Finite Group Databasebeta

← C2×#20243864 #26218138

Subgroups — C2×#20243864 #26218138

Order 12032.

1654 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094055C211yesmaximal, characteristic
2C2×#15689889C211yesmaximal, characteristic
3C2×#15689139C211yesmaximal, characteristic
4C2×#15689132C211yesmaximal, characteristic, complemented
5#20243864C218yesmaximal, direct product factor
6C2×#15688895C211yesmaximal, characteristic, complemented
7C2×C47⋊#338C211yesmaximal, characteristic, complemented
8C22×#101×C47C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C2×#13094055—22no—
11C2×#13094055—22no—
12C2×#13094055—22no—
13C2×#13094055—22no—
14C2×#13094055C414yescomplemented
15C2×#13094055C2214yes—
16C22×#10625337C412yescomplemented
17C22×#10625336C412yescomplemented
18#15689889—22no—
19#15689889—22no—
20#15689889—22no—
21#15689889C2214yes—
22C2×#13094032—22no—
23C2×#13094030—22no—
24C22×#10625329C2211yescharacteristic
25C22×#10625329C2211yescharacteristic
26C2×M16×D47—22no—
27C2×#13093983C2211yescharacteristic
28#15689139—22no—
29#15689139C2214yes—
30C2×#13093950—22no—
31#15689132—22no—
32#15689132C2214yescomplemented
33C2×#13093948—22no—
34#15688895C2214yescomplemented
35C47⋊#338C2214yescomplemented
36C23×Q8×C47C2211yescharacteristic
37C22×M16×C47C2211yescharacteristic
38C22×M16×C47C2211yescharacteristic
39C2×#101×C47—22no—
40C2×#101×C47—22no—
41C2×#101×C47C2214yescomplemented
42C2×#10625350—21no—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350C2×C412yes—
49C2×#10625350D412yes—
50C2×#10625350D412yes—
51C2×#10625350D412yes—
52C2×#10625350D412yes—
53C2×#10625350C2312yes—
54C22×Dic94C2×C411yescharacteristic
55C22×D188C2×C411yescharacteristic
56C22×C22⋊D47—21no—
57C22×C4×D47—21no—
58#13094055—28no—
59#13094055—28no—
60#13094055—28no—
61#13094055—28no—
62C2×#10625337—24no—
63C2×#10625337—24no—
64C2×#10625337C2×C418yescomplemented
65C2×#10625336—24no—
66C2×#10625336—24no—
67C2×#10625336C2×C418yescomplemented
68#13094032—28no—
69#13094032—28no—
70#13094030—28no—
71#13094030—28no—
72C2×#10625329—21no—
73C2×#10625329—21no—
74C2×#10625329—21no—
75C2×#10625329—21no—
76C2×#10625329—21no—
77C2×#10625329—21no—
78C2×#10625329—21no—
79C2×#10625329—21no—
80C2×#10625329C2×C412yes—
81C2×#10625329D412yes—
82C2×#10625329C2312yes—
83C2×#10625329C2312yes—
84C2×#10625324—24no—
85M16×D47—28no—
86M16×D47—28no—
87C22×C47⋊C8C2×C412yes—
88C22×C47⋊C8D412yes—
89C2×C8×D47—24no—
90#13093983—21no—
91#13093983—21no—
92#13093983—21no—
93#13093983C2312yes—
94C2×C4⋊Dic47—21no—
95C2×C22⋊Dic47—21no—
96C2×C4×Dic47—21no—
97#13093950—28no—
98#13093948—28no—
99C22×Q8×C47—21no—
100C22×Q8×C47—21no—
101C22×Q8×C47—21no—
102C22×Q8×C47—21no—
103C22×Q8×C47—21no—
104C22×Q8×C47—21no—
105C22×Q8×C47—21no—
106C22×Q8×C47—21no—
107C22×Q8×C47—21no—
108C22×Q8×C47—21no—
109C22×Q8×C47—21no—
110C22×Q8×C47C2×C412yes—
111C22×Q8×C47C2×C412yes—
112C22×Q8×C47C2312yes—
113C23×C4×C47—21no—
114C23×C4×C47C2311yescharacteristic
115C2×M16×C47—21no—
116C2×M16×C47—21no—
117C2×M16×C47—21no—
118C2×M16×C47—21no—
119C2×M16×C47—21no—
120C2×M16×C47—21no—
121C2×M16×C47—21no—
122C2×M16×C47—21no—
123C2×M16×C47D412yes—
124C2×M16×C47D412yes—
125C2×M16×C47C2312yes—
126C2×M16×C47C2312yes—
127C22×C8×C47—21no—
128C22×C8×C47—21no—
129#101×C47—28no—
130C24×C47#4111yescharacteristic
131C23×D47—21no—
132C2×Q8×C47—22no—
133C2×Q8×C47—22no—
134C2×Q8×C47—22no—
135C2×Q8×C47—22no—
136C2×Q8×C47—22no—
137C2×Q8×C47—22no—
138C2×Q8×C47—22no—
139C2×Q8×C47—22no—
140C2×Q8×C47—22no—
141C2×Q8×C47—22no—
142C2×Q8×C47—22no—
143C2×Q8×C47—22no—
144C2×Q8×C47—22no—
145C2×Q8×C47—22no—
146C2×Q8×C47—22no—
147C2×Q8×C47—41no—
148C2×Q8×C47—41no—
149C2×Q8×C47—41no—
150C2×Q8×C47—41no—
151C2×Q8×C47—41no—
152C2×Q8×C47—41no—
153C2×Q8×C47—41no—
154C2×Q8×C47—41no—
155C2×Q8×C47—41no—
156C2×Q8×C47—41no—
157C2×Q8×C47—41no—
158C2×Q8×C47—41no—
159C2×Q8×C47C22×C414yes—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—41no—
164C22×C4×C47—41no—
165C22×C4×C47—41no—
166C22×C4×C47—41no—
167C22×C4×C47C22×C411yescharacteristic
168C22×C4×C47C22×C411yescharacteristic
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47#4111yescharacteristic
178C22×C4×C47#4111yescharacteristic
179C22×C4×C47#4111yescharacteristic
180C22×C4×C47C2411yescharacteristic
181C2×C22⋊D47—22no—
182C2×C22⋊D47—22no—
183C2×C22⋊D47—22no—
184C2×C22⋊D47—22no—
185C2×C22⋊D47—22no—
186C2×C22⋊D47—22no—
187C22×Dic47—21no—
188C22×Dic47—41no—
189#10625350—22no—
190#10625350—22no—
191#10625350—22no—
192#10625350—22no—
193#10625350—22no—
194#10625350—22no—
195#10625350—22no—
196#10625350—22no—
197#10625350—22no—
198#10625350—22no—
199#10625350—22no—
200#10625350—22no—
201#10625350C22⋊C414yes—
202#10625350C22⋊C414yes—
203#10625350C2×D414yes—
204#10625350C2×D414yes—
205C2×D188—21no—
206C2×D188—21no—
207C2×D188—21no—
208C2×D188C22⋊C412yes—
209C2×D188C22⋊C412yes—
210C2×D188C22×C412yes—
211C2×C4×D47—22no—
212C2×C4×D47—22no—
213C2×C4×D47—22no—
214C2×C4×D47—22no—
215C2×C4×D47—22no—
216C2×C4×D47—22no—
217C2×Dic94—21no—
218C2×Dic94—21no—
219C2×Dic94—21no—
220C2×Dic94C22⋊C412yes—
221C2×Dic94C22⋊C412yes—
222C2×Dic94C22×C412yes—
223M16×C47—22no—
224M16×C47—22no—
225M16×C47—22no—
226M16×C47—22no—
227M16×C47—22no—
228M16×C47—41no—
229M16×C47—41no—
230M16×C47C2×D414yes—
231C2×C8×C47—22no—
232C2×C8×C47—22no—
233C2×C8×C47—22no—
234C2×C8×C47—22no—
235C2×C8×C47—41no—
236C2×C8×C47—41no—
237C22⋊Dic47—22no—
238C22⋊Dic47—41no—
239#10625337—216no—
240#10625336—216no—
241C4⋊Dic47—22no—
242C4⋊Dic47—41no—
243C4×Dic47—22no—
244C4×Dic47—41no—
245#10625329—22no—
246#10625329—22no—
247#10625329—22no—
248#10625329—22no—
249#10625329—22no—
250#10625329—22no—
251#10625329—22no—
252#10625329—22no—
253C2×C47⋊C8—22no—
254C2×C47⋊C8—22no—
255C2×C47⋊C8—22no—
256C2×C47⋊C8—22no—
257C2×C47⋊C8C22×C414yes—
258C2×C47⋊C8C2×D414yes—
259#10625324—216no—
260C8×D47—216no—
261C23×C47—42no—
262C23×C47C4×D411yescharacteristic
263C23×C47C4×D411yescharacteristic
264C23×C47#12111yescharacteristic
265C23×C47#12111yescharacteristic
266C23×C47#12311yescharacteristic
267C23×C47#12311yescharacteristic
268C23×C47C2×#4111yescharacteristic
269C22×D47—22no—
270C22×D47—22no—
271C22×D47—22no—
272C22×D47—82no—
273Q8×C47—24no—
274Q8×C47—24no—
275Q8×C47—42no—
276Q8×C47—42no—
277Q8×C47—42no—
278Q8×C47—42no—
279Q8×C47—42no—
280Q8×C47—42no—
281C2×C4×C47—24no—
282C2×C4×C47—42no—
283C2×C4×C47—42no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47C2×C22⋊C411yescharacteristic
289C2×C4×C47C2×C22⋊C411yescharacteristic
290C2×C4×C47C2×C22⋊C411yescharacteristic
291C2×C4×C47C2×C22⋊C411yescharacteristic
292C2×C4×C47C4×D411yescharacteristic
293C2×C4×C47C4×D411yescharacteristic
294C2×C4×C47C4×D411yescharacteristic
295C2×C4×C47C4×D411yescharacteristic
296C2×C4×C47C4×D411yescharacteristic
297C2×C4×C47C4×D411yescharacteristic
298C2×C4×C47#12011yescharacteristic
299C2×C4×C47#12011yescharacteristic
300C2×C4×C47#12011yescharacteristic
301C2×C4×C47#12011yescharacteristic
302C2×C4×C47#12111yescharacteristic
303C2×C4×C47#12111yescharacteristic
304C2×C4×C47#12111yescharacteristic
305C2×C4×C47#12111yescharacteristic
306C2×C4×C47#12111yescharacteristic
307C2×C4×C47#12111yescharacteristic
308C2×C4×C47#12311yescharacteristic
309C2×C4×C47#12311yescharacteristic
310C2×C4×C47C23×C411yescharacteristic
311C2×C4×C47C22×D411yescharacteristic
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C2×#4111yescharacteristic
316C22⋊D47—24no—
317C22⋊D47—24no—
318C22⋊D47—24no—
319C22⋊D47—24no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—42no—
324C2×Dic47—82no—
325D188—22no—
326D188—22no—
327D188—22no—
328D188C2×C22⋊C414yes—
329C4×D47—24no—
330C4×D47—24no—
331C4×D47—24no—
332C4×D47—24no—
333Dic94—22no—
334Dic94—22no—
335Dic94—22no—
336Dic94C2×C22⋊C414yes—
337C8×C47—24no—
338C8×C47—42no—
339C47⋊C8—24no—
340C47⋊C8—24no—
341C2×#1902—471nomaximal, Sylow
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47#38611yescharacteristic
350C22×C47#38611yescharacteristic
351C22×C47#38611yescharacteristic
352C22×C47#38611yescharacteristic
353C22×C47C2×C4×D411yescharacteristic
354C22×C47C2×#12111yescharacteristic
355C22×C47C2×#12311yescharacteristic
356C2×D47—24no—
357C2×D47—44no—
358C2×D47—82no—
359C2×D47—82no—
360C4×C47—44no—
361C4×C47#38611yescharacteristic
362C4×C47#38611yescharacteristic
363C4×C47#38611yescharacteristic
364C4×C47#38611yescharacteristic
365C4×C47C22×C22⋊C411yescharacteristic
366C4×C47C2×C4×D411yescharacteristic
367C4×C47C2×#12011yescharacteristic
368C4×C47C2×#12111yescharacteristic
369Dic47—24no—
370Dic47—82no—
371C22×#137—471no—
372C2×#568—471no—
373C2×#421—471no—
374C2×#419—471no—
375C22×#101D4711yescharacteristic, complemented
376#1902—478no—
377C2×#344—471no—
378C2×#338—471no—
379C2×C47—21no—
380C2×C47—21no—
381C2×C47—21no—
382C2×C47—21no—
383C2×C47—21no—
384C2×C47—21no—
385C2×C47#190212yescomplemented
386C2×C47C2×#38611yescharacteristic
387D47—44no—
388C22×#41—471no—
389C23×Q8C2×D4711yescharacteristic
390C2×#137—474no—
391C2×#137—474no—
392C2×#137—942no—
393C2×#137—942no—
394C2×#137—942no—
395C2×#137—942no—
396C22×Q16—472no—
397C22×SD16—472no—
398#568—474no—
399#568—942no—
400#568—942no—
401#568—942no—
402C2×#131—942no—
403C2×#131—942no—
404C22×M16—471no—
405C22×M16—471no—
406C22×M16—942no—
407C22×M16C2×D4711yescharacteristic
408C22×M16C2×D4711yescharacteristic
409C2×#117—471no—
410#421—474no—
411#421—942no—
412C2×#104—942no—
413#419—474no—
414#419—942no—
415C2×#103—942no—
416C2×#101—22no—
417C2×#101—22no—
418C2×#101C2×D4714yescomplemented
419#344—474no—
420#338—474no—
421C47C2×#190211yescharacteristic, complemented, Sylow
422C2×#41—472no—
423C2×#41—472no—
424C2×#41—472no—
425C2×#41—472no—
426C2×#41—472no—
427C2×#41—472no—
428C2×#41—941no—
429C2×#41—941no—
430C2×#41—941no—
431C2×#41—941no—
432C2×#41—941no—
433C2×#41—941no—
434C22×Q8—21no—
435C22×Q8—21no—
436C22×Q8—21no—
437C22×Q8—21no—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8—471no—
446C22×Q8C4×D4712yes—
447C22×Q8C4×D4712yes—
448C22×Q8C22×D4712yes—
449C22×D4—471no—
450C22×D4—941no—
451C23×C4—21no—
452C23×C4—941no—
453C23×C4C22×D4711yescharacteristic
454#137—948no—
455#137—948no—
456#137—948no—
457#137—948no—
458C2×Q16—478no—
459C2×Q16—944no—
460C2×Q16—944no—
461C2×SD16—478no—
462C2×SD16—944no—
463C2×SD16—944no—
464#131—948no—
465#131—948no—
466#131—948no—
467#131—948no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—472no—
477C2×M16—472no—
478C2×M16—472no—
479C2×M16—472no—
480C2×M16—944no—
481C2×M16—948no—
482C2×M16—941no—
483C2×M16—941no—
484C2×M16—941no—
485C2×M16—941no—
486C2×M16—941no—
487C2×M16—941no—
488C2×M16—941no—
489C2×M16—941no—
490C2×M16—948no—
491C2×M16C22⋊D4712yes—
492C2×M16C22⋊D4712yes—
493C2×M16C22×D4712yes—
494C2×M16C22×D4712yes—
495C22×C8—21no—
496C22×C8—21no—
497C22×C8—472no—
498C22×C8—472no—
499C22×C8—944no—
500#117—472no—
501#117—941no—
502#117—941no—
503#117—941no—
504C2×C4⋊C4—941no—
505C2×C22⋊C4—941no—
506C2×C42—941no—
507#104—948no—
508#103—948no—
509#101—28no—
510C24—941no—
511C24#1062535011yescharacteristic
512#41—474no—
513#41—474no—
514#41—474no—
515#41—474no—
516#41—942no—
517#41—942no—
518#41—942no—
519#41—942no—
520#41—942no—
521#41—942no—
522#41—942no—
523#41—942no—
524#41—942no—
525#41—942no—
526#41—942no—
527#41—942no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—472no—
556C2×Q8—472no—
557C2×Q8—472no—
558C2×Q8—941no—
559C2×Q8—941no—
560C2×Q8—941no—
561C2×Q8C2×C4×D4714yes—
562C2×D4—472no—
563C2×D4—472no—
564C2×D4—472no—
565C2×D4—942no—
566C2×D4—942no—
567C2×D4—942no—
568C2×D4—942no—
569C2×D4—942no—
570C2×D4—942no—
571C2×D4—941no—
572C2×D4—941no—
573C2×D4—941no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—941no—
582C22×C4—942no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—1881no—
589C22×C4C2×C4×D4711yescharacteristic
590C22×C4C2×C4×D4711yescharacteristic
591C22×C4#1062535011yescharacteristic
592C22×C4D4×D4711yescharacteristic
593C22×C4D4×D4711yescharacteristic
594C22×C4D4×D4711yescharacteristic
595C22×C4D4×D4711yescharacteristic
596C22×C4D4×D4711yescharacteristic
597C22×C4D4×D4711yescharacteristic
598C22×C4#1062535211yescharacteristic
599C22×C4#1062535211yescharacteristic
600C22×C4C2×C22⋊D4711yescharacteristic
601C22×C4C2×C22⋊D4711yescharacteristic
602C22×C4C23×D4711yescharacteristic
603Q16—9416no—
604SD16—9416no—
605M16—22no—
606M16—22no—
607M16—22no—
608M16—22no—
609M16—22no—
610M16—41no—
611M16—41no—
612M16—9416no—
613M16—942no—
614M16—942no—
615M16—942no—
616M16—942no—
617M16—942no—
618M16—942no—
619M16—942no—
620M16—942no—
621M16C2×C22⋊D4714yes—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—474no—
629C2×C8—474no—
630C2×C8—9416no—
631C2×C8—942no—
632C2×C8—942no—
633C2×C8—942no—
634C2×C8—942no—
635C4⋊C4—942no—
636C4⋊C4—1881no—
637C22⋊C4—942no—
638C22⋊C4—1881no—
639C42—942no—
640C42—1881no—
641C23—42no—
642C23—942no—
643C23—942no—
644C23—942no—
645C23—3762no—
646C23C4×C22⋊D4711yescharacteristic
647C23C4×C22⋊D4711yescharacteristic
648C23#1309399711yescharacteristic
649C23#1309399711yescharacteristic
650C23#1309400611yescharacteristic
651C23#1309400611yescharacteristic
652C23C2×#1062535011yescharacteristic
653Q8—24no—
654Q8—24no—
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661Q8—474no—
662Q8—942no—
663Q8—942no—
664Q8—942no—
665D4—474no—
666D4—944no—
667D4—944no—
668D4—944no—
669D4—944no—
670D4—942no—
671D4—942no—
672D4—942no—
673C2×C4—24no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—944no—
684C2×C4—944no—
685C2×C4—944no—
686C2×C4—944no—
687C2×C4—3762no—
688C2×C4—1882no—
689C2×C4C22⋊C4×D4711yescharacteristic
690C2×C4C22⋊C4×D4711yescharacteristic
691C2×C4C22⋊C4×D4711yescharacteristic
692C2×C4C22⋊C4×D4711yescharacteristic
693C2×C4(C22⋊D47)⋊C411yescharacteristic
694C2×C4(C22⋊D47)⋊C411yescharacteristic
695C2×C4(C22⋊D47)⋊C411yescharacteristic
696C2×C4(C22⋊D47)⋊C411yescharacteristic
697C2×C4C4×C22⋊D4711yescharacteristic
698C2×C4C4×C22⋊D4711yescharacteristic
699C2×C4#1309399211yescharacteristic
700C2×C4#1309399211yescharacteristic
701C2×C4#1309399211yescharacteristic
702C2×C4#1309399211yescharacteristic
703C2×C4#1309399511yescharacteristic
704C2×C4#1309399511yescharacteristic
705C2×C4#1309399511yescharacteristic
706C2×C4#1309399511yescharacteristic
707C2×C4#1309399711yescharacteristic
708C2×C4#1309399711yescharacteristic
709C2×C4#1309400611yescharacteristic
710C2×C4#1309400611yescharacteristic
711C2×C4C22×C4×D4711yescharacteristic
712C2×C4C2×D4×D4711yescharacteristic
713C2×C4C2×D4×D4711yescharacteristic
714C2×C4C2×D4×D4711yescharacteristic
715C2×C4C22×C22⋊D4711yescharacteristic
716C2×C4C2×#1062535211yescharacteristic
717C8—24no—
718C8—42no—
719C8—944no—
720C8—944no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—944no—
729C22—3762no—
730C22—3762no—
731C22—1884no—
732C22#1568899911yescharacteristic
733C22#1568899911yescharacteristic
734C22#1568899911yescharacteristic
735C22#1568899911yescharacteristic
736C22C2×C4×C22⋊D4711yescharacteristic
737C22C2×#1309399711yescharacteristic
738C22C2×#1309400611yescharacteristic
739C4—44no—
740C4—944no—
741C4—3762no—
742C4#1568899911yescharacteristic
743C4#1568899911yescharacteristic
744C4#1568899911yescharacteristic
745C4#1568899911yescharacteristic
746C4C2×C22⋊C4×D4711yescharacteristic
747C4C2×(C22⋊D47)⋊C411yescharacteristic
748C4C2×#1309399211yescharacteristic
749C4C2×#1309399511yescharacteristic
750C2—21no—
751C2—21no—
752C2—21no—
753C2—21no—
754C2—21no—
755C2—21no—
756C2—1884no—
757C2#2024386412yesdirect product factor
758C2C2×#1568899911yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#101×C47C2
socleC22×C47#386
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC22×#101D47
hypocenterC47C2×#1902
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
4. C2×#15689132C2semidirect
5. #20243864C2direct (N × H)
6. C2×#15688895C2semidirect
7. C2×C47⋊#338C2semidirect
8. C22×#101×C47C2semidirect
14. C2×#13094055C4semidirect
16. C22×#10625337C4semidirect
17. C22×#10625336C4semidirect
32. #15689132C22semidirect
34. #15688895C22semidirect
35. C47⋊#338C22semidirect
41. C2×#101×C47C22semidirect
64. C2×#10625337C2×C4semidirect
67. C2×#10625336C2×C4semidirect
375. C22×#101D47semidirect
385. C2×C47#1902semidirect
418. C2×#101C2×D47semidirect
421. C47C2×#1902semidirect
757. C2#20243864direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940552
C2×#156898892
C2×#156891392
C2×#156891322
#202438642
C2×#156888952
C2×C47⋊#3382
C22×#101×C472
C2×#190247