Finite Group Databasebeta

← C2×#20252895 #27083168

Subgroups — C2×#20252895 #27083168

Order 12032.

2882 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094051C211yesmaximal, characteristic
2C22×SD16×D47C211yesmaximal, characteristic, complemented
3C2×#15689698C211yesmaximal, characteristic, complemented
4C2×#15689595C211yesmaximal, characteristic, complemented
5#20252895C2116yesmaximal, direct product factor
6C2×#15689341C211yesmaximal, characteristic, complemented
7C2×#15689340C211yesmaximal, characteristic, complemented
8C2×#15689339C211yesmaximal, characteristic, complemented
9C2×#15689338C211yesmaximal, characteristic, complemented
10C2×#15689327C211yesmaximal, characteristic, complemented
11C2×#15689326C211yesmaximal, characteristic, complemented
12C2×#15689325C211yesmaximal, characteristic, complemented
13C2×#15689148C211yesmaximal, characteristic, complemented
14C2×#15689130C211yesmaximal, characteristic, complemented
15C2×#15689118C211yesmaximal, characteristic, complemented
16C2×C47×#461C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C22×D4×D47C2211yescharacteristic
20C2×#13094051—28no—
21C2×#13094051C2218yes—
22C22×#10625325C2211yescharacteristic
23C22×#10625335C2211yescharacteristic
24C22×#10625336C2211yescharacteristic
25C22×#10625336C2211yescharacteristic
26C2×SD16×D47—28no—
27C2×SD16×D47C2218yescomplemented
28C22×D376C2211yescharacteristic
29C22×#10625334C2211yescharacteristic
30C22×#10625324C2211yescharacteristic
31C22×C8×D47C2211yescharacteristic
32#15689698—24no—
33#15689698C2218yescomplemented
34C2×#13094022C2211yescharacteristic, complemented
35C2×#13094013C2211yescharacteristic, complemented
36C2×#13094012C2211yescharacteristic, complemented
37C2×#13094009—21no—
38C2×#13094009—21no—
39C2×#13094002—21no—
40C2×#13094002—21no—
41#15689595—24no—
42#15689595C2218yescomplemented
43C2×C4×D188C2211yescharacteristic
44C2×D4×Dic47C2211yescharacteristic
45C2×#13093986C2211yescharacteristic
46C2×C4×C22⋊D47—21no—
47C2×(C22⋊D47)⋊C4—21no—
48C2×#13093982C2211yescharacteristic
49C2×#13093981C2211yescharacteristic
50C22×(C2×D47)⋊C4—21no—
51C2×C22⋊C4×D47—21no—
52#15689341C2218yescomplemented
53#15689340C2218yescomplemented
54#15689339C2218yescomplemented
55#15689338C2218yescomplemented
56#15689327C2218yescomplemented
57#15689326C2218yescomplemented
58#15689325C2218yescomplemented
59#15689148C2218yescomplemented
60C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
61C2×Dic47⋊C8C2211yescharacteristic, complemented
62C2×Dic47⋊C8C2211yescharacteristic, complemented
63#15689130C2218yescomplemented
64#15689118C2218yescomplemented
65C2×#13093949C2211yescharacteristic, complemented
66C2×#13093948C2211yescharacteristic, complemented
67C2×#13093948C2211yescharacteristic, complemented
68C2×#13093947C2211yescharacteristic, complemented
69C2×#13093946C2211yescharacteristic, complemented
70C2×#13093944C2211yescharacteristic, complemented
71C22×SD16×C47C2211yescharacteristic
72C22×SD16×C47C2211yescharacteristic
73C2×C4⋊Q8×C47C2211yescharacteristic, complemented
74C2×C4×D4×C47C2211yescharacteristic
75C47×#461C2218yescomplemented
76C2×C4⋊C8×C47C2211yescharacteristic, complemented
77C2×#103×C47C2211yescharacteristic, complemented
78C2×#103×C47C2211yescharacteristic, complemented
79C24×D47—21no—
80C2×#10625354—22no—
81C2×#10625354—24no—
82C2×#10625354—24no—
83C2×#10625354C2314yes—
84C22×Dic94—21no—
85C22×Dic94C2311yescharacteristic
86C2×Q8×D47—22no—
87C2×Q8×D47—24no—
88C2×Q8×D47—24no—
89C2×Q8×D47C2314yes—
90C22×D188—21no—
91C22×D188C2311yescharacteristic
92C22×D188C2311yescharacteristic
93C22×C22⋊D47—21no—
94C2×D4×D47—22no—
95C2×D4×D47—24no—
96C2×D4×D47D418yes—
97C2×D4×D47C2314yes—
98C23×Dic47—21no—
99C22×C4×D47—21no—
100C22×C4×D47—21no—
101C22×C4×D47—21no—
102C22×C4×D47—21no—
103C22×C4×D47C2311yescharacteristic
104#13094051—232no—
105C2×#10625325—24no—
106C2×#10625325C2314yes—
107C2×#10625335—24no—
108C2×#10625335C2314yes—
109C2×#10625336—24no—
110C2×#10625336—24no—
111C2×#10625336C2314yes—
112C2×#10625336C2314yes—
113SD16×D47—232no—
114C2×D376—24no—
115C2×D376C2314yes—
116C2×#10625334—24no—
117C2×#10625334C2314yes—
118C2×#10625324—24no—
119C2×#10625324C2314yes—
120C22×C47⋊C8C2311yescharacteristic
121C22×C47⋊C8C2311yescharacteristic
122C2×C8×D47—24no—
123C2×C8×D47C2314yes—
124#13094022—22no—
125#13094022C2314yescomplemented
126#13094013—22no—
127#13094013C2314yescomplemented
128#13094012—22no—
129#13094012C2314yescomplemented
130#13094009—28no—
131#13094009—28no—
132#13094002—28no—
133#13094002—28no—
134C4×D188—22no—
135C4×D188C2314yes—
136D4×Dic47—22no—
137D4×Dic47C2314yes—
138#13093986—22no—
139#13093986C2314yes—
140C4×C22⋊D47—28no—
141(C22⋊D47)⋊C4—28no—
142#13093982—22no—
143#13093982C2314yes—
144#13093981D414yes—
145#13093981C2314yes—
146C2×C4⋊Dic47C2311yescharacteristic
147C2×Dic47⋊C4—21no—
148C2×Dic47⋊C4—21no—
149C2×Dic47⋊C4D411yescharacteristic
150C2×Dic47⋊C4D411yescharacteristic
151C2×C22⋊Dic47—21no—
152C2×(C2×D47)⋊C4—21no—
153C2×(C2×D47)⋊C4—21no—
154C2×(C2×D47)⋊C4—21no—
155C2×(C2×D47)⋊C4—21no—
156C2×(C2×D47)⋊C4—21no—
157C2×(C2×D47)⋊C4—21no—
158C2×(C2×D47)⋊C4—21no—
159C2×(C2×D47)⋊C4—28no—
160C2×(C2×D47)⋊C4D411yescharacteristic
161C2×(C2×D47)⋊C4D411yescharacteristic
162C22⋊C4×D47—28no—
163C2×C4×Dic47—21no—
164C2×C4×Dic47C2311yescharacteristic
165C4⋊(C47⋊C8)C2314yescomplemented
166Dic47⋊C8C2314yescomplemented
167Dic47⋊C8C2314yescomplemented
168#13093949C2314yescomplemented
169#13093948C2314yescomplemented
170#13093948C2314yescomplemented
171#13093947C2314yescomplemented
172#13093946C2314yescomplemented
173#13093944C2314yescomplemented
174C22×Q8×C47C2311yescharacteristic
175C22×Q8×C47C2311yescharacteristic
176C22×D4×C47C2311yescharacteristic
177C23×C4×C47—21no—
178C2×SD16×C47—24no—
179C2×SD16×C47—24no—
180C2×SD16×C47C2314yes—
181C2×SD16×C47C2314yes—
182C22×C8×C47C2311yescharacteristic
183C22×C8×C47C2311yescharacteristic
184C4⋊Q8×C47—22no—
185C4⋊Q8×C47C2314yescomplemented
186C4×D4×C47—22no—
187C4×D4×C47C2314yes—
188C2×C4⋊C4×C47—21no—
189C2×C4⋊C4×C47—21no—
190C2×C4⋊C4×C47C2311yescharacteristic
191C2×C22⋊C4×C47—21no—
192C2×C42×C47C2311yescharacteristic
193C4⋊C8×C47C2314yescomplemented
194#103×C47C2314yescomplemented
195#103×C47C2314yescomplemented
196C24×C47—21no—
197C23×D47—21no—
198C23×D47—28no—
199C23×D47—24no—
200C23×D47—21no—
201C23×D47—82no—
202C23×D47—82no—
203C23×D47C2×D411yescharacteristic
204C2×Q8×C47—21no—
205C2×Q8×C47—21no—
206C2×Q8×C47—22no—
207C2×Q8×C47—22no—
208C2×Q8×C47—22no—
209C2×Q8×C47—22no—
210C2×Q8×C47C2412yes—
211C2×Q8×C47C2412yes—
212C2×D4×C47—21no—
213C2×D4×C47—22no—
214C2×D4×C47C2×D414yes—
215C2×D4×C47C2412yes—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—24no—
220C22×C4×C47—82no—
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2411yescharacteristic
224C2×C22⋊D47—28no—
225C2×C22⋊D47—24no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—24no—
229C22×Dic47—82no—
230C22×Dic47C2×D411yescharacteristic
231C22×Dic47C2×D411yescharacteristic
232C22×Dic47C2×D411yescharacteristic
233#10625354—28no—
234#10625354—28no—
235#10625354—48no—
236Q8×D47—28no—
237Q8×D47—28no—
238Q8×D47—48no—
239D4×D47—216no—
240D4×D47—28no—
241D4×D47C2×D4116yes—
242C2×D188—21no—
243C2×D188—22no—
244C2×D188—22no—
245C2×D188—22no—
246C2×D188—24no—
247C2×D188—21no—
248C2×D188—44no—
249C2×D188C2×D414yes—
250C2×D188C2412yes—
251C2×D188C2412yes—
252C2×C4×D47—24no—
253C2×C4×D47—24no—
254C2×C4×D47—24no—
255C2×C4×D47—24no—
256C2×C4×D47—44no—
257C2×C4×D47—44no—
258C2×C4×D47—82no—
259C2×C4×D47—82no—
260C2×C4×D47C2×D412yes—
261C2×C4×D47C2×D414yes—
262C2×C4×D47#4114yes—
263C2×C4×D47C2412yes—
264C2×Dic94—22no—
265C2×Dic94—22no—
266C2×Dic94—21no—
267C2×Dic94—24no—
268C2×Dic94—44no—
269C2×Dic94C2412yes—
270SD16×C47—28no—
271SD16×C47—28no—
272C2×C8×C47—22no—
273C2×C8×C47—22no—
274C2×C8×C47C2412yes—
275C2×C8×C47C2412yes—
276C4⋊C4×C47—24no—
277C4⋊C4×C47—24no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47C2412yes—
280C22⋊C4×C47—24no—
281C42×C47C2×D412yes—
282C42×C47C2412yes—
283C22⋊Dic47—24no—
284#10625336—28no—
285#10625336—28no—
286#10625335—28no—
287#10625334—28no—
288(C2×D47)⋊C4—24no—
289(C2×D47)⋊C4—24no—
290(C2×D47)⋊C4—24no—
291(C2×D47)⋊C4—24no—
292(C2×D47)⋊C4—24no—
293(C2×D47)⋊C4—24no—
294(C2×D47)⋊C4—24no—
295(C2×D47)⋊C4C2×D414yes—
296(C2×D47)⋊C4C2×D414yes—
297C4⋊Dic47—21no—
298C4⋊Dic47C2412yes—
299Dic47⋊C4—24no—
300Dic47⋊C4—24no—
301Dic47⋊C4C2×D414yes—
302Dic47⋊C4C2×D414yes—
303C4×Dic47—24no—
304C4×Dic47C2×D412yes—
305C4×Dic47C2412yes—
306C2×C47⋊C8—22no—
307C2×C47⋊C8—22no—
308C2×C47⋊C8C2412yes—
309C2×C47⋊C8C2412yes—
310D376—28no—
311#10625325—28no—
312#10625324—28no—
313C8×D47—28no—
314C23×C47—24no—
315C23×C47—22no—
316C23×C47—42no—
317C23×C47—42no—
318C23×C47C22×D411yescharacteristic
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—24no—
322C22×D47—22no—
323C22×D47—216no—
324C22×D47—22no—
325C22×D47—42no—
326C22×D47—42no—
327C22×D47—42no—
328C22×D47—42no—
329C22×D47—42no—
330C22×D47—816no—
331C22×D47—84no—
332C22×D47—84no—
333C22×D47#12114yes—
334C22×D47C22×D412yes—
335Q8×C47—22no—
336Q8×C47—22no—
337Q8×C47—22no—
338Q8×C47—22no—
339Q8×C47—42no—
340Q8×C47—42no—
341D4×C47—24no—
342D4×C47—22no—
343D4×C47C22×D414yes—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—42no—
350C2×C4×C47—42no—
351C2×C4×C47—42no—
352C2×C4×C47—84no—
353C2×C4×C47C22×D412yes—
354C2×C4×C47C22×D412yes—
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47C22×D412yes—
357C2×C4×C47C2×#4112yes—
358C2×C4×C47C2511yescharacteristic
359C22⋊D47—216no—
360C2×Dic47—22no—
361C2×Dic47—22no—
362C2×Dic47—22no—
363C2×Dic47—22no—
364C2×Dic47—42no—
365C2×Dic47—42no—
366C2×Dic47—84no—
367C2×Dic47#12114yes—
368C2×Dic47C22×D412yes—
369C2×Dic47C22×D412yes—
370C2×Dic47C22×D412yes—
371D188—24no—
372D188—22no—
373D188—22no—
374D188—22no—
375D188—48no—
376D188—42no—
377D188C22×D414yes—
378C4×D47—48no—
379C4×D47—48no—
380C4×D47—84no—
381C4×D47—84no—
382C4×D47#12118yes—
383C4×D47C22×D414yes—
384C4×D47C2×#4114yes—
385Dic94—22no—
386Dic94—22no—
387Dic94—42no—
388Dic94—48no—
389C8×C47—22no—
390C8×C47—22no—
391C47⋊C8—22no—
392C47⋊C8—22no—
393C2×#3042—471nomaximal, Sylow
394C22×C47—24no—
395C22×C47—48no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47C2×#12112yes—
399C22×C47#57712yes—
400C22×C47#57712yes—
401C22×C47C23×D411yescharacteristic
402C2×D47—28no—
403C2×D47—22no—
404C2×D47—22no—
405C2×D47—24no—
406C2×D47—48no—
407C2×D47—42no—
408C2×D47—42no—
409C2×D47—42no—
410C2×D47—42no—
411C2×D47—42no—
412C2×D47—816no—
413C2×D47—84no—
414C2×D47C2×#12114yes—
415C4×C47—22no—
416C4×C47—22no—
417C4×C47—42no—
418C4×C47—42no—
419C4×C47—42no—
420C4×C47C2×#12112yes—
421C4×C47C23×D411yescharacteristic
422C4×C47C22×#4111yescharacteristic
423Dic47—22no—
424Dic47—22no—
425Dic47—42no—
426Dic47—42no—
427Dic47C2×#12114yes—
428C22×AGL(1,ℤ/8)—471no—
429C23×SD16—471no—
430C2×#536—471no—
431C2×#518—471no—
432#3042—4716no—
433C2×#463—471no—
434C2×#463—471no—
435C2×#463—471no—
436C2×#463—471no—
437C2×#461—471no—
438C2×#461—471no—
439C2×#461—471no—
440C2×#461D4711yescharacteristic, complemented
441C2×#424—471no—
442C2×#419—471no—
443C2×#416—471no—
444C2×C47—44no—
445C2×C47#304214yescomplemented
446C2×C47C22×#12111yescharacteristic
447C2×C47C2×#57711yescharacteristic
448C2×C47C2×#57711yescharacteristic
449D47—24no—
450D47—44no—
451D47—82no—
452C22×#41—471no—
453C23×Q8—471no—
454C23×D4—471no—
455C2×AGL(1,ℤ/8)—478no—
456C2×AGL(1,ℤ/8)—948no—
457C22×SD16—471no—
458C22×SD16—471no—
459C22×SD16—471no—
460C22×SD16—478no—
461C22×SD16—471no—
462C22×SD16—948no—
463C22×SD16C2×D4711yescharacteristic
464C22×SD16C2×D4711yescharacteristic
465C22×D8—471no—
466C22×D8—471no—
467C22×M16—471no—
468C23×C8—471no—
469#536—478no—
470#536—944no—
471C2×C4⋊Q8—471no—
472C2×C4⋊Q8C2×D4711yescharacteristic, complemented
473C2×#124—471no—
474C2×#124—471no—
475C2×#123—941no—
476C2×#123—941no—
477C2×C22⋊Q8—941no—
478C2×C22⋊Q8—941no—
479#518—478no—
480#518—944no—
481C2×C4×D4—471no—
482C2×C4×D4—471no—
483C2×C4×D4—471no—
484C2×C4×D4—941no—
485C2×C4×D4—941no—
486C2×C4×D4C2×D4711yescharacteristic
487C2×#117—471no—
488C2×#117—471no—
489C22×C22⋊C4—941no—
490C22×C22⋊C4—941no—
491#463—478no—
492#463—478no—
493#463—478no—
494#463—478no—
495#461—478no—
496#461—478no—
497#461—478no—
498#461C2×D4718yescomplemented
499#424—478no—
500C2×C4⋊C8—471no—
501C2×C4⋊C8—471no—
502C2×C4⋊C8—471no—
503C2×C4⋊C8C2×D4711yescharacteristic, complemented
504#419—478no—
505#416—478no—
506C2×#103—471no—
507C2×#103—471no—
508C2×#103—471no—
509C2×#103—471no—
510C2×#103C2×D4711yescharacteristic, complemented
511C2×#103C2×D4711yescharacteristic, complemented
512C2×#102—471no—
513C2×#102—471no—
514C47C2×#304211yescharacteristic, complemented, Sylow
515C25—941no—
516C2×#41—474no—
517C2×#41—942no—
518C2×#41—944no—
519C2×#41—944no—
520C22×Q8—474no—
521C22×Q8—471no—
522C22×Q8—941no—
523C22×Q8—942no—
524C22×Q8—944no—
525C22×Q8—944no—
526C22×Q8C22×D4711yescharacteristic
527C22×Q8C22×D4711yescharacteristic
528C22×D4—478no—
529C22×D4—474no—
530C22×D4—471no—
531C22×D4—471no—
532C22×D4—941no—
533C22×D4—942no—
534C22×D4—944no—
535C22×D4—941no—
536C22×D4C22×D4711yescharacteristic
537C23×C4—21no—
538C23×C4—471no—
539C23×C4—941no—
540C23×C4—941no—
541C23×C4—941no—
542C23×C4—941no—
543C23×C4—941no—
544AGL(1,ℤ/8)—9432no—
545C2×SD16—24no—
546C2×SD16—24no—
547C2×SD16—474no—
548C2×SD16—474no—
549C2×SD16—474no—
550C2×SD16—474no—
551C2×SD16—944no—
552C2×SD16—9432no—
553C2×SD16—944no—
554C2×SD16—944no—
555C2×SD16—944no—
556C2×SD16C22×D4714yes—
557C2×SD16C22×D4714yes—
558C2×D8—474no—
559C2×D8—474no—
560C2×D8—944no—
561C2×D8—944no—
562C2×M16—474no—
563C2×M16—944no—
564C22×C8—471no—
565C22×C8—471no—
566C22×C8—474no—
567C22×C8—944no—
568C22×C8C22×D4711yescharacteristic
569C22×C8C22×D4711yescharacteristic
570C4⋊Q8—22no—
571C4⋊Q8—474no—
572C4⋊Q8—942no—
573C4⋊Q8C22×D4714yescomplemented
574#124—474no—
575#124—474no—
576#124—942no—
577#124—942no—
578#123—948no—
579#123—948no—
580C22⋊Q8—948no—
581C22⋊Q8—948no—
582C4×D4—22no—
583C4×D4—474no—
584C4×D4—474no—
585C4×D4—474no—
586C4×D4—942no—
587C4×D4—942no—
588C4×D4—948no—
589C4×D4—948no—
590C4×D4—942no—
591C4×D4C22×D4714yes—
592#117—474no—
593#117—474no—
594#117—474no—
595#117—942no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—471no—
599C2×C4⋊C4—471no—
600C2×C4⋊C4—471no—
601C2×C4⋊C4—941no—
602C2×C4⋊C4—941no—
603C2×C4⋊C4C22×D4711yescharacteristic
604C2×C22⋊C4—21no—
605C2×C22⋊C4—471no—
606C2×C22⋊C4—471no—
607C2×C22⋊C4—948no—
608C2×C22⋊C4—948no—
609C2×C22⋊C4—941no—
610C2×C22⋊C4—941no—
611C2×C22⋊C4—941no—
612C2×C22⋊C4—941no—
613C2×C22⋊C4—941no—
614C2×C22⋊C4—941no—
615C2×C22⋊C4—941no—
616C2×C22⋊C4—941no—
617C2×C42—471no—
618C2×C42—941no—
619C2×C42C22×D4711yescharacteristic
620C4⋊C8—474no—
621C4⋊C8—474no—
622C4⋊C8—474no—
623C4⋊C8C22×D4714yescomplemented
624#103—474no—
625#103—474no—
626#103—474no—
627#103—474no—
628#103C22×D4714yescomplemented
629#103C22×D4714yescomplemented
630#102—474no—
631#102—474no—
632C24—21no—
633C24—471no—
634C24—944no—
635C24—948no—
636C24—941no—
637C24—941no—
638C24—3762no—
639C24—3762no—
640#41—948no—
641#41—948no—
642#41—1888no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—472no—
650C2×Q8—944no—
651C2×Q8—948no—
652C2×Q8—948no—
653C2×Q8—941no—
654C2×Q8—942no—
655C2×Q8—942no—
656C2×Q8—1884no—
657C2×Q8—1888no—
658C2×Q8C23×D4712yes—
659C2×Q8C23×D4712yes—
660C2×D4—21no—
661C2×D4—22no—
662C2×D4—4716no—
663C2×D4—474no—
664C2×D4—472no—
665C2×D4—472no—
666C2×D4—944no—
667C2×D4—9416no—
668C2×D4—948no—
669C2×D4—944no—
670C2×D4—948no—
671C2×D4—941no—
672C2×D4—942no—
673C2×D4—941no—
674C2×D4—942no—
675C2×D4—942no—
676C2×D4—1884no—
677C2×D4D4×D4714yes—
678C2×D4C23×D4712yes—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—82no—
684C22×C4—471no—
685C22×C4—472no—
686C22×C4—474no—
687C22×C4—474no—
688C22×C4—472no—
689C22×C4—471no—
690C22×C4—471no—
691C22×C4—944no—
692C22×C4—944no—
693C22×C4—944no—
694C22×C4—944no—
695C22×C4—941no—
696C22×C4—941no—
697C22×C4—944no—
698C22×C4—3762no—
699C22×C4—3762no—
700C22×C4—3762no—
701C22×C4—1884no—
702C22×C4—1884no—
703C22×C4D4×D4711yescharacteristic
704C22×C4D4×D4711yescharacteristic
705C22×C4C23×D4711yescharacteristic
706SD16—28no—
707SD16—28no—
708SD16—948no—
709SD16—948no—
710SD16—948no—
711SD16—948no—
712D8—948no—
713D8—948no—
714M16—948no—
715C2×C8—22no—
716C2×C8—22no—
717C2×C8—472no—
718C2×C8—472no—
719C2×C8—948no—
720C2×C8—942no—
721C2×C8—942no—
722C2×C8C23×D4712yes—
723C2×C8C23×D4712yes—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—21no—
727C4⋊C4—474no—
728C4⋊C4—474no—
729C4⋊C4—472no—
730C4⋊C4—944no—
731C4⋊C4—944no—
732C4⋊C4—941no—
733C4⋊C4C23×D4712yes—
734C22⋊C4—24no—
735C22⋊C4—474no—
736C22⋊C4—474no—
737C22⋊C4—944no—
738C22⋊C4—944no—
739C22⋊C4—944no—
740C22⋊C4—944no—
741C22⋊C4—944no—
742C22⋊C4—944no—
743C22⋊C4—944no—
744C22⋊C4—944no—
745C42—472no—
746C42—472no—
747C42—944no—
748C42D4×D4712yes—
749C42C23×D4712yes—
750C23—24no—
751C23—22no—
752C23—42no—
753C23—42no—
754C23—474no—
755C23—472no—
756C23—9416no—
757C23—942no—
758C23—942no—
759C23—944no—
760C23—942no—
761C23—942no—
762C23—3764no—
763C23—3764no—
764C23—37616no—
765C23—1882no—
766C23—1882no—
767C23—1882no—
768C23—1882no—
769C23—1882no—
770C23C2×D4×D4711yescharacteristic
771Q8—22no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—42no—
776Q8—42no—
777Q8—942no—
778Q8—942no—
779Q8—1888no—
780Q8—1882no—
781D4—24no—
782D4—22no—
783D4—474no—
784D4—9416no—
785D4—944no—
786D4—942no—
787D4—942no—
788D4—942no—
789D4—1888no—
790D4—1882no—
791D4C2×D4×D4714yes—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—84no—
801C2×C4—474no—
802C2×C4—472no—
803C2×C4—478no—
804C2×C4—474no—
805C2×C4—474no—
806C2×C4—472no—
807C2×C4—472no—
808C2×C4—942no—
809C2×C4—942no—
810C2×C4—942no—
811C2×C4—942no—
812C2×C4—3764no—
813C2×C4—3764no—
814C2×C4—3764no—
815C2×C4—1888no—
816C2×C4—1888no—
817C2×C4—1882no—
818C2×C4—1882no—
819C2×C4C2×D4×D4712yes—
820C2×C4C2×D4×D4712yes—
821C2×C4C2×D4×D4711yescharacteristic
822C2×C4C2×D4×D4712yes—
823C2×C4#41×D4712yes—
824C2×C4C24×D4711yescharacteristic
825C8—22no—
826C8—22no—
827C8—942no—
828C8—942no—
829C22—24no—
830C22—42no—
831C22—42no—
832C22—48no—
833C22—474no—
834C22—942no—
835C22—942no—
836C22—948no—
837C22—944no—
838C22—37616no—
839C22—3764no—
840C22—1882no—
841C22—1882no—
842C22—1882no—
843C22—1882no—
844C22—1882no—
845C22—1888no—
846C22#121×D4712yes—
847C22#1568992912yes—
848C22#1568993212yes—
849C22C22×D4×D4711yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—474no—
856C4—942no—
857C4—942no—
858C4—1882no—
859C4—1882no—
860C4#121×D4712yes—
861C4C22×D4×D4711yescharacteristic
862C4C2×#41×D4711yescharacteristic
863C2—44no—
864C2—944no—
865C2—3762no—
866C2—1884no—
867C2#2025289514yesdirect product factor
868C2C2×#121×D4711yescharacteristic
869C2C2×#1568992911yescharacteristic
870C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#461C2
socleC23×C47C22×D4
prime radicalC22×#13094051C2
hypercenterC2×#461D47
hypocenterC47C2×#3042
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
2. C22×SD16×D47C2semidirect
3. C2×#15689698C2semidirect
4. C2×#15689595C2semidirect
5. #20252895C2direct (N × H)
6. C2×#15689341C2semidirect
7. C2×#15689340C2semidirect
8. C2×#15689339C2semidirect
9. C2×#15689338C2semidirect
10. C2×#15689327C2semidirect
11. C2×#15689326C2semidirect
12. C2×#15689325C2semidirect
13. C2×#15689148C2semidirect
14. C2×#15689130C2semidirect
15. C2×#15689118C2semidirect
16. C2×C47×#461C2semidirect
27. C2×SD16×D47C22semidirect
33. #15689698C22semidirect
34. C2×#13094022C22semidirect
35. C2×#13094013C22semidirect
36. C2×#13094012C22semidirect
42. #15689595C22semidirect
52. #15689341C22semidirect
53. #15689340C22semidirect
54. #15689339C22semidirect
55. #15689338C22semidirect
56. #15689327C22semidirect
57. #15689326C22semidirect
58. #15689325C22semidirect
59. #15689148C22semidirect
60. C2×C4⋊(C47⋊C8)C22semidirect
61. C2×Dic47⋊C8C22semidirect
62. C2×Dic47⋊C8C22semidirect
63. #15689130C22semidirect
64. #15689118C22semidirect
65. C2×#13093949C22semidirect
66. C2×#13093948C22semidirect
67. C2×#13093948C22semidirect
68. C2×#13093947C22semidirect
69. C2×#13093946C22semidirect
70. C2×#13093944C22semidirect
73. C2×C4⋊Q8×C47C22semidirect
75. C47×#461C22semidirect
76. C2×C4⋊C8×C47C22semidirect
77. C2×#103×C47C22semidirect
78. C2×#103×C47C22semidirect
125. #13094022C23semidirect
127. #13094013C23semidirect
129. #13094012C23semidirect
165. C4⋊(C47⋊C8)C23semidirect
166. Dic47⋊C8C23semidirect
167. Dic47⋊C8C23semidirect
168. #13093949C23semidirect
169. #13093948C23semidirect
170. #13093948C23semidirect
171. #13093947C23semidirect
172. #13093946C23semidirect
173. #13093944C23semidirect
185. C4⋊Q8×C47C23semidirect
193. C4⋊C8×C47C23semidirect
194. #103×C47C23semidirect
195. #103×C47C23semidirect
440. C2×#461D47semidirect
445. C2×C47#3042semidirect
472. C2×C4⋊Q8C2×D47semidirect
498. #461C2×D47semidirect
503. C2×C4⋊C8C2×D47semidirect
510. C2×#103C2×D47semidirect
511. C2×#103C2×D47semidirect
514. C47C2×#3042semidirect
573. C4⋊Q8C22×D47semidirect
623. C4⋊C8C22×D47semidirect
628. #103C22×D47semidirect
629. #103C22×D47semidirect
867. C2#20252895direct (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×SD16×D472
C2×#156896982
C2×#156895952
#202528952
C2×#156893412
C2×#156893402
C2×#156893392
C2×#156893382
C2×#156893272
C2×#156893262
C2×#156893252
C2×#156891482
C2×#156891302
C2×#156891182
C2×C47×#4612
C2×#304247