Finite Group Databasebeta

← #26140094

Subgroups — #26140094

Order 12032.

1838 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689030C212yesmaximal
2C2×#15689022C211yesmaximal, characteristic
3C2×C4⋊C4×Dic47C211yesmaximal, characteristic
4#20241659C212yesmaximal
5#20241641C212yesmaximal
6#20241620C212yesmaximal
7#20241618C211yesmaximal, characteristic
8#20241617C211yesmaximal, characteristic
9#20241617C211yesmaximal, characteristic
10C4×C47⋊#95C211yesmaximal, characteristic
11C22×C4⋊Q8×C47C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2212yes—
14C22×C4⋊Dic47C2211yescharacteristic
15C22×C4×Dic47C2211yescharacteristic
16C22×C4×Dic47C2212yes—
17C22×C4×Dic47C2211yescharacteristic
18#15689030—28no—
19#15689022—24no—
20C4⋊C4×Dic47—24no—
21C2×C47⋊#95C2212yes—
22C2×C47⋊#95C2212yes—
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2211yescharacteristic
26C2×C47⋊#95C2211yescharacteristic
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C23×Q8×C47C2212yes—
34C2×C4⋊Q8×C47—24no—
35C2×C4⋊Q8×C47—24no—
36C2×C4⋊Q8×C47C418yescomplemented
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C4⋊C4×C47C2212yes—
39C22×C4⋊C4×C47C2211yescharacteristic
40C22×C42×C47C2211yescharacteristic
41C23×Dic47C2312yes—
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2312yes—
46C23×Dic47C2311yescharacteristic
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—24no—
50C2×C4⋊Dic47—22no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—22no—
53C2×C4⋊Dic47—24no—
54C2×C4⋊Dic47—42no—
55C2×C4⋊Dic47Q814yescomplemented
56C2×C4×Dic47—22no—
57C2×C4×Dic47—22no—
58C2×C4×Dic47—24no—
59C2×C4×Dic47—22no—
60C2×C4×Dic47—22no—
61C2×C4×Dic47—22no—
62C2×C4×Dic47—24no—
63C2×C4×Dic47—42no—
64C2×C4×Dic47Q814yescomplemented
65C47⋊#95—24no—
66C47⋊#95—24no—
67C47⋊#95—24no—
68C47⋊#95—22no—
69C47⋊#95—22no—
70C47⋊#95—24no—
71C47⋊#95—24no—
72C47⋊#95—24no—
73C47⋊#95—42no—
74C47⋊#95—42no—
75C47⋊#95D414yes—
76C47⋊#95Q814yescomplemented
77C22×Q8×C47—24no—
78C22×Q8×C47—24no—
79C22×Q8×C47—24no—
80C22×Q8×C47—24no—
81C22×Q8×C47—42no—
82C22×Q8×C47—42no—
83C22×Q8×C47C2×C418yes—
84C23×C4×C47C2312yes—
85C23×C4×C47C2312yes—
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2311yescharacteristic
88C23×C4×C47C2311yescharacteristic
89C4⋊Q8×C47—232no—
90C2×C4⋊C4×C47—24no—
91C2×C4⋊C4×C47—24no—
92C2×C4⋊C4×C47—22no—
93C2×C4⋊C4×C47—22no—
94C2×C4⋊C4×C47C2×C414yes—
95C2×C4⋊C4×C47C2×C418yes—
96C2×C4⋊C4×C47C2×C414yes—
97C2×C4⋊C4×C47D414yes—
98C2×C4⋊C4×C47D414yes—
99C2×C42×C47—22no—
100C2×C42×C47—22no—
101C2×C42×C47C2×C414yes—
102C24×C47C2411yescharacteristic
103C2×Q8×C47—216no—
104C2×Q8×C47—216no—
105C2×Q8×C47—48no—
106C2×Q8×C47—48no—
107C2×Q8×C47—48no—
108C2×Q8×C47—48no—
109C2×Q8×C47—48no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—21no—
117C22×C4×C47—21no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47C22×C414yes—
129C22×C4×C47C22×C414yes—
130C22×C4×C47C22×C412yes—
131C22×C4×C47C22×C412yes—
132C22×C4×C47C22×C412yes—
133C22×C4×C47C2×D414yes—
134C22×C4×C47C2×D414yes—
135C22×C4×C47C2×D412yes—
136C22×C4×C47C2×D412yes—
137C22×C4×C47C2×D412yes—
138C22×C4×C47C2×Q812yes—
139C22×C4×C47C2×Q812yes—
140C22×C4×C47C2×Q812yes—
141C22×C4×C47#4112yes—
142C22×C4×C47#4112yes—
143C22×C4×C47#4112yes—
144C22×C4×C47#4112yes—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—21no—
156C22×Dic47—21no—
157C22×Dic47—21no—
158C22×Dic47—22no—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—22no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—22no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—22no—
172C22×Dic47—21no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47C2×D412yes—
181C22×Dic47C2×D412yes—
182C22×Dic47C2×Q812yes—
183C22×Dic47C2×Q812yes—
184C22×Dic47C2×Q814yes—
185C22×Dic47C2×Q812yes—
186C22×Dic47C2×Q812yes—
187C4⋊C4×C47—216no—
188C4⋊C4×C47—28no—
189C4⋊C4×C47C22⋊C4116yes—
190C42×C47—28no—
191C4⋊Dic47—28no—
192C4⋊Dic47—48no—
193C4⋊Dic47—44no—
194C4×Dic47—28no—
195C4×Dic47—48no—
196C4×Dic47—44no—
197C23×C47C23×C411yescharacteristic
198C23×C47C22×D411yescharacteristic
199C23×C47C22×D411yescharacteristic
200C23×C47C22×D411yescharacteristic
201C23×C47C22×Q811yescharacteristic
202C23×C47C22×Q811yescharacteristic
203C23×C47C22×Q811yescharacteristic
204C23×C47C2×#4111yescharacteristic
205C23×C47C2×#4111yescharacteristic
206C23×C47C2×#4111yescharacteristic
207C23×C47C2×#4111yescharacteristic
208C23×C47H(5,𝔽2)11yescharacteristic
209C23×C47H(5,𝔽2)11yescharacteristic
210C23×C472−1+411yescharacteristic
211C23×C472−1+411yescharacteristic
212Q8×C47—432no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—24no—
216C2×C4×C47—24no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—24no—
220C2×C4×C47—24no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—24no—
224C2×C4×C47—24no—
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—24no—
232C2×C4×C47—24no—
233C2×C4×C47—24no—
234C2×C4×C47—42no—
235C2×C4×C47—42no—
236C2×C4×C47—42no—
237C2×C4×C47—42no—
238C2×C4×C47C2×C22⋊C418yes—
239C2×C4×C47C2×C22⋊C414yes—
240C2×C4×C47C4×D414yes—
241C2×C4×C47C4×Q814yes—
242C2×C4×C47C4×Q814yes—
243C2×C4×C47C4×Q814yes—
244C2×C4×C47C22⋊Q814yes—
245C2×C4×C47C22⋊Q814yes—
246C2×C4×C47#12414yes—
247C2×C4×C47C4⋊Q814yes—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—22no—
253C2×Dic47—22no—
254C2×Dic47—22no—
255C2×Dic47—24no—
256C2×Dic47—22no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—22no—
262C2×Dic47—22no—
263C2×Dic47—24no—
264C2×Dic47—24no—
265C2×Dic47—22no—
266C2×Dic47—41no—
267C2×Dic47—41no—
268C2×Dic47—42no—
269C2×Dic47—42no—
270C2×Dic47—41no—
271C2×Dic47—41no—
272C2×Dic47—42no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275C2×Dic47—41no—
276C2×Dic47—42no—
277C2×Dic47—41no—
278C2×Dic47—41no—
279C2×Dic47—41no—
280C2×Dic47—41no—
281C2×Dic47—41no—
282C2×Dic47—42no—
283C2×Dic47—42no—
284C2×Dic47—42no—
285C2×Dic47—42no—
286C2×Dic47—42no—
287C2×Dic47—42no—
288C2×Dic47—42no—
289C2×Dic47C4⋊Q814yescomplemented
290#14053—471nomaximal, Sylow
291C22×C47C22×C22⋊C411yescharacteristic
292C22×C47C2×C4×D411yescharacteristic
293C22×C47C2×C4×Q811yescharacteristic
294C22×C47C2×C4×Q811yescharacteristic
295C22×C47C2×C4×Q811yescharacteristic
296C22×C47#51811yescharacteristic
297C22×C47#51911yescharacteristic
298C22×C47C2×C22⋊Q811yescharacteristic
299C22×C47C2×C22⋊Q811yescharacteristic
300C22×C47C2×#12411yescharacteristic
301C22×C47C2×C4⋊Q811yescharacteristic
302C22×C47C2×C4⋊Q811yescharacteristic
303C22×C47#53211yescharacteristic
304C22×C47#53311yescharacteristic
305C22×C47#53311yescharacteristic
306C22×C47#54211yescharacteristic
307C22×C47#54211yescharacteristic
308C22×C47#54411yescharacteristic
309C22×C47#54411yescharacteristic
310C22×C47D4211yescharacteristic
311C22×C47D4211yescharacteristic
312C22×C47#54611yescharacteristic
313C22×C47#54611yescharacteristic
314C22×C47#54711yescharacteristic
315C22×C47#54811yescharacteristic
316C22×C47#54811yescharacteristic
317C22×C47D4×Q811yescharacteristic
318C22×C47D4×Q811yescharacteristic
319C22×C47D4×Q811yescharacteristic
320C22×C47#55411yescharacteristic
321C22×C47#55411yescharacteristic
322C22×C47#55511yescharacteristic
323C22×C47#55611yescharacteristic
324C22×C47#55711yescharacteristic
325C22×C47Q8211yescharacteristic
326C4×C47—28no—
327C4×C47—24no—
328C4×C47—24no—
329C4×C47—44no—
330C4×C47#39118yescomplemented
331Dic47—24no—
332Dic47—42no—
333Dic47—44no—
334Dic47—42no—
335Dic47—42no—
336Dic47—82no—
337C22×C4⋊Q8D4711yescharacteristic
338C2×#391—472no—
339C2×#389—471no—
340C2×C4×C4⋊C4—471no—
341#1446—472no—
342#1441—472no—
343#1436—472no—
344C4⋊#95—471no—
345C4⋊#95—471no—
346C4⋊#95—471no—
347C4×#95—471no—
348C2×C47C2×#39111yescharacteristic
349C2×C47C4×C4⋊Q811yescharacteristic
350C2×C47#233111yescharacteristic
351C2×C47D4×C22⋊C411yescharacteristic
352C2×C47Q8×C22⋊C411yescharacteristic
353C2×C47#236511yescharacteristic
354C2×C47#236911yescharacteristic
355C2×C47#243911yescharacteristic
356C2×C47#244011yescharacteristic
357C2×C47#245111yescharacteristic
358C2×C47#245211yescharacteristic
359C2×C47#249111yescharacteristic
360C2×C47#249211yescharacteristic
361C2×C47#255011yescharacteristic
362C2×C47#255111yescharacteristic
363C23×Q8C2×D4712yes—
364C2×C4⋊Q8—24no—
365C2×C4⋊Q8—24no—
366C2×C4⋊Q8Dic4718yescomplemented
367C22×C4⋊C4—471no—
368C22×C4⋊C4—471no—
369C22×C4⋊C4—472no—
370C22×C4⋊C4C2×D4711yescharacteristic
371C22×C4⋊C4C2×D4712yes—
372C22×C4⋊C4C2×D4711yescharacteristic
373C22×C42—471no—
374C22×C42—471no—
375C22×C42—472no—
376C22×C42C2×D4711yescharacteristic
377#391—948no—
378#389—944no—
379C4×C4⋊C4—944no—
380C2×#95—471no—
381C2×#95—471no—
382C2×#95—471no—
383C2×#95—471no—
384C2×#95—472no—
385C2×#95—472no—
386C2×#95—472no—
387C2×#95—472no—
388C2×#95—472no—
389C2×#95—472no—
390C2×#95—472no—
391C2×#95—472no—
392C47#1405311yescharacteristic, complemented, Sylow
393C22×Q8—24no—
394C22×Q8—24no—
395C22×Q8—24no—
396C22×Q8—24no—
397C22×Q8—42no—
398C22×Q8—42no—
399C22×Q8C2×Dic4718yes—
400C23×C4—471no—
401C23×C4—471no—
402C23×C4—472no—
403C23×C4—471no—
404C23×C4—471no—
405C23×C4—472no—
406C23×C4C22×D4712yes—
407C23×C4C22×D4711yescharacteristic
408C23×C4C22×D4711yescharacteristic
409C23×C4C22×D4712yes—
410C23×C4C22×D4711yescharacteristic
411C4⋊Q8—232no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—474no—
417C2×C4⋊C4—942no—
418C2×C4⋊C4—942no—
419C2×C4⋊C4—944no—
420C2×C4⋊C4—942no—
421C2×C4⋊C4—942no—
422C2×C4⋊C4—944no—
423C2×C4⋊C4—942no—
424C2×C4⋊C4—1882no—
425C2×C4⋊C4C2×Dic4714yes—
426C2×C4⋊C4C2×Dic4718yes—
427C2×C4⋊C4C2×Dic4714yes—
428C2×C4⋊C4C22⋊D4714yes—
429C2×C4⋊C4C22⋊D4714yes—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—474no—
433C2×C42—942no—
434C2×C42—942no—
435C2×C42—944no—
436C2×C42—942no—
437C2×C42—942no—
438C2×C42—944no—
439C2×C42—942no—
440C2×C42—1882no—
441C2×C42C2×Dic4714yes—
442#95—474no—
443#95—474no—
444#95—944no—
445#95—944no—
446#95—944no—
447#95—942no—
448#95—942no—
449#95—944no—
450#95—944no—
451#95—944no—
452#95—1882no—
453#95—1882no—
454C24C23×D4711yescharacteristic
455C2×Q8—216no—
456C2×Q8—216no—
457C2×Q8—48no—
458C2×Q8—48no—
459C2×Q8—48no—
460C2×Q8—48no—
461C2×Q8—48no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—472no—
481C22×C4—472no—
482C22×C4—472no—
483C22×C4—472no—
484C22×C4—472no—
485C22×C4—472no—
486C22×C4—474no—
487C22×C4—941no—
488C22×C4—941no—
489C22×C4—941no—
490C22×C4—941no—
491C22×C4—942no—
492C22×C4—941no—
493C22×C4—941no—
494C22×C4—942no—
495C22×C4—941no—
496C22×C4—941no—
497C22×C4—941no—
498C22×C4—942no—
499C22×C4—941no—
500C22×C4—941no—
501C22×C4—941no—
502C22×C4—941no—
503C22×C4—941no—
504C22×C4—941no—
505C22×C4—941no—
506C22×C4—942no—
507C22×C4—941no—
508C22×C4—941no—
509C22×C4—942no—
510C22×C4—941no—
511C22×C4—941no—
512C22×C4—941no—
513C22×C4—941no—
514C22×C4—942no—
515C22×C4—942no—
516C22×C4—942no—
517C22×C4—942no—
518C22×C4—942no—
519C22×C4—942no—
520C22×C4—942no—
521C22×C4—942no—
522C22×C4D4×D4712yes—
523C22×C4#1062535212yes—
524C22×C4Q8×D4712yes—
525C22×C4Q8×D4712yes—
526C22×C4Q8×D4712yes—
527C22×C4#1062535412yes—
528C22×C4#1062535412yes—
529C22×C4#1062535412yes—
530C22×C4C22×Dic4714yes—
531C22×C4C22×Dic4714yes—
532C22×C4C22×Dic4712yes—
533C22×C4C22×Dic4712yes—
534C22×C4C22×Dic4712yes—
535C22×C4C2×C22⋊D4714yes—
536C22×C4C2×C22⋊D4714yes—
537C22×C4C2×C22⋊D4712yes—
538C22×C4C2×C22⋊D4712yes—
539C4⋊C4—216no—
540C4⋊C4—28no—
541C4⋊C4—948no—
542C4⋊C4—1888no—
543C4⋊C4—1884no—
544C4⋊C4C22⋊Dic47116yes—
545C42—28no—
546C42—948no—
547C42—1888no—
548C42—1884no—
549C23C23×Dic4711yescharacteristic
550C23C2×D4×D4711yescharacteristic
551C23C22×C22⋊D4711yescharacteristic
552C23C22×C22⋊D4711yescharacteristic
553C23C2×Q8×D4711yescharacteristic
554C23C2×Q8×D4711yescharacteristic
555C23C2×Q8×D4711yescharacteristic
556C23C2×#1062535211yescharacteristic
557C23C2×#1062535411yescharacteristic
558C23C2×#1062535411yescharacteristic
559C23C2×#1062535411yescharacteristic
560C23#1309406911yescharacteristic
561C23#1309406911yescharacteristic
562C23#1309407211yescharacteristic
563C23#1309407211yescharacteristic
564Q8—432no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—474no—
591C2×C4—942no—
592C2×C4—942no—
593C2×C4—942no—
594C2×C4—942no—
595C2×C4—942no—
596C2×C4—942no—
597C2×C4—942no—
598C2×C4—942no—
599C2×C4—942no—
600C2×C4—942no—
601C2×C4—944no—
602C2×C4—944no—
603C2×C4—942no—
604C2×C4—942no—
605C2×C4—944no—
606C2×C4—942no—
607C2×C4—942no—
608C2×C4—942no—
609C2×C4—1882no—
610C2×C4—1882no—
611C2×C4—1882no—
612C2×C4—1882no—
613C2×C4—1882no—
614C2×C4—1882no—
615C2×C4—1882no—
616C2×C4—1882no—
617C2×C4—1881no—
618C2×C4—1881no—
619C2×C4—1882no—
620C2×C4—1881no—
621C2×C4—1881no—
622C2×C4—1881no—
623C2×C4—1882no—
624C2×C4—1881no—
625C2×C4—1881no—
626C2×C4—1881no—
627C2×C4—1881no—
628C2×C4—1881no—
629C2×C4—1881no—
630C2×C4—1881no—
631C2×C4—1882no—
632C2×C4C2×C22⋊Dic4718yes—
633C2×C4C2×C22⋊Dic4714yes—
634C2×C4D4×Dic4714yes—
635C2×C4Q8×Dic4714yes—
636C2×C4Q8×Dic4714yes—
637C2×C4Q8×Dic4714yes—
638C2×C4#1309400014yes—
639C2×C4#1309400014yes—
640C2×C4#1309401314yes—
641C2×C4#1309402214yes—
642C22C22×C22⋊Dic4711yescharacteristic
643C22C2×D4×Dic4711yescharacteristic
644C22C2×Q8×Dic4711yescharacteristic
645C22C2×Q8×Dic4711yescharacteristic
646C22C2×Q8×Dic4711yescharacteristic
647C22#1568959811yescharacteristic
648C22#1568960111yescharacteristic
649C22C2×#1309400011yescharacteristic
650C22C2×#1309400011yescharacteristic
651C22C2×#1309401311yescharacteristic
652C22C4⋊Q8×D4711yescharacteristic
653C22C2×#1309402211yescharacteristic
654C22#1568967411yescharacteristic
655C22#1568967811yescharacteristic
656C22#1568967811yescharacteristic
657C22#1568974711yescharacteristic
658C22#1568974711yescharacteristic
659C22#1568975011yescharacteristic
660C22#1568975011yescharacteristic
661C22D4×C22⋊D4711yescharacteristic
662C22D4×C22⋊D4711yescharacteristic
663C22#1568976711yescharacteristic
664C22#1568976711yescharacteristic
665C22#1568977611yescharacteristic
666C22#1568978411yescharacteristic
667C22#1568978411yescharacteristic
668C22Q8×C22⋊D4711yescharacteristic
669C22Q8×C22⋊D4711yescharacteristic
670C22#1568978811yescharacteristic
671C22#1568983411yescharacteristic
672C22#1568983411yescharacteristic
673C22#1568983911yescharacteristic
674C22#1568984711yescharacteristic
675C22#1568984811yescharacteristic
676C22#1568985311yescharacteristic
677C4—28no—
678C4—24no—
679C4—24no—
680C4—44no—
681C4—944no—
682C4—3762no—
683C4—1882no—
684C4—1884no—
685C4—1882no—
686C4—1882no—
687C4#1568903018yescomplemented
688C2C2×#1568903011yescharacteristic
689C2C4⋊Q8×Dic4711yescharacteristic
690C2#2024613711yescharacteristic
691C2D4×C22⋊Dic4711yescharacteristic
692C2Q8×C22⋊Dic4711yescharacteristic
693C2#2024644811yescharacteristic
694C2#2024647811yescharacteristic
695C2#2024707511yescharacteristic
696C2#2024708611yescharacteristic
697C2#2024722311yescharacteristic
698C2#2024723411yescharacteristic
699C2#2024775411yescharacteristic
700C2#2024776511yescharacteristic
701C2#2024840511yescharacteristic
702C2#2024841511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC22×C4⋊Q8×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC22×C4⋊Q8D47
hypocenterC47#14053
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
36. C2×C4⋊Q8×C47C4semidirect
55. C2×C4⋊Dic47Q8semidirect
64. C2×C4×Dic47Q8semidirect
76. C47⋊#95Q8semidirect
289. C2×Dic47C4⋊Q8semidirect
330. C4×C47#391semidirect
366. C2×C4⋊Q8Dic47semidirect
392. C47#14053semidirect
687. C4#15689030semidirect

Maximal subgroups

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

subgroupindex
C2×#156890302
C2×#156890222
C2×C4⋊C4×Dic472
#202416592
#202416412
#202416202
#202416182
#202416172
C4×C47⋊#952
C22×C4⋊Q8×C472
#1405347