Finite Group Databasebeta

← C2×#20255466 #27092801

Subgroups — C2×#20255466 #27092801

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×#15689834C211yesmaximal, characteristic, complemented
2C2×#15689768C211yesmaximal, characteristic
3#20255466C2116yesmaximal, direct product factor
4C2×#15689485C211yesmaximal, characteristic, complemented
5C2×#15689460C211yesmaximal, characteristic, complemented
6C2×#15689438C211yesmaximal, characteristic, complemented
7C2×#15689370C211yesmaximal, characteristic, complemented
8C2×#15689365C211yesmaximal, characteristic, complemented
9C2×#15689346C211yesmaximal, characteristic, complemented
10C2×#15689286C211yesmaximal, characteristic, complemented
11C2×#15689275C211yesmaximal, characteristic, complemented
12C2×#15689223C211yesmaximal, characteristic, complemented
13C2×#15689193C211yesmaximal, characteristic, complemented
14C2×#15689121C211yesmaximal, characteristic, complemented
15C2×#102×D47C211yesmaximal, characteristic, complemented
16C2×C47×#474C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C22×Dic188C2211yescharacteristic, complemented
20C22×#10625325C2211yescharacteristic
21C22×#10625335C2211yescharacteristic
22C22×#10625324C2211yescharacteristic, complemented
23C22×C8×D47C2211yescharacteristic
24#15689834—24no—
25#15689834C2218yescomplemented
26#15689768—24no—
27#15689768C2218yes—
28C2×#13094015—21no—
29C2×#13094012C2211yescharacteristic
30C2×#13094008—21no—
31C2×#13094004C2211yescharacteristic
32C2×#13094004C2211yescharacteristic
33C2×#13094004C2211yescharacteristic, complemented
34C2×#13094000—21no—
35C2×#13094000—21no—
36C2×#13093999C2211yescharacteristic
37C2×#13093998—21no—
38C2×#13093994—21no—
39C2×C4×Dic94C2211yescharacteristic, complemented
40C2×C4×D188C2211yescharacteristic
41C2×#13093986—21no—
42C2×C4⋊C4×D47C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic, complemented
44C22×(C2×D47)⋊C4—21no—
45#15689485C2218yescomplemented
46#15689460C2218yescomplemented
47#15689438C2218yescomplemented
48#15689370C2218yescomplemented
49#15689365C2218yescomplemented
50#15689346C2218yescomplemented
51#15689286C2218yescomplemented
52#15689275C2218yescomplemented
53#15689223C2218yescomplemented
54#15689193C2218yescomplemented
55C2×#13093957C2211yescharacteristic, complemented
56#15689121C2218yescomplemented
57C2×#13093949C2211yescharacteristic, complemented
58C2×#13093947C2211yescharacteristic, complemented
59C2×#13093947C2211yescharacteristic, complemented
60C2×#13093947C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65#102×D47C2218yescomplemented
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×#13093935C2211yescharacteristic, complemented
69C2×C4⋊Q8×C47C2211yescharacteristic, complemented
70C2×C4×D4×C47C2211yescharacteristic
71C47×#474C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#107×C47C2211yescharacteristic, complemented
74C2×C4⋊C8×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C24×D47—21no—
78C2×#10625352—24no—
79C2×#10625352—22no—
80C2×#10625352—42no—
81C2×#10625352C2314yes—
82C22×Dic94C2311yescharacteristic
83C22×Dic94C2311yescharacteristic
84C22×D188—21no—
85C22×D188D411yescharacteristic
86C22×D188C2311yescharacteristic
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C2×D4×D47—24no—
90C2×D4×D47—22no—
91C2×D4×D47—42no—
92C2×D4×D47C2314yes—
93C23×Dic47—21no—
94C22×C4×D47—21no—
95C22×C4×D47—21no—
96C22×C4×D47C2311yescharacteristic
97C22×C4×D47C2311yescharacteristic
98C2×Dic188—42no—
99C2×Dic188C2314yescomplemented
100C2×#10625325—42no—
101C2×#10625325C2314yes—
102C2×#10625335—24no—
103C2×#10625335C2314yes—
104C2×#10625324—42no—
105C2×#10625324C2314yescomplemented
106C22×C47⋊C8C2311yescharacteristic
107C22×C47⋊C8C2311yescharacteristic
108C2×C8×D47—42no—
109C2×C8×D47C2314yes—
110#13094015—28no—
111#13094012—22no—
112#13094012C2314yes—
113#13094008—28no—
114#13094004—22no—
115#13094004—22no—
116#13094004—22no—
117#13094004C2314yes—
118#13094004C2314yes—
119#13094004C2314yescomplemented
120#13094000—28no—
121#13094000—28no—
122#13093999—22no—
123#13093999C2314yes—
124#13093998—28no—
125#13093994—28no—
126C4×Dic94—22no—
127C4×Dic94C2314yescomplemented
128C4×D188D414yes—
129C4×D188C2314yes—
130#13093986—28no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47—21no—
133C2×C4⋊Dic47—21no—
134C2×C4⋊Dic47D411yescharacteristic
135C2×C4⋊Dic47C2311yescharacteristic
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C4⋊C4×D47—22no—
140C4⋊C4×D47—22no—
141C4⋊C4×D47C2314yes—
142C4⋊C4×D47C2314yescomplemented
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4—28no—
150C2×(C2×D47)⋊C4D411yescharacteristic
151C2×(C2×D47)⋊C4D411yescharacteristic
152C2×C4×Dic47—21no—
153#13093957C2314yescomplemented
154#13093949C2314yescomplemented
155#13093947C2314yescomplemented
156#13093947C2314yescomplemented
157#13093947C2314yescomplemented
158#13093946C2314yes—
159#13093945C2314yes—
160#13093944C2314yes—
161#13093944C2314yes—
162(C2×D47)⋊C8C2314yes—
163(C2×D47)⋊C8C2314yescomplemented
164#13093935C2314yescomplemented
165C22×Q8×C47—21no—
166C22×D4×C47C2311yescharacteristic
167C23×C4×C47—21no—
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C4⋊Q8×C47—22no—
171C4⋊Q8×C47C2314yescomplemented
172C4×D4×C47—22no—
173C4×D4×C47C2314yes—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C22⋊C4×C47—21no—
179C2×C42×C47C2311yescharacteristic
180#107×C47C2314yescomplemented
181#107×C47C2314yescomplemented
182C4⋊C8×C47C2314yescomplemented
183#102×C47C2314yes—
184#102×C47C2314yes—
185C24×C47—21no—
186C23×D47—21no—
187C23×D47—24no—
188C23×D47—44no—
189C23×D47—44no—
190C23×D47—82no—
191C23×D47C2×D411yescharacteristic
192C23×D47C2×D411yescharacteristic
193C2×Q8×C47—24no—
194C2×Q8×C47—82no—
195C2×D4×C47—21no—
196C2×D4×C47—22no—
197C2×D4×C47#4114yes—
198C2×D4×C47C2412yes—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—24no—
203C22×C4×C47—82no—
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2411yescharacteristic
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47—44no—
210C2×C22⋊D47—44no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—24no—
215C22×Dic47—44no—
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D411yescharacteristic
218#10625352—28no—
219#10625352—44no—
220#10625352—48no—
221D4×D47—28no—
222D4×D47—44no—
223D4×D47—48no—
224C2×D188—24no—
225C2×D188—22no—
226C2×D188—22no—
227C2×D188—21no—
228C2×D188—24no—
229C2×D188—82no—
230C2×D188C2×D414yes—
231C2×D188C2412yes—
232C2×C4×D47—22no—
233C2×C4×D47—22no—
234C2×C4×D47—22no—
235C2×C4×D47—22no—
236C2×C4×D47—24no—
237C2×C4×D47—24no—
238C2×C4×D47—82no—
239C2×C4×D47—82no—
240C2×C4×D47C2×D412yes—
241C2×C4×D47C2×D412yes—
242C2×C4×D47C2412yes—
243C2×C4×D47C2412yes—
244C2×Dic94—22no—
245C2×Dic94—22no—
246C2×Dic94—22no—
247C2×Dic94—22no—
248C2×Dic94—21no—
249C2×Dic94—21no—
250C2×Dic94C2412yes—
251C2×Dic94C2412yes—
252C2×C8×C47—22no—
253C2×C8×C47—22no—
254C2×C8×C47C2412yes—
255C2×C8×C47C2412yes—
256C4⋊C4×C47—24no—
257C4⋊C4×C47—21no—
258C4⋊C4×C47—21no—
259C4⋊C4×C47—21no—
260C4⋊C4×C47C2412yes—
261C4⋊C4×C47C2412yes—
262C4⋊C4×C47C2412yes—
263C22⋊C4×C47—24no—
264C42×C47C2×D412yes—
265C42×C47C2412yes—
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)⋊C4—24no—
273(C2×D47)⋊C4C2×D414yes—
274(C2×D47)⋊C4C2×D414yes—
275C4⋊Dic47—21no—
276C4⋊Dic47—24no—
277C4⋊Dic47—24no—
278C4⋊Dic47—24no—
279C4⋊Dic47C2×D414yes—
280C4⋊Dic47C2412yes—
281Dic47⋊C4—24no—
282Dic47⋊C4—24no—
283Dic47⋊C4—24no—
284C4×Dic47—24no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8C2412yes—
288C2×C47⋊C8C2412yes—
289Dic188—44no—
290#10625325—44no—
291#10625324—44no—
292C8×D47—44no—
293C23×C47—24no—
294C23×C47—22no—
295C23×C47—42no—
296C23×C47—42no—
297C23×C47C22×D411yescharacteristic
298C22×D47—22no—
299C22×D47—22no—
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—84no—
310C22×D47—816no—
311C22×D47#13714yes—
312C22×D47C22×D412yes—
313C22×D47C22×D412yes—
314Q8×C47—84no—
315D4×C47—24no—
316D4×C47—22no—
317D4×C47C2×#4114yes—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—42no—
324C2×C4×C47—42no—
325C2×C4×C47—42no—
326C2×C4×C47—84no—
327C2×C4×C47C22×D412yes—
328C2×C4×C47C22×D412yes—
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C2×#4112yes—
331C2×C4×C47H(5,𝔽2)12yes—
332C2×C4×C47C2511yescharacteristic
333C22⋊D47—48no—
334C22⋊D47—48no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—48no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343C2×Dic47—42no—
344C2×Dic47C22×D412yes—
345C2×Dic47C22×D412yes—
346D188—28no—
347D188—22no—
348D188—22no—
349D188—42no—
350D188—84no—
351C4×D47—24no—
352C4×D47—24no—
353C4×D47—22no—
354C4×D47—22no—
355C4×D47—22no—
356C4×D47—22no—
357C4×D47—84no—
358C4×D47—84no—
359Dic94—22no—
360Dic94—22no—
361Dic94—22no—
362Dic94—22no—
363Dic94—42no—
364Dic94—42no—
365C8×C47—22no—
366C8×C47—22no—
367C47⋊C8—22no—
368C47⋊C8—22no—
369C2×#3314—471nomaximal, Sylow
370C22×C47—24no—
371C22×C47—48no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47#54612yes—
375C22×C47C2×#13712yes—
376C22×C47#57612yes—
377C22×C47C23×D411yescharacteristic
378C2×D47—22no—
379C2×D47—28no—
380C2×D47—22no—
381C2×D47—22no—
382C2×D47—22no—
383C2×D47—22no—
384C2×D47—44no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—816no—
389C2×D47—84no—
390C2×D47C2×#13714yes—
391C4×C47—22no—
392C4×C47—22no—
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—42no—
402Dic47—42no—
403Dic47—42no—
404C2×#554—471no—
405C2×#546—471no—
406#3314—4716no—
407C2×#489—471no—
408C2×#484—471no—
409C2×#480—471no—
410C2×#474D4711yescharacteristic, complemented
411C2×#468—471no—
412C2×#467—471no—
413C2×#464—471no—
414C2×#452—471no—
415C2×#450—471no—
416C2×#440—471no—
417C2×#435—471no—
418C2×#417—471no—
419C22×#102—471no—
420C2×C47—44no—
421C2×C47#331414yescomplemented
422C2×C47C2×#54611yescharacteristic
423C2×C47C22×#13711yescharacteristic
424C2×C47C2×#57611yescharacteristic
425D47—24no—
426D47—42no—
427D47—82no—
428C22×#41—471no—
429C23×D4—471no—
430C22×Q16—471no—
431C22×SD16—471no—
432C22×SD16—471no—
433C22×M16—471no—
434C23×C8—471no—
435#554—478no—
436#554—944no—
437#546—478no—
438#546—944no—
439C2×C4⋊Q8C2×D4711yescharacteristic, complemented
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—941no—
454C2×C4×D4C2×D4711yescharacteristic
455C22×C4⋊C4—471no—
456C22×C4⋊C4—471no—
457C22×C22⋊C4—941no—
458#489—478no—
459#484—478no—
460#480—478no—
461#474C2×D4718yescomplemented
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×#107C2×D4711yescharacteristic, complemented
471C2×#107C2×D4711yescharacteristic, complemented
472C2×C4⋊C8C2×D4711yescharacteristic, complemented
473#417—478no—
474C2×#103—471no—
475C2×#103—471no—
476C2×#103—471no—
477C2×#103—471no—
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—474no—
491C2×#41—942no—
492C2×#41—944no—
493C2×#41—1882no—
494C22×Q8—21no—
495C22×Q8—471no—
496C22×Q8—471no—
497C22×D4—474no—
498C22×D4—471no—
499C22×D4—471no—
500C22×D4—941no—
501C22×D4—942no—
502C22×D4—941no—
503C22×D4—944no—
504C22×D4—941no—
505C22×D4—1882no—
506C22×D4C22×D4711yescharacteristic
507C23×C4—21no—
508C23×C4—471no—
509C23×C4—471no—
510C23×C4—941no—
511C23×C4—941no—
512C23×C4—941no—
513C2×Q16—474no—
514C2×Q16—1882no—
515C2×SD16—474no—
516C2×SD16—474no—
517C2×SD16—944no—
518C2×SD16—1882no—
519C2×M16—474no—
520C2×M16—1882no—
521C22×C8—471no—
522C22×C8—471no—
523C22×C8—474no—
524C22×C8—1882no—
525C22×C8C22×D4711yescharacteristic
526C22×C8C22×D4711yescharacteristic
527C4⋊Q8—22no—
528C4⋊Q8C22×D4714yescomplemented
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—22no—
548C4×D4—474no—
549C4×D4—474no—
550C4×D4—948no—
551C4×D4C22×D4714yes—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—471no—
554C2×C4⋊C4—471no—
555C2×C4⋊C4—474no—
556C2×C4⋊C4—474no—
557C2×C4⋊C4—942no—
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×D4711yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—471no—
570C2×C22⋊C4—471no—
571C2×C22⋊C4—948no—
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—941no—
579C2×C42C22×D4711yescharacteristic
580#107—474no—
581#107C22×D4714yescomplemented
582#107C22×D4714yescomplemented
583C4⋊C8C22×D4714yescomplemented
584#103—474no—
585#103—474no—
586#103—474no—
587#103—474no—
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—471no—
600C24—944no—
601C24—941no—
602C24—3762no—
603C24—1884no—
604C24—1884no—
605#41—948no—
606#41—1884no—
607#41—1888no—
608C2×Q8—24no—
609C2×Q8—82no—
610C2×Q8—472no—
611C2×Q8—472no—
612C2×Q8—941no—
613C2×Q8—941no—
614C2×Q8—942no—
615C2×Q8—942no—
616C2×Q8—942no—
617C2×Q8—942no—
618C2×D4—21no—
619C2×D4—22no—
620C2×D4—474no—
621C2×D4—472no—
622C2×D4—944no—
623C2×D4—944no—
624C2×D4—944no—
625C2×D4—948no—
626C2×D4—944no—
627C2×D4—941no—
628C2×D4—942no—
629C2×D4—942no—
630C2×D4—3762no—
631C2×D4—1884no—
632C2×D4—1888no—
633C2×D4—1884no—
634C2×D4—1884no—
635C2×D4#1062535414yes—
636C2×D4C23×D4712yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—82no—
642C22×C4—471no—
643C22×C4—471no—
644C22×C4—472no—
645C22×C4—472no—
646C22×C4—472no—
647C22×C4—472no—
648C22×C4—944no—
649C22×C4—944no—
650C22×C4—944no—
651C22×C4—942no—
652C22×C4—942no—
653C22×C4—942no—
654C22×C4—942no—
655C22×C4—941no—
656C22×C4—941no—
657C22×C4—941no—
658C22×C4—3762no—
659C22×C4—3762no—
660C22×C4—1884no—
661C22×C4D4×D4711yescharacteristic
662C22×C4D4×D4711yescharacteristic
663C22×C4C23×D4711yescharacteristic
664Q16—1884no—
665SD16—948no—
666SD16—1884no—
667M16—1884no—
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—24no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—474no—
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⋊C4C23×D4712yes—
691C4⋊C4C23×D4712yes—
692C4⋊C4C23×D4712yes—
693C22⋊C4—24no—
694C22⋊C4—474no—
695C22⋊C4—474no—
696C22⋊C4—944no—
697C22⋊C4—944no—
698C22⋊C4—944no—
699C22⋊C4—944no—
700C22⋊C4—944no—
701C22⋊C4—944no—
702C42—944no—
703C42D4×D4712yes—
704C42C23×D4712yes—
705C23—24no—
706C23—22no—
707C23—42no—
708C23—42no—
709C23—474no—
710C23—472no—
711C23—472no—
712C23—942no—
713C23—942no—
714C23—942no—
715C23—942no—
716C23—942no—
717C23—942no—
718C23—37616no—
719C23—3764no—
720C23—1888no—
721C23—1888no—
722C23—1882no—
723C23—1882no—
724C23—1882no—
725C23C2×D4×D4711yescharacteristic
726Q8—84no—
727Q8—942no—
728Q8—942no—
729Q8—942no—
730Q8—942no—
731Q8—1882no—
732Q8—1882no—
733D4—24no—
734D4—22no—
735D4—948no—
736D4—942no—
737D4—942no—
738D4—3764no—
739D4—1888no—
740D4—1888no—
741D4—1882no—
742D4C2×#1062535414yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—472no—
753C2×C4—472no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—944no—
757C2×C4—944no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—3764no—
766C2×C4—3764no—
767C2×C4—1888no—
768C2×C4—1882no—
769C2×C4—1882no—
770C2×C4—1882no—
771C2×C4C2×D4×D4712yes—
772C2×C4C2×D4×D4712yes—
773C2×C4C2×D4×D4711yescharacteristic
774C2×C4C2×#1062535412yes—
775C2×C4#1309407012yes—
776C2×C4C24×D4711yescharacteristic
777C8—22no—
778C8—22no—
779C8—942no—
780C8—942no—
781C22—24no—
782C22—42no—
783C22—42no—
784C22—48no—
785C22—474no—
786C22—942no—
787C22—942no—
788C22—948no—
789C22—942no—
790C22—942no—
791C22—942no—
792C22—37616no—
793C22—3764no—
794C22—1882no—
795C22—1882no—
796C22—1882no—
797C22—1884no—
798C22#1568976412yes—
799C22#137×D4712yes—
800C22#1568992412yes—
801C22C22×D4×D4711yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—942no—
808C4—942no—
809C4—1882no—
810C4—1882no—
811C4—1882no—
812C4#1568976412yes—
813C4C22×#1062535411yescharacteristic
814C4C2×#1309407011yescharacteristic
815C2—44no—
816C2—944no—
817C2—3762no—
818C2—1882no—
819C2#2025546614yesdirect product factor
820C2C2×#1568976411yescharacteristic
821C2C2×#137×D4711yescharacteristic
822C2C2×#1568992411yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#474C2
socleC23×C47C22×D4
prime radicalC2×#15689768C2
hypercenterC2×#474D47
hypocenterC47C2×#3314
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#15689834C2semidirect
3. #20255466C2direct (N × H)
4. C2×#15689485C2semidirect
5. C2×#15689460C2semidirect
6. C2×#15689438C2semidirect
7. C2×#15689370C2semidirect
8. C2×#15689365C2semidirect
9. C2×#15689346C2semidirect
10. C2×#15689286C2semidirect
11. C2×#15689275C2semidirect
12. C2×#15689223C2semidirect
13. C2×#15689193C2semidirect
14. C2×#15689121C2semidirect
15. C2×#102×D47C2semidirect
16. C2×C47×#474C2semidirect
19. C22×Dic188C22semidirect
22. C22×#10625324C22semidirect
25. #15689834C22semidirect
33. C2×#13094004C22semidirect
39. C2×C4×Dic94C22semidirect
43. C2×C4⋊C4×D47C22semidirect
45. #15689485C22semidirect
46. #15689460C22semidirect
47. #15689438C22semidirect
48. #15689370C22semidirect
49. #15689365C22semidirect
50. #15689346C22semidirect
51. #15689286C22semidirect
52. #15689275C22semidirect
53. #15689223C22semidirect
54. #15689193C22semidirect
55. C2×#13093957C22semidirect
56. #15689121C22semidirect
57. C2×#13093949C22semidirect
58. C2×#13093947C22semidirect
59. C2×#13093947C22semidirect
60. C2×#13093947C22semidirect
65. #102×D47C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×#13093935C22semidirect
69. C2×C4⋊Q8×C47C22semidirect
71. C47×#474C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#107×C47C22semidirect
74. C2×C4⋊C8×C47C22semidirect
99. C2×Dic188C23semidirect
105. C2×#10625324C23semidirect
119. #13094004C23semidirect
127. C4×Dic94C23semidirect
142. C4⋊C4×D47C23semidirect
153. #13093957C23semidirect
154. #13093949C23semidirect
155. #13093947C23semidirect
156. #13093947C23semidirect
157. #13093947C23semidirect
163. (C2×D47)⋊C8C23semidirect
164. #13093935C23semidirect
171. C4⋊Q8×C47C23semidirect
180. #107×C47C23semidirect
181. #107×C47C23semidirect
182. C4⋊C8×C47C23semidirect
410. C2×#474D47semidirect
421. C2×C47#3314semidirect
439. C2×C4⋊Q8C2×D47semidirect
461. #474C2×D47semidirect
470. C2×#107C2×D47semidirect
471. C2×#107C2×D47semidirect
472. C2×C4⋊C8C2×D47semidirect
488. C47C2×#3314semidirect
528. C4⋊Q8C22×D47semidirect
581. #107C22×D47semidirect
582. #107C22×D47semidirect
583. C4⋊C8C22×D47semidirect
819. C2#20255466direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898342
C2×#156897682
#202554662
C2×#156894852
C2×#156894602
C2×#156894382
C2×#156893702
C2×#156893652
C2×#156893462
C2×#156892862
C2×#156892752
C2×#156892232
C2×#156891932
C2×#156891212
C2×#102×D472
C2×C47×#4742
C2×#331447