Finite Group Databasebeta

← C2×#20255794 #27094755

Subgroups — C2×#20255794 #27094755

Order 12032.

1918 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689844C211yesmaximal, characteristic, complemented
2C2×#15689836C211yesmaximal, characteristic
3#20255794C2116yesmaximal, direct product factor
4C2×#15689520C211yesmaximal, characteristic, complemented
5C2×#15689462C211yesmaximal, characteristic, complemented
6C2×#15689449C211yesmaximal, characteristic, complemented
7C2×#15689448C211yesmaximal, characteristic, complemented
8C2×#15689416C211yesmaximal, characteristic, complemented
9C2×#15689402C211yesmaximal, characteristic, complemented
10C2×#15689355C211yesmaximal, characteristic, complemented
11C2×#15689354C211yesmaximal, characteristic, complemented
12C2×#15689208C211yesmaximal, characteristic, complemented
13C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
14C2×#15689160C211yesmaximal, characteristic, complemented
15C2×#15689159C211yesmaximal, characteristic, complemented
16C2×C47×#485C211yesmaximal, characteristic, complemented
17C22×#10625336C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20#15689844—24no—
21#15689844C2218yescomplemented
22#15689836—24no—
23#15689836C2218yes—
24C2×#13094023C2211yescharacteristic
25C2×#13094023C2211yescharacteristic
26C2×#13094019—21no—
27C2×#13094017—21no—
28C2×#13094012—21no—
29C2×#13094010—21no—
30C2×#13094010—21no—
31C2×#13094000C2211yescharacteristic
32C2×#13093999C2211yescharacteristic
33C2×#13093998C2211yescharacteristic
34C2×#13093997—21no—
35C2×Q8×Dic47C2211yescharacteristic
36C2×#13093989—21no—
37C2×#13093986C2211yescharacteristic
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×#13093983C2211yescharacteristic
40C2×#13093982C2211yescharacteristic
41C2×#13093982C2211yescharacteristic
42C2×#13093981—21no—
43#15689520C2218yescomplemented
44#15689462C2218yescomplemented
45#15689449C2218yescomplemented
46#15689448C2218yescomplemented
47#15689416C2218yescomplemented
48#15689402C2218yescomplemented
49#15689355C2218yescomplemented
50#15689354C2218yescomplemented
51#15689208C2218yescomplemented
52(C22⋊D47)⋊C8C2218yescomplemented
53#15689160C2218yescomplemented
54#15689159C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×#13093955C2211yescharacteristic
60C2×#13093955C2211yescharacteristic
61C2×#13093955C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×C22⋊Q8×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C47×#485C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×D188—21no—
80C22×D188C2311yescharacteristic
81C22×C22⋊D47—21no—
82C22×C22⋊D47D411yescharacteristic
83C22×C4×D47—21no—
84C22×C4×D47C2311yescharacteristic
85C2×#10625336—24no—
86C2×#10625336C2314yes—
87C22×C47⋊C8—24no—
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2314yes—
90C22×C47⋊C8C2311yescharacteristic
91C2×C8×D47—24no—
92C2×C8×D47C2314yes—
93#13094023—22no—
94#13094023—22no—
95#13094023C2314yes—
96#13094023C2314yes—
97#13094019—28no—
98#13094017—28no—
99#13094012—28no—
100#13094010—28no—
101#13094010—28no—
102#13094000—22no—
103#13094000C2314yes—
104#13093999—22no—
105#13093999C2314yes—
106#13093998—22no—
107#13093998C2314yes—
108#13093997—28no—
109Q8×Dic47—22no—
110Q8×Dic47C2314yes—
111#13093989—28no—
112#13093986—22no—
113#13093986C2314yes—
114C4×C22⋊D47D414yes—
115C4×C22⋊D47C2314yes—
116#13093983—22no—
117#13093983C2314yes—
118#13093982—22no—
119#13093982—22no—
120#13093982C2314yes—
121#13093982C2314yes—
122#13093981—28no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4D411yescharacteristic
131C2×C22⋊Dic47—21no—
132C2×C22⋊Dic47D411yescharacteristic
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4D411yescharacteristic
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47C2311yescharacteristic
145#13093958C2314yes—
146#13093957C2314yes—
147#13093957C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150#13093955C2314yes—
151#13093955C2314yes—
152Dic47⋊C8C2314yes—
153#13093948C2314yes—
154#13093946C2314yes—
155#13093946C2314yes—
156#13093944C2314yes—
157(C2×D47)⋊C8C2314yes—
158C8×Dic47C2314yes—
159C22×Q8×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C22×C8×C47C2311yescharacteristic
162C22×C8×C47C2311yescharacteristic
163C22⋊Q8×C47—22no—
164C22⋊Q8×C47C2314yes—
165#117×C47—22no—
166#117×C47C2314yes—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C22⋊C4×C47—21no—
172C2×C22⋊C4×C47—21no—
173C2×C42×C47—21no—
174#107×C47C2314yes—
175#106×C47C2314yes—
176#103×C47C2314yes—
177#103×C47C2314yes—
178C22⋊C8×C47C2314yes—
179C24×C47C2×D411yescharacteristic
180C23×D47—21no—
181C23×D47C2×D411yescharacteristic
182C2×Q8×C47—21no—
183C2×Q8×C47—22no—
184C2×Q8×C47—22no—
185C2×Q8×C47C2412yes—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2411yescharacteristic
196C2×C22⋊D47—24no—
197C2×C22⋊D47—24no—
198C2×C22⋊D47—82no—
199C2×C22⋊D47C2×D414yes—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47C2×D411yescharacteristic
204C22×Dic47C2×D411yescharacteristic
205C22×Dic47C2×D411yescharacteristic
206C2×D188—22no—
207C2×D188—22no—
208C2×D188—21no—
209C2×D188—24no—
210C2×D188—82no—
211C2×D188C2412yes—
212C2×C4×D47—22no—
213C2×C4×D47—22no—
214C2×C4×D47—24no—
215C2×C4×D47—44no—
216C2×C4×D47C2×D412yes—
217C2×C4×D47C2412yes—
218C2×Dic94—24no—
219C2×Dic94—24no—
220C2×Dic94—44no—
221C2×Dic94—82no—
222C2×C8×C47—22no—
223C2×C8×C47—22no—
224C2×C8×C47C2412yes—
225C2×C8×C47C2412yes—
226C4⋊C4×C47—24no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47C2412yes—
231C4⋊C4×C47C2412yes—
232C4⋊C4×C47C2412yes—
233C22⋊C4×C47—24no—
234C22⋊C4×C47—24no—
235C42×C47—24no—
236C22⋊Dic47—24no—
237C22⋊Dic47C2×D414yes—
238#10625336—28no—
239(C2×D47)⋊C4—24no—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4C2×D414yes—
246C4⋊Dic47—21no—
247C4⋊Dic47—21no—
248C4⋊Dic47—21no—
249C4⋊Dic47—24no—
250C4⋊Dic47C2412yes—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4C2×D414yes—
257C4×Dic47—24no—
258C4×Dic47—24no—
259C4×Dic47—24no—
260C4×Dic47—24no—
261C4×Dic47C2×D412yes—
262C4×Dic47C2412yes—
263C2×C47⋊C8—22no—
264C2×C47⋊C8—28no—
265C2×C47⋊C8#4114yes—
266C2×C47⋊C8C2412yes—
267C2×C47⋊C8C2412yes—
268C8×D47—28no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47C22×D412yes—
273C23×C47C22×D411yescharacteristic
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—42no—
279C22×D47—42no—
280C22×D47—42no—
281C22×D47C22×D412yes—
282Q8×C47—22no—
283Q8×C47—22no—
284Q8×C47—42no—
285C2×C4×C47—22no—
286C2×C4×C47—24no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D411yescharacteristic
299C2×C4×C47C2×#4112yes—
300C2×C4×C472−1+412yes—
301C2×C4×C47C2511yescharacteristic
302C22⋊D47—28no—
303C22⋊D47—84no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47#13514yes—
313C2×Dic47C22×D412yes—
314C2×Dic47C22×D412yes—
315C2×Dic47C22×D412yes—
316D188—22no—
317D188—22no—
318D188—42no—
319D188—84no—
320C4×D47—24no—
321C4×D47—22no—
322C4×D47—22no—
323C4×D47—48no—
324Dic94—48no—
325Dic94—84no—
326C8×C47—22no—
327C8×C47—22no—
328C47⋊C8—22no—
329C47⋊C8C2×#4114yes—
330C2×#3340—471nomaximal, Sylow
331C22×C47—22no—
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—44no—
335C22×C47#54712yes—
336C22×C47C2×#13512yes—
337C22×C47#57712yes—
338C22×C47C23×D411yescharacteristic
339C2×D47—22no—
340C2×D47—22no—
341C2×D47—22no—
342C2×D47—44no—
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—42no—
346C2×D47—84no—
347C4×C47—22no—
348C4×C47—42no—
349C4×C47—42no—
350C4×C47—42no—
351C4×C47—42no—
352C4×C47#54712yes—
353C4×C47C22×#4111yescharacteristic
354C4×C47C2×2−1+411yescharacteristic
355Dic47—22no—
356Dic47—22no—
357Dic47—42no—
358Dic47—42no—
359Dic47—42no—
360Dic47C2×#13514yes—
361C2×#556—471no—
362C2×#555—471no—
363#3340—4716no—
364C2×#498—471no—
365C2×#485—471no—
366C2×#485D4711yescharacteristic, complemented
367C2×#482—471no—
368C2×#482—471no—
369C2×#477—471no—
370C2×#474—471no—
371C2×#465—471no—
372C2×#465—471no—
373C2×C4×SD16—471no—
374C2×C8×D4—471no—
375C2×#427—471no—
376C2×#427—471no—
377C2×C47—42no—
378C2×C47#334014yescomplemented
379C2×C47C2×#54711yescharacteristic
380C2×C47C22×#13511yescharacteristic
381C2×C47C2×#57711yescharacteristic
382D47—42no—
383D47—82no—
384C22×SD16—471no—
385C23×C8—471no—
386C23×C8—471no—
387#556—478no—
388#556—944no—
389#555—478no—
390#555—944no—
391C2×C4⋊Q8—471no—
392C2×C4⋊Q8—471no—
393C2×#126—941no—
394C2×#126—941no—
395C2×#124—941no—
396C2×#124—941no—
397C2×#124—941no—
398C2×C22⋊Q8—471no—
399C2×C22⋊Q8C2×D4711yescharacteristic
400C2×#121—471no—
401C2×#121—471no—
402C2×#121—941no—
403C2×C4×Q8—471no—
404C2×C4×Q8—941no—
405C2×C4×D4—471no—
406C2×C4×D4—471no—
407C2×#117—471no—
408C2×#117—471no—
409C2×#117—471no—
410C2×#117—941no—
411C2×#117C2×D4711yescharacteristic
412#498—478no—
413#485—478no—
414#485C2×D4718yescomplemented
415#482—478no—
416#482—478no—
417#477—478no—
418#474—478no—
419#465—478no—
420#465—478no—
421C4×SD16—478no—
422C8×D4—478no—
423#427—478no—
424#427—478no—
425C2×#107—471no—
426C2×#107—471no—
427C2×#107—471no—
428C2×#107C2×D4711yescharacteristic
429C2×#106—471no—
430C2×#106—471no—
431C2×#106—471no—
432C2×#106—471no—
433C2×#106C2×D4711yescharacteristic
434C2×C4⋊C8—471no—
435C2×#103—471no—
436C2×#103C2×D4711yescharacteristic
437C2×#103C2×D4711yescharacteristic
438C2×#102—471no—
439C2×#102—471no—
440C2×#102—471no—
441C2×C22⋊C8—471no—
442C2×C22⋊C8C2×D4711yescharacteristic
443C2×C4×C8—471no—
444C47C2×#334011yescharacteristic, complemented, Sylow
445C22×Q8—941no—
446C22×Q8—941no—
447C22×Q8C22×D4711yescharacteristic
448C22×D4—471no—
449C22×D4—471no—
450C22×D4—941no—
451C22×D4—941no—
452C23×C4—471no—
453C23×C4—941no—
454C23×C4C22×D4711yescharacteristic
455C2×SD16—474no—
456C2×SD16—944no—
457C22×C8—471no—
458C22×C8—471no—
459C22×C8—474no—
460C22×C8—474no—
461C22×C8—944no—
462C22×C8—944no—
463C22×C8C22×D4711yescharacteristic
464C22×C8C22×D4711yescharacteristic
465C4⋊Q8—474no—
466C4⋊Q8—474no—
467C4⋊Q8—942no—
468C4⋊Q8—942no—
469#126—948no—
470#126—948no—
471#124—948no—
472#124—948no—
473#124—948no—
474C22⋊Q8—22no—
475C22⋊Q8—474no—
476C22⋊Q8—942no—
477C22⋊Q8C22×D4714yes—
478#121—474no—
479#121—474no—
480#121—948no—
481#121—942no—
482#121—942no—
483C4×Q8—474no—
484C4×Q8—942no—
485C4×Q8—948no—
486C4×D4—474no—
487C4×D4—474no—
488C4×D4—474no—
489C4×D4—942no—
490#117—22no—
491#117—474no—
492#117—474no—
493#117—474no—
494#117—948no—
495#117—942no—
496#117—942no—
497#117—942no—
498#117C22×D4714yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—471no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4—941no—
508C2×C4⋊C4C22×D4711yescharacteristic
509C2×C4⋊C4C22×D4711yescharacteristic
510C2×C4⋊C4C22×D4711yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—471no—
514C2×C22⋊C4—471no—
515C2×C22⋊C4—941no—
516C2×C22⋊C4—941no—
517C2×C22⋊C4—941no—
518C2×C22⋊C4—941no—
519C2×C22⋊C4—941no—
520C2×C22⋊C4—941no—
521C2×C22⋊C4—941no—
522C2×C42—21no—
523C2×C42—471no—
524C2×C42—941no—
525C2×C42—941no—
526C2×C42—941no—
527C2×C42—941no—
528#107—474no—
529#107—474no—
530#107—474no—
531#107C22×D4714yes—
532#106—474no—
533#106—474no—
534#106—474no—
535#106—474no—
536#106C22×D4714yes—
537C4⋊C8—474no—
538#103—474no—
539#103C22×D4714yes—
540#103C22×D4714yes—
541#102—474no—
542#102—474no—
543#102—474no—
544C22⋊C8—474no—
545C22⋊C8C22×D4714yes—
546C4×C8—474no—
547C24—471no—
548C24—941no—
549C24D4×D4711yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—944no—
554C2×Q8—944no—
555C2×Q8—3762no—
556C2×Q8—1884no—
557C2×Q8C23×D4712yes—
558C2×D4—474no—
559C2×D4—472no—
560C2×D4—944no—
561C2×D4—944no—
562C2×D4—944no—
563C2×D4—941no—
564C2×D4—942no—
565C2×D4—942no—
566C2×D4—3762no—
567C2×D4—3762no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—471no—
575C22×C4—471no—
576C22×C4—471no—
577C22×C4—472no—
578C22×C4—472no—
579C22×C4—944no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—1884no—
586C22×C4D4×D4712yes—
587C22×C4D4×D4711yescharacteristic
588C22×C4C23×D4712yes—
589C22×C4C23×D4711yescharacteristic
590SD16—948no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—474no—
594C2×C8—472no—
595C2×C8—472no—
596C2×C8—948no—
597C2×C8—948no—
598C2×C8—942no—
599C2×C8C23×D4712yes—
600C2×C8C23×D4712yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—474no—
606C4⋊C4—472no—
607C4⋊C4—472no—
608C4⋊C4—472no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4—941no—
614C4⋊C4—941no—
615C4⋊C4—941no—
616C4⋊C4C23×D4712yes—
617C4⋊C4C23×D4712yes—
618C4⋊C4C23×D4712yes—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—474no—
622C22⋊C4—474no—
623C22⋊C4—944no—
624C22⋊C4—944no—
625C22⋊C4—944no—
626C22⋊C4—944no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C22⋊C4—944no—
630C42—24no—
631C42—472no—
632C42—472no—
633C42—944no—
634C42—944no—
635C42—944no—
636C42—944no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—472no—
641C23—942no—
642C23—942no—
643C23—942no—
644C23—942no—
645C23—1882no—
646C23—1882no—
647C23—1882no—
648C23C2×D4×D4712yes—
649C23C2×D4×D4711yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—3764no—
654Q8—1888no—
655D4—948no—
656D4—942no—
657D4—942no—
658D4—3764no—
659D4—3764no—
660D4—1882no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—474no—
674C2×C4—472no—
675C2×C4—472no—
676C2×C4—472no—
677C2×C4—942no—
678C2×C4—942no—
679C2×C4—944no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—1888no—
686C2×C4—1882no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4C2×D4×D4712yes—
690C2×C4C2×D4×D4711yescharacteristic
691C2×C4#41×D4712yes—
692C2×C4#1309407112yes—
693C2×C4C24×D4711yescharacteristic
694C8—22no—
695C8—22no—
696C8—474no—
697C8—942no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—942no—
703C22—942no—
704C22—942no—
705C22—3764no—
706C22—1882no—
707C22—1882no—
708C22—1882no—
709C22—1884no—
710C22#1568977112yes—
711C22#135×D4712yes—
712C22#1568993212yes—
713C22C22×D4×D4711yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—474no—
720C4—942no—
721C4—942no—
722C4—1882no—
723C4—1882no—
724C4—1882no—
725C4#1568977112yes—
726C4C2×#41×D4711yescharacteristic
727C4C2×#1309407111yescharacteristic
728C2—42no—
729C2—3762no—
730C2—1882no—
731C2#2025579414yesdirect product factor
732C2C2×#1568977111yescharacteristic
733C2C2×#135×D4711yescharacteristic
734C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#485C2
socleC23×C47C22×D4
prime radicalC2×#15689836C2
hypercenterC2×#485D47
hypocenterC47C2×#3340
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#15689844C2semidirect
3. #20255794C2direct (N × H)
4. C2×#15689520C2semidirect
5. C2×#15689462C2semidirect
6. C2×#15689449C2semidirect
7. C2×#15689448C2semidirect
8. C2×#15689416C2semidirect
9. C2×#15689402C2semidirect
10. C2×#15689355C2semidirect
11. C2×#15689354C2semidirect
12. C2×#15689208C2semidirect
13. C2×(C22⋊D47)⋊C8C2semidirect
14. C2×#15689160C2semidirect
15. C2×#15689159C2semidirect
16. C2×C47×#485C2semidirect
21. #15689844C22semidirect
43. #15689520C22semidirect
44. #15689462C22semidirect
45. #15689449C22semidirect
46. #15689448C22semidirect
47. #15689416C22semidirect
48. #15689402C22semidirect
49. #15689355C22semidirect
50. #15689354C22semidirect
51. #15689208C22semidirect
52. (C22⋊D47)⋊C8C22semidirect
53. #15689160C22semidirect
54. #15689159C22semidirect
71. C47×#485C22semidirect
366. C2×#485D47semidirect
378. C2×C47#3340semidirect
414. #485C2×D47semidirect
444. C47C2×#3340semidirect
731. C2#20255794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898442
C2×#156898362
#202557942
C2×#156895202
C2×#156894622
C2×#156894492
C2×#156894482
C2×#156894162
C2×#156894022
C2×#156893552
C2×#156893542
C2×#156892082
C2×(C22⋊D47)⋊C82
C2×#156891602
C2×#156891592
C2×C47×#4852
C2×#334047