Finite Group Databasebeta

← C2×#20244665 #26244113

Subgroups — C2×#20244665 #26244113

Order 12032.

1322 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689171C211yesmaximal, characteristic, complemented
2C2×#15689140C211yesmaximal, characteristic
3C2×#15689132C211yesmaximal, characteristic, complemented
4C2×#15689107C211yesmaximal, characteristic
5C22×#13093943C211yesmaximal, characteristic, complemented
6#20244665C218yesmaximal, direct product factor
7C2×#15688895C211yesmaximal, characteristic, complemented
8C22×#137×C47C211yesmaximal, characteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12C2×#13093983C2211yescharacteristic
13#15689171—22no—
14#15689171C2214yescomplemented
15C2×#13093959—22no—
16#15689140—22no—
17#15689140C2214yes—
18C2×#13093951—22no—
19#15689132—22no—
20#15689132C2214yescomplemented
21C2×#13093948—22no—
22#15689107—22no—
23#15689107C2214yes—
24C2×#13093943—22no—
25C2×#13093943—22no—
26C2×#13093943—21no—
27C2×#13093943C2214yescomplemented
28C2×#13093941—21no—
29#15688895C2214yescomplemented
30C22×#41×C47C2211yescharacteristic
31C23×Q8×C47C2211yescharacteristic
32C2×#137×C47—22no—
33C2×#137×C47—22no—
34C2×#137×C47—22no—
35C2×#137×C47—22no—
36C2×#137×C47—22no—
37C2×#137×C47C2214yes—
38C22×Q16×C47—21no—
39C22×SD16×C47—21no—
40C22×M16×C47C2211yescharacteristic
41C2×#10625329—21no—
42C2×#10625329—21no—
43C2×#10625329—21no—
44C2×#10625329—21no—
45C2×#10625329—21no—
46C2×#10625329—21no—
47C2×#10625329—21no—
48C2×#10625329—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329D412yes—
55C2×#10625329D412yes—
56C2×#10625329C2312yes—
57C2×#10625329C2312yes—
58C2×#10625329C2312yes—
59C22×C47⋊C8—21no—
60C22×C47⋊C8—21no—
61C22×C47⋊C8—21no—
62#13093983—21no—
63#13093983—21no—
64#13093983—21no—
65#13093983C2312yes—
66C2×C4⋊Dic47—21no—
67C2×C22⋊Dic47—21no—
68C2×C4×Dic47—21no—
69#13093959—28no—
70#13093951—28no—
71#13093948—28no—
72#13093943—24no—
73#13093943—28no—
74#13093941—24no—
75C2×#41×C47—21no—
76C2×#41×C47—21no—
77C2×#41×C47—21no—
78C2×#41×C47—21no—
79C2×#41×C47—21no—
80C2×#41×C47—21no—
81C2×#41×C47—21no—
82C2×#41×C47—21no—
83C2×#41×C47—21no—
84C2×#41×C47—21no—
85C2×#41×C47D412yes—
86C2×#41×C47C2312yes—
87C22×Q8×C47—21no—
88C22×Q8×C47—21no—
89C22×Q8×C47—21no—
90C22×Q8×C47—21no—
91C22×Q8×C47—21no—
92C22×Q8×C47—21no—
93C22×Q8×C47—21no—
94C22×Q8×C47—21no—
95C22×Q8×C47—21no—
96C22×Q8×C47—21no—
97C22×Q8×C47—21no—
98C22×Q8×C47D411yescharacteristic
99C22×Q8×C47D412yes—
100C22×Q8×C47D412yes—
101C22×Q8×C47C2312yes—
102C22×D4×C47—21no—
103C22×D4×C47D411yescharacteristic
104C23×C4×C47—21no—
105C23×C4×C47—21no—
106C23×C4×C47C2311yescharacteristic
107#137×C47—28no—
108#137×C47—28no—
109#137×C47—28no—
110#137×C47—28no—
111C2×Q16×C47—24no—
112C2×Q16×C47—24no—
113C2×Q16×C47—24no—
114C2×SD16×C47—24no—
115C2×SD16×C47—24no—
116C2×SD16×C47—24no—
117C2×M16×C47—21no—
118C2×M16×C47—21no—
119C2×M16×C47—21no—
120C2×M16×C47D412yes—
121C2×M16×C47D412yes—
122C2×M16×C47C2312yes—
123C22×C8×C47—21no—
124C24×C47—21no—
125C24×C47#4111yescharacteristic
126#41×C47—22no—
127#41×C47—22no—
128#41×C47—22no—
129#41×C47—22no—
130#41×C47—22no—
131#41×C47—22no—
132#41×C47—22no—
133#41×C47—22no—
134#41×C47—41no—
135#41×C47—41no—
136#41×C47—41no—
137#41×C47—41no—
138#41×C47—41no—
139#41×C47—41no—
140#41×C47—41no—
141#41×C47—41no—
142C2×Q8×C47—22no—
143C2×Q8×C47—22no—
144C2×Q8×C47—21no—
145C2×Q8×C47—22no—
146C2×Q8×C47—22no—
147C2×Q8×C47—22no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—22no—
151C2×Q8×C47—22no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—22no—
155C2×Q8×C47—22no—
156C2×Q8×C47—22no—
157C2×Q8×C47—22no—
158C2×Q8×C47—22no—
159C2×Q8×C47—22no—
160C2×Q8×C47—22no—
161C2×Q8×C47—22no—
162C2×Q8×C47—41no—
163C2×Q8×C47—41no—
164C2×Q8×C47—41no—
165C2×Q8×C47—41no—
166C2×Q8×C47—41no—
167C2×Q8×C47—41no—
168C2×Q8×C47—41no—
169C2×Q8×C47—41no—
170C2×Q8×C47—41no—
171C2×Q8×C47—41no—
172C2×Q8×C47—41no—
173C2×Q8×C47—41no—
174C2×Q8×C47C2×D412yes—
175C2×Q8×C47C2×D414yes—
176C2×D4×C47—22no—
177C2×D4×C47—22no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47—21no—
183C2×D4×C47—41no—
184C2×D4×C47—41no—
185C2×D4×C47—41no—
186C2×D4×C47—41no—
187C2×D4×C47C2×D412yes—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47—21no—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—41no—
195C22×C4×C47—41no—
196C22×C4×C47—41no—
197C22×C4×C47—41no—
198C22×C4×C47—41no—
199C22×C4×C47—41no—
200C22×C4×C47—41no—
201C22×C4×C47—41no—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47#4111yescharacteristic
211C22×C4×C47#4111yescharacteristic
212C22×C4×C47#4111yescharacteristic
213C22×C4×C47#4111yescharacteristic
214C22×C4×C47#4111yescharacteristic
215C22×C4×C47C2411yescharacteristic
216C22×Dic47—41no—
217Q16×C47—216no—
218SD16×C47—216no—
219M16×C47—22no—
220M16×C47—22no—
221M16×C47—22no—
222M16×C47C2×D414yes—
223C2×C8×C47—22no—
224C2×C8×C47—22no—
225C2×C8×C47—22no—
226C22⋊Dic47—22no—
227C22⋊Dic47—41no—
228C4⋊Dic47—22no—
229C4⋊Dic47—41no—
230C4×Dic47—22no—
231C4×Dic47—41no—
232#10625329—22no—
233#10625329—22no—
234#10625329—22no—
235#10625329—22no—
236#10625329—22no—
237#10625329—22no—
238#10625329—22no—
239#10625329—41no—
240#10625329—41no—
241#10625329—41no—
242#10625329—41no—
243#10625329C2×D414yes—
244C2×C47⋊C8—22no—
245C2×C47⋊C8—22no—
246C2×C47⋊C8—22no—
247C2×C47⋊C8—22no—
248C2×C47⋊C8—22no—
249C2×C47⋊C8—41no—
250C2×C47⋊C8—41no—
251C2×C47⋊C8—41no—
252C2×C47⋊C8—41no—
253C23×C47—22no—
254C23×C47—42no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—82no—
258C23×C47#12111yescharacteristic
259C23×C47#12111yescharacteristic
260C23×C47#12311yescharacteristic
261C23×C47#12311yescharacteristic
262C23×C47#12411yescharacteristic
263C23×C47#12411yescharacteristic
264C23×C47C2×#4111yescharacteristic
265Q8×C47—24no—
266Q8×C47—22no—
267Q8×C47—22no—
268Q8×C47—24no—
269Q8×C47—42no—
270Q8×C47—42no—
271Q8×C47—42no—
272Q8×C47—42no—
273Q8×C47—42no—
274Q8×C47—42no—
275Q8×C47—41no—
276Q8×C47—41no—
277D4×C47—22no—
278D4×C47—22no—
279D4×C47—42no—
280D4×C47—42no—
281D4×C47—42no—
282D4×C47—42no—
283D4×C47—41no—
284D4×C47—41no—
285C2×C4×C47—24no—
286C2×C4×C47—22no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47#12011yescharacteristic
300C2×C4×C47#12011yescharacteristic
301C2×C4×C47#12011yescharacteristic
302C2×C4×C47#12011yescharacteristic
303C2×C4×C47#12111yescharacteristic
304C2×C4×C47#12111yescharacteristic
305C2×C4×C47#12111yescharacteristic
306C2×C4×C47#12111yescharacteristic
307C2×C4×C47#12111yescharacteristic
308C2×C4×C47#12111yescharacteristic
309C2×C4×C47#12111yescharacteristic
310C2×C4×C47#12111yescharacteristic
311C2×C4×C47#12111yescharacteristic
312C2×C4×C47#12111yescharacteristic
313C2×C4×C47#12311yescharacteristic
314C2×C4×C47#12311yescharacteristic
315C2×C4×C47#12311yescharacteristic
316C2×C4×C47#12311yescharacteristic
317C2×C4×C47#12311yescharacteristic
318C2×C4×C47#12311yescharacteristic
319C2×C4×C47#12411yescharacteristic
320C2×C4×C47#12411yescharacteristic
321C2×C4×C47C22×D411yescharacteristic
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C22×D411yescharacteristic
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C2×#4111yescharacteristic
326C2×C4×C47C2×#4111yescharacteristic
327C2×Dic47—42no—
328C2×Dic47—82no—
329C8×C47—24no—
330C47⋊C8—24no—
331C47⋊C8—42no—
332C47⋊C8—42no—
333C2×#2049—471nomaximal, Sylow
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—42no—
342C22×C47—82no—
343C22×C47—82no—
344C22×C47—82no—
345C22×C47#39411yescharacteristic
346C22×C47#39411yescharacteristic
347C22×C47#39411yescharacteristic
348C22×C47#39411yescharacteristic
349C22×C47C2×#12111yescharacteristic
350C22×C47C2×#12311yescharacteristic
351C22×C47C2×#12411yescharacteristic
352C4×C47—42no—
353C4×C47—44no—
354C4×C47#39411yescharacteristic
355C4×C47#39411yescharacteristic
356C4×C47#39411yescharacteristic
357C4×C47#39411yescharacteristic
358C4×C47C2×#12011yescharacteristic
359C4×C47C2×#12111yescharacteristic
360C4×C47C2×#12111yescharacteristic
361C4×C47C2×#12311yescharacteristic
362Dic47—82no—
363C22×#137D4711yescharacteristic
364C2×#430—471no—
365C2×#421—471no—
366C2×#419—471no—
367C2×#413—471no—
368C22×#101—471no—
369#2049—478no—
370C2×#344—471no—
371C2×C47—21no—
372C2×C47—21no—
373C2×C47—21no—
374C2×C47—21no—
375C2×C47—21no—
376C2×C47—21no—
377C2×C47—82no—
378C2×C47#204912yescomplemented
379C2×C47C2×#39411yescharacteristic
380C22×#41C2×D4711yescharacteristic
381C23×Q8C2×D4711yescharacteristic
382C2×#137—22no—
383C2×#137—22no—
384C2×#137—22no—
385C2×#137—22no—
386C2×#137—22no—
387C2×#137C2×D4714yes—
388C22×Q16—21no—
389C22×SD16—21no—
390C22×M16—471no—
391C22×M16—471no—
392C22×M16—471no—
393C22×M16C2×D4711yescharacteristic
394C2×#117—471no—
395#430—474no—
396#430—942no—
397C2×#108—942no—
398#421—474no—
399#421—942no—
400C2×#104—942no—
401#419—474no—
402#419—942no—
403C2×#103—942no—
404#413—474no—
405#413—942no—
406C2×#101—474no—
407C2×#101—942no—
408C2×#101—942no—
409C2×#101—941no—
410C2×#100—941no—
411#344—474no—
412C47C2×#204911yescharacteristic, complemented, Sylow
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41C22⋊D4712yes—
424C2×#41C22×D4712yes—
425C22×Q8—21no—
426C22×Q8—21no—
427C22×Q8—21no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—21no—
432C22×Q8—21no—
433C22×Q8—21no—
434C22×Q8—21no—
435C22×Q8—21no—
436C22×Q8C22⋊D4711yescharacteristic
437C22×Q8C22⋊D4712yes—
438C22×Q8C22⋊D4712yes—
439C22×Q8C22×D4712yes—
440C22×D4—21no—
441C22×D4C22⋊D4711yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4C22×D4711yescharacteristic
445#137—28no—
446#137—28no—
447#137—28no—
448#137—28no—
449C2×Q16—24no—
450C2×Q16—24no—
451C2×Q16—24no—
452C2×SD16—24no—
453C2×SD16—24no—
454C2×SD16—24no—
455C2×M16—21no—
456C2×M16—21no—
457C2×M16—21no—
458C2×M16—472no—
459C2×M16—472no—
460C2×M16—472no—
461C2×M16—472no—
462C2×M16—472no—
463C2×M16—941no—
464C2×M16—941no—
465C2×M16—941no—
466C2×M16—941no—
467C2×M16—941no—
468C2×M16—941no—
469C2×M16—941no—
470C2×M16—941no—
471C2×M16—941no—
472C2×M16—941no—
473C2×M16—941no—
474C2×M16—941no—
475C2×M16—941no—
476C2×M16C22⋊D4712yes—
477C2×M16C22⋊D4712yes—
478C2×M16C22×D4712yes—
479C22×C8—21no—
480C22×C8—941no—
481C22×C8—941no—
482C22×C8—941no—
483#117—472no—
484#117—941no—
485#117—941no—
486#117—941no—
487C2×C4⋊C4—941no—
488C2×C22⋊C4—941no—
489C2×C42—941no—
490#108—948no—
491#104—948no—
492#103—948no—
493#101—948no—
494#101—944no—
495#100—944no—
496C24—21no—
497C24#1062535211yescharacteristic
498#41—22no—
499#41—22no—
500#41—22no—
501#41—22no—
502#41—22no—
503#41—22no—
504#41—22no—
505#41—22no—
506#41—41no—
507#41—41no—
508#41—41no—
509#41—41no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—41no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—21no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8C2×C22⋊D4712yes—
547C2×Q8C2×C22⋊D4714yes—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4C2×C22⋊D4712yes—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—1881no—
575C22×C4D4×D4711yescharacteristic
576C22×C4D4×D4711yescharacteristic
577C22×C4#1062535211yescharacteristic
578C22×C4#1062535211yescharacteristic
579C22×C4#1062535211yescharacteristic
580C22×C4#1062535211yescharacteristic
581C22×C4#1062535211yescharacteristic
582C22×C4C2×C22⋊D4711yescharacteristic
583C22×C4C2×C22⋊D4711yescharacteristic
584C22×C4C2×C22⋊D4711yescharacteristic
585C22×C4C2×C22⋊D4711yescharacteristic
586C22×C4C2×C22⋊D4711yescharacteristic
587C22×C4C2×C22⋊D4711yescharacteristic
588C22×C4C23×D4711yescharacteristic
589Q16—216no—
590SD16—216no—
591M16—22no—
592M16—22no—
593M16—22no—
594M16—474no—
595M16—942no—
596M16—942no—
597M16—942no—
598M16—942no—
599M16—942no—
600M16—942no—
601M16—942no—
602M16—1881no—
603M16—1881no—
604M16—1881no—
605M16—1881no—
606M16C2×C22⋊D4714yes—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—942no—
611C2×C8—942no—
612C2×C8—942no—
613C2×C8—942no—
614C2×C8—942no—
615C2×C8—1881no—
616C2×C8—1881no—
617C2×C8—1881no—
618C2×C8—1881no—
619C4⋊C4—942no—
620C4⋊C4—1881no—
621C22⋊C4—942no—
622C22⋊C4—1881no—
623C42—942no—
624C42—1881no—
625C23—22no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—82no—
630C23#1309399611yescharacteristic
631C23#1309399611yescharacteristic
632C23#1309400511yescharacteristic
633C23#1309400511yescharacteristic
634C23#1309401111yescharacteristic
635C23#1309401111yescharacteristic
636C23C2×#1062535211yescharacteristic
637Q8—24no—
638Q8—22no—
639Q8—22no—
640Q8—24no—
641Q8—42no—
642Q8—42no—
643Q8—42no—
644Q8—42no—
645Q8—41no—
646Q8—41no—
647Q8—42no—
648Q8—42no—
649D4—22no—
650D4—22no—
651D4—42no—
652D4—42no—
653D4—42no—
654D4—42no—
655D4—41no—
656D4—41no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—3762no—
672C2×C4—1882no—
673C2×C4#1309399311yescharacteristic
674C2×C4#1309399311yescharacteristic
675C2×C4#1309399311yescharacteristic
676C2×C4#1309399311yescharacteristic
677C2×C4#1309399511yescharacteristic
678C2×C4#1309399511yescharacteristic
679C2×C4#1309399511yescharacteristic
680C2×C4#1309399511yescharacteristic
681C2×C4#1309399611yescharacteristic
682C2×C4#1309399611yescharacteristic
683C2×C4#1309399611yescharacteristic
684C2×C4#1309399611yescharacteristic
685C2×C4#1309399611yescharacteristic
686C2×C4#1309399611yescharacteristic
687C2×C4#1309400511yescharacteristic
688C2×C4#1309400511yescharacteristic
689C2×C4#1309400511yescharacteristic
690C2×C4#1309400511yescharacteristic
691C2×C4#1309400511yescharacteristic
692C2×C4#1309400511yescharacteristic
693C2×C4#1309401111yescharacteristic
694C2×C4#1309401111yescharacteristic
695C2×C4C2×D4×D4711yescharacteristic
696C2×C4C22×C22⋊D4711yescharacteristic
697C2×C4C22×C22⋊D4711yescharacteristic
698C2×C4C22×C22⋊D4711yescharacteristic
699C2×C4C2×#1062535211yescharacteristic
700C2×C4C2×#1062535211yescharacteristic
701C8—24no—
702C8—944no—
703C8—1882no—
704C8—1882no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22#1568903711yescharacteristic
717C22#1568903711yescharacteristic
718C22#1568903711yescharacteristic
719C22#1568903711yescharacteristic
720C22C2×#1309399611yescharacteristic
721C22C2×#1309400511yescharacteristic
722C22C2×#1309401111yescharacteristic
723C4—42no—
724C4—44no—
725C4—3762no—
726C4#1568903711yescharacteristic
727C4#1568903711yescharacteristic
728C4#1568903711yescharacteristic
729C4#1568903711yescharacteristic
730C4C2×#1309399311yescharacteristic
731C4C2×#1309399511yescharacteristic
732C4C2×#1309399611yescharacteristic
733C4C2×#1309400511yescharacteristic
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—82no—
741C2#2024466512yesdirect product factor
742C2C2×#1568903711yescharacteristic
subgroupG/H
centerC22#15689037
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×#137×C47C2
socleC22×C47#394
prime radicalC22×#41×C47C22
hypercenterC22×#137D47
hypocenterC47C2×#2049
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C2×#15689171C2semidirect
3. C2×#15689132C2semidirect
5. C22×#13093943C2semidirect
6. #20244665C2direct (N × H)
7. C2×#15688895C2semidirect
14. #15689171C22semidirect
20. #15689132C22semidirect
27. C2×#13093943C22semidirect
29. #15688895C22semidirect
378. C2×C47#2049semidirect
412. C47C2×#2049semidirect
741. C2#20244665direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156891712
C2×#156891402
C2×#156891322
C2×#156891072
C22×#130939432
#202446652
C2×#156888952
C22×#137×C472
C2×#204947