Finite Group Databasebeta

← C2×#20255501 #27092870

Subgroups — C2×#20255501 #27092870

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×#15689830C211yesmaximal, characteristic, complemented
2C2×#15689782C211yesmaximal, characteristic
3#20255501C2116yesmaximal, direct product factor
4C2×#15689483C211yesmaximal, characteristic, complemented
5C2×#15689442C211yesmaximal, characteristic, complemented
6C2×#15689454C211yesmaximal, characteristic, complemented
7C2×#15689409C211yesmaximal, characteristic, complemented
8C2×#15689381C211yesmaximal, characteristic, complemented
9C2×#15689352C211yesmaximal, characteristic, complemented
10C2×#15689346C211yesmaximal, characteristic, complemented
11C2×#15689287C211yesmaximal, characteristic, complemented
12C2×#15689281C211yesmaximal, characteristic, complemented
13C2×#15689231C211yesmaximal, characteristic, complemented
14C2×#15689125C211yesmaximal, characteristic, complemented
15C22×#13093949C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×Dic94C2211yescharacteristic
19C22×Dic188C2211yescharacteristic
20C22×Dic188C2211yescharacteristic
21C22×#10625325C2211yescharacteristic
22#15689830—24no—
23#15689830C2218yescomplemented
24#15689782—24no—
25#15689782C2218yes—
26C2×#13094024C2211yescharacteristic
27C2×#13094015—21no—
28C2×#13094012C2211yescharacteristic
29C2×#13094010—21no—
30C2×#13094003C2211yescharacteristic
31C2×#13094003C2211yescharacteristic
32C2×#13094003C2211yescharacteristic
33C2×#13094002—21no—
34C2×#13094001—21no—
35C2×#13094001—21no—
36C2×#13093998C2211yescharacteristic
37C2×#13093996—21no—
38C2×C4×Dic94C2211yescharacteristic
39C2×C4×Dic94C2211yescharacteristic
40C2×D4×Dic47—21no—
41C2×(C22⋊D47)⋊C4—21no—
42C22×C4⋊Dic47C2211yescharacteristic
43C22×C4⋊Dic47C2211yescharacteristic
44#15689483C2218yescomplemented
45#15689454C2218yescomplemented
46#15689442C2218yescomplemented
47#15689409C2218yescomplemented
48#15689381C2218yescomplemented
49#15689352C2218yescomplemented
50#15689346C2218yescomplemented
51#15689287C2218yescomplemented
52#15689281C2218yescomplemented
53#15689231C2218yescomplemented
54C2×#13093956C2211yescharacteristic
55C2×#13093956C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57#15689125C2218yescomplemented
58C2×#13093949C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093949C2218yescomplemented
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C22×M16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#435C2218yescomplemented
73C2×C4⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×C22⋊C8×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350—42no—
80C2×#10625350C2314yes—
81C22×Dic94—24no—
82C22×Dic94—22no—
83C22×Dic94—21no—
84C22×Dic94—21no—
85C22×Dic94—42no—
86C22×Dic94C2311yescharacteristic
87C22×Dic94C2311yescharacteristic
88C22×Dic94C2314yes—
89C22×Dic94C2311yescharacteristic
90C22×D188C2311yescharacteristic
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C23×Dic47—21no—
94C23×Dic47—21no—
95C23×Dic47—21no—
96C22×C4×D47—21no—
97C2×Dic188—24no—
98C2×Dic188—42no—
99C2×Dic188C2314yes—
100C2×Dic188C2314yes—
101C2×#10625325—42no—
102C2×#10625325C2314yes—
103#13094024—22no—
104#13094024C2314yes—
105#13094015—28no—
106#13094012—22no—
107#13094012C2314yes—
108#13094010—28no—
109#13094003—22no—
110#13094003—22no—
111#13094003—22no—
112#13094003C2314yes—
113#13094003C2314yes—
114#13094003C2314yes—
115#13094002—28no—
116#13094001—28no—
117#13094001—28no—
118#13093998—22no—
119#13093998C2314yes—
120#13093996—28no—
121C4×Dic94—22no—
122C4×Dic94—22no—
123C4×Dic94C2314yes—
124C4×Dic94C2314yes—
125D4×Dic47—28no—
126(C22⋊D47)⋊C4—28no—
127C2×C4⋊Dic47—22no—
128C2×C4⋊Dic47—22no—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2314yes—
134C2×C4⋊Dic47C2314yes—
135C2×C4⋊Dic47C2311yescharacteristic
136C2×C4⋊Dic47C2311yescharacteristic
137C2×C4⋊Dic47C2311yescharacteristic
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4—21no—
142C2×Dic47⋊C4—21no—
143C2×C22⋊Dic47—21no—
144C2×C22⋊Dic47—21no—
145C2×C22⋊Dic47—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151#13093956C2314yes—
152#13093956C2314yes—
153#13093956C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093949C2314yes—
157#13093949C2314yes—
158#13093949C2314yes—
159#13093949C2314yes—
160#13093949C2314yes—
161#13093946C2314yes—
162#13093946C2314yes—
163#13093946C2314yes—
164C22×D4×C47D411yescharacteristic
165C23×C4×C47C2311yescharacteristic
166C23×C4×C47C2311yescharacteristic
167C2×M16×C47—42no—
168C2×M16×C47C2314yes—
169C22×C8×C47—42no—
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2314yes—
175C4×D4×C47D414yes—
176C4×D4×C47C2314yes—
177C2×C4⋊C4×C47D411yescharacteristic
178C2×C22⋊C4×C47D411yescharacteristic
179C2×C22⋊C4×C47D411yescharacteristic
180C2×C42×C47C2311yescharacteristic
181C4⋊C8×C47C2314yes—
182C22⋊C8×C47C2314yes—
183C22⋊C8×C47C2314yes—
184#97×C47C2314yes—
185C24×C47C2×D411yescharacteristic
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C2×D4×C47—24no—
189C2×D4×C47C2×D414yes—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D412yes—
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2411yescharacteristic
203C2×C22⋊D47—24no—
204C2×C22⋊D47—24no—
205C2×C22⋊D47—44no—
206C2×C22⋊D47—44no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—24no—
215C22×Dic47—24no—
216C22×Dic47—24no—
217C22×Dic47—44no—
218C22×Dic47—82no—
219C22×Dic47—82no—
220#10625350—28no—
221#10625350—44no—
222#10625350—48no—
223C2×D188—22no—
224C2×D188—22no—
225C2×D188—21no—
226C2×D188C2412yes—
227C2×C4×D47—24no—
228C2×C4×D47—44no—
229C2×Dic94—21no—
230C2×Dic94—22no—
231C2×Dic94—22no—
232C2×Dic94—22no—
233C2×Dic94—22no—
234C2×Dic94—22no—
235C2×Dic94—28no—
236C2×Dic94—21no—
237C2×Dic94—24no—
238C2×Dic94—21no—
239C2×Dic94—24no—
240C2×Dic94—44no—
241C2×Dic94—48no—
242C2×Dic94—44no—
243C2×Dic94—82no—
244C2×Dic94#4114yes—
245C2×Dic94C2412yes—
246C2×Dic94C2412yes—
247C2×Dic94C2412yes—
248M16×C47—44no—
249C2×C8×C47—22no—
250C2×C8×C47—22no—
251C2×C8×C47—22no—
252C2×C8×C47—22no—
253C2×C8×C47—44no—
254C2×C8×C47C2412yes—
255C2×C8×C47C2412yes—
256C2×C8×C47C2412yes—
257C2×C8×C47C2412yes—
258C4⋊C4×C47C2×D414yes—
259C22⋊C4×C47C2×D414yes—
260C22⋊C4×C47C2×D414yes—
261C42×C47C2×D412yes—
262C42×C47C2412yes—
263C22⋊Dic47—24no—
264C22⋊Dic47—24no—
265C22⋊Dic47—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269C4⋊Dic47—21no—
270C4⋊Dic47—24no—
271C4⋊Dic47—24no—
272C4⋊Dic47—21no—
273C4⋊Dic47—21no—
274C4⋊Dic47—24no—
275C4⋊Dic47—21no—
276C4⋊Dic47C2412yes—
277C4⋊Dic47C2412yes—
278C4⋊Dic47C2412yes—
279C4⋊Dic47C2412yes—
280Dic47⋊C4—24no—
281Dic47⋊C4—24no—
282Dic47⋊C4—24no—
283Dic47⋊C4—24no—
284Dic47⋊C4—24no—
285C4×Dic47—24no—
286C4×Dic47—24no—
287Dic188—28no—
288Dic188—44no—
289#10625325—44no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47#13714yes—
296C23×C47C22×D412yes—
297C23×C47C22×D412yes—
298C23×C47C22×D411yescharacteristic
299C22×D47—22no—
300C22×D47—42no—
301C22×D47—42no—
302C22×D47—42no—
303D4×C47—28no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—24no—
309C2×C4×C47—24no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47C22×D412yes—
315C2×C4×C47C22×D412yes—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D412yes—
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C2×#4112yes—
320C2×C4×C47H(5,𝔽2)12yes—
321C2×C4×C47C2511yescharacteristic
322C22⋊D47—48no—
323C22⋊D47—48no—
324C2×Dic47—24no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—48no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47—42no—
339C2×Dic47—84no—
340C2×Dic47—84no—
341D188—22no—
342D188—22no—
343D188—42no—
344C4×D47—48no—
345Dic94—24no—
346Dic94—22no—
347Dic94—22no—
348Dic94—22no—
349Dic94—22no—
350Dic94—22no—
351Dic94—48no—
352Dic94—42no—
353Dic94—42no—
354Dic94—84no—
355Dic94C2×#4114yes—
356C8×C47—22no—
357C8×C47—22no—
358C8×C47—22no—
359C8×C47—22no—
360C2×#3316—471nomaximal, Sylow
361C22×C47—22no—
362C22×C47—28no—
363C22×C47—22no—
364C22×C47—22no—
365C22×C47—22no—
366C22×C47—22no—
367C22×C47—44no—
368C22×C47#54612yes—
369C22×C47C2×#13714yes—
370C22×C47C2×#13712yes—
371C22×C47#57712yes—
372C22×C47C23×D411yescharacteristic
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—84no—
377C4×C47—22no—
378C4×C47—22no—
379C4×C47—22no—
380C4×C47—22no—
381C4×C47#54612yes—
382C4×C47C22×#4111yescharacteristic
383C4×C47C2×H(5,𝔽2)11yescharacteristic
384Dic47—24no—
385Dic47—42no—
386Dic47—42no—
387Dic47—42no—
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×#451—471no—
403C2×#441—471no—
404C2×#435D4711yescharacteristic, complemented
405C2×#417—471no—
406C22×#103—471no—
407C2×C47—24no—
408C2×C47—42no—
409C2×C47#331614yescomplemented
410C2×C47C2×#54611yescharacteristic
411C2×C47C22×#13711yescharacteristic
412C2×C47C2×#57711yescharacteristic
413D47—82no—
414C22×#41—471no—
415C23×Q8—471no—
416C22×Q16—471no—
417C22×Q16—471no—
418C22×SD16—471no—
419C22×M16C2×D4711yescharacteristic
420C23×C8C2×D4711yescharacteristic
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—471no—
432C2×C22⋊Q8—941no—
433C2×C22⋊Q8—941no—
434C2×C22⋊Q8—941no—
435C2×#121—471no—
436C2×#121—941no—
437C2×C4×Q8—471no—
438C2×C4×Q8—471no—
439C2×C4×D4—941no—
440C2×C4×D4—941no—
441C2×C4×D4C2×D4711yescharacteristic
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#451—478no—
453#441—478no—
454#435C2×D4718yescomplemented
455C2×#106—471no—
456C2×#106—471no—
457C2×#106—471no—
458C2×C4⋊C8C2×D4711yescharacteristic
459#417—478no—
460C2×#103—471no—
461C2×#103—471no—
462C2×#103—471no—
463C2×#103—471no—
464C2×#103—471no—
465C2×#103—471no—
466C2×#103—478no—
467C2×#103—471no—
468C2×#102—471no—
469C2×#102—471no—
470C2×#102—471no—
471C2×C22⋊C8C2×D4711yescharacteristic
472C2×C22⋊C8C2×D4711yescharacteristic
473C2×#97C2×D4711yescharacteristic
474C47C2×#331611yescharacteristic, complemented, Sylow
475C2×#41—474no—
476C2×#41—944no—
477C2×#41—942no—
478C2×#41—1882no—
479C22×Q8—471no—
480C22×Q8—471no—
481C22×Q8—471no—
482C22×Q8—474no—
483C22×Q8—944no—
484C22×Q8—941no—
485C22×Q8—941no—
486C22×Q8—942no—
487C22×Q8—1882no—
488C22×D4—471no—
489C22×D4—941no—
490C22×D4—941no—
491C22×D4D18811yescharacteristic
492C23×C4—941no—
493C23×C4—941no—
494C23×C4—941no—
495C23×C4—941no—
496C23×C4C22×D4711yescharacteristic
497C23×C4C22×D4711yescharacteristic
498C2×Q16—474no—
499C2×Q16—474no—
500C2×Q16—944no—
501C2×Q16—1882no—
502C2×SD16—474no—
503C2×SD16—1882no—
504C2×M16—42no—
505C2×M16C22×D4714yes—
506C22×C8—42no—
507C22×C8C22×D4711yescharacteristic
508C22×C8C22×D4711yescharacteristic
509C22×C8C22×D4711yescharacteristic
510C22×C8C22×D4711yescharacteristic
511C22×C8C22×D4714yes—
512C4⋊Q8—474no—
513C4⋊Q8—942no—
514#125—948no—
515#124—474no—
516#124—948no—
517#124—942no—
518C22⋊Q8—474no—
519C22⋊Q8—474no—
520C22⋊Q8—474no—
521C22⋊Q8—942no—
522C22⋊Q8—942no—
523C22⋊Q8—942no—
524C22⋊Q8—948no—
525C22⋊Q8—948no—
526C22⋊Q8—948no—
527#121—474no—
528#121—948no—
529#121—942no—
530C4×Q8—474no—
531C4×Q8—474no—
532C4×Q8—942no—
533C4×Q8—942no—
534C4×D4—948no—
535C4×D4—948no—
536C4×D4D18814yes—
537C4×D4C22×D4714yes—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—471no—
540C2×C4⋊C4—471no—
541C2×C4⋊C4—474no—
542C2×C4⋊C4—474no—
543C2×C4⋊C4—471no—
544C2×C4⋊C4—941no—
545C2×C4⋊C4—941no—
546C2×C4⋊C4—942no—
547C2×C4⋊C4—942no—
548C2×C4⋊C4—941no—
549C2×C4⋊C4—941no—
550C2×C4⋊C4—941no—
551C2×C4⋊C4—941no—
552C2×C4⋊C4—941no—
553C2×C4⋊C4—941no—
554C2×C4⋊C4D18811yescharacteristic
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C22⋊C4—941no—
558C2×C22⋊C4—941no—
559C2×C22⋊C4—941no—
560C2×C22⋊C4—941no—
561C2×C22⋊C4D18811yescharacteristic
562C2×C22⋊C4D18811yescharacteristic
563C2×C42—941no—
564C2×C42—941no—
565C2×C42C22×D4711yescharacteristic
566#106—474no—
567#106—474no—
568#106—474no—
569C4⋊C8C22×D4714yes—
570#103—474no—
571#103—474no—
572#103—474no—
573#103—474no—
574#103—474no—
575#103—474no—
576#103—474no—
577#102—474no—
578#102—474no—
579#102—474no—
580C22⋊C8C22×D4714yes—
581C22⋊C8C22×D4714yes—
582#97C22×D4714yes—
583C24—941no—
584C24C2×D18811yescharacteristic
585C24C2×D18811yescharacteristic
586#41—948no—
587#41—1884no—
588#41—1888no—
589C2×Q8—474no—
590C2×Q8—472no—
591C2×Q8—472no—
592C2×Q8—472no—
593C2×Q8—948no—
594C2×Q8—941no—
595C2×Q8—944no—
596C2×Q8—941no—
597C2×Q8—944no—
598C2×Q8—941no—
599C2×Q8—942no—
600C2×Q8—942no—
601C2×Q8—942no—
602C2×Q8—942no—
603C2×Q8—942no—
604C2×Q8—3762no—
605C2×Q8—1884no—
606C2×Q8—1884no—
607C2×Q8—1888no—
608C2×D4—24no—
609C2×D4—472no—
610C2×D4—944no—
611C2×D4—944no—
612C2×D4—941no—
613C2×D4—942no—
614C2×D4—942no—
615C2×D4—1884no—
616C2×D4—1884no—
617C2×D4C2×D18814yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—941no—
623C22×C4—944no—
624C22×C4—944no—
625C22×C4—944no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—941no—
631C22×C4—941no—
632C22×C4—944no—
633C22×C4—3762no—
634C22×C4—3762no—
635C22×C4—1884no—
636C22×C4—1884no—
637C22×C4C2×D18812yes—
638C22×C4C2×D18812yes—
639C22×C4C2×D18811yescharacteristic
640C22×C4C2×D18811yescharacteristic
641C22×C4C2×D18811yescharacteristic
642C22×C4C2×D18811yescharacteristic
643C22×C4C23×D4712yes—
644C22×C4C23×D4712yes—
645C22×C4C23×D4711yescharacteristic
646Q16—948no—
647Q16—1884no—
648SD16—1884no—
649M16—44no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—44no—
655C2×C8C23×D4712yes—
656C2×C8C23×D4712yes—
657C2×C8C23×D4712yes—
658C2×C8C23×D4712yes—
659C4⋊C4—472no—
660C4⋊C4—472no—
661C4⋊C4—472no—
662C4⋊C4—472no—
663C4⋊C4—944no—
664C4⋊C4—944no—
665C4⋊C4—944no—
666C4⋊C4—944no—
667C4⋊C4—944no—
668C4⋊C4—941no—
669C4⋊C4—944no—
670C4⋊C4—944no—
671C4⋊C4—941no—
672C4⋊C4—941no—
673C4⋊C4—941no—
674C4⋊C4—944no—
675C4⋊C4C2×D18814yes—
676C22⋊C4—944no—
677C22⋊C4—944no—
678C22⋊C4—944no—
679C22⋊C4—944no—
680C22⋊C4—944no—
681C22⋊C4—944no—
682C22⋊C4C2×D18814yes—
683C22⋊C4C2×D18814yes—
684C42—944no—
685C42—944no—
686C42C2×D18812yes—
687C42C23×D4712yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—942no—
694C23—1882no—
695C23—1882no—
696C23—1882no—
697C23#1309405714yes—
698C23C22×D18812yes—
699C23C22×D18812yes—
700C23C22×D18811yescharacteristic
701Q8—474no—
702Q8—944no—
703Q8—942no—
704Q8—942no—
705Q8—942no—
706Q8—942no—
707Q8—942no—
708Q8—3764no—
709Q8—1888no—
710Q8—1882no—
711Q8—1882no—
712D4—28no—
713D4—942no—
714D4—942no—
715D4—1888no—
716D4—1888no—
717D4—1882no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—944no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—3764no—
737C2×C4—3764no—
738C2×C4—1888no—
739C2×C4—1888no—
740C2×C4—1882no—
741C2×C4—1882no—
742C2×C4—1882no—
743C2×C4—1882no—
744C2×C4—1882no—
745C2×C4—1882no—
746C2×C4C22×D18812yes—
747C2×C4C22×D18812yes—
748C2×C4C22×D18812yes—
749C2×C4C22×D18812yes—
750C2×C4C22×D18811yescharacteristic
751C2×C4#41×D4712yes—
752C2×C4#1309406912yes—
753C2×C4C24×D4711yescharacteristic
754C8—22no—
755C8—22no—
756C8—22no—
757C8—22no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—3764no—
766C22—1882no—
767C22—1882no—
768C22—1882no—
769C22#1568976812yes—
770C22C2×#1309405714yes—
771C22C2×#1309405712yes—
772C22#1568993512yes—
773C22C23×D18811yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—944no—
779C4—1882no—
780C4—1882no—
781C4—1882no—
782C4—1882no—
783C4—1882no—
784C4—1882no—
785C4#1568976812yes—
786C4C2×#41×D4711yescharacteristic
787C4C2×#1309406911yescharacteristic
788C2—24no—
789C2—42no—
790C2—3762no—
791C2#2025550114yesdirect product factor
792C2C2×#1568976811yescharacteristic
793C2C22×#1309405711yescharacteristic
794C2C2×#1568993511yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C22×D4
prime radicalC2×#15689782C2
hypercenterC2×#435D47
hypocenterC47C2×#3316
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#15689830C2semidirect
3. #20255501C2direct (N × H)
4. C2×#15689483C2semidirect
5. C2×#15689442C2semidirect
6. C2×#15689454C2semidirect
7. C2×#15689409C2semidirect
8. C2×#15689381C2semidirect
9. C2×#15689352C2semidirect
10. C2×#15689346C2semidirect
11. C2×#15689287C2semidirect
12. C2×#15689281C2semidirect
13. C2×#15689231C2semidirect
14. C2×#15689125C2semidirect
15. C22×#13093949C2semidirect
16. C2×C47×#435C2semidirect
23. #15689830C22semidirect
44. #15689483C22semidirect
45. #15689454C22semidirect
46. #15689442C22semidirect
47. #15689409C22semidirect
48. #15689381C22semidirect
49. #15689352C22semidirect
50. #15689346C22semidirect
51. #15689287C22semidirect
52. #15689281C22semidirect
53. #15689231C22semidirect
57. #15689125C22semidirect
65. C2×#13093949C22semidirect
72. C47×#435C22semidirect
404. C2×#435D47semidirect
409. C2×C47#3316semidirect
454. #435C2×D47semidirect
474. C47C2×#3316semidirect
791. C2#20255501direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898302
C2×#156897822
#202555012
C2×#156894832
C2×#156894422
C2×#156894542
C2×#156894092
C2×#156893812
C2×#156893522
C2×#156893462
C2×#156892872
C2×#156892812
C2×#156892312
C2×#156891252
C22×#130939492
C2×C47×#4352
C2×#331647