect
50. #14583235C22semidirect
51. #14583230C22semidirect
52. #14583224C22semidirect
53. #14583218C22semidirect
54. #14583218C22semidirect
55. #14583213C22semidirect
56. #14583213C22semidirect
57. #14583152C22semidirect
58. #14583145C22semidirect
59. #14583135C22semidirect
60. #14583128C22semidirect
61. #14583052C22semidirect
62. #14583052C22semidirect
63. #14583046C22semidirect
64. #14583040C22semidirect
65. #14583035C22semidirect
66. #14583035C22semidirect
67. #14583035C22semidirect
68. #14582941C22semidirect
69. #14582905C22semidirect
70. #14582901C22semidirect
72. C22×M16×C43C22semidirect
73. C43×#407C22semidirect
74. C43×#407C22semidirect
75. C43×#407C22semidirect
76. C43×#407C22semidirect
77. C2×C22⋊C8×C43C22semidirect
78. C2×C22⋊C8×C43C22semidirect
84. C2×#10621898C23semidirect
85. C22×Dic86C23semidirect
93. C22×D172C23semidirect
107. C2×#10621873C23semidirect
108. C2×D344C23semidirect
119. #13063304C23semidirect
120. #13063304C23semidirect
143. #13063299C23semidirect
144. #13063299C23semidirect
160. #13063284C23semidirect
167. C2×C4⋊Dic43C23semidirect
168. C2×C4⋊Dic43C23semidirect
183. #13063259C23semidirect
184. #13063257C23semidirect
185. #13063250C23semidirect
186. #13063247C23semidirect
187. #13063247C23semidirect
188. #13063247C23semidirect
207. C2×M16×C43C23semidirect
208. C22×C8×C43C23semidirect
211. C22⋊C8×C43C23semidirect
212. C22⋊C8×C43C23semidirect
376. C23×C43AGL(1,ℤ/8)semidirect
531. C2×#407D43semidirect
549. C22×M16C2×D43semidirect
602. #407C2×D43semidirect
603. #407C2×D43semidirect
604. #407C2×D43semidirect
605. #407C2×D43semidirect
606. C2×C22⋊C8C2×D43semidirect
607. C2×C22⋊C8C2×D43semidirect
608. C43#60750semidirect
657. C2×M16C22×D43semidirect
658. C22×C8C22×D43semidirect
741. C22⋊C8C22×D43semidirect
742. C22⋊C8C22×D43semidirect
921. C23#13063353semidirect

Maximal subgroups

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

subgroupindex
C2×#145834102
C22×#130632992
#191454112
#191454022
#191453952
#191453622
#191453532
#191453462
#191445362
#191445202
#191442142
#191438492
#191438252
C2×C43×#4072
#6075043