Finite Group Databasebeta

← C2×#20253574 #27084511

Subgroups — C2×#20253574 #27084511

Order 12032.

2274 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×#15689744C211yesmaximal, characteristic, complemented
2C2×#15689597C211yesmaximal, characteristic, complemented
3#20253574C2116yesmaximal, direct product factor
4C2×#15689465C211yesmaximal, characteristic, complemented
5C2×#15689448C211yesmaximal, characteristic, complemented
6C2×#15689414C211yesmaximal, characteristic, complemented
7C2×#15689404C211yesmaximal, characteristic, complemented
8C2×#15689339C211yesmaximal, characteristic, complemented
9C2×#15689339C211yesmaximal, characteristic, complemented
10C2×#15689276C211yesmaximal, characteristic, complemented
11C2×#15689259C211yesmaximal, characteristic
12C2×#15689236C211yesmaximal, characteristic, complemented
13C2×#15689225C211yesmaximal, characteristic, complemented
14C2×C4×#10625325C211yesmaximal, characteristic, complemented
15C2×C4×D376C211yesmaximal, characteristic, complemented
16C2×C47×#433C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×D376C2211yescharacteristic
21C22×D376C2211yescharacteristic
22#15689744—24no—
23#15689744C2218yescomplemented
24C2×#13094024C2211yescharacteristic, complemented
25C2×#13094019—21no—
26C2×#13094012C2211yescharacteristic, complemented
27C2×#13094010—21no—
28C2×#13094006—21no—
29C2×#13094003C2211yescharacteristic
30C2×#13094002—21no—
31C2×#13093998C2211yescharacteristic
32#15689597—24no—
33#15689597C2218yescomplemented
34C2×C4×Dic94C2211yescharacteristic, complemented
35C2×C4×D188C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37C2×C4×D188C2211yescharacteristic
38C2×C4×D188C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic, complemented
40C2×#13093986—21no—
41C2×#13093986—21no—
42C2×#13093983C2211yescharacteristic
43C2×C22⋊C4×D47—21no—
44C2×C22⋊C4×D47—21no—
45#15689465C2218yescomplemented
46#15689448C2218yescomplemented
47#15689414C2218yescomplemented
48#15689404C2218yescomplemented
49#15689339C2218yescomplemented
50#15689339C2218yescomplemented
51#15689276C2218yescomplemented
52#15689259C2218yes—
53#15689236C2218yescomplemented
54#15689225C2218yescomplemented
55C4×#10625325C2218yescomplemented
56C4×D376C2218yescomplemented
57C2×#13093958C2211yescharacteristic, complemented
58C2×#13093958C2211yescharacteristic, complemented
59C2×#13093956C2211yescharacteristic, complemented
60C2×#13093956C2211yescharacteristic, complemented
61C2×#13093949C2211yescharacteristic, complemented
62C2×#13093949C2211yescharacteristic, complemented
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic, complemented
68C2×#13093946C2211yescharacteristic, complemented
69C2×#117×C47C2211yescharacteristic
70C47×#433C2218yescomplemented
71C2×C4⋊C8×C47C2211yescharacteristic, complemented
72C2×C4⋊C8×C47C2211yescharacteristic, complemented
73C2×C22⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×#97×C47C2211yescharacteristic, complemented
76C2×C4×C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C22×Dic94—21no—
79C22×Dic94C2311yescharacteristic
80C22×D188—21no—
81C22×D188—22no—
82C22×D188—24no—
83C22×D188—24no—
84C22×D188C2314yes—
85C22×D188C2311yescharacteristic
86C22×D188C2311yescharacteristic
87C22×D188C2311yescharacteristic
88C22×C22⋊D47—21no—
89C22×C4×D47—21no—
90C22×C4×D47—21no—
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C2×#10625325—24no—
95C2×#10625325—24no—
96C2×#10625325C2314yes—
97C2×#10625325C2314yes—
98C2×D376—24no—
99C2×D376—24no—
100C2×D376C2314yes—
101C2×D376C2314yes—
102#13094024—22no—
103#13094024C2314yescomplemented
104#13094019—28no—
105#13094012—22no—
106#13094012C2314yescomplemented
107#13094010—28no—
108#13094006—28no—
109#13094003—22no—
110#13094003C2314yes—
111#13094002—28no—
112#13093998—22no—
113#13093998C2314yes—
114C4×Dic94—22no—
115C4×Dic94C2314yescomplemented
116C4×D188—22no—
117C4×D188—22no—
118C4×D188—22no—
119C4×D188—22no—
120C4×D188—22no—
121C4×D188C2314yes—
122C4×D188C2314yes—
123C4×D188C2314yes—
124C4×D188C2314yes—
125C4×D188C2314yescomplemented
126#13093986—28no—
127#13093986—28no—
128#13093983—22no—
129#13093983C2314yes—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47C2311yescharacteristic
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2311yescharacteristic
134C2×C4⋊Dic47C2311yescharacteristic
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×(C2×D47)⋊C4—21no—
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—21no—
146C2×(C2×D47)⋊C4—21no—
147C22⋊C4×D47—28no—
148C22⋊C4×D47—28no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151#13093958C2314yescomplemented
152#13093958C2314yescomplemented
153#13093956C2314yescomplemented
154#13093956C2314yescomplemented
155#13093949C2314yescomplemented
156#13093949C2314yescomplemented
157#13093946C2314yes—
158#13093946C2314yes—
159#13093946C2314yes—
160#13093946C2314yes—
161#13093946C2314yescomplemented
162#13093946C2314yescomplemented
163C23×C4×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168#117×C47D414yes—
169#117×C47C2314yes—
170C2×C4⋊C4×C47D411yescharacteristic
171C2×C4⋊C4×C47D411yescharacteristic
172C2×C22⋊C4×C47D411yescharacteristic
173C2×C22⋊C4×C47D411yescharacteristic
174C2×C42×C47C2311yescharacteristic
175C2×C42×C47C2311yescharacteristic
176C4⋊C8×C47C2314yescomplemented
177C4⋊C8×C47C2314yescomplemented
178C22⋊C8×C47C2314yes—
179C22⋊C8×C47C2314yes—
180#97×C47C2314yescomplemented
181C4×C8×C47C2314yescomplemented
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C23×D47—21no—
185C23×D47—28no—
186C23×D47—24no—
187C23×D47—21no—
188C23×D47—82no—
189C23×D47—82no—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D412yes—
198C22×C4×C47C2412yes—
199C22×C4×C47C2411yescharacteristic
200C2×C22⋊D47—24no—
201C2×C22⋊D47—82no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C2×D188—28no—
208C2×D188—216no—
209C2×D188—24no—
210C2×D188—21no—
211C2×D188—21no—
212C2×D188—22no—
213C2×D188—22no—
214C2×D188—28no—
215C2×D188—28no—
216C2×D188—22no—
217C2×D188—22no—
218C2×D188—21no—
219C2×D188#4114yes—
220C2×D188#4114yes—
221C2×D188C2412yes—
222C2×D188C2412yes—
223C2×D188C2412yes—
224C2×C4×D47—24no—
225C2×C4×D47—24no—
226C2×C4×D47—24no—
227C2×C4×D47—24no—
228C2×C4×D47—24no—
229C2×C4×D47—82no—
230C2×C4×D47—82no—
231C2×C4×D47—82no—
232C2×C4×D47—82no—
233C2×C4×D47—82no—
234C2×Dic94—22no—
235C2×Dic94—22no—
236C2×Dic94—21no—
237C2×Dic94—24no—
238C2×Dic94—82no—
239C2×Dic94C2412yes—
240C2×C8×C47—22no—
241C2×C8×C47—22no—
242C2×C8×C47—22no—
243C2×C8×C47—22no—
244C2×C8×C47C2412yes—
245C2×C8×C47C2412yes—
246C2×C8×C47C2412yes—
247C2×C8×C47C2412yes—
248C4⋊C4×C47C2×D414yes—
249C4⋊C4×C47C2×D414yes—
250C22⋊C4×C47C2×D414yes—
251C22⋊C4×C47C2×D414yes—
252C42×C47C2×D412yes—
253C42×C47C2×D412yes—
254C42×C47C2412yes—
255C42×C47C2412yes—
256C22⋊Dic47—24no—
257C22⋊Dic47—24no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4—24no—
266C4⋊Dic47—24no—
267C4⋊Dic47—21no—
268C4⋊Dic47—21no—
269C4⋊Dic47—21no—
270C4⋊Dic47—21no—
271C4⋊Dic47C2412yes—
272C4⋊Dic47C2412yes—
273C4⋊Dic47C2412yes—
274C4⋊Dic47C2412yes—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277C4×Dic47—24no—
278C4×Dic47—24no—
279D376—28no—
280D376—28no—
281#10625325—28no—
282#10625325—28no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47C22×D412yes—
287C23×C47C22×D411yescharacteristic
288C22×D47—24no—
289C22×D47—24no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—216no—
293C22×D47—22no—
294C22×D47—42no—
295C22×D47—42no—
296C22×D47—42no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47—42no—
300C22×D47—42no—
301C22×D47—84no—
302C22×D47—84no—
303C22×D47—816no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—24no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47C22×D412yes—
313C2×C4×C47C22×D412yes—
314C2×C4×C47C22×D412yes—
315C2×C4×C47C22×D412yes—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C2×#4112yes—
319C2×C4×C47C2×#4112yes—
320C2×C4×C47C2511yescharacteristic
321C22⋊D47—84no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332D188—216no—
333D188—24no—
334D188—24no—
335D188—22no—
336D188—22no—
337D188—22no—
338D188—22no—
339D188—42no—
340D188C2×#4114yes—
341D188C2×#4114yes—
342C4×D47—84no—
343C4×D47—84no—
344C4×D47—84no—
345C4×D47—84no—
346C4×D47—84no—
347Dic94—22no—
348Dic94—22no—
349Dic94—42no—
350Dic94—84no—
351C8×C47—22no—
352C8×C47—22no—
353C8×C47—22no—
354C8×C47—22no—
355C2×#3118—471nomaximal, Sylow
356C22×C47—22no—
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—44no—
360C22×C47#52512yes—
361C22×C47#57612yes—
362C22×C47#57712yes—
363C22×C47C23×D411yescharacteristic
364C2×D47—24no—
365C2×D47—24no—
366C2×D47—48no—
367C2×D47—48no—
368C2×D47—42no—
369C2×D47—42no—
370C2×D47—42no—
371C2×D47—42no—
372C2×D47—42no—
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—816no—
376C2×D47—84no—
377C4×C47—22no—
378C4×C47—22no—
379C4×C47—22no—
380C4×C47—22no—
381C4×C47—22no—
382C4×C47#52512yes—
383C4×C47C22×#4111yescharacteristic
384C4×C47C22×#4111yescharacteristic
385Dic47—42no—
386Dic47—42no—
387Dic47—42no—
388Dic47—42no—
389Dic47—42no—
390C2×#542—471no—
391C2×#518—471no—
392#3118—4716no—
393C2×#485—471no—
394C2×#482—471no—
395C2×#476—471no—
396C2×#474—471no—
397C2×#463—471no—
398C2×#463—471no—
399C2×#450—471no—
400C2×#447—471no—
401C2×#442—471no—
402C2×#440—471no—
403C2×C4×SD16—471no—
404C2×C4×D8—471no—
405C2×#433D4711yescharacteristic, complemented
406C2×C47—42no—
407C2×C47#311814yescomplemented
408C2×C47C2×#52511yescharacteristic
409C2×C47C2×#57611yescharacteristic
410C2×C47C2×#57711yescharacteristic
411D47—44no—
412D47—44no—
413D47—82no—
414C23×D4—471no—
415C22×SD16—471no—
416C22×SD16—471no—
417C22×D8—471no—
418C22×D8—471no—
419#542—478no—
420#542—944no—
421C2×C4⋊Q8—471no—
422C2×#126—941no—
423C2×#124—471no—
424C2×#124—941no—
425C2×#123—941no—
426C2×C22⋊Q8—471no—
427C2×C22⋊Q8—941no—
428C2×#121—471no—
429#518—478no—
430#518—944no—
431C2×C4×Q8—471no—
432C2×C4×D4—471no—
433C2×C4×D4—471no—
434C2×C4×D4—471no—
435C2×C4×D4—471no—
436C2×C4×D4—471no—
437C2×C4×D4—941no—
438C2×C4×D4—941no—
439C2×#117—471no—
440C2×#117C2×D4711yescharacteristic
441C22×C22⋊C4—941no—
442C22×C22⋊C4—941no—
443#485—478no—
444#482—478no—
445#476—478no—
446#474—478no—
447#463—478no—
448#463—478no—
449#450—478no—
450#447—478no—
451#442—478no—
452#440—478no—
453C4×SD16—478no—
454C4×D8—478no—
455#433C2×D4718yescomplemented
456C2×#107—471no—
457C2×#107—471no—
458C2×#106—471no—
459C2×#106—471no—
460C2×C4⋊C8C2×D4711yescharacteristic, complemented
461C2×C4⋊C8C2×D4711yescharacteristic, complemented
462C2×#103—471no—
463C2×#103—471no—
464C2×#102—471no—
465C2×#102—471no—
466C2×#102—471no—
467C2×#102—471no—
468C2×#102—471no—
469C2×#102—471no—
470C2×C22⋊C8C2×D4711yescharacteristic
471C2×C22⋊C8C2×D4711yescharacteristic
472C2×#97C2×D4711yescharacteristic, complemented
473C2×C4×C8C2×D4711yescharacteristic, complemented
474C47C2×#311811yescharacteristic, complemented, Sylow
475C25—941no—
476C22×Q8—471no—
477C22×Q8—941no—
478C22×D4—471no—
479C22×D4—471no—
480C22×D4—471no—
481C22×D4—474no—
482C22×D4—944no—
483C22×D4—944no—
484C22×D4—941no—
485C22×D4—941no—
486C22×D4—942no—
487C23×C4—941no—
488C23×C4—941no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4—941no—
492C23×C4C22×D4711yescharacteristic
493C2×SD16—474no—
494C2×SD16—474no—
495C2×SD16—944no—
496C2×SD16—944no—
497C2×D8—474no—
498C2×D8—474no—
499C2×D8—944no—
500C2×D8—944no—
501C22×C8C22×D4711yescharacteristic
502C22×C8C22×D4711yescharacteristic
503C22×C8C22×D4711yescharacteristic
504C22×C8C22×D4711yescharacteristic
505C4⋊Q8—474no—
506C4⋊Q8—942no—
507#126—948no—
508#124—474no—
509#124—948no—
510#124—942no—
511#123—948no—
512C22⋊Q8—474no—
513C22⋊Q8—942no—
514C22⋊Q8—948no—
515#121—474no—
516#121—942no—
517C4×Q8—474no—
518C4×Q8—942no—
519C4×D4—474no—
520C4×D4—474no—
521C4×D4—474no—
522C4×D4—474no—
523C4×D4—474no—
524C4×D4—948no—
525C4×D4—948no—
526C4×D4—942no—
527C4×D4—942no—
528C4×D4—942no—
529C4×D4—942no—
530C4×D4—942no—
531#117—474no—
532#117—942no—
533#117D18814yes—
534#117C22×D4714yes—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4D18811yescharacteristic
543C2×C4⋊C4D18811yescharacteristic
544C2×C22⋊C4—941no—
545C2×C22⋊C4—941no—
546C2×C22⋊C4—941no—
547C2×C22⋊C4—941no—
548C2×C22⋊C4—941no—
549C2×C22⋊C4—941no—
550C2×C22⋊C4—941no—
551C2×C22⋊C4—941no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—948no—
555C2×C22⋊C4—948no—
556C2×C22⋊C4D18811yescharacteristic
557C2×C22⋊C4D18811yescharacteristic
558C2×C42—941no—
559C2×C42—941no—
560C2×C42C22×D4711yescharacteristic
561C2×C42C22×D4711yescharacteristic
562#107—474no—
563#107—474no—
564#106—474no—
565#106—474no—
566C4⋊C8C22×D4714yescomplemented
567C4⋊C8C22×D4714yescomplemented
568#103—474no—
569#103—474no—
570#102—474no—
571#102—474no—
572#102—474no—
573#102—474no—
574#102—474no—
575#102—474no—
576C22⋊C8C22×D4714yes—
577C22⋊C8C22×D4714yes—
578#97C22×D4714yescomplemented
579C4×C8C22×D4714yescomplemented
580C24—948no—
581C24—944no—
582C24—941no—
583C24—941no—
584C24—941no—
585C24—3762no—
586C24—3762no—
587C24C2×D18811yescharacteristic
588C2×Q8—472no—
589C2×Q8—944no—
590C2×Q8—941no—
591C2×Q8—942no—
592C2×Q8—942no—
593C2×Q8—3762no—
594C2×D4—474no—
595C2×D4—474no—
596C2×D4—472no—
597C2×D4—472no—
598C2×D4—472no—
599C2×D4—948no—
600C2×D4—948no—
601C2×D4—948no—
602C2×D4—9416no—
603C2×D4—944no—
604C2×D4—944no—
605C2×D4—941no—
606C2×D4—941no—
607C2×D4—941no—
608C2×D4—942no—
609C2×D4—942no—
610C2×D4—942no—
611C2×D4—942no—
612C2×D4—3762no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—941no—
616C22×C4—941no—
617C22×C4—941no—
618C22×C4—941no—
619C22×C4—941no—
620C22×C4—944no—
621C22×C4—944no—
622C22×C4—944no—
623C22×C4—944no—
624C22×C4—944no—
625C22×C4—3762no—
626C22×C4—3762no—
627C22×C4—3762no—
628C22×C4—3762no—
629C22×C4—3762no—
630C22×C4C2×D18812yes—
631C22×C4C2×D18811yescharacteristic
632C22×C4C2×D18811yescharacteristic
633C22×C4C2×D18811yescharacteristic
634C22×C4C2×D18811yescharacteristic
635C22×C4C2×D18811yescharacteristic
636C22×C4C23×D4712yes—
637C22×C4C23×D4711yescharacteristic
638SD16—948no—
639SD16—948no—
640D8—948no—
641D8—948no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8C23×D4712yes—
647C2×C8C23×D4712yes—
648C2×C8C23×D4712yes—
649C2×C8C23×D4712yes—
650C4⋊C4—472no—
651C4⋊C4—472no—
652C4⋊C4—472no—
653C4⋊C4—472no—
654C4⋊C4—944no—
655C4⋊C4—944no—
656C4⋊C4—941no—
657C4⋊C4—941no—
658C4⋊C4—941no—
659C4⋊C4—941no—
660C4⋊C4—944no—
661C4⋊C4C2×D18814yes—
662C4⋊C4C2×D18814yes—
663C22⋊C4—944no—
664C22⋊C4—944no—
665C22⋊C4—944no—
666C22⋊C4—944no—
667C22⋊C4—944no—
668C22⋊C4—944no—
669C22⋊C4—944no—
670C22⋊C4—944no—
671C22⋊C4—944no—
672C22⋊C4—944no—
673C22⋊C4C2×D18814yes—
674C22⋊C4C2×D18814yes—
675C42—944no—
676C42—944no—
677C42C2×D18812yes—
678C42C2×D18812yes—
679C42C23×D4712yes—
680C42C23×D4712yes—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—9416no—
685C23—944no—
686C23—944no—
687C23—942no—
688C23—942no—
689C23—942no—
690C23—3764no—
691C23—3764no—
692C23—37616no—
693C23—1882no—
694C23—1882no—
695C23—1882no—
696C23—1882no—
697C23—1882no—
698C23—1882no—
699C23—1882no—
700C23C22×D18812yes—
701C23C22×D18811yescharacteristic
702Q8—942no—
703Q8—942no—
704Q8—3764no—
705Q8—1882no—
706D4—474no—
707D4—474no—
708D4—9416no—
709D4—944no—
710D4—944no—
711D4—942no—
712D4—942no—
713D4—942no—
714D4—942no—
715D4—3764no—
716D4—1882no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—3764no—
731C2×C4—3764no—
732C2×C4—3764no—
733C2×C4—3764no—
734C2×C4—3764no—
735C2×C4—1882no—
736C2×C4—1882no—
737C2×C4—1882no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4C22×D18812yes—
741C2×C4C22×D18812yes—
742C2×C4C22×D18812yes—
743C2×C4C22×D18812yes—
744C2×C4C22×D18812yes—
745C2×C4C22×D18811yescharacteristic
746C2×C4#41×D4712yes—
747C2×C4#41×D4712yes—
748C2×C4C24×D4711yescharacteristic
749C8—22no—
750C8—22no—
751C8—22no—
752C8—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—944no—
758C22—944no—
759C22—37616no—
760C22—3764no—
761C22—1882no—
762C22—1882no—
763C22—1882no—
764C22—1882no—
765C22—1882no—
766C22—1882no—
767C22—1882no—
768C22—1888no—
769C22—1888no—
770C22#1568963512yes—
771C22#1568992812yes—
772C22#1568993512yes—
773C22C23×D18811yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—1882no—
780C4—1882no—
781C4—1882no—
782C4—1882no—
783C4—1882no—
784C4#1568963512yes—
785C4C2×#41×D4711yescharacteristic
786C4C2×#41×D4711yescharacteristic
787C2—42no—
788C2—3762no—
789C2—1884no—
790C2—1884no—
791C2#2025357414yesdirect product factor
792C2C2×#1568963511yescharacteristic
793C2C2×#1568992811yescharacteristic
794C2C2×#1568993511yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#433C2
socleC23×C47C22×D4
prime radicalC2×#15689259C2
hypercenterC2×#433D47
hypocenterC47C2×#3118
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#15689744C2semidirect
2. C2×#15689597C2semidirect
3. #20253574C2direct (N × H)
4. C2×#15689465C2semidirect
5. C2×#15689448C2semidirect
6. C2×#15689414C2semidirect
7. C2×#15689404C2semidirect
8. C2×#15689339C2semidirect
9. C2×#15689339C2semidirect
10. C2×#15689276C2semidirect
12. C2×#15689236C2semidirect
13. C2×#15689225C2semidirect
14. C2×C4×#10625325C2semidirect
15. C2×C4×D376C2semidirect
16. C2×C47×#433C2semidirect
23. #15689744C22semidirect
24. C2×#13094024C22semidirect
26. C2×#13094012C22semidirect
33. #15689597C22semidirect
34. C2×C4×Dic94C22semidirect
39. C2×C4×D188C22semidirect
45. #15689465C22semidirect
46. #15689448C22semidirect
47. #15689414C22semidirect
48. #15689404C22semidirect
49. #15689339C22semidirect
50. #15689339C22semidirect
51. #15689276C22semidirect
53. #15689236C22semidirect
54. #15689225C22semidirect
55. C4×#10625325C22semidirect
56. C4×D376C22semidirect
57. C2×#13093958C22semidirect
58. C2×#13093958C22semidirect
59. C2×#13093956C22semidirect
60. C2×#13093956C22semidirect
61. C2×#13093949C22semidirect
62. C2×#13093949C22semidirect
67. C2×#13093946C22semidirect
68. C2×#13093946C22semidirect
70. C47×#433C22semidirect
71. C2×C4⋊C8×C47C22semidirect
72. C2×C4⋊C8×C47C22semidirect
75. C2×#97×C47C22semidirect
76. C2×C4×C8×C47C22semidirect
103. #13094024C23semidirect
106. #13094012C23semidirect
115. C4×Dic94C23semidirect
125. C4×D188C23semidirect
151. #13093958C23semidirect
152. #13093958C23semidirect
153. #13093956C23semidirect
154. #13093956C23semidirect
155. #13093949C23semidirect
156. #13093949C23semidirect
161. #13093946C23semidirect
162. #13093946C23semidirect
176. C4⋊C8×C47C23semidirect
177. C4⋊C8×C47C23semidirect
180. #97×C47C23semidirect
181. C4×C8×C47C23semidirect
405. C2×#433D47semidirect
407. C2×C47#3118semidirect
455. #433C2×D47semidirect
460. C2×C4⋊C8C2×D47semidirect
461. C2×C4⋊C8C2×D47semidirect
472. C2×#97C2×D47semidirect
473. C2×C4×C8C2×D47semidirect
474. C47C2×#3118semidirect
566. C4⋊C8C22×D47semidirect
567. C4⋊C8C22×D47semidirect
578. #97C22×D47semidirect
579. C4×C8C22×D47semidirect
791. C2#20253574direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897442
C2×#156895972
#202535742
C2×#156894652
C2×#156894482
C2×#156894142
C2×#156894042
C2×#156893392
C2×#156892762
C2×#156892592
C2×#156892362
C2×#156892252
C2×C4×#106253252
C2×C4×D3762
C2×C47×#4332
C2×#311847