Finite Group Databasebeta

← C2×#20256347 #27096820

Subgroups — C2×#20256347 #27096820

Order 12032.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689832C211yesmaximal, characteristic, complemented
2C2×#15689830C211yesmaximal, characteristic, complemented
3#20256347C2116yesmaximal, direct product factor
4C2×#15689532C211yesmaximal, characteristic, complemented
5C2×#15689530C211yesmaximal, characteristic, complemented
6C2×#15689523C211yesmaximal, characteristic, complemented
7C2×#15689425C211yesmaximal, characteristic, complemented
8C2×#15689425C211yesmaximal, characteristic, complemented
9C2×#15689423C211yesmaximal, characteristic, complemented
10C2×#15689421C211yesmaximal, characteristic, complemented
11C2×#15689403C211yesmaximal, characteristic, complemented
12C2×#15689401C211yesmaximal, characteristic, complemented
13C2×#15689251C211yesmaximal, characteristic, complemented
14C2×#15689235C211yesmaximal, characteristic
15C2×D8×Dic47C211yesmaximal, characteristic
16C2×C47×#442C211yesmaximal, characteristic
17#15689832—24no—
18#15689832C2218yescomplemented
19#15689830—24no—
20#15689830C2218yescomplemented
21C2×#13094024C2211yescharacteristic
22C2×#13094023C2211yescharacteristic
23C2×#13094016C2211yescharacteristic
24C2×#13094015C2211yescharacteristic
25C2×#13094015C2211yescharacteristic
26C2×#13094015C2211yescharacteristic
27C2×#13094003—21no—
28C2×#13094003—21no—
29C2×#13094001—21no—
30C2×#13094001—21no—
31C2×#13094001—21no—
32C2×#13094001—21no—
33C2×C4×Dic94C2211yescharacteristic
34C2×D4×Dic47C2211yescharacteristic
35C2×D4×Dic47C2211yescharacteristic
36C2×D4×Dic47C2211yescharacteristic
37C2×D4×Dic47C2211yescharacteristic
38C22×C4⋊Dic47—21no—
39C22×Dic47⋊C4—21no—
40#15689532C2218yescomplemented
41#15689530C2218yescomplemented
42#15689523C2218yescomplemented
43#15689425C2218yescomplemented
44#15689425C2218yescomplemented
45#15689423C2218yescomplemented
46#15689421C2218yescomplemented
47#15689403C2218yescomplemented
48#15689401C2218yescomplemented
49#15689251C2218yescomplemented
50#15689235C2218yes—
51D8×Dic47C2218yes—
52C2×#13093958C2211yescharacteristic
53C2×#13093958C2211yescharacteristic
54C2×#13093957C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×#13093955C2211yescharacteristic
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093945C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×D8×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#442C2218yes—
73C2×#106×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×Dic94D411yescharacteristic
80C23×Dic47—21no—
81C23×Dic47—21no—
82C23×Dic47—21no—
83C23×Dic47—21no—
84C22×C47⋊C8C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86#13094024—22no—
87#13094024C2314yes—
88#13094023—22no—
89#13094023C2314yes—
90#13094016—22no—
91#13094016C2314yes—
92#13094015—22no—
93#13094015—22no—
94#13094015—22no—
95#13094015C2314yes—
96#13094015C2314yes—
97#13094015C2314yes—
98#13094003—28no—
99#13094003—28no—
100#13094001—28no—
101#13094001—28no—
102#13094001—28no—
103#13094001—28no—
104C4×Dic94D414yes—
105C4×Dic94C2314yes—
106D4×Dic47—22no—
107D4×Dic47—22no—
108D4×Dic47—22no—
109D4×Dic47—22no—
110D4×Dic47C2314yes—
111D4×Dic47C2314yes—
112D4×Dic47C2314yes—
113D4×Dic47C2314yes—
114C2×C4⋊Dic47—21no—
115C2×C4⋊Dic47—21no—
116C2×C4⋊Dic47—21no—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47—28no—
119C2×C4⋊Dic47D411yescharacteristic
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2311yescharacteristic
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—28no—
131C2×Dic47⋊C4D411yescharacteristic
132C2×Dic47⋊C4D411yescharacteristic
133C2×C22⋊Dic47—21no—
134C2×C22⋊Dic47—21no—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×C4×Dic47C2311yescharacteristic
138C2×C4×Dic47C2311yescharacteristic
139#13093958C2314yes—
140#13093958C2314yes—
141#13093957C2314yes—
142#13093957C2314yes—
143#13093957C2314yes—
144#13093956C2314yes—
145#13093956C2314yes—
146#13093955C2314yes—
147C4⋊(C47⋊C8)C2314yes—
148Dic47⋊C8C2314yes—
149Dic47⋊C8C2314yes—
150#13093945C2314yes—
151#13093945C2314yes—
152#13093945C2314yes—
153#13093945C2314yes—
154#13093934C2314yes—
155C8×Dic47C2314yes—
156C22×D4×C47C2311yescharacteristic
157C22×D4×C47C2311yescharacteristic
158C23×C4×C47—21no—
159C23×C4×C47—21no—
160C2×D8×C47Q818yescomplemented
161C2×D8×C47C2314yes—
162C22×C8×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164C4×D4×C47—22no—
165C4×D4×C47—22no—
166C4×D4×C47C2314yes—
167C4×D4×C47C2314yes—
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C22⋊C4×C47—21no—
171C2×C22⋊C4×C47—21no—
172C2×C42×C47C2311yescharacteristic
173#106×C47C2314yes—
174#102×C47C2314yes—
175#102×C47C2314yes—
176#97×C47C2314yes—
177C24×C47—21no—
178C24×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—22no—
182C2×D4×C47—22no—
183C2×D4×C47C2×Q814yes—
184C2×D4×C47C2×Q814yes—
185C2×D4×C47C2412yes—
186C2×D4×C47C2412yes—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—24no—
190C22×C4×C47—24no—
191C22×C4×C47—44no—
192C22×C4×C47—82no—
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—24no—
201C22×Dic47—24no—
202C22×Dic47—24no—
203C22×Dic47—24no—
204C22×Dic47—44no—
205C22×Dic47—82no—
206C22×Dic47—82no—
207C22×Dic47—82no—
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C2×Dic94—24no—
213C2×Dic94—24no—
214C2×Dic94—42no—
215C2×Dic94—82no—
216C2×Dic94—82no—
217C2×Dic94C2×D414yes—
218D8×C47C2×Q8116yescomplemented
219C2×C8×C47—22no—
220C2×C8×C47C2×Q814yes—
221C2×C8×C47C2412yes—
222C2×C8×C47C2412yes—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47C2412yes—
226C4⋊C4×C47C2412yes—
227C22⋊C4×C47—24no—
228C22⋊C4×C47—24no—
229C42×C47C2×D412yes—
230C42×C47C2412yes—
231C22⋊Dic47—24no—
232C22⋊Dic47—24no—
233C22⋊Dic47—24no—
234C22⋊Dic47—24no—
235C4⋊Dic47—24no—
236C4⋊Dic47—21no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47—24no—
241C4⋊Dic47—24no—
242C4⋊Dic47—24no—
243C4⋊Dic47C2×D414yes—
244C4⋊Dic47C2412yes—
245C4⋊Dic47C2412yes—
246C4⋊Dic47C2412yes—
247C4⋊Dic47C2412yes—
248Dic47⋊C4—24no—
249Dic47⋊C4—24no—
250Dic47⋊C4—24no—
251Dic47⋊C4—24no—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4C2×D414yes—
255Dic47⋊C4C2×D414yes—
256C4×Dic47C2×D412yes—
257C4×Dic47C2×D412yes—
258C4×Dic47C2412yes—
259C4×Dic47C2412yes—
260C2×C47⋊C8—22no—
261C2×C47⋊C8—22no—
262C2×C47⋊C8C2412yes—
263C2×C47⋊C8C2412yes—
264C23×C47—24no—
265C23×C47—24no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—42no—
269C23×C47—42no—
270C23×C47—42no—
271C23×C47—42no—
272C23×C47C22×D411yescharacteristic
273D4×C47—24no—
274D4×C47—24no—
275D4×C47—22no—
276D4×C47—22no—
277D4×C47C22×Q814yes—
278D4×C47C22×Q814yes—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—48no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—84no—
287C2×C4×C47C22×D412yes—
288C2×C4×C47C22×D412yes—
289C2×C4×C47C22×D411yescharacteristic
290C2×C4×C47C22×Q812yes—
291C2×C4×C472−1+412yes—
292C2×C4×C47C2511yescharacteristic
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—48no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306C2×Dic47—84no—
307C2×Dic47—84no—
308C2×Dic47—84no—
309C2×Dic47C22×D412yes—
310C2×Dic47C22×D412yes—
311C2×Dic47C22×D412yes—
312C2×Dic47C22×D412yes—
313Dic94—44no—
314Dic94—84no—
315Dic94—84no—
316C8×C47—22no—
317C8×C47C22×Q814yes—
318C47⋊C8—22no—
319C47⋊C8—22no—
320C2×#3389—471nomaximal, Sylow
321C22×C47—24no—
322C22×C47—24no—
323C22×C47—48no—
324C22×C47—48no—
325C22×C47—42no—
326C22×C47—42no—
327C22×C47—42no—
328C22×C47—42no—
329C22×C47D4×Q812yes—
330C22×C47#57512yes—
331C22×C47#57612yes—
332C22×C47C23×D411yescharacteristic
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—42no—
336C4×C47—42no—
337C4×C47D4×Q812yes—
338C4×C47C23×Q811yescharacteristic
339C4×C47C2×2−1+411yescharacteristic
340Dic47—22no—
341Dic47—22no—
342Dic47—22no—
343Dic47—22no—
344Dic47—42no—
345Dic47—42no—
346Dic47—42no—
347Dic47—42no—
348C2×#554—471no—
349C2×#554—471no—
350#3389—4716no—
351C2×#501—471no—
352C2×#501—471no—
353C2×#499—471no—
354C2×#478—471no—
355C2×#478—471no—
356C2×#478—471no—
357C2×#478—471no—
358C2×#474—471no—
359C2×#474—471no—
360C2×#446—471no—
361C2×#442—471no—
362C2×#442D4711yescharacteristic
363C2×C4×D8—471no—
364C2×C47—44no—
365C2×C47—44no—
366C2×C47#338914yescomplemented
367C2×C47C2×D4×Q811yescharacteristic
368C2×C47C2×#57511yescharacteristic
369C2×C47C2×#57611yescharacteristic
370C22×D8C2×D4711yescharacteristic
371#554—478no—
372#554—478no—
373#554—944no—
374#554—944no—
375C2×C4⋊Q8—471no—
376C2×C4⋊Q8—471no—
377C2×#125—471no—
378C2×#125—471no—
379C2×#125—471no—
380C2×#125—471no—
381C2×C22⋊Q8—941no—
382C2×C22⋊Q8—941no—
383C2×C22⋊Q8—941no—
384C2×C22⋊Q8—941no—
385C2×C22⋊Q8—941no—
386C2×C22⋊Q8—941no—
387C2×C4×Q8—471no—
388C2×C4×D4—471no—
389C2×C4×D4—471no—
390C2×C4×D4—471no—
391C2×C4×D4—471no—
392C2×C4×D4C2×D4711yescharacteristic
393C2×C4×D4C2×D4711yescharacteristic
394C22×C4⋊C4—941no—
395C22×C4⋊C4—941no—
396#501—478no—
397#501—478no—
398#499—478no—
399#478—478no—
400#478—478no—
401#478—478no—
402#478—478no—
403#474—478no—
404#474—478no—
405#446—478no—
406#442—478no—
407#442C2×D4718yes—
408C4×D8—478no—
409C2×#107—471no—
410C2×#107—471no—
411C2×#107—471no—
412C2×#107—471no—
413C2×#107—471no—
414C2×#106—471no—
415C2×#106—471no—
416C2×#106—471no—
417C2×#106C2×D4711yescharacteristic
418C2×C4⋊C8—471no—
419C2×C4⋊C8—471no—
420C2×C4⋊C8—471no—
421C2×#102—471no—
422C2×#102—471no—
423C2×#102—471no—
424C2×#102—471no—
425C2×#102C2×D4711yescharacteristic
426C2×#102C2×D4711yescharacteristic
427C2×#97—471no—
428C2×#97C2×D4711yescharacteristic
429C2×C4×C8—471no—
430C47C2×#338911yescharacteristic, complemented, Sylow
431C22×Q8—471no—
432C22×Q8—941no—
433C22×Q8—941no—
434C22×D4C22×D4711yescharacteristic
435C22×D4C22×D4711yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—941no—
439C23×C4—941no—
440C23×C4—941no—
441C23×C4—941no—
442C2×D8Dic9418yescomplemented
443C2×D8C22×D4714yes—
444C22×C8—471no—
445C22×C8—471no—
446C22×C8C22×D4711yescharacteristic
447C22×C8C22×D4711yescharacteristic
448C4⋊Q8—474no—
449C4⋊Q8—474no—
450C4⋊Q8—942no—
451C4⋊Q8—942no—
452#125—474no—
453#125—474no—
454#125—474no—
455#125—474no—
456#125—942no—
457#125—942no—
458#125—942no—
459#125—942no—
460C22⋊Q8—948no—
461C22⋊Q8—948no—
462C22⋊Q8—948no—
463C22⋊Q8—948no—
464C22⋊Q8—948no—
465C22⋊Q8—948no—
466C4×Q8—474no—
467C4×Q8—474no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—474no—
471C4×D4—474no—
472C4×D4—474no—
473C4×D4—474no—
474C4×D4—942no—
475C4×D4—942no—
476C4×D4—942no—
477C4×D4—942no—
478C4×D4C22×D4714yes—
479C4×D4C22×D4714yes—
480C2×C4⋊C4—471no—
481C2×C4⋊C4—471no—
482C2×C4⋊C4—471no—
483C2×C4⋊C4—471no—
484C2×C4⋊C4—471no—
485C2×C4⋊C4—471no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—948no—
488C2×C4⋊C4—948no—
489C2×C4⋊C4—941no—
490C2×C4⋊C4—941no—
491C2×C4⋊C4—941no—
492C2×C4⋊C4—941no—
493C2×C4⋊C4—941no—
494C2×C4⋊C4—941no—
495C2×C4⋊C4—941no—
496C2×C4⋊C4—941no—
497C2×C4⋊C4—941no—
498C2×C4⋊C4—941no—
499C2×C4⋊C4C22×D4711yescharacteristic
500C2×C4⋊C4C22×D4711yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—941no—
504C2×C22⋊C4—941no—
505C2×C22⋊C4—941no—
506C2×C22⋊C4—941no—
507C2×C42—471no—
508C2×C42—471no—
509C2×C42C22×D4711yescharacteristic
510#107—474no—
511#107—474no—
512#107—474no—
513#107—474no—
514#107—474no—
515#106—474no—
516#106—474no—
517#106—474no—
518#106C22×D4714yes—
519C4⋊C8—474no—
520C4⋊C8—474no—
521C4⋊C8—474no—
522#102—474no—
523#102—474no—
524#102—474no—
525#102—474no—
526#102C22×D4714yes—
527#102C22×D4714yes—
528#97—474no—
529#97C22×D4714yes—
530C4×C8—474no—
531C24—21no—
532C24—21no—
533C2×Q8—474no—
534C2×Q8—944no—
535C2×Q8—944no—
536C2×Q8—3762no—
537C2×Q8—3762no—
538C2×Q8—1882no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4C2×Dic9414yes—
544C2×D4C2×Dic9414yes—
545C2×D4C23×D4712yes—
546C2×D4C23×D4712yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—44no—
552C22×C4—82no—
553C22×C4—471no—
554C22×C4—471no—
555C22×C4—471no—
556C22×C4—471no—
557C22×C4—944no—
558C22×C4—944no—
559C22×C4—944no—
560C22×C4—944no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—3762no—
566C22×C4—3762no—
567C22×C4—3762no—
568C22×C4—1884no—
569C22×C4D4×D4711yescharacteristic
570C22×C4D4×D4711yescharacteristic
571C22×C4C23×D4711yescharacteristic
572D8C2×Dic94116yescomplemented
573C2×C8—22no—
574C2×C8—472no—
575C2×C8—472no—
576C2×C8—942no—
577C2×C8—942no—
578C2×C8C2×Dic9414yes—
579C2×C8C23×D4712yes—
580C2×C8C23×D4712yes—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—474no—
584C4⋊C4—474no—
585C4⋊C4—474no—
586C4⋊C4—472no—
587C4⋊C4—472no—
588C4⋊C4—472no—
589C4⋊C4—472no—
590C4⋊C4—944no—
591C4⋊C4—944no—
592C4⋊C4—944no—
593C4⋊C4—944no—
594C4⋊C4—944no—
595C4⋊C4—944no—
596C4⋊C4—944no—
597C4⋊C4—944no—
598C4⋊C4—944no—
599C4⋊C4—941no—
600C4⋊C4—941no—
601C4⋊C4—941no—
602C4⋊C4—941no—
603C4⋊C4—944no—
604C4⋊C4C23×D4712yes—
605C4⋊C4C23×D4712yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—944no—
609C22⋊C4—944no—
610C22⋊C4—944no—
611C22⋊C4—944no—
612C42—472no—
613C42—472no—
614C42—472no—
615C42—472no—
616C42D4×D4712yes—
617C42C23×D4712yes—
618C23—24no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23C2×D4×D4711yescharacteristic
627Q8—3764no—
628Q8—3764no—
629Q8—1884no—
630D4—24no—
631D4—24no—
632D4—22no—
633D4—22no—
634D4C22×Dic9414yes—
635D4C22×Dic9414yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—48no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—84no—
644C2×C4—472no—
645C2×C4—472no—
646C2×C4—472no—
647C2×C4—472no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—942no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—3764no—
657C2×C4—3764no—
658C2×C4—3764no—
659C2×C4—1888no—
660C2×C4—1882no—
661C2×C4—1882no—
662C2×C4—1882no—
663C2×C4—1882no—
664C2×C4C2×D4×D4712yes—
665C2×C4C2×D4×D4712yes—
666C2×C4C2×D4×D4711yescharacteristic
667C2×C4C22×Dic9412yes—
668C2×C4#1309407112yes—
669C2×C4C24×D4711yescharacteristic
670C8—22no—
671C8—942no—
672C8—942no—
673C8C22×Dic9414yes—
674C22—24no—
675C22—24no—
676C22—42no—
677C22—42no—
678C22—48no—
679C22—48no—
680C22—42no—
681C22—42no—
682C22D4×Dic9412yes—
683C22#1568991912yes—
684C22#1568992712yes—
685C22C22×D4×D4711yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—942no—
691C4—942no—
692C4—942no—
693C4—942no—
694C4—1882no—
695C4—1882no—
696C4—1882no—
697C4—1882no—
698C4D4×Dic9412yes—
699C4C23×Dic9411yescharacteristic
700C4C2×#1309407111yescharacteristic
701C2—44no—
702C2—44no—
703C2#2025634714yesdirect product factor
704C2C2×D4×Dic9411yescharacteristic
705C2C2×#1568991911yescharacteristic
706C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#442C2
socleC23×C47C22×D4
prime radicalC22×D8×C47C22
hypercenterC2×#442D47
hypocenterC47C2×#3389
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#15689832C2semidirect
2. C2×#15689830C2semidirect
3. #20256347C2direct (N × H)
4. C2×#15689532C2semidirect
5. C2×#15689530C2semidirect
6. C2×#15689523C2semidirect
7. C2×#15689425C2semidirect
8. C2×#15689425C2semidirect
9. C2×#15689423C2semidirect
10. C2×#15689421C2semidirect
11. C2×#15689403C2semidirect
12. C2×#15689401C2semidirect
13. C2×#15689251C2semidirect
18. #15689832C22semidirect
20. #15689830C22semidirect
40. #15689532C22semidirect
41. #15689530C22semidirect
42. #15689523C22semidirect
43. #15689425C22semidirect
44. #15689425C22semidirect
45. #15689423C22semidirect
46. #15689421C22semidirect
47. #15689403C22semidirect
48. #15689401C22semidirect
49. #15689251C22semidirect
160. C2×D8×C47Q8semidirect
218. D8×C47C2×Q8semidirect
366. C2×C47#3389semidirect
430. C47C2×#3389semidirect
442. C2×D8Dic94semidirect
572. D8C2×Dic94semidirect
703. C2#20256347direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898322
C2×#156898302
#202563472
C2×#156895322
C2×#156895302
C2×#156895232
C2×#156894252
C2×#156894232
C2×#156894212
C2×#156894032
C2×#156894012
C2×#156892512
C2×#156892352
C2×D8×Dic472
C2×C47×#4422
C2×#338947