Finite Group Databasebeta

← C2×#20252941 #27083218

Subgroups — C2×#20252941 #27083218

Order 12032.

2742 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094056C211yesmaximal, characteristic, complemented
2C22×#13094045C211yesmaximal, characteristic
3C2×#15689693C211yesmaximal, characteristic, complemented
4C2×#15689605C211yesmaximal, characteristic, complemented
5#20252941C2116yesmaximal, direct product factor
6C2×#15689343C211yesmaximal, characteristic, complemented
7C2×#15689333C211yesmaximal, characteristic, complemented
8C2×#15689331C211yesmaximal, characteristic, complemented
9C2×#15689337C211yesmaximal, characteristic, complemented
10C2×#15689335C211yesmaximal, characteristic, complemented
11C2×#15689329C211yesmaximal, characteristic, complemented
12C2×#15689327C211yesmaximal, characteristic, complemented
13C2×#15689148C211yesmaximal, characteristic, complemented
14C2×#15689121C211yesmaximal, characteristic, complemented
15C2×#103×D47C211yesmaximal, characteristic, complemented
16C2×C47×#464C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625352C2211yescharacteristic
19C22×Q8×D47C2211yescharacteristic
20C2×#13094056—28no—
21C2×#13094056C2218yescomplemented
22C2×#13094045—28no—
23C2×#13094045C2218yes—
24C22×#10625337C2211yescharacteristic
25C22×#10625337C2211yescharacteristic
26C22×#10625325C2211yescharacteristic
27C22×#10625325C2211yescharacteristic
28C22×#10625336C2211yescharacteristic
29C22×#10625334C2211yescharacteristic
30C22×#10625324C2211yescharacteristic
31C22×C8×D47C2211yescharacteristic
32#15689693—24no—
33#15689693C2218yescomplemented
34C2×#13094024C2211yescharacteristic
35C2×#13094022C2211yescharacteristic
36C2×#13094011C2211yescharacteristic
37C2×#13094006—21no—
38C2×#13094006—21no—
39C2×#13094001—21no—
40C2×#13094001—21no—
41#15689605—24no—
42#15689605C2218yescomplemented
43C2×Q8×Dic47C2211yescharacteristic
44C2×C4×D188—21no—
45C2×C4×D188C2211yescharacteristic
46C2×#13093986—21no—
47C2×#13093986C2211yescharacteristic
48C2×#13093981—21no—
49C2×#13093981C2211yescharacteristic
50C2×C4⋊C4×D47—21no—
51C2×C4⋊C4×D47C2211yescharacteristic
52#15689343C2218yescomplemented
53#15689337C2218yescomplemented
54#15689335C2218yescomplemented
55#15689333C2218yescomplemented
56#15689331C2218yescomplemented
57#15689329C2218yescomplemented
58#15689327C2218yescomplemented
59#15689148C2218yescomplemented
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63#15689121C2218yescomplemented
64C2×#13093949C2211yescharacteristic
65C2×#13093949C2211yescharacteristic
66C2×#13093948C2211yescharacteristic
67C2×#13093947C2211yescharacteristic
68C2×#13093947C2211yescharacteristic
69#103×D47C2218yescomplemented
70C2×#13093945C2211yescharacteristic
71C22×Q16×C47C2211yescharacteristic
72C22×SD16×C47C2211yescharacteristic
73C2×#124×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic
75C47×#464C2218yescomplemented
76C2×C4⋊C8×C47C2211yescharacteristic
77C2×#103×C47C2211yescharacteristic
78C2×#102×C47C2211yescharacteristic
79C2×#10625354—22no—
80C2×#10625354—24no—
81C2×#10625354D418yes—
82C2×#10625354C2314yes—
83C2×#10625352—24no—
84C2×#10625352—22no—
85C2×#10625352—24no—
86C2×#10625352C2314yes—
87C22×Dic94—21no—
88C22×Dic94C2311yescharacteristic
89C22×Dic94C2311yescharacteristic
90C2×Q8×D47—22no—
91C2×Q8×D47—24no—
92C2×Q8×D47—24no—
93C2×Q8×D47C2314yes—
94C22×D188—21no—
95C22×D188C2311yescharacteristic
96C22×C22⋊D47—21no—
97C23×Dic47—21no—
98C22×C4×D47—21no—
99C22×C4×D47—21no—
100C22×C4×D47—21no—
101C22×C4×D47—21no—
102C22×C4×D47—21no—
103C22×C4×D47C2311yescharacteristic
104#13094056—232no—
105#13094045—232no—
106C2×#10625337—24no—
107C2×#10625337—24no—
108C2×#10625337C2314yes—
109C2×#10625337C2314yes—
110C2×#10625325—24no—
111C2×#10625325—24no—
112C2×#10625325C2314yes—
113C2×#10625325C2314yes—
114C2×#10625336—24no—
115C2×#10625336C2314yes—
116C2×#10625334—24no—
117C2×#10625334C2314yes—
118C2×#10625324—24no—
119C2×#10625324C2314yes—
120C22×C47⋊C8C2311yescharacteristic
121C22×C47⋊C8C2311yescharacteristic
122C2×C8×D47—24no—
123C2×C8×D47C2314yes—
124#13094024—22no—
125#13094024C2314yes—
126#13094022—22no—
127#13094022C2314yes—
128#13094011—22no—
129#13094011C2314yes—
130#13094006—28no—
131#13094006—28no—
132#13094001—28no—
133#13094001—28no—
134Q8×Dic47—22no—
135Q8×Dic47C2314yes—
136C4×D188—22no—
137C4×D188—28no—
138C4×D188C2314yes—
139#13093986—28no—
140#13093986—22no—
141#13093986C2314yes—
142#13093981—28no—
143#13093981D414yes—
144#13093981C2314yes—
145C2×C4⋊Dic47—21no—
146C2×C4⋊Dic47—21no—
147C2×C4⋊Dic47—21no—
148C2×C4⋊Dic47C2311yescharacteristic
149C2×Dic47⋊C4—21no—
150C2×Dic47⋊C4—21no—
151C2×Dic47⋊C4—21no—
152C2×Dic47⋊C4D411yescharacteristic
153C2×Dic47⋊C4D411yescharacteristic
154C4⋊C4×D47—22no—
155C4⋊C4×D47—28no—
156C4⋊C4×D47C2314yes—
157C2×C22⋊Dic47—21no—
158C2×C22⋊Dic47—21no—
159C2×(C2×D47)⋊C4—21no—
160C2×(C2×D47)⋊C4—21no—
161C2×(C2×D47)⋊C4D411yescharacteristic
162C2×(C2×D47)⋊C4D411yescharacteristic
163C2×C4×Dic47—21no—
164C2×C4×Dic47C2311yescharacteristic
165C4⋊(C47⋊C8)C2314yes—
166Dic47⋊C8C2314yes—
167Dic47⋊C8C2314yes—
168#13093949C2314yes—
169#13093949C2314yes—
170#13093948C2314yes—
171#13093947C2314yes—
172#13093947C2314yes—
173#13093945C2314yes—
174C22×Q8×C47C2311yescharacteristic
175C22×Q8×C47C2311yescharacteristic
176C22×D4×C47C2311yescharacteristic
177C2×Q16×C47—24no—
178C2×Q16×C47C2314yes—
179C2×SD16×C47—24no—
180C2×SD16×C47C2314yes—
181C22×C8×C47C2311yescharacteristic
182C22×C8×C47C2311yescharacteristic
183#124×C47—22no—
184#124×C47C2314yes—
185C4×Q8×C47—22no—
186C4×Q8×C47C2314yes—
187C2×C4⋊C4×C47—21no—
188C2×C4⋊C4×C47C2311yescharacteristic
189C2×C22⋊C4×C47—21no—
190C2×C22⋊C4×C47—21no—
191C2×C42×C47—21no—
192C2×C42×C47C2311yescharacteristic
193C4⋊C8×C47C2314yes—
194#103×C47C2314yes—
195#102×C47C2314yes—
196C24×C47—21no—
197C23×D47—21no—
198C23×D47C2×D411yescharacteristic
199C2×Q8×C47—21no—
200C2×Q8×C47—21no—
201C2×Q8×C47—22no—
202C2×Q8×C47—22no—
203C2×Q8×C47—22no—
204C2×Q8×C47C2×D414yes—
205C2×Q8×C47C2412yes—
206C2×Q8×C47C2412yes—
207C2×D4×C47—22no—
208C2×D4×C47—21no—
209C2×D4×C47—22no—
210C2×D4×C47C2412yes—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2411yescharacteristic
217C2×C22⋊D47—24no—
218C2×C22⋊D47—44no—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—24no—
223C22×Dic47—44no—
224C22×Dic47C2×D411yescharacteristic
225C22×Dic47C2×D411yescharacteristic
226C22×Dic47C2×D411yescharacteristic
227#10625354—216no—
228#10625354—28no—
229#10625354C2×D4116yes—
230Q8×D47—28no—
231Q8×D47—28no—
232Q8×D47—48no—
233#10625352—28no—
234#10625352—28no—
235#10625352—48no—
236C2×D188—28no—
237C2×D188—24no—
238C2×D188—21no—
239C2×D188—22no—
240C2×D188C2×D414yes—
241C2×D188C2412yes—
242C2×C4×D47—28no—
243C2×C4×D47—24no—
244C2×C4×D47—24no—
245C2×C4×D47—24no—
246C2×C4×D47—24no—
247C2×C4×D47—24no—
248C2×C4×D47—44no—
249C2×C4×D47—82no—
250C2×C4×D47—82no—
251C2×C4×D47—82no—
252C2×C4×D47C2×D412yes—
253C2×C4×D47C2×D414yes—
254C2×C4×D47#4114yes—
255C2×C4×D47C2412yes—
256C2×Dic94—22no—
257C2×Dic94—22no—
258C2×Dic94—22no—
259C2×Dic94—22no—
260C2×Dic94—21no—
261C2×Dic94—21no—
262C2×Dic94—24no—
263C2×Dic94—44no—
264C2×Dic94C2412yes—
265C2×Dic94C2412yes—
266Q16×C47—28no—
267SD16×C47—28no—
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⋊C4×C47—24no—
277C42×C47—24no—
278C42×C47C2×D412yes—
279C42×C47C2412yes—
280C22⋊Dic47—24no—
281C22⋊Dic47—24no—
282#10625337—28no—
283#10625337—28no—
284#10625336—28no—
285#10625334—28no—
286(C2×D47)⋊C4—24no—
287(C2×D47)⋊C4—24no—
288(C2×D47)⋊C4C2×D414yes—
289(C2×D47)⋊C4C2×D414yes—
290C4⋊Dic47—21no—
291C4⋊Dic47—24no—
292C4⋊Dic47—24no—
293C4⋊Dic47—24no—
294C4⋊Dic47C2412yes—
295Dic47⋊C4—24no—
296Dic47⋊C4—24no—
297Dic47⋊C4—24no—
298Dic47⋊C4C2×D414yes—
299Dic47⋊C4C2×D414yes—
300C4×Dic47—24no—
301C4×Dic47C2×D412yes—
302C4×Dic47C2412yes—
303C2×C47⋊C8—22no—
304C2×C47⋊C8—22no—
305C2×C47⋊C8C2412yes—
306C2×C47⋊C8C2412yes—
307#10625325—28no—
308#10625325—28no—
309#10625324—28no—
310C8×D47—28no—
311C23×C47—22no—
312C23×C47—42no—
313C23×C47—42no—
314C23×C47—42no—
315C23×C47C22×D411yescharacteristic
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—24no—
319C22×D47—22no—
320C22×D47—42no—
321C22×D47—42no—
322C22×D47#12114yes—
323C22×D47C22×D412yes—
324Q8×C47—24no—
325Q8×C47—22no—
326Q8×C47—22no—
327Q8×C47—22no—
328Q8×C47—42no—
329Q8×C47C22×D414yes—
330D4×C47—22no—
331D4×C47—22no—
332D4×C47—42no—
333C2×C4×C47—24no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—42no—
340C2×C4×C47—42no—
341C2×C4×C47C22×D412yes—
342C2×C4×C47C22×D412yes—
343C2×C4×C47C22×D411yescharacteristic
344C2×C4×C47C22×D412yes—
345C2×C4×C47C2×#4112yes—
346C2×C4×C47C2511yescharacteristic
347C22⋊D47—48no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47—22no—
353C2×Dic47—42no—
354C2×Dic47—42no—
355C2×Dic47—42no—
356C2×Dic47—48no—
357C2×Dic47#12114yes—
358C2×Dic47C22×D412yes—
359C2×Dic47C22×D412yes—
360C2×Dic47C22×D412yes—
361D188—216no—
362D188—24no—
363D188—22no—
364D188C22×D414yes—
365C4×D47—216no—
366C4×D47—48no—
367C4×D47—84no—
368C4×D47—84no—
369C4×D47—84no—
370C4×D47#12118yes—
371C4×D47C22×D414yes—
372C4×D47C2×#4114yes—
373Dic94—22no—
374Dic94—22no—
375Dic94—22no—
376Dic94—22no—
377Dic94—42no—
378Dic94—42no—
379Dic94—48no—
380C8×C47—22no—
381C8×C47—22no—
382C47⋊C8—22no—
383C47⋊C8—22no—
384C2×#3046—471nomaximal, Sylow
385C22×C47—42no—
386C22×C47—42no—
387C22×C47—42no—
388C22×C47—84no—
389C22×C47C2×#12112yes—
390C22×C47#57712yes—
391C22×C47#57812yes—
392C22×C47C23×D411yescharacteristic
393C2×D47—28no—
394C2×D47—22no—
395C2×D47—22no—
396C2×D47—24no—
397C2×D47—48no—
398C2×D47—42no—
399C2×D47—42no—
400C2×D47C2×#12114yes—
401C4×C47—24no—
402C4×C47—22no—
403C4×C47—22no—
404C4×C47—42no—
405C4×C47—42no—
406C4×C47C2×#12112yes—
407C4×C47C23×D411yescharacteristic
408C4×C47C22×#4111yescharacteristic
409Dic47—22no—
410Dic47—22no—
411Dic47—42no—
412Dic47—42no—
413Dic47—42no—
414Dic47C2×#12114yes—
415C22×#137—471no—
416C22×#135—471no—
417C2×#536—471no—
418C2×#520—471no—
419#3046—4716no—
420C2×#464—471no—
421C2×#464D4711yescharacteristic, complemented
422C2×#462—471no—
423C2×#462—471no—
424C2×#463—471no—
425C2×#463—471no—
426C2×#461—471no—
427C2×#461—471no—
428C2×#424—471no—
429C2×#417—471no—
430C22×#103—471no—
431C2×C47—82no—
432C2×C47#304614yescomplemented
433C2×C47C22×#12111yescharacteristic
434C2×C47C2×#57711yescharacteristic
435C2×C47C2×#57811yescharacteristic
436D47—24no—
437D47—44no—
438C22×#41—471no—
439C22×#41—471no—
440C23×Q8—471no—
441C2×#137—478no—
442C2×#137—948no—
443C2×#135—478no—
444C2×#135—948no—
445C22×Q16—471no—
446C22×Q16—471no—
447C22×Q16C2×D4711yescharacteristic
448C22×SD16—471no—
449C22×SD16—471no—
450C22×SD16—471no—
451C22×SD16C2×D4711yescharacteristic
452C22×D8—471no—
453C22×M16—471no—
454C23×C8—471no—
455#536—478no—
456#536—944no—
457C2×C4⋊Q8—471no—
458C2×C4⋊Q8—471no—
459C2×#124—471no—
460C2×#124C2×D4711yescharacteristic
461C2×#123—941no—
462C2×#123—941no—
463C2×C22⋊Q8—941no—
464C2×C22⋊Q8—941no—
465#520—478no—
466#520—944no—
467C2×C4×Q8—471no—
468C2×C4×Q8C2×D4711yescharacteristic
469C2×C4×D4—471no—
470C2×C4×D4—471no—
471C2×C4×D4—941no—
472C2×C4×D4—941no—
473C2×#117—471no—
474C2×#117—941no—
475C22×C4⋊C4—471no—
476C22×C4⋊C4—941no—
477#464—478no—
478#464C2×D4718yescomplemented
479#463—478no—
480#463—478no—
481#462—478no—
482#462—478no—
483#461—478no—
484#461—478no—
485#424—478no—
486C2×C4⋊C8—471no—
487C2×C4⋊C8—471no—
488C2×C4⋊C8—471no—
489C2×C4⋊C8C2×D4711yescharacteristic
490#417—478no—
491C2×#103—471no—
492C2×#103—471no—
493C2×#103—471no—
494C2×#103—471no—
495C2×#103—471no—
496C2×#103—478no—
497C2×#103C2×D4711yescharacteristic
498C2×#102—471no—
499C2×#102C2×D4711yescharacteristic
500C47C2×#304611yescharacteristic, complemented, Sylow
501C2×#41—478no—
502C2×#41—474no—
503C2×#41—474no—
504C2×#41—942no—
505C2×#41—942no—
506C2×#41—944no—
507C2×#41—944no—
508C2×#41—944no—
509C22×Q8—474no—
510C22×Q8—471no—
511C22×Q8—471no—
512C22×Q8—941no—
513C22×Q8—942no—
514C22×Q8—944no—
515C22×Q8—944no—
516C22×Q8C22×D4711yescharacteristic
517C22×Q8C22×D4711yescharacteristic
518C22×D4—471no—
519C22×D4—941no—
520C22×D4—941no—
521C22×D4C22×D4711yescharacteristic
522C23×C4—471no—
523C23×C4—941no—
524C23×C4—941no—
525C23×C4—941no—
526C23×C4—941no—
527C23×C4—941no—
528C23×C4—941no—
529#137—9432no—
530#135—9432no—
531C2×Q16—24no—
532C2×Q16—474no—
533C2×Q16—474no—
534C2×Q16—944no—
535C2×Q16—944no—
536C2×Q16C22×D4714yes—
537C2×SD16—24no—
538C2×SD16—474no—
539C2×SD16—474no—
540C2×SD16—474no—
541C2×SD16—944no—
542C2×SD16—944no—
543C2×SD16—944no—
544C2×SD16C22×D4714yes—
545C2×D8—474no—
546C2×D8—944no—
547C2×M16—474no—
548C2×M16—944no—
549C22×C8—471no—
550C22×C8—471no—
551C22×C8—474no—
552C22×C8—944no—
553C22×C8C22×D4711yescharacteristic
554C22×C8C22×D4711yescharacteristic
555C4⋊Q8—474no—
556C4⋊Q8—474no—
557C4⋊Q8—942no—
558C4⋊Q8—942no—
559#124—22no—
560#124—474no—
561#124—942no—
562#124C22×D4714yes—
563#123—948no—
564#123—948no—
565C22⋊Q8—948no—
566C22⋊Q8—948no—
567C4×Q8—22no—
568C4×Q8—474no—
569C4×Q8—942no—
570C4×Q8C22×D4714yes—
571C4×D4—474no—
572C4×D4—474no—
573C4×D4—948no—
574C4×D4—942no—
575C4×D4—948no—
576C4×D4—942no—
577#117—474no—
578#117—474no—
579#117—948no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—471no—
582C2×C4⋊C4—471no—
583C2×C4⋊C4—471no—
584C2×C4⋊C4—474no—
585C2×C4⋊C4—948no—
586C2×C4⋊C4—942no—
587C2×C4⋊C4—941no—
588C2×C4⋊C4—941no—
589C2×C4⋊C4—941no—
590C2×C4⋊C4—941no—
591C2×C4⋊C4—941no—
592C2×C4⋊C4—941no—
593C2×C4⋊C4C22×D4711yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—471no—
597C2×C22⋊C4—471no—
598C2×C22⋊C4—941no—
599C2×C22⋊C4—941no—
600C2×C22⋊C4—941no—
601C2×C22⋊C4—941no—
602C2×C42—21no—
603C2×C42—471no—
604C2×C42—941no—
605C2×C42C22×D4711yescharacteristic
606C4⋊C8—474no—
607C4⋊C8—474no—
608C4⋊C8—474no—
609C4⋊C8C22×D4714yes—
610#103—474no—
611#103—474no—
612#103—474no—
613#103—474no—
614#103—474no—
615#103C22×D4714yes—
616#102—474no—
617#102C22×D4714yes—
618C24—21no—
619C24—471no—
620C24—941no—
621#41—4716no—
622#41—9416no—
623#41—948no—
624#41—948no—
625#41—948no—
626#41—1888no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—472no—
633C2×Q8—472no—
634C2×Q8—944no—
635C2×Q8—948no—
636C2×Q8—948no—
637C2×Q8—941no—
638C2×Q8—941no—
639C2×Q8—942no—
640C2×Q8—942no—
641C2×Q8—942no—
642C2×Q8—942no—
643C2×Q8—1884no—
644C2×Q8—1888no—
645C2×Q8D4×D4714yes—
646C2×Q8C23×D4712yes—
647C2×Q8C23×D4712yes—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—22no—
651C2×D4—474no—
652C2×D4—472no—
653C2×D4—944no—
654C2×D4—948no—
655C2×D4—944no—
656C2×D4—941no—
657C2×D4—942no—
658C2×D4—1884no—
659C2×D4C23×D4712yes—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—471no—
664C22×C4—472no—
665C22×C4—474no—
666C22×C4—474no—
667C22×C4—472no—
668C22×C4—471no—
669C22×C4—471no—
670C22×C4—944no—
671C22×C4—948no—
672C22×C4—944no—
673C22×C4—944no—
674C22×C4—944no—
675C22×C4—944no—
676C22×C4—941no—
677C22×C4—941no—
678C22×C4—941no—
679C22×C4—944no—
680C22×C4—3762no—
681C22×C4—3762no—
682C22×C4—3762no—
683C22×C4—1884no—
684C22×C4—1884no—
685C22×C4D4×D4711yescharacteristic
686C22×C4D4×D4711yescharacteristic
687C22×C4C23×D4711yescharacteristic
688Q16—28no—
689Q16—948no—
690Q16—948no—
691SD16—28no—
692SD16—948no—
693SD16—948no—
694SD16—948no—
695D8—948no—
696M16—948no—
697C2×C8—22no—
698C2×C8—22no—
699C2×C8—472no—
700C2×C8—472no—
701C2×C8—948no—
702C2×C8—942no—
703C2×C8—942no—
704C2×C8C23×D4712yes—
705C2×C8C23×D4712yes—
706C4⋊C4—24no—
707C4⋊C4—21no—
708C4⋊C4—474no—
709C4⋊C4—474no—
710C4⋊C4—472no—
711C4⋊C4—944no—
712C4⋊C4—944no—
713C4⋊C4—944no—
714C4⋊C4—944no—
715C4⋊C4—941no—
716C4⋊C4—944no—
717C4⋊C4—944no—
718C4⋊C4C23×D4712yes—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—474no—
722C22⋊C4—474no—
723C22⋊C4—944no—
724C22⋊C4—944no—
725C22⋊C4—944no—
726C22⋊C4—944no—
727C42—24no—
728C42—472no—
729C42—472no—
730C42—944no—
731C42D4×D4712yes—
732C42C23×D4712yes—
733C23—22no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—474no—
738C23—472no—
739C23—942no—
740C23—942no—
741C23—944no—
742C23—942no—
743C23—1882no—
744C23—1882no—
745C23C2×D4×D4711yescharacteristic
746Q8—24no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—42no—
751Q8—942no—
752Q8—942no—
753Q8—942no—
754Q8—942no—
755Q8—1888no—
756Q8—1882no—
757Q8—1882no—
758Q8C2×D4×D4714yes—
759D4—22no—
760D4—22no—
761D4—42no—
762D4—474no—
763D4—9416no—
764D4—944no—
765D4—942no—
766D4—1888no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—474no—
776C2×C4—472no—
777C2×C4—478no—
778C2×C4—474no—
779C2×C4—474no—
780C2×C4—472no—
781C2×C4—472no—
782C2×C4—9416no—
783C2×C4—942no—
784C2×C4—942no—
785C2×C4—942no—
786C2×C4—942no—
787C2×C4—942no—
788C2×C4—3764no—
789C2×C4—3764no—
790C2×C4—3764no—
791C2×C4—1888no—
792C2×C4—1888no—
793C2×C4—1882no—
794C2×C4—1882no—
795C2×C4—1882no—
796C2×C4C2×D4×D4712yes—
797C2×C4C2×D4×D4712yes—
798C2×C4C2×D4×D4711yescharacteristic
799C2×C4C2×D4×D4712yes—
800C2×C4#41×D4712yes—
801C2×C4C24×D4711yescharacteristic
802C8—22no—
803C8—22no—
804C8—942no—
805C8—942no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—84no—
810C22—474no—
811C22—948no—
812C22—942no—
813C22—942no—
814C22—944no—
815C22—1888no—
816C22—1882no—
817C22—1882no—
818C22#121×D4712yes—
819C22#1568993012yes—
820C22#1568993912yes—
821C22C22×D4×D4711yescharacteristic
822C4—24no—
823C4—22no—
824C4—22no—
825C4—42no—
826C4—42no—
827C4—474no—
828C4—942no—
829C4—942no—
830C4—1882no—
831C4—1882no—
832C4—1882no—
833C4#121×D4712yes—
834C4C22×D4×D4711yescharacteristic
835C4C2×#41×D4711yescharacteristic
836C2—82no—
837C2—944no—
838C2—1884no—
839C2#2025294114yesdirect product factor
840C2C2×#121×D4711yescharacteristic
841C2C2×#1568993011yescharacteristic
842C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#464C2
socleC23×C47C22×D4
prime radicalC22×#13094045C2
hypercenterC2×#464D47
hypocenterC47C2×#3046
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×#13094056C2semidirect
3. C2×#15689693C2semidirect
4. C2×#15689605C2semidirect
5. #20252941C2direct (N × H)
6. C2×#15689343C2semidirect
7. C2×#15689333C2semidirect
8. C2×#15689331C2semidirect
9. C2×#15689337C2semidirect
10. C2×#15689335C2semidirect
11. C2×#15689329C2semidirect
12. C2×#15689327C2semidirect
13. C2×#15689148C2semidirect
14. C2×#15689121C2semidirect
15. C2×#103×D47C2semidirect
16. C2×C47×#464C2semidirect
21. C2×#13094056C22semidirect
33. #15689693C22semidirect
42. #15689605C22semidirect
52. #15689343C22semidirect
53. #15689337C22semidirect
54. #15689335C22semidirect
55. #15689333C22semidirect
56. #15689331C22semidirect
57. #15689329C22semidirect
58. #15689327C22semidirect
59. #15689148C22semidirect
63. #15689121C22semidirect
69. #103×D47C22semidirect
75. C47×#464C22semidirect
421. C2×#464D47semidirect
432. C2×C47#3046semidirect
478. #464C2×D47semidirect
500. C47C2×#3046semidirect
839. C2#20252941direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940562
C22×#130940452
C2×#156896932
C2×#156896052
#202529412
C2×#156893432
C2×#156893332
C2×#156893312
C2×#156893372
C2×#156893352
C2×#156893292
C2×#156893272
C2×#156891482
C2×#156891212
C2×#103×D472
C2×C47×#4642
C2×#304647