Finite Group Databasebeta

← C2×#20245039 #26369011

Subgroups — C2×#20245039 #26369011

Order 12032.

1406 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689687C211yesmaximal, characteristic
2C2×#15689097C211yesmaximal, characteristic, complemented
3#20245039C218yesmaximal, direct product factor
4C2×#15688911C214yesmaximal, complemented
5C2×C47×#413C211yesmaximal, characteristic, complemented
6C23×D188C411yescharacteristic, complemented
7#15689687—22no—
8#15689687—22no—
9#15689687C414yescomplemented
10#15689687C2214yes—
11C2×#13094020—21no—
12C2×#13094013—21no—
13C2×#13093998—21no—
14C2×#13093998—21no—
15C2×#13093992C412yescomplemented
16C2×#13093992C2212yes—
17C2×#13093983—21no—
18C2×#13093983C411yescharacteristic, complemented
19#15689097—22no—
20#15689097C2214yescomplemented
21C2×#13093939—21no—
22C2×#13093939C2212yes—
23#15688911C22116yescomplemented
24C22×#41×C47C2211yescharacteristic
25C22×M16×C47—21no—
26C47×#413—22no—
27C47×#413C2214yescomplemented
28C2×#101×C47—21no—
29C2×#100×C47C2212yes—
30C24×D47C2×C412yes—
31C22×D188—21no—
32C22×D188—21no—
33C22×D188—22no—
34C22×D188—42no—
35C22×D188—41no—
36C22×D188—41no—
37C22×D188C2×C414yescomplemented
38C22×C22⋊D47—22no—
39C22×C22⋊D47—22no—
40#13094020—24no—
41#13094020—24no—
42#13094013—24no—
43#13094013—24no—
44#13093998—24no—
45#13093998—24no—
46#13093998—24no—
47#13093998—24no—
48#13093992—24no—
49#13093992—22no—
50#13093992—22no—
51#13093992C2×C414yes—
52#13093992C2×C418yescomplemented
53#13093992C2314yes—
54#13093983—22no—
55#13093983—24no—
56#13093983—42no—
57#13093983C2×C414yescomplemented
58C2×C4⋊Dic47—21no—
59C2×C4⋊Dic47—41no—
60C2×C22⋊Dic47—22no—
61C2×C22⋊Dic47C2×C412yes—
62C2×(C2×D47)⋊C4—22no—
63C2×(C2×D47)⋊C4—22no—
64C2×C4×Dic47—21no—
65C2×C4×Dic47—41no—
66#13093939—24no—
67#13093939—22no—
68#13093939C2314yes—
69C2×#41×C47—41no—
70C2×#41×C47—41no—
71C2×#41×C47—42no—
72C2×#41×C47C2×C412yes—
73C2×#41×C47D412yes—
74C2×#41×C47D412yes—
75C2×#41×C47C2312yes—
76C22×Q8×C47D411yescharacteristic
77C22×D4×C47C2×C411yescharacteristic
78C22×D4×C47D411yescharacteristic
79C22×D4×C47C2311yescharacteristic
80C23×C4×C47C2×C411yescharacteristic
81C23×C4×C47D411yescharacteristic
82C23×C4×C47D411yescharacteristic
83C2×M16×C47—22no—
84C2×M16×C47—24no—
85C2×M16×C47—41no—
86C2×M16×C47—42no—
87C22×C8×C47—41no—
88#101×C47—24no—
89#100×C47—22no—
90#100×C47C2314yes—
91C24×C47C22⋊C411yescharacteristic
92C24×C47C22×C411yescharacteristic
93C24×C47C2×D411yescharacteristic
94C23×D47—22no—
95C23×D47—22no—
96C23×D47—42no—
97C23×D47—42no—
98C23×D47—84no—
99C23×D47C22×C414yes—
100#41×C47—42no—
101#41×C47—42no—
102#41×C47—42no—
103#41×C47—42no—
104#41×C47—42no—
105#41×C47—42no—
106#41×C47—42no—
107#41×C47—42no—
108C2×Q8×C47—41no—
109C2×Q8×C47—41no—
110C2×Q8×C47C22⋊C412yes—
111C2×Q8×C47C2×D412yes—
112C2×D4×C47—41no—
113C2×D4×C47—41no—
114C2×D4×C47—41no—
115C2×D4×C47—41no—
116C2×D4×C47—41no—
117C2×D4×C47—41no—
118C2×D4×C47C22⋊C412yes—
119C2×D4×C47C22⋊C412yes—
120C2×D4×C47C22×C412yes—
121C2×D4×C47C22×C411yescharacteristic
122C2×D4×C47C2×D412yes—
123C2×D4×C47C2×D411yescharacteristic
124C2×D4×C47C2×D411yescharacteristic
125C2×D4×C47C2411yescharacteristic
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—22no—
135C22×C4×C47C22⋊C411yescharacteristic
136C22×C4×C47C22⋊C412yes—
137C22×C4×C47C22⋊C411yescharacteristic
138C22×C4×C47C22⋊C412yes—
139C22×C4×C47C22⋊C412yes—
140C22×C4×C47C22⋊C411yescharacteristic
141C22×C4×C47C22×C412yes—
142C22×C4×C47C2×D412yes—
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D412yes—
145C2×C22⋊D47—24no—
146C2×C22⋊D47—28no—
147C2×C22⋊D47—24no—
148C2×C22⋊D47—84no—
149C2×C22⋊D47—84no—
150C22×Dic47—22no—
151C22×Dic47—42no—
152C2×D188—24no—
153C2×D188—24no—
154C2×D188—42no—
155C2×D188—42no—
156C2×D188—44no—
157C2×D188—44no—
158C2×D188—42no—
159C2×D188—41no—
160C2×D188—41no—
161C2×D188—44no—
162C2×D188—44no—
163M16×C47—24no—
164M16×C47—42no—
165M16×C47—44no—
166C2×C8×C47—42no—
167C2×C8×C47—44no—
168C22⋊Dic47—22no—
169C22⋊Dic47—24no—
170C22⋊Dic47—42no—
171C22⋊Dic47C22×C414yes—
172(C2×D47)⋊C4—24no—
173(C2×D47)⋊C4—28no—
174(C2×D47)⋊C4—24no—
175C4⋊Dic47—24no—
176C4⋊Dic47—44no—
177C4×Dic47—24no—
178C4×Dic47—44no—
179C23×C47—21no—
180C23×C47—21no—
181C23×C47—21no—
182C23×C47—21no—
183C23×C47—21no—
184C23×C47—21no—
185C23×C47—42no—
186C23×C47—42no—
187C23×C47—42no—
188C23×C47C2×C22⋊C411yescharacteristic
189C23×C47C2×C22⋊C411yescharacteristic
190C23×C47C2×C22⋊C411yescharacteristic
191C23×C47C2×C22⋊C412yes—
192C23×C47C23×C411yescharacteristic
193C23×C47C22×D411yescharacteristic
194C22×D47—24no—
195C22×D47—44no—
196C22×D47—44no—
197C22×D47—44no—
198C22×D47—42no—
199C22×D47—42no—
200C22×D47—44no—
201C22×D47—84no—
202C22×D47—84no—
203C22×D47—88no—
204C22×D47—88no—
205Q8×C47—42no—
206Q8×C47—42no—
207D4×C47—42no—
208D4×C47—42no—
209D4×C47—42no—
210D4×C47—41no—
211D4×C47—42no—
212D4×C47—41no—
213D4×C47—41no—
214D4×C47—41no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47#9912yes—
234C2×C4×C47#9911yescharacteristic
235C2×C4×C47#9911yescharacteristic
236C2×C4×C47C2×C22⋊C412yes—
237C2×C4×C47C2×C22⋊C412yes—
238C2×C4×C47C2×C22⋊C411yescharacteristic
239C2×C4×C47C2×C22⋊C412yes—
240C2×C4×C47C22×D411yescharacteristic
241C22⋊D47—84no—
242C22⋊D47—88no—
243C22⋊D47—84no—
244C2×Dic47—24no—
245C2×Dic47—44no—
246C2×Dic47—44no—
247C2×Dic47—84no—
248D188—48no—
249D188—44no—
250D188—44no—
251C8×C47—44no—
252C2×#2122—471nomaximal, Sylow
253C22×C47—22no—
254C22×C47—21no—
255C22×C47—21no—
256C22×C47—21no—
257C22×C47—22no—
258C22×C47—21no—
259C22×C47—42no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47—42no—
265C22×C47—42no—
266C22×C47—42no—
267C22×C47—42no—
268C22×C47—81no—
269C22×C47—81no—
270C22×C47C2×#9911yescharacteristic
271C22×C47C2×#9911yescharacteristic
272C22×C47C22×C22⋊C411yescharacteristic
273C2×D47—44no—
274C2×D47—44no—
275C2×D47—44no—
276C2×D47—84no—
277C2×D47—88no—
278C2×D47—84no—
279C2×D47—88no—
280C4×C47—21no—
281C4×C47—22no—
282C4×C47—21no—
283C4×C47—22no—
284C4×C47C2×#9912yes—
285C4×C47C2×#9912yes—
286Dic47—44no—
287Dic47—84no—
288C2×#535—471no—
289C2×#413D4711yescharacteristic, complemented
290C2×#410—471no—
291#2122—478no—
292C2×AΣL(1,𝔽16)—474no—
293C2×C47—21no—
294C2×C47—21no—
295C2×C47—41no—
296C2×C47—41no—
297C2×C47—41no—
298C2×C47—41no—
299C2×C47—42no—
300C2×C47#212212yescomplemented
301C2×C47C22×#9911yescharacteristic
302D47—84no—
303C22×#41C2×D4711yescharacteristic
304C23×D4—471no—
305C22×M16—21no—
306#535—474no—
307#535—474no—
308#535—942no—
309#535—942no—
310C2×#127—941no—
311C2×#124—941no—
312C2×#121—941no—
313C2×#121—941no—
314C2×#120—472no—
315C2×#120—472no—
316C2×#117—471no—
317C2×#117—941no—
318#413—22no—
319#413C2×D4714yescomplemented
320C2×#101—21no—
321C2×#100C2×D4712yes—
322#410—474no—
323#410—942no—
324C2×#99—472no—
325C2×#99—941no—
326AΣL(1,𝔽16)—4716no—
327C47C2×#212211yescharacteristic, complemented, Sylow
328C25—472no—
329C2×#41—41no—
330C2×#41—41no—
331C2×#41—42no—
332C2×#41C4×D4712yes—
333C2×#41D18812yes—
334C2×#41C22⋊D4712yes—
335C2×#41C22×D4712yes—
336C22×Q8C22⋊D4711yescharacteristic
337C22×D4—474no—
338C22×D4—942no—
339C22×D4—942no—
340C22×D4—941no—
341C22×D4—942no—
342C22×D4—941no—
343C22×D4—1882no—
344C22×D4—1881no—
345C22×D4—1881no—
346C22×D4C4×D4711yescharacteristic
347C22×D4D18811yescharacteristic
348C22×D4C22×D4711yescharacteristic
349C23×C4C4×D4711yescharacteristic
350C23×C4D18811yescharacteristic
351C23×C4C22⋊D4711yescharacteristic
352C2×M16—22no—
353C2×M16—24no—
354C2×M16—41no—
355C2×M16—42no—
356C22×C8—41no—
357#127—944no—
358#127—944no—
359#124—944no—
360#124—944no—
361#121—944no—
362#121—944no—
363#121—944no—
364#121—944no—
365#120—474no—
366#120—478no—
367#120—474no—
368#120—944no—
369#120—942no—
370#120—942no—
371#117—474no—
372#117—942no—
373#117—944no—
374#117—1882no—
375C2×C4⋊C4—941no—
376C2×C4⋊C4—1881no—
377C2×C22⋊C4—472no—
378C2×C22⋊C4—942no—
379C2×C22⋊C4—942no—
380C2×C22⋊C4—942no—
381C2×C42—941no—
382C2×C42—1881no—
383#101—24no—
384#100—22no—
385#100C22×D4714yes—
386#99—474no—
387#99—942no—
388#99—944no—
389C24—474no—
390C24—942no—
391C24—942no—
392C24—3764no—
393C24—1882no—
394C24—1882no—
395C24(C2×D47)⋊C411yescharacteristic
396C24C2×C4×D4711yescharacteristic
397C24C2×D18811yescharacteristic
398#41—42no—
399#41—42no—
400#41—42no—
401#41—42no—
402#41—42no—
403#41—42no—
404#41—42no—
405#41—42no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8(C2×D47)⋊C412yes—
409C2×Q8C2×C22⋊D4712yes—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—944no—
417C2×D4—948no—
418C2×D4—944no—
419C2×D4—944no—
420C2×D4—944no—
421C2×D4—3764no—
422C2×D4—3764no—
423C2×D4—1882no—
424C2×D4—1882no—
425C2×D4—1884no—
426C2×D4—1884no—
427C2×D4—1884no—
428C2×D4—1884no—
429C2×D4—1882no—
430C2×D4—1881no—
431C2×D4—1881no—
432C2×D4(C2×D47)⋊C412yes—
433C2×D4(C2×D47)⋊C412yes—
434C2×D4C2×C4×D4712yes—
435C2×D4C2×C4×D4711yescharacteristic
436C2×D4C2×D18811yescharacteristic
437C2×D4C2×D18812yes—
438C2×D4C2×C22⋊D4711yescharacteristic
439C2×D4C23×D4711yescharacteristic
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—942no—
450C22×C4—1882no—
451C22×C4(C2×D47)⋊C411yescharacteristic
452C22×C4(C2×D47)⋊C411yescharacteristic
453C22×C4(C2×D47)⋊C412yes—
454C22×C4(C2×D47)⋊C412yes—
455C22×C4(C2×D47)⋊C412yes—
456C22×C4(C2×D47)⋊C411yescharacteristic
457C22×C4C2×C4×D4712yes—
458C22×C4C2×D18812yes—
459C22×C4C2×C22⋊D4711yescharacteristic
460C22×C4C2×C22⋊D4712yes—
461M16—24no—
462M16—42no—
463M16—44no—
464C2×C8—42no—
465C2×C8—44no—
466C4⋊C4—944no—
467C4⋊C4—1884no—
468C22⋊C4—474no—
469C22⋊C4—942no—
470C22⋊C4—948no—
471C22⋊C4—944no—
472C22⋊C4—944no—
473C22⋊C4—944no—
474C22⋊C4—1882no—
475C42—944no—
476C42—1884no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—944no—
487C23—3768no—
488C23—3768no—
489C23—3764no—
490C23—3764no—
491C23—1884no—
492C23—1884no—
493C23—1884no—
494C23—1884no—
495C23—1882no—
496C23—1882no—
497C23C2×(C2×D47)⋊C411yescharacteristic
498C23C2×(C2×D47)⋊C411yescharacteristic
499C23C2×(C2×D47)⋊C411yescharacteristic
500C23C2×(C2×D47)⋊C412yes—
501C23C22×C4×D4711yescharacteristic
502C23C22×D18811yescharacteristic
503Q8—42no—
504Q8—42no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—41no—
509D4—42no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—3768no—
514D4—3764no—
515D4—3764no—
516D4—1888no—
517D4—1884no—
518D4—1884no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—944no—
538C2×C4—3764no—
539C2×C4—1884no—
540C2×C4—1884no—
541C2×C4#1309393812yes—
542C2×C4#1309393811yescharacteristic
543C2×C4#1309393811yescharacteristic
544C2×C4C2×(C2×D47)⋊C412yes—
545C2×C4C2×(C2×D47)⋊C412yes—
546C2×C4C2×(C2×D47)⋊C411yescharacteristic
547C2×C4C2×(C2×D47)⋊C412yes—
548C2×C4C22×C22⋊D4711yescharacteristic
549C8—44no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—22no—
555C22—21no—
556C22—42no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—3764no—
568C22—3768no—
569C22—3768no—
570C22—3764no—
571C22—1884no—
572C22—1884no—
573C22—1884no—
574C22C2×#1309393811yescharacteristic
575C22C2×#1309393811yescharacteristic
576C22C22×(C2×D47)⋊C411yescharacteristic
577C4—21no—
578C4—22no—
579C4—21no—
580C4—22no—
581C4—3764no—
582C4—1884no—
583C4C2×#1309393812yes—
584C4C2×#1309393812yes—
585C2—21no—
586C2—21no—
587C2—41no—
588C2—41no—
589C2—41no—
590C2—41no—
591C2—42no—
592C2—3764no—
593C2#2024503912yesdirect product factor
594C2C22×#1309393811yescharacteristic
subgroupG/H
centerC22C2×#13093938
commutatorC23×C47C23×C4
FrattiniC2×D4C23×D47
FittingC2×C47×#413C2
socleC22×C47C2×#99
prime radicalC2×#15689687C2
cosocleC2×D4×C47C24
hypercenterC2×#413D47
hypocenterC47C2×#2122
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#15689097C2semidirect
3. #20245039C2direct (N × H)
4. C2×#15688911C2semidirect
5. C2×C47×#413C2semidirect
6. C23×D188C4semidirect
9. #15689687C4semidirect
15. C2×#13093992C4semidirect
18. C2×#13093983C4semidirect
20. #15689097C22semidirect
23. #15688911C22semidirect
27. C47×#413C22semidirect
37. C22×D188C2×C4semidirect
52. #13093992C2×C4semidirect
57. #13093983C2×C4semidirect
289. C2×#413D47semidirect
300. C2×C47#2122semidirect
319. #413C2×D47semidirect
327. C47C2×#2122semidirect
593. C2#20245039direct (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×#156890972
#202450392
C2×#156889112
C2×C47×#4132
C2×#212247