Finite Group Databasebeta

← #26226924

Subgroups — #26226924

Order 12032.

930 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2#20243996C211yesmaximal, characteristic, complemented
3#20243945C211yesmaximal, characteristic, complemented
4#20243943C211yesmaximal, characteristic, complemented
5#20243677C211yesmaximal, characteristic
6#20243677C211yesmaximal, characteristic
7#20243567C211yesmaximal, characteristic, complemented
8#20243564C211yesmaximal, characteristic, complemented
9#20243530C211yesmaximal, characteristic, complemented
10#20243504C211yesmaximal, characteristic, complemented
11#20243454C211yesmaximal, characteristic, complemented
12#20243366C211yesmaximal, characteristic, complemented
13C4×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
14#336×D47C211yesmaximal, characteristic, complemented
15C47×#1923C211yesmaximal, characteristic, complemented
16C22×C8×D47C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C2×C4×C22⋊D47C2211yescharacteristic
19C2×(C22⋊D47)⋊C4C411yescharacteristic
20C2×(C22⋊D47)⋊C4C411yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22C2×C42×D47C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25C2×Dic47⋊C8C2211yescharacteristic
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×C22⋊(C47⋊C8)C2211yescharacteristic
28C2×(C2×D47)⋊C8C2211yescharacteristic
29C2×(C2×D47)⋊C8C2211yescharacteristic
30C2×C4×C47⋊C8C2211yescharacteristic
31C4×Dic47⋊C4C2211yescharacteristic
32#15688974C411yescharacteristic
33#15688974C411yescharacteristic
34C22⋊C4×Dic47C411yescharacteristic
35C22⋊C4×Dic47C411yescharacteristic
36C4×(C2×D47)⋊C4C2211yescharacteristic
37#15688970C411yescharacteristic
38#15688970C411yescharacteristic
39C42×Dic47C2211yescharacteristic
40#15688878C2211yescharacteristic
41#15688878C2211yescharacteristic
42#15688877C2211yescharacteristic
43#15688877C2211yescharacteristic
44#15688877C2211yescharacteristic
45#15688877C2211yescharacteristic
46#15688877C2211yescharacteristic
47#15688877C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52C2×C4⋊C8×C47C2211yescharacteristic
53C2×C22⋊C8×C47C2211yescharacteristic
54C2×C22⋊C8×C47C2211yescharacteristic
55C2×C4×C8×C47C2211yescharacteristic
56C4×C22⋊C4×C47C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×C22⋊D47C2×C411yescharacteristic
60C23×Dic47C2×C411yescharacteristic
61C23×Dic47C2×C411yescharacteristic
62C22×C4×D47C2×C411yescharacteristic
63C22×C4×D47C2×C411yescharacteristic
64C22×C4×D47C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C2×C8×D47—22no—
70C2×C8×D47—22no—
71C2×C8×D47—41no—
72C2×C8×D47—41no—
73C2×C8×D47—41no—
74C2×C8×D47—41no—
75C4×C22⋊D47—22no—
76C4×C22⋊D47—22no—
77(C22⋊D47)⋊C4—24no—
78(C22⋊D47)⋊C4C818yescomplemented
79C2×Dic47⋊C4C2×C411yescharacteristic
80C2×Dic47⋊C4C2×C411yescharacteristic
81C2×Dic47⋊C4C2×C411yescharacteristic
82C2×C22⋊Dic47C2×C411yescharacteristic
83C2×(C2×D47)⋊C4C2×C411yescharacteristic
84C2×(C2×D47)⋊C4C2×C411yescharacteristic
85C2×(C2×D47)⋊C4C2×C411yescharacteristic
86C2×C4×Dic47—41no—
87C2×C4×Dic47—41no—
88C2×C4×Dic47C2×C411yescharacteristic
89C2×C4×Dic47C2×C411yescharacteristic
90C2×C4×Dic47C2×C411yescharacteristic
91C2×C4×Dic47C2×C411yescharacteristic
92C2×C4×Dic47C2×C411yescharacteristic
93C2×C4×Dic47C2×C411yescharacteristic
94C2×C4×Dic47C2×C411yescharacteristic
95C2×C4×Dic47C2×C411yescharacteristic
96C2×C4×Dic47C2311yescharacteristic
97C2×C4×Dic47C2311yescharacteristic
98C2×C4×Dic47C2311yescharacteristic
99C42×D47—41no—
100C42×D47—41no—
101C4⋊(C47⋊C8)—41no—
102Dic47⋊C8—41no—
103Dic47⋊C8—41no—
104C22⋊(C47⋊C8)—41no—
105C22⋊(C47⋊C8)—41no—
106(C2×D47)⋊C8—22no—
107(C2×D47)⋊C8—22no—
108C4×C47⋊C8—41no—
109C47⋊#95C2×C411yescharacteristic
110C47⋊#95C2×C411yescharacteristic
111C47⋊#95C2×C411yescharacteristic
112C47⋊#95C2×C411yescharacteristic
113C23×C4×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116C22×C8×C47C2311yescharacteristic
117C22×C8×C47C2311yescharacteristic
118C2×C22⋊C4×C47C2×C411yescharacteristic
119C2×C22⋊C4×C47C2×C411yescharacteristic
120C2×C42×C47C2311yescharacteristic
121C2×C42×C47C2311yescharacteristic
122C4⋊C8×C47—41no—
123C22⋊C8×C47—41no—
124C22⋊C8×C47—41no—
125C4×C8×C47—41no—
126#95×C47C2×C411yescharacteristic
127#95×C47C2×C411yescharacteristic
128C24×C47C22×C411yescharacteristic
129C23×D47C22×C411yescharacteristic
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47C22×C411yescharacteristic
137C22×C4×C47C22×C411yescharacteristic
138C22×C4×C47C22×C411yescharacteristic
139C22×C4×C47C22×C411yescharacteristic
140C22×C4×C47C22×C411yescharacteristic
141C22×C4×C47C2411yescharacteristic
142C2×C22⋊D47—22no—
143C2×C22⋊D47—22no—
144C2×C22⋊D47C2×C814yes—
145C22×Dic47—22no—
146C22×Dic47—41no—
147C22×Dic47—41no—
148C22×Dic47—41no—
149C22×Dic47—41no—
150C22×Dic47C2×C814yescomplemented
151C22×Dic47C22×C411yescharacteristic
152C22×Dic47C22×C411yescharacteristic
153C22×Dic47C22×C411yescharacteristic
154C22×Dic47C22×C411yescharacteristic
155C22×Dic47C22×C411yescharacteristic
156C22×Dic47C22×C411yescharacteristic
157C22×Dic47C22×C411yescharacteristic
158C2×C4×D47—21no—
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47—21no—
162C2×C4×D47—41no—
163C2×C4×D47—41no—
164C2×C4×D47—41no—
165C2×C4×D47—41no—
166C2×C4×D47C2×C814yes—
167C2×C4×D47M1614yes—
168C2×C4×D47#4112yes—
169C2×C4×D47#4112yes—
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C22⋊C4×C47—22no—
183C22⋊C4×C47C2×C814yescomplemented
184C42×C47—21no—
185C42×C47—21no—
186C42×C47—21no—
187C42×C47—21no—
188C22⋊Dic47—22no—
189(C2×D47)⋊C4—22no—
190(C2×D47)⋊C4—22no—
191(C2×D47)⋊C4C2×C814yes—
192Dic47⋊C4—22no—
193Dic47⋊C4—22no—
194Dic47⋊C4C2×C814yescomplemented
195C4×Dic47—21no—
196C4×Dic47—21no—
197C4×Dic47—21no—
198C4×Dic47—21no—
199C4×Dic47—21no—
200C4×Dic47—21no—
201C4×Dic47—22no—
202C4×Dic47—41no—
203C4×Dic47—41no—
204C4×Dic47—41no—
205C4×Dic47—41no—
206C4×Dic47—41no—
207C4×Dic47—41no—
208C4×Dic47C2×C814yescomplemented
209C2×C47⋊C8—21no—
210C2×C47⋊C8—21no—
211C2×C47⋊C8—21no—
212C2×C47⋊C8—21no—
213C2×C47⋊C8—21no—
214C2×C47⋊C8—21no—
215C2×C47⋊C8—21no—
216C2×C47⋊C8—21no—
217C2×C47⋊C8—21no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8—21no—
221C8×D47—44no—
222C8×D47—44no—
223C23×C47—21no—
224C23×C47—21no—
225C23×C47—21no—
226C23×C47—21no—
227C23×C47—21no—
228C23×C47—21no—
229C23×C47C22×C812yes—
230C23×C47C23×C411yescharacteristic
231C22×D47—21no—
232C22×D47—21no—
233C22×D47—21no—
234C22×D47—21no—
235C22×D47#11712yes—
236C22×D47C22×C812yes—
237C22×D47C2×M1612yes—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47C22×C812yes—
255C2×C4×C47C22×C812yes—
256C2×C4×C47C2×M1612yes—
257C2×C4×C47C2×#4111yescharacteristic
258C2×C4×C47C2×#4111yescharacteristic
259C2×C4×C47H(5,𝔽2)11yescharacteristic
260C2×C4×C47H(5,𝔽2)11yescharacteristic
261C2×C4×C47H(5,𝔽2)11yescharacteristic
262C2×C4×C472−1+411yescharacteristic
263C22⋊D47—28no—
264C2×Dic47—21no—
265C2×Dic47—21no—
266C2×Dic47—21no—
267C2×Dic47—21no—
268C2×Dic47—21no—
269C2×Dic47—21no—
270C2×Dic47—21no—
271C2×Dic47—21no—
272C2×Dic47—21no—
273C2×Dic47—21no—
274C2×Dic47—21no—
275C2×Dic47—21no—
276C2×Dic47—21no—
277C2×Dic47—21no—
278C2×Dic47—21no—
279C2×Dic47—21no—
280C2×Dic47—44no—
281C2×Dic47—44no—
282C2×Dic47#11712yes—
283C2×Dic47C22×C812yes—
284C2×Dic47C22×C812yes—
285C2×Dic47C22×C812yes—
286C2×Dic47C2×M1612yes—
287C4×D47—22no—
288C4×D47—22no—
289C4×D47—22no—
290C4×D47—22no—
291C4×D47—44no—
292C4×D47—44no—
293C8×C47—41no—
294C8×C47—41no—
295C8×C47—41no—
296C8×C47—41no—
297C47⋊C8—41no—
298C47⋊C8—41no—
299C47⋊C8—41no—
300C47⋊C8—41no—
301#21996—471nomaximal, Sylow
302C22×C47—22no—
303C22×C47—22no—
304C22×C47—22no—
305C22×C47—41no—
306C22×C47—41no—
307C22×C47—41no—
308C22×C47—41no—
309C22×C47C2×#11711yescharacteristic
310C22×C47#51811yescharacteristic
311C22×C47#52011yescharacteristic
312C22×C47C23×C811yescharacteristic
313C22×C47C22×M1611yescharacteristic
314C22×C47#56811yescharacteristic
315C22×C47#56811yescharacteristic
316C2×D47—22no—
317C2×D47—22no—
318C2×D47—22no—
319C2×D47—22no—
320C2×D47—22no—
321C2×D47—22no—
322C2×D47#43114yes—
323C4×C47—22no—
324C4×C47—22no—
325C4×C47—22no—
326C4×C47—41no—
327C4×C47—41no—
328C4×C47#53811yescharacteristic
329C4×C47#53811yescharacteristic
330C4×C47#53911yescharacteristic
331C4×C47#53911yescharacteristic
332Dic47—22no—
333Dic47—22no—
334Dic47—22no—
335Dic47—22no—
336Dic47—22no—
337Dic47—41no—
338Dic47—41no—
339C42×D4—471no—
340#1923—471no—
341#1923D4711yescharacteristic, complemented
342#1916—471no—
343#1916—471no—
344#1869—471no—
345#1869—471no—
346#1850—471no—
347#1850—471no—
348#1839—471no—
349#1831—471no—
350#1817—471no—
351#1797—471no—
352C4×C22⋊C8—471no—
353C2×#336—471no—
354C2×C47—42no—
355C2×C47#231811yescharacteristic
356C2×C47C2×#43111yescharacteristic
357C2×C47#292311yescharacteristic
358C2×C47#297211yescharacteristic
359C2×C47#297311yescharacteristic
360C2×C47#298811yescharacteristic
361C2×C47#298911yescharacteristic
362D47—24no—
363C23×C8—471no—
364C23×C8—471no—
365C2×C4×D4—471no—
366C2×C4×D4—471no—
367C2×C4×D4—471no—
368C22×C42—471no—
369C22×C42—471no—
370C2×C4⋊C8—471no—
371C2×C4⋊C8—471no—
372C2×C4⋊C8—471no—
373C2×C4⋊C8C2×D4711yescharacteristic
374C2×C22⋊C8—471no—
375C2×C22⋊C8—471no—
376C2×C22⋊C8—471no—
377C2×C22⋊C8—471no—
378C2×C22⋊C8C2×D4711yescharacteristic
379C2×C22⋊C8C2×D4711yescharacteristic
380C2×C4×C8—471no—
381C2×C4×C8C2×D4711yescharacteristic
382C4×C4⋊C4—471no—
383C4×C4⋊C4—471no—
384C4×C4⋊C4—471no—
385C4×C22⋊C4—471no—
386C4×C22⋊C4—471no—
387C4×C22⋊C4—471no—
388C4×C22⋊C4—471no—
389C4×C22⋊C4—471no—
390C4×C22⋊C4C2×D4711yescharacteristic
391C43—471no—
392#336—471no—
393#336—471no—
394#336—471no—
395#336—471no—
396#336—471no—
397#336—471no—
398#336—471no—
399#336—471no—
400#336—471no—
401#336—471no—
402#336—471no—
403#336—471no—
404#336C2×D4711yescharacteristic
405#336C2×D4711yescharacteristic
406C47#2199611yescharacteristic, complemented, Sylow
407C22×D4—471no—
408C23×C4—471no—
409C23×C4—471no—
410C23×C4—471no—
411C23×C4—471no—
412C23×C4—471no—
413C23×C4C22×D4711yescharacteristic
414C22×C8—471no—
415C22×C8—471no—
416C22×C8—471no—
417C22×C8—471no—
418C22×C8—942no—
419C22×C8—942no—
420C22×C8—1881no—
421C22×C8—1881no—
422C22×C8—1881no—
423C22×C8—1881no—
424C22×C8C22×D4711yescharacteristic
425C22×C8C22×D4711yescharacteristic
426C22×C8C22×D4711yescharacteristic
427C22×C8C22×D4711yescharacteristic
428C4×D4—478no—
429C4×D4—944no—
430C4×D4—942no—
431C4×D4—942no—
432C2×C4⋊C4—471no—
433C2×C4⋊C4—471no—
434C2×C4⋊C4—471no—
435C2×C22⋊C4—471no—
436C2×C22⋊C4—471no—
437C2×C22⋊C4—471no—
438C2×C22⋊C4—471no—
439C2×C22⋊C4C4×D4711yescharacteristic
440C2×C22⋊C4C4×D4711yescharacteristic
441C2×C42—471no—
442C2×C42—471no—
443C2×C42—471no—
444C2×C42—471no—
445C2×C42—471no—
446C2×C42—471no—
447C2×C42—471no—
448C2×C42—471no—
449C2×C42—471no—
450C2×C42—471no—
451C2×C42—471no—
452C2×C42—1881no—
453C2×C42—1881no—
454C2×C42—1881no—
455C2×C42—1881no—
456C2×C42C22×D4711yescharacteristic
457C2×C42C22×D4711yescharacteristic
458C4⋊C8—41no—
459C4⋊C8—1881no—
460C4⋊C8—1881no—
461C4⋊C8—1881no—
462C22⋊C8—41no—
463C22⋊C8—41no—
464C22⋊C8—942no—
465C22⋊C8—942no—
466C22⋊C8—1881no—
467C22⋊C8—1881no—
468C4×C8—41no—
469C4×C8—1881no—
470#95—471no—
471#95—471no—
472#95—471no—
473#95—471no—
474#95C4×D4711yescharacteristic
475#95C4×D4711yescharacteristic
476C24—471no—
477C24C2×C4×D4711yescharacteristic
478C2×D4—474no—
479C2×D4—942no—
480C2×D4—942no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—471no—
488C22×C4—471no—
489C22×C4—471no—
490C22×C4—471no—
491C22×C4—471no—
492C22×C4—474no—
493C22×C4—472no—
494C22×C4—472no—
495C22×C4—474no—
496C22×C4—474no—
497C22×C4—471no—
498C22×C4—471no—
499C22×C4—942no—
500C22×C4—941no—
501C22×C4—941no—
502C22×C4—941no—
503C22×C4—941no—
504C22×C4—1881no—
505C22×C4—1881no—
506C22×C4—1881no—
507C22×C4—1881no—
508C22×C4—1881no—
509C22×C4—1881no—
510C22×C4—1881no—
511C22×C4—1881no—
512C22×C4C2×C4×D4711yescharacteristic
513C22×C4C2×C4×D4711yescharacteristic
514C22×C4C2×C4×D4711yescharacteristic
515C22×C4C2×C4×D4711yescharacteristic
516C22×C4C2×C4×D4711yescharacteristic
517C22×C4C23×D4711yescharacteristic
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—941no—
531C2×C8—941no—
532C2×C8—941no—
533C2×C8—941no—
534C2×C8—941no—
535C2×C8—941no—
536C2×C8—941no—
537C2×C8—941no—
538C2×C8—941no—
539C2×C8—941no—
540C2×C8—941no—
541C2×C8—941no—
542C2×C8—1884no—
543C2×C8—1884no—
544C4⋊C4—474no—
545C4⋊C4—942no—
546C4⋊C4—942no—
547C22⋊C4—22no—
548C22⋊C4—474no—
549C22⋊C4—942no—
550C22⋊C4—942no—
551C22⋊C4—942no—
552C22⋊C4C8×D4714yescomplemented
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—474no—
558C42—942no—
559C42—941no—
560C42—941no—
561C42—941no—
562C42—941no—
563C42—941no—
564C42—941no—
565C42—1881no—
566C42—1881no—
567C42—1881no—
568C42—1881no—
569C42—1881no—
570C42—1881no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—472no—
578C23—472no—
579C23—472no—
580C23—941no—
581C23—941no—
582C23—941no—
583C23—941no—
584C23C2×C8×D4712yes—
585C23C22×C4×D4711yescharacteristic
586D4—948no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—472no—
604C2×C4—472no—
605C2×C4—472no—
606C2×C4—472no—
607C2×C4—472no—
608C2×C4—941no—
609C2×C4—941no—
610C2×C4—941no—
611C2×C4—941no—
612C2×C4—941no—
613C2×C4—941no—
614C2×C4—941no—
615C2×C4—941no—
616C2×C4—941no—
617C2×C4—941no—
618C2×C4—942no—
619C2×C4—942no—
620C2×C4—942no—
621C2×C4—942no—
622C2×C4—941no—
623C2×C4—941no—
624C2×C4—941no—
625C2×C4—941no—
626C2×C4—941no—
627C2×C4—941no—
628C2×C4—1884no—
629C2×C4—1884no—
630C2×C4—1884no—
631C2×C4—1884no—
632C2×C4C2×C8×D4712yes—
633C2×C4C2×C8×D4712yes—
634C2×C4M16×D4712yes—
635C2×C4#41×D4711yescharacteristic
636C2×C4#41×D4711yescharacteristic
637C2×C4#1309406911yescharacteristic
638C2×C4#1309406911yescharacteristic
639C2×C4#1309407011yescharacteristic
640C2×C4#1309407111yescharacteristic
641C8—41no—
642C8—41no—
643C8—41no—
644C8—41no—
645C8—1881no—
646C8—1881no—
647C8—1881no—
648C8—1881no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—474no—
657C22—942no—
658C22—942no—
659C22—942no—
660C22—942no—
661C22—942no—
662C22—942no—
663C22#117×D4711yescharacteristic
664C22#1568959511yescharacteristic
665C22#1568960211yescharacteristic
666C22C22×C8×D4711yescharacteristic
667C22C2×M16×D4711yescharacteristic
668C22#1568988811yescharacteristic
669C22#1568988811yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—41no—
674C4—41no—
675C4—942no—
676C4—942no—
677C4—942no—
678C4—942no—
679C4—942no—
680C4—1881no—
681C4—1881no—
682C4#1568970511yescharacteristic
683C4#1568970711yescharacteristic
684C4#1568971411yescharacteristic
685C4#1568971611yescharacteristic
686C2—42no—
687C2—944no—
688C2#2024601811yescharacteristic
689C2#431×D4711yescharacteristic
690C2#2025203611yescharacteristic
691C2#2025240911yescharacteristic
692C2#2025241311yescharacteristic
693C2#2025249511yescharacteristic
694C2#2025250311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C23×C8
FittingC47×#1923C2
socleC23×C47C23×C4
prime radicalC22×C22⋊D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1923D47
hypocenterC47#21996
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #20243996C2semidirect
3. #20243945C2semidirect
4. #20243943C2semidirect
7. #20243567C2semidirect
8. #20243564C2semidirect
9. #20243530C2semidirect
10. #20243504C2semidirect
11. #20243454C2semidirect
12. #20243366C2semidirect
13. C4×(C2×D47)⋊C8C2semidirect
14. #336×D47C2semidirect
15. C47×#1923C2semidirect
78. (C22⋊D47)⋊C4C8semidirect
150. C22×Dic47C2×C8semidirect
183. C22⋊C4×C47C2×C8semidirect
194. Dic47⋊C4C2×C8semidirect
208. C4×Dic47C2×C8semidirect
341. #1923D47semidirect
406. C47#21996semidirect
552. C22⋊C4C8×D47semidirect

Maximal subgroups

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

subgroupindex
C4×(C22⋊D47)⋊C42
#202439962
#202439452
#202439432
#202436772
#202435672
#202435642
#202435302
#202435042
#202434542
#202433662
C4×(C2×D47)⋊C82
#336×D472
C47×#19232
#2199647