Finite Group Databasebeta

← #27087015

Subgroups — #27087015

Order 12032.

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
1C22×#13093998C211yesmaximal, characteristic, complemented
2#20254198C214yesmaximal, complemented
3#20254190C212yesmaximal, complemented
4#20254185C212yesmaximal, complemented
5#20254149C214yesmaximal, complemented
6#20254141C212yesmaximal, complemented
7#20254136C212yesmaximal, complemented
8#20253328C212yesmaximal, complemented
9#20253308C212yesmaximal, complemented
10#20253009C214yesmaximal, complemented
11#20252640C212yesmaximal, complemented
12#20252614C212yesmaximal, complemented
13C2×#15689087C211yesmaximal, characteristic, complemented
14C2×C47×#525C211yesmaximal, characteristic, complemented
15C23×D188C2211yescharacteristic, complemented
16C23×C22⋊D47—21no—
17C2×#13094049C2214yescomplemented
18C22×#10625329C2212yescomplemented
19C2×#13093998—21no—
20C2×#13093998—21no—
21C2×#13093998—21no—
22C2×#13093998—21no—
23C2×#13093998—21no—
24C2×#13093998—21no—
25C2×#13093998C2212yes—
26C2×#13093998C2212yes—
27C2×#13093998C2212yes—
28C2×#13093998C2212yescomplemented
29C2×#13093998C2212yescomplemented
30C2×#13093998C2212yescomplemented
31C22×C4⋊Dic47C2211yescharacteristic, complemented
32C22×(C2×D47)⋊C4—21no—
33#15689456C2214yescomplemented
34#15689451C2214yescomplemented
35#15689447C2218yescomplemented
36#15689441C2214yescomplemented
37#15689439C2214yescomplemented
38#15689436C2214yescomplemented
39#15689434C2214yescomplemented
40#15689374C2218yescomplemented
41#15689371C2218yescomplemented
42#15689357C2218yescomplemented
43#15689354C2218yescomplemented
44#15689273C2214yescomplemented
45#15689273C2214yescomplemented
46#15689268C2218yescomplemented
47#15689262C2214yescomplemented
48#15689257C2214yescomplemented
49#15689256C2214yescomplemented
50#15689256C2214yescomplemented
51#15689166C2214yescomplemented
52#15689127C2214yescomplemented
53#15689124C2214yescomplemented
54#15689087C2212yescomplemented
55#15689087C2212yescomplemented
56#15689087C2212yescomplemented
57#15689087C2212yescomplemented
58C2×C22⋊(C47⋊C8)C2212yescomplemented
59C2×C22⋊(C47⋊C8)C2212yescomplemented
60C22×#41×C47C2211yescharacteristic, complemented
61C24×C4×C47C2211yescharacteristic
62C47×#525—21no—
63C47×#525—21no—
64C47×#525—21no—
65C47×#525—21no—
66C47×#525C2212yes—
67C47×#525C2212yescomplemented
68C47×#525C2212yescomplemented
69C47×#525C2212yescomplemented
70C2×#123×C47—21no—
71C2×C22⋊Q8×C47C2211yescharacteristic, complemented
72C2×C22⋊Q8×C47C2211yescharacteristic, complemented
73C2×#121×C47C2211yescharacteristic, complemented
74C2×#121×C47C2211yescharacteristic, complemented
75C2×#120×C47—21no—
76C2×C4×D4×C47—21no—
77C2×C4×D4×C47—21no—
78C2×#117×C47C2211yescharacteristic, complemented
79C24×D47—21no—
80C22×D188—21no—
81C22×D188—21no—
82C22×D188—21no—
83C22×D188—44no—
84C22×D188C2312yes—
85C22×D188C2312yes—
86C22×D188C2312yes—
87C22×C22⋊D47—22no—
88C22×C22⋊D47—22no—
89C22×C22⋊D47—22no—
90C22×C22⋊D47—22no—
91C22×C22⋊D47—22no—
92C22×C22⋊D47—22no—
93C22×C22⋊D47—48no—
94C23×Dic47—21no—
95#13094049—48no—
96C2×#10625336C2318yescomplemented
97C2×#10625334C2318yescomplemented
98C2×#10625329—44no—
99C2×#10625329C2314yes—
100C2×#10625329C2314yescomplemented
101C22×C47⋊C8C2314yescomplemented
102#13093998—22no—
103#13093998—22no—
104#13093998—22no—
105#13093998—22no—
106#13093998—22no—
107#13093998—22no—
108#13093998—22no—
109#13093998—22no—
110#13093998—22no—
111#13093998—22no—
112#13093998—22no—
113#13093998—22no—
114#13093998C2314yes—
115#13093998C2314yes—
116#13093998C2314yes—
117#13093998C2314yes—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47C2312yes—
122C2×C4⋊Dic47C2312yes—
123C2×C4⋊Dic47C2312yes—
124C2×(C2×D47)⋊C4—22no—
125C2×(C2×D47)⋊C4—22no—
126C2×(C2×D47)⋊C4—22no—
127C2×(C2×D47)⋊C4—22no—
128C2×(C2×D47)⋊C4—22no—
129C2×(C2×D47)⋊C4—22no—
130#13093957C2318yescomplemented
131#13093955C2318yescomplemented
132#13093948C2318yescomplemented
133#13093945C2318yescomplemented
134#13093944C2318yescomplemented
135#13093944C2318yescomplemented
136C22⋊(C47⋊C8)C2314yes—
137C22⋊(C47⋊C8)C2314yes—
138C22⋊(C47⋊C8)C2314yescomplemented
139C22⋊(C47⋊C8)C2314yescomplemented
140C25×C47D411yescharacteristic
141C2×#41×C47—21no—
142C2×#41×C47—21no—
143C2×#41×C47—44no—
144C2×#41×C47C2312yes—
145C2×#41×C47C2312yescomplemented
146C22×Q8×C47C2311yescharacteristic, complemented
147C22×D4×C47—21no—
148C22×D4×C47—21no—
149C22×D4×C47—21no—
150C22×D4×C47C2311yescharacteristic, complemented
151C23×C4×C47—21no—
152C23×C4×C47—44no—
153C23×C4×C47D411yescharacteristic
154C23×C4×C47D411yescharacteristic
155C23×C4×C47D411yescharacteristic
156C23×C4×C47D411yescharacteristic
157C23×C4×C47D411yescharacteristic
158C23×C4×C47D411yescharacteristic
159C23×C4×C47D411yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C23×C4×C47C2311yescharacteristic
162C23×C4×C47C2311yescharacteristic
163C23×C4×C47C2311yescharacteristic
164C23×C4×C47C2311yescharacteristic
165C23×C4×C47C2311yescharacteristic
166C23×C4×C47C2311yescharacteristic
167#123×C47—22no—
168#123×C47—22no—
169#123×C47—22no—
170#123×C47—22no—
171C22⋊Q8×C47—21no—
172C22⋊Q8×C47—21no—
173C22⋊Q8×C47—21no—
174C22⋊Q8×C47—21no—
175C22⋊Q8×C47C2312yes—
176C22⋊Q8×C47C2312yes—
177C22⋊Q8×C47C2312yescomplemented
178C22⋊Q8×C47C2312yescomplemented
179#121×C47—21no—
180#121×C47—21no—
181#121×C47—21no—
182#121×C47—21no—
183#121×C47C2312yes—
184#121×C47C2312yes—
185#121×C47C2312yescomplemented
186#121×C47C2312yescomplemented
187#120×C47—22no—
188#120×C47—22no—
189#120×C47—22no—
190#120×C47—22no—
191C4×D4×C47—22no—
192C4×D4×C47—22no—
193C4×D4×C47—22no—
194C4×D4×C47—22no—
195C4×D4×C47—22no—
196C4×D4×C47—22no—
197C4×D4×C47—22no—
198C4×D4×C47—22no—
199#117×C47—21no—
200#117×C47—21no—
201#117×C47C2312yes—
202#117×C47C2312yescomplemented
203C2×C4⋊C4×C47—21no—
204C2×C4⋊C4×C47—21no—
205C2×C4⋊C4×C47C2311yescharacteristic, complemented
206C2×C4⋊C4×C47C2311yescharacteristic, complemented
207C2×C22⋊C4×C47—21no—
208C2×C22⋊C4×C47—21no—
209C2×C22⋊C4×C47—21no—
210C2×C22⋊C4×C47—21no—
211C2×C22⋊C4×C47—21no—
212C2×C42×C47—21no—
213C24×C47—24no—
214C24×C47—21no—
215C24×C47—42no—
216C24×C47—42no—
217C24×C47C2×D411yescharacteristic
218C24×C47C2×D411yescharacteristic
219C24×C47C2×D411yescharacteristic
220C24×C47C2×D411yescharacteristic
221C24×C47C2×D411yescharacteristic
222C24×C47C2×D411yescharacteristic
223C24×C47C2×D411yescharacteristic
224C23×D47—22no—
225C23×D47—22no—
226C23×D47—22no—
227C23×D47—44no—
228C23×D47—44no—
229C23×D47—44no—
230#41×C47—28no—
231#41×C47—44no—
232#41×C47—44no—
233#41×C47—44no—
234C2×Q8×C47—21no—
235C2×Q8×C47—42no—
236C2×Q8×C47C2412yes—
237C2×D4×C47—22no—
238C2×D4×C47—22no—
239C2×D4×C47—22no—
240C2×D4×C47—22no—
241C2×D4×C47—22no—
242C2×D4×C47—22no—
243C2×D4×C47—21no—
244C2×D4×C47—42no—
245C2×D4×C47—44no—
246C2×D4×C47—44no—
247C2×D4×C47—44no—
248C2×D4×C47C2412yes—
249C22×C4×C47—24no—
250C22×C4×C47—24no—
251C22×C4×C47—24no—
252C22×C4×C47—21no—
253C22×C4×C47—21no—
254C22×C4×C47—21no—
255C22×C4×C47—22no—
256C22×C4×C47—22no—
257C22×C4×C47—42no—
258C22×C4×C47—42no—
259C22×C4×C47—42no—
260C22×C4×C47—42no—
261C22×C4×C47—42no—
262C22×C4×C47—42no—
263C22×C4×C47—42no—
264C22×C4×C47—42no—
265C22×C4×C47—42no—
266C22×C4×C47—42no—
267C22×C4×C47—42no—
268C22×C4×C47—44no—
269C22×C4×C47C2×D411yescharacteristic
270C22×C4×C47C2×D411yescharacteristic
271C22×C4×C47C2×D411yescharacteristic
272C22×C4×C47C2×D411yescharacteristic
273C22×C4×C47C2×D411yescharacteristic
274C22×C4×C47C2×D411yescharacteristic
275C22×C4×C47C2×D411yescharacteristic
276C22×C4×C47C2×D411yescharacteristic
277C22×C4×C47C2×D411yescharacteristic
278C22×C4×C47C2×D411yescharacteristic
279C22×C4×C47C2×D411yescharacteristic
280C22×C4×C47C2×D411yescharacteristic
281C22×C4×C47C2×D411yescharacteristic
282C22×C4×C47C2×D411yescharacteristic
283C22×C4×C47C2×D411yescharacteristic
284C22×C4×C47C2×D411yescharacteristic
285C22×C4×C47C2×D411yescharacteristic
286C22×C4×C47C2×D411yescharacteristic
287C22×C4×C47C2×D411yescharacteristic
288C22×C4×C47C2×D411yescharacteristic
289C22×C4×C47C2×D411yescharacteristic
290C22×C4×C47C2411yescharacteristic
291C22×C4×C47C2411yescharacteristic
292C22×C4×C47C2411yescharacteristic
293C22×C4×C47C2411yescharacteristic
294C22×C4×C47C2411yescharacteristic
295C22×C4×C47C2411yescharacteristic
296C22×C4×C47C2411yescharacteristic
297C2×C22⋊D47—24no—
298C2×C22⋊D47—24no—
299C2×C22⋊D47—24no—
300C2×C22⋊D47—24no—
301C2×C22⋊D47—48no—
302C2×C22⋊D47—48no—
303C2×C22⋊D47—48no—
304C2×C22⋊D47—48no—
305C2×C22⋊D47—48no—
306C2×C22⋊D47—48no—
307C22×Dic47—22no—
308C22×Dic47—22no—
309C22×Dic47—22no—
310C22×Dic47—44no—
311C2×D188—28no—
312C2×D188—22no—
313C2×D188—22no—
314C2×D188—22no—
315C2×D188—44no—
316C2×D188—44no—
317C2×D188—44no—
318C2×D188—44no—
319C2×D188—44no—
320C2×D188C2414yes—
321C4⋊C4×C47—22no—
322C4⋊C4×C47—22no—
323C4⋊C4×C47—22no—
324C4⋊C4×C47—22no—
325C4⋊C4×C47—21no—
326C4⋊C4×C47—21no—
327C4⋊C4×C47C2412yes—
328C4⋊C4×C47C2412yes—
329C22⋊C4×C47—22no—
330C22⋊C4×C47—22no—
331C22⋊C4×C47—22no—
332C22⋊C4×C47—22no—
333C22⋊C4×C47—22no—
334C22⋊C4×C47—22no—
335C22⋊C4×C47—22no—
336C22⋊C4×C47—22no—
337C22⋊C4×C47—22no—
338C22⋊C4×C47—22no—
339C42×C47—22no—
340C42×C47—22no—
341#10625336—48no—
342#10625334—48no—
343(C2×D47)⋊C4—24no—
344(C2×D47)⋊C4—24no—
345(C2×D47)⋊C4—24no—
346(C2×D47)⋊C4—24no—
347C4⋊Dic47—22no—
348C4⋊Dic47—22no—
349C4⋊Dic47—22no—
350C4⋊Dic47C2414yes—
351#10625329—28no—
352#10625329—44no—
353C2×C47⋊C8—44no—
354C2×C47⋊C8C2418yes—
355C23×C47—22no—
356C23×C47—22no—
357C23×C47—22no—
358C23×C47—22no—
359C23×C47—22no—
360C23×C47—22no—
361C23×C47—22no—
362C23×C47—22no—
363C23×C47—22no—
364C23×C47—22no—
365C23×C47—22no—
366C23×C47—22no—
367C23×C47—22no—
368C23×C47—41no—
369C23×C47—41no—
370C23×C47—41no—
371C23×C47—41no—
372C23×C47—41no—
373C23×C47—41no—
374C23×C47—41no—
375C23×C47—41no—
376C23×C47—416no—
377C23×C47—42no—
378C23×C47—42no—
379C23×C47—42no—
380C23×C47AGL(1,ℤ/8)14yescomplemented
381C23×C47C22×D411yescharacteristic
382C23×C47C22×D411yescharacteristic
383C23×C47C22×D411yescharacteristic
384C23×C47C22×D411yescharacteristic
385C23×C47C22×D411yescharacteristic
386C23×C47C22×D411yescharacteristic
387C23×C47C22×D411yescharacteristic
388C22×D47—24no—
389C22×D47—44no—
390C22×D47—44no—
391C22×D47—44no—
392C22×D47—44no—
393C22×D47—44no—
394C22×D47—44no—
395C22×D47—44no—
396C22×D47—44no—
397C22×D47—44no—
398C22×D47—816no—
399Q8×C47—24no—
400Q8×C47—42no—
401D4×C47—24no—
402D4×C47—42no—
403D4×C47—44no—
404D4×C47—44no—
405D4×C47—44no—
406D4×C47—44no—
407D4×C47—44no—
408D4×C47—44no—
409C2×C4×C47—22no—
410C2×C4×C47—22no—
411C2×C4×C47—22no—
412C2×C4×C47—22no—
413C2×C4×C47—22no—
414C2×C4×C47—22no—
415C2×C4×C47—22no—
416C2×C4×C47—22no—
417C2×C4×C47—22no—
418C2×C4×C47—22no—
419C2×C4×C47—22no—
420C2×C4×C47—22no—
421C2×C4×C47—22no—
422C2×C4×C47—22no—
423C2×C4×C47—22no—
424C2×C4×C47—22no—
425C2×C4×C47—22no—
426C2×C4×C47—22no—
427C2×C4×C47—41no—
428C2×C4×C47—41no—
429C2×C4×C47—41no—
430C2×C4×C47—41no—
431C2×C4×C47—41no—
432C2×C4×C47—41no—
433C2×C4×C47—41no—
434C2×C4×C47—41no—
435C2×C4×C47—41no—
436C2×C4×C47—41no—
437C2×C4×C47—41no—
438C2×C4×C47—41no—
439C2×C4×C47—44no—
440C2×C4×C47—42no—
441C2×C4×C47—42no—
442C2×C4×C47—42no—
443C2×C4×C47—44no—
444C2×C4×C47C22×D411yescharacteristic
445C2×C4×C47C22×D411yescharacteristic
446C2×C4×C47C22×D411yescharacteristic
447C2×C4×C47C22×D411yescharacteristic
448C2×C4×C47C22×D411yescharacteristic
449C2×C4×C47C22×D411yescharacteristic
450C2×C4×C47C22×D411yescharacteristic
451C2×C4×C47H(5,𝔽2)14yes—
452C2×C4×C47C2511yescharacteristic
453C22⋊D47—48no—
454C22⋊D47—48no—
455C22⋊D47—48no—
456C22⋊D47—48no—
457C2×Dic47—24no—
458C2×Dic47—44no—
459C2×Dic47—44no—
460C2×Dic47—44no—
461D188—28no—
462D188—44no—
463D188—44no—
464D188—44no—
465C47⋊C8—28no—
466#60750—471nomaximal, Sylow
467C22×C47—28no—
468C22×C47—21no—
469C22×C47—21no—
470C22×C47—21no—
471C22×C47—21no—
472C22×C47—21no—
473C22×C47—21no—
474C22×C47—21no—
475C22×C47—21no—
476C22×C47—21no—
477C22×C47—21no—
478C22×C47—21no—
479C22×C47—21no—
480C22×C47—21no—
481C22×C47—21no—
482C22×C47—21no—
483C22×C47—21no—
484C22×C47—44no—
485C22×C47—44no—
486C22×C47—44no—
487C22×C47—44no—
488C22×C47—44no—
489C22×C47—44no—
490C22×C47—42no—
491C22×C47—42no—
492C22×C47—42no—
493C22×C47—84no—
494C22×C47#53412yes—
495C22×C47C2×AGL(1,ℤ/8)12yes—
496C22×C47C2×AGL(1,ℤ/8)12yes—
497C22×C47C2×AGL(1,ℤ/8)12yes—
498C22×C47#57512yes—
499C22×C47C23×D411yescharacteristic
500C2×D47—44no—
501C2×D47—44no—
502C2×D47—44no—
503C2×D47—88no—
504C2×D47—88no—
505C2×D47—88no—
506C4×C47—21no—
507C4×C47—21no—
508C4×C47—21no—
509C4×C47—21no—
510C4×C47—21no—
511C4×C47—21no—
512C4×C47—42no—
513C4×C47—42no—
514C4×C47—42no—
515C4×C47#53412yes—
516C4×C47C2×H(5,𝔽2)12yes—
517Dic47—44no—
518C2×#525D4711yescharacteristic, complemented
519C22×#121—471no—
520#3194—474no—
521#3193—472no—
522#3192—472no—
523#3188—474no—
524#3187—472no—
525#3186—472no—
526#3094—472no—
527#3092—472no—
528#3055—474no—
529#3006—472no—
530#3003—472no—
531C2×#407—471no—
532C2×C47—22no—
533C2×C47—22no—
534C2×C47—22no—
535C2×C47—22no—
536C2×C47—22no—
537C2×C47—41no—
538C2×C47—41no—
539C2×C47—82no—
540C2×C47C2×#53411yescharacteristic
541C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
542C2×C47C2×#57511yescharacteristic
543D47—84no—
544C22×#41C2×D4711yescharacteristic, complemented
545C23×D4—471no—
546C23×D4—941no—
547C24×C4C2×D4711yescharacteristic
548C2×AGL(1,ℤ/8)—474no—
549C22×M16—472no—
550#525—21no—
551#525—21no—
552#525—21no—
553#525—21no—
554#525C2×D4712yes—
555#525C2×D4712yescomplemented
556#525C2×D4712yescomplemented
557#525C2×D4712yescomplemented
558C2×#123—21no—
559C2×C22⋊Q8C2×D4711yescharacteristic, complemented
560C2×C22⋊Q8C2×D4711yescharacteristic, complemented
561C2×#121—472no—
562C2×#121—472no—
563C2×#121—472no—
564C2×#121—472no—
565C2×#121—472no—
566C2×#121—472no—
567C2×#121—941no—
568C2×#121—941no—
569C2×#121—941no—
570C2×#121—941no—
571C2×#121—941no—
572C2×#121—941no—
573C2×#121C2×D4711yescharacteristic, complemented
574C2×#121C2×D4711yescharacteristic, complemented
575C2×#120—21no—
576C2×C4×D4—21no—
577C2×C4×D4—21no—
578C2×#117C2×D4711yescharacteristic, complemented
579C22×C4⋊C4—471no—
580C22×C22⋊C4—941no—
581#484—474no—
582#483—474no—
583#482—478no—
584#481—474no—
585#481—474no—
586#480—474no—
587#480—474no—
588#469—478no—
589#468—478no—
590#466—478no—
591#465—478no—
592#450—474no—
593#450—474no—
594#449—478no—
595#448—474no—
596#447—474no—
597#447—474no—
598#447—474no—
599#428—474no—
600#418—474no—
601#417—474no—
602#407—472no—
603#407—472no—
604#407—472no—
605#407—472no—
606C2×C22⋊C8—472no—
607C2×C22⋊C8—472no—
608C47#6075011yescharacteristic, complemented, Sylow
609C25—941no—
610C25C22⋊D4711yescharacteristic
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—44no—
614C2×#41C22×D4712yes—
615C2×#41C22×D4712yescomplemented
616C22×Q8C22×D4711yescharacteristic, complemented
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4—472no—
621C22×D4—472no—
622C22×D4—472no—
623C22×D4—942no—
624C22×D4—942no—
625C22×D4—942no—
626C22×D4—942no—
627C22×D4—942no—
628C22×D4—942no—
629C22×D4—941no—
630C22×D4—941no—
631C22×D4—941no—
632C22×D4—1884no—
633C22×D4—1888no—
634C22×D4C22×D4711yescharacteristic, complemented
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—941no—
638C23×C4C22⋊D4711yescharacteristic
639C23×C4C22⋊D4711yescharacteristic
640C23×C4C22⋊D4711yescharacteristic
641C23×C4C22⋊D4711yescharacteristic
642C23×C4C22⋊D4711yescharacteristic
643C23×C4C22⋊D4711yescharacteristic
644C23×C4C22⋊D4711yescharacteristic
645C23×C4C22×D4711yescharacteristic
646C23×C4C22×D4711yescharacteristic
647C23×C4C22×D4711yescharacteristic
648C23×C4C22×D4711yescharacteristic
649C23×C4C22×D4711yescharacteristic
650C23×C4C22×D4711yescharacteristic
651C23×C4C22×D4711yescharacteristic
652AGL(1,ℤ/8)—1888no—
653C2×SD16—478no—
654C2×D8—478no—
655C2×M16—474no—
656C2×M16—474no—
657C2×M16—1884no—
658C22×C8—474no—
659#123—22no—
660#123—22no—
661#123—22no—
662#123—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8C22×D4712yes—
668C22⋊Q8C22×D4712yes—
669C22⋊Q8C22×D4712yescomplemented
670C22⋊Q8C22×D4712yescomplemented
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—474no—
676#121—474no—
677#121—474no—
678#121—474no—
679#121—942no—
680#121—942no—
681#121—942no—
682#121—942no—
683#121—942no—
684#121—942no—
685#121—942no—
686#121—942no—
687#121—942no—
688#121—942no—
689#121—942no—
690#121—942no—
691#121C22×D4712yes—
692#121C22×D4712yes—
693#121C22×D4712yescomplemented
694#121C22×D4712yescomplemented
695#120—22no—
696#120—22no—
697#120—22no—
698#120—22no—
699C4×D4—22no—
700C4×D4—22no—
701C4×D4—22no—
702C4×D4—22no—
703C4×D4—22no—
704C4×D4—22no—
705C4×D4—22no—
706C4×D4—22no—
707#117—21no—
708#117—21no—
709#117C22×D4712yes—
710#117C22×D4712yescomplemented
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—472no—
714C2×C4⋊C4—472no—
715C2×C4⋊C4—472no—
716C2×C4⋊C4—941no—
717C2×C4⋊C4—941no—
718C2×C4⋊C4—941no—
719C2×C4⋊C4C22×D4711yescharacteristic, complemented
720C2×C4⋊C4C22×D4711yescharacteristic, complemented
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—942no—
727C2×C22⋊C4—942no—
728C2×C22⋊C4—942no—
729C2×C22⋊C4—942no—
730C2×C22⋊C4—942no—
731C2×C22⋊C4—942no—
732C2×C42—21no—
733#107—478no—
734#106—478no—
735#103—478no—
736#102—478no—
737#102—478no—
738#102—478no—
739C22⋊C8—474no—
740C22⋊C8—474no—
741C22⋊C8—474no—
742C22⋊C8—474no—
743C24—24no—
744C24—21no—
745C24—42no—
746C24—42no—
747C24—942no—
748C24—942no—
749C24—942no—
750C24—1884no—
751C24—1884no—
752C24—1884no—
753C24C2×C22⋊D4711yescharacteristic
754C24C2×C22⋊D4711yescharacteristic
755C24C2×C22⋊D4711yescharacteristic
756C24C2×C22⋊D4711yescharacteristic
757C24C2×C22⋊D4711yescharacteristic
758C24C2×C22⋊D4711yescharacteristic
759C24C2×C22⋊D4711yescharacteristic
760#41—28no—
761#41—44no—
762#41—44no—
763#41—44no—
764C2×Q8—21no—
765C2×Q8—42no—
766C2×Q8C23×D4712yes—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—21no—
774C2×D4—42no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—474no—
779C2×D4—944no—
780C2×D4—944no—
781C2×D4—944no—
782C2×D4—944no—
783C2×D4—942no—
784C2×D4—942no—
785C2×D4—942no—
786C2×D4—948no—
787C2×D4—1884no—
788C2×D4—1884no—
789C2×D4—1884no—
790C2×D4—1884no—
791C2×D4—1884no—
792C2×D4—1888no—
793C2×D4—1888no—
794C2×D4—1888no—
795C2×D4—1888no—
796C2×D4—1888no—
797C2×D4—1888no—
798C2×D4C23×D4712yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
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—42no—
817C22×C4—42no—
818C22×C4—44no—
819C22×C4—942no—
820C22×C4—942no—
821C22×C4—942no—
822C22×C4—1884no—
823C22×C4C2×C22⋊D4711yescharacteristic
824C22×C4C2×C22⋊D4711yescharacteristic
825C22×C4C2×C22⋊D4711yescharacteristic
826C22×C4C2×C22⋊D4711yescharacteristic
827C22×C4C2×C22⋊D4711yescharacteristic
828C22×C4C2×C22⋊D4711yescharacteristic
829C22×C4C2×C22⋊D4711yescharacteristic
830C22×C4C2×C22⋊D4711yescharacteristic
831C22×C4C2×C22⋊D4711yescharacteristic
832C22×C4C2×C22⋊D4711yescharacteristic
833C22×C4C2×C22⋊D4711yescharacteristic
834C22×C4C2×C22⋊D4711yescharacteristic
835C22×C4C2×C22⋊D4711yescharacteristic
836C22×C4C2×C22⋊D4711yescharacteristic
837C22×C4C2×C22⋊D4711yescharacteristic
838C22×C4C2×C22⋊D4711yescharacteristic
839C22×C4C2×C22⋊D4711yescharacteristic
840C22×C4C2×C22⋊D4711yescharacteristic
841C22×C4C2×C22⋊D4711yescharacteristic
842C22×C4C2×C22⋊D4711yescharacteristic
843C22×C4C2×C22⋊D4711yescharacteristic
844C22×C4C23×D4711yescharacteristic
845C22×C4C23×D4711yescharacteristic
846C22×C4C23×D4711yescharacteristic
847C22×C4C23×D4711yescharacteristic
848C22×C4C23×D4711yescharacteristic
849C22×C4C23×D4711yescharacteristic
850C22×C4C23×D4711yescharacteristic
851SD16—1888no—
852D8—1888no—
853M16—948no—
854M16—1884no—
855C2×C8—478no—
856C2×C8—1884no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—474no—
864C4⋊C4—942no—
865C4⋊C4—942no—
866C4⋊C4—942no—
867C4⋊C4C23×D4712yes—
868C4⋊C4C23×D4712yes—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—944no—
880C22⋊C4—944no—
881C22⋊C4—944no—
882C22⋊C4—944no—
883C42—22no—
884C42—22no—
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—22no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—944no—
911C23—37616no—
912C23—1884no—
913C23—1884no—
914C23—1884no—
915C23—1884no—
916C23—1884no—
917C23—1884no—
918C23—1884no—
919C23—1884no—
920C23—1884no—
921C23#1309404914yescomplemented
922C23C22×C22⋊D4711yescharacteristic
923C23C22×C22⋊D4711yescharacteristic
924C23C22×C22⋊D4711yescharacteristic
925C23C22×C22⋊D4711yescharacteristic
926C23C22×C22⋊D4711yescharacteristic
927C23C22×C22⋊D4711yescharacteristic
928C23C22×C22⋊D4711yescharacteristic
929Q8—24no—
930Q8—42no—
931D4—24no—
932D4—42no—
933D4—44no—
934D4—44no—
935D4—44no—
936D4—44no—
937D4—44no—
938D4—44no—
939D4—948no—
940D4—1884no—
941D4—1884no—
942D4—1888no—
943D4—1888no—
944D4—1888no—
945D4—1888no—
946D4—1884no—
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—22no—
963C2×C4—22no—
964C2×C4—22no—
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—41no—
976C2×C4—41no—
977C2×C4—44no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—44no—
982C2×C4—944no—
983C2×C4—1884no—
984C2×C4—1884no—
985C2×C4—1884no—
986C2×C4C22×C22⋊D4711yescharacteristic
987C2×C4C22×C22⋊D4711yescharacteristic
988C2×C4C22×C22⋊D4711yescharacteristic
989C2×C4C22×C22⋊D4711yescharacteristic
990C2×C4C22×C22⋊D4711yescharacteristic
991C2×C4C22×C22⋊D4711yescharacteristic
992C2×C4C22×C22⋊D4711yescharacteristic
993C2×C4#1309406914yes—
994C2×C4C24×D4711yescharacteristic
995C8—948no—
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—42no—
1020C22—42no—
1021C22—42no—
1022C22—84no—
1023C22—3768no—
1024C22—3768no—
1025C22—3768no—
1026C22—1884no—
1027C22—1884no—
1028C22—1884no—
1029C22#1568968212yes—
1030C22C2×#1309404912yes—
1031C22C2×#1309404912yes—
1032C22C2×#1309404912yes—
1033C22#1568992112yes—
1034C22C23×C22⋊D4711yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—1884no—
1045C4#1568968212yes—
1046C4C2×#1309406912yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—82no—
1055C2—3764no—
1056C2C2×#1568968211yescharacteristic
1057C2C22×#1309404911yescharacteristic
1058C2C2×#1568992111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#525C2
socleC22×C47C23×D4
hypercenterC2×#525D47
hypocenterC47#60750
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C22×#13093998C2semidirect
2. #20254198C2semidirect
3. #20254190C2semidirect
4. #20254185C2semidirect
5. #20254149C2semidirect
6. #20254141C2semidirect
7. #20254136C2semidirect
8. #20253328C2semidirect
9. #20253308C2semidirect
10. #20253009C2semidirect
11. #20252640C2semidirect
12. #20252614C2semidirect
13. C2×#15689087C2semidirect
14. C2×C47×#525C2semidirect
15. C23×D188C22semidirect
17. C2×#13094049C22semidirect
18. C22×#10625329C22semidirect
28. C2×#13093998C22semidirect
29. C2×#13093998C22semidirect
30. C2×#13093998C22semidirect
31. C22×C4⋊Dic47C22semidirect
33. #15689456C22semidirect
34. #15689451C22semidirect
35. #15689447C22semidirect
36. #15689441C22semidirect
37. #15689439C22semidirect
38. #15689436C22semidirect
39. #15689434C22semidirect
40. #15689374C22semidirect
41. #15689371C22semidirect
42. #15689357C22semidirect
43. #15689354C22semidirect
44. #15689273C22semidirect
45. #15689273C22semidirect
46. #15689268C22semidirect
47. #15689262C22semidirect
48. #15689257C22semidirect
49. #15689256C22semidirect
50. #15689256C22semidirect
51. #15689166C22semidirect
52. #15689127C22semidirect
53. #15689124C22semidirect
54. #15689087C22semidirect
55. #15689087C22semidirect
56. #15689087C22semidirect
57. #15689087C22semidirect
58. C2×C22⋊(C47⋊C8)C22semidirect
59. C2×C22⋊(C47⋊C8)C22semidirect
60. C22×#41×C47C22semidirect
67. C47×#525C22semidirect
68. C47×#525C22semidirect
69. C47×#525C22semidirect
71. C2×C22⋊Q8×C47C22semidirect
72. C2×C22⋊Q8×C47C22semidirect
73. C2×#121×C47C22semidirect
74. C2×#121×C47C22semidirect
78. C2×#117×C47C22semidirect
96. C2×#10625336C23semidirect
97. C2×#10625334C23semidirect
100. C2×#10625329C23semidirect
101. C22×C47⋊C8C23semidirect
130. #13093957C23semidirect
131. #13093955C23semidirect
132. #13093948C23semidirect
133. #13093945C23semidirect
134. #13093944C23semidirect
135. #13093944C23semidirect
138. C22⋊(C47⋊C8)C23semidirect
139. C22⋊(C47⋊C8)C23semidirect
145. C2×#41×C47C23semidirect
146. C22×Q8×C47C23semidirect
150. C22×D4×C47C23semidirect
177. C22⋊Q8×C47C23semidirect
178. C22⋊Q8×C47C23semidirect
185. #121×C47C23semidirect
186. #121×C47C23semidirect
202. #117×C47C23semidirect
205. C2×C4⋊C4×C47C23semidirect
206. C2×C4⋊C4×C47C23semidirect
380. C23×C47AGL(1,ℤ/8)semidirect
518. C2×#525D47semidirect
544. C22×#41C2×D47semidirect
555. #525C2×D47semidirect
556. #525C2×D47semidirect
557. #525C2×D47semidirect
559. C2×C22⋊Q8C2×D47semidirect
560. C2×C22⋊Q8C2×D47semidirect
573. C2×#121C2×D47semidirect
574. C2×#121C2×D47semidirect
578. C2×#117C2×D47semidirect
608. C47#60750semidirect
615. C2×#41C22×D47semidirect
616. C22×Q8C22×D47semidirect
634. C22×D4C22×D47semidirect
669. C22⋊Q8C22×D47semidirect
670. C22⋊Q8C22×D47semidirect
693. #121C22×D47semidirect
694. #121C22×D47semidirect
710. #117C22×D47semidirect
719. C2×C4⋊C4C22×D47semidirect
720. C2×C4⋊C4C22×D47semidirect
921. C23#13094049semidirect

Maximal subgroups

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

subgroupindex
C22×#130939982
#202541982
#202541902
#202541852
#202541492
#202541412
#202541362
#202533282
#202533082
#202530092
#202526402
#202526142
C2×#156890872
C2×C47×#5252
#6075047