Finite Group Databasebeta

← #26125195

Subgroups — #26125195

Order 12032.

1254 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094023C211yesmaximal, characteristic
2C2×#15688886C211yesmaximal, characteristic
3C2×#15688885C211yesmaximal, characteristic
4C2×#15688885C211yesmaximal, characteristic
5C2×#15688877C211yesmaximal, characteristic
6#20241617C211yesmaximal, characteristic
7C2×C47×#340C211yesmaximal, characteristic
8C23×Dic94—21no—
9C23×C47⋊C8C2211yescharacteristic
10C2×#13094023—22no—
11C2×#13094023—22no—
12C2×#13094023—22no—
13C2×#13094023—22no—
14C2×#13094023—22no—
15C2×#13094023C414yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×Dic47⋊C4—21no—
19C22×C4×Dic47C2211yescharacteristic
20C2×C47⋊#95—21no—
21C2×C47⋊#95—21no—
22#15688886—22no—
23#15688885—22no—
24#15688885—22no—
25#15688877—22no—
26C23×C8×C47C2211yescharacteristic
27C22×C4⋊C4×C47C2211yescharacteristic
28C22×C4⋊C4×C47C2211yescharacteristic
29C47×#340—22no—
30C22×Dic94—24no—
31C22×Dic94—24no—
32C22×Dic94—24no—
33C22×Dic94—42no—
34C22×Dic94—42no—
35C22×Dic94—42no—
36C22×Dic94—42no—
37C23×Dic47—21no—
38C23×Dic47—21no—
39C23×Dic47D411yescharacteristic
40C23×Dic47D411yescharacteristic
41C22×C47⋊C8—21no—
42C22×C47⋊C8—21no—
43C22×C47⋊C8—21no—
44C22×C47⋊C8—21no—
45C22×C47⋊C8—21no—
46C22×C47⋊C8—21no—
47C22×C47⋊C8Q812yescomplemented
48#13094023—28no—
49#13094023—28no—
50#13094023—28no—
51#13094023—28no—
52C2×C4⋊Dic47—21no—
53C2×C4⋊Dic47—21no—
54C2×C4⋊Dic47—21no—
55C2×C4⋊Dic47—21no—
56C2×C4⋊Dic47—21no—
57C2×C4⋊Dic47—21no—
58C2×C4⋊Dic47—21no—
59C2×C4⋊Dic47—21no—
60C2×C4⋊Dic47C2×C412yes—
61C2×C4⋊Dic47D412yes—
62C2×C4⋊Dic47D412yes—
63C2×C4⋊Dic47Q812yescomplemented
64C2×Dic47⋊C4—24no—
65C2×Dic47⋊C4—24no—
66C2×Dic47⋊C4—24no—
67C2×C4×Dic47—21no—
68C2×C4×Dic47—21no—
69C2×C4×Dic47—21no—
70C2×C4×Dic47—21no—
71C2×C4×Dic47C2×C412yes—
72C2×C4×Dic47D412yes—
73C47⋊#95—42no—
74C47⋊#95—42no—
75C23×C4×C47—21no—
76C23×C4×C47—21no—
77C23×C4×C47C2311yescharacteristic
78C22×C8×C47—21no—
79C22×C8×C47—21no—
80C22×C8×C47—21no—
81C22×C8×C47—21no—
82C22×C8×C47—21no—
83C22×C8×C47—21no—
84C22×C8×C47Q812yescomplemented
85C2×C4⋊C4×C47—21no—
86C2×C4⋊C4×C47—21no—
87C2×C4⋊C4×C47—21no—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47C2×C412yes—
94C2×C4⋊C4×C47D412yes—
95C2×C4⋊C4×C47D412yes—
96C2×C4⋊C4×C47Q812yescomplemented
97C24×C47C2×D411yescharacteristic
98C22×C4×C47—22no—
99C22×C4×C47—22no—
100C22×C4×C47—22no—
101C22×C4×C47—22no—
102C22×C4×C47—41no—
103C22×C4×C47—41no—
104C22×C4×C47—41no—
105C22×C4×C47—41no—
106C22×C4×C47—41no—
107C22×C4×C47—41no—
108C22×C4×C47—41no—
109C22×C4×C47—41no—
110C22×C4×C47—41no—
111C22×C4×C47—41no—
112C22×C4×C47C22×C411yescharacteristic
113C22×C4×C47C2×D411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2×D411yescharacteristic
118C22×C4×C47C2×Q811yescharacteristic
119C22×C4×C47C2×Q811yescharacteristic
120C22×C4×C47C2×Q811yescharacteristic
121C22×C4×C47C2×Q811yescharacteristic
122C22×C4×C47#4111yescharacteristic
123C22×C4×C47#4111yescharacteristic
124C22×C4×C47#4111yescharacteristic
125C22×C4×C47#4111yescharacteristic
126C22×Dic47—21no—
127C22×Dic47—21no—
128C22×Dic47—21no—
129C22×Dic47—21no—
130C22×Dic47—21no—
131C22×Dic47—21no—
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—41no—
139C22×Dic47—41no—
140C22×Dic47—41no—
141C22×Dic47—41no—
142C22×Dic47—41no—
143C22×Dic47—41no—
144C22×Dic47—41no—
145C22×Dic47—41no—
146C22×Dic47—41no—
147C22×Dic47—41no—
148C22×Dic47C22⋊C412yes—
149C22×Dic47C22⋊C412yes—
150C22×Dic47D812yes—
151C22×Dic47SD1612yes—
152C22×Dic47SD1612yes—
153C22×Dic47Q1612yes—
154C2×Dic94—216no—
155C2×Dic94—48no—
156C2×Dic94—48no—
157C2×Dic94—48no—
158C2×Dic94—48no—
159C2×Dic94—48no—
160C2×Dic94—48no—
161C2×C8×C47—22no—
162C2×C8×C47—22no—
163C2×C8×C47—22no—
164C2×C8×C47—41no—
165C2×C8×C47—41no—
166C2×C8×C47—41no—
167C2×C8×C47—41no—
168C4⋊C4×C47—22no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—22no—
171C4⋊C4×C47—22no—
172C4⋊C4×C47—22no—
173C4⋊C4×C47—41no—
174C4⋊C4×C47—41no—
175C4⋊C4×C47C22⋊C414yes—
176C4⋊Dic47—22no—
177C4⋊Dic47—22no—
178C4⋊Dic47—22no—
179C4⋊Dic47—22no—
180C4⋊Dic47—22no—
181C4⋊Dic47—41no—
182C4⋊Dic47—41no—
183C4⋊Dic47C22⋊C414yes—
184Dic47⋊C4—216no—
185C4×Dic47—22no—
186C4×Dic47—22no—
187C4×Dic47—22no—
188C4×Dic47—22no—
189C2×C47⋊C8—22no—
190C2×C47⋊C8—22no—
191C2×C47⋊C8—22no—
192C2×C47⋊C8—41no—
193C2×C47⋊C8—41no—
194C2×C47⋊C8—41no—
195C2×C47⋊C8—41no—
196C23×C47C2×C22⋊C411yescharacteristic
197C23×C47#12011yescharacteristic
198C23×C47#12011yescharacteristic
199C23×C47C22⋊Q811yescharacteristic
200C23×C47C22⋊Q811yescharacteristic
201C23×C47#12411yescharacteristic
202C23×C47C4⋊Q811yescharacteristic
203C23×C47C2×D811yescharacteristic
204C23×C47C2×SD1611yescharacteristic
205C23×C47C2×SD1611yescharacteristic
206C23×C47C2×Q1611yescharacteristic
207C23×C47AGL(1,ℤ/8)11yescharacteristic
208C23×C47AGL(1,ℤ/8)11yescharacteristic
209C23×C47#13711yescharacteristic
210C23×C47#13711yescharacteristic
211C2×C4×C47—24no—
212C2×C4×C47—42no—
213C2×C4×C47—42no—
214C2×C4×C47—42no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—81no—
222C2×C4×C47—81no—
223C2×C4×C47—81no—
224C2×C4×C47—81no—
225C2×C4×C47C2×C22⋊C411yescharacteristic
226C2×C4×C47C2×C22⋊C411yescharacteristic
227C2×C4×C47C4×Q811yescharacteristic
228C2×C4×C47C4×Q811yescharacteristic
229C2×C4×C47C4×Q811yescharacteristic
230C2×C4×C47C4×Q811yescharacteristic
231C2×C4×C47#12011yescharacteristic
232C2×C4×C47#12011yescharacteristic
233C2×C4×C47C22⋊Q811yescharacteristic
234C2×C4×C47C22⋊Q811yescharacteristic
235C2×C4×C47C22⋊Q811yescharacteristic
236C2×C4×C47C22⋊Q811yescharacteristic
237C2×C4×C47C22⋊Q811yescharacteristic
238C2×C4×C47C22⋊Q811yescharacteristic
239C2×C4×C47C22⋊Q811yescharacteristic
240C2×C4×C47C22⋊Q811yescharacteristic
241C2×C4×C47C22⋊Q811yescharacteristic
242C2×C4×C47C22⋊Q811yescharacteristic
243C2×C4×C47#12411yescharacteristic
244C2×C4×C47#12411yescharacteristic
245C2×C4×C47#12411yescharacteristic
246C2×C4×C47#12411yescharacteristic
247C2×C4×C47#12411yescharacteristic
248C2×C4×C47C4⋊Q811yescharacteristic
249C2×C4×C47C4⋊Q811yescharacteristic
250C2×C4×C47C4⋊Q811yescharacteristic
251C2×C4×C47C4⋊Q811yescharacteristic
252C2×C4×C47C4⋊Q811yescharacteristic
253C2×Dic47—22no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—22no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—22no—
262C2×Dic47—22no—
263C2×Dic47—22no—
264C2×Dic47—22no—
265C2×Dic47—24no—
266C2×Dic47—42no—
267C2×Dic47—42no—
268C2×Dic47—42no—
269C2×Dic47—42no—
270C2×Dic47—42no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C2×Dic47—42no—
274C2×Dic47—42no—
275C2×Dic47—81no—
276C2×Dic47—81no—
277C2×Dic47—81no—
278C2×Dic47—81no—
279C2×Dic47#10214yes—
280C2×Dic47#10314yes—
281Dic94—432no—
282C8×C47—42no—
283C47⋊C8—42no—
284#11384—471nomaximal, Sylow
285C22×C47#37911yescharacteristic
286C22×C47#39111yescharacteristic
287C22×C47#39111yescharacteristic
288C22×C47#39311yescharacteristic
289C22×C47#39311yescharacteristic
290C22×C47#39511yescharacteristic
291C22×C47#39511yescharacteristic
292C22×C47C2×#10211yescharacteristic
293C22×C47C2×#10311yescharacteristic
294C22×C47#41811yescharacteristic
295C22×C47#41911yescharacteristic
296C22×C47#44711yescharacteristic
297C22×C47#44711yescharacteristic
298C22×C47#44811yescharacteristic
299C22×C47#44811yescharacteristic
300C22×C47#45011yescharacteristic
301C22×C47#45011yescharacteristic
302C22×C47#45111yescharacteristic
303C22×C47#45111yescharacteristic
304C22×C47#47411yescharacteristic
305C22×C47#47411yescharacteristic
306C22×C47#47511yescharacteristic
307C22×C47#47511yescharacteristic
308C22×C47#47611yescharacteristic
309C22×C47#47611yescharacteristic
310C22×C47#47711yescharacteristic
311C22×C47#47711yescharacteristic
312C22×C47#48611yescharacteristic
313C22×C47#48711yescharacteristic
314C22×C47#48911yescharacteristic
315C22×C47#48911yescharacteristic
316C22×C47#49811yescharacteristic
317C22×C47#50011yescharacteristic
318C22×C47#50111yescharacteristic
319C22×C47#50111yescharacteristic
320C4×C47—44no—
321C4×C47—82no—
322C4×C47#39111yescharacteristic
323C4×C47#39111yescharacteristic
324C4×C47#39111yescharacteristic
325C4×C47#39111yescharacteristic
326C4×C47#39311yescharacteristic
327C4×C47#39311yescharacteristic
328C4×C47#39511yescharacteristic
329C4×C47#39511yescharacteristic
330Dic47—24no—
331Dic47—24no—
332Dic47—44no—
333Dic47—82no—
334C22×C4⋊Q8—471no—
335C2×#340—471no—
336C2×#340—471no—
337C2×#340—471no—
338C2×#340D4711yescharacteristic
339C2×#336—471no—
340C4⋊#95—471no—
341C2×C47#144611yescharacteristic
342C2×C47#178611yescharacteristic
343C2×C47#178711yescharacteristic
344C2×C47#198711yescharacteristic
345C2×C47#198811yescharacteristic
346C2×C47#199011yescharacteristic
347C2×C47#199311yescharacteristic
348C2×C47#202311yescharacteristic
349C2×C47#202311yescharacteristic
350C2×C47#202411yescharacteristic
351C2×C47#202411yescharacteristic
352C2×C47#205711yescharacteristic
353C2×C47#205711yescharacteristic
354C2×C47#205811yescharacteristic
355C2×C47#205811yescharacteristic
356C23×Q8—941no—
357C23×C8—471no—
358C23×C8C2×D4711yescharacteristic
359C2×C4⋊Q8—474no—
360C2×C4⋊Q8—942no—
361C2×C4⋊Q8—942no—
362C2×C4⋊Q8—942no—
363C2×C4⋊Q8—942no—
364C2×C4⋊Q8—942no—
365C22×C4⋊C4—471no—
366C22×C4⋊C4—471no—
367C22×C4⋊C4—941no—
368C22×C4⋊C4C2×D4711yescharacteristic
369C22×C4⋊C4C2×D4711yescharacteristic
370C22×C42—471no—
371C2×#95—941no—
372C2×#95—941no—
373#340—22no—
374#340—942no—
375#340—942no—
376#340—942no—
377#336—942no—
378C47#1138411yescharacteristic, complemented, Sylow
379C22×Q8—944no—
380C22×Q8—944no—
381C22×Q8—944no—
382C22×Q8—1882no—
383C22×Q8—1882no—
384C22×Q8—1882no—
385C22×Q8—1882no—
386C23×C4—21no—
387C23×C4—21no—
388C23×C4—471no—
389C23×C4—471no—
390C23×C4—941no—
391C23×C4—941no—
392C23×C4C22×D4711yescharacteristic
393C22×C8—21no—
394C22×C8—21no—
395C22×C8—21no—
396C22×C8—21no—
397C22×C8—21no—
398C22×C8—21no—
399C22×C8—472no—
400C22×C8—941no—
401C22×C8—941no—
402C22×C8—941no—
403C22×C8—941no—
404C22×C8—941no—
405C22×C8—941no—
406C22×C8Dic9412yescomplemented
407C4⋊Q8—948no—
408C4⋊Q8—948no—
409C4⋊Q8—948no—
410C4⋊Q8—948no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—472no—
420C2×C4⋊C4—472no—
421C2×C4⋊C4—472no—
422C2×C4⋊C4—472no—
423C2×C4⋊C4—944no—
424C2×C4⋊C4—944no—
425C2×C4⋊C4—944no—
426C2×C4⋊C4—941no—
427C2×C4⋊C4—941no—
428C2×C4⋊C4—941no—
429C2×C4⋊C4—941no—
430C2×C4⋊C4—941no—
431C2×C4⋊C4—941no—
432C2×C4⋊C4—941no—
433C2×C4⋊C4—941no—
434C2×C4⋊C4Dic9412yescomplemented
435C2×C4⋊C4C4×D4712yes—
436C2×C4⋊C4D18812yes—
437C2×C4⋊C4C22⋊D4712yes—
438C2×C42—472no—
439C2×C42—472no—
440C2×C42—941no—
441C2×C42—941no—
442C2×C42—941no—
443C2×C42—941no—
444#95—1882no—
445#95—1882no—
446C24D4×D4711yescharacteristic
447C2×Q8—9416no—
448C2×Q8—1888no—
449C2×Q8—1888no—
450C2×Q8—1888no—
451C2×Q8—1888no—
452C2×Q8—1888no—
453C2×Q8—1888no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—472no—
469C22×C4—472no—
470C22×C4—472no—
471C22×C4—472no—
472C22×C4—472no—
473C22×C4—472no—
474C22×C4—941no—
475C22×C4—941no—
476C22×C4—941no—
477C22×C4—941no—
478C22×C4—941no—
479C22×C4—941no—
480C22×C4—941no—
481C22×C4—941no—
482C22×C4—942no—
483C22×C4—942no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4—1881no—
487C22×C4—1881no—
488C22×C4—1881no—
489C22×C4—1881no—
490C22×C4—1881no—
491C22×C4—1881no—
492C22×C4—1881no—
493C22×C4—1881no—
494C22×C4—1881no—
495C22×C4—1881no—
496C22×C4C2×Dic9411yescharacteristic
497C22×C4C2×Dic9411yescharacteristic
498C22×C4C2×C4×D4711yescharacteristic
499C22×C4C2×D18811yescharacteristic
500C22×C4#1062535011yescharacteristic
501C22×C4#1062535011yescharacteristic
502C22×C4D4×D4711yescharacteristic
503C22×C4D4×D4711yescharacteristic
504C22×C4D4×D4711yescharacteristic
505C22×C4#1062535211yescharacteristic
506C22×C4#1062535211yescharacteristic
507C22×C4Q8×D4711yescharacteristic
508C22×C4Q8×D4711yescharacteristic
509C22×C4C2×C22⋊D4711yescharacteristic
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—942no—
518C2×C8—942no—
519C2×C8—942no—
520C2×C8—1881no—
521C2×C8—1881no—
522C2×C8—1881no—
523C2×C8—1881no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—474no—
532C4⋊C4—9416no—
533C4⋊C4—942no—
534C4⋊C4—942no—
535C4⋊C4—942no—
536C4⋊C4—942no—
537C4⋊C4—942no—
538C4⋊C4—1881no—
539C4⋊C4—1881no—
540C4⋊C4(C2×D47)⋊C414yes—
541C42—942no—
542C42—942no—
543C42—942no—
544C42—942no—
545C23C22⋊C4×D4711yescharacteristic
546C23#1309399211yescharacteristic
547C23#1309399411yescharacteristic
548C23#1309400111yescharacteristic
549C23#1309400211yescharacteristic
550C23#1309401011yescharacteristic
551C23#1309402311yescharacteristic
552C23D8×D4711yescharacteristic
553C23SD16×D4711yescharacteristic
554C23SD16×D4711yescharacteristic
555C23Q16×D4711yescharacteristic
556C23#1309404811yescharacteristic
557C23#1309405111yescharacteristic
558C23#1309405311yescharacteristic
559C23#1309405611yescharacteristic
560Q8—18832no—
561C2×C4—24no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—81no—
572C2×C4—81no—
573C2×C4—81no—
574C2×C4—81no—
575C2×C4—474no—
576C2×C4—474no—
577C2×C4—942no—
578C2×C4—942no—
579C2×C4—942no—
580C2×C4—942no—
581C2×C4—942no—
582C2×C4—942no—
583C2×C4—942no—
584C2×C4—942no—
585C2×C4—942no—
586C2×C4—942no—
587C2×C4—942no—
588C2×C4—942no—
589C2×C4—944no—
590C2×C4—3761no—
591C2×C4—3761no—
592C2×C4—3761no—
593C2×C4—3761no—
594C2×C4—1882no—
595C2×C4—1882no—
596C2×C4—1882no—
597C2×C4—1882no—
598C2×C4—1882no—
599C2×C4—1882no—
600C2×C4—1882no—
601C2×C4—1882no—
602C2×C4—1882no—
603C2×C4C22⋊C4×D4711yescharacteristic
604C2×C4C2×(C2×D47)⋊C411yescharacteristic
605C2×C4#1309398911yescharacteristic
606C2×C4#1309398911yescharacteristic
607C2×C4C4×Dic9411yescharacteristic
608C2×C4C4×Dic9411yescharacteristic
609C2×C4#1309399211yescharacteristic
610C2×C4#1309399411yescharacteristic
611C2×C4#1309400111yescharacteristic
612C2×C4#1309400111yescharacteristic
613C2×C4#1309400111yescharacteristic
614C2×C4#1309400211yescharacteristic
615C2×C4#1309400211yescharacteristic
616C2×C4#1309400211yescharacteristic
617C2×C4#1309400311yescharacteristic
618C2×C4#1309400311yescharacteristic
619C2×C4#1309400411yescharacteristic
620C2×C4#1309400411yescharacteristic
621C2×C4#1309401011yescharacteristic
622C2×C4#1309401011yescharacteristic
623C2×C4#1309401011yescharacteristic
624C2×C4#1309401111yescharacteristic
625C2×C4#1309401211yescharacteristic
626C2×C4#1309402211yescharacteristic
627C2×C4#1309402311yescharacteristic
628C2×C4#1309402311yescharacteristic
629C2×C4#1309402311yescharacteristic
630C2×C4#1309402411yescharacteristic
631C8—42no—
632C8—1882no—
633C22#1568897811yescharacteristic
634C22#1568902711yescharacteristic
635C22#1568902711yescharacteristic
636C22#1568903511yescharacteristic
637C22#1568903611yescharacteristic
638C22#1568904311yescharacteristic
639C22#1568904411yescharacteristic
640C22#102×D4711yescharacteristic
641C22#103×D4711yescharacteristic
642C22#1568912611yescharacteristic
643C22#1568913011yescharacteristic
644C22#1568925511yescharacteristic
645C22#1568925811yescharacteristic
646C22#1568926011yescharacteristic
647C22#1568926311yescharacteristic
648C22#1568927211yescharacteristic
649C22#1568927511yescharacteristic
650C22#1568927711yescharacteristic
651C22#1568928011yescharacteristic
652C22#1568940111yescharacteristic
653C22#1568940211yescharacteristic
654C22#1568940611yescharacteristic
655C22#1568940711yescharacteristic
656C22#1568941111yescharacteristic
657C22#1568941211yescharacteristic
658C22#1568941611yescharacteristic
659C22#1568941711yescharacteristic
660C22#1568946811yescharacteristic
661C22#1568947211yescharacteristic
662C22#1568948111yescharacteristic
663C22#1568948411yescharacteristic
664C22#1568952011yescharacteristic
665C22#1568952711yescharacteristic
666C22#1568953011yescharacteristic
667C22#1568953111yescharacteristic
668C4—44no—
669C4—82no—
670C4—944no—
671C4—944no—
672C4—3762no—
673C4—1884no—
674C4#1568902711yescharacteristic
675C4#1568902711yescharacteristic
676C4#1568902811yescharacteristic
677C4#1568902911yescharacteristic
678C4#1568903511yescharacteristic
679C4#1568903611yescharacteristic
680C4#1568904311yescharacteristic
681C4#1568904411yescharacteristic
682C2#2024165811yescharacteristic
683C2#2024331711yescharacteristic
684C2#2024332111yescharacteristic
685C2#2024433411yescharacteristic
686C2#2024433811yescharacteristic
687C2#2024434711yescharacteristic
688C2#2024435911yescharacteristic
689C2#2024452211yescharacteristic
690C2#2024452311yescharacteristic
691C2#2024452711yescharacteristic
692C2#2024452811yescharacteristic
693C2#2024471411yescharacteristic
694C2#2024471511yescharacteristic
695C2#2024471911yescharacteristic
696C2#2024472011yescharacteristic
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#11384
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×#13094023C4semidirect
47. C22×C47⋊C8Q8semidirect
63. C2×C4⋊Dic47Q8semidirect
84. C22×C8×C47Q8semidirect
96. C2×C4⋊C4×C47Q8semidirect
378. C47#11384semidirect
406. C22×C8Dic94semidirect
434. C2×C4⋊C4Dic94semidirect

Maximal subgroups

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

subgroupindex
C22×#130940232
C2×#156888862
C2×#156888852
C2×#156888772
#202416172
C2×C47×#3402
#1138447