Finite Group Databasebeta

← #26121937

Subgroups — #26121937

Order 12032.

914 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic47C211yesmaximal, characteristic
2C2×#15688886C211yesmaximal, characteristic
3C2×#15688885C211yesmaximal, characteristic
4C2×#15688885C211yesmaximal, characteristic
5C2×#15688877C211yesmaximal, characteristic
6#20241617C211yesmaximal, characteristic
7C2×C47×#340C211yesmaximal, characteristic
8C23×C47⋊C8C2211yescharacteristic
9C22×C4⋊Dic47C2211yescharacteristic
10C22×C4⋊Dic47C2211yescharacteristic
11C22×C4×Dic47—21no—
12C22×C4×Dic47C2211yescharacteristic
13C4⋊C4×Dic47—22no—
14C4⋊C4×Dic47C414yescomplemented
15C2×C47⋊#95—21no—
16C2×C47⋊#95—21no—
17C2×C47⋊#95—21no—
18#15688886—22no—
19#15688885—22no—
20#15688885C414yescomplemented
21#15688877—22no—
22C23×C8×C47C2211yescharacteristic
23C22×C4⋊C4×C47C2211yescharacteristic
24C22×C4⋊C4×C47C2211yescharacteristic
25C47×#340C414yescomplemented
26C23×Dic47—21no—
27C23×Dic47—21no—
28C23×Dic47D411yescharacteristic
29C23×Dic47D411yescharacteristic
30C22×C47⋊C8—21no—
31C22×C47⋊C8—21no—
32C22×C47⋊C8—21no—
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36C22×C47⋊C8C2×C412yes—
37C2×C4⋊Dic47—21no—
38C2×C4⋊Dic47—21no—
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⋊Dic47C2×C412yes—
46C2×C4⋊Dic47C2×C412yes—
47C2×C4⋊Dic47D412yes—
48C2×C4⋊Dic47Q812yes—
49C2×C4×Dic47—21no—
50C2×C4×Dic47—21no—
51C2×C4×Dic47—21no—
52C2×C4×Dic47—21no—
53C2×C4×Dic47—24no—
54C2×C4×Dic47—42no—
55C2×C4×Dic47—42no—
56C2×C4×Dic47C2×C412yes—
57C2×C4×Dic47D412yes—
58C47⋊#95—24no—
59C47⋊#95—42no—
60C47⋊#95—42no—
61C23×C4×C47—21no—
62C23×C4×C47—21no—
63C23×C4×C47C2311yescharacteristic
64C22×C8×C47—21no—
65C22×C8×C47—21no—
66C22×C8×C47—21no—
67C22×C8×C47—21no—
68C22×C8×C47—21no—
69C22×C8×C47—21no—
70C22×C8×C47C2×C412yes—
71C2×C4⋊C4×C47—21no—
72C2×C4⋊C4×C47—21no—
73C2×C4⋊C4×C47—21no—
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×C47C2×C412yes—
80C2×C4⋊C4×C47C2×C412yes—
81C2×C4⋊C4×C47C2×C412yes—
82C2×C4⋊C4×C47C2×C412yes—
83C24×C47C2×D411yescharacteristic
84C22×C4×C47—22no—
85C22×C4×C47—22no—
86C22×C4×C47—22no—
87C22×C4×C47—22no—
88C22×C4×C47—41no—
89C22×C4×C47—41no—
90C22×C4×C47—41no—
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×C47C22×C411yescharacteristic
99C22×C4×C47C22×C411yescharacteristic
100C22×C4×C47C22×C411yescharacteristic
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47C2×Q811yescharacteristic
104C22×C4×C47#4111yescharacteristic
105C22×C4×C47#4111yescharacteristic
106C22×C4×C47#4111yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C22×C4×C47#4111yescharacteristic
111C22×C4×C47#4111yescharacteristic
112C22×Dic47—21no—
113C22×Dic47—21no—
114C22×Dic47—21no—
115C22×Dic47—21no—
116C22×Dic47—22no—
117C22×Dic47—22no—
118C22×Dic47—22no—
119C22×Dic47—21no—
120C22×Dic47—21no—
121C22×Dic47—21no—
122C22×Dic47—21no—
123C22×Dic47—21no—
124C22×Dic47—21no—
125C22×Dic47—22no—
126C22×Dic47—41no—
127C22×Dic47—41no—
128C22×Dic47—41no—
129C22×Dic47—41no—
130C22×Dic47—41no—
131C22×Dic47—41no—
132C22×Dic47—41no—
133C22×Dic47—41no—
134C22×Dic47—41no—
135C22×Dic47—41no—
136C22×Dic47C22⋊C412yes—
137C22×Dic47C22⋊C412yes—
138C22×Dic47SD1612yes—
139C22×Dic47Q1612yes—
140C2×C8×C47—22no—
141C2×C8×C47—22no—
142C2×C8×C47—22no—
143C2×C8×C47—41no—
144C2×C8×C47—41no—
145C2×C8×C47—41no—
146C2×C8×C47—41no—
147C4⋊C4×C47—22no—
148C4⋊C4×C47—22no—
149C4⋊C4×C47—22no—
150C4⋊C4×C47—22no—
151C4⋊C4×C47—22no—
152C4⋊C4×C47—41no—
153C4⋊C4×C47—41no—
154C4⋊C4×C47C4214yes—
155C4⋊Dic47—22no—
156C4⋊Dic47—22no—
157C4⋊Dic47—22no—
158C4⋊Dic47—22no—
159C4⋊Dic47—22no—
160C4⋊Dic47—41no—
161C4⋊Dic47—41no—
162C4⋊Dic47C4⋊C414yes—
163C4×Dic47—22no—
164C4×Dic47—22no—
165C4×Dic47—22no—
166C4×Dic47—22no—
167C4×Dic47—48no—
168C2×C47⋊C8—22no—
169C2×C47⋊C8—22no—
170C2×C47⋊C8—22no—
171C2×C47⋊C8—41no—
172C2×C47⋊C8—41no—
173C2×C47⋊C8—41no—
174C2×C47⋊C8—41no—
175C23×C47C2×C22⋊C411yescharacteristic
176C23×C47C4×D411yescharacteristic
177C23×C47C4×D411yescharacteristic
178C23×C47#12111yescharacteristic
179C23×C47C22⋊Q811yescharacteristic
180C23×C47#12311yescharacteristic
181C23×C47#12311yescharacteristic
182C23×C47C2×SD1611yescharacteristic
183C23×C47C2×Q1611yescharacteristic
184C23×C47#13511yescharacteristic
185C23×C47#13511yescharacteristic
186C23×C47AGL(1,ℤ/8)11yescharacteristic
187C23×C47AGL(1,ℤ/8)11yescharacteristic
188C23×C47AGL(1,ℤ/8)11yescharacteristic
189C23×C47#13711yescharacteristic
190C2×C4×C47—24no—
191C2×C4×C47—42no—
192C2×C4×C47—42no—
193C2×C4×C47—42no—
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—81no—
201C2×C4×C47—81no—
202C2×C4×C47—81no—
203C2×C4×C47—81no—
204C2×C4×C47C2×C4211yescharacteristic
205C2×C4×C47C2×C4⋊C411yescharacteristic
206C2×C4×C47#11711yescharacteristic
207C2×C4×C47#11711yescharacteristic
208C2×C4×C47#11711yescharacteristic
209C2×C4×C47#11711yescharacteristic
210C2×C4×C47#11711yescharacteristic
211C2×C4×C47#11711yescharacteristic
212C2×C4×C47#11711yescharacteristic
213C2×C4×C47#11711yescharacteristic
214C2×C4×C47C4×D411yescharacteristic
215C2×C4×C47C4×D411yescharacteristic
216C2×C4×C47C4×D411yescharacteristic
217C2×C4×C47C4×D411yescharacteristic
218C2×C4×C47C4×Q811yescharacteristic
219C2×C4×C47C4×Q811yescharacteristic
220C2×C4×C47#12111yescharacteristic
221C2×C4×C47C22⋊Q811yescharacteristic
222C2×C4×C47#12311yescharacteristic
223C2×C4×C47#12311yescharacteristic
224C2×C4×C47#12411yescharacteristic
225C2×C4×C47#12411yescharacteristic
226C2×C4×C47#12511yescharacteristic
227C2×C4×C47#12511yescharacteristic
228C2×C4×C47#12611yescharacteristic
229C2×C4×C47#12611yescharacteristic
230C2×C4×C47#12611yescharacteristic
231C2×C4×C47#12611yescharacteristic
232C2×Dic47—22no—
233C2×Dic47—22no—
234C2×Dic47—22no—
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—22no—
238C2×Dic47—24no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—22no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244C2×Dic47—42no—
245C2×Dic47—42no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47—81no—
256C2×Dic47—81no—
257C2×Dic47—81no—
258C2×Dic47—81no—
259C2×Dic47#10314yes—
260C8×C47—42no—
261C47⋊C8—42no—
262#10807—471nomaximal, Sylow
263C22×C47C4×C22⋊C411yescharacteristic
264C22×C47#38011yescharacteristic
265C22×C47#38111yescharacteristic
266C22×C47#38711yescharacteristic
267C22×C47#38711yescharacteristic
268C22×C47#38811yescharacteristic
269C22×C47#38811yescharacteristic
270C22×C47C2×#10311yescharacteristic
271C22×C47#41611yescharacteristic
272C22×C47#41711yescharacteristic
273C22×C47#41811yescharacteristic
274C22×C47C4×SD1611yescharacteristic
275C22×C47C4×SD1611yescharacteristic
276C22×C47C4×Q1611yescharacteristic
277C22×C47C4×Q1611yescharacteristic
278C22×C47#44011yescharacteristic
279C22×C47#44011yescharacteristic
280C22×C47#44211yescharacteristic
281C22×C47#44211yescharacteristic
282C22×C47#46011yescharacteristic
283C22×C47#46211yescharacteristic
284C22×C47#46311yescharacteristic
285C22×C47#46311yescharacteristic
286C22×C47#47511yescharacteristic
287C22×C47#47711yescharacteristic
288C22×C47#47811yescharacteristic
289C22×C47#47811yescharacteristic
290C22×C47#48111yescharacteristic
291C22×C47#48111yescharacteristic
292C22×C47#48211yescharacteristic
293C22×C47#48211yescharacteristic
294C22×C47#48411yescharacteristic
295C22×C47#48411yescharacteristic
296C22×C47#48511yescharacteristic
297C22×C47#48511yescharacteristic
298C4×C47—44no—
299C4×C47—82no—
300C4×C47#37611yescharacteristic
301C4×C47C4×C4⋊C411yescharacteristic
302C4×C47#38211yescharacteristic
303C4×C47#38311yescharacteristic
304C4×C47#38711yescharacteristic
305C4×C47#38711yescharacteristic
306C4×C47#38811yescharacteristic
307C4×C47#38811yescharacteristic
308Dic47—24no—
309Dic47—44no—
310Dic47—42no—
311Dic47—82no—
312C2×C4×C4⋊C4—471no—
313C2×#340—471no—
314C2×#340—471no—
315C2×#340—471no—
316C2×#340D4711yescharacteristic
317C2×#336—471no—
318C4⋊#95—471no—
319C2×C47#143411yescharacteristic
320C2×C47C4×#10311yescharacteristic
321C2×C47#176211yescharacteristic
322C2×C47#180311yescharacteristic
323C2×C47#180411yescharacteristic
324C2×C47#182411yescharacteristic
325C2×C47#182511yescharacteristic
326C2×C47#191911yescharacteristic
327C2×C47#191911yescharacteristic
328C2×C47#192111yescharacteristic
329C2×C47#192111yescharacteristic
330C2×C47#192611yescharacteristic
331C2×C47#192611yescharacteristic
332C2×C47#192811yescharacteristic
333C2×C47#192811yescharacteristic
334C23×C8—471no—
335C23×C8C2×D4711yescharacteristic
336C22×C4⋊C4—471no—
337C22×C4⋊C4—471no—
338C22×C4⋊C4C2×D4711yescharacteristic
339C22×C4⋊C4C2×D4711yescharacteristic
340C22×C42—471no—
341C22×C42—941no—
342C4×C4⋊C4—474no—
343C4×C4⋊C4—942no—
344C2×#95—941no—
345C2×#95—941no—
346C2×#95—941no—
347#340—474no—
348#340—942no—
349#340—942no—
350#340Dic4714yescomplemented
351#336—942no—
352C47#1080711yescharacteristic, complemented, Sylow
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—471no—
356C23×C4—471no—
357C23×C4—941no—
358C23×C4—941no—
359C23×C4C22×D4711yescharacteristic
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—472no—
367C22×C8—941no—
368C22×C8—941no—
369C22×C8—941no—
370C22×C8—941no—
371C22×C8—941no—
372C22×C8—941no—
373C22×C8C2×Dic4712yes—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—472no—
383C2×C4⋊C4—472no—
384C2×C4⋊C4—472no—
385C2×C4⋊C4—472no—
386C2×C4⋊C4—941no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4—941no—
389C2×C4⋊C4—941no—
390C2×C4⋊C4—941no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4—941no—
393C2×C4⋊C4—941no—
394C2×C4⋊C4C4×D4712yes—
395C2×C4⋊C4C4×D4712yes—
396C2×C4⋊C4C2×Dic4712yes—
397C2×C4⋊C4C2×Dic4712yes—
398C2×C42—472no—
399C2×C42—472no—
400C2×C42—941no—
401C2×C42—941no—
402C2×C42—941no—
403C2×C42—941no—
404C2×C42—944no—
405C2×C42—1882no—
406C2×C42—1882no—
407#95—944no—
408#95—1882no—
409#95—1882no—
410C24D4×D4711yescharacteristic
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—472no—
426C22×C4—472no—
427C22×C4—472no—
428C22×C4—472no—
429C22×C4—941no—
430C22×C4—941no—
431C22×C4—941no—
432C22×C4—941no—
433C22×C4—942no—
434C22×C4—942no—
435C22×C4—942no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4—941no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—942no—
443C22×C4—1881no—
444C22×C4—1881no—
445C22×C4—1881no—
446C22×C4—1881no—
447C22×C4—1881no—
448C22×C4—1881no—
449C22×C4—1881no—
450C22×C4—1881no—
451C22×C4—1881no—
452C22×C4—1881no—
453C22×C4C2×C4×D4711yescharacteristic
454C22×C4C2×C4×D4711yescharacteristic
455C22×C4#1062535011yescharacteristic
456C22×C4#1062535011yescharacteristic
457C22×C4#1062535011yescharacteristic
458C22×C4#1062535011yescharacteristic
459C22×C4D4×D4711yescharacteristic
460C22×C4D4×D4711yescharacteristic
461C22×C4#1062535211yescharacteristic
462C22×C4#1062535211yescharacteristic
463C22×C4#1062535211yescharacteristic
464C22×C4Q8×D4711yescharacteristic
465C22×C4#1062535411yescharacteristic
466C22×C4C22×Dic4711yescharacteristic
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—942no—
475C2×C8—942no—
476C2×C8—942no—
477C2×C8—1881no—
478C2×C8—1881no—
479C2×C8—1881no—
480C2×C8—1881no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—474no—
489C4⋊C4—942no—
490C4⋊C4—942no—
491C4⋊C4—942no—
492C4⋊C4—942no—
493C4⋊C4—942no—
494C4⋊C4—1881no—
495C4⋊C4—1881no—
496C4⋊C4C4×Dic4714yes—
497C42—942no—
498C42—942no—
499C42—942no—
500C42—942no—
501C42—1888no—
502C23C22⋊C4×D4711yescharacteristic
503C23(C22⋊D47)⋊C411yescharacteristic
504C23D4×Dic4711yescharacteristic
505C23#1309399711yescharacteristic
506C23#1309400211yescharacteristic
507C23#1309400611yescharacteristic
508C23#1309400911yescharacteristic
509C23SD16×D4711yescharacteristic
510C23Q16×D4711yescharacteristic
511C23#1309404511yescharacteristic
512C23#1309404711yescharacteristic
513C23#1309404811yescharacteristic
514C23#1309404811yescharacteristic
515C23#1309405111yescharacteristic
516C23#1309405311yescharacteristic
517C2×C4—24no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—81no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—474no—
532C2×C4—942no—
533C2×C4—942no—
534C2×C4—942no—
535C2×C4—942no—
536C2×C4—942no—
537C2×C4—942no—
538C2×C4—944no—
539C2×C4—942no—
540C2×C4—942no—
541C2×C4—942no—
542C2×C4—3761no—
543C2×C4—3761no—
544C2×C4—3761no—
545C2×C4—3761no—
546C2×C4—1882no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4—1882no—
552C2×C4—1882no—
553C2×C4—1882no—
554C2×C4—1882no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4C2×C4×Dic4711yescharacteristic
560C2×C4C4⋊C4×D4711yescharacteristic
561C2×C4#1309398011yescharacteristic
562C2×C4#1309398111yescharacteristic
563C2×C4#1309398111yescharacteristic
564C2×C4#1309398111yescharacteristic
565C2×C4#1309398111yescharacteristic
566C2×C4#1309398211yescharacteristic
567C2×C4#1309398311yescharacteristic
568C2×C4#1309398311yescharacteristic
569C2×C4(C22⋊D47)⋊C411yescharacteristic
570C2×C4#1309398611yescharacteristic
571C2×C4D4×Dic4711yescharacteristic
572C2×C4D4×Dic4711yescharacteristic
573C2×C4#1309398911yescharacteristic
574C2×C4Q8×Dic4711yescharacteristic
575C2×C4#1309399711yescharacteristic
576C2×C4#1309400211yescharacteristic
577C2×C4#1309400611yescharacteristic
578C2×C4#1309400911yescharacteristic
579C2×C4#1309401011yescharacteristic
580C2×C4#1309401011yescharacteristic
581C2×C4#1309401411yescharacteristic
582C2×C4#1309401411yescharacteristic
583C2×C4#1309401711yescharacteristic
584C2×C4#1309401711yescharacteristic
585C2×C4#1309401911yescharacteristic
586C2×C4#1309401911yescharacteristic
587C8—42no—
588C8—1882no—
589C22C22⋊C4×Dic4711yescharacteristic
590C22#1568898211yescharacteristic
591C22#1568898511yescharacteristic
592C22#1568900511yescharacteristic
593C22#1568900911yescharacteristic
594C22#1568901211yescharacteristic
595C22#1568901611yescharacteristic
596C22#103×D4711yescharacteristic
597C22#1568911811yescharacteristic
598C22#1568912111yescharacteristic
599C22#1568912611yescharacteristic
600C22#1568920811yescharacteristic
601C22SD16×Dic4711yescharacteristic
602C22#1568921511yescharacteristic
603C22Q16×Dic4711yescharacteristic
604C22#1568922011yescharacteristic
605C22#1568922411yescharacteristic
606C22#1568923211yescharacteristic
607C22#1568923511yescharacteristic
608C22#1568932211yescharacteristic
609C22#1568933211yescharacteristic
610C22#1568933711yescharacteristic
611C22#1568934111yescharacteristic
612C22#1568940711yescharacteristic
613C22#1568941711yescharacteristic
614C22#1568942211yescharacteristic
615C22#1568942611yescharacteristic
616C22#1568944011yescharacteristic
617C22#1568944311yescharacteristic
618C22#1568944611yescharacteristic
619C22#1568945011yescharacteristic
620C22#1568945711yescharacteristic
621C22#1568946011yescharacteristic
622C22#1568946311yescharacteristic
623C22#1568946711yescharacteristic
624C4—44no—
625C4—82no—
626C4—944no—
627C4—3762no—
628C4—1882no—
629C4—1884no—
630C4#1568896911yescharacteristic
631C4C4⋊C4×Dic4711yescharacteristic
632C4#1568898711yescharacteristic
633C4#1568899011yescharacteristic
634C4#1568900511yescharacteristic
635C4#1568900911yescharacteristic
636C4#1568901211yescharacteristic
637C4#1568901611yescharacteristic
638C2#2024161311yescharacteristic
639C2#103×Dic4711yescharacteristic
640C2#2024321511yescharacteristic
641C2#2024339211yescharacteristic
642C2#2024339711yescharacteristic
643C2#2024347711yescharacteristic
644C2#2024348211yescharacteristic
645C2#2024396411yescharacteristic
646C2#2024396811yescharacteristic
647C2#2024397811yescharacteristic
648C2#2024398211yescharacteristic
649C2#2024401311yescharacteristic
650C2#2024401711yescharacteristic
651C2#2024402711yescharacteristic
652C2#2024403111yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#340C2
socle, prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC2×#340D47
hypocenterC47#10807
LCSG ▷ C2×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
14. C4⋊C4×Dic47C4semidirect
20. #15688885C4semidirect
25. C47×#340C4semidirect
350. #340Dic47semidirect
352. C47#10807semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic472
C2×#156888862
C2×#156888852
C2×#156888772
#202416172
C2×C47×#3402
#1080747