Finite Group Databasebeta

← #26137846

Subgroups — #26137846

Order 12032.

2666 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093986C211yesmaximal, characteristic
2C2×#15689025C211yesmaximal, characteristic
3C2×#15689024C211yesmaximal, characteristic
4C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D47)⋊C4C212yesmaximal, complemented
6#20241626C212yesmaximal, complemented
7#20241624C212yesmaximal, complemented
8#20241617C211yesmaximal, characteristic, complemented
9(C2×D47)⋊#95C212yesmaximal, complemented
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
12C23×D188C2211yescharacteristic
13C23×C4×D47C2212yes—
14C2×#13093986—24no—
15C2×#13093986—24no—
16C2×#13093986C418yescomplemented
17C22×C4⋊Dic47C2211yescharacteristic
18C22×(C2×D47)⋊C4C2212yes—
19C22×(C2×D47)⋊C4C2212yes—
20C22×(C2×D47)⋊C4C2212yes—
21C22×(C2×D47)⋊C4C2212yes—
22C22×(C2×D47)⋊C4C2212yes—
23C22×C4×Dic47C2212yes—
24C22×C4×Dic47C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26#15689025C418yescomplemented
27#15689024C418yescomplemented
28C4⋊C4×Dic47—24no—
29C4×(C2×D47)⋊C4—28no—
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2211yescharacteristic
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C4⋊C4×C47C2211yescharacteristic
39C22×C42×C47C2212yes—
40C22×C42×C47C2211yescharacteristic
41C4×C4⋊C4×C47—24no—
42C2×#95×C47C2212yes—
43C24×D47C2312yes—
44C22×D188—22no—
45C22×D188—22no—
46C22×D188—22no—
47C22×D188—22no—
48C22×D188C2×C414yes—
49C22×D188C2×C414yes—
50C22×D188C2×C414yes—
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2312yes—
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2311yescharacteristic
56C22×C4×D47—24no—
57C22×C4×D47—24no—
58C22×C4×D47—24no—
59C22×C4×D47—24no—
60C22×C4×D47—42no—
61C22×C4×D47—42no—
62C22×C4×D47C2×C418yes—
63#13093986—232no—
64C2×C4⋊Dic47—22no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47C2×C414yescomplemented
67C2×(C2×D47)⋊C4—24no—
68C2×(C2×D47)⋊C4—24no—
69C2×(C2×D47)⋊C4—24no—
70C2×(C2×D47)⋊C4—24no—
71C2×(C2×D47)⋊C4—24no—
72C2×(C2×D47)⋊C4—24no—
73C2×(C2×D47)⋊C4—42no—
74C2×(C2×D47)⋊C4—42no—
75C2×(C2×D47)⋊C4—42no—
76C2×(C2×D47)⋊C4—42no—
77C2×(C2×D47)⋊C4C2×C418yes—
78C2×(C2×D47)⋊C4C2×C418yescomplemented
79C2×(C2×D47)⋊C4C2×C418yescomplemented
80C2×(C2×D47)⋊C4C2×C418yescomplemented
81C2×(C2×D47)⋊C4C2×C418yescomplemented
82C2×C4×Dic47—22no—
83C2×C4×Dic47—22no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47—22no—
86C2×C4×Dic47—24no—
87C2×C4×Dic47—24no—
88C2×C4×Dic47—42no—
89C2×C4×Dic47C2×C414yes—
90C2×C4×Dic47C2×C414yescomplemented
91C47⋊#95—24no—
92C47⋊#95—22no—
93C47⋊#95—24no—
94C47⋊#95—22no—
95C47⋊#95—22no—
96C47⋊#95—42no—
97C47⋊#95D414yescomplemented
98C23×C4×C47C2312yes—
99C23×C4×C47C2311yescharacteristic
100C23×C4×C47C2312yes—
101C23×C4×C47C2311yescharacteristic
102C23×C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47—22no—
104C2×C4⋊C4×C47—22no—
105C2×C4⋊C4×C47C2×C414yes—
106C2×C4⋊C4×C47C2×C414yescomplemented
107C2×C4⋊C4×C47D414yes—
108C2×C4⋊C4×C47D414yes—
109C2×C42×C47—22no—
110C2×C42×C47—22no—
111C2×C42×C47—24no—
112C2×C42×C47—24no—
113C2×C42×C47—42no—
114C2×C42×C47C2×C414yescomplemented
115#95×C47—24no—
116C24×C47C2411yescharacteristic
117C23×D47—22no—
118C23×D47—22no—
119C23×D47—22no—
120C23×D47—22no—
121C23×D47—22no—
122C23×D47—22no—
123C23×D47—22no—
124C23×D47—22no—
125C23×D47—22no—
126C23×D47—22no—
127C23×D47—22no—
128C23×D47—22no—
129C23×D47C22×C414yes—
130C23×D47C22×C414yes—
131C23×D47C22×C414yes—
132C22×C4×C47—21no—
133C22×C4×C47—22no—
134C22×C4×C47—21no—
135C22×C4×C47—22no—
136C22×C4×C47—21no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—21no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—22no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47C22×C412yes—
153C22×C4×C47C22×C414yes—
154C22×C4×C47C22×C414yes—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C22×C412yes—
157C22×C4×C47C22×C412yes—
158C22×C4×C47C22×C412yes—
159C22×C4×C47C2×D414yes—
160C22×C4×C47C2×D414yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2×D412yes—
163C22×C4×C47C2×D412yes—
164C22×C4×C47#4112yes—
165C22×C4×C47#4112yes—
166C22×C4×C47#4112yes—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—21no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47C22×C412yes—
194C22×Dic47C22×C412yes—
195C22×Dic47C22×C414yes—
196C22×Dic47C22×C412yes—
197C22×Dic47C22×C412yes—
198C22×Dic47C2×D412yes—
199C22×Dic47C2×D412yes—
200C22×Dic47#4112yes—
201C22×Dic47#4112yes—
202C2×D188—28no—
203C2×D188—28no—
204C2×D188—28no—
205C2×D188—28no—
206C2×D188—28no—
207C2×D188—28no—
208C2×D188C42116yescomplemented
209C2×C4×D47—216no—
210C2×C4×D47—216no—
211C2×C4×D47—48no—
212C2×C4×D47—48no—
213C2×C4×D47—48no—
214C2×C4×D47—48no—
215C2×C4×D47—48no—
216C4⋊C4×C47—28no—
217C4⋊C4×C47C22⋊C4116yescomplemented
218C42×C47—28no—
219C42×C47—48no—
220(C2×D47)⋊C4—216no—
221(C2×D47)⋊C4—216no—
222(C2×D47)⋊C4—216no—
223(C2×D47)⋊C4—48no—
224(C2×D47)⋊C4—48no—
225C4⋊Dic47—28no—
226C4×Dic47—28no—
227C4×Dic47—28no—
228C4×Dic47—48no—
229C23×C47C23×C411yescharacteristic
230C23×C47C23×C411yescharacteristic
231C23×C47C23×C411yescharacteristic
232C23×C47C22×D411yescharacteristic
233C23×C47C22×D411yescharacteristic
234C23×C47C22×D411yescharacteristic
235C23×C47C2×#4111yescharacteristic
236C23×C47C2×#4111yescharacteristic
237C23×C47C2×#4111yescharacteristic
238C23×C47C2×#4111yescharacteristic
239C23×C47C2×#4111yescharacteristic
240C23×C47H(5,𝔽2)11yescharacteristic
241C23×C47H(5,𝔽2)11yescharacteristic
242C23×C47H(5,𝔽2)11yescharacteristic
243C23×C472−1+411yescharacteristic
244C22×D47—24no—
245C22×D47—24no—
246C22×D47—24no—
247C22×D47—24no—
248C22×D47—24no—
249C22×D47—24no—
250C22×D47—24no—
251C22×D47—24no—
252C22×D47—24no—
253C22×D47—24no—
254C22×D47—24no—
255C22×D47—24no—
256C22×D47—24no—
257C22×D47—24no—
258C22×D47—24no—
259C22×D47—24no—
260C22×D47—24no—
261C22×D47—24no—
262C22×D47—42no—
263C22×D47—42no—
264C22×D47—42no—
265C22×D47—42no—
266C22×D47—42no—
267C22×D47—42no—
268C22×D47—42no—
269C22×D47—42no—
270C22×D47—42no—
271C22×D47—42no—
272C22×D47—42no—
273C22×D47—42no—
274C22×D47—42no—
275C22×D47—42no—
276C22×D47—42no—
277C22×D47—42no—
278C22×D47C2×C4218yes—
279C2×C4×C47—22no—
280C2×C4×C47—24no—
281C2×C4×C47—24no—
282C2×C4×C47—22no—
283C2×C4×C47—24no—
284C2×C4×C47—22no—
285C2×C4×C47—24no—
286C2×C4×C47—24no—
287C2×C4×C47—24no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—24no—
292C2×C4×C47—22no—
293C2×C4×C47—24no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—24no—
297C2×C4×C47—42no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—42no—
305C2×C4×C47C2×C4214yes—
306C2×C4×C47C2×C22⋊C418yes—
307C2×C4×C47C2×C22⋊C414yes—
308C2×C4×C47#11714yes—
309C2×C4×C47C4×D414yes—
310C2×C4×C47C4×D414yes—
311C2×C4×C47C4×D414yes—
312C2×C4×C47C4×D414yes—
313C2×C4×C47C4×D414yescomplemented
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—24no—
329C2×Dic47—24no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—24no—
334C2×Dic47—22no—
335C2×Dic47—42no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—42no—
341C2×Dic47—41no—
342C2×Dic47—41no—
343C2×Dic47—42no—
344C2×Dic47—41no—
345C2×Dic47—41no—
346C2×Dic47—42no—
347C2×Dic47C4×D414yes—
348C2×Dic47C4×D414yescomplemented
349D188—232no—
350C4×D47—432no—
351#13820—471nomaximal, Sylow
352C22×C47C22×C4211yescharacteristic
353C22×C47C22×C22⋊C411yescharacteristic
354C22×C47C2×#11711yescharacteristic
355C22×C47C2×C4×D411yescharacteristic
356C22×C47C2×C4×D411yescharacteristic
357C22×C47C2×C4×D411yescharacteristic
358C22×C47C2×C4×D411yescharacteristic
359C22×C47C2×C4×D411yescharacteristic
360C22×C47C2×C4×D411yescharacteristic
361C22×C47C2×C4×D411yescharacteristic
362C22×C47C4×#4111yescharacteristic
363C22×C47C4×#4111yescharacteristic
364C22×C47C4×#4111yescharacteristic
365C22×C47#51811yescharacteristic
366C22×C47#51811yescharacteristic
367C22×C47#51811yescharacteristic
368C22×C47#52011yescharacteristic
369C22×C47#52011yescharacteristic
370C22×C47#52011yescharacteristic
371C22×C47D4211yescharacteristic
372C22×C47D4211yescharacteristic
373C22×C47#54611yescharacteristic
374C22×C47#54611yescharacteristic
375C22×C47#54711yescharacteristic
376C22×C47#54811yescharacteristic
377C22×C47#54811yescharacteristic
378C22×C47#55011yescharacteristic
379C22×C47#55011yescharacteristic
380C22×C47#55011yescharacteristic
381C22×C47#55311yescharacteristic
382C22×C47#55311yescharacteristic
383C22×C47#55511yescharacteristic
384C22×C47#55611yescharacteristic
385C22×C47#55911yescharacteristic
386C22×C47#55911yescharacteristic
387C2×D47—28no—
388C2×D47—28no—
389C2×D47—28no—
390C2×D47—44no—
391C2×D47—44no—
392C2×D47—44no—
393C2×D47—44no—
394C2×D47—44no—
395C2×D47—44no—
396C2×D47—44no—
397C2×D47—44no—
398C2×D47—44no—
399C2×D47—44no—
400C2×D47—44no—
401C2×D47—44no—
402C4×C47—28no—
403C4×C47—24no—
404C4×C47—42no—
405C4×C47—44no—
406C4×C47C4×C22⋊C418yescomplemented
407Dic47—24no—
408Dic47—24no—
409Dic47—42no—
410Dic47—42no—
411Dic47—44no—
412C22×C4×D4—471no—
413C2×#390—471no—
414C2×#390—471no—
415C2×C4×C4⋊C4—471no—
416C2×C4×C4⋊C4D4711yescharacteristic, complemented
417C2×C4×C22⋊C4—472no—
418#1437—472no—
419#1437—472no—
420C4⋊#95—471no—
421C22⋊#95—472no—
422C4×#95—471no—
423C2×C47C2×C4×C22⋊C411yescharacteristic
424C2×C47C42×D411yescharacteristic
425C2×C47#227511yescharacteristic
426C2×C47D4×C22⋊C411yescharacteristic
427C2×C47#234111yescharacteristic
428C2×C47#235411yescharacteristic
429C2×C47#235711yescharacteristic
430C2×C47#236111yescharacteristic
431C2×C47#236111yescharacteristic
432C2×C47#236311yescharacteristic
433C2×C47#236311yescharacteristic
434C2×C47#236611yescharacteristic
435C2×C47#236611yescharacteristic
436C2×C47#236711yescharacteristic
437C2×C47#236711yescharacteristic
438D47—48no—
439C23×D4—471no—
440C24×C4—472no—
441C2×C4×D4—478no—
442C2×C4×D4—944no—
443C2×C4×D4—944no—
444C22×C4⋊C4—471no—
445C22×C4⋊C4C2×D4711yescharacteristic
446C22×C4⋊C4C2×D4711yescharacteristic
447C22×C22⋊C4—472no—
448C22×C22⋊C4—472no—
449C22×C22⋊C4—472no—
450C22×C22⋊C4—472no—
451C22×C22⋊C4—472no—
452C22×C42—471no—
453C22×C42—471no—
454C22×C42—472no—
455C22×C42C2×D4712yes—
456C22×C42C2×D4711yescharacteristic
457#390—478no—
458#390—478no—
459C4×C4⋊C4—24no—
460C4×C4⋊C4—944no—
461C4×C22⋊C4—948no—
462C2×#95—471no—
463C2×#95—471no—
464C2×#95—471no—
465C2×#95—471no—
466C2×#95—472no—
467C2×#95—472no—
468C2×#95—472no—
469C2×#95C2×D4712yes—
470C47#1382011yescharacteristic, complemented, Sylow
471C25—472no—
472C22×D4—474no—
473C22×D4—474no—
474C22×D4—474no—
475C22×D4—942no—
476C22×D4—942no—
477C22×D4—942no—
478C22×D4—942no—
479C23×C4—471no—
480C23×C4—471no—
481C23×C4—472no—
482C23×C4—471no—
483C23×C4—471no—
484C23×C4—478no—
485C23×C4—944no—
486C23×C4—944no—
487C23×C4—944no—
488C23×C4—944no—
489C23×C4—1882no—
490C23×C4—1882no—
491C23×C4C22×D4712yes—
492C23×C4C22×D4711yescharacteristic
493C23×C4C22×D4712yes—
494C23×C4C22×D4711yescharacteristic
495C23×C4C22×D4711yescharacteristic
496C4×D4—9432no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—474no—
500C2×C4⋊C4—942no—
501C2×C4⋊C4—942no—
502C2×C4⋊C4C4×D4714yes—
503C2×C4⋊C4C4×D4714yescomplemented
504C2×C4⋊C4D18814yes—
505C2×C4⋊C4C22⋊D4714yes—
506C2×C22⋊C4—478no—
507C2×C22⋊C4—478no—
508C2×C22⋊C4—478no—
509C2×C22⋊C4—478no—
510C2×C22⋊C4—478no—
511C2×C22⋊C4—944no—
512C2×C22⋊C4—944no—
513C2×C22⋊C4—944no—
514C2×C22⋊C4—944no—
515C2×C22⋊C4—944no—
516C2×C22⋊C4—944no—
517C2×C22⋊C4—1882no—
518C2×C22⋊C4—1882no—
519C2×C22⋊C4—1882no—
520C2×C22⋊C4—1882no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—24no—
524C2×C42—24no—
525C2×C42—42no—
526C2×C42—474no—
527C2×C42—474no—
528C2×C42—942no—
529C2×C42—942no—
530C2×C42—942no—
531C2×C42—942no—
532C2×C42—944no—
533C2×C42—944no—
534C2×C42—1882no—
535C2×C42C4×D4714yescomplemented
536#95—24no—
537#95—474no—
538#95—942no—
539#95—942no—
540#95—944no—
541#95—944no—
542#95—942no—
543#95—1882no—
544C24—474no—
545C24—474no—
546C24—474no—
547C24—942no—
548C24—942no—
549C24—942no—
550C24—942no—
551C24—942no—
552C24—942no—
553C24—942no—
554C24—942no—
555C24—942no—
556C24—942no—
557C24—942no—
558C24—942no—
559C24C23×D4711yescharacteristic
560C2×D4—4716no—
561C2×D4—948no—
562C2×D4—948no—
563C2×D4—948no—
564C2×D4—948no—
565C2×D4—948no—
566C2×D4—948no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—472no—
588C22×C4—472no—
589C22×C4—472no—
590C22×C4—472no—
591C22×C4—472no—
592C22×C4—472no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—474no—
596C22×C4—9416no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—942no—
606C22×C4—941no—
607C22×C4—941no—
608C22×C4—942no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—941no—
613C22×C4—942no—
614C22×C4—941no—
615C22×C4—941no—
616C22×C4—942no—
617C22×C4—941no—
618C22×C4—941no—
619C22×C4—942no—
620C22×C4—942no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—9416no—
624C22×C4—1888no—
625C22×C4—1888no—
626C22×C4—1888no—
627C22×C4—1888no—
628C22×C4—1888no—
629C22×C4C2×C4×D4712yes—
630C22×C4C2×C4×D4714yes—
631C22×C4C2×C4×D4714yes—
632C22×C4C2×C4×D4712yes—
633C22×C4C2×C4×D4712yes—
634C22×C4C2×C4×D4712yes—
635C22×C4C2×C4×D4712yes—
636C22×C4C2×D18814yes—
637C22×C4C2×D18812yes—
638C22×C4#1062535012yes—
639C22×C4#1062535012yes—
640C22×C4D4×D4712yes—
641C22×C4#1062535412yes—
642C22×C4C2×C22⋊D4714yes—
643C22×C4C2×C22⋊D4712yes—
644C4⋊C4—28no—
645C4⋊C4—948no—
646C4⋊C4(C2×D47)⋊C4116yescomplemented
647C22⋊C4—9416no—
648C22⋊C4—9416no—
649C22⋊C4—9416no—
650C22⋊C4—1888no—
651C22⋊C4—1888no—
652C42—28no—
653C42—48no—
654C42—948no—
655C42—948no—
656C42—1888no—
657C23—478no—
658C23—944no—
659C23—944no—
660C23—944no—
661C23—944no—
662C23—944no—
663C23—944no—
664C23—944no—
665C23—944no—
666C23—944no—
667C23—944no—
668C23—944no—
669C23—944no—
670C23—944no—
671C23—944no—
672C23—944no—
673C23—944no—
674C23—944no—
675C23—944no—
676C23—1882no—
677C23—1882no—
678C23—1882no—
679C23—1882no—
680C23—1882no—
681C23—1882no—
682C23—1882no—
683C23—1882no—
684C23—1882no—
685C23—1882no—
686C23—1882no—
687C23—1882no—
688C23—1882no—
689C23—1882no—
690C23—1882no—
691C23—1882no—
692C23C22×C4×D4711yescharacteristic
693C23C22×C4×D4711yescharacteristic
694C23C22×C4×D4711yescharacteristic
695C23C2×D4×D4711yescharacteristic
696C23C22×C22⋊D4711yescharacteristic
697C23C22×D18811yescharacteristic
698C23#41×D4711yescharacteristic
699C23#41×D4711yescharacteristic
700C23C2×#1062535011yescharacteristic
701C23C2×#1062535011yescharacteristic
702C23C2×#1062535411yescharacteristic
703C23#1309406911yescharacteristic
704C23#1309407011yescharacteristic
705C23#1309407011yescharacteristic
706C23#1309407211yescharacteristic
707D4—9432no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—474no—
735C2×C4—474no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—942no—
748C2×C4—942no—
749C2×C4—944no—
750C2×C4—942no—
751C2×C4—944no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—944no—
756C2×C4—942no—
757C2×C4—18832no—
758C2×C4—1882no—
759C2×C4—1881no—
760C2×C4—1881no—
761C2×C4—1881no—
762C2×C4—1881no—
763C2×C4—1882no—
764C2×C4—1881no—
765C2×C4—1882no—
766C2×C4—1881no—
767C2×C4—1881no—
768C2×C4—1881no—
769C2×C4—1882no—
770C2×C4C42×D4714yes—
771C2×C4C2×(C2×D47)⋊C418yes—
772C2×C4C2×(C2×D47)⋊C414yes—
773C2×C4#1309398114yes—
774C2×C4C4×C22⋊D4714yes—
775C2×C4C4×C22⋊D4714yes—
776C2×C4#1309398614yescomplemented
777C2×C4C4×D18814yes—
778C2×C4C4×D18814yes—
779C22—948no—
780C22—948no—
781C22—948no—
782C22—1884no—
783C22—1884no—
784C22—1884no—
785C22—1884no—
786C22—1884no—
787C22—1884no—
788C22—1884no—
789C22—1884no—
790C22—1884no—
791C22—1884no—
792C22—1884no—
793C22—1884no—
794C22C2×C42×D4711yescharacteristic
795C22C22×(C2×D47)⋊C411yescharacteristic
796C22C2×#1309398111yescharacteristic
797C22C4×D4×D4711yescharacteristic
798C22C4×D4×D4711yescharacteristic
799C22C2×C4×C22⋊D4711yescharacteristic
800C22C2×C4×C22⋊D4711yescharacteristic
801C22C2×#1309398611yescharacteristic
802C22C2×C4×D18811yescharacteristic
803C22C2×C4×D18811yescharacteristic
804C22#1568959111yescharacteristic
805C22C4×#1062535411yescharacteristic
806C22C4×#1062535411yescharacteristic
807C22#1568959511yescharacteristic
808C22#1568959511yescharacteristic
809C22#1568959711yescharacteristic
810C22#1568960411yescharacteristic
811C22#1568960511yescharacteristic
812C22#1568960511yescharacteristic
813C22D4×C22⋊D4711yescharacteristic
814C22D4×D18811yescharacteristic
815C22#1568976111yescharacteristic
816C22#1568976811yescharacteristic
817C22#1568977411yescharacteristic
818C22#1568978411yescharacteristic
819C22#1568978511yescharacteristic
820C22#1568979211yescharacteristic
821C22#1568979411yescharacteristic
822C22#1568979511yescharacteristic
823C22#1568981711yescharacteristic
824C22#1568982111yescharacteristic
825C22#1568983611yescharacteristic
826C22#1568984511yescharacteristic
827C22#1568985611yescharacteristic
828C22#1568985811yescharacteristic
829C4—24no—
830C4—28no—
831C4—42no—
832C4—44no—
833C4—944no—
834C4—944no—
835C4—1882no—
836C4—1884no—
837C4—1882no—
838C4C4×(C2×D47)⋊C418yescomplemented
839C2—1888no—
840C2C2×C4×(C2×D47)⋊C411yescharacteristic
841C2C4×#1309398611yescharacteristic
842C2#2024574811yescharacteristic
843C2D4×(C2×D47)⋊C411yescharacteristic
844C2#2024622611yescharacteristic
845C2#2024633311yescharacteristic
846C2#2024635711yescharacteristic
847C2#2024640411yescharacteristic
848C2#2024640611yescharacteristic
849C2#2024642611yescharacteristic
850C2#2024642811yescharacteristic
851C2#2024645011yescharacteristic
852C2#2024645211yescharacteristic
853C2#2024645511yescharacteristic
854C2#2024645911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C4×C4⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC23×D188C22
hypercenterC2×C4×C4⋊C4D47
hypocenterC47#13820
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊C4×Dic47C2semidirect
5. C2×C4×(C2×D47)⋊C4C2semidirect
6. #20241626C2semidirect
7. #20241624C2semidirect
8. #20241617C2semidirect
9. (C2×D47)⋊#95C2semidirect
10. C4×C47⋊#95C2semidirect
11. C2×C4×C4⋊C4×C47C2semidirect
16. C2×#13093986C4semidirect
26. #15689025C4semidirect
27. #15689024C4semidirect
66. C2×C4⋊Dic47C2×C4semidirect
78. C2×(C2×D47)⋊C4C2×C4semidirect
79. C2×(C2×D47)⋊C4C2×C4semidirect
80. C2×(C2×D47)⋊C4C2×C4semidirect
81. C2×(C2×D47)⋊C4C2×C4semidirect
90. C2×C4×Dic47C2×C4semidirect
97. C47⋊#95D4semidirect
106. C2×C4⋊C4×C47C2×C4semidirect
114. C2×C42×C47C2×C4semidirect
208. C2×D188C42semidirect
217. C4⋊C4×C47C22⋊C4semidirect
313. C2×C4×C47C4×D4semidirect
348. C2×Dic47C4×D4semidirect
406. C4×C47C4×C22⋊C4semidirect
416. C2×C4×C4⋊C4D47semidirect
470. C47#13820semidirect
503. C2×C4⋊C4C4×D47semidirect
535. C2×C42C4×D47semidirect
646. C4⋊C4(C2×D47)⋊C4semidirect
776. C2×C4#13093986semidirect
838. C4C4×(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130939862
C2×#156890252
C2×#156890242
C2×C4⋊C4×Dic472
C2×C4×(C2×D47)⋊C42
#202416262
#202416242
#202416172
(C2×D47)⋊#952
C4×C47⋊#952
C2×C4×C4⋊C4×C472
#1382047