Finite Group Databasebeta

← #26139491

Subgroups — #26139491

Order 12032.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689019C211yesmaximal, characteristic, complemented
2C2×#15688998C211yesmaximal, characteristic
3C2×#15688996C211yesmaximal, characteristic
4C2×#15688981C211yesmaximal, characteristic
5C2×C22⋊C4×Dic47C211yesmaximal, characteristic
6C22×C47⋊#95C211yesmaximal, characteristic
7#20241651C211yesmaximal, characteristic, complemented
8#20241647C211yesmaximal, characteristic, complemented
9#20241640C211yesmaximal, characteristic, complemented
10#20241640C211yesmaximal, characteristic, complemented
11#20241619C211yesmaximal, characteristic, complemented
12#20241619C211yesmaximal, characteristic, complemented
13#20241617C211yesmaximal, characteristic, complemented
14#20241610C211yesmaximal, characteristic
15C2×C47×#385C211yesmaximal, characteristic
16C24×Dic47C2211yescharacteristic
17C24×Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28#15689019—24no—
29#15688998C418yescomplemented
30#15688996—24no—
31#15688981—24no—
32C22⋊C4×Dic47—24no—
33C2×C47⋊#95—24no—
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2211yescharacteristic
38C2×C47⋊#95C2211yescharacteristic
39C2×C47⋊#95C2211yescharacteristic
40C2×C47⋊#95C2211yescharacteristic
41C2×C47⋊#95C2211yescharacteristic
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2211yescharacteristic
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C2×C47⋊#95C2211yescharacteristic
49C2×C47⋊#95C2211yescharacteristic
50C24×C4×C47C2211yescharacteristic
51C22×C4⋊C4×C47C2211yescharacteristic
52C22×C4⋊C4×C47C2211yescharacteristic
53C22×C22⋊C4×C47C2211yescharacteristic
54C22×C22⋊C4×C47C2211yescharacteristic
55C47×#385—24no—
56C2×#95×C47C2211yescharacteristic
57C2×#95×C47C2211yescharacteristic
58C23×Dic47—22no—
59C23×Dic47—22no—
60C23×Dic47—22no—
61C23×Dic47—22no—
62C23×Dic47—22no—
63C23×Dic47—22no—
64C23×Dic47—22no—
65C23×Dic47—22no—
66C23×Dic47—41no—
67C23×Dic47—41no—
68C23×Dic47—41no—
69C23×Dic47—41no—
70C23×Dic47C2×C414yes—
71C23×Dic47Q814yes—
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C2×C4⋊Dic47—22no—
81C2×C4⋊Dic47—22no—
82C2×C4⋊Dic47—41no—
83C2×C4⋊Dic47—41no—
84C2×C4⋊Dic47C2×C414yescomplemented
85C2×C4⋊Dic47C2×C414yescomplemented
86C2×Dic47⋊C4—22no—
87C2×Dic47⋊C4—22no—
88C2×Dic47⋊C4—22no—
89C2×Dic47⋊C4—22no—
90C2×Dic47⋊C4—22no—
91C2×Dic47⋊C4—22no—
92C2×Dic47⋊C4—22no—
93C2×Dic47⋊C4—22no—
94C2×Dic47⋊C4—41no—
95C2×Dic47⋊C4—41no—
96C2×Dic47⋊C4—41no—
97C2×Dic47⋊C4—41no—
98C2×C22⋊Dic47—22no—
99C2×C22⋊Dic47—22no—
100C2×C22⋊Dic47—22no—
101C2×C22⋊Dic47—22no—
102C2×C22⋊Dic47C2×C414yes—
103C2×C22⋊Dic47D414yes—
104C2×C4×Dic47—22no—
105C2×C4×Dic47—22no—
106C2×C4×Dic47—22no—
107C2×C4×Dic47—22no—
108C2×C4×Dic47—41no—
109C2×C4×Dic47—41no—
110C47⋊#95—22no—
111C47⋊#95—22no—
112C47⋊#95—22no—
113C47⋊#95—22no—
114C47⋊#95—22no—
115C47⋊#95—22no—
116C47⋊#95—22no—
117C47⋊#95—22no—
118C47⋊#95—22no—
119C47⋊#95—22no—
120C47⋊#95—22no—
121C47⋊#95—41no—
122C47⋊#95—41no—
123C47⋊#95C2×C414yescomplemented
124C47⋊#95C2×C414yescomplemented
125C47⋊#95D414yes—
126C25×C47C2311yescharacteristic
127C23×C4×C47—22no—
128C23×C4×C47—22no—
129C23×C4×C47—22no—
130C23×C4×C47—22no—
131C23×C4×C47—22no—
132C23×C4×C47—41no—
133C23×C4×C47—41no—
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47—22no—
141C2×C4⋊C4×C47—22no—
142C2×C4⋊C4×C47—22no—
143C2×C4⋊C4×C47—22no—
144C2×C4⋊C4×C47—41no—
145C2×C4⋊C4×C47—41no—
146C2×C22⋊C4×C47—22no—
147C2×C22⋊C4×C47—22no—
148C2×C22⋊C4×C47—22no—
149C2×C22⋊C4×C47C2×C414yes—
150C2×C22⋊C4×C47D414yes—
151C2×C22⋊C4×C47Q814yes—
152#95×C47—22no—
153#95×C47—22no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47—21no—
157C24×C47—21no—
158C24×C47—21no—
159C24×C47—21no—
160C24×C47—21no—
161C24×C47—21no—
162C24×C47C22×C412yes—
163C24×C47C2×D412yes—
164C24×C47C2×D412yes—
165C24×C47C2×Q812yes—
166C24×C47C2×Q812yes—
167C24×C47#4112yes—
168C24×C47#4112yes—
169C24×C47C2411yescharacteristic
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—28no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—44no—
206C22×C4×C47—44no—
207C22×C4×C47—44no—
208C22×C4×C47—44no—
209C22×C4×C47—44no—
210C22×C4×C47—44no—
211C22×C4×C47C22×C412yes—
212C22×C4×C47C22×C412yes—
213C22×C4×C47C2×D412yes—
214C22×C4×C47C2×D412yes—
215C22×C4×C47C2×D412yes—
216C22×C4×C47C2×Q812yes—
217C22×C4×C47C2×Q812yes—
218C22×C4×C47#4112yes—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—28no—
228C22×Dic47—28no—
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—21no—
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—21no—
239C22×Dic47—21no—
240C22×Dic47—21no—
241C22×Dic47—21no—
242C22×Dic47—21no—
243C22×Dic47—21no—
244C22×Dic47—21no—
245C22×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—21no—
249C22×Dic47—21no—
250C22×Dic47—21no—
251C22×Dic47—21no—
252C22×Dic47—21no—
253C22×Dic47—21no—
254C22×Dic47—21no—
255C22×Dic47—21no—
256C22×Dic47—21no—
257C22×Dic47—21no—
258C22×Dic47—21no—
259C22×Dic47—21no—
260C22×Dic47—21no—
261C22×Dic47—21no—
262C22×Dic47—21no—
263C22×Dic47—21no—
264C22×Dic47—21no—
265C22×Dic47—28no—
266C22×Dic47—28no—
267C22×Dic47—44no—
268C22×Dic47—44no—
269C22×Dic47—44no—
270C22×Dic47—44no—
271C22×Dic47—44no—
272C22×Dic47—44no—
273C22×Dic47—44no—
274C22×Dic47—44no—
275C22×Dic47—44no—
276C22×Dic47—44no—
277C22×Dic47C22×C412yes—
278C22×Dic47C22×C412yes—
279C22×Dic47C22×C412yes—
280C22×Dic47C22×C412yes—
281C22×Dic47C2×D412yes—
282C22×Dic47C2×D412yes—
283C22×Dic47C2×D412yes—
284C22×Dic47C2×D412yes—
285C22×Dic47C2×Q812yes—
286C22×Dic47C2×Q812yes—
287C22×Dic47#4112yes—
288C22×Dic47#4112yes—
289C4⋊C4×C47—44no—
290C4⋊C4×C47—44no—
291C22⋊C4×C47—44no—
292C22⋊C4×C47C4⋊C4116yescomplemented
293C22⋊Dic47—28no—
294C22⋊Dic47—28no—
295C4⋊Dic47—28no—
296C4⋊Dic47—44no—
297Dic47⋊C4—44no—
298Dic47⋊C4—44no—
299Dic47⋊C4—44no—
300Dic47⋊C4—44no—
301C4×Dic47—44no—
302C4×Dic47—44no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—22no—
318C23×C47—22no—
319C23×C47—22no—
320C23×C47—22no—
321C23×C47—22no—
322C23×C47—22no—
323C23×C47—22no—
324C23×C47—22no—
325C23×C47—22no—
326C23×C47—22no—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47—22no—
331C23×C47C2×C4⋊C414yes—
332C23×C47C4×D414yes—
333C23×C47C4×Q814yes—
334C23×C47#12114yes—
335C23×C47C22⋊Q814yes—
336C23×C47#12514yes—
337C23×C47C4⋊Q814yes—
338C23×C47C23×C411yescharacteristic
339C23×C47C22×D411yescharacteristic
340C23×C47C22×D411yescharacteristic
341C23×C47C22×D411yescharacteristic
342C23×C47C22×Q811yescharacteristic
343C23×C47C22×Q811yescharacteristic
344C23×C47C2×#4111yescharacteristic
345C23×C47C2×#4111yescharacteristic
346C23×C47C2×#4111yescharacteristic
347C23×C47C2×#4111yescharacteristic
348C23×C47C2×#4111yescharacteristic
349C23×C47H(5,𝔽2)11yescharacteristic
350C23×C47H(5,𝔽2)11yescharacteristic
351C23×C47H(5,𝔽2)11yescharacteristic
352C23×C472−1+411yescharacteristic
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—416no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—41no—
394C2×C4×C47C2×C4⋊C414yes—
395C2×C4×C47C2×C4⋊C414yes—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—22no—
401C2×Dic47—22no—
402C2×Dic47—22no—
403C2×Dic47—22no—
404C2×Dic47—22no—
405C2×Dic47—22no—
406C2×Dic47—22no—
407C2×Dic47—22no—
408C2×Dic47—22no—
409C2×Dic47—22no—
410C2×Dic47—22no—
411C2×Dic47—22no—
412C2×Dic47—22no—
413C2×Dic47—22no—
414C2×Dic47—22no—
415C2×Dic47—22no—
416C2×Dic47—22no—
417C2×Dic47—22no—
418C2×Dic47—22no—
419C2×Dic47—22no—
420C2×Dic47—22no—
421C2×Dic47—22no—
422C2×Dic47—22no—
423C2×Dic47—22no—
424C2×Dic47—22no—
425C2×Dic47—22no—
426C2×Dic47—416no—
427C2×Dic47—416no—
428C2×Dic47—41no—
429C2×Dic47—41no—
430C2×Dic47—41no—
431C2×Dic47—41no—
432C2×Dic47—41no—
433C2×Dic47—41no—
434C2×Dic47—41no—
435C2×Dic47—41no—
436C2×Dic47—41no—
437C2×Dic47—41no—
438C2×Dic47—41no—
439C2×Dic47—41no—
440C2×Dic47—41no—
441C2×Dic47—41no—
442C2×Dic47—41no—
443C2×Dic47—41no—
444C2×Dic47—41no—
445C2×Dic47—41no—
446C2×Dic47—41no—
447C2×Dic47—41no—
448C2×Dic47—41no—
449C2×Dic47—41no—
450C2×Dic47—41no—
451C2×Dic47—41no—
452C2×Dic47C4×D414yes—
453C2×Dic47C22⋊Q814yes—
454#14004—471nomaximal, Sylow
455C22×C47—24no—
456C22×C47—24no—
457C22×C47—24no—
458C22×C47—24no—
459C22×C47—24no—
460C22×C47—24no—
461C22×C47—24no—
462C22×C47—24no—
463C22×C47—24no—
464C22×C47—24no—
465C22×C47—24no—
466C22×C47—24no—
467C22×C47—24no—
468C22×C47—24no—
469C22×C47#38918yescomplemented
470C22×C47C22×C4⋊C411yescharacteristic
471C22×C47C2×C4×D411yescharacteristic
472C22×C47C2×C4×D411yescharacteristic
473C22×C47C2×C4×Q811yescharacteristic
474C22×C47C4×#4111yescharacteristic
475C22×C47#51811yescharacteristic
476C22×C47#52011yescharacteristic
477C22×C47C2×#12111yescharacteristic
478C22×C47C2×C22⋊Q811yescharacteristic
479C22×C47C2×C22⋊Q811yescharacteristic
480C22×C47#52511yescharacteristic
481C22×C47C2×#12511yescharacteristic
482C22×C47#52911yescharacteristic
483C22×C47C2×C4⋊Q811yescharacteristic
484C22×C47#53311yescharacteristic
485C22×C47#53811yescharacteristic
486C22×C47#53911yescharacteristic
487C22×C47#54311yescharacteristic
488C22×C47#54411yescharacteristic
489C22×C47D4211yescharacteristic
490C22×C47D4211yescharacteristic
491C22×C47#54611yescharacteristic
492C22×C47#54611yescharacteristic
493C22×C47#54611yescharacteristic
494C22×C47#54611yescharacteristic
495C22×C47#54611yescharacteristic
496C22×C47#54711yescharacteristic
497C22×C47#54711yescharacteristic
498C22×C47D4×Q811yescharacteristic
499C22×C47#55111yescharacteristic
500C22×C47#55111yescharacteristic
501C22×C47#55211yescharacteristic
502C22×C47#55411yescharacteristic
503C22×C47#55411yescharacteristic
504C22×C47#55411yescharacteristic
505C4×C47—24no—
506C4×C47—24no—
507C4×C47—42no—
508C4×C47—42no—
509C4×C47—81no—
510C4×C47—81no—
511Dic47—24no—
512Dic47—24no—
513Dic47—42no—
514Dic47—42no—
515Dic47—42no—
516Dic47—42no—
517Dic47—42no—
518Dic47—42no—
519C2×#389—471no—
520C2×#385—471no—
521C2×#385—471no—
522C2×#385D4711yescharacteristic
523C2×#380—471no—
524C2×C4×C22⋊C4—471no—
525C22×#95—471no—
526#1444—471no—
527#1442—471no—
528#1441—471no—
529#1441—471no—
530#1436—471no—
531#1436—471no—
532C4⋊#95—471no—
533C22⋊#95—471no—
534C2×C47—28no—
535C2×C47C2×#38911yescharacteristic
536C2×C47C4×C22⋊Q811yescharacteristic
537C2×C47#232911yescharacteristic
538C2×C47D4×C4⋊C411yescharacteristic
539C2×C47#234911yescharacteristic
540C2×C47#235811yescharacteristic
541C2×C47#235911yescharacteristic
542C2×C47#242411yescharacteristic
543C2×C47#242511yescharacteristic
544C2×C47#243711yescharacteristic
545C2×C47#243811yescharacteristic
546C2×C47#244011yescharacteristic
547C2×C47#247311yescharacteristic
548C2×C47#250511yescharacteristic
549C2×C47#254911yescharacteristic
550C24×C4—471no—
551C24×C4—471no—
552C24×C4C2×D4711yescharacteristic
553C22×C4⋊C4—471no—
554C22×C4⋊C4—471no—
555C22×C4⋊C4—471no—
556C22×C4⋊C4—471no—
557C22×C4⋊C4—471no—
558C22×C4⋊C4—471no—
559C22×C4⋊C4C2×D4711yescharacteristic
560C22×C4⋊C4C2×D4711yescharacteristic
561C22×C22⋊C4—471no—
562C22×C22⋊C4—471no—
563C22×C22⋊C4C2×D4711yescharacteristic
564C22×C22⋊C4C2×D4711yescharacteristic
565C22×C42—471no—
566C22×C42—471no—
567#389—944no—
568#385—24no—
569#385—478no—
570#385—944no—
571#380—944no—
572C4×C22⋊C4—944no—
573C2×#95—471no—
574C2×#95—471no—
575C2×#95—471no—
576C2×#95—471no—
577C2×#95—471no—
578C2×#95—471no—
579C2×#95—471no—
580C2×#95—471no—
581C2×#95—471no—
582C2×#95—471no—
583C2×#95—471no—
584C2×#95—471no—
585C2×#95—471no—
586C2×#95—471no—
587C2×#95—471no—
588C2×#95—471no—
589C2×#95—944no—
590C2×#95C2×D4711yescharacteristic
591C2×#95C2×D4711yescharacteristic
592C47#1400411yescharacteristic, complemented, Sylow
593C25C22×D4711yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—22no—
599C23×C4—41no—
600C23×C4—41no—
601C23×C4—471no—
602C23×C4—471no—
603C23×C4—471no—
604C23×C4—471no—
605C23×C4—471no—
606C23×C4—471no—
607C23×C4—471no—
608C23×C4—471no—
609C23×C4—474no—
610C23×C4—474no—
611C23×C4—942no—
612C23×C4—942no—
613C23×C4—942no—
614C23×C4—942no—
615C23×C4—942no—
616C23×C4—942no—
617C23×C4—942no—
618C23×C4—942no—
619C23×C4—1881no—
620C23×C4—1881no—
621C23×C4—1881no—
622C23×C4—1881no—
623C23×C4C22×D4711yescharacteristic
624C23×C4C22×D4711yescharacteristic
625C23×C4C22×D4711yescharacteristic
626C23×C4C22×D4711yescharacteristic
627C23×C4C22×D4711yescharacteristic
628C23×C4C22×D4711yescharacteristic
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—474no—
636C2×C4⋊C4—474no—
637C2×C4⋊C4—942no—
638C2×C4⋊C4—942no—
639C2×C4⋊C4—942no—
640C2×C4⋊C4—942no—
641C2×C4⋊C4—942no—
642C2×C4⋊C4—942no—
643C2×C4⋊C4—942no—
644C2×C4⋊C4—942no—
645C2×C4⋊C4—942no—
646C2×C4⋊C4—942no—
647C2×C4⋊C4—1881no—
648C2×C4⋊C4—1881no—
649C2×C4⋊C4—1881no—
650C2×C4⋊C4—1881no—
651C2×C4⋊C4—1881no—
652C2×C4⋊C4—1881no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—474no—
657C2×C22⋊C4—474no—
658C2×C22⋊C4—942no—
659C2×C22⋊C4—942no—
660C2×C22⋊C4—942no—
661C2×C22⋊C4—942no—
662C2×C22⋊C4Dic9414yes—
663C2×C22⋊C4C4×D4714yes—
664C2×C22⋊C4C22⋊D4714yes—
665C2×C42—942no—
666C2×C42—942no—
667C2×C42—942no—
668C2×C42—942no—
669C2×C42—1881no—
670C2×C42—1881no—
671#95—22no—
672#95—22no—
673#95—474no—
674#95—474no—
675#95—474no—
676#95—942no—
677#95—942no—
678#95—942no—
679#95—942no—
680#95—942no—
681#95—942no—
682#95—942no—
683#95—942no—
684#95—942no—
685#95—942no—
686#95—942no—
687#95—1881no—
688#95—1881no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×Dic9412yes—
698C24C2×C4×D4712yes—
699C24D4×D4712yes—
700C24#1062535212yes—
701C24Q8×D4712yes—
702C24#1062535412yes—
703C24C2×C22⋊D4712yes—
704C24C23×D4711yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—28no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—472no—
747C22×C4—472no—
748C22×C4—472no—
749C22×C4—472no—
750C22×C4—472no—
751C22×C4—472no—
752C22×C4—472no—
753C22×C4—472no—
754C22×C4—472no—
755C22×C4—472no—
756C22×C4—472no—
757C22×C4—472no—
758C22×C4—948no—
759C22×C4—948no—
760C22×C4—941no—
761C22×C4—941no—
762C22×C4—941no—
763C22×C4—941no—
764C22×C4—941no—
765C22×C4—941no—
766C22×C4—941no—
767C22×C4—941no—
768C22×C4—948no—
769C22×C4—948no—
770C22×C4—941no—
771C22×C4—941no—
772C22×C4—941no—
773C22×C4—941no—
774C22×C4—941no—
775C22×C4—941no—
776C22×C4—941no—
777C22×C4—941no—
778C22×C4—941no—
779C22×C4—941no—
780C22×C4—941no—
781C22×C4—941no—
782C22×C4—941no—
783C22×C4—941no—
784C22×C4—941no—
785C22×C4—941no—
786C22×C4—941no—
787C22×C4—941no—
788C22×C4—941no—
789C22×C4—941no—
790C22×C4—941no—
791C22×C4—941no—
792C22×C4—941no—
793C22×C4—941no—
794C22×C4—941no—
795C22×C4—941no—
796C22×C4—941no—
797C22×C4—941no—
798C22×C4—941no—
799C22×C4—941no—
800C22×C4—941no—
801C22×C4—941no—
802C22×C4—941no—
803C22×C4—941no—
804C22×C4—941no—
805C22×C4—941no—
806C22×C4—1884no—
807C22×C4—1884no—
808C22×C4—1884no—
809C22×C4—1884no—
810C22×C4—1884no—
811C22×C4—1884no—
812C22×C4—1884no—
813C22×C4—1884no—
814C22×C4—1884no—
815C22×C4—1884no—
816C22×C4C2×Dic9412yes—
817C22×C4C2×Dic9412yes—
818C22×C4C2×C4×D4712yes—
819C22×C4C2×C4×D4712yes—
820C22×C4D4×D4712yes—
821C22×C4#1062535212yes—
822C22×C4C2×C22⋊D4712yes—
823C22×C4C2×C22⋊D4712yes—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—948no—
827C4⋊C4—1884no—
828C4⋊C4—1884no—
829C4⋊C4—1884no—
830C4⋊C4—1884no—
831C4⋊C4—1884no—
832C22⋊C4—44no—
833C22⋊C4—948no—
834C22⋊C4—948no—
835C22⋊C4Dic47⋊C4116yescomplemented
836C42—1884no—
837C42—1884no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C2×Dic47⋊C414yes—
867C23#1309398614yes—
868C23#1309398914yes—
869C23#1309399514yes—
870C23#1309400014yes—
871C23#1309401514yes—
872C23#1309402314yes—
873C23C22×C4×D4711yescharacteristic
874C23C2×D4×D4711yescharacteristic
875C23C2×D4×D4711yescharacteristic
876C23C22×C22⋊D4711yescharacteristic
877C23C2×Q8×D4711yescharacteristic
878C23C22×Dic9411yescharacteristic
879C23#41×D4711yescharacteristic
880C23#41×D4711yescharacteristic
881C23C2×#1062535211yescharacteristic
882C23C2×#1062535211yescharacteristic
883C23C2×#1062535411yescharacteristic
884C23#1309406911yescharacteristic
885C23#1309406911yescharacteristic
886C23#1309407011yescharacteristic
887C23#1309407111yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—416no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—474no—
930C2×C4—474no—
931C2×C4—942no—
932C2×C4—942no—
933C2×C4—942no—
934C2×C4—942no—
935C2×C4—942no—
936C2×C4—942no—
937C2×C4—942no—
938C2×C4—942no—
939C2×C4—942no—
940C2×C4—942no—
941C2×C4—942no—
942C2×C4—942no—
943C2×C4—942no—
944C2×C4—942no—
945C2×C4—942no—
946C2×C4—942no—
947C2×C4—942no—
948C2×C4—942no—
949C2×C4—942no—
950C2×C4—942no—
951C2×C4—942no—
952C2×C4—942no—
953C2×C4—942no—
954C2×C4—942no—
955C2×C4—942no—
956C2×C4—942no—
957C2×C4—942no—
958C2×C4—942no—
959C2×C4—942no—
960C2×C4—942no—
961C2×C4—18816no—
962C2×C4—18816no—
963C2×C4—1881no—
964C2×C4—1881no—
965C2×C4—1881no—
966C2×C4—1881no—
967C2×C4—1881no—
968C2×C4—1881no—
969C2×C4—1881no—
970C2×C4—1881no—
971C2×C4—1881no—
972C2×C4—1881no—
973C2×C4—1881no—
974C2×C4—1881no—
975C2×C4—1881no—
976C2×C4—1881no—
977C2×C4—1881no—
978C2×C4—1881no—
979C2×C4—1881no—
980C2×C4—1881no—
981C2×C4—1881no—
982C2×C4—1881no—
983C2×C4—1881no—
984C2×C4—1881no—
985C2×C4—1881no—
986C2×C4—1881no—
987C2×C4C2×Dic47⋊C414yes—
988C2×C4C2×Dic47⋊C414yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22#1568901918yescomplemented
1004C22C22×Dic47⋊C411yescharacteristic
1005C22C4×D4×D4711yescharacteristic
1006C22C2×#1309398611yescharacteristic
1007C22C2×#1309398911yescharacteristic
1008C22C4×#1062535211yescharacteristic
1009C22#1568959511yescharacteristic
1010C22#1568960211yescharacteristic
1011C22C2×#1309399511yescharacteristic
1012C22C22⋊Q8×D4711yescharacteristic
1013C22C2×#1309400011yescharacteristic
1014C22#1568962911yescharacteristic
1015C22C2×#1309401511yescharacteristic
1016C22#1568965011yescharacteristic
1017C22C2×#1309402311yescharacteristic
1018C22#1568967511yescharacteristic
1019C22#1568970811yescharacteristic
1020C22#1568971711yescharacteristic
1021C22#1568974811yescharacteristic
1022C22#1568975211yescharacteristic
1023C22#1568975511yescharacteristic
1024C22D4×C22⋊D4711yescharacteristic
1025C22#1568976011yescharacteristic
1026C22#1568976111yescharacteristic
1027C22#1568976411yescharacteristic
1028C22#1568976511yescharacteristic
1029C22#1568976711yescharacteristic
1030C22#1568977111yescharacteristic
1031C22#1568977211yescharacteristic
1032C22D4×Dic9411yescharacteristic
1033C22#1568980011yescharacteristic
1034C22#1568980011yescharacteristic
1035C22#1568981511yescharacteristic
1036C22#1568983011yescharacteristic
1037C22#1568983211yescharacteristic
1038C22#1568983211yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—42no—
1042C4—42no—
1043C4—81no—
1044C4—81no—
1045C4—944no—
1046C4—944no—
1047C4—1882no—
1048C4—1882no—
1049C4—1882no—
1050C4—1882no—
1051C4—1882no—
1052C4—1882no—
1053C2—28no—
1054C2C2×#1568901911yescharacteristic
1055C2#2024592011yescharacteristic
1056C2#2024611911yescharacteristic
1057C2D4×Dic47⋊C411yescharacteristic
1058C2#2024629311yescharacteristic
1059C2#2024636411yescharacteristic
1060C2#2024637811yescharacteristic
1061C2#2024692011yescharacteristic
1062C2#2024693511yescharacteristic
1063C2#2024705111yescharacteristic
1064C2#2024706011yescharacteristic
1065C2#2024708911yescharacteristic
1066C2#2024752811yescharacteristic
1067C2#2024789511yescharacteristic
1068C2#2024840111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#385C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#385D47
hypocenterC47#14004
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#15689019C2semidirect
7. #20241651C2semidirect
8. #20241647C2semidirect
9. #20241640C2semidirect
10. #20241640C2semidirect
11. #20241619C2semidirect
12. #20241619C2semidirect
13. #20241617C2semidirect
29. #15688998C4semidirect
84. C2×C4⋊Dic47C2×C4semidirect
85. C2×C4⋊Dic47C2×C4semidirect
123. C47⋊#95C2×C4semidirect
124. C47⋊#95C2×C4semidirect
292. C22⋊C4×C47C4⋊C4semidirect
469. C22×C47#389semidirect
592. C47#14004semidirect
835. C22⋊C4Dic47⋊C4semidirect
1003. C22#15689019semidirect

Maximal subgroups

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

subgroupindex
C2×#156890192
C2×#156889982
C2×#156889962
C2×#156889812
C2×C22⋊C4×Dic472
C22×C47⋊#952
#202416512
#202416472
#202416402
#202416192
#202416172
#202416102
C2×C47×#3852
#1400447