Finite Group Databasebeta

← #26153027

Subgroups — #26153027

Order 12032.

1922 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689058C212yesmaximal, complemented
2C2×#15689025C211yesmaximal, characteristic
3C2×#15689024C211yesmaximal, characteristic
4C2×#15689024C211yesmaximal, characteristic
5C2×#15689019C211yesmaximal, characteristic, complemented
6C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
7#20241632C212yesmaximal, complemented
8#20241632C212yesmaximal, complemented
9#20241630C212yesmaximal, complemented
10#20241617C211yesmaximal, characteristic, complemented
11C2×C47×#389C211yesmaximal, characteristic, complemented
12C23×D188C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×Dic47⋊C4C2211yescharacteristic
15C22×Dic47⋊C4C2212yes—
16C22×Dic47⋊C4C2211yescharacteristic
17C22×(C2×D47)⋊C4C2212yes—
18C22×(C2×D47)⋊C4C2212yes—
19C22×(C2×D47)⋊C4C2212yes—
20C22×(C2×D47)⋊C4C2212yes—
21C22×(C2×D47)⋊C4C2212yes—
22C22×(C2×D47)⋊C4C2212yes—
23C22×C4×Dic47C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25#15689058—28no—
26#15689025—24no—
27#15689024—24no—
28#15689024—24no—
29#15689019—24no—
30C4×Dic47⋊C4—24no—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2212yes—
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C4⋊C4×C47C2212yes—
38C22×C4⋊C4×C47C2211yescharacteristic
39C22×C42×C47C2211yescharacteristic
40C47×#389—24no—
41C2×#95×C47C2212yes—
42C24×D47C2312yes—
43C22×D188—22no—
44C22×D188—22no—
45C22×D188—22no—
46C22×D188—22no—
47C22×D188—22no—
48C22×D188—22no—
49C22×D188Q814yes—
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2312yes—
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2311yescharacteristic
55C2×C4⋊Dic47—22no—
56C2×C4⋊Dic47—22no—
57C2×C4⋊Dic47D414yes—
58C2×Dic47⋊C4—22no—
59C2×Dic47⋊C4—22no—
60C2×Dic47⋊C4—22no—
61C2×Dic47⋊C4—22no—
62C2×Dic47⋊C4—22no—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4—24no—
65C2×Dic47⋊C4—42no—
66C2×Dic47⋊C4D414yescomplemented
67C2×(C2×D47)⋊C4—24no—
68C2×(C2×D47)⋊C4—24no—
69C2×(C2×D47)⋊C4—24no—
70C2×(C2×D47)⋊C4—24no—
71C2×(C2×D47)⋊C4—24no—
72C2×(C2×D47)⋊C4—24no—
73C2×(C2×D47)⋊C4—24no—
74C2×(C2×D47)⋊C4—24no—
75C2×(C2×D47)⋊C4—24no—
76C2×(C2×D47)⋊C4—24no—
77C2×(C2×D47)⋊C4—24no—
78C2×(C2×D47)⋊C4—24no—
79C2×(C2×D47)⋊C4—42no—
80C2×(C2×D47)⋊C4—42no—
81C2×(C2×D47)⋊C4—42no—
82C2×(C2×D47)⋊C4—42no—
83C2×(C2×D47)⋊C4—42no—
84C2×(C2×D47)⋊C4—42no—
85C2×C4×Dic47—22no—
86C2×C4×Dic47—22no—
87C2×C4×Dic47—22no—
88C2×C4×Dic47—22no—
89C2×C4×Dic47—22no—
90C2×C4×Dic47D414yes—
91C47⋊#95—22no—
92C47⋊#95—22no—
93C47⋊#95—24no—
94C47⋊#95—24no—
95C47⋊#95—42no—
96C23×C4×C47C2312yes—
97C23×C4×C47C2312yes—
98C23×C4×C47C2311yescharacteristic
99C23×C4×C47C2311yescharacteristic
100C23×C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47—22no—
102C2×C4⋊C4×C47—22no—
103C2×C4⋊C4×C47—22no—
104C2×C4⋊C4×C47—22no—
105C2×C4⋊C4×C47—24no—
106C2×C4⋊C4×C47—24no—
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47—42no—
109C2×C4⋊C4×C47D414yes—
110C2×C42×C47—22no—
111C2×C42×C47—22no—
112C2×C42×C47—22no—
113#95×C47—24no—
114C24×C47C2411yescharacteristic
115C23×D47—22no—
116C23×D47—22no—
117C23×D47—22no—
118C23×D47—22no—
119C23×D47—22no—
120C23×D47—22no—
121C23×D47—22no—
122C23×D47—22no—
123C23×D47—22no—
124C23×D47—22no—
125C23×D47—22no—
126C23×D47—22no—
127C23×D47—22no—
128C23×D47—22no—
129C23×D47C2×Q814yes—
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×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47C2×D412yes—
156C22×C4×C47C2×D414yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2×D412yes—
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×Q812yes—
161C22×C4×C47#4112yes—
162C22×C4×C47#4112yes—
163C22×C4×C47#4112yes—
164C22×C4×C47#4112yes—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—22no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—22no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—21no—
184C22×Dic47—22no—
185C22×Dic47—21no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—22no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47C2×D412yes—
194C22×Dic47C2×D414yes—
195C22×Dic47C2×D412yes—
196C22×Dic47C2×D412yes—
197C22×Dic47C2×D412yes—
198C22×Dic47#4112yes—
199C22×Dic47#4112yes—
200C2×D188—28no—
201C2×D188—28no—
202C2×D188—28no—
203C2×D188—44no—
204C2×D188—44no—
205C2×D188—44no—
206C2×D188—44no—
207C4⋊C4×C47—28no—
208C4⋊C4×C47—48no—
209C4⋊C4×C47—44no—
210C42×C47—44no—
211(C2×D47)⋊C4—48no—
212(C2×D47)⋊C4—48no—
213(C2×D47)⋊C4—48no—
214(C2×D47)⋊C4—48no—
215(C2×D47)⋊C4—48no—
216(C2×D47)⋊C4—48no—
217C4⋊Dic47—28no—
218Dic47⋊C4—28no—
219Dic47⋊C4—28no—
220Dic47⋊C4—48no—
221C4×Dic47—28no—
222C4×Dic47—44no—
223C23×C47C22×D411yescharacteristic
224C23×C47C22×D411yescharacteristic
225C23×C47C22×D411yescharacteristic
226C23×C47C22×D411yescharacteristic
227C23×C47C22×Q811yescharacteristic
228C23×C47C2×#4111yescharacteristic
229C23×C47C2×#4111yescharacteristic
230C23×C47C2×#4111yescharacteristic
231C23×C47C2×#4111yescharacteristic
232C23×C47C2×#4111yescharacteristic
233C23×C47C2×#4111yescharacteristic
234C23×C47H(5,𝔽2)11yescharacteristic
235C23×C47H(5,𝔽2)11yescharacteristic
236C23×C47H(5,𝔽2)11yescharacteristic
237C23×C472−1+411yescharacteristic
238C22×D47—24no—
239C22×D47—24no—
240C22×D47—24no—
241C22×D47—24no—
242C22×D47—24no—
243C22×D47—24no—
244C22×D47—24no—
245C22×D47—42no—
246C22×D47—42no—
247C22×D47—42no—
248C22×D47—42no—
249C22×D47—42no—
250C22×D47—42no—
251C22×D47—42no—
252C22×D47—42no—
253C22×D47—42no—
254C22×D47—42no—
255C22×D47—42no—
256C22×D47—42no—
257C22×D47—42no—
258C22×D47—42no—
259C22×D47—42no—
260C22×D47—42no—
261C22×D47—42no—
262C22×D47—42no—
263C22×D47—42no—
264C22×D47—42no—
265C22×D47—42no—
266C22×D47—42no—
267C22×D47—42no—
268C22×D47—42no—
269C22×D47—42no—
270C22×D47—42no—
271C22×D47—42no—
272C22×D47—42no—
273C2×C4×C47—22no—
274C2×C4×C47—24no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—24no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—24no—
281C2×C4×C47—22no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—42no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—42no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47C22⋊Q814yes—
302C2×C4×C47C22⋊Q814yes—
303C2×C4×C47C22⋊Q814yes—
304C2×C4×C47#12314yes—
305C2×C4×C47#12314yes—
306C2×C4×C47#12314yes—
307C2×C4×C47#12714yes—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—24no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—24no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—24no—
325C2×Dic47—22no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—42no—
329C2×Dic47—41no—
330C2×Dic47—41no—
331C2×Dic47—41no—
332C2×Dic47—42no—
333C2×Dic47—41no—
334C2×Dic47—41no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47#12114yes—
343D188—416no—
344#15148—471nomaximal, Sylow
345C22×C47C2×#12111yescharacteristic
346C22×C47C2×C22⋊Q811yescharacteristic
347C22×C47C2×C22⋊Q811yescharacteristic
348C22×C47C2×C22⋊Q811yescharacteristic
349C22×C47C2×#12311yescharacteristic
350C22×C47C2×#12311yescharacteristic
351C22×C47C2×#12311yescharacteristic
352C22×C47#52511yescharacteristic
353C22×C47#52911yescharacteristic
354C22×C47#52911yescharacteristic
355C22×C47C2×#12711yescharacteristic
356C22×C47#53211yescharacteristic
357C22×C47#53211yescharacteristic
358C22×C47#53511yescharacteristic
359C22×C47#53711yescharacteristic
360C22×C47#54011yescharacteristic
361C22×C47#54011yescharacteristic
362C22×C47#54211yescharacteristic
363C22×C47#54211yescharacteristic
364C22×C47D4211yescharacteristic
365C22×C47D4211yescharacteristic
366C22×C47#54611yescharacteristic
367C22×C47#54611yescharacteristic
368C22×C47#54811yescharacteristic
369C22×C47#54811yescharacteristic
370C22×C47D4×Q811yescharacteristic
371C22×C47#55011yescharacteristic
372C22×C47#55011yescharacteristic
373C22×C47#55011yescharacteristic
374C22×C47#55411yescharacteristic
375C22×C47#55411yescharacteristic
376C22×C47#55411yescharacteristic
377C22×C47#55611yescharacteristic
378C22×C47#55911yescharacteristic
379C22×C47#55911yescharacteristic
380C2×D47—44no—
381C2×D47—44no—
382C2×D47—44no—
383C2×D47—44no—
384C2×D47—44no—
385C2×D47—44no—
386C2×D47—44no—
387C2×D47—82no—
388C2×D47—82no—
389C2×D47—82no—
390C2×D47—82no—
391C2×D47—82no—
392C2×D47—82no—
393C2×D47—82no—
394C2×D47—82no—
395C4×C47—44no—
396C4×C47—42no—
397C4×C47—42no—
398C4×C47—82no—
399C4×C47#39918yescomplemented
400Dic47—24no—
401Dic47—42no—
402Dic47—44no—
403Dic47—42no—
404Dic47—42no—
405C2×#399—472no—
406C2×#390—471no—
407C2×#390—471no—
408C2×#390—471no—
409C2×#389—471no—
410C2×#389D4711yescharacteristic, complemented
411C2×C4×C4⋊C4—471no—
412#1439—472no—
413#1439—472no—
414#1439—472no—
415C4⋊#95—471no—
416C2×C47C2×#39911yescharacteristic
417C2×C47#244511yescharacteristic
418C2×C47#244511yescharacteristic
419C2×C47#244811yescharacteristic
420C2×C47#244811yescharacteristic
421C2×C47#245211yescharacteristic
422C2×C47#245211yescharacteristic
423C2×C47#245411yescharacteristic
424C2×C47#245411yescharacteristic
425C2×C47#253811yescharacteristic
426C2×C47#254011yescharacteristic
427C2×C47#254111yescharacteristic
428C2×C47#258011yescharacteristic
429C2×C47#262411yescharacteristic
430C2×C47#285411yescharacteristic
431D47—84no—
432C23×D4—471no—
433C22×C4⋊C4—471no—
434C22×C4⋊C4—471no—
435C22×C4⋊C4—471no—
436C22×C4⋊C4—472no—
437C22×C4⋊C4C2×D4711yescharacteristic
438C22×C4⋊C4C2×D4712yes—
439C22×C4⋊C4C2×D4711yescharacteristic
440C22×C22⋊C4—472no—
441C22×C22⋊C4—472no—
442C22×C22⋊C4—472no—
443C22×C22⋊C4—472no—
444C22×C22⋊C4—472no—
445C22×C22⋊C4—472no—
446C22×C42—471no—
447C22×C42—471no—
448C22×C42C2×D4711yescharacteristic
449#399—948no—
450#390—944no—
451#390—944no—
452#390—944no—
453#389—24no—
454#389—944no—
455C4×C4⋊C4—944no—
456C2×#95—472no—
457C2×#95—471no—
458C2×#95—471no—
459C2×#95—472no—
460C2×#95—472no—
461C2×#95C2×D4712yes—
462C47#1514811yescharacteristic, complemented, Sylow
463C25—472no—
464C22×D4—474no—
465C22×D4—942no—
466C22×D4—942no—
467C22×D4—942no—
468C22×D4—942no—
469C22×D4—942no—
470C22×D4—942no—
471C23×C4—471no—
472C23×C4—471no—
473C23×C4—472no—
474C23×C4—471no—
475C23×C4—471no—
476C23×C4C22×D4712yes—
477C23×C4C22×D4711yescharacteristic
478C23×C4C22×D4711yescharacteristic
479C23×C4C22×D4712yes—
480C23×C4C22×D4711yescharacteristic
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—474no—
490C2×C4⋊C4—474no—
491C2×C4⋊C4—942no—
492C2×C4⋊C4—942no—
493C2×C4⋊C4—942no—
494C2×C4⋊C4—942no—
495C2×C4⋊C4—942no—
496C2×C4⋊C4—942no—
497C2×C4⋊C4—942no—
498C2×C4⋊C4—944no—
499C2×C4⋊C4—944no—
500C2×C4⋊C4—1882no—
501C2×C4⋊C4C22⋊D4714yes—
502C2×C22⋊C4—944no—
503C2×C22⋊C4—944no—
504C2×C22⋊C4—944no—
505C2×C22⋊C4—944no—
506C2×C22⋊C4—944no—
507C2×C22⋊C4—944no—
508C2×C22⋊C4—944no—
509C2×C22⋊C4—944no—
510C2×C22⋊C4—944no—
511C2×C22⋊C4—944no—
512C2×C22⋊C4—944no—
513C2×C22⋊C4—944no—
514C2×C22⋊C4—1882no—
515C2×C22⋊C4—1882no—
516C2×C22⋊C4—1882no—
517C2×C22⋊C4—1882no—
518C2×C22⋊C4—1882no—
519C2×C22⋊C4—1882no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—474no—
524C2×C42—942no—
525C2×C42—942no—
526C2×C42—942no—
527C2×C42—942no—
528C2×C42—942no—
529#95—24no—
530#95—942no—
531#95—942no—
532#95—944no—
533#95—944no—
534#95—1882no—
535C24—474no—
536C24—942no—
537C24—942no—
538C24—942no—
539C24—942no—
540C24—942no—
541C24—942no—
542C24—942no—
543C24—942no—
544C24—942no—
545C24—942no—
546C24—942no—
547C24—942no—
548C24—942no—
549C24—942no—
550C24C23×D4711yescharacteristic
551C2×D4—948no—
552C2×D4—948no—
553C2×D4—948no—
554C2×D4—1884no—
555C2×D4—1884no—
556C2×D4—1884no—
557C2×D4—1884no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—472no—
584C22×C4—472no—
585C22×C4—472no—
586C22×C4—472no—
587C22×C4—474no—
588C22×C4—472no—
589C22×C4—472no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—942no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—942no—
604C22×C4—941no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—941no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—942no—
612C22×C4—941no—
613C22×C4—941no—
614C22×C4—942no—
615C22×C4—941no—
616C22×C4—941no—
617C22×C4—941no—
618C22×C4#1062535012yes—
619C22×C4#1062535012yes—
620C22×C4D4×D4712yes—
621C22×C4D4×D4712yes—
622C22×C4D4×D4712yes—
623C22×C4Q8×D4712yes—
624C22×C4#1062535412yes—
625C22×C4#1062535412yes—
626C22×C4C2×C22⋊D4714yes—
627C22×C4C2×C22⋊D4712yes—
628C4⋊C4—28no—
629C4⋊C4—48no—
630C4⋊C4—44no—
631C4⋊C4—948no—
632C4⋊C4—948no—
633C4⋊C4—948no—
634C4⋊C4—1888no—
635C22⋊C4—1888no—
636C22⋊C4—1888no—
637C22⋊C4—1888no—
638C22⋊C4—1888no—
639C22⋊C4—1888no—
640C22⋊C4—1888no—
641C42—44no—
642C42—948no—
643C42—1884no—
644C23—944no—
645C23—944no—
646C23—944no—
647C23—944no—
648C23—944no—
649C23—944no—
650C23—944no—
651C23—1882no—
652C23—1882no—
653C23—1882no—
654C23—1882no—
655C23—1882no—
656C23—1882no—
657C23—1882no—
658C23—1882no—
659C23—1882no—
660C23—1882no—
661C23—1882no—
662C23—1882no—
663C23—1882no—
664C23—1882no—
665C23—1882no—
666C23—1882no—
667C23—1882no—
668C23—1882no—
669C23—1882no—
670C23—1882no—
671C23—1882no—
672C23—1882no—
673C23—1882no—
674C23—1882no—
675C23—1882no—
676C23—1882no—
677C23—1882no—
678C23—1882no—
679C23C2×D4×D4711yescharacteristic
680C23C2×D4×D4711yescharacteristic
681C23C2×D4×D4711yescharacteristic
682C23C22×C22⋊D4711yescharacteristic
683C23C2×Q8×D4711yescharacteristic
684C23#41×D4711yescharacteristic
685C23#41×D4711yescharacteristic
686C23C2×#1062535011yescharacteristic
687C23C2×#1062535011yescharacteristic
688C23C2×#1062535411yescharacteristic
689C23C2×#1062535411yescharacteristic
690C23#1309406911yescharacteristic
691C23#1309407011yescharacteristic
692C23#1309407011yescharacteristic
693C23#1309407211yescharacteristic
694D4—18816no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—474no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—944no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—944no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—944no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—1881no—
743C2×C4—1882no—
744C2×C4—1881no—
745C2×C4—1881no—
746C2×C4—1881no—
747C2×C4—1881no—
748C2×C4—1881no—
749C2×C4—1881no—
750C2×C4—1882no—
751C2×C4—1882no—
752C2×C4—1881no—
753C2×C4—1881no—
754C2×C4—1882no—
755C2×C4—1881no—
756C2×C4—1881no—
757C2×C4—1881no—
758C2×C4#1309400014yes—
759C2×C4#1309400214yes—
760C2×C4#1309400214yes—
761C2×C4#1309400714yes—
762C2×C4#1309400914yes—
763C2×C4#1309400914yes—
764C2×C4#1309402014yes—
765C22—3762no—
766C22—3762no—
767C22—3762no—
768C22—3762no—
769C22—3762no—
770C22—3762no—
771C22—3762no—
772C22—3762no—
773C22—1884no—
774C22—1884no—
775C22—1884no—
776C22—1884no—
777C22—1884no—
778C22—1884no—
779C22—1884no—
780C22#121×D4711yescharacteristic
781C22C2×#1309400011yescharacteristic
782C22C2×#1309400211yescharacteristic
783C22C2×#1309400211yescharacteristic
784C22C2×#1309400711yescharacteristic
785C22C2×#1309400911yescharacteristic
786C22C2×#1309400911yescharacteristic
787C22#1568963611yescharacteristic
788C22#1568965811yescharacteristic
789C22#1568966011yescharacteristic
790C22C2×#1309402011yescharacteristic
791C22#1568967011yescharacteristic
792C22#1568967411yescharacteristic
793C22#1568968911yescharacteristic
794C22#1568970311yescharacteristic
795C22#1568972411yescharacteristic
796C22#1568972911yescharacteristic
797C22#1568974511yescharacteristic
798C22#1568974711yescharacteristic
799C22D4×C22⋊D4711yescharacteristic
800C22#1568975711yescharacteristic
801C22#1568976111yescharacteristic
802C22#1568976411yescharacteristic
803C22#1568978311yescharacteristic
804C22#1568978411yescharacteristic
805C22#1568978811yescharacteristic
806C22#1568979111yescharacteristic
807C22#1568979211yescharacteristic
808C22#1568979411yescharacteristic
809C22#1568982911yescharacteristic
810C22#1568982911yescharacteristic
811C22#1568983411yescharacteristic
812C22#1568984511yescharacteristic
813C22#1568985611yescharacteristic
814C22#1568985811yescharacteristic
815C4—42no—
816C4—42no—
817C4—44no—
818C4—82no—
819C4—944no—
820C4—1882no—
821C4—1882no—
822C4—1882no—
823C4—1884no—
824C4#1568905818yescomplemented
825C2—3764no—
826C2C2×#1568905811yescharacteristic
827C2#2024714711yescharacteristic
828C2#2024715511yescharacteristic
829C2#2024718011yescharacteristic
830C2#2024718811yescharacteristic
831C2#2024723411yescharacteristic
832C2#2024723911yescharacteristic
833C2#2024725611yescharacteristic
834C2#2024726111yescharacteristic
835C2#2024830911yescharacteristic
836C2#2024832611yescharacteristic
837C2#2024833111yescharacteristic
838C2#2024874811yescharacteristic
839C2#2024918211yescharacteristic
840C2#2025172111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutator, socle, cosocleC24×C47C24
FittingC2×C47×#389C2
prime radicalC23×D188C22
hypercenterC2×#389D47
hypocenterC47#15148
LCSG ▷ C24×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×#15689058C2semidirect
5. C2×#15689019C2semidirect
6. C2×C4×Dic47⋊C4C2semidirect
7. #20241632C2semidirect
8. #20241632C2semidirect
9. #20241630C2semidirect
10. #20241617C2semidirect
11. C2×C47×#389C2semidirect
66. C2×Dic47⋊C4D4semidirect
399. C4×C47#399semidirect
410. C2×#389D47semidirect
462. C47#15148semidirect
824. C4#15689058semidirect

Maximal subgroups

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

subgroupindex
C2×#156890582
C2×#156890252
C2×#156890242
C2×#156890192
C2×C4×Dic47⋊C42
#202416322
#202416302
#202416172
C2×C47×#3892
#1514847