Finite Group Databasebeta

← C2×#20255823 #27094804

Subgroups — C2×#20255823 #27094804

Order 12032.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689807C211yesmaximal, characteristic, complemented
2C2×#15689773C211yesmaximal, characteristic
3#20255823C2116yesmaximal, direct product factor
4C2×#15689531C211yesmaximal, characteristic, complemented
5C2×#15689456C211yesmaximal, characteristic, complemented
6C2×#15689444C211yesmaximal, characteristic, complemented
7C2×#15689452C211yesmaximal, characteristic, complemented
8C2×#15689435C211yesmaximal, characteristic, complemented
9C2×#15689416C211yesmaximal, characteristic, complemented
10C2×#15689425C211yesmaximal, characteristic, complemented
11C2×#15689349C211yesmaximal, characteristic, complemented
12C2×#15689224C211yesmaximal, characteristic, complemented
13C2×#15689192C211yesmaximal, characteristic, complemented
14C2×#15689165C211yesmaximal, characteristic, complemented
15C2×#107×D47C211yesmaximal, characteristic, complemented
16C2×C47×#468C211yesmaximal, characteristic, complemented
17C22×#10625352—21no—
18C22×C8×D47C2211yescharacteristic
19#15689807—24no—
20#15689807C2218yescomplemented
21#15689773—24no—
22#15689773C2218yes—
23C2×#13094023C2211yescharacteristic
24C2×#13094017—21no—
25C2×#13094015C2211yescharacteristic
26C2×#13094014—21no—
27C2×#13094006—21no—
28C2×#13094006—21no—
29C2×#13094005—21no—
30C2×#13094001—21no—
31C2×#13094000C2211yescharacteristic
32C2×#13093995C2211yescharacteristic
33C2×Q8×Dic47C2211yescharacteristic
34C2×D4×Dic47C2211yescharacteristic
35C2×C4×C22⋊D47C2211yescharacteristic
36C2×#13093983C2211yescharacteristic
37C2×#13093982—21no—
38C22×C4⋊Dic47C2211yescharacteristic
39C2×C4⋊C4×D47C2211yescharacteristic
40C2×C4⋊C4×D47C2211yescharacteristic
41#15689531C2218yescomplemented
42#15689456C2218yescomplemented
43#15689452C2218yescomplemented
44#15689444C2218yescomplemented
45#15689435C2218yescomplemented
46#15689425C2218yescomplemented
47#15689416C2218yescomplemented
48#15689349C2218yescomplemented
49#15689224C2218yescomplemented
50#15689192C2218yescomplemented
51#15689165C2218yescomplemented
52C2×#13093958C2211yescharacteristic
53C2×#13093958C2211yescharacteristic
54C2×#13093957C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57#107×D47C2218yescomplemented
58C2×#13093956C2211yescharacteristic
59C2×#13093956C2211yescharacteristic
60C2×#13093955C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C47×#468C2218yescomplemented
74C2×#107×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C2×#10625352—28no—
78C2×#10625352—48no—
79C22×Dic94—21no—
80C22×C22⋊D47—21no—
81C22×C22⋊D47D411yescharacteristic
82C23×Dic47—21no—
83C23×Dic47—21no—
84C22×C4×D47—21no—
85C22×C4×D47—21no—
86C22×C4×D47C2311yescharacteristic
87C22×C47⋊C8C2311yescharacteristic
88C22×C47⋊C8C2311yescharacteristic
89C2×C8×D47—24no—
90C2×C8×D47C2314yes—
91#13094023—22no—
92#13094023C2314yes—
93#13094017—28no—
94#13094015—22no—
95#13094015C2314yes—
96#13094014—28no—
97#13094006—28no—
98#13094006—28no—
99#13094005—28no—
100#13094001—28no—
101#13094000—22no—
102#13094000C2314yes—
103#13093995—22no—
104#13093995C2314yes—
105Q8×Dic47—22no—
106Q8×Dic47C2314yes—
107D4×Dic47—22no—
108D4×Dic47C2314yes—
109C4×C22⋊D47D414yes—
110C4×C22⋊D47C2314yes—
111#13093983—22no—
112#13093983C2314yes—
113#13093982—28no—
114C2×C4⋊Dic47—22no—
115C2×C4⋊Dic47—21no—
116C2×C4⋊Dic47—21no—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47C2314yes—
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4D411yescharacteristic
129C4⋊C4×D47—22no—
130C4⋊C4×D47—22no—
131C4⋊C4×D47C2314yes—
132C4⋊C4×D47C2314yes—
133C2×C22⋊Dic47—21no—
134C2×C22⋊Dic47—21no—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47D411yescharacteristic
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4D411yescharacteristic
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47C2311yescharacteristic
142#13093958C2314yes—
143#13093958C2314yes—
144#13093957C2314yes—
145#13093957C2314yes—
146#13093957C2314yes—
147#13093956C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150Dic47⋊C8C2314yes—
151#13093948C2314yes—
152#13093948C2314yes—
153#13093945C2314yes—
154#13093945C2314yes—
155C22⋊(C47⋊C8)C2314yes—
156(C2×D47)⋊C8C2314yes—
157#13093934C2314yes—
158C22×Q8×C47C2311yescharacteristic
159C22×D4×C47—21no—
160C22×D4×C47C2311yescharacteristic
161C23×C4×C47C2311yescharacteristic
162C2×SD16×C47—24no—
163C2×SD16×C47C2314yes—
164C2×M16×C47—24no—
165C2×M16×C47C2314yes—
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168C22⋊Q8×C47—22no—
169C22⋊Q8×C47C2314yes—
170#121×C47—22no—
171#121×C47C2314yes—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177#107×C47C2314yes—
178#103×C47C2314yes—
179#102×C47C2314yes—
180C24×C47—21no—
181C24×C47C2×D411yescharacteristic
182C23×D47C2×D411yescharacteristic
183C2×Q8×C47—21no—
184C2×Q8×C47—22no—
185C2×Q8×C47—22no—
186C2×Q8×C47C2412yes—
187C2×D4×C47—24no—
188C2×D4×C47—21no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—44no—
192C2×D4×C47C2412yes—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2411yescharacteristic
202C2×C22⋊D47—24no—
203C2×C22⋊D47—24no—
204C2×C22⋊D47—44no—
205C2×C22⋊D47C2×D414yes—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—24no—
211C22×Dic47—24no—
212C22×Dic47—44no—
213C22×Dic47—44no—
214C22×Dic47C2×D411yescharacteristic
215C22×Dic47C2×D411yescharacteristic
216C22×Dic47C2×D411yescharacteristic
217#10625352—432no—
218C2×C4×D47—22no—
219C2×C4×D47—22no—
220C2×C4×D47—24no—
221C2×C4×D47—24no—
222C2×C4×D47—44no—
223C2×C4×D47—44no—
224C2×C4×D47C2×D412yes—
225C2×C4×D47C2412yes—
226C2×Dic94—24no—
227C2×Dic94—44no—
228SD16×C47—28no—
229M16×C47—28no—
230C2×C8×C47—22no—
231C2×C8×C47#4114yescomplemented
232C2×C8×C47C2412yes—
233C2×C8×C47C2412yes—
234C4⋊C4×C47—24no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47C2412yes—
238C4⋊C4×C47C2412yes—
239C22⋊C4×C47—24no—
240C22⋊C4×C47—24no—
241C22⋊Dic47—24no—
242C22⋊Dic47—24no—
243C22⋊Dic47—24no—
244C22⋊Dic47C2×D414yes—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4C2×D414yes—
247C4⋊Dic47—21no—
248C4⋊Dic47—21no—
249C4⋊Dic47—21no—
250C4⋊Dic47—24no—
251C4⋊Dic47—21no—
252C4⋊Dic47—24no—
253C4⋊Dic47—24no—
254C4⋊Dic47C2412yes—
255C4⋊Dic47C2412yes—
256C4⋊Dic47C2412yes—
257C4⋊Dic47C2412yes—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4C2×D414yes—
264C4×Dic47—24no—
265C4×Dic47—24no—
266C4×Dic47C2×D412yes—
267C4×Dic47C2412yes—
268C2×C47⋊C8—22no—
269C2×C47⋊C8—22no—
270C2×C47⋊C8C2412yes—
271C2×C47⋊C8C2412yes—
272C8×D47—28no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—42no—
278C23×C47—42no—
279C23×C47—42no—
280C23×C47C22×D412yes—
281C23×C47C22×D411yescharacteristic
282C22×D47—22no—
283C22×D47—22no—
284C22×D47AGL(1,ℤ/8)14yes—
285C22×D47C22×D412yes—
286Q8×C47—22no—
287Q8×C47—22no—
288Q8×C47—42no—
289D4×C47—22no—
290D4×C47—22no—
291D4×C47—48no—
292D4×C47—42no—
293C2×C4×C47—22no—
294C2×C4×C47—24no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C2×#4112yes—
306C2×C4×C472−1+412yes—
307C2×C4×C47C2511yescharacteristic
308C22⋊D47—28no—
309C22⋊D47—48no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—48no—
318C2×Dic47—48no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47C22×D412yes—
324C2×Dic47C22×D412yes—
325C2×Dic47C22×D412yes—
326C4×D47—24no—
327C4×D47—22no—
328C4×D47—22no—
329C4×D47—48no—
330C4×D47—48no—
331Dic94—48no—
332C8×C47—22no—
333C8×C47C2×#4114yescomplemented
334C47⋊C8—22no—
335C47⋊C8—22no—
336C2×#3343—471nomaximal, Sylow
337C22×C47—22no—
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—44no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—84no—
345C22×C47#54712yes—
346C22×C47C2×AGL(1,ℤ/8)12yes—
347C22×C47#57812yes—
348C22×C47C23×D411yescharacteristic
349C2×D47—28no—
350C2×D47—22no—
351C2×D47—22no—
352C2×D47C2×AGL(1,ℤ/8)14yes—
353C4×C47—22no—
354C4×C47—42no—
355C4×C47—42no—
356C4×C47—42no—
357C4×C47#54712yes—
358C4×C47C22×#4111yescharacteristic
359C4×C47C2×2−1+411yescharacteristic
360Dic47—22no—
361Dic47—22no—
362Dic47—22no—
363Dic47—42no—
364Dic47—42no—
365Dic47—42no—
366Dic47—42no—
367C2×#552—471no—
368C2×#547—471no—
369#3343—4716no—
370C2×#501—471no—
371C2×#484—471no—
372C2×#482—471no—
373C2×#483—471no—
374C2×#480—471no—
375C2×#477—471no—
376C2×#478—471no—
377C2×#468D4711yescharacteristic, complemented
378C2×#465—471no—
379C2×#440—471no—
380C2×#435—471no—
381C2×#428—471no—
382C22×#107—471no—
383C2×C47—42no—
384C2×C47—82no—
385C2×C47#334314yescomplemented
386C2×C47C2×#54711yescharacteristic
387C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
388C2×C47C2×#57811yescharacteristic
389D47—24no—
390C22×#41—941no—
391C22×SD16C2×D4711yescharacteristic
392C22×M16C2×D4711yescharacteristic
393C23×C8—471no—
394#552—478no—
395#552—944no—
396#547—478no—
397#547—944no—
398C2×C4⋊Q8—471no—
399C2×#126—941no—
400C2×#125—471no—
401C2×#125—941no—
402C2×#123—941no—
403C2×#123—941no—
404C2×#123—941no—
405C2×C22⋊Q8—471no—
406C2×C22⋊Q8—941no—
407C2×C22⋊Q8C2×D4711yescharacteristic
408C2×#121—471no—
409C2×#121C2×D4711yescharacteristic
410C2×C4×Q8—471no—
411C2×C4×D4—471no—
412C2×C4×D4—471no—
413C2×#117—471no—
414C2×#117—941no—
415C22×C4⋊C4—471no—
416C22×C4⋊C4—471no—
417C22×C4⋊C4—471no—
418#501—478no—
419#484—478no—
420#483—478no—
421#482—478no—
422#480—478no—
423#478—478no—
424#477—478no—
425#468C2×D4718yescomplemented
426#465—478no—
427#440—478no—
428#435—478no—
429#428—478no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#107—471no—
433C2×#107—471no—
434C2×#107—471no—
435C2×#107—478no—
436C2×#107C2×D4711yescharacteristic
437C2×#106—471no—
438C2×#106—471no—
439C2×#106—471no—
440C2×C4⋊C8—471no—
441C2×#103—471no—
442C2×#103—471no—
443C2×#103C2×D4711yescharacteristic
444C2×#102—471no—
445C2×#102—471no—
446C2×#102C2×D4711yescharacteristic
447C2×C22⋊C8—471no—
448C2×C22⋊C8—471no—
449C2×#97—471no—
450C47C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—948no—
452C2×#41—1888no—
453C22×Q8—941no—
454C22×Q8C22×D4711yescharacteristic
455C22×D4—21no—
456C22×D4—471no—
457C22×D4—941no—
458C22×D4C22×D4711yescharacteristic
459C23×C4—471no—
460C23×C4—941no—
461C23×C4—941no—
462C23×C4—941no—
463C23×C4—941no—
464C23×C4C22×D4711yescharacteristic
465C2×SD16—24no—
466C2×SD16C22×D4714yes—
467C2×M16—24no—
468C2×M16C22×D4714yes—
469C22×C8—471no—
470C22×C8—471no—
471C22×C8—474no—
472C22×C8—944no—
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475C4⋊Q8—474no—
476C4⋊Q8—942no—
477#126—948no—
478#125—474no—
479#125—942no—
480#125—948no—
481#123—948no—
482#123—948no—
483#123—948no—
484C22⋊Q8—22no—
485C22⋊Q8—474no—
486C22⋊Q8—948no—
487C22⋊Q8—942no—
488C22⋊Q8C22×D4714yes—
489#121—22no—
490#121—474no—
491#121—942no—
492#121C22×D4714yes—
493C4×Q8—474no—
494C4×Q8—942no—
495C4×D4—474no—
496C4×D4—474no—
497C4×D4—474no—
498C4×D4—942no—
499#117—474no—
500#117—948no—
501#117—942no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—474no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—474no—
510C2×C4⋊C4—474no—
511C2×C4⋊C4—942no—
512C2×C4⋊C4—942no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4—942no—
522C2×C4⋊C4C22×D4711yescharacteristic
523C2×C4⋊C4C22×D4711yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—471no—
527C2×C22⋊C4—471no—
528C2×C22⋊C4—941no—
529C2×C22⋊C4—941no—
530C2×C22⋊C4—941no—
531C2×C22⋊C4—941no—
532C2×C42—471no—
533C2×C42—941no—
534C2×C42—941no—
535#107—474no—
536#107—474no—
537#107—474no—
538#107—474no—
539#107—474no—
540#107C22×D4714yes—
541#106—474no—
542#106—474no—
543#106—474no—
544C4⋊C8—474no—
545#103—474no—
546#103—474no—
547#103C22×D4714yes—
548#102—474no—
549#102—474no—
550#102C22×D4714yes—
551C22⋊C8—474no—
552C22⋊C8—474no—
553#97—474no—
554C24—21no—
555C24—471no—
556C24D4×D4711yescharacteristic
557#41—18832no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—944no—
562C2×Q8—1884no—
563C2×Q8C23×D4712yes—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—44no—
569C2×D4—474no—
570C2×D4—944no—
571C2×D4—944no—
572C2×D4—1884no—
573C2×D4C23×D4712yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—471no—
580C22×C4—471no—
581C22×C4—471no—
582C22×C4—472no—
583C22×C4—472no—
584C22×C4—944no—
585C22×C4—944no—
586C22×C4—944no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—944no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—1884no—
595C22×C4—1884no—
596C22×C4—1884no—
597C22×C4—1884no—
598C22×C4D4×D4712yes—
599C22×C4D4×D4711yescharacteristic
600C22×C4C23×D4712yes—
601C22×C4C23×D4711yescharacteristic
602SD16—28no—
603M16—28no—
604C2×C8—22no—
605C2×C8—472no—
606C2×C8—472no—
607C2×C8—942no—
608C2×C8—942no—
609C2×C8—948no—
610C2×C8#1062535214yescomplemented
611C2×C8C23×D4712yes—
612C2×C8C23×D4712yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—474no—
617C4⋊C4—472no—
618C4⋊C4—472no—
619C4⋊C4—472no—
620C4⋊C4—472no—
621C4⋊C4—944no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—944no—
628C4⋊C4—941no—
629C4⋊C4—941no—
630C4⋊C4—941no—
631C4⋊C4—944no—
632C4⋊C4—941no—
633C4⋊C4C23×D4712yes—
634C4⋊C4C23×D4712yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—474no—
638C22⋊C4—474no—
639C22⋊C4—944no—
640C22⋊C4—944no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C42—472no—
644C42—472no—
645C42—944no—
646C42—944no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—474no—
655C23—472no—
656C23—942no—
657C23—942no—
658C23C2×D4×D4712yes—
659C23C2×D4×D4711yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—1888no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—42no—
668D4—948no—
669D4—1888no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—472no—
681C2×C4—472no—
682C2×C4—472no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—944no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—1888no—
694C2×C4—1888no—
695C2×C4—1888no—
696C2×C4—1888no—
697C2×C4—1882no—
698C2×C4—1882no—
699C2×C4—1882no—
700C2×C4—1882no—
701C2×C4C2×D4×D4712yes—
702C2×C4C2×D4×D4711yescharacteristic
703C2×C4C2×#1062535212yes—
704C2×C4#1309407112yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—942no—
708C8—942no—
709C8C2×#1062535214yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—474no—
719C22—942no—
720C22—948no—
721C22—942no—
722C22#1568977312yes—
723C22AGL(1,ℤ/8)×D4712yes—
724C22#1568993912yes—
725C22C22×D4×D4711yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—942no—
731C4—942no—
732C4—942no—
733C4—1882no—
734C4—1882no—
735C4—1882no—
736C4—1882no—
737C4#1568977312yes—
738C4C22×#1062535211yescharacteristic
739C4C2×#1309407111yescharacteristic
740C2—42no—
741C2—82no—
742C2—944no—
743C2#2025582314yesdirect product factor
744C2C2×#1568977311yescharacteristic
745C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
746C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
prime radicalC2×#15689773C2
hypercenterC2×#468D47
hypocenterC47C2×#3343
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#15689807C2semidirect
3. #20255823C2direct (N × H)
4. C2×#15689531C2semidirect
5. C2×#15689456C2semidirect
6. C2×#15689444C2semidirect
7. C2×#15689452C2semidirect
8. C2×#15689435C2semidirect
9. C2×#15689416C2semidirect
10. C2×#15689425C2semidirect
11. C2×#15689349C2semidirect
12. C2×#15689224C2semidirect
13. C2×#15689192C2semidirect
14. C2×#15689165C2semidirect
15. C2×#107×D47C2semidirect
16. C2×C47×#468C2semidirect
20. #15689807C22semidirect
41. #15689531C22semidirect
42. #15689456C22semidirect
43. #15689452C22semidirect
44. #15689444C22semidirect
45. #15689435C22semidirect
46. #15689425C22semidirect
47. #15689416C22semidirect
48. #15689349C22semidirect
49. #15689224C22semidirect
50. #15689192C22semidirect
51. #15689165C22semidirect
57. #107×D47C22semidirect
73. C47×#468C22semidirect
231. C2×C8×C47#41semidirect
333. C8×C47C2×#41semidirect
377. C2×#468D47semidirect
385. C2×C47#3343semidirect
425. #468C2×D47semidirect
450. C47C2×#3343semidirect
610. C2×C8#10625352semidirect
709. C8C2×#10625352semidirect
743. C2#20255823direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898072
C2×#156897732
#202558232
C2×#156895312
C2×#156894562
C2×#156894442
C2×#156894522
C2×#156894352
C2×#156894162
C2×#156894252
C2×#156893492
C2×#156892242
C2×#156891922
C2×#156891652
C2×#107×D472
C2×C47×#4682
C2×#334347