Finite Group Databasebeta

← #26222419

Subgroups — #26222419

Order 12032.

1052 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689193C211yesmaximal, characteristic, complemented
2C2×#15689193C211yesmaximal, characteristic, complemented
3C2×#15689188C211yesmaximal, characteristic, complemented
4C2×#15689077C211yesmaximal, characteristic, complemented
5#20246628C211yesmaximal, characteristic
6#20244182C211yesmaximal, characteristic, complemented
7#20243993C211yesmaximal, characteristic, complemented
8#20243993C211yesmaximal, characteristic, complemented
9#20243684C211yesmaximal, characteristic, complemented
10#20243684C211yesmaximal, characteristic, complemented
11#20243369C211yesmaximal, characteristic, complemented
12#20243263C211yesmaximal, characteristic, complemented
13#20243168C211yesmaximal, characteristic, complemented
14#20243163C211yesmaximal, characteristic, complemented
15C47×#1939C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20C2×C4×D188C2211yescharacteristic
21C2×C4×D188C2211yescharacteristic
22C2×C4×D188C2211yescharacteristic
23C2×#13093981C2211yescharacteristic
24#15689193—24no—
25#15689193—24no—
26#15689188—24no—
27C2×C4⋊(C47⋊C8)C2211yescharacteristic
28C2×(C2×D47)⋊C8C2211yescharacteristic
29C2×(C2×D47)⋊C8C2211yescharacteristic
30C2×(C2×D47)⋊C8C2211yescharacteristic
31C2×(C2×D47)⋊C8C2211yescharacteristic
32C2×(C2×D47)⋊C8C2211yescharacteristic
33C2×(C2×D47)⋊C8C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×(C2×D47)⋊C8C2211yescharacteristic
36#15689077—24no—
37C2×#13093935C2211yescharacteristic
38C2×#13093935C2211yescharacteristic
39C2×#13093934C2211yescharacteristic
40C2×C4×C47⋊C8C2211yescharacteristic
41C2×C8×Dic47C2211yescharacteristic
42#15689055C411yescharacteristic
43#15689050C411yescharacteristic
44#15689045C411yescharacteristic
45#15689045C411yescharacteristic
46#15689041C411yescharacteristic
47#15689040C411yescharacteristic
48#15689040C411yescharacteristic
49#15689033C411yescharacteristic
50C4×(C2×D47)⋊C4C2211yescharacteristic
51C4×(C2×D47)⋊C4C2211yescharacteristic
52#15688878C2211yescharacteristic
53#15688878C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C2×C4⋊C8×C47C2211yescharacteristic
57C2×C4⋊C8×C47C2211yescharacteristic
58C2×C4⋊C8×C47C2211yescharacteristic
59C2×C4×C8×C47C2211yescharacteristic
60C4×C4⋊C4×C47C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×D188C2×C411yescharacteristic
64C22×D188C2×C411yescharacteristic
65C22×D188C2×C411yescharacteristic
66C22×C4×D47C2311yescharacteristic
67C22×C4×D47C2311yescharacteristic
68C22×C4×D47C2311yescharacteristic
69C2×#10625324—22no—
70C2×#10625324—22no—
71C2×#10625324—22no—
72C2×#10625324—22no—
73C2×#10625324—22no—
74C2×#10625324—22no—
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C22×C47⋊C8C2311yescharacteristic
79C2×C8×D47—22no—
80C2×C8×D47—22no—
81C2×C8×D47—22no—
82C2×C8×D47—22no—
83C2×C8×D47—22no—
84C2×C8×D47D414yescomplemented
85C4×D188—22no—
86C4×D188—22no—
87C4×D188—22no—
88C4×D188—22no—
89C4×D188—22no—
90C4×D188—22no—
91#13093981—22no—
92#13093981—22no—
93C2×C4⋊Dic47C2×C411yescharacteristic
94C2×C4⋊Dic47C2×C411yescharacteristic
95C2×C4⋊Dic47C2×C411yescharacteristic
96C2×Dic47⋊C4C2×C411yescharacteristic
97C2×Dic47⋊C4C2×C411yescharacteristic
98C2×(C2×D47)⋊C4C2×C411yescharacteristic
99C2×(C2×D47)⋊C4C2×C411yescharacteristic
100C2×(C2×D47)⋊C4C2×C411yescharacteristic
101C2×(C2×D47)⋊C4C2×C411yescharacteristic
102C2×(C2×D47)⋊C4C2×C411yescharacteristic
103C2×(C2×D47)⋊C4C2×C411yescharacteristic
104C2×(C2×D47)⋊C4C2×C411yescharacteristic
105C2×(C2×D47)⋊C4C2×C411yescharacteristic
106C2×(C2×D47)⋊C4C2×C411yescharacteristic
107C2×(C2×D47)⋊C4C2×C411yescharacteristic
108C2×(C2×D47)⋊C4C2×C411yescharacteristic
109C2×(C2×D47)⋊C4C2×C411yescharacteristic
110C2×C4×Dic47C2311yescharacteristic
111C4⋊(C47⋊C8)—22no—
112(C2×D47)⋊C8—22no—
113(C2×D47)⋊C8—22no—
114(C2×D47)⋊C8—22no—
115(C2×D47)⋊C8—22no—
116(C2×D47)⋊C8—22no—
117(C2×D47)⋊C8—22no—
118(C2×D47)⋊C8—22no—
119(C2×D47)⋊C8—22no—
120#13093935—22no—
121#13093935D414yescomplemented
122#13093934—22no—
123C4×C47⋊C8—22no—
124C8×Dic47—22no—
125C47⋊#95C2×C411yescharacteristic
126C47⋊#95C2×C411yescharacteristic
127C47⋊#95C2×C411yescharacteristic
128C47⋊#95C2×C411yescharacteristic
129C22×C8×C47C2311yescharacteristic
130C22×C8×C47C2311yescharacteristic
131C22×C8×C47C2311yescharacteristic
132C22×C8×C47C2311yescharacteristic
133C2×C4⋊C4×C47C2×C411yescharacteristic
134C2×C4⋊C4×C47C2×C411yescharacteristic
135C2×C42×C47C2311yescharacteristic
136C2×C42×C47C2311yescharacteristic
137C2×C42×C47C2311yescharacteristic
138C4⋊C8×C47—22no—
139C4⋊C8×C47—22no—
140C4⋊C8×C47—22no—
141C4×C8×C47—22no—
142#95×C47C2×C411yescharacteristic
143#95×C47C2×C411yescharacteristic
144C23×D47C22×C411yescharacteristic
145C23×D47C22×C411yescharacteristic
146C23×D47C22×C411yescharacteristic
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C22×C411yescharacteristic
150C22×C4×C47C22×C411yescharacteristic
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C2411yescharacteristic
154C22×Dic47C22×C411yescharacteristic
155C22×Dic47C22×C411yescharacteristic
156C22×Dic47C22×C411yescharacteristic
157C22×Dic47C22×C411yescharacteristic
158C22×Dic47C22×C411yescharacteristic
159C2×D188—22no—
160C2×D188—22no—
161C2×D188—22no—
162C2×D188—22no—
163C2×D188—22no—
164C2×D188—22no—
165C2×D188—41no—
166C2×D188—41no—
167C2×D188—41no—
168C2×C4×D47—21no—
169C2×C4×D47—21no—
170C2×C4×D47—21no—
171C2×C4×D47—21no—
172C2×C4×D47—21no—
173C2×C4×D47—21no—
174C2×C4×D47—21no—
175C2×C4×D47—21no—
176C2×C4×D47—21no—
177C2×C4×D47—21no—
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47C2×D412yes—
185C2×C4×D47#4112yes—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47C2×D412yes—
197C2×C8×C47#4112yes—
198C4⋊C4×C47—22no—
199C4⋊C4×C47—41no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47—21no—
203C42×C47—21no—
204C42×C47C2×D412yes—
205C42×C47#4112yes—
206(C2×D47)⋊C4—22no—
207(C2×D47)⋊C4—22no—
208(C2×D47)⋊C4—22no—
209(C2×D47)⋊C4—22no—
210(C2×D47)⋊C4—22no—
211(C2×D47)⋊C4—22no—
212(C2×D47)⋊C4—22no—
213(C2×D47)⋊C4—22no—
214(C2×D47)⋊C4—22no—
215(C2×D47)⋊C4—22no—
216(C2×D47)⋊C4—41no—
217(C2×D47)⋊C4—41no—
218C4⋊Dic47—22no—
219C4⋊Dic47—22no—
220C4⋊Dic47—22no—
221Dic47⋊C4—22no—
222Dic47⋊C4—22no—
223C4×Dic47—21no—
224C4×Dic47—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8C2×D412yes—
234C2×C47⋊C8C2×D412yes—
235C2×C47⋊C8C2×D412yes—
236C2×C47⋊C8#4112yes—
237#10625324—28no—
238#10625324—44no—
239C8×D47—28no—
240C8×D47—44no—
241C23×C47C23×C411yescharacteristic
242C22×D47—21no—
243C22×D47—21no—
244C22×D47—21no—
245C22×D47—21no—
246C22×D47—21no—
247C22×D47—21no—
248C22×D47—21no—
249C22×D47—21no—
250C22×D47—21no—
251C22×D47—21no—
252C22×D47—21no—
253C22×D47—21no—
254C22×D47—21no—
255C22×D47—21no—
256C22×D47—21no—
257C22×D47—21no—
258C22×D47—21no—
259C22×D47—21no—
260C22×D47—21no—
261C22×D47C4×D412yes—
262C22×D47#13112yes—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
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×C47C4×D412yes—
279C2×C4×C47C4×D412yes—
280C2×C4×C47#13112yes—
281C2×C4×C47C22×D411yescharacteristic
282C2×C4×C47C22×D411yescharacteristic
283C2×C4×C47C2×#4111yescharacteristic
284C2×C4×C47C2×#4111yescharacteristic
285C2×C4×C47C2×#4111yescharacteristic
286C2×C4×C47C2×#4111yescharacteristic
287C2×Dic47—21no—
288C2×Dic47—21no—
289C2×Dic47—21no—
290C2×Dic47—21no—
291C2×Dic47—21no—
292C2×Dic47—21no—
293C2×Dic47—21no—
294C2×Dic47—21no—
295C2×Dic47—21no—
296C2×Dic47—21no—
297C2×Dic47—21no—
298C2×Dic47—21no—
299C2×Dic47—21no—
300C2×Dic47—21no—
301C2×Dic47C4×D412yes—
302D188—28no—
303D188—44no—
304D188—44no—
305C4×D47—22no—
306C4×D47—22no—
307C4×D47—22no—
308C4×D47—22no—
309C4×D47—41no—
310C4×D47—41no—
311C4×D47—41no—
312C4×D47—41no—
313C4×D47—41no—
314C4×D47—41no—
315C4×D47—41no—
316C4×D47—41no—
317C8×C47—22no—
318C8×C47—22no—
319C8×C47—41no—
320C8×C47—41no—
321C47⋊C8—22no—
322C47⋊C8—41no—
323C47⋊C8—41no—
324C47⋊C8#12114yes—
325#21495—471nomaximal, Sylow
326C22×C47C2×C4×D411yescharacteristic
327C22×C47C2×C4×D411yescharacteristic
328C22×C47C4×#4111yescharacteristic
329C22×C47C2×#13111yescharacteristic
330C22×C47C2×#13111yescharacteristic
331C22×C47#56811yescharacteristic
332C22×C47#56811yescharacteristic
333C2×D47—22no—
334C2×D47—22no—
335C2×D47—22no—
336C2×D47—22no—
337C2×D47—22no—
338C2×D47—22no—
339C2×D47—41no—
340C2×D47—41no—
341C2×D47—41no—
342C2×D47—41no—
343C2×D47—41no—
344C2×D47—41no—
345C2×D47—41no—
346C2×D47—41no—
347C2×D47—41no—
348C2×D47—41no—
349C2×D47—41no—
350C2×D47—41no—
351C2×D47—41no—
352C2×D47—41no—
353C2×D47—41no—
354C4×C47—22no—
355C4×C47—22no—
356C4×C47—22no—
357C4×C47—41no—
358C4×C47—41no—
359C4×C47—41no—
360C4×C47C2×#12111yescharacteristic
361C4×C47#52511yescharacteristic
362C4×C47#52911yescharacteristic
363C4×C47#53211yescharacteristic
364Dic47—22no—
365Dic47—41no—
366Dic47—41no—
367Dic47—41no—
368Dic47—41no—
369C2×#435—471no—
370C2×#435—471no—
371C2×C8×D4—471no—
372C2×#405—471no—
373#2392—471no—
374#1954—471no—
375#1939D4711yescharacteristic, complemented
376#1923—471no—
377#1923—471no—
378#1870—471no—
379#1870—471no—
380#1798—471no—
381#1771—471no—
382#1753—471no—
383#1752—471no—
384C2×C47C4×#12111yescharacteristic
385C2×C47#292911yescharacteristic
386C2×C47#293011yescharacteristic
387C2×C47#293311yescharacteristic
388C2×C47#293511yescharacteristic
389C2×C47#296811yescharacteristic
390C2×C47#296911yescharacteristic
391D47—42no—
392D47—42no—
393D47—81no—
394C22×M16—471no—
395C22×M16—471no—
396C23×C8—471no—
397C23×C8—471no—
398C2×C4×D4—471no—
399C2×C4×D4—471no—
400C2×C4×D4—471no—
401C2×#117—471no—
402#435—944no—
403#435—944no—
404C8×D4—944no—
405C2×C4⋊C8—471no—
406C2×C4⋊C8C2×D4711yescharacteristic
407C2×C4⋊C8C2×D4711yescharacteristic
408C2×C4⋊C8C2×D4711yescharacteristic
409C2×C22⋊C8—471no—
410C2×C22⋊C8—471no—
411C2×C22⋊C8—471no—
412C2×C22⋊C8—471no—
413C2×C22⋊C8—471no—
414C2×C22⋊C8—471no—
415C2×C22⋊C8—471no—
416C2×C22⋊C8—471no—
417#405—944no—
418C2×#97—471no—
419C2×#97—471no—
420C2×#97—471no—
421C2×C4×C8—471no—
422C2×C4×C8—471no—
423C2×C4×C8C2×D4711yescharacteristic
424#398—471no—
425#397—471no—
426#396—471no—
427#396—471no—
428#394—471no—
429#394—471no—
430#394—471no—
431#392—471no—
432C4×C4⋊C4C2×D4711yescharacteristic
433C4×C22⋊C4—471no—
434C4×C22⋊C4—471no—
435#336—471no—
436#336—471no—
437#336—471no—
438#336—471no—
439#336C2×D4711yescharacteristic
440#336C2×D4711yescharacteristic
441C47#2149511yescharacteristic, complemented, Sylow
442C22×D4—471no—
443C22×D4—471no—
444C22×D4—471no—
445C23×C4—471no—
446C23×C4—471no—
447C23×C4—471no—
448C2×M16—942no—
449C2×M16—942no—
450C2×M16—942no—
451C2×M16—942no—
452C2×M16—942no—
453C2×M16—942no—
454C22×C8—471no—
455C22×C8—471no—
456C22×C8—474no—
457C22×C8—471no—
458C22×C8—471no—
459C22×C8—942no—
460C22×C8—942no—
461C22×C8—942no—
462C22×C8—942no—
463C22×C8—942no—
464C22×C8C22×D4711yescharacteristic
465C22×C8C22×D4711yescharacteristic
466C22×C8C22×D4711yescharacteristic
467C22×C8C22×D4711yescharacteristic
468C4×D4—942no—
469C4×D4—942no—
470C4×D4—942no—
471C4×D4—942no—
472C4×D4—942no—
473C4×D4—942no—
474#117—942no—
475#117—942no—
476C2×C4⋊C4—471no—
477C2×C4⋊C4—471no—
478C2×C4⋊C4—471no—
479C2×C4⋊C4—471no—
480C2×C4⋊C4—471no—
481C2×C4⋊C4C4×D4711yescharacteristic
482C2×C4⋊C4C4×D4711yescharacteristic
483C2×C22⋊C4—471no—
484C2×C22⋊C4—471no—
485C2×C22⋊C4—471no—
486C2×C22⋊C4—471no—
487C2×C22⋊C4—471no—
488C2×C22⋊C4—471no—
489C2×C22⋊C4—471no—
490C2×C22⋊C4—471no—
491C2×C22⋊C4—471no—
492C2×C22⋊C4—471no—
493C2×C22⋊C4—471no—
494C2×C22⋊C4—471no—
495C2×C42—471no—
496C2×C42C22×D4711yescharacteristic
497C2×C42C22×D4711yescharacteristic
498C2×C42C22×D4711yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—22no—
502C4⋊C8—942no—
503C22⋊C8—942no—
504C22⋊C8—942no—
505C22⋊C8—942no—
506C22⋊C8—942no—
507C22⋊C8—942no—
508C22⋊C8—942no—
509C22⋊C8—942no—
510C22⋊C8—942no—
511#97—474no—
512#97—942no—
513#97—942no—
514C4×C8—22no—
515C4×C8—942no—
516C4×C8—942no—
517#95—471no—
518#95—471no—
519#95—471no—
520#95—471no—
521#95C4×D4711yescharacteristic
522#95C4×D4711yescharacteristic
523C24—471no—
524C24—471no—
525C24—471no—
526C2×D4—942no—
527C2×D4—942no—
528C2×D4—942no—
529C2×D4—942no—
530C2×D4—942no—
531C2×D4—942no—
532C2×D4—1881no—
533C2×D4—1881no—
534C2×D4—1881no—
535C22×C4—471no—
536C22×C4—472no—
537C22×C4—472no—
538C22×C4—471no—
539C22×C4—471no—
540C22×C4—471no—
541C22×C4—471no—
542C22×C4—941no—
543C22×C4—941no—
544C22×C4—941no—
545C22×C4—941no—
546C22×C4—941no—
547C22×C4—941no—
548C22×C4—941no—
549C22×C4—941no—
550C22×C4—941no—
551C22×C4—941no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4—941no—
558C22×C4C2×C4×D4711yescharacteristic
559C22×C4C2×C4×D4711yescharacteristic
560C22×C4C2×C4×D4711yescharacteristic
561C22×C4C2×C4×D4711yescharacteristic
562C22×C4C2×C4×D4711yescharacteristic
563C22×C4C2×C4×D4711yescharacteristic
564C22×C4C23×D4711yescharacteristic
565M16—948no—
566M16—1884no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—472no—
578C2×C8—472no—
579C2×C8—472no—
580C2×C8—472no—
581C2×C8—948no—
582C2×C8—941no—
583C2×C8—941no—
584C2×C8—941no—
585C2×C8—941no—
586C2×C8—941no—
587C2×C8—941no—
588C2×C8—941no—
589C2×C8—941no—
590C2×C8—1884no—
591C2×C8D4×D4712yes—
592C2×C8#1062535412yes—
593C4⋊C4—22no—
594C4⋊C4—41no—
595C4⋊C4—942no—
596C4⋊C4—942no—
597C4⋊C4—942no—
598C4⋊C4—942no—
599C4⋊C4—942no—
600C22⋊C4—942no—
601C22⋊C4—942no—
602C22⋊C4—942no—
603C22⋊C4—942no—
604C22⋊C4—942no—
605C22⋊C4—942no—
606C22⋊C4—942no—
607C22⋊C4—942no—
608C22⋊C4—942no—
609C22⋊C4—942no—
610C22⋊C4—1881no—
611C22⋊C4—1881no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—941no—
617C42—941no—
618C42D4×D4712yes—
619C42#1062535412yes—
620C23—472no—
621C23—472no—
622C23—941no—
623C23—941no—
624C23—941no—
625C23—941no—
626C23—941no—
627C23—941no—
628C23—941no—
629C23—941no—
630C23—941no—
631C23—941no—
632C23—941no—
633C23—941no—
634C23—941no—
635C23—941no—
636C23—941no—
637C23—941no—
638C23—941no—
639C23—941no—
640C23—941no—
641C23C22×C4×D4711yescharacteristic
642D4—948no—
643D4—1884no—
644D4—1884no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—472no—
661C2×C4—941no—
662C2×C4—941no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—941no—
668C2×C4—941no—
669C2×C4—941no—
670C2×C4—941no—
671C2×C4—941no—
672C2×C4—941no—
673C2×C4—941no—
674C2×C4—941no—
675C2×C4—941no—
676C2×C4—941no—
677C2×C4—941no—
678C2×C4—941no—
679C2×C4—1881no—
680C2×C4—1881no—
681C2×C4—1881no—
682C2×C4—1881no—
683C2×C4—1881no—
684C2×C4—1881no—
685C2×C4—1881no—
686C2×C4—1881no—
687C2×C4#1309398612yes—
688C2×C4#1309398612yes—
689C2×C4#1309403012yes—
690C2×C4C2×D4×D4711yescharacteristic
691C2×C4C2×D4×D4711yescharacteristic
692C2×C4#41×D4711yescharacteristic
693C2×C4#41×D4711yescharacteristic
694C2×C4C2×#1062535411yescharacteristic
695C2×C4C2×#1062535411yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—474no—
701C8—942no—
702C8—1881no—
703C8—1881no—
704C22—942no—
705C22—942no—
706C22—942no—
707C22—942no—
708C22—942no—
709C22—942no—
710C22—1881no—
711C22—1881no—
712C22—1881no—
713C22—1881no—
714C22—1881no—
715C22—1881no—
716C22—1881no—
717C22—1881no—
718C22—1881no—
719C22—1881no—
720C22—1881no—
721C22—1881no—
722C22—1881no—
723C22—1881no—
724C22—1881no—
725C22C4×D4×D4711yescharacteristic
726C22C2×#1309398611yescharacteristic
727C22C4×#1062535411yescharacteristic
728C22#131×D4711yescharacteristic
729C22C2×#1309403011yescharacteristic
730C22#1568988811yescharacteristic
731C22#1568988911yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—942no—
739C4—1881no—
740C4—1881no—
741C4—1881no—
742C4—1881no—
743C4#121×D4711yescharacteristic
744C4#1568963611yescharacteristic
745C4#1568965811yescharacteristic
746C4#1568967411yescharacteristic
747C2—3761no—
748C2—1882no—
749C2—1882no—
750C2#2024589611yescharacteristic
751C2#2025207711yescharacteristic
752C2#2025208811yescharacteristic
753C2#2025211211yescharacteristic
754C2#2025213111yescharacteristic
755C2#2025238111yescharacteristic
756C2#2025239111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1939C2
prime radical#15689033C4
cosocleC22×C4×C47C24
hypercenter#1939D47
hypocenterC47#21495
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. C2×#15689193C2semidirect
2. C2×#15689193C2semidirect
3. C2×#15689188C2semidirect
4. C2×#15689077C2semidirect
6. #20244182C2semidirect
7. #20243993C2semidirect
8. #20243993C2semidirect
9. #20243684C2semidirect
10. #20243684C2semidirect
11. #20243369C2semidirect
12. #20243263C2semidirect
13. #20243168C2semidirect
14. #20243163C2semidirect
15. C47×#1939C2semidirect
84. C2×C8×D47D4semidirect
121. #13093935D4semidirect
375. #1939D47semidirect
441. C47#21495semidirect

Maximal subgroups

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

subgroupindex
C2×#156891932
C2×#156891882
C2×#156890772
#202466282
#202441822
#202439932
#202436842
#202433692
#202432632
#202431682
#202431632
C47×#19392
#2149547