Finite Group Databasebeta

← C2×#20253981 #27086041

Subgroups — C2×#20253981 #27086041

Order 12032.

2266 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689670C211yesmaximal, characteristic, complemented
2C2×#15689655C211yesmaximal, characteristic, complemented
3#20253981C2116yesmaximal, direct product factor
4C2×#15689531C211yesmaximal, characteristic, complemented
5C2×#15689511C211yesmaximal, characteristic, complemented
6C2×#15689486C211yesmaximal, characteristic, complemented
7C2×#15689481C211yesmaximal, characteristic, complemented
8C2×#15689375C211yesmaximal, characteristic, complemented
9C2×#15689373C211yesmaximal, characteristic, complemented
10C2×#15689370C211yesmaximal, characteristic, complemented
11C2×#15689368C211yesmaximal, characteristic, complemented
12C2×C4×#10625325C211yesmaximal, characteristic, complemented
13C2×C4×#10625335C211yesmaximal, characteristic, complemented
14C2×C4×#10625334C211yesmaximal, characteristic, complemented
15C2×C4×#10625324C211yesmaximal, characteristic, complemented
16C2×C4×D8×C47C211yesmaximal, characteristic, complemented
17C22×#10625350—21no—
18C22×#10625325C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22C22×#10625324C2211yescharacteristic
23#15689670—24no—
24#15689670C2218yescomplemented
25C2×#13094023C2211yescharacteristic
26C2×#13094020C2211yescharacteristic
27#15689655—24no—
28#15689655C2218yescomplemented
29C2×#13094017—21no—
30C2×#13094015C2211yescharacteristic
31C2×#13094011C2211yescharacteristic
32C2×#13094010—21no—
33C2×#13094006—21no—
34C2×#13094004C2211yescharacteristic
35C2×#13093999C2211yescharacteristic
36C2×#13093997—21no—
37C2×#13093995C2211yescharacteristic
38C2×#13093995C2211yescharacteristic
39C2×C4×Dic94C2211yescharacteristic
40C2×C4×D188C2211yescharacteristic
41C2×C4×C22⋊D47—21no—
42C2×C4×C22⋊D47—21no—
43C2×#13093983—21no—
44C2×C42×D47C2211yescharacteristic
45#15689531C2218yescomplemented
46#15689511C2218yescomplemented
47#15689486C2218yescomplemented
48#15689481C2218yescomplemented
49#15689375C2218yescomplemented
50#15689373C2218yescomplemented
51#15689370C2218yescomplemented
52#15689368C2218yescomplemented
53C4×#10625325C2218yescomplemented
54C4×#10625335C2218yescomplemented
55C4×#10625334C2218yescomplemented
56C2×#13093957C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093947C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C4×#10625324C2218yescomplemented
66C2×#13093934C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C4×C47⋊C8C2211yescharacteristic
69C22×D8×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C4×D8×C47C2218yescomplemented
73C2×#107×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C2×#10625350—28no—
78C2×#10625350—48no—
79C22×Dic94—21no—
80C22×Dic94C2311yescharacteristic
81C22×D188—21no—
82C22×D188C2311yescharacteristic
83C22×C22⋊D47—21no—
84C22×C22⋊D47—21no—
85C22×C22⋊D47—21no—
86C22×C22⋊D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47D411yescharacteristic
89C22×C4×D47D411yescharacteristic
90C22×C4×D47C2311yescharacteristic
91C2×#10625325—24no—
92C2×#10625325C2314yes—
93C2×#10625335—24no—
94C2×#10625335C2314yes—
95C2×#10625334—24no—
96C2×#10625334C2314yes—
97C2×#10625324—24no—
98C2×#10625324—24no—
99C2×#10625324C2314yes—
100C2×#10625324C2314yes—
101C22×C47⋊C8C2311yescharacteristic
102C22×C47⋊C8C2311yescharacteristic
103#13094023—22no—
104#13094023C2314yes—
105#13094020—22no—
106#13094020C2314yes—
107#13094017—28no—
108#13094015—22no—
109#13094015C2314yes—
110#13094011—22no—
111#13094011C2314yes—
112#13094010—28no—
113#13094006—28no—
114#13094004—22no—
115#13094004C2314yes—
116#13093999—22no—
117#13093999C2314yes—
118#13093997—28no—
119#13093995—22no—
120#13093995—22no—
121#13093995C2314yes—
122#13093995C2314yes—
123C4×Dic94—22no—
124C4×Dic94C2314yes—
125C4×D188—22no—
126C4×D188C2314yes—
127C4×C22⋊D47—28no—
128C4×C22⋊D47—28no—
129#13093983—28no—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2311yescharacteristic
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47D411yescharacteristic
146C2×C4×Dic47D411yescharacteristic
147C2×C4×Dic47C2311yescharacteristic
148C42×D47D414yes—
149C42×D47C2314yes—
150#13093957C2314yes—
151#13093956C2314yes—
152#13093955C2314yes—
153#13093949C2314yes—
154#13093947C2314yes—
155#13093946C2314yes—
156#13093945C2314yes—
157#13093945C2314yes—
158#13093944C2314yes—
159#13093934C2314yes—
160#13093934C2314yes—
161C4×C47⋊C8C2314yes—
162C22×D4×C47C2311yescharacteristic
163C22×D4×C47C2311yescharacteristic
164C23×C4×C47—21no—
165C23×C4×C47—21no—
166C2×D8×C47—24no—
167C2×D8×C47C2314yes—
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C4×D4×C47—22no—
171C4×D4×C47—22no—
172C4×D4×C47C2314yes—
173C4×D4×C47C2314yes—
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C22⋊C4×C47—21no—
177C2×C22⋊C4×C47—21no—
178C2×C42×C47C2311yescharacteristic
179#107×C47C2314yes—
180#102×C47C2314yes—
181#102×C47C2314yes—
182C4×C8×C47C2314yes—
183C24×C47—21no—
184C24×C47—21no—
185C23×D47—21no—
186C23×D47C2×D411yescharacteristic
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47C2412yes—
194C2×D4×C47C2412yes—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—24no—
198C22×C4×C47—24no—
199C22×C4×C47—44no—
200C22×C4×C47—44no—
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2411yescharacteristic
204C2×C22⋊D47—24no—
205C2×C22⋊D47—24no—
206C2×C22⋊D47—24no—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—44no—
209C2×C22⋊D47—44no—
210C2×C22⋊D47—44no—
211C2×C22⋊D47—44no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47C2×D411yescharacteristic
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D411yescharacteristic
218#10625350—432no—
219C2×D188—22no—
220C2×D188—22no—
221C2×D188—24no—
222C2×D188—21no—
223C2×D188—44no—
224C2×D188C2412yes—
225C2×C4×D47—24no—
226C2×C4×D47—22no—
227C2×C4×D47—22no—
228C2×C4×D47—24no—
229C2×C4×D47—42no—
230C2×C4×D47—44no—
231C2×C4×D47C2×D412yes—
232C2×C4×D47C2×D414yes—
233C2×C4×D47C2×D414yes—
234C2×C4×D47C2412yes—
235C2×Dic94—22no—
236C2×Dic94—22no—
237C2×Dic94—21no—
238C2×Dic94—24no—
239C2×Dic94—44no—
240C2×Dic94C2412yes—
241D8×C47—28no—
242C2×C8×C47—22no—
243C2×C8×C47#4114yescomplemented
244C2×C8×C47C2412yes—
245C2×C8×C47C2412yes—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47C2412yes—
249C4⋊C4×C47C2412yes—
250C22⋊C4×C47—24no—
251C22⋊C4×C47—24no—
252C42×C47C2×D412yes—
253C42×C47C2412yes—
254C22⋊Dic47—24no—
255C22⋊Dic47—24no—
256C22⋊Dic47—24no—
257C22⋊Dic47—24no—
258#10625335—28no—
259#10625334—28no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263C4⋊Dic47—21no—
264C4⋊Dic47—21no—
265C4⋊Dic47—24no—
266C4⋊Dic47—24no—
267C4⋊Dic47C2412yes—
268C4⋊Dic47C2412yes—
269Dic47⋊C4—24no—
270Dic47⋊C4—24no—
271Dic47⋊C4—24no—
272C4×Dic47—24no—
273C4×Dic47C2×D412yes—
274C4×Dic47C2×D414yes—
275C4×Dic47C2×D414yes—
276C4×Dic47C2412yes—
277C2×C47⋊C8—22no—
278C2×C47⋊C8#4114yescomplemented
279C2×C47⋊C8C2412yes—
280C2×C47⋊C8C2412yes—
281#10625325—28no—
282#10625324—28no—
283#10625324—28no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—42no—
287C23×C47—42no—
288C23×C47—42no—
289C23×C47—42no—
290C23×C47—42no—
291C23×C47—42no—
292C23×C47C22×D411yescharacteristic
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47—42no—
300C22×D47C22×D412yes—
301D4×C47—22no—
302D4×C47—22no—
303D4×C47—22no—
304D4×C47—22no—
305D4×C47—42no—
306D4×C47—42no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—48no—
313C2×C4×C47—48no—
314C2×C4×C47AGL(1,ℤ/8)14yes—
315C2×C4×C47C22×D412yes—
316C2×C4×C47C22×D411yescharacteristic
317C2×C4×C47C22×D412yes—
318C2×C4×C47C2×#4112yes—
319C2×C4×C47C2×#4112yes—
320C2×C4×C47C2511yescharacteristic
321C22⋊D47—48no—
322C22⋊D47—48no—
323C22⋊D47—48no—
324C22⋊D47—48no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47C22×D412yes—
335C2×Dic47C22×D412yes—
336C2×Dic47C22×D412yes—
337D188—22no—
338D188—22no—
339D188—48no—
340D188—42no—
341C4×D47—24no—
342C4×D47—28no—
343C4×D47—22no—
344C4×D47—22no—
345C4×D47—44no—
346C4×D47—48no—
347Dic94—22no—
348Dic94—22no—
349Dic94—48no—
350Dic94—42no—
351C8×C47—22no—
352C8×C47C2×#4114yescomplemented
353C47⋊C8—22no—
354C47⋊C8C2×#4114yescomplemented
355C2×#3171—471nomaximal, Sylow
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47—42no—
362C22×C47—84no—
363C22×C47—84no—
364C22×C47#53212yes—
365C22×C47C2×AGL(1,ℤ/8)12yes—
366C22×C47#57512yes—
367C22×C47C23×D411yescharacteristic
368C2×D47—22no—
369C2×D47—22no—
370C2×D47—22no—
371C2×D47—44no—
372C2×D47—42no—
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—84no—
376C4×C47—22no—
377C4×C47—42no—
378C4×C47—42no—
379C4×C47#53212yes—
380C4×C47C2×AGL(1,ℤ/8)14yes—
381C4×C47C22×#4111yescharacteristic
382C4×C47C22×#4111yescharacteristic
383Dic47—22no—
384Dic47—22no—
385Dic47—22no—
386Dic47—42no—
387Dic47—42no—
388Dic47—42no—
389C2×#532—471no—
390C2×#529—471no—
391#3171—4716no—
392C2×#501—471no—
393C2×#496—471no—
394C2×#490—471no—
395C2×#489—471no—
396C2×#469—471no—
397C2×#469—471no—
398C2×#468—471no—
399C2×#468—471no—
400C2×C4×SD16—471no—
401C2×C4×SD16—471no—
402C2×C4×D8—471no—
403C2×C4×D8D4711yescharacteristic, complemented
404C2×C4×M16—471no—
405C2×C47—82no—
406C2×C47—82no—
407C2×C47#317114yescomplemented
408C2×C47C2×#53211yescharacteristic
409C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
410C2×C47C2×#57511yescharacteristic
411D47—42no—
412D47—82no—
413C22×#41—941no—
414C22×SD16—471no—
415C22×SD16—471no—
416C22×D8—471no—
417C22×D8C2×D4711yescharacteristic
418C22×M16—471no—
419C22×M16—471no—
420#532—478no—
421#532—944no—
422C2×C4⋊Q8—471no—
423C2×#127—471no—
424#529—478no—
425#529—944no—
426C2×#126—941no—
427C2×#125—471no—
428C2×#124—471no—
429C2×#124—941no—
430C2×#123—941no—
431C2×C22⋊Q8—471no—
432C2×#121—471no—
433C2×#121—471no—
434C2×#121—471no—
435C2×#121—941no—
436C2×C4×Q8—471no—
437C2×C4×D4—471no—
438C2×C4×D4—941no—
439C2×C4×D4—941no—
440C2×C4×D4C2×D4711yescharacteristic
441C2×C4×D4C2×D4711yescharacteristic
442C2×#117—941no—
443C22×C42—471no—
444#501—478no—
445#496—478no—
446#490—478no—
447#489—478no—
448#469—478no—
449#469—478no—
450#468—478no—
451#468—478no—
452C4×SD16—478no—
453C4×SD16—478no—
454C4×D8—478no—
455C4×D8C2×D4718yescomplemented
456C2×#107—471no—
457C2×#107C2×D4711yescharacteristic
458C2×#106—471no—
459C2×#106—471no—
460C2×#103—471no—
461C2×#103—471no—
462C2×#102—471no—
463C2×#102—471no—
464C2×#102—471no—
465C2×#102—471no—
466C2×#102C2×D4711yescharacteristic
467C2×#102C2×D4711yescharacteristic
468C4×M16—478no—
469C2×#97—471no—
470C2×#97—471no—
471C2×C4×C8—471no—
472C2×C4×C8C2×D4711yescharacteristic
473C47C2×#317111yescharacteristic, complemented, Sylow
474C2×#41—948no—
475C2×#41—1888no—
476C22×Q8—471no—
477C22×Q8—941no—
478C22×D4—471no—
479C22×D4—941no—
480C22×D4—941no—
481C22×D4—941no—
482C22×D4—941no—
483C22×D4—941no—
484C22×D4C22×D4711yescharacteristic
485C22×D4C22×D4711yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—471no—
489C23×C4—471no—
490C23×C4—471no—
491C23×C4—941no—
492C2×SD16—474no—
493C2×SD16—474no—
494C2×SD16—944no—
495C2×SD16—944no—
496C2×D8—24no—
497C2×D8—474no—
498C2×D8—944no—
499C2×D8C22×D4714yes—
500C2×M16—474no—
501C2×M16—474no—
502C2×M16—944no—
503C2×M16—944no—
504C22×C8—471no—
505C22×C8—471no—
506C22×C8C22×D4711yescharacteristic
507C22×C8C22×D4711yescharacteristic
508C4⋊Q8—474no—
509C4⋊Q8—942no—
510#127—474no—
511#127—942no—
512#126—948no—
513#125—474no—
514#125—942no—
515#124—474no—
516#124—948no—
517#124—942no—
518#123—948no—
519C22⋊Q8—474no—
520C22⋊Q8—942no—
521#121—474no—
522#121—474no—
523#121—474no—
524#121—948no—
525#121—942no—
526#121—942no—
527#121—942no—
528C4×Q8—474no—
529C4×Q8—942no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—474no—
533C4×D4—948no—
534C4×D4—948no—
535C4×D4—942no—
536C4×D4C22×D4714yes—
537C4×D4C22×D4714yes—
538#117—948no—
539C2×C4⋊C4—471no—
540C2×C4⋊C4—471no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4—941no—
544C2×C4⋊C4—941no—
545C2×C4⋊C4—941no—
546C2×C4⋊C4C22×D4711yescharacteristic
547C2×C4⋊C4C22×D4711yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—941no—
551C2×C22⋊C4—941no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C42—471no—
558C2×C42—471no—
559C2×C42—471no—
560C2×C42—474no—
561C2×C42—474no—
562C2×C42—941no—
563C2×C42C22×D4711yescharacteristic
564#107—474no—
565#107C22×D4714yes—
566#106—474no—
567#106—474no—
568#103—474no—
569#103—474no—
570#102—474no—
571#102—474no—
572#102—474no—
573#102—474no—
574#102C22×D4714yes—
575#102C22×D4714yes—
576#97—474no—
577#97—474no—
578C4×C8—474no—
579C4×C8C22×D4714yes—
580C24—21no—
581C24—21no—
582C24—471no—
583C24—941no—
584#41—18832no—
585C2×Q8—472no—
586C2×Q8—944no—
587C2×Q8—941no—
588C2×Q8—942no—
589C2×Q8—942no—
590C2×Q8—1884no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—472no—
598C2×D4—944no—
599C2×D4—944no—
600C2×D4—944no—
601C2×D4—944no—
602C2×D4—944no—
603C2×D4—941no—
604C2×D4—942no—
605C2×D4—942no—
606C2×D4—1884no—
607C2×D4—1884no—
608C2×D4—1884no—
609C2×D4—1884no—
610C2×D4—1884no—
611C2×D4C23×D4712yes—
612C2×D4C23×D4712yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—471no—
620C22×C4—471no—
621C22×C4—471no—
622C22×C4—474no—
623C22×C4—472no—
624C22×C4—472no—
625C22×C4—474no—
626C22×C4—944no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—941no—
630C22×C4—941no—
631C22×C4—941no—
632C22×C4—944no—
633C22×C4—1882no—
634C22×C4—1884no—
635C22×C4D4×D4711yescharacteristic
636C22×C4D4×D4711yescharacteristic
637C22×C4C23×D4711yescharacteristic
638SD16—948no—
639SD16—948no—
640D8—28no—
641D8—948no—
642M16—948no—
643M16—948no—
644C2×C8—22no—
645C2×C8—474no—
646C2×C8—472no—
647C2×C8—472no—
648C2×C8—942no—
649C2×C8#1062535014yescomplemented
650C2×C8C23×D4712yes—
651C2×C8C23×D4712yes—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—472no—
655C4⋊C4—472no—
656C4⋊C4—944no—
657C4⋊C4—944no—
658C4⋊C4—944no—
659C4⋊C4—944no—
660C4⋊C4—944no—
661C4⋊C4—941no—
662C4⋊C4—941no—
663C4⋊C4C23×D4712yes—
664C4⋊C4C23×D4712yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—944no—
668C22⋊C4—944no—
669C22⋊C4—944no—
670C22⋊C4—944no—
671C22⋊C4—944no—
672C22⋊C4—944no—
673C22⋊C4—944no—
674C42—474no—
675C42—474no—
676C42—472no—
677C42—472no—
678C42—944no—
679C42D4×D4712yes—
680C42C23×D4712yes—
681C23—22no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—472no—
690C23—942no—
691C23—942no—
692C23—942no—
693C23—942no—
694C23—1882no—
695C23—1882no—
696C23—1882no—
697C23C2×D4×D4711yescharacteristic
698Q8—942no—
699Q8—942no—
700Q8—1888no—
701Q8—1882no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—42no—
707D4—42no—
708D4—942no—
709D4—942no—
710D4—1888no—
711D4—1888no—
712D4—1888no—
713D4—1888no—
714D4—1888no—
715D4—1882no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—48no—
722C2×C4—48no—
723C2×C4—472no—
724C2×C4—472no—
725C2×C4—472no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—948no—
730C2×C4—944no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—1884no—
737C2×C4—1882no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4—1888no—
741C2×C4#1309404814yes—
742C2×C4C2×D4×D4712yes—
743C2×C4C2×D4×D4712yes—
744C2×C4C2×D4×D4711yescharacteristic
745C2×C4#41×D4712yes—
746C2×C4C2×#1062535012yes—
747C2×C4C24×D4711yescharacteristic
748C8—22no—
749C8—474no—
750C8—942no—
751C8C2×#1062535014yescomplemented
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—84no—
759C22—84no—
760C22—942no—
761C22—942no—
762C22—942no—
763C22—3764no—
764C22—1882no—
765C22—1882no—
766C22—1882no—
767C22—1884no—
768C22#1568967012yes—
769C22C2×#1309404812yes—
770C22#1568992012yes—
771C22C22×D4×D4711yescharacteristic
772C4—22no—
773C4—42no—
774C4—42no—
775C4—942no—
776C4—942no—
777C4—942no—
778C4—1882no—
779C4—1882no—
780C4—1882no—
781C4#1568967012yes—
782C4C2×#1309404814yes—
783C4C2×#41×D4711yescharacteristic
784C4C22×#1062535011yescharacteristic
785C2—82no—
786C2—82no—
787C2—3762no—
788C2—1882no—
789C2#2025398114yesdirect product factor
790C2C2×#1568967011yescharacteristic
791C2C22×#1309404811yescharacteristic
792C2C2×#1568992011yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×D8×C47C2
socleC23×C47C22×D4
hypercenterC2×C4×D8D47
hypocenterC47C2×#3171
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#15689670C2semidirect
2. C2×#15689655C2semidirect
3. #20253981C2direct (N × H)
4. C2×#15689531C2semidirect
5. C2×#15689511C2semidirect
6. C2×#15689486C2semidirect
7. C2×#15689481C2semidirect
8. C2×#15689375C2semidirect
9. C2×#15689373C2semidirect
10. C2×#15689370C2semidirect
11. C2×#15689368C2semidirect
12. C2×C4×#10625325C2semidirect
13. C2×C4×#10625335C2semidirect
14. C2×C4×#10625334C2semidirect
15. C2×C4×#10625324C2semidirect
16. C2×C4×D8×C47C2semidirect
24. #15689670C22semidirect
28. #15689655C22semidirect
45. #15689531C22semidirect
46. #15689511C22semidirect
47. #15689486C22semidirect
48. #15689481C22semidirect
49. #15689375C22semidirect
50. #15689373C22semidirect
51. #15689370C22semidirect
52. #15689368C22semidirect
53. C4×#10625325C22semidirect
54. C4×#10625335C22semidirect
55. C4×#10625334C22semidirect
65. C4×#10625324C22semidirect
72. C4×D8×C47C22semidirect
243. C2×C8×C47#41semidirect
278. C2×C47⋊C8#41semidirect
352. C8×C47C2×#41semidirect
354. C47⋊C8C2×#41semidirect
403. C2×C4×D8D47semidirect
407. C2×C47#3171semidirect
455. C4×D8C2×D47semidirect
473. C47C2×#3171semidirect
649. C2×C8#10625350semidirect
751. C8C2×#10625350semidirect
789. C2#20253981direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896702
C2×#156896552
#202539812
C2×#156895312
C2×#156895112
C2×#156894862
C2×#156894812
C2×#156893752
C2×#156893732
C2×#156893702
C2×#156893682
C2×C4×#106253252
C2×C4×#106253352
C2×C4×#106253342
C2×C4×#106253242
C2×C4×D8×C472
C2×#317147