Finite Group Databasebeta

← C2×#20253605 #27084544

Subgroups — C2×#20253605 #27084544

Order 12032.

2070 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×#15689733C211yesmaximal, characteristic, complemented
2C2×#15689604C211yesmaximal, characteristic
3#20253605C2116yesmaximal, direct product factor
4C2×#15689458C211yesmaximal, characteristic, complemented
5C2×#15689433C211yesmaximal, characteristic, complemented
6C2×#15689422C211yesmaximal, characteristic, complemented
7C2×#15689332C211yesmaximal, characteristic, complemented
8C2×#15689327C211yesmaximal, characteristic, complemented
9C2×#15689287C211yesmaximal, characteristic
10C2×#15689283C211yesmaximal, characteristic
11C2×#15689229C211yesmaximal, characteristic, complemented
12C2×#15689226C211yesmaximal, characteristic, complemented
13C2×#15689215C211yesmaximal, characteristic, complemented
14C2×#15689210C211yesmaximal, characteristic, complemented
15C2×#15689181C211yesmaximal, characteristic, complemented
16C2×C47×#483C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22#15689733—24no—
23#15689733C2218yescomplemented
24C2×#13094022C2211yescharacteristic
25C2×#13094017—21no—
26C2×#13094017—21no—
27C2×#13094015—21no—
28C2×#13094015C2211yescharacteristic
29C2×#13094014—21no—
30C2×#13094003C2211yescharacteristic
31#15689604—24no—
32#15689604C2218yes—
33C2×Q8×Dic47C2211yescharacteristic
34C2×#13093989C2211yescharacteristic
35C2×#13093989C2211yescharacteristic
36C2×#13093989C2211yescharacteristic
37C2×#13093986C2211yescharacteristic
38C2×#13093986C2211yescharacteristic
39C2×C4×C22⋊D47—21no—
40C2×C4×C22⋊D47—21no—
41C2×#13093983C2211yescharacteristic
42C2×#13093982—21no—
43C2×C4⋊C4×D47—21no—
44#15689458C2218yescomplemented
45#15689433C2218yescomplemented
46#15689422C2218yescomplemented
47#15689332C2218yescomplemented
48#15689327C2218yescomplemented
49#15689287C2218yes—
50#15689283C2218yes—
51#15689229C2218yescomplemented
52#15689226C2218yescomplemented
53#15689215C2218yescomplemented
54#15689210C2218yescomplemented
55#15689181C2218yescomplemented
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×C22⋊Q8×C47C2211yescharacteristic
70C22×C4⋊C4×C47C2211yescharacteristic
71C47×#483C2218yescomplemented
72C2×#106×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350—24no—
80C2×#10625350C2314yes—
81C22×Dic94C2311yescharacteristic
82C22×Dic94C2311yescharacteristic
83C22×D188C2311yescharacteristic
84C22×C22⋊D47—21no—
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C2×Dic188—24no—
89C2×Dic188C2314yes—
90C2×#10625337—24no—
91C2×#10625337C2314yes—
92C2×#10625325—24no—
93C2×#10625325C2314yes—
94C2×#10625336—24no—
95C2×#10625336C2314yes—
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2311yescharacteristic
98#13094022—22no—
99#13094022C2314yes—
100#13094017—28no—
101#13094017—28no—
102#13094015—28no—
103#13094015—22no—
104#13094015C2314yes—
105#13094014—28no—
106#13094003—22no—
107#13094003C2314yes—
108Q8×Dic47—22no—
109Q8×Dic47C2314yes—
110#13093989—22no—
111#13093989—22no—
112#13093989—22no—
113#13093989C2314yes—
114#13093989C2314yes—
115#13093989C2314yes—
116#13093986—22no—
117#13093986—22no—
118#13093986C2314yes—
119#13093986C2314yes—
120C4×C22⋊D47—28no—
121C4×C22⋊D47—28no—
122#13093983D414yes—
123#13093983C2314yes—
124#13093982—28no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47D411yescharacteristic
128C2×C4⋊Dic47D411yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C4⋊C4×D47—28no—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47D411yescharacteristic
140C2×C22⋊Dic47D411yescharacteristic
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47C2311yescharacteristic
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yes—
150#13093957C2314yes—
151Dic47⋊C8C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093947C2314yes—
155#13093947C2314yes—
156#13093947C2314yes—
157#13093946C2314yes—
158#13093944C2314yes—
159C22⋊(C47⋊C8)C2314yes—
160#13093934C2314yes—
161C8×Dic47C2314yes—
162C22×Q8×C47C2311yescharacteristic
163C23×C4×C47—21no—
164C23×C4×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22⋊Q8×C47—22no—
168C22⋊Q8×C47C2314yes—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47—22no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2314yes—
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C22⋊C4×C47—21no—
177#106×C47C2314yes—
178#106×C47C2314yes—
179#103×C47C2314yes—
180#103×C47C2314yes—
181C22⋊C8×C47C2314yes—
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—22no—
186C2×Q8×C47—22no—
187C2×Q8×C47C2412yes—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—24no—
195C22×C4×C47—82no—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D412yes—
198C22×C4×C47C2412yes—
199C22×C4×C47C2411yescharacteristic
200C2×C22⋊D47—28no—
201C2×C22⋊D47—24no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209#10625350—216no—
210#10625350—28no—
211#10625350—28no—
212C2×D188—21no—
213C2×D188—22no—
214C2×D188#4114yes—
215C2×D188C2412yes—
216C2×C4×D47—28no—
217C2×C4×D47—24no—
218C2×C4×D47—24no—
219C2×C4×D47—24no—
220C2×C4×D47—82no—
221C2×C4×D47—82no—
222C2×Dic94—21no—
223C2×Dic94—22no—
224C2×Dic94—22no—
225C2×Dic94—22no—
226C2×Dic94—21no—
227C2×Dic94#4114yes—
228C2×Dic94C2412yes—
229C2×Dic94C2412yes—
230C2×C8×C47—22no—
231C2×C8×C47—22no—
232C2×C8×C47C2412yes—
233C2×C8×C47C2412yes—
234C4⋊C4×C47—24no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—24no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47C2412yes—
240C4⋊C4×C47C2412yes—
241C4⋊C4×C47C2412yes—
242C22⋊C4×C47—24no—
243C22⋊Dic47—24no—
244C22⋊Dic47C2×D414yes—
245C22⋊Dic47C2×D414yes—
246#10625337—28no—
247#10625336—28no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250C4⋊Dic47—21no—
251C4⋊Dic47—24no—
252C4⋊Dic47—24no—
253C4⋊Dic47C2×D414yes—
254C4⋊Dic47C2×D414yes—
255C4⋊Dic47C2412yes—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263C4×Dic47—24no—
264C4×Dic47—24no—
265C4×Dic47—24no—
266C4×Dic47—24no—
267C4×Dic47C2×D412yes—
268C4×Dic47C2×D412yes—
269C4×Dic47C2412yes—
270C4×Dic47C2412yes—
271C2×C47⋊C8—22no—
272C2×C47⋊C8—22no—
273C2×C47⋊C8C2412yes—
274C2×C47⋊C8C2412yes—
275Dic188—28no—
276#10625325—28no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47C22×D412yes—
281C23×C47C22×D411yescharacteristic
282C22×D47—24no—
283C22×D47—22no—
284C22×D47—42no—
285C22×D47—42no—
286Q8×C47—22no—
287Q8×C47—22no—
288Q8×C47—42no—
289C2×C4×C47—22no—
290C2×C4×C47—24no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—84no—
302C2×C4×C47C22×D412yes—
303C2×C4×C47C22×D411yescharacteristic
304C2×C4×C47C2×#4112yes—
305C2×C4×C47C2×#4112yes—
306C2×C4×C47C2511yescharacteristic
307C22⋊D47—216no—
308C2×Dic47—24no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47C22×D412yes—
319C2×Dic47C22×D412yes—
320C2×Dic47C22×D412yes—
321C2×Dic47C22×D412yes—
322D188—24no—
323D188—22no—
324D188C2×#4114yes—
325C4×D47—216no—
326C4×D47—84no—
327C4×D47—84no—
328Dic94—24no—
329Dic94—22no—
330Dic94—22no—
331Dic94—22no—
332Dic94—42no—
333Dic94C2×#4114yes—
334C8×C47—22no—
335C8×C47—22no—
336C47⋊C8—22no—
337C47⋊C8—22no—
338C2×#3120—471nomaximal, Sylow
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—44no—
343C22×C47#52512yes—
344C22×C47#57712yes—
345C22×C47#57812yes—
346C22×C47C23×D411yescharacteristic
347C2×D47—24no—
348C2×D47—48no—
349C2×D47—42no—
350C2×D47—42no—
351C4×C47—22no—
352C4×C47—42no—
353C4×C47—42no—
354C4×C47—42no—
355C4×C47—42no—
356C4×C47#52512yes—
357C4×C47C22×#4111yescharacteristic
358C4×C47C22×#4111yescharacteristic
359Dic47—24no—
360Dic47—22no—
361Dic47—22no—
362Dic47—22no—
363Dic47—22no—
364Dic47—42no—
365Dic47—42no—
366C2×#541—471no—
367C2×#520—471no—
368#3120—4716no—
369C2×#484—471no—
370C2×#483D4711yescharacteristic, complemented
371C2×#479—471no—
372C2×#478—471no—
373C2×#462—471no—
374C2×#461—471no—
375C2×#452—471no—
376C2×#452—471no—
377C2×#441—471no—
378C2×#440—471no—
379C2×C4×Q16—471no—
380C2×C4×SD16—471no—
381C2×#433—471no—
382C2×C47—42no—
383C2×C47#312014yescomplemented
384C2×C47C2×#52511yescharacteristic
385C2×C47C2×#57711yescharacteristic
386C2×C47C2×#57811yescharacteristic
387D47—44no—
388C22×#41—471no—
389C22×Q16—471no—
390C22×Q16—471no—
391C22×SD16—471no—
392C22×SD16—471no—
393#541—478no—
394#541—944no—
395C2×C4⋊Q8—471no—
396C2×#126—941no—
397C2×#126—941no—
398C2×#125—471no—
399C2×#125—941no—
400C2×#125—941no—
401C2×C22⋊Q8—471no—
402C2×C22⋊Q8C2×D4711yescharacteristic
403#520—478no—
404#520—944no—
405C2×C4×Q8—471no—
406C2×C4×Q8—471no—
407C2×C4×Q8—471no—
408C2×C4×Q8—471no—
409C2×C4×D4—471no—
410C2×C4×D4—471no—
411C2×C4×D4—941no—
412C2×C4×D4—941no—
413C2×#117—471no—
414C2×#117—941no—
415C22×C4⋊C4—941no—
416C22×C4⋊C4C2×D4711yescharacteristic
417#484—478no—
418#483C2×D4718yescomplemented
419#479—478no—
420#478—478no—
421#462—478no—
422#461—478no—
423#452—478no—
424#452—478no—
425#441—478no—
426#440—478no—
427C4×Q16—478no—
428C4×SD16—478no—
429#433—478no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#106C2×D4711yescharacteristic
433C2×#106C2×D4711yescharacteristic
434C2×C4⋊C8—471no—
435C2×C4⋊C8—471no—
436C2×#103—471no—
437C2×#103—471no—
438C2×#103—471no—
439C2×#103—471no—
440C2×#103C2×D4711yescharacteristic
441C2×#103C2×D4711yescharacteristic
442C2×#102—471no—
443C2×#102—471no—
444C2×C22⋊C8—471no—
445C2×C22⋊C8C2×D4711yescharacteristic
446C2×#97—471no—
447C2×C4×C8—471no—
448C47C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—474no—
450C2×#41—944no—
451C2×#41—944no—
452C2×#41—942no—
453C22×Q8—471no—
454C22×Q8—471no—
455C22×Q8C22×D4711yescharacteristic
456C22×D4—471no—
457C22×D4—941no—
458C23×C4—21no—
459C23×C4—941no—
460C23×C4—941no—
461C23×C4—941no—
462C23×C4C22×D4711yescharacteristic
463C2×Q16—474no—
464C2×Q16—474no—
465C2×Q16—944no—
466C2×Q16—944no—
467C2×SD16—474no—
468C2×SD16—474no—
469C2×SD16—944no—
470C2×SD16—944no—
471C22×C8—471no—
472C22×C8—471no—
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475C4⋊Q8—474no—
476C4⋊Q8—942no—
477#126—948no—
478#126—948no—
479#125—474no—
480#125—942no—
481#125—948no—
482#125—948no—
483C22⋊Q8—22no—
484C22⋊Q8—474no—
485C22⋊Q8—942no—
486C22⋊Q8C22×D4714yes—
487C4×Q8—474no—
488C4×Q8—474no—
489C4×Q8—474no—
490C4×Q8—474no—
491C4×Q8—942no—
492C4×Q8—942no—
493C4×Q8—942no—
494C4×Q8—942no—
495C4×D4—474no—
496C4×D4—474no—
497C4×D4—942no—
498C4×D4—942no—
499C4×D4—948no—
500C4×D4—948no—
501#117—474no—
502#117—474no—
503#117—948no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—948no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4C22×D4711yescharacteristic
521C2×C4⋊C4C22×D4711yescharacteristic
522C2×C4⋊C4C22×D4714yes—
523C2×C4⋊C4C22×D4711yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—471no—
526C2×C22⋊C4—471no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4—941no—
529C2×C22⋊C4—941no—
530C2×C42—471no—
531C2×C42—471no—
532C2×C42—941no—
533C2×C42—941no—
534C2×C42—941no—
535C2×C42—941no—
536#107—474no—
537#107—474no—
538#106C22×D4714yes—
539#106C22×D4714yes—
540C4⋊C8—474no—
541C4⋊C8—474no—
542#103—474no—
543#103—474no—
544#103—474no—
545#103—474no—
546#103C22×D4714yes—
547#103C22×D4714yes—
548#102—474no—
549#102—474no—
550C22⋊C8—474no—
551C22⋊C8C22×D4714yes—
552#97—474no—
553C4×C8—474no—
554C24—941no—
555C24D4×D4711yescharacteristic
556#41—948no—
557#41—948no—
558#41—9416no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—474no—
563C2×Q8—472no—
564C2×Q8—472no—
565C2×Q8—941no—
566C2×Q8—941no—
567C2×Q8—942no—
568C2×Q8—942no—
569C2×Q8—942no—
570C2×Q8C23×D4712yes—
571C2×D4—474no—
572C2×D4—472no—
573C2×D4—948no—
574C2×D4—944no—
575C2×D4—941no—
576C2×D4—942no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—82no—
585C22×C4—471no—
586C22×C4—471no—
587C22×C4—471no—
588C22×C4—471no—
589C22×C4—944no—
590C22×C4—944no—
591C22×C4—948no—
592C22×C4—941no—
593C22×C4—944no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—3762no—
597C22×C4—3762no—
598C22×C4D4×D4712yes—
599C22×C4D4×D4711yescharacteristic
600C22×C4C23×D4712yes—
601C22×C4C23×D4711yescharacteristic
602Q16—948no—
603Q16—948no—
604SD16—948no—
605SD16—948no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—472no—
609C2×C8—472no—
610C2×C8—942no—
611C2×C8—942no—
612C2×C8C23×D4712yes—
613C2×C8C23×D4712yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—474no—
620C4⋊C4—474no—
621C4⋊C4—472no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—944no—
628C4⋊C4—944no—
629C4⋊C4—944no—
630C4⋊C4—944no—
631C4⋊C4—941no—
632C4⋊C4C23×D4712yes—
633C4⋊C4C23×D4712yes—
634C4⋊C4C23×D4712yes—
635C22⋊C4—24no—
636C22⋊C4—474no—
637C22⋊C4—474no—
638C22⋊C4—944no—
639C22⋊C4—944no—
640C22⋊C4—944no—
641C42—472no—
642C42—472no—
643C42—472no—
644C42—472no—
645C42—944no—
646C42—944no—
647C42—944no—
648C42—944no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—944no—
653C23—942no—
654C23—1882no—
655C23—1882no—
656C23C2×D4×D4712yes—
657C23C2×D4×D4711yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—474no—
662Q8—944no—
663Q8—942no—
664Q8—942no—
665Q8—942no—
666Q8—1882no—
667D4—474no—
668D4—9416no—
669D4—944no—
670D4—942no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—84no—
684C2×C4—472no—
685C2×C4—472no—
686C2×C4—472no—
687C2×C4—472no—
688C2×C4—9416no—
689C2×C4—944no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—3764no—
698C2×C4—3764no—
699C2×C4—1882no—
700C2×C4—1882no—
701C2×C4C2×D4×D4712yes—
702C2×C4C2×D4×D4711yescharacteristic
703C2×C4#41×D4712yes—
704C2×C4#41×D4712yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—22no—
708C8—942no—
709C8—942no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—944no—
715C22—1882no—
716C22—1882no—
717C22—1888no—
718C22#1568963112yes—
719C22#1568992912yes—
720C22#1568993912yes—
721C22C22×D4×D4711yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—942no—
728C4—942no—
729C4—942no—
730C4—942no—
731C4—944no—
732C4—1882no—
733C4—1882no—
734C4#1568963112yes—
735C4C2×#41×D4711yescharacteristic
736C4C2×#41×D4711yescharacteristic
737C2—42no—
738C2—1884no—
739C2#2025360514yesdirect product factor
740C2C2×#1568963111yescharacteristic
741C2C2×#1568992911yescharacteristic
742C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#483C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
hypercenterC2×#483D47
hypocenterC47C2×#3120
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#15689733C2semidirect
3. #20253605C2direct (N × H)
4. C2×#15689458C2semidirect
5. C2×#15689433C2semidirect
6. C2×#15689422C2semidirect
7. C2×#15689332C2semidirect
8. C2×#15689327C2semidirect
11. C2×#15689229C2semidirect
12. C2×#15689226C2semidirect
13. C2×#15689215C2semidirect
14. C2×#15689210C2semidirect
15. C2×#15689181C2semidirect
16. C2×C47×#483C2semidirect
23. #15689733C22semidirect
44. #15689458C22semidirect
45. #15689433C22semidirect
46. #15689422C22semidirect
47. #15689332C22semidirect
48. #15689327C22semidirect
51. #15689229C22semidirect
52. #15689226C22semidirect
53. #15689215C22semidirect
54. #15689210C22semidirect
55. #15689181C22semidirect
71. C47×#483C22semidirect
370. C2×#483D47semidirect
383. C2×C47#3120semidirect
418. #483C2×D47semidirect
448. C47C2×#3120semidirect
739. C2#20253605direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897332
C2×#156896042
#202536052
C2×#156894582
C2×#156894332
C2×#156894222
C2×#156893322
C2×#156893272
C2×#156892872
C2×#156892832
C2×#156892292
C2×#156892262
C2×#156892152
C2×#156892102
C2×#156891812
C2×C47×#4832
C2×#312047