Finite Group Databasebeta

← #26124261

Subgroups — #26124261

Order 12032.

886 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093957C211yesmaximal, characteristic
2C2×#15689022C211yesmaximal, characteristic
3C2×#15688886C211yesmaximal, characteristic
4C2×#15688885C211yesmaximal, characteristic
5C2×#15688877C211yesmaximal, characteristic
6#20241617C211yesmaximal, characteristic
7C2×C47×#340C211yesmaximal, characteristic
8C23×C47⋊C8C2211yescharacteristic
9C22×C4⋊Dic47—21no—
10C22×C4⋊Dic47C2211yescharacteristic
11C22×C4⋊Dic47C2211yescharacteristic
12C22×C4×Dic47C2211yescharacteristic
13C2×#13093957—22no—
14C2×#13093957—22no—
15C2×#13093957C414yescomplemented
16#15689022—22no—
17#15689022—22no—
18C2×C47⋊#95—21no—
19C2×C47⋊#95—21no—
20C2×C47⋊#95—21no—
21#15688886—22no—
22#15688885—22no—
23#15688877—22no—
24C23×C8×C47C2211yescharacteristic
25C22×C4⋊C4×C47C2211yescharacteristic
26C22×C4⋊C4×C47C2211yescharacteristic
27C47×#340—22no—
28C23×Dic47—21no—
29C23×Dic47—21no—
30C23×Dic47D411yescharacteristic
31C23×Dic47D411yescharacteristic
32C22×C47⋊C8—21no—
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36C22×C47⋊C8C2×C412yes—
37C22×C47⋊C8D412yes—
38C22×C47⋊C8Q812yes—
39C2×C4⋊Dic47—21no—
40C2×C4⋊Dic47—21no—
41C2×C4⋊Dic47—21no—
42C2×C4⋊Dic47—21no—
43C2×C4⋊Dic47—21no—
44C2×C4⋊Dic47—21no—
45C2×C4⋊Dic47—21no—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47—24no—
48C2×C4⋊Dic47—21no—
49C2×C4⋊Dic47—21no—
50C2×C4⋊Dic47—42no—
51C2×C4⋊Dic47—42no—
52C2×C4⋊Dic47C2×C412yes—
53C2×C4⋊Dic47D412yes—
54C2×C4×Dic47—21no—
55C2×C4×Dic47—21no—
56C2×C4×Dic47—21no—
57C2×C4×Dic47—21no—
58C2×C4×Dic47—21no—
59C2×C4×Dic47—21no—
60#13093957—28no—
61C47⋊#95—24no—
62C47⋊#95—42no—
63C47⋊#95—42no—
64C23×C4×C47—21no—
65C23×C4×C47—21no—
66C23×C4×C47C2311yescharacteristic
67C22×C8×C47—21no—
68C22×C8×C47—21no—
69C22×C8×C47—21no—
70C22×C8×C47—21no—
71C22×C8×C47—21no—
72C22×C8×C47—21no—
73C22×C8×C47Q812yes—
74C2×C4⋊C4×C47—21no—
75C2×C4⋊C4×C47—21no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—21no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47—21no—
82C2×C4⋊C4×C47C2×C412yes—
83C2×C4⋊C4×C47D412yes—
84C2×C4⋊C4×C47D412yes—
85C2×C4⋊C4×C47Q812yes—
86C24×C47C2×D411yescharacteristic
87C22×C4×C47—22no—
88C22×C4×C47—22no—
89C22×C4×C47—22no—
90C22×C4×C47—22no—
91C22×C4×C47—41no—
92C22×C4×C47—41no—
93C22×C4×C47—41no—
94C22×C4×C47—41no—
95C22×C4×C47—41no—
96C22×C4×C47—41no—
97C22×C4×C47—41no—
98C22×C4×C47—41no—
99C22×C4×C47—41no—
100C22×C4×C47—41no—
101C22×C4×C47C22×C411yescharacteristic
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47C2×D411yescharacteristic
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47C2×Q811yescharacteristic
107C22×C4×C47C2×Q811yescharacteristic
108C22×C4×C47C2×Q811yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C22×C4×C47#4111yescharacteristic
111C22×C4×C47#4111yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C22×C4×C47#4111yescharacteristic
114C22×C4×C47#4111yescharacteristic
115C22×Dic47—21no—
116C22×Dic47—21no—
117C22×Dic47—21no—
118C22×Dic47—21no—
119C22×Dic47—21no—
120C22×Dic47—21no—
121C22×Dic47—21no—
122C22×Dic47—21no—
123C22×Dic47—21no—
124C22×Dic47—21no—
125C22×Dic47—21no—
126C22×Dic47—21no—
127C22×Dic47—22no—
128C22×Dic47—22no—
129C22×Dic47—41no—
130C22×Dic47—41no—
131C22×Dic47—41no—
132C22×Dic47—41no—
133C22×Dic47—41no—
134C22×Dic47—41no—
135C22×Dic47—41no—
136C22×Dic47—41no—
137C22×Dic47—41no—
138C22×Dic47—41no—
139C22×Dic47—41no—
140C22×Dic47—41no—
141C22×Dic47D812yes—
142C22×Dic47Q1612yes—
143C2×C8×C47—22no—
144C2×C8×C47—22no—
145C2×C8×C47—22no—
146C2×C8×C47—41no—
147C2×C8×C47—41no—
148C2×C8×C47—41no—
149C2×C8×C47—41no—
150C4⋊C4×C47—22no—
151C4⋊C4×C47—22no—
152C4⋊C4×C47—22no—
153C4⋊C4×C47—22no—
154C4⋊C4×C47—22no—
155C4⋊C4×C47—41no—
156C4⋊C4×C47—41no—
157C4⋊C4×C47C22⋊C414yes—
158C4⋊Dic47—22no—
159C4⋊Dic47—22no—
160C4⋊Dic47—22no—
161C4⋊Dic47—22no—
162C4⋊Dic47—48no—
163C4⋊Dic47—41no—
164C4⋊Dic47—41no—
165C4⋊Dic47—41no—
166C4⋊Dic47—41no—
167C4×Dic47—41no—
168C4×Dic47—41no—
169C4×Dic47—41no—
170C4×Dic47—41no—
171C2×C47⋊C8—22no—
172C2×C47⋊C8—22no—
173C2×C47⋊C8—22no—
174C2×C47⋊C8—22no—
175C2×C47⋊C8—22no—
176C2×C47⋊C8—22no—
177C2×C47⋊C8C4⋊C414yescomplemented
178C23×C47C4×D411yescharacteristic
179C23×C47#12011yescharacteristic
180C23×C47#12111yescharacteristic
181C23×C47#12111yescharacteristic
182C23×C47C22⋊Q811yescharacteristic
183C23×C47#12311yescharacteristic
184C23×C47C4⋊Q811yescharacteristic
185C23×C47C2×D811yescharacteristic
186C23×C47C2×Q1611yescharacteristic
187C23×C47#13511yescharacteristic
188C23×C47#13511yescharacteristic
189C23×C47AGL(1,ℤ/8)11yescharacteristic
190C23×C47AGL(1,ℤ/8)11yescharacteristic
191C23×C47#13711yescharacteristic
192C23×C47#13711yescharacteristic
193C2×C4×C47—24no—
194C2×C4×C47—42no—
195C2×C4×C47—42no—
196C2×C4×C47—42no—
197C2×C4×C47—42no—
198C2×C4×C47—42no—
199C2×C4×C47—42no—
200C2×C4×C47—42no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47—81no—
204C2×C4×C47—81no—
205C2×C4×C47—81no—
206C2×C4×C47—81no—
207C2×C4×C47C2×C22⋊C411yescharacteristic
208C2×C4×C47C2×C4⋊C411yescharacteristic
209C2×C4×C47#11711yescharacteristic
210C2×C4×C47C4×D411yescharacteristic
211C2×C4×C47C4×Q811yescharacteristic
212C2×C4×C47C4×Q811yescharacteristic
213C2×C4×C47#12111yescharacteristic
214C2×C4×C47#12111yescharacteristic
215C2×C4×C47#12111yescharacteristic
216C2×C4×C47#12111yescharacteristic
217C2×C4×C47C22⋊Q811yescharacteristic
218C2×C4×C47C22⋊Q811yescharacteristic
219C2×C4×C47C22⋊Q811yescharacteristic
220C2×C4×C47C22⋊Q811yescharacteristic
221C2×C4×C47C22⋊Q811yescharacteristic
222C2×C4×C47C22⋊Q811yescharacteristic
223C2×C4×C47C22⋊Q811yescharacteristic
224C2×C4×C47#12311yescharacteristic
225C2×C4×C47#12311yescharacteristic
226C2×C4×C47#12411yescharacteristic
227C2×C4×C47#12511yescharacteristic
228C2×C4×C47#12511yescharacteristic
229C2×C4×C47#12511yescharacteristic
230C2×C4×C47#12511yescharacteristic
231C2×C4×C47#12611yescharacteristic
232C2×C4×C47#12611yescharacteristic
233C2×C4×C47C4⋊Q811yescharacteristic
234C2×C4×C47C4⋊Q811yescharacteristic
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47—81no—
256C2×Dic47—81no—
257C2×Dic47—81no—
258C2×Dic47—81no—
259C2×Dic47—81no—
260C2×Dic47—81no—
261C2×Dic47—81no—
262C2×Dic47—81no—
263C8×C47—42no—
264C47⋊C8—24no—
265#11219—471nomaximal, Sylow
266C22×C47#38611yescharacteristic
267C22×C47#38711yescharacteristic
268C22×C47#38911yescharacteristic
269C22×C47#39411yescharacteristic
270C22×C47#39511yescharacteristic
271C22×C47#39611yescharacteristic
272C22×C47#39811yescharacteristic
273C22×C47C4×D811yescharacteristic
274C22×C47C4×Q1611yescharacteristic
275C22×C47#44111yescharacteristic
276C22×C47#44211yescharacteristic
277C22×C47#44711yescharacteristic
278C22×C47#44911yescharacteristic
279C22×C47#45111yescharacteristic
280C22×C47#45211yescharacteristic
281C22×C47#45911yescharacteristic
282C22×C47#46211yescharacteristic
283C22×C47#46311yescharacteristic
284C22×C47#46411yescharacteristic
285C22×C47#46611yescharacteristic
286C22×C47#46711yescharacteristic
287C22×C47#46811yescharacteristic
288C22×C47#46811yescharacteristic
289C22×C47#47411yescharacteristic
290C22×C47#47711yescharacteristic
291C22×C47#47811yescharacteristic
292C22×C47#47911yescharacteristic
293C22×C47#48011yescharacteristic
294C22×C47#48211yescharacteristic
295C22×C47#48411yescharacteristic
296C22×C47#48511yescharacteristic
297C22×C47#49911yescharacteristic
298C22×C47#50011yescharacteristic
299C22×C47#50111yescharacteristic
300C22×C47#50111yescharacteristic
301C4×C47—44no—
302C4×C47—82no—
303C4×C47#38011yescharacteristic
304C4×C47#38711yescharacteristic
305C4×C47#38911yescharacteristic
306C4×C47#39111yescharacteristic
307C4×C47#39611yescharacteristic
308C4×C47#39811yescharacteristic
309C4×C47#39811yescharacteristic
310C4×C47#40011yescharacteristic
311Dic47—42no—
312Dic47—42no—
313Dic47—82no—
314Dic47—82no—
315C22×#107—471no—
316C2×#389—471no—
317C2×#340—471no—
318C2×#340—471no—
319C2×#340D4711yescharacteristic
320C2×#336—471no—
321C4⋊#95—471no—
322C2×C47#144111yescharacteristic
323C2×C47#187811yescharacteristic
324C2×C47#187911yescharacteristic
325C2×C47#191811yescharacteristic
326C2×C47#192111yescharacteristic
327C2×C47#194211yescharacteristic
328C2×C47#194311yescharacteristic
329C2×C47#203311yescharacteristic
330C2×C47#203611yescharacteristic
331C2×C47#205711yescharacteristic
332C2×C47#205911yescharacteristic
333C2×C47#206711yescharacteristic
334C2×C47#206811yescharacteristic
335C2×C47#208311yescharacteristic
336C2×C47#208511yescharacteristic
337C23×C8—471no—
338C23×C8C2×D4711yescharacteristic
339C22×C4⋊C4—471no—
340C22×C4⋊C4—471no—
341C22×C4⋊C4—941no—
342C22×C4⋊C4C2×D4711yescharacteristic
343C22×C4⋊C4C2×D4711yescharacteristic
344C22×C42—471no—
345C2×#107—474no—
346C2×#107—942no—
347C2×#107—942no—
348#389—942no—
349#389—942no—
350C2×#95—941no—
351C2×#95—941no—
352C2×#95—941no—
353#340—22no—
354#340—942no—
355#340—942no—
356#336—942no—
357C47#1121911yescharacteristic, complemented, Sylow
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—471no—
361C23×C4—471no—
362C23×C4—941no—
363C23×C4—941no—
364C23×C4C22×D4711yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—472no—
372C22×C8—472no—
373C22×C8—472no—
374C22×C8—941no—
375C22×C8—941no—
376C22×C8—941no—
377C22×C8—941no—
378C22×C8Dic9412yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—472no—
388C2×C4⋊C4—472no—
389C2×C4⋊C4—941no—
390C2×C4⋊C4—941no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4—941no—
393C2×C4⋊C4—941no—
394C2×C4⋊C4—941no—
395C2×C4⋊C4—941no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—944no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—1882no—
401C2×C4⋊C4—1882no—
402C2×C4⋊C4Dic9412yes—
403C2×C4⋊C4C4×D4712yes—
404C2×C4⋊C4D18812yes—
405C2×C4⋊C4C22⋊D4712yes—
406C2×C42—941no—
407C2×C42—941no—
408C2×C42—941no—
409C2×C42—941no—
410C2×C42—941no—
411C2×C42—941no—
412#107—948no—
413#95—944no—
414#95—1882no—
415#95—1882no—
416C24D4×D4711yescharacteristic
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—472no—
432C22×C4—472no—
433C22×C4—941no—
434C22×C4—941no—
435C22×C4—941no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4—941no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—941no—
443C22×C4—941no—
444C22×C4—941no—
445C22×C4—942no—
446C22×C4—942no—
447C22×C4—1881no—
448C22×C4—1881no—
449C22×C4—1881no—
450C22×C4—1881no—
451C22×C4—1881no—
452C22×C4—1881no—
453C22×C4—1881no—
454C22×C4—1881no—
455C22×C4—1881no—
456C22×C4—1881no—
457C22×C4—1881no—
458C22×C4—1881no—
459C22×C4C2×Dic9411yescharacteristic
460C22×C4C2×Dic9411yescharacteristic
461C22×C4C2×C4×D4711yescharacteristic
462C22×C4C2×D18811yescharacteristic
463C22×C4#1062535011yescharacteristic
464C22×C4#1062535011yescharacteristic
465C22×C4D4×D4711yescharacteristic
466C22×C4D4×D4711yescharacteristic
467C22×C4#1062535211yescharacteristic
468C22×C4#1062535211yescharacteristic
469C22×C4#1062535211yescharacteristic
470C22×C4Q8×D4711yescharacteristic
471C22×C4#1062535411yescharacteristic
472C22×C4C2×C22⋊D4711yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—474no—
481C2×C8—942no—
482C2×C8—942no—
483C2×C8—942no—
484C2×C8—942no—
485C2×C8—942no—
486C2×C8—942no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—942no—
495C4⋊C4—942no—
496C4⋊C4—942no—
497C4⋊C4—942no—
498C4⋊C4—1888no—
499C4⋊C4—1881no—
500C4⋊C4—1881no—
501C4⋊C4—1881no—
502C4⋊C4—1881no—
503C4⋊C4(C2×D47)⋊C414yes—
504C42—1881no—
505C42—1881no—
506C42—1881no—
507C42—1881no—
508C23(C22⋊D47)⋊C411yescharacteristic
509C23#1309399411yescharacteristic
510C23#1309399611yescharacteristic
511C23#1309399711yescharacteristic
512C23#1309400111yescharacteristic
513C23#1309400911yescharacteristic
514C23#1309402311yescharacteristic
515C23D8×D4711yescharacteristic
516C23Q16×D4711yescharacteristic
517C23#1309404511yescharacteristic
518C23#1309404511yescharacteristic
519C23#1309404811yescharacteristic
520C23#1309405111yescharacteristic
521C23#1309405311yescharacteristic
522C23#1309405611yescharacteristic
523C2×C4—24no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—942no—
538C2×C4—942no—
539C2×C4—942no—
540C2×C4—942no—
541C2×C4—942no—
542C2×C4—942no—
543C2×C4—3761no—
544C2×C4—3761no—
545C2×C4—3761no—
546C2×C4—3761no—
547C2×C4—3761no—
548C2×C4—3761no—
549C2×C4—3761no—
550C2×C4—3761no—
551C2×C4—1882no—
552C2×C4—1882no—
553C2×C4—1882no—
554C2×C4—1882no—
555C2×C4—1882no—
556C2×C4—1882no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4—1881no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4C2×(C2×D47)⋊C411yescharacteristic
566C2×C4C4⋊C4×D4711yescharacteristic
567C2×C4#1309398211yescharacteristic
568C2×C4(C22⋊D47)⋊C411yescharacteristic
569C2×C4C4×Dic9411yescharacteristic
570C2×C4C4×Dic9411yescharacteristic
571C2×C4#1309399511yescharacteristic
572C2×C4#1309399611yescharacteristic
573C2×C4#1309399711yescharacteristic
574C2×C4#1309399911yescharacteristic
575C2×C4#1309400011yescharacteristic
576C2×C4#1309400111yescharacteristic
577C2×C4#1309400111yescharacteristic
578C2×C4#1309400111yescharacteristic
579C2×C4#1309400311yescharacteristic
580C2×C4#1309400311yescharacteristic
581C2×C4#1309400411yescharacteristic
582C2×C4#1309400811yescharacteristic
583C2×C4#1309400911yescharacteristic
584C2×C4#1309401211yescharacteristic
585C2×C4#1309401411yescharacteristic
586C2×C4#1309401411yescharacteristic
587C2×C4#1309401511yescharacteristic
588C2×C4#1309401511yescharacteristic
589C2×C4#1309401711yescharacteristic
590C2×C4#1309401711yescharacteristic
591C2×C4#1309402311yescharacteristic
592C2×C4#1309402411yescharacteristic
593C8—42no—
594C8—944no—
595C22#1568900011yescharacteristic
596C22#1568901011yescharacteristic
597C22#1568902011yescharacteristic
598C22#1568904111yescharacteristic
599C22#1568904411yescharacteristic
600C22#1568904611yescharacteristic
601C22#1568905611yescharacteristic
602C22#1568920311yescharacteristic
603C22#1568921511yescharacteristic
604C22#1568922711yescharacteristic
605C22#1568923211yescharacteristic
606C22#1568925811yescharacteristic
607C22#1568926911yescharacteristic
608C22#1568928011yescharacteristic
609C22#1568928811yescharacteristic
610C22#1568931611yescharacteristic
611C22#1568933111yescharacteristic
612C22#1568934011yescharacteristic
613C22#1568934311yescharacteristic
614C22#1568935811yescharacteristic
615C22#1568936311yescharacteristic
616C22#1568936811yescharacteristic
617C22#1568937211yescharacteristic
618C22#1568940111yescharacteristic
619C22#1568941611yescharacteristic
620C22#1568942511yescharacteristic
621C22#1568942811yescharacteristic
622C22#1568943811yescharacteristic
623C22#1568944911yescharacteristic
624C22#1568946011yescharacteristic
625C22#1568946711yescharacteristic
626C22#1568952311yescharacteristic
627C22#1568952711yescharacteristic
628C22#1568953011yescharacteristic
629C22#1568953111yescharacteristic
630C4—44no—
631C4—82no—
632C4—3762no—
633C4—3762no—
634C4—1882no—
635C4—1882no—
636C4#1568898011yescharacteristic
637C4#1568901011yescharacteristic
638C4#1568902011yescharacteristic
639C4#1568902911yescharacteristic
640C4#1568904611yescharacteristic
641C4#1568905511yescharacteristic
642C4#1568905611yescharacteristic
643C4#1568906311yescharacteristic
644C2#2024164211yescharacteristic
645C2#2024372711yescharacteristic
646C2#2024373411yescharacteristic
647C2#2024396211yescharacteristic
648C2#2024398311yescharacteristic
649C2#2024412011yescharacteristic
650C2#2024412511yescharacteristic
651C2#2024457311yescharacteristic
652C2#2024459411yescharacteristic
653C2#2024471511yescharacteristic
654C2#2024472511yescharacteristic
655C2#2024477211yescharacteristic
656C2#2024477911yescharacteristic
657C2#2024486211yescharacteristic
658C2#2024487311yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#340C2
socle, prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC2×#340D47
hypocenterC47#11219
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
15. C2×#13093957C4semidirect
177. C2×C47⋊C8C4⋊C4semidirect
357. C47#11219semidirect

Maximal subgroups

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

subgroupindex
C22×#130939572
C2×#156890222
C2×#156888862
C2×#156888852
C2×#156888772
#202416172
C2×C47×#3402
#1121947