Finite Group Databasebeta

← #27087035

Subgroups — #27087035

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
2#20254218C214yesmaximal, complemented
3#20254209C212yesmaximal, complemented
4#20254190C212yesmaximal, complemented
5#20254169C214yesmaximal, complemented
6#20254160C212yesmaximal, complemented
7#20254141C212yesmaximal, complemented
8#20253332C212yesmaximal, complemented
9#20253311C212yesmaximal, complemented
10#20253014C214yesmaximal, complemented
11#20252646C212yesmaximal, complemented
12#20252622C212yesmaximal, complemented
13C2×#15689087C211yesmaximal, characteristic, complemented
14C22×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
15C22×#10625350C2211yescharacteristic
16C2×#13094055C2214yescomplemented
17C22×#10625329C2212yescomplemented
18#15689634—21no—
19#15689634—21no—
20#15689634—21no—
21#15689634—21no—
22#15689634C2212yes—
23#15689634C2212yes—
24#15689634C2212yes—
25#15689634C2212yes—
26C2×#13094007—21no—
27C2×#13094003C2211yescharacteristic
28C2×#13094003C2211yescharacteristic
29C2×#13093998C2211yescharacteristic
30C2×#13093998C2211yescharacteristic
31C2×#13093993—21no—
32C2×C4×C22⋊D47—21no—
33C2×C4×C22⋊D47—21no—
34C2×#13093983C2211yescharacteristic
35#15689461C2218yescomplemented
36#15689458C2214yescomplemented
37#15689456C2214yescomplemented
38#15689453C2214yescomplemented
39#15689451C2214yescomplemented
40#15689441C2214yescomplemented
41#15689436C2214yescomplemented
42#15689379C2218yescomplemented
43#15689371C2218yescomplemented
44#15689362C2218yescomplemented
45#15689354C2218yescomplemented
46#15689283C2218yescomplemented
47#15689279C2214yescomplemented
48#15689279C2214yescomplemented
49#15689278C2214yescomplemented
50#15689273C2214yescomplemented
51#15689262C2214yescomplemented
52#15689262C2214yescomplemented
53#15689163C2214yescomplemented
54#15689132C2214yescomplemented
55#15689122C2214yescomplemented
56#15689087C2212yes—
57#15689087C2212yes—
58#15689087C2212yescomplemented
59#15689087C2212yescomplemented
60C2×C22⋊(C47⋊C8)C2212yes—
61C2×C22⋊(C47⋊C8)C2212yescomplemented
62C23×Q8×C47C2211yescharacteristic, complemented
63C24×C4×C47C2211yescharacteristic
64C2×C22⋊Q8×C47—21no—
65C2×C22⋊Q8×C47—21no—
66C2×C22⋊Q8×C47—21no—
67C2×C22⋊Q8×C47—21no—
68C2×C22⋊Q8×C47—21no—
69C2×C22⋊Q8×C47—21no—
70C2×C22⋊Q8×C47C2212yes—
71C2×C22⋊Q8×C47C2212yes—
72C2×C22⋊Q8×C47C2212yes—
73C2×C22⋊Q8×C47C2212yescomplemented
74C2×C22⋊Q8×C47C2212yescomplemented
75C2×C22⋊Q8×C47C2212yescomplemented
76C22×C4⋊C4×C47—21no—
77C22×C4⋊C4×C47C2211yescharacteristic, complemented
78C22×C22⋊C4×C47—21no—
79C2×#10625350—21no—
80C2×#10625350—21no—
81C2×#10625350—44no—
82C2×#10625350C2312yes—
83C2×#10625350C2312yes—
84C22×Dic94C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C22×C4×D47—21no—
90#13094055—48no—
91C2×#10625337C2318yescomplemented
92C2×#10625336C2318yescomplemented
93C2×#10625329—44no—
94C2×#10625329C2314yes—
95C2×#10625329C2314yes—
96C22×C47⋊C8C2314yes—
97#13094007—22no—
98#13094007—22no—
99#13094007—22no—
100#13094007—22no—
101#13094003—21no—
102#13094003—21no—
103#13094003—21no—
104#13094003—21no—
105#13094003C2312yes—
106#13094003C2312yes—
107#13094003C2312yes—
108#13094003C2312yes—
109#13093998—21no—
110#13093998—21no—
111#13093998—21no—
112#13093998—21no—
113#13093998C2312yes—
114#13093998C2312yes—
115#13093998C2312yes—
116#13093998C2312yes—
117#13093993—22no—
118#13093993—22no—
119#13093993—22no—
120#13093993—22no—
121C4×C22⋊D47—22no—
122C4×C22⋊D47—22no—
123C4×C22⋊D47—22no—
124C4×C22⋊D47—22no—
125C4×C22⋊D47—22no—
126C4×C22⋊D47—22no—
127C4×C22⋊D47—22no—
128C4×C22⋊D47—22no—
129#13093983—21no—
130#13093983—21no—
131#13093983C2312yes—
132#13093983C2312yes—
133C2×C4⋊Dic47C2311yescharacteristic
134C2×C4⋊Dic47C2311yescharacteristic
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×C4×Dic47—21no—
143#13093957C2318yescomplemented
144#13093955C2318yescomplemented
145#13093948C2318yescomplemented
146#13093948C2318yescomplemented
147#13093947C2318yescomplemented
148#13093944C2318yescomplemented
149C22⋊(C47⋊C8)C2314yes—
150C22⋊(C47⋊C8)C2314yes—
151C22⋊(C47⋊C8)C2314yes—
152C22⋊(C47⋊C8)C2314yes—
153C25×C47D411yescharacteristic
154C22×Q8×C47—21no—
155C22×Q8×C47—21no—
156C22×Q8×C47—21no—
157C22×Q8×C47—44no—
158C22×Q8×C47C2312yes—
159C22×Q8×C47C2312yes—
160C22×Q8×C47C2312yes—
161C23×C4×C47—21no—
162C23×C4×C47—21no—
163C23×C4×C47—44no—
164C23×C4×C47D411yescharacteristic
165C23×C4×C47D411yescharacteristic
166C23×C4×C47D411yescharacteristic
167C23×C4×C47D411yescharacteristic
168C23×C4×C47D411yescharacteristic
169C23×C4×C47D411yescharacteristic
170C23×C4×C47D411yescharacteristic
171C23×C4×C47C2311yescharacteristic
172C23×C4×C47C2311yescharacteristic
173C23×C4×C47C2311yescharacteristic
174C23×C4×C47C2311yescharacteristic
175C23×C4×C47C2311yescharacteristic
176C23×C4×C47C2311yescharacteristic
177C23×C4×C47C2311yescharacteristic
178C22⋊Q8×C47—22no—
179C22⋊Q8×C47—22no—
180C22⋊Q8×C47—22no—
181C22⋊Q8×C47—22no—
182C22⋊Q8×C47—22no—
183C22⋊Q8×C47—22no—
184C22⋊Q8×C47—22no—
185C22⋊Q8×C47—22no—
186C22⋊Q8×C47—22no—
187C22⋊Q8×C47—22no—
188C22⋊Q8×C47—22no—
189C22⋊Q8×C47—22no—
190C22⋊Q8×C47C2314yes—
191C22⋊Q8×C47C2314yes—
192C22⋊Q8×C47C2314yes—
193C22⋊Q8×C47C2314yes—
194C2×C4⋊C4×C47—22no—
195C2×C4⋊C4×C47—22no—
196C2×C4⋊C4×C47—22no—
197C2×C4⋊C4×C47—22no—
198C2×C4⋊C4×C47—22no—
199C2×C4⋊C4×C47—22no—
200C2×C4⋊C4×C47—21no—
201C2×C4⋊C4×C47—21no—
202C2×C4⋊C4×C47—21no—
203C2×C4⋊C4×C47C2312yes—
204C2×C4⋊C4×C47C2312yes—
205C2×C4⋊C4×C47C2312yes—
206C2×C22⋊C4×C47—22no—
207C2×C22⋊C4×C47—22no—
208C2×C22⋊C4×C47—22no—
209C2×C22⋊C4×C47—22no—
210C2×C22⋊C4×C47—22no—
211C2×C22⋊C4×C47—22no—
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—
223C2×Q8×C47—22no—
224C2×Q8×C47—22no—
225C2×Q8×C47—22no—
226C2×Q8×C47—28no—
227C2×Q8×C47—44no—
228C2×Q8×C47—44no—
229C2×Q8×C47—44no—
230C2×Q8×C47—44no—
231C2×Q8×C47—44no—
232C2×Q8×C47C2414yes—
233C22×C4×C47—24no—
234C22×C4×C47—24no—
235C22×C4×C47—24no—
236C22×C4×C47—22no—
237C22×C4×C47—22no—
238C22×C4×C47—22no—
239C22×C4×C47—22no—
240C22×C4×C47—22no—
241C22×C4×C47—22no—
242C22×C4×C47—42no—
243C22×C4×C47—42no—
244C22×C4×C47—42no—
245C22×C4×C47—42no—
246C22×C4×C47—42no—
247C22×C4×C47—42no—
248C22×C4×C47—42no—
249C22×C4×C47—42no—
250C22×C4×C47—42no—
251C22×C4×C47—42no—
252C22×C4×C47—42no—
253C22×C4×C47—44no—
254C22×C4×C47—44no—
255C22×C4×C47C2×D411yescharacteristic
256C22×C4×C47C2×D411yescharacteristic
257C22×C4×C47C2×D411yescharacteristic
258C22×C4×C47C2×D411yescharacteristic
259C22×C4×C47C2×D411yescharacteristic
260C22×C4×C47C2×D411yescharacteristic
261C22×C4×C47C2×D411yescharacteristic
262C22×C4×C47C2×D411yescharacteristic
263C22×C4×C47C2×D411yescharacteristic
264C22×C4×C47C2×D411yescharacteristic
265C22×C4×C47C2×D411yescharacteristic
266C22×C4×C47C2×D411yescharacteristic
267C22×C4×C47C2×D411yescharacteristic
268C22×C4×C47C2×D411yescharacteristic
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×C47C2411yescharacteristic
277C22×C4×C47C2411yescharacteristic
278C22×C4×C47C2411yescharacteristic
279C22×C4×C47C2411yescharacteristic
280C22×C4×C47C2411yescharacteristic
281C22×C4×C47C2411yescharacteristic
282C22×C4×C47C2411yescharacteristic
283C2×C22⋊D47—22no—
284C2×C22⋊D47—22no—
285C2×C22⋊D47—22no—
286C2×C22⋊D47—22no—
287C2×C22⋊D47—22no—
288C2×C22⋊D47—22no—
289C2×C22⋊D47—44no—
290C2×C22⋊D47—44no—
291C2×C22⋊D47—44no—
292C22×Dic47—21no—
293C22×Dic47—21no—
294C22×Dic47—21no—
295#10625350—28no—
296#10625350—44no—
297#10625350—44no—
298#10625350—44no—
299C2×D188—21no—
300C2×D188—42no—
301C2×D188C2412yes—
302C2×C4×D47—22no—
303C2×C4×D47—22no—
304C2×C4×D47—44no—
305C2×Dic94—21no—
306C2×Dic94—42no—
307C2×Dic94C2412yes—
308C4⋊C4×C47—24no—
309C4⋊C4×C47—24no—
310C4⋊C4×C47—24no—
311C4⋊C4×C47—24no—
312C4⋊C4×C47—22no—
313C4⋊C4×C47—22no—
314C4⋊C4×C47—22no—
315C4⋊C4×C47C2414yes—
316C22⋊C4×C47—24no—
317C22⋊C4×C47—24no—
318C22⋊C4×C47—24no—
319C22⋊C4×C47—24no—
320C22⋊Dic47—22no—
321C22⋊Dic47—22no—
322C22⋊Dic47—22no—
323C22⋊Dic47—22no—
324C22⋊Dic47—22no—
325C22⋊Dic47—22no—
326#10625337—48no—
327#10625336—48no—
328(C2×D47)⋊C4—22no—
329(C2×D47)⋊C4—22no—
330(C2×D47)⋊C4—22no—
331(C2×D47)⋊C4—22no—
332C4⋊Dic47—21no—
333C4⋊Dic47—21no—
334C4⋊Dic47C2412yes—
335C4⋊Dic47C2412yes—
336Dic47⋊C4—22no—
337Dic47⋊C4—22no—
338Dic47⋊C4—22no—
339Dic47⋊C4—22no—
340C4×Dic47—22no—
341C4×Dic47—22no—
342#10625329—28no—
343#10625329—44no—
344C2×C47⋊C8—44no—
345C2×C47⋊C8C2418yes—
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—
379Q8×C47—28no—
380Q8×C47—44no—
381Q8×C47—44no—
382Q8×C47—44no—
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—22no—
395C2×C4×C47—22no—
396C2×C4×C47—22no—
397C2×C4×C47—22no—
398C2×C4×C47—24no—
399C2×C4×C47—24no—
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×C47—41no—
407C2×C4×C47—41no—
408C2×C4×C47—41no—
409C2×C4×C47—41no—
410C2×C4×C47—41no—
411C2×C4×C47—41no—
412C2×C4×C47—44no—
413C2×C4×C47—44no—
414C2×C4×C47—44no—
415C2×C4×C47—44no—
416C2×C4×C47—44no—
417C2×C4×C47—44no—
418C2×C4×C47C22×D411yescharacteristic
419C2×C4×C47C22×D411yescharacteristic
420C2×C4×C47C22×D411yescharacteristic
421C2×C4×C47C22×D411yescharacteristic
422C2×C4×C47C22×D411yescharacteristic
423C2×C4×C47C22×D411yescharacteristic
424C2×C4×C47C22×D411yescharacteristic
425C2×C4×C47H(5,𝔽2)14yes—
426C2×C4×C47C2511yescharacteristic
427C22⋊D47—44no—
428C22⋊D47—44no—
429C22⋊D47—44no—
430C22⋊D47—44no—
431C22⋊D47—44no—
432C22⋊D47—44no—
433C2×Dic47—22no—
434C2×Dic47—22no—
435C2×Dic47—22no—
436C2×Dic47—42no—
437C2×Dic47—42no—
438C2×Dic47—42no—
439D188—24no—
440D188—42no—
441C4×D47—44no—
442C4×D47—44no—
443Dic94—24no—
444Dic94—42no—
445C47⋊C8—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—44no—
487C4×C47—44no—
488C4×C47#53412yes—
489C4×C47C2×H(5,𝔽2)12yes—
490Dic47—42no—
491Dic47—42no—
492Dic47—42no—
493C2×#525—471no—
494C22×C22⋊Q8D4711yescharacteristic, complemented
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×#407—471no—
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×Q8C2×D4711yescharacteristic, complemented
520C24×C4C2×D4711yescharacteristic
521C2×#137—474no—
522C22×M16—472no—
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—21no—
533C2×C22⋊Q8—21no—
534C2×C22⋊Q8—21no—
535C2×C22⋊Q8—21no—
536C2×C22⋊Q8—21no—
537C2×C22⋊Q8—21no—
538C2×C22⋊Q8—471no—
539C2×C22⋊Q8—471no—
540C2×C22⋊Q8C2×D4712yes—
541C2×C22⋊Q8C2×D4712yes—
542C2×C22⋊Q8C2×D4712yes—
543C2×C22⋊Q8C2×D4712yescomplemented
544C2×C22⋊Q8C2×D4712yescomplemented
545C2×C22⋊Q8C2×D4712yescomplemented
546C2×#121—471no—
547C2×#121—471no—
548C2×#120—941no—
549C2×C4×D4—941no—
550C2×C4×D4—941no—
551C2×#117—471no—
552C22×C4⋊C4—21no—
553C22×C4⋊C4C2×D4711yescharacteristic, complemented
554C22×C22⋊C4—21no—
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#407—472no—
577#407—472no—
578#407—472no—
579#407—472no—
580C2×C22⋊C8—472no—
581C2×C22⋊C8—472no—
582C47#6075111yescharacteristic, complemented, Sylow
583C25C22⋊D4711yescharacteristic
584C2×#41—472no—
585C2×#41—472no—
586C2×#41—941no—
587C2×#41—941no—
588C2×#41—1884no—
589C22×Q8—21no—
590C22×Q8—21no—
591C22×Q8—21no—
592C22×Q8—44no—
593C22×Q8—471no—
594C22×Q8C22×D4712yes—
595C22×Q8C22×D4712yes—
596C22×Q8C22×D4712yes—
597C22×D4—471no—
598C22×D4—941no—
599C22×D4—941no—
600C22×D4—941no—
601C23×C4—21no—
602C23×C4—21no—
603C23×C4—44no—
604C23×C4—941no—
605C23×C4C22⋊D4711yescharacteristic
606C23×C4C22⋊D4711yescharacteristic
607C23×C4C22⋊D4711yescharacteristic
608C23×C4C22⋊D4711yescharacteristic
609C23×C4C22⋊D4711yescharacteristic
610C23×C4C22⋊D4711yescharacteristic
611C23×C4C22⋊D4711yescharacteristic
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—474no—
623C2×M16—474no—
624C2×M16—1884no—
625C22×C8—474no—
626#123—942no—
627#123—942no—
628#123—942no—
629#123—942no—
630C22⋊Q8—22no—
631C22⋊Q8—22no—
632C22⋊Q8—22no—
633C22⋊Q8—22no—
634C22⋊Q8—22no—
635C22⋊Q8—22no—
636C22⋊Q8—22no—
637C22⋊Q8—22no—
638C22⋊Q8—22no—
639C22⋊Q8—22no—
640C22⋊Q8—22no—
641C22⋊Q8—22no—
642C22⋊Q8—472no—
643C22⋊Q8—472no—
644C22⋊Q8—472no—
645C22⋊Q8—472no—
646C22⋊Q8—941no—
647C22⋊Q8—941no—
648C22⋊Q8—941no—
649C22⋊Q8—941no—
650C22⋊Q8C22×D4714yes—
651C22⋊Q8C22×D4714yes—
652C22⋊Q8C22×D4714yes—
653C22⋊Q8C22×D4714yes—
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—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—471no—
688C2×C4⋊C4—471no—
689C2×C4⋊C4—941no—
690C2×C4⋊C4—941no—
691C2×C4⋊C4C22×D4712yes—
692C2×C4⋊C4C22×D4712yes—
693C2×C4⋊C4C22×D4712yes—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
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⋊C8—474no—
713C22⋊C8—474no—
714C22⋊C8—474no—
715C22⋊C8—474no—
716C24—24no—
717C24—42no—
718C24—42no—
719C24—941no—
720C24C2×C22⋊D4711yescharacteristic
721C24C2×C22⋊D4711yescharacteristic
722C24C2×C22⋊D4711yescharacteristic
723C24C2×C22⋊D4711yescharacteristic
724C24C2×C22⋊D4711yescharacteristic
725C24C2×C22⋊D4711yescharacteristic
726C24C2×C22⋊D4711yescharacteristic
727#41—948no—
728#41—1884no—
729#41—1884no—
730#41—1884no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—22no—
734C2×Q8—28no—
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—44no—
739C2×Q8—44no—
740C2×Q8—472no—
741C2×Q8—941no—
742C2×Q8—1882no—
743C2×Q8C23×D4714yes—
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—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—941no—
779C22×C4—941no—
780C22×C4—941no—
781C22×C4—942no—
782C22×C4—942no—
783C22×C4—1884no—
784C22×C4C2×C22⋊D4711yescharacteristic
785C22×C4C2×C22⋊D4711yescharacteristic
786C22×C4C2×C22⋊D4711yescharacteristic
787C22×C4C2×C22⋊D4711yescharacteristic
788C22×C4C2×C22⋊D4711yescharacteristic
789C22×C4C2×C22⋊D4711yescharacteristic
790C22×C4C2×C22⋊D4711yescharacteristic
791C22×C4C2×C22⋊D4711yescharacteristic
792C22×C4C2×C22⋊D4711yescharacteristic
793C22×C4C2×C22⋊D4711yescharacteristic
794C22×C4C2×C22⋊D4711yescharacteristic
795C22×C4C2×C22⋊D4711yescharacteristic
796C22×C4C2×C22⋊D4711yescharacteristic
797C22×C4C2×C22⋊D4711yescharacteristic
798C22×C4C2×C22⋊D4711yescharacteristic
799C22×C4C2×C22⋊D4711yescharacteristic
800C22×C4C2×C22⋊D4711yescharacteristic
801C22×C4C2×C22⋊D4711yescharacteristic
802C22×C4C2×C22⋊D4711yescharacteristic
803C22×C4C2×C22⋊D4711yescharacteristic
804C22×C4C2×C22⋊D4711yescharacteristic
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—948no—
815M16—1884no—
816C2×C8—478no—
817C2×C8—1884no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—472no—
826C4⋊C4—472no—
827C4⋊C4—942no—
828C4⋊C4—942no—
829C4⋊C4—942no—
830C4⋊C4—942no—
831C4⋊C4—941no—
832C4⋊C4—941no—
833C4⋊C4C23×D4714yes—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—24no—
837C22⋊C4—24no—
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#1309405514yescomplemented
876C23C22×C22⋊D4711yescharacteristic
877C23C22×C22⋊D4711yescharacteristic
878C23C22×C22⋊D4711yescharacteristic
879C23C22×C22⋊D4711yescharacteristic
880C23C22×C22⋊D4711yescharacteristic
881C23C22×C22⋊D4711yescharacteristic
882C23C22×C22⋊D4711yescharacteristic
883Q8—28no—
884Q8—44no—
885Q8—44no—
886Q8—44no—
887Q8—944no—
888Q8—1882no—
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—24no—
913C2×C4—24no—
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—41no—
925C2×C4—41no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—942no—
933C2×C4—942no—
934C2×C4—942no—
935C2×C4—1884no—
936C2×C4—1882no—
937C2×C4—1882no—
938C2×C4—1882no—
939C2×C4—1884no—
940C2×C4C22×C22⋊D4711yescharacteristic
941C2×C4C22×C22⋊D4711yescharacteristic
942C2×C4C22×C22⋊D4711yescharacteristic
943C2×C4C22×C22⋊D4711yescharacteristic
944C2×C4C22×C22⋊D4711yescharacteristic
945C2×C4C22×C22⋊D4711yescharacteristic
946C2×C4C22×C22⋊D4711yescharacteristic
947C2×C4#1309406914yes—
948C2×C4C24×D4711yescharacteristic
949C8—948no—
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#1568968212yes—
978C22C2×#1309405512yes—
979C22C2×#1309405512yes—
980C22C2×#1309405512yes—
981C22#1568992112yes—
982C22C23×C22⋊D4711yescharacteristic
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—44no—
990C4—44no—
991C4—1882no—
992C4—1882no—
993C4—1882no—
994C4#1568968212yes—
995C4C2×#1309406912yes—
996C2—22no—
997C2—22no—
998C2—22no—
999C2—22no—
1000C2—22no—
1001C2—41no—
1002C2—41no—
1003C2—3762no—
1004C2C2×#1568968211yescharacteristic
1005C2C22×#1309405511yescharacteristic
1006C2C2×#1568992111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC22×C22⋊Q8×C47C2
socleC22×C47C23×D4
prime radicalC2×#15689634C2
hypercenterC22×C22⋊Q8D47
hypocenterC47#60751
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #20254218C2semidirect
3. #20254209C2semidirect
4. #20254190C2semidirect
5. #20254169C2semidirect
6. #20254160C2semidirect
7. #20254141C2semidirect
8. #20253332C2semidirect
9. #20253311C2semidirect
10. #20253014C2semidirect
11. #20252646C2semidirect
12. #20252622C2semidirect
13. C2×#15689087C2semidirect
14. C22×C22⋊Q8×C47C2semidirect
16. C2×#13094055C22semidirect
17. C22×#10625329C22semidirect
35. #15689461C22semidirect
36. #15689458C22semidirect
37. #15689456C22semidirect
38. #15689453C22semidirect
39. #15689451C22semidirect
40. #15689441C22semidirect
41. #15689436C22semidirect
42. #15689379C22semidirect
43. #15689371C22semidirect
44. #15689362C22semidirect
45. #15689354C22semidirect
46. #15689283C22semidirect
47. #15689279C22semidirect
48. #15689279C22semidirect
49. #15689278C22semidirect
50. #15689273C22semidirect
51. #15689262C22semidirect
52. #15689262C22semidirect
53. #15689163C22semidirect
54. #15689132C22semidirect
55. #15689122C22semidirect
58. #15689087C22semidirect
59. #15689087C22semidirect
61. C2×C22⋊(C47⋊C8)C22semidirect
62. C23×Q8×C47C22semidirect
73. C2×C22⋊Q8×C47C22semidirect
74. C2×C22⋊Q8×C47C22semidirect
75. C2×C22⋊Q8×C47C22semidirect
77. C22×C4⋊C4×C47C22semidirect
91. C2×#10625337C23semidirect
92. C2×#10625336C23semidirect
143. #13093957C23semidirect
144. #13093955C23semidirect
145. #13093948C23semidirect
146. #13093948C23semidirect
147. #13093947C23semidirect
148. #13093944C23semidirect
367. C23×C47#137semidirect
494. C22×C22⋊Q8D47semidirect
519. C23×Q8C2×D47semidirect
543. C2×C22⋊Q8C2×D47semidirect
544. C2×C22⋊Q8C2×D47semidirect
545. C2×C22⋊Q8C2×D47semidirect
553. C22×C4⋊C4C2×D47semidirect
582. C47#60751semidirect
875. C23#13094055semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
#202542182
#202542092
#202541902
#202541692
#202541602
#202541412
#202533322
#202533112
#202530142
#202526462
#202526222
C2×#156890872
C22×C22⋊Q8×C472
#6075147