Finite Group Databasebeta

← #26182593

Subgroups — #26182593

Order 12032.

1022 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252423C212yesmaximal, complemented
2#20241757C212yesmaximal, complemented
3#20241748C212yesmaximal, complemented
4#20241736C212yesmaximal, complemented
5#20241726C211yesmaximal, characteristic, complemented
6#20241722C211yesmaximal, characteristic, complemented
7#20241718C211yesmaximal, characteristic, complemented
8#20241706C211yesmaximal, characteristic, complemented
9#20241702C211yesmaximal, characteristic, complemented
10C2×#15688849C211yesmaximal, characteristic, complemented
11C2×C47×#553C211yesmaximal, characteristic
12#15689201—22no—
13#15689195—22no—
14#15689195—22no—
15D4×C47⋊C8—22no—
16#15689180C2212yes—
17#15689176C2212yes—
18#15689087C2212yes—
19#15689087C2212yes—
20C2×C22⋊(C47⋊C8)C2212yes—
21C2×C22⋊(C47⋊C8)C2212yes—
22#15688849C2211yescharacteristic
23#15688849C2211yescharacteristic
24#15688849C2212yes—
25#15688849C2211yescharacteristic
26#15688849C2211yescharacteristic
27#15688849C2212yes—
28#15688847C2212yes—
29#15688847C2212yes—
30#15688847C2212yes—
31#15688847C2212yes—
32C47×#553—22no—
33C47×#553—22no—
34C47×#553—22no—
35C47×#553—22no—
36C2×#126×C47C411yescharacteristic
37C2×#126×C47C2211yescharacteristic
38C2×#125×C47C411yescharacteristic
39C2×#123×C47C411yescharacteristic
40C2×#123×C47C2211yescharacteristic
41C2×#121×C47C411yescharacteristic
42C2×#121×C47C411yescharacteristic
43C2×#121×C47C411yescharacteristic
44C2×#121×C47C2211yescharacteristic
45C2×C4×D4×C47C411yescharacteristic
46C2×C4×D4×C47C411yescharacteristic
47C2×C4×D4×C47C2211yescharacteristic
48C2×C4×D4×C47C2211yescharacteristic
49C2×#117×C47C2211yescharacteristic
50C22×C4⋊C4×C47C2211yescharacteristic
51C2×#10625329—22no—
52C2×#10625329—22no—
53C22×C47⋊C8—22no—
54C22×C47⋊C8—22no—
55C4⋊(C47⋊C8)—22no—
56C4⋊(C47⋊C8)—22no—
57C22⋊(C47⋊C8)—22no—
58C22⋊(C47⋊C8)—22no—
59C22⋊(C47⋊C8)—22no—
60C22⋊(C47⋊C8)—22no—
61C22⋊(C47⋊C8)C2312yes—
62C22⋊(C47⋊C8)C2312yes—
63C22⋊(C47⋊C8)C2312yes—
64C22⋊(C47⋊C8)C2312yes—
65#13093935—22no—
66C4×C47⋊C8—22no—
67C22×D4×C47C2×C411yescharacteristic
68C22×D4×C47C2×C411yescharacteristic
69C22×D4×C47C2×C411yescharacteristic
70C22×D4×C47C2×C411yescharacteristic
71C22×D4×C47C2×C411yescharacteristic
72C22×D4×C47C2×C411yescharacteristic
73C23×C4×C47C2×C411yescharacteristic
74C23×C4×C47C2×C411yescharacteristic
75C23×C4×C47C2×C411yescharacteristic
76C23×C4×C47C2×C411yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2311yescharacteristic
79#126×C47—22no—
80#126×C47—22no—
81#126×C47—22no—
82#126×C47—22no—
83#125×C47—22no—
84#125×C47—22no—
85#123×C47—22no—
86#123×C47—22no—
87#123×C47—22no—
88#123×C47—22no—
89#121×C47—22no—
90#121×C47—22no—
91#121×C47—22no—
92#121×C47—22no—
93#121×C47—22no—
94#121×C47—22no—
95#121×C47—22no—
96#121×C47—22no—
97C4×D4×C47—22no—
98C4×D4×C47—22no—
99C4×D4×C47—21no—
100C4×D4×C47—21no—
101C4×D4×C47—21no—
102C4×D4×C47—21no—
103C4×D4×C47—21no—
104C4×D4×C47—21no—
105C4×D4×C47—21no—
106C4×D4×C47—21no—
107C4×D4×C47D412yes—
108C4×D4×C47D412yes—
109C4×D4×C47D412yes—
110C4×D4×C47D412yes—
111#117×C47—22no—
112#117×C47—22no—
113C2×C4⋊C4×C47—22no—
114C2×C4⋊C4×C47—22no—
115C2×C4⋊C4×C47C2×C411yescharacteristic
116C2×C4⋊C4×C47C2×C411yescharacteristic
117C2×C4⋊C4×C47C2×C411yescharacteristic
118C2×C4⋊C4×C47C2×C411yescharacteristic
119C2×C4⋊C4×C47C2×C411yescharacteristic
120C2×C4⋊C4×C47C2×C411yescharacteristic
121C2×C4⋊C4×C47C2×C411yescharacteristic
122C2×C4⋊C4×C47C2×C411yescharacteristic
123C2×C4⋊C4×C47C2311yescharacteristic
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C22⋊C4×C47C2×C411yescharacteristic
126C2×C22⋊C4×C47C2×C411yescharacteristic
127C2×C22⋊C4×C47C2×C411yescharacteristic
128C2×C22⋊C4×C47C2×C411yescharacteristic
129C2×C22⋊C4×C47C2×C411yescharacteristic
130C2×C22⋊C4×C47C2×C411yescharacteristic
131C2×C22⋊C4×C47C2×C411yescharacteristic
132C2×C22⋊C4×C47C2×C411yescharacteristic
133C2×C22⋊C4×C47C2311yescharacteristic
134C2×C22⋊C4×C47C2311yescharacteristic
135C2×C42×C47C2×C411yescharacteristic
136C2×C42×C47C2×C411yescharacteristic
137C2×C42×C47C2311yescharacteristic
138C24×C47C22×C411yescharacteristic
139C24×C47C22×C411yescharacteristic
140C24×C47C22×C411yescharacteristic
141C24×C47C22×C411yescharacteristic
142C2×D4×C47—22no—
143C2×D4×C47—21no—
144C2×D4×C47—21no—
145C2×D4×C47—21no—
146C2×D4×C47—21no—
147C2×D4×C47—22no—
148C2×D4×C47—22no—
149C2×D4×C47—22no—
150C2×D4×C47—41no—
151C2×D4×C47—42no—
152C2×D4×C47—42no—
153C2×D4×C47—42no—
154C2×D4×C47—81no—
155C2×D4×C47—81no—
156C2×D4×C47C22⋊C412yes—
157C2×D4×C47C22⋊C412yes—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—41no—
169C22×C4×C47—41no—
170C22×C4×C47—81no—
171C22×C4×C47—81no—
172C22×C4×C47—81no—
173C22×C4×C47—81no—
174C22×C4×C47C22×C411yescharacteristic
175C22×C4×C47C22×C411yescharacteristic
176C22×C4×C47C22×C411yescharacteristic
177C22×C4×C47C22×C411yescharacteristic
178C22×C4×C47C22×C411yescharacteristic
179C22×C4×C47C22×C411yescharacteristic
180C22×C4×C47C22×C411yescharacteristic
181C22×C4×C47C22×C411yescharacteristic
182C22×C4×C47C22×C411yescharacteristic
183C22×C4×C47C22×C411yescharacteristic
184C22×C4×C47C2×D412yes—
185C22×C4×C47C2×D412yes—
186C22×C4×C47C2×D412yes—
187C22×C4×C47C2×D412yes—
188C22×C4×C47C2411yescharacteristic
189C4⋊C4×C47—22no—
190C4⋊C4×C47—22no—
191C4⋊C4×C47—22no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—22no—
197C4⋊C4×C47—22no—
198C4⋊C4×C47—22no—
199C4⋊C4×C47—22no—
200C4⋊C4×C47C22⋊C412yes—
201C4⋊C4×C47C22⋊C412yes—
202C22⋊C4×C47—22no—
203C22⋊C4×C47—22no—
204C22⋊C4×C47—22no—
205C22⋊C4×C47—21no—
206C22⋊C4×C47—21no—
207C22⋊C4×C47—21no—
208C22⋊C4×C47—21no—
209C22⋊C4×C47—22no—
210C22⋊C4×C47—22no—
211C22⋊C4×C47—22no—
212C22⋊C4×C47C22⋊C411yescharacteristic
213C22⋊C4×C47C22⋊C411yescharacteristic
214C22⋊C4×C47C22⋊C411yescharacteristic
215C22⋊C4×C47C22⋊C411yescharacteristic
216C22⋊C4×C47C22⋊C412yes—
217C22⋊C4×C47C22⋊C412yes—
218C42×C47—21no—
219C42×C47—21no—
220C42×C47—21no—
221C42×C47—21no—
222C42×C47C2×D412yes—
223C42×C47C2×D412yes—
224#10625329—82no—
225#10625329—82no—
226C2×C47⋊C8—22no—
227C2×C47⋊C8—22no—
228C2×C47⋊C8—22no—
229C2×C47⋊C8—22no—
230C2×C47⋊C8—82no—
231C2×C47⋊C8—82no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47—22no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—41no—
250C23×C47C2×C22⋊C412yes—
251C23×C47C2×C22⋊C411yescharacteristic
252C23×C47C2×C22⋊C411yescharacteristic
253C23×C47C23×C411yescharacteristic
254D4×C47—24no—
255D4×C47—42no—
256D4×C47—44no—
257D4×C47—42no—
258D4×C47—42no—
259D4×C47—42no—
260D4×C47—42no—
261D4×C47—82no—
262D4×C47—82no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—42no—
275C2×C4×C47—42no—
276C2×C4×C47—42no—
277C2×C4×C47—42no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—42no—
283C2×C4×C47—42no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—81no—
291C2×C4×C47—81no—
292C2×C4×C47—81no—
293C2×C4×C47—81no—
294C2×C4×C47C2×C22⋊C411yescharacteristic
295C2×C4×C47C2×C22⋊C411yescharacteristic
296C2×C4×C47C2×C22⋊C411yescharacteristic
297C2×C4×C47C2×C22⋊C411yescharacteristic
298C2×C4×C47C2×C22⋊C412yes—
299C2×C4×C47C2×C22⋊C412yes—
300C2×C4×C47#13112yes—
301C2×C4×C47C22×D412yes—
302C47⋊C8—42no—
303C47⋊C8—42no—
304C47⋊C8—42no—
305C47⋊C8—42no—
306#17427—471nomaximal, Sylow
307C22×C47—21no—
308C22×C47—21no—
309C22×C47—21no—
310C22×C47—21no—
311C22×C47—21no—
312C22×C47—22no—
313C22×C47—21no—
314C22×C47—22no—
315C22×C47—22no—
316C22×C47—21no—
317C22×C47—42no—
318C22×C47—42no—
319C22×C47—41no—
320C22×C47—41no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47—41no—
324C22×C47—41no—
325C22×C47—81no—
326C22×C47—81no—
327C22×C47—81no—
328C22×C47—81no—
329C22×C47—81no—
330C22×C47—81no—
331C22×C47#41312yes—
332C22×C47C22×C22⋊C411yescharacteristic
333C22×C47C2×#13111yescharacteristic
334C22×C47#56811yescharacteristic
335C4×C47—22no—
336C4×C47—21no—
337C4×C47—21no—
338C4×C47—22no—
339C4×C47—21no—
340C4×C47—21no—
341C4×C47—22no—
342C4×C47—22no—
343C4×C47—41no—
344C4×C47—41no—
345C4×C47—41no—
346C4×C47—41no—
347C4×C47—41no—
348C2×#553D4711yescharacteristic
349#2974—472no—
350#1473—472no—
351#1471—472no—
352#1468—472no—
353#1465—471no—
354#1464—471no—
355#1463—471no—
356#1459—471no—
357#1458—471no—
358C2×#324—471no—
359C2×C47—21no—
360C2×C47—21no—
361C2×C47—22no—
362C2×C47—41no—
363C2×C47—42no—
364C2×C47—81no—
365C2×C47—81no—
366C2×C47#288011yescharacteristic
367C2×C47#288311yescharacteristic
368C2×C47C2×#41311yescharacteristic
369#553—22no—
370#553—22no—
371#553—22no—
372#553—22no—
373C2×#126Dic4711yescharacteristic
374C2×#126C2×D4711yescharacteristic
375C2×#125Dic4711yescharacteristic
376C2×#123Dic4711yescharacteristic
377C2×#123C2×D4711yescharacteristic
378C2×#121Dic4711yescharacteristic
379C2×#121Dic4711yescharacteristic
380C2×#121Dic4711yescharacteristic
381C2×#121C2×D4711yescharacteristic
382C2×C4×D4Dic4711yescharacteristic
383C2×C4×D4Dic4711yescharacteristic
384C2×C4×D4C2×D4711yescharacteristic
385C2×C4×D4C2×D4711yescharacteristic
386C2×#117C2×D4711yescharacteristic
387C22×C4⋊C4C2×D4711yescharacteristic
388#436—942no—
389#435—942no—
390#435—942no—
391C8×D4—942no—
392#432—472no—
393#431—472no—
394#407—472no—
395#407—472no—
396C2×C22⋊C8—472no—
397C2×C22⋊C8—472no—
398#324—471no—
399#324—471no—
400#324—472no—
401#324—471no—
402#324—471no—
403#324—472no—
404#323—472no—
405#323—472no—
406#323—472no—
407#323—472no—
408C47#1742711yescharacteristic, complemented, Sylow
409C22×D4C2×Dic4711yescharacteristic
410C22×D4C2×Dic4711yescharacteristic
411C22×D4C2×Dic4711yescharacteristic
412C22×D4C2×Dic4711yescharacteristic
413C22×D4C2×Dic4711yescharacteristic
414C22×D4C2×Dic4711yescharacteristic
415C23×C4C2×Dic4711yescharacteristic
416C23×C4C2×Dic4711yescharacteristic
417C23×C4C2×Dic4711yescharacteristic
418C23×C4C2×Dic4711yescharacteristic
419C23×C4C22×D4711yescharacteristic
420C23×C4C22×D4711yescharacteristic
421C2×M16—942no—
422C2×M16—942no—
423C22×C8—942no—
424C22×C8—942no—
425#126—22no—
426#126—22no—
427#126—22no—
428#126—22no—
429#125—22no—
430#125—22no—
431#123—22no—
432#123—22no—
433#123—22no—
434#123—22no—
435#121—22no—
436#121—22no—
437#121—22no—
438#121—22no—
439#121—22no—
440#121—22no—
441#121—22no—
442#121—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4C22⋊D4712yes—
454C4×D4C22⋊D4712yes—
455C4×D4C22⋊D4712yes—
456C4×D4C22⋊D4712yes—
457#117—22no—
458#117—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4C2×Dic4711yescharacteristic
462C2×C4⋊C4C2×Dic4711yescharacteristic
463C2×C4⋊C4C2×Dic4711yescharacteristic
464C2×C4⋊C4C2×Dic4711yescharacteristic
465C2×C4⋊C4C2×Dic4711yescharacteristic
466C2×C4⋊C4C2×Dic4711yescharacteristic
467C2×C4⋊C4C2×Dic4711yescharacteristic
468C2×C4⋊C4C2×Dic4711yescharacteristic
469C2×C4⋊C4C22×D4711yescharacteristic
470C2×C4⋊C4C22×D4711yescharacteristic
471C2×C22⋊C4C2×Dic4711yescharacteristic
472C2×C22⋊C4C2×Dic4711yescharacteristic
473C2×C22⋊C4C2×Dic4711yescharacteristic
474C2×C22⋊C4C2×Dic4711yescharacteristic
475C2×C22⋊C4C2×Dic4711yescharacteristic
476C2×C22⋊C4C2×Dic4711yescharacteristic
477C2×C22⋊C4C2×Dic4711yescharacteristic
478C2×C22⋊C4C2×Dic4711yescharacteristic
479C2×C22⋊C4C22×D4711yescharacteristic
480C2×C22⋊C4C22×D4711yescharacteristic
481C2×C42C2×Dic4711yescharacteristic
482C2×C42C2×Dic4711yescharacteristic
483C2×C42C22×D4711yescharacteristic
484C4⋊C8—942no—
485C4⋊C8—942no—
486C22⋊C8—472no—
487C22⋊C8—472no—
488C22⋊C8—472no—
489C22⋊C8—472no—
490C22⋊C8—942no—
491C22⋊C8—942no—
492C22⋊C8—942no—
493C22⋊C8—942no—
494#97—942no—
495C4×C8—942no—
496C24C22×Dic4711yescharacteristic
497C24C22×Dic4711yescharacteristic
498C24C22×Dic4711yescharacteristic
499C24C22×Dic4711yescharacteristic
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—41no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4C22⋊Dic4712yes—
515C2×D4C22⋊Dic4712yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4C22×Dic4711yescharacteristic
533C22×C4C22×Dic4711yescharacteristic
534C22×C4C22×Dic4711yescharacteristic
535C22×C4C22×Dic4711yescharacteristic
536C22×C4C22×Dic4711yescharacteristic
537C22×C4C22×Dic4711yescharacteristic
538C22×C4C22×Dic4711yescharacteristic
539C22×C4C22×Dic4711yescharacteristic
540C22×C4C22×Dic4711yescharacteristic
541C22×C4C22×Dic4711yescharacteristic
542C22×C4C2×C22⋊D4712yes—
543C22×C4C2×C22⋊D4712yes—
544C22×C4C2×C22⋊D4712yes—
545C22×C4C2×C22⋊D4712yes—
546C22×C4C23×D4711yescharacteristic
547M16—3762no—
548M16—3762no—
549C2×C8—942no—
550C2×C8—942no—
551C2×C8—942no—
552C2×C8—942no—
553C2×C8—3762no—
554C2×C8—3762no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4C22⋊Dic4712yes—
567C4⋊C4C22⋊Dic4712yes—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4C22⋊Dic4711yescharacteristic
579C22⋊C4C22⋊Dic4711yescharacteristic
580C22⋊C4C22⋊Dic4711yescharacteristic
581C22⋊C4C22⋊Dic4711yescharacteristic
582C22⋊C4C22⋊Dic4712yes—
583C22⋊C4C22⋊Dic4712yes—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42C2×C22⋊D4712yes—
589C42C2×C22⋊D4712yes—
590C23—22no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23C2×C22⋊Dic4712yes—
609C23C2×C22⋊Dic4711yescharacteristic
610C23C2×C22⋊Dic4711yescharacteristic
611C23C23×Dic4711yescharacteristic
612D4—24no—
613D4—42no—
614D4—44no—
615D4—42no—
616D4—42no—
617D4—42no—
618D4—42no—
619D4—82no—
620D4—82no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4C2×C22⋊Dic4711yescharacteristic
653C2×C4C2×C22⋊Dic4711yescharacteristic
654C2×C4C2×C22⋊Dic4711yescharacteristic
655C2×C4C2×C22⋊Dic4711yescharacteristic
656C2×C4C2×C22⋊Dic4712yes—
657C2×C4C2×C22⋊Dic4712yes—
658C2×C4#1309403112yes—
659C2×C4C22×C22⋊D4712yes—
660C8—1882no—
661C8—1882no—
662C8—1882no—
663C8—1882no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—22no—
670C22—21no—
671C22—22no—
672C22—22no—
673C22—21no—
674C22—42no—
675C22—42no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22#1568910712yes—
689C22C22×C22⋊Dic4711yescharacteristic
690C22C2×#1309403111yescharacteristic
691C22#1568989011yescharacteristic
692C4—22no—
693C4—21no—
694C4—21no—
695C4—22no—
696C4—21no—
697C4—21no—
698C4—22no—
699C4—22no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—41no—
705C2—21no—
706C2—21no—
707C2—22no—
708C2—41no—
709C2—42no—
710C2—81no—
711C2—81no—
712C2#2025183711yescharacteristic
713C2#2025184911yescharacteristic
714C2C2×#1568910711yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic47
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#553C2
socleC22×C47C22×C22⋊C4
cosocleC22×C4×C47C24
hypercenterC2×#553D47
hypocenterC47#17427
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. #20252423C2semidirect
2. #20241757C2semidirect
3. #20241748C2semidirect
4. #20241736C2semidirect
5. #20241726C2semidirect
6. #20241722C2semidirect
7. #20241718C2semidirect
8. #20241706C2semidirect
9. #20241702C2semidirect
10. C2×#15688849C2semidirect
408. C47#17427semidirect

Maximal subgroups

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

subgroupindex
#202524232
#202417572
#202417482
#202417362
#202417262
#202417222
#202417182
#202417062
#202417022
C2×#156888492
C2×C47×#5532
#1742747