Finite Group Databasebeta

← #25967340

Subgroups — #25967340

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
2#19145409C214yesmaximal, complemented
3#19145401C212yesmaximal, complemented
4#19145392C212yesmaximal, complemented
5#19145360C214yesmaximal, complemented
6#19145352C212yesmaximal, complemented
7#19145343C212yesmaximal, complemented
8#19144531C212yesmaximal, complemented
9#19144518C212yesmaximal, complemented
10#19144210C214yesmaximal, complemented
11#19143845C212yesmaximal, complemented
12#19143822C212yesmaximal, complemented
13C2×#14582863C211yesmaximal, characteristic, complemented
14C22×#121×C43C211yesmaximal, characteristic, complemented
15C22×#10621898C2211yescharacteristic, complemented
16C2×#13063351C2214yescomplemented
17C22×#10621877C2212yescomplemented
18#14583410—21no—
19#14583410—21no—
20#14583410—21no—
21#14583410—21no—
22#14583410C2212yes—
23#14583410C2212yescomplemented
24#14583410C2212yescomplemented
25#14583410C2212yescomplemented
26C2×#13063308—21no—
27C2×#13063304C2211yescharacteristic, complemented
28C2×#13063304C2211yescharacteristic, complemented
29C2×#13063299C2211yescharacteristic, complemented
30C2×#13063299C2211yescharacteristic, complemented
31C2×#13063294—21no—
32C2×C4×C22⋊D43—21no—
33C2×C4×C22⋊D43—21no—
34C2×#13063284C2211yescharacteristic, complemented
35#14583234C2214yescomplemented
36#14583229C2214yescomplemented
37#14583220C2218yescomplemented
38#14583217C2214yescomplemented
39#14583215C2214yescomplemented
40#14583212C2214yescomplemented
41#14583210C2214yescomplemented
42#14583150C2218yescomplemented
43#14583143C2218yescomplemented
44#14583133C2218yescomplemented
45#14583126C2218yescomplemented
46#14583050C2214yescomplemented
47#14583050C2214yescomplemented
48#14583042C2218yescomplemented
49#14583037C2214yescomplemented
50#14583033C2214yescomplemented
51#14583033C2214yescomplemented
52#14583032C2214yescomplemented
53#14582939C2214yescomplemented
54#14582904C2214yescomplemented
55#14582898C2214yescomplemented
56#14582863C2212yescomplemented
57#14582863C2212yescomplemented
58#14582863C2212yescomplemented
59#14582863C2212yescomplemented
60C2×C22⋊(C43⋊C8)C2212yescomplemented
61C2×C22⋊(C43⋊C8)C2212yescomplemented
62C23×D4×C43—21no—
63C23×D4×C43C2211yescharacteristic, complemented
64C24×C4×C43C2211yescharacteristic
65C2×#121×C43—21no—
66C2×#121×C43—21no—
67C2×#121×C43—21no—
68C2×#121×C43—21no—
69C2×#121×C43—21no—
70C2×#121×C43—21no—
71C2×#121×C43C2212yes—
72C2×#121×C43C2212yes—
73C2×#121×C43C2212yes—
74C2×#121×C43C2212yescomplemented
75C2×#121×C43C2212yescomplemented
76C2×#121×C43C2212yescomplemented
77C22×C4⋊C4×C43C2211yescharacteristic, complemented
78C22×C22⋊C4×C43—21no—
79C2×#10621898—21no—
80C2×#10621898—21no—
81C2×#10621898—44no—
82C2×#10621898C2312yes—
83C2×#10621898C2312yescomplemented
84C22×Dic86C2311yescharacteristic, complemented
85C22×D172C2311yescharacteristic, complemented
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C4×D43—21no—
90#13063351—48no—
91C2×#10621883C2318yescomplemented
92C2×#10621882C2318yescomplemented
93C2×#10621877—44no—
94C2×#10621877C2314yes—
95C2×#10621877C2314yescomplemented
96C22×C43⋊C8C2314yescomplemented
97#13063308—22no—
98#13063308—22no—
99#13063308—22no—
100#13063308—22no—
101#13063304—21no—
102#13063304—21no—
103#13063304—21no—
104#13063304—21no—
105#13063304C2312yes—
106#13063304C2312yes—
107#13063304C2312yescomplemented
108#13063304C2312yescomplemented
109#13063299—21no—
110#13063299—21no—
111#13063299—21no—
112#13063299—21no—
113#13063299C2312yes—
114#13063299C2312yes—
115#13063299C2312yescomplemented
116#13063299C2312yescomplemented
117#13063294—22no—
118#13063294—22no—
119#13063294—22no—
120#13063294—22no—
121C4×C22⋊D43—22no—
122C4×C22⋊D43—22no—
123C4×C22⋊D43—22no—
124C4×C22⋊D43—22no—
125C4×C22⋊D43—22no—
126C4×C22⋊D43—22no—
127C4×C22⋊D43—22no—
128C4×C22⋊D43—22no—
129#13063284—21no—
130#13063284—21no—
131#13063284C2312yes—
132#13063284C2312yescomplemented
133C2×C4⋊Dic43C2311yescharacteristic, complemented
134C2×C4⋊Dic43C2311yescharacteristic, complemented
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×C4×Dic43—21no—
143#13063258C2318yescomplemented
144#13063256C2318yescomplemented
145#13063248C2318yescomplemented
146#13063246C2318yescomplemented
147#13063246C2318yescomplemented
148#13063245C2318yescomplemented
149C22⋊(C43⋊C8)C2314yes—
150C22⋊(C43⋊C8)C2314yes—
151C22⋊(C43⋊C8)C2314yescomplemented
152C22⋊(C43⋊C8)C2314yescomplemented
153C25×C43—21no—
154C25×C43D411yescharacteristic
155C22×D4×C43—22no—
156C22×D4×C43—22no—
157C22×D4×C43—22no—
158C22×D4×C43—22no—
159C22×D4×C43—22no—
160C22×D4×C43—22no—
161C22×D4×C43—21no—
162C22×D4×C43—21no—
163C22×D4×C43—21no—
164C22×D4×C43—44no—
165C22×D4×C43—48no—
166C22×D4×C43C2312yes—
167C22×D4×C43C2312yes—
168C22×D4×C43C2312yes—
169C23×C4×C43—21no—
170C23×C4×C43—44no—
171C23×C4×C43D411yescharacteristic
172C23×C4×C43D411yescharacteristic
173C23×C4×C43D411yescharacteristic
174C23×C4×C43D411yescharacteristic
175C23×C4×C43D411yescharacteristic
176C23×C4×C43D411yescharacteristic
177C23×C4×C43D411yescharacteristic
178C23×C4×C43C2311yescharacteristic
179C23×C4×C43C2311yescharacteristic
180C23×C4×C43C2311yescharacteristic
181C23×C4×C43C2311yescharacteristic
182C23×C4×C43C2311yescharacteristic
183C23×C4×C43C2311yescharacteristic
184C23×C4×C43C2311yescharacteristic
185#121×C43—22no—
186#121×C43—22no—
187#121×C43—22no—
188#121×C43—22no—
189#121×C43—22no—
190#121×C43—22no—
191#121×C43—22no—
192#121×C43—22no—
193#121×C43—22no—
194#121×C43—22no—
195#121×C43—22no—
196#121×C43—22no—
197#121×C43C2314yes—
198#121×C43C2314yes—
199#121×C43C2314yes—
200#121×C43C2314yes—
201C2×C4⋊C4×C43—21no—
202C2×C4⋊C4×C43—21no—
203C2×C4⋊C4×C43—21no—
204C2×C4⋊C4×C43C2312yes—
205C2×C4⋊C4×C43C2312yes—
206C2×C4⋊C4×C43C2312yes—
207C2×C22⋊C4×C43—22no—
208C2×C22⋊C4×C43—22no—
209C2×C22⋊C4×C43—22no—
210C2×C22⋊C4×C43—22no—
211C2×C22⋊C4×C43—22no—
212C2×C22⋊C4×C43—22no—
213C24×C43—24no—
214C24×C43—22no—
215C24×C43—22no—
216C24×C43—22no—
217C24×C43—42no—
218C24×C43—42no—
219C24×C43—44no—
220C24×C43—44no—
221C24×C43—44no—
222C24×C43C2×D411yescharacteristic
223C24×C43C2×D411yescharacteristic
224C24×C43C2×D411yescharacteristic
225C24×C43C2×D411yescharacteristic
226C24×C43C2×D411yescharacteristic
227C24×C43C2×D411yescharacteristic
228C24×C43C2×D411yescharacteristic
229C23×D43—21no—
230C2×D4×C43—22no—
231C2×D4×C43—22no—
232C2×D4×C43—22no—
233C2×D4×C43—24no—
234C2×D4×C43—24no—
235C2×D4×C43—24no—
236C2×D4×C43—24no—
237C2×D4×C43—28no—
238C2×D4×C43—48no—
239C2×D4×C43—48no—
240C2×D4×C43—48no—
241C2×D4×C43—48no—
242C2×D4×C43—48no—
243C2×D4×C43—44no—
244C2×D4×C43—44no—
245C2×D4×C43—44no—
246C2×D4×C43—44no—
247C2×D4×C43—44no—
248C2×D4×C43—48no—
249C2×D4×C43C2414yes—
250C22×C4×C43—24no—
251C22×C4×C43—24no—
252C22×C4×C43—24no—
253C22×C4×C43—22no—
254C22×C4×C43—22no—
255C22×C4×C43—22no—
256C22×C4×C43—42no—
257C22×C4×C43—42no—
258C22×C4×C43—42no—
259C22×C4×C43—44no—
260C22×C4×C43—42no—
261C22×C4×C43—42no—
262C22×C4×C43—42no—
263C22×C4×C43—42no—
264C22×C4×C43—42no—
265C22×C4×C43—42no—
266C22×C4×C43—42no—
267C22×C4×C43—42no—
268C22×C4×C43C2×D411yescharacteristic
269C22×C4×C43C2×D411yescharacteristic
270C22×C4×C43C2×D411yescharacteristic
271C22×C4×C43C2×D411yescharacteristic
272C22×C4×C43C2×D411yescharacteristic
273C22×C4×C43C2×D411yescharacteristic
274C22×C4×C43C2×D411yescharacteristic
275C22×C4×C43C2×D411yescharacteristic
276C22×C4×C43C2×D411yescharacteristic
277C22×C4×C43C2×D411yescharacteristic
278C22×C4×C43C2×D411yescharacteristic
279C22×C4×C43C2×D411yescharacteristic
280C22×C4×C43C2×D411yescharacteristic
281C22×C4×C43C2×D411yescharacteristic
282C22×C4×C43C2×D411yescharacteristic
283C22×C4×C43C2×D411yescharacteristic
284C22×C4×C43C2×D411yescharacteristic
285C22×C4×C43C2×D411yescharacteristic
286C22×C4×C43C2×D411yescharacteristic
287C22×C4×C43C2×D411yescharacteristic
288C22×C4×C43C2×D411yescharacteristic
289C22×C4×C43C2411yescharacteristic
290C22×C4×C43C2411yescharacteristic
291C22×C4×C43C2411yescharacteristic
292C22×C4×C43C2411yescharacteristic
293C22×C4×C43C2411yescharacteristic
294C22×C4×C43C2411yescharacteristic
295C22×C4×C43C2411yescharacteristic
296C2×C22⋊D43—22no—
297C2×C22⋊D43—22no—
298C2×C22⋊D43—22no—
299C2×C22⋊D43—22no—
300C2×C22⋊D43—22no—
301C2×C22⋊D43—22no—
302C2×C22⋊D43—44no—
303C2×C22⋊D43—44no—
304C2×C22⋊D43—44no—
305C22×Dic43—21no—
306C22×Dic43—21no—
307C22×Dic43—21no—
308#10621898—28no—
309#10621898—44no—
310#10621898—44no—
311#10621898—44no—
312C2×D172—21no—
313C2×D172—42no—
314C2×D172C2412yes—
315C2×C4×D43—22no—
316C2×C4×D43—22no—
317C2×C4×D43—44no—
318C2×Dic86—21no—
319C2×Dic86—42no—
320C2×Dic86C2412yes—
321C4⋊C4×C43—22no—
322C4⋊C4×C43—22no—
323C4⋊C4×C43—22no—
324C4⋊C4×C43C2414yes—
325C22⋊C4×C43—24no—
326C22⋊C4×C43—24no—
327C22⋊C4×C43—24no—
328C22⋊C4×C43—24no—
329C22⋊Dic43—22no—
330C22⋊Dic43—22no—
331C22⋊Dic43—22no—
332C22⋊Dic43—22no—
333C22⋊Dic43—22no—
334C22⋊Dic43—22no—
335#10621883—48no—
336#10621882—48no—
337(C2×D43)⋊C4—22no—
338(C2×D43)⋊C4—22no—
339(C2×D43)⋊C4—22no—
340(C2×D43)⋊C4—22no—
341C4⋊Dic43—21no—
342C4⋊Dic43—21no—
343C4⋊Dic43C2412yes—
344C4⋊Dic43C2412yes—
345Dic43⋊C4—22no—
346Dic43⋊C4—22no—
347Dic43⋊C4—22no—
348Dic43⋊C4—22no—
349C4×Dic43—22no—
350C4×Dic43—22no—
351#10621877—28no—
352#10621877—44no—
353C2×C43⋊C8—44no—
354C2×C43⋊C8C2418yes—
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—24no—
368C23×C43—41no—
369C23×C43—41no—
370C23×C43—41no—
371C23×C43—41no—
372C23×C43—41no—
373C23×C43—41no—
374C23×C43—41no—
375C23×C43—41no—
376C23×C43—416no—
377C23×C43—44no—
378C23×C43—44no—
379C23×C43—44no—
380C23×C43—44no—
381C23×C43—44no—
382C23×C43—44no—
383C23×C43—44no—
384C23×C43—44no—
385C23×C43—44no—
386C23×C43—816no—
387C23×C43AGL(1,ℤ/8)14yescomplemented
388C23×C43C22×D411yescharacteristic
389C23×C43C22×D411yescharacteristic
390C23×C43C22×D411yescharacteristic
391C23×C43C22×D411yescharacteristic
392C23×C43C22×D411yescharacteristic
393C23×C43C22×D411yescharacteristic
394C23×C43C22×D411yescharacteristic
395C22×D43—22no—
396C22×D43—42no—
397C22×D43—42no—
398C22×D43—42no—
399D4×C43—28no—
400D4×C43—44no—
401D4×C43—44no—
402D4×C43—48no—
403D4×C43—48no—
404D4×C43—48no—
405D4×C43—48no—
406D4×C43—44no—
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—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—24no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—41no—
427C2×C4×C43—41no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—44no—
436C2×C4×C43—44no—
437C2×C4×C43—44no—
438C2×C4×C43C22×D411yescharacteristic
439C2×C4×C43C22×D411yescharacteristic
440C2×C4×C43C22×D411yescharacteristic
441C2×C4×C43C22×D411yescharacteristic
442C2×C4×C43C22×D411yescharacteristic
443C2×C4×C43C22×D411yescharacteristic
444C2×C4×C43C22×D411yescharacteristic
445C2×C4×C43H(5,𝔽2)14yes—
446C2×C4×C43C2511yescharacteristic
447C22⋊D43—44no—
448C22⋊D43—44no—
449C22⋊D43—44no—
450C22⋊D43—44no—
451C22⋊D43—44no—
452C22⋊D43—44no—
453C2×Dic43—22no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—42no—
457C2×Dic43—42no—
458C2×Dic43—42no—
459D172—24no—
460D172—42no—
461C4×D43—44no—
462C4×D43—44no—
463Dic86—24no—
464Dic86—42no—
465C43⋊C8—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—44no—
491C22×C43—44no—
492C22×C43—44no—
493C22×C43—88no—
494C22×C43—88no—
495C22×C43—88no—
496C22×C43#53412yes—
497C22×C43C2×AGL(1,ℤ/8)12yes—
498C22×C43C2×AGL(1,ℤ/8)12yes—
499C22×C43C2×AGL(1,ℤ/8)12yes—
500C22×C43#57512yes—
501C22×C43C23×D411yescharacteristic
502C2×D43—42no—
503C2×D43—42no—
504C2×D43—42no—
505C2×D43—84no—
506C4×C43—21no—
507C4×C43—21no—
508C4×C43—21no—
509C4×C43—21no—
510C4×C43—21no—
511C4×C43—21no—
512C4×C43—44no—
513C4×C43#53412yes—
514C4×C43C2×H(5,𝔽2)12yes—
515Dic43—42no—
516Dic43—42no—
517Dic43—42no—
518C2×#525—431no—
519C22×#121D4311yescharacteristic, complemented
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×#407—431no—
532C2×C43—22no—
533C2×C43—22no—
534C2×C43—22no—
535C2×C43—22no—
536C2×C43—22no—
537C2×C43—41no—
538C2×C43—41no—
539C2×C43—84no—
540C2×C43C2×#53411yescharacteristic
541C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
542C2×C43C2×#57511yescharacteristic
543D43—82no—
544C22×#41—431no—
545C23×D4—21no—
546C23×D4C2×D4311yescharacteristic, complemented
547C24×C4C2×D4311yescharacteristic
548C2×AGL(1,ℤ/8)—434no—
549C22×M16—432no—
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—21no—
562C2×#121—21no—
563C2×#121—21no—
564C2×#121—21no—
565C2×#121—21no—
566C2×#121—21no—
567C2×#121—431no—
568C2×#121—431no—
569C2×#121C2×D4312yes—
570C2×#121C2×D4312yes—
571C2×#121C2×D4312yes—
572C2×#121C2×D4312yescomplemented
573C2×#121C2×D4312yescomplemented
574C2×#121C2×D4312yescomplemented
575C2×#120—861no—
576C2×C4×D4—861no—
577C2×C4×D4—861no—
578C2×#117—431no—
579C22×C4⋊C4C2×D4311yescharacteristic, complemented
580C22×C22⋊C4—21no—
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#407—432no—
603#407—432no—
604#407—432no—
605#407—432no—
606C2×C22⋊C8—432no—
607C2×C22⋊C8—432no—
608C43#6075011yescharacteristic, complemented, Sylow
609C25—21no—
610C25C22⋊D4311yescharacteristic
611C2×#41—432no—
612C2×#41—432no—
613C2×#41—861no—
614C2×#41—861no—
615C2×#41—1724no—
616C22×Q8—431no—
617C22×D4—22no—
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—21no—
626C22×D4—44no—
627C22×D4—48no—
628C22×D4—431no—
629C22×D4—861no—
630C22×D4—861no—
631C22×D4—861no—
632C22×D4C22×D4312yes—
633C22×D4C22×D4312yes—
634C22×D4C22×D4312yes—
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—861no—
638C23×C4C22⋊D4311yescharacteristic
639C23×C4C22⋊D4311yescharacteristic
640C23×C4C22⋊D4311yescharacteristic
641C23×C4C22⋊D4311yescharacteristic
642C23×C4C22⋊D4311yescharacteristic
643C23×C4C22⋊D4311yescharacteristic
644C23×C4C22⋊D4311yescharacteristic
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—434no—
656C2×M16—434no—
657C2×M16—1724no—
658C22×C8—434no—
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—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—22no—
680#121—22no—
681#121—22no—
682#121—22no—
683#121—432no—
684#121—432no—
685#121—432no—
686#121—432no—
687#121—861no—
688#121—861no—
689#121—861no—
690#121—861no—
691#121C22×D4314yes—
692#121C22×D4314yes—
693#121C22×D4314yes—
694#121C22×D4314yes—
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—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—431no—
715C2×C4⋊C4—431no—
716C2×C4⋊C4—861no—
717C2×C4⋊C4—861no—
718C2×C4⋊C4C22×D4312yes—
719C2×C4⋊C4C22×D4312yes—
720C2×C4⋊C4C22×D4312yes—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—861no—
728C2×C22⋊C4—861no—
729C2×C22⋊C4—861no—
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⋊C8—434no—
740C22⋊C8—434no—
741C22⋊C8—434no—
742C22⋊C8—434no—
743C24—24no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—42no—
748C24—42no—
749C24—44no—
750C24—44no—
751C24—44no—
752C24—861no—
753C24C2×C22⋊D4311yescharacteristic
754C24C2×C22⋊D4311yescharacteristic
755C24C2×C22⋊D4311yescharacteristic
756C24C2×C22⋊D4311yescharacteristic
757C24C2×C22⋊D4311yescharacteristic
758C24C2×C22⋊D4311yescharacteristic
759C24C2×C22⋊D4311yescharacteristic
760#41—868no—
761#41—1724no—
762#41—1724no—
763#41—1724no—
764C2×Q8—432no—
765C2×Q8—861no—
766C2×Q8—1722no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—28no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—432no—
787C2×D4—862no—
788C2×D4—862no—
789C2×D4—862no—
790C2×D4—862no—
791C2×D4—862no—
792C2×D4—862no—
793C2×D4—861no—
794C2×D4—1722no—
795C2×D4—1724no—
796C2×D4—1724no—
797C2×D4—1724no—
798C2×D4C23×D4314yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
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—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—44no—
817C22×C4—861no—
818C22×C4—861no—
819C22×C4—861no—
820C22×C4—862no—
821C22×C4—862no—
822C22×C4—1724no—
823C22×C4C2×C22⋊D4311yescharacteristic
824C22×C4C2×C22⋊D4311yescharacteristic
825C22×C4C2×C22⋊D4311yescharacteristic
826C22×C4C2×C22⋊D4311yescharacteristic
827C22×C4C2×C22⋊D4311yescharacteristic
828C22×C4C2×C22⋊D4311yescharacteristic
829C22×C4C2×C22⋊D4311yescharacteristic
830C22×C4C2×C22⋊D4311yescharacteristic
831C22×C4C2×C22⋊D4311yescharacteristic
832C22×C4C2×C22⋊D4311yescharacteristic
833C22×C4C2×C22⋊D4311yescharacteristic
834C22×C4C2×C22⋊D4311yescharacteristic
835C22×C4C2×C22⋊D4311yescharacteristic
836C22×C4C2×C22⋊D4311yescharacteristic
837C22×C4C2×C22⋊D4311yescharacteristic
838C22×C4C2×C22⋊D4311yescharacteristic
839C22×C4C2×C22⋊D4311yescharacteristic
840C22×C4C2×C22⋊D4311yescharacteristic
841C22×C4C2×C22⋊D4311yescharacteristic
842C22×C4C2×C22⋊D4311yescharacteristic
843C22×C4C2×C22⋊D4311yescharacteristic
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—868no—
854M16—1724no—
855C2×C8—438no—
856C2×C8—1724no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—432no—
861C4⋊C4—432no—
862C4⋊C4—861no—
863C4⋊C4—861no—
864C4⋊C4—862no—
865C4⋊C4—862no—
866C4⋊C4—862no—
867C4⋊C4—862no—
868C4⋊C4C23×D4314yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—862no—
874C22⋊C4—862no—
875C22⋊C4—862no—
876C22⋊C4—862no—
877C22⋊C4—862no—
878C22⋊C4—862no—
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—24no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—44no—
916C23—816no—
917C23—862no—
918C23—1722no—
919C23—1722no—
920C23—1722no—
921C23#1306335114yescomplemented
922C23C22×C22⋊D4311yescharacteristic
923C23C22×C22⋊D4311yescharacteristic
924C23C22×C22⋊D4311yescharacteristic
925C23C22×C22⋊D4311yescharacteristic
926C23C22×C22⋊D4311yescharacteristic
927C23C22×C22⋊D4311yescharacteristic
928C23C22×C22⋊D4311yescharacteristic
929Q8—864no—
930Q8—1722no—
931D4—28no—
932D4—44no—
933D4—44no—
934D4—48no—
935D4—48no—
936D4—48no—
937D4—48no—
938D4—44no—
939D4—864no—
940D4—1722no—
941D4—1724no—
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—24no—
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—41no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—44no—
978C2×C4—862no—
979C2×C4—862no—
980C2×C4—862no—
981C2×C4—1724no—
982C2×C4—1722no—
983C2×C4—1722no—
984C2×C4—1722no—
985C2×C4—1724no—
986C2×C4C22×C22⋊D4311yescharacteristic
987C2×C4C22×C22⋊D4311yescharacteristic
988C2×C4C22×C22⋊D4311yescharacteristic
989C2×C4C22×C22⋊D4311yescharacteristic
990C2×C4C22×C22⋊D4311yescharacteristic
991C2×C4C22×C22⋊D4311yescharacteristic
992C2×C4C22×C22⋊D4311yescharacteristic
993C2×C4#1306337014yes—
994C2×C4C24×D4311yescharacteristic
995C8—868no—
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—44no—
1020C22—44no—
1021C22—44no—
1022C22—88no—
1023C22—88no—
1024C22—88no—
1025C22—3444no—
1026C22—1722no—
1027C22—1722no—
1028C22—1722no—
1029C22#1458345812yes—
1030C22C2×#1306335112yes—
1031C22C2×#1306335112yes—
1032C22C2×#1306335112yes—
1033C22#1458369712yes—
1034C22C23×C22⋊D4311yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—44no—
1042C4—1722no—
1043C4—1722no—
1044C4—1722no—
1045C4#1458345812yes—
1046C4C2×#1306337012yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—84no—
1055C2—3442no—
1056C2C2×#1458345811yescharacteristic
1057C2C22×#1306335111yescharacteristic
1058C2C2×#1458369711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#121×C43C2
socleC22×C43C23×D4
hypercenterC22×#121D43
hypocenterC43#60750
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14583410C2semidirect
2. #19145409C2semidirect
3. #19145401C2semidirect
4. #19145392C2semidirect
5. #19145360C2semidirect
6. #19145352C2semidirect
7. #19145343C2semidirect
8. #19144531C2semidirect
9. #19144518C2semidirect
10. #19144210C2semidirect
11. #19143845C2semidirect
12. #19143822C2semidirect
13. C2×#14582863C2semidirect
14. C22×#121×C43C2semidirect
15. C22×#10621898C22semidirect
16. C2×#13063351C22semidirect
17. C22×#10621877C22semidirect
23. #14583410C22semidirect
24. #14583410C22semidirect
25. #14583410C22semidirect
27. C2×#13063304C22semidirect
28. C2×#13063304C22semidirect
29. C2×#13063299C22semidirect
30. C2×#13063299C22semidirect
34. C2×#13063284C22semidirect
35. #14583234C22semidirect
36. #14583229C22semidirect
37. #14583220C22semidirect
38. #14583217C22semidirect
39. #14583215C22semidirect
40. #14583212C22semidirect
41. #14583210C22semidirect
42. #14583150C22semidirect
43. #14583143C22semidirect
44. #14583133C22semidirect
45. #14583126C22semidirect
46. #14583050C22semidirect
47. #14583050C22semidirect
48. #14583042C22semidirect
49. #14583037C22semidirect
50. #14583033C22semidirect
51. #14583033C22semidirect
52. #14583032C22semidirect
53. #14582939C22semidirect
54. #14582904C22semidirect
55. #14582898C22semidirect
56. #14582863C22semidirect
57. #14582863C22semidirect
58. #14582863C22semidirect
59. #14582863C22semidirect
60. C2×C22⋊(C43⋊C8)C22semidirect
61. C2×C22⋊(C43⋊C8)C22semidirect
63. C23×D4×C43C22semidirect
74. C2×#121×C43C22semidirect
75. C2×#121×C43C22semidirect
76. C2×#121×C43C22semidirect
77. C22×C4⋊C4×C43C22semidirect
83. C2×#10621898C23semidirect
84. C22×Dic86C23semidirect
85. C22×D172C23semidirect
91. C2×#10621883C23semidirect
92. C2×#10621882C23semidirect
95. C2×#10621877C23semidirect
96. C22×C43⋊C8C23semidirect
107. #13063304C23semidirect
108. #13063304C23semidirect
115. #13063299C23semidirect
116. #13063299C23semidirect
132. #13063284C23semidirect
133. C2×C4⋊Dic43C23semidirect
134. C2×C4⋊Dic43C23semidirect
143. #13063258C23semidirect
144. #13063256C23semidirect
145. #13063248C23semidirect
146. #13063246C23semidirect
147. #13063246C23semidirect
148. #13063245C23semidirect
151. C22⋊(C43⋊C8)C23semidirect
152. C22⋊(C43⋊C8)C23semidirect
387. C23×C43AGL(1,ℤ/8)semidirect
519. C22×#121D43semidirect
546. C23×D4C2×D43semidirect
572. C2×#121C2×D43semidirect
573. C2×#121C2×D43semidirect
574. C2×#121C2×D43semidirect
579. C22×C4⋊C4C2×D43semidirect
608. C43#60750semidirect
921. C23#13063351semidirect

Maximal subgroups

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

subgroupindex
C2×#145834102
#191454092
#191454012
#191453922
#191453602
#191453522
#191453432
#191445312
#191445182
#191442102
#191438452
#191438222
C2×#145828632
C22×#121×C432
#6075043