Finite Group Databasebeta

← #26121841

Subgroups — #26121841

Order 12032.

1802 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093986C211yesmaximal, characteristic
2C22×#13093946C211yesmaximal, characteristic
3C22×#13093944C211yesmaximal, characteristic
4C2×#15688885C211yesmaximal, characteristic, complemented
5C2×#15688877C211yesmaximal, characteristic, complemented
6#20241617C211yesmaximal, characteristic, complemented
7C2×C47×#340C211yesmaximal, characteristic, complemented
8C23×D188C2211yescharacteristic
9C23×C4×D47—21no—
10C23×C47⋊C8C2211yescharacteristic
11C2×#13093986—22no—
12C2×#13093986—22no—
13C2×#13093986—22no—
14C2×#13093986—22no—
15C2×#13093986—22no—
16C2×#13093986C414yescomplemented
17C22×C4⋊Dic47C2211yescharacteristic
18C22×(C2×D47)⋊C4—21no—
19C22×C4×Dic47C2211yescharacteristic
20C2×#13093946—22no—
21C2×#13093946—22no—
22C2×#13093946C414yescomplemented
23C2×#13093944—22no—
24C2×#13093944—22no—
25C2×#13093944C414yescomplemented
26C2×C47⋊#95—21no—
27C2×C47⋊#95—21no—
28#15688885—22no—
29#15688877—22no—
30C23×C8×C47C2211yescharacteristic
31C22×C4⋊C4×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C47×#340—22no—
34C24×D47—21no—
35C22×D188—21no—
36C22×D188—21no—
37C22×D188—21no—
38C22×D188—21no—
39C22×D188—21no—
40C22×D188—21no—
41C22×D188—21no—
42C22×D188C2×C412yes—
43C22×D188C2×C412yes—
44C22×D188C2×C412yes—
45C22×D188D412yes—
46C22×D188D412yes—
47C22×D188D412yes—
48C22×D188Q812yes—
49C23×Dic47—21no—
50C23×Dic47D411yescharacteristic
51C23×Dic47D411yescharacteristic
52C22×C4×D47—24no—
53C22×C4×D47—24no—
54C22×C4×D47—24no—
55C22×C4×D47—42no—
56C22×C4×D47—42no—
57C22×C4×D47—42no—
58C22×C4×D47—42no—
59C22×C47⋊C8—21no—
60C22×C47⋊C8—21no—
61C22×C47⋊C8—21no—
62C22×C47⋊C8—21no—
63C22×C47⋊C8—21no—
64C22×C47⋊C8—21no—
65C22×C47⋊C8C2×C412yescomplemented
66#13093986—28no—
67#13093986—28no—
68#13093986—28no—
69#13093986—28no—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47C2×C412yescomplemented
76C2×(C2×D47)⋊C4—24no—
77C2×(C2×D47)⋊C4—24no—
78C2×(C2×D47)⋊C4—24no—
79C2×C4×Dic47—21no—
80C2×C4×Dic47—21no—
81C2×C4×Dic47—21no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47C2×C412yes—
84C2×C4×Dic47D412yes—
85#13093946—28no—
86#13093944—28no—
87C47⋊#95—42no—
88C47⋊#95—42no—
89C23×C4×C47—21no—
90C23×C4×C47—21no—
91C23×C4×C47C2311yescharacteristic
92C22×C8×C47—21no—
93C22×C8×C47—21no—
94C22×C8×C47—21no—
95C22×C8×C47—21no—
96C22×C8×C47—21no—
97C22×C8×C47—21no—
98C22×C8×C47C2×C412yescomplemented
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47C2×C412yes—
108C2×C4⋊C4×C47C2×C412yescomplemented
109C2×C4⋊C4×C47D412yes—
110C2×C4⋊C4×C47D412yes—
111C24×C47C2×D411yescharacteristic
112C23×D47—22no—
113C23×D47—22no—
114C23×D47—22no—
115C23×D47—22no—
116C23×D47—22no—
117C23×D47—22no—
118C23×D47—22no—
119C23×D47—41no—
120C23×D47—41no—
121C23×D47—41no—
122C23×D47—41no—
123C23×D47—41no—
124C23×D47—41no—
125C23×D47—41no—
126C23×D47—41no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—41no—
132C22×C4×C47—41no—
133C22×C4×C47—41no—
134C22×C4×C47—41no—
135C22×C4×C47—41no—
136C22×C4×C47—41no—
137C22×C4×C47—41no—
138C22×C4×C47—41no—
139C22×C4×C47—41no—
140C22×C4×C47—41no—
141C22×C4×C47C22×C411yescharacteristic
142C22×C4×C47C22×C411yescharacteristic
143C22×C4×C47C22×C411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×Q811yescharacteristic
151C22×C4×C47#4111yescharacteristic
152C22×C4×C47#4111yescharacteristic
153C22×C4×C47#4111yescharacteristic
154C22×C4×C47#4111yescharacteristic
155C22×Dic47—21no—
156C22×Dic47—21no—
157C22×Dic47—21no—
158C22×Dic47—21no—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—22no—
166C22×Dic47—41no—
167C22×Dic47—41no—
168C22×Dic47—41no—
169C22×Dic47—41no—
170C22×Dic47—41no—
171C22×Dic47—41no—
172C22×Dic47C22⋊C412yes—
173C22×Dic47C22⋊C412yes—
174C22×Dic47D812yes—
175C22×Dic47SD1612yes—
176C2×D188—22no—
177C2×D188—22no—
178C2×D188—22no—
179C2×D188—22no—
180C2×D188—22no—
181C2×D188—22no—
182C2×D188—22no—
183C2×D188—22no—
184C2×D188—22no—
185C2×D188—22no—
186C2×D188—22no—
187C2×D188—22no—
188C2×D188—22no—
189C2×D188—22no—
190C2×D188—22no—
191C2×D188—22no—
192C2×D188—22no—
193C2×D188—22no—
194C2×D188—22no—
195C2×D188—22no—
196C2×D188—22no—
197C2×D188C4214yes—
198C2×D188C22⋊C414yes—
199C2×D188C22⋊C414yes—
200C2×D188C22⋊C414yes—
201C2×D188C4⋊C414yes—
202C2×D188C4⋊C414yes—
203C2×D188C4⋊C414yes—
204C2×C4×D47—216no—
205C2×C4×D47—48no—
206C2×C4×D47—48no—
207C2×C4×D47—48no—
208C2×C4×D47—48no—
209C2×C4×D47—48no—
210C2×C4×D47—48no—
211C2×C8×C47—22no—
212C2×C8×C47—22no—
213C2×C8×C47—22no—
214C2×C8×C47—41no—
215C2×C8×C47—41no—
216C2×C8×C47—41no—
217C2×C8×C47—41no—
218C4⋊C4×C47—22no—
219C4⋊C4×C47—22no—
220C4⋊C4×C47—22no—
221C4⋊C4×C47—22no—
222C4⋊C4×C47—22no—
223C4⋊C4×C47—41no—
224C4⋊C4×C47—41no—
225C4⋊C4×C47C22⋊C414yes—
226(C2×D47)⋊C4—216no—
227C4⋊Dic47—22no—
228C4⋊Dic47—22no—
229C4⋊Dic47—41no—
230C4⋊Dic47—41no—
231C4×Dic47—22no—
232C4×Dic47—22no—
233C4×Dic47—22no—
234C4×Dic47—22no—
235C2×C47⋊C8—22no—
236C2×C47⋊C8—22no—
237C2×C47⋊C8—22no—
238C2×C47⋊C8—41no—
239C2×C47⋊C8—41no—
240C2×C47⋊C8—41no—
241C2×C47⋊C8—41no—
242C23×C47C2×C22⋊C411yescharacteristic
243C23×C47C4×D411yescharacteristic
244C23×C47C4×D411yescharacteristic
245C23×C47#12011yescharacteristic
246C23×C47#12011yescharacteristic
247C23×C47#12111yescharacteristic
248C23×C47C22⋊Q811yescharacteristic
249C23×C47C2×D811yescharacteristic
250C23×C47C2×SD1611yescharacteristic
251C23×C47#13511yescharacteristic
252C23×C47#13511yescharacteristic
253C23×C47AGL(1,ℤ/8)11yescharacteristic
254C23×C47AGL(1,ℤ/8)11yescharacteristic
255C23×C47AGL(1,ℤ/8)11yescharacteristic
256C23×C47#13711yescharacteristic
257C22×D47—24no—
258C22×D47—24no—
259C22×D47—24no—
260C22×D47—24no—
261C22×D47—24no—
262C22×D47—24no—
263C22×D47—24no—
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×D47—42no—
279C22×D47—42no—
280C22×D47—42no—
281C22×D47—42no—
282C22×D47—42no—
283C22×D47—42no—
284C22×D47—42no—
285C22×D47—42no—
286C22×D47—42no—
287C22×D47—42no—
288C22×D47—42no—
289C22×D47—42no—
290C22×D47—42no—
291C22×D47—42no—
292C2×C4×C47—24no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—81no—
303C2×C4×C47—81no—
304C2×C4×C47—81no—
305C2×C4×C47—81no—
306C2×C4×C47C2×C4211yescharacteristic
307C2×C4×C47C2×C22⋊C411yescharacteristic
308C2×C4×C47C2×C22⋊C411yescharacteristic
309C2×C4×C47C2×C22⋊C411yescharacteristic
310C2×C4×C47C2×C22⋊C411yescharacteristic
311C2×C4×C47C2×C4⋊C411yescharacteristic
312C2×C4×C47C2×C4⋊C411yescharacteristic
313C2×C4×C47C2×C4⋊C411yescharacteristic
314C2×C4×C47#11711yescharacteristic
315C2×C4×C47#11711yescharacteristic
316C2×C4×C47C4×D411yescharacteristic
317C2×C4×C47C4×D411yescharacteristic
318C2×C4×C47C4×D411yescharacteristic
319C2×C4×C47C4×D411yescharacteristic
320C2×C4×C47C4×D411yescharacteristic
321C2×C4×C47C4×D411yescharacteristic
322C2×C4×C47#12011yescharacteristic
323C2×C4×C47#12011yescharacteristic
324C2×C4×C47#12111yescharacteristic
325C2×C4×C47#12111yescharacteristic
326C2×C4×C47#12111yescharacteristic
327C2×C4×C47C22⋊Q811yescharacteristic
328C2×C4×C47C22⋊Q811yescharacteristic
329C2×C4×C47C22⋊Q811yescharacteristic
330C2×C4×C47#12311yescharacteristic
331C2×C4×C47#12311yescharacteristic
332C2×C4×C47#12311yescharacteristic
333C2×C4×C47#12311yescharacteristic
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—41no—
344C2×Dic47—41no—
345C2×Dic47—41no—
346C2×Dic47—41no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349C2×Dic47—42no—
350C2×Dic47—81no—
351C2×Dic47—81no—
352C2×Dic47—81no—
353C2×Dic47—81no—
354C2×Dic47#10214yescomplemented
355D188—24no—
356D188—24no—
357D188—24no—
358D188—24no—
359D188—24no—
360D188—24no—
361D188—24no—
362D188#9518yescomplemented
363C4×D47—432no—
364C8×C47—42no—
365C47⋊C8—42no—
366#10788—471nomaximal, Sylow
367C22×C47C4×C22⋊C411yescharacteristic
368C22×C47#37911yescharacteristic
369C22×C47#38011yescharacteristic
370C22×C47#38511yescharacteristic
371C22×C47#38511yescharacteristic
372C22×C47#38611yescharacteristic
373C22×C47#38611yescharacteristic
374C22×C47C2×#10211yescharacteristic
375C22×C47#41611yescharacteristic
376C22×C47#41711yescharacteristic
377C22×C47#41811yescharacteristic
378C22×C47C4×D811yescharacteristic
379C22×C47C4×D811yescharacteristic
380C22×C47C4×SD1611yescharacteristic
381C22×C47C4×SD1611yescharacteristic
382C22×C47#44011yescharacteristic
383C22×C47#44011yescharacteristic
384C22×C47#44211yescharacteristic
385C22×C47#44211yescharacteristic
386C22×C47#44711yescharacteristic
387C22×C47#44711yescharacteristic
388C22×C47#44911yescharacteristic
389C22×C47#44911yescharacteristic
390C22×C47#45011yescharacteristic
391C22×C47#45011yescharacteristic
392C22×C47#45211yescharacteristic
393C22×C47#45211yescharacteristic
394C22×C47#45911yescharacteristic
395C22×C47#46111yescharacteristic
396C22×C47#46311yescharacteristic
397C22×C47#46311yescharacteristic
398C22×C47#47411yescharacteristic
399C22×C47#47611yescharacteristic
400C22×C47#47811yescharacteristic
401C22×C47#47811yescharacteristic
402C2×D47—28no—
403C2×D47—44no—
404C2×D47—44no—
405C2×D47—44no—
406C2×D47—44no—
407C2×D47—44no—
408C2×D47—44no—
409C2×D47—44no—
410C2×D47—44no—
411C2×D47—44no—
412C2×D47—44no—
413C2×D47—44no—
414C2×D47—44no—
415C2×D47—44no—
416C2×D47—44no—
417C4×C47—44no—
418C4×C47—82no—
419C4×C47C2×#9511yescharacteristic
420C4×C47C4×C22⋊C411yescharacteristic
421C4×C47#38011yescharacteristic
422C4×C47#38111yescharacteristic
423C4×C47#38511yescharacteristic
424C4×C47#38511yescharacteristic
425C4×C47#38611yescharacteristic
426C4×C47#38611yescharacteristic
427Dic47—24no—
428Dic47—42no—
429Dic47—82no—
430C22×C4×D4—471no—
431C22×#102—471no—
432C22×#102—471no—
433C2×#340—471no—
434C2×#340D4711yescharacteristic, complemented
435C2×#336—471no—
436C4⋊#95—471no—
437C2×C47C22⋊#9511yescharacteristic
438C2×C47C4×#10211yescharacteristic
439C2×C47#176211yescharacteristic
440C2×C47#178611yescharacteristic
441C2×C47#178811yescharacteristic
442C2×C47#180211yescharacteristic
443C2×C47#180411yescharacteristic
444C2×C47#186211yescharacteristic
445C2×C47#186211yescharacteristic
446C2×C47#186411yescharacteristic
447C2×C47#186411yescharacteristic
448C2×C47#187711yescharacteristic
449C2×C47#187711yescharacteristic
450C2×C47#187911yescharacteristic
451C2×C47#187911yescharacteristic
452D47—48no—
453C23×D4—471no—
454C24×C4—941no—
455C23×C8—471no—
456C23×C8C2×D4711yescharacteristic
457C2×C4×D4—474no—
458C2×C4×D4—942no—
459C2×C4×D4—942no—
460C2×C4×D4—942no—
461C2×C4×D4—942no—
462C2×C4×D4—942no—
463C22×C4⋊C4—471no—
464C22×C4⋊C4C2×D4711yescharacteristic
465C22×C4⋊C4C2×D4711yescharacteristic
466C22×C22⋊C4—941no—
467C22×C42—471no—
468C2×#102—474no—
469C2×#102—474no—
470C2×#102—942no—
471C2×#102—942no—
472C2×#102—942no—
473C2×#102—942no—
474C2×#95—941no—
475C2×#95—941no—
476#340—22no—
477#340—942no—
478#336—942no—
479C47#1078811yescharacteristic, complemented, Sylow
480C25—941no—
481C22×D4—472no—
482C22×D4—472no—
483C22×D4—472no—
484C22×D4—472no—
485C22×D4—472no—
486C22×D4—472no—
487C22×D4—472no—
488C22×D4—941no—
489C22×D4—941no—
490C22×D4—941no—
491C22×D4—941no—
492C22×D4—941no—
493C22×D4—941no—
494C22×D4—941no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—471no—
498C23×C4—471no—
499C23×C4—944no—
500C23×C4—944no—
501C23×C4—944no—
502C23×C4—941no—
503C23×C4—1882no—
504C23×C4—1882no—
505C23×C4—1882no—
506C23×C4—1882no—
507C23×C4C22×D4711yescharacteristic
508C22×C8—21no—
509C22×C8—21no—
510C22×C8—21no—
511C22×C8—21no—
512C22×C8—21no—
513C22×C8—21no—
514C22×C8—472no—
515C22×C8—941no—
516C22×C8—941no—
517C22×C8—941no—
518C22×C8—941no—
519C22×C8—941no—
520C22×C8—941no—
521C22×C8C4×D4712yescomplemented
522C4×D4—948no—
523C4×D4—948no—
524C4×D4—948no—
525C4×D4—948no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—472no—
535C2×C4⋊C4—941no—
536C2×C4⋊C4—941no—
537C2×C4⋊C4—941no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4C4×D4712yes—
541C2×C4⋊C4C4×D4712yescomplemented
542C2×C4⋊C4D18812yes—
543C2×C4⋊C4C22⋊D4712yes—
544C2×C22⋊C4—944no—
545C2×C22⋊C4—944no—
546C2×C22⋊C4—944no—
547C2×C42—472no—
548C2×C42—472no—
549C2×C42—941no—
550C2×C42—941no—
551C2×C42—941no—
552C2×C42—941no—
553#102—948no—
554#102—948no—
555#95—1882no—
556#95—1882no—
557C24—942no—
558C24—942no—
559C24—942no—
560C24—942no—
561C24—942no—
562C24—942no—
563C24—942no—
564C24—1881no—
565C24—1881no—
566C24—1881no—
567C24—1881no—
568C24—1881no—
569C24—1881no—
570C24—1881no—
571C24—1881no—
572C24D4×D4711yescharacteristic
573C2×D4—474no—
574C2×D4—474no—
575C2×D4—474no—
576C2×D4—474no—
577C2×D4—474no—
578C2×D4—474no—
579C2×D4—474no—
580C2×D4—942no—
581C2×D4—942no—
582C2×D4—942no—
583C2×D4—942no—
584C2×D4—942no—
585C2×D4—942no—
586C2×D4—942no—
587C2×D4—942no—
588C2×D4—942no—
589C2×D4—942no—
590C2×D4—942no—
591C2×D4—942no—
592C2×D4—942no—
593C2×D4—942no—
594C2×D4—942no—
595C2×D4—942no—
596C2×D4—942no—
597C2×D4—942no—
598C2×D4—942no—
599C2×D4—942no—
600C2×D4—942no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—472no—
616C22×C4—472no—
617C22×C4—472no—
618C22×C4—472no—
619C22×C4—9416no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—941no—
624C22×C4—941no—
625C22×C4—941no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—942no—
631C22×C4—1888no—
632C22×C4—1888no—
633C22×C4—1888no—
634C22×C4—1888no—
635C22×C4—1888no—
636C22×C4—1888no—
637C22×C4—1881no—
638C22×C4—1881no—
639C22×C4—1881no—
640C22×C4—1881no—
641C22×C4—1881no—
642C22×C4—1881no—
643C22×C4C2×C4×D4711yescharacteristic
644C22×C4C2×C4×D4711yescharacteristic
645C22×C4C2×C4×D4711yescharacteristic
646C22×C4C2×D18811yescharacteristic
647C22×C4#1062535011yescharacteristic
648C22×C4#1062535011yescharacteristic
649C22×C4D4×D4711yescharacteristic
650C22×C4D4×D4711yescharacteristic
651C22×C4D4×D4711yescharacteristic
652C22×C4D4×D4711yescharacteristic
653C22×C4#1062535211yescharacteristic
654C22×C4Q8×D4711yescharacteristic
655C22×C4#1062535411yescharacteristic
656C22×C4C2×C22⋊D4711yescharacteristic
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8—41no—
663C2×C8—41no—
664C2×C8—942no—
665C2×C8—942no—
666C2×C8—942no—
667C2×C8—1881no—
668C2×C8—1881no—
669C2×C8—1881no—
670C2×C8—1881no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4—942no—
679C4⋊C4—942no—
680C4⋊C4—1881no—
681C4⋊C4—1881no—
682C4⋊C4(C2×D47)⋊C414yes—
683C22⋊C4—9416no—
684C42—942no—
685C42—942no—
686C42—942no—
687C42—942no—
688C23—944no—
689C23—944no—
690C23—944no—
691C23—944no—
692C23—944no—
693C23—944no—
694C23—944no—
695C23—1882no—
696C23—1882no—
697C23—1882no—
698C23—1882no—
699C23—1882no—
700C23—1882no—
701C23—1882no—
702C23—1882no—
703C23—1882no—
704C23—1882no—
705C23—1882no—
706C23—1882no—
707C23—1882no—
708C23—1882no—
709C23—1882no—
710C23—1882no—
711C23—1882no—
712C23—1882no—
713C23—1882no—
714C23—1882no—
715C23—1882no—
716C23—1882no—
717C23—1882no—
718C23—1882no—
719C23—1882no—
720C23—1882no—
721C23—1882no—
722C23—1882no—
723C23C22⋊C4×D4711yescharacteristic
724C23(C22⋊D47)⋊C411yescharacteristic
725C23#1309398611yescharacteristic
726C23#1309399211yescharacteristic
727C23#1309399411yescharacteristic
728C23#1309399711yescharacteristic
729C23#1309400211yescharacteristic
730C23D8×D4711yescharacteristic
731C23SD16×D4711yescharacteristic
732C23#1309404511yescharacteristic
733C23#1309404711yescharacteristic
734C23#1309404811yescharacteristic
735C23#1309405111yescharacteristic
736C23#1309405111yescharacteristic
737C23#1309405611yescharacteristic
738D4—478no—
739D4—944no—
740D4—944no—
741D4—944no—
742D4—944no—
743D4—944no—
744D4—944no—
745D4—944no—
746C2×C4—24no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—474no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—942no—
768C2×C4—942no—
769C2×C4—942no—
770C2×C4—3761no—
771C2×C4—3761no—
772C2×C4—3761no—
773C2×C4—3761no—
774C2×C4—18832no—
775C2×C4—1882no—
776C2×C4—1882no—
777C2×C4—1882no—
778C2×C4—1881no—
779C2×C4—1881no—
780C2×C4—1881no—
781C2×C4—1881no—
782C2×C4C42×D4711yescharacteristic
783C2×C4C22⋊C4×D4711yescharacteristic
784C2×C4C22⋊C4×D4711yescharacteristic
785C2×C4C22⋊C4×D4711yescharacteristic
786C2×C4C2×(C2×D47)⋊C411yescharacteristic
787C2×C4C4⋊C4×D4711yescharacteristic
788C2×C4C4⋊C4×D4711yescharacteristic
789C2×C4C4⋊C4×D4711yescharacteristic
790C2×C4#1309398111yescharacteristic
791C2×C4#1309398211yescharacteristic
792C2×C4(C22⋊D47)⋊C411yescharacteristic
793C2×C4C4×C22⋊D4711yescharacteristic
794C2×C4C4×C22⋊D4711yescharacteristic
795C2×C4#1309398611yescharacteristic
796C2×C4C4×D18811yescharacteristic
797C2×C4C4×D18811yescharacteristic
798C2×C4#1309399211yescharacteristic
799C2×C4#1309399411yescharacteristic
800C2×C4#1309399511yescharacteristic
801C2×C4#1309399711yescharacteristic
802C2×C4#1309399911yescharacteristic
803C2×C4#1309400011yescharacteristic
804C2×C4#1309400211yescharacteristic
805C2×C4#1309400411yescharacteristic
806C2×C4#1309400611yescharacteristic
807C2×C4#1309400611yescharacteristic
808C2×C4#1309400911yescharacteristic
809C2×C4#1309400911yescharacteristic
810C8—42no—
811C8—1882no—
812C22—948no—
813C22—1884no—
814C22—1884no—
815C22—1884no—
816C22—1884no—
817C22—1884no—
818C22—1884no—
819C22—1884no—
820C22—1884no—
821C22—1884no—
822C22—1884no—
823C22—1884no—
824C22—1884no—
825C22—1884no—
826C22—1884no—
827C22#1568897011yescharacteristic
828C22#1568897811yescharacteristic
829C22#1568898211yescharacteristic
830C22#1568899411yescharacteristic
831C22#1568899711yescharacteristic
832C22#1568899911yescharacteristic
833C22#1568900111yescharacteristic
834C22#102×D4711yescharacteristic
835C22#1568911811yescharacteristic
836C22#1568912311yescharacteristic
837C22#1568912611yescharacteristic
838C22#1568920311yescharacteristic
839C22#1568920511yescharacteristic
840C22#1568920811yescharacteristic
841C22#1568921011yescharacteristic
842C22#1568922211yescharacteristic
843C22#1568922611yescharacteristic
844C22#1568923211yescharacteristic
845C22#1568923411yescharacteristic
846C22#1568925511yescharacteristic
847C22#1568925811yescharacteristic
848C22#1568926711yescharacteristic
849C22#1568927111yescharacteristic
850C22#1568927211yescharacteristic
851C22#1568927511yescharacteristic
852C22#1568928411yescharacteristic
853C22#1568928811yescharacteristic
854C22#1568931711yescharacteristic
855C22#1568932711yescharacteristic
856C22#1568933711yescharacteristic
857C22#1568934111yescharacteristic
858C22#1568940211yescharacteristic
859C22#1568941211yescharacteristic
860C22#1568942211yescharacteristic
861C22#1568942611yescharacteristic
862C4—44no—
863C4—82no—
864C4—944no—
865C4—3762no—
866C4—1882no—
867C4#95×D4711yescharacteristic
868C4C4×(C2×D47)⋊C411yescharacteristic
869C4#1568898011yescharacteristic
870C4#1568898511yescharacteristic
871C4#1568899411yescharacteristic
872C4#1568899711yescharacteristic
873C4#1568899911yescharacteristic
874C4#1568900111yescharacteristic
875C2—1888no—
876C2(C2×D47)⋊#9511yescharacteristic
877C2#2024320211yescharacteristic
878C2#2024321211yescharacteristic
879C2#2024331711yescharacteristic
880C2#2024332711yescharacteristic
881C2#2024338711yescharacteristic
882C2#2024339711yescharacteristic
883C2#2024363211yescharacteristic
884C2#2024363611yescharacteristic
885C2#2024364611yescharacteristic
886C2#2024365011yescharacteristic
887C2#2024371911yescharacteristic
888C2#2024372311yescharacteristic
889C2#2024373311yescharacteristic
890C2#2024373711yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#340C2
socleC24×C47C2×D4
prime radicalC23×D188C22
cosocleC23×C4×C47C23
hypercenterC2×#340D47
hypocenterC47#10788
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
4. C2×#15688885C2semidirect
5. C2×#15688877C2semidirect
6. #20241617C2semidirect
7. C2×C47×#340C2semidirect
16. C2×#13093986C4semidirect
22. C2×#13093946C4semidirect
25. C2×#13093944C4semidirect
65. C22×C47⋊C8C2×C4semidirect
75. C2×C4⋊Dic47C2×C4semidirect
98. C22×C8×C47C2×C4semidirect
108. C2×C4⋊C4×C47C2×C4semidirect
354. C2×Dic47#102semidirect
362. D188#95semidirect
434. C2×#340D47semidirect
479. C47#10788semidirect
521. C22×C8C4×D47semidirect
541. C2×C4⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×#130939862
C22×#130939462
C22×#130939442
C2×#156888852
C2×#156888772
#202416172
C2×C47×#3402
#1078847