Finite Group Databasebeta

← C2×#20253608 #27084547

Subgroups — C2×#20253608 #27084547

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×#15689731C211yesmaximal, characteristic, complemented
2C2×#15689605C211yesmaximal, characteristic
3#20253608C2116yesmaximal, direct product factor
4C2×#15689460C211yesmaximal, characteristic, complemented
5C2×#15689452C211yesmaximal, characteristic, complemented
6C2×#15689428C211yesmaximal, characteristic, complemented
7C2×#15689426C211yesmaximal, characteristic, complemented
8C2×#15689331C211yesmaximal, characteristic, complemented
9C2×#15689327C211yesmaximal, characteristic, complemented
10C2×#15689288C211yesmaximal, characteristic
11C2×#15689284C211yesmaximal, characteristic
12C2×#15689228C211yesmaximal, characteristic, complemented
13C2×#15689221C211yesmaximal, characteristic, complemented
14C2×C4×#10625325C211yesmaximal, characteristic, complemented
15C2×#15689182C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C47C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21#15689731—24no—
22#15689731C2218yescomplemented
23C2×#13094022C2211yescharacteristic
24C2×#13094019—21no—
25C2×#13094018—21no—
26C2×#13094016—21no—
27C2×#13094015C2211yescharacteristic
28C2×#13094014—21no—
29C2×#13094004C2211yescharacteristic
30C2×#13094000C2211yescharacteristic
31#15689605—24no—
32#15689605C2218yes—
33C2×Q8×Dic47C2211yescharacteristic
34C2×C4×Dic94C2211yescharacteristic
35C2×C4×D188—21no—
36C2×C4×D188C2211yescharacteristic
37C2×#13093986—21no—
38C2×#13093986C2211yescharacteristic
39C2×#13093981—21no—
40C2×#13093981C2211yescharacteristic
41C2×C4⋊C4×D47—21no—
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689460C2218yescomplemented
44#15689452C2218yescomplemented
45#15689428C2218yescomplemented
46#15689426C2218yescomplemented
47#15689331C2218yescomplemented
48#15689327C2218yescomplemented
49#15689288C2218yes—
50#15689284C2218yes—
51#15689228C2218yescomplemented
52#15689221C2218yescomplemented
53C4×#10625325C2218yescomplemented
54#15689182C2218yescomplemented
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093935C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×Q8×C47C2211yescharacteristic
72C4×Q16×C47C2218yescomplemented
73C2×#107×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C2×#10625354—24no—
78C2×#10625354—24no—
79C2×#10625354—22no—
80C2×#10625354C2314yes—
81C22×Dic94C2311yescharacteristic
82C22×D188—21no—
83C22×D188C2311yescharacteristic
84C22×C4×D47—21no—
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47C2311yescharacteristic
89C2×#10625337—24no—
90C2×#10625337C2314yes—
91C2×#10625325—24no—
92C2×#10625325C2314yes—
93C2×#10625336—24no—
94C2×#10625336C2314yes—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97#13094022—22no—
98#13094022C2314yes—
99#13094019—28no—
100#13094018—28no—
101#13094016—28no—
102#13094015—22no—
103#13094015C2314yes—
104#13094014—28no—
105#13094004—22no—
106#13094004C2314yes—
107#13094000—22no—
108#13094000C2314yes—
109Q8×Dic47—22no—
110Q8×Dic47C2314yes—
111C4×Dic94—22no—
112C4×Dic94C2314yes—
113C4×D188—22no—
114C4×D188—28no—
115C4×D188C2314yes—
116#13093986—28no—
117#13093986—22no—
118#13093986C2314yes—
119#13093981—28no—
120#13093981D414yes—
121#13093981C2314yes—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4D411yescharacteristic
134C2×Dic47⋊C4D411yescharacteristic
135C4⋊C4×D47—22no—
136C4⋊C4×D47—28no—
137C4⋊C4×D47C2314yes—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4D411yescharacteristic
143C2×(C2×D47)⋊C4D411yescharacteristic
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47C2311yescharacteristic
147#13093957C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150Dic47⋊C8C2314yes—
151Dic47⋊C8C2314yes—
152#13093949C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093947C2314yes—
156#13093946C2314yes—
157#13093944C2314yes—
158(C2×D47)⋊C8C2314yes—
159(C2×D47)⋊C8C2314yes—
160#13093935C2314yes—
161C22×Q8×C47C2311yescharacteristic
162C22×Q8×C47C2311yescharacteristic
163C2×Q16×C47—24no—
164C2×Q16×C47C2314yes—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C4×Q8×C47—22no—
168C4×Q8×C47—22no—
169C4×Q8×C47C2314yes—
170C4×Q8×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C42×C47—21no—
176C2×C42×C47—21no—
177C2×C42×C47C2311yescharacteristic
178#107×C47C2314yes—
179#103×C47C2314yes—
180#103×C47C2314yes—
181C4×C8×C47C2314yes—
182C23×D47—21no—
183C23×D47C2×D411yescharacteristic
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47#4114yes—
190C2×Q8×C47C2412yes—
191C2×Q8×C47C2412yes—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47C2×D411yescharacteristic
203C22×Dic47C2×D411yescharacteristic
204C22×Dic47C2×D411yescharacteristic
205#10625354—216no—
206#10625354—28no—
207#10625354—28no—
208C2×D188—28no—
209C2×D188—24no—
210C2×D188—21no—
211C2×D188—22no—
212C2×D188#4114yes—
213C2×D188C2412yes—
214C2×C4×D47—28no—
215C2×C4×D47—22no—
216C2×C4×D47—22no—
217C2×C4×D47—24no—
218C2×C4×D47—24no—
219C2×C4×D47—24no—
220C2×C4×D47—24no—
221C2×C4×D47—82no—
222C2×C4×D47—82no—
223C2×C4×D47—82no—
224C2×C4×D47C2×D412yes—
225C2×C4×D47C2412yes—
226C2×Dic94—22no—
227C2×Dic94—22no—
228C2×Dic94—21no—
229C2×Dic94C2412yes—
230Q16×C47—28no—
231C2×C8×C47—22no—
232C2×C8×C47—22no—
233C2×C8×C47C2412yes—
234C2×C8×C47C2412yes—
235C4⋊C4×C47—24no—
236C4⋊C4×C47—24no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47C2412yes—
240C4⋊C4×C47C2412yes—
241C42×C47—24no—
242C42×C47—24no—
243C42×C47C2×D412yes—
244C42×C47C2412yes—
245#10625337—28no—
246#10625336—28no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4C2×D414yes—
252(C2×D47)⋊C4C2×D414yes—
253C4⋊Dic47—21no—
254C4⋊Dic47—21no—
255C4⋊Dic47—24no—
256C4⋊Dic47—24no—
257C4⋊Dic47—24no—
258C4⋊Dic47C2412yes—
259C4⋊Dic47C2412yes—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266Dic47⋊C4C2×D414yes—
267Dic47⋊C4C2×D414yes—
268C4×Dic47—24no—
269C4×Dic47—24no—
270C4×Dic47C2×D412yes—
271C4×Dic47C2412yes—
272C2×C47⋊C8—22no—
273C2×C47⋊C8—22no—
274C2×C47⋊C8C2412yes—
275C2×C47⋊C8C2412yes—
276#10625325—28no—
277C23×C47C22×D411yescharacteristic
278C22×D47—22no—
279C22×D47—24no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—42no—
284C22×D47—42no—
285C22×D47C22×D412yes—
286Q8×C47—24no—
287Q8×C47—22no—
288Q8×C47—22no—
289Q8×C47—22no—
290Q8×C47—42no—
291Q8×C47C2×#4114yes—
292C2×C4×C47—24no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47C22×D412yes—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C2×#4112yes—
306C2×C4×C47C2×#4112yes—
307C2×C4×C47C2511yescharacteristic
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47C22×D412yes—
318C2×Dic47C22×D412yes—
319C2×Dic47C22×D412yes—
320D188—216no—
321D188—24no—
322D188—22no—
323D188C2×#4114yes—
324C4×D47—216no—
325C4×D47—24no—
326C4×D47—22no—
327C4×D47—22no—
328C4×D47—84no—
329C4×D47—84no—
330C4×D47—84no—
331Dic94—22no—
332Dic94—22no—
333Dic94—42no—
334C8×C47—22no—
335C8×C47—22no—
336C47⋊C8—22no—
337C47⋊C8—22no—
338C2×#3120—471nomaximal, Sylow
339C22×C47#52512yes—
340C22×C47#57712yes—
341C22×C47#57812yes—
342C22×C47C23×D411yescharacteristic
343C2×D47—22no—
344C2×D47—24no—
345C2×D47—22no—
346C2×D47—22no—
347C2×D47—44no—
348C2×D47—48no—
349C2×D47—42no—
350C2×D47—42no—
351C4×C47—24no—
352C4×C47—22no—
353C4×C47—22no—
354C4×C47—42no—
355C4×C47—42no—
356C4×C47—42no—
357C4×C47#52512yes—
358C4×C47C22×#4111yescharacteristic
359C4×C47C22×#4111yescharacteristic
360Dic47—22no—
361Dic47—22no—
362Dic47—22no—
363Dic47—42no—
364Dic47—42no—
365Dic47—42no—
366C2×#541—471no—
367C2×#520—471no—
368#3120—4716no—
369C2×#484—471no—
370C2×#483—471no—
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×Q16D4711yescharacteristic, complemented
380C2×C4×SD16—471no—
381C2×#433—471no—
382C2×C47#312014yescomplemented
383C2×C47C2×#52511yescharacteristic
384C2×C47C2×#57711yescharacteristic
385C2×C47C2×#57811yescharacteristic
386D47—42no—
387D47—44no—
388C22×#41—471no—
389C22×Q16—471no—
390C22×Q16C2×D4711yescharacteristic
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⋊Q8—471no—
403#520—478no—
404#520—944no—
405C2×C4×Q8—471no—
406C2×C4×Q8—471no—
407C2×C4×Q8C2×D4711yescharacteristic
408C2×C4×Q8C2×D4711yescharacteristic
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—471no—
416C22×C4⋊C4—941no—
417#484—478no—
418#483—478no—
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×Q16C2×D4718yescomplemented
428C4×SD16—478no—
429#433—478no—
430C2×#107—471no—
431C2×#107C2×D4711yescharacteristic
432C2×#106—471no—
433C2×#106—471no—
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⋊C8—471no—
446C2×#97—471no—
447C2×C4×C8C2×D4711yescharacteristic
448C47C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—474no—
450C2×#41—942no—
451C2×#41—944no—
452C2×#41—944no—
453C22×Q8—471no—
454C22×Q8C22×D4711yescharacteristic
455C22×Q8C22×D4711yescharacteristic
456C22×D4—471no—
457C22×D4—941no—
458C23×C4—471no—
459C23×C4—941no—
460C23×C4—941no—
461C23×C4—941no—
462C23×C4—941no—
463C2×Q16—24no—
464C2×Q16—474no—
465C2×Q16—944no—
466C2×Q16C22×D4714yes—
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—948no—
481#125—942no—
482#125—948no—
483C22⋊Q8—474no—
484C22⋊Q8—474no—
485C22⋊Q8—942no—
486C22⋊Q8—942no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—474no—
490C4×Q8—474no—
491C4×Q8—942no—
492C4×Q8—942no—
493C4×Q8C22×D4714yes—
494C4×Q8C22×D4714yes—
495C4×D4—474no—
496C4×D4—474no—
497C4×D4—948no—
498C4×D4—942no—
499C4×D4—948no—
500C4×D4—942no—
501#117—474no—
502#117—474no—
503#117—948no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—474no—
511C2×C4⋊C4—948no—
512C2×C4⋊C4—942no—
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⋊C4—941no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4C22×D4711yescharacteristic
523C2×C4⋊C4C22×D4711yescharacteristic
524C2×C22⋊C4—471no—
525C2×C22⋊C4—471no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4—941no—
529C2×C22⋊C4—941no—
530C2×C42—21no—
531C2×C42—21no—
532C2×C42—471no—
533C2×C42—941no—
534C2×C42—941no—
535C2×C42C22×D4711yescharacteristic
536#107—474no—
537#107C22×D4714yes—
538#106—474no—
539#106—474no—
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⋊C8—474no—
552#97—474no—
553C4×C8C22×D4714yes—
554C24—471no—
555C24—941no—
556#41—948no—
557#41—9416no—
558#41—948no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—472no—
565C2×Q8—941no—
566C2×Q8—942no—
567C2×Q8—942no—
568C2×Q8#1062535014yes—
569C2×Q8C23×D4712yes—
570C2×Q8C23×D4712yes—
571C2×D4—474no—
572C2×D4—472no—
573C2×D4—944no—
574C2×D4—948no—
575C2×D4—941no—
576C2×D4—942no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—471no—
582C22×C4—471no—
583C22×C4—471no—
584C22×C4—472no—
585C22×C4—472no—
586C22×C4—944no—
587C22×C4—944no—
588C22×C4—948no—
589C22×C4—944no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—944no—
596C22×C4—3762no—
597C22×C4—3762no—
598C22×C4—3762no—
599C22×C4D4×D4711yescharacteristic
600C22×C4D4×D4711yescharacteristic
601C22×C4C23×D4711yescharacteristic
602Q16—28no—
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—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—474no—
619C4⋊C4—474no—
620C4⋊C4—472no—
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⋊C4—941no—
633C4⋊C4C23×D4712yes—
634C4⋊C4C23×D4712yes—
635C22⋊C4—474no—
636C22⋊C4—474no—
637C22⋊C4—944no—
638C22⋊C4—944no—
639C22⋊C4—944no—
640C22⋊C4—944no—
641C42—24no—
642C42—24no—
643C42—472no—
644C42—472no—
645C42—944no—
646C42—944no—
647C42D4×D4712yes—
648C42C23×D4712yes—
649C23—472no—
650C23—944no—
651C23—942no—
652C23—942no—
653C23—942no—
654C23—942no—
655C23—1882no—
656C23—1882no—
657C23C2×D4×D4711yescharacteristic
658Q8—24no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—942no—
664Q8—942no—
665Q8—1882no—
666Q8C2×#1062535014yes—
667D4—474no—
668D4—9416no—
669D4—944no—
670D4—942no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—472no—
682C2×C4—472no—
683C2×C4—472no—
684C2×C4—9416no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—944no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—3764no—
695C2×C4—3764no—
696C2×C4—3764no—
697C2×C4—1882no—
698C2×C4—1882no—
699C2×C4—1882no—
700C2×C4C2×D4×D4712yes—
701C2×C4C2×D4×D4712yes—
702C2×C4C2×D4×D4711yescharacteristic
703C2×C4#41×D4712yes—
704C2×C4C2×#1062535012yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—22no—
708C8—942no—
709C8—942no—
710C22—942no—
711C22—942no—
712C22—944no—
713C22—942no—
714C22—1882no—
715C22—1882no—
716C22—1884no—
717C22—1888no—
718C22#1568963212yes—
719C22#1568993012yes—
720C22#1568993612yes—
721C22C22×D4×D4711yescharacteristic
722C4—22no—
723C4—22no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—942no—
729C4—942no—
730C4—942no—
731C4—1882no—
732C4—1882no—
733C4—1882no—
734C4#1568963212yes—
735C4C2×#41×D4711yescharacteristic
736C4C22×#1062535011yescharacteristic
737C2—1882no—
738C2—1884no—
739C2#2025360814yesdirect product factor
740C2C2×#1568963211yescharacteristic
741C2C2×#1568993011yescharacteristic
742C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×Q16×C47C2
socleC23×C47C22×D4
prime radicalC22×#10625354C22
hypercenterC2×C4×Q16D47
hypocenterC47C2×#3120
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#15689731C2semidirect
3. #20253608C2direct (N × H)
4. C2×#15689460C2semidirect
5. C2×#15689452C2semidirect
6. C2×#15689428C2semidirect
7. C2×#15689426C2semidirect
8. C2×#15689331C2semidirect
9. C2×#15689327C2semidirect
12. C2×#15689228C2semidirect
13. C2×#15689221C2semidirect
14. C2×C4×#10625325C2semidirect
15. C2×#15689182C2semidirect
16. C2×C4×Q16×C47C2semidirect
22. #15689731C22semidirect
43. #15689460C22semidirect
44. #15689452C22semidirect
45. #15689428C22semidirect
46. #15689426C22semidirect
47. #15689331C22semidirect
48. #15689327C22semidirect
51. #15689228C22semidirect
52. #15689221C22semidirect
53. C4×#10625325C22semidirect
54. #15689182C22semidirect
72. C4×Q16×C47C22semidirect
379. C2×C4×Q16D47semidirect
382. C2×C47#3120semidirect
427. C4×Q16C2×D47semidirect
448. C47C2×#3120semidirect
739. C2#20253608direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897312
C2×#156896052
#202536082
C2×#156894602
C2×#156894522
C2×#156894282
C2×#156894262
C2×#156893312
C2×#156893272
C2×#156892882
C2×#156892842
C2×#156892282
C2×#156892212
C2×C4×#106253252
C2×#156891822
C2×C4×Q16×C472
C2×#312047