Finite Group Databasebeta

← #26233538

Subgroups — #26233538

Order 12032.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689127C211yesmaximal, characteristic
2C22⋊C4×D188C211yesmaximal, characteristic
3#20244084C211yesmaximal, characteristic, complemented
4#20244070C211yesmaximal, characteristic, complemented
5#20244015C211yesmaximal, characteristic, complemented
6#20244008C211yesmaximal, characteristic, complemented
7#20243648C211yesmaximal, characteristic, complemented
8#20243634C211yesmaximal, characteristic, complemented
9#20243483C211yesmaximal, characteristic, complemented
10#20243419C211yesmaximal, characteristic, complemented
11#20243318C211yesmaximal, characteristic
12#20243216C211yesmaximal, characteristic, complemented
13C4×#13093944C211yesmaximal, characteristic, complemented
14#20243172C211yesmaximal, characteristic, complemented
15C47×#2347C211yesmaximal, characteristic, complemented
16C23×D188C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C2×C4×D188C2211yescharacteristic
19C2×C4×D188C2211yescharacteristic
20C2×C22⋊C4×D47—21no—
21C2×#13093957C2211yescharacteristic, complemented
22C2×#13093955C2211yescharacteristic, complemented
23#15689127C418yescomplemented
24C2×#13093944C2211yescharacteristic
25C2×#13093944C2211yescharacteristic
26C2×#13093944C2211yescharacteristic
27C2×#13093944C2211yescharacteristic
28C2×#13093944C2211yescharacteristic
29C2×#13093944C2211yescharacteristic
30C2×#13093944C2211yescharacteristic
31C2×#13093944C2211yescharacteristic
32C2×C22⋊(C47⋊C8)C2211yescharacteristic
33C2×#13093935C2211yescharacteristic, complemented
34C2×C4×C47⋊C8C2211yescharacteristic, complemented
35#15689025C2211yescharacteristic
36#15689025C2211yescharacteristic
37#15689001—21no—
38#15689001—21no—
39#15688983C2211yescharacteristic
40#15688978—21no—
41#15688885C2211yescharacteristic, complemented
42#15688885C2211yescharacteristic, complemented
43#15688885C2211yescharacteristic, complemented
44#15688885C2211yescharacteristic, complemented
45#15688885C2211yescharacteristic, complemented
46#15688885C2211yescharacteristic, complemented
47#15688878C2211yescharacteristic, complemented
48#15688878C2211yescharacteristic, complemented
49C2×#117×C47C2211yescharacteristic
50C47×#389C2211yescharacteristic, complemented
51C47×#389C2211yescharacteristic, complemented
52C47×#388—21no—
53C47×#388—21no—
54C47×#383—21no—
55C47×#380C2211yescharacteristic
56C4×C4⋊C4×C47—21no—
57C4×C4⋊C4×C47C2211yescharacteristic, complemented
58C4×C4⋊C4×C47C2211yescharacteristic, complemented
59C4×C22⋊C4×C47C2211yescharacteristic
60C24×D47—21no—
61C22×D188—22no—
62C22×D188—22no—
63C22×D188—21no—
64C22×D188—22no—
65C22×D188—41no—
66C22×D188—41no—
67C22×D188C2×C414yes—
68C22×D188C2311yescharacteristic
69C22×D188C2311yescharacteristic
70C22×C4×D47—21no—
71C22×C4×D47—21no—
72C2×#10625329—41no—
73C2×#10625329—41no—
74C2×#10625329C2×C414yescomplemented
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C22×C47⋊C8C2311yescharacteristic
79C4×D188—22no—
80C4×D188—22no—
81C4×D188—41no—
82C4×D188—41no—
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C4⋊Dic47C2311yescharacteristic
85C2×C22⋊Dic47—21no—
86C2×(C2×D47)⋊C4—21no—
87C2×(C2×D47)⋊C4—21no—
88C2×(C2×D47)⋊C4—21no—
89C2×(C2×D47)⋊C4—21no—
90C2×(C2×D47)⋊C4—21no—
91C2×(C2×D47)⋊C4—21no—
92C22⋊C4×D47—44no—
93#13093957—41no—
94#13093955—41no—
95#13093944—22no—
96#13093944—22no—
97#13093944—41no—
98#13093944—41no—
99#13093944C2×C414yes—
100#13093944C2×C414yes—
101#13093944C2×C414yescomplemented
102#13093944C2×C414yescomplemented
103C22⋊(C47⋊C8)—22no—
104#13093935—41no—
105C4×C47⋊C8—41no—
106C47⋊#95—21no—
107C23×C4×C47C2311yescharacteristic
108#117×C47—22no—
109#117×C47C2×C414yescomplemented
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47D411yescharacteristic
119C2×C22⋊C4×C47D411yescharacteristic
120C2×C42×C47—21no—
121C2×C42×C47—21no—
122C2×C42×C47—21no—
123C2×C42×C47C2311yescharacteristic
124C2×C42×C47C2311yescharacteristic
125#95×C47—21no—
126#95×C47—21no—
127#95×C47—21no—
128#95×C47—21no—
129#95×C47—21no—
130#95×C47D411yescharacteristic
131#95×C47D411yescharacteristic
132C24×C47C2×D411yescharacteristic
133C23×D47—21no—
134C23×D47—21no—
135C23×D47—24no—
136C23×D47—42no—
137C23×D47—42no—
138C23×D47—42no—
139C23×D47—42no—
140C23×D47—81no—
141C23×D47—81no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47C22×C412yes—
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47#4112yes—
157C22×C4×C47C2411yescharacteristic
158C22×Dic47—21no—
159C22×Dic47—21no—
160C2×D188—21no—
161C2×D188—21no—
162C2×D188—21no—
163C2×D188—21no—
164C2×D188—21no—
165C2×D188—21no—
166C2×D188—21no—
167C2×D188—28no—
168C2×D188—24no—
169C2×D188—21no—
170C2×D188—44no—
171C2×D188—44no—
172C2×D188—44no—
173C2×D188—42no—
174C2×D188—42no—
175C2×D188C22×C412yes—
176C2×D188C22×C412yes—
177C2×D188#4112yes—
178C2×D188#4112yes—
179C2×C4×D47—42no—
180C2×C4×D47—42no—
181C2×C4×D47—42no—
182C2×C4×D47—42no—
183C2×C4×D47—81no—
184C2×C4×D47—81no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—42no—
192C4⋊C4×C47—42no—
193C4⋊C4×C47C22×C412yes—
194C4⋊C4×C47C22×C412yes—
195C22⋊C4×C47—24no—
196C22⋊C4×C47—22no—
197C22⋊C4×C47—41no—
198C22⋊C4×C47—81no—
199C42×C47—24no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47—21no—
203C42×C47—21no—
204C42×C47—81no—
205C42×C47—81no—
206C22⋊Dic47—42no—
207(C2×D47)⋊C4—42no—
208(C2×D47)⋊C4—42no—
209(C2×D47)⋊C4—42no—
210(C2×D47)⋊C4—42no—
211(C2×D47)⋊C4—81no—
212(C2×D47)⋊C4—81no—
213C4⋊Dic47—21no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217#10625329—44no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8C22×C412yes—
229C2×C47⋊C8C22×C412yes—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47C4×D412yes—
237C23×C47C22×D411yescharacteristic
238C22×D47—22no—
239C22×D47—22no—
240C22×D47—22no—
241C22×D47—22no—
242C22×D47—48no—
243C22×D47—41no—
244C22×D47—41no—
245C22×D47—41no—
246C22×D47—41no—
247C22×D47—48no—
248C22×D47—41no—
249C22×D47—41no—
250C22×D47—41no—
251C22×D47—41no—
252C22×D47—41no—
253C22×D47—41no—
254C22×D47—84no—
255C22×D47—84no—
256C22×D47—84no—
257C22×D47—84no—
258C22×D47—84no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47C4×D412yes—
289C2×C4×C47AGL(1,ℤ/8)12yes—
290C2×C4×C47C23×C411yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C47C2×#4111yescharacteristic
293C2×C4×C47C2×#4111yescharacteristic
294C2×C4×C47H(5,𝔽2)11yescharacteristic
295C2×C4×C47H(5,𝔽2)11yescharacteristic
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302D188—22no—
303D188—22no—
304D188—22no—
305D188—22no—
306D188—22no—
307D188—48no—
308D188—41no—
309D188—41no—
310D188#11714yes—
311C4×D47—84no—
312C4×D47—84no—
313C47⋊C8—22no—
314C47⋊C8—22no—
315C47⋊C8—41no—
316C47⋊C8—41no—
317#22580—471nomaximal, Sylow
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47—41no—
324C22×C47—41no—
325C22×C47C2×C4×D411yescharacteristic
326C22×C47#54611yescharacteristic
327C22×C47#54611yescharacteristic
328C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C47#57511yescharacteristic
330C22×C47#57611yescharacteristic
331C22×C47#57711yescharacteristic
332C2×D47—24no—
333C2×D47—42no—
334C2×D47—42no—
335C2×D47—42no—
336C2×D47—42no—
337C2×D47—42no—
338C2×D47—42no—
339C2×D47—42no—
340C2×D47—42no—
341C2×D47—42no—
342C2×D47—816no—
343C2×D47—81no—
344C2×D47—81no—
345C2×D47—81no—
346C2×D47—81no—
347C4×C47—22no—
348C4×C47—22no—
349C4×C47—42no—
350C4×C47—42no—
351C4×C47—41no—
352C4×C47—41no—
353C4×C47—41no—
354C4×C47—81no—
355C4×C47—81no—
356C4×C47C2×#11711yescharacteristic
357C4×C47#51811yescharacteristic
358C4×C47#55111yescharacteristic
359C4×C47#55111yescharacteristic
360Dic47—81no—
361Dic47—81no—
362C2×#418—471no—
363#2347D4711yescharacteristic, complemented
364D4×C22⋊C4—471no—
365#1936—471no—
366#1934—471no—
367#1926—471no—
368#1925—471no—
369#1864—471no—
370#1862—471no—
371#1825—471no—
372#1809—471no—
373#1786—471no—
374#1762—471no—
375C4×#102—471no—
376#1753—471no—
377C2×C47—42no—
378C2×C47#234211yescharacteristic
379C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
380C2×C47#294611yescharacteristic
381C2×C47#331111yescharacteristic
382C2×C47#331811yescharacteristic
383C2×C47#332211yescharacteristic
384C2×C47#332411yescharacteristic
385D47—44no—
386D47—82no—
387C23×D4—471no—
388C22×M16—471no—
389C2×C4×D4—471no—
390C2×C4×D4—471no—
391C2×#117C2×D4711yescharacteristic
392C22×C22⋊C4—941no—
393C2×#107—471no—
394C2×#106—471no—
395#418—478no—
396C2×#102—471no—
397C2×#102—471no—
398C2×#102—471no—
399C2×#102—471no—
400C2×#102—471no—
401C2×#102—471no—
402C2×#102—471no—
403C2×#102—471no—
404C2×C22⋊C8—471no—
405C2×#97—471no—
406C2×C4×C8—471no—
407#390—471no—
408#390—471no—
409#389C2×D4711yescharacteristic, complemented
410#389C2×D4711yescharacteristic, complemented
411#388—21no—
412#388—21no—
413#386—941no—
414#386—941no—
415#383—21no—
416#380—471no—
417#380C2×D4711yescharacteristic
418#379—941no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4C2×D4711yescharacteristic, complemented
421C4×C4⋊C4C2×D4711yescharacteristic, complemented
422C4×C22⋊C4C2×D4711yescharacteristic
423#340—471no—
424#340—471no—
425#340—471no—
426#340—471no—
427#340—471no—
428#340—471no—
429#336—471no—
430#336—471no—
431C47#2258011yescharacteristic, complemented, Sylow
432C25—941no—
433C22×D4—474no—
434C22×D4—471no—
435C22×D4—471no—
436C22×D4—942no—
437C22×D4—942no—
438C22×D4—942no—
439C22×D4—941no—
440C22×D4—1881no—
441C22×D4—1881no—
442C23×C4—941no—
443C23×C4—941no—
444C23×C4C22×D4711yescharacteristic
445C2×M16—474no—
446C2×M16—1881no—
447C2×M16—1881no—
448C22×C8—471no—
449C22×C8—471no—
450C22×C8—471no—
451C22×C8—471no—
452C4×D4—942no—
453C4×D4—942no—
454C4×D4—1881no—
455C4×D4—1881no—
456#117—22no—
457#117C4×D4714yescomplemented
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—471no—
461C2×C4⋊C4—471no—
462C2×C4⋊C4C22×D4711yescharacteristic
463C2×C4⋊C4C22×D4711yescharacteristic
464C2×C4⋊C4C22×D4711yescharacteristic
465C2×C4⋊C4C22×D4711yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—941no—
469C2×C22⋊C4—941no—
470C2×C22⋊C4—941no—
471C2×C22⋊C4—941no—
472C2×C22⋊C4—941no—
473C2×C22⋊C4—941no—
474C2×C22⋊C4—941no—
475C2×C22⋊C4—1884no—
476C2×C22⋊C4C22⋊D4711yescharacteristic
477C2×C22⋊C4C22⋊D4711yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42C22×D4711yescharacteristic
482C2×C42C22×D4711yescharacteristic
483#107—1881no—
484#106—1881no—
485#102—474no—
486#102—474no—
487#102—474no—
488#102—474no—
489#102—942no—
490#102—942no—
491#102—1881no—
492#102—1881no—
493C22⋊C8—942no—
494#97—1881no—
495C4×C8—1881no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—941no—
502#95C22⋊D4711yescharacteristic
503#95C22⋊D4711yescharacteristic
504C24—941no—
505C24—944no—
506C24—941no—
507C24—3761no—
508C24—3761no—
509C24—1882no—
510C24—1882no—
511C24—1882no—
512C24—1882no—
513C24C2×C22⋊D4711yescharacteristic
514C2×D4—472no—
515C2×D4—472no—
516C2×D4—472no—
517C2×D4—472no—
518C2×D4—948no—
519C2×D4—944no—
520C2×D4—941no—
521C2×D4—941no—
522C2×D4—941no—
523C2×D4—941no—
524C2×D4—941no—
525C2×D4—941no—
526C2×D4—941no—
527C2×D4—941no—
528C2×D4—1884no—
529C2×D4—1884no—
530C2×D4—1884no—
531C2×D4—1882no—
532C2×D4—1882no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—941no—
542C22×C4—941no—
543C22×C4—3761no—
544C22×C4—3761no—
545C22×C4—1882no—
546C22×C4—1882no—
547C22×C4—1882no—
548C22×C4—1882no—
549C22×C4C2×C4×D4712yes—
550C22×C4#1062535012yes—
551C22×C4C2×C22⋊D4711yescharacteristic
552C22×C4C2×C22⋊D4711yescharacteristic
553C22×C4C2×C22⋊D4711yescharacteristic
554C22×C4C2×C22⋊D4711yescharacteristic
555C22×C4C2×C22⋊D4711yescharacteristic
556C22×C4C23×D4711yescharacteristic
557M16—1884no—
558C2×C8—472no—
559C2×C8—472no—
560C2×C8—941no—
561C2×C8—941no—
562C2×C8—941no—
563C2×C8—941no—
564C2×C8—941no—
565C2×C8—941no—
566C2×C8—941no—
567C2×C8—941no—
568C2×C8—941no—
569C2×C8—941no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—941no—
579C4⋊C4—941no—
580C4⋊C4—941no—
581C4⋊C4—941no—
582C4⋊C4C2×C4×D4712yes—
583C4⋊C4C2×C4×D4712yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—81no—
588C22⋊C4—3761no—
589C22⋊C4—3761no—
590C22⋊C4—1882no—
591C22⋊C4—1882no—
592C22⋊C4—1882no—
593C22⋊C4—1882no—
594C22⋊C4—1882no—
595C42—24no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—81no—
601C42—81no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—942no—
609C23—942no—
610C23—942no—
611C23—942no—
612C23—3764no—
613C23—3764no—
614C23—3764no—
615C23—3764no—
616C23—3764no—
617C23—1888no—
618C23—1888no—
619C23—1881no—
620C23—1881no—
621C23—1881no—
622C23—1881no—
623C23—1881no—
624C23—1881no—
625C23—1881no—
626C23—1881no—
627C23—1881no—
628C23—1881no—
629C23C4×C22⋊D4712yes—
630C23C22×C22⋊D4711yescharacteristic
631D4—474no—
632D4—942no—
633D4—942no—
634D4—942no—
635D4—942no—
636D4—942no—
637D4—1888no—
638D4—1881no—
639D4—1881no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—3764no—
670C2×C4—3764no—
671C2×C4—1881no—
672C2×C4—1881no—
673C2×C4—1881no—
674C2×C4—1881no—
675C2×C4—1881no—
676C2×C4—1881no—
677C2×C4C4×C22⋊D4712yes—
678C2×C4#1309404912yes—
679C2×C4C22×C4×D4711yescharacteristic
680C2×C4#41×D4711yescharacteristic
681C2×C4#41×D4711yescharacteristic
682C2×C4C2×#1062535011yescharacteristic
683C2×C4#1309407011yescharacteristic
684C2×C4#1309407011yescharacteristic
685C8—942no—
686C8—942no—
687C8—1881no—
688C8—1881no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—944no—
697C22—37616no—
698C22—3761no—
699C22—3761no—
700C22—3761no—
701C22—3761no—
702C22—1882no—
703C22—1882no—
704C22—1882no—
705C22—1882no—
706C22—1882no—
707C22—1882no—
708C22—1882no—
709C22—1882no—
710C22—1882no—
711C22C2×C4×C22⋊D4711yescharacteristic
712C22#1568976111yescharacteristic
713C22#1568976111yescharacteristic
714C22C2×#1309404911yescharacteristic
715C22#1568992111yescharacteristic
716C22#1568992611yescharacteristic
717C22#1568993111yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—81no—
726C4—81no—
727C4—3761no—
728C4—3761no—
729C4#117×D4711yescharacteristic
730C4#1568959711yescharacteristic
731C4#1568979711yescharacteristic
732C4#1568979711yescharacteristic
733C2—42no—
734C2—3762no—
735C2—1884no—
736C2#2024623811yescharacteristic
737C2C4×#1309404911yescharacteristic
738C2#2025221611yescharacteristic
739C2#2025541811yescharacteristic
740C2#2025552311yescharacteristic
741C2#2025558311yescharacteristic
742C2#2025561311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2347C2
socleC23×C47C22×D4
prime radicalC23×D188C22
cosocleC22×C4×C47C24
hypercenter#2347D47
hypocenterC47#22580
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2347

Complements

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

NH ≅ G/Ntype
3. #20244084C2semidirect
4. #20244070C2semidirect
5. #20244015C2semidirect
6. #20244008C2semidirect
7. #20243648C2semidirect
8. #20243634C2semidirect
9. #20243483C2semidirect
10. #20243419C2semidirect
12. #20243216C2semidirect
13. C4×#13093944C2semidirect
14. #20243172C2semidirect
15. C47×#2347C2semidirect
21. C2×#13093957C22semidirect
22. C2×#13093955C22semidirect
23. #15689127C4semidirect
33. C2×#13093935C22semidirect
34. C2×C4×C47⋊C8C22semidirect
41. #15688885C22semidirect
42. #15688885C22semidirect
43. #15688885C22semidirect
44. #15688885C22semidirect
45. #15688885C22semidirect
46. #15688885C22semidirect
47. #15688878C22semidirect
48. #15688878C22semidirect
50. C47×#389C22semidirect
51. C47×#389C22semidirect
57. C4×C4⋊C4×C47C22semidirect
58. C4×C4⋊C4×C47C22semidirect
74. C2×#10625329C2×C4semidirect
101. #13093944C2×C4semidirect
102. #13093944C2×C4semidirect
109. #117×C47C2×C4semidirect
363. #2347D47semidirect
409. #389C2×D47semidirect
410. #389C2×D47semidirect
420. C4×C4⋊C4C2×D47semidirect
421. C4×C4⋊C4C2×D47semidirect
431. C47#22580semidirect
457. #117C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156891272
C22⋊C4×D1882
#202440842
#202440702
#202440152
#202440082
#202436482
#202436342
#202434832
#202434192
#202433182
#202432162
C4×#130939442
#202431722
C47×#23472
#2258047