Finite Group Databasebeta

← C4×#15689358 #26222772

Subgroups — C4×#15689358 #26222772

Order 12032.

1222 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689358C211yesmaximal, characteristic
2C2×C4×#10625334C211yesmaximal, characteristic, complemented
3C2×C4×C8×D47C211yesmaximal, characteristic, complemented
4C4×#13093999C211yesmaximal, characteristic, complemented
5C4×#13093995C211yesmaximal, characteristic, complemented
6#20244251C211yesmaximal, characteristic, complemented
7#20244120C211yesmaximal, characteristic, complemented
8#20244073C211yesmaximal, characteristic, complemented
9#20244069C211yesmaximal, characteristic, complemented
10#20243815C211yesmaximal, characteristic, complemented
11#20243813C211yesmaximal, characteristic, complemented
12#20243416C211yesmaximal, characteristic, complemented
13C4×#13093957C211yesmaximal, characteristic, complemented
14C4×#13093946C211yesmaximal, characteristic, complemented
15C4×#102×C47C211yesmaximal, characteristic, complemented
16C22×#10625334C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19C2×#13093999C2211yescharacteristic
20C2×#13093995C2211yescharacteristic
21C2×C4×D188—21no—
22C2×C4×D188C2211yescharacteristic
23C2×C4×C22⋊D47—21no—
24C2×C42×D47C2211yescharacteristic
25#15689358C418yesdirect product factor
26C4×#10625334—24no—
27C2×#13093957C2211yescharacteristic
28C2×#13093957C2211yescharacteristic
29C2×#13093957C2211yescharacteristic
30C2×#13093946C2211yescharacteristic
31C2×#13093946C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×#13093944C2211yescharacteristic
34C2×C4×C47⋊C8C2211yescharacteristic
35C2×C8×Dic47C2211yescharacteristic
36C2×C8×Dic47C2211yescharacteristic
37C4×C8×D47—24no—
38#15689026C2211yescharacteristic
39#15689024C2211yescharacteristic
40#15689022C2211yescharacteristic
41#15689019C2211yescharacteristic
42#15689015—21no—
43#15689011—21no—
44#15689001—21no—
45#15688999—21no—
46#15688980C2211yescharacteristic
47#15688980C2211yescharacteristic
48C4×C4⋊Dic47C2211yescharacteristic
49C4×(C2×D47)⋊C4—21no—
50C4×C22⋊Dic47—21no—
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55C2×C4×D4×C47C2211yescharacteristic
56C2×#102×C47C2211yescharacteristic
57C2×#102×C47C2211yescharacteristic
58C2×C4×C8×C47C2211yescharacteristic
59C4×C4⋊C4×C47C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×D188—21no—
63C22×D188C2311yescharacteristic
64C22×C22⋊D47—21no—
65C22×C4×D47—21no—
66C22×C4×D47D411yescharacteristic
67C22×C4×D47D411yescharacteristic
68C22×C4×D47C2311yescharacteristic
69C2×#10625334—22no—
70C2×#10625334—22no—
71C2×#10625334C2×C414yescomplemented
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C2×C8×D47—22no—
75C2×C8×D47—22no—
76C2×C8×D47—22no—
77C2×C8×D47—22no—
78C2×C8×D47—22no—
79C2×C8×D47C2×C414yescomplemented
80#13093999—22no—
81#13093999C2×C414yescomplemented
82#13093995—22no—
83#13093995C2×C414yescomplemented
84C4×D188—22no—
85C4×D188—22no—
86C4×D188—44no—
87C4×C22⋊D47—44no—
88C2×C4⋊Dic47—21no—
89C2×C4⋊Dic47C2311yescharacteristic
90C2×C4⋊Dic47C2311yescharacteristic
91C2×C4⋊Dic47C2311yescharacteristic
92C2×Dic47⋊C4—21no—
93C2×C22⋊Dic47—21no—
94C2×C22⋊Dic47—21no—
95C2×C22⋊Dic47—21no—
96C2×(C2×D47)⋊C4—21no—
97C2×(C2×D47)⋊C4—21no—
98C2×(C2×D47)⋊C4—21no—
99C2×(C2×D47)⋊C4—21no—
100C2×(C2×D47)⋊C4—21no—
101C2×(C2×D47)⋊C4—21no—
102C2×C4×Dic47—21no—
103C2×C4×Dic47D411yescharacteristic
104C2×C4×Dic47D411yescharacteristic
105C2×C4×Dic47C2311yescharacteristic
106C42×D47—22no—
107C42×D47—22no—
108#13093957—22no—
109#13093957—22no—
110#13093957C2×C414yescomplemented
111#13093946—22no—
112#13093946C2×C414yescomplemented
113#13093945—22no—
114#13093944—22no—
115C4×C47⋊C8D414yescomplemented
116C8×Dic47—22no—
117C8×Dic47—22no—
118C47⋊#95—21no—
119C47⋊#95—21no—
120C47⋊#95—21no—
121C47⋊#95—21no—
122C47⋊#95—21no—
123C22×D4×C47C2311yescharacteristic
124C23×C4×C47—21no—
125C22×C8×C47C2311yescharacteristic
126C22×C8×C47C2311yescharacteristic
127C4×D4×C47—22no—
128C4×D4×C47—22no—
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C22⋊C4×C47—21no—
133C2×C42×C47—21no—
134C2×C42×C47C2311yescharacteristic
135#102×C47—22no—
136#102×C47C2×C414yescomplemented
137C4×C8×C47—22no—
138#95×C47—21no—
139C24×C47—21no—
140C23×D47—21no—
141C23×D47C2×D411yescharacteristic
142C2×D4×C47—21no—
143C2×D4×C47—21no—
144C2×D4×C47—21no—
145C2×D4×C47—21no—
146C2×D4×C47—21no—
147C2×D4×C47C22×C412yes—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—42no—
152C22×C4×C47—42no—
153C22×C4×C47—42no—
154C22×C4×C47C2×D411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2411yescharacteristic
157C2×C22⋊D47—24no—
158C2×C22⋊D47—42no—
159C2×C22⋊D47—42no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47C2×D411yescharacteristic
164C22×Dic47C2×D411yescharacteristic
165C22×Dic47C2×D411yescharacteristic
166C2×D188—21no—
167C2×D188—21no—
168C2×D188—21no—
169C2×D188—21no—
170C2×D188—24no—
171C2×D188—21no—
172C2×D188—42no—
173C2×D188—42no—
174C2×D188C22×C412yes—
175C2×C4×D47—22no—
176C2×C4×D47—22no—
177C2×C4×D47—22no—
178C2×C4×D47—22no—
179C2×C4×D47—21no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—21no—
183C2×C4×D47—22no—
184C2×C4×D47—42no—
185C2×C4×D47—42no—
186C2×C4×D47—42no—
187C2×C4×D47D814yescomplemented
188C2×C4×D47C22×C412yes—
189C2×C4×D47#4112yes—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47C22×C412yes—
195C2×C8×C47#4112yes—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—21no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47C22×C412yes—
202C22⋊C4×C47—42no—
203C42×C47—42no—
204C42×C47C2×D412yes—
205C42×C47#4112yes—
206C22⋊Dic47—24no—
207C22⋊Dic47—42no—
208C22⋊Dic47—42no—
209#10625334—28no—
210(C2×D47)⋊C4—24no—
211(C2×D47)⋊C4—42no—
212(C2×D47)⋊C4—42no—
213(C2×D47)⋊C4—42no—
214(C2×D47)⋊C4—42no—
215(C2×D47)⋊C4—42no—
216C4⋊Dic47—21no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47—21no—
220C4⋊Dic47—21no—
221C4⋊Dic47—42no—
222C4⋊Dic47C22×C412yes—
223Dic47⋊C4—42no—
224C4×Dic47—22no—
225C4×Dic47—22no—
226C4×Dic47—21no—
227C4×Dic47—21no—
228C4×Dic47—42no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8C22×C412yes—
232C2×C47⋊C8C2×D412yes—
233C2×C47⋊C8C2×D412yes—
234C2×C47⋊C8#4112yes—
235C8×D47—28no—
236C8×D47—28no—
237C23×C47—22no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47C22×D411yescharacteristic
245C22×D47—21no—
246C22×D47—21no—
247C22×D47—21no—
248C22×D47—21no—
249C22×D47—22no—
250C22×D47—41no—
251C22×D47—41no—
252C22×D47—41no—
253C22×D47—41no—
254C22×D47—41no—
255C22×D47—41no—
256C22×D47C4×D412yes—
257C22×D47C2×D812yes—
258C22×D47#13512yes—
259D4×C47—22no—
260D4×C47—22no—
261D4×C47—41no—
262D4×C47—41no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—22no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47—41no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—84no—
275C2×C4×C47#12112yes—
276C2×C4×C47#12112yes—
277C2×C4×C47C2×D812yes—
278C2×C4×C47#13512yes—
279C2×C4×C47C23×C411yescharacteristic
280C2×C4×C47C22×D411yescharacteristic
281C2×C4×C47C2×#4111yescharacteristic
282C2×C4×C47C2×#4111yescharacteristic
283C2×C4×C47C2×#4111yescharacteristic
284C2×C4×C47C2×#4111yescharacteristic
285C22⋊D47—48no—
286C2×Dic47—21no—
287C2×Dic47—21no—
288C2×Dic47—21no—
289C2×Dic47—21no—
290C2×Dic47—21no—
291C2×Dic47—21no—
292C2×Dic47—22no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47C4×D412yes—
302C2×Dic47C2×D812yes—
303C2×Dic47#13512yes—
304D188—22no—
305D188—22no—
306D188—48no—
307D188—41no—
308D188—41no—
309C4×D47—28no—
310C4×D47—22no—
311C4×D47—22no—
312C4×D47—22no—
313C4×D47—22no—
314C4×D47—28no—
315C4×D47—84no—
316C8×C47—22no—
317C8×C47—22no—
318C47⋊C8—22no—
319C47⋊C8C4×D414yescomplemented
320C4×#466—471nomaximal, Sylow
321C22×C47—42no—
322C22×C47—42no—
323C22×C47—42no—
324C22×C47—81no—
325C22×C47—81no—
326C22×C47—81no—
327C22×C47—81no—
328C22×C47C2×C4×D411yescharacteristic
329C22×C47C2×#12111yescharacteristic
330C22×C47#53211yescharacteristic
331C22×C47C22×D811yescharacteristic
332C22×C47C2×#13511yescharacteristic
333C22×C47C2×#13511yescharacteristic
334C22×C47C2×#13511yescharacteristic
335C2×D47—22no—
336C2×D47—22no—
337C2×D47—22no—
338C2×D47—22no—
339C2×D47—22no—
340C2×D47—22no—
341C2×D47—42no—
342C2×D47—42no—
343C2×D47—42no—
344C2×D47—81no—
345C2×D47—81no—
346C2×D47—81no—
347C2×D47—81no—
348C2×D47C4×D814yescomplemented
349C4×C47—22no—
350C4×C47—42no—
351C4×C47—81no—
352C4×C47—81no—
353C4×C47#46614yescomplemented
354C4×C47C2×C4×D411yescharacteristic
355C4×C47C4×#4111yescharacteristic
356C4×C47#52511yescharacteristic
357C4×C47#52911yescharacteristic
358Dic47—22no—
359Dic47—22no—
360Dic47—22no—
361Dic47—42no—
362Dic47—81no—
363Dic47—81no—
364C2×#466—471no—
365C2×C4×D8—471no—
366C22×C4×C8—471no—
367C4×#121—471no—
368C4×#121—471no—
369#1970—471no—
370#1942—471no—
371#1934—471no—
372#1934—471no—
373#1893—471no—
374#1893—471no—
375#1808—471no—
376C4×#107—471no—
377C4×#102—471no—
378C4×#102D4711yescharacteristic, complemented
379C2×C47—82no—
380C2×C47C4×#12111yescharacteristic
381C2×C47C2×C4×D811yescharacteristic
382C2×C47C4×#13511yescharacteristic
383C2×C47C2×#46611yescharacteristic
384C2×C47#305011yescharacteristic
385C2×C47#316811yescharacteristic
386C2×C47#316911yescharacteristic
387D47—24no—
388D47—82no—
389C22×D8—471no—
390C23×C8—471no—
391C23×C8—471no—
392C2×#121—471no—
393C2×#121—471no—
394C2×C4×D4—471no—
395C2×C4×D4—941no—
396C2×C4×D4—941no—
397C2×C4×D4C2×D4711yescharacteristic
398C22×C42—471no—
399#466—478no—
400C4×D8—944no—
401C2×#107—471no—
402C2×#107—471no—
403C2×#107—471no—
404C2×#102—471no—
405C2×#102—471no—
406C2×#102—471no—
407C2×#102—471no—
408C2×#102C2×D4711yescharacteristic
409C2×#102C2×D4711yescharacteristic
410C2×C4×C8—471no—
411C2×C4×C8—471no—
412C2×C4×C8—471no—
413C2×C4×C8—944no—
414C2×C4×C8C2×D4711yescharacteristic
415#390—471no—
416#390—471no—
417#389—471no—
418#389—471no—
419#388—941no—
420#388—941no—
421#386—941no—
422#386—941no—
423#380—471no—
424#380—471no—
425C4×C4⋊C4—471no—
426C4×C4⋊C4C2×D4711yescharacteristic
427C4×C22⋊C4—941no—
428C4×C22⋊C4—941no—
429#340—471no—
430#340—471no—
431#340—471no—
432#340—471no—
433#340C2×D4711yescharacteristic
434#340C2×D4711yescharacteristic
435C47C4×#46611yescharacteristic, complemented, Sylow
436C22×D4—471no—
437C22×D4—941no—
438C22×D4—941no—
439C22×D4C22×D4711yescharacteristic
440C23×C4—21no—
441C23×C4—471no—
442C23×C4—471no—
443C23×C4—471no—
444C23×C4—941no—
445C2×D8—474no—
446C2×D8—942no—
447C2×D8—942no—
448C22×C8—471no—
449C22×C8—471no—
450C22×C8—474no—
451C22×C8—942no—
452C22×C8—942no—
453C22×C8—942no—
454C22×C8—942no—
455C22×C8—942no—
456C22×C8C22×D4711yescharacteristic
457C22×C8C22×D4711yescharacteristic
458#121—474no—
459#121—474no—
460#121—942no—
461#121—942no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—942no—
465C4×D4—942no—
466C4×D4—1884no—
467C4×D4—1884no—
468C2×C4⋊C4—471no—
469C2×C4⋊C4—471no—
470C2×C4⋊C4—471no—
471C2×C4⋊C4—941no—
472C2×C4⋊C4—941no—
473C2×C4⋊C4C22×D4711yescharacteristic
474C2×C4⋊C4C22×D4711yescharacteristic
475C2×C4⋊C4C22×D4711yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—941no—
478C2×C22⋊C4—941no—
479C2×C22⋊C4—941no—
480C2×C22⋊C4—941no—
481C2×C22⋊C4—941no—
482C2×C22⋊C4—941no—
483C2×C22⋊C4—941no—
484C2×C22⋊C4—941no—
485C2×C22⋊C4—941no—
486C2×C42—21no—
487C2×C42—471no—
488C2×C42—471no—
489C2×C42—471no—
490C2×C42—942no—
491C2×C42—942no—
492C2×C42—941no—
493C2×C42C22×D4711yescharacteristic
494#107—474no—
495#107—942no—
496#107—942no—
497#102—22no—
498#102—474no—
499#102—942no—
500#102—942no—
501#102—942no—
502#102C4×D4714yescomplemented
503C4×C8—22no—
504C4×C8—474no—
505C4×C8—942no—
506C4×C8—942no—
507#95—21no—
508#95—941no—
509#95—941no—
510#95—941no—
511#95—941no—
512#95—941no—
513C24—21no—
514C24—471no—
515C24—941no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—472no—
522C2×D4—944no—
523C2×D4—944no—
524C2×D4—941no—
525C2×D4—941no—
526C2×D4—941no—
527C2×D4—941no—
528C2×D4—941no—
529C2×D4—1882no—
530C2×D4—1882no—
531C2×D4—1882no—
532C2×D4—1882no—
533C2×D4C2×C4×D4712yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—471no—
541C22×C4—471no—
542C22×C4—471no—
543C22×C4—474no—
544C22×C4—472no—
545C22×C4—472no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—941no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4—941no—
558C22×C4—1882no—
559C22×C4—1882no—
560C22×C4—1882no—
561C22×C4D4×D4711yescharacteristic
562C22×C4D4×D4711yescharacteristic
563C22×C4C23×D4711yescharacteristic
564D8—948no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—472no—
570C2×C8—472no—
571C2×C8—472no—
572C2×C8—472no—
573C2×C8—948no—
574C2×C8—948no—
575C2×C8—941no—
576C2×C8—941no—
577C2×C8C2×C4×D4712yes—
578C2×C8#1062535012yes—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—472no—
585C4⋊C4—941no—
586C4⋊C4—941no—
587C4⋊C4—941no—
588C4⋊C4—941no—
589C4⋊C4—941no—
590C4⋊C4—1882no—
591C4⋊C4—1882no—
592C4⋊C4C2×C4×D4712yes—
593C22⋊C4—42no—
594C22⋊C4—944no—
595C22⋊C4—944no—
596C22⋊C4—1882no—
597C22⋊C4—1882no—
598C22⋊C4—1882no—
599C22⋊C4—1882no—
600C22⋊C4—1882no—
601C22⋊C4—1882no—
602C22⋊C4—1882no—
603C42—42no—
604C42—942no—
605C42—942no—
606C42—941no—
607C42—941no—
608C42—1882no—
609C42#1062535012yes—
610C42D4×D4712yes—
611C23—22no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—472no—
619C23—472no—
620C23—472no—
621C23—941no—
622C23—941no—
623C23—941no—
624C23—941no—
625C23—942no—
626C23—1881no—
627C23—1881no—
628C23—1881no—
629C23—1881no—
630C23—1881no—
631C23—1881no—
632C23C2×D4×D4711yescharacteristic
633D4—22no—
634D4—22no—
635D4—41no—
636D4—41no—
637D4—942no—
638D4—942no—
639D4—1888no—
640D4—1888no—
641D4—1881no—
642D4—1881no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—84no—
655C2×C4—472no—
656C2×C4—472no—
657C2×C4—472no—
658C2×C4—948no—
659C2×C4—941no—
660C2×C4—941no—
661C2×C4—941no—
662C2×C4—941no—
663C2×C4—941no—
664C2×C4—941no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—948no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—3764no—
672C2×C4—1881no—
673C2×C4—1881no—
674C2×C4—1881no—
675C2×C4—1881no—
676C2×C4—1881no—
677C2×C4—1881no—
678C2×C4—1881no—
679C2×C4—1881no—
680C2×C4#1309399712yes—
681C2×C4#1309399712yes—
682C2×C4D8×D4712yes—
683C2×C4#1309404512yes—
684C2×C4C22×C4×D4711yescharacteristic
685C2×C4C2×D4×D4711yescharacteristic
686C2×C4#41×D4711yescharacteristic
687C2×C4#41×D4711yescharacteristic
688C2×C4C2×#1062535011yescharacteristic
689C2×C4C2×#1062535011yescharacteristic
690C8—22no—
691C8—22no—
692C8—474no—
693C8—942no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—474no—
702C22—942no—
703C22—942no—
704C22—942no—
705C22—942no—
706C22—942no—
707C22—942no—
708C22—3761no—
709C22—3761no—
710C22—3761no—
711C22—3761no—
712C22—1882no—
713C22—1882no—
714C22—1882no—
715C22C4×D4×D4711yescharacteristic
716C22C2×#1309399711yescharacteristic
717C22#1568967011yescharacteristic
718C22C2×D8×D4711yescharacteristic
719C22#135×D4711yescharacteristic
720C22#135×D4711yescharacteristic
721C22C2×#1309404511yescharacteristic
722C4—22no—
723C4—42no—
724C4—81no—
725C4—81no—
726C4—942no—
727C4—942no—
728C4—942no—
729C4—3761no—
730C4—3761no—
731C4—1882no—
732C4#1568935814yesdirect product factor
733C4C4×D4×D4711yescharacteristic
734C4C4×#1062535011yescharacteristic
735C4#1568963211yescharacteristic
736C4#1568965111yescharacteristic
737C2—82no—
738C2—944no—
739C2—3762no—
740C2C4×#1309399711yescharacteristic
741C2C4×D8×D4711yescharacteristic
742C2C4×#1309404511yescharacteristic
743C2C2×#1568935811yescharacteristic
744C2#2025296811yescharacteristic
745C2#2025395411yescharacteristic
746C2#2025396411yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#102×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689358C2
cosocleC22×C4×C47C24
hypercenterC4×#102D47
hypocenterC47C4×#466
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10625334C2semidirect
3. C2×C4×C8×D47C2semidirect
4. C4×#13093999C2semidirect
5. C4×#13093995C2semidirect
6. #20244251C2semidirect
7. #20244120C2semidirect
8. #20244073C2semidirect
9. #20244069C2semidirect
10. #20243815C2semidirect
11. #20243813C2semidirect
12. #20243416C2semidirect
13. C4×#13093957C2semidirect
14. C4×#13093946C2semidirect
15. C4×#102×C47C2semidirect
25. #15689358C4direct (N × H)
71. C2×#10625334C2×C4semidirect
79. C2×C8×D47C2×C4semidirect
81. #13093999C2×C4semidirect
83. #13093995C2×C4semidirect
110. #13093957C2×C4semidirect
112. #13093946C2×C4semidirect
115. C4×C47⋊C8D4semidirect
136. #102×C47C2×C4semidirect
187. C2×C4×D47D8semidirect
319. C47⋊C8C4×D4semidirect
348. C2×D47C4×D8semidirect
353. C4×C47#466semidirect
378. C4×#102D47semidirect
435. C47C4×#466semidirect
502. #102C4×D47semidirect
732. C4#15689358direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156893582
C2×C4×#106253342
C2×C4×C8×D472
C4×#130939992
C4×#130939952
#202442512
#202441202
#202440732
#202440692
#202438152
#202438132
#202434162
C4×#130939572
C4×#130939462
C4×#102×C472
C4×#46647