Finite Group Databasebeta

← C2×#20255470 #27092805

Subgroups — C2×#20255470 #27092805

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×#15689828C211yesmaximal, characteristic, complemented
2C2×#15689761C211yesmaximal, characteristic
3#20255470C2116yesmaximal, direct product factor
4C2×#15689484C211yesmaximal, characteristic, complemented
5C2×#15689457C211yesmaximal, characteristic, complemented
6C2×#15689436C211yesmaximal, characteristic, complemented
7C2×#15689401C211yesmaximal, characteristic, complemented
8C2×#15689369C211yesmaximal, characteristic, complemented
9C2×#15689363C211yesmaximal, characteristic, complemented
10C2×#15689348C211yesmaximal, characteristic, complemented
11C2×#15689285C211yesmaximal, characteristic, complemented
12C2×#15689275C211yesmaximal, characteristic, complemented
13C2×#15689220C211yesmaximal, characteristic, complemented
14C2×#15689192C211yesmaximal, characteristic, complemented
15C2×#102×D47C211yesmaximal, characteristic, complemented
16C2×C47×#417C211yesmaximal, characteristic, complemented
17C22×D4×D47C2211yescharacteristic
18C22×#10625337C2211yescharacteristic, complemented
19C22×#10625325C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×C8×D47C2211yescharacteristic
22#15689828—24no—
23#15689828C2218yescomplemented
24#15689761—24no—
25#15689761C2218yes—
26C2×#13094023C2211yescharacteristic, complemented
27C2×#13094014—21no—
28C2×#13094013C2211yescharacteristic
29C2×#13094007—21no—
30C2×#13094004C2211yescharacteristic
31C2×#13094003—21no—
32C2×#13094003C2211yescharacteristic, complemented
33C2×#13094002—21no—
34C2×#13094000C2211yescharacteristic
35C2×#13093998C2211yescharacteristic
36C2×#13093996—21no—
37C2×#13093992—21no—
38C2×#13093989C2211yescharacteristic, complemented
39C2×D4×Dic47C2211yescharacteristic
40C2×C4×C22⋊D47—21no—
41C2×C4×C22⋊D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43C22×(C2×D47)⋊C4—21no—
44#15689484C2218yescomplemented
45#15689457C2218yescomplemented
46#15689436C2218yescomplemented
47#15689401C2218yescomplemented
48#15689369C2218yescomplemented
49#15689363C2218yescomplemented
50#15689348C2218yescomplemented
51#15689285C2218yescomplemented
52#15689275C2218yescomplemented
53#15689220C2218yescomplemented
54#15689192C2218yescomplemented
55C2×#13093958C2211yescharacteristic, complemented
56C2×#13093957C2211yescharacteristic, complemented
57C2×#13093957C2211yescharacteristic, complemented
58C2×Dic47⋊C8C2211yescharacteristic, complemented
59C2×#13093949C2211yescharacteristic, complemented
60C2×#13093948C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65#102×D47C2218yescomplemented
66C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic, complemented
69C22×#41×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic, complemented
71C22×C4⋊C4×C47C2211yescharacteristic, complemented
72C47×#417C2218yescomplemented
73C2×#103×C47C2211yescharacteristic, complemented
74C2×#103×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C24×D47—21no—
78C22×Dic94—21no—
79C22×Dic94C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C22×C22⋊D47—21no—
82C22×C22⋊D47—21no—
83C22×C22⋊D47D411yescharacteristic
84C2×D4×D47—24no—
85C2×D4×D47—22no—
86C2×D4×D47—42no—
87C2×D4×D47C2314yes—
88C23×Dic47—21no—
89C22×C4×D47—21no—
90C22×C4×D47C2311yescharacteristic
91C2×#10625337—42no—
92C2×#10625337C2314yescomplemented
93C2×#10625325—42no—
94C2×#10625325C2314yes—
95C2×#10625335—24no—
96C2×#10625335C2314yes—
97C22×C47⋊C8C2311yescharacteristic
98C22×C47⋊C8C2311yescharacteristic
99C2×C8×D47—42no—
100C2×C8×D47C2314yes—
101#13094023—22no—
102#13094023C2314yescomplemented
103#13094014—28no—
104#13094013—22no—
105#13094013C2314yes—
106#13094007—28no—
107#13094004—22no—
108#13094004C2314yes—
109#13094003—22no—
110#13094003—28no—
111#13094003C2314yescomplemented
112#13094002—28no—
113#13094000—22no—
114#13094000C2314yes—
115#13093998—22no—
116#13093998C2314yes—
117#13093996—28no—
118#13093992—28no—
119#13093989—22no—
120#13093989C2314yescomplemented
121D4×Dic47—22no—
122D4×Dic47C2314yes—
123C4×C22⋊D47—28no—
124C4×C22⋊D47D414yes—
125C4×C22⋊D47C2314yes—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4D411yescharacteristic
135C4⋊C4×D47—22no—
136C4⋊C4×D47C2314yes—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
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)⋊C4—28no—
146C2×(C2×D47)⋊C4D411yescharacteristic
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093958C2314yescomplemented
150#13093957C2314yescomplemented
151#13093957C2314yescomplemented
152Dic47⋊C8C2314yescomplemented
153#13093949C2314yescomplemented
154#13093948C2314yescomplemented
155#13093946C2314yes—
156#13093945C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159C22⋊(C47⋊C8)C2314yescomplemented
160(C2×D47)⋊C8C2314yes—
161#13093934C2314yescomplemented
162C2×#41×C47—22no—
163C2×#41×C47—24no—
164C2×#41×C47—42no—
165C2×#41×C47C2314yes—
166C22×Q8×C47C2311yescharacteristic
167C22×D4×C47—21no—
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C23×C4×C47—21no—
171C23×C4×C47C2311yescharacteristic
172C2×M16×C47—42no—
173C2×M16×C47C2314yescomplemented
174C22×C8×C47C2311yescharacteristic
175C22×C8×C47C2311yescharacteristic
176C2×C4⋊C4×C47—22no—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C4⋊C4×C47C2314yescomplemented
181#103×C47C2314yescomplemented
182#103×C47C2314yescomplemented
183#102×C47C2314yes—
184#102×C47C2314yes—
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47—24no—
189C23×D47—44no—
190C23×D47—44no—
191C23×D47—82no—
192C23×D47C2×D411yescharacteristic
193#41×C47—28no—
194#41×C47—44no—
195#41×C47—48no—
196C2×Q8×C47—21no—
197C2×Q8×C47—22no—
198C2×Q8×C47—22no—
199C2×Q8×C47C2412yes—
200C2×D4×C47—24no—
201C2×D4×C47—21no—
202C2×D4×C47—22no—
203C2×D4×C47—44no—
204C2×D4×C47#4114yes—
205C2×D4×C47C2412yes—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—24no—
212C22×C4×C47—24no—
213C22×C4×C47—44no—
214C22×C4×C47—82no—
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D412yes—
217C22×C4×C47C2412yes—
218C22×C4×C47C2411yescharacteristic
219C2×C22⋊D47—24no—
220C2×C22⋊D47—24no—
221C2×C22⋊D47—24no—
222C2×C22⋊D47—44no—
223C2×C22⋊D47—82no—
224C2×C22⋊D47C2×D414yes—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—24no—
229C22×Dic47—82no—
230C22×Dic47C2×D411yescharacteristic
231C22×Dic47C2×D411yescharacteristic
232C22×Dic47C2×D411yescharacteristic
233D4×D47—28no—
234D4×D47—44no—
235D4×D47—48no—
236C2×D188—22no—
237C2×D188—22no—
238C2×D188—21no—
239C2×D188C2412yes—
240C2×C4×D47—22no—
241C2×C4×D47—22no—
242C2×C4×D47—24no—
243C2×C4×D47—82no—
244C2×C4×D47C2×D412yes—
245C2×C4×D47C2412yes—
246C2×Dic94—22no—
247C2×Dic94—22no—
248C2×Dic94—21no—
249C2×Dic94—24no—
250C2×Dic94—82no—
251C2×Dic94C2412yes—
252M16×C47—44no—
253C2×C8×C47—22no—
254C2×C8×C47—22no—
255C2×C8×C47C2412yes—
256C2×C8×C47C2412yes—
257C4⋊C4×C47—21no—
258C4⋊C4×C47—21no—
259C4⋊C4×C47—24no—
260C4⋊C4×C47C2412yes—
261C4⋊C4×C47C2412yes—
262C22⋊Dic47—24no—
263C22⋊Dic47—24no—
264C22⋊Dic47C2×D414yes—
265#10625337—44no—
266#10625335—28no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4—24no—
272(C2×D47)⋊C4C2×D414yes—
273C4⋊Dic47—21no—
274C4⋊Dic47—21no—
275C4⋊Dic47—24no—
276C4⋊Dic47C2412yes—
277C4⋊Dic47C2412yes—
278Dic47⋊C4—24no—
279Dic47⋊C4—24no—
280Dic47⋊C4—24no—
281Dic47⋊C4—24no—
282Dic47⋊C4—24no—
283Dic47⋊C4C2×D414yes—
284C4×Dic47—24no—
285C4×Dic47C2×D412yes—
286C4×Dic47C2412yes—
287C2×C47⋊C8—22no—
288C2×C47⋊C8—22no—
289C2×C47⋊C8C2412yes—
290C2×C47⋊C8C2412yes—
291#10625325—44no—
292C8×D47—44no—
293C23×C47—24no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—42no—
299C23×C47—42no—
300C23×C47C22×D412yes—
301C23×C47C22×D411yescharacteristic
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—48no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—42no—
309C22×D47—48no—
310C22×D47—84no—
311C22×D47—816no—
312C22×D47#13714yes—
313C22×D47C22×D412yes—
314Q8×C47—22no—
315Q8×C47—22no—
316Q8×C47—42no—
317D4×C47—24no—
318D4×C47—22no—
319D4×C47—48no—
320D4×C47C2×#4114yes—
321C2×C4×C47—22no—
322C2×C4×C47—24no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—48no—
329C2×C4×C47—42no—
330C2×C4×C47—42no—
331C2×C4×C47—42no—
332C2×C4×C47—84no—
333C2×C4×C47C22×D412yes—
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C2×#4112yes—
336C2×C4×C47H(5,𝔽2)12yes—
337C2×C4×C47C2511yescharacteristic
338C22⋊D47—28no—
339C22⋊D47—48no—
340C22⋊D47—84no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349C2×Dic47—42no—
350C2×Dic47—84no—
351C2×Dic47C22×D412yes—
352C2×Dic47C22×D412yes—
353C2×Dic47C22×D412yes—
354D188—22no—
355D188—22no—
356D188—42no—
357C4×D47—24no—
358C4×D47—22no—
359C4×D47—22no—
360C4×D47—84no—
361Dic94—22no—
362Dic94—22no—
363Dic94—42no—
364Dic94—84no—
365C8×C47—22no—
366C8×C47—22no—
367C47⋊C8—22no—
368C47⋊C8—22no—
369C2×#3314—471nomaximal, Sylow
370C22×C47—24no—
371C22×C47—22no—
372C22×C47—22no—
373C22×C47—22no—
374C22×C47—48no—
375C22×C47—44no—
376C22×C47—42no—
377C22×C47—42no—
378C22×C47#54612yes—
379C22×C47C2×#13712yes—
380C22×C47#57612yes—
381C22×C47C23×D411yescharacteristic
382C2×D47—22no—
383C2×D47—28no—
384C2×D47—22no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—816no—
389C2×D47—84no—
390C2×D47C2×#13714yes—
391C4×C47—22no—
392C4×C47—42no—
393C4×C47—42no—
394C4×C47—42no—
395C4×C47#54612yes—
396C4×C47C22×#4111yescharacteristic
397C4×C47C2×H(5,𝔽2)11yescharacteristic
398Dic47—22no—
399Dic47—22no—
400Dic47—22no—
401Dic47—42no—
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×#467—471no—
413C2×#464—471no—
414C2×#452—471no—
415C2×#450—471no—
416C2×#440—471no—
417C2×#435—471no—
418C2×#417D4711yescharacteristic, complemented
419C22×#102—471no—
420C2×C47—44no—
421C2×C47—42no—
422C2×C47#331414yescomplemented
423C2×C47C2×#54611yescharacteristic
424C2×C47C22×#13711yescharacteristic
425C2×C47C2×#57611yescharacteristic
426D47—24no—
427D47—82no—
428C22×#41C2×D4711yescharacteristic
429C23×D4—471no—
430C22×Q16—471no—
431C22×SD16—471no—
432C22×SD16—471no—
433C22×M16C2×D4711yescharacteristic, complemented
434C23×C8—471no—
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—471no—
445C2×C22⋊Q8—471no—
446C2×C22⋊Q8—941no—
447C2×C22⋊Q8—941no—
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⋊C4C2×D4711yescharacteristic, complemented
457C22×C22⋊C4—941no—
458#489—478no—
459#484—478no—
460#480—478no—
461#474—478no—
462#468—478no—
463#467—478no—
464#464—478no—
465#452—478no—
466#450—478no—
467#440—478no—
468#435—478no—
469C2×#107—471no—
470C2×#107—471no—
471C2×#107—471no—
472C2×C4⋊C8—471no—
473#417C2×D4718yescomplemented
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×#102C2×D4711yescharacteristic
484C2×#102C2×D4711yescharacteristic
485C2×C22⋊C8—471no—
486C2×C22⋊C8—471no—
487C2×#97—471no—
488C47C2×#331411yescharacteristic, complemented, Sylow
489C25—941no—
490C2×#41—22no—
491C2×#41—24no—
492C2×#41—42no—
493C2×#41C22×D4714yes—
494C22×Q8—471no—
495C22×Q8—941no—
496C22×Q8C22×D4711yescharacteristic
497C22×D4—21no—
498C22×D4—471no—
499C22×D4—474no—
500C22×D4—471no—
501C22×D4—942no—
502C22×D4—941no—
503C22×D4—944no—
504C22×D4—941no—
505C22×D4—1882no—
506C22×D4C22×D4711yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—471no—
510C23×C4—941no—
511C23×C4—941no—
512C23×C4C22×D4711yescharacteristic
513C2×Q16—474no—
514C2×Q16—1882no—
515C2×SD16—474no—
516C2×SD16—474no—
517C2×SD16—944no—
518C2×SD16—1882no—
519C2×M16—42no—
520C2×M16C22×D4714yescomplemented
521C22×C8—471no—
522C22×C8—471no—
523C22×C8—474no—
524C22×C8—1882no—
525C22×C8C22×D4711yescharacteristic
526C22×C8C22×D4711yescharacteristic
527C4⋊Q8—474no—
528C4⋊Q8—942no—
529#125—948no—
530#124—474no—
531#124—942no—
532#123—948no—
533C22⋊Q8—474no—
534C22⋊Q8—474no—
535C22⋊Q8—474no—
536C22⋊Q8—948no—
537C22⋊Q8—948no—
538C22⋊Q8—942no—
539C22⋊Q8—942no—
540C22⋊Q8—942no—
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—22no—
554C2×C4⋊C4—471no—
555C2×C4⋊C4—471no—
556C2×C4⋊C4—471no—
557C2×C4⋊C4—474no—
558C2×C4⋊C4—942no—
559C2×C4⋊C4—941no—
560C2×C4⋊C4—941no—
561C2×C4⋊C4—941no—
562C2×C4⋊C4—941no—
563C2×C4⋊C4—941no—
564C2×C4⋊C4—941no—
565C2×C4⋊C4C22×D4711yescharacteristic
566C2×C4⋊C4C22×D4711yescharacteristic
567C2×C4⋊C4C22×D4714yescomplemented
568C2×C22⋊C4—471no—
569C2×C22⋊C4—471no—
570C2×C22⋊C4—948no—
571C2×C22⋊C4—941no—
572C2×C22⋊C4—941no—
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#107—474no—
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#102C22×D4714yes—
593#102C22×D4714yes—
594C22⋊C8—474no—
595C22⋊C8—474no—
596#97—474no—
597C24—21no—
598C24—471no—
599C24—944no—
600C24—941no—
601C24—3762no—
602C24—1884no—
603C24—1884no—
604C24D4×D4711yescharacteristic
605#41—28no—
606#41—44no—
607#41—48no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—472no—
612C2×Q8—944no—
613C2×Q8—941no—
614C2×Q8—942no—
615C2×Q8—942no—
616C2×Q8—3762no—
617C2×Q8C23×D4712yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—44no—
622C2×D4—474no—
623C2×D4—472no—
624C2×D4—944no—
625C2×D4—944no—
626C2×D4—948no—
627C2×D4—944no—
628C2×D4—941no—
629C2×D4—942no—
630C2×D4—942no—
631C2×D4—3762no—
632C2×D4—1884no—
633C2×D4—1888no—
634C2×D4—1884no—
635C2×D4#1062535014yes—
636C2×D4C23×D4712yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—82no—
646C22×C4—471no—
647C22×C4—471no—
648C22×C4—471no—
649C22×C4—472no—
650C22×C4—472no—
651C22×C4—944no—
652C22×C4—944no—
653C22×C4—942no—
654C22×C4—942no—
655C22×C4—941no—
656C22×C4—941no—
657C22×C4—941no—
658C22×C4—3762no—
659C22×C4—3762no—
660C22×C4D4×D4712yes—
661C22×C4D4×D4711yescharacteristic
662C22×C4C23×D4712yes—
663C22×C4C23×D4711yescharacteristic
664Q16—1884no—
665SD16—948no—
666SD16—1884no—
667M16—44no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—472no—
671C2×C8—472no—
672C2×C8—942no—
673C2×C8—942no—
674C2×C8—1884no—
675C2×C8C23×D4712yes—
676C2×C8C23×D4712yes—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—24no—
680C4⋊C4—474no—
681C4⋊C4—472no—
682C4⋊C4—472no—
683C4⋊C4—944no—
684C4⋊C4—944no—
685C4⋊C4—944no—
686C4⋊C4—944no—
687C4⋊C4—944no—
688C4⋊C4—944no—
689C4⋊C4—941no—
690C4⋊C4—941no—
691C4⋊C4C23×D4712yes—
692C4⋊C4C23×D4712yes—
693C22⋊C4—474no—
694C22⋊C4—474no—
695C22⋊C4—944no—
696C22⋊C4—944no—
697C22⋊C4—944no—
698C22⋊C4—944no—
699C22⋊C4—944no—
700C22⋊C4—944no—
701C22⋊C4—944no—
702C42—472no—
703C42—472no—
704C42—944no—
705C23—22no—
706C23—24no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—474no—
713C23—472no—
714C23—942no—
715C23—942no—
716C23—942no—
717C23—37616no—
718C23—3764no—
719C23—1888no—
720C23—1888no—
721C23—1882no—
722C23—1882no—
723C23—1882no—
724C23C2×D4×D4712yes—
725C23C2×D4×D4711yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—942no—
730Q8—942no—
731Q8—3764no—
732Q8—1882no—
733D4—24no—
734D4—22no—
735D4—48no—
736D4—948no—
737D4—942no—
738D4—942no—
739D4—3764no—
740D4—1888no—
741D4—1882no—
742D4C2×#1062535014yes—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—84no—
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—942no—
767C2×C4—3764no—
768C2×C4—3764no—
769C2×C4—1882no—
770C2×C4—1882no—
771C2×C4—1882no—
772C2×C4C2×D4×D4712yes—
773C2×C4C2×D4×D4711yescharacteristic
774C2×C4C2×#1062535012yes—
775C2×C4#1309406912yes—
776C2×C4C24×D4711yescharacteristic
777C8—22no—
778C8—22no—
779C8—942no—
780C8—942no—
781C22—22no—
782C22—24no—
783C22—22no—
784C22—22no—
785C22—42no—
786C22—42no—
787C22—44no—
788C22—48no—
789C22—474no—
790C22—942no—
791C22—942no—
792C22—948no—
793C22—37616no—
794C22—3764no—
795C22—1882no—
796C22—1882no—
797C22—1882no—
798C22#1568976312yes—
799C22#137×D4712yes—
800C22#1568992712yes—
801C22C22×D4×D4711yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—942no—
807C4—942no—
808C4—942no—
809C4—1882no—
810C4—1882no—
811C4—1882no—
812C4#1568976312yes—
813C4C22×#1062535011yescharacteristic
814C4C2×#1309406911yescharacteristic
815C2—42no—
816C2—44no—
817C2—944no—
818C2—3762no—
819C2#2025547014yesdirect product factor
820C2C2×#1568976311yescharacteristic
821C2C2×#137×D4711yescharacteristic
822C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#417C2
socleC23×C47C22×D4
prime radicalC2×#15689761C2
hypercenterC2×#417D47
hypocenterC47C2×#3314
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#15689828C2semidirect
3. #20255470C2direct (N × H)
4. C2×#15689484C2semidirect
5. C2×#15689457C2semidirect
6. C2×#15689436C2semidirect
7. C2×#15689401C2semidirect
8. C2×#15689369C2semidirect
9. C2×#15689363C2semidirect
10. C2×#15689348C2semidirect
11. C2×#15689285C2semidirect
12. C2×#15689275C2semidirect
13. C2×#15689220C2semidirect
14. C2×#15689192C2semidirect
15. C2×#102×D47C2semidirect
16. C2×C47×#417C2semidirect
18. C22×#10625337C22semidirect
23. #15689828C22semidirect
26. C2×#13094023C22semidirect
32. C2×#13094003C22semidirect
38. C2×#13093989C22semidirect
44. #15689484C22semidirect
45. #15689457C22semidirect
46. #15689436C22semidirect
47. #15689401C22semidirect
48. #15689369C22semidirect
49. #15689363C22semidirect
50. #15689348C22semidirect
51. #15689285C22semidirect
52. #15689275C22semidirect
53. #15689220C22semidirect
54. #15689192C22semidirect
55. C2×#13093958C22semidirect
56. C2×#13093957C22semidirect
57. C2×#13093957C22semidirect
58. C2×Dic47⋊C8C22semidirect
59. C2×#13093949C22semidirect
60. C2×#13093948C22semidirect
65. #102×D47C22semidirect
66. C2×C22⋊(C47⋊C8)C22semidirect
68. C2×#13093934C22semidirect
70. C22×M16×C47C22semidirect
71. C22×C4⋊C4×C47C22semidirect
72. C47×#417C22semidirect
73. C2×#103×C47C22semidirect
74. C2×#103×C47C22semidirect
92. C2×#10625337C23semidirect
102. #13094023C23semidirect
111. #13094003C23semidirect
120. #13093989C23semidirect
149. #13093958C23semidirect
150. #13093957C23semidirect
151. #13093957C23semidirect
152. Dic47⋊C8C23semidirect
153. #13093949C23semidirect
154. #13093948C23semidirect
159. C22⋊(C47⋊C8)C23semidirect
161. #13093934C23semidirect
173. C2×M16×C47C23semidirect
180. C2×C4⋊C4×C47C23semidirect
181. #103×C47C23semidirect
182. #103×C47C23semidirect
418. C2×#417D47semidirect
422. C2×C47#3314semidirect
433. C22×M16C2×D47semidirect
456. C22×C4⋊C4C2×D47semidirect
473. #417C2×D47semidirect
476. C2×#103C2×D47semidirect
477. C2×#103C2×D47semidirect
488. C47C2×#3314semidirect
520. C2×M16C22×D47semidirect
567. C2×C4⋊C4C22×D47semidirect
586. #103C22×D47semidirect
587. #103C22×D47semidirect
819. C2#20255470direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898282
C2×#156897612
#202554702
C2×#156894842
C2×#156894572
C2×#156894362
C2×#156894012
C2×#156893692
C2×#156893632
C2×#156893482
C2×#156892852
C2×#156892752
C2×#156892202
C2×#156891922
C2×#102×D472
C2×C47×#4172
C2×#331447