Finite Group Databasebeta

← C2×#20254523 #27088335

Subgroups — C2×#20254523 #27088335

Order 12032.

2058 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689679C211yesmaximal, characteristic, complemented
2C2×#15689670C211yesmaximal, characteristic
3#20254523C2116yesmaximal, direct product factor
4C2×#15689527C211yesmaximal, characteristic, complemented
5C2×#15689520C211yesmaximal, characteristic, complemented
6C2×#15689468C211yesmaximal, characteristic, complemented
7C2×#15689468C211yesmaximal, characteristic, complemented
8C2×#15689450C211yesmaximal, characteristic, complemented
9C2×#15689449C211yesmaximal, characteristic, complemented
10C2×#15689446C211yesmaximal, characteristic, complemented
11C2×#15689445C211yesmaximal, characteristic, complemented
12C2×#15689424C211yesmaximal, characteristic, complemented
13C2×#15689423C211yesmaximal, characteristic, complemented
14C2×#15689420C211yesmaximal, characteristic, complemented
15C2×#15689175C211yesmaximal, characteristic, complemented
16C2×C47×#478C211yesmaximal, characteristic, complemented
17C22×#10625350—21no—
18#15689679—24no—
19#15689679C2218yescomplemented
20#15689670—24no—
21#15689670C2218yes—
22C2×#13094023C2211yescharacteristic
23C2×#13094023C2211yescharacteristic
24C2×#13094023C2211yescharacteristic
25C2×#13094020C2211yescharacteristic
26C2×#13094016C2211yescharacteristic
27C2×#13094010—21no—
28C2×#13094002—21no—
29C2×#13094002—21no—
30C2×#13093999C2211yescharacteristic
31C2×#13093997—21no—
32C2×#13093995C2211yescharacteristic
33C2×#13093989—21no—
34C2×#13093989—21no—
35C2×C4×D188C2211yescharacteristic
36C2×C4×C22⋊D47—21no—
37C2×#13093982C2211yescharacteristic
38C2×#13093982C2211yescharacteristic
39C2×C42×D47C2211yescharacteristic
40#15689527C2218yescomplemented
41#15689520C2218yescomplemented
42#15689468C2218yescomplemented
43#15689468C2218yescomplemented
44#15689450C2218yescomplemented
45#15689449C2218yescomplemented
46#15689446C2218yescomplemented
47#15689445C2218yescomplemented
48#15689424C2218yescomplemented
49#15689423C2218yescomplemented
50#15689420C2218yescomplemented
51#15689175C2218yescomplemented
52C2×#13093958C2211yescharacteristic
53C2×#13093957C2211yescharacteristic
54C2×#13093957C2211yescharacteristic
55C2×#13093956C2211yescharacteristic
56C2×#13093955C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×#13093946C2211yescharacteristic
60C2×#13093946C2211yescharacteristic
61C2×#13093945C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
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
77C2×#10625350—28no—
78C2×#10625350—48no—
79C22×Dic94—21no—
80C22×Dic94—21no—
81C22×Dic94—21no—
82C22×D188—21no—
83C22×D188C2311yescharacteristic
84C22×C22⋊D47—21no—
85C22×C22⋊D47—21no—
86C22×C22⋊D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47D411yescharacteristic
89C22×C4×D47D411yescharacteristic
90C22×C4×D47C2311yescharacteristic
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2311yescharacteristic
93#13094023—22no—
94#13094023—22no—
95#13094023—22no—
96#13094023C2314yes—
97#13094023C2314yes—
98#13094023C2314yes—
99#13094020—22no—
100#13094020C2314yes—
101#13094016—22no—
102#13094016C2314yes—
103#13094010—28no—
104#13094002—28no—
105#13094002—28no—
106#13093999—22no—
107#13093999C2314yes—
108#13093997—28no—
109#13093995—22no—
110#13093995C2314yes—
111#13093989—28no—
112#13093989—28no—
113C4×D188—22no—
114C4×D188C2314yes—
115C4×C22⋊D47—28no—
116#13093982—22no—
117#13093982—22no—
118#13093982C2314yes—
119#13093982C2314yes—
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×C22⋊Dic47—21no—
129C2×(C2×D47)⋊C4—21no—
130C2×(C2×D47)⋊C4—21no—
131C2×(C2×D47)⋊C4—21no—
132C2×(C2×D47)⋊C4—21no—
133C2×C4×Dic47—21no—
134C2×C4×Dic47—21no—
135C2×C4×Dic47D411yescharacteristic
136C2×C4×Dic47D411yescharacteristic
137C2×C4×Dic47C2311yescharacteristic
138C42×D47D414yes—
139C42×D47C2314yes—
140#13093958C2314yes—
141#13093957C2314yes—
142#13093957C2314yes—
143#13093956C2314yes—
144#13093955C2314yes—
145#13093955C2314yes—
146C4⋊(C47⋊C8)C2314yes—
147#13093946C2314yes—
148#13093946C2314yes—
149#13093945C2314yes—
150#13093945C2314yes—
151#13093944C2314yes—
152#13093944C2314yes—
153(C2×D47)⋊C8C2314yes—
154(C2×D47)⋊C8C2314yes—
155C8×Dic47C2314yes—
156C8×Dic47C2314yes—
157C22×D4×C47C2311yescharacteristic
158C23×C4×C47—21no—
159C22×C8×C47C2311yescharacteristic
160C22×C8×C47C2311yescharacteristic
161#125×C47—22no—
162#125×C47C2314yes—
163C4×D4×C47—22no—
164C4×D4×C47C2314yes—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47C2311yescharacteristic
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C22⋊C4×C47—21no—
171C2×C42×C47C2311yescharacteristic
172#107×C47C2314yes—
173#106×C47C2314yes—
174C4⋊C8×C47C2314yes—
175#102×C47C2314yes—
176#102×C47C2314yes—
177C24×C47—21no—
178C23×D47—21no—
179C23×D47C2×D411yescharacteristic
180C2×D4×C47—21no—
181C2×D4×C47—22no—
182C2×D4×C47—22no—
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
192C2×C22⋊D47—24no—
193C2×C22⋊D47—24no—
194C2×C22⋊D47—24no—
195C2×C22⋊D47—44no—
196C2×C22⋊D47—44no—
197C2×C22⋊D47—44no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47C2×D411yescharacteristic
202C22×Dic47C2×D411yescharacteristic
203C22×Dic47C2×D411yescharacteristic
204#10625350—432no—
205C2×D188—22no—
206C2×D188—22no—
207C2×D188—24no—
208C2×D188—21no—
209C2×D188—44no—
210C2×D188C2412yes—
211C2×C4×D47—22no—
212C2×C4×D47—22no—
213C2×C4×D47—24no—
214C2×C4×D47—24no—
215C2×C4×D47—24no—
216C2×C4×D47—44no—
217C2×C4×D47C2×D412yes—
218C2×C4×D47C2×D414yes—
219C2×C4×D47C2×D414yes—
220C2×C4×D47C2412yes—
221C2×Dic94—24no—
222C2×Dic94—24no—
223C2×Dic94—24no—
224C2×Dic94—44no—
225C2×Dic94—44no—
226C2×Dic94—44no—
227C2×C8×C47—22no—
228C2×C8×C47—22no—
229C2×C8×C47C2412yes—
230C2×C8×C47C2412yes—
231C4⋊C4×C47—24no—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C4⋊C4×C47C2412yes—
239C22⋊C4×C47—24no—
240C42×C47C2×D412yes—
241C42×C47C2412yes—
242C22⋊Dic47—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247C4⋊Dic47—21no—
248C4⋊Dic47—21no—
249C4⋊Dic47—21no—
250C4⋊Dic47C2412yes—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258C4×Dic47—24no—
259C4×Dic47—24no—
260C4×Dic47C2×D412yes—
261C4×Dic47C2×D414yes—
262C4×Dic47C2×D414yes—
263C4×Dic47C2412yes—
264C2×C47⋊C8—22no—
265C2×C47⋊C8—22no—
266C2×C47⋊C8C2412yes—
267C2×C47⋊C8C2412yes—
268C23×C47—22no—
269C23×C47—42no—
270C23×C47—42no—
271C23×C47—42no—
272C23×C47C22×D411yescharacteristic
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—42no—
278C22×D47—42no—
279C22×D47—42no—
280C22×D47C22×D412yes—
281D4×C47—22no—
282D4×C47—22no—
283D4×C47—42no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—48no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47C22×D412yes—
294C2×C4×C47C22×D412yes—
295C2×C4×C47C22×D411yescharacteristic
296C2×C4×C472−1+412yes—
297C2×C4×C472−1+412yes—
298C2×C4×C47C2511yescharacteristic
299C22⋊D47—48no—
300C22⋊D47—48no—
301C22⋊D47—48no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47#13514yes—
310C2×Dic47AGL(1,ℤ/8)14yes—
311C2×Dic47C22×D412yes—
312C2×Dic47C22×D412yes—
313C2×Dic47C22×D412yes—
314D188—22no—
315D188—22no—
316D188—48no—
317D188—42no—
318C4×D47—24no—
319C4×D47—22no—
320C4×D47—22no—
321C4×D47—28no—
322C4×D47—28no—
323C4×D47—48no—
324Dic94—48no—
325Dic94—48no—
326Dic94—48no—
327C8×C47—22no—
328C8×C47—22no—
329C47⋊C8—22no—
330C47⋊C8—22no—
331C2×#3228—471nomaximal, Sylow
332C22×C47—42no—
333C22×C47—42no—
334C22×C47—42no—
335C22×C47—84no—
336C22×C47#53612yes—
337C22×C47C2×#13512yes—
338C22×C47C2×AGL(1,ℤ/8)12yes—
339C22×C47C23×D411yescharacteristic
340C2×D47—22no—
341C2×D47—22no—
342C2×D47—22no—
343C2×D47—44no—
344C2×D47—42no—
345C2×D47—42no—
346C2×D47—42no—
347C2×D47—84no—
348C4×C47—22no—
349C4×C47—22no—
350C4×C47—42no—
351C4×C47—42no—
352C4×C47—42no—
353C4×C47#53612yes—
354C4×C47C2×2−1+411yescharacteristic
355C4×C47C2×2−1+411yescharacteristic
356Dic47—22no—
357Dic47—42no—
358Dic47—42no—
359Dic47—42no—
360Dic47C2×#13514yes—
361Dic47C2×AGL(1,ℤ/8)14yes—
362C2×#533—471no—
363C2×#532—471no—
364#3228—4716no—
365C2×#500—471no—
366C2×#498—471no—
367C2×#486—471no—
368C2×#486—471no—
369C2×#482—471no—
370C2×#482—471no—
371C2×#482—471no—
372C2×#482—471no—
373C2×#478—471no—
374C2×#478—471no—
375C2×#478—471no—
376C2×#478D4711yescharacteristic, complemented
377C2×#431—471no—
378C2×C47—82no—
379C2×C47#322814yescomplemented
380C2×C47C2×#53611yescharacteristic
381C2×C47C22×#13511yescharacteristic
382C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
383D47—42no—
384D47—82no—
385C22×#41—941no—
386#533—478no—
387#533—944no—
388#532—478no—
389#532—944no—
390C2×C4⋊Q8—471no—
391C2×C4⋊Q8—471no—
392C2×C4⋊Q8—471no—
393C2×#127—471no—
394C2×#125—471no—
395C2×#125C2×D4711yescharacteristic
396C2×#124—941no—
397C2×C22⋊Q8—941no—
398C2×C22⋊Q8—941no—
399C2×#121—471no—
400C2×#121—471no—
401C2×#121—941no—
402C2×C4×Q8—941no—
403C2×C4×Q8—941no—
404C2×C4×D4—471no—
405C2×C4×D4—941no—
406C2×C4×D4C2×D4711yescharacteristic
407C2×#117—471no—
408C2×#117—471no—
409C22×C42—471no—
410#500—478no—
411#498—478no—
412#486—478no—
413#486—478no—
414#482—478no—
415#482—478no—
416#482—478no—
417#482—478no—
418#478—478no—
419#478—478no—
420#478—478no—
421#478C2×D4718yescomplemented
422#431—478no—
423C2×#107—471no—
424C2×#107—471no—
425C2×#107—471no—
426C2×#107C2×D4711yescharacteristic
427C2×#106—471no—
428C2×#106—471no—
429C2×#106—471no—
430C2×#106C2×D4711yescharacteristic
431C2×C4⋊C8—471no—
432C2×C4⋊C8C2×D4711yescharacteristic
433C2×#102—471no—
434C2×#102—471no—
435C2×#102—471no—
436C2×#102—471no—
437C2×#102—471no—
438C2×#102—471no—
439C2×#102C2×D4711yescharacteristic
440C2×#102C2×D4711yescharacteristic
441C2×C22⋊C8—471no—
442C2×C22⋊C8—471no—
443C2×C4×C8—471no—
444C2×C4×C8—471no—
445C47C2×#322811yescharacteristic, complemented, Sylow
446C2×#41—948no—
447C2×#41—1888no—
448C22×Q8—941no—
449C22×Q8—941no—
450C22×Q8—941no—
451C22×D4—471no—
452C22×D4—941no—
453C22×D4—941no—
454C22×D4—941no—
455C22×D4—941no—
456C22×D4C22×D4711yescharacteristic
457C23×C4—21no—
458C23×C4—471no—
459C23×C4—471no—
460C23×C4—471no—
461C23×C4—941no—
462C22×C8—471no—
463C22×C8—471no—
464C22×C8C22×D4711yescharacteristic
465C22×C8C22×D4711yescharacteristic
466C4⋊Q8—474no—
467C4⋊Q8—474no—
468C4⋊Q8—474no—
469C4⋊Q8—942no—
470C4⋊Q8—942no—
471C4⋊Q8—942no—
472#127—474no—
473#127—942no—
474#125—22no—
475#125—474no—
476#125—942no—
477#125C22×D4714yes—
478#124—948no—
479C22⋊Q8—948no—
480C22⋊Q8—948no—
481#121—474no—
482#121—474no—
483#121—948no—
484#121—942no—
485#121—942no—
486C4×Q8—948no—
487C4×Q8—948no—
488C4×D4—22no—
489C4×D4—474no—
490C4×D4—948no—
491C4×D4—942no—
492C4×D4C22×D4714yes—
493#117—474no—
494#117—474no—
495#117—942no—
496#117—942no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C4⋊C4C22×D4711yescharacteristic
509C2×C4⋊C4C22×D4711yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C22⋊C4—941no—
515C2×C22⋊C4—941no—
516C2×C42—471no—
517C2×C42—471no—
518C2×C42—471no—
519C2×C42—474no—
520C2×C42—474no—
521C2×C42—941no—
522C2×C42—941no—
523C2×C42C22×D4711yescharacteristic
524#107—474no—
525#107—474no—
526#107—474no—
527#107C22×D4714yes—
528#106—474no—
529#106—474no—
530#106—474no—
531#106C22×D4714yes—
532C4⋊C8—474no—
533C4⋊C8C22×D4714yes—
534#102—474no—
535#102—474no—
536#102—474no—
537#102—474no—
538#102—474no—
539#102—474no—
540#102C22×D4714yes—
541#102C22×D4714yes—
542C22⋊C8—474no—
543C22⋊C8—474no—
544C4×C8—474no—
545C4×C8—474no—
546C24—21no—
547C24—471no—
548C24—941no—
549#41—18832no—
550C2×Q8—944no—
551C2×Q8—944no—
552C2×Q8—944no—
553C2×Q8—1884no—
554C2×Q8—1884no—
555C2×Q8—1884no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—472no—
560C2×D4—944no—
561C2×D4—944no—
562C2×D4—944no—
563C2×D4—944no—
564C2×D4—941no—
565C2×D4—942no—
566C2×D4—942no—
567C2×D4—1884no—
568C2×D4—1884no—
569C2×D4—1884no—
570C2×D4—1884no—
571C2×D4C23×D4712yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—44no—
577C22×C4—471no—
578C22×C4—471no—
579C22×C4—471no—
580C22×C4—472no—
581C22×C4—474no—
582C22×C4—474no—
583C22×C4—472no—
584C22×C4—944no—
585C22×C4—944no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—944no—
592C22×C4—1884no—
593C22×C4D4×D4711yescharacteristic
594C22×C4D4×D4711yescharacteristic
595C22×C4C23×D4711yescharacteristic
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—472no—
599C2×C8—472no—
600C2×C8—942no—
601C2×C8—942no—
602C2×C8C23×D4712yes—
603C2×C8C23×D4712yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—472no—
610C4⋊C4—472no—
611C4⋊C4—472no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—944no—
616C4⋊C4—944no—
617C4⋊C4—941no—
618C4⋊C4—941no—
619C4⋊C4—941no—
620C4⋊C4C23×D4712yes—
621C4⋊C4C23×D4712yes—
622C4⋊C4C23×D4712yes—
623C22⋊C4—24no—
624C22⋊C4—944no—
625C22⋊C4—944no—
626C22⋊C4—944no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C42—474no—
630C42—474no—
631C42—472no—
632C42—472no—
633C42—944no—
634C42—944no—
635C42D4×D4712yes—
636C42C23×D4712yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—472no—
642C23—942no—
643C23—942no—
644C23—942no—
645C23—942no—
646C23—1882no—
647C23—1882no—
648C23—1882no—
649C23C2×D4×D4711yescharacteristic
650Q8—1888no—
651Q8—1888no—
652Q8—1888no—
653D4—22no—
654D4—22no—
655D4—42no—
656D4—942no—
657D4—942no—
658D4—1888no—
659D4—1888no—
660D4—1888no—
661D4—1888no—
662D4—1882no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—48no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—474no—
673C2×C4—474no—
674C2×C4—472no—
675C2×C4—472no—
676C2×C4—472no—
677C2×C4—948no—
678C2×C4—948no—
679C2×C4—942no—
680C2×C4—944no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—1888no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4—1882no—
690C2×C4C2×D4×D4712yes—
691C2×C4C2×D4×D4712yes—
692C2×C4C2×D4×D4711yescharacteristic
693C2×C4#1309407112yes—
694C2×C4#1309407212yes—
695C2×C4C24×D4711yescharacteristic
696C8—22no—
697C8—22no—
698C8—942no—
699C8—942no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—942no—
705C22—942no—
706C22—942no—
707C22—3764no—
708C22—1882no—
709C22—1882no—
710C22—1882no—
711C22—1884no—
712C22#1568969612yes—
713C22#135×D4712yes—
714C22AGL(1,ℤ/8)×D4712yes—
715C22C22×D4×D4711yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—474no—
722C4—474no—
723C4—942no—
724C4—1882no—
725C4—1882no—
726C4—1882no—
727C4#1568969612yes—
728C4C2×#1309407111yescharacteristic
729C4C2×#1309407211yescharacteristic
730C2—82no—
731C2—3762no—
732C2—1882no—
733C2#2025452314yesdirect product factor
734C2C2×#1568969611yescharacteristic
735C2C2×#135×D4711yescharacteristic
736C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#478C2
socleC23×C47C22×D4
prime radicalC2×#15689670C2
hypercenterC2×#478D47
hypocenterC47C2×#3228
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×#15689679C2semidirect
3. #20254523C2direct (N × H)
4. C2×#15689527C2semidirect
5. C2×#15689520C2semidirect
6. C2×#15689468C2semidirect
7. C2×#15689468C2semidirect
8. C2×#15689450C2semidirect
9. C2×#15689449C2semidirect
10. C2×#15689446C2semidirect
11. C2×#15689445C2semidirect
12. C2×#15689424C2semidirect
13. C2×#15689423C2semidirect
14. C2×#15689420C2semidirect
15. C2×#15689175C2semidirect
16. C2×C47×#478C2semidirect
19. #15689679C22semidirect
40. #15689527C22semidirect
41. #15689520C22semidirect
42. #15689468C22semidirect
43. #15689468C22semidirect
44. #15689450C22semidirect
45. #15689449C22semidirect
46. #15689446C22semidirect
47. #15689445C22semidirect
48. #15689424C22semidirect
49. #15689423C22semidirect
50. #15689420C22semidirect
51. #15689175C22semidirect
71. C47×#478C22semidirect
376. C2×#478D47semidirect
379. C2×C47#3228semidirect
421. #478C2×D47semidirect
445. C47C2×#3228semidirect
733. C2#20254523direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896792
C2×#156896702
#202545232
C2×#156895272
C2×#156895202
C2×#156894682
C2×#156894502
C2×#156894492
C2×#156894462
C2×#156894452
C2×#156894242
C2×#156894232
C2×#156894202
C2×#156891752
C2×C47×#4782
C2×#322847