Finite Group Databasebeta

← #26215679

Subgroups — #26215679

Order 12032.

1690 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689595C211yesmaximal, characteristic
2C2×#99×D47C212yesmaximal
3#20246001C212yesmaximal, complemented
4#20243376C211yesmaximal, characteristic, complemented
5#20243375C212yesmaximal, complemented
6#20243374C212yesmaximal, complemented
7#20243373C212yesmaximal, complemented
8#342×D47C212yesmaximal, complemented
9C47×#1799C211yesmaximal, characteristic, complemented
10C22×D4×D47C2211yescharacteristic
11#15689595—24no—
12#15689595—24no—
13C2×C4×D188C411yescharacteristic, complemented
14C2×D4×Dic47C2211yescharacteristic
15C2×#13093986C411yescharacteristic, complemented
16C2×C4×C22⋊D47C411yescharacteristic, complemented
17C2×C4×C22⋊D47C2211yescharacteristic
18C2×(C22⋊D47)⋊C4C411yescharacteristic, complemented
19C2×(C22⋊D47)⋊C4C2211yescharacteristic
20C2×#13093982C411yescharacteristic, complemented
21C2×#13093981C411yescharacteristic, complemented
22C22×(C2×D47)⋊C4C411yescharacteristic, complemented
23C22×(C2×D47)⋊C4C2211yescharacteristic
24C2×C22⋊C4×D47C411yescharacteristic, complemented
25C2×C22⋊C4×D47C2214yes—
26C2×C22⋊C4×D47C2211yescharacteristic
27C2×#13093939C2212yes—
28C2×#13093938C2214yes—
29#99×D47—28no—
30#15688997—24no—
31#15688994—24no—
32#15688983C2212yescomplemented
33#15688981C2214yescomplemented
34#15688890C2212yescomplemented
35#15688889C2214yescomplemented
36C2×C4×D4×C47C2211yescharacteristic
37C2×#99×C47C2212yes—
38C47×#380C2212yescomplemented
39C47×#342C2212yescomplemented
40C24×D47C2×C411yescharacteristic
41C24×D47C2311yescharacteristic
42C22×D188C2×C411yescharacteristic
43C22×C22⋊D47C2×C411yescharacteristic
44C22×C22⋊D47C2311yescharacteristic
45C2×D4×D47—24no—
46C2×D4×D47—24no—
47C2×D4×D47D414yes—
48C2×D4×D47Q814yes—
49C23×Dic47C2×C411yescharacteristic, complemented
50C23×Dic47C2311yescharacteristic
51C22×C4×D47—24no—
52C22×C4×D47C2×C411yescharacteristic
53C22×C4×D47C2×C411yescharacteristic
54C22×C4×D47C2×C411yescharacteristic
55C22×C4×D47C2×C411yescharacteristic, complemented
56C22×C4×D47C2×C411yescharacteristic, complemented
57C4×D188—22no—
58C4×D188—22no—
59D4×Dic47—24no—
60#13093986—24no—
61C4×C22⋊D47—22no—
62C4×C22⋊D47—22no—
63C4×C22⋊D47—22no—
64C4×C22⋊D47—22no—
65(C22⋊D47)⋊C4—24no—
66(C22⋊D47)⋊C4—24no—
67#13093982—24no—
68#13093981—22no—
69#13093981—22no—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47C2×C411yescharacteristic, complemented
72C2×Dic47⋊C4—24no—
73C2×Dic47⋊C4C2×C411yescharacteristic, complemented
74C2×Dic47⋊C4C2×C411yescharacteristic, complemented
75C2×C22⋊Dic47C2×C411yescharacteristic, complemented
76C2×C22⋊Dic47C2314yes—
77C2×C22⋊Dic47C2311yescharacteristic
78C2×(C2×D47)⋊C4—22no—
79C2×(C2×D47)⋊C4—22no—
80C2×(C2×D47)⋊C4—24no—
81C2×(C2×D47)⋊C4C2×C411yescharacteristic
82C2×(C2×D47)⋊C4C2×C411yescharacteristic
83C2×(C2×D47)⋊C4C2×C411yescharacteristic
84C2×(C2×D47)⋊C4C2×C411yescharacteristic
85C2×(C2×D47)⋊C4C2×C411yescharacteristic
86C2×(C2×D47)⋊C4C2×C411yescharacteristic
87C2×(C2×D47)⋊C4C2×C411yescharacteristic, complemented
88C2×(C2×D47)⋊C4C2×C411yescharacteristic, complemented
89C2×(C2×D47)⋊C4D414yes—
90C2×(C2×D47)⋊C4D414yes—
91C22⋊C4×D47—24no—
92C22⋊C4×D47—24no—
93C22⋊C4×D47—28no—
94C22⋊C4×D47—28no—
95C2×C4×Dic47C2×C411yescharacteristic, complemented
96C2×C4×Dic47C2×C411yescharacteristic, complemented
97C2×C4×Dic47C2×C411yescharacteristic, complemented
98#13093939—24no—
99#13093938—28no—
100C47⋊#95—22no—
101C47⋊#95—24no—
102C22×D4×C47C2311yescharacteristic
103C23×C4×C47C2×C411yescharacteristic, complemented
104C23×C4×C47C2311yescharacteristic
105C4×D4×C47—22no—
106C4×D4×C47—22no—
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47C2×C411yescharacteristic, complemented
109C2×C22⋊C4×C47C2×C411yescharacteristic, complemented
110C2×C22⋊C4×C47C2314yes—
111C2×C22⋊C4×C47C2311yescharacteristic
112C2×C42×C47C2×C411yescharacteristic, complemented
113#99×C47—24no—
114#95×C47—22no—
115C24×C47C22×C411yescharacteristic
116C24×C47C2411yescharacteristic
117C23×D47—22no—
118C23×D47—22no—
119C23×D47—81no—
120C23×D47—81no—
121C23×D47—81no—
122C23×D47—81no—
123C23×D47C4⋊C414yescomplemented
124C23×D47C22×C411yescharacteristic
125C23×D47C22×C411yescharacteristic
126C23×D47C22×C411yescharacteristic
127C23×D47C2×D414yes—
128C23×D47C2×D412yes—
129C23×D47C2×Q812yes—
130C23×D47#4114yes—
131C2×D4×C47—22no—
132C2×D4×C47—22no—
133C2×D4×C47C2×D412yes—
134C2×D4×C47C2×Q812yes—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—24no—
138C22×C4×C47—81no—
139C22×C4×C47—81no—
140C22×C4×C47C22×C411yescharacteristic
141C22×C4×C47C22×C411yescharacteristic
142C22×C4×C47C22×C411yescharacteristic
143C22×C4×C47C22×C411yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D412yes—
146C22×C4×C47C2×D412yes—
147C2×C22⋊D47—22no—
148C2×C22⋊D47—22no—
149C2×C22⋊D47—22no—
150C2×C22⋊D47—22no—
151C2×C22⋊D47C4⋊C414yescomplemented
152C2×C22⋊D47C2×D412yes—
153C2×C22⋊D47C2×Q812yes—
154C22×Dic47—22no—
155C22×Dic47—24no—
156C22×Dic47—81no—
157C22×Dic47—81no—
158C22×Dic47C22×C411yescharacteristic
159C22×Dic47C22×C411yescharacteristic
160C22×Dic47C22×C411yescharacteristic
161C22×Dic47C22×C411yescharacteristic
162C22×Dic47C22×C411yescharacteristic
163C22×Dic47C2×D414yes—
164D4×D47—216no—
165D4×D47—216no—
166C2×D188—22no—
167C2×D188—22no—
168C2×D188C4⋊C414yescomplemented
169C2×C4×D47—22no—
170C2×C4×D47—22no—
171C2×C4×D47—22no—
172C2×C4×D47—22no—
173C2×C4×D47—22no—
174C2×C4×D47—22no—
175C2×C4×D47—48no—
176C2×C4×D47—84no—
177C2×C4×D47—84no—
178C2×C4×D47—81no—
179C2×C4×D47—81no—
180C2×C4×D47—81no—
181C2×C4×D47—81no—
182C2×C4×D47C4⋊C414yescomplemented
183C4⋊C4×C47—22no—
184C4⋊C4×C47—82no—
185C22⋊C4×C47—22no—
186C22⋊C4×C47—22no—
187C22⋊C4×C47—24no—
188C22⋊C4×C47—24no—
189C42×C47—21no—
190C42×C47—21no—
191C22⋊Dic47—22no—
192C22⋊Dic47—22no—
193C22⋊Dic47—24no—
194C22⋊Dic47—24no—
195(C2×D47)⋊C4—22no—
196(C2×D47)⋊C4—22no—
197(C2×D47)⋊C4—21no—
198(C2×D47)⋊C4—21no—
199(C2×D47)⋊C4—22no—
200(C2×D47)⋊C4—48no—
201(C2×D47)⋊C4C22⋊C414yes—
202(C2×D47)⋊C4C22⋊C412yes—
203(C2×D47)⋊C4C22⋊C412yes—
204(C2×D47)⋊C4C22⋊C414yes—
205(C2×D47)⋊C4C22⋊C412yes—
206(C2×D47)⋊C4C22⋊C412yes—
207C4⋊Dic47—22no—
208C4⋊Dic47—82no—
209Dic47⋊C4—21no—
210Dic47⋊C4—21no—
211Dic47⋊C4—22no—
212Dic47⋊C4—84no—
213C4×Dic47—22no—
214C4×Dic47—22no—
215C4×Dic47—22no—
216C23×C47—21no—
217C23×C47—21no—
218C23×C47—41no—
219C23×C47—41no—
220C23×C47—41no—
221C23×C47—41no—
222C23×C47C2×C4⋊C412yes—
223C23×C47C23×C411yescharacteristic
224C23×C47C22×D412yes—
225C23×C47C22×D411yescharacteristic
226C23×C47C22×Q811yescharacteristic
227C23×C47C2×#4112yes—
228C22×D47—21no—
229C22×D47—21no—
230C22×D47—28no—
231C22×D47—41no—
232C22×D47—41no—
233C22×D47—44no—
234C22×D47—44no—
235C22×D47—41no—
236C22×D47—41no—
237C22×D47—41no—
238C22×D47—41no—
239C22×D47—82no—
240C22×D47—82no—
241C22×D47—82no—
242C22×D47—82no—
243C22×D47—84no—
244C22×D47—84no—
245C22×D47—84no—
246C22×D47C2×C22⋊C412yes—
247C22×D47C2×C22⋊C412yes—
248C22×D47C2×C4⋊C412yes—
249C22×D47C2×C4⋊C412yes—
250C22×D47C2×C4⋊C412yes—
251C22×D47#11712yes—
252C22×D47#11712yes—
253C22×D47#12118yes—
254C22×D47C22⋊Q818yes—
255D4×C47—24no—
256D4×C47—24no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—42no—
262C2×C4×C47—42no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—44no—
268C2×C4×C47—44no—
269C2×C4×C47—44no—
270C2×C4×C47—81no—
271C2×C4×C47—81no—
272C2×C4×C47C2×C22⋊C412yes—
273C2×C4×C47C2×C22⋊C411yescharacteristic
274C2×C4×C47C2×C22⋊C411yescharacteristic
275C2×C4×C47C2×C4⋊C412yes—
276C22⋊D47—24no—
277C22⋊D47—24no—
278C22⋊D47—28no—
279C2×Dic47—21no—
280C2×Dic47—21no—
281C2×Dic47—21no—
282C2×Dic47—21no—
283C2×Dic47—44no—
284C2×Dic47—41no—
285C2×Dic47—41no—
286C2×Dic47—41no—
287C2×Dic47—41no—
288C2×Dic47—44no—
289C2×Dic47—44no—
290C2×Dic47—44no—
291C2×Dic47—82no—
292C2×Dic47C2×C22⋊C412yes—
293C2×Dic47C2×C22⋊C412yes—
294C2×Dic47C2×C4⋊C412yes—
295D188—28no—
296C4×D47—28no—
297C4×D47—82no—
298C4×D47—82no—
299C4×D47—82no—
300C4×D47—82no—
301C4×D47—816no—
302#20633—471nomaximal, Sylow
303C22×C47—22no—
304C22×C47—21no—
305C22×C47—22no—
306C22×C47—21no—
307C22×C47—22no—
308C22×C47—41no—
309C22×C47—41no—
310C22×C47—42no—
311C22×C47—42no—
312C22×C47—42no—
313C22×C47—41no—
314C22×C47—41no—
315C22×C47C22×C22⋊C411yescharacteristic
316C22×C47C22×C4⋊C411yescharacteristic
317C22×C47C2×#11711yescharacteristic
318C22×C47C2×#12112yes—
319C22×C47C2×C22⋊Q812yes—
320C2×D47—22no—
321C2×D47—22no—
322C2×D47—22no—
323C2×D47—22no—
324C2×D47—22no—
325C2×D47—48no—
326C2×D47—42no—
327C2×D47—42no—
328C2×D47—42no—
329C2×D47—42no—
330C2×D47—48no—
331C2×D47—42no—
332C2×D47—41no—
333C2×D47—41no—
334C2×D47—42no—
335C2×D47—88no—
336C2×D47#38014yes—
337C2×D47#38014yes—
338C4×C47—22no—
339C4×C47—21no—
340C4×C47—21no—
341C4×C47—22no—
342C4×C47—41no—
343C4×C47—41no—
344C4×C47—84no—
345Dic47—22no—
346Dic47—22no—
347Dic47—22no—
348Dic47—41no—
349Dic47—41no—
350Dic47—84no—
351C2×#518—471no—
352C22×#99—472no—
353#2315—472no—
354#1799—472no—
355#1799—472no—
356#1799—472no—
357#1799—471no—
358#1799D4711yescharacteristic, complemented
359C2×#342—472no—
360C2×C47—22no—
361C2×C47—21no—
362C2×C47—21no—
363C2×C47—22no—
364C2×C47—42no—
365C2×C47C2×#38011yescharacteristic
366C2×C47#288311yescharacteristic
367C2×C47#288311yescharacteristic
368D47—24no—
369D47—24no—
370D47—42no—
371C23×D4—471no—
372#518—944no—
373#518—944no—
374C2×C4×D4—471no—
375C2×C4×D4—471no—
376C2×C4×D4—471no—
377C2×C4×D4—471no—
378C2×C4×D4—471no—
379C2×C4×D4—471no—
380C2×C4×D4—471no—
381C2×C4×D4C2×D4711yescharacteristic
382C2×#117—471no—
383C2×#117—471no—
384C22×C22⋊C4—471no—
385C22×C22⋊C4—471no—
386C22×C22⋊C4—471no—
387C22×C22⋊C4—471no—
388C22×C22⋊C4—474no—
389C2×#99—472no—
390C2×#99—474no—
391C2×#99—948no—
392C2×#99C2×D4712yes—
393#385—944no—
394#385—944no—
395#380—472no—
396#380—474no—
397#380C2×D4712yescomplemented
398#342—474no—
399#342—472no—
400#342C2×D4712yescomplemented
401C47#2063311yescharacteristic, complemented, Sylow
402C25—471no—
403C25—471no—
404C22×D4—471no—
405C22×D4—471no—
406C22×D4—474no—
407C22×D4—474no—
408C22×D4—471no—
409C22×D4—944no—
410C22×D4—944no—
411C22×D4C22×D4711yescharacteristic
412C23×C4—471no—
413C23×C4—471no—
414C23×C4—471no—
415C23×C4—471no—
416C23×C4—471no—
417C23×C4—471no—
418C23×C4—471no—
419C23×C4—944no—
420C23×C4C4×D4711yescharacteristic, complemented
421C23×C4C22×D4711yescharacteristic
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—942no—
425C4×D4—942no—
426C4×D4—944no—
427C4×D4—944no—
428C4×D4—944no—
429C4×D4—942no—
430C4×D4—942no—
431C4×D4—944no—
432C4×D4—942no—
433C4×D4—942no—
434#117—942no—
435#117—942no—
436#117—944no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—471no—
439C2×C4⋊C4—471no—
440C2×C4⋊C4—471no—
441C2×C4⋊C4—944no—
442C2×C4⋊C4—942no—
443C2×C4⋊C4C4×D4711yescharacteristic, complemented
444C2×C22⋊C4—471no—
445C2×C22⋊C4—471no—
446C2×C22⋊C4—471no—
447C2×C22⋊C4—471no—
448C2×C22⋊C4—474no—
449C2×C22⋊C4—474no—
450C2×C22⋊C4—471no—
451C2×C22⋊C4—471no—
452C2×C22⋊C4—471no—
453C2×C22⋊C4—471no—
454C2×C22⋊C4—471no—
455C2×C22⋊C4—471no—
456C2×C22⋊C4—474no—
457C2×C22⋊C4—944no—
458C2×C22⋊C4—944no—
459C2×C22⋊C4—948no—
460C2×C22⋊C4—948no—
461C2×C22⋊C4—942no—
462C2×C22⋊C4—942no—
463C2×C22⋊C4—944no—
464C2×C22⋊C4C4×D4711yescharacteristic, complemented
465C2×C22⋊C4C22×D4714yes—
466C2×C22⋊C4C22×D4711yescharacteristic
467C2×C42—471no—
468C2×C42—471no—
469C2×C42—471no—
470C2×C42C4×D4711yescharacteristic, complemented
471#99—24no—
472#99—948no—
473#99—944no—
474#95—22no—
475#95—944no—
476#95—942no—
477C24—472no—
478C24—472no—
479C24—474no—
480C24—471no—
481C24—471no—
482C24—474no—
483C24—474no—
484C24—471no—
485C24—942no—
486C24—942no—
487C24—3761no—
488C24—3761no—
489C24—3761no—
490C24—3761no—
491C24C2×C4×D4711yescharacteristic
492C24C23×D4711yescharacteristic
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—474no—
496C2×D4—472no—
497C2×D4—472no—
498C2×D4—474no—
499C2×D4—942no—
500C2×D4—942no—
501C2×D4—9416no—
502C2×D4—9416no—
503C2×D4—942no—
504C2×D4—942no—
505C2×D4—942no—
506C2×D4—942no—
507C2×D4D4×D4712yes—
508C2×D4Q8×D4712yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4—471no—
515C22×C4—471no—
516C22×C4—471no—
517C22×C4—474no—
518C22×C4—474no—
519C22×C4—471no—
520C22×C4—471no—
521C22×C4—942no—
522C22×C4—942no—
523C22×C4—942no—
524C22×C4—942no—
525C22×C4—942no—
526C22×C4—942no—
527C22×C4—942no—
528C22×C4—944no—
529C22×C4—3764no—
530C22×C4—3764no—
531C22×C4—3761no—
532C22×C4—3761no—
533C22×C4—3761no—
534C22×C4—3761no—
535C22×C4—3761no—
536C22×C4—3761no—
537C22×C4—1888no—
538C22×C4C2×C4×D4711yescharacteristic
539C22×C4C2×C4×D4711yescharacteristic
540C22×C4C2×C4×D4711yescharacteristic
541C22×C4C2×C4×D4711yescharacteristic
542C22×C4C2×C4×D4711yescharacteristic
543C22×C4D4×D4712yes—
544C22×C4D4×D4712yes—
545C4⋊C4—22no—
546C4⋊C4—82no—
547C4⋊C4—942no—
548C4⋊C4—942no—
549C4⋊C4—941no—
550C4⋊C4—941no—
551C4⋊C4—3764no—
552C4⋊C4—3762no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—24no—
556C22⋊C4—24no—
557C22⋊C4—472no—
558C22⋊C4—472no—
559C22⋊C4—474no—
560C22⋊C4—472no—
561C22⋊C4—472no—
562C22⋊C4—474no—
563C22⋊C4—942no—
564C22⋊C4—942no—
565C22⋊C4—942no—
566C22⋊C4—942no—
567C22⋊C4—942no—
568C22⋊C4—941no—
569C22⋊C4—941no—
570C22⋊C4—944no—
571C22⋊C4—944no—
572C22⋊C4—1888no—
573C42—21no—
574C42—21no—
575C42—942no—
576C42—942no—
577C42—942no—
578C23—21no—
579C23—21no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—472no—
585C23—472no—
586C23—472no—
587C23—472no—
588C23—472no—
589C23—472no—
590C23—478no—
591C23—478no—
592C23—472no—
593C23—948no—
594C23—941no—
595C23—941no—
596C23—3762no—
597C23—3762no—
598C23—3764no—
599C23—3764no—
600C23—3762no—
601C23—3762no—
602C23—3764no—
603C23—1884no—
604C23—1881no—
605C23—1884no—
606C23—1881no—
607C23—1881no—
608C23—1881no—
609C23—1881no—
610C23—1881no—
611C23C4⋊C4×D4712yes—
612C23C22×C4×D4711yescharacteristic
613C23C2×D4×D4712yes—
614C23C2×D4×D4711yescharacteristic
615C23C2×Q8×D4711yescharacteristic
616C23#41×D4712yes—
617D4—24no—
618D4—24no—
619D4—948no—
620D4—948no—
621D4—944no—
622D4—944no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—44no—
634C2×C4—44no—
635C2×C4—44no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—472no—
639C2×C4—472no—
640C2×C4—472no—
641C2×C4—948no—
642C2×C4—941no—
643C2×C4—941no—
644C2×C4—941no—
645C2×C4—941no—
646C2×C4—3762no—
647C2×C4—3762no—
648C2×C4—3762no—
649C2×C4—3762no—
650C2×C4—37616no—
651C2×C4—3762no—
652C2×C4—1884no—
653C2×C4—1881no—
654C2×C4—1881no—
655C2×C4—1884no—
656C2×C4—1884no—
657C2×C4—1884no—
658C2×C4—1881no—
659C2×C4—1881no—
660C2×C4C22⋊C4×D4711yescharacteristic
661C2×C4C22⋊C4×D4711yescharacteristic
662C2×C4C22⋊C4×D4712yes—
663C2×C4C4⋊C4×D4712yes—
664C22—22no—
665C22—21no—
666C22—22no—
667C22—21no—
668C22—22no—
669C22—41no—
670C22—41no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—41no—
675C22—41no—
676C22—474no—
677C22—474no—
678C22—942no—
679C22—942no—
680C22—942no—
681C22—942no—
682C22—942no—
683C22—3768no—
684C22—1888no—
685C22—1882no—
686C22—1882no—
687C22—1882no—
688C22—1882no—
689C22—1888no—
690C22—1882no—
691C22—1882no—
692C22—1881no—
693C22—1881no—
694C22C2×C22⋊C4×D4711yescharacteristic
695C22C2×C4⋊C4×D4711yescharacteristic
696C22#117×D4711yescharacteristic
697C22#121×D4712yes—
698C22C22⋊Q8×D4712yes—
699C4—21no—
700C4—21no—
701C4—22no—
702C4—22no—
703C4—41no—
704C4—41no—
705C4—84no—
706C4—942no—
707C4—942no—
708C4—942no—
709C4—3764no—
710C4—1881no—
711C4—1881no—
712C2—22no—
713C2—21no—
714C2—21no—
715C2—22no—
716C2—42no—
717C2—944no—
718C2—944no—
719C2—1882no—
720C2#380×D4711yescharacteristic
721C2#2025184611yescharacteristic
722C2#2025184711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#1799C2
socleC22×C47C22×C22⋊C4
prime radicalC22×D4×D47C22
cosocleC24×C47C24
hypercenter#1799D47
hypocenterC47#20633
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #20246001C2semidirect
4. #20243376C2semidirect
5. #20243375C2semidirect
6. #20243374C2semidirect
7. #20243373C2semidirect
8. #342×D47C2semidirect
9. C47×#1799C2semidirect
13. C2×C4×D188C4semidirect
15. C2×#13093986C4semidirect
16. C2×C4×C22⋊D47C4semidirect
18. C2×(C22⋊D47)⋊C4C4semidirect
20. C2×#13093982C4semidirect
21. C2×#13093981C4semidirect
22. C22×(C2×D47)⋊C4C4semidirect
24. C2×C22⋊C4×D47C4semidirect
32. #15688983C22semidirect
33. #15688981C22semidirect
34. #15688890C22semidirect
35. #15688889C22semidirect
38. C47×#380C22semidirect
39. C47×#342C22semidirect
49. C23×Dic47C2×C4semidirect
55. C22×C4×D47C2×C4semidirect
56. C22×C4×D47C2×C4semidirect
71. C2×C4⋊Dic47C2×C4semidirect
73. C2×Dic47⋊C4C2×C4semidirect
74. C2×Dic47⋊C4C2×C4semidirect
75. C2×C22⋊Dic47C2×C4semidirect
87. C2×(C2×D47)⋊C4C2×C4semidirect
88. C2×(C2×D47)⋊C4C2×C4semidirect
95. C2×C4×Dic47C2×C4semidirect
96. C2×C4×Dic47C2×C4semidirect
97. C2×C4×Dic47C2×C4semidirect
103. C23×C4×C47C2×C4semidirect
108. C2×C4⋊C4×C47C2×C4semidirect
109. C2×C22⋊C4×C47C2×C4semidirect
112. C2×C42×C47C2×C4semidirect
123. C23×D47C4⋊C4semidirect
151. C2×C22⋊D47C4⋊C4semidirect
168. C2×D188C4⋊C4semidirect
182. C2×C4×D47C4⋊C4semidirect
358. #1799D47semidirect
397. #380C2×D47semidirect
400. #342C2×D47semidirect
401. C47#20633semidirect
420. C23×C4C4×D47semidirect
443. C2×C4⋊C4C4×D47semidirect
464. C2×C22⋊C4C4×D47semidirect
470. C2×C42C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156895952
C2×#99×D472
#202460012
#202433762
#202433752
#202433742
#202433732
#342×D472
C47×#17992
#2063347