Finite Group Databasebeta

← #26233321

Subgroups — #26233321

Order 12032.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689181C211yesmaximal, characteristic, complemented
2C2×#15689088C211yesmaximal, characteristic
3#20245878C211yesmaximal, characteristic
4#20244002C211yesmaximal, characteristic, complemented
5#20244001C211yesmaximal, characteristic, complemented
6#20244001C211yesmaximal, characteristic, complemented
7#20243995C211yesmaximal, characteristic, complemented
8#20243572C211yesmaximal, characteristic, complemented
9#20243567C211yesmaximal, characteristic, complemented
10#20243457C211yesmaximal, characteristic, complemented
11#20243368C211yesmaximal, characteristic, complemented
12#20243299C211yesmaximal, characteristic
13#20243173C211yesmaximal, characteristic, complemented
14#20243165C211yesmaximal, characteristic, complemented
15C47×#1749C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19C2×#13093983C2211yescharacteristic
20#15689181—24no—
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23C2×Dic47⋊C8C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25#15689088—24no—
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×C22⋊(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×#13093934C2211yescharacteristic
35C2×C8×Dic47C2211yescharacteristic
36#15689029C411yescharacteristic
37#15689029C411yescharacteristic
38#15689025C411yescharacteristic
39#15689025C411yescharacteristic
40#15689002C411yescharacteristic
41#15689002C411yescharacteristic
42#15689002C411yescharacteristic
43#15689002C411yescharacteristic
44C4×(C2×D47)⋊C4C2211yescharacteristic
45C4×(C2×D47)⋊C4C2211yescharacteristic
46C4×(C2×D47)⋊C4C2211yescharacteristic
47C4×(C2×D47)⋊C4C2211yescharacteristic
48#15688878C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C22×C42×C47C2211yescharacteristic
55C2×C22⋊C8×C47C2211yescharacteristic
56C2×C22⋊C8×C47C2211yescharacteristic
57C2×#97×C47C2211yescharacteristic
58C2×#97×C47C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C2×#10625350—22no—
62C2×#10625350—22no—
63C2×#10625350—22no—
64C2×#10625350—22no—
65C2×#10625350—41no—
66C2×#10625350—41no—
67C22×Dic94C2×C411yescharacteristic
68C22×D188C2×C411yescharacteristic
69C22×C22⋊D47C2×C411yescharacteristic
70C22×C22⋊D47C2×C411yescharacteristic
71C22×C4×D47C2311yescharacteristic
72C22×C4×D47C2311yescharacteristic
73C2×#10625324—22no—
74C2×#10625324—22no—
75C2×#10625324—41no—
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C22×C47⋊C8C2311yescharacteristic
79C22×C47⋊C8C2311yescharacteristic
80C2×C8×D47—22no—
81C2×C8×D47—22no—
82C2×C8×D47—41no—
83#13093983—22no—
84#13093983—22no—
85C2×C4⋊Dic47C2×C411yescharacteristic
86C2×C4⋊Dic47C2×C411yescharacteristic
87C2×C22⋊Dic47C2×C411yescharacteristic
88C2×C22⋊Dic47C2×C411yescharacteristic
89C2×(C2×D47)⋊C4C2×C411yescharacteristic
90C2×(C2×D47)⋊C4C2×C411yescharacteristic
91C2×(C2×D47)⋊C4C2×C411yescharacteristic
92C2×(C2×D47)⋊C4C2×C411yescharacteristic
93C2×(C2×D47)⋊C4C2×C411yescharacteristic
94C2×(C2×D47)⋊C4C2×C411yescharacteristic
95C2×(C2×D47)⋊C4C2×C411yescharacteristic
96C2×(C2×D47)⋊C4C2×C411yescharacteristic
97C2×C4×Dic47C2311yescharacteristic
98C2×C4×Dic47C2311yescharacteristic
99C4⋊(C47⋊C8)—41no—
100C4⋊(C47⋊C8)—41no—
101Dic47⋊C8—22no—
102Dic47⋊C8—22no—
103C22⋊(C47⋊C8)—22no—
104C22⋊(C47⋊C8)—22no—
105(C2×D47)⋊C8—22no—
106(C2×D47)⋊C8—22no—
107(C2×D47)⋊C8—22no—
108(C2×D47)⋊C8—22no—
109(C2×D47)⋊C8—41no—
110(C2×D47)⋊C8—41no—
111#13093934—22no—
112C8×Dic47—22no—
113C47⋊#95C2×C411yescharacteristic
114C47⋊#95C2×C411yescharacteristic
115C47⋊#95C2×C411yescharacteristic
116C47⋊#95C2×C411yescharacteristic
117C47⋊#95C2×C411yescharacteristic
118C47⋊#95C2×C411yescharacteristic
119C47⋊#95C2×C411yescharacteristic
120C47⋊#95C2×C411yescharacteristic
121C23×C4×C47C2×C411yescharacteristic
122C23×C4×C47C2×C411yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C22×C8×C47C2311yescharacteristic
125C22×C8×C47C2311yescharacteristic
126C22×C8×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128C2×C42×C47—41no—
129C2×C42×C47—41no—
130C2×C42×C47C2×C411yescharacteristic
131C2×C42×C47C2×C411yescharacteristic
132C2×C42×C47C2311yescharacteristic
133C2×C42×C47C2311yescharacteristic
134C22⋊C8×C47—22no—
135C22⋊C8×C47D414yes—
136#97×C47—41no—
137#97×C47—41no—
138C24×C47C22×C411yescharacteristic
139C23×D47C22×C411yescharacteristic
140C23×D47C22×C411yescharacteristic
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—22no—
146C22×C4×C47—41no—
147C22×C4×C47—41no—
148C22×C4×C47—41no—
149C22×C4×C47—41no—
150C22×C4×C47—41no—
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C22×C411yescharacteristic
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C2×D412yes—
157C22×C4×C47#4112yes—
158C22×C4×C47C2411yescharacteristic
159C2×C22⋊D47—22no—
160C2×C22⋊D47—22no—
161C2×C22⋊D47—22no—
162C2×C22⋊D47—22no—
163C2×C22⋊D47—41no—
164C2×C22⋊D47—41no—
165C22×Dic47C22×C411yescharacteristic
166C22×Dic47C22×C411yescharacteristic
167C22×Dic47C22×C411yescharacteristic
168C22×Dic47C22×C411yescharacteristic
169C22×Dic47C22×C411yescharacteristic
170C22×Dic47C22×C411yescharacteristic
171#10625350—44no—
172#10625350—44no—
173#10625350—44no—
174#10625350—44no—
175C2×D188—22no—
176C2×D188—22no—
177C2×D188—41no—
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×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—21no—
187C2×C4×D47—21no—
188C2×C4×D47#4112yes—
189C2×C4×D47#4112yes—
190C2×Dic94—22no—
191C2×Dic94—22no—
192C2×Dic94—41no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47C2×D412yes—
204C2×C8×C47C2×D412yes—
205C42×C47—21no—
206C42×C47—21no—
207C42×C47—21no—
208C42×C47—21no—
209C42×C47—41no—
210C42×C47—41no—
211C22⋊Dic47—22no—
212C22⋊Dic47—22no—
213(C2×D47)⋊C4—22no—
214(C2×D47)⋊C4—22no—
215(C2×D47)⋊C4—41no—
216(C2×D47)⋊C4—41no—
217(C2×D47)⋊C4—41no—
218(C2×D47)⋊C4—41no—
219(C2×D47)⋊C4—41no—
220(C2×D47)⋊C4—41no—
221C4⋊Dic47—22no—
222C4⋊Dic47—22no—
223C4×Dic47—21no—
224C4×Dic47—21no—
225C4×Dic47—21no—
226C4×Dic47—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⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—21no—
239#10625324—44no—
240C8×D47—44no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47C4×D412yes—
248C23×C47C23×C411yescharacteristic
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×D47—21no—
262C22×D47#11712yes—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
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×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—44no—
281C2×C4×C47—44no—
282C2×C4×C47C4×D412yes—
283C2×C4×C47#13112yes—
284C2×C4×C47C22×D411yescharacteristic
285C2×C4×C47C2×#4111yescharacteristic
286C2×C4×C47C2×#4111yescharacteristic
287C2×C4×C47C2×#4111yescharacteristic
288C2×C4×C47H(5,𝔽2)11yescharacteristic
289C2×C4×C47H(5,𝔽2)11yescharacteristic
290C22⋊D47—44no—
291C22⋊D47—44no—
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×Dic47—21no—
302C2×Dic47—21no—
303C2×Dic47—21no—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—21no—
307C2×Dic47—21no—
308C2×Dic47—21no—
309C2×Dic47#11712yes—
310D188—44no—
311C4×D47—22no—
312C4×D47—22no—
313C4×D47—22no—
314C4×D47—22no—
315C4×D47—41no—
316C4×D47—41no—
317C4×D47—41no—
318C4×D47—41no—
319Dic94—44no—
320C8×C47—22no—
321C8×C47—22no—
322C8×C47—41no—
323C8×C47—41no—
324C47⋊C8—41no—
325C47⋊C8—41no—
326C47⋊C8—41no—
327C47⋊C8—41no—
328#22561—471nomaximal, Sylow
329C22×C47—22no—
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47C2×#11711yescharacteristic
337C22×C47C2×C4×D411yescharacteristic
338C22×C47#51811yescharacteristic
339C22×C47C2×#13111yescharacteristic
340C22×C47#56811yescharacteristic
341C22×C47#56811yescharacteristic
342C22×C47#56811yescharacteristic
343C2×D47—22no—
344C2×D47—22no—
345C2×D47—22no—
346C2×D47—41no—
347C2×D47—41no—
348C2×D47—41no—
349C2×D47—41no—
350C2×D47—41no—
351C2×D47—41no—
352C2×D47—41no—
353C2×D47—41no—
354C2×D47—41no—
355C2×D47—41no—
356C2×D47—41no—
357C4×C47—22no—
358C4×C47—22no—
359C4×C47—41no—
360C4×C47—41no—
361C4×C47—41no—
362C4×C47#54611yescharacteristic
363C4×C47#54611yescharacteristic
364C4×C47#55111yescharacteristic
365C4×C47#55111yescharacteristic
366Dic47—22no—
367Dic47—41no—
368Dic47—41no—
369Dic47—41no—
370Dic47—41no—
371Dic47—41no—
372C2×#433—471no—
373C2×#408—471no—
374#2297—471no—
375#1924—471no—
376#1924—471no—
377#1924—471no—
378#1923—471no—
379#1851—471no—
380#1850—471no—
381#1818—471no—
382#1797—471no—
383#1780—471no—
384#1753—471no—
385#1752—471no—
386#1749D4711yescharacteristic, complemented
387C2×C47—42no—
388C2×C47#234211yescharacteristic
389C2×C47#292311yescharacteristic
390C2×C47#292511yescharacteristic
391C2×C47#293211yescharacteristic
392C2×C47#293511yescharacteristic
393C2×C47#297611yescharacteristic
394C2×C47#297811yescharacteristic
395D47—42no—
396D47—81no—
397C22×#41—471no—
398C22×M16—471no—
399C23×C8—471no—
400C2×#117—471no—
401C22×C42C2×D4711yescharacteristic
402#433—944no—
403C2×C4⋊C8—471no—
404C2×C4⋊C8—471no—
405C2×C4⋊C8—471no—
406C2×C4⋊C8—471no—
407#408—944no—
408C2×C22⋊C8—471no—
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⋊C8C2×D4711yescharacteristic
417C2×C22⋊C8C2×D4711yescharacteristic
418C2×#97—471no—
419C2×#97C2×D4711yescharacteristic
420C2×#97C2×D4711yescharacteristic
421C2×C4×C8—471no—
422#391—471no—
423#391—471no—
424#390—471no—
425#390—471no—
426#386—471no—
427#386—471no—
428#386—471no—
429#386—471no—
430C4×C22⋊C4—471no—
431C4×C22⋊C4—471no—
432C4×C22⋊C4—471no—
433C4×C22⋊C4—471no—
434#336—471no—
435#336—471no—
436#336—471no—
437#336—471no—
438#336—471no—
439#336—471no—
440#336C2×D4711yescharacteristic
441#336C2×D4711yescharacteristic
442C47#2256111yescharacteristic, complemented, Sylow
443C2×#41—942no—
444C2×#41—942no—
445C2×#41—942no—
446C2×#41—942no—
447C2×#41—1881no—
448C2×#41—1881no—
449C22×Q8—471no—
450C22×D4—471no—
451C22×D4—471no—
452C22×D4—471no—
453C23×C4—471no—
454C23×C4—471no—
455C23×C4C4×D4711yescharacteristic
456C23×C4C4×D4711yescharacteristic
457C23×C4C22×D4711yescharacteristic
458C2×M16—942no—
459C2×M16—942no—
460C2×M16—1881no—
461C22×C8—471no—
462C22×C8—471no—
463C22×C8—471no—
464C22×C8—471no—
465C22×C8—942no—
466C22×C8—942no—
467C22×C8—1881no—
468C22×C8C22×D4711yescharacteristic
469C22×C8C22×D4711yescharacteristic
470C22×C8C22×D4711yescharacteristic
471C22×C8C22×D4711yescharacteristic
472#117—942no—
473#117—942no—
474C2×C4⋊C4—471no—
475C2×C4⋊C4—471no—
476C2×C22⋊C4—471no—
477C2×C22⋊C4—471no—
478C2×C22⋊C4—471no—
479C2×C22⋊C4—471no—
480C2×C22⋊C4—471no—
481C2×C22⋊C4—471no—
482C2×C22⋊C4—471no—
483C2×C22⋊C4—471no—
484C2×C22⋊C4—471no—
485C2×C22⋊C4—471no—
486C2×C42—41no—
487C2×C42—41no—
488C2×C42—471no—
489C2×C42—471no—
490C2×C42C4×D4711yescharacteristic
491C2×C42C4×D4711yescharacteristic
492C2×C42C22×D4711yescharacteristic
493C2×C42C22×D4711yescharacteristic
494C4⋊C8—942no—
495C4⋊C8—942no—
496C4⋊C8—1881no—
497C4⋊C8—1881no—
498C22⋊C8—22no—
499C22⋊C8—942no—
500C22⋊C8—942no—
501C22⋊C8—942no—
502C22⋊C8—942no—
503C22⋊C8—942no—
504C22⋊C8—942no—
505C22⋊C8—1881no—
506C22⋊C8—1881no—
507C22⋊C8D18814yes—
508#97—41no—
509#97—41no—
510#97—942no—
511C4×C8—942no—
512#95—471no—
513#95—471no—
514#95—471no—
515#95—471no—
516#95—471no—
517#95—471no—
518#95—471no—
519#95—471no—
520C24—471no—
521C24—471no—
522C24C2×C4×D4711yescharacteristic
523#41—1884no—
524#41—1884no—
525#41—1884no—
526#41—1884no—
527C2×Q8—942no—
528C2×Q8—942no—
529C2×Q8—1881no—
530C2×D4—942no—
531C2×D4—942no—
532C2×D4—942no—
533C2×D4—942no—
534C2×D4—942no—
535C2×D4—942no—
536C2×D4—1881no—
537C2×D4—1881no—
538C2×D4—1881no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—471no—
550C22×C4—472no—
551C22×C4—472no—
552C22×C4—471no—
553C22×C4—471no—
554C22×C4—471no—
555C22×C4—471no—
556C22×C4—471no—
557C22×C4—941no—
558C22×C4—941no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4C2×C4×D4711yescharacteristic
568C22×C4C2×C4×D4711yescharacteristic
569C22×C4C2×C4×D4711yescharacteristic
570C22×C4C2×C4×D4711yescharacteristic
571C22×C4C2×C4×D4711yescharacteristic
572C22×C4C2×D18812yes—
573C22×C4#1062535012yes—
574C22×C4C23×D4711yescharacteristic
575M16—1884no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—941no—
587C2×C8—941no—
588C2×C8—941no—
589C2×C8—941no—
590C2×C8—941no—
591C2×C8—941no—
592C2×C8—941no—
593C2×C8—941no—
594C2×C8—941no—
595C2×C8—941no—
596C2×C8—941no—
597C2×C8—941no—
598C2×C8—1884no—
599C2×C8C2×D18812yes—
600C2×C8C2×D18812yes—
601C4⋊C4—942no—
602C4⋊C4—942no—
603C22⋊C4—942no—
604C22⋊C4—942no—
605C22⋊C4—942no—
606C22⋊C4—942no—
607C22⋊C4—1881no—
608C22⋊C4—1881no—
609C22⋊C4—1881no—
610C22⋊C4—1881no—
611C22⋊C4—1881no—
612C22⋊C4—1881no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—41no—
618C42—41no—
619C42—941no—
620C42—941no—
621C42—941no—
622C42—941no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—472no—
630C23—941no—
631C23—941no—
632C23—941no—
633C23—941no—
634C23—941no—
635C23—941no—
636C23—941no—
637C23—941no—
638C23—941no—
639C23—941no—
640C23—941no—
641C23—941no—
642C23—941no—
643C23C4×D18812yes—
644C23C22×C4×D4711yescharacteristic
645Q8—1884no—
646D4—1884no—
647D4—1884no—
648D4—1884no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—472no—
669C2×C4—941no—
670C2×C4—941no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—941no—
676C2×C4—941no—
677C2×C4—941no—
678C2×C4—941no—
679C2×C4—941no—
680C2×C4—941no—
681C2×C4—941no—
682C2×C4—941no—
683C2×C4—941no—
684C2×C4—941no—
685C2×C4—941no—
686C2×C4—941no—
687C2×C4—941no—
688C2×C4—941no—
689C2×C4—941no—
690C2×C4—1881no—
691C2×C4—1881no—
692C2×C4—1881no—
693C2×C4—1881no—
694C2×C4C4×D18812yes—
695C2×C4#1309403212yes—
696C2×C4C22×D18811yescharacteristic
697C2×C4#41×D4711yescharacteristic
698C2×C4#41×D4711yescharacteristic
699C2×C4C2×#1062535011yescharacteristic
700C2×C4#1309406911yescharacteristic
701C2×C4#1309406911yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C8—1881no—
707C8—1881no—
708C8—1881no—
709C8—1881no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—942no—
718C22—942no—
719C22—942no—
720C22—1881no—
721C22—1881no—
722C22—1881no—
723C22—1881no—
724C22—1881no—
725C22—1881no—
726C22—1881no—
727C22—1881no—
728C22—1881no—
729C22—1881no—
730C22—1881no—
731C22#117×D4711yescharacteristic
732C22C2×C4×D18811yescharacteristic
733C22#1568959611yescharacteristic
734C22C2×#1309403211yescharacteristic
735C22#1568988911yescharacteristic
736C22#1568988911yescharacteristic
737C22#1568988911yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—942no—
744C4—1881no—
745C4—1881no—
746C4—1881no—
747C4—1881no—
748C4—1881no—
749C4#1568976811yescharacteristic
750C4#1568976811yescharacteristic
751C4#1568980211yescharacteristic
752C4#1568980211yescharacteristic
753C2—42no—
754C2—3761no—
755C2—1882no—
756C2#2024624011yescharacteristic
757C2#2025203411yescharacteristic
758C2#2025205511yescharacteristic
759C2#2025210711yescharacteristic
760C2#2025213411yescharacteristic
761C2#2025243811yescharacteristic
762C2#2025244811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1749C2
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenter#1749D47
hypocenterC47#22561
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
1. C2×#15689181C2semidirect
4. #20244002C2semidirect
5. #20244001C2semidirect
6. #20244001C2semidirect
7. #20243995C2semidirect
8. #20243572C2semidirect
9. #20243567C2semidirect
10. #20243457C2semidirect
11. #20243368C2semidirect
13. #20243173C2semidirect
14. #20243165C2semidirect
15. C47×#1749C2semidirect
386. #1749D47semidirect
442. C47#22561semidirect

Maximal subgroups

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

subgroupindex
C2×#156891812
C2×#156890882
#202458782
#202440022
#202440012
#202439952
#202435722
#202435672
#202434572
#202433682
#202432992
#202431732
#202431652
C47×#17492
#2256147