Finite Group Databasebeta

← C4×#15689095 #26213927

Subgroups — C4×#15689095 #26213927

Order 12032.

1666 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625352C211yesmaximal, characteristic
2C2×#15689095C212yesmaximal
3C4×#13093980C212yesmaximal, complemented
4#99×Dic47C212yesmaximal, complemented
5C4×#13093938C212yesmaximal, complemented
6C4×#13093939C211yesmaximal, characteristic, complemented
7#20243175C212yesmaximal, complemented
8#20243119C212yesmaximal, complemented
9C4×#99×C47C211yesmaximal, characteristic, complemented
10C22×#10625352C2211yescharacteristic
11C4×#10625352—22no—
12C4×#10625352—22no—
13C4×#10625352—22no—
14C4×#10625352—22no—
15C2×C4×Dic94C411yescharacteristic, complemented
16C2×#13093989C411yescharacteristic, complemented
17C2×D4×Dic47C2211yescharacteristic
18C2×C4×C22⋊D47C411yescharacteristic, complemented
19C2×C4×C22⋊D47C2211yescharacteristic
20C2×(C22⋊D47)⋊C4C411yescharacteristic, complemented
21C2×(C22⋊D47)⋊C4C2211yescharacteristic
22C2×#13093982C411yescharacteristic, complemented
23C2×#13093980C411yescharacteristic, complemented
24C2×#13093980C2214yes—
25C2×#13093980C2211yescharacteristic
26C22×C4×Dic47C411yescharacteristic, complemented
27C22×C4×Dic47C2211yescharacteristic
28C2×C42×D47C411yescharacteristic, complemented
29#15689095C4116yesdirect product factor
30C2×#13093939C2212yes—
31C2×#13093938C2214yes—
32C4×Dic47⋊C4—22no—
33#15688974—22no—
34C22⋊C4×Dic47C2214yes—
35C4×C22⋊Dic47C2212yes—
36#15688968—22no—
37C42×Dic47—22no—
38#15688890C2212yes—
39#15688889C2214yes—
40C2×C4×D4×C47C2211yescharacteristic
41C2×#99×C47C2212yes—
42C4×C22⋊C4×C47C2212yes—
43C47×#342C2212yes—
44C2×#10625352—22no—
45C2×#10625352—22no—
46C2×#10625352—24no—
47C2×#10625352C2×C418yes—
48C22×Dic94C2×C411yescharacteristic
49C22×C22⋊D47C2×C411yescharacteristic
50C22×C22⋊D47C2311yescharacteristic
51C23×Dic47C2×C411yescharacteristic
52C23×Dic47C2×C411yescharacteristic
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2311yescharacteristic
55C22×C4×D47C2×C411yescharacteristic
56C22×C4×D47C2×C411yescharacteristic
57C22×C4×D47C2×C411yescharacteristic
58C4×Dic94—22no—
59C4×Dic94—22no—
60#13093989—22no—
61#13093989—22no—
62D4×Dic47—22no—
63D4×Dic47—22no—
64C4×C22⋊D47—22no—
65C4×C22⋊D47—22no—
66C4×C22⋊D47—22no—
67C4×C22⋊D47—22no—
68(C22⋊D47)⋊C4—22no—
69(C22⋊D47)⋊C4—22no—
70(C22⋊D47)⋊C4—22no—
71(C22⋊D47)⋊C4—22no—
72#13093982—22no—
73#13093982—22no—
74#13093980—22no—
75#13093980—22no—
76#13093980—28no—
77#13093980—22no—
78#13093980—22no—
79#13093980C2×C4116yescomplemented
80C2×C4⋊Dic47C2×C411yescharacteristic
81C2×Dic47⋊C4—24no—
82C2×Dic47⋊C4C2×C411yescharacteristic
83C2×Dic47⋊C4C2×C411yescharacteristic
84C2×Dic47⋊C4C2×C411yescharacteristic
85C2×Dic47⋊C4C2×C411yescharacteristic
86C2×C22⋊Dic47C2×C411yescharacteristic
87C2×C22⋊Dic47C2311yescharacteristic
88C2×C22⋊Dic47C2314yes—
89C2×(C2×D47)⋊C4C2×C411yescharacteristic
90C2×(C2×D47)⋊C4C2×C411yescharacteristic
91C2×C4×Dic47—24no—
92C2×C4×Dic47—21no—
93C2×C4×Dic47—21no—
94C2×C4×Dic47—21no—
95C2×C4×Dic47—21no—
96C2×C4×Dic47—22no—
97C2×C4×Dic47—24no—
98C2×C4×Dic47C2×C411yescharacteristic
99C2×C4×Dic47C2×C411yescharacteristic
100C2×C4×Dic47C2×C411yescharacteristic
101C2×C4×Dic47C2×C411yescharacteristic
102C2×C4×Dic47C2×C411yescharacteristic
103C2×C4×Dic47C2×C411yescharacteristic
104C2×C4×Dic47C2×C411yescharacteristic
105C2×C4×Dic47C2×C411yescharacteristic
106C2×C4×Dic47C2×C411yescharacteristic
107C2×C4×Dic47D412yes—
108C2×C4×Dic47D412yes—
109C2×C4×Dic47D412yes—
110C2×C4×Dic47D412yes—
111C42×D47—21no—
112C42×D47—21no—
113C42×D47—21no—
114C42×D47—21no—
115#13093939C2×C418yescomplemented
116#13093938C2×C4116yescomplemented
117C47⋊#95—22no—
118C47⋊#95—24no—
119C22×D4×C47C2311yescharacteristic
120C23×C4×C47C2×C411yescharacteristic
121C23×C4×C47C2311yescharacteristic
122C4×D4×C47—22no—
123C4×D4×C47—22no—
124C2×C4⋊C4×C47C2×C411yescharacteristic
125C2×C22⋊C4×C47C2×C411yescharacteristic
126C2×C22⋊C4×C47C2311yescharacteristic
127C2×C22⋊C4×C47C2314yes—
128C2×C42×C47—22no—
129C2×C42×C47C2×C411yescharacteristic
130#99×C47C2×C418yescomplemented
131#95×C47—22no—
132C24×C47C22×C411yescharacteristic
133C24×C47C2411yescharacteristic
134C23×D47C22×C411yescharacteristic
135C2×D4×C47—22no—
136C2×D4×C47—22no—
137C2×D4×C47C22×C414yes—
138C22×C4×C47—24no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—42no—
142C22×C4×C47—42no—
143C22×C4×C47C22×C411yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C22×C411yescharacteristic
146C22×C4×C47C22×C411yescharacteristic
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C2×D412yes—
149C22×C4×C47C2×D412yes—
150C2×C22⋊D47—22no—
151C2×C22⋊D47—22no—
152C2×C22⋊D47—22no—
153C2×C22⋊D47—22no—
154C2×C22⋊D47C4214yescomplemented
155C2×C22⋊D47C22×C414yes—
156C22×Dic47—21no—
157C22×Dic47—21no—
158C22×Dic47—22no—
159C22×Dic47—24no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—42no—
163C22×Dic47—42no—
164C22×Dic47C4214yescomplemented
165C22×Dic47C22×C411yescharacteristic
166C22×Dic47C22×C411yescharacteristic
167C22×Dic47C22×C411yescharacteristic
168C22×Dic47C22×C411yescharacteristic
169C22×Dic47C22×C411yescharacteristic
170C22×Dic47C22×C411yescharacteristic
171C22×Dic47C22×C411yescharacteristic
172C22×Dic47C22×C414yes—
173C22×Dic47C2×D412yes—
174C22×Dic47C2×D412yes—
175C22×Dic47C2×D412yes—
176C22×Dic47C2×D412yes—
177C22×Dic47#4114yes—
178#10625352—216no—
179#10625352—216no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—22no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—21no—
187C2×C4×D47—42no—
188C2×C4×D47—42no—
189C2×C4×D47C4214yescomplemented
190C2×Dic94—22no—
191C2×Dic94—22no—
192C2×Dic94C4214yescomplemented
193C4⋊C4×C47—22no—
194C22⋊C4×C47—22no—
195C22⋊C4×C47—24no—
196C22⋊C4×C47—22no—
197C22⋊C4×C47C22×C418yes—
198C42×C47—21no—
199C42×C47—21no—
200C42×C47—44no—
201C22⋊Dic47—22no—
202C22⋊Dic47—24no—
203C22⋊Dic47—22no—
204C22⋊Dic47C22×C418yes—
205(C2×D47)⋊C4—22no—
206(C2×D47)⋊C4—22no—
207C4⋊Dic47—22no—
208Dic47⋊C4—22no—
209Dic47⋊C4—22no—
210Dic47⋊C4—22no—
211Dic47⋊C4—22no—
212Dic47⋊C4—216no—
213C4×Dic47—21no—
214C4×Dic47—21no—
215C4×Dic47—21no—
216C4×Dic47—21no—
217C4×Dic47—21no—
218C4×Dic47—21no—
219C4×Dic47—21no—
220C4×Dic47—21no—
221C4×Dic47—21no—
222C4×Dic47—21no—
223C4×Dic47—216no—
224C4×Dic47—48no—
225C4×Dic47—44no—
226C4×Dic47C22⋊C411yescharacteristic
227C4×Dic47C22⋊C411yescharacteristic
228C4×Dic47C22⋊C411yescharacteristic
229C4×Dic47C22⋊C411yescharacteristic
230C4×Dic47C22⋊C412yes—
231C4×Dic47C22⋊C412yes—
232C4×Dic47C22⋊C412yes—
233C4×Dic47C22⋊C412yes—
234C4×Dic47C22⋊C412yes—
235C4×Dic47C22⋊C412yes—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47C2×C4212yes—
243C23×C47C23×C411yescharacteristic
244C23×C47C23×C412yes—
245C23×C47C22×D412yes—
246C23×C47C2×#4112yes—
247C22×D47—21no—
248C22×D47—21no—
249C22×D47—41no—
250C22×D47—41no—
251C22×D47C2×C4212yes—
252D4×C47—28no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—24no—
256C2×C4×C47—22no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—28no—
260C2×C4×C47—41no—
261C2×C4×C47—42no—
262C2×C4×C47—42no—
263C2×C4×C47—44no—
264C2×C4×C47—44no—
265C2×C4×C47—42no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47C2×C4212yes—
269C2×C4×C47C2×C22⋊C411yescharacteristic
270C2×C4×C47C2×C22⋊C412yes—
271C2×C4×C47C2×C22⋊C411yescharacteristic
272C22⋊D47—28no—
273C22⋊D47—28no—
274C2×Dic47—21no—
275C2×Dic47—21no—
276C2×Dic47—24no—
277C2×Dic47—24no—
278C2×Dic47—24no—
279C2×Dic47—22no—
280C2×Dic47—21no—
281C2×Dic47—21no—
282C2×Dic47—28no—
283C2×Dic47—41no—
284C2×Dic47—42no—
285C2×Dic47—42no—
286C2×Dic47—44no—
287C2×Dic47—44no—
288C2×Dic47—42no—
289C2×Dic47—41no—
290C2×Dic47—41no—
291C2×Dic47C2×C4212yes—
292C2×Dic47C2×C4212yes—
293C2×Dic47C2×C4212yes—
294C2×Dic47C2×C22⋊C411yescharacteristic
295C2×Dic47C2×C22⋊C412yes—
296C2×Dic47C2×C22⋊C411yescharacteristic
297C2×Dic47C2×C22⋊C411yescharacteristic
298C2×Dic47C2×C22⋊C412yes—
299C2×Dic47C2×C22⋊C411yescharacteristic
300C2×Dic47#11712yes—
301C2×Dic47#11712yes—
302C2×Dic47C4×D418yes—
303C2×Dic47C4×D418yes—
304C4×D47—24no—
305C4×D47—24no—
306C4×D47—42no—
307C4×D47—42no—
308C4×D47—42no—
309C4×D47—42no—
310Dic94—28no—
311C4×#410—471nomaximal, Sylow
312C22×C47—22no—
313C22×C47—21no—
314C22×C47—22no—
315C22×C47—21no—
316C22×C47—22no—
317C22×C47—42no—
318C22×C47—42no—
319C22×C47—42no—
320C22×C47—42no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47C22×C4211yescharacteristic
324C22×C47C22×C22⋊C411yescharacteristic
325C22×C47C2×#11711yescharacteristic
326C22×C47C2×C4×D414yes—
327C2×D47—22no—
328C2×D47—42no—
329C2×D47—41no—
330C2×D47—41no—
331C2×D47—42no—
332C4×C47—21no—
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—48no—
336C4×C47—41no—
337C4×C47—41no—
338C4×C47#41012yescomplemented
339Dic47—21no—
340Dic47—22no—
341Dic47—22no—
342Dic47—48no—
343Dic47—41no—
344Dic47—41no—
345Dic47C4×C22⋊C414yes—
346Dic47C4×C22⋊C412yes—
347Dic47C4×C22⋊C412yes—
348Dic47#41012yescomplemented
349C2×C4×#41—471no—
350C2×#410—472no—
351C4×#117—472no—
352C4×#99—472no—
353C4×#99—472no—
354C4×#99—472no—
355C4×#99—471no—
356C4×#99D4711yescharacteristic, complemented
357#1740—472no—
358C2×C47—24no—
359C2×C47—21no—
360C2×C47—21no—
361C2×C47—42no—
362C2×C47C2×C4×C22⋊C411yescharacteristic
363C2×C47C2×#41011yescharacteristic
364C2×C47C2×#41011yescharacteristic
365D47—42no—
366C22×#41—471no—
367C4×#41—942no—
368C4×#41—942no—
369C4×#41—942no—
370C4×#41—942no—
371C2×C4×Q8—471no—
372C2×C4×Q8—471no—
373C2×C4×D4—471no—
374C2×C4×D4—471no—
375C2×C4×D4—471no—
376C2×C4×D4—471no—
377C2×C4×D4—471no—
378C2×C4×D4C2×D4711yescharacteristic
379C2×#117—471no—
380C2×#117—471no—
381C2×#117—471no—
382C2×#117—474no—
383C22×C42—471no—
384C22×C42—471no—
385C22×C42—471no—
386#410—4716no—
387C2×#99—472no—
388C2×#99—474no—
389C2×#99C2×D4712yes—
390C4×C4⋊C4—942no—
391C4×C4⋊C4—942no—
392C4×C22⋊C4—472no—
393C4×C22⋊C4—474no—
394C4×C22⋊C4C2×D4712yes—
395#376—942no—
396C43—942no—
397#342—474no—
398#342—472no—
399#342C2×D4712yes—
400C47C4×#41011yescharacteristic, complemented, Sylow
401C2×#41—478no—
402C2×#41—942no—
403C2×#41—942no—
404C2×#41—944no—
405C22×Q8—471no—
406C22×D4—471no—
407C22×D4—471no—
408C22×D4C22×D4711yescharacteristic
409C23×C4—471no—
410C23×C4—471no—
411C23×C4—471no—
412C23×C4—471no—
413C23×C4—471no—
414C23×C4—471no—
415C23×C4—471no—
416C23×C4C4×D4711yescharacteristic
417C23×C4C22×D4711yescharacteristic
418C4×Q8—942no—
419C4×Q8—942no—
420C4×Q8—942no—
421C4×Q8—942no—
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—942no—
425C4×D4—942no—
426C4×D4—942no—
427C4×D4—942no—
428C4×D4—942no—
429C4×D4—942no—
430C4×D4—942no—
431C4×D4—942no—
432C4×D4—942no—
433C4×D4—942no—
434#117—4716no—
435#117—942no—
436#117—942no—
437#117—942no—
438#117—942no—
439#117—942no—
440#117—942no—
441#117—948no—
442C2×C4⋊C4—471no—
443C2×C4⋊C4—471no—
444C2×C4⋊C4—471no—
445C2×C4⋊C4—471no—
446C2×C4⋊C4—471no—
447C2×C4⋊C4—944no—
448C2×C4⋊C4C4×D4711yescharacteristic
449C2×C22⋊C4—474no—
450C2×C22⋊C4—471no—
451C2×C22⋊C4—471no—
452C2×C22⋊C4—471no—
453C2×C22⋊C4—471no—
454C2×C22⋊C4C4×D4711yescharacteristic
455C2×C22⋊C4C22×D4711yescharacteristic
456C2×C22⋊C4C22×D4714yes—
457C2×C42—22no—
458C2×C42—471no—
459C2×C42—471no—
460C2×C42—471no—
461C2×C42—471no—
462C2×C42—472no—
463C2×C42—472no—
464C2×C42—472no—
465C2×C42—472no—
466C2×C42—471no—
467C2×C42—471no—
468C2×C42—471no—
469C2×C42—471no—
470C2×C42—471no—
471C2×C42—941no—
472C2×C42—941no—
473C2×C42—941no—
474C2×C42—941no—
475C2×C42—941no—
476C2×C42—941no—
477C2×C42—941no—
478C2×C42—941no—
479C2×C42—944no—
480C2×C42—944no—
481C2×C42—942no—
482C2×C42C4×D4711yescharacteristic
483#99—478no—
484#99—4716no—
485#99C4×D4718yescomplemented
486#95—22no—
487#95—944no—
488#95—942no—
489C24—471no—
490C24C2×C4×D4711yescharacteristic
491C24C23×D4711yescharacteristic
492#41—9416no—
493#41—9416no—
494C2×Q8—474no—
495C2×Q8—942no—
496C2×Q8—942no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—474no—
500C2×D4—474no—
501C2×D4—942no—
502C2×D4—942no—
503C2×D4—942no—
504C2×D4—942no—
505C2×D4C2×C4×D4714yes—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—471no—
512C22×C4—471no—
513C22×C4—474no—
514C22×C4—472no—
515C22×C4—472no—
516C22×C4—474no—
517C22×C4—474no—
518C22×C4—471no—
519C22×C4—471no—
520C22×C4—472no—
521C22×C4—471no—
522C22×C4—472no—
523C22×C4—474no—
524C22×C4—471no—
525C22×C4—471no—
526C22×C4—941no—
527C22×C4—941no—
528C22×C4—942no—
529C22×C4—941no—
530C22×C4—941no—
531C22×C4—941no—
532C22×C4—941no—
533C22×C4—942no—
534C22×C4—941no—
535C22×C4—941no—
536C22×C4—944no—
537C22×C4—941no—
538C22×C4—941no—
539C22×C4—1882no—
540C22×C4—1882no—
541C22×C4—1882no—
542C22×C4—1882no—
543C22×C4C2×C4×D4711yescharacteristic
544C22×C4C2×C4×D4711yescharacteristic
545C22×C4C2×C4×D4711yescharacteristic
546C22×C4C2×C4×D4711yescharacteristic
547C22×C4C2×C4×D4711yescharacteristic
548C22×C4D4×D4712yes—
549C22×C4D4×D4712yes—
550C4⋊C4—22no—
551C4⋊C4—942no—
552C4⋊C4—942no—
553C4⋊C4—942no—
554C4⋊C4—9416no—
555C4⋊C4—942no—
556C4⋊C4—942no—
557C22⋊C4—22no—
558C22⋊C4—24no—
559C22⋊C4—22no—
560C22⋊C4—478no—
561C22⋊C4—942no—
562C22⋊C4—942no—
563C22⋊C4—942no—
564C22⋊C4—944no—
565C22⋊C4—942no—
566C22⋊C4C2×C4×D4718yes—
567C42—21no—
568C42—21no—
569C42—44no—
570C42—471no—
571C42—471no—
572C42—472no—
573C42—472no—
574C42—472no—
575C42—472no—
576C42—472no—
577C42—471no—
578C42—471no—
579C42—472no—
580C42—941no—
581C42—941no—
582C42—941no—
583C42—941no—
584C42—941no—
585C42—941no—
586C42—941no—
587C42—941no—
588C42—9416no—
589C42—941no—
590C42—941no—
591C42—1884no—
592C42—1888no—
593C23—21no—
594C23—21no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—472no—
600C23—941no—
601C23—941no—
602C23—1881no—
603C23—1881no—
604C23C42×D4712yes—
605C23C22×C4×D4711yescharacteristic
606C23C22×C4×D4712yes—
607C23C2×D4×D4712yes—
608C23#41×D4712yes—
609Q8—948no—
610D4—28no—
611D4—948no—
612D4—948no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—28no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—472no—
629C2×C4—472no—
630C2×C4—471no—
631C2×C4—471no—
632C2×C4—471no—
633C2×C4—472no—
634C2×C4—472no—
635C2×C4—472no—
636C2×C4—478no—
637C2×C4—478no—
638C2×C4—472no—
639C2×C4—471no—
640C2×C4—472no—
641C2×C4—944no—
642C2×C4—944no—
643C2×C4—944no—
644C2×C4—944no—
645C2×C4—944no—
646C2×C4—942no—
647C2×C4—941no—
648C2×C4—941no—
649C2×C4—941no—
650C2×C4—941no—
651C2×C4—948no—
652C2×C4—1882no—
653C2×C4—1882no—
654C2×C4—1882no—
655C2×C4—1882no—
656C2×C4—1882no—
657C2×C4—1881no—
658C2×C4—1882no—
659C2×C4—1884no—
660C2×C4—1884no—
661C2×C4—1882no—
662C2×C4—1881no—
663C2×C4—1881no—
664C2×C4C42×D4712yes—
665C2×C4C22⋊C4×D4711yescharacteristic
666C2×C4C22⋊C4×D4712yes—
667C2×C4C22⋊C4×D4711yescharacteristic
668C22—22no—
669C22—21no—
670C22—22no—
671C22—21no—
672C22—22no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—41no—
678C22—41no—
679C22—942no—
680C22—1882no—
681C22—1882no—
682C22—1881no—
683C22—1881no—
684C22C2×C42×D4711yescharacteristic
685C22C2×C22⋊C4×D4711yescharacteristic
686C22#117×D4711yescharacteristic
687C22C4×D4×D4714yes—
688C4—21no—
689C4—22no—
690C4—22no—
691C4—48no—
692C4—41no—
693C4—41no—
694C4—472no—
695C4—472no—
696C4—472no—
697C4—474no—
698C4—941no—
699C4—942no—
700C4—942no—
701C4—1888no—
702C4—1881no—
703C4—1881no—
704C4#1568909512yesdirect product factor
705C2—24no—
706C2—21no—
707C2—21no—
708C2—42no—
709C2—1882no—
710C2C4×C22⋊C4×D4711yescharacteristic
711C2#410×D4711yescharacteristic
712C2C2×#1568909511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC4×#99×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC22×#10625352C22
cosocleC24×C47C24
hypercenterC4×#99D47
hypocenterC47C4×#410
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. C4×#13093980C2semidirect
4. #99×Dic47C2semidirect
5. C4×#13093938C2semidirect
6. C4×#13093939C2semidirect
7. #20243175C2semidirect
8. #20243119C2semidirect
9. C4×#99×C47C2semidirect
15. C2×C4×Dic94C4semidirect
16. C2×#13093989C4semidirect
18. C2×C4×C22⋊D47C4semidirect
20. C2×(C22⋊D47)⋊C4C4semidirect
22. C2×#13093982C4semidirect
23. C2×#13093980C4semidirect
26. C22×C4×Dic47C4semidirect
28. C2×C42×D47C4semidirect
29. #15689095C4direct (N × H)
79. #13093980C2×C4semidirect
115. #13093939C2×C4semidirect
116. #13093938C2×C4semidirect
130. #99×C47C2×C4semidirect
154. C2×C22⋊D47C42semidirect
164. C22×Dic47C42semidirect
189. C2×C4×D47C42semidirect
192. C2×Dic94C42semidirect
338. C4×C47#410semidirect
348. Dic47#410semidirect
356. C4×#99D47semidirect
400. C47C4×#410semidirect
485. #99C4×D47semidirect
704. C4#15689095direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#106253522
C2×#156890952
C4×#130939802
#99×Dic472
C4×#130939382
C4×#130939392
#202431752
#202431192
C4×#99×C472
C4×#41047