Finite Group Databasebeta

← C2×#20252183 #27080326

Subgroups — C2×#20252183 #27080326

Order 12032.

2854 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094045C211yesmaximal, characteristic
2C2×C4×#10625354C211yesmaximal, characteristic, complemented
3C2×C4×#10625352C211yesmaximal, characteristic, complemented
4#20252183C2116yesmaximal, direct product factor
5C2×#15689233C211yesmaximal, characteristic, complemented
6C2×#15689232C211yesmaximal, characteristic, complemented
7C2×#15689228C211yesmaximal, characteristic, complemented
8C2×#15689227C211yesmaximal, characteristic, complemented
9C2×#15689225C211yesmaximal, characteristic, complemented
10C2×#15689224C211yesmaximal, characteristic, complemented
11C2×#15689222C211yesmaximal, characteristic, complemented
12C2×#15689160C211yesmaximal, characteristic, complemented
13C2×#15689118C211yesmaximal, characteristic, complemented
14C2×#15689116C211yesmaximal, characteristic, complemented
15C2×#97×D47C211yesmaximal, characteristic, complemented
16C2×C47×#440C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625352C2211yescharacteristic
19C2×#13094045C4116yescomplemented
20C2×#13094045C2218yes—
21C22×#10625337C2211yescharacteristic
22C22×#10625325C2211yescharacteristic
23C22×#10625334C2211yescharacteristic
24C22×C8×D47C2211yescharacteristic
25C22×C8×D47C2211yescharacteristic
26C4×#10625354—24no—
27C4×#10625354C2218yescomplemented
28C4×#10625352—24no—
29C4×#10625352C2218yescomplemented
30C2×Q8×Dic47C2211yescharacteristic
31C2×C4×Dic94C2211yescharacteristic
32C2×#13093989C2211yescharacteristic
33C2×C4×D188—21no—
34C2×C4×D188C2211yescharacteristic
35C2×D4×Dic47C2211yescharacteristic
36C2×#13093986—21no—
37C2×#13093986C2211yescharacteristic
38C2×C4×C22⋊D47—21no—
39C2×(C22⋊D47)⋊C4—21no—
40C2×#13093982—21no—
41C2×#13093982C2211yescharacteristic
42C2×#13093982C2211yescharacteristic
43C2×#13093980—21no—
44C22×C4×Dic47—21no—
45C2×C42×D47—21no—
46C2×C42×D47C2211yescharacteristic
47#15689233C2218yescomplemented
48#15689232C2218yescomplemented
49#15689228C2218yescomplemented
50#15689227C2218yescomplemented
51#15689225C2218yescomplemented
52#15689224C2218yescomplemented
53#15689222C2218yescomplemented
54#15689160C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093955C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58#15689118C2218yescomplemented
59#15689116C2218yescomplemented
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×#13093935C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69#97×D47C2218yescomplemented
70C22×SD16×C47C2211yescharacteristic
71C2×C4×Q8×C47C2211yescharacteristic
72C2×C4×D4×C47C2211yescharacteristic
73C47×#440C2218yescomplemented
74C2×#107×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C2×#97×C47C2211yescharacteristic
78C2×#10625354—22no—
79C2×#10625354—24no—
80C2×#10625354C2×C418yescomplemented
81C2×#10625354C2314yes—
82C2×#10625352—22no—
83C2×#10625352—24no—
84C2×#10625352C2×C418yescomplemented
85C2×#10625352C2314yes—
86C22×Dic94C2311yescharacteristic
87C22×D188—21no—
88C22×D188C2311yescharacteristic
89C22×C22⋊D47—21no—
90C23×Dic47—21no—
91C23×Dic47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47—21no—
95C22×C4×D47D411yescharacteristic
96C22×C4×D47D411yescharacteristic
97C22×C4×D47C2311yescharacteristic
98#13094045C2×C4164yescomplemented
99C2×#10625337C2×C418yescomplemented
100C2×#10625337C2314yes—
101C2×#10625325C2×C418yescomplemented
102C2×#10625325C2314yes—
103C2×#10625334C2×C418yescomplemented
104C2×#10625334C2314yes—
105C22×C47⋊C8C2311yescharacteristic
106C22×C47⋊C8C2311yescharacteristic
107C2×C8×D47—24no—
108C2×C8×D47C2×C418yescomplemented
109C2×C8×D47C2314yes—
110C2×C8×D47C2314yes—
111Q8×Dic47—22no—
112Q8×Dic47C2314yes—
113C4×Dic94—22no—
114C4×Dic94C2314yes—
115#13093989—22no—
116#13093989C2314yes—
117C4×D188—28no—
118C4×D188—22no—
119C4×D188C2314yes—
120D4×Dic47—22no—
121D4×Dic47C2314yes—
122#13093986—28no—
123#13093986—22no—
124#13093986C2314yes—
125C4×C22⋊D47—28no—
126(C22⋊D47)⋊C4—28no—
127#13093982—22no—
128#13093982—22no—
129#13093982—28no—
130#13093982C2314yes—
131#13093982C2314yes—
132#13093980—28no—
133C2×C4⋊Dic47—21no—
134C2×C4⋊Dic47C2311yescharacteristic
135C2×C4⋊Dic47C2311yescharacteristic
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×C22⋊Dic47—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47—28no—
149C2×C4×Dic47D411yescharacteristic
150C2×C4×Dic47D411yescharacteristic
151C2×C4×Dic47C2311yescharacteristic
152C42×D47—28no—
153C42×D47D414yes—
154C42×D47C2314yes—
155#13093958C2314yes—
156#13093955C2314yes—
157#13093955C2314yes—
158#13093949C2314yes—
159#13093948C2314yes—
160#13093947C2314yes—
161#13093946C2314yes—
162#13093945C2314yes—
163#13093944C2314yes—
164#13093935C2314yes—
165#13093934C2314yes—
166#13093934C2314yes—
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×C47C2314yes—
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×C47C2314yes—
185#103×C47C2314yes—
186#102×C47C2314yes—
187#97×C47C2314yes—
188C24×C47—21no—
189C23×D47—21no—
190C23×D47C2×D411yescharacteristic
191C2×Q8×C47—21no—
192C2×Q8×C47—22no—
193C2×Q8×C47C22×C414yes—
194C2×Q8×C47C2412yes—
195C2×D4×C47—21no—
196C2×D4×C47—22no—
197C2×D4×C47C22×C414yes—
198C2×D4×C47C2412yes—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—24no—
203C22×C4×C47—44no—
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2411yescharacteristic
207C2×C22⋊D47—28no—
208C2×C22⋊D47—24no—
209C22×Dic47—21no—
210C22×Dic47—28no—
211C22×Dic47—24no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—24no—
215C22×Dic47—44no—
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D411yescharacteristic
218C22×Dic47C2×D411yescharacteristic
219#10625354—216no—
220#10625354—28no—
221#10625354C22×C4116yescomplemented
222#10625352—216no—
223#10625352—28no—
224#10625352C22×C4116yescomplemented
225C2×D188—28no—
226C2×D188—24no—
227C2×D188—21no—
228C2×D188—22no—
229C2×D188C22×C414yes—
230C2×D188C2412yes—
231C2×C4×D47—28no—
232C2×C4×D47—24no—
233C2×C4×D47—24no—
234C2×C4×D47—24no—
235C2×C4×D47—42no—
236C2×C4×D47—42no—
237C2×C4×D47—44no—
238C2×C4×D47—44no—
239C2×C4×D47C22×C414yes—
240C2×C4×D47C2×D414yes—
241C2×C4×D47C2×D414yes—
242C2×C4×D47C2×D412yes—
243C2×C4×D47#4114yes—
244C2×C4×D47C2412yes—
245C2×Dic94—21no—
246C2×Dic94—22no—
247C2×Dic94C22×C414yes—
248C2×Dic94C2412yes—
249SD16×C47C22×C4116yescomplemented
250C2×C8×C47—22no—
251C2×C8×C47C22×C414yes—
252C2×C8×C47C2412yes—
253C2×C8×C47C2412yes—
254C4⋊C4×C47—24no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47—21no—
257C4⋊C4×C47C2412yes—
258C4⋊C4×C47C2412yes—
259C22⋊C4×C47—24no—
260C42×C47—24no—
261C42×C47C2×D412yes—
262C42×C47C2412yes—
263C22⋊Dic47—24no—
264#10625337C22×C4116yescomplemented
265#10625334C22×C4116yescomplemented
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4—24no—
270C4⋊Dic47—21no—
271C4⋊Dic47—21no—
272C4⋊Dic47—24no—
273C4⋊Dic47C2412yes—
274C4⋊Dic47C2412yes—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277C4×Dic47—24no—
278C4×Dic47—24no—
279C4×Dic47—24no—
280C4×Dic47—24no—
281C4×Dic47—24no—
282C4×Dic47C2×D414yes—
283C4×Dic47C2×D412yes—
284C4×Dic47C2×D414yes—
285C4×Dic47C2412yes—
286C2×C47⋊C8—22no—
287C2×C47⋊C8C22×C414yes—
288C2×C47⋊C8C2412yes—
289C2×C47⋊C8C2412yes—
290#10625325C22×C4116yescomplemented
291C8×D47—28no—
292C8×D47C22×C4116yescomplemented
293C23×C47—24no—
294C23×C47—22no—
295C23×C47—42no—
296C23×C47—42no—
297C23×C47C22×D411yescharacteristic
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—24no—
301C22×D47—22no—
302C22×D47—42no—
303C22×D47—42no—
304C22×D47C4×D414yes—
305C22×D47C22×D412yes—
306Q8×C47—24no—
307Q8×C47—22no—
308Q8×C47C23×C414yes—
309D4×C47—24no—
310D4×C47—22no—
311D4×C47C23×C414yes—
312C2×C4×C47—24no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—48no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47C23×C412yes—
322C2×C4×C47C22×D412yes—
323C2×C4×C47C22×D412yes—
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C2×#4112yes—
326C2×C4×C47C2511yescharacteristic
327C22⋊D47—216no—
328C2×Dic47—24no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—216no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—48no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47C4×D414yes—
339C2×Dic47C22×D412yes—
340C2×Dic47C22×D412yes—
341C2×Dic47C22×D412yes—
342D188—216no—
343D188—24no—
344D188—22no—
345D188C23×C414yes—
346C4×D47—216no—
347C4×D47—44no—
348C4×D47—44no—
349C4×D47—48no—
350C4×D47—48no—
351C4×D47C4×D418yes—
352C4×D47C23×C414yes—
353C4×D47C2×#4114yes—
354Dic94—24no—
355Dic94—22no—
356Dic94C23×C414yes—
357C8×C47—22no—
358C8×C47C23×C414yes—
359C47⋊C8—22no—
360C47⋊C8C23×C414yes—
361C2×#2943—471nomaximal, Sylow
362C22×C47—24no—
363C22×C47—48no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47C2×C4×D412yes—
367C22×C47#57512yes—
368C22×C47#57512yes—
369C22×C47C23×D411yescharacteristic
370C2×D47—28no—
371C2×D47—22no—
372C2×D47—22no—
373C2×D47—24no—
374C2×D47—48no—
375C2×D47—42no—
376C2×D47—42no—
377C2×D47C2×C4×D414yes—
378C4×C47—24no—
379C4×C47—22no—
380C4×C47—22no—
381C4×C47—42no—
382C4×C47—42no—
383C4×C47C2×C4×D412yes—
384C4×C47C24×C411yescharacteristic
385C4×C47C22×#4111yescharacteristic
386Dic47—24no—
387Dic47—22no—
388Dic47—22no—
389Dic47—42no—
390Dic47—42no—
391Dic47C2×C4×D414yes—
392C22×#135—471no—
393C2×C4×#41—471no—
394C2×C4×#41—471no—
395#2943—4716no—
396C2×#442—471no—
397C2×#442—471no—
398C2×#441—471no—
399C2×#441—471no—
400C2×#440—471no—
401C2×#440—471no—
402C2×#440—471no—
403C2×#440D4711yescharacteristic, complemented
404C2×#427—471no—
405C2×#416—471no—
406C2×#416—471no—
407C22×#97—471no—
408C2×C47—44no—
409C2×C47#294314yescomplemented
410C2×C47C22×C4×D411yescharacteristic
411C2×C47C2×#57511yescharacteristic
412C2×C47C2×#57511yescharacteristic
413D47—24no—
414D47—44no—
415C22×#41—471no—
416C22×#41—471no—
417C2×#135—4716no—
418C2×#135—478no—
419C22×Q16—471no—
420C22×SD16—471no—
421C22×SD16C2×D4711yescharacteristic
422C22×D8—471no—
423C23×C8—471no—
424C23×C8—471no—
425C4×#41—478no—
426C4×#41—478no—
427C4×#41—944no—
428C4×#41—944no—
429C2×C4×Q8—471no—
430C2×C4×Q8—471no—
431C2×C4×Q8—471no—
432C2×C4×Q8C2×D4711yescharacteristic
433C2×C4×D4—471no—
434C2×C4×D4—471no—
435C2×C4×D4—471no—
436C2×C4×D4—941no—
437C2×C4×D4—941no—
438C2×C4×D4—941no—
439C2×C4×D4—941no—
440C2×C4×D4C2×D4711yescharacteristic
441C2×#117—471no—
442C2×#117—471no—
443C2×#117—941no—
444C2×#117—941no—
445C22×C42—471no—
446C22×C42—941no—
447C22×C42—941no—
448#442—478no—
449#442—478no—
450#441—478no—
451#441—478no—
452#440—478no—
453#440—478no—
454#440—478no—
455#440C2×D4718yescomplemented
456#427—478no—
457C2×#107—471no—
458C2×#107C2×D4711yescharacteristic
459C2×#106—471no—
460C2×#106—471no—
461#416—478no—
462#416—478no—
463C2×#103—471no—
464C2×#103—471no—
465C2×#103—471no—
466C2×#103C2×D4711yescharacteristic
467C2×#102—471no—
468C2×#102—471no—
469C2×#102—471no—
470C2×#102C2×D4711yescharacteristic
471C2×#97—471no—
472C2×#97—471no—
473C2×#97—471no—
474C2×#97—478no—
475C2×#97C2×D4711yescharacteristic
476C47C2×#294311yescharacteristic, complemented, Sylow
477C2×#41—478no—
478C2×#41—474no—
479C2×#41—478no—
480C2×#41—474no—
481C2×#41—942no—
482C2×#41—944no—
483C2×#41—942no—
484C2×#41—944no—
485C22×Q8—471no—
486C22×Q8C22×D4711yescharacteristic
487C22×D4—471no—
488C22×D4—941no—
489C22×D4—941no—
490C22×D4C22×D4711yescharacteristic
491C23×C4—21no—
492C23×C4—471no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—941no—
496C23×C4—941no—
497C23×C4—941no—
498C23×C4—941no—
499C23×C4—941no—
500#135—4764no—
501C2×Q16—478no—
502C2×Q16—474no—
503C2×SD16—478no—
504C2×SD16—474no—
505C2×SD16C4×D4718yescomplemented
506C2×SD16C22×D4714yes—
507C2×D8—478no—
508C2×D8—474no—
509C22×C8—471no—
510C22×C8—478no—
511C22×C8—474no—
512C22×C8—471no—
513C22×C8—474no—
514C22×C8—944no—
515C22×C8C22×D4711yescharacteristic
516C22×C8C22×D4711yescharacteristic
517C4×Q8—22no—
518C4×Q8—474no—
519C4×Q8—474no—
520C4×Q8—474no—
521C4×Q8—942no—
522C4×Q8—942no—
523C4×Q8—942no—
524C4×Q8C22×D4714yes—
525C4×D4—22no—
526C4×D4—474no—
527C4×D4—474no—
528C4×D4—474no—
529C4×D4—948no—
530C4×D4—942no—
531C4×D4—942no—
532C4×D4—948no—
533C4×D4—948no—
534C4×D4—948no—
535C4×D4—942no—
536C4×D4C22×D4714yes—
537#117—474no—
538#117—474no—
539#117—948no—
540#117—948no—
541#117—942no—
542#117—942no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—471no—
545C2×C4⋊C4—471no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4—941no—
548C2×C4⋊C4—941no—
549C2×C4⋊C4C22×D4711yescharacteristic
550C2×C4⋊C4C22×D4711yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C42—21no—
558C2×C42—471no—
559C2×C42—471no—
560C2×C42—471no—
561C2×C42—474no—
562C2×C42—474no—
563C2×C42—948no—
564C2×C42—948no—
565C2×C42—941no—
566C2×C42—941no—
567C2×C42—941no—
568C2×C42—941no—
569C2×C42—941no—
570C2×C42C22×D4711yescharacteristic
571#107—474no—
572#107C22×D4714yes—
573#106—474no—
574#106—474no—
575#103—474no—
576#103—474no—
577#103—474no—
578#103C22×D4714yes—
579#102—474no—
580#102—474no—
581#102—474no—
582#102C22×D4714yes—
583#97—474no—
584#97—474no—
585#97—474no—
586#97C22×D4714yes—
587C24—21no—
588C24—471no—
589C24—941no—
590#41—4716no—
591#41—4716no—
592#41—9416no—
593#41—948no—
594#41—9416no—
595#41—948no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—474no—
599C2×Q8—472no—
600C2×Q8—941no—
601C2×Q8—942no—
602C2×Q8C2×C4×D4714yes—
603C2×Q8C23×D4712yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—474no—
607C2×D4—472no—
608C2×D4—944no—
609C2×D4—948no—
610C2×D4—944no—
611C2×D4—948no—
612C2×D4—941no—
613C2×D4—942no—
614C2×D4C2×C4×D4714yes—
615C2×D4C23×D4712yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—44no—
621C22×C4—471no—
622C22×C4—474no—
623C22×C4—472no—
624C22×C4—474no—
625C22×C4—472no—
626C22×C4—471no—
627C22×C4—471no—
628C22×C4—474no—
629C22×C4—474no—
630C22×C4—944no—
631C22×C4—948no—
632C22×C4—944no—
633C22×C4—944no—
634C22×C4—948no—
635C22×C4—944no—
636C22×C4—941no—
637C22×C4—941no—
638C22×C4—941no—
639C22×C4—944no—
640C22×C4—1882no—
641C22×C4—1882no—
642C22×C4—1884no—
643C22×C4—1884no—
644C22×C4—1884no—
645C22×C4D4×D4711yescharacteristic
646C22×C4D4×D4711yescharacteristic
647C22×C4C23×D4711yescharacteristic
648Q16—4716no—
649SD16—4716no—
650SD16C2×C4×D47116yescomplemented
651D8—4716no—
652C2×C8—22no—
653C2×C8—474no—
654C2×C8—472no—
655C2×C8—4716no—
656C2×C8—472no—
657C2×C8—948no—
658C2×C8—942no—
659C2×C8C2×C4×D4714yes—
660C2×C8C23×D4712yes—
661C2×C8C23×D4712yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—472no—
666C4⋊C4—472no—
667C4⋊C4—944no—
668C4⋊C4—944no—
669C4⋊C4—944no—
670C4⋊C4—941no—
671C4⋊C4—941no—
672C4⋊C4C23×D4712yes—
673C4⋊C4C23×D4712yes—
674C22⋊C4—24no—
675C22⋊C4—944no—
676C22⋊C4—944no—
677C22⋊C4—944no—
678C22⋊C4—944no—
679C22⋊C4—944no—
680C42—24no—
681C42—474no—
682C42—474no—
683C42—472no—
684C42—472no—
685C42—944no—
686C42—944no—
687C42—944no—
688C42—944no—
689C42—944no—
690C42D4×D4712yes—
691C42C23×D4712yes—
692C23—24no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—474no—
697C23—472no—
698C23—942no—
699C23—942no—
700C23—944no—
701C23—942no—
702C23—1882no—
703C23—1882no—
704C23C2×D4×D4711yescharacteristic
705Q8—24no—
706Q8—22no—
707Q8—474no—
708Q8—944no—
709Q8—942no—
710Q8C22×C4×D4714yes—
711D4—24no—
712D4—22no—
713D4—474no—
714D4—9416no—
715D4—9416no—
716D4—944no—
717D4—942no—
718D4C22×C4×D4714yes—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—48no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—474no—
729C2×C4—472no—
730C2×C4—478no—
731C2×C4—474no—
732C2×C4—474no—
733C2×C4—472no—
734C2×C4—472no—
735C2×C4—9416no—
736C2×C4—9416no—
737C2×C4—944no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—1884no—
744C2×C4—1884no—
745C2×C4—1888no—
746C2×C4—1888no—
747C2×C4—1888no—
748C2×C4—1882no—
749C2×C4—1882no—
750C2×C4C22×C4×D4712yes—
751C2×C4C2×D4×D4712yes—
752C2×C4C2×D4×D4712yes—
753C2×C4C2×D4×D4711yescharacteristic
754C2×C4#41×D4712yes—
755C2×C4C24×D4711yescharacteristic
756C8—22no—
757C8—474no—
758C8—942no—
759C8C22×C4×D4714yes—
760C22—24no—
761C22—48no—
762C22—42no—
763C22—42no—
764C22—474no—
765C22—948no—
766C22—942no—
767C22—942no—
768C22—944no—
769C22—1888no—
770C22—1882no—
771C22—1882no—
772C22C4×D4×D4712yes—
773C22#1568991912yes—
774C22#1568992212yes—
775C22C22×D4×D4711yescharacteristic
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—474no—
782C4—944no—
783C4—942no—
784C4—942no—
785C4—1882no—
786C4—1882no—
787C4C4×D4×D4712yes—
788C4C23×C4×D4711yescharacteristic
789C4C2×#41×D4711yescharacteristic
790C2—44no—
791C2—944no—
792C2—1884no—
793C2#2025218314yesdirect product factor
794C2C2×C4×D4×D4711yescharacteristic
795C2C2×#1568991911yescharacteristic
796C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#440C2
socleC23×C47C22×D4
prime radicalC22×#13094045C2
cosocleC2×C4×C47C25
hypercenterC2×#440D47
hypocenterC47C2×#2943
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×C4×#10625354C2semidirect
3. C2×C4×#10625352C2semidirect
4. #20252183C2direct (N × H)
5. C2×#15689233C2semidirect
6. C2×#15689232C2semidirect
7. C2×#15689228C2semidirect
8. C2×#15689227C2semidirect
9. C2×#15689225C2semidirect
10. C2×#15689224C2semidirect
11. C2×#15689222C2semidirect
12. C2×#15689160C2semidirect
13. C2×#15689118C2semidirect
14. C2×#15689116C2semidirect
15. C2×#97×D47C2semidirect
16. C2×C47×#440C2semidirect
19. C2×#13094045C4semidirect
27. C4×#10625354C22semidirect
29. C4×#10625352C22semidirect
47. #15689233C22semidirect
48. #15689232C22semidirect
49. #15689228C22semidirect
50. #15689227C22semidirect
51. #15689225C22semidirect
52. #15689224C22semidirect
53. #15689222C22semidirect
54. #15689160C22semidirect
58. #15689118C22semidirect
59. #15689116C22semidirect
69. #97×D47C22semidirect
73. C47×#440C22semidirect
80. C2×#10625354C2×C4semidirect
84. C2×#10625352C2×C4semidirect
98. #13094045C2×C4semidirect
99. C2×#10625337C2×C4semidirect
101. C2×#10625325C2×C4semidirect
103. C2×#10625334C2×C4semidirect
108. C2×C8×D47C2×C4semidirect
170. C2×SD16×C47C2×C4semidirect
221. #10625354C22×C4semidirect
224. #10625352C22×C4semidirect
249. SD16×C47C22×C4semidirect
264. #10625337C22×C4semidirect
265. #10625334C22×C4semidirect
290. #10625325C22×C4semidirect
292. C8×D47C22×C4semidirect
403. C2×#440D47semidirect
409. C2×C47#2943semidirect
455. #440C2×D47semidirect
476. C47C2×#2943semidirect
505. C2×SD16C4×D47semidirect
650. SD16C2×C4×D47semidirect
793. C2#20252183direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940452
C2×C4×#106253542
C2×C4×#106253522
#202521832
C2×#156892332
C2×#156892322
C2×#156892282
C2×#156892272
C2×#156892252
C2×#156892242
C2×#156892222
C2×#156891602
C2×#156891182
C2×#156891162
C2×#97×D472
C2×C47×#4402
C2×#294347