Finite Group Databasebeta

← C2×#20255503 #27092872

Subgroups — C2×#20255503 #27092872

Order 12032.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689831C211yesmaximal, characteristic, complemented
2C2×#15689784C211yesmaximal, characteristic
3#20255503C2116yesmaximal, direct product factor
4C2×#15689484C211yesmaximal, characteristic, complemented
5C2×#15689442C211yesmaximal, characteristic, complemented
6C2×#15689452C211yesmaximal, characteristic, complemented
7C2×#15689406C211yesmaximal, characteristic, complemented
8C2×#15689378C211yesmaximal, characteristic, complemented
9C2×#15689354C211yesmaximal, characteristic, complemented
10C2×#15689347C211yesmaximal, characteristic, complemented
11C2×#15689284C211yesmaximal, characteristic, complemented
12C2×#15689230C211yesmaximal, characteristic, complemented
13C2×#15689191C211yesmaximal, characteristic, complemented
14C2×#15689123C211yesmaximal, characteristic, complemented
15C22×#13093948C211yesmaximal, characteristic, complemented
16C2×C47×#451C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C23×C47⋊C8C2211yescharacteristic
21#15689831—24no—
22#15689831C2218yescomplemented
23#15689784—24no—
24#15689784C2218yes—
25C2×#13094023C2211yescharacteristic
26C2×#13094014—21no—
27C2×#13094013—21no—
28C2×#13094013C2211yescharacteristic
29C2×#13094004—21no—
30C2×#13094001—21no—
31C2×#13094000—21no—
32C2×#13094000C2211yescharacteristic
33C2×#13094000C2211yescharacteristic
34C2×#13093998—21no—
35C2×#13093998C2211yescharacteristic
36C2×Q8×Dic47C2211yescharacteristic
37C2×Q8×Dic47C2211yescharacteristic
38C2×C4×C22⋊D47—21no—
39C2×C4×C22⋊D47C2211yescharacteristic
40C2×(C22⋊D47)⋊C4—21no—
41C22×C4⋊Dic47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689484C2218yescomplemented
44#15689452C2218yescomplemented
45#15689442C2218yescomplemented
46#15689406C2218yescomplemented
47#15689378C2218yescomplemented
48#15689354C2218yescomplemented
49#15689347C2218yescomplemented
50#15689284C2218yescomplemented
51#15689230C2218yescomplemented
52#15689191C2218yescomplemented
53C2×#13093956C2211yescharacteristic
54C2×#13093956C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56C2×Dic47⋊C8C2211yescharacteristic
57#15689123C2218yescomplemented
58C2×#13093948C2211yescharacteristic
59C2×#13093948C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2218yescomplemented
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C23×Q8×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C22×Q16×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#451C2218yescomplemented
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625354—22no—
78C2×#10625354—24no—
79C2×#10625354—42no—
80C2×#10625354C2314yes—
81C22×Dic94—21no—
82C22×D188—21no—
83C22×D188C2311yescharacteristic
84C22×C22⋊D47—21no—
85C22×C22⋊D47D411yescharacteristic
86C23×Dic47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47C2311yescharacteristic
90C2×#10625336—42no—
91C2×#10625336C2314yes—
92C2×#10625324—42no—
93C2×#10625324C2314yes—
94C22×C47⋊C8—42no—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2314yes—
98#13094023—22no—
99#13094023C2314yes—
100#13094014—28no—
101#13094013—28no—
102#13094013—22no—
103#13094013C2314yes—
104#13094004—28no—
105#13094001—28no—
106#13094000—22no—
107#13094000—22no—
108#13094000—28no—
109#13094000C2314yes—
110#13094000C2314yes—
111#13093998—22no—
112#13093998—28no—
113#13093998C2314yes—
114Q8×Dic47—22no—
115Q8×Dic47—22no—
116Q8×Dic47C2314yes—
117Q8×Dic47C2314yes—
118C4×C22⋊D47—28no—
119C4×C22⋊D47D414yes—
120C4×C22⋊D47C2314yes—
121(C22⋊D47)⋊C4—28no—
122C2×C4⋊Dic47—22no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2314yes—
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4D411yescharacteristic
135C4⋊C4×D47—22no—
136C4⋊C4×D47C2314yes—
137C2×C22⋊Dic47D411yescharacteristic
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4D411yescharacteristic
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47C2311yescharacteristic
147#13093956C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150Dic47⋊C8C2314yes—
151#13093948C2314yes—
152#13093948C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093946C2314yes—
157#13093946C2314yes—
158#13093944C2314yes—
159(C2×D47)⋊C8C2314yes—
160#13093934C2314yes—
161C22×Q8×C47—22no—
162C22×Q8×C47—21no—
163C22×Q8×C47—24no—
164C22×Q8×C47—42no—
165C22×Q8×C47C2311yescharacteristic
166C22×Q8×C47C2311yescharacteristic
167C22×Q8×C47C2314yes—
168C22×Q8×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C23×C4×C47C2311yescharacteristic
171C2×Q16×C47—24no—
172C2×Q16×C47—42no—
173C2×Q16×C47C2314yes—
174C2×Q16×C47C2314yes—
175C22×C8×C47C2311yescharacteristic
176C22×C8×C47C2311yescharacteristic
177C22⋊Q8×C47—22no—
178C22⋊Q8×C47C2314yes—
179C2×C4⋊C4×C47—21no—
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47—21no—
182#103×C47C2314yes—
183#103×C47C2314yes—
184C22⋊C8×C47C2314yes—
185C24×C47C2×D411yescharacteristic
186C23×D47—21no—
187C23×D47C2×D411yescharacteristic
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—24no—
191C2×Q8×C47—21no—
192C2×Q8×C47—22no—
193C2×Q8×C47—28no—
194C2×Q8×C47—22no—
195C2×Q8×C47—22no—
196C2×Q8×C47—22no—
197C2×Q8×C47—22no—
198C2×Q8×C47—44no—
199C2×Q8×C47—44no—
200C2×Q8×C47—48no—
201C2×Q8×C47#4114yes—
202C2×Q8×C47C2412yes—
203C2×Q8×C47C2412yes—
204C2×Q8×C47C2412yes—
205C22×C4×C47—21no—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—24no—
212C22×C4×C47—44no—
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D412yes—
215C22×C4×C47C2412yes—
216C22×C4×C47C2411yescharacteristic
217C2×C22⋊D47—24no—
218C2×C22⋊D47—24no—
219C2×C22⋊D47—44no—
220C2×C22⋊D47C2×D414yes—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—24no—
225C22×Dic47—82no—
226C22×Dic47C2×D411yescharacteristic
227C22×Dic47C2×D411yescharacteristic
228C22×Dic47C2×D411yescharacteristic
229#10625354—28no—
230#10625354—44no—
231#10625354—48no—
232C2×D188—22no—
233C2×D188—22no—
234C2×D188—24no—
235C2×D188—21no—
236C2×D188—44no—
237C2×D188C2412yes—
238C2×C4×D47—22no—
239C2×C4×D47—22no—
240C2×C4×D47—24no—
241C2×C4×D47—24no—
242C2×C4×D47—44no—
243C2×C4×D47—82no—
244C2×C4×D47C2×D412yes—
245C2×C4×D47C2412yes—
246C2×Dic94—24no—
247C2×Dic94—82no—
248Q16×C47—28no—
249Q16×C47—44no—
250C2×C8×C47—22no—
251C2×C8×C47—22no—
252C2×C8×C47C2412yes—
253C2×C8×C47C2412yes—
254C4⋊C4×C47—24no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47C2412yes—
257C22⋊C4×C47—24no—
258C22⋊Dic47C2×D414yes—
259#10625336—44no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4C2×D414yes—
266C4⋊Dic47—21no—
267C4⋊Dic47—21no—
268C4⋊Dic47—24no—
269C4⋊Dic47—21no—
270C4⋊Dic47—24no—
271C4⋊Dic47—24no—
272C4⋊Dic47C2412yes—
273C4⋊Dic47C2412yes—
274C4⋊Dic47C2412yes—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279Dic47⋊C4C2×D414yes—
280C4×Dic47—24no—
281C4×Dic47—24no—
282C4×Dic47C2×D412yes—
283C4×Dic47C2412yes—
284C2×C47⋊C8—22no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—44no—
287C2×C47⋊C8C2412yes—
288C2×C47⋊C8C2412yes—
289#10625324—44no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47#13714yes—
293C23×C47C22×D412yes—
294C23×C47C22×D411yescharacteristic
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—42no—
300C22×D47—42no—
301C22×D47—42no—
302C22×D47C22×D412yes—
303Q8×C47—24no—
304Q8×C47—22no—
305Q8×C47—22no—
306Q8×C47—22no—
307Q8×C47—22no—
308Q8×C47—22no—
309Q8×C47—48no—
310Q8×C47—42no—
311Q8×C47—42no—
312Q8×C47C2×#4114yes—
313C2×C4×C47—24no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—24no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—48no—
323C2×C4×C47—42no—
324C2×C4×C47—42no—
325C2×C4×C47—42no—
326C2×C4×C47C22×D412yes—
327C2×C4×C47C22×D411yescharacteristic
328C2×C4×C47C2×#4112yes—
329C2×C4×C47H(5,𝔽2)12yes—
330C2×C4×C47C2511yescharacteristic
331C22⋊D47—28no—
332C22⋊D47—48no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—42no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—84no—
343C2×Dic47C22×D412yes—
344C2×Dic47C22×D412yes—
345C2×Dic47C22×D412yes—
346D188—22no—
347D188—22no—
348D188—48no—
349D188—42no—
350C4×D47—24no—
351C4×D47—22no—
352C4×D47—22no—
353C4×D47—48no—
354C4×D47—84no—
355Dic94—84no—
356C8×C47—22no—
357C8×C47—22no—
358C47⋊C8—22no—
359C47⋊C8—22no—
360C2×#3316—471nomaximal, Sylow
361C22×C47—22no—
362C22×C47—28no—
363C22×C47—22no—
364C22×C47#54612yes—
365C22×C47C2×#13714yes—
366C22×C47C2×#13712yes—
367C22×C47#57712yes—
368C22×C47C23×D411yescharacteristic
369C2×D47—22no—
370C2×D47—22no—
371C2×D47—22no—
372C2×D47—44no—
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—84no—
377C4×C47—24no—
378C4×C47—22no—
379C4×C47—42no—
380C4×C47—42no—
381C4×C47—42no—
382C4×C47#54612yes—
383C4×C47C22×#4111yescharacteristic
384C4×C47C2×H(5,𝔽2)11yescharacteristic
385Dic47—22no—
386Dic47—22no—
387Dic47—22no—
388Dic47—42no—
389Dic47—42no—
390Dic47—42no—
391C2×#554—471no—
392C2×#548—471no—
393#3316—4716no—
394C2×#489—471no—
395C2×#481—471no—
396C2×#483—471no—
397C2×#475—471no—
398C2×#470—471no—
399C2×#465—471no—
400C2×#464—471no—
401C2×#452—471no—
402C2×#451D4711yescharacteristic, complemented
403C2×#441—471no—
404C2×#435—471no—
405C2×#417—471no—
406C22×#103—471no—
407C2×C47—24no—
408C2×C47#331614yescomplemented
409C2×C47C2×#54611yescharacteristic
410C2×C47C22×#13711yescharacteristic
411C2×C47C2×#57711yescharacteristic
412D47—42no—
413D47—82no—
414C22×#41—471no—
415C23×Q8C2×D4711yescharacteristic
416C22×Q16C2×D4711yescharacteristic
417C22×Q16C2×D4711yescharacteristic
418C22×SD16—471no—
419C22×M16—471no—
420C23×C8—471no—
421#554—478no—
422#554—944no—
423#548—478no—
424#548—944no—
425C2×C4⋊Q8—471no—
426C2×#125—941no—
427C2×#124—471no—
428C2×#124—941no—
429C2×C22⋊Q8—471no—
430C2×C22⋊Q8—471no—
431C2×C22⋊Q8—941no—
432C2×C22⋊Q8—941no—
433C2×C22⋊Q8—941no—
434C2×C22⋊Q8C2×D4711yescharacteristic
435C2×#121—471no—
436C2×#121—941no—
437C2×C4×Q8—471no—
438C2×C4×Q8—471no—
439C2×C4×D4—471no—
440C2×C4×D4—941no—
441C2×C4×D4—941no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4—471no—
444#489—478no—
445#483—478no—
446#481—478no—
447#475—478no—
448#470—478no—
449#465—478no—
450#464—478no—
451#452—478no—
452#451C2×D4718yescomplemented
453#441—478no—
454#435—478no—
455C2×#106—471no—
456C2×#106—471no—
457C2×#106—471no—
458C2×C4⋊C8—471no—
459#417—478no—
460C2×#103—471no—
461C2×#103—471no—
462C2×#103—471no—
463C2×#103—471no—
464C2×#103—478no—
465C2×#103—471no—
466C2×#103C2×D4711yescharacteristic
467C2×#103C2×D4711yescharacteristic
468C2×#102—471no—
469C2×#102—471no—
470C2×#102—471no—
471C2×C22⋊C8—471no—
472C2×C22⋊C8C2×D4711yescharacteristic
473C2×#97—471no—
474C47C2×#331611yescharacteristic, complemented, Sylow
475C2×#41—474no—
476C2×#41—942no—
477C2×#41—944no—
478C2×#41—1882no—
479C22×Q8—21no—
480C22×Q8—22no—
481C22×Q8—24no—
482C22×Q8—42no—
483C22×Q8—941no—
484C22×Q8C22×D4711yescharacteristic
485C22×Q8C22×D4711yescharacteristic
486C22×Q8C22×D4714yes—
487C22×Q8C22×D4711yescharacteristic
488C22×D4—471no—
489C22×D4—471no—
490C22×D4—941no—
491C22×D4—941no—
492C23×C4—21no—
493C23×C4—471no—
494C23×C4—941no—
495C23×C4—941no—
496C23×C4—941no—
497C23×C4C22×D4711yescharacteristic
498C2×Q16—24no—
499C2×Q16—42no—
500C2×Q16C22×D4714yes—
501C2×Q16C22×D4714yes—
502C2×SD16—474no—
503C2×SD16—1882no—
504C2×M16—474no—
505C2×M16—1882no—
506C22×C8—471no—
507C22×C8—471no—
508C22×C8—474no—
509C22×C8—1882no—
510C22×C8C22×D4711yescharacteristic
511C22×C8C22×D4711yescharacteristic
512C4⋊Q8—474no—
513C4⋊Q8—942no—
514#125—948no—
515#124—474no—
516#124—942no—
517#124—948no—
518C22⋊Q8—22no—
519C22⋊Q8—474no—
520C22⋊Q8—474no—
521C22⋊Q8—948no—
522C22⋊Q8—948no—
523C22⋊Q8—948no—
524C22⋊Q8—942no—
525C22⋊Q8—942no—
526C22⋊Q8C22×D4714yes—
527#121—474no—
528#121—948no—
529#121—942no—
530C4×Q8—474no—
531C4×Q8—474no—
532C4×Q8—942no—
533C4×Q8—942no—
534C4×D4—474no—
535C4×D4—474no—
536C4×D4—948no—
537C4×D4—948no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—471no—
540C2×C4⋊C4—471no—
541C2×C4⋊C4—471no—
542C2×C4⋊C4—474no—
543C2×C4⋊C4—471no—
544C2×C4⋊C4—474no—
545C2×C4⋊C4—942no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4—941no—
548C2×C4⋊C4—941no—
549C2×C4⋊C4—941no—
550C2×C4⋊C4—941no—
551C2×C4⋊C4—941no—
552C2×C4⋊C4—941no—
553C2×C4⋊C4—942no—
554C2×C4⋊C4C22×D4711yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—471no—
557C2×C22⋊C4—471no—
558C2×C22⋊C4—941no—
559C2×C22⋊C4—941no—
560C2×C22⋊C4—941no—
561C2×C22⋊C4—941no—
562C2×C22⋊C4—941no—
563C2×C42—471no—
564C2×C42—941no—
565C2×C42—941no—
566#106—474no—
567#106—474no—
568#106—474no—
569C4⋊C8—474no—
570#103—474no—
571#103—474no—
572#103—474no—
573#103—474no—
574#103—474no—
575#103C22×D4714yes—
576#103C22×D4714yes—
577#102—474no—
578#102—474no—
579#102—474no—
580C22⋊C8—474no—
581C22⋊C8C22×D4714yes—
582#97—474no—
583C24—471no—
584C24—941no—
585C24D4×D4711yescharacteristic
586#41—948no—
587#41—1884no—
588#41—1888no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—24no—
592C2×Q8—21no—
593C2×Q8—22no—
594C2×Q8—28no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—22no—
598C2×Q8—22no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8—48no—
602C2×Q8—944no—
603C2×Q8—3762no—
604C2×Q8#1062535214yes—
605C2×Q8C23×D4712yes—
606C2×Q8C23×D4712yes—
607C2×Q8C23×D4712yes—
608C2×D4—474no—
609C2×D4—472no—
610C2×D4—944no—
611C2×D4—944no—
612C2×D4—944no—
613C2×D4—941no—
614C2×D4—942no—
615C2×D4—942no—
616C2×D4—1884no—
617C2×D4—1884no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—24no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—44no—
626C22×C4—471no—
627C22×C4—471no—
628C22×C4—471no—
629C22×C4—472no—
630C22×C4—472no—
631C22×C4—944no—
632C22×C4—944no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—944no—
636C22×C4—941no—
637C22×C4—941no—
638C22×C4—941no—
639C22×C4—3762no—
640C22×C4—3762no—
641C22×C4—1884no—
642C22×C4D4×D4712yes—
643C22×C4D4×D4711yescharacteristic
644C22×C4C23×D4712yes—
645C22×C4C23×D4711yescharacteristic
646Q16—28no—
647Q16—44no—
648SD16—1884no—
649M16—1884no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—472no—
653C2×C8—472no—
654C2×C8—942no—
655C2×C8—942no—
656C2×C8—1884no—
657C2×C8C23×D4712yes—
658C2×C8C23×D4712yes—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—474no—
662C4⋊C4—472no—
663C4⋊C4—472no—
664C4⋊C4—472no—
665C4⋊C4—944no—
666C4⋊C4—944no—
667C4⋊C4—944no—
668C4⋊C4—944no—
669C4⋊C4—944no—
670C4⋊C4—944no—
671C4⋊C4—941no—
672C4⋊C4—944no—
673C4⋊C4—941no—
674C4⋊C4—941no—
675C4⋊C4C23×D4712yes—
676C22⋊C4—24no—
677C22⋊C4—474no—
678C22⋊C4—474no—
679C22⋊C4—944no—
680C22⋊C4—944no—
681C22⋊C4—944no—
682C22⋊C4—944no—
683C22⋊C4—944no—
684C42—472no—
685C42—472no—
686C42—944no—
687C42—944no—
688C23—22no—
689C23—22no—
690C23—472no—
691C23—942no—
692C23—942no—
693C23—942no—
694C23—942no—
695C23—1882no—
696C23—1882no—
697C23—1882no—
698C23#1309405614yes—
699C23C2×D4×D4712yes—
700C23C2×D4×D4711yescharacteristic
701Q8—24no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—48no—
708Q8—42no—
709Q8—42no—
710Q8—3764no—
711Q8C2×#1062535214yes—
712D4—948no—
713D4—942no—
714D4—942no—
715D4—1888no—
716D4—1888no—
717D4—1882no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—48no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—472no—
732C2×C4—472no—
733C2×C4—472no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—944no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—3764no—
744C2×C4—3764no—
745C2×C4—1888no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4—1882no—
749C2×C4C2×D4×D4712yes—
750C2×C4C2×D4×D4711yescharacteristic
751C2×C4C2×#1062535212yes—
752C2×C4#1309406912yes—
753C2×C4C24×D4711yescharacteristic
754C8—22no—
755C8—22no—
756C8—942no—
757C8—942no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—942no—
762C22—942no—
763C22—942no—
764C22—3764no—
765C22—1882no—
766C22—1882no—
767C22—1882no—
768C22—1884no—
769C22#1568976012yes—
770C22C2×#1309405614yes—
771C22C2×#1309405612yes—
772C22#1568993212yes—
773C22C22×D4×D4711yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—942no—
780C4—942no—
781C4—942no—
782C4—1882no—
783C4—1882no—
784C4—1882no—
785C4#1568976012yes—
786C4C22×#1062535211yescharacteristic
787C4C2×#1309406911yescharacteristic
788C2—24no—
789C2—3762no—
790C2—1882no—
791C2#2025550314yesdirect product factor
792C2C2×#1568976011yescharacteristic
793C2C22×#1309405611yescharacteristic
794C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#451C2
socleC23×C47C22×D4
prime radicalC2×#15689784C2
hypercenterC2×#451D47
hypocenterC47C2×#3316
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×#15689831C2semidirect
3. #20255503C2direct (N × H)
4. C2×#15689484C2semidirect
5. C2×#15689442C2semidirect
6. C2×#15689452C2semidirect
7. C2×#15689406C2semidirect
8. C2×#15689378C2semidirect
9. C2×#15689354C2semidirect
10. C2×#15689347C2semidirect
11. C2×#15689284C2semidirect
12. C2×#15689230C2semidirect
13. C2×#15689191C2semidirect
14. C2×#15689123C2semidirect
15. C22×#13093948C2semidirect
16. C2×C47×#451C2semidirect
22. #15689831C22semidirect
43. #15689484C22semidirect
44. #15689452C22semidirect
45. #15689442C22semidirect
46. #15689406C22semidirect
47. #15689378C22semidirect
48. #15689354C22semidirect
49. #15689347C22semidirect
50. #15689284C22semidirect
51. #15689230C22semidirect
52. #15689191C22semidirect
57. #15689123C22semidirect
63. C2×#13093948C22semidirect
73. C47×#451C22semidirect
402. C2×#451D47semidirect
408. C2×C47#3316semidirect
452. #451C2×D47semidirect
474. C47C2×#3316semidirect
791. C2#20255503direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898312
C2×#156897842
#202555032
C2×#156894842
C2×#156894422
C2×#156894522
C2×#156894062
C2×#156893782
C2×#156893542
C2×#156893472
C2×#156892842
C2×#156892302
C2×#156891912
C2×#156891232
C22×#130939482
C2×C47×#4512
C2×#331647