Finite Group Databasebeta

← #26137422

Subgroups — #26137422

Order 12032.

3366 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2C23×C4×Dic47C211yesmaximal, characteristic, complemented
3C2×#15689002C211yesmaximal, characteristic
4C2×#15689000C211yesmaximal, characteristic
5C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
6C2×#15688970C212yesmaximal, complemented
7#20241624C212yesmaximal, complemented
8#20241619C212yesmaximal, complemented
9#20241610C211yesmaximal, characteristic, complemented
10#95×Dic47C212yesmaximal, complemented
11C47×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C24×Dic47C2211yescharacteristic
15C23×C4×D47C2211yescharacteristic
16C2×(C22⋊D47)⋊C4—24no—
17C2×(C22⋊D47)⋊C4—24no—
18C2×(C22⋊D47)⋊C4C418yescomplemented
19C22×Dic47⋊C4C2211yescharacteristic
20C22×C22⋊Dic47C2211yescharacteristic
21C22×(C2×D47)⋊C4C2211yescharacteristic
22C22×(C2×D47)⋊C4C2212yes—
23C22×(C2×D47)⋊C4C2212yes—
24C22×C4×Dic47—24no—
25C22×C4×Dic47—28no—
26C22×C4×Dic47C2212yes—
27C22×C4×Dic47C2212yes—
28C22×C4×Dic47C2211yescharacteristic
29C22×C4×Dic47C2212yes—
30#15689002C418yescomplemented
31#15689000C418yescomplemented
32C22⋊C4×Dic47—24no—
33#15688970—28no—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C2×C47⋊#95C2212yes—
38C2×C47⋊#95C2212yes—
39C24×C4×C47C2211yescharacteristic
40C22×C22⋊C4×C47C2211yescharacteristic
41C22×C22⋊C4×C47C2211yescharacteristic
42C2×#95×C47C2212yes—
43C2×#95×C47C2212yes—
44C24×D47C2311yescharacteristic
45C22×C22⋊D47—22no—
46C22×C22⋊D47—22no—
47C22×C22⋊D47—22no—
48C22×C22⋊D47—22no—
49C22×C22⋊D47C2×C414yes—
50C22×C22⋊D47C2×C414yes—
51C22×C22⋊D47C2×C414yes—
52C23×Dic47—22no—
53C23×Dic47—22no—
54C23×Dic47—24no—
55C23×Dic47—24no—
56C23×Dic47—24no—
57C23×Dic47—24no—
58C23×Dic47C2×C414yes—
59C23×Dic47C2×C414yescomplemented
60C23×Dic47D414yes—
61C23×Dic47D414yes—
62C23×Dic47C2312yes—
63C23×Dic47C2311yescharacteristic
64C23×Dic47C2311yescharacteristic
65C23×Dic47C2312yes—
66C23×Dic47C2311yescharacteristic
67C22×C4×D47—24no—
68C22×C4×D47—22no—
69C22×C4×D47—22no—
70C22×C4×D47—24no—
71C22×C4×D47C2×C414yescomplemented
72(C22⋊D47)⋊C4—232no—
73C2×Dic47⋊C4—22no—
74C2×Dic47⋊C4—22no—
75C2×Dic47⋊C4C2×C414yescomplemented
76C2×C22⋊Dic47—22no—
77C2×C22⋊Dic47—22no—
78C2×C22⋊Dic47C2×C414yescomplemented
79C2×(C2×D47)⋊C4—24no—
80C2×(C2×D47)⋊C4—24no—
81C2×(C2×D47)⋊C4—24no—
82C2×(C2×D47)⋊C4—22no—
83C2×(C2×D47)⋊C4—22no—
84C2×(C2×D47)⋊C4—24no—
85C2×(C2×D47)⋊C4C2×C418yescomplemented
86C2×(C2×D47)⋊C4C2×C418yescomplemented
87C2×(C2×D47)⋊C4C2×C414yescomplemented
88C2×C4×Dic47—232no—
89C2×C4×Dic47—24no—
90C2×C4×Dic47—24no—
91C2×C4×Dic47—24no—
92C2×C4×Dic47—24no—
93C2×C4×Dic47—24no—
94C2×C4×Dic47—22no—
95C2×C4×Dic47—22no—
96C2×C4×Dic47—24no—
97C2×C4×Dic47—24no—
98C2×C4×Dic47—24no—
99C2×C4×Dic47C2×C414yescomplemented
100C2×C4×Dic47D418yescomplemented
101C47⋊#95—24no—
102C47⋊#95—24no—
103C47⋊#95—24no—
104C47⋊#95C2×C418yescomplemented
105C47⋊#95C2×C418yescomplemented
106C25×C47C2311yescharacteristic
107C23×C4×C47—22no—
108C23×C4×C47—22no—
109C23×C4×C47—24no—
110C23×C4×C47—24no—
111C23×C4×C47C2×C414yescomplemented
112C23×C4×C47C2312yes—
113C23×C4×C47C2311yescharacteristic
114C23×C4×C47C2311yescharacteristic
115C23×C4×C47C2312yes—
116C2×C22⋊C4×C47—22no—
117C2×C22⋊C4×C47—22no—
118C2×C22⋊C4×C47—22no—
119C2×C22⋊C4×C47—22no—
120C2×C22⋊C4×C47C2×C414yes—
121C2×C22⋊C4×C47C2×C414yescomplemented
122#95×C47—24no—
123#95×C47—24no—
124C24×C47—22no—
125C24×C47—22no—
126C24×C47—22no—
127C24×C47—22no—
128C24×C47C22×C412yes—
129C24×C47C22×C412yes—
130C24×C47C22×C412yes—
131C24×C47C2×D412yes—
132C24×C47C2×D412yes—
133C24×C47#4112yes—
134C24×C47#4112yes—
135C24×C47C2411yescharacteristic
136C23×D47—22no—
137C23×D47—21no—
138C23×D47—21no—
139C23×D47—22no—
140C23×D47—22no—
141C23×D47—22no—
142C23×D47—21no—
143C23×D47—21no—
144C23×D47C22×C412yes—
145C23×D47C22×C412yes—
146C23×D47C22×C412yes—
147C22×C4×C47—216no—
148C22×C4×C47—28no—
149C22×C4×C47—28no—
150C22×C4×C47—28no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—216no—
156C22×C4×C47—22no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47C22×C412yes—
171C22×C4×C47C22×C412yes—
172C22×C4×C47C22×C414yes—
173C22×C4×C47C22×C414yes—
174C22×C4×C47C2×D414yes—
175C22×C4×C47#4114yes—
176C2×C22⋊D47—28no—
177C2×C22⋊D47—28no—
178C2×C22⋊D47—28no—
179C2×C22⋊D47—28no—
180C2×C22⋊D47—28no—
181C2×C22⋊D47—28no—
182C2×C22⋊D47C42116yescomplemented
183C22×Dic47—28no—
184C22×Dic47—216no—
185C22×Dic47—28no—
186C22×Dic47—28no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—216no—
198C22×Dic47—216no—
199C22×Dic47—28no—
200C22×Dic47—216no—
201C22×Dic47—28no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47C22⋊C4116yescomplemented
209C22×Dic47C22×C414yes—
210C22×Dic47C22×C412yes—
211C22×Dic47C22×C412yes—
212C22×Dic47C22×C412yes—
213C22×Dic47C22×C412yes—
214C22×Dic47C22×C414yes—
215C22×Dic47C22×C412yes—
216C22×Dic47C2×D412yes—
217C22×Dic47C2×D412yes—
218C22×Dic47C2×D414yes—
219C22×Dic47C2×D412yes—
220C22×Dic47C2×D412yes—
221C22×Dic47C2×D414yes—
222C22×Dic47#4114yes—
223C22×Dic47#4114yes—
224C2×C4×D47—28no—
225C2×C4×D47—216no—
226C2×C4×D47—44no—
227C2×C4×D47—48no—
228C2×C4×D47—44no—
229C22⋊C4×C47—28no—
230C22⋊C4×C47—28no—
231C22⋊Dic47—28no—
232(C2×D47)⋊C4—216no—
233(C2×D47)⋊C4—28no—
234(C2×D47)⋊C4—216no—
235Dic47⋊C4—28no—
236C4×Dic47—216no—
237C4×Dic47—28no—
238C4×Dic47—216no—
239C4×Dic47—48no—
240C23×C47—24no—
241C23×C47—24no—
242C23×C47—24no—
243C23×C47—24no—
244C23×C47—24no—
245C23×C47—24no—
246C23×C47—22no—
247C23×C47—24no—
248C23×C47—22no—
249C23×C47—22no—
250C23×C47—24no—
251C23×C47—22no—
252C23×C47—24no—
253C23×C47—24no—
254C23×C47—24no—
255C23×C47—24no—
256C23×C47C2×C4214yes—
257C23×C47C2×C22⋊C414yes—
258C23×C47#11714yes—
259C23×C47C4×D414yes—
260C23×C47C4×D414yes—
261C23×C47C4×D414yes—
262C23×C47C4×D414yes—
263C23×C47C23×C411yescharacteristic
264C23×C47C23×C411yescharacteristic
265C23×C47C23×C411yescharacteristic
266C23×C47C22×D411yescharacteristic
267C23×C47C22×D411yescharacteristic
268C23×C47C22×D412yes—
269C23×C47C2×#4112yes—
270C23×C47C2×#4112yes—
271C23×C47C2×#4111yescharacteristic
272C23×C47C2×#4112yes—
273C23×C47C2×#4111yescharacteristic
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—24no—
277C22×D47—24no—
278C22×D47—24no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—24no—
284C22×D47—24no—
285C22×D47—24no—
286C22×D47—41no—
287C22×D47—42no—
288C22×D47—41no—
289C22×D47—42no—
290C22×D47—41no—
291C22×D47—41no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47—42no—
296C22×D47C2×C4214yescomplemented
297C2×C4×C47—232no—
298C2×C4×C47—24no—
299C2×C4×C47—24no—
300C2×C4×C47—24no—
301C2×C4×C47—24no—
302C2×C4×C47—24no—
303C2×C4×C47—24no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—24no—
307C2×C4×C47—24no—
308C2×C4×C47—24no—
309C2×C4×C47—24no—
310C2×C4×C47—24no—
311C2×C4×C47—41no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—42no—
317C2×C4×C47—41no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47C4×D418yescomplemented
322C22⋊D47—232no—
323C2×Dic47—232no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—24no—
327C2×Dic47—24no—
328C2×Dic47—24no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—24no—
335C2×Dic47—24no—
336C2×Dic47—22no—
337C2×Dic47—24no—
338C2×Dic47—24no—
339C2×Dic47—24no—
340C2×Dic47—232no—
341C2×Dic47—24no—
342C2×Dic47—24no—
343C2×Dic47—24no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47C2×C4214yescomplemented
349C2×Dic47C2×C22⋊C414yes—
350C2×Dic47C2×C22⋊C414yes—
351C2×Dic47C4×D418yes—
352C2×Dic47C4×D418yescomplemented
353C2×Dic47#12014yes—
354C2×Dic47#12118yes—
355C2×Dic47#12314yes—
356C4×D47—416no—
357C4×#386—471nomaximal, Sylow
358C22×C47—28no—
359C22×C47—24no—
360C22×C47—28no—
361C22×C47—24no—
362C22×C47—24no—
363C22×C47—24no—
364C22×C47—28no—
365C22×C47—28no—
366C22×C47—24no—
367C22×C47—24no—
368C22×C47C4×C22⋊C418yescomplemented
369C22×C47C22×C4211yescharacteristic
370C22×C47C22×C22⋊C411yescharacteristic
371C22×C47C2×#11711yescharacteristic
372C22×C47C2×C4×D412yes—
373C22×C47C2×C4×D412yes—
374C22×C47C2×C4×D411yescharacteristic
375C22×C47C2×C4×D411yescharacteristic
376C22×C47C2×C4×D412yes—
377C22×C47C2×C4×D411yescharacteristic
378C22×C47C2×C4×D411yescharacteristic
379C22×C47C4×#4112yes—
380C22×C47C4×#4112yes—
381C22×C47C4×#4112yes—
382C22×C47C2×#12011yescharacteristic
383C22×C47C2×#12112yes—
384C22×C47C2×#12311yescharacteristic
385C22×C47#52512yes—
386C22×C47#52511yescharacteristic
387C22×C47#52511yescharacteristic
388C22×C47#52512yes—
389C22×C47#52912yes—
390C22×C47#52912yes—
391C22×C47#53212yes—
392C2×D47—24no—
393C2×D47—28no—
394C2×D47—42no—
395C2×D47—44no—
396C2×D47—42no—
397C2×D47—42no—
398C2×D47—42no—
399C2×D47—44no—
400C2×D47—44no—
401C2×D47—42no—
402C2×D47—42no—
403C4×C47—28no—
404C4×C47—42no—
405C4×C47—42no—
406C4×C47—44no—
407Dic47—24no—
408Dic47—24no—
409Dic47—28no—
410Dic47—44no—
411Dic47#38618yescomplemented
412C22×C4×D4—471no—
413C23×C42—471no—
414C2×#386—471no—
415C2×#386—471no—
416C2×C4×C22⋊C4—472no—
417C2×C4×C22⋊C4—471no—
418#1437—472no—
419#1436—472no—
420C22⋊#95—471no—
421C22⋊#95D4711yescharacteristic, complemented
422C4×#95—472no—
423C2×C47—28no—
424C2×C47C2×C4×C22⋊C411yescharacteristic
425C2×C47C42×D412yes—
426C2×C47C2×#38611yescharacteristic
427C2×C47#229012yes—
428C2×C47#229711yescharacteristic
429C2×C47C4×#12011yescharacteristic
430C2×C47C4×#12011yescharacteristic
431C2×C47C4×#12112yes—
432C2×C47C4×#12112yes—
433C2×C47C4×#12311yescharacteristic
434C2×C47C4×#12311yescharacteristic
435D47—44no—
436C23×D4—471no—
437C24×C4—471no—
438C24×C4—471no—
439C24×C4—471no—
440C24×C4C2×D4711yescharacteristic
441C2×C4×D4—478no—
442C2×C4×D4—944no—
443C2×C4×D4—944no—
444C22×C4⋊C4—471no—
445C22×C22⋊C4—471no—
446C22×C22⋊C4—471no—
447C22×C22⋊C4—472no—
448C22×C22⋊C4—472no—
449C22×C22⋊C4C2×D4711yescharacteristic
450C22×C22⋊C4C2×D4711yescharacteristic
451C22×C42—472no—
452C22×C42—471no—
453C22×C42—472no—
454C22×C42—472no—
455C22×C42—948no—
456C22×C42—944no—
457#386—478no—
458#386—478no—
459C4×C22⋊C4—948no—
460C4×C22⋊C4—944no—
461C2×#95—472no—
462C2×#95—472no—
463C2×#95—472no—
464C2×#95—472no—
465C2×#95—472no—
466C2×#95C2×D4712yes—
467C2×#95C2×D4712yes—
468C47C4×#38611yescharacteristic, complemented, Sylow
469C25—471no—
470C25C22×D4711yescharacteristic
471C22×D4—474no—
472C22×D4—474no—
473C22×D4—474no—
474C22×D4—942no—
475C22×D4—942no—
476C22×D4—942no—
477C22×D4—942no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—471no—
483C23×C4—474no—
484C23×C4—474no—
485C23×C4—474no—
486C23×C4—471no—
487C23×C4—472no—
488C23×C4—471no—
489C23×C4—474no—
490C23×C4—472no—
491C23×C4—474no—
492C23×C4—942no—
493C23×C4—942no—
494C23×C4—944no—
495C23×C4—944no—
496C23×C4—944no—
497C23×C4—944no—
498C23×C4—944no—
499C23×C4—944no—
500C23×C4—942no—
501C23×C4—942no—
502C23×C4C4×D4714yescomplemented
503C23×C4C22×D4712yes—
504C23×C4C22×D4711yescharacteristic
505C23×C4C22×D4711yescharacteristic
506C23×C4C22×D4712yes—
507C4×D4—9432no—
508C2×C4⋊C4—474no—
509C2×C4⋊C4—942no—
510C2×C4⋊C4—942no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—478no—
518C2×C22⋊C4—478no—
519C2×C22⋊C4—942no—
520C2×C22⋊C4—942no—
521C2×C22⋊C4—944no—
522C2×C22⋊C4—944no—
523C2×C22⋊C4—942no—
524C2×C22⋊C4—942no—
525C2×C22⋊C4—944no—
526C2×C22⋊C4—944no—
527C2×C22⋊C4C4×D4714yes—
528C2×C22⋊C4C4×D4714yescomplemented
529C2×C42—474no—
530C2×C42—478no—
531C2×C42—942no—
532C2×C42—942no—
533C2×C42—944no—
534C2×C42—944no—
535C2×C42—944no—
536C2×C42—944no—
537C2×C42—9432no—
538C2×C42—944no—
539C2×C42—944no—
540C2×C42—944no—
541C2×C42—944no—
542#95—24no—
543#95—24no—
544#95—478no—
545#95—478no—
546#95—944no—
547#95—944no—
548#95—944no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—472no—
554C24—472no—
555C24—472no—
556C24—942no—
557C24—941no—
558C24—941no—
559C24—942no—
560C24—942no—
561C24—942no—
562C24—941no—
563C24—941no—
564C24C2×C4×D4712yes—
565C24C2×C4×D4712yes—
566C24C2×C4×D4712yes—
567C24D4×D4712yes—
568C24D4×D4712yes—
569C24#1062535212yes—
570C24#1062535412yes—
571C24C23×D4711yescharacteristic
572C2×D4—4716no—
573C2×D4—948no—
574C2×D4—948no—
575C2×D4—948no—
576C2×D4—948no—
577C2×D4—948no—
578C2×D4—948no—
579C22×C4—28no—
580C22×C4—216no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—216no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—472no—
603C22×C4—474no—
604C22×C4—472no—
605C22×C4—472no—
606C22×C4—474no—
607C22×C4—4716no—
608C22×C4—472no—
609C22×C4—472no—
610C22×C4—474no—
611C22×C4—472no—
612C22×C4—472no—
613C22×C4—472no—
614C22×C4—474no—
615C22×C4—472no—
616C22×C4—474no—
617C22×C4—474no—
618C22×C4—948no—
619C22×C4—9416no—
620C22×C4—948no—
621C22×C4—9416no—
622C22×C4—9416no—
623C22×C4—948no—
624C22×C4—9416no—
625C22×C4—948no—
626C22×C4—948no—
627C22×C4—9416no—
628C22×C4—948no—
629C22×C4—942no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—941no—
633C22×C4—941no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—941no—
637C22×C4—942no—
638C22×C4—941no—
639C22×C4—942no—
640C22×C4—942no—
641C22×C4—942no—
642C22×C4—942no—
643C22×C4—942no—
644C22×C4—942no—
645C22×C4—1884no—
646C22×C4—1888no—
647C22×C4—1884no—
648C22×C4C2×C4×D4714yes—
649C22×C4C2×C4×D4712yes—
650C22×C4C2×C4×D4712yes—
651C22×C4C2×C4×D4714yes—
652C22×C4D4×D4714yes—
653C22×C4#1062535214yes—
654C4⋊C4—948no—
655C22⋊C4—28no—
656C22⋊C4—28no—
657C22⋊C4—9416no—
658C22⋊C4—948no—
659C22⋊C4—948no—
660C22⋊C4—9416no—
661C42—9416no—
662C42—948no—
663C42—9416no—
664C42—1888no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—24no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—22no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—474no—
682C23—942no—
683C23—942no—
684C23—944no—
685C23—944no—
686C23—944no—
687C23—942no—
688C23—942no—
689C23—942no—
690C23—942no—
691C23—944no—
692C23—944no—
693C23—944no—
694C23—1881no—
695C23—1882no—
696C23—1881no—
697C23—1882no—
698C23—1881no—
699C23—1881no—
700C23—1882no—
701C23—1882no—
702C23—1882no—
703C23—1882no—
704C23C42×D4714yes—
705C23C22⋊C4×D4714yes—
706C23#1309398214yes—
707C23(C22⋊D47)⋊C414yes—
708C23(C22⋊D47)⋊C414yes—
709C23#1309398614yes—
710C23#1309398614yes—
711C23C22×C4×D4711yescharacteristic
712C23C22×C4×D4711yescharacteristic
713C23C22×C4×D4711yescharacteristic
714C23C2×D4×D4711yescharacteristic
715C23C2×D4×D4711yescharacteristic
716C23C2×D4×D4712yes—
717C23#41×D4712yes—
718C23#41×D4712yes—
719C23C2×#1062535211yescharacteristic
720C23C2×#1062535212yes—
721C23C2×#1062535411yescharacteristic
722D4—9432no—
723C2×C4—232no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—474no—
748C2×C4—478no—
749C2×C4—474no—
750C2×C4—478no—
751C2×C4—474no—
752C2×C4—474no—
753C2×C4—474no—
754C2×C4—478no—
755C2×C4—9432no—
756C2×C4—9432no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—944no—
760C2×C4—944no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—944no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—944no—
768C2×C4—944no—
769C2×C4—942no—
770C2×C4—944no—
771C2×C4—944no—
772C2×C4—944no—
773C2×C4—944no—
774C2×C4—944no—
775C2×C4—944no—
776C2×C4—18816no—
777C2×C4—1882no—
778C2×C4—1882no—
779C2×C4—1882no—
780C2×C4—1882no—
781C2×C4(C22⋊D47)⋊C418yescomplemented
782C22—24no—
783C22—28no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—28no—
788C22—28no—
789C22—24no—
790C22—24no—
791C22—28no—
792C22—944no—
793C22—948no—
794C22—1882no—
795C22—1884no—
796C22—1882no—
797C22—1882no—
798C22—1882no—
799C22—1884no—
800C22—1884no—
801C22—1882no—
802C22—1882no—
803C22#1568897018yescomplemented
804C22C2×C42×D4711yescharacteristic
805C22C2×C22⋊C4×D4711yescharacteristic
806C22C2×#1309398211yescharacteristic
807C22C4×D4×D4712yes—
808C22C4×D4×D4712yes—
809C22C2×(C22⋊D47)⋊C412yes—
810C22C2×(C22⋊D47)⋊C411yescharacteristic
811C22C2×(C22⋊D47)⋊C411yescharacteristic
812C22C2×#1309398611yescharacteristic
813C22C2×#1309398611yescharacteristic
814C22C4×#1062535212yes—
815C22C4×#1062535212yes—
816C22#1568959112yes—
817C22#120×D4711yescharacteristic
818C22#121×D4712yes—
819C22#123×D4711yescharacteristic
820C22#1568962912yes—
821C22#1568962911yescharacteristic
822C22#1568963111yescharacteristic
823C22#1568963612yes—
824C22#1568965012yes—
825C22#1568965912yes—
826C22#1568966812yes—
827C4—28no—
828C4—42no—
829C4—42no—
830C4—44no—
831C4—478no—
832C4—944no—
833C4—948no—
834C4—944no—
835C4—1884no—
836C2—28no—
837C2—1884no—
838C2C2×#1568897011yescharacteristic
839C2C4×(C22⋊D47)⋊C412yes—
840C2#386×D4711yescharacteristic
841C2#2024582412yes—
842C2#2024587311yescharacteristic
843C2#2024588711yescharacteristic
844C2#2024588911yescharacteristic
845C2#2024589412yes—
846C2#2024589812yes—
847C2#2024590511yescharacteristic
848C2#2024590711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×C22⋊#95C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC22⋊#95D47
hypocenterC47C4×#386
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C23×C4×Dic47C2semidirect
5. C2×C22⋊C4×Dic47C2semidirect
6. C2×#15688970C2semidirect
7. #20241624C2semidirect
8. #20241619C2semidirect
9. #20241610C2semidirect
10. #95×Dic47C2semidirect
11. C47×C22⋊#95C2semidirect
18. C2×(C22⋊D47)⋊C4C4semidirect
30. #15689002C4semidirect
31. #15689000C4semidirect
59. C23×Dic47C2×C4semidirect
71. C22×C4×D47C2×C4semidirect
75. C2×Dic47⋊C4C2×C4semidirect
78. C2×C22⋊Dic47C2×C4semidirect
85. C2×(C2×D47)⋊C4C2×C4semidirect
86. C2×(C2×D47)⋊C4C2×C4semidirect
87. C2×(C2×D47)⋊C4C2×C4semidirect
99. C2×C4×Dic47C2×C4semidirect
100. C2×C4×Dic47D4semidirect
104. C47⋊#95C2×C4semidirect
105. C47⋊#95C2×C4semidirect
111. C23×C4×C47C2×C4semidirect
121. C2×C22⋊C4×C47C2×C4semidirect
182. C2×C22⋊D47C42semidirect
208. C22×Dic47C22⋊C4semidirect
296. C22×D47C2×C42semidirect
321. C2×C4×C47C4×D4semidirect
348. C2×Dic47C2×C42semidirect
352. C2×Dic47C4×D4semidirect
368. C22×C47C4×C22⋊C4semidirect
411. Dic47#386semidirect
421. C22⋊#95D47semidirect
468. C47C4×#386semidirect
502. C23×C4C4×D47semidirect
528. C2×C22⋊C4C4×D47semidirect
781. C2×C4(C22⋊D47)⋊C4semidirect
803. C22#15688970semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D47)⋊C42
C23×C4×Dic472
C2×#156890022
C2×#156890002
C2×C22⋊C4×Dic472
C2×#156889702
#202416242
#202416192
#202416102
#95×Dic472
C47×C22⋊#952
C4×#38647