Finite Group Databasebeta

← #26234392

Subgroups — #26234392

Order 12032.

1126 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic
2C22×#13093957C211yesmaximal, characteristic, complemented
3C2×#107×D47C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D47C211yesmaximal, characteristic
5#20246284C211yesmaximal, characteristic
6#20244145C211yesmaximal, characteristic, complemented
7#20244143C211yesmaximal, characteristic, complemented
8#20243578C211yesmaximal, characteristic, complemented
9#20243577C211yesmaximal, characteristic, complemented
10#20243574C211yesmaximal, characteristic, complemented
11#20243546C211yesmaximal, characteristic, complemented
12#20243416C211yesmaximal, characteristic, complemented
13#20243415C211yesmaximal, characteristic, complemented
14#20243280C211yesmaximal, characteristic, complemented
15C47×#1852C211yesmaximal, characteristic, complemented
16C23×C47⋊C8C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C2×C4×C22⋊D47—21no—
19C2×C4×C22⋊D47C2211yescharacteristic
20C2×(C22⋊D47)⋊C4—21no—
21C22×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊C4×D47C2211yescharacteristic
23C2×C4⋊C4×D47C2211yescharacteristic
24(C22⋊D47)⋊C8C418yescomplemented
25C2×#13093958C2211yescharacteristic
26C2×#13093958C2211yescharacteristic
27C2×#13093957—24no—
28C2×#13093957C2211yescharacteristic
29C2×#13093957C2211yescharacteristic
30C2×#13093957C2211yescharacteristic
31C2×#13093957C2211yescharacteristic
32C2×#13093957C2211yescharacteristic
33C2×#13093957C2211yescharacteristic
34#107×D47—24no—
35C2×Dic47⋊C8C2211yescharacteristic
36C2×(C2×D47)⋊C8C2211yescharacteristic
37C2×C8×Dic47C2211yescharacteristic
38#15689020—21no—
39#15689018—21no—
40#15688997—21no—
41#15688996—21no—
42#15688995—21no—
43#15688994—21no—
44#15688992C2211yescharacteristic
45#15688992C2211yescharacteristic
46#15688983C2211yescharacteristic
47#15688980C2211yescharacteristic
48#15688980C2211yescharacteristic
49C4⋊C4×Dic47C2211yescharacteristic
50C4⋊C4×Dic47C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55C22×C4⋊C4×C47C2211yescharacteristic
56C2×#107×C47C2211yescharacteristic
57C2×#107×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C47×#380C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×C22⋊D47D411yescharacteristic
63C23×Dic47—21no—
64C22×C4×D47—21no—
65C22×C4×D47—21no—
66C22×C4×D47C2311yescharacteristic
67C22×C47⋊C8—22no—
68C22×C47⋊C8—22no—
69C22×C47⋊C8C2×C414yescomplemented
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C2×C8×D47—22no—
73C2×C8×D47—22no—
74C2×C8×D47C2×C414yescomplemented
75C4×C22⋊D47—44no—
76C4×C22⋊D47C2×C414yes—
77C4×C22⋊D47Q814yes—
78(C22⋊D47)⋊C4—44no—
79C2×C4⋊Dic47—22no—
80C2×C4⋊Dic47—21no—
81C2×C4⋊Dic47—41no—
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C4⋊Dic47C2311yescharacteristic
85C2×C4⋊Dic47C2311yescharacteristic
86C2×Dic47⋊C4—21no—
87C2×Dic47⋊C4—21no—
88C2×Dic47⋊C4—21no—
89C2×Dic47⋊C4—21no—
90C2×Dic47⋊C4—21no—
91C2×Dic47⋊C4—21no—
92C2×Dic47⋊C4D411yescharacteristic
93C4⋊C4×D47—22no—
94C4⋊C4×D47—22no—
95C4⋊C4×D47—41no—
96C4⋊C4×D47—41no—
97C2×C22⋊Dic47—21no—
98C2×C22⋊Dic47D411yescharacteristic
99C2×(C2×D47)⋊C4—21no—
100C2×(C2×D47)⋊C4—21no—
101C2×(C2×D47)⋊C4D411yescharacteristic
102C2×C4×Dic47—21no—
103C2×C4×Dic47—21no—
104C2×C4×Dic47C2311yescharacteristic
105#13093958—22no—
106#13093958—41no—
107#13093957—22no—
108#13093957—22no—
109#13093957—22no—
110#13093957—22no—
111#13093957—22no—
112#13093957D414yescomplemented
113Dic47⋊C8C2×C414yescomplemented
114(C2×D47)⋊C8C2×C414yescomplemented
115C8×Dic47C2×C414yescomplemented
116C47⋊#95—21no—
117C47⋊#95—21no—
118C47⋊#95—21no—
119C47⋊#95—21no—
120C47⋊#95—21no—
121C23×C4×C47—21no—
122C23×C4×C47C2311yescharacteristic
123C22×C8×C47C2311yescharacteristic
124C22×C8×C47C2311yescharacteristic
125C2×C4⋊C4×C47—22no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—41no—
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C22⋊C4×C47—21no—
133#107×C47—22no—
134#107×C47—41no—
135C22⋊C8×C47C2×C414yescomplemented
136#95×C47—21no—
137C24×C47C2×D411yescharacteristic
138C23×D47C2×D411yescharacteristic
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—42no—
148C22×C4×C47—42no—
149C22×C4×C47—81no—
150C22×C4×C47C22×C412yes—
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×Q812yes—
153C22×C4×C47C2411yescharacteristic
154C2×C22⋊D47C4⋊C414yes—
155C2×C22⋊D47D814yes—
156C2×C22⋊D47Q1614yes—
157C22×Dic47—21no—
158C22×Dic47—21no—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47—42no—
162C22×Dic47—42no—
163C22×Dic47—81no—
164C22×Dic47C2×D411yescharacteristic
165C22×Dic47C2×D411yescharacteristic
166C22×Dic47C2×D411yescharacteristic
167C2×C4×D47—21no—
168C2×C4×D47—21no—
169C2×C4×D47—21no—
170C2×C4×D47—21no—
171C2×C4×D47—42no—
172C2×C4×D47—42no—
173C2×C4×D47—42no—
174C2×C4×D47—42no—
175C2×C4×D47—81no—
176C2×C4×D47—81no—
177C2×C4×D47C22×C412yes—
178C2×C4×D47C2×Q812yes—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C2×C8×C47—21no—
183C2×C8×C47C22×C412yes—
184C2×C8×C47C22×C412yes—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—21no—
192C4⋊C4×C47—42no—
193C4⋊C4×C47C2×D412yes—
194C22⋊C4×C47—42no—
195C22⋊Dic47—42no—
196C22⋊Dic47C4⋊C414yes—
197(C2×D47)⋊C4—42no—
198(C2×D47)⋊C4—42no—
199(C2×D47)⋊C4C4⋊C414yes—
200C4⋊Dic47—21no—
201C4⋊Dic47—21no—
202C4⋊Dic47—21no—
203C4⋊Dic47—21no—
204C4⋊Dic47—21no—
205C4⋊Dic47—21no—
206C4⋊Dic47—21no—
207C4⋊Dic47—42no—
208C4⋊Dic47C2×D412yes—
209Dic47⋊C4—42no—
210Dic47⋊C4—42no—
211Dic47⋊C4—42no—
212Dic47⋊C4—42no—
213Dic47⋊C4—81no—
214Dic47⋊C4—81no—
215Dic47⋊C4C4⋊C414yes—
216C4×Dic47—42no—
217C4×Dic47—42no—
218C4×Dic47C22×C412yes—
219C4×Dic47C2×Q812yes—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—28no—
223C2×C47⋊C8C22×C412yes—
224C2×C47⋊C8C22×C412yes—
225C2×C47⋊C8C2×D412yes—
226C2×C47⋊C8#4112yes—
227C8×D47—28no—
228C23×C47—21no—
229C23×C47—21no—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47C2×C4⋊C412yes—
233C23×C47C2×D812yes—
234C23×C47C2×Q1612yes—
235C23×C47C22×D411yescharacteristic
236C22×D47—21no—
237C22×D47—21no—
238C22×D47—21no—
239C22×D47—21no—
240C22×D47C2×C4⋊C412yes—
241C22×D47C2×D812yes—
242C22×D47C2×Q1612yes—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—22no—
246C2×C4×C47—22no—
247C2×C4×C47—22no—
248C2×C4×C47—22no—
249C2×C4×C47—22no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—84no—
262C2×C4×C47C2×C4⋊C412yes—
263C2×C4×C47C23×C411yescharacteristic
264C2×C4×C47C22×D411yescharacteristic
265C2×C4×C47C22×Q811yescharacteristic
266C2×C4×C47C2×#4111yescharacteristic
267C2×C4×C47H(5,𝔽2)11yescharacteristic
268C2×C4×C472−1+411yescharacteristic
269C22⋊D47#107116yescomplemented
270C2×Dic47—21no—
271C2×Dic47—21no—
272C2×Dic47—21no—
273C2×Dic47—21no—
274C2×Dic47—22no—
275C2×Dic47—41no—
276C2×Dic47—41no—
277C2×Dic47—41no—
278C2×Dic47—41no—
279C2×Dic47—41no—
280C2×Dic47—41no—
281C2×Dic47—41no—
282C2×Dic47—41no—
283C2×Dic47—41no—
284C2×Dic47—41no—
285C2×Dic47—41no—
286C2×Dic47—84no—
287C2×Dic47C2×C4⋊C412yes—
288C2×Dic47C2×C4⋊C412yes—
289C2×Dic47C2×C4⋊C412yes—
290C2×Dic47C2×D812yes—
291C2×Dic47C2×Q1612yes—
292C4×D47—22no—
293C4×D47—22no—
294C4×D47—22no—
295C4×D47—22no—
296C4×D47—84no—
297C4×D47—84no—
298C8×C47—22no—
299C8×C47—22no—
300C47⋊C8—22no—
301C47⋊C8C4×D414yescomplemented
302D4×#107—471nomaximal, Sylow
303C22×C47—22no—
304C22×C47—22no—
305C22×C47—22no—
306C22×C47—22no—
307C22×C47—22no—
308C22×C47—22no—
309C22×C47C2×#10714yescomplemented
310C22×C47C22×C4⋊C411yescharacteristic
311C22×C47D4211yescharacteristic
312C22×C47#54711yescharacteristic
313C22×C47C22×D811yescharacteristic
314C22×C47C22×Q1611yescharacteristic
315C22×C47#57611yescharacteristic
316C22×C47#57811yescharacteristic
317C2×D47—22no—
318C2×D47—22no—
319C2×D47—22no—
320C2×D47—22no—
321C2×D47—22no—
322C2×D47—22no—
323C2×D47C2×#10714yescomplemented
324C4×C47—22no—
325C4×C47—42no—
326C4×C47—81no—
327C4×C47—81no—
328C4×C47—81no—
329C4×C47C2×C4×D411yescharacteristic
330C4×C47#52011yescharacteristic
331C4×C47D4×Q811yescharacteristic
332C4×C47#55411yescharacteristic
333Dic47—22no—
334Dic47—22no—
335Dic47—42no—
336Dic47—81no—
337Dic47—81no—
338Dic47—81no—
339Dic47C2×#10714yescomplemented
340C2×C8×D4—471no—
341C22×#107—471no—
342C22×#107—471no—
343D4×C4⋊C4—471no—
344D4×C4⋊C4—471no—
345#1947—471no—
346#1947—471no—
347#1852—471no—
348#1852—471no—
349#1852—471no—
350#1852D4711yescharacteristic, complemented
351#1845—471no—
352#1808—471no—
353#1808—471no—
354C4×#107—471no—
355C2×C47—24no—
356C2×C47D4×C4⋊C411yescharacteristic
357C2×C47C22×#10711yescharacteristic
358C2×C47#291311yescharacteristic
359C2×C47D4×D811yescharacteristic
360C2×C47D4×Q1611yescharacteristic
361C2×C47#333411yescharacteristic
362C2×C47#333811yescharacteristic
363D47—24no—
364C23×C8—471no—
365C23×C8—471no—
366C2×C4×D4—471no—
367C2×C4×D4—941no—
368C2×C4×D4—941no—
369C22×C4⋊C4—471no—
370C22×C4⋊C4—471no—
371C22×C4⋊C4—471no—
372C22×C4⋊C4C2×D4711yescharacteristic
373C8×D4—478no—
374C2×#107—471no—
375C2×#107—471no—
376C2×#107—471no—
377C2×#107—471no—
378C2×#107—471no—
379C2×#107—471no—
380C2×#107—471no—
381C2×#107—471no—
382C2×#107—944no—
383C2×#107—944no—
384C2×#107C2×D4711yescharacteristic
385C2×#107C2×D4711yescharacteristic
386C2×C4⋊C8—471no—
387C2×C22⋊C8—471no—
388C2×C22⋊C8C2×D4711yescharacteristic
389C2×C4×C8—471no—
390#389—941no—
391#389—941no—
392#385—941no—
393#385—941no—
394#385—941no—
395#385—941no—
396#384—471no—
397#384—471no—
398#380—471no—
399#380—471no—
400#380—471no—
401#380C2×D4711yescharacteristic
402C4×C4⋊C4—471no—
403C4×C4⋊C4—471no—
404#340—471no—
405#340—471no—
406#340—471no—
407#340—471no—
408#340C2×D4711yescharacteristic
409#340C2×D4711yescharacteristic
410C47D4×#10711yescharacteristic, complemented, Sylow
411C22×D4—471no—
412C23×C4—21no—
413C23×C4—471no—
414C23×C4—941no—
415C23×C4—941no—
416C23×C4—941no—
417C23×C4C22×D4711yescharacteristic
418C22×C8—471no—
419C22×C8—474no—
420C22×C8—471no—
421C22×C8—474no—
422C22×C8—942no—
423C22×C8—942no—
424C22×C8—942no—
425C22×C8—942no—
426C22×C8C22×D4711yescharacteristic
427C22×C8C22×D4711yescharacteristic
428C4×D4—474no—
429C4×D4—474no—
430C4×D4—1884no—
431C4×D4—1884no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—471no—
436C2×C4⋊C4—471no—
437C2×C4⋊C4—471no—
438C2×C4⋊C4—471no—
439C2×C4⋊C4—471no—
440C2×C4⋊C4—942no—
441C2×C4⋊C4—942no—
442C2×C4⋊C4—942no—
443C2×C4⋊C4—941no—
444C2×C4⋊C4—941no—
445C2×C4⋊C4—941no—
446C2×C4⋊C4—941no—
447C2×C4⋊C4—941no—
448C2×C4⋊C4—941no—
449C2×C4⋊C4—941no—
450C2×C4⋊C4—1881no—
451C2×C4⋊C4—1881no—
452C2×C4⋊C4—1881no—
453C2×C4⋊C4C22×D4711yescharacteristic
454C2×C4⋊C4C22×D4711yescharacteristic
455C2×C4⋊C4C22×D4711yescharacteristic
456C2×C4⋊C4C22×D4711yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—471no—
459C2×C22⋊C4—471no—
460C2×C22⋊C4—941no—
461C2×C22⋊C4—941no—
462C2×C22⋊C4—941no—
463C2×C42—471no—
464C2×C42—941no—
465C2×C42—941no—
466#107—22no—
467#107—41no—
468#107—474no—
469#107—942no—
470#107—942no—
471#107—942no—
472#107—942no—
473#107—942no—
474#107—942no—
475#107—1881no—
476C4⋊C8—474no—
477C22⋊C8—474no—
478C22⋊C8C4×D4714yescomplemented
479C4×C8—474no—
480#95—21no—
481#95—941no—
482#95—941no—
483#95—941no—
484#95—941no—
485#95—941no—
486C24—471no—
487C24D4×D4711yescharacteristic
488C2×D4—474no—
489C2×D4—474no—
490C2×D4—474no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—81no—
502C22×C4—471no—
503C22×C4—471no—
504C22×C4—471no—
505C22×C4—472no—
506C22×C4—472no—
507C22×C4—941no—
508C22×C4—941no—
509C22×C4—941no—
510C22×C4—941no—
511C22×C4—941no—
512C22×C4—941no—
513C22×C4—941no—
514C22×C4—941no—
515C22×C4—3761no—
516C22×C4—3761no—
517C22×C4—3761no—
518C22×C4—1882no—
519C22×C4—1882no—
520C22×C4—1882no—
521C22×C4—1882no—
522C22×C4—1882no—
523C22×C4—1882no—
524C22×C4C2×C4×D4712yes—
525C22×C4D4×D4711yescharacteristic
526C22×C4Q8×D4712yes—
527C22×C4C23×D4711yescharacteristic
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—472no—
533C2×C8—472no—
534C2×C8—472no—
535C2×C8—472no—
536C2×C8—948no—
537C2×C8—948no—
538C2×C8—941no—
539C2×C8—941no—
540C2×C8C2×C4×D4712yes—
541C2×C8C2×C4×D4712yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—474no—
551C4⋊C4—472no—
552C4⋊C4—941no—
553C4⋊C4—941no—
554C4⋊C4—941no—
555C4⋊C4—941no—
556C4⋊C4—941no—
557C4⋊C4—941no—
558C4⋊C4—941no—
559C4⋊C4—3761no—
560C4⋊C4—3761no—
561C4⋊C4—1882no—
562C4⋊C4—1882no—
563C4⋊C4—1882no—
564C4⋊C4—1882no—
565C4⋊C4—1882no—
566C4⋊C4D4×D4712yes—
567C22⋊C4—42no—
568C22⋊C4—474no—
569C22⋊C4—474no—
570C22⋊C4—1882no—
571C22⋊C4—1882no—
572C22⋊C4—1882no—
573C42—472no—
574C42—472no—
575C42—1882no—
576C42—1882no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—472no—
582C23—472no—
583C23—472no—
584C23—941no—
585C23—941no—
586C23—941no—
587C23—941no—
588C23C4⋊C4×D4712yes—
589C23D8×D4712yes—
590C23Q16×D4712yes—
591C23C2×D4×D4711yescharacteristic
592D4—4716no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—84no—
612C2×C4—472no—
613C2×C4—472no—
614C2×C4—472no—
615C2×C4—472no—
616C2×C4—472no—
617C2×C4—941no—
618C2×C4—941no—
619C2×C4—941no—
620C2×C4—941no—
621C2×C4—942no—
622C2×C4—942no—
623C2×C4—942no—
624C2×C4—942no—
625C2×C4—942no—
626C2×C4—3764no—
627C2×C4—3764no—
628C2×C4—3764no—
629C2×C4—1881no—
630C2×C4—1881no—
631C2×C4—1881no—
632C2×C4—1881no—
633C2×C4—1881no—
634C2×C4—1881no—
635C2×C4—1881no—
636C2×C4—1881no—
637C2×C4—1881no—
638C2×C4—1881no—
639C2×C4—1881no—
640C2×C4C4⋊C4×D4712yes—
641C2×C4C22×C4×D4711yescharacteristic
642C2×C4C2×D4×D4711yescharacteristic
643C2×C4C2×Q8×D4711yescharacteristic
644C2×C4#41×D4711yescharacteristic
645C2×C4#1309406911yescharacteristic
646C2×C4#1309407111yescharacteristic
647C8—22no—
648C8—22no—
649C8—474no—
650C8—942no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—474no—
658C22—942no—
659C22—942no—
660C22—942no—
661C22—942no—
662C22—942no—
663C22—942no—
664C22#107×D4714yescomplemented
665C22C2×C4⋊C4×D4711yescharacteristic
666C22#1568975511yescharacteristic
667C22#1568977111yescharacteristic
668C22C2×D8×D4711yescharacteristic
669C22C2×Q16×D4711yescharacteristic
670C22#1568992711yescharacteristic
671C22#1568993911yescharacteristic
672C4—22no—
673C4—42no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—474no—
678C4—942no—
679C4—942no—
680C4—3761no—
681C4—3761no—
682C4—3761no—
683C4—1882no—
684C4C4×D4×D4711yescharacteristic
685C4#1568960211yescharacteristic
686C4#1568978611yescharacteristic
687C4#1568982711yescharacteristic
688C2—24no—
689C2—944no—
690C2#2024628611yescharacteristic
691C2C2×#107×D4711yescharacteristic
692C2#2025198711yescharacteristic
693C2#2025505811yescharacteristic
694C2#2025513311yescharacteristic
695C2#2025573011yescharacteristic
696C2#2025577511yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1852C2
socleC23×C47C22×D4
prime radicalC22×C22⋊D47D4
cosocleC22×C4×C47C24
hypercenter#1852D47
hypocenterC47D4×#107
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. C22×#13093957C2semidirect
3. C2×#107×D47C2semidirect
6. #20244145C2semidirect
7. #20244143C2semidirect
8. #20243578C2semidirect
9. #20243577C2semidirect
10. #20243574C2semidirect
11. #20243546C2semidirect
12. #20243416C2semidirect
13. #20243415C2semidirect
14. #20243280C2semidirect
15. C47×#1852C2semidirect
24. (C22⋊D47)⋊C8C4semidirect
69. C22×C47⋊C8C2×C4semidirect
74. C2×C8×D47C2×C4semidirect
112. #13093957D4semidirect
113. Dic47⋊C8C2×C4semidirect
114. (C2×D47)⋊C8C2×C4semidirect
115. C8×Dic47C2×C4semidirect
135. C22⋊C8×C47C2×C4semidirect
269. C22⋊D47#107semidirect
301. C47⋊C8C4×D4semidirect
309. C22×C47C2×#107semidirect
323. C2×D47C2×#107semidirect
339. Dic47C2×#107semidirect
350. #1852D47semidirect
410. C47D4×#107semidirect
478. C22⋊C8C4×D47semidirect
664. C22#107×D47semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D47)⋊C82
C22×#130939572
C2×#107×D472
C4⋊C4×C22⋊D472
#202462842
#202441452
#202441432
#202435782
#202435772
#202435742
#202435462
#202434162
#202434152
#202432802
C47×#18522
D4×#10747