Finite Group Databasebeta

← #26233288

Subgroups — #26233288

Order 12032.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689185C211yesmaximal, characteristic, complemented
2C2×#15689086C211yesmaximal, characteristic
3#20245769C211yesmaximal, characteristic
4#20244001C211yesmaximal, characteristic, complemented
5#20243999C211yesmaximal, characteristic, complemented
6#20243994C211yesmaximal, characteristic, complemented
7#20243992C211yesmaximal, characteristic, complemented
8#20243571C211yesmaximal, characteristic, complemented
9#20243570C211yesmaximal, characteristic, complemented
10#20243458C211yesmaximal, characteristic, complemented
11#20243371C211yesmaximal, characteristic, complemented
12#20243297C211yesmaximal, characteristic
13#20243172C211yesmaximal, characteristic, complemented
14#20243155C211yesmaximal, characteristic, complemented
15C47×#1753C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C2×#13093981C2211yescharacteristic
19C2×#13093981C2211yescharacteristic
20#15689185—24no—
21C2×Dic47⋊C8C2211yescharacteristic, complemented
22C2×Dic47⋊C8C2211yescharacteristic, complemented
23C2×Dic47⋊C8C2211yescharacteristic, complemented
24C2×Dic47⋊C8C2211yescharacteristic, complemented
25#15689086—24no—
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×(C2×D47)⋊C8C2211yescharacteristic
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×#13093935C2211yescharacteristic, complemented
36C2×C4×C47⋊C8C2211yescharacteristic, complemented
37#15688985C411yescharacteristic
38#15688985C411yescharacteristic
39#15688982C411yescharacteristic
40#15688982C411yescharacteristic
41#15688981C411yescharacteristic
42#15688981C411yescharacteristic
43#15688978C411yescharacteristic
44#15688978C411yescharacteristic
45C4×(C2×D47)⋊C4C2211yescharacteristic
46C4×(C2×D47)⋊C4C2211yescharacteristic
47C4×C22⋊Dic47C2211yescharacteristic
48#15688878C2211yescharacteristic, complemented
49#15688878C2211yescharacteristic, complemented
50#15688877C2211yescharacteristic, complemented
51#15688877C2211yescharacteristic, complemented
52#15688877C2211yescharacteristic, complemented
53#15688877C2211yescharacteristic, complemented
54C22×M16×C47C2211yescharacteristic
55C2×C22⋊C8×C47C2211yescharacteristic
56C2×#97×C47C2211yescharacteristic, complemented
57C2×C4×C8×C47C2211yescharacteristic, complemented
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#336C2211yescharacteristic, complemented
60C47×#336C2211yescharacteristic, complemented
61C24×D47C2×C411yescharacteristic
62C23×Dic47C2×C411yescharacteristic
63C22×C4×D47—22no—
64C22×C4×D47—22no—
65C22×C4×D47—22no—
66C22×C4×D47—22no—
67C22×C4×D47—41no—
68C22×C4×D47—41no—
69C22×C4×D47C2×C411yescharacteristic
70C22×C4×D47C2×C411yescharacteristic
71C22×C4×D47C2311yescharacteristic
72C22×C4×D47C2311yescharacteristic
73C2×#10625329—22no—
74C2×#10625329—22no—
75C2×#10625329—41no—
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C22×C47⋊C8C2311yescharacteristic
79C22×C47⋊C8C2311yescharacteristic
80#13093981—22no—
81#13093981—22no—
82#13093981—41no—
83#13093981—41no—
84C2×Dic47⋊C4C2×C411yescharacteristic
85C2×Dic47⋊C4C2×C411yescharacteristic
86C2×Dic47⋊C4C2×C411yescharacteristic
87C2×Dic47⋊C4C2×C411yescharacteristic
88C2×C22⋊Dic47C2×C411yescharacteristic
89C2×C22⋊Dic47C2×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×(C2×D47)⋊C4C2×C411yescharacteristic
98C2×C4×Dic47C2311yescharacteristic
99C2×C4×Dic47C2311yescharacteristic
100Dic47⋊C8—22no—
101Dic47⋊C8—22no—
102Dic47⋊C8—41no—
103Dic47⋊C8—41no—
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—22no—
110(C2×D47)⋊C8—41no—
111(C2×D47)⋊C8—41no—
112(C2×D47)⋊C8D414yes—
113#13093935—41no—
114C4×C47⋊C8—22no—
115C47⋊#95C2×C411yescharacteristic
116C47⋊#95C2×C411yescharacteristic
117C47⋊#95C2×C411yescharacteristic
118C47⋊#95C2×C411yescharacteristic
119C47⋊#95C2×C411yescharacteristic
120C47⋊#95C2×C411yescharacteristic
121C23×C4×C47C2311yescharacteristic
122C2×M16×C47—22no—
123C2×M16×C47—22no—
124C2×M16×C47—41no—
125C22×C8×C47C2311yescharacteristic
126C22×C8×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C2×C22⋊C4×C47C2×C411yescharacteristic
130C2×C22⋊C4×C47C2×C411yescharacteristic
131C2×C42×C47C2311yescharacteristic
132C2×C42×C47C2311yescharacteristic
133C22⋊C8×C47—22no—
134#97×C47—22no—
135C4×C8×C47—41no—
136#95×C47C2×C411yescharacteristic
137#95×C47C2×C411yescharacteristic
138C24×C47C22×C411yescharacteristic
139C23×D47—22no—
140C23×D47—22no—
141C23×D47—22no—
142C23×D47—41no—
143C23×D47—41no—
144C23×D47—41no—
145C23×D47—41no—
146C23×D47C22×C411yescharacteristic
147C23×D47C22×C411yescharacteristic
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C22×C411yescharacteristic
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C22×C411yescharacteristic
157C22×C4×C47#4112yes—
158C22×C4×C47#4112yes—
159C22×C4×C47C2411yescharacteristic
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—41no—
163C22×Dic47C22×C411yescharacteristic
164C22×Dic47C22×C411yescharacteristic
165C22×Dic47C22×C411yescharacteristic
166C22×Dic47C22×C411yescharacteristic
167C22×Dic47C22×C411yescharacteristic
168C22×Dic47C22×C411yescharacteristic
169C2×C4×D47—21no—
170C2×C4×D47—21no—
171C2×C4×D47—21no—
172C2×C4×D47—21no—
173C2×C4×D47—22no—
174C2×C4×D47—22no—
175C2×C4×D47—22no—
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—22no—
183C2×C4×D47—44no—
184C2×C4×D47—44no—
185C2×C4×D47—44no—
186C2×C4×D47—44no—
187C2×C4×D47—41no—
188C2×C4×D47—41no—
189C2×C4×D47C2×D412yes—
190C2×C4×D47#4112yes—
191M16×C47—44no—
192C2×C8×C47—21no—
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—
204C22⋊C4×C47—41no—
205C22⋊C4×C47—41no—
206C42×C47—21no—
207C42×C47—21no—
208C42×C47—21no—
209C42×C47—21no—
210C22⋊Dic47—41no—
211C22⋊Dic47—41no—
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—
218(C2×D47)⋊C4—41no—
219(C2×D47)⋊C4—41no—
220Dic47⋊C4—22no—
221Dic47⋊C4—22no—
222Dic47⋊C4—41no—
223Dic47⋊C4—41no—
224C4×Dic47—21no—
225C4×Dic47—21no—
226C4×Dic47—21no—
227C4×Dic47—21no—
228#10625329—44no—
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—
239C2×C47⋊C8—21no—
240C2×C47⋊C8C2×D412yes—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47#11712yes—
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—44no—
262C22×D47—44no—
263C22×D47—44no—
264C22×D47—44no—
265C22×D47—44no—
266C22×D47—44no—
267C22×D47—44no—
268C22×D47C4×D412yes—
269C22×D47#13112yes—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47#11712yes—
289C2×C4×C47C22×D411yescharacteristic
290C2×C4×C47C2×#4111yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C47C2×#4111yescharacteristic
293C2×C4×C47H(5,𝔽2)11yescharacteristic
294C2×C4×C47H(5,𝔽2)11yescharacteristic
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—21no—
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—44no—
313C2×Dic47C4×D412yes—
314C4×D47—22no—
315C4×D47—22no—
316C4×D47—22no—
317C4×D47—22no—
318C4×D47—44no—
319C4×D47—44no—
320C4×D47—41no—
321C4×D47—41no—
322C4×D47—41no—
323C4×D47—41no—
324C8×C47—22no—
325C8×C47—41no—
326C8×C47—41no—
327C8×C47—41no—
328C47⋊C8—22no—
329C47⋊C8—41no—
330C47⋊C8—41no—
331C47⋊C8—41no—
332#22559—471nomaximal, Sylow
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47C2×#11711yescharacteristic
341C22×C47C2×C4×D411yescharacteristic
342C22×C47#51811yescharacteristic
343C22×C47C2×#13111yescharacteristic
344C22×C47#56811yescharacteristic
345C22×C47#56811yescharacteristic
346C22×C47#56811yescharacteristic
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—22no—
351C2×D47—22no—
352C2×D47—22no—
353C2×D47—416no—
354C2×D47—41no—
355C2×D47—41no—
356C2×D47—41no—
357C2×D47—41no—
358C2×D47—41no—
359C2×D47—41no—
360C2×D47—41no—
361C2×D47—41no—
362C4×C47—22no—
363C4×C47—41no—
364C4×C47—41no—
365C4×C47—41no—
366C4×C47—41no—
367C4×C47#54611yescharacteristic
368C4×C47#54611yescharacteristic
369C4×C47#55111yescharacteristic
370C4×C47#55111yescharacteristic
371Dic47—22no—
372Dic47—41no—
373Dic47—41no—
374Dic47—41no—
375Dic47—41no—
376Dic47—41no—
377C2×#433—471no—
378C2×#407—471no—
379#2280—471no—
380#1924—471no—
381#1924—471no—
382#1923—471no—
383#1923—471no—
384#1851—471no—
385#1851—471no—
386#1818—471no—
387#1798—471no—
388#1779—471no—
389#1753—471no—
390#1753D4711yescharacteristic, complemented
391#1750—471no—
392C2×C47—42no—
393C2×C47#234211yescharacteristic
394C2×C47#292111yescharacteristic
395C2×C47#292411yescharacteristic
396C2×C47#293011yescharacteristic
397C2×C47#293311yescharacteristic
398C2×C47#297611yescharacteristic
399C2×C47#297811yescharacteristic
400D47—42no—
401D47—42no—
402C24×C4—471no—
403C22×M16—471no—
404C22×M16C2×D4711yescharacteristic
405C2×#117—471no—
406C2×#117—471no—
407#433—944no—
408C2×C4⋊C8—471no—
409C2×C4⋊C8—471no—
410C2×C4⋊C8—471no—
411C2×C4⋊C8—471no—
412#407—944no—
413C2×C22⋊C8—471no—
414C2×C22⋊C8—471no—
415C2×C22⋊C8—471no—
416C2×C22⋊C8—471no—
417C2×C22⋊C8—471no—
418C2×C22⋊C8—471no—
419C2×C22⋊C8—471no—
420C2×C22⋊C8—471no—
421C2×C22⋊C8—471no—
422C2×C22⋊C8C2×D4711yescharacteristic
423C2×#97—471no—
424C2×#97C2×D4711yescharacteristic, complemented
425C2×C4×C8—471no—
426C2×C4×C8C2×D4711yescharacteristic, complemented
427#381—471no—
428#381—471no—
429#380—471no—
430#380—471no—
431#380—471no—
432#380—471no—
433#379—471no—
434#379—471no—
435C4×C22⋊C4—471no—
436C4×C22⋊C4—471no—
437C4×C22⋊C4—471no—
438C4×C22⋊C4C2×D4711yescharacteristic
439#336—471no—
440#336—471no—
441#336—471no—
442#336—471no—
443#336—471no—
444#336—471no—
445#336C2×D4711yescharacteristic, complemented
446#336C2×D4711yescharacteristic, complemented
447C47#2255911yescharacteristic, complemented, Sylow
448C25—471no—
449C23×C4—471no—
450C23×C4—471no—
451C23×C4—471no—
452C23×C4—471no—
453C23×C4—471no—
454C23×C4—942no—
455C23×C4—942no—
456C23×C4—942no—
457C23×C4—942no—
458C23×C4—1881no—
459C23×C4—1881no—
460C23×C4C22×D4711yescharacteristic
461C2×M16—22no—
462C2×M16—22no—
463C2×M16—41no—
464C2×M16—942no—
465C2×M16—942no—
466C2×M16—1881no—
467C22×C8—471no—
468C22×C8—471no—
469C22×C8—471no—
470C22×C8—471no—
471C22×C8C22×D4711yescharacteristic
472C22×C8C22×D4711yescharacteristic
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475#117—942no—
476#117—942no—
477#117—1881no—
478#117—1881no—
479C2×C4⋊C4—471no—
480C2×C4⋊C4—471no—
481C2×C4⋊C4—471no—
482C2×C4⋊C4—471no—
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⋊C4C4×D4711yescharacteristic
494C2×C22⋊C4C4×D4711yescharacteristic
495C2×C42—471no—
496C2×C42—471no—
497C2×C42C22×D4711yescharacteristic
498C2×C42C22×D4711yescharacteristic
499C4⋊C8—942no—
500C4⋊C8—942no—
501C4⋊C8—1881no—
502C4⋊C8—1881no—
503C22⋊C8—22no—
504C22⋊C8—474no—
505C22⋊C8—942no—
506C22⋊C8—942no—
507C22⋊C8—942no—
508C22⋊C8—942no—
509C22⋊C8—942no—
510C22⋊C8—942no—
511C22⋊C8—1881no—
512C22⋊C8—1881no—
513#97—22no—
514#97—1881no—
515C4×C8—41no—
516C4×C8—942no—
517#95—471no—
518#95—471no—
519#95—471no—
520#95—471no—
521#95—471no—
522#95—471no—
523#95C4×D4711yescharacteristic
524#95C4×D4711yescharacteristic
525C24—471no—
526C24—471no—
527C24—942no—
528C24—942no—
529C24—942no—
530C24—1881no—
531C24—1881no—
532C24—1881no—
533C24—1881no—
534C24C2×C4×D4711yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—471no—
540C22×C4—472no—
541C22×C4—472no—
542C22×C4—471no—
543C22×C4—471no—
544C22×C4—471no—
545C22×C4—471no—
546C22×C4—471no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—941no—
551C22×C4—941no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4—941no—
558C22×C4—941no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—1881no—
564C22×C4—1881no—
565C22×C4—1884no—
566C22×C4—1884no—
567C22×C4—1884no—
568C22×C4—1884no—
569C22×C4—1881no—
570C22×C4C2×C4×D4711yescharacteristic
571C22×C4C2×C4×D4711yescharacteristic
572C22×C4C2×C4×D4711yescharacteristic
573C22×C4C2×C4×D4711yescharacteristic
574C22×C4C2×C4×D4711yescharacteristic
575C22×C4#1062535012yes—
576C22×C4#1062535012yes—
577C22×C4C23×D4711yescharacteristic
578M16—44no—
579M16—1884no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—472no—
592C2×C8—941no—
593C2×C8—941no—
594C2×C8—941no—
595C2×C8—941no—
596C2×C8—941no—
597C2×C8—941no—
598C2×C8—941no—
599C2×C8—941no—
600C2×C8—941no—
601C2×C8—941no—
602C2×C8—941no—
603C2×C8D4×D4712yes—
604C4⋊C4—942no—
605C4⋊C4—942no—
606C4⋊C4—1881no—
607C4⋊C4—1881no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—942no—
611C22⋊C4—942no—
612C22⋊C4—942no—
613C22⋊C4—942no—
614C22⋊C4—1881no—
615C22⋊C4—1881no—
616C22⋊C4—1881no—
617C22⋊C4—1881no—
618C22⋊C4—1881no—
619C22⋊C4—1881no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—941no—
625C42—941no—
626C42—941no—
627C42—941no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—472no—
635C23—472no—
636C23—941no—
637C23—941no—
638C23—941no—
639C23—941no—
640C23—941no—
641C23—941no—
642C23—941no—
643C23—941no—
644C23—941no—
645C23—941no—
646C23—941no—
647C23—941no—
648C23—1884no—
649C23—1884no—
650C23—1884no—
651C23—1884no—
652C23—1884no—
653C23—1884no—
654C23—1884no—
655C23#1309398112yes—
656C23C22×C4×D4711yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—472no—
676C2×C4—941no—
677C2×C4—941no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
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—941no—
691C2×C4—941no—
692C2×C4—941no—
693C2×C4—941no—
694C2×C4—941no—
695C2×C4—941no—
696C2×C4—941no—
697C2×C4—1884no—
698C2×C4—1884no—
699C2×C4—1884no—
700C2×C4—1881no—
701C2×C4—1881no—
702C2×C4—1881no—
703C2×C4—1881no—
704C2×C4#1309398112yes—
705C2×C4C2×D4×D4711yescharacteristic
706C2×C4#41×D4711yescharacteristic
707C2×C4C2×#1062535011yescharacteristic
708C2×C4C2×#1062535011yescharacteristic
709C2×C4#1309406911yescharacteristic
710C2×C4#1309407011yescharacteristic
711C8—22no—
712C8—41no—
713C8—41no—
714C8—41no—
715C8—942no—
716C8—1881no—
717C8—1881no—
718C8—1881no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—942no—
727C22—942no—
728C22—942no—
729C22—942no—
730C22—942no—
731C22—942no—
732C22—18816no—
733C22—1881no—
734C22—1881no—
735C22—1881no—
736C22—1881no—
737C22—1881no—
738C22—1881no—
739C22—1881no—
740C22—1881no—
741C22C2×#1309398111yescharacteristic
742C22C4×D4×D4711yescharacteristic
743C22#1568959511yescharacteristic
744C22#131×D4711yescharacteristic
745C22#1568988811yescharacteristic
746C22#1568988911yescharacteristic
747C22#1568988911yescharacteristic
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—942no—
754C4—1881no—
755C4—1881no—
756C4—1881no—
757C4—1881no—
758C4—1881no—
759C4#1568976311yescharacteristic
760C4#1568976911yescharacteristic
761C4#1568979711yescharacteristic
762C4#1568980211yescharacteristic
763C2—42no—
764C2—1882no—
765C2—1882no—
766C2#2024623111yescharacteristic
767C2#2025202411yescharacteristic
768C2#2025204311yescharacteristic
769C2#2025208811yescharacteristic
770C2#2025211711yescharacteristic
771C2#2025243511yescharacteristic
772C2#2025244711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1753C2
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1753D47
hypocenterC47#22559
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#15689185C2semidirect
4. #20244001C2semidirect
5. #20243999C2semidirect
6. #20243994C2semidirect
7. #20243992C2semidirect
8. #20243571C2semidirect
9. #20243570C2semidirect
10. #20243458C2semidirect
11. #20243371C2semidirect
13. #20243172C2semidirect
14. #20243155C2semidirect
15. C47×#1753C2semidirect
21. C2×Dic47⋊C8C22semidirect
22. C2×Dic47⋊C8C22semidirect
23. C2×Dic47⋊C8C22semidirect
24. C2×Dic47⋊C8C22semidirect
35. C2×#13093935C22semidirect
36. C2×C4×C47⋊C8C22semidirect
48. #15688878C22semidirect
49. #15688878C22semidirect
50. #15688877C22semidirect
51. #15688877C22semidirect
52. #15688877C22semidirect
53. #15688877C22semidirect
56. C2×#97×C47C22semidirect
57. C2×C4×C8×C47C22semidirect
59. C47×#336C22semidirect
60. C47×#336C22semidirect
390. #1753D47semidirect
424. C2×#97C2×D47semidirect
426. C2×C4×C8C2×D47semidirect
445. #336C2×D47semidirect
446. #336C2×D47semidirect
447. C47#22559semidirect

Maximal subgroups

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

subgroupindex
C2×#156891852
C2×#156890862
#202457692
#202440012
#202439992
#202439942
#202439922
#202435712
#202435702
#202434582
#202433712
#202432972
#202431722
#202431552
C47×#17532
#2255947