Finite Group Databasebeta

← C2×#20256143 #27096029

Subgroups — C2×#20256143 #27096029

Order 12032.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689858C211yesmaximal, characteristic, complemented
2C2×#15689833C211yesmaximal, characteristic, complemented
3#20256143C2116yesmaximal, direct product factor
4C2×#15689488C211yesmaximal, characteristic, complemented
5C2×#15689483C211yesmaximal, characteristic, complemented
6C2×#15689478C211yesmaximal, characteristic, complemented
7C2×#15689431C211yesmaximal, characteristic, complemented
8C2×#15689424C211yesmaximal, characteristic, complemented
9C2×#15689404C211yesmaximal, characteristic, complemented
10C2×#15689339C211yesmaximal, characteristic, complemented
11C2×#15689339C211yesmaximal, characteristic, complemented
12C2×#15689319C211yesmaximal, characteristic
13C2×#15689236C211yesmaximal, characteristic, complemented
14C2×#15689225C211yesmaximal, characteristic, complemented
15C2×C4×D376C211yesmaximal, characteristic, complemented
16C2×C47×#446C211yesmaximal, characteristic, complemented
17C22×#10625325C2211yescharacteristic
18C22×D376C2211yescharacteristic
19C22×D376C2211yescharacteristic
20#15689858—24no—
21#15689858C2218yescomplemented
22#15689833—24no—
23#15689833C2218yescomplemented
24C2×#13094024C2211yescharacteristic
25C2×#13094021C2211yescharacteristic
26C2×#13094016C2211yescharacteristic
27C2×#13094016C2211yescharacteristic
28C2×#13094013—21no—
29C2×#13094012C2211yescharacteristic
30C2×#13094012C2211yescharacteristic
31C2×#13094009—21no—
32C2×#13094009—21no—
33C2×#13094002—21no—
34C2×#13094002—21no—
35C2×#13094000—21no—
36C2×C4×Dic94C2211yescharacteristic
37C2×C4×D188C2211yescharacteristic
38C2×C4×D188C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic
40C2×C4×D188C2211yescharacteristic
41C2×C4×D188C2211yescharacteristic
42C2×#13093986—21no—
43C2×C4⋊C4×D47—21no—
44#15689488C2218yescomplemented
45#15689483C2218yescomplemented
46#15689478C2218yescomplemented
47#15689431C2218yescomplemented
48#15689424C2218yescomplemented
49#15689404C2218yescomplemented
50#15689339C2218yescomplemented
51#15689339C2218yescomplemented
52#15689319C2218yes—
53#15689236C2218yescomplemented
54#15689225C2218yescomplemented
55C4×D376C2218yescomplemented
56C2×#13093958C2211yescharacteristic
57C2×#13093958C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C2×C4×Q8×C47C2211yescharacteristic
70C47×#446C2218yescomplemented
71C2×C4⋊C8×C47C2211yescharacteristic
72C2×C4⋊C8×C47C2211yescharacteristic
73C2×C4⋊C8×C47C2211yescharacteristic
74C2×#97×C47C2211yescharacteristic
75C2×#97×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188—21no—
80C22×D188—21no—
81C22×D188C2311yescharacteristic
82C22×D188C2311yescharacteristic
83C22×D188C2311yescharacteristic
84C22×C4×D47—21no—
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C2×#10625325—24no—
90C2×#10625325C2314yes—
91C2×D376—24no—
92C2×D376—24no—
93C2×D376C2314yes—
94C2×D376C2314yes—
95#13094024—22no—
96#13094024C2314yes—
97#13094021—22no—
98#13094021C2314yes—
99#13094016—22no—
100#13094016—22no—
101#13094016C2314yes—
102#13094016C2314yes—
103#13094013—28no—
104#13094012—22no—
105#13094012—22no—
106#13094012C2314yes—
107#13094012C2314yes—
108#13094009—28no—
109#13094009—28no—
110#13094002—28no—
111#13094002—28no—
112#13094000—28no—
113C4×Dic94—22no—
114C4×Dic94C2314yes—
115C4×D188—22no—
116C4×D188—22no—
117C4×D188—22no—
118C4×D188—22no—
119C4×D188—22no—
120C4×D188C2314yes—
121C4×D188C2314yes—
122C4×D188C2314yes—
123C4×D188C2314yes—
124C4×D188C2314yes—
125#13093986—28no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×C4⋊Dic47C2311yescharacteristic
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C4⋊C4×D47—28no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×C4×Dic47—21no—
147#13093958C2314yes—
148#13093958C2314yes—
149#13093956C2314yes—
150#13093949C2314yes—
151#13093949C2314yes—
152#13093949C2314yes—
153#13093946C2314yes—
154#13093946C2314yes—
155#13093946C2314yes—
156#13093946C2314yes—
157#13093946C2314yes—
158#13093946C2314yes—
159#13093946C2314yes—
160C22×Q8×C47D411yescharacteristic
161C22×C8×C47C2311yescharacteristic
162C22×C8×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C4×Q8×C47D414yes—
166C4×Q8×C47C2314yes—
167C2×C4⋊C4×C47D411yescharacteristic
168C2×C4⋊C4×C47D411yescharacteristic
169C2×C4⋊C4×C47D411yescharacteristic
170C2×C42×C47C2311yescharacteristic
171C2×C42×C47C2311yescharacteristic
172C2×C42×C47C2311yescharacteristic
173C4⋊C8×C47C2314yes—
174C4⋊C8×C47C2314yes—
175C4⋊C8×C47C2314yes—
176#97×C47C2314yes—
177#97×C47C2314yes—
178C4×C8×C47C2314yes—
179C23×D47—21no—
180C23×D47—21no—
181C23×D47—21no—
182C2×Q8×C47—42no—
183C2×Q8×C47C2×D414yes—
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2411yescharacteristic
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C2×D188—21no—
197C2×D188—22no—
198C2×D188—22no—
199C2×D188—22no—
200C2×D188—22no—
201C2×D188—22no—
202C2×D188—24no—
203C2×D188—21no—
204C2×D188—21no—
205C2×D188—24no—
206C2×D188—44no—
207C2×D188—82no—
208C2×D188#4114yes—
209C2×D188C2412yes—
210C2×D188C2412yes—
211C2×D188C2412yes—
212C2×C4×D47—24no—
213C2×C4×D47—24no—
214C2×C4×D47—24no—
215C2×C4×D47—24no—
216C2×C4×D47—24no—
217C2×C4×D47—44no—
218C2×C4×D47—82no—
219C2×C4×D47—82no—
220C2×C4×D47—82no—
221C2×C4×D47—82no—
222C2×Dic94—22no—
223C2×Dic94—22no—
224C2×Dic94—21no—
225C2×Dic94—24no—
226C2×Dic94—82no—
227C2×Dic94C2412yes—
228C2×C8×C47—22no—
229C2×C8×C47—22no—
230C2×C8×C47—22no—
231C2×C8×C47—22no—
232C2×C8×C47C2412yes—
233C2×C8×C47C2412yes—
234C2×C8×C47C2412yes—
235C2×C8×C47C2412yes—
236C4⋊C4×C47C2×D414yes—
237C4⋊C4×C47C2×D414yes—
238C4⋊C4×C47C2×D414yes—
239C42×C47C2×D412yes—
240C42×C47C2×D412yes—
241C42×C47C2×D412yes—
242C42×C47C2412yes—
243C42×C47C2412yes—
244C42×C47C2412yes—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254C4⋊Dic47—24no—
255C4⋊Dic47—21no—
256C4⋊Dic47—21no—
257C4⋊Dic47—21no—
258C4⋊Dic47—21no—
259C4⋊Dic47C2412yes—
260C4⋊Dic47C2412yes—
261C4⋊Dic47C2412yes—
262C4⋊Dic47C2412yes—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268C4×Dic47—24no—
269D376—28no—
270D376—28no—
271#10625325—28no—
272C23×C47C22×D411yescharacteristic
273C22×D47—24no—
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—42no—
278C22×D47—42no—
279C22×D47—42no—
280C22×D47—42no—
281C22×D47—42no—
282C22×D47—42no—
283C22×D47—42no—
284C22×D47—42no—
285Q8×C47—44no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47C22×D412yes—
293C2×C4×C47C22×D412yes—
294C2×C4×C47C22×D412yes—
295C2×C4×C47C22×D412yes—
296C2×C4×C47C22×D412yes—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D411yescharacteristic
299C2×C4×C47C2×#4112yes—
300C2×C4×C472−1+412yes—
301C2×C4×C47C2511yescharacteristic
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312D188—24no—
313D188—22no—
314D188—22no—
315D188—22no—
316D188—22no—
317D188—22no—
318D188—48no—
319D188—42no—
320D188—42no—
321D188—84no—
322D188C2×#4114yes—
323C4×D47—48no—
324C4×D47—84no—
325C4×D47—84no—
326C4×D47—84no—
327C4×D47—84no—
328Dic94—22no—
329Dic94—22no—
330Dic94—42no—
331Dic94—84no—
332C8×C47—22no—
333C8×C47—22no—
334C8×C47—22no—
335C8×C47—22no—
336C2×#3370—471nomaximal, Sylow
337C22×C47#54812yes—
338C22×C47#57512yes—
339C22×C47#57612yes—
340C22×C47C23×D411yescharacteristic
341C2×D47—24no—
342C2×D47—48no—
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—42no—
346C2×D47—42no—
347C2×D47—42no—
348C2×D47—42no—
349C2×D47—42no—
350C2×D47—42no—
351C2×D47—84no—
352C2×D47—84no—
353C4×C47—22no—
354C4×C47—22no—
355C4×C47—22no—
356C4×C47—22no—
357C4×C47—22no—
358C4×C47—22no—
359C4×C47#54812yes—
360C4×C47C22×#4111yescharacteristic
361C4×C47C2×2−1+411yescharacteristic
362Dic47—42no—
363Dic47—42no—
364Dic47—42no—
365Dic47—42no—
366Dic47—42no—
367C2×#559—471no—
368C2×#554—471no—
369#3370—4716no—
370C2×#490—471no—
371C2×#489—471no—
372C2×#488—471no—
373C2×#479—471no—
374C2×#478—471no—
375C2×#474—471no—
376C2×#463—471no—
377C2×#463—471no—
378C2×#459—471no—
379C2×#446D4711yescharacteristic, complemented
380C2×#442—471no—
381C2×#440—471no—
382C2×C4×D8—471no—
383C2×C47#337014yescomplemented
384C2×C47C2×#54811yescharacteristic
385C2×C47C2×#57511yescharacteristic
386C2×C47C2×#57611yescharacteristic
387D47—44no—
388D47—82no—
389D47—82no—
390C22×SD16—471no—
391C22×D8—471no—
392C22×D8—471no—
393#559—478no—
394#559—944no—
395#554—478no—
396#554—944no—
397C2×C4⋊Q8—471no—
398C2×#127—471no—
399C2×#125—471no—
400C2×#125—471no—
401C2×#124—471no—
402C2×#124—471no—
403C2×#124—941no—
404C2×#123—941no—
405C2×#123—941no—
406C2×C22⋊Q8—941no—
407C2×C22⋊Q8—941no—
408C2×C22⋊Q8—941no—
409C2×C4×Q8—471no—
410C2×C4×Q8C2×D4711yescharacteristic
411C2×C4×D4—471no—
412C2×C4×D4—471no—
413C2×C4×D4—471no—
414C2×C4×D4—471no—
415C2×C4×D4—471no—
416C2×C4×D4—941no—
417C22×C4⋊C4—941no—
418#490—478no—
419#489—478no—
420#488—478no—
421#479—478no—
422#478—478no—
423#474—478no—
424#463—478no—
425#463—478no—
426#459—478no—
427#446C2×D4718yescomplemented
428#442—478no—
429#440—478no—
430C4×D8—478no—
431C2×#107—471no—
432C2×#107—471no—
433C2×#106—471no—
434C2×C4⋊C8C2×D4711yescharacteristic
435C2×C4⋊C8C2×D4711yescharacteristic
436C2×C4⋊C8C2×D4711yescharacteristic
437C2×#103—471no—
438C2×#103—471no—
439C2×#103—471no—
440C2×#102—471no—
441C2×#102—471no—
442C2×#102—471no—
443C2×#102—471no—
444C2×#102—471no—
445C2×#102—471no—
446C2×#102—471no—
447C2×#97C2×D4711yescharacteristic
448C2×#97C2×D4711yescharacteristic
449C2×C4×C8C2×D4711yescharacteristic
450C47C2×#337011yescharacteristic, complemented, Sylow
451C22×Q8—471no—
452C22×Q8—941no—
453C22×Q8D18811yescharacteristic
454C22×D4—471no—
455C22×D4—471no—
456C22×D4—471no—
457C22×D4—941no—
458C22×D4—941no—
459C23×C4—941no—
460C23×C4—941no—
461C23×C4—941no—
462C23×C4—941no—
463C23×C4—941no—
464C2×SD16—474no—
465C2×SD16—944no—
466C2×D8—474no—
467C2×D8—474no—
468C2×D8—944no—
469C2×D8—944no—
470C22×C8C22×D4711yescharacteristic
471C22×C8C22×D4711yescharacteristic
472C22×C8C22×D4711yescharacteristic
473C22×C8C22×D4711yescharacteristic
474C4⋊Q8—474no—
475C4⋊Q8—942no—
476#127—474no—
477#127—942no—
478#125—474no—
479#125—474no—
480#125—942no—
481#125—942no—
482#124—474no—
483#124—474no—
484#124—948no—
485#124—942no—
486#124—942no—
487#123—948no—
488#123—948no—
489C22⋊Q8—948no—
490C22⋊Q8—948no—
491C22⋊Q8—948no—
492C4×Q8—474no—
493C4×Q8—942no—
494C4×Q8D18814yes—
495C4×Q8C22×D4714yes—
496C4×D4—474no—
497C4×D4—474no—
498C4×D4—474no—
499C4×D4—474no—
500C4×D4—474no—
501C4×D4—948no—
502C4×D4—942no—
503C4×D4—942no—
504C4×D4—942no—
505C4×D4—942no—
506C4×D4—942no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—471no—
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—948no—
518C2×C4⋊C4D18811yescharacteristic
519C2×C4⋊C4D18811yescharacteristic
520C2×C4⋊C4D18811yescharacteristic
521C2×C22⋊C4—941no—
522C2×C22⋊C4—941no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4—941no—
529C2×C22⋊C4—941no—
530C2×C42—941no—
531C2×C42C22×D4711yescharacteristic
532C2×C42C22×D4711yescharacteristic
533C2×C42C22×D4711yescharacteristic
534#107—474no—
535#107—474no—
536#106—474no—
537C4⋊C8C22×D4714yes—
538C4⋊C8C22×D4714yes—
539C4⋊C8C22×D4714yes—
540#103—474no—
541#103—474no—
542#103—474no—
543#102—474no—
544#102—474no—
545#102—474no—
546#102—474no—
547#102—474no—
548#102—474no—
549#102—474no—
550#97C22×D4714yes—
551#97C22×D4714yes—
552C4×C8C22×D4714yes—
553C24—941no—
554C24—941no—
555C24—941no—
556C2×Q8—42no—
557C2×Q8—472no—
558C2×Q8—944no—
559C2×Q8—941no—
560C2×Q8—942no—
561C2×Q8—942no—
562C2×Q8—3762no—
563C2×Q8C2×D18814yes—
564C2×D4—474no—
565C2×D4—472no—
566C2×D4—472no—
567C2×D4—472no—
568C2×D4—941no—
569C2×D4—944no—
570C2×D4—944no—
571C2×D4—941no—
572C2×D4—941no—
573C2×D4—942no—
574C2×D4—942no—
575C2×D4—942no—
576C2×D4—942no—
577C2×D4—942no—
578C2×D4—3762no—
579C2×D4—1884no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—944no—
586C22×C4—944no—
587C22×C4—944no—
588C22×C4—944no—
589C22×C4—944no—
590C22×C4—3762no—
591C22×C4—3762no—
592C22×C4—3762no—
593C22×C4—3762no—
594C22×C4—1884no—
595C22×C4C2×D18811yescharacteristic
596C22×C4C2×D18811yescharacteristic
597C22×C4C2×D18811yescharacteristic
598C22×C4C2×D18811yescharacteristic
599C22×C4C2×D18811yescharacteristic
600C22×C4C2×D18811yescharacteristic
601C22×C4C23×D4711yescharacteristic
602SD16—948no—
603D8—948no—
604D8—948no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8C23×D4712yes—
610C2×C8C23×D4712yes—
611C2×C8C23×D4712yes—
612C2×C8C23×D4712yes—
613C4⋊C4—472no—
614C4⋊C4—472no—
615C4⋊C4—472no—
616C4⋊C4—472no—
617C4⋊C4—944no—
618C4⋊C4—944no—
619C4⋊C4—944no—
620C4⋊C4—944no—
621C4⋊C4—944no—
622C4⋊C4—941no—
623C4⋊C4—941no—
624C4⋊C4—941no—
625C4⋊C4—941no—
626C4⋊C4—944no—
627C4⋊C4C2×D18814yes—
628C4⋊C4C2×D18814yes—
629C4⋊C4C2×D18814yes—
630C22⋊C4—944no—
631C22⋊C4—944no—
632C22⋊C4—944no—
633C22⋊C4—944no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C22⋊C4—944no—
639C42—944no—
640C42C2×D18812yes—
641C42C2×D18812yes—
642C42C2×D18812yes—
643C42C23×D4712yes—
644C42C23×D4712yes—
645C42C23×D4712yes—
646C23—944no—
647C23—942no—
648C23—942no—
649C23—942no—
650C23—1882no—
651C23—1882no—
652C23—1882no—
653C23—1882no—
654C23—1882no—
655C23—1882no—
656C23—1882no—
657C23—1882no—
658C23C22×D18811yescharacteristic
659Q8—44no—
660Q8—942no—
661Q8—942no—
662Q8—3764no—
663Q8—1882no—
664D4—474no—
665D4—944no—
666D4—942no—
667D4—942no—
668D4—942no—
669D4—942no—
670D4—942no—
671D4—3764no—
672D4—1888no—
673D4—1882no—
674D4—1882no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—3764no—
687C2×C4—3764no—
688C2×C4—3764no—
689C2×C4—3764no—
690C2×C4—1888no—
691C2×C4—1882no—
692C2×C4—1882no—
693C2×C4—1882no—
694C2×C4—1882no—
695C2×C4—1882no—
696C2×C4C22×D18812yes—
697C2×C4C22×D18812yes—
698C2×C4C22×D18812yes—
699C2×C4C22×D18812yes—
700C2×C4C22×D18812yes—
701C2×C4C22×D18812yes—
702C2×C4C22×D18811yescharacteristic
703C2×C4#41×D4712yes—
704C2×C4#1309407212yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—944no—
711C22—3764no—
712C22—3764no—
713C22—1882no—
714C22—1882no—
715C22—1882no—
716C22—1882no—
717C22—1882no—
718C22—1882no—
719C22—1882no—
720C22—1882no—
721C22—1888no—
722C22#1568978512yes—
723C22#1568992312yes—
724C22#1568992812yes—
725C22C23×D18811yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—1882no—
733C4—1882no—
734C4—1882no—
735C4—1882no—
736C4—1882no—
737C4#1568978512yes—
738C4C2×#41×D4711yescharacteristic
739C4C2×#1309407211yescharacteristic
740C2—3762no—
741C2—3762no—
742C2—1884no—
743C2#2025614314yesdirect product factor
744C2C2×#1568978511yescharacteristic
745C2C2×#1568992311yescharacteristic
746C2C2×#1568992811yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#446C2
socleC23×C47C22×D4
prime radicalC2×#15689319C2
hypercenterC2×#446D47
hypocenterC47C2×#3370
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×#15689858C2semidirect
2. C2×#15689833C2semidirect
3. #20256143C2direct (N × H)
4. C2×#15689488C2semidirect
5. C2×#15689483C2semidirect
6. C2×#15689478C2semidirect
7. C2×#15689431C2semidirect
8. C2×#15689424C2semidirect
9. C2×#15689404C2semidirect
10. C2×#15689339C2semidirect
11. C2×#15689339C2semidirect
13. C2×#15689236C2semidirect
14. C2×#15689225C2semidirect
15. C2×C4×D376C2semidirect
16. C2×C47×#446C2semidirect
21. #15689858C22semidirect
23. #15689833C22semidirect
44. #15689488C22semidirect
45. #15689483C22semidirect
46. #15689478C22semidirect
47. #15689431C22semidirect
48. #15689424C22semidirect
49. #15689404C22semidirect
50. #15689339C22semidirect
51. #15689339C22semidirect
53. #15689236C22semidirect
54. #15689225C22semidirect
55. C4×D376C22semidirect
70. C47×#446C22semidirect
379. C2×#446D47semidirect
383. C2×C47#3370semidirect
427. #446C2×D47semidirect
450. C47C2×#3370semidirect
743. C2#20256143direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898582
C2×#156898332
#202561432
C2×#156894882
C2×#156894832
C2×#156894782
C2×#156894312
C2×#156894242
C2×#156894042
C2×#156893392
C2×#156893192
C2×#156892362
C2×#156892252
C2×C4×D3762
C2×C47×#4462
C2×#337047