Finite Group Databasebeta

← #26236471

Subgroups — #26236471

Order 12032.

1306 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689202C211yesmaximal, characteristic, complemented
2C2×#15689191C211yesmaximal, characteristic, complemented
3C2×#15689085C211yesmaximal, characteristic, complemented
4C22×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
5C4×#13093994C211yesmaximal, characteristic
6#20244182C211yesmaximal, characteristic, complemented
7#20244002C211yesmaximal, characteristic, complemented
8#20243994C211yesmaximal, characteristic, complemented
9#20243684C211yesmaximal, characteristic, complemented
10#20243684C211yesmaximal, characteristic, complemented
11#20243680C211yesmaximal, characteristic, complemented
12#20243572C211yesmaximal, characteristic, complemented
13#20243568C211yesmaximal, characteristic, complemented
14#20243171C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C47C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×#10625324C2211yescharacteristic, complemented
20C23×C47⋊C8C2211yescharacteristic
21C2×#13093994C411yescharacteristic
22C2×C4×D188C2211yescharacteristic
23C2×C4×D188C2211yescharacteristic
24C2×C4×C22⋊D47C2211yescharacteristic
25#15689202—24no—
26#15689191—24no—
27C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
28C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
29C2×Dic47⋊C8C2211yescharacteristic, complemented
30#15689085—24no—
31C2×C22⋊(C47⋊C8)C2211yescharacteristic
32C2×(C2×D47)⋊C8—24no—
33C2×(C2×D47)⋊C8C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×(C2×D47)⋊C8C2211yescharacteristic
36C2×(C2×D47)⋊C8C2211yescharacteristic
37C2×(C2×D47)⋊C8C2211yescharacteristic
38C2×(C2×D47)⋊C8C2211yescharacteristic
39C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
40C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
41C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
42C2×#13093934C2211yescharacteristic, complemented
43#15689001C411yescharacteristic
44#15689001C411yescharacteristic
45#15689000C411yescharacteristic
46#15688998C411yescharacteristic
47#15688997C411yescharacteristic
48#15688997C411yescharacteristic
49#15688978C411yescharacteristic
50C4×(C2×D47)⋊C4C2211yescharacteristic
51C4×(C2×D47)⋊C4C2211yescharacteristic
52#15688878C2211yescharacteristic, complemented
53#15688878C2211yescharacteristic, complemented
54#15688877C2211yescharacteristic, complemented
55#15688877C2211yescharacteristic, complemented
56C23×C8×C47C2211yescharacteristic
57C2×C22⋊C8×C47C2211yescharacteristic
58C2×C4×C8×C47C2211yescharacteristic, complemented
59C2×C4×C8×C47C2211yescharacteristic, complemented
60C4×C22⋊C4×C47C2211yescharacteristic
61C47×#336C2211yescharacteristic, complemented
62C47×#336C2211yescharacteristic, complemented
63C24×D47C2×C411yescharacteristic
64C22×D188C2×C411yescharacteristic
65C22×D188C2×C411yescharacteristic
66C22×C22⋊D47C2×C411yescharacteristic
67C23×Dic47C2×C411yescharacteristic
68C22×C4×D47—22no—
69C22×C4×D47—22no—
70C22×C4×D47—22no—
71C22×C4×D47—22no—
72C22×C4×D47—41no—
73C22×C4×D47—41no—
74C22×C4×D47C2×C411yescharacteristic
75C22×C4×D47C2×C411yescharacteristic
76C22×C4×D47C2311yescharacteristic
77C22×C4×D47C2311yescharacteristic
78C22×C4×D47C2311yescharacteristic
79C2×#10625324—22no—
80C2×#10625324—22no—
81C2×#10625324—22no—
82C2×#10625324—22no—
83C2×#10625324—22no—
84C2×#10625324—22no—
85C2×#10625324—41no—
86C2×#10625324—41no—
87C2×#10625324—41no—
88C22×C47⋊C8—22no—
89C22×C47⋊C8—22no—
90C22×C47⋊C8—41no—
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95#13093994—24no—
96C4×D188—22no—
97C4×D188—22no—
98C4×D188—41no—
99C4×D188—41no—
100C4×C22⋊D47—22no—
101C4×C22⋊D47—22no—
102C2×C4⋊Dic47C2×C411yescharacteristic
103C2×C4⋊Dic47C2×C411yescharacteristic
104C2×Dic47⋊C4C2×C411yescharacteristic
105C2×C22⋊Dic47C2×C411yescharacteristic
106C2×(C2×D47)⋊C4C2×C411yescharacteristic
107C2×(C2×D47)⋊C4C2×C411yescharacteristic
108C2×(C2×D47)⋊C4C2×C411yescharacteristic
109C2×(C2×D47)⋊C4C2×C411yescharacteristic
110C2×(C2×D47)⋊C4C2×C411yescharacteristic
111C2×(C2×D47)⋊C4C2×C411yescharacteristic
112C2×(C2×D47)⋊C4C2×C411yescharacteristic
113C2×(C2×D47)⋊C4C2×C411yescharacteristic
114C2×(C2×D47)⋊C4C2×C411yescharacteristic
115C2×C4×Dic47C2311yescharacteristic
116C4⋊(C47⋊C8)—22no—
117C4⋊(C47⋊C8)—41no—
118Dic47⋊C8—22no—
119C22⋊(C47⋊C8)—22no—
120(C2×D47)⋊C8—22no—
121(C2×D47)⋊C8—22no—
122(C2×D47)⋊C8—22no—
123(C2×D47)⋊C8—22no—
124(C2×D47)⋊C8—22no—
125(C2×D47)⋊C8—22no—
126(C2×D47)⋊C8—22no—
127(C2×D47)⋊C8—41no—
128(C2×D47)⋊C8D414yescomplemented
129#13093934—22no—
130C47⋊#95C2×C411yescharacteristic
131C47⋊#95C2×C411yescharacteristic
132C47⋊#95C2×C411yescharacteristic
133C47⋊#95C2×C411yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C22×C8×C47—22no—
136C22×C8×C47—22no—
137C22×C8×C47—41no—
138C22×C8×C47C2311yescharacteristic
139C22×C8×C47C2311yescharacteristic
140C22×C8×C47C2311yescharacteristic
141C22×C8×C47C2311yescharacteristic
142C2×C22⋊C4×C47C2×C411yescharacteristic
143C2×C22⋊C4×C47C2×C411yescharacteristic
144C2×C42×C47C2311yescharacteristic
145C2×C42×C47C2311yescharacteristic
146C22⋊C8×C47D414yescomplemented
147C4×C8×C47—22no—
148C4×C8×C47—41no—
149#95×C47C2×C411yescharacteristic
150#95×C47C2×C411yescharacteristic
151C24×C47C22×C411yescharacteristic
152C23×D47—22no—
153C23×D47—22no—
154C23×D47—22no—
155C23×D47—22no—
156C23×D47—22no—
157C23×D47—41no—
158C23×D47—41no—
159C23×D47C22×C411yescharacteristic
160C23×D47C22×C411yescharacteristic
161C23×D47C22×C411yescharacteristic
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47C22×C411yescharacteristic
167C22×C4×C47C22×C411yescharacteristic
168C22×C4×C47C22×C411yescharacteristic
169C22×C4×C47C22×C411yescharacteristic
170C22×C4×C47C22×C411yescharacteristic
171C22×C4×C47C2×D412yes—
172C22×C4×C47#4112yes—
173C22×C4×C47C2411yescharacteristic
174C2×C22⋊D47—22no—
175C2×C22⋊D47—22no—
176C2×C22⋊D47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—41no—
180C22×Dic47C22×C411yescharacteristic
181C22×Dic47C22×C411yescharacteristic
182C22×Dic47C22×C411yescharacteristic
183C22×Dic47C22×C411yescharacteristic
184C22×Dic47C22×C411yescharacteristic
185C2×D188—22no—
186C2×D188—22no—
187C2×D188—22no—
188C2×D188—22no—
189C2×D188—41no—
190C2×D188—41no—
191C2×C4×D47—21no—
192C2×C4×D47—21no—
193C2×C4×D47—21no—
194C2×C4×D47—21no—
195C2×C4×D47—22no—
196C2×C4×D47—22no—
197C2×C4×D47—22no—
198C2×C4×D47—21no—
199C2×C4×D47—21no—
200C2×C4×D47—21no—
201C2×C4×D47—21no—
202C2×C4×D47—21no—
203C2×C4×D47—21no—
204C2×C4×D47—21no—
205C2×C4×D47—21no—
206C2×C4×D47—21no—
207C2×C4×D47—21no—
208C2×C4×D47—21no—
209C2×C4×D47—21no—
210C2×C4×D47—22no—
211C2×C4×D47—44no—
212C2×C4×D47—44no—
213C2×C4×D47—44no—
214C2×C4×D47—44no—
215C2×C4×D47—41no—
216C2×C4×D47—41no—
217C2×C4×D47C2×D412yes—
218C2×C4×D47#4112yes—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—44no—
229C2×C8×C47C2×D412yes—
230C2×C8×C47C2×D412yes—
231C2×C8×C47C2×D412yes—
232C22⋊C4×C47—22no—
233C22⋊C4×C47M1614yescomplemented
234C42×C47—21no—
235C42×C47—21no—
236C42×C47—21no—
237C42×C47—21no—
238C22⋊Dic47—22no—
239(C2×D47)⋊C4—22no—
240(C2×D47)⋊C4—22no—
241(C2×D47)⋊C4—22no—
242(C2×D47)⋊C4—22no—
243(C2×D47)⋊C4—22no—
244(C2×D47)⋊C4—22no—
245(C2×D47)⋊C4—41no—
246(C2×D47)⋊C4—41no—
247(C2×D47)⋊C4—41no—
248C4⋊Dic47—22no—
249C4⋊Dic47—41no—
250Dic47⋊C4—22no—
251C4×Dic47—21no—
252C4×Dic47—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257C2×C47⋊C8—21no—
258C2×C47⋊C8—21no—
259C2×C47⋊C8—21no—
260C2×C47⋊C8—21no—
261C2×C47⋊C8—21no—
262C2×C47⋊C8—21no—
263C2×C47⋊C8—21no—
264C2×C47⋊C8—44no—
265C2×C47⋊C8C2×D412yes—
266#10625324—44no—
267#10625324—44no—
268#10625324—44no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47C4×D412yes—
274C23×C47C2×M1612yes—
275C23×C47#13112yes—
276C23×C47C23×C411yescharacteristic
277C22×D47—28no—
278C22×D47—21no—
279C22×D47—21no—
280C22×D47—21no—
281C22×D47—21no—
282C22×D47—21no—
283C22×D47—21no—
284C22×D47—21no—
285C22×D47—21no—
286C22×D47—21no—
287C22×D47—21no—
288C22×D47—21no—
289C22×D47—21no—
290C22×D47—21no—
291C22×D47—21no—
292C22×D47—21no—
293C22×D47—21no—
294C22×D47—21no—
295C22×D47—21no—
296C22×D47—21no—
297C22×D47—44no—
298C22×D47—44no—
299C22×D47—44no—
300C22×D47—44no—
301C22×D47—44no—
302C22×D47—44no—
303C22×D47C4×D412yes—
304C22×D47#13112yes—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47C4×D412yes—
322C2×C4×C47C2×M1612yes—
323C2×C4×C47C2×M1612yes—
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C22×D411yescharacteristic
326C2×C4×C47C2×#4111yescharacteristic
327C2×C4×C47C2×#4111yescharacteristic
328C2×C4×C47H(5,𝔽2)11yescharacteristic
329C2×C4×C47H(5,𝔽2)11yescharacteristic
330C22⋊D47—44no—
331C2×Dic47—21no—
332C2×Dic47—21no—
333C2×Dic47—21no—
334C2×Dic47—21no—
335C2×Dic47—21no—
336C2×Dic47—21no—
337C2×Dic47—21no—
338C2×Dic47—21no—
339C2×Dic47—21no—
340C2×Dic47—21no—
341C2×Dic47—21no—
342C2×Dic47—21no—
343C2×Dic47—21no—
344C2×Dic47—21no—
345C2×Dic47—44no—
346C2×Dic47C4×D412yes—
347D188—44no—
348D188—44no—
349C4×D47—22no—
350C4×D47—22no—
351C4×D47—22no—
352C4×D47—22no—
353C4×D47—44no—
354C4×D47—44no—
355C4×D47—41no—
356C4×D47—41no—
357C4×D47—41no—
358C4×D47—41no—
359C4×D47—41no—
360C4×D47—41no—
361C4×D47—41no—
362C4×D47—41no—
363C8×C47—22no—
364C8×C47—22no—
365C8×C47—22no—
366C8×C47—41no—
367C47⋊C8—22no—
368C47⋊C8—41no—
369C47⋊C8—41no—
370C47⋊C8—41no—
371#22848—471nomaximal, Sylow
372C22×C47—22no—
373C22×C47—22no—
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47#43614yescomplemented
379C22×C47C2×C4×D411yescharacteristic
380C22×C47C2×C4×D411yescharacteristic
381C22×C47#51811yescharacteristic
382C22×C47C22×M1611yescharacteristic
383C22×C47C2×#13111yescharacteristic
384C22×C47C2×#13111yescharacteristic
385C22×C47#56811yescharacteristic
386C2×D47—22no—
387C2×D47—22no—
388C2×D47—22no—
389C2×D47—22no—
390C2×D47—22no—
391C2×D47—22no—
392C2×D47—416no—
393C2×D47—41no—
394C2×D47—41no—
395C2×D47—41no—
396C2×D47—41no—
397C2×D47—41no—
398C2×D47—41no—
399C2×D47—41no—
400C2×D47—41no—
401C2×D47—41no—
402C2×D47—41no—
403C2×D47—41no—
404C2×D47—41no—
405C2×D47—41no—
406C2×D47—41no—
407C2×D47—41no—
408C4×C47—22no—
409C4×C47—22no—
410C4×C47—22no—
411C4×C47—41no—
412C4×C47—41no—
413C4×C47D4211yescharacteristic
414C4×C47#54611yescharacteristic
415C4×C47#54611yescharacteristic
416C4×C47#55111yescharacteristic
417Dic47—22no—
418Dic47—41no—
419Dic47—41no—
420Dic47—41no—
421Dic47—41no—
422C2×#436—471no—
423C2×#435—471no—
424C2×#407—471no—
425C22×C22⋊C8—471no—
426C4×#120—471no—
427#1954—471no—
428#1924—471no—
429#1923—471no—
430#1870—471no—
431#1870—471no—
432#1869—471no—
433#1851—471no—
434#1850—471no—
435#1753—471no—
436C8×C22⋊C4D4711yescharacteristic, complemented
437C2×C47—24no—
438C2×C47#235811yescharacteristic
439C2×C47C2×#43611yescharacteristic
440C2×C47#292911yescharacteristic
441C2×C47#293311yescharacteristic
442C2×C47D4×M1611yescharacteristic
443C2×C47#297411yescharacteristic
444C2×C47#297611yescharacteristic
445D47—42no—
446D47—42no—
447D47—81no—
448C24×C4—471no—
449C22×M16—471no—
450C22×M16—471no—
451C22×M16—471no—
452C23×C8—471no—
453C23×C8C2×D4711yescharacteristic
454C2×#120—471no—
455C2×C4×D4—471no—
456C2×C4×D4—471no—
457C2×C4×D4—471no—
458#436—944no—
459#435—944no—
460C2×C4⋊C8—471no—
461C2×C4⋊C8—471no—
462C2×C4⋊C8—471no—
463#407—944no—
464C2×C22⋊C8—471no—
465C2×C22⋊C8—471no—
466C2×C22⋊C8—471no—
467C2×C22⋊C8—471no—
468C2×C22⋊C8—471no—
469C2×C22⋊C8—471no—
470C2×C22⋊C8—471no—
471C2×C22⋊C8—471no—
472C2×C22⋊C8—471no—
473C2×C22⋊C8—471no—
474C2×C22⋊C8—944no—
475C2×C22⋊C8C2×D4711yescharacteristic
476C2×#97—471no—
477C2×C4×C8C2×D4711yescharacteristic, complemented
478C2×C4×C8C2×D4711yescharacteristic, complemented
479#386—471no—
480#386—471no—
481#386—471no—
482#385—471no—
483#385—471no—
484#385—471no—
485#379—471no—
486C4×C22⋊C4—471no—
487C4×C22⋊C4—471no—
488C4×C22⋊C4C2×D4711yescharacteristic
489#336—471no—
490#336—471no—
491#336—471no—
492#336—471no—
493#336C2×D4711yescharacteristic, complemented
494#336C2×D4711yescharacteristic, complemented
495C47#2284811yescharacteristic, complemented, Sylow
496C25—471no—
497C22×D4—471no—
498C22×D4—471no—
499C22×D4—471no—
500C23×C4—471no—
501C23×C4—471no—
502C23×C4—471no—
503C23×C4—471no—
504C23×C4—471no—
505C23×C4—471no—
506C23×C4—942no—
507C23×C4—942no—
508C23×C4—942no—
509C23×C4—942no—
510C23×C4—1881no—
511C23×C4—1881no—
512C23×C4C22×D4711yescharacteristic
513C2×M16—942no—
514C2×M16—942no—
515C2×M16—942no—
516C2×M16—942no—
517C2×M16—942no—
518C2×M16—942no—
519C2×M16—1881no—
520C2×M16—1881no—
521C2×M16—1881no—
522C22×C8—22no—
523C22×C8—22no—
524C22×C8—41no—
525C22×C8—471no—
526C22×C8—471no—
527C22×C8—471no—
528C22×C8—471no—
529C22×C8—942no—
530C22×C8—942no—
531C22×C8—1881no—
532C22×C8C22×D4711yescharacteristic
533C22×C8C22×D4711yescharacteristic
534C22×C8C22×D4711yescharacteristic
535C22×C8C22×D4711yescharacteristic
536#120—944no—
537C4×D4—942no—
538C4×D4—942no—
539C4×D4—942no—
540C4×D4—942no—
541C4×D4—1881no—
542C4×D4—1881no—
543C2×C4⋊C4—471no—
544C2×C4⋊C4—471no—
545C2×C4⋊C4—471no—
546C2×C22⋊C4—471no—
547C2×C22⋊C4—471no—
548C2×C22⋊C4—471no—
549C2×C22⋊C4—471no—
550C2×C22⋊C4—471no—
551C2×C22⋊C4—471no—
552C2×C22⋊C4—471no—
553C2×C22⋊C4—471no—
554C2×C22⋊C4—471no—
555C2×C22⋊C4—471no—
556C2×C22⋊C4C4×D4711yescharacteristic
557C2×C22⋊C4C4×D4711yescharacteristic
558C2×C42—471no—
559C2×C42C22×D4711yescharacteristic
560C2×C42C22×D4711yescharacteristic
561C4⋊C8—942no—
562C4⋊C8—942no—
563C4⋊C8—1881no—
564C22⋊C8—474no—
565C22⋊C8—942no—
566C22⋊C8—942no—
567C22⋊C8—942no—
568C22⋊C8—942no—
569C22⋊C8—942no—
570C22⋊C8—942no—
571C22⋊C8—942no—
572C22⋊C8—942no—
573C22⋊C8—1881no—
574C22⋊C8D18814yescomplemented
575#97—942no—
576C4×C8—22no—
577C4×C8—41no—
578#95—471no—
579#95—471no—
580#95—471no—
581#95—471no—
582#95C4×D4711yescharacteristic
583#95C4×D4711yescharacteristic
584C24—471no—
585C24—471no—
586C24—471no—
587C24—942no—
588C24—942no—
589C24—942no—
590C24—942no—
591C24—942no—
592C24—1881no—
593C24—1881no—
594C24C2×C4×D4711yescharacteristic
595C2×D4—942no—
596C2×D4—942no—
597C2×D4—942no—
598C2×D4—942no—
599C2×D4—942no—
600C2×D4—942no—
601C2×D4—942no—
602C2×D4—1881no—
603C2×D4—1881no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—471no—
609C22×C4—472no—
610C22×C4—472no—
611C22×C4—471no—
612C22×C4—471no—
613C22×C4—471no—
614C22×C4—471no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—941no—
619C22×C4—941no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—942no—
623C22×C4—942no—
624C22×C4—942no—
625C22×C4—941no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—941no—
631C22×C4—941no—
632C22×C4—941no—
633C22×C4—941no—
634C22×C4—941no—
635C22×C4—941no—
636C22×C4—941no—
637C22×C4—1881no—
638C22×C4—1881no—
639C22×C4—1884no—
640C22×C4—1884no—
641C22×C4—1884no—
642C22×C4—1884no—
643C22×C4—1881no—
644C22×C4C2×C4×D4711yescharacteristic
645C22×C4C2×C4×D4711yescharacteristic
646C22×C4C2×C4×D4711yescharacteristic
647C22×C4C2×C4×D4711yescharacteristic
648C22×C4C2×C4×D4711yescharacteristic
649C22×C4C2×D18812yes—
650C22×C4#1062535012yes—
651C22×C4C23×D4711yescharacteristic
652M16—1884no—
653M16—1884no—
654M16—1884no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—44no—
665C2×C8—472no—
666C2×C8—941no—
667C2×C8—941no—
668C2×C8—941no—
669C2×C8—941no—
670C2×C8—941no—
671C2×C8—941no—
672C2×C8—941no—
673C2×C8—941no—
674C2×C8—941no—
675C2×C8—941no—
676C2×C8—941no—
677C2×C8—1884no—
678C2×C8C2×D18812yes—
679C2×C8C2×D18812yes—
680C2×C8D4×D4712yes—
681C4⋊C4—942no—
682C4⋊C4—942no—
683C4⋊C4—1881no—
684C22⋊C4—22no—
685C22⋊C4—942no—
686C22⋊C4—942no—
687C22⋊C4—942no—
688C22⋊C4—942no—
689C22⋊C4—942no—
690C22⋊C4—942no—
691C22⋊C4—942no—
692C22⋊C4—1881no—
693C22⋊C4—1881no—
694C22⋊C4—1881no—
695C22⋊C4#1062532414yescomplemented
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—941no—
701C42—941no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—472no—
707C23—472no—
708C23—948no—
709C23—941no—
710C23—941no—
711C23—941no—
712C23—941no—
713C23—941no—
714C23—941no—
715C23—941no—
716C23—941no—
717C23—941no—
718C23—941no—
719C23—941no—
720C23—941no—
721C23—941no—
722C23—941no—
723C23—941no—
724C23—941no—
725C23—941no—
726C23—941no—
727C23—941no—
728C23—1884no—
729C23—1884no—
730C23—1884no—
731C23—1884no—
732C23—1884no—
733C23—1884no—
734C23C4×D18812yes—
735C23C2×#1062532412yes—
736C23#1309403012yes—
737C23C22×C4×D4711yescharacteristic
738D4—1884no—
739D4—1884no—
740D4—1884no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—472no—
758C2×C4—941no—
759C2×C4—941no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—941no—
765C2×C4—941no—
766C2×C4—941no—
767C2×C4—941no—
768C2×C4—941no—
769C2×C4—941no—
770C2×C4—941no—
771C2×C4—941no—
772C2×C4—941no—
773C2×C4—941no—
774C2×C4—941no—
775C2×C4—941no—
776C2×C4—1884no—
777C2×C4—1884no—
778C2×C4—1884no—
779C2×C4—1881no—
780C2×C4—1881no—
781C2×C4—1881no—
782C2×C4—1881no—
783C2×C4—1881no—
784C2×C4—1881no—
785C2×C4—1881no—
786C2×C4—1881no—
787C2×C4C4×D18812yes—
788C2×C4C2×#1062532412yes—
789C2×C4C2×#1062532412yes—
790C2×C4C2×D4×D4711yescharacteristic
791C2×C4C22×D18811yescharacteristic
792C2×C4#41×D4711yescharacteristic
793C2×C4C2×#1062535011yescharacteristic
794C2×C4#1309406911yescharacteristic
795C2×C4#1309407011yescharacteristic
796C8—22no—
797C8—22no—
798C8—22no—
799C8—41no—
800C8—942no—
801C8—1881no—
802C8—1881no—
803C8—1881no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—942no—
811C22—942no—
812C22—942no—
813C22—942no—
814C22—942no—
815C22—942no—
816C22—18816no—
817C22—1881no—
818C22—1881no—
819C22—1881no—
820C22—1881no—
821C22—1881no—
822C22—1881no—
823C22—1881no—
824C22—1881no—
825C22—1881no—
826C22—1881no—
827C22—1881no—
828C22—1881no—
829C22—1881no—
830C22—1881no—
831C22—1881no—
832C22#1568920214yescomplemented
833C22C4×D4×D4711yescharacteristic
834C22C2×C4×D18811yescharacteristic
835C22#1568959511yescharacteristic
836C22C22×#1062532411yescharacteristic
837C22#131×D4711yescharacteristic
838C22C2×#1309403011yescharacteristic
839C22#1568988811yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—41no—
844C4—41no—
845C4—942no—
846C4—1881no—
847C4—1881no—
848C4—1881no—
849C4—1881no—
850C4D4×D18811yescharacteristic
851C4#1568976311yescharacteristic
852C4#1568976811yescharacteristic
853C4#1568979711yescharacteristic
854C2—24no—
855C2—3761no—
856C2—1882no—
857C2—1882no—
858C2#2024637011yescharacteristic
859C2C2×#1568920211yescharacteristic
860C2#2025207711yescharacteristic
861C2#2025211611yescharacteristic
862C2D4×#1062532411yescharacteristic
863C2#2025242111yescharacteristic
864C2#2025243011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC8×C22⋊C4×C47C2
prime radicalC2×#13093994C4
cosocleC22×C4×C47C24
hypercenterC8×C22⋊C4D47
hypocenterC47#22848
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#15689202C2semidirect
2. C2×#15689191C2semidirect
3. C2×#15689085C2semidirect
4. C22×(C2×D47)⋊C8C2semidirect
6. #20244182C2semidirect
7. #20244002C2semidirect
8. #20243994C2semidirect
9. #20243684C2semidirect
10. #20243684C2semidirect
11. #20243680C2semidirect
12. #20243572C2semidirect
13. #20243568C2semidirect
14. #20243171C2semidirect
15. C8×C22⋊C4×C47C2semidirect
19. C22×#10625324C22semidirect
27. C2×C4⋊(C47⋊C8)C22semidirect
28. C2×C4⋊(C47⋊C8)C22semidirect
29. C2×Dic47⋊C8C22semidirect
39. C2×(C2×D47)⋊C8C22semidirect
40. C2×(C2×D47)⋊C8C22semidirect
41. C2×(C2×D47)⋊C8C22semidirect
42. C2×#13093934C22semidirect
52. #15688878C22semidirect
53. #15688878C22semidirect
54. #15688877C22semidirect
55. #15688877C22semidirect
58. C2×C4×C8×C47C22semidirect
59. C2×C4×C8×C47C22semidirect
61. C47×#336C22semidirect
62. C47×#336C22semidirect
128. (C2×D47)⋊C8D4semidirect
146. C22⋊C8×C47D4semidirect
233. C22⋊C4×C47M16semidirect
378. C22×C47#436semidirect
436. C8×C22⋊C4D47semidirect
477. C2×C4×C8C2×D47semidirect
478. C2×C4×C8C2×D47semidirect
493. #336C2×D47semidirect
494. #336C2×D47semidirect
495. C47#22848semidirect
574. C22⋊C8D188semidirect
695. C22⋊C4#10625324semidirect
832. C22#15689202semidirect

Maximal subgroups

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

subgroupindex
C2×#156892022
C2×#156891912
C2×#156890852
C22×(C2×D47)⋊C82
C4×#130939942
#202441822
#202440022
#202439942
#202436842
#202436802
#202435722
#202435682
#202431712
C8×C22⋊C4×C472
#2284847