Finite Group Databasebeta

← #27087037

Subgroups — #27087037

Order 12032.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2C22×#13094003C211yesmaximal, characteristic, complemented
3#20254220C214yesmaximal, complemented
4#20254212C212yesmaximal, complemented
5#20254195C212yesmaximal, complemented
6#20254171C214yesmaximal, complemented
7#20254163C212yesmaximal, complemented
8#20254146C212yesmaximal, complemented
9#20253337C212yesmaximal, complemented
10#20253313C212yesmaximal, complemented
11#20253018C214yesmaximal, complemented
12#20252650C212yesmaximal, complemented
13#20252625C212yesmaximal, complemented
14C2×C47×#407C211yesmaximal, characteristic, complemented
15C22×#10625350C2211yescharacteristic
16C23×Dic94C2211yescharacteristic, complemented
17C2×#13094057C2214yescomplemented
18#15689634—21no—
19#15689634—21no—
20#15689634—21no—
21#15689634—21no—
22#15689634C2212yes—
23#15689634C2212yes—
24#15689634C2212yes—
25#15689634C2212yes—
26C2×#13094007—21no—
27C2×#13094003—21no—
28C2×#13094003—21no—
29C2×#13094003—21no—
30C2×#13094003—21no—
31C2×#13094003—21no—
32C2×#13094003—21no—
33C2×#13094003C2211yescharacteristic
34C2×#13094003C2212yes—
35C2×#13094003C2212yes—
36C2×#13094003C2212yes—
37C2×#13094003C2211yescharacteristic
38C2×#13094003C2212yescomplemented
39C2×#13094003C2212yescomplemented
40C2×#13094003C2212yescomplemented
41C2×#13093998C2211yescharacteristic
42C2×#13093998C2211yescharacteristic
43C2×#13093993—21no—
44C2×C4×C22⋊D47—21no—
45C2×C4×C22⋊D47—21no—
46C2×#13093983C2211yescharacteristic
47C22×C4⋊Dic47C2211yescharacteristic, complemented
48C22×Dic47⋊C4—21no—
49C22×C22⋊Dic47—21no—
50#15689465C2218yescomplemented
51#15689459C2214yescomplemented
52#15689459C2214yescomplemented
53#15689454C2214yescomplemented
54#15689454C2214yescomplemented
55#15689442C2214yescomplemented
56#15689437C2214yescomplemented
57#15689381C2218yescomplemented
58#15689369C2218yescomplemented
59#15689364C2218yescomplemented
60#15689352C2218yescomplemented
61#15689287C2218yescomplemented
62#15689281C2214yescomplemented
63#15689281C2214yescomplemented
64#15689281C2214yescomplemented
65#15689276C2214yescomplemented
66#15689264C2214yescomplemented
67#15689264C2214yescomplemented
68#15689165C2214yescomplemented
69#15689133C2214yescomplemented
70#15689125C2214yescomplemented
71C24×C4×C47C2211yescharacteristic
72C22×M16×C47C2212yescomplemented
73C47×#407C2212yes—
74C47×#407C2212yes—
75C47×#407C2212yescomplemented
76C47×#407C2212yescomplemented
77C2×C22⋊C8×C47C2212yes—
78C2×C22⋊C8×C47C2212yescomplemented
79C2×#10625350—21no—
80C2×#10625350—21no—
81C2×#10625350—44no—
82C2×#10625350C2312yes—
83C2×#10625350C2312yes—
84C22×Dic94—21no—
85C22×Dic94—21no—
86C22×Dic94—21no—
87C22×Dic94—44no—
88C22×Dic94C2312yes—
89C22×Dic94C2312yes—
90C22×Dic94C2312yes—
91C22×Dic94C2311yescharacteristic
92C22×D188C2311yescharacteristic
93C22×C22⋊D47—21no—
94C22×C22⋊D47—21no—
95C22×C22⋊D47—21no—
96C23×Dic47—21no—
97C23×Dic47—21no—
98C22×C4×D47—21no—
99#13094057—48no—
100C2×Dic188C2318yescomplemented
101C2×#10625325C2318yescomplemented
102#13094007—22no—
103#13094007—22no—
104#13094007—22no—
105#13094007—22no—
106#13094003—22no—
107#13094003—22no—
108#13094003—22no—
109#13094003—22no—
110#13094003—22no—
111#13094003—22no—
112#13094003—22no—
113#13094003—22no—
114#13094003—22no—
115#13094003—22no—
116#13094003—22no—
117#13094003—22no—
118#13094003—21no—
119#13094003—21no—
120#13094003—21no—
121#13094003—21no—
122#13094003C2314yes—
123#13094003C2312yes—
124#13094003C2312yes—
125#13094003C2314yes—
126#13094003C2314yes—
127#13094003C2312yes—
128#13094003C2314yes—
129#13094003C2312yes—
130#13093998—21no—
131#13093998—21no—
132#13093998—21no—
133#13093998—21no—
134#13093998C2312yes—
135#13093998C2312yes—
136#13093998C2312yes—
137#13093998C2312yes—
138#13093993—22no—
139#13093993—22no—
140#13093993—22no—
141#13093993—22no—
142C4×C22⋊D47—22no—
143C4×C22⋊D47—22no—
144C4×C22⋊D47—22no—
145C4×C22⋊D47—22no—
146C4×C22⋊D47—22no—
147C4×C22⋊D47—22no—
148C4×C22⋊D47—22no—
149C4×C22⋊D47—22no—
150#13093983—21no—
151#13093983—21no—
152#13093983C2312yes—
153#13093983C2312yes—
154C2×C4⋊Dic47—21no—
155C2×C4⋊Dic47—21no—
156C2×C4⋊Dic47—21no—
157C2×C4⋊Dic47C2312yes—
158C2×C4⋊Dic47C2312yes—
159C2×C4⋊Dic47C2312yes—
160C2×C4⋊Dic47C2311yescharacteristic
161C2×C4⋊Dic47C2311yescharacteristic
162C2×Dic47⋊C4—22no—
163C2×Dic47⋊C4—22no—
164C2×Dic47⋊C4—22no—
165C2×Dic47⋊C4—22no—
166C2×Dic47⋊C4—22no—
167C2×Dic47⋊C4—22no—
168C2×Dic47⋊C4—21no—
169C2×Dic47⋊C4—21no—
170C2×C22⋊Dic47—22no—
171C2×C22⋊Dic47—22no—
172C2×C22⋊Dic47—22no—
173C2×C22⋊Dic47—22no—
174C2×C22⋊Dic47—22no—
175C2×C22⋊Dic47—22no—
176C2×C22⋊Dic47—21no—
177C2×C22⋊Dic47—21no—
178C2×C22⋊Dic47—21no—
179C2×(C2×D47)⋊C4—21no—
180C2×(C2×D47)⋊C4—21no—
181C2×C4×Dic47—21no—
182#13093958C2318yescomplemented
183#13093956C2318yescomplemented
184#13093949C2318yescomplemented
185#13093949C2318yescomplemented
186#13093949C2318yescomplemented
187#13093946C2318yescomplemented
188C25×C47D411yescharacteristic
189C23×C4×C47—44no—
190C23×C4×C47D411yescharacteristic
191C23×C4×C47D411yescharacteristic
192C23×C4×C47D411yescharacteristic
193C23×C4×C47D411yescharacteristic
194C23×C4×C47D411yescharacteristic
195C23×C4×C47D411yescharacteristic
196C23×C4×C47D411yescharacteristic
197C23×C4×C47C2311yescharacteristic
198C23×C4×C47C2311yescharacteristic
199C23×C4×C47C2311yescharacteristic
200C23×C4×C47C2311yescharacteristic
201C23×C4×C47C2311yescharacteristic
202C23×C4×C47C2311yescharacteristic
203C23×C4×C47C2311yescharacteristic
204C2×M16×C47—44no—
205C2×M16×C47C2314yes—
206C2×M16×C47C2314yes—
207C22×C8×C47C2314yes—
208C22⋊C8×C47C2314yes—
209C22⋊C8×C47C2314yes—
210C22⋊C8×C47C2314yes—
211C22⋊C8×C47C2314yes—
212C24×C47—24no—
213C24×C47—42no—
214C24×C47—42no—
215C24×C47C2×D411yescharacteristic
216C24×C47C2×D411yescharacteristic
217C24×C47C2×D411yescharacteristic
218C24×C47C2×D411yescharacteristic
219C24×C47C2×D411yescharacteristic
220C24×C47C2×D411yescharacteristic
221C24×C47C2×D411yescharacteristic
222C23×D47—21no—
223C22×C4×C47—24no—
224C22×C4×C47—24no—
225C22×C4×C47—24no—
226C22×C4×C47—42no—
227C22×C4×C47—42no—
228C22×C4×C47—42no—
229C22×C4×C47—42no—
230C22×C4×C47—42no—
231C22×C4×C47—42no—
232C22×C4×C47—42no—
233C22×C4×C47—42no—
234C22×C4×C47—42no—
235C22×C4×C47—42no—
236C22×C4×C47—42no—
237C22×C4×C47C2×D411yescharacteristic
238C22×C4×C47C2×D411yescharacteristic
239C22×C4×C47C2×D411yescharacteristic
240C22×C4×C47C2×D411yescharacteristic
241C22×C4×C47C2×D411yescharacteristic
242C22×C4×C47C2×D411yescharacteristic
243C22×C4×C47C2×D411yescharacteristic
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2×D411yescharacteristic
252C22×C4×C47C2×D411yescharacteristic
253C22×C4×C47C2×D411yescharacteristic
254C22×C4×C47C2×D411yescharacteristic
255C22×C4×C47C2×D411yescharacteristic
256C22×C4×C47C2×D411yescharacteristic
257C22×C4×C47C2×D411yescharacteristic
258C22×C4×C47C2411yescharacteristic
259C22×C4×C47C2411yescharacteristic
260C22×C4×C47C2411yescharacteristic
261C22×C4×C47C2411yescharacteristic
262C22×C4×C47C2411yescharacteristic
263C22×C4×C47C2411yescharacteristic
264C22×C4×C47C2411yescharacteristic
265C2×C22⋊D47—22no—
266C2×C22⋊D47—22no—
267C2×C22⋊D47—22no—
268C2×C22⋊D47—22no—
269C2×C22⋊D47—22no—
270C2×C22⋊D47—22no—
271C2×C22⋊D47—44no—
272C2×C22⋊D47—44no—
273C2×C22⋊D47—44no—
274C22×Dic47—21no—
275C22×Dic47—21no—
276C22×Dic47—22no—
277C22×Dic47—22no—
278C22×Dic47—22no—
279C22×Dic47—21no—
280C22×Dic47—22no—
281C22×Dic47—22no—
282C22×Dic47—22no—
283C22×Dic47—44no—
284C22×Dic47—44no—
285#10625350—28no—
286#10625350—44no—
287#10625350—44no—
288#10625350—44no—
289C2×D188—21no—
290C2×D188—42no—
291C2×D188C2412yes—
292C2×C4×D47—22no—
293C2×C4×D47—22no—
294C2×C4×D47—44no—
295C2×Dic94—28no—
296C2×Dic94—22no—
297C2×Dic94—22no—
298C2×Dic94—22no—
299C2×Dic94—21no—
300C2×Dic94—44no—
301C2×Dic94—44no—
302C2×Dic94—42no—
303C2×Dic94—44no—
304C2×Dic94—44no—
305C2×Dic94—44no—
306C2×Dic94C2414yes—
307C2×Dic94C2412yes—
308M16×C47—28no—
309M16×C47—44no—
310C2×C8×C47—44no—
311C2×C8×C47C2418yes—
312C22⋊Dic47—24no—
313C22⋊Dic47—24no—
314C22⋊Dic47—24no—
315C22⋊Dic47—24no—
316C22⋊Dic47—22no—
317C22⋊Dic47—22no—
318C22⋊Dic47—22no—
319C22⋊Dic47—22no—
320C22⋊Dic47—22no—
321C22⋊Dic47—22no—
322(C2×D47)⋊C4—22no—
323(C2×D47)⋊C4—22no—
324(C2×D47)⋊C4—22no—
325(C2×D47)⋊C4—22no—
326C4⋊Dic47—22no—
327C4⋊Dic47—22no—
328C4⋊Dic47—22no—
329C4⋊Dic47—21no—
330C4⋊Dic47—21no—
331C4⋊Dic47C2414yes—
332C4⋊Dic47C2412yes—
333C4⋊Dic47C2412yes—
334Dic47⋊C4—24no—
335Dic47⋊C4—24no—
336Dic47⋊C4—24no—
337Dic47⋊C4—24no—
338Dic47⋊C4—22no—
339Dic47⋊C4—22no—
340Dic47⋊C4—22no—
341Dic47⋊C4—22no—
342C4×Dic47—22no—
343C4×Dic47—22no—
344Dic188—48no—
345#10625325—48no—
346C23×C47—22no—
347C23×C47—22no—
348C23×C47—22no—
349C23×C47—22no—
350C23×C47—22no—
351C23×C47—22no—
352C23×C47—22no—
353C23×C47—22no—
354C23×C47—22no—
355C23×C47—22no—
356C23×C47—22no—
357C23×C47—22no—
358C23×C47—41no—
359C23×C47—41no—
360C23×C47—41no—
361C23×C47—41no—
362C23×C47—41no—
363C23×C47—41no—
364C23×C47—41no—
365C23×C47—41no—
366C23×C47—416no—
367C23×C47#13714yescomplemented
368C23×C47C22×D411yescharacteristic
369C23×C47C22×D411yescharacteristic
370C23×C47C22×D411yescharacteristic
371C23×C47C22×D411yescharacteristic
372C23×C47C22×D411yescharacteristic
373C23×C47C22×D411yescharacteristic
374C23×C47C22×D411yescharacteristic
375C22×D47—22no—
376C22×D47—42no—
377C22×D47—42no—
378C22×D47—42no—
379C2×C4×C47—22no—
380C2×C4×C47—22no—
381C2×C4×C47—22no—
382C2×C4×C47—22no—
383C2×C4×C47—22no—
384C2×C4×C47—22no—
385C2×C4×C47—22no—
386C2×C4×C47—22no—
387C2×C4×C47—22no—
388C2×C4×C47—22no—
389C2×C4×C47—22no—
390C2×C4×C47—22no—
391C2×C4×C47—22no—
392C2×C4×C47—22no—
393C2×C4×C47—22no—
394C2×C4×C47—41no—
395C2×C4×C47—41no—
396C2×C4×C47—41no—
397C2×C4×C47—41no—
398C2×C4×C47—41no—
399C2×C4×C47—41no—
400C2×C4×C47—41no—
401C2×C4×C47—41no—
402C2×C4×C47—41no—
403C2×C4×C47—41no—
404C2×C4×C47—41no—
405C2×C4×C47—41no—
406C2×C4×C47C22×D411yescharacteristic
407C2×C4×C47C22×D411yescharacteristic
408C2×C4×C47C22×D411yescharacteristic
409C2×C4×C47C22×D411yescharacteristic
410C2×C4×C47C22×D411yescharacteristic
411C2×C4×C47C22×D411yescharacteristic
412C2×C4×C47C22×D411yescharacteristic
413C2×C4×C47H(5,𝔽2)14yes—
414C2×C4×C47C2511yescharacteristic
415C22⋊D47—44no—
416C22⋊D47—44no—
417C22⋊D47—44no—
418C22⋊D47—44no—
419C22⋊D47—44no—
420C22⋊D47—44no—
421C2×Dic47—22no—
422C2×Dic47—22no—
423C2×Dic47—24no—
424C2×Dic47—24no—
425C2×Dic47—22no—
426C2×Dic47—44no—
427C2×Dic47—44no—
428C2×Dic47—42no—
429C2×Dic47—44no—
430C2×Dic47—44no—
431C2×Dic47—42no—
432C2×Dic47—44no—
433C2×Dic47—42no—
434C2×Dic47—44no—
435D188—24no—
436D188—42no—
437C4×D47—44no—
438C4×D47—44no—
439Dic94—28no—
440Dic94—24no—
441Dic94—44no—
442Dic94—44no—
443Dic94—42no—
444Dic94—44no—
445C8×C47—28no—
446#60751—471nomaximal, Sylow
447C22×C47—28no—
448C22×C47—21no—
449C22×C47—21no—
450C22×C47—21no—
451C22×C47—21no—
452C22×C47—21no—
453C22×C47—21no—
454C22×C47—21no—
455C22×C47—21no—
456C22×C47—21no—
457C22×C47—21no—
458C22×C47—21no—
459C22×C47—21no—
460C22×C47—21no—
461C22×C47—21no—
462C22×C47—21no—
463C22×C47—21no—
464C22×C47—44no—
465C22×C47—44no—
466C22×C47—44no—
467C22×C47—44no—
468C22×C47—44no—
469C22×C47—44no—
470C22×C47#53412yes—
471C22×C47C2×#13712yes—
472C22×C47C2×#13712yes—
473C22×C47C2×#13712yes—
474C22×C47#57512yes—
475C22×C47C23×D411yescharacteristic
476C2×D47—42no—
477C2×D47—42no—
478C2×D47—42no—
479C2×D47—84no—
480C4×C47—21no—
481C4×C47—21no—
482C4×C47—21no—
483C4×C47—21no—
484C4×C47—21no—
485C4×C47—21no—
486C4×C47#53412yes—
487C4×C47C2×H(5,𝔽2)12yes—
488Dic47—44no—
489Dic47—42no—
490Dic47—42no—
491Dic47—44no—
492Dic47—42no—
493C2×#525—471no—
494C22×C22⋊Q8—471no—
495#3196—474no—
496#3195—472no—
497#3193—472no—
498#3190—474no—
499#3189—472no—
500#3187—472no—
501#3095—472no—
502#3092—472no—
503#3056—474no—
504#3007—472no—
505#3004—472no—
506C2×#407D4711yescharacteristic, complemented
507C2×C47—22no—
508C2×C47—22no—
509C2×C47—22no—
510C2×C47—22no—
511C2×C47—22no—
512C2×C47—41no—
513C2×C47—41no—
514C2×C47C2×#53411yescharacteristic
515C2×C47C22×#13711yescharacteristic
516C2×C47C2×#57511yescharacteristic
517D47—82no—
518C22×#41—471no—
519C23×Q8—471no—
520C24×C4C2×D4711yescharacteristic
521C2×#137—474no—
522C22×M16C2×D4712yescomplemented
523#525—472no—
524#525—472no—
525#525—472no—
526#525—472no—
527#525—941no—
528#525—941no—
529#525—941no—
530#525—941no—
531C2×#123—941no—
532C2×C22⋊Q8—472no—
533C2×C22⋊Q8—472no—
534C2×C22⋊Q8—472no—
535C2×C22⋊Q8—472no—
536C2×C22⋊Q8—472no—
537C2×C22⋊Q8—472no—
538C2×C22⋊Q8—471no—
539C2×C22⋊Q8—471no—
540C2×C22⋊Q8—941no—
541C2×C22⋊Q8—941no—
542C2×C22⋊Q8—941no—
543C2×C22⋊Q8—941no—
544C2×C22⋊Q8—941no—
545C2×C22⋊Q8—941no—
546C2×#121—471no—
547C2×#121—471no—
548C2×#120—941no—
549C2×C4×D4—941no—
550C2×C4×D4—941no—
551C2×#117—471no—
552C22×C4⋊C4—471no—
553C22×C4⋊C4—941no—
554C22×C22⋊C4—941no—
555#485—478no—
556#484—474no—
557#484—474no—
558#483—474no—
559#483—474no—
560#481—474no—
561#480—474no—
562#470—478no—
563#468—478no—
564#467—478no—
565#465—478no—
566#452—478no—
567#451—474no—
568#451—474no—
569#451—474no—
570#450—474no—
571#448—474no—
572#448—474no—
573#428—474no—
574#419—474no—
575#417—474no—
576#407C2×D4712yes—
577#407C2×D4712yes—
578#407C2×D4712yescomplemented
579#407C2×D4712yescomplemented
580C2×C22⋊C8C2×D4712yes—
581C2×C22⋊C8C2×D4712yescomplemented
582C47#6075111yescharacteristic, complemented, Sylow
583C25D18811yescharacteristic
584C2×#41—472no—
585C2×#41—472no—
586C2×#41—941no—
587C2×#41—941no—
588C2×#41—1884no—
589C22×Q8—472no—
590C22×Q8—472no—
591C22×Q8—472no—
592C22×Q8—471no—
593C22×Q8—941no—
594C22×Q8—941no—
595C22×Q8—941no—
596C22×Q8—1884no—
597C22×D4—471no—
598C22×D4—941no—
599C22×D4—941no—
600C22×D4—941no—
601C23×C4—44no—
602C23×C4—941no—
603C23×C4—941no—
604C23×C4—941no—
605C23×C4D18811yescharacteristic
606C23×C4D18811yescharacteristic
607C23×C4D18811yescharacteristic
608C23×C4D18811yescharacteristic
609C23×C4D18811yescharacteristic
610C23×C4D18811yescharacteristic
611C23×C4D18811yescharacteristic
612C23×C4C22×D4711yescharacteristic
613C23×C4C22×D4711yescharacteristic
614C23×C4C22×D4711yescharacteristic
615C23×C4C22×D4711yescharacteristic
616C23×C4C22×D4711yescharacteristic
617C23×C4C22×D4711yescharacteristic
618C23×C4C22×D4711yescharacteristic
619#137—1888no—
620C2×Q16—478no—
621C2×SD16—478no—
622C2×M16—44no—
623C2×M16C22×D4714yes—
624C2×M16C22×D4714yes—
625C22×C8C22×D4714yes—
626#123—942no—
627#123—942no—
628#123—942no—
629#123—942no—
630C22⋊Q8—474no—
631C22⋊Q8—474no—
632C22⋊Q8—474no—
633C22⋊Q8—474no—
634C22⋊Q8—472no—
635C22⋊Q8—472no—
636C22⋊Q8—472no—
637C22⋊Q8—472no—
638C22⋊Q8—942no—
639C22⋊Q8—942no—
640C22⋊Q8—942no—
641C22⋊Q8—942no—
642C22⋊Q8—942no—
643C22⋊Q8—942no—
644C22⋊Q8—942no—
645C22⋊Q8—942no—
646C22⋊Q8—942no—
647C22⋊Q8—942no—
648C22⋊Q8—942no—
649C22⋊Q8—942no—
650C22⋊Q8—941no—
651C22⋊Q8—941no—
652C22⋊Q8—941no—
653C22⋊Q8—941no—
654#121—472no—
655#121—472no—
656#121—472no—
657#121—472no—
658#121—941no—
659#121—941no—
660#121—941no—
661#121—941no—
662#120—942no—
663#120—942no—
664#120—942no—
665#120—942no—
666C4×D4—942no—
667C4×D4—942no—
668C4×D4—942no—
669C4×D4—942no—
670C4×D4—942no—
671C4×D4—942no—
672C4×D4—942no—
673C4×D4—942no—
674#117—472no—
675#117—472no—
676#117—941no—
677#117—941no—
678C2×C4⋊C4—472no—
679C2×C4⋊C4—472no—
680C2×C4⋊C4—472no—
681C2×C4⋊C4—471no—
682C2×C4⋊C4—471no—
683C2×C4⋊C4—941no—
684C2×C4⋊C4—941no—
685C2×C4⋊C4—941no—
686C2×C4⋊C4—942no—
687C2×C4⋊C4—942no—
688C2×C4⋊C4—942no—
689C2×C4⋊C4—942no—
690C2×C4⋊C4—942no—
691C2×C4⋊C4—942no—
692C2×C4⋊C4—941no—
693C2×C4⋊C4—941no—
694C2×C22⋊C4—942no—
695C2×C22⋊C4—942no—
696C2×C22⋊C4—942no—
697C2×C22⋊C4—942no—
698C2×C22⋊C4—942no—
699C2×C22⋊C4—942no—
700C2×C22⋊C4—941no—
701C2×C22⋊C4—941no—
702C2×C22⋊C4—941no—
703C2×C22⋊C4—941no—
704C2×C22⋊C4—941no—
705C2×C42—941no—
706#107—478no—
707#106—478no—
708#103—478no—
709#103—478no—
710#103—478no—
711#102—478no—
712C22⋊C8C22×D4714yes—
713C22⋊C8C22×D4714yes—
714C22⋊C8C22×D4714yes—
715C22⋊C8C22×D4714yes—
716C24—24no—
717C24—42no—
718C24—42no—
719C24—941no—
720C24C2×D18811yescharacteristic
721C24C2×D18811yescharacteristic
722C24C2×D18811yescharacteristic
723C24C2×D18811yescharacteristic
724C24C2×D18811yescharacteristic
725C24C2×D18811yescharacteristic
726C24C2×D18811yescharacteristic
727#41—948no—
728#41—1884no—
729#41—1884no—
730#41—1884no—
731C2×Q8—474no—
732C2×Q8—472no—
733C2×Q8—942no—
734C2×Q8—942no—
735C2×Q8—942no—
736C2×Q8—941no—
737C2×Q8—948no—
738C2×Q8—1884no—
739C2×Q8—1884no—
740C2×Q8—1882no—
741C2×Q8—1884no—
742C2×Q8—1884no—
743C2×Q8—1884no—
744C2×D4—472no—
745C2×D4—942no—
746C2×D4—942no—
747C2×D4—942no—
748C2×D4—942no—
749C2×D4—942no—
750C2×D4—942no—
751C2×D4—941no—
752C2×D4—1882no—
753C2×D4—1884no—
754C2×D4—1884no—
755C2×D4—1884no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—941no—
771C22×C4—941no—
772C22×C4—942no—
773C22×C4—942no—
774C22×C4—942no—
775C22×C4—941no—
776C22×C4—942no—
777C22×C4—942no—
778C22×C4—942no—
779C22×C4—942no—
780C22×C4—942no—
781C22×C4—1884no—
782C22×C4—1884no—
783C22×C4—1884no—
784C22×C4C2×D18811yescharacteristic
785C22×C4C2×D18811yescharacteristic
786C22×C4C2×D18811yescharacteristic
787C22×C4C2×D18811yescharacteristic
788C22×C4C2×D18811yescharacteristic
789C22×C4C2×D18811yescharacteristic
790C22×C4C2×D18811yescharacteristic
791C22×C4C2×D18811yescharacteristic
792C22×C4C2×D18811yescharacteristic
793C22×C4C2×D18811yescharacteristic
794C22×C4C2×D18811yescharacteristic
795C22×C4C2×D18811yescharacteristic
796C22×C4C2×D18811yescharacteristic
797C22×C4C2×D18811yescharacteristic
798C22×C4C2×D18811yescharacteristic
799C22×C4C2×D18811yescharacteristic
800C22×C4C2×D18811yescharacteristic
801C22×C4C2×D18811yescharacteristic
802C22×C4C2×D18811yescharacteristic
803C22×C4C2×D18811yescharacteristic
804C22×C4C2×D18811yescharacteristic
805C22×C4C23×D4711yescharacteristic
806C22×C4C23×D4711yescharacteristic
807C22×C4C23×D4711yescharacteristic
808C22×C4C23×D4711yescharacteristic
809C22×C4C23×D4711yescharacteristic
810C22×C4C23×D4711yescharacteristic
811C22×C4C23×D4711yescharacteristic
812Q16—1888no—
813SD16—1888no—
814M16—28no—
815M16—44no—
816C2×C8—44no—
817C2×C8C23×D4718yes—
818C4⋊C4—474no—
819C4⋊C4—472no—
820C4⋊C4—472no—
821C4⋊C4—944no—
822C4⋊C4—944no—
823C4⋊C4—944no—
824C4⋊C4—944no—
825C4⋊C4—942no—
826C4⋊C4—942no—
827C4⋊C4—942no—
828C4⋊C4—942no—
829C4⋊C4—942no—
830C4⋊C4—942no—
831C4⋊C4—942no—
832C4⋊C4—941no—
833C4⋊C4—941no—
834C22⋊C4—944no—
835C22⋊C4—944no—
836C22⋊C4—944no—
837C22⋊C4—944no—
838C22⋊C4—942no—
839C22⋊C4—942no—
840C22⋊C4—942no—
841C22⋊C4—942no—
842C22⋊C4—942no—
843C22⋊C4—942no—
844C22⋊C4—942no—
845C22⋊C4—942no—
846C22⋊C4—942no—
847C22⋊C4—942no—
848C42—942no—
849C42—942no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—416no—
871C23—942no—
872C23—1882no—
873C23—1882no—
874C23—1882no—
875C23#1309405714yescomplemented
876C23C22×D18811yescharacteristic
877C23C22×D18811yescharacteristic
878C23C22×D18811yescharacteristic
879C23C22×D18811yescharacteristic
880C23C22×D18811yescharacteristic
881C23C22×D18811yescharacteristic
882C23C22×D18811yescharacteristic
883Q8—948no—
884Q8—944no—
885Q8—1884no—
886Q8—1884no—
887Q8—1882no—
888Q8—1884no—
889D4—944no—
890D4—1882no—
891D4—1884no—
892D4—1884no—
893D4—1884no—
894D4—1884no—
895D4—1884no—
896D4—1884no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—942no—
925C2×C4—942no—
926C2×C4—944no—
927C2×C4—942no—
928C2×C4—944no—
929C2×C4—1884no—
930C2×C4—1884no—
931C2×C4—1884no—
932C2×C4—1882no—
933C2×C4—1884no—
934C2×C4—1884no—
935C2×C4—1882no—
936C2×C4—1882no—
937C2×C4—1884no—
938C2×C4—1884no—
939C2×C4—1884no—
940C2×C4C22×D18811yescharacteristic
941C2×C4C22×D18811yescharacteristic
942C2×C4C22×D18811yescharacteristic
943C2×C4C22×D18811yescharacteristic
944C2×C4C22×D18811yescharacteristic
945C2×C4C22×D18811yescharacteristic
946C2×C4C22×D18811yescharacteristic
947C2×C4#1309406914yes—
948C2×C4C24×D4711yescharacteristic
949C8—28no—
950C22—28no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—3764no—
974C22—1882no—
975C22—1882no—
976C22—1882no—
977C22#1568968512yes—
978C22C2×#1309405712yes—
979C22C2×#1309405712yes—
980C22C2×#1309405712yes—
981C22#1568992312yes—
982C22C23×D18811yescharacteristic
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—1882no—
990C4—1884no—
991C4—1882no—
992C4—1882no—
993C4—1884no—
994C4#1568968512yes—
995C4C2×#1309406912yes—
996C2—22no—
997C2—22no—
998C2—22no—
999C2—22no—
1000C2—22no—
1001C2—41no—
1002C2—41no—
1003C2—3762no—
1004C2C2×#1568968511yescharacteristic
1005C2C22×#1309405711yescharacteristic
1006C2C2×#1568992311yescharacteristic
subgroupG/H
centerC22C23×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#407C2
socleC22×C47C23×D4
prime radicalC2×#15689634C2
hypercenterC2×#407D47
hypocenterC47#60751
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C22×#13094003C2semidirect
3. #20254220C2semidirect
4. #20254212C2semidirect
5. #20254195C2semidirect
6. #20254171C2semidirect
7. #20254163C2semidirect
8. #20254146C2semidirect
9. #20253337C2semidirect
10. #20253313C2semidirect
11. #20253018C2semidirect
12. #20252650C2semidirect
13. #20252625C2semidirect
14. C2×C47×#407C2semidirect
16. C23×Dic94C22semidirect
17. C2×#13094057C22semidirect
38. C2×#13094003C22semidirect
39. C2×#13094003C22semidirect
40. C2×#13094003C22semidirect
47. C22×C4⋊Dic47C22semidirect
50. #15689465C22semidirect
51. #15689459C22semidirect
52. #15689459C22semidirect
53. #15689454C22semidirect
54. #15689454C22semidirect
55. #15689442C22semidirect
56. #15689437C22semidirect
57. #15689381C22semidirect
58. #15689369C22semidirect
59. #15689364C22semidirect
60. #15689352C22semidirect
61. #15689287C22semidirect
62. #15689281C22semidirect
63. #15689281C22semidirect
64. #15689281C22semidirect
65. #15689276C22semidirect
66. #15689264C22semidirect
67. #15689264C22semidirect
68. #15689165C22semidirect
69. #15689133C22semidirect
70. #15689125C22semidirect
72. C22×M16×C47C22semidirect
75. C47×#407C22semidirect
76. C47×#407C22semidirect
78. C2×C22⋊C8×C47C22semidirect
100. C2×Dic188C23semidirect
101. C2×#10625325C23semidirect
182. #13093958C23semidirect
183. #13093956C23semidirect
184. #13093949C23semidirect
185. #13093949C23semidirect
186. #13093949C23semidirect
187. #13093946C23semidirect
367. C23×C47#137semidirect
506. C2×#407D47semidirect
522. C22×M16C2×D47semidirect
578. #407C2×D47semidirect
579. #407C2×D47semidirect
581. C2×C22⋊C8C2×D47semidirect
582. C47#60751semidirect
875. C23#13094057semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
C22×#130940032
#202542202
#202542122
#202541952
#202541712
#202541632
#202541462
#202533372
#202533132
#202530182
#202526502
#202526252
C2×C47×#4072
#6075147