Finite Group Databasebeta

← C2×#20255237 #27092644

Subgroups — C2×#20255237 #27092644

Order 12032.

2350 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689826C211yesmaximal, characteristic, complemented
2C2×#15689766C211yesmaximal, characteristic, complemented
3#20255237C2116yesmaximal, direct product factor
4C2×#15689457C211yesmaximal, characteristic, complemented
5C2×#15689445C211yesmaximal, characteristic, complemented
6C2×#15689420C211yesmaximal, characteristic, complemented
7C2×#15689358C211yesmaximal, characteristic, complemented
8C2×#15689355C211yesmaximal, characteristic, complemented
9C2×#15689335C211yesmaximal, characteristic, complemented
10C2×#15689271C211yesmaximal, characteristic, complemented
11C2×#15689258C211yesmaximal, characteristic, complemented
12C2×C4×D376C211yesmaximal, characteristic, complemented
13C2×C8×D188C211yesmaximal, characteristic, complemented
14C2×#15689118C211yesmaximal, characteristic, complemented
15C2×#102×D47C211yesmaximal, characteristic, complemented
16C2×C47×#488C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C22×#10625336C2211yescharacteristic, complemented
20C22×D376C2211yescharacteristic
21C22×#10625334C2211yescharacteristic
22C22×C8×D47C2211yescharacteristic
23C22×C8×D47C2211yescharacteristic, complemented
24#15689826—24no—
25#15689826C2218yescomplemented
26#15689766—24no—
27#15689766C2218yescomplemented
28C2×#13094019—21no—
29C2×#13094009—21no—
30C2×#13094006—21no—
31C2×#13094000C2211yescharacteristic
32C2×#13093999—21no—
33C2×#13093999C2211yescharacteristic
34C2×#13093999C2211yescharacteristic, complemented
35C2×#13093997—21no—
36C2×#13093995C2211yescharacteristic
37C2×#13093994—21no—
38C2×C4×D188C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic
40C2×C4×D188C2211yescharacteristic, complemented
41C2×#13093986—21no—
42C2×#13093982C2211yescharacteristic, complemented
43C2×C4⋊C4×D47C2211yescharacteristic
44C2×C22⋊C4×D47—21no—
45#15689457C2218yescomplemented
46#15689445C2218yescomplemented
47#15689420C2218yescomplemented
48#15689358C2218yescomplemented
49#15689355C2218yescomplemented
50#15689335C2218yescomplemented
51#15689271C2218yescomplemented
52#15689258C2218yescomplemented
53C4×D376C2218yescomplemented
54C8×D188C2218yescomplemented
55C2×#13093958C2211yescharacteristic, complemented
56C2×#13093957C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
59#15689118C2218yescomplemented
60C2×#13093948C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic, complemented
63C2×#13093945C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66#102×D47C2218yescomplemented
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
69C2×#125×C47C2211yescharacteristic, complemented
70C2×#124×C47C2211yescharacteristic
71C47×#488C2218yescomplemented
72C2×#103×C47C2211yescharacteristic, complemented
73C2×#103×C47C2211yescharacteristic, complemented
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625354—22no—
79C2×#10625354—24no—
80C2×#10625354—42no—
81C2×#10625354C2314yes—
82C22×D188—21no—
83C22×D188—21no—
84C22×D188—21no—
85C22×D188D411yescharacteristic
86C22×D188C2311yescharacteristic
87C22×D188C2311yescharacteristic
88C22×C22⋊D47—21no—
89C22×C22⋊D47—21no—
90C2×D4×D47—24no—
91C2×D4×D47—22no—
92C2×D4×D47—42no—
93C2×D4×D47C2314yes—
94C22×C4×D47—21no—
95C22×C4×D47—21no—
96C22×C4×D47—21no—
97C22×C4×D47—21no—
98C22×C4×D47C2311yescharacteristic
99C22×C4×D47C2311yescharacteristic
100C2×#10625336—42no—
101C2×#10625336C2314yescomplemented
102C2×D376—24no—
103C2×D376C2314yes—
104C2×#10625334—42no—
105C2×#10625334C2314yes—
106C22×C47⋊C8C2311yescharacteristic
107C22×C47⋊C8C2311yescharacteristic
108C2×C8×D47—42no—
109C2×C8×D47—42no—
110C2×C8×D47C2314yes—
111C2×C8×D47C2314yescomplemented
112#13094019—28no—
113#13094009—28no—
114#13094006—28no—
115#13094000—22no—
116#13094000C2314yes—
117#13093999—28no—
118#13093999—22no—
119#13093999—22no—
120#13093999C2314yes—
121#13093999C2314yescomplemented
122#13093997—28no—
123#13093995—22no—
124#13093995C2314yes—
125#13093994—28no—
126C4×D188—22no—
127C4×D188—22no—
128C4×D188D414yes—
129C4×D188C2314yes—
130C4×D188C2314yes—
131C4×D188C2314yescomplemented
132#13093986—28no—
133#13093982—22no—
134#13093982C2314yescomplemented
135C2×C4⋊Dic47D411yescharacteristic
136C2×C4⋊Dic47C2311yescharacteristic
137C2×C4⋊Dic47C2311yescharacteristic
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C4⋊C4×D47—22no—
141C4⋊C4×D47C2314yes—
142C2×C22⋊Dic47—21no—
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)⋊C4D411yescharacteristic
150C2×(C2×D47)⋊C4D411yescharacteristic
151C22⋊C4×D47—28no—
152C2×C4×Dic47—21no—
153#13093958C2314yescomplemented
154#13093957C2314yescomplemented
155#13093955C2314yescomplemented
156C4⋊(C47⋊C8)C2314yescomplemented
157#13093948C2314yescomplemented
158#13093946C2314yes—
159#13093946C2314yescomplemented
160#13093945C2314yes—
161#13093944C2314yes—
162#13093944C2314yes—
163(C2×D47)⋊C8C2314yes—
164(C2×D47)⋊C8C2314yescomplemented
165C22×Q8×C47C2311yescharacteristic
166C22×D4×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169#125×C47—22no—
170#125×C47C2314yescomplemented
171#124×C47—22no—
172#124×C47C2314yes—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179C2×C42×C47C2311yescharacteristic
180#103×C47C2314yescomplemented
181#103×C47C2314yescomplemented
182#102×C47C2314yes—
183#102×C47C2314yes—
184C4×C8×C47C2314yescomplemented
185C24×C47—21no—
186C23×D47—21no—
187C23×D47—21no—
188C23×D47—24no—
189C23×D47—44no—
190C23×D47—44no—
191C23×D47—82no—
192C23×D47C2×D411yescharacteristic
193C23×D47C2×D411yescharacteristic
194C2×Q8×C47—21no—
195C2×Q8×C47—22no—
196C2×Q8×C47—22no—
197C2×Q8×C47C2412yes—
198C2×D4×C47—21no—
199C2×D4×C47—22no—
200C2×D4×C47—22no—
201C2×D4×C47C2412yes—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2411yescharacteristic
208C2×C22⋊D47—24no—
209C2×C22⋊D47—24no—
210C2×C22⋊D47—44no—
211C2×C22⋊D47—82no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47C2×D411yescharacteristic
215C22×Dic47C2×D411yescharacteristic
216#10625354—28no—
217#10625354—44no—
218#10625354—48no—
219D4×D47—28no—
220D4×D47—44no—
221D4×D47—48no—
222C2×D188—24no—
223C2×D188—21no—
224C2×D188—22no—
225C2×D188—22no—
226C2×D188—22no—
227C2×D188—24no—
228C2×D188—24no—
229C2×D188—21no—
230C2×D188—24no—
231C2×D188—44no—
232C2×D188—44no—
233C2×D188—82no—
234C2×D188C2×D414yes—
235C2×D188#4114yes—
236C2×D188C2412yes—
237C2×D188C2412yes—
238C2×C4×D47—22no—
239C2×C4×D47—22no—
240C2×C4×D47—22no—
241C2×C4×D47—22no—
242C2×C4×D47—24no—
243C2×C4×D47—24no—
244C2×C4×D47—24no—
245C2×C4×D47—24no—
246C2×C4×D47—44no—
247C2×C4×D47—82no—
248C2×C4×D47—82no—
249C2×C4×D47—82no—
250C2×C4×D47C2×D412yes—
251C2×C4×D47C2×D412yes—
252C2×C4×D47C2412yes—
253C2×C4×D47C2412yes—
254C2×C8×C47—22no—
255C2×C8×C47—22no—
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—
266C42×C47C2×D412yes—
267C42×C47C2412yes—
268C22⋊Dic47—24no—
269#10625336—44no—
270#10625334—44no—
271(C2×D47)⋊C4—24no—
272(C2×D47)⋊C4—24no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4—24no—
275(C2×D47)⋊C4—24no—
276(C2×D47)⋊C4—24no—
277(C2×D47)⋊C4C2×D414yes—
278(C2×D47)⋊C4C2×D414yes—
279C4⋊Dic47—21no—
280C4⋊Dic47—21no—
281C4⋊Dic47C2×D414yes—
282C4⋊Dic47C2412yes—
283C4⋊Dic47C2412yes—
284Dic47⋊C4—24no—
285Dic47⋊C4—24no—
286C4×Dic47—24no—
287C2×C47⋊C8—22no—
288C2×C47⋊C8—22no—
289C2×C47⋊C8C2412yes—
290C2×C47⋊C8C2412yes—
291D376—28no—
292C8×D47—44no—
293C8×D47—44no—
294C23×C47—22no—
295C23×C47—42no—
296C23×C47—42no—
297C23×C47—42no—
298C23×C47C22×D411yescharacteristic
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—24no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—48no—
308C22×D47—42no—
309C22×D47—42no—
310C22×D47—42no—
311C22×D47—42no—
312C22×D47—42no—
313C22×D47—48no—
314C22×D47—84no—
315C22×D47—816no—
316C22×D47#13514yes—
317C22×D47C22×D412yes—
318C22×D47C22×D412yes—
319Q8×C47—22no—
320Q8×C47—22no—
321Q8×C47—42no—
322D4×C47—22no—
323D4×C47—22no—
324D4×C47—42no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—42no—
331C2×C4×C47—42no—
332C2×C4×C47—42no—
333C2×C4×C47C22×D412yes—
334C2×C4×C47C22×D412yes—
335C2×C4×C47C22×D411yescharacteristic
336C2×C4×C47C2×#4112yes—
337C2×C4×C47H(5,𝔽2)12yes—
338C2×C4×C47C2511yescharacteristic
339C22⋊D47—48no—
340C22⋊D47—84no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47C22×D412yes—
348C2×Dic47C22×D412yes—
349D188—28no—
350D188—24no—
351D188—22no—
352D188—22no—
353D188—22no—
354D188—48no—
355D188—48no—
356D188—42no—
357D188—84no—
358D188C2×#4114yes—
359C4×D47—24no—
360C4×D47—24no—
361C4×D47—22no—
362C4×D47—22no—
363C4×D47—22no—
364C4×D47—22no—
365C4×D47—48no—
366C4×D47—84no—
367C4×D47—84no—
368C4×D47—84no—
369C8×C47—22no—
370C8×C47—22no—
371C47⋊C8—22no—
372C47⋊C8—22no—
373C2×#3297—471nomaximal, Sylow
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—42no—
377C22×C47—84no—
378C22×C47#54612yes—
379C22×C47C2×#13512yes—
380C22×C47#57612yes—
381C22×C47C23×D411yescharacteristic
382C2×D47—22no—
383C2×D47—28no—
384C2×D47—22no—
385C2×D47—22no—
386C2×D47—24no—
387C2×D47—22no—
388C2×D47—22no—
389C2×D47—44no—
390C2×D47—48no—
391C2×D47—42no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—816no—
397C2×D47—84no—
398C2×D47C2×#13514yes—
399C4×C47—22no—
400C4×C47—22no—
401C4×C47—42no—
402C4×C47—42no—
403C4×C47—42no—
404C4×C47#54612yes—
405C4×C47C22×#4111yescharacteristic
406C4×C47C2×H(5,𝔽2)11yescharacteristic
407Dic47—22no—
408Dic47—22no—
409Dic47—42no—
410Dic47—42no—
411C2×#553—471no—
412C2×#546—471no—
413#3297—4716no—
414C2×#488D4711yescharacteristic, complemented
415C2×#484—471no—
416C2×#482—471no—
417C2×#478—471no—
418C2×#466—471no—
419C2×#465—471no—
420C2×#463—471no—
421C2×#449—471no—
422C2×#447—471no—
423C2×C4×D8—471no—
424C2×C8×D4—471no—
425C2×#416—471no—
426C22×#102—471no—
427C2×C47—82no—
428C2×C47#329714yescomplemented
429C2×C47C2×#54611yescharacteristic
430C2×C47C22×#13511yescharacteristic
431C2×C47C2×#57611yescharacteristic
432D47—24no—
433D47—42no—
434D47—44no—
435D47—82no—
436C22×#41—471no—
437C23×D4—471no—
438C22×SD16—471no—
439C22×D8—471no—
440C22×D8—471no—
441C23×C8—471no—
442C23×C8—471no—
443#553—478no—
444#553—944no—
445#546—478no—
446#546—944no—
447C2×#126—941no—
448C2×#125C2×D4711yescharacteristic, complemented
449C2×#124C2×D4711yescharacteristic
450C2×#123—941no—
451C2×#123—941no—
452C2×C22⋊Q8—471no—
453C2×#121—471no—
454C2×#121—471no—
455C2×#121—471no—
456C2×#121—941no—
457C2×#121—941no—
458C2×#120—941no—
459C2×C4×D4—471no—
460C2×C4×D4—471no—
461C2×C4×D4—471no—
462C2×C4×D4—941no—
463C2×#117—471no—
464C22×C4⋊C4—471no—
465C22×C22⋊C4—941no—
466#488C2×D4718yescomplemented
467#484—478no—
468#482—478no—
469#478—478no—
470#466—478no—
471#465—478no—
472#463—478no—
473#449—478no—
474#447—478no—
475C4×D8—478no—
476C8×D4—478no—
477C2×#107—471no—
478C2×#107—471no—
479C2×#106—471no—
480C2×C4⋊C8—471no—
481#416—478no—
482C2×#103—471no—
483C2×#103C2×D4711yescharacteristic, complemented
484C2×#103C2×D4711yescharacteristic, complemented
485C2×#102—471no—
486C2×#102—471no—
487C2×#102—471no—
488C2×#102—471no—
489C2×#102—471no—
490C2×#102—478no—
491C2×#102C2×D4711yescharacteristic
492C2×#102C2×D4711yescharacteristic
493C2×C22⋊C8—471no—
494C2×C22⋊C8—471no—
495C2×C4×C8C2×D4711yescharacteristic, complemented
496C47C2×#329711yescharacteristic, complemented, Sylow
497C25—941no—
498C2×#41—474no—
499C2×#41—942no—
500C2×#41—944no—
501C2×#41—1882no—
502C22×Q8C22×D4711yescharacteristic
503C22×D4—474no—
504C22×D4—471no—
505C22×D4—471no—
506C22×D4—471no—
507C22×D4—941no—
508C22×D4—941no—
509C22×D4—941no—
510C22×D4—942no—
511C22×D4—941no—
512C22×D4—944no—
513C22×D4—941no—
514C22×D4—1882no—
515C22×D4C22×D4711yescharacteristic
516C23×C4—471no—
517C23×C4—471no—
518C23×C4—941no—
519C23×C4—941no—
520C23×C4—941no—
521C23×C4—941no—
522C2×SD16—474no—
523C2×SD16—1882no—
524C2×D8—474no—
525C2×D8—474no—
526C2×D8—944no—
527C2×D8—1882no—
528C22×C8—471no—
529C22×C8—471no—
530C22×C8—474no—
531C22×C8—474no—
532C22×C8—1882no—
533C22×C8—1882no—
534C22×C8C22×D4711yescharacteristic
535C22×C8C22×D4711yescharacteristic
536#126—948no—
537#125—22no—
538#125C22×D4714yescomplemented
539#124—22no—
540#124C22×D4714yes—
541#123—948no—
542#123—948no—
543C22⋊Q8—474no—
544C22⋊Q8—942no—
545#121—474no—
546#121—474no—
547#121—474no—
548#121—948no—
549#121—942no—
550#121—942no—
551#121—948no—
552#121—942no—
553#120—948no—
554C4×D4—474no—
555C4×D4—474no—
556C4×D4—474no—
557C4×D4—474no—
558C4×D4—948no—
559C4×D4—942no—
560C4×D4—942no—
561#117—474no—
562#117—942no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—471no—
566C2×C4⋊C4—471no—
567C2×C4⋊C4—471no—
568C2×C4⋊C4—474no—
569C2×C4⋊C4—942no—
570C2×C4⋊C4—941no—
571C2×C4⋊C4—941no—
572C2×C4⋊C4C22×D4711yescharacteristic
573C2×C4⋊C4C22×D4711yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—471no—
577C2×C22⋊C4—471no—
578C2×C22⋊C4—948no—
579C2×C22⋊C4—941no—
580C2×C22⋊C4—941no—
581C2×C22⋊C4—941no—
582C2×C22⋊C4—941no—
583C2×C22⋊C4—941no—
584C2×C22⋊C4—941no—
585C2×C22⋊C4—941no—
586C2×C42—941no—
587C2×C42C22×D4711yescharacteristic
588#107—474no—
589#107—474no—
590#106—474no—
591C4⋊C8—474no—
592#103—474no—
593#103C22×D4714yescomplemented
594#103C22×D4714yescomplemented
595#102—474no—
596#102—474no—
597#102—474no—
598#102—474no—
599#102—474no—
600#102C22×D4714yes—
601#102C22×D4714yes—
602C22⋊C8—474no—
603C22⋊C8—474no—
604C4×C8C22×D4714yescomplemented
605C24—21no—
606C24—471no—
607C24—471no—
608C24—944no—
609C24—941no—
610C24—941no—
611C24—3762no—
612C24—1884no—
613C24—1884no—
614#41—948no—
615#41—1884no—
616#41—1888no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D4712yes—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—474no—
625C2×D4—474no—
626C2×D4—472no—
627C2×D4—472no—
628C2×D4—944no—
629C2×D4—944no—
630C2×D4—944no—
631C2×D4—944no—
632C2×D4—944no—
633C2×D4—948no—
634C2×D4—944no—
635C2×D4—941no—
636C2×D4—941no—
637C2×D4—942no—
638C2×D4—942no—
639C2×D4—942no—
640C2×D4—3762no—
641C2×D4—3762no—
642C2×D4—1884no—
643C2×D4—1884no—
644C2×D4—1884no—
645C2×D4—1888no—
646C2×D4—1884no—
647C2×D4C23×D4712yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—471no—
652C22×C4—471no—
653C22×C4—472no—
654C22×C4—472no—
655C22×C4—472no—
656C22×C4—472no—
657C22×C4—944no—
658C22×C4—944no—
659C22×C4—942no—
660C22×C4—942no—
661C22×C4—942no—
662C22×C4—942no—
663C22×C4—941no—
664C22×C4—941no—
665C22×C4—944no—
666C22×C4—944no—
667C22×C4—3762no—
668C22×C4—3762no—
669C22×C4—3762no—
670C22×C4—1884no—
671C22×C4D4×D4711yescharacteristic
672C22×C4D4×D4711yescharacteristic
673C22×C4C23×D4711yescharacteristic
674SD16—1884no—
675D8—948no—
676D8—1884no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—472no—
680C2×C8—472no—
681C2×C8—942no—
682C2×C8—942no—
683C2×C8—1884no—
684C2×C8—1884no—
685C2×C8C23×D4712yes—
686C2×C8C23×D4712yes—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—474no—
692C4⋊C4—472no—
693C4⋊C4—472no—
694C4⋊C4—944no—
695C4⋊C4—944no—
696C4⋊C4—941no—
697C4⋊C4—941no—
698C4⋊C4C23×D4712yes—
699C4⋊C4C23×D4712yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—474no—
703C22⋊C4—474no—
704C22⋊C4—944no—
705C22⋊C4—944no—
706C22⋊C4—944no—
707C22⋊C4—944no—
708C22⋊C4—944no—
709C22⋊C4—944no—
710C22⋊C4—944no—
711C42—944no—
712C42D4×D4712yes—
713C42C23×D4712yes—
714C23—22no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—474no—
719C23—472no—
720C23—472no—
721C23—942no—
722C23—942no—
723C23—942no—
724C23—944no—
725C23—942no—
726C23—942no—
727C23—942no—
728C23—942no—
729C23—3764no—
730C23—37616no—
731C23—1888no—
732C23—1888no—
733C23—1882no—
734C23—1882no—
735C23—1882no—
736C23—1882no—
737C23—1882no—
738C23C2×D4×D4711yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—474no—
746D4—948no—
747D4—944no—
748D4—942no—
749D4—942no—
750D4—942no—
751D4—3764no—
752D4—3764no—
753D4—1888no—
754D4—1888no—
755D4—1888no—
756D4—1882no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—472no—
766C2×C4—472no—
767C2×C4—942no—
768C2×C4—942no—
769C2×C4—944no—
770C2×C4—944no—
771C2×C4—942no—
772C2×C4—942no—
773C2×C4—942no—
774C2×C4—942no—
775C2×C4—942no—
776C2×C4—942no—
777C2×C4—3764no—
778C2×C4—3764no—
779C2×C4—3764no—
780C2×C4—1888no—
781C2×C4—1882no—
782C2×C4—1882no—
783C2×C4C2×D4×D4712yes—
784C2×C4C2×D4×D4712yes—
785C2×C4C2×D4×D4711yescharacteristic
786C2×C4#41×D4712yes—
787C2×C4#1309407012yes—
788C2×C4C24×D4711yescharacteristic
789C8—22no—
790C8—22no—
791C8—942no—
792C8—942no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—84no—
797C22—474no—
798C22—948no—
799C22—942no—
800C22—942no—
801C22—942no—
802C22—942no—
803C22—944no—
804C22—942no—
805C22—37616no—
806C22—3764no—
807C22—1882no—
808C22—1882no—
809C22—1882no—
810C22—1884no—
811C22—1888no—
812C22—1882no—
813C22—1882no—
814C22#1568976612yes—
815C22#135×D4712yes—
816C22#1568992512yes—
817C22C22×D4×D4711yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—942no—
824C4—942no—
825C4—1882no—
826C4—1882no—
827C4#1568976612yes—
828C4C2×#41×D4711yescharacteristic
829C4C2×#1309407011yescharacteristic
830C2—82no—
831C2—944no—
832C2—3762no—
833C2—1882no—
834C2—1884no—
835C2#2025523714yesdirect product factor
836C2C2×#1568976611yescharacteristic
837C2C2×#135×D4711yescharacteristic
838C2C2×#1568992511yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#488C2
socleC23×C47C22×D4
hypercenterC2×#488D47
hypocenterC47C2×#3297
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#15689826C2semidirect
2. C2×#15689766C2semidirect
3. #20255237C2direct (N × H)
4. C2×#15689457C2semidirect
5. C2×#15689445C2semidirect
6. C2×#15689420C2semidirect
7. C2×#15689358C2semidirect
8. C2×#15689355C2semidirect
9. C2×#15689335C2semidirect
10. C2×#15689271C2semidirect
11. C2×#15689258C2semidirect
12. C2×C4×D376C2semidirect
13. C2×C8×D188C2semidirect
14. C2×#15689118C2semidirect
15. C2×#102×D47C2semidirect
16. C2×C47×#488C2semidirect
19. C22×#10625336C22semidirect
23. C22×C8×D47C22semidirect
25. #15689826C22semidirect
27. #15689766C22semidirect
34. C2×#13093999C22semidirect
40. C2×C4×D188C22semidirect
42. C2×#13093982C22semidirect
45. #15689457C22semidirect
46. #15689445C22semidirect
47. #15689420C22semidirect
48. #15689358C22semidirect
49. #15689355C22semidirect
50. #15689335C22semidirect
51. #15689271C22semidirect
52. #15689258C22semidirect
53. C4×D376C22semidirect
54. C8×D188C22semidirect
55. C2×#13093958C22semidirect
56. C2×#13093957C22semidirect
57. C2×#13093955C22semidirect
58. C2×C4⋊(C47⋊C8)C22semidirect
59. #15689118C22semidirect
60. C2×#13093948C22semidirect
62. C2×#13093946C22semidirect
66. #102×D47C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
69. C2×#125×C47C22semidirect
71. C47×#488C22semidirect
72. C2×#103×C47C22semidirect
73. C2×#103×C47C22semidirect
76. C2×C4×C8×C47C22semidirect
101. C2×#10625336C23semidirect
111. C2×C8×D47C23semidirect
121. #13093999C23semidirect
131. C4×D188C23semidirect
134. #13093982C23semidirect
153. #13093958C23semidirect
154. #13093957C23semidirect
155. #13093955C23semidirect
156. C4⋊(C47⋊C8)C23semidirect
157. #13093948C23semidirect
159. #13093946C23semidirect
164. (C2×D47)⋊C8C23semidirect
170. #125×C47C23semidirect
180. #103×C47C23semidirect
181. #103×C47C23semidirect
184. C4×C8×C47C23semidirect
414. C2×#488D47semidirect
428. C2×C47#3297semidirect
448. C2×#125C2×D47semidirect
466. #488C2×D47semidirect
483. C2×#103C2×D47semidirect
484. C2×#103C2×D47semidirect
495. C2×C4×C8C2×D47semidirect
496. C47C2×#3297semidirect
538. #125C22×D47semidirect
593. #103C22×D47semidirect
594. #103C22×D47semidirect
604. C4×C8C22×D47semidirect
835. C2#20255237direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898262
C2×#156897662
#202552372
C2×#156894572
C2×#156894452
C2×#156894202
C2×#156893582
C2×#156893552
C2×#156893352
C2×#156892712
C2×#156892582
C2×C4×D3762
C2×C8×D1882
C2×#156891182
C2×#102×D472
C2×C47×#4882
C2×#329747