Finite Group Databasebeta

← C2×#20254180 #27086842

Subgroups — C2×#20254180 #27086842

Order 12032.

2394 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689636C211yesmaximal, characteristic, complemented
2C2×#15689630C211yesmaximal, characteristic, complemented
3#20254180C2116yesmaximal, direct product factor
4C2×#15689462C211yesmaximal, characteristic, complemented
5C2×#15689461C211yesmaximal, characteristic, complemented
6C2×#15689448C211yesmaximal, characteristic, complemented
7C2×#15689445C211yesmaximal, characteristic, complemented
8C2×#15689361C211yesmaximal, characteristic, complemented
9C2×#15689358C211yesmaximal, characteristic, complemented
10C2×#15689355C211yesmaximal, characteristic, complemented
11C2×#15689349C211yesmaximal, characteristic, complemented
12C2×#15689284C211yesmaximal, characteristic, complemented
13C2×#15689268C211yesmaximal, characteristic, complemented
14C2×#15689267C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D47C211yesmaximal, characteristic, complemented
16C2×C47×#452C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C22×#10625336C2211yescharacteristic, complemented
20C22×#10625334C2211yescharacteristic, complemented
21C22×C8×D47C2211yescharacteristic
22C22×C8×D47C2211yescharacteristic
23#15689636—24no—
24#15689636C2218yescomplemented
25#15689630—24no—
26#15689630C2218yescomplemented
27C2×#13094009—21no—
28C2×#13094005—21no—
29C2×#13094000C2211yescharacteristic
30C2×#13094000C2211yescharacteristic
31C2×#13094000C2211yescharacteristic
32C2×#13093999C2211yescharacteristic
33C2×#13093998C2211yescharacteristic
34C2×#13093995C2211yescharacteristic
35C2×#13093995C2211yescharacteristic
36C2×#13093994—21no—
37C2×#13093992—21no—
38C2×#13093986—21no—
39C2×C4×C22⋊D47—21no—
40C2×C4×C22⋊D47—21no—
41C2×(C22⋊D47)⋊C4—21no—
42C2×#13093983C2211yescharacteristic
43C2×#13093982C2211yescharacteristic
44#15689462C2218yescomplemented
45#15689461C2218yescomplemented
46#15689448C2218yescomplemented
47#15689445C2218yescomplemented
48#15689361C2218yescomplemented
49#15689358C2218yescomplemented
50#15689355C2218yescomplemented
51#15689349C2218yescomplemented
52#15689284C2218yescomplemented
53#15689268C2218yescomplemented
54#15689267C2218yescomplemented
55C2×#13093958C2211yescharacteristic, complemented
56C2×#13093957C2211yescharacteristic, complemented
57C2×#13093956C2211yescharacteristic, complemented
58C2×#13093955C2211yescharacteristic, complemented
59C2×#13093948C2211yescharacteristic, complemented
60C2×#13093948C2211yescharacteristic, complemented
61C2×#13093948C2211yescharacteristic, complemented
62C2×#13093946C2211yescharacteristic, complemented
63C2×#13093946C2211yescharacteristic, complemented
64C2×#13093945C2211yescharacteristic, complemented
65C2×C22⋊(C47⋊C8)C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C22⋊C8×D47C2218yescomplemented
69C22×#41×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic, complemented
71C22×SD16×C47C2211yescharacteristic, complemented
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#452C2218yescomplemented
74C2×#103×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic
77C24×D47D411yescharacteristic
78C2×#10625354—22no—
79C2×#10625354—42no—
80C2×#10625354—42no—
81C2×#10625354C2314yes—
82C22×D188—21no—
83C22×D188—21no—
84C22×D188C2311yescharacteristic
85C22×C22⋊D47—21no—
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C23×Dic47D411yescharacteristic
89C22×C4×D47—21no—
90C22×C4×D47—42no—
91C22×C4×D47—42no—
92C22×C4×D47D411yescharacteristic
93C22×C4×D47D411yescharacteristic
94C22×C4×D47D414yes—
95C22×C4×D47C2311yescharacteristic
96C22×C4×D47C2311yescharacteristic
97C22×C4×D47C2314yes—
98C2×#10625336—42no—
99C2×#10625336C2314yescomplemented
100C2×#10625334—42no—
101C2×#10625334C2314yescomplemented
102C22×C47⋊C8C2311yescharacteristic
103C22×C47⋊C8C2311yescharacteristic
104C2×C8×D47—42no—
105C2×C8×D47—42no—
106C2×C8×D47C2314yes—
107C2×C8×D47C2314yes—
108#13094009—28no—
109#13094005—28no—
110#13094000—22no—
111#13094000—22no—
112#13094000—22no—
113#13094000C2314yes—
114#13094000C2314yes—
115#13094000C2314yes—
116#13093999—22no—
117#13093999C2314yes—
118#13093998—22no—
119#13093998C2314yes—
120#13093995—22no—
121#13093995—22no—
122#13093995C2314yes—
123#13093995C2314yes—
124#13093994—28no—
125#13093992—28no—
126#13093986—28no—
127C4×C22⋊D47—28no—
128C4×C22⋊D47—28no—
129(C22⋊D47)⋊C4—28no—
130#13093983—22no—
131#13093983C2314yes—
132#13093982—22no—
133#13093982C2314yes—
134C2×C4⋊Dic47C2311yescharacteristic
135C2×C4⋊Dic47C2311yescharacteristic
136C2×C4⋊Dic47C2311yescharacteristic
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×C22⋊Dic47—21no—
141C2×C22⋊Dic47—21no—
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—21no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151#13093958C2314yescomplemented
152#13093957C2314yescomplemented
153#13093956C2314yescomplemented
154#13093955C2314yescomplemented
155#13093948C2314yescomplemented
156#13093948C2314yescomplemented
157#13093948C2314yescomplemented
158#13093946C2314yescomplemented
159#13093946C2314yescomplemented
160#13093945C2314yescomplemented
161C22⋊(C47⋊C8)C2314yes—
162(C2×D47)⋊C8C2314yes—
163(C2×D47)⋊C8C2314yes—
164C2×#41×C47—22no—
165C2×#41×C47—42no—
166C2×#41×C47—42no—
167C2×#41×C47C2314yes—
168C22×Q8×C47C2311yescharacteristic
169C22×Q8×C47C2311yescharacteristic
170C22×D4×C47—21no—
171C22×D4×C47C2311yescharacteristic
172C23×C4×C47—21no—
173C23×C4×C47C2311yescharacteristic
174C2×Q16×C47—42no—
175C2×Q16×C47C2314yescomplemented
176C2×SD16×C47—42no—
177C2×SD16×C47C2314yescomplemented
178C22×C8×C47C2311yescharacteristic
179C22×C8×C47C2311yescharacteristic
180C22⋊Q8×C47—22no—
181C22⋊Q8×C47C2314yes—
182C2×C4⋊C4×C47—21no—
183C2×C4⋊C4×C47C2311yescharacteristic
184C2×C22⋊C4×C47—21no—
185#103×C47C2314yescomplemented
186#102×C47C2314yescomplemented
187C22⋊C8×C47C2314yes—
188C24×C47—21no—
189C24×C47C2×D411yescharacteristic
190C23×D47—24no—
191C23×D47—21no—
192C23×D47—42no—
193C23×D47—42no—
194C23×D47C2×D411yescharacteristic
195C23×D47C2×D411yescharacteristic
196C23×D47C2×D414yes—
197#41×C47—44no—
198#41×C47—44no—
199#41×C47—48no—
200C2×Q8×C47—21no—
201C2×Q8×C47—21no—
202C2×Q8×C47—22no—
203C2×Q8×C47—22no—
204C2×Q8×C47—22no—
205C2×Q8×C47—22no—
206C2×Q8×C47C2412yes—
207C2×Q8×C47C2412yes—
208C2×D4×C47—24no—
209C2×D4×C47—21no—
210C2×D4×C47—22no—
211C2×D4×C47—22no—
212C2×D4×C47—44no—
213C2×D4×C47C2412yes—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—24no—
220C22×C4×C47—44no—
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D412yes—
223C22×C4×C47C2412yes—
224C22×C4×C47C2411yescharacteristic
225C2×C22⋊D47—24no—
226C2×C22⋊D47—24no—
227C2×C22⋊D47—24no—
228C2×C22⋊D47—44no—
229C2×C22⋊D47—44no—
230C2×C22⋊D47—44no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—21no—
234C22×Dic47—42no—
235C22×Dic47C2×D411yescharacteristic
236C22×Dic47C2×D411yescharacteristic
237C22×Dic47C2×D414yes—
238#10625354—44no—
239#10625354—44no—
240#10625354—48no—
241C2×D188—22no—
242C2×D188—22no—
243C2×D188—24no—
244C2×D188—24no—
245C2×D188—21no—
246C2×D188—44no—
247C2×D188—44no—
248C2×D188C2412yes—
249C2×C4×D47—22no—
250C2×C4×D47—22no—
251C2×C4×D47—22no—
252C2×C4×D47—22no—
253C2×C4×D47—24no—
254C2×C4×D47—48no—
255C2×C4×D47—44no—
256C2×C4×D47—44no—
257C2×C4×D47—42no—
258C2×C4×D47—42no—
259C2×C4×D47—44no—
260C2×C4×D47C2×D412yes—
261C2×C4×D47C2×D412yes—
262C2×C4×D47C2×D414yes—
263C2×C4×D47C2×D414yes—
264C2×C4×D47C2412yes—
265C2×C4×D47C2412yes—
266Q16×C47—44no—
267SD16×C47—44no—
268C2×C8×C47—22no—
269C2×C8×C47—22no—
270C2×C8×C47C2412yes—
271C2×C8×C47C2412yes—
272C4⋊C4×C47—24no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47C2412yes—
275C22⋊C4×C47—24no—
276C22⋊Dic47—24no—
277C22⋊Dic47—24no—
278C22⋊Dic47—24no—
279#10625336—44no—
280#10625334—44no—
281(C2×D47)⋊C4—24no—
282(C2×D47)⋊C4—24no—
283(C2×D47)⋊C4—24no—
284(C2×D47)⋊C4—24no—
285(C2×D47)⋊C4—24no—
286(C2×D47)⋊C4—24no—
287C4⋊Dic47—21no—
288C4⋊Dic47—21no—
289C4⋊Dic47—21no—
290C4⋊Dic47C2412yes—
291C4⋊Dic47C2412yes—
292C4⋊Dic47C2412yes—
293Dic47⋊C4—24no—
294Dic47⋊C4—24no—
295Dic47⋊C4—24no—
296C4×Dic47—24no—
297C4×Dic47—24no—
298C2×C47⋊C8—22no—
299C2×C47⋊C8—22no—
300C2×C47⋊C8C2412yes—
301C2×C47⋊C8C2412yes—
302C8×D47—44no—
303C8×D47—44no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—42no—
309C23×C47—42no—
310C23×C47—42no—
311C23×C47C22×D412yes—
312C23×C47C22×D411yescharacteristic
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—28no—
319C22×D47—22no—
320C22×D47—44no—
321C22×D47—44no—
322C22×D47—416no—
323C22×D47—42no—
324C22×D47—42no—
325C22×D47—42no—
326C22×D47#13514yes—
327C22×D47C22×D412yes—
328C22×D47C22×D412yes—
329Q8×C47—22no—
330Q8×C47—22no—
331Q8×C47—22no—
332Q8×C47—22no—
333Q8×C47—42no—
334Q8×C47—42no—
335D4×C47—22no—
336D4×C47—22no—
337D4×C47—48no—
338D4×C47—42no—
339C2×C4×C47—22no—
340C2×C4×C47—24no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—48no—
347C2×C4×C47—42no—
348C2×C4×C47—42no—
349C2×C4×C47—42no—
350C2×C4×C47C22×D412yes—
351C2×C4×C47C22×D411yescharacteristic
352C2×C4×C47H(5,𝔽2)12yes—
353C2×C4×C47H(5,𝔽2)12yes—
354C2×C4×C47C2511yescharacteristic
355C22⋊D47—48no—
356C22⋊D47—48no—
357C22⋊D47—48no—
358C2×Dic47—22no—
359C2×Dic47—22no—
360C2×Dic47—22no—
361C2×Dic47—22no—
362C2×Dic47—22no—
363C2×Dic47—44no—
364C2×Dic47—42no—
365C2×Dic47—42no—
366C2×Dic47—42no—
367C2×Dic47C22×D412yes—
368C2×Dic47C22×D412yes—
369D188—22no—
370D188—22no—
371D188—48no—
372D188—48no—
373D188—42no—
374C4×D47—24no—
375C4×D47—24no—
376C4×D47—22no—
377C4×D47—22no—
378C4×D47—22no—
379C4×D47—22no—
380C4×D47—44no—
381C4×D47—44no—
382C4×D47—48no—
383C8×C47—22no—
384C8×C47—22no—
385C47⋊C8—22no—
386C47⋊C8—22no—
387C2×#3191—471nomaximal, Sylow
388C22×C47—22no—
389C22×C47—22no—
390C22×C47—22no—
391C22×C47—44no—
392C22×C47—42no—
393C22×C47—42no—
394C22×C47—42no—
395C22×C47—84no—
396C22×C47#53412yes—
397C22×C47C2×#13512yes—
398C22×C47#57512yes—
399C22×C47C23×D411yescharacteristic
400C2×D47—22no—
401C2×D47—28no—
402C2×D47—22no—
403C2×D47—22no—
404C2×D47—22no—
405C2×D47—22no—
406C2×D47—416no—
407C2×D47—44no—
408C2×D47—42no—
409C2×D47—42no—
410C2×D47—42no—
411C2×D47—84no—
412C2×D47C2×#13514yes—
413C4×C47—22no—
414C4×C47—42no—
415C4×C47—42no—
416C4×C47—42no—
417C4×C47#53412yes—
418C4×C47C2×H(5,𝔽2)11yescharacteristic
419C4×C47C2×H(5,𝔽2)11yescharacteristic
420Dic47—22no—
421Dic47—22no—
422Dic47—42no—
423Dic47—42no—
424Dic47—42no—
425C2×#525—471no—
426C2×#525—471no—
427#3191—4716no—
428C2×#485—471no—
429C2×#485—471no—
430C2×#482—471no—
431C2×#482—471no—
432C2×#467—471no—
433C2×#466—471no—
434C2×#465—471no—
435C2×#465—471no—
436C2×#452—471no—
437C2×#452D4711yescharacteristic, complemented
438C2×#449—471no—
439C2×#449—471no—
440C22×C22⋊C8—471no—
441C2×C47—42no—
442C2×C47—82no—
443C2×C47#319114yescomplemented
444C2×C47C2×#53411yescharacteristic
445C2×C47C22×#13511yescharacteristic
446C2×C47C2×#57511yescharacteristic
447D47—24no—
448D47—42no—
449D47—82no—
450C22×#41—471no—
451C22×#41C2×D4711yescharacteristic
452C24×C4—471no—
453C22×Q16C2×D4711yescharacteristic, complemented
454C22×SD16—471no—
455C22×SD16C2×D4711yescharacteristic, complemented
456C22×D8—471no—
457C23×C8—471no—
458C23×C8—471no—
459#525—478no—
460#525—478no—
461#525—944no—
462#525—944no—
463C2×#123—941no—
464C2×#123—941no—
465C2×C22⋊Q8—471no—
466C2×C22⋊Q8—471no—
467C2×C22⋊Q8—471no—
468C2×C22⋊Q8C2×D4711yescharacteristic
469C2×#121—471no—
470C2×#121—471no—
471C2×#121—471no—
472C2×#121—471no—
473C2×#120—941no—
474C2×#120—941no—
475C2×C4×D4—941no—
476C2×C4×D4—941no—
477C2×C4×D4—941no—
478C2×C4×D4—941no—
479C2×#117—471no—
480C2×#117—471no—
481#485—478no—
482#485—478no—
483#482—478no—
484#482—478no—
485#467—478no—
486#466—478no—
487#465—478no—
488#465—478no—
489#452—478no—
490#452C2×D4718yescomplemented
491#449—478no—
492#449—478no—
493C2×#107—471no—
494C2×#107—471no—
495C2×#106—471no—
496C2×#106—471no—
497C2×#103—471no—
498C2×#103—471no—
499C2×#103—471no—
500C2×#103C2×D4711yescharacteristic, complemented
501C2×#102—471no—
502C2×#102—471no—
503C2×#102—471no—
504C2×#102C2×D4711yescharacteristic, complemented
505C2×C22⋊C8—471no—
506C2×C22⋊C8—471no—
507C2×C22⋊C8—471no—
508C2×C22⋊C8—478no—
509C2×C22⋊C8C2×D4711yescharacteristic
510C47C2×#319111yescharacteristic, complemented, Sylow
511C25—471no—
512C2×#41—22no—
513C2×#41—42no—
514C2×#41—42no—
515C2×#41—474no—
516C2×#41—942no—
517C2×#41—1882no—
518C2×#41—1882no—
519C2×#41C22×D4714yes—
520C22×Q8C22×D4711yescharacteristic
521C22×Q8C22×D4711yescharacteristic
522C22×D4—21no—
523C22×D4—471no—
524C22×D4—941no—
525C22×D4—941no—
526C22×D4—941no—
527C22×D4—941no—
528C22×D4—941no—
529C22×D4C22×D4711yescharacteristic
530C23×C4—21no—
531C23×C4—471no—
532C23×C4—471no—
533C23×C4—471no—
534C23×C4—471no—
535C23×C4—471no—
536C23×C4—474no—
537C23×C4—474no—
538C23×C4—941no—
539C23×C4—1882no—
540C23×C4—1882no—
541C23×C4C22×D4711yescharacteristic
542C2×Q16—42no—
543C2×Q16C22×D4714yescomplemented
544C2×SD16—42no—
545C2×SD16—474no—
546C2×SD16—1882no—
547C2×SD16C22×D4714yescomplemented
548C2×D8—474no—
549C2×D8—1882no—
550C22×C8—471no—
551C22×C8—471no—
552C22×C8—474no—
553C22×C8—474no—
554C22×C8—1882no—
555C22×C8—1882no—
556C22×C8C22×D4711yescharacteristic
557C22×C8C22×D4711yescharacteristic
558#123—948no—
559#123—948no—
560C22⋊Q8—22no—
561C22⋊Q8—474no—
562C22⋊Q8—474no—
563C22⋊Q8—474no—
564C22⋊Q8—942no—
565C22⋊Q8—942no—
566C22⋊Q8—942no—
567C22⋊Q8C22×D4714yes—
568#121—474no—
569#121—474no—
570#121—474no—
571#121—474no—
572#121—942no—
573#121—942no—
574#121—942no—
575#121—942no—
576#120—948no—
577#120—948no—
578C4×D4—948no—
579C4×D4—948no—
580C4×D4—948no—
581C4×D4—948no—
582#117—474no—
583#117—474no—
584#117—942no—
585#117—942no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—471no—
588C2×C4⋊C4—471no—
589C2×C4⋊C4—471no—
590C2×C4⋊C4—941no—
591C2×C4⋊C4—941no—
592C2×C4⋊C4—941no—
593C2×C4⋊C4C22×D4711yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—941no—
596C2×C22⋊C4—941no—
597C2×C22⋊C4—941no—
598C2×C22⋊C4—941no—
599C2×C22⋊C4—941no—
600C2×C22⋊C4—941no—
601C2×C22⋊C4—941no—
602C2×C22⋊C4—941no—
603C2×C22⋊C4—941no—
604C2×C42—941no—
605C2×C42—941no—
606#107—474no—
607#107—474no—
608#106—474no—
609#106—474no—
610#103—474no—
611#103—474no—
612#103—474no—
613#103C22×D4714yescomplemented
614#102—474no—
615#102—474no—
616#102—474no—
617#102C22×D4714yescomplemented
618C22⋊C8—474no—
619C22⋊C8—474no—
620C22⋊C8—474no—
621C22⋊C8C22×D4714yes—
622C24—21no—
623C24—471no—
624C24—471no—
625C24—474no—
626C24—944no—
627C24—941no—
628C24—1882no—
629C24—1882no—
630C24D4×D4711yescharacteristic
631#41—44no—
632#41—44no—
633#41—48no—
634#41—1884no—
635#41—1884no—
636#41—1888no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8—22no—
643C2×Q8C23×D4712yes—
644C2×Q8C23×D4712yes—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—44no—
650C2×D4—472no—
651C2×D4—944no—
652C2×D4—944no—
653C2×D4—944no—
654C2×D4—944no—
655C2×D4—944no—
656C2×D4—941no—
657C2×D4—942no—
658C2×D4—942no—
659C2×D4—1884no—
660C2×D4—1884no—
661C2×D4—1884no—
662C2×D4—1884no—
663C2×D4—1884no—
664C2×D4C23×D4712yes—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—24no—
671C22×C4—44no—
672C22×C4—471no—
673C22×C4—471no—
674C22×C4—474no—
675C22×C4—472no—
676C22×C4—472no—
677C22×C4—472no—
678C22×C4—472no—
679C22×C4—474no—
680C22×C4—474no—
681C22×C4—944no—
682C22×C4—942no—
683C22×C4—942no—
684C22×C4—942no—
685C22×C4—942no—
686C22×C4—941no—
687C22×C4—941no—
688C22×C4—941no—
689C22×C4—1888no—
690C22×C4—1884no—
691C22×C4—1884no—
692C22×C4—1882no—
693C22×C4—1882no—
694C22×C4—1884no—
695C22×C4—1882no—
696C22×C4D4×D4712yes—
697C22×C4D4×D4711yescharacteristic
698C22×C4C23×D4712yes—
699C22×C4C23×D4711yescharacteristic
700Q16—44no—
701SD16—44no—
702SD16—1884no—
703D8—1884no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—472no—
707C2×C8—472no—
708C2×C8—942no—
709C2×C8—942no—
710C2×C8—1884no—
711C2×C8—1884no—
712C2×C8C23×D4712yes—
713C2×C8C23×D4712yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—472no—
717C4⋊C4—472no—
718C4⋊C4—472no—
719C4⋊C4—944no—
720C4⋊C4—944no—
721C4⋊C4—944no—
722C4⋊C4—941no—
723C4⋊C4—941no—
724C4⋊C4—941no—
725C4⋊C4C23×D4712yes—
726C22⋊C4—24no—
727C22⋊C4—944no—
728C22⋊C4—944no—
729C22⋊C4—944no—
730C22⋊C4—944no—
731C22⋊C4—944no—
732C22⋊C4—944no—
733C22⋊C4—944no—
734C22⋊C4—944no—
735C22⋊C4—944no—
736C42—944no—
737C42—944no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—474no—
746C23—472no—
747C23—472no—
748C23—948no—
749C23—942no—
750C23—942no—
751C23—942no—
752C23—942no—
753C23—942no—
754C23—942no—
755C23—1884no—
756C23—1884no—
757C23—18816no—
758C23—1882no—
759C23—1882no—
760C23—1882no—
761C23C2×D4×D4712yes—
762C23C2×D4×D4711yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—22no—
766Q8—22no—
767Q8—42no—
768Q8—42no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—42no—
773D4—942no—
774D4—942no—
775D4—1888no—
776D4—1888no—
777D4—1888no—
778D4—1888no—
779D4—1888no—
780D4—1882no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—48no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—472no—
793C2×C4—472no—
794C2×C4—942no—
795C2×C4—942no—
796C2×C4—944no—
797C2×C4—944no—
798C2×C4—942no—
799C2×C4—942no—
800C2×C4—942no—
801C2×C4—942no—
802C2×C4—942no—
803C2×C4—942no—
804C2×C4—942no—
805C2×C4—1884no—
806C2×C4—1884no—
807C2×C4—1888no—
808C2×C4—1884no—
809C2×C4—1882no—
810C2×C4—1882no—
811C2×C4—1882no—
812C2×C4C2×D4×D4712yes—
813C2×C4C2×D4×D4711yescharacteristic
814C2×C4#1309406912yes—
815C2×C4#1309406912yes—
816C2×C4C24×D4711yescharacteristic
817C8—22no—
818C8—22no—
819C8—942no—
820C8—942no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—84no—
829C22—474no—
830C22—942no—
831C22—942no—
832C22—948no—
833C22—942no—
834C22—942no—
835C22—942no—
836C22—3764no—
837C22—18816no—
838C22—1882no—
839C22—1882no—
840C22—1882no—
841C22—1884no—
842C22#1568968312yes—
843C22#135×D4712yes—
844C22#1568992212yes—
845C22C22×D4×D4711yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—942no—
851C4—942no—
852C4—1882no—
853C4—1882no—
854C4—1882no—
855C4#1568968312yes—
856C4C2×#1309406911yescharacteristic
857C4C2×#1309406911yescharacteristic
858C2—42no—
859C2—82no—
860C2—944no—
861C2—3762no—
862C2—1882no—
863C2#2025418014yesdirect product factor
864C2C2×#1568968311yescharacteristic
865C2C2×#135×D4711yescharacteristic
866C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#452C2
socleC23×C47C22×D4
hypercenterC2×#452D47
hypocenterC47C2×#3191
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#15689636C2semidirect
2. C2×#15689630C2semidirect
3. #20254180C2direct (N × H)
4. C2×#15689462C2semidirect
5. C2×#15689461C2semidirect
6. C2×#15689448C2semidirect
7. C2×#15689445C2semidirect
8. C2×#15689361C2semidirect
9. C2×#15689358C2semidirect
10. C2×#15689355C2semidirect
11. C2×#15689349C2semidirect
12. C2×#15689284C2semidirect
13. C2×#15689268C2semidirect
14. C2×#15689267C2semidirect
15. C2×C22⋊C8×D47C2semidirect
16. C2×C47×#452C2semidirect
19. C22×#10625336C22semidirect
20. C22×#10625334C22semidirect
24. #15689636C22semidirect
26. #15689630C22semidirect
44. #15689462C22semidirect
45. #15689461C22semidirect
46. #15689448C22semidirect
47. #15689445C22semidirect
48. #15689361C22semidirect
49. #15689358C22semidirect
50. #15689355C22semidirect
51. #15689349C22semidirect
52. #15689284C22semidirect
53. #15689268C22semidirect
54. #15689267C22semidirect
55. C2×#13093958C22semidirect
56. C2×#13093957C22semidirect
57. C2×#13093956C22semidirect
58. C2×#13093955C22semidirect
59. C2×#13093948C22semidirect
60. C2×#13093948C22semidirect
61. C2×#13093948C22semidirect
62. C2×#13093946C22semidirect
63. C2×#13093946C22semidirect
64. C2×#13093945C22semidirect
68. C22⋊C8×D47C22semidirect
70. C22×Q16×C47C22semidirect
71. C22×SD16×C47C22semidirect
73. C47×#452C22semidirect
74. C2×#103×C47C22semidirect
75. C2×#102×C47C22semidirect
99. C2×#10625336C23semidirect
101. C2×#10625334C23semidirect
151. #13093958C23semidirect
152. #13093957C23semidirect
153. #13093956C23semidirect
154. #13093955C23semidirect
155. #13093948C23semidirect
156. #13093948C23semidirect
157. #13093948C23semidirect
158. #13093946C23semidirect
159. #13093946C23semidirect
160. #13093945C23semidirect
175. C2×Q16×C47C23semidirect
177. C2×SD16×C47C23semidirect
185. #103×C47C23semidirect
186. #102×C47C23semidirect
437. C2×#452D47semidirect
443. C2×C47#3191semidirect
453. C22×Q16C2×D47semidirect
455. C22×SD16C2×D47semidirect
490. #452C2×D47semidirect
500. C2×#103C2×D47semidirect
504. C2×#102C2×D47semidirect
510. C47C2×#3191semidirect
543. C2×Q16C22×D47semidirect
547. C2×SD16C22×D47semidirect
613. #103C22×D47semidirect
617. #102C22×D47semidirect
863. C2#20254180direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896362
C2×#156896302
#202541802
C2×#156894622
C2×#156894612
C2×#156894482
C2×#156894452
C2×#156893612
C2×#156893582
C2×#156893552
C2×#156893492
C2×#156892842
C2×#156892682
C2×#156892672
C2×C22⋊C8×D472
C2×C47×#4522
C2×#319147