Finite Group Databasebeta

← C2×#20243917 #26218267

Subgroups — C2×#20243917 #26218267

Order 12032.

1974 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689687C211yesmaximal, characteristic
2C2×#15689597C211yesmaximal, characteristic, complemented
3C2×#15689140C211yesmaximal, characteristic, complemented
4C22×#13093940C211yesmaximal, characteristic, complemented
5#20243917C218yesmaximal, direct product factor
6C2×#15688880C211yesmaximal, characteristic, complemented
7C2×#15688879C211yesmaximal, characteristic, complemented
8C2×C47×#421C211yesmaximal, characteristic, complemented
9C23×D188C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11#15689687—22no—
12#15689687—22no—
13#15689687C414yescomplemented
14#15689687C2214yes—
15C2×#13094020C412yescomplemented
16C2×#13094013C412yescomplemented
17C2×#13093998—22no—
18C2×#13093992—22no—
19#15689597—22no—
20#15689597—22no—
21#15689597—22no—
22#15689597C2214yescomplemented
23C2×C4×D188—22no—
24C2×#13093986—22no—
25C2×#13093983C2211yescharacteristic
26C2×#13093983C2211yescharacteristic
27C2×C22⋊C4×D47—22no—
28#15689140—22no—
29#15689140C2214yescomplemented
30C2×#13093951—22no—
31C2×#13093940—22no—
32C2×#13093940—22no—
33C2×#13093940C2214yescomplemented
34#15688880C2214yescomplemented
35#15688879C2214yescomplemented
36C22×#41×C47C2211yescharacteristic
37C22×M16×C47C2211yescharacteristic
38C2×#117×C47C2211yescharacteristic
39C47×#421—22no—
40C47×#421C2214yescomplemented
41C2×#104×C47—22no—
42C24×D47D412yes—
43C22×D188—21no—
44C22×D188—21no—
45C22×D188—21no—
46C22×D188—21no—
47C22×D188—21no—
48C22×D188—21no—
49C22×D188—21no—
50C22×D188—21no—
51C22×D188C2×C412yes—
52C22×D188C2×C412yes—
53C22×D188D412yes—
54C22×D188D412yes—
55C22×D188D412yes—
56C22×D188C2312yes—
57C22×C22⋊D47—24no—
58C22×C4×D47—24no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329—21no—
62C2×#10625329—21no—
63C2×#10625329—21no—
64C2×#10625329C2312yes—
65C22×C47⋊C8—21no—
66#13094020—24no—
67#13094020C2×C418yescomplemented
68#13094013—24no—
69#13094013C2×C418yescomplemented
70#13093998—28no—
71#13093998—28no—
72#13093992—28no—
73#13093992—28no—
74C4×D188—28no—
75C4×D188—28no—
76#13093986—28no—
77#13093986—28no—
78#13093983—21no—
79#13093983—21no—
80#13093983—21no—
81#13093983—21no—
82#13093983C2×C412yescomplemented
83#13093983D412yescomplemented
84#13093983C2312yes—
85#13093983C2312yes—
86C2×C4⋊Dic47—21no—
87C2×C4⋊Dic47—21no—
88C2×C22⋊Dic47—21no—
89C2×C22⋊Dic47—21no—
90C2×(C2×D47)⋊C4—24no—
91C2×(C2×D47)⋊C4—24no—
92C22⋊C4×D47—28no—
93C22⋊C4×D47—28no—
94C2×C4×Dic47C2×C412yescomplemented
95C2×C4×Dic47D412yescomplemented
96#13093951—28no—
97#13093940—28no—
98C2×#41×C47—21no—
99C2×#41×C47—21no—
100C2×#41×C47—21no—
101C2×#41×C47—21no—
102C2×#41×C47—21no—
103C2×#41×C47—21no—
104C2×#41×C47—21no—
105C2×#41×C47—21no—
106C2×#41×C47—21no—
107C2×#41×C47—21no—
108C2×#41×C47C2×C412yescomplemented
109C2×#41×C47C2312yes—
110C22×Q8×C47C2×C411yescharacteristic, complemented
111C22×D4×C47—21no—
112C22×D4×C47C2×C411yescharacteristic, complemented
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×C47C2312yes—
121C22×C8×C47—21no—
122#117×C47—21no—
123#117×C47—21no—
124#117×C47D412yescomplemented
125#117×C47C2312yes—
126C2×C4⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C42×C47D412yescomplemented
129#104×C47—28no—
130C24×C47—21no—
131C24×C47C2×D411yescharacteristic
132C23×D47—22no—
133C23×D47—22no—
134C23×D47—22no—
135C23×D47—22no—
136C23×D47—84no—
137C23×D47C22⋊C414yes—
138C23×D47C22⋊C414yes—
139C23×D47C2×D414yes—
140#41×C47—22no—
141#41×C47—22no—
142#41×C47—22no—
143#41×C47—22no—
144#41×C47—22no—
145#41×C47—22no—
146#41×C47—22no—
147#41×C47—22no—
148#41×C47—41no—
149#41×C47—41no—
150#41×C47—41no—
151#41×C47—41no—
152#41×C47—41no—
153#41×C47—41no—
154#41×C47—41no—
155#41×C47—41no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47C22×C412yescomplemented
162C2×D4×C47—22no—
163C2×D4×C47—22no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—41no—
170C2×D4×C47—41no—
171C2×D4×C47—41no—
172C2×D4×C47—41no—
173C2×D4×C47C22×C412yescomplemented
174C22×C4×C47—21no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—41no—
179C22×C4×C47—41no—
180C22×C4×C47—41no—
181C22×C4×C47—41no—
182C22×C4×C47C22×C411yescharacteristic
183C22×C4×C47C22×C411yescharacteristic
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×C47C2×D411yescharacteristic
191C22×C4×C47#4111yescharacteristic
192C22×C4×C47#4111yescharacteristic
193C22×C4×C47#4111yescharacteristic
194C22×C4×C47#4111yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C2×C22⋊D47—216no—
197C2×C22⋊D47—88no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C2×D188—22no—
201C2×D188—22no—
202C2×D188—22no—
203C2×D188—22no—
204C2×D188—22no—
205C2×D188—22no—
206C2×D188—22no—
207C2×D188—22no—
208C2×D188—22no—
209C2×D188—22no—
210C2×D188—22no—
211C2×D188—22no—
212C2×D188—22no—
213C2×D188—22no—
214C2×D188—22no—
215C2×D188—22no—
216C2×D188—22no—
217C2×D188—22no—
218C2×D188—22no—
219C2×D188—22no—
220C2×D188—22no—
221C2×D188—22no—
222C2×D188—22no—
223C2×D188—22no—
224C2×D188C22⋊C414yes—
225C2×D188C22⋊C414yes—
226C2×D188C22×C414yes—
227C2×D188C2×D414yes—
228C2×C4×D47—216no—
229C2×C4×D47—88no—
230M16×C47—22no—
231M16×C47—22no—
232M16×C47—41no—
233M16×C47—41no—
234C2×C8×C47—22no—
235C2×C8×C47—41no—
236C2×C8×C47—41no—
237C4⋊C4×C47—22no—
238C4⋊C4×C47—22no—
239C22⋊C4×C47—22no—
240C22⋊C4×C47—22no—
241C42×C47—22no—
242C42×C47C2×D414yescomplemented
243C22⋊Dic47—22no—
244C22⋊Dic47—22no—
245C22⋊Dic47—22no—
246C22⋊Dic47—22no—
247(C2×D47)⋊C4—216no—
248(C2×D47)⋊C4—216no—
249C4⋊Dic47—22no—
250C4⋊Dic47—22no—
251C4⋊Dic47—22no—
252C4⋊Dic47—22no—
253C4×Dic47—22no—
254C4×Dic47—22no—
255C4×Dic47C22×C414yescomplemented
256C4×Dic47C2×D414yescomplemented
257#10625329—22no—
258#10625329—22no—
259#10625329—41no—
260#10625329—41no—
261C2×C47⋊C8—22no—
262C2×C47⋊C8—41no—
263C2×C47⋊C8—41no—
264C23×C47—22no—
265C23×C47—42no—
266C23×C47—44no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47C2×C22⋊C411yescharacteristic
270C23×C47C2×C22⋊C411yescharacteristic
271C23×C47#12011yescharacteristic
272C23×C47#12011yescharacteristic
273C23×C47#12311yescharacteristic
274C23×C47#12311yescharacteristic
275C23×C47C22×D411yescharacteristic
276C22×D47—24no—
277C22×D47—24no—
278C22×D47—24no—
279C22×D47—24no—
280C22×D47—24no—
281C22×D47—24no—
282C22×D47—48no—
283C22×D47—48no—
284C22×D47—84no—
285C22×D47—84no—
286C22×D47—84no—
287C22×D47—84no—
288C22×D47—84no—
289C22×D47C2×C22⋊C418yes—
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—41no—
293Q8×C47—41no—
294D4×C47—22no—
295D4×C47—22no—
296D4×C47—42no—
297D4×C47—42no—
298D4×C47—42no—
299D4×C47—42no—
300D4×C47—41no—
301D4×C47—41no—
302C2×C4×C47—22no—
303C2×C4×C47—24no—
304C2×C4×C47—44no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—42no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47C2×C22⋊C411yescharacteristic
312C2×C4×C47C2×C22⋊C411yescharacteristic
313C2×C4×C47C4×D411yescharacteristic
314C2×C4×C47C4×D411yescharacteristic
315C2×C4×C47C4×D411yescharacteristic
316C2×C4×C47C4×D411yescharacteristic
317C2×C4×C47C4×D411yescharacteristic
318C2×C4×C47C4×D411yescharacteristic
319C2×C4×C47C4×D411yescharacteristic
320C2×C4×C47C4×D411yescharacteristic
321C2×C4×C47#12011yescharacteristic
322C2×C4×C47#12011yescharacteristic
323C2×C4×C47#12111yescharacteristic
324C2×C4×C47#12111yescharacteristic
325C2×C4×C47#12111yescharacteristic
326C2×C4×C47#12111yescharacteristic
327C2×C4×C47#12111yescharacteristic
328C2×C4×C47#12111yescharacteristic
329C2×C4×C47#12111yescharacteristic
330C2×C4×C47#12111yescharacteristic
331C2×C4×C47#12311yescharacteristic
332C2×C4×C47#12311yescharacteristic
333C2×C4×C47C23×C411yescharacteristic
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C22×D411yescharacteristic
336C2×C4×C47C22×D411yescharacteristic
337C2×C4×C47C2×#4111yescharacteristic
338C2×C4×C47C2×#4111yescharacteristic
339C22⋊D47—816no—
340C2×Dic47—24no—
341C2×Dic47—24no—
342C2×Dic47—44no—
343C2×Dic47—44no—
344D188—24no—
345D188—24no—
346D188—24no—
347D188—24no—
348D188—24no—
349D188—24no—
350D188—24no—
351D188—24no—
352C4×D47—816no—
353C8×C47—42no—
354C47⋊C8—42no—
355C2×#1911—471nomaximal, Sylow
356C22×C47—22no—
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—44no—
364C22×C47—42no—
365C22×C47—82no—
366C22×C47—82no—
367C22×C47#38611yescharacteristic
368C22×C47#38611yescharacteristic
369C22×C47#38611yescharacteristic
370C22×C47#38611yescharacteristic
371C22×C47C22×C22⋊C411yescharacteristic
372C22×C47C2×#12011yescharacteristic
373C22×C47C2×#12311yescharacteristic
374C2×D47—28no—
375C2×D47—48no—
376C2×D47—48no—
377C2×D47—48no—
378C2×D47—48no—
379C2×D47—84no—
380C2×D47—84no—
381C2×D47—84no—
382C4×C47—44no—
383C4×C47—42no—
384C4×C47#38611yescharacteristic
385C4×C47#38611yescharacteristic
386C4×C47#38611yescharacteristic
387C4×C47#38611yescharacteristic
388C4×C47C2×C4×D411yescharacteristic
389C4×C47C2×C4×D411yescharacteristic
390C4×C47C2×#12111yescharacteristic
391C4×C47C2×#12111yescharacteristic
392Dic47—44no—
393Dic47—44no—
394C2×#535—471no—
395C2×#518—471no—
396C2×#421—471no—
397C2×#421D4711yescharacteristic, complemented
398C22×#100—471no—
399#1911—478no—
400C2×H(3,ℤ/4)—471no—
401C2×H(3,ℤ/4)—471no—
402C2×C47—21no—
403C2×C47—21no—
404C2×C47—21no—
405C2×C47—21no—
406C2×C47—21no—
407C2×C47—21no—
408C2×C47—82no—
409C2×C47#191112yescomplemented
410C2×C47C2×#38611yescharacteristic
411D47—48no—
412C22×#41C2×D4711yescharacteristic
413C23×D4—471no—
414C22×M16—471no—
415C22×M16C2×D4711yescharacteristic
416#535—474no—
417#535—474no—
418#535—942no—
419#535—942no—
420C2×#127—472no—
421C2×#124—472no—
422C2×#121—942no—
423C2×#120—942no—
424#518—474no—
425#518—942no—
426#518—942no—
427#518—942no—
428C2×C4×D4—942no—
429C2×C4×D4—942no—
430C2×#117—471no—
431C2×#117—471no—
432C2×#117C2×D4711yescharacteristic
433C22×C22⋊C4—942no—
434#421—22no—
435#421—474no—
436#421—942no—
437#421C2×D4714yescomplemented
438C2×#104—22no—
439C2×#104—942no—
440C2×#100—474no—
441C2×#100—942no—
442C2×#100—942no—
443H(3,ℤ/4)—474no—
444H(3,ℤ/4)—474no—
445C47C2×#191111yescharacteristic, complemented, Sylow
446C25—472no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41C4×D4712yescomplemented
458C2×#41C22×D4712yes—
459C22×Q8C4×D4711yescharacteristic, complemented
460C22×D4—21no—
461C22×D4—472no—
462C22×D4—472no—
463C22×D4—472no—
464C22×D4—472no—
465C22×D4—472no—
466C22×D4—472no—
467C22×D4—944no—
468C22×D4—941no—
469C22×D4—941no—
470C22×D4—941no—
471C22×D4—941no—
472C22×D4—941no—
473C22×D4—941no—
474C22×D4—941no—
475C22×D4—941no—
476C22×D4C4×D4711yescharacteristic, complemented
477C23×C4—21no—
478C23×C4—944no—
479C23×C4C22×D4711yescharacteristic
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—472no—
486C2×M16—941no—
487C2×M16—941no—
488C2×M16—941no—
489C2×M16—941no—
490C2×M16—941no—
491C2×M16C22×D4712yes—
492C22×C8—21no—
493C22×C8—941no—
494#127—478no—
495#127—944no—
496#124—478no—
497#124—944no—
498#121—948no—
499#121—948no—
500#120—948no—
501#120—948no—
502C4×D4—948no—
503C4×D4—948no—
504C4×D4—948no—
505C4×D4—948no—
506#117—21no—
507#117—21no—
508#117—472no—
509#117—472no—
510#117—472no—
511#117—472no—
512#117—941no—
513#117—941no—
514#117—941no—
515#117—941no—
516#117C22⋊D4712yescomplemented
517#117C22×D4712yes—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—948no—
523C2×C22⋊C4—948no—
524C2×C22⋊C4—944no—
525C2×C22⋊C4—944no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C42—472no—
529C2×C42—472no—
530C2×C42C22⋊D4712yescomplemented
531#104—28no—
532#104—948no—
533#100—948no—
534C24—21no—
535C24—474no—
536C24—474no—
537C24—474no—
538C24—942no—
539C24—942no—
540C24—942no—
541C24—942no—
542C24—3764no—
543C24D4×D4711yescharacteristic
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8C2×C4×D4712yescomplemented
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—474no—
578C2×D4—474no—
579C2×D4—474no—
580C2×D4—474no—
581C2×D4—9416no—
582C2×D4—942no—
583C2×D4—942no—
584C2×D4—942no—
585C2×D4—942no—
586C2×D4—942no—
587C2×D4—942no—
588C2×D4—942no—
589C2×D4—942no—
590C2×D4—942no—
591C2×D4—942no—
592C2×D4—942no—
593C2×D4—942no—
594C2×D4—942no—
595C2×D4—942no—
596C2×D4—942no—
597C2×D4—942no—
598C2×D4—942no—
599C2×D4—942no—
600C2×D4—942no—
601C2×D4—942no—
602C2×D4—942no—
603C2×D4—942no—
604C2×D4—942no—
605C2×D4—942no—
606C2×D4—3768no—
607C2×D4C2×C4×D4712yescomplemented
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—9416no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—3768no—
620C22×C4C2×C4×D4711yescharacteristic
621C22×C4C2×C4×D4711yescharacteristic
622C22×C4#1062535011yescharacteristic
623C22×C4#1062535011yescharacteristic
624C22×C4D4×D4711yescharacteristic
625C22×C4D4×D4711yescharacteristic
626C22×C4D4×D4711yescharacteristic
627C22×C4D4×D4711yescharacteristic
628C22×C4D4×D4711yescharacteristic
629C22×C4#1062535211yescharacteristic
630C22×C4#1062535211yescharacteristic
631C22×C4C2×C22⋊D4711yescharacteristic
632C22×C4C2×C22⋊D4711yescharacteristic
633C22×C4C23×D4711yescharacteristic
634M16—22no—
635M16—22no—
636M16—41no—
637M16—41no—
638M16—942no—
639M16—942no—
640M16—1881no—
641M16—1881no—
642C2×C8—22no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—942no—
646C2×C8—1881no—
647C2×C8—1881no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—942no—
651C4⋊C4—942no—
652C4⋊C4—942no—
653C4⋊C4—942no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—9416no—
657C22⋊C4—9416no—
658C22⋊C4—942no—
659C22⋊C4—942no—
660C22⋊C4—942no—
661C22⋊C4—942no—
662C42—22no—
663C42—474no—
664C42—474no—
665C42—942no—
666C42—942no—
667C42C2×C22⋊D4714yescomplemented
668C23—22no—
669C23—42no—
670C23—44no—
671C23—41no—
672C23—41no—
673C23—478no—
674C23—944no—
675C23—944no—
676C23—944no—
677C23—944no—
678C23—944no—
679C23—944no—
680C23—3764no—
681C23—3764no—
682C23—3764no—
683C23—3764no—
684C23—3764no—
685C23—1888no—
686C23—1888no—
687C23C22⋊C4×D4711yescharacteristic
688C23C22⋊C4×D4711yescharacteristic
689C23#1309399211yescharacteristic
690C23#1309399211yescharacteristic
691C23#1309400611yescharacteristic
692C23#1309400611yescharacteristic
693C23C2×D4×D4711yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—41no—
697Q8—41no—
698D4—22no—
699D4—22no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—41no—
705D4—41no—
706D4—944no—
707D4—944no—
708D4—944no—
709D4—944no—
710D4—944no—
711D4—944no—
712D4—944no—
713D4—944no—
714D4—37616no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—44no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—944no—
725C2×C4—944no—
726C2×C4—37616no—
727C2×C4—1884no—
728C2×C4—1884no—
729C2×C4C22⋊C4×D4711yescharacteristic
730C2×C4C22⋊C4×D4711yescharacteristic
731C2×C4(C22⋊D47)⋊C411yescharacteristic
732C2×C4(C22⋊D47)⋊C411yescharacteristic
733C2×C4(C22⋊D47)⋊C411yescharacteristic
734C2×C4(C22⋊D47)⋊C411yescharacteristic
735C2×C4C4×C22⋊D4711yescharacteristic
736C2×C4C4×C22⋊D4711yescharacteristic
737C2×C4C4×C22⋊D4711yescharacteristic
738C2×C4C4×C22⋊D4711yescharacteristic
739C2×C4#1309399211yescharacteristic
740C2×C4#1309399211yescharacteristic
741C2×C4#1309399511yescharacteristic
742C2×C4#1309399511yescharacteristic
743C2×C4#1309399511yescharacteristic
744C2×C4#1309399511yescharacteristic
745C2×C4#1309399711yescharacteristic
746C2×C4#1309399711yescharacteristic
747C2×C4#1309399711yescharacteristic
748C2×C4#1309399711yescharacteristic
749C2×C4#1309400611yescharacteristic
750C2×C4#1309400611yescharacteristic
751C2×C4C22×C4×D4711yescharacteristic
752C2×C4C2×D4×D4711yescharacteristic
753C2×C4C2×D4×D4711yescharacteristic
754C2×C4C22×C22⋊D4711yescharacteristic
755C2×C4C2×#1062535211yescharacteristic
756C2×C4C2×#1062535011yescharacteristic
757C8—42no—
758C8—1882no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—44no—
767C22—42no—
768C22—82no—
769C22—82no—
770C22—948no—
771C22—3764no—
772C22—3764no—
773C22—3764no—
774C22—1888no—
775C22—1888no—
776C22—1888no—
777C22—1888no—
778C22#1568899911yescharacteristic
779C22#1568899911yescharacteristic
780C22#1568899911yescharacteristic
781C22#1568899911yescharacteristic
782C22C2×C22⋊C4×D4711yescharacteristic
783C22C2×#1309399211yescharacteristic
784C22C2×#1309400611yescharacteristic
785C4—44no—
786C4—42no—
787C4—1884no—
788C4—1884no—
789C4#1568899911yescharacteristic
790C4#1568899911yescharacteristic
791C4#1568899911yescharacteristic
792C4#1568899911yescharacteristic
793C4C2×(C22⋊D47)⋊C411yescharacteristic
794C4C2×C4×C22⋊D4711yescharacteristic
795C4C2×#1309399511yescharacteristic
796C4C2×#1309399711yescharacteristic
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—82no—
804C2—1888no—
805C2#2024391712yesdirect product factor
806C2C2×#1568899911yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#421C2
socleC22×C47#386
prime radicalC2×#15689687C2
cosocleC22×C4×C47C24
hypercenterC2×#421D47
hypocenterC47C2×#1911
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#15689597C2semidirect
3. C2×#15689140C2semidirect
4. C22×#13093940C2semidirect
5. #20243917C2direct (N × H)
6. C2×#15688880C2semidirect
7. C2×#15688879C2semidirect
8. C2×C47×#421C2semidirect
13. #15689687C4semidirect
15. C2×#13094020C4semidirect
16. C2×#13094013C4semidirect
22. #15689597C22semidirect
29. #15689140C22semidirect
33. C2×#13093940C22semidirect
34. #15688880C22semidirect
35. #15688879C22semidirect
40. C47×#421C22semidirect
67. #13094020C2×C4semidirect
69. #13094013C2×C4semidirect
82. #13093983C2×C4semidirect
83. #13093983D4semidirect
94. C2×C4×Dic47C2×C4semidirect
95. C2×C4×Dic47D4semidirect
108. C2×#41×C47C2×C4semidirect
110. C22×Q8×C47C2×C4semidirect
112. C22×D4×C47C2×C4semidirect
124. #117×C47D4semidirect
128. C2×C42×C47D4semidirect
161. C2×Q8×C47C22×C4semidirect
173. C2×D4×C47C22×C4semidirect
242. C42×C47C2×D4semidirect
255. C4×Dic47C22×C4semidirect
256. C4×Dic47C2×D4semidirect
397. C2×#421D47semidirect
409. C2×C47#1911semidirect
437. #421C2×D47semidirect
445. C47C2×#1911semidirect
457. C2×#41C4×D47semidirect
459. C22×Q8C4×D47semidirect
476. C22×D4C4×D47semidirect
516. #117C22⋊D47semidirect
530. C2×C42C22⋊D47semidirect
565. C2×Q8C2×C4×D47semidirect
607. C2×D4C2×C4×D47semidirect
667. C42C2×C22⋊D47semidirect
805. C2#20243917direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896872
C2×#156895972
C2×#156891402
C22×#130939402
#202439172
C2×#156888802
C2×#156888792
C2×C47×#4212
C2×#191147