Finite Group Databasebeta

← C2×#20255494 #27092863

Subgroups — C2×#20255494 #27092863

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×#15689783C211yesmaximal, characteristic
3#20255494C2116yesmaximal, direct product factor
4C2×#15689484C211yesmaximal, characteristic, complemented
5C2×#15689443C211yesmaximal, characteristic, complemented
6C2×#15689451C211yesmaximal, characteristic, complemented
7C2×#15689407C211yesmaximal, characteristic, complemented
8C2×#15689355C211yesmaximal, characteristic, complemented
9C2×#15689347C211yesmaximal, characteristic, complemented
10C2×#15689283C211yesmaximal, characteristic, complemented
11C2×#15689277C211yesmaximal, characteristic, complemented
12C2×#15689227C211yesmaximal, characteristic, complemented
13C2×#15689192C211yesmaximal, characteristic, complemented
14C2×#15689125C211yesmaximal, characteristic, complemented
15C2×#103×D47C211yesmaximal, characteristic, complemented
16C2×C47×#470C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×C8×D47C2211yescharacteristic
22#15689831—24no—
23#15689831C2218yescomplemented
24#15689783—24no—
25#15689783C2218yes—
26C2×#13094023C2211yescharacteristic
27C2×#13094014—21no—
28C2×#13094013C2211yescharacteristic
29C2×#13094010—21no—
30C2×#13094004—21no—
31C2×#13094002—21no—
32C2×#13094001—21no—
33C2×#13094000C2211yescharacteristic
34C2×#13093999C2211yescharacteristic
35C2×#13093997—21no—
36C2×Q8×Dic47C2211yescharacteristic
37C2×#13093989C2211yescharacteristic
38C2×#13093986—21no—
39C2×C4×C22⋊D47C2211yescharacteristic
40C2×(C22⋊D47)⋊C4—21no—
41C22×C4⋊Dic47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689484C2218yescomplemented
44#15689451C2218yescomplemented
45#15689443C2218yescomplemented
46#15689407C2218yescomplemented
47#15689355C2218yescomplemented
48#15689347C2218yescomplemented
49#15689283C2218yescomplemented
50#15689277C2218yescomplemented
51#15689227C2218yescomplemented
52#15689192C2218yescomplemented
53C2×#13093955C2211yescharacteristic
54C2×#13093955C2211yescharacteristic
55C2×Dic47⋊C8C2211yescharacteristic
56#15689125C2218yescomplemented
57C2×#13093949C2211yescharacteristic
58C2×#13093949C2211yescharacteristic
59C2×#13093948C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62#103×D47C2218yescomplemented
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#470C2218yescomplemented
74C2×#106×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350—42no—
80C2×#10625350C2314yes—
81C22×Dic94—21no—
82C22×Dic94—21no—
83C22×Dic94C2311yescharacteristic
84C2×Q8×D47—22no—
85C2×Q8×D47—24no—
86C2×Q8×D47—42no—
87C2×Q8×D47C2314yes—
88C22×D188—21no—
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C22×C22⋊D47D411yescharacteristic
92C23×Dic47—21no—
93C22×C4×D47—21no—
94C22×C4×D47—21no—
95C22×C4×D47—21no—
96C22×C4×D47C2311yescharacteristic
97C2×#10625337—24no—
98C2×#10625337C2314yes—
99C2×#10625336—42no—
100C2×#10625336C2314yes—
101C22×C47⋊C8C2311yescharacteristic
102C22×C47⋊C8C2311yescharacteristic
103C2×C8×D47—42no—
104C2×C8×D47C2314yes—
105#13094023—22no—
106#13094023C2314yes—
107#13094014—28no—
108#13094013—22no—
109#13094013C2314yes—
110#13094010—28no—
111#13094004—28no—
112#13094002—28no—
113#13094001—28no—
114#13094000—22no—
115#13094000C2314yes—
116#13093999—22no—
117#13093999C2314yes—
118#13093997—28no—
119Q8×Dic47—22no—
120Q8×Dic47C2314yes—
121#13093989—22no—
122#13093989C2314yes—
123#13093986—28no—
124C4×C22⋊D47D414yes—
125C4×C22⋊D47C2314yes—
126(C22⋊D47)⋊C4—28no—
127C2×C4⋊Dic47—22no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47C2311yescharacteristic
131C2×C4⋊Dic47C2314yes—
132C2×C4⋊Dic47C2311yescharacteristic
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4D411yescharacteristic
138C4⋊C4×D47—22no—
139C4⋊C4×D47C2314yes—
140C2×C22⋊Dic47D411yescharacteristic
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4D411yescharacteristic
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093955C2314yes—
150#13093955C2314yes—
151Dic47⋊C8C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093947C2314yes—
157#13093946C2314yes—
158#13093946C2314yes—
159#13093944C2314yes—
160C22⋊(C47⋊C8)C2314yes—
161(C2×D47)⋊C8C2314yes—
162#13093934C2314yes—
163C22×Q8×C47C2311yescharacteristic
164C22×Q8×C47C2311yescharacteristic
165C23×C4×C47C2311yescharacteristic
166C2×Q16×C47—42no—
167C2×Q16×C47C2314yes—
168C2×M16×C47—42no—
169C2×M16×C47C2314yes—
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172C22⋊Q8×C47—22no—
173C22⋊Q8×C47—22no—
174C22⋊Q8×C47C2314yes—
175C22⋊Q8×C47C2314yes—
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182#106×C47C2314yes—
183#103×C47C2314yes—
184#103×C47C2314yes—
185C24×C47C2×D411yescharacteristic
186C23×D47—21no—
187C23×D47C2×D411yescharacteristic
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47—22no—
193C2×Q8×C47—22no—
194C2×Q8×C47C2412yes—
195C2×Q8×C47C2412yes—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D412yes—
204C22×C4×C47C2412yes—
205C22×C4×C47C2411yescharacteristic
206C2×C22⋊D47—24no—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—44no—
209C2×C22⋊D47C2×D414yes—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—24no—
214C22×Dic47—82no—
215C22×Dic47C2×D411yescharacteristic
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D411yescharacteristic
218Q8×D47—28no—
219Q8×D47—44no—
220Q8×D47—48no—
221#10625350—28no—
222#10625350—44no—
223#10625350—48no—
224C2×D188—22no—
225C2×D188—22no—
226C2×D188—24no—
227C2×D188—21no—
228C2×D188—44no—
229C2×D188C2412yes—
230C2×C4×D47—22no—
231C2×C4×D47—22no—
232C2×C4×D47—24no—
233C2×C4×D47—24no—
234C2×C4×D47—24no—
235C2×C4×D47—44no—
236C2×C4×D47—44no—
237C2×C4×D47—82no—
238C2×C4×D47C2×D412yes—
239C2×C4×D47C2412yes—
240C2×Dic94—21no—
241C2×Dic94—22no—
242C2×Dic94—24no—
243C2×Dic94—24no—
244C2×Dic94—44no—
245C2×Dic94—82no—
246C2×Dic94#4114yes—
247C2×Dic94C2412yes—
248Q16×C47—44no—
249M16×C47—44no—
250C2×C8×C47—22no—
251C2×C8×C47—22no—
252C2×C8×C47C2412yes—
253C2×C8×C47C2412yes—
254C4⋊C4×C47—24no—
255C4⋊C4×C47—24no—
256C4⋊C4×C47—21no—
257C4⋊C4×C47—21no—
258C4⋊C4×C47C2412yes—
259C4⋊C4×C47C2412yes—
260C22⋊C4×C47—24no—
261C22⋊C4×C47—24no—
262C22⋊Dic47C2×D414yes—
263#10625337—28no—
264#10625336—44no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4C2×D414yes—
270C4⋊Dic47—21no—
271C4⋊Dic47—21no—
272C4⋊Dic47—24no—
273C4⋊Dic47—24no—
274C4⋊Dic47C2412yes—
275C4⋊Dic47C2412yes—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279Dic47⋊C4—24no—
280Dic47⋊C4C2×D414yes—
281C4×Dic47—24no—
282C4×Dic47—24no—
283C4×Dic47C2×D412yes—
284C4×Dic47C2412yes—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8C2412yes—
288C2×C47⋊C8C2412yes—
289C8×D47—44no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47C22×D412yes—
294C23×C47C22×D411yescharacteristic
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—42no—
299C22×D47—42no—
300C22×D47—42no—
301C22×D47#13714yes—
302C22×D47C22×D412yes—
303Q8×C47—22no—
304Q8×C47—22no—
305Q8×C47—22no—
306Q8×C47—22no—
307Q8×C47—42no—
308Q8×C47—42no—
309C2×C4×C47—22no—
310C2×C4×C47—24no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47C22×D412yes—
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C2×#4112yes—
324C2×C4×C47H(5,𝔽2)12yes—
325C2×C4×C47C2511yescharacteristic
326C22⋊D47—28no—
327C22⋊D47—48no—
328C2×Dic47—24no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—84no—
338C2×Dic47C22×D412yes—
339C2×Dic47C22×D412yes—
340C2×Dic47C22×D412yes—
341D188—22no—
342D188—22no—
343D188—48no—
344D188—42no—
345C4×D47—24no—
346C4×D47—22no—
347C4×D47—22no—
348C4×D47—48no—
349C4×D47—48no—
350C4×D47—84no—
351Dic94—24no—
352Dic94—22no—
353Dic94—48no—
354Dic94—84no—
355Dic94C2×#4114yes—
356C8×C47—22no—
357C8×C47—22no—
358C47⋊C8—22no—
359C47⋊C8—22no—
360C2×#3316—471nomaximal, Sylow
361C22×C47—22no—
362C22×C47—22no—
363C22×C47—22no—
364C22×C47—44no—
365C22×C47#54612yes—
366C22×C47C2×#13712yes—
367C22×C47#57712yes—
368C22×C47C23×D411yescharacteristic
369C2×D47—22no—
370C2×D47—28no—
371C2×D47—22no—
372C2×D47—42no—
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—84no—
376C2×D47C2×#13714yes—
377C4×C47—22no—
378C4×C47—42no—
379C4×C47—42no—
380C4×C47—42no—
381C4×C47—42no—
382C4×C47#54612yes—
383C4×C47C22×#4111yescharacteristic
384C4×C47C2×H(5,𝔽2)11yescharacteristic
385Dic47—24no—
386Dic47—22no—
387Dic47—22no—
388Dic47—22no—
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×#470D4711yescharacteristic, complemented
399C2×#465—471no—
400C2×#464—471no—
401C2×#452—471no—
402C2×#451—471no—
403C2×#441—471no—
404C2×#435—471no—
405C2×#417—471no—
406C22×#103—471no—
407C2×C47—42no—
408C2×C47#331614yescomplemented
409C2×C47C2×#54611yescharacteristic
410C2×C47C22×#13711yescharacteristic
411C2×C47C2×#57711yescharacteristic
412D47—24no—
413D47—82no—
414C22×#41—471no—
415C23×Q8—471no—
416C22×Q16—471no—
417C22×Q16C2×D4711yescharacteristic
418C22×SD16—471no—
419C22×M16C2×D4711yescharacteristic
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—941no—
431C2×C22⋊Q8—941no—
432C2×C22⋊Q8—941no—
433C2×C22⋊Q8C2×D4711yescharacteristic
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#470C2×D4718yescomplemented
449#465—478no—
450#464—478no—
451#452—478no—
452#451—478no—
453#441—478no—
454#435—478no—
455C2×#106—471no—
456C2×#106—471no—
457C2×#106C2×D4711yescharacteristic
458C2×C4⋊C8—471no—
459#417—478no—
460C2×#103—471no—
461C2×#103—471no—
462C2×#103—471no—
463C2×#103—471no—
464C2×#103—471no—
465C2×#103—478no—
466C2×#103C2×D4711yescharacteristic
467C2×#103C2×D4711yescharacteristic
468C2×#102—471no—
469C2×#102—471no—
470C2×#102—471no—
471C2×C22⋊C8—471no—
472C2×C22⋊C8—471no—
473C2×#97—471no—
474C47C2×#331611yescharacteristic, complemented, Sylow
475C2×#41—474no—
476C2×#41—944no—
477C2×#41—942no—
478C2×#41—1882no—
479C22×Q8—474no—
480C22×Q8—471no—
481C22×Q8—941no—
482C22×Q8—941no—
483C22×Q8—942no—
484C22×Q8—944no—
485C22×Q8—1882no—
486C22×Q8C22×D4711yescharacteristic
487C22×Q8C22×D4711yescharacteristic
488C22×D4—471no—
489C22×D4—471no—
490C22×D4—941no—
491C22×D4—941no—
492C23×C4—471no—
493C23×C4—941no—
494C23×C4—941no—
495C23×C4—941no—
496C23×C4—941no—
497C23×C4C22×D4711yescharacteristic
498C2×Q16—42no—
499C2×Q16—474no—
500C2×Q16—944no—
501C2×Q16C22×D4714yes—
502C2×SD16—474no—
503C2×SD16—1882no—
504C2×M16—42no—
505C2×M16C22×D4714yes—
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—22no—
520C22⋊Q8—474no—
521C22⋊Q8—948no—
522C22⋊Q8—948no—
523C22⋊Q8—948no—
524C22⋊Q8—942no—
525C22⋊Q8C22×D4714yes—
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—21no—
540C2×C4⋊C4—471no—
541C2×C4⋊C4—471no—
542C2×C4⋊C4—471no—
543C2×C4⋊C4—474no—
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—942no—
553C2×C4⋊C4C22×D4711yescharacteristic
554C2×C4⋊C4C22×D4711yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—471no—
558C2×C22⋊C4—471no—
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#106C22×D4714yes—
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⋊C8—474no—
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—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—474no—
596C2×Q8—472no—
597C2×Q8—944no—
598C2×Q8—944no—
599C2×Q8—941no—
600C2×Q8—942no—
601C2×Q8—948no—
602C2×Q8—3762no—
603C2×Q8—1884no—
604C2×Q8—1884no—
605C2×Q8—1888no—
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—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—471no—
625C22×C4—471no—
626C22×C4—471no—
627C22×C4—472no—
628C22×C4—472no—
629C22×C4—944no—
630C22×C4—944no—
631C22×C4—941no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4—944no—
635C22×C4—941no—
636C22×C4—941no—
637C22×C4—944no—
638C22×C4—3762no—
639C22×C4—3762no—
640C22×C4—1884no—
641C22×C4—1884no—
642C22×C4D4×D4712yes—
643C22×C4D4×D4711yescharacteristic
644C22×C4C23×D4712yes—
645C22×C4C23×D4711yescharacteristic
646Q16—44no—
647Q16—948no—
648SD16—1884no—
649M16—44no—
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—24no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—474no—
664C4⋊C4—472no—
665C4⋊C4—472no—
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⋊C4C23×D4712yes—
675C4⋊C4C23×D4712yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—474no—
679C22⋊C4—474no—
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—22no—
691C23—474no—
692C23—472no—
693C23—942no—
694C23—942no—
695C23—942no—
696C23—1882no—
697C23—1882no—
698C23—1882no—
699C23C2×D4×D4712yes—
700C23C2×D4×D4711yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—42no—
706Q8—42no—
707Q8—474no—
708Q8—944no—
709Q8—942no—
710Q8—3764no—
711Q8—1888no—
712D4—948no—
713D4—942no—
714D4—942no—
715D4—1888no—
716D4—1888no—
717D4—1882no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—472no—
731C2×C4—472no—
732C2×C4—472no—
733C2×C4—942no—
734C2×C4—944no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—944no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—3764no—
744C2×C4—3764no—
745C2×C4—1888no—
746C2×C4—1888no—
747C2×C4—1882no—
748C2×C4—1882no—
749C2×C4C2×D4×D4712yes—
750C2×C4C2×D4×D4711yescharacteristic
751C2×C4#41×D4712yes—
752C2×C4#1309406912yes—
753C2×C4C24×D4711yescharacteristic
754C8—22no—
755C8—22no—
756C8—942no—
757C8—942no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—474no—
763C22—948no—
764C22—942no—
765C22—942no—
766C22—3764no—
767C22—1882no—
768C22—1882no—
769C22—1882no—
770C22#1568976212yes—
771C22#137×D4712yes—
772C22#1568993212yes—
773C22C22×D4×D4711yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—942no—
780C4—944no—
781C4—942no—
782C4—942no—
783C4—1882no—
784C4—1882no—
785C4#1568976212yes—
786C4C2×#41×D4711yescharacteristic
787C4C2×#1309406911yescharacteristic
788C2—42no—
789C2—944no—
790C2—3762no—
791C2#2025549414yesdirect product factor
792C2C2×#1568976211yescharacteristic
793C2C2×#137×D4711yescharacteristic
794C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#470C2
socleC23×C47C22×D4
prime radicalC2×#15689783C2
hypercenterC2×#470D47
hypocenterC47C2×#3316
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C2×#15689831C2semidirect
3. #20255494C2direct (N × H)
4. C2×#15689484C2semidirect
5. C2×#15689443C2semidirect
6. C2×#15689451C2semidirect
7. C2×#15689407C2semidirect
8. C2×#15689355C2semidirect
9. C2×#15689347C2semidirect
10. C2×#15689283C2semidirect
11. C2×#15689277C2semidirect
12. C2×#15689227C2semidirect
13. C2×#15689192C2semidirect
14. C2×#15689125C2semidirect
15. C2×#103×D47C2semidirect
16. C2×C47×#470C2semidirect
23. #15689831C22semidirect
43. #15689484C22semidirect
44. #15689451C22semidirect
45. #15689443C22semidirect
46. #15689407C22semidirect
47. #15689355C22semidirect
48. #15689347C22semidirect
49. #15689283C22semidirect
50. #15689277C22semidirect
51. #15689227C22semidirect
52. #15689192C22semidirect
56. #15689125C22semidirect
62. #103×D47C22semidirect
73. C47×#470C22semidirect
398. C2×#470D47semidirect
408. C2×C47#3316semidirect
448. #470C2×D47semidirect
474. C47C2×#3316semidirect
791. C2#20255494direct (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×#156897832
#202554942
C2×#156894842
C2×#156894432
C2×#156894512
C2×#156894072
C2×#156893552
C2×#156893472
C2×#156892832
C2×#156892772
C2×#156892272
C2×#156891922
C2×#156891252
C2×#103×D472
C2×C47×#4702
C2×#331647