Finite Group Databasebeta

← C2×#20256290 #27096758

Subgroups — C2×#20256290 #27096758

Order 12032.

2082 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689829C211yesmaximal, characteristic, complemented
2C2×D4×Dic94C211yesmaximal, characteristic, complemented
3#20256290C2116yesmaximal, direct product factor
4C2×#15689533C211yesmaximal, characteristic, complemented
5C2×#15689531C211yesmaximal, characteristic, complemented
6C2×#15689520C211yesmaximal, characteristic, complemented
7C2×#15689425C211yesmaximal, characteristic, complemented
8C2×#15689414C211yesmaximal, characteristic, complemented
9C2×#15689412C211yesmaximal, characteristic, complemented
10C2×#15689411C211yesmaximal, characteristic, complemented
11C2×#15689402C211yesmaximal, characteristic, complemented
12C2×#15689252C211yesmaximal, characteristic, complemented
13C2×#15689233C211yesmaximal, characteristic
14C2×#15689232C211yesmaximal, characteristic
15C2×#15689203C211yesmaximal, characteristic
16C2×C47×#478C211yesmaximal, characteristic, complemented
17C23×Dic94—21no—
18C22×#10625334C2211yescharacteristic
19#15689829—24no—
20#15689829C2218yescomplemented
21D4×Dic94—24no—
22D4×Dic94C2218yescomplemented
23C2×#13094024C2211yescharacteristic
24C2×#13094023C2211yescharacteristic
25C2×#13094023C2211yescharacteristic
26C2×#13094023C2211yescharacteristic
27C2×#13094015C2211yescharacteristic
28C2×#13094004—21no—
29C2×#13094003—21no—
30C2×#13094002—21no—
31C2×#13094002—21no—
32C2×#13094001—21no—
33C2×#13094001—21no—
34C2×C4×Dic94C2211yescharacteristic
35C2×C4×D188C2211yescharacteristic
36C2×D4×Dic47C2211yescharacteristic
37C2×D4×Dic47C2211yescharacteristic
38C2×#13093986C2211yescharacteristic
39C2×#13093986C2211yescharacteristic
40C2×C4⋊C4×D47—21no—
41#15689533C2218yescomplemented
42#15689531C2218yescomplemented
43#15689520C2218yescomplemented
44#15689425C2218yescomplemented
45#15689414C2218yescomplemented
46#15689412C2218yescomplemented
47#15689411C2218yescomplemented
48#15689402C2218yescomplemented
49#15689252C2218yescomplemented
50#15689233C2218yes—
51#15689232C2218yes—
52#15689203C2218yes—
53C2×#13093957C2211yescharacteristic
54C2×#13093957C2211yescharacteristic
55C2×#13093956C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59C2×#13093955C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×#13093935C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×#125×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C47×#478C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×Dic94—21no—
80C22×Dic94—21no—
81C22×Dic94—28no—
82C22×Dic94—48no—
83C22×Dic94D411yescharacteristic
84C22×D188C2311yescharacteristic
85C23×Dic47—21no—
86C23×Dic47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C2×#10625334Q818yescomplemented
91C2×#10625334C2314yes—
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94#13094024—22no—
95#13094024C2314yes—
96#13094023—22no—
97#13094023—22no—
98#13094023—22no—
99#13094023C2314yes—
100#13094023C2314yes—
101#13094023C2314yes—
102#13094015—22no—
103#13094015C2314yes—
104#13094004—28no—
105#13094003—28no—
106#13094002—28no—
107#13094002—28no—
108#13094001—28no—
109#13094001—28no—
110C4×Dic94D414yes—
111C4×Dic94C2314yes—
112C4×D188—22no—
113C4×D188C2314yes—
114D4×Dic47—22no—
115D4×Dic47—22no—
116D4×Dic47C2314yes—
117D4×Dic47C2314yes—
118#13093986—22no—
119#13093986—22no—
120#13093986C2314yes—
121#13093986C2314yes—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47D411yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4D411yescharacteristic
133C2×Dic47⋊C4D411yescharacteristic
134C4⋊C4×D47—28no—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×C4×Dic47C2311yescharacteristic
141C2×C4×Dic47C2311yescharacteristic
142#13093957C2314yes—
143#13093957C2314yes—
144#13093956C2314yes—
145#13093956C2314yes—
146#13093955C2314yes—
147#13093955C2314yes—
148#13093955C2314yes—
149Dic47⋊C8C2314yes—
150Dic47⋊C8C2314yes—
151#13093946C2314yes—
152#13093946C2314yes—
153#13093945C2314yes—
154#13093944C2314yes—
155#13093935C2314yes—
156#13093934C2314yes—
157C8×Dic47C2314yes—
158C22×D4×C47C2311yescharacteristic
159C23×C4×C47—21no—
160C22×C8×C47C2311yescharacteristic
161C22×C8×C47C2311yescharacteristic
162#125×C47—22no—
163#125×C47C2314yes—
164C4×D4×C47—22no—
165C4×D4×C47C2314yes—
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C22⋊C4×C47—21no—
172C2×C42×C47C2311yescharacteristic
173#107×C47C2314yes—
174#106×C47C2314yes—
175C4⋊C8×C47C2314yes—
176#102×C47C2314yes—
177#102×C47C2314yes—
178C24×C47—21no—
179C23×D47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—22no—
182C2×D4×C47C2×Q814yes—
183C2×D4×C47C2412yes—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—24no—
188C22×C4×C47—44no—
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2411yescharacteristic
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—24no—
196C22×Dic47—24no—
197C22×Dic47—44no—
198C22×Dic47—44no—
199C22×Dic47C2×D411yescharacteristic
200C22×Dic47C2×D411yescharacteristic
201C22×Dic47C2×D411yescharacteristic
202C22×Dic47C2×D411yescharacteristic
203C2×D188—21no—
204C2×D188—22no—
205C2×D188C2×Q814yescomplemented
206C2×D188C2412yes—
207C2×C4×D47—24no—
208C2×C4×D47—24no—
209C2×C4×D47—24no—
210C2×C4×D47—44no—
211C2×C4×D47—82no—
212C2×C4×D47—82no—
213C2×Dic94—24no—
214C2×Dic94—24no—
215C2×Dic94—24no—
216C2×Dic94—24no—
217C2×Dic94—24no—
218C2×Dic94—432no—
219C2×Dic94—44no—
220C2×Dic94—44no—
221C2×Dic94—44no—
222C2×Dic94—82no—
223C2×Dic94C2×D414yes—
224C2×C8×C47—22no—
225C2×C8×C47—22no—
226C2×C8×C47C2412yes—
227C2×C8×C47C2412yes—
228C4⋊C4×C47—24no—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47C2412yes—
234C4⋊C4×C47C2412yes—
235C4⋊C4×C47C2412yes—
236C22⋊C4×C47—24no—
237C42×C47C2×D412yes—
238C42×C47C2412yes—
239C22⋊Dic47—24no—
240C22⋊Dic47—24no—
241#10625334C2×Q8116yescomplemented
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245C4⋊Dic47—24no—
246C4⋊Dic47—21no—
247C4⋊Dic47—21no—
248C4⋊Dic47—21no—
249C4⋊Dic47—24no—
250C4⋊Dic47C2×D414yes—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253C4⋊Dic47C2412yes—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4C2×D414yes—
259Dic47⋊C4C2×D414yes—
260C4×Dic47C2×D412yes—
261C4×Dic47C2×D412yes—
262C4×Dic47C2412yes—
263C4×Dic47C2412yes—
264C2×C47⋊C8—22no—
265C2×C47⋊C8C2×Q814yescomplemented
266C2×C47⋊C8C2412yes—
267C2×C47⋊C8C2412yes—
268C23×C47—24no—
269C23×C47—22no—
270C23×C47—42no—
271C23×C47—42no—
272C23×C47C22×D411yescharacteristic
273C22×D47—24no—
274C22×D47—22no—
275C22×D47—42no—
276C22×D47—42no—
277D4×C47—24no—
278D4×C47—22no—
279D4×C47C22×Q814yes—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—48no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47C22×D412yes—
290C2×C4×C47C22×D412yes—
291C2×C4×C47C22×D411yescharacteristic
292C2×C4×C47C22×Q812yes—
293C2×C4×C472−1+412yes—
294C2×C4×C47C2511yescharacteristic
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—48no—
306C2×Dic47AGL(1,ℤ/8)14yes—
307C2×Dic47C22×D412yes—
308C2×Dic47C22×D412yes—
309C2×Dic47C22×D412yes—
310C2×Dic47C22×D412yes—
311D188—24no—
312D188—22no—
313D188C22×Q814yescomplemented
314C4×D47—48no—
315C4×D47—84no—
316C4×D47—84no—
317Dic94—28no—
318Dic94—48no—
319Dic94—48no—
320Dic94—48no—
321Dic94—84no—
322C8×C47—22no—
323C8×C47—22no—
324C47⋊C8—22no—
325C47⋊C8C22×Q814yescomplemented
326C2×#3384—471nomaximal, Sylow
327C22×C47—24no—
328C22×C47—48no—
329C22×C47—42no—
330C22×C47—42no—
331C22×C47D4×Q812yes—
332C22×C47C2×AGL(1,ℤ/8)12yes—
333C22×C47#57712yes—
334C22×C47C23×D411yescharacteristic
335C2×D47—24no—
336C2×D47—48no—
337C2×D47—42no—
338C2×D47—42no—
339C4×C47—22no—
340C4×C47—22no—
341C4×C47—42no—
342C4×C47—42no—
343C4×C47—42no—
344C4×C47D4×Q812yes—
345C4×C47C23×Q811yescharacteristic
346C4×C47C2×2−1+411yescharacteristic
347Dic47—22no—
348Dic47—22no—
349Dic47—22no—
350Dic47—42no—
351Dic47—42no—
352Dic47—42no—
353Dic47C2×AGL(1,ℤ/8)14yes—
354C2×#554—471no—
355C2×D4×Q8—471no—
356#3384—4716no—
357C2×#501—471no—
358C2×#501—471no—
359C2×#498—471no—
360C2×#478—471no—
361C2×#478D4711yescharacteristic, complemented
362C2×#476—471no—
363C2×#476—471no—
364C2×#476—471no—
365C2×#474—471no—
366C2×#446—471no—
367C2×#442—471no—
368C2×#442—471no—
369C2×C4×D8—471no—
370C2×C47—44no—
371C2×C47#338414yescomplemented
372C2×C47C2×D4×Q811yescharacteristic
373C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
374C2×C47C2×#57711yescharacteristic
375D47—44no—
376C23×Q8—941no—
377C22×D8—471no—
378#554—478no—
379#554—944no—
380D4×Q8—478no—
381D4×Q8—944no—
382C2×C4⋊Q8—471no—
383C2×C4⋊Q8—471no—
384C2×C4⋊Q8—471no—
385C2×C4⋊Q8—471no—
386C2×#125—471no—
387C2×#125C2×D4711yescharacteristic
388C2×C22⋊Q8—941no—
389C2×C22⋊Q8—941no—
390C2×C22⋊Q8—941no—
391C2×C22⋊Q8—941no—
392C2×C22⋊Q8—941no—
393C2×C22⋊Q8—941no—
394C2×C4×Q8—471no—
395C2×C4×D4—471no—
396C2×C4×D4—471no—
397C2×C4×D4—471no—
398C2×C4×D4—471no—
399C2×C4×D4—471no—
400C2×C4×D4C2×D4711yescharacteristic
401C22×C4⋊C4—941no—
402#501—478no—
403#501—478no—
404#498—478no—
405#478—478no—
406#478C2×D4718yescomplemented
407#476—478no—
408#476—478no—
409#476—478no—
410#474—478no—
411#446—478no—
412#442—478no—
413#442—478no—
414C4×D8—478no—
415C2×#107—471no—
416C2×#107—471no—
417C2×#107C2×D4711yescharacteristic
418C2×#106—471no—
419C2×#106—471no—
420C2×#106—471no—
421C2×#106—471no—
422C2×#106—471no—
423C2×#106C2×D4711yescharacteristic
424C2×C4⋊C8—471no—
425C2×C4⋊C8—471no—
426C2×C4⋊C8C2×D4711yescharacteristic
427C2×#102—471no—
428C2×#102—471no—
429C2×#102—471no—
430C2×#102—471no—
431C2×#102C2×D4711yescharacteristic
432C2×#102C2×D4711yescharacteristic
433C2×#97—471no—
434C2×#97—471no—
435C2×C4×C8—471no—
436C47C2×#338411yescharacteristic, complemented, Sylow
437C22×Q8—471no—
438C22×Q8—941no—
439C22×Q8—941no—
440C22×Q8—941no—
441C22×Q8—948no—
442C22×Q8—941no—
443C22×Q8—1888no—
444C22×D4—471no—
445C22×D4C22×D4711yescharacteristic
446C23×C4—21no—
447C23×C4—941no—
448C23×C4—941no—
449C23×C4—941no—
450C23×C4—941no—
451C23×C4—941no—
452C2×D8—478no—
453C2×D8—474no—
454C22×C8—471no—
455C22×C8—471no—
456C22×C8C22×D4711yescharacteristic
457C22×C8C22×D4711yescharacteristic
458C4⋊Q8—474no—
459C4⋊Q8—474no—
460C4⋊Q8—474no—
461C4⋊Q8—474no—
462C4⋊Q8—942no—
463C4⋊Q8—942no—
464C4⋊Q8—942no—
465C4⋊Q8—942no—
466#125—22no—
467#125—474no—
468#125—942no—
469#125C22×D4714yes—
470C22⋊Q8—948no—
471C22⋊Q8—948no—
472C22⋊Q8—948no—
473C22⋊Q8—948no—
474C22⋊Q8—948no—
475C22⋊Q8—948no—
476C4×Q8—474no—
477C4×Q8—474no—
478C4×D4—22no—
479C4×D4—474no—
480C4×D4—474no—
481C4×D4—474no—
482C4×D4—474no—
483C4×D4—474no—
484C4×D4—942no—
485C4×D4—942no—
486C4×D4—942no—
487C4×D4—942no—
488C4×D4—942no—
489C4×D4C22×D4714yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—471no—
493C2×C4⋊C4—471no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—948no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C42—471no—
515C2×C42—471no—
516C2×C42C22×D4711yescharacteristic
517#107—474no—
518#107—474no—
519#107C22×D4714yes—
520#106—474no—
521#106—474no—
522#106—474no—
523#106—474no—
524#106—474no—
525#106C22×D4714yes—
526C4⋊C8—474no—
527C4⋊C8—474no—
528C4⋊C8C22×D4714yes—
529#102—474no—
530#102—474no—
531#102—474no—
532#102—474no—
533#102C22×D4714yes—
534#102C22×D4714yes—
535#97—474no—
536#97—474no—
537C4×C8—474no—
538C24—21no—
539C24—941no—
540C2×Q8—474no—
541C2×Q8—944no—
542C2×Q8—944no—
543C2×Q8—944no—
544C2×Q8—944no—
545C2×Q8—944no—
546C2×Q8—3762no—
547C2×Q8—1884no—
548C2×Q8—1884no—
549C2×Q8—1884no—
550C2×Q8—18832no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—474no—
554C2×D4—472no—
555C2×D4—941no—
556C2×D4—942no—
557C2×D4Q8×D4714yes—
558C2×D4C23×D4712yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—44no—
564C22×C4—471no—
565C22×C4—471no—
566C22×C4—471no—
567C22×C4—471no—
568C22×C4—944no—
569C22×C4—944no—
570C22×C4—944no—
571C22×C4—944no—
572C22×C4—941no—
573C22×C4—941no—
574C22×C4—941no—
575C22×C4—944no—
576C22×C4—3762no—
577C22×C4—3762no—
578C22×C4—1884no—
579C22×C4—1884no—
580C22×C4—1884no—
581C22×C4D4×D4711yescharacteristic
582C22×C4D4×D4711yescharacteristic
583C22×C4C23×D4711yescharacteristic
584D8—4716no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—474no—
588C2×C8—472no—
589C2×C8—472no—
590C2×C8—942no—
591C2×C8C23×D4712yes—
592C2×C8C23×D4712yes—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—474no—
599C4⋊C4—474no—
600C4⋊C4—474no—
601C4⋊C4—472no—
602C4⋊C4—472no—
603C4⋊C4—472no—
604C4⋊C4—944no—
605C4⋊C4—944no—
606C4⋊C4—944no—
607C4⋊C4—944no—
608C4⋊C4—944no—
609C4⋊C4—941no—
610C4⋊C4—941no—
611C4⋊C4—941no—
612C4⋊C4—944no—
613C4⋊C4C23×D4712yes—
614C4⋊C4C23×D4712yes—
615C4⋊C4C23×D4712yes—
616C22⋊C4—24no—
617C22⋊C4—944no—
618C22⋊C4—944no—
619C22⋊C4—944no—
620C22⋊C4—944no—
621C22⋊C4—944no—
622C42—472no—
623C42—472no—
624C42—472no—
625C42—472no—
626C42D4×D4712yes—
627C42C23×D4712yes—
628C23—24no—
629C23—22no—
630C23—42no—
631C23—42no—
632C23—944no—
633C23—942no—
634C23—1882no—
635C23—1882no—
636C23C2×D4×D4711yescharacteristic
637Q8—948no—
638Q8—3764no—
639Q8—1888no—
640Q8—1888no—
641Q8—1888no—
642D4—24no—
643D4—22no—
644D4—474no—
645D4—944no—
646D4—942no—
647D4C2×Q8×D4714yes—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—48no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—474no—
658C2×C4—472no—
659C2×C4—472no—
660C2×C4—472no—
661C2×C4—472no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—942no—
668C2×C4—3764no—
669C2×C4—3764no—
670C2×C4—1888no—
671C2×C4—1888no—
672C2×C4—1888no—
673C2×C4—1882no—
674C2×C4—1882no—
675C2×C4—1882no—
676C2×C4C2×D4×D4712yes—
677C2×C4C2×D4×D4712yes—
678C2×C4C2×D4×D4711yescharacteristic
679C2×C4C2×Q8×D4712yes—
680C2×C4#1309407112yes—
681C2×C4C24×D4711yescharacteristic
682C8—22no—
683C8—22no—
684C8—474no—
685C8—942no—
686C22—24no—
687C22—48no—
688C22—42no—
689C22—42no—
690C22—944no—
691C22—1888no—
692C22—1882no—
693C22—1882no—
694C22#1568978612yes—
695C22AGL(1,ℤ/8)×D4712yes—
696C22#1568993012yes—
697C22C22×D4×D4711yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—474no—
704C4—942no—
705C4—942no—
706C4—942no—
707C4—1882no—
708C4—1882no—
709C4—1882no—
710C4#1568978612yes—
711C4C22×Q8×D4711yescharacteristic
712C4C2×#1309407111yescharacteristic
713C2—44no—
714C2—1884no—
715C2#2025629014yesdirect product factor
716C2C2×#1568978611yescharacteristic
717C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
718C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#478C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
hypercenterC2×#478D47
hypocenterC47C2×#3384
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#15689829C2semidirect
2. C2×D4×Dic94C2semidirect
3. #20256290C2direct (N × H)
4. C2×#15689533C2semidirect
5. C2×#15689531C2semidirect
6. C2×#15689520C2semidirect
7. C2×#15689425C2semidirect
8. C2×#15689414C2semidirect
9. C2×#15689412C2semidirect
10. C2×#15689411C2semidirect
11. C2×#15689402C2semidirect
12. C2×#15689252C2semidirect
16. C2×C47×#478C2semidirect
20. #15689829C22semidirect
22. D4×Dic94C22semidirect
41. #15689533C22semidirect
42. #15689531C22semidirect
43. #15689520C22semidirect
44. #15689425C22semidirect
45. #15689414C22semidirect
46. #15689412C22semidirect
47. #15689411C22semidirect
48. #15689402C22semidirect
49. #15689252C22semidirect
71. C47×#478C22semidirect
90. C2×#10625334Q8semidirect
205. C2×D188C2×Q8semidirect
241. #10625334C2×Q8semidirect
265. C2×C47⋊C8C2×Q8semidirect
313. D188C22×Q8semidirect
325. C47⋊C8C22×Q8semidirect
361. C2×#478D47semidirect
371. C2×C47#3384semidirect
406. #478C2×D47semidirect
436. C47C2×#3384semidirect
715. C2#20256290direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898292
C2×D4×Dic942
#202562902
C2×#156895332
C2×#156895312
C2×#156895202
C2×#156894252
C2×#156894142
C2×#156894122
C2×#156894112
C2×#156894022
C2×#156892522
C2×#156892332
C2×#156892322
C2×#156892032
C2×C47×#4782
C2×#338447