Finite Group Databasebeta

← #26233649

Subgroups — #26233649

Order 12032.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252046C211yesmaximal, characteristic, complemented
2#20251837C211yesmaximal, characteristic
3#20244101C211yesmaximal, characteristic, complemented
4#20244094C211yesmaximal, characteristic, complemented
5#20244038C211yesmaximal, characteristic, complemented
6#20244038C211yesmaximal, characteristic, complemented
7#20243665C211yesmaximal, characteristic, complemented
8#20243665C211yesmaximal, characteristic, complemented
9#20243487C211yesmaximal, characteristic, complemented
10#20243430C211yesmaximal, characteristic, complemented
11#20243332C211yesmaximal, characteristic
12#20243235C211yesmaximal, characteristic, complemented
13#20243228C211yesmaximal, characteristic, complemented
14#20243169C211yesmaximal, characteristic, complemented
15C47×#2896C211yesmaximal, characteristic
16C2×#13094031C2211yescharacteristic
17C2×#13094031C2211yescharacteristic
18#15689184—21no—
19#15689184—21no—
20#15689180—21no—
21#15689176—21no—
22C2×#13093960C2211yescharacteristic, complemented
23C2×#13093960C2211yescharacteristic, complemented
24#15689150C2211yescharacteristic, complemented
25#15689150C2211yescharacteristic, complemented
26C2×#13093951C2211yescharacteristic
27C2×#13093951C2211yescharacteristic
28C2×#13093951C2211yescharacteristic
29C2×#13093951C2211yescharacteristic
30#15689090—21no—
31#15689090—21no—
32#15689090C2211yescharacteristic
33#15689090C2211yescharacteristic
34#15689087—21no—
35#15689087C2211yescharacteristic
36#15689087C2211yescharacteristic
37C2×C22⋊(C47⋊C8)—21no—
38C2×C22⋊(C47⋊C8)C2211yescharacteristic
39#15689079C2211yescharacteristic, complemented
40#15689079C2211yescharacteristic, complemented
41C2×#13093934C2211yescharacteristic, complemented
42C2×C8×Dic47C2211yescharacteristic, complemented
43C4×C22⋊Dic47C2211yescharacteristic
44#15688888C2211yescharacteristic, complemented
45#15688888C2211yescharacteristic, complemented
46#15688882C2211yescharacteristic, complemented
47#15688882C2211yescharacteristic, complemented
48#15688882C2211yescharacteristic, complemented
49#15688882C2211yescharacteristic, complemented
50#15688877C2211yescharacteristic, complemented
51#15688877C2211yescharacteristic, complemented
52C22×#41×C47C2211yescharacteristic
53C22×M16×C47C2211yescharacteristic
54C2×#117×C47C2211yescharacteristic
55C47×#419C411yescharacteristic, complemented
56C47×#419C411yescharacteristic, complemented
57C47×#418C411yescharacteristic, complemented
58C47×#418C411yescharacteristic, complemented
59C47×#417C411yescharacteristic, complemented
60C47×#417C411yescharacteristic, complemented
61C47×#417C411yescharacteristic, complemented
62C47×#417C411yescharacteristic, complemented
63C47×#416C2211yescharacteristic
64C47×#416C2211yescharacteristic
65C47×#416C2211yescharacteristic
66C47×#416C2211yescharacteristic
67#13094031—22no—
68#13094031—22no—
69#13094031—41no—
70#13094031—41no—
71C2×#10625329—21no—
72C2×#10625329—21no—
73C2×#10625329C2311yescharacteristic
74C2×#10625329C2311yescharacteristic
75C2×#10625329C2311yescharacteristic
76C2×#10625329C2311yescharacteristic
77C22×C47⋊C8—21no—
78C22×C47⋊C8—21no—
79C22×C47⋊C8C2311yescharacteristic
80C22×C47⋊C8C2311yescharacteristic
81C2×C22⋊Dic47—21no—
82C2×C4×Dic47C2311yescharacteristic
83C2×C4×Dic47C2311yescharacteristic
84#13093960—41no—
85#13093960—41no—
86C4⋊(C47⋊C8)—21no—
87C4⋊(C47⋊C8)—21no—
88C4⋊(C47⋊C8)—21no—
89C4⋊(C47⋊C8)—21no—
90#13093951—22no—
91#13093951—22no—
92#13093951—41no—
93#13093951—41no—
94C22⋊(C47⋊C8)—21no—
95C22⋊(C47⋊C8)—21no—
96C22⋊(C47⋊C8)—21no—
97C22⋊(C47⋊C8)—21no—
98C22⋊(C47⋊C8)—21no—
99C22⋊(C47⋊C8)—21no—
100C22⋊(C47⋊C8)—21no—
101C22⋊(C47⋊C8)—21no—
102C22⋊(C47⋊C8)D411yescharacteristic
103C22⋊(C47⋊C8)D411yescharacteristic
104C22⋊(C47⋊C8)D411yescharacteristic
105C22⋊(C47⋊C8)D411yescharacteristic
106#13093935—21no—
107#13093935—21no—
108#13093934—41no—
109C4×C47⋊C8—21no—
110C4×C47⋊C8—21no—
111C8×Dic47—41no—
112C47⋊#95—21no—
113C2×#41×C47—21no—
114C2×#41×C47—21no—
115C2×#41×C47—22no—
116C2×#41×C47—22no—
117C2×#41×C47—41no—
118C2×#41×C47—41no—
119C2×#41×C47C2×C411yescharacteristic
120C2×#41×C47C2×C411yescharacteristic
121C2×#41×C47C2311yescharacteristic
122C2×#41×C47C2311yescharacteristic
123C22×Q8×C47C2×C411yescharacteristic
124C22×D4×C47—21no—
125C22×D4×C47C2×C411yescharacteristic
126C23×C4×C47—21no—
127C23×C4×C47C2311yescharacteristic
128C2×M16×C47—41no—
129C2×M16×C47—41no—
130C2×M16×C47C2×C411yescharacteristic
131C2×M16×C47C2×C411yescharacteristic
132C2×M16×C47C2×C411yescharacteristic
133C2×M16×C47C2×C411yescharacteristic
134C22×C8×C47C2311yescharacteristic
135C22×C8×C47C2311yescharacteristic
136#117×C47—21no—
137#117×C47—21no—
138#117×C47C2×C411yescharacteristic
139#117×C47C2×C411yescharacteristic
140#117×C47C2311yescharacteristic
141#117×C47C2311yescharacteristic
142C2×C4⋊C4×C47C2×C411yescharacteristic
143C2×C4⋊C4×C47C2×C411yescharacteristic
144C2×C22⋊C4×C47—21no—
145C2×C42×C47—21no—
146#103×C47C2×C411yescharacteristic
147#103×C47C2×C411yescharacteristic
148#103×C47C2×C411yescharacteristic
149#103×C47C2×C411yescharacteristic
150#103×C47C2×C411yescharacteristic
151#103×C47C2×C411yescharacteristic
152#103×C47C2×C411yescharacteristic
153#103×C47C2×C411yescharacteristic
154#102×C47C2×C411yescharacteristic
155#102×C47C2×C411yescharacteristic
156#102×C47C2×C411yescharacteristic
157#102×C47C2×C411yescharacteristic
158#102×C47C2×C411yescharacteristic
159#102×C47C2×C411yescharacteristic
160#102×C47C2×C411yescharacteristic
161#102×C47C2×C411yescharacteristic
162C24×C47—21no—
163C24×C47#4111yescharacteristic
164#41×C47—21no—
165#41×C47—21no—
166#41×C47—22no—
167#41×C47—22no—
168#41×C47—21no—
169#41×C47—21no—
170#41×C47—21no—
171#41×C47—21no—
172#41×C47—42no—
173#41×C47—42no—
174#41×C47—41no—
175#41×C47—41no—
176#41×C47—42no—
177#41×C47—42no—
178#41×C47#4112yes—
179#41×C47#4112yes—
180C2×Q8×C47—21no—
181C2×Q8×C47—22no—
182C2×Q8×C47—41no—
183C2×Q8×C47C22×C411yescharacteristic
184C2×Q8×C47C22×C411yescharacteristic
185C2×D4×C47—21no—
186C2×D4×C47—22no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—41no—
192C2×D4×C47—42no—
193C2×D4×C47—42no—
194C2×D4×C47C22×C411yescharacteristic
195C2×D4×C47C22×C411yescharacteristic
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—42no—
208C22×C4×C47—42no—
209C22×C4×C47C22×C411yescharacteristic
210C22×C4×C47C22×C411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47#4111yescharacteristic
214C22×C4×C47C2411yescharacteristic
215C22×Dic47—21no—
216C22×Dic47—21no—
217M16×C47—41no—
218M16×C47—41no—
219M16×C47—41no—
220M16×C47—41no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47C22×C411yescharacteristic
226C2×C8×C47C22×C411yescharacteristic
227C2×C8×C47C22×C411yescharacteristic
228C2×C8×C47C22×C411yescharacteristic
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47C22×C411yescharacteristic
232C4⋊C4×C47C22×C411yescharacteristic
233C4⋊C4×C47C22×C411yescharacteristic
234C4⋊C4×C47C22×C411yescharacteristic
235C22⋊C4×C47—21no—
236C22⋊C4×C47—21no—
237C22⋊C4×C47—21no—
238C22⋊C4×C47—21no—
239C42×C47—21no—
240C42×C47—21no—
241C42×C47—21no—
242C42×C47—21no—
243C22⋊Dic47—42no—
244C4×Dic47—21no—
245C4×Dic47—21no—
246C4×Dic47—21no—
247C4×Dic47—21no—
248#10625329—21no—
249#10625329—21no—
250#10625329—21no—
251#10625329—21no—
252#10625329—21no—
253#10625329—21no—
254#10625329—21no—
255#10625329—21no—
256#10625329—42no—
257#10625329—42no—
258C2×C47⋊C8—21no—
259C2×C47⋊C8—21no—
260C2×C47⋊C8—21no—
261C2×C47⋊C8—21no—
262C2×C47⋊C8—21no—
263C2×C47⋊C8—21no—
264C2×C47⋊C8—21no—
265C2×C47⋊C8—21no—
266C2×C47⋊C8—42no—
267C2×C47⋊C8—42no—
268C2×C47⋊C8C2×D411yescharacteristic
269C2×C47⋊C8C2×D411yescharacteristic
270C2×C47⋊C8C2×D411yescharacteristic
271C2×C47⋊C8C2×D411yescharacteristic
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—42no—
279C23×C47—42no—
280C23×C47—81no—
281C23×C47C4×D411yescharacteristic
282C23×C47C4×D411yescharacteristic
283C23×C47C2×#4111yescharacteristic
284Q8×C47—21no—
285Q8×C47—21no—
286Q8×C47—21no—
287Q8×C47—42no—
288Q8×C47#11712yes—
289D4×C47—22no—
290D4×C47—22no—
291D4×C47—21no—
292D4×C47—21no—
293D4×C47—21no—
294D4×C47—42no—
295D4×C47—42no—
296D4×C47—42no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47#11712yes—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—81no—
325C2×C4×C47C4×D411yescharacteristic
326C2×C4×C47C4×D411yescharacteristic
327C2×C4×C47C23×C411yescharacteristic
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C2×#4111yescharacteristic
330C2×C4×C47C2×#4111yescharacteristic
331C2×C4×C47H(5,𝔽2)11yescharacteristic
332C2×C4×C47H(5,𝔽2)11yescharacteristic
333C2×Dic47—22no—
334C2×Dic47—41no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C8×C47—21no—
340C8×C47—21no—
341C8×C47—21no—
342C8×C47—21no—
343C47⋊C8—21no—
344C47⋊C8—21no—
345C47⋊C8—21no—
346C47⋊C8—21no—
347C47⋊C8—41no—
348C47⋊C8—41no—
349C47⋊C8—41no—
350C47⋊C8—41no—
351#22588—471nomaximal, Sylow
352C22×C47—21no—
353C22×C47—21no—
354C22×C47—21no—
355C22×C47—21no—
356C22×C47—22no—
357C22×C47—21no—
358C22×C47—21no—
359C22×C47—21no—
360C22×C47—21no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47—84no—
369C22×C47C2×C4×D411yescharacteristic
370C22×C47#55111yescharacteristic
371C22×C47#55111yescharacteristic
372C4×C47—21no—
373C4×C47—21no—
374C4×C47—22no—
375C4×C47—41no—
376C4×C47—41no—
377C4×C47—41no—
378C4×C47—41no—
379C4×C47—41no—
380C4×C47C2×#11711yescharacteristic
381C4×C47#51811yescharacteristic
382C4×C47#54611yescharacteristic
383C4×C47#54611yescharacteristic
384Dic47—42no—
385Dic47—81no—
386#2924—471no—
387#2896D4711yescharacteristic
388#2880—471no—
389#1938—471no—
390#1937—471no—
391#1929—471no—
392#1929—471no—
393#1866—471no—
394#1866—471no—
395#1826—471no—
396#1811—471no—
397#1789—471no—
398#1765—471no—
399#1764—471no—
400#1753—471no—
401C2×C47—21no—
402C2×C47—21no—
403C2×C47—41no—
404C2×C47—41no—
405C2×C47—42no—
406C2×C47—81no—
407C2×C47#234211yescharacteristic
408C2×C47#295511yescharacteristic
409C2×C47#295611yescharacteristic
410C22×#41C2×D4711yescharacteristic
411C2×#131—471no—
412C2×#131—471no—
413C22×M16C2×D4711yescharacteristic
414C2×#117C2×D4711yescharacteristic
415#433—941no—
416#433—941no—
417#432—941no—
418#431—941no—
419C2×#108—471no—
420C2×#108—471no—
421#424—471no—
422#424—471no—
423C2×#104—471no—
424C2×#104—471no—
425C2×#104—471no—
426C2×#104—471no—
427#419Dic4711yescharacteristic, complemented
428#419Dic4711yescharacteristic, complemented
429#418Dic4711yescharacteristic, complemented
430#418Dic4711yescharacteristic, complemented
431#417Dic4711yescharacteristic, complemented
432#417Dic4711yescharacteristic, complemented
433#417Dic4711yescharacteristic, complemented
434#417Dic4711yescharacteristic, complemented
435#416C2×D4711yescharacteristic
436#416C2×D4711yescharacteristic
437#416C2×D4711yescharacteristic
438#416C2×D4711yescharacteristic
439#408—471no—
440#408—471no—
441#408—941no—
442#408—941no—
443#407—471no—
444#407—471no—
445#407—941no—
446C2×C22⋊C8—471no—
447C2×C22⋊C8—941no—
448#405—471no—
449#405—471no—
450C2×#97—471no—
451C2×C4×C8—471no—
452C4×C22⋊C4—471no—
453#341—471no—
454#341—471no—
455#339—471no—
456#339—471no—
457#339—471no—
458#339—471no—
459#336—471no—
460#336—471no—
461C47#2258811yescharacteristic, complemented, Sylow
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×Dic4711yescharacteristic
469C2×#41C2×Dic4711yescharacteristic
470C2×#41C22×D4711yescharacteristic
471C2×#41C22×D4711yescharacteristic
472C22×Q8C2×Dic4711yescharacteristic
473C22×D4—21no—
474C22×D4C2×Dic4711yescharacteristic
475C23×C4—21no—
476C23×C4C22×D4711yescharacteristic
477#131—942no—
478#131—942no—
479#131—1881no—
480#131—1881no—
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—471no—
484C2×M16—471no—
485C2×M16—471no—
486C2×M16—471no—
487C2×M16—941no—
488C2×M16—941no—
489C2×M16C2×Dic4711yescharacteristic
490C2×M16C2×Dic4711yescharacteristic
491C2×M16C2×Dic4711yescharacteristic
492C2×M16C2×Dic4711yescharacteristic
493C22×C8—471no—
494C22×C8—471no—
495C22×C8—941no—
496C22×C8—941no—
497C22×C8C22×D4711yescharacteristic
498C22×C8C22×D4711yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×Dic4711yescharacteristic
502#117C2×Dic4711yescharacteristic
503#117C22×D4711yescharacteristic
504#117C22×D4711yescharacteristic
505C2×C4⋊C4C2×Dic4711yescharacteristic
506C2×C4⋊C4C2×Dic4711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—941no—
509C2×C42—21no—
510C2×C42—471no—
511C2×C42—471no—
512#108—1881no—
513#108—1881no—
514C4⋊C8—941no—
515C4⋊C8—941no—
516C4⋊C8—941no—
517C4⋊C8—941no—
518#104—942no—
519#104—942no—
520#104—1881no—
521#104—1881no—
522#103C2×Dic4711yescharacteristic
523#103C2×Dic4711yescharacteristic
524#103C2×Dic4711yescharacteristic
525#103C2×Dic4711yescharacteristic
526#103C2×Dic4711yescharacteristic
527#103C2×Dic4711yescharacteristic
528#103C2×Dic4711yescharacteristic
529#103C2×Dic4711yescharacteristic
530#102C2×Dic4711yescharacteristic
531#102C2×Dic4711yescharacteristic
532#102C2×Dic4711yescharacteristic
533#102C2×Dic4711yescharacteristic
534#102C2×Dic4711yescharacteristic
535#102C2×Dic4711yescharacteristic
536#102C2×Dic4711yescharacteristic
537#102C2×Dic4711yescharacteristic
538C22⋊C8—471no—
539C22⋊C8—471no—
540C22⋊C8—471no—
541C22⋊C8—471no—
542C22⋊C8—941no—
543C22⋊C8—941no—
544C22⋊C8—941no—
545C22⋊C8—941no—
546C22⋊C8—941no—
547C22⋊C8—941no—
548C22⋊C8—941no—
549C22⋊C8—941no—
550#97—941no—
551#97—941no—
552#97—1881no—
553C4×C8—941no—
554C4×C8—941no—
555C4×C8—1881no—
556#95—941no—
557C24—21no—
558C24#1062535211yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1062535012yes—
574#41#1062535012yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×Dic4711yescharacteristic
579C2×Q8C22×Dic4711yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×Dic4711yescharacteristic
590C2×D4C22×Dic4711yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4D4×D4711yescharacteristic
607C22×C4D4×D4711yescharacteristic
608C22×C4#1062535211yescharacteristic
609C22×C4C22×Dic4711yescharacteristic
610C22×C4C22×Dic4711yescharacteristic
611C22×C4C23×D4711yescharacteristic
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616M16—941no—
617M16—941no—
618M16—941no—
619M16—941no—
620M16—941no—
621M16—941no—
622M16—941no—
623M16—941no—
624M16—1882no—
625M16—1882no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—471no—
631C2×C8—471no—
632C2×C8—471no—
633C2×C8—471no—
634C2×C8—941no—
635C2×C8—941no—
636C2×C8—941no—
637C2×C8—941no—
638C2×C8—941no—
639C2×C8—941no—
640C2×C8—941no—
641C2×C8—941no—
642C2×C8—1882no—
643C2×C8—1882no—
644C2×C8C22×Dic4711yescharacteristic
645C2×C8C22×Dic4711yescharacteristic
646C2×C8C22×Dic4711yescharacteristic
647C2×C8C22×Dic4711yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×Dic4711yescharacteristic
651C4⋊C4C22×Dic4711yescharacteristic
652C4⋊C4C22×Dic4711yescharacteristic
653C4⋊C4C22×Dic4711yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—1882no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—941no—
664C42—941no—
665C42—941no—
666C42—941no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23D4×Dic4711yescharacteristic
677C23D4×Dic4711yescharacteristic
678C23C2×#1062535211yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1309398312yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1309398312yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—81no—
720C2×C4—942no—
721C2×C4—1881no—
722C2×C4—1881no—
723C2×C4—1881no—
724C2×C4—1881no—
725C2×C4—1881no—
726C2×C4D4×Dic4711yescharacteristic
727C2×C4D4×Dic4711yescharacteristic
728C2×C4C23×Dic4711yescharacteristic
729C2×C4C2×D4×D4711yescharacteristic
730C2×C4C2×#1062535011yescharacteristic
731C2×C4C2×#1062535011yescharacteristic
732C2×C4#1309406911yescharacteristic
733C2×C4#1309406911yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—941no—
739C8—941no—
740C8—941no—
741C8—941no—
742C8—1881no—
743C8—1881no—
744C8—1881no—
745C8—1881no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×D4×Dic4711yescharacteristic
764C22#1568979911yescharacteristic
765C22#1568979911yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—3761no—
775C4—1882no—
776C4C2×#1309398311yescharacteristic
777C4#1568959811yescharacteristic
778C4#1568976311yescharacteristic
779C4#1568976311yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2024623711yescharacteristic
787C2#2025229111yescharacteristic
788C2#2025229811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2896C2
socleC22×C47C2×C4×D4
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenter#2896D47
hypocenterC47#22588
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #20252046C2semidirect
3. #20244101C2semidirect
4. #20244094C2semidirect
5. #20244038C2semidirect
6. #20244038C2semidirect
7. #20243665C2semidirect
8. #20243665C2semidirect
9. #20243487C2semidirect
10. #20243430C2semidirect
12. #20243235C2semidirect
13. #20243228C2semidirect
14. #20243169C2semidirect
22. C2×#13093960C22semidirect
23. C2×#13093960C22semidirect
24. #15689150C22semidirect
25. #15689150C22semidirect
39. #15689079C22semidirect
40. #15689079C22semidirect
41. C2×#13093934C22semidirect
42. C2×C8×Dic47C22semidirect
44. #15688888C22semidirect
45. #15688888C22semidirect
46. #15688882C22semidirect
47. #15688882C22semidirect
48. #15688882C22semidirect
49. #15688882C22semidirect
50. #15688877C22semidirect
51. #15688877C22semidirect
55. C47×#419C4semidirect
56. C47×#419C4semidirect
57. C47×#418C4semidirect
58. C47×#418C4semidirect
59. C47×#417C4semidirect
60. C47×#417C4semidirect
61. C47×#417C4semidirect
62. C47×#417C4semidirect
427. #419Dic47semidirect
428. #419Dic47semidirect
429. #418Dic47semidirect
430. #418Dic47semidirect
431. #417Dic47semidirect
432. #417Dic47semidirect
433. #417Dic47semidirect
434. #417Dic47semidirect
461. C47#22588semidirect

Maximal subgroups

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

subgroupindex
#202520462
#202518372
#202441012
#202440942
#202440382
#202436652
#202434872
#202434302
#202433322
#202432352
#202432282
#202431692
C47×#28962
#2258847