Finite Group Databasebeta

← #26375476

Subgroups — #26375476

Order 12032.

5646 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10625350C211yesmaximal, characteristic
2C2×#15689591C212yesmaximal, complemented
3#20246225C212yesmaximal, complemented
4#20246220C212yesmaximal, complemented
5#20246216C212yesmaximal, complemented
6#20246212C214yesmaximal, complemented
7#20246208C212yesmaximal, complemented
8#20246204C214yesmaximal, complemented
9#20245876C212yesmaximal, complemented
10#20245874C214yesmaximal, complemented
11#20245769C212yesmaximal, complemented
12C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
13C4×C22⋊C4×D47C212yesmaximal, complemented
14C47×#2280C211yesmaximal, characteristic, complemented
15C22×#10625350—216no—
16C22×#10625350C4116yescomplemented
17C22×#10625350C2212yes—
18C22×#10625350C2211yescharacteristic
19C22×#10625350C2212yes—
20C22×#10625350C2211yescharacteristic
21C22×#10625350C2211yescharacteristic
22C22×#10625350C2211yescharacteristic
23C23×Dic94C2211yescharacteristic
24C23×D188C2211yescharacteristic
25C23×C22⋊D47C2212yes—
26C23×C4×D47C2212yes—
27#15689591—216no—
28C2×#13093989C2214yescomplemented
29C2×#13093986C2214yescomplemented
30C2×(C22⋊D47)⋊C4C2218yescomplemented
31C2×#13093981C2214yescomplemented
32C22×C22⋊Dic47C2212yes—
33C2×C22⋊C4×D47C2214yes—
34C22×C4×Dic47C2212yescomplemented
35C2×C42×D47C2214yescomplemented
36#15689028C2214yescomplemented
37#15689027C2218yescomplemented
38#15689024C2214yescomplemented
39#15689023C2218yescomplemented
40#15689001C2218yescomplemented
41#15689000C2218yescomplemented
42#15688999C2218yescomplemented
43#15688985C2214yescomplemented
44#15688982C2214yescomplemented
45#15688981C2214yes—
46#15688978C2214yes—
47C22⋊C4×Dic47C2214yes—
48C4×(C2×D47)⋊C4C2214yescomplemented
49C4×(C2×D47)⋊C4C2214yescomplemented
50C4×C22⋊Dic47C2211yescharacteristic
51C4×C22⋊Dic47C2212yes—
52C4×C22⋊Dic47C2211yescharacteristic
53C4×C22⋊Dic47C2212yescomplemented
54C4×C22⋊Dic47C2212yescomplemented
55#15688970C2214yescomplemented
56C2×C47⋊#95C2212yescomplemented
57#95×D47C2214yescomplemented
58C24×C4×C47C2211yescharacteristic
59C2×#117×C47C2212yescomplemented
60C47×#381C2212yescomplemented
61C47×#380C2212yes—
62C47×#380C2212yescomplemented
63C47×#379C2212yes—
64C4×C22⋊C4×C47C2212yes—
65C4×C22⋊C4×C47C2212yescomplemented
66C24×D47C2312yes—
67C2×#10625350—28no—
68C2×#10625350—216no—
69C2×#10625350—2128no—
70C2×#10625350—28no—
71C2×#10625350—216no—
72C2×#10625350—28no—
73C2×#10625350C2×C418yes—
74C2×#10625350C2×C418yescomplemented
75C2×#10625350C2×C4116yescomplemented
76C2×#10625350C2×C418yescomplemented
77C2×#10625350C2×C4116yescomplemented
78C2×#10625350C2×C418yescomplemented
79C2×#10625350D4116yes—
80C22×Dic94—28no—
81C22×Dic94C2×C418yescomplemented
82C22×Dic94C2312yes—
83C22×Dic94C2311yescharacteristic
84C22×Dic94C2311yescharacteristic
85C22×D188—28no—
86C22×D188C2×C418yescomplemented
87C22×D188C2312yes—
88C22×D188C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—216no—
91C22×C22⋊D47C2×C4116yescomplemented
92C22×C22⋊D47C2312yes—
93C22×C22⋊D47C2312yes—
94C22×C22⋊D47C2312yes—
95C22×C22⋊D47C2312yes—
96C23×Dic47C2314yes—
97C23×Dic47C2312yes—
98C22×C4×D47—216no—
99C22×C4×D47C2×C4116yescomplemented
100C22×C4×D47C2318yes—
101C22×C4×D47C2312yes—
102C22×C4×D47C2312yes—
103C22×C4×D47C2312yes—
104C22×C4×D47C2312yes—
105#13093989—216no—
106#13093986—216no—
107(C22⋊D47)⋊C4—232no—
108#13093981—216no—
109C2×Dic47⋊C4C2318yes—
110C2×C22⋊Dic47—28no—
111C2×C22⋊Dic47C2312yes—
112C2×C22⋊Dic47C2314yes—
113C2×C22⋊Dic47C2312yes—
114C2×(C2×D47)⋊C4C2318yes—
115C2×(C2×D47)⋊C4C2318yes—
116C2×(C2×D47)⋊C4C2318yes—
117C22⋊C4×D47—216no—
118C2×C4×Dic47—28no—
119C2×C4×Dic47C2318yes—
120C2×C4×Dic47C2312yes—
121C2×C4×Dic47C2312yes—
122C2×C4×Dic47C2314yes—
123C42×D47—216no—
124C47⋊#95C2312yes—
125C47⋊#95C2318yes—
126C47⋊#95C2312yes—
127C47⋊#95C2314yes—
128C47⋊#95C2318yes—
129C25×C47C2311yescharacteristic
130C23×C4×C47—28no—
131C23×C4×C47C2×C418yescomplemented
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138#117×C47—28no—
139C2×C4⋊C4×C47C2314yes—
140C2×C22⋊C4×C47C2314yes—
141C2×C22⋊C4×C47C2314yes—
142C2×C22⋊C4×C47C2314yes—
143C2×C42×C47C2314yes—
144#95×C47C2314yes—
145#95×C47C2314yes—
146C24×C47—24no—
147C24×C47—24no—
148C24×C47—42no—
149C24×C47C22×C414yes—
150C24×C47C2411yescharacteristic
151C24×C47C2411yescharacteristic
152C24×C47C2411yescharacteristic
153C23×D47—28no—
154C23×D47—28no—
155C23×D47—44no—
156C23×D47C22×C418yes—
157C23×D47C2412yes—
158C23×D47C2412yes—
159C22×C4×C47—24no—
160C22×C4×C47—232no—
161C22×C4×C47—24no—
162C22×C4×C47—24no—
163C22×C4×C47—24no—
164C22×C4×C47—24no—
165C22×C4×C47C22×C414yes—
166C22×C4×C47C22×C414yes—
167C22×C4×C47C22×C414yes—
168C22×C4×C47C22×C414yes—
169C22×C4×C47C22×C414yes—
170C22×C4×C47C22×C414yes—
171C22×C4×C47C2×D418yes—
172C22×C4×C47C2418yes—
173C22×C4×C47C2411yescharacteristic
174C22×C4×C47C2411yescharacteristic
175C22×C4×C47C2411yescharacteristic
176C22×C4×C47C2411yescharacteristic
177C2×C22⋊D47—28no—
178C2×C22⋊D47—28no—
179C2×C22⋊D47—264no—
180C2×C22⋊D47—28no—
181C2×C22⋊D47C22×C418yes—
182C2×C22⋊D47C22×C418yes—
183C2×C22⋊D47C22×C418yes—
184C2×C22⋊D47C22×C418yes—
185C2×C22⋊D47C2×D4116yes—
186C22×Dic47—28no—
187C22×Dic47—28no—
188C22×Dic47—28no—
189C22×Dic47—44no—
190C22×Dic47C22×C418yes—
191C22×Dic47C2414yes—
192C22×Dic47C2412yes—
193C22×Dic47C2414yes—
194C22×Dic47C2412yes—
195#10625350—232no—
196#10625350—264no—
197#10625350—232no—
198#10625350—264no—
199#10625350—232no—
200#10625350C22⋊C4164yescomplemented
201C2×D188—28no—
202C2×D188—24no—
203C2×D188—232no—
204C2×D188C22×C418yes—
205C2×D188C22×C414yes—
206C2×D188C22×C414yes—
207C2×D188C2×D418yes—
208C2×C4×D47—28no—
209C2×C4×D47—28no—
210C2×C4×D47—28no—
211C2×C4×D47—264no—
212C2×C4×D47—216no—
213C2×C4×D47—216no—
214C2×C4×D47—48no—
215C2×C4×D47C22×C418yes—
216C2×C4×D47C22×C418yes—
217C2×C4×D47C22×C418yes—
218C2×C4×D47C22×C418yes—
219C2×C4×D47C2×D4116yes—
220C2×Dic94—24no—
221C2×Dic94—28no—
222C2×Dic94—232no—
223C2×Dic94C22×C414yes—
224C2×Dic94C22×C418yes—
225C2×Dic94C22×C414yes—
226C2×Dic94C2×D418yes—
227C4⋊C4×C47—28no—
228C22⋊C4×C47—28no—
229C22⋊C4×C47—28no—
230C22⋊C4×C47—44no—
231C42×C47—28no—
232C22⋊Dic47—24no—
233C22⋊Dic47—28no—
234C22⋊Dic47#4118yescomplemented
235(C2×D47)⋊C4—216no—
236(C2×D47)⋊C4—216no—
237(C2×D47)⋊C4—48no—
238Dic47⋊C4—216no—
239C4×Dic47—24no—
240C4×Dic47—24no—
241C4×Dic47—28no—
242C4×Dic47—216no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—28no—
248C23×C47—28no—
249C23×C47—22no—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—44no—
253C23×C47—416no—
254C23×C47C23×C412yes—
255C23×C47C23×C412yes—
256C23×C47C23×C412yes—
257C23×C47C22×D414yes—
258C23×C47C2×#4114yes—
259C23×C47C2511yescharacteristic
260C22×D47—24no—
261C22×D47—24no—
262C22×D47—216no—
263C22×D47—24no—
264C22×D47—24no—
265C22×D47—24no—
266C22×D47—216no—
267C22×D47—48no—
268C22×D47—432no—
269C22×D47C23×C414yes—
270C22×D47C23×C414yes—
271C22×D47C22×D418yes—
272C2×C4×C47—28no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—28no—
276C2×C4×C47—28no—
277C2×C4×C47—28no—
278C2×C4×C47—28no—
279C2×C4×C47—28no—
280C2×C4×C47—28no—
281C2×C4×C47—28no—
282C2×C4×C47C2×C22⋊C4116yescomplemented
283C2×C4×C47C23×C412yes—
284C2×C4×C47C23×C412yes—
285C2×C4×C47C23×C412yes—
286C2×C4×C47C23×C412yes—
287C2×C4×C47C22×D414yes—
288C2×C4×C47C22×D414yes—
289C22⋊D47—216no—
290C22⋊D47—216no—
291C22⋊D47—216no—
292C22⋊D47C2×C22⋊C4132yescomplemented
293C2×Dic47—24no—
294C2×Dic47—24no—
295C2×Dic47—24no—
296C2×Dic47—216no—
297C2×Dic47—24no—
298C2×Dic47—24no—
299C2×Dic47—24no—
300C2×Dic47—416no—
301C2×Dic47C23×C414yes—
302C2×Dic47C23×C414yes—
303C2×Dic47C22×D418yes—
304C2×Dic47C2×#4118yescomplemented
305D188—216no—
306D188—28no—
307D188C2×C22⋊C4116yescomplemented
308C4×D47—216no—
309C4×D47—216no—
310C4×D47—216no—
311C4×D47—432no—
312C4×D47C2×C22⋊C4132yescomplemented
313Dic94—28no—
314Dic94—216no—
315Dic94C2×C22⋊C4116yescomplemented
316C22⋊C4×#41—471nomaximal, Sylow
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—28no—
322C22×C47—28no—
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—416no—
327C22×C47—44no—
328C22×C47C22×C22⋊C414yes—
329C22×C47C4×#4114yescomplemented
330C22×C47C24×C411yescharacteristic
331C22×C47C23×D412yes—
332C22×C47C22×#4112yes—
333C22×C47#58512yes—
334C2×D47—24no—
335C2×D47—24no—
336C2×D47—216no—
337C2×D47—24no—
338C2×D47—24no—
339C2×D47—24no—
340C2×D47—432no—
341C2×D47—48no—
342C2×D47C22×C22⋊C418yes—
343C4×C47—22no—
344C4×C47—22no—
345C4×C47—48no—
346C4×C47C22×C22⋊C414yes—
347C4×C47C22×C22⋊C414yes—
348Dic47—24no—
349Dic47—28no—
350Dic47—44no—
351Dic47C22×C22⋊C418yes—
352C23×#41—471no—
353C2×C4×#41—472no—
354#2341—472no—
355Q8×C22⋊C4—472no—
356#2339—474no—
357#2339—472no—
358D4×C22⋊C4—472no—
359D4×C22⋊C4—474no—
360#2297—474no—
361#2297—472no—
362#2280—472no—
363#2280D4711yescharacteristic, complemented
364C2×C4×C22⋊C4—472no—
365C2×C4×C22⋊C4—471no—
366C2×C47—24no—
367C2×C47—24no—
368C2×C47—42no—
369C2×C47C23×C22⋊C411yescharacteristic
370C2×C47C2×C4×#4111yescharacteristic
371C2×C47#342811yescharacteristic
372C2×C47D4×#4114yes—
373D47—28no—
374D47—44no—
375C22×#41—4716no—
376C22×#41—471no—
377C22×#41—471no—
378C22×#41—472no—
379C22×#41—471no—
380C22×#41—472no—
381C22×#41—471no—
382C22×#41—9416no—
383C23×Q8—471no—
384C23×D4—472no—
385C23×D4—471no—
386C24×C4—472no—
387C24×C4C2×D4711yescharacteristic
388C4×#41—9416no—
389C2×C4×Q8—474no—
390C2×C4×D4—474no—
391C2×C4×D4—478no—
392C2×#117—474no—
393C2×#117C2×D4712yescomplemented
394C22×C22⋊C4—472no—
395C22×C22⋊C4—474no—
396C22×C42—472no—
397C22×C42—474no—
398#391—474no—
399#391—478no—
400#390—474no—
401#390—478no—
402#386—478no—
403#386—478no—
404#386—478no—
405#381—474no—
406#381C2×D4712yescomplemented
407#380—474no—
408#380—474no—
409#380C2×D4712yes—
410#380C2×D4712yescomplemented
411#379—474no—
412#379C2×D4712yes—
413C4×C22⋊C4—472no—
414C4×C22⋊C4—471no—
415C4×C22⋊C4—471no—
416C4×C22⋊C4—472no—
417C4×C22⋊C4—472no—
418C4×C22⋊C4—474no—
419C4×C22⋊C4—474no—
420C4×C22⋊C4—474no—
421C4×C22⋊C4—474no—
422C4×C22⋊C4C2×D4712yes—
423C4×C22⋊C4C2×D4712yescomplemented
424C2×#95—472no—
425C2×#95—474no—
426C47C22⋊C4×#4111yescharacteristic, complemented, Sylow
427C25—472no—
428C25C22×D4711yescharacteristic
429C2×#41—478no—
430C2×#41—4716no—
431C2×#41—4716no—
432C2×#41—478no—
433C2×#41—478no—
434C2×#41—478no—
435C2×#41—4716no—
436C2×#41—9416no—
437C2×#41—9416no—
438C2×#41—948no—
439C2×#41—948no—
440C2×#41—94128no—
441C2×#41—948no—
442C22×Q8—478no—
443C22×Q8—471no—
444C22×Q8—472no—
445C22×Q8—471no—
446C22×Q8—948no—
447C22×D4—472no—
448C22×D4—4716no—
449C22×D4—472no—
450C22×D4—472no—
451C22×D4—472no—
452C22×D4—478no—
453C22×D4—471no—
454C22×D4—472no—
455C22×D4—471no—
456C22×D4—948no—
457C22×D4—9416no—
458C23×C4—28no—
459C23×C4—472no—
460C23×C4—472no—
461C23×C4—4716no—
462C23×C4—472no—
463C23×C4—472no—
464C23×C4—472no—
465C23×C4—474no—
466C23×C4—478no—
467C23×C4—9416no—
468C23×C4C4×D4718yescomplemented
469C23×C4C22×D4711yescharacteristic
470C23×C4C22×D4711yescharacteristic
471C23×C4C22×D4711yescharacteristic
472C23×C4C22×D4711yescharacteristic
473C23×C4C22×D4711yescharacteristic
474C23×C4C22×D4711yescharacteristic
475C4×Q8—9416no—
476C4×D4—9432no—
477C4×D4—9416no—
478#117—28no—
479#117—9416no—
480C2×C4⋊C4—478no—
481C2×C4⋊C4C22×D4714yes—
482C2×C22⋊C4—472no—
483C2×C22⋊C4—472no—
484C2×C22⋊C4—474no—
485C2×C22⋊C4—478no—
486C2×C22⋊C4—478no—
487C2×C22⋊C4—478no—
488C2×C22⋊C4—9416no—
489C2×C22⋊C4—948no—
490C2×C22⋊C4C22×D4714yes—
491C2×C22⋊C4C22×D4714yes—
492C2×C22⋊C4C22×D4714yes—
493C2×C42—478no—
494C2×C42—474no—
495C2×C42—472no—
496C2×C42—472no—
497C2×C42—9416no—
498C2×C42—948no—
499C2×C42C22×D4714yes—
500#95—472no—
501#95—472no—
502#95—478no—
503#95—474no—
504#95—478no—
505#95C22×D4714yes—
506#95C22×D4714yes—
507C24—24no—
508C24—24no—
509C24—42no—
510C24—472no—
511C24—472no—
512C24—478no—
513C24—948no—
514C24—948no—
515C24—1884no—
516C24C2×C4×D4714yes—
517C24C23×D4711yescharacteristic
518C24C23×D4711yescharacteristic
519C24C23×D4711yescharacteristic
520#41—4764no—
521#41—9464no—
522#41—9464no—
523#41—9432no—
524#41—9432no—
525#41—9432no—
526C2×Q8—474no—
527C2×Q8—478no—
528C2×Q8—474no—
529C2×Q8—478no—
530C2×Q8—948no—
531C2×Q8—9432no—
532C2×Q8—944no—
533C2×D4—478no—
534C2×D4—4716no—
535C2×D4—478no—
536C2×D4—478no—
537C2×D4—478no—
538C2×D4—474no—
539C2×D4—478no—
540C2×D4—474no—
541C2×D4—478no—
542C2×D4—9432no—
543C2×D4—948no—
544C2×D4—948no—
545C2×D4—9464no—
546C2×D4—948no—
547C2×D4—948no—
548C2×D4—944no—
549C22×C4—24no—
550C22×C4—232no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—472no—
556C22×C4—478no—
557C22×C4—4716no—
558C22×C4—478no—
559C22×C4—472no—
560C22×C4—474no—
561C22×C4—478no—
562C22×C4—478no—
563C22×C4—478no—
564C22×C4—474no—
565C22×C4—948no—
566C22×C4—9464no—
567C22×C4—9416no—
568C22×C4—948no—
569C22×C4—9416no—
570C22×C4—948no—
571C22×C4—948no—
572C22×C4—948no—
573C22×C4—948no—
574C22×C4—1888no—
575C22×C4—1884no—
576C22×C4C2×C4×D4714yes—
577C22×C4C2×C4×D4714yes—
578C22×C4C2×C4×D4714yes—
579C22×C4C2×C4×D4714yes—
580C22×C4C2×C4×D4714yes—
581C22×C4C2×C4×D4714yes—
582C22×C4D4×D4718yes—
583C22×C4C23×D4718yes—
584C22×C4C23×D4711yescharacteristic
585C22×C4C23×D4711yescharacteristic
586C22×C4C23×D4711yescharacteristic
587C22×C4C23×D4711yescharacteristic
588C4⋊C4—28no—
589C4⋊C4—9416no—
590C22⋊C4—28no—
591C22⋊C4—28no—
592C22⋊C4—44no—
593C22⋊C4—478no—
594C22⋊C4—9416no—
595C22⋊C4—9416no—
596C22⋊C4—948no—
597C22⋊C4—944no—
598C22⋊C4—1888no—
599C42—28no—
600C42—9416no—
601C42—944no—
602C42—944no—
603C42—948no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—28no—
609C23—28no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—44no—
614C23—416no—
615C23—474no—
616C23—478no—
617C23—474no—
618C23—9416no—
619C23—944no—
620C23—944no—
621C23—9416no—
622C23—944no—
623C23—944no—
624C23—944no—
625C23—1888no—
626C23—18832no—
627C23C22×C4×D4712yes—
628C23C22×C4×D4712yes—
629C23C22×C4×D4712yes—
630C23C2×D4×D4714yes—
631C23#41×D4714yes—
632C23C24×D4711yescharacteristic
633Q8—4716no—
634Q8—9416no—
635Q8—948no—
636D4—4732no—
637D4—4716no—
638D4—9416no—
639D4—9416no—
640D4—9416no—
641D4—9416no—
642D4—948no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—28no—
652C2×C4—28no—
653C2×C4—474no—
654C2×C4—478no—
655C2×C4—4732no—
656C2×C4—474no—
657C2×C4—478no—
658C2×C4—9416no—
659C2×C4—9416no—
660C2×C4—9416no—
661C2×C4—944no—
662C2×C4—944no—
663C2×C4—944no—
664C2×C4—9416no—
665C2×C4—944no—
666C2×C4—944no—
667C2×C4—944no—
668C2×C4—18832no—
669C2×C4—18816no—
670C2×C4C22⋊C4×D47116yescomplemented
671C2×C4C22×C4×D4712yes—
672C2×C4C22×C4×D4712yes—
673C2×C4C22×C4×D4712yes—
674C2×C4C22×C4×D4712yes—
675C2×C4C2×D4×D4714yes—
676C2×C4C2×D4×D4714yes—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—28no—
682C22—28no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—416no—
687C22—44no—
688C22—478no—
689C22—944no—
690C22—944no—
691C22—9416no—
692C22—944no—
693C22—944no—
694C22—944no—
695C22—18832no—
696C22—1888no—
697C22C2×C22⋊C4×D4714yes—
698C22#1568959114yescomplemented
699C22C23×C4×D4711yescharacteristic
700C22C22×D4×D4712yes—
701C22C2×#41×D4712yes—
702C22#1568995912yes—
703C4—22no—
704C4—22no—
705C4—48no—
706C4—478no—
707C4—944no—
708C4—948no—
709C4—1884no—
710C4C2×C22⋊C4×D4714yes—
711C4C2×C22⋊C4×D4714yes—
712C2—24no—
713C2—24no—
714C2—42no—
715C2—948no—
716C2—1884no—
717C2C22×C22⋊C4×D4711yescharacteristic
718C2C2×#1568959111yescharacteristic
719C2#2025658911yescharacteristic
720C2#2025687114yes—
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC47×#2280C2
socle, cosocleC23×C47C25
prime radicalC23×#10625350C2
hypercenter#2280D47
hypocenterC47C22⋊C4×#41
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#15689591C2semidirect
3. #20246225C2semidirect
4. #20246220C2semidirect
5. #20246216C2semidirect
6. #20246212C2semidirect
7. #20246208C2semidirect
8. #20246204C2semidirect
9. #20245876C2semidirect
10. #20245874C2semidirect
11. #20245769C2semidirect
12. C2×C4×C22⋊Dic47C2semidirect
13. C4×C22⋊C4×D47C2semidirect
14. C47×#2280C2semidirect
16. C22×#10625350C4semidirect
28. C2×#13093989C22semidirect
29. C2×#13093986C22semidirect
30. C2×(C22⋊D47)⋊C4C22semidirect
31. C2×#13093981C22semidirect
34. C22×C4×Dic47C22semidirect
35. C2×C42×D47C22semidirect
36. #15689028C22semidirect
37. #15689027C22semidirect
38. #15689024C22semidirect
39. #15689023C22semidirect
40. #15689001C22semidirect
41. #15689000C22semidirect
42. #15688999C22semidirect
43. #15688985C22semidirect
44. #15688982C22semidirect
48. C4×(C2×D47)⋊C4C22semidirect
49. C4×(C2×D47)⋊C4C22semidirect
53. C4×C22⋊Dic47C22semidirect
54. C4×C22⋊Dic47C22semidirect
55. #15688970C22semidirect
56. C2×C47⋊#95C22semidirect
57. #95×D47C22semidirect
59. C2×#117×C47C22semidirect
60. C47×#381C22semidirect
62. C47×#380C22semidirect
65. C4×C22⋊C4×C47C22semidirect
74. C2×#10625350C2×C4semidirect
75. C2×#10625350C2×C4semidirect
76. C2×#10625350C2×C4semidirect
77. C2×#10625350C2×C4semidirect
78. C2×#10625350C2×C4semidirect
81. C22×Dic94C2×C4semidirect
86. C22×D188C2×C4semidirect
91. C22×C22⋊D47C2×C4semidirect
99. C22×C4×D47C2×C4semidirect
131. C23×C4×C47C2×C4semidirect
200. #10625350C22⋊C4semidirect
234. C22⋊Dic47#41semidirect
282. C2×C4×C47C2×C22⋊C4semidirect
292. C22⋊D47C2×C22⋊C4semidirect
304. C2×Dic47C2×#41semidirect
307. D188C2×C22⋊C4semidirect
312. C4×D47C2×C22⋊C4semidirect
315. Dic94C2×C22⋊C4semidirect
329. C22×C47C4×#41semidirect
363. #2280D47semidirect
393. C2×#117C2×D47semidirect
406. #381C2×D47semidirect
410. #380C2×D47semidirect
423. C4×C22⋊C4C2×D47semidirect
426. C47C22⋊C4×#41semidirect
468. C23×C4C4×D47semidirect
670. C2×C4C22⋊C4×D47semidirect
698. C22#15689591semidirect

Maximal subgroups

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

subgroupindex
C23×#106253502
C2×#156895912
#202462252
#202462202
#202462162
#202462122
#202462082
#202462042
#202458762
#202458742
#202457692
C2×C4×C22⋊Dic472
C4×C22⋊C4×D472
C47×#22802
C22⋊C4×#4147