Finite Group Databasebeta

← C2×#20252219 #27080374

Subgroups — C2×#20252219 #27080374

Order 12032.

2946 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094051C211yesmaximal, characteristic
2C2×#15689605C211yesmaximal, characteristic, complemented
3C2×#15689595C211yesmaximal, characteristic, complemented
4#20252219C2116yesmaximal, direct product factor
5C2×#15689236C211yesmaximal, characteristic, complemented
6C2×#15689232C211yesmaximal, characteristic, complemented
7C2×#15689226C211yesmaximal, characteristic, complemented
8C2×SD16×Dic47C211yesmaximal, characteristic, complemented
9C2×C4×#10625336C211yesmaximal, characteristic, complemented
10C2×#15689205C211yesmaximal, characteristic, complemented
11C2×C4×#10625334C211yesmaximal, characteristic, complemented
12C2×#15689164C211yesmaximal, characteristic, complemented
13C2×#15689118C211yesmaximal, characteristic, complemented
14C2×#102×D47C211yesmaximal, characteristic, complemented
15C2×#15689080C211yesmaximal, characteristic, complemented
16C2×C47×#440C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C2×#13094051C4116yescomplemented
20C2×#13094051C2218yes—
21C22×#10625336C2211yescharacteristic
22C22×D376C2211yescharacteristic
23C22×#10625334C2211yescharacteristic
24C22×#10625324C2211yescharacteristic
25C22×C8×D47C2211yescharacteristic
26#15689605—24no—
27#15689605C2218yescomplemented
28#15689595—24no—
29#15689595C2218yescomplemented
30C2×Q8×Dic47C2211yescharacteristic, complemented
31C2×C4×D188—21no—
32C2×C4×D188C2211yescharacteristic
33C2×C4×D188C2211yescharacteristic, complemented
34C2×D4×Dic47C2211yescharacteristic
35C2×#13093986—21no—
36C2×#13093986C2211yescharacteristic
37C2×#13093986C2211yescharacteristic, complemented
38C2×C4×C22⋊D47—21no—
39C2×(C22⋊D47)⋊C4—21no—
40C2×#13093982C2211yescharacteristic
41C2×#13093981—21no—
42C2×#13093981C2211yescharacteristic
43C2×C4⋊C4×D47—21no—
44C2×C4⋊C4×D47C2211yescharacteristic
45C22×(C2×D47)⋊C4—21no—
46C2×C22⋊C4×D47—21no—
47#15689236C2218yescomplemented
48#15689232C2218yescomplemented
49#15689226C2218yescomplemented
50SD16×Dic47C2218yescomplemented
51C4×#10625336C2218yescomplemented
52#15689205C2218yescomplemented
53C4×#10625334C2218yescomplemented
54#15689164C2218yescomplemented
55C2×#13093957C2211yescharacteristic, complemented
56C2×#13093956C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58#15689118C2218yescomplemented
59C2×#13093948C2211yescharacteristic, complemented
60C2×#13093946C2211yescharacteristic
61C2×#13093946C2211yescharacteristic, complemented
62C2×#13093945C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic, complemented
65#102×D47C2218yescomplemented
66#15689080C2218yescomplemented
67C2×#13093934C2211yescharacteristic, complemented
68C2×C4×C47⋊C8C2211yescharacteristic, complemented
69C2×C8×Dic47C2211yescharacteristic, complemented
70C22×SD16×C47C2211yescharacteristic
71C2×C4×Q8×C47C2211yescharacteristic, complemented
72C2×C4×D4×C47C2211yescharacteristic
73C47×#440C2218yescomplemented
74C2×#107×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×#102×C47C2211yescharacteristic
77C2×#97×C47C2211yescharacteristic, complemented
78C24×D47—21no—
79C2×#10625354—22no—
80C2×#10625354—24no—
81C2×#10625354C2×C418yescomplemented
82C2×#10625354C2314yes—
83C22×D188—21no—
84C22×D188C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C2×D4×D47—22no—
88C2×D4×D47—24no—
89C2×D4×D47C2×C418yescomplemented
90C2×D4×D47C2314yes—
91C23×Dic47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47—21no—
95C22×C4×D47—21no—
96C22×C4×D47—21no—
97C22×C4×D47—21no—
98C22×C4×D47C2311yescharacteristic
99#13094051C2×C4164yescomplemented
100C2×#10625336C2×C418yescomplemented
101C2×#10625336C2314yes—
102C2×D376C2×C418yescomplemented
103C2×D376C2314yes—
104C2×#10625334C2×C418yescomplemented
105C2×#10625334C2314yes—
106C2×#10625324C2×C418yescomplemented
107C2×#10625324C2314yes—
108C22×C47⋊C8C2311yescharacteristic
109C22×C47⋊C8C2311yescharacteristic
110C2×C8×D47—24no—
111C2×C8×D47C2314yes—
112Q8×Dic47—22no—
113Q8×Dic47C2314yescomplemented
114C4×D188—22no—
115C4×D188—22no—
116C4×D188—28no—
117C4×D188C2314yes—
118C4×D188C2314yescomplemented
119D4×Dic47—22no—
120D4×Dic47C2314yes—
121#13093986—28no—
122#13093986—22no—
123#13093986—22no—
124#13093986C2314yes—
125#13093986C2314yescomplemented
126C4×C22⋊D47—28no—
127(C22⋊D47)⋊C4—28no—
128#13093982—22no—
129#13093982C2314yes—
130#13093981—28no—
131#13093981D414yes—
132#13093981C2314yes—
133C2×C4⋊Dic47—21no—
134C2×C4⋊Dic47C2311yescharacteristic
135C2×C4⋊Dic47C2311yescharacteristic
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4D411yescharacteristic
138C2×Dic47⋊C4D411yescharacteristic
139C4⋊C4×D47—22no—
140C4⋊C4×D47—28no—
141C4⋊C4×D47C2314yes—
142C2×C22⋊Dic47—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—28no—
149C2×(C2×D47)⋊C4D411yescharacteristic
150C2×(C2×D47)⋊C4D411yescharacteristic
151C22⋊C4×D47—28no—
152C2×C4×Dic47—21no—
153C2×C4×Dic47—21no—
154C2×C4×Dic47C2311yescharacteristic
155#13093957C2314yescomplemented
156#13093956C2314yescomplemented
157#13093955C2314yescomplemented
158#13093948C2314yescomplemented
159#13093946C2314yes—
160#13093946C2314yescomplemented
161#13093945C2314yes—
162#13093944C2314yes—
163#13093944C2314yescomplemented
164#13093934C2314yescomplemented
165C4×C47⋊C8C2314yescomplemented
166C8×Dic47C2314yescomplemented
167C22×Q8×C47C2311yescharacteristic
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C2×SD16×C47C2×C418yescomplemented
171C2×SD16×C47C2314yes—
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174C4×Q8×C47—22no—
175C4×Q8×C47C2314yescomplemented
176C4×D4×C47—22no—
177C4×D4×C47C2314yes—
178C2×C4⋊C4×C47—21no—
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47—21no—
182C2×C42×C47—21no—
183C2×C42×C47C2311yescharacteristic
184#107×C47C2314yescomplemented
185#103×C47C2314yescomplemented
186#102×C47C2314yes—
187#97×C47C2314yescomplemented
188C24×C47—21no—
189C23×D47—21no—
190C23×D47—21no—
191C23×D47—28no—
192C23×D47—24no—
193C23×D47—82no—
194C23×D47—82no—
195C23×D47C2×D411yescharacteristic
196C2×Q8×C47—21no—
197C2×Q8×C47—22no—
198C2×Q8×C47C22×C414yes—
199C2×Q8×C47C2412yes—
200C2×D4×C47—21no—
201C2×D4×C47—22no—
202C2×D4×C47C22×C414yes—
203C2×D4×C47C2412yes—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—24no—
208C22×C4×C47—82no—
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2411yescharacteristic
212C2×C22⋊D47—28no—
213C2×C22⋊D47—24no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—24no—
217C22×Dic47—82no—
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D411yescharacteristic
220C22×Dic47C2×D411yescharacteristic
221#10625354—216no—
222#10625354—28no—
223#10625354C22×C4116yescomplemented
224D4×D47—216no—
225D4×D47—28no—
226D4×D47C22×C4116yescomplemented
227C2×D188—28no—
228C2×D188—24no—
229C2×D188—21no—
230C2×D188—21no—
231C2×D188—22no—
232C2×D188—22no—
233C2×D188C22×C414yes—
234C2×D188C22×C414yes—
235C2×D188C2412yes—
236C2×D188C2412yes—
237C2×C4×D47—28no—
238C2×C4×D47—24no—
239C2×C4×D47—24no—
240C2×C4×D47—24no—
241C2×C4×D47—24no—
242C2×C4×D47—24no—
243C2×C4×D47—24no—
244C2×C4×D47—82no—
245C2×C4×D47—82no—
246C2×C4×D47—82no—
247C2×C4×D47—82no—
248C2×C4×D47—82no—
249C2×C4×D47C22×C414yes—
250C2×C4×D47C2×D412yes—
251C2×C4×D47#4114yes—
252C2×C4×D47C2412yes—
253SD16×C47C22×C4116yescomplemented
254C2×C8×C47—22no—
255C2×C8×C47C22×C414yes—
256C2×C8×C47C2412yes—
257C2×C8×C47C2412yes—
258C4⋊C4×C47—24no—
259C4⋊C4×C47—21no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47C2412yes—
262C4⋊C4×C47C2412yes—
263C22⋊C4×C47—24no—
264C42×C47—24no—
265C42×C47C2×D412yes—
266C42×C47C2412yes—
267C22⋊Dic47—24no—
268#10625336C22×C4116yescomplemented
269#10625334C22×C4116yescomplemented
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4—24no—
272(C2×D47)⋊C4—24no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4—24no—
275(C2×D47)⋊C4C2×D414yes—
276(C2×D47)⋊C4C2×D414yes—
277C4⋊Dic47—21no—
278C4⋊Dic47—21no—
279C4⋊Dic47—24no—
280C4⋊Dic47C2412yes—
281C4⋊Dic47C2412yes—
282Dic47⋊C4—24no—
283Dic47⋊C4C2×D414yes—
284Dic47⋊C4C2×D414yes—
285C4×Dic47—24no—
286C4×Dic47—24no—
287C4×Dic47C2×D412yes—
288C4×Dic47C2412yes—
289C2×C47⋊C8—22no—
290C2×C47⋊C8C22×C414yes—
291C2×C47⋊C8C2412yes—
292C2×C47⋊C8C2412yes—
293D376C22×C4116yescomplemented
294#10625324C22×C4116yescomplemented
295C8×D47—28no—
296C23×C47—24no—
297C23×C47—22no—
298C23×C47—42no—
299C23×C47—42no—
300C23×C47C22×D411yescharacteristic
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—24no—
304C22×D47—24no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—216no—
308C22×D47—42no—
309C22×D47—42no—
310C22×D47—42no—
311C22×D47—42no—
312C22×D47—816no—
313C22×D47—84no—
314C22×D47—84no—
315C22×D47C4×D414yes—
316C22×D47C22×D412yes—
317Q8×C47—24no—
318Q8×C47—22no—
319Q8×C47C23×C414yes—
320D4×C47—24no—
321D4×C47—22no—
322D4×C47C23×C414yes—
323C2×C4×C47—24no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—42no—
330C2×C4×C47—42no—
331C2×C4×C47—84no—
332C2×C4×C47C23×C412yes—
333C2×C4×C47C22×D412yes—
334C2×C4×C47C22×D412yes—
335C2×C4×C47C22×D411yescharacteristic
336C2×C4×C47C2×#4112yes—
337C2×C4×C47C2511yescharacteristic
338C22⋊D47—216no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47—84no—
346C2×Dic47C4×D414yes—
347C2×Dic47C22×D412yes—
348C2×Dic47C22×D412yes—
349C2×Dic47C22×D412yes—
350D188—216no—
351D188—24no—
352D188—24no—
353D188—22no—
354D188—22no—
355D188C23×C414yes—
356D188C23×C414yes—
357C4×D47—216no—
358C4×D47—84no—
359C4×D47—84no—
360C4×D47—84no—
361C4×D47—84no—
362C4×D47—84no—
363C4×D47C4×D418yes—
364C4×D47C23×C414yes—
365C4×D47C2×#4114yes—
366C8×C47—22no—
367C8×C47C23×C414yes—
368C47⋊C8—22no—
369C47⋊C8C23×C414yes—
370C2×#2946—471nomaximal, Sylow
371C22×C47—24no—
372C22×C47—48no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47C2×C4×D412yes—
376C22×C47#57612yes—
377C22×C47#57712yes—
378C22×C47C23×D411yescharacteristic
379C2×D47—28no—
380C2×D47—22no—
381C2×D47—22no—
382C2×D47—24no—
383C2×D47—24no—
384C2×D47—48no—
385C2×D47—48no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—42no—
389C2×D47—42no—
390C2×D47—816no—
391C2×D47C2×C4×D414yes—
392C4×C47—24no—
393C4×C47—22no—
394C4×C47—22no—
395C4×C47—42no—
396C4×C47—42no—
397C4×C47C2×C4×D412yes—
398C4×C47C24×C411yescharacteristic
399C4×C47C22×#4111yescharacteristic
400Dic47—22no—
401Dic47—22no—
402Dic47—42no—
403Dic47—42no—
404Dic47C2×C4×D414yes—
405C22×AGL(1,ℤ/8)—471no—
406C2×#520—471no—
407C2×#518—471no—
408#2946—4716no—
409C2×#442—471no—
410C2×#442—471no—
411C2×#440—471no—
412C2×#440D4711yescharacteristic, complemented
413C2×C4×SD16—471no—
414C2×C4×SD16—471no—
415C2×C4×D8—471no—
416C2×C4×D8—471no—
417C2×#428—471no—
418C2×#416—471no—
419C22×#102—471no—
420C2×#405—471no—
421C2×C47—44no—
422C2×C47#294614yescomplemented
423C2×C47C22×C4×D411yescharacteristic
424C2×C47C2×#57611yescharacteristic
425C2×C47C2×#57711yescharacteristic
426D47—24no—
427D47—44no—
428D47—44no—
429C22×#41—471no—
430C23×D4—471no—
431C2×AGL(1,ℤ/8)—4716no—
432C2×AGL(1,ℤ/8)—478no—
433C22×SD16—471no—
434C22×SD16C2×D4711yescharacteristic
435C22×D8—471no—
436C22×D8—471no—
437C22×M16—471no—
438C23×C8—471no—
439#520—478no—
440#520—944no—
441#518—478no—
442#518—944no—
443C2×C4×Q8—471no—
444C2×C4×Q8C2×D4711yescharacteristic, complemented
445C2×C4×D4—471no—
446C2×C4×D4—471no—
447C2×C4×D4—471no—
448C2×C4×D4—471no—
449C2×C4×D4—471no—
450C2×C4×D4—941no—
451C2×C4×D4—941no—
452C2×C4×D4—941no—
453C2×C4×D4—941no—
454C2×C4×D4C2×D4711yescharacteristic
455C2×#117—471no—
456C2×#117—471no—
457C2×#117—941no—
458C22×C4⋊C4—471no—
459C22×C4⋊C4—941no—
460C22×C22⋊C4—941no—
461C22×C22⋊C4—941no—
462#442—478no—
463#442—478no—
464#440—478no—
465#440C2×D4718yescomplemented
466C4×SD16—478no—
467C4×SD16—478no—
468C4×D8—478no—
469C4×D8—478no—
470#428—478no—
471C2×#107—471no—
472C2×#107C2×D4711yescharacteristic, complemented
473C2×#106—471no—
474C2×#106—471no—
475#416—478no—
476C2×#103—471no—
477C2×#103C2×D4711yescharacteristic, complemented
478C2×#102—471no—
479C2×#102—471no—
480C2×#102—471no—
481C2×#102—471no—
482C2×#102—471no—
483C2×#102—478no—
484C2×#102C2×D4711yescharacteristic
485#405—478no—
486C2×#97—471no—
487C2×#97C2×D4711yescharacteristic, complemented
488C2×C4×C8—471no—
489C2×C4×C8—471no—
490C47C2×#294611yescharacteristic, complemented, Sylow
491C25—941no—
492C2×#41—478no—
493C2×#41—474no—
494C2×#41—942no—
495C2×#41—944no—
496C22×Q8C22×D4711yescharacteristic
497C22×D4—478no—
498C22×D4—474no—
499C22×D4—471no—
500C22×D4—471no—
501C22×D4—941no—
502C22×D4—942no—
503C22×D4—944no—
504C22×D4—941no—
505C22×D4C22×D4711yescharacteristic
506C23×C4—21no—
507C23×C4—471no—
508C23×C4—941no—
509C23×C4—941no—
510C23×C4—941no—
511C23×C4—941no—
512C23×C4—941no—
513C23×C4—941no—
514C23×C4—941no—
515AGL(1,ℤ/8)—4764no—
516C2×SD16—478no—
517C2×SD16—474no—
518C2×SD16C4×D4718yescomplemented
519C2×SD16C22×D4714yes—
520C2×D8—478no—
521C2×D8—474no—
522C2×D8—478no—
523C2×D8—474no—
524C2×M16—478no—
525C2×M16—474no—
526C22×C8—471no—
527C22×C8—471no—
528C22×C8—474no—
529C22×C8—944no—
530C22×C8C22×D4711yescharacteristic
531C22×C8C22×D4711yescharacteristic
532C4×Q8—22no—
533C4×Q8—474no—
534C4×Q8—942no—
535C4×Q8C22×D4714yescomplemented
536C4×D4—22no—
537C4×D4—474no—
538C4×D4—474no—
539C4×D4—474no—
540C4×D4—474no—
541C4×D4—474no—
542C4×D4—948no—
543C4×D4—942no—
544C4×D4—942no—
545C4×D4—942no—
546C4×D4—948no—
547C4×D4—948no—
548C4×D4—948no—
549C4×D4—942no—
550C4×D4—942no—
551C4×D4C22×D4714yes—
552#117—474no—
553#117—474no—
554#117—474no—
555#117—948no—
556#117—942no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—471no—
559C2×C4⋊C4—471no—
560C2×C4⋊C4—471no—
561C2×C4⋊C4—471no—
562C2×C4⋊C4—474no—
563C2×C4⋊C4—948no—
564C2×C4⋊C4—942no—
565C2×C4⋊C4—941no—
566C2×C4⋊C4—941no—
567C2×C4⋊C4C22×D4711yescharacteristic
568C2×C4⋊C4C22×D4711yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—471no—
571C2×C22⋊C4—471no—
572C2×C22⋊C4—948no—
573C2×C22⋊C4—948no—
574C2×C22⋊C4—941no—
575C2×C22⋊C4—941no—
576C2×C22⋊C4—941no—
577C2×C22⋊C4—941no—
578C2×C22⋊C4—941no—
579C2×C22⋊C4—941no—
580C2×C42—21no—
581C2×C42—471no—
582C2×C42—941no—
583C2×C42—941no—
584C2×C42C22×D4711yescharacteristic
585#107—474no—
586#107C22×D4714yescomplemented
587#106—474no—
588#106—474no—
589#103—474no—
590#103C22×D4714yescomplemented
591#102—474no—
592#102—474no—
593#102—474no—
594#102—474no—
595#102—474no—
596#102C22×D4714yes—
597#97—474no—
598#97C22×D4714yescomplemented
599C4×C8—474no—
600C4×C8—474no—
601C24—21no—
602C24—471no—
603C24—944no—
604C24—948no—
605C24—941no—
606C24—941no—
607C24—3762no—
608C24—3762no—
609#41—4716no—
610#41—9416no—
611#41—948no—
612C2×Q8—21no—
613C2×Q8—22no—
614C2×Q8C2×C4×D4714yes—
615C2×Q8C23×D4712yes—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—4716no—
619C2×D4—474no—
620C2×D4—474no—
621C2×D4—472no—
622C2×D4—472no—
623C2×D4—944no—
624C2×D4—948no—
625C2×D4—9416no—
626C2×D4—948no—
627C2×D4—944no—
628C2×D4—948no—
629C2×D4—941no—
630C2×D4—941no—
631C2×D4—942no—
632C2×D4—942no—
633C2×D4C2×C4×D4714yes—
634C2×D4C23×D4712yes—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—82no—
640C22×C4—471no—
641C22×C4—474no—
642C22×C4—472no—
643C22×C4—474no—
644C22×C4—472no—
645C22×C4—471no—
646C22×C4—471no—
647C22×C4—944no—
648C22×C4—948no—
649C22×C4—944no—
650C22×C4—944no—
651C22×C4—944no—
652C22×C4—944no—
653C22×C4—941no—
654C22×C4—941no—
655C22×C4—944no—
656C22×C4—944no—
657C22×C4—3762no—
658C22×C4—3762no—
659C22×C4—3762no—
660C22×C4—3762no—
661C22×C4—3762no—
662C22×C4—3762no—
663C22×C4D4×D4711yescharacteristic
664C22×C4D4×D4711yescharacteristic
665C22×C4C23×D4711yescharacteristic
666SD16—4716no—
667SD16C2×C4×D47116yescomplemented
668D8—4716no—
669D8—4716no—
670M16—4716no—
671C2×C8—22no—
672C2×C8—474no—
673C2×C8—472no—
674C2×C8—472no—
675C2×C8—948no—
676C2×C8—942no—
677C2×C8C2×C4×D4714yes—
678C2×C8C23×D4712yes—
679C2×C8C23×D4712yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—474no—
684C4⋊C4—474no—
685C4⋊C4—472no—
686C4⋊C4—472no—
687C4⋊C4—944no—
688C4⋊C4—944no—
689C4⋊C4—941no—
690C4⋊C4—941no—
691C4⋊C4C23×D4712yes—
692C4⋊C4C23×D4712yes—
693C22⋊C4—24no—
694C22⋊C4—474no—
695C22⋊C4—474no—
696C22⋊C4—944no—
697C22⋊C4—944no—
698C22⋊C4—944no—
699C22⋊C4—944no—
700C22⋊C4—944no—
701C22⋊C4—944no—
702C42—24no—
703C42—472no—
704C42—472no—
705C42—944no—
706C42—944no—
707C42D4×D4712yes—
708C42C23×D4712yes—
709C23—24no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—474no—
714C23—472no—
715C23—9416no—
716C23—942no—
717C23—942no—
718C23—944no—
719C23—944no—
720C23—942no—
721C23—942no—
722C23—37616no—
723C23—3764no—
724C23—3764no—
725C23—1882no—
726C23—1882no—
727C23—1882no—
728C23—1882no—
729C23C2×D4×D4711yescharacteristic
730Q8—24no—
731Q8—22no—
732Q8C22×C4×D4714yes—
733D4—24no—
734D4—22no—
735D4—474no—
736D4—474no—
737D4—9416no—
738D4—9416no—
739D4—944no—
740D4—944no—
741D4—942no—
742D4—942no—
743D4C22×C4×D4714yes—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—84no—
753C2×C4—474no—
754C2×C4—472no—
755C2×C4—478no—
756C2×C4—474no—
757C2×C4—474no—
758C2×C4—472no—
759C2×C4—472no—
760C2×C4—9416no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—3764no—
766C2×C4—3764no—
767C2×C4—3764no—
768C2×C4—3764no—
769C2×C4—3764no—
770C2×C4—3764no—
771C2×C4—1882no—
772C2×C4—1882no—
773C2×C4C22×C4×D4712yes—
774C2×C4C2×D4×D4712yes—
775C2×C4C2×D4×D4712yes—
776C2×C4C2×D4×D4711yescharacteristic
777C2×C4#41×D4712yes—
778C2×C4C24×D4711yescharacteristic
779C8—22no—
780C8—474no—
781C8—942no—
782C8C22×C4×D4714yes—
783C22—24no—
784C22—48no—
785C22—42no—
786C22—42no—
787C22—474no—
788C22—948no—
789C22—942no—
790C22—942no—
791C22—944no—
792C22—944no—
793C22—37616no—
794C22—1888no—
795C22—1888no—
796C22—1882no—
797C22—1882no—
798C22—1882no—
799C22—1882no—
800C22C4×D4×D4712yes—
801C22#1568992712yes—
802C22#1568993212yes—
803C22C22×D4×D4711yescharacteristic
804C4—24no—
805C4—22no—
806C4—22no—
807C4—42no—
808C4—42no—
809C4—474no—
810C4—942no—
811C4—942no—
812C4—1882no—
813C4—1882no—
814C4C4×D4×D4712yes—
815C4C23×C4×D4711yescharacteristic
816C4C2×#41×D4711yescharacteristic
817C2—44no—
818C2—944no—
819C2—1884no—
820C2—1884no—
821C2#2025221914yesdirect product factor
822C2C2×C4×D4×D4711yescharacteristic
823C2C2×#1568992711yescharacteristic
824C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#440C2
socleC23×C47C22×D4
prime radicalC22×#13094051C2
cosocleC2×C4×C47C25
hypercenterC2×#440D47
hypocenterC47C2×#2946
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#15689605C2semidirect
3. C2×#15689595C2semidirect
4. #20252219C2direct (N × H)
5. C2×#15689236C2semidirect
6. C2×#15689232C2semidirect
7. C2×#15689226C2semidirect
8. C2×SD16×Dic47C2semidirect
9. C2×C4×#10625336C2semidirect
10. C2×#15689205C2semidirect
11. C2×C4×#10625334C2semidirect
12. C2×#15689164C2semidirect
13. C2×#15689118C2semidirect
14. C2×#102×D47C2semidirect
15. C2×#15689080C2semidirect
16. C2×C47×#440C2semidirect
19. C2×#13094051C4semidirect
27. #15689605C22semidirect
29. #15689595C22semidirect
30. C2×Q8×Dic47C22semidirect
33. C2×C4×D188C22semidirect
37. C2×#13093986C22semidirect
47. #15689236C22semidirect
48. #15689232C22semidirect
49. #15689226C22semidirect
50. SD16×Dic47C22semidirect
51. C4×#10625336C22semidirect
52. #15689205C22semidirect
53. C4×#10625334C22semidirect
54. #15689164C22semidirect
55. C2×#13093957C22semidirect
56. C2×#13093956C22semidirect
57. C2×#13093955C22semidirect
58. #15689118C22semidirect
59. C2×#13093948C22semidirect
61. C2×#13093946C22semidirect
64. C2×#13093944C22semidirect
65. #102×D47C22semidirect
66. #15689080C22semidirect
67. C2×#13093934C22semidirect
68. C2×C4×C47⋊C8C22semidirect
69. C2×C8×Dic47C22semidirect
71. C2×C4×Q8×C47C22semidirect
73. C47×#440C22semidirect
74. C2×#107×C47C22semidirect
75. C2×#103×C47C22semidirect
77. C2×#97×C47C22semidirect
81. C2×#10625354C2×C4semidirect
89. C2×D4×D47C2×C4semidirect
99. #13094051C2×C4semidirect
100. C2×#10625336C2×C4semidirect
102. C2×D376C2×C4semidirect
104. C2×#10625334C2×C4semidirect
106. C2×#10625324C2×C4semidirect
113. Q8×Dic47C23semidirect
118. C4×D188C23semidirect
125. #13093986C23semidirect
155. #13093957C23semidirect
156. #13093956C23semidirect
157. #13093955C23semidirect
158. #13093948C23semidirect
160. #13093946C23semidirect
163. #13093944C23semidirect
164. #13093934C23semidirect
165. C4×C47⋊C8C23semidirect
166. C8×Dic47C23semidirect
170. C2×SD16×C47C2×C4semidirect
175. C4×Q8×C47C23semidirect
184. #107×C47C23semidirect
185. #103×C47C23semidirect
187. #97×C47C23semidirect
223. #10625354C22×C4semidirect
226. D4×D47C22×C4semidirect
253. SD16×C47C22×C4semidirect
268. #10625336C22×C4semidirect
269. #10625334C22×C4semidirect
293. D376C22×C4semidirect
294. #10625324C22×C4semidirect
412. C2×#440D47semidirect
422. C2×C47#2946semidirect
444. C2×C4×Q8C2×D47semidirect
465. #440C2×D47semidirect
472. C2×#107C2×D47semidirect
477. C2×#103C2×D47semidirect
487. C2×#97C2×D47semidirect
490. C47C2×#2946semidirect
518. C2×SD16C4×D47semidirect
535. C4×Q8C22×D47semidirect
586. #107C22×D47semidirect
590. #103C22×D47semidirect
598. #97C22×D47semidirect
667. SD16C2×C4×D47semidirect
821. C2#20252219direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940512
C2×#156896052
C2×#156895952
#202522192
C2×#156892362
C2×#156892322
C2×#156892262
C2×SD16×Dic472
C2×C4×#106253362
C2×#156892052
C2×C4×#106253342
C2×#156891642
C2×#156891182
C2×#102×D472
C2×#156890802
C2×C47×#4402
C2×#294647