Finite Group Databasebeta

← C2×#20255475 #27092810

Subgroups — C2×#20255475 #27092810

Order 12032.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689831C211yesmaximal, characteristic, complemented
2C2×#15689764C211yesmaximal, characteristic
3#20255475C2116yesmaximal, direct product factor
4C2×#15689484C211yesmaximal, characteristic, complemented
5C2×#15689456C211yesmaximal, characteristic, complemented
6C2×#15689438C211yesmaximal, characteristic, complemented
7C2×#15689402C211yesmaximal, characteristic, complemented
8C2×#15689372C211yesmaximal, characteristic, complemented
9C2×#15689347C211yesmaximal, characteristic, complemented
10C2×#15689284C211yesmaximal, characteristic, complemented
11C2×#15689273C211yesmaximal, characteristic, complemented
12C2×#15689226C211yesmaximal, characteristic, complemented
13C2×#15689194C211yesmaximal, characteristic, complemented
14C2×#15689123C211yesmaximal, characteristic, complemented
15C22×#13093946C211yesmaximal, characteristic, complemented
16C2×C47×#467C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625324C2211yescharacteristic, complemented
22#15689831—24no—
23#15689831C2218yescomplemented
24#15689764—24no—
25#15689764C2218yes—
26C2×#13094023C2211yescharacteristic, complemented
27C2×#13094014—21no—
28C2×#13094013C2211yescharacteristic
29C2×#13094009—21no—
30C2×#13094004—21no—
31C2×#13094001—21no—
32C2×#13094000C2211yescharacteristic, complemented
33C2×#13093999—21no—
34C2×#13093999C2211yescharacteristic
35C2×#13093994—21no—
36C2×Q8×Dic47C2211yescharacteristic, complemented
37C2×#13093986C2211yescharacteristic
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×(C22⋊D47)⋊C4—21no—
40C22×C4⋊Dic47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic, complemented
42C2×C22⋊C4×D47—21no—
43#15689484C2218yescomplemented
44#15689456C2218yescomplemented
45#15689438C2218yescomplemented
46#15689402C2218yescomplemented
47#15689372C2218yescomplemented
48#15689347C2218yescomplemented
49#15689284C2218yescomplemented
50#15689273C2218yescomplemented
51#15689226C2218yescomplemented
52#15689194C2218yescomplemented
53C2×#13093957C2211yescharacteristic, complemented
54C2×#13093957C2211yescharacteristic, complemented
55C2×Dic47⋊C8C2211yescharacteristic, complemented
56#15689123C2218yescomplemented
57C2×#13093948C2211yescharacteristic, complemented
58C2×#13093948C2211yescharacteristic, complemented
59C2×#13093946C2211yescharacteristic
60C2×#13093946C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2218yescomplemented
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×#13093934C2211yescharacteristic, complemented
69C22×Q16×C47C2211yescharacteristic, complemented
70C23×C8×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#467C2218yescomplemented
74C2×#107×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×#103×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625354—22no—
79C2×#10625354—24no—
80C2×#10625354—42no—
81C2×#10625354C2314yes—
82C22×Dic94—21no—
83C22×D188—24no—
84C22×D188—21no—
85C22×D188—22no—
86C22×D188—21no—
87C22×D188—21no—
88C22×D188—42no—
89C22×D188C2311yescharacteristic
90C22×D188C2314yes—
91C22×D188C2311yescharacteristic
92C22×C22⋊D47D411yescharacteristic
93C23×Dic47—21no—
94C22×C4×D47—21no—
95C22×C4×D47—21no—
96C22×C4×D47—21no—
97C22×C4×D47C2311yescharacteristic
98C2×#10625336—24no—
99C2×#10625336—42no—
100C2×#10625336C2314yes—
101C2×#10625336C2314yes—
102C2×#10625324—42no—
103C2×#10625324C2314yescomplemented
104C22×C47⋊C8C2311yescharacteristic
105C22×C47⋊C8C2311yescharacteristic
106#13094023—22no—
107#13094023C2314yescomplemented
108#13094014—28no—
109#13094013—22no—
110#13094013C2314yes—
111#13094009—28no—
112#13094004—28no—
113#13094001—28no—
114#13094000—22no—
115#13094000C2314yescomplemented
116#13093999—22no—
117#13093999—28no—
118#13093999C2314yes—
119#13093994—28no—
120Q8×Dic47—22no—
121Q8×Dic47C2314yescomplemented
122#13093986—22no—
123#13093986C2314yes—
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⋊C4D411yescharacteristic
137C4⋊C4×D47—22no—
138C4⋊C4×D47C2314yescomplemented
139C2×C22⋊Dic47D411yescharacteristic
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4D411yescharacteristic
146C22⋊C4×D47—28no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yescomplemented
150#13093957C2314yescomplemented
151Dic47⋊C8C2314yescomplemented
152#13093948C2314yescomplemented
153#13093948C2314yescomplemented
154#13093946C2314yes—
155#13093946C2314yes—
156#13093946C2314yes—
157#13093946C2314yes—
158#13093944C2314yes—
159#13093944C2314yes—
160C22⋊(C47⋊C8)C2314yes—
161(C2×D47)⋊C8C2314yescomplemented
162#13093934C2314yescomplemented
163C22×Q8×C47C2311yescharacteristic
164C22×Q8×C47C2311yescharacteristic
165C23×C4×C47C2311yescharacteristic
166C2×Q16×C47—42no—
167C2×Q16×C47C2314yescomplemented
168C22×C8×C47—42no—
169C22×C8×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2314yes—
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#107×C47C2314yescomplemented
183#103×C47C2314yescomplemented
184#103×C47C2314yescomplemented
185C24×C47C2×D411yescharacteristic
186C23×D47—21no—
187C23×D47—21no—
188C23×D47—24no—
189C23×D47—44no—
190C23×D47—44no—
191C23×D47—82no—
192C23×D47C2×D411yescharacteristic
193C2×Q8×C47—21no—
194C2×Q8×C47—21no—
195C2×Q8×C47—22no—
196C2×Q8×C47—22no—
197C2×Q8×C47—22no—
198C2×Q8×C47—22no—
199C2×Q8×C47C2412yes—
200C2×Q8×C47C2412yes—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D412yes—
209C22×C4×C47C2412yes—
210C22×C4×C47C2411yescharacteristic
211C2×C22⋊D47—24no—
212C2×C22⋊D47C2×D414yes—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—24no—
216C22×Dic47—82no—
217C22×Dic47C2×D411yescharacteristic
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D411yescharacteristic
220#10625354—28no—
221#10625354—44no—
222#10625354—48no—
223C2×D188—21no—
224C2×D188—22no—
225C2×D188—22no—
226C2×D188—22no—
227C2×D188—28no—
228C2×D188—24no—
229C2×D188—24no—
230C2×D188—21no—
231C2×D188—24no—
232C2×D188—44no—
233C2×D188—48no—
234C2×D188—44no—
235C2×D188—44no—
236C2×D188—82no—
237C2×D188#4114yes—
238C2×D188C2412yes—
239C2×D188C2412yes—
240C2×C4×D47—22no—
241C2×C4×D47—22no—
242C2×C4×D47—24no—
243C2×C4×D47—24no—
244C2×C4×D47—24no—
245C2×C4×D47—44no—
246C2×C4×D47—82no—
247C2×C4×D47—82no—
248C2×C4×D47C2×D412yes—
249C2×C4×D47C2412yes—
250C2×Dic94—24no—
251C2×Dic94—82no—
252Q16×C47—44no—
253C2×C8×C47—22no—
254C2×C8×C47—22no—
255C2×C8×C47—44no—
256C2×C8×C47C2412yes—
257C2×C8×C47C2412yes—
258C4⋊C4×C47—24no—
259C4⋊C4×C47—24no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47C2412yes—
263C4⋊C4×C47C2412yes—
264C22⋊C4×C47—24no—
265C22⋊C4×C47—24no—
266C22⋊Dic47C2×D414yes—
267#10625336—28no—
268#10625336—44no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4—24no—
272(C2×D47)⋊C4—24no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4C2×D414yes—
275C4⋊Dic47—21no—
276C4⋊Dic47—21no—
277C4⋊Dic47—24no—
278C4⋊Dic47—24no—
279C4⋊Dic47C2412yes—
280C4⋊Dic47C2412yes—
281Dic47⋊C4—24no—
282Dic47⋊C4—24no—
283Dic47⋊C4—24no—
284Dic47⋊C4C2×D414yes—
285C4×Dic47—24no—
286C4×Dic47C2×D412yes—
287C4×Dic47C2412yes—
288C2×C47⋊C8—22no—
289C2×C47⋊C8—22no—
290C2×C47⋊C8C2412yes—
291C2×C47⋊C8C2412yes—
292#10625324—44no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47#13714yes—
296C23×C47C22×D412yes—
297C23×C47C22×D411yescharacteristic
298C22×D47—22no—
299C22×D47—24no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—48no—
305C22×D47—42no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—48no—
309C22×D47—42no—
310C22×D47—42no—
311C22×D47—84no—
312C22×D47—816no—
313C22×D47C22×D412yes—
314Q8×C47—22no—
315Q8×C47—22no—
316Q8×C47—22no—
317Q8×C47—22no—
318Q8×C47—42no—
319Q8×C47—42no—
320C2×C4×C47—22no—
321C2×C4×C47—24no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—42no—
329C2×C4×C47—42no—
330C2×C4×C47—42no—
331C2×C4×C47—42no—
332C2×C4×C47C22×D412yes—
333C2×C4×C47C22×D411yescharacteristic
334C2×C4×C47C2×#4112yes—
335C2×C4×C47H(5,𝔽2)12yes—
336C2×C4×C47C2511yescharacteristic
337C22⋊D47—28no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47—84no—
346C2×Dic47C22×D412yes—
347C2×Dic47C22×D412yes—
348C2×Dic47C22×D412yes—
349D188—24no—
350D188—22no—
351D188—22no—
352D188—22no—
353D188—48no—
354D188—48no—
355D188—42no—
356D188—84no—
357D188C2×#4114yes—
358C4×D47—24no—
359C4×D47—22no—
360C4×D47—22no—
361C4×D47—48no—
362C4×D47—84no—
363C4×D47—84no—
364Dic94—84no—
365C8×C47—22no—
366C8×C47—22no—
367C47⋊C8—22no—
368C47⋊C8—22no—
369C2×#3314—471nomaximal, Sylow
370C22×C47—22no—
371C22×C47—28no—
372C22×C47—22no—
373C22×C47#54612yes—
374C22×C47C2×#13714yes—
375C22×C47C2×#13712yes—
376C22×C47#57612yes—
377C22×C47C23×D411yescharacteristic
378C2×D47—22no—
379C2×D47—24no—
380C2×D47—22no—
381C2×D47—22no—
382C2×D47—44no—
383C2×D47—48no—
384C2×D47—42no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—42no—
389C2×D47—816no—
390C2×D47—84no—
391C4×C47—22no—
392C4×C47—42no—
393C4×C47—42no—
394C4×C47—42no—
395C4×C47—42no—
396C4×C47#54612yes—
397C4×C47C22×#4111yescharacteristic
398C4×C47C2×H(5,𝔽2)11yescharacteristic
399Dic47—22no—
400Dic47—22no—
401Dic47—22no—
402Dic47—42no—
403Dic47—42no—
404C2×#554—471no—
405C2×#546—471no—
406#3314—4716no—
407C2×#489—471no—
408C2×#484—471no—
409C2×#480—471no—
410C2×#474—471no—
411C2×#468—471no—
412C2×#467D4711yescharacteristic, complemented
413C2×#464—471no—
414C2×#452—471no—
415C2×#450—471no—
416C2×#440—471no—
417C2×#435—471no—
418C2×#417—471no—
419C22×#102—471no—
420C2×C47—24no—
421C2×C47#331414yescomplemented
422C2×C47C2×#54611yescharacteristic
423C2×C47C22×#13711yescharacteristic
424C2×C47C2×#57611yescharacteristic
425D47—42no—
426D47—44no—
427D47—82no—
428C22×#41—471no—
429C23×D4—471no—
430C22×Q16C2×D4711yescharacteristic, complemented
431C22×SD16—471no—
432C22×SD16—471no—
433C22×M16—471no—
434C23×C8C2×D4711yescharacteristic
435#554—478no—
436#554—944no—
437#546—478no—
438#546—944no—
439C2×C4⋊Q8—471no—
440C2×#125—941no—
441C2×#124—471no—
442C2×#123—941no—
443C2×C22⋊Q8—471no—
444C2×C22⋊Q8—941no—
445C2×C22⋊Q8—941no—
446C2×C22⋊Q8C2×D4711yescharacteristic
447C2×C22⋊Q8C2×D4711yescharacteristic
448C2×#121—471no—
449C2×#121—941no—
450C2×#120—941no—
451C2×C4×Q8—471no—
452C2×C4×D4—471no—
453C2×C4×D4—471no—
454C2×C4×D4—941no—
455C22×C4⋊C4—471no—
456C22×C4⋊C4—471no—
457C22×C22⋊C4—941no—
458#489—478no—
459#484—478no—
460#480—478no—
461#474—478no—
462#468—478no—
463#467C2×D4718yescomplemented
464#464—478no—
465#452—478no—
466#450—478no—
467#440—478no—
468#435—478no—
469C2×#107—471no—
470C2×#107—471no—
471C2×#107C2×D4711yescharacteristic, complemented
472C2×C4⋊C8—471no—
473#417—478no—
474C2×#103—471no—
475C2×#103—471no—
476C2×#103C2×D4711yescharacteristic, complemented
477C2×#103C2×D4711yescharacteristic, complemented
478C2×#102—471no—
479C2×#102—471no—
480C2×#102—471no—
481C2×#102—471no—
482C2×#102—478no—
483C2×#102—471no—
484C2×#102—471no—
485C2×C22⋊C8—471no—
486C2×C22⋊C8—471no—
487C2×#97—471no—
488C47C2×#331411yescharacteristic, complemented, Sylow
489C25—941no—
490C2×#41—474no—
491C2×#41—942no—
492C2×#41—944no—
493C2×#41—1882no—
494C22×Q8—941no—
495C22×Q8C22×D4711yescharacteristic
496C22×Q8C22×D4711yescharacteristic
497C22×D4—471no—
498C22×D4—471no—
499C22×D4—471no—
500C22×D4—474no—
501C22×D4—944no—
502C22×D4—941no—
503C22×D4—941no—
504C22×D4—941no—
505C22×D4—942no—
506C22×D4—1882no—
507C23×C4—471no—
508C23×C4—941no—
509C23×C4—941no—
510C23×C4—941no—
511C23×C4—941no—
512C23×C4C22×D4711yescharacteristic
513C2×Q16—42no—
514C2×Q16C22×D4714yescomplemented
515C2×SD16—474no—
516C2×SD16—474no—
517C2×SD16—944no—
518C2×SD16—1882no—
519C2×M16—474no—
520C2×M16—1882no—
521C22×C8—42no—
522C22×C8—471no—
523C22×C8—471no—
524C22×C8C22×D4711yescharacteristic
525C22×C8C22×D4711yescharacteristic
526C22×C8C22×D4714yes—
527C4⋊Q8—474no—
528C4⋊Q8—942no—
529#125—948no—
530#124—474no—
531#124—942no—
532#123—948no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—474no—
536C22⋊Q8—948no—
537C22⋊Q8—948no—
538C22⋊Q8—942no—
539C22⋊Q8C22×D4714yes—
540C22⋊Q8C22×D4714yes—
541#121—474no—
542#121—948no—
543#121—942no—
544#120—948no—
545C4×Q8—474no—
546C4×Q8—942no—
547C4×D4—474no—
548C4×D4—474no—
549C4×D4—474no—
550C4×D4—942no—
551C4×D4—948no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—471no—
555C2×C4⋊C4—471no—
556C2×C4⋊C4—471no—
557C2×C4⋊C4—474no—
558C2×C4⋊C4—474no—
559C2×C4⋊C4—942no—
560C2×C4⋊C4—941no—
561C2×C4⋊C4—941no—
562C2×C4⋊C4—941no—
563C2×C4⋊C4—941no—
564C2×C4⋊C4—941no—
565C2×C4⋊C4—942no—
566C2×C4⋊C4C22×D4711yescharacteristic
567C2×C4⋊C4C22×D4711yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—471no—
571C2×C22⋊C4—471no—
572C2×C22⋊C4—948no—
573C2×C22⋊C4—941no—
574C2×C22⋊C4—941no—
575C2×C22⋊C4—941no—
576C2×C22⋊C4—941no—
577C2×C22⋊C4—941no—
578C2×C42—471no—
579C2×C42—941no—
580#107—474no—
581#107—474no—
582#107C22×D4714yescomplemented
583C4⋊C8—474no—
584#103—474no—
585#103—474no—
586#103C22×D4714yescomplemented
587#103C22×D4714yescomplemented
588#102—474no—
589#102—474no—
590#102—474no—
591#102—474no—
592#102—474no—
593#102—474no—
594C22⋊C8—474no—
595C22⋊C8—474no—
596#97—474no—
597C24—471no—
598C24—941no—
599C24—944no—
600C24—941no—
601C24—3762no—
602C24—1884no—
603C24—1884no—
604C24D4×D4711yescharacteristic
605#41—948no—
606#41—1884no—
607#41—1888no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—944no—
615C2×Q8—3762no—
616C2×Q8C23×D4712yes—
617C2×Q8C23×D4712yes—
618C2×D4—474no—
619C2×D4—474no—
620C2×D4—472no—
621C2×D4—472no—
622C2×D4—948no—
623C2×D4—944no—
624C2×D4—944no—
625C2×D4—944no—
626C2×D4—941no—
627C2×D4—944no—
628C2×D4—941no—
629C2×D4—942no—
630C2×D4—942no—
631C2×D4—942no—
632C2×D4—3762no—
633C2×D4—1884no—
634C2×D4—1888no—
635C2×D4—1884no—
636C2×D4—1884no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—471no—
644C22×C4—471no—
645C22×C4—471no—
646C22×C4—472no—
647C22×C4—472no—
648C22×C4—944no—
649C22×C4—944no—
650C22×C4—944no—
651C22×C4—942no—
652C22×C4—942no—
653C22×C4—944no—
654C22×C4—941no—
655C22×C4—941no—
656C22×C4—3762no—
657C22×C4—3762no—
658C22×C4—3762no—
659C22×C4—1884no—
660C22×C4D4×D4712yes—
661C22×C4D4×D4711yescharacteristic
662C22×C4C23×D4712yes—
663C22×C4C23×D4711yescharacteristic
664Q16—44no—
665SD16—948no—
666SD16—1884no—
667M16—1884no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—44no—
671C2×C8—472no—
672C2×C8—472no—
673C2×C8—942no—
674C2×C8—942no—
675C2×C8C23×D4712yes—
676C2×C8C23×D4712yes—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—474no—
682C4⋊C4—472no—
683C4⋊C4—472no—
684C4⋊C4—944no—
685C4⋊C4—944no—
686C4⋊C4—944no—
687C4⋊C4—944no—
688C4⋊C4—941no—
689C4⋊C4—944no—
690C4⋊C4—941no—
691C4⋊C4C23×D4712yes—
692C4⋊C4C23×D4712yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—474no—
696C22⋊C4—474no—
697C22⋊C4—944no—
698C22⋊C4—944no—
699C22⋊C4—944no—
700C22⋊C4—944no—
701C22⋊C4—944no—
702C42—472no—
703C42—472no—
704C42—944no—
705C23—22no—
706C23—22no—
707C23—472no—
708C23—942no—
709C23—944no—
710C23—942no—
711C23—942no—
712C23—942no—
713C23—942no—
714C23—37616no—
715C23—3764no—
716C23—1888no—
717C23—1882no—
718C23—1888no—
719C23—1882no—
720C23—1882no—
721C23—1882no—
722C23—1882no—
723C23#1309405614yes—
724C23C2×D4×D4712yes—
725C23C2×D4×D4711yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—42no—
731Q8—42no—
732Q8—3764no—
733D4—474no—
734D4—948no—
735D4—944no—
736D4—942no—
737D4—942no—
738D4—942no—
739D4—3764no—
740D4—1888no—
741D4—1888no—
742D4—1882no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—472no—
756C2×C4—472no—
757C2×C4—472no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—944no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—3764no—
767C2×C4—3764no—
768C2×C4—3764no—
769C2×C4—1888no—
770C2×C4—1882no—
771C2×C4—1882no—
772C2×C4C2×D4×D4712yes—
773C2×C4C2×D4×D4711yescharacteristic
774C2×C4#41×D4712yes—
775C2×C4#1309406912yes—
776C2×C4C24×D4711yescharacteristic
777C8—22no—
778C8—22no—
779C8—942no—
780C8—942no—
781C22—22no—
782C22—22no—
783C22—28no—
784C22—942no—
785C22—944no—
786C22—942no—
787C22—942no—
788C22—37616no—
789C22—3764no—
790C22—1882no—
791C22—1882no—
792C22—1882no—
793C22—1882no—
794C22—1882no—
795C22—1884no—
796C22—1888no—
797C22#1568976212yes—
798C22C2×#1309405614yes—
799C22C2×#1309405612yes—
800C22#1568992512yes—
801C22C22×D4×D4711yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—942no—
808C4—942no—
809C4—942no—
810C4—1882no—
811C4—1882no—
812C4#1568976212yes—
813C4C2×#41×D4711yescharacteristic
814C4C2×#1309406911yescharacteristic
815C2—24no—
816C2—3762no—
817C2—1882no—
818C2—1884no—
819C2#2025547514yesdirect product factor
820C2C2×#1568976211yescharacteristic
821C2C22×#1309405611yescharacteristic
822C2C2×#1568992511yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#467C2
socleC23×C47C22×D4
prime radicalC2×#15689764C2
hypercenterC2×#467D47
hypocenterC47C2×#3314
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#15689831C2semidirect
3. #20255475C2direct (N × H)
4. C2×#15689484C2semidirect
5. C2×#15689456C2semidirect
6. C2×#15689438C2semidirect
7. C2×#15689402C2semidirect
8. C2×#15689372C2semidirect
9. C2×#15689347C2semidirect
10. C2×#15689284C2semidirect
11. C2×#15689273C2semidirect
12. C2×#15689226C2semidirect
13. C2×#15689194C2semidirect
14. C2×#15689123C2semidirect
15. C22×#13093946C2semidirect
16. C2×C47×#467C2semidirect
21. C22×#10625324C22semidirect
23. #15689831C22semidirect
26. C2×#13094023C22semidirect
32. C2×#13094000C22semidirect
36. C2×Q8×Dic47C22semidirect
41. C2×C4⋊C4×D47C22semidirect
43. #15689484C22semidirect
44. #15689456C22semidirect
45. #15689438C22semidirect
46. #15689402C22semidirect
47. #15689372C22semidirect
48. #15689347C22semidirect
49. #15689284C22semidirect
50. #15689273C22semidirect
51. #15689226C22semidirect
52. #15689194C22semidirect
53. C2×#13093957C22semidirect
54. C2×#13093957C22semidirect
55. C2×Dic47⋊C8C22semidirect
56. #15689123C22semidirect
57. C2×#13093948C22semidirect
58. C2×#13093948C22semidirect
63. C2×#13093946C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×#13093934C22semidirect
69. C22×Q16×C47C22semidirect
73. C47×#467C22semidirect
74. C2×#107×C47C22semidirect
75. C2×#103×C47C22semidirect
76. C2×#103×C47C22semidirect
103. C2×#10625324C23semidirect
107. #13094023C23semidirect
115. #13094000C23semidirect
121. Q8×Dic47C23semidirect
138. C4⋊C4×D47C23semidirect
149. #13093957C23semidirect
150. #13093957C23semidirect
151. Dic47⋊C8C23semidirect
152. #13093948C23semidirect
153. #13093948C23semidirect
161. (C2×D47)⋊C8C23semidirect
162. #13093934C23semidirect
167. C2×Q16×C47C23semidirect
182. #107×C47C23semidirect
183. #103×C47C23semidirect
184. #103×C47C23semidirect
412. C2×#467D47semidirect
421. C2×C47#3314semidirect
430. C22×Q16C2×D47semidirect
463. #467C2×D47semidirect
471. C2×#107C2×D47semidirect
476. C2×#103C2×D47semidirect
477. C2×#103C2×D47semidirect
488. C47C2×#3314semidirect
514. C2×Q16C22×D47semidirect
582. #107C22×D47semidirect
586. #103C22×D47semidirect
587. #103C22×D47semidirect
819. C2#20255475direct (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×#156897642
#202554752
C2×#156894842
C2×#156894562
C2×#156894382
C2×#156894022
C2×#156893722
C2×#156893472
C2×#156892842
C2×#156892732
C2×#156892262
C2×#156891942
C2×#156891232
C22×#130939462
C2×C47×#4672
C2×#331447