Finite Group Databasebeta

← C2×#20254923 #27091286

Subgroups — C2×#20254923 #27091286

Order 12032.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094051C211yesmaximal, characteristic, complemented
2C22×#13094047C211yesmaximal, characteristic, complemented
3C2×#15689795C211yesmaximal, characteristic, complemented
4C2×#15689766C211yesmaximal, characteristic, complemented
5#20254923C2116yesmaximal, direct product factor
6C2×#15689513C211yesmaximal, characteristic, complemented
7C2×#15689372C211yesmaximal, characteristic, complemented
8C2×#15689358C211yesmaximal, characteristic, complemented
9C2×#15689319C211yesmaximal, characteristic, complemented
10C2×#15689284C211yesmaximal, characteristic, complemented
11C2×#15689271C211yesmaximal, characteristic, complemented
12C2×#15689267C211yesmaximal, characteristic, complemented
13C2×#15689258C211yesmaximal, characteristic, complemented
14C2×#15689221C211yesmaximal, characteristic, complemented
15C2×#15689193C211yesmaximal, characteristic, complemented
16C2×C47×#464C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625354C2211yescharacteristic
19C22×#10625354C2211yescharacteristic, complemented
20C22×D4×D47C2211yescharacteristic
21C2×#13094051—28no—
22C2×#13094051C2218yescomplemented
23C2×#13094047—28no—
24C2×#13094047C2218yescomplemented
25C22×#10625336C2211yescharacteristic
26C22×#10625336C2211yescharacteristic, complemented
27C22×#10625336C2211yescharacteristic, complemented
28C22×D376C2211yescharacteristic
29C22×D376C2211yescharacteristic
30C22×#10625334C2211yescharacteristic
31C22×#10625334C2211yescharacteristic
32C22×#10625324C2211yescharacteristic
33C22×C8×D47C2211yescharacteristic, complemented
34#15689795—24no—
35#15689795C2218yescomplemented
36#15689766—24no—
37#15689766C2218yescomplemented
38C2×#13094021—21no—
39C2×#13094021C2211yescharacteristic, complemented
40C2×#13094006—21no—
41C2×#13094000C2211yescharacteristic
42C2×#13093999—21no—
43C2×#13093999—21no—
44C2×#13093999C2211yescharacteristic
45C2×#13093999C2211yescharacteristic, complemented
46C2×#13093997—21no—
47C2×#13093995C2211yescharacteristic
48C2×#13093994—21no—
49C2×C4×D188—21no—
50C2×C4×D188C2211yescharacteristic
51C2×C4×D188C2211yescharacteristic
52C2×C22⋊C4×D47—21no—
53#15689513C2218yescomplemented
54#15689372C2218yescomplemented
55#15689358C2218yescomplemented
56#15689319C2218yescomplemented
57#15689284C2218yescomplemented
58#15689271C2218yescomplemented
59#15689267C2218yescomplemented
60#15689258C2218yescomplemented
61#15689221C2218yescomplemented
62#15689193C2218yescomplemented
63C2×#13093957C2211yescharacteristic, complemented
64C2×#13093948C2211yescharacteristic, complemented
65C2×#13093946C2211yescharacteristic, complemented
66C2×#13093946C2211yescharacteristic, complemented
67C2×#13093944C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
70C2×#13093935C2211yescharacteristic, complemented
71C22×Q16×C47C2211yescharacteristic, complemented
72C22×SD16×C47C2211yescharacteristic
73C2×#124×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic, complemented
75C47×#464C2218yescomplemented
76C2×C4⋊C8×C47C2211yescharacteristic, complemented
77C2×#103×C47C2211yescharacteristic, complemented
78C2×#102×C47C2211yescharacteristic
79C24×D47—21no—
80C2×#10625354—22no—
81C2×#10625354—22no—
82C2×#10625354—22no—
83C2×#10625354—24no—
84C2×#10625354—24no—
85C2×#10625354—24no—
86C2×#10625354—42no—
87C2×#10625354—42no—
88C2×#10625354—42no—
89C2×#10625354C2314yes—
90C2×#10625354C2314yes—
91C2×#10625354C2314yescomplemented
92C22×D188—21no—
93C22×D188—21no—
94C22×D188—21no—
95C22×D188—21no—
96C22×D188—21no—
97C22×D188—21no—
98C22×D188—21no—
99C22×D188D411yescharacteristic
100C22×D188C2311yescharacteristic
101C22×D188C2311yescharacteristic
102C22×D188C2311yescharacteristic
103C22×C22⋊D47—21no—
104C22×C22⋊D47—21no—
105C2×D4×D47—24no—
106C2×D4×D47—22no—
107C2×D4×D47—42no—
108C2×D4×D47C2314yes—
109C22×C4×D47—21no—
110C22×C4×D47—21no—
111C22×C4×D47—21no—
112C22×C4×D47—21no—
113C22×C4×D47C2311yescharacteristic
114C22×C4×D47C2311yescharacteristic
115#13094051—232no—
116#13094047—232no—
117C2×#10625336—24no—
118C2×#10625336—42no—
119C2×#10625336D418yescomplemented
120C2×#10625336C2314yes—
121C2×#10625336C2314yescomplemented
122C2×#10625336C2314yescomplemented
123C2×D376—24no—
124C2×D376—24no—
125C2×D376C2314yes—
126C2×D376C2314yes—
127C2×#10625334—24no—
128C2×#10625334—42no—
129C2×#10625334C2314yes—
130C2×#10625334C2314yes—
131C2×#10625324—24no—
132C2×#10625324C2314yes—
133C22×C47⋊C8C2311yescharacteristic
134C22×C47⋊C8C2311yescharacteristic
135C2×C8×D47—24no—
136C2×C8×D47C2314yescomplemented
137#13094021—28no—
138#13094021—22no—
139#13094021C2314yescomplemented
140#13094006—28no—
141#13094000—22no—
142#13094000C2314yes—
143#13093999—22no—
144#13093999—22no—
145#13093999—28no—
146#13093999—28no—
147#13093999C2314yes—
148#13093999C2314yescomplemented
149#13093997—28no—
150#13093995—22no—
151#13093995C2314yes—
152#13093994—28no—
153C4×D188—22no—
154C4×D188—28no—
155C4×D188D414yes—
156C4×D188C2314yes—
157C4×D188C2314yes—
158C2×C4⋊Dic47D411yescharacteristic
159C2×C4⋊Dic47C2311yescharacteristic
160C2×Dic47⋊C4—21no—
161C2×C22⋊Dic47—21no—
162C2×(C2×D47)⋊C4—21no—
163C2×(C2×D47)⋊C4—21no—
164C2×(C2×D47)⋊C4—21no—
165C2×(C2×D47)⋊C4—21no—
166C2×(C2×D47)⋊C4D411yescharacteristic
167C2×(C2×D47)⋊C4D411yescharacteristic
168C22⋊C4×D47—28no—
169#13093957C2314yescomplemented
170#13093948C2314yescomplemented
171#13093946C2314yescomplemented
172#13093946C2314yescomplemented
173#13093944C2314yes—
174(C2×D47)⋊C8C2314yes—
175(C2×D47)⋊C8C2314yescomplemented
176#13093935C2314yescomplemented
177C22×Q8×C47C2311yescharacteristic
178C22×Q8×C47C2311yescharacteristic
179C22×D4×C47C2311yescharacteristic
180C2×Q16×C47—24no—
181C2×Q16×C47C2314yescomplemented
182C2×SD16×C47—24no—
183C2×SD16×C47C2314yes—
184C22×C8×C47C2311yescharacteristic
185C22×C8×C47C2311yescharacteristic
186#124×C47—22no—
187#124×C47C2314yes—
188C4×Q8×C47—22no—
189C4×Q8×C47C2314yescomplemented
190C2×C4⋊C4×C47—21no—
191C2×C4⋊C4×C47C2311yescharacteristic
192C2×C22⋊C4×C47—21no—
193C2×C22⋊C4×C47—21no—
194C2×C42×C47—21no—
195C2×C42×C47C2311yescharacteristic
196C4⋊C8×C47C2314yescomplemented
197#103×C47C2314yescomplemented
198#102×C47C2314yes—
199C24×C47—21no—
200C23×D47—21no—
201C23×D47—21no—
202C23×D47—21no—
203C23×D47—24no—
204C23×D47—44no—
205C23×D47—44no—
206C23×D47—82no—
207C23×D47C2×D411yescharacteristic
208C23×D47C2×D411yescharacteristic
209C2×Q8×C47—21no—
210C2×Q8×C47—21no—
211C2×Q8×C47—22no—
212C2×Q8×C47—22no—
213C2×Q8×C47—22no—
214C2×Q8×C47C2×D414yes—
215C2×Q8×C47C2412yes—
216C2×Q8×C47C2412yes—
217C2×D4×C47—22no—
218C2×D4×C47—21no—
219C2×D4×C47—22no—
220C2×D4×C47C2412yes—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2411yescharacteristic
227C2×C22⋊D47—24no—
228C2×C22⋊D47—24no—
229C2×C22⋊D47—44no—
230C2×C22⋊D47—82no—
231C22×Dic47—21no—
232C22×Dic47C2×D411yescharacteristic
233C22×Dic47C2×D411yescharacteristic
234#10625354—28no—
235#10625354—28no—
236#10625354—28no—
237#10625354—44no—
238#10625354—44no—
239#10625354—44no—
240#10625354—48no—
241#10625354—48no—
242#10625354—48no—
243D4×D47—28no—
244D4×D47—44no—
245D4×D47—48no—
246C2×D188—21no—
247C2×D188—22no—
248C2×D188—22no—
249C2×D188—22no—
250C2×D188—22no—
251C2×D188—22no—
252C2×D188—24no—
253C2×D188—24no—
254C2×D188—24no—
255C2×D188—24no—
256C2×D188—21no—
257C2×D188—21no—
258C2×D188—24no—
259C2×D188—24no—
260C2×D188—24no—
261C2×D188—42no—
262C2×D188—44no—
263C2×D188—44no—
264C2×D188—44no—
265C2×D188—44no—
266C2×D188—82no—
267C2×D188—82no—
268C2×D188—82no—
269C2×D188C2×D414yes—
270C2×D188C2×D414yes—
271C2×D188C2412yes—
272C2×D188C2412yes—
273C2×D188C2412yes—
274C2×C4×D47—22no—
275C2×C4×D47—22no—
276C2×C4×D47—22no—
277C2×C4×D47—22no—
278C2×C4×D47—24no—
279C2×C4×D47—24no—
280C2×C4×D47—24no—
281C2×C4×D47—24no—
282C2×C4×D47—44no—
283C2×C4×D47—44no—
284C2×C4×D47—44no—
285C2×C4×D47—82no—
286C2×C4×D47C2×D412yes—
287C2×C4×D47C2×D412yes—
288C2×C4×D47C2412yes—
289C2×C4×D47C2412yes—
290Q16×C47—28no—
291SD16×C47—28no—
292C2×C8×C47—22no—
293C2×C8×C47—22no—
294C2×C8×C47C2412yes—
295C2×C8×C47C2412yes—
296C4⋊C4×C47—24no—
297C4⋊C4×C47—21no—
298C4⋊C4×C47C2412yes—
299C22⋊C4×C47—24no—
300C22⋊C4×C47—24no—
301C42×C47—24no—
302C42×C47C2×D412yes—
303C42×C47C2412yes—
304C22⋊Dic47—24no—
305#10625336—28no—
306#10625336—44no—
307#10625336C2×D4116yescomplemented
308#10625334—28no—
309#10625334—44no—
310(C2×D47)⋊C4—24no—
311(C2×D47)⋊C4—24no—
312(C2×D47)⋊C4—24no—
313(C2×D47)⋊C4—24no—
314(C2×D47)⋊C4C2×D414yes—
315(C2×D47)⋊C4C2×D414yes—
316C4⋊Dic47—21no—
317C4⋊Dic47C2×D414yes—
318C4⋊Dic47C2412yes—
319Dic47⋊C4—24no—
320C2×C47⋊C8—22no—
321C2×C47⋊C8C2×D414yes—
322C2×C47⋊C8C2412yes—
323C2×C47⋊C8C2412yes—
324D376—28no—
325D376—28no—
326#10625324—28no—
327C8×D47—28no—
328C23×C47—22no—
329C23×C47—42no—
330C23×C47—42no—
331C23×C47—42no—
332C23×C47C22×D411yescharacteristic
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—24no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—22no—
343C22×D47—48no—
344C22×D47—48no—
345C22×D47—42no—
346C22×D47—42no—
347C22×D47—42no—
348C22×D47—42no—
349C22×D47—42no—
350C22×D47—42no—
351C22×D47—42no—
352C22×D47—42no—
353C22×D47—84no—
354C22×D47—816no—
355C22×D47C22×D412yes—
356C22×D47C22×D412yes—
357Q8×C47—24no—
358Q8×C47—22no—
359Q8×C47—22no—
360Q8×C47—22no—
361Q8×C47—42no—
362Q8×C47C22×D414yes—
363D4×C47—22no—
364D4×C47—22no—
365D4×C47—42no—
366C2×C4×C47—24no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—42no—
373C2×C4×C47—42no—
374C2×C4×C47C22×D412yes—
375C2×C4×C47C22×D412yes—
376C2×C4×C47C22×D411yescharacteristic
377C2×C4×C47C22×D412yes—
378C2×C4×C47H(5,𝔽2)12yes—
379C2×C4×C47C2511yescharacteristic
380C22⋊D47—48no—
381C22⋊D47—84no—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—42no—
386C2×Dic47C22×D412yes—
387C2×Dic47C22×D412yes—
388D188—24no—
389D188—22no—
390D188—22no—
391D188—22no—
392D188—22no—
393D188—22no—
394D188—44no—
395D188—48no—
396D188—48no—
397D188—48no—
398D188—48no—
399D188—42no—
400D188—42no—
401D188—84no—
402D188—84no—
403D188—84no—
404D188C22×D414yes—
405C4×D47—24no—
406C4×D47—24no—
407C4×D47—22no—
408C4×D47—22no—
409C4×D47—22no—
410C4×D47—22no—
411C4×D47—48no—
412C4×D47—48no—
413C4×D47—48no—
414C4×D47—84no—
415C8×C47—22no—
416C8×C47—22no—
417C47⋊C8—22no—
418C47⋊C8C22×D414yes—
419C2×#3268—471nomaximal, Sylow
420C22×C47—42no—
421C22×C47—42no—
422C22×C47—42no—
423C22×C47—84no—
424C22×C47D4212yes—
425C22×C47#57512yes—
426C22×C47#57612yes—
427C22×C47C23×D411yescharacteristic
428C2×D47—22no—
429C2×D47—22no—
430C2×D47—24no—
431C2×D47—22no—
432C2×D47—22no—
433C2×D47—22no—
434C2×D47—22no—
435C2×D47—44no—
436C2×D47—44no—
437C2×D47—48no—
438C2×D47—42no—
439C2×D47—42no—
440C2×D47—42no—
441C2×D47—42no—
442C2×D47—42no—
443C2×D47—42no—
444C2×D47—42no—
445C2×D47—42no—
446C2×D47—816no—
447C2×D47—84no—
448C2×D47—84no—
449C4×C47—24no—
450C4×C47—22no—
451C4×C47—22no—
452C4×C47—42no—
453C4×C47—42no—
454C4×C47D4212yes—
455C4×C47C23×D411yescharacteristic
456C4×C47C2×H(5,𝔽2)11yescharacteristic
457Dic47—22no—
458Dic47—22no—
459Dic47—42no—
460C22×AGL(1,ℤ/8)—471no—
461C22×#135—471no—
462C2×#550—471no—
463C2×#546—471no—
464#3268—4716no—
465C2×#496—471no—
466C2×#468—471no—
467C2×#466—471no—
468C2×#464D4711yescharacteristic, complemented
469C2×#459—471no—
470C2×#452—471no—
471C2×#449—471no—
472C2×#449—471no—
473C2×#447—471no—
474C2×#440—471no—
475C2×#435—471no—
476C2×C47—82no—
477C2×C47#326814yescomplemented
478C2×C47C2×D4211yescharacteristic
479C2×C47C2×#57511yescharacteristic
480C2×C47C2×#57611yescharacteristic
481D47—42no—
482D47—42no—
483D47—44no—
484D47—82no—
485D47—82no—
486C22×#41—471no—
487C22×#41—471no—
488C22×#41—471no—
489C23×D4—471no—
490C2×AGL(1,ℤ/8)—478no—
491C2×AGL(1,ℤ/8)—948no—
492C2×#135—478no—
493C2×#135—948no—
494C22×Q16C2×D4711yescharacteristic, complemented
495C22×SD16—471no—
496C22×SD16—471no—
497C22×SD16—471no—
498C22×SD16C2×D4711yescharacteristic
499C22×D8—471no—
500C22×D8—471no—
501C22×D8—471no—
502C22×D8—471no—
503C22×M16—471no—
504C23×C8—471no—
505#550—478no—
506#550—944no—
507#546—478no—
508#546—944no—
509C2×#127—471no—
510C2×#127—941no—
511C2×#124C2×D4711yescharacteristic
512C2×#123—941no—
513C2×C22⋊Q8—471no—
514C2×#121—471no—
515C2×#121—471no—
516C2×#121—471no—
517C2×#121—941no—
518C2×#121—941no—
519C2×#121—941no—
520C2×#120—941no—
521C2×C4×Q8C2×D4711yescharacteristic, complemented
522C2×C4×D4—471no—
523C2×C4×D4—471no—
524C2×C4×D4—941no—
525C22×C22⋊C4—941no—
526#496—478no—
527#468—478no—
528#466—478no—
529#464C2×D4718yescomplemented
530#459—478no—
531#452—478no—
532#449—478no—
533#449—478no—
534#447—478no—
535#440—478no—
536#435—478no—
537C2×#107—471no—
538C2×C4⋊C8C2×D4711yescharacteristic, complemented
539C2×#103—471no—
540C2×#103C2×D4711yescharacteristic, complemented
541C2×#102—471no—
542C2×#102—471no—
543C2×#102—471no—
544C2×#102C2×D4711yescharacteristic
545C2×C22⋊C8—471no—
546C2×C22⋊C8—471no—
547C2×#97—471no—
548C47C2×#326811yescharacteristic, complemented, Sylow
549C25—941no—
550C2×#41—474no—
551C2×#41—474no—
552C2×#41—474no—
553C2×#41—942no—
554C2×#41—942no—
555C2×#41—942no—
556C2×#41—944no—
557C2×#41—944no—
558C2×#41—944no—
559C2×#41—1882no—
560C2×#41—1882no—
561C2×#41—1882no—
562C22×Q8C22×D4711yescharacteristic
563C22×Q8C22×D4711yescharacteristic
564C22×D4—474no—
565C22×D4—471no—
566C22×D4—471no—
567C22×D4—471no—
568C22×D4—471no—
569C22×D4—941no—
570C22×D4—941no—
571C22×D4—941no—
572C22×D4—941no—
573C22×D4—941no—
574C22×D4—942no—
575C22×D4—941no—
576C22×D4—944no—
577C22×D4—941no—
578C22×D4—941no—
579C22×D4—941no—
580C22×D4—1882no—
581C22×D4C22×D4711yescharacteristic
582C23×C4—471no—
583C23×C4—471no—
584C23×C4—941no—
585C23×C4—941no—
586C23×C4—941no—
587C23×C4—941no—
588AGL(1,ℤ/8)—9432no—
589#135—9432no—
590C2×Q16—24no—
591C2×Q16C22×D4714yescomplemented
592C2×SD16—24no—
593C2×SD16—478no—
594C2×SD16—474no—
595C2×SD16—474no—
596C2×SD16—474no—
597C2×SD16—944no—
598C2×SD16—1882no—
599C2×SD16C22×D4714yes—
600C2×D8—474no—
601C2×D8—474no—
602C2×D8—474no—
603C2×D8—474no—
604C2×D8—944no—
605C2×D8—944no—
606C2×D8—944no—
607C2×D8—1882no—
608C2×M16—474no—
609C2×M16—944no—
610C22×C8—471no—
611C22×C8—471no—
612C22×C8—474no—
613C22×C8—944no—
614C22×C8C22×D4711yescharacteristic
615C22×C8C22×D4711yescharacteristic
616#127—474no—
617#127—948no—
618#127—942no—
619#124—22no—
620#124C22×D4714yes—
621#123—948no—
622C22⋊Q8—474no—
623C22⋊Q8—942no—
624#121—474no—
625#121—474no—
626#121—474no—
627#121—948no—
628#121—948no—
629#121—948no—
630#121—942no—
631#121—942no—
632#121—942no—
633#120—948no—
634C4×Q8—22no—
635C4×Q8C22×D4714yescomplemented
636C4×D4—474no—
637C4×D4—474no—
638C4×D4—474no—
639C4×D4—948no—
640C4×D4—942no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—471no—
643C2×C4⋊C4—471no—
644C2×C4⋊C4—941no—
645C2×C4⋊C4C22×D4711yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—471no—
649C2×C22⋊C4—471no—
650C2×C22⋊C4—948no—
651C2×C22⋊C4—941no—
652C2×C22⋊C4—941no—
653C2×C22⋊C4—941no—
654C2×C22⋊C4—941no—
655C2×C22⋊C4—941no—
656C2×C42—21no—
657C2×C42C22×D4711yescharacteristic
658#107—474no—
659C4⋊C8C22×D4714yescomplemented
660#103—474no—
661#103C22×D4714yescomplemented
662#102—474no—
663#102—474no—
664#102—474no—
665#102C22×D4714yes—
666C22⋊C8—474no—
667C22⋊C8—474no—
668#97—474no—
669C24—21no—
670C24—471no—
671C24—471no—
672C24—944no—
673C24—941no—
674C24—941no—
675C24—941no—
676C24—3762no—
677C24—1884no—
678C24—1884no—
679#41—948no—
680#41—948no—
681#41—948no—
682#41—1884no—
683#41—1884no—
684#41—1884no—
685#41—1888no—
686#41—1888no—
687#41—1888no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—22no—
691C2×Q8—22no—
692C2×Q8—22no—
693C2×Q8D4×D4714yes—
694C2×Q8C23×D4712yes—
695C2×Q8C23×D4712yes—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—22no—
699C2×D4—474no—
700C2×D4—474no—
701C2×D4—472no—
702C2×D4—472no—
703C2×D4—472no—
704C2×D4—944no—
705C2×D4—944no—
706C2×D4—944no—
707C2×D4—944no—
708C2×D4—944no—
709C2×D4—944no—
710C2×D4—948no—
711C2×D4—944no—
712C2×D4—941no—
713C2×D4—942no—
714C2×D4—942no—
715C2×D4—944no—
716C2×D4—944no—
717C2×D4—941no—
718C2×D4—941no—
719C2×D4—942no—
720C2×D4—942no—
721C2×D4—942no—
722C2×D4—3762no—
723C2×D4—3762no—
724C2×D4—3762no—
725C2×D4—3762no—
726C2×D4—1882no—
727C2×D4—1884no—
728C2×D4—1884no—
729C2×D4—1884no—
730C2×D4—1884no—
731C2×D4—1884no—
732C2×D4—1888no—
733C2×D4—1884no—
734C2×D4C23×D4712yes—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—471no—
739C22×C4—471no—
740C22×C4—472no—
741C22×C4—472no—
742C22×C4—472no—
743C22×C4—472no—
744C22×C4—944no—
745C22×C4—944no—
746C22×C4—944no—
747C22×C4—942no—
748C22×C4—942no—
749C22×C4—942no—
750C22×C4—942no—
751C22×C4—941no—
752C22×C4—944no—
753C22×C4—3762no—
754C22×C4—1884no—
755C22×C4—1884no—
756C22×C4—1884no—
757C22×C4D4×D4711yescharacteristic
758C22×C4D4×D4711yescharacteristic
759C22×C4C23×D4711yescharacteristic
760Q16—28no—
761SD16—28no—
762SD16—4716no—
763SD16—948no—
764SD16—1884no—
765D8—948no—
766D8—948no—
767D8—948no—
768D8—1884no—
769M16—948no—
770C2×C8—22no—
771C2×C8—22no—
772C2×C8—474no—
773C2×C8—472no—
774C2×C8—472no—
775C2×C8—948no—
776C2×C8—942no—
777C2×C8C23×D4712yes—
778C2×C8C23×D4712yes—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—474no—
782C4⋊C4—472no—
783C4⋊C4—944no—
784C4⋊C4—941no—
785C4⋊C4C23×D4712yes—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—474no—
789C22⋊C4—474no—
790C22⋊C4—944no—
791C22⋊C4—944no—
792C22⋊C4—944no—
793C22⋊C4—944no—
794C22⋊C4—944no—
795C42—24no—
796C42D4×D4712yes—
797C42C23×D4712yes—
798C23—22no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—472no—
803C23—472no—
804C23—942no—
805C23—942no—
806C23—944no—
807C23—942no—
808C23—942no—
809C23—942no—
810C23—942no—
811C23—942no—
812C23—942no—
813C23—942no—
814C23—3764no—
815C23—37616no—
816C23—1888no—
817C23—1888no—
818C23—1882no—
819C23—1882no—
820C23—1882no—
821C23—1882no—
822C23—1882no—
823C23—1882no—
824C23—1882no—
825C23—1882no—
826C23C2×D4×D4711yescharacteristic
827Q8—24no—
828Q8—22no—
829Q8—22no—
830Q8—22no—
831Q8—42no—
832Q8C2×D4×D4714yes—
833D4—22no—
834D4—22no—
835D4—42no—
836D4—474no—
837D4—944no—
838D4—942no—
839D4—942no—
840D4—942no—
841D4—942no—
842D4—942no—
843D4—3764no—
844D4—3764no—
845D4—3764no—
846D4—3764no—
847D4—1884no—
848D4—1888no—
849D4—1888no—
850D4—1888no—
851D4—1888no—
852D4—1888no—
853D4—1882no—
854D4—1882no—
855C2×C4—24no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—472no—
864C2×C4—472no—
865C2×C4—942no—
866C2×C4—942no—
867C2×C4—944no—
868C2×C4—944no—
869C2×C4—942no—
870C2×C4—942no—
871C2×C4—942no—
872C2×C4—942no—
873C2×C4—942no—
874C2×C4—3764no—
875C2×C4—1888no—
876C2×C4—1888no—
877C2×C4—1888no—
878C2×C4—1882no—
879C2×C4C2×D4×D4712yes—
880C2×C4C2×D4×D4712yes—
881C2×C4C2×D4×D4711yescharacteristic
882C2×C4C2×D4×D4712yes—
883C2×C4#1309407012yes—
884C2×C4C24×D4711yescharacteristic
885C8—22no—
886C8—22no—
887C8—474no—
888C8—942no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—84no—
893C22—942no—
894C22—942no—
895C22—944no—
896C22—942no—
897C22—942no—
898C22—942no—
899C22—942no—
900C22—37616no—
901C22—3764no—
902C22—3764no—
903C22—1882no—
904C22—1882no—
905C22—1882no—
906C22—1882no—
907C22—1882no—
908C22—1882no—
909C22—1882no—
910C22—1882no—
911C22—1884no—
912C22—1884no—
913C22—1888no—
914C22#1568975712yes—
915C22#1568992212yes—
916C22#1568992512yes—
917C22C22×D4×D4711yescharacteristic
918C4—24no—
919C4—22no—
920C4—22no—
921C4—42no—
922C4—42no—
923C4—942no—
924C4—942no—
925C4—1882no—
926C4#1568975712yes—
927C4C22×D4×D4711yescharacteristic
928C4C2×#1309407011yescharacteristic
929C2—82no—
930C2—3762no—
931C2—3762no—
932C2—1882no—
933C2—1882no—
934C2—1884no—
935C2#2025492314yesdirect product factor
936C2C2×#1568975711yescharacteristic
937C2C2×#1568992211yescharacteristic
938C2C2×#1568992511yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#464C2
socleC23×C47C22×D4
hypercenterC2×#464D47
hypocenterC47C2×#3268
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#13094051C2semidirect
2. C22×#13094047C2semidirect
3. C2×#15689795C2semidirect
4. C2×#15689766C2semidirect
5. #20254923C2direct (N × H)
6. C2×#15689513C2semidirect
7. C2×#15689372C2semidirect
8. C2×#15689358C2semidirect
9. C2×#15689319C2semidirect
10. C2×#15689284C2semidirect
11. C2×#15689271C2semidirect
12. C2×#15689267C2semidirect
13. C2×#15689258C2semidirect
14. C2×#15689221C2semidirect
15. C2×#15689193C2semidirect
16. C2×C47×#464C2semidirect
19. C22×#10625354C22semidirect
22. C2×#13094051C22semidirect
24. C2×#13094047C22semidirect
26. C22×#10625336C22semidirect
27. C22×#10625336C22semidirect
33. C22×C8×D47C22semidirect
35. #15689795C22semidirect
37. #15689766C22semidirect
39. C2×#13094021C22semidirect
45. C2×#13093999C22semidirect
53. #15689513C22semidirect
54. #15689372C22semidirect
55. #15689358C22semidirect
56. #15689319C22semidirect
57. #15689284C22semidirect
58. #15689271C22semidirect
59. #15689267C22semidirect
60. #15689258C22semidirect
61. #15689221C22semidirect
62. #15689193C22semidirect
63. C2×#13093957C22semidirect
64. C2×#13093948C22semidirect
65. C2×#13093946C22semidirect
66. C2×#13093946C22semidirect
69. C2×(C2×D47)⋊C8C22semidirect
70. C2×#13093935C22semidirect
71. C22×Q16×C47C22semidirect
74. C2×C4×Q8×C47C22semidirect
75. C47×#464C22semidirect
76. C2×C4⋊C8×C47C22semidirect
77. C2×#103×C47C22semidirect
91. C2×#10625354C23semidirect
119. C2×#10625336D4semidirect
121. C2×#10625336C23semidirect
122. C2×#10625336C23semidirect
136. C2×C8×D47C23semidirect
139. #13094021C23semidirect
148. #13093999C23semidirect
169. #13093957C23semidirect
170. #13093948C23semidirect
171. #13093946C23semidirect
172. #13093946C23semidirect
175. (C2×D47)⋊C8C23semidirect
176. #13093935C23semidirect
181. C2×Q16×C47C23semidirect
189. C4×Q8×C47C23semidirect
196. C4⋊C8×C47C23semidirect
197. #103×C47C23semidirect
307. #10625336C2×D4semidirect
468. C2×#464D47semidirect
477. C2×C47#3268semidirect
494. C22×Q16C2×D47semidirect
521. C2×C4×Q8C2×D47semidirect
529. #464C2×D47semidirect
538. C2×C4⋊C8C2×D47semidirect
540. C2×#103C2×D47semidirect
548. C47C2×#3268semidirect
591. C2×Q16C22×D47semidirect
635. C4×Q8C22×D47semidirect
659. C4⋊C8C22×D47semidirect
661. #103C22×D47semidirect
935. C2#20254923direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940512
C22×#130940472
C2×#156897952
C2×#156897662
#202549232
C2×#156895132
C2×#156893722
C2×#156893582
C2×#156893192
C2×#156892842
C2×#156892712
C2×#156892672
C2×#156892582
C2×#156892212
C2×#156891932
C2×C47×#4642
C2×#326847