Finite Group Databasebeta

← #26238812

Subgroups — #26238812

Order 12032.

864 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×#15689245C211yesmaximal, characteristic, complemented
2C2×#15689240C211yesmaximal, characteristic, complemented
3#20252132C211yesmaximal, characteristic, complemented
4#20251956C211yesmaximal, characteristic, complemented
5#20244221C211yesmaximal, characteristic, complemented
6#20244164C211yesmaximal, characteristic, complemented
7#20244101C211yesmaximal, characteristic, complemented
8#20244094C211yesmaximal, characteristic, complemented
9#20243717C211yesmaximal, characteristic, complemented
10#20243717C211yesmaximal, characteristic, complemented
11#20243665C211yesmaximal, characteristic, complemented
12#20243665C211yesmaximal, characteristic, complemented
13#20243247C211yesmaximal, characteristic, complemented
14#20243198C211yesmaximal, characteristic, complemented
15C47×#3035C211yesmaximal, characteristic
16C2×#13094031C2211yescharacteristic
17C2×#13094031C2211yescharacteristic
18C2×#13094031C2211yescharacteristic
19C2×#13094031C2211yescharacteristic
20#15689245—24no—
21#15689240—24no—
22#15689201—21no—
23#15689195—21no—
24#15689195—21no—
25D4×C47⋊C8—21no—
26C2×#13093960C2211yescharacteristic
27C2×#13093960C2211yescharacteristic
28#15689150—21no—
29#15689150—21no—
30#15689150C2211yescharacteristic
31#15689150C2211yescharacteristic
32#15689147—21no—
33#15689147C2211yescharacteristic
34C2×C4⋊(C47⋊C8)—21no—
35C2×C4⋊(C47⋊C8)C2211yescharacteristic
36C2×#13093951C2211yescharacteristic
37C2×#13093951C2211yescharacteristic
38C2×#13093951C2211yescharacteristic
39C2×#13093951C2211yescharacteristic
40C2×#13093951C2211yescharacteristic
41C2×#13093951C2211yescharacteristic
42#15689090C2211yescharacteristic
43#15689090C2211yescharacteristic
44C4×#10625329C2211yescharacteristic
45C2×#13093934C2211yescharacteristic
46C2×C8×Dic47C2211yescharacteristic
47#15688969C2211yescharacteristic
48#15688888C2211yescharacteristic
49#15688888C2211yescharacteristic
50#15688882C2211yescharacteristic
51#15688882C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C2×#135×C47C2211yescharacteristic
55C2×#135×C47C2211yescharacteristic
56C47×#532C2211yescharacteristic
57C4×#41×C47C2211yescharacteristic
58C47×#464C411yescharacteristic, complemented
59C47×#464C411yescharacteristic, complemented
60C47×#463C411yescharacteristic, complemented
61C47×#463C411yescharacteristic, complemented
62C47×#462C411yescharacteristic, complemented
63C47×#461C411yescharacteristic, complemented
64C47×#460C411yescharacteristic, complemented
65C47×#459C411yescharacteristic, complemented
66C2×C4⋊C8×C47C2211yescharacteristic
67C47×#416C2211yescharacteristic
68C47×#416C2211yescharacteristic
69#13094031—22no—
70#13094031—22no—
71#13094031—22no—
72#13094031—22no—
73#13094031—41no—
74#13094031—41no—
75#13094031—41no—
76#13094031—41no—
77C2×#10625329—21no—
78C2×#10625329—21no—
79C2×#10625329—21no—
80C2×#10625329—21no—
81C2×#10625329C2311yescharacteristic
82C2×#10625329C2311yescharacteristic
83C2×#10625329C2311yescharacteristic
84C2×#10625329C2311yescharacteristic
85C22×C47⋊C8—21no—
86C22×C47⋊C8—21no—
87C22×C47⋊C8—21no—
88C22×C47⋊C8—21no—
89C22×C47⋊C8C2311yescharacteristic
90C22×C47⋊C8C2311yescharacteristic
91C2×C4×Dic47C2311yescharacteristic
92C2×C4×Dic47C2311yescharacteristic
93#13093960—22no—
94#13093960—22no—
95C4⋊(C47⋊C8)—21no—
96C4⋊(C47⋊C8)—21no—
97C4⋊(C47⋊C8)—21no—
98C4⋊(C47⋊C8)—21no—
99C4⋊(C47⋊C8)—21no—
100C4⋊(C47⋊C8)—21no—
101C4⋊(C47⋊C8)D411yescharacteristic
102C4⋊(C47⋊C8)D411yescharacteristic
103C4⋊(C47⋊C8)D411yescharacteristic
104C4⋊(C47⋊C8)D411yescharacteristic
105#13093951—22no—
106#13093951—22no—
107#13093951—22no—
108#13093951—41no—
109#13093951—41no—
110#13093951D414yescomplemented
111C22⋊(C47⋊C8)—21no—
112C22⋊(C47⋊C8)—21no—
113C22⋊(C47⋊C8)—21no—
114C22⋊(C47⋊C8)—21no—
115#13093935—21no—
116#13093934—22no—
117C4×C47⋊C8—21no—
118C8×Dic47—22no—
119C47⋊#95—21no—
120C47⋊#95—21no—
121C2×#41×C47C2311yescharacteristic
122C2×#41×C47C2311yescharacteristic
123C2×#41×C47C2311yescharacteristic
124#135×C47—22no—
125#135×C47—22no—
126#135×C47—22no—
127#135×C47—22no—
128C2×Q16×C47C2×C411yescharacteristic
129C2×Q16×C47C2×C411yescharacteristic
130C2×SD16×C47C2×C411yescharacteristic
131C2×SD16×C47C2×C411yescharacteristic
132C2×SD16×C47C2×C411yescharacteristic
133C2×SD16×C47C2×C411yescharacteristic
134C2×D8×C47C2×C411yescharacteristic
135C2×D8×C47C2×C411yescharacteristic
136C22×C8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C4⋊Q8×C47C2×C411yescharacteristic
139#127×C47C2×C411yescharacteristic
140#124×C47C2×C411yescharacteristic
141#124×C47C2×C411yescharacteristic
142#121×C47—21no—
143#121×C47—21no—
144C4×Q8×C47C2×C411yescharacteristic
145C4×Q8×C47C2×C411yescharacteristic
146C4×D4×C47—21no—
147C4×D4×C47—21no—
148C4×D4×C47—21no—
149C4×D4×C47—21no—
150C4×D4×C47C2×C411yescharacteristic
151C4×D4×C47C2×C411yescharacteristic
152#117×C47—21no—
153#117×C47C2311yescharacteristic
154C2×C42×C47—21no—
155C2×C42×C47C2311yescharacteristic
156C4⋊C8×C47C2×C411yescharacteristic
157C4⋊C8×C47C2×C411yescharacteristic
158C4⋊C8×C47C2×C411yescharacteristic
159C4⋊C8×C47C2×C411yescharacteristic
160#103×C47C2×C411yescharacteristic
161#103×C47C2×C411yescharacteristic
162#103×C47C2×C411yescharacteristic
163#103×C47C2×C411yescharacteristic
164#102×C47C2×C411yescharacteristic
165#102×C47C2×C411yescharacteristic
166#102×C47C2×C411yescharacteristic
167#102×C47C2×C411yescharacteristic
168#41×C47—21no—
169#41×C47—21no—
170#41×C47—21no—
171#41×C47—21no—
172#41×C47—21no—
173#41×C47—21no—
174#41×C47—21no—
175#41×C47—21no—
176#41×C47—21no—
177#41×C47—21no—
178#41×C47C2×D412yes—
179#41×C47#4112yes—
180C2×Q8×C47C22×C411yescharacteristic
181C2×Q8×C47C22×C411yescharacteristic
182C2×Q8×C47C22×C411yescharacteristic
183C2×D4×C47—21no—
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47C22×C411yescharacteristic
189C2×D4×C47C22×C411yescharacteristic
190C2×D4×C47C22×C411yescharacteristic
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47#4111yescharacteristic
197C22×C4×C47#4111yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C22×Dic47—21no—
200C22×Dic47—21no—
201Q16×C47—22no—
202Q16×C47—22no—
203SD16×C47—22no—
204SD16×C47—22no—
205SD16×C47—22no—
206SD16×C47—22no—
207D8×C47—22no—
208D8×C47—22no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47C22×C411yescharacteristic
214C2×C8×C47C22×C411yescharacteristic
215C2×C8×C47C22×C411yescharacteristic
216C2×C8×C47C22×C411yescharacteristic
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47C22×C411yescharacteristic
222C4⋊C4×C47C22×C411yescharacteristic
223C22⋊C4×C47—21no—
224C22⋊C4×C47—21no—
225C22⋊C4×C47—21no—
226C22⋊C4×C47—21no—
227C22⋊C4×C47—21no—
228C22⋊C4×C47—21no—
229C22⋊C4×C47—21no—
230C42×C47—21no—
231C42×C47—21no—
232C42×C47—21no—
233C42×C47C22×C411yescharacteristic
234C42×C47C22×C411yescharacteristic
235C42×C47C2×D411yescharacteristic
236C42×C47C2×D411yescharacteristic
237C4×Dic47—21no—
238C4×Dic47—21no—
239C4×Dic47—21no—
240C4×Dic47C2×D412yes—
241#10625329—21no—
242#10625329—21no—
243#10625329—21no—
244#10625329—21no—
245#10625329—21no—
246#10625329—21no—
247#10625329—21no—
248#10625329—42no—
249#10625329—42no—
250#10625329—42no—
251#10625329—42no—
252#10625329C2×D412yes—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257C2×C47⋊C8—21no—
258C2×C47⋊C8—21no—
259C2×C47⋊C8—21no—
260C2×C47⋊C8—21no—
261C2×C47⋊C8—42no—
262C2×C47⋊C8—42no—
263C2×C47⋊C8—42no—
264C2×C47⋊C8—42no—
265C2×C47⋊C8C2×D411yescharacteristic
266C2×C47⋊C8C2×D411yescharacteristic
267C2×C47⋊C8C2×D411yescharacteristic
268C2×C47⋊C8C2×D411yescharacteristic
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47C2×#4111yescharacteristic
273Q8×C47—21no—
274Q8×C47—21no—
275Q8×C47—21no—
276Q8×C47—21no—
277Q8×C47—21no—
278Q8×C47C4×D412yes—
279D4×C47—22no—
280D4×C47—22no—
281D4×C47—21no—
282D4×C47—21no—
283D4×C47—21no—
284D4×C47—21no—
285D4×C47—21no—
286D4×C47—42no—
287D4×C47—41no—
288D4×C47—41no—
289D4×C47—41no—
290D4×C47—41no—
291D4×C47—81no—
292D4×C47C4×D412yes—
293C2×C4×C47—21no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—42no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—81no—
308C2×C4×C47C4×D411yescharacteristic
309C2×C4×C47C4×D411yescharacteristic
310C2×C4×C47C4×D411yescharacteristic
311C2×C4×C47C4×D411yescharacteristic
312C2×C4×C47C23×C411yescharacteristic
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C2×#4111yescharacteristic
316C2×C4×C47H(5,𝔽2)11yescharacteristic
317C2×C4×C472−1+411yescharacteristic
318C2×Dic47—22no—
319C2×Dic47—41no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C8×C47—21no—
325C8×C47—21no—
326C8×C47—21no—
327C8×C47—21no—
328C47⋊C8—21no—
329C47⋊C8—21no—
330C47⋊C8—21no—
331C47⋊C8—21no—
332C47⋊C8—22no—
333C47⋊C8—41no—
334C47⋊C8—41no—
335C47⋊C8—41no—
336#23017—471nomaximal, Sylow
337C22×C47—21no—
338C22×C47—21no—
339C22×C47—22no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47C2×C4×D411yescharacteristic
349C22×C47#54711yescharacteristic
350C22×C47#55311yescharacteristic
351C4×C47—22no—
352C4×C47—21no—
353C4×C47—21no—
354C4×C47—21no—
355C4×C47—21no—
356C4×C47—41no—
357C4×C47—41no—
358C4×C47—41no—
359C4×C47—41no—
360C4×C47C2×C4×D411yescharacteristic
361C4×C47#52011yescharacteristic
362C4×C47D4211yescharacteristic
363C4×C47#54811yescharacteristic
364Dic47—42no—
365Dic47—81no—
366#3035D4711yescharacteristic
367C2×#444—471no—
368C2×#443—471no—
369#2935—471no—
370#2906—471no—
371#1963—471no—
372#1950—471no—
373#1938—471no—
374#1937—471no—
375#1876—471no—
376#1876—471no—
377#1866—471no—
378#1866—471no—
379#1768—471no—
380#1759—471no—
381C2×C47—21no—
382C2×C47—21no—
383C2×C47—42no—
384C2×C47—81no—
385C2×C47—81no—
386C2×C47#236111yescharacteristic
387C2×C47#295511yescharacteristic
388C2×C47#295711yescharacteristic
389C2×#135C2×D4711yescharacteristic
390C2×#135C2×D4711yescharacteristic
391C2×#131—471no—
392C2×#131—471no—
393C2×#131—471no—
394C2×#131—471no—
395#532C2×D4711yescharacteristic
396C4×#41C2×D4711yescharacteristic
397#464Dic4711yescharacteristic, complemented
398#464Dic4711yescharacteristic, complemented
399#463Dic4711yescharacteristic, complemented
400#463Dic4711yescharacteristic, complemented
401#462Dic4711yescharacteristic, complemented
402#461Dic4711yescharacteristic, complemented
403#460Dic4711yescharacteristic, complemented
404#459Dic4711yescharacteristic, complemented
405#444—944no—
406#443—944no—
407#436—941no—
408#435—941no—
409#435—941no—
410C8×D4—941no—
411C2×#108—471no—
412C2×#108—471no—
413#424—471no—
414#424—471no—
415#424—941no—
416#424—941no—
417#423—471no—
418#423—941no—
419C2×C4⋊C8—471no—
420C2×C4⋊C8—941no—
421C2×C4⋊C8C2×D4711yescharacteristic
422C2×#104—471no—
423C2×#104—471no—
424C2×#104—471no—
425C2×#104—471no—
426C2×#104—471no—
427C2×#104—471no—
428#416C2×D4711yescharacteristic
429#416C2×D4711yescharacteristic
430#408—471no—
431#408—471no—
432C4×M16—471no—
433C2×#97—471no—
434C2×C4×C8—471no—
435#376—471no—
436#341—471no—
437#341—471no—
438#339—471no—
439#339—471no—
440#336—471no—
441#336—471no—
442C47#2301711yescharacteristic, complemented, Sylow
443C2×#41C22×D4711yescharacteristic
444C2×#41C22×D4711yescharacteristic
445C2×#41C22×D4711yescharacteristic
446#135—22no—
447#135—22no—
448#135—22no—
449#135—22no—
450C2×Q16C2×Dic4711yescharacteristic
451C2×Q16C2×Dic4711yescharacteristic
452C2×SD16C2×Dic4711yescharacteristic
453C2×SD16C2×Dic4711yescharacteristic
454C2×SD16C2×Dic4711yescharacteristic
455C2×SD16C2×Dic4711yescharacteristic
456C2×D8C2×Dic4711yescharacteristic
457C2×D8C2×Dic4711yescharacteristic
458#131—942no—
459#131—942no—
460#131—942no—
461#131—942no—
462#131—1881no—
463#131—1881no—
464#131—1881no—
465#131—1881no—
466C2×M16—471no—
467C2×M16—471no—
468C2×M16—471no—
469C2×M16—471no—
470C2×M16—941no—
471C2×M16—941no—
472C2×M16—941no—
473C2×M16—941no—
474C22×C8—471no—
475C22×C8—471no—
476C22×C8—941no—
477C22×C8—941no—
478C22×C8—941no—
479C22×C8—941no—
480C22×C8C22×D4711yescharacteristic
481C22×C8C22×D4711yescharacteristic
482C4⋊Q8C2×Dic4711yescharacteristic
483#127C2×Dic4711yescharacteristic
484#124C2×Dic4711yescharacteristic
485#124C2×Dic4711yescharacteristic
486#121—21no—
487#121—21no—
488C4×Q8C2×Dic4711yescharacteristic
489C4×Q8C2×Dic4711yescharacteristic
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4C2×Dic4711yescharacteristic
495C4×D4C2×Dic4711yescharacteristic
496#117—21no—
497#117C22×D4711yescharacteristic
498C2×C42—21no—
499C2×C42—471no—
500C2×C42—471no—
501C2×C42C22×D4711yescharacteristic
502#108—942no—
503#108—942no—
504C4⋊C8—471no—
505C4⋊C8—471no—
506C4⋊C8—471no—
507C4⋊C8—471no—
508C4⋊C8—941no—
509C4⋊C8—941no—
510C4⋊C8—941no—
511C4⋊C8—941no—
512C4⋊C8—941no—
513C4⋊C8—941no—
514C4⋊C8C2×Dic4711yescharacteristic
515C4⋊C8C2×Dic4711yescharacteristic
516C4⋊C8C2×Dic4711yescharacteristic
517C4⋊C8C2×Dic4711yescharacteristic
518#104—474no—
519#104—942no—
520#104—942no—
521#104—942no—
522#104—1881no—
523#104—1881no—
524#103C2×Dic4711yescharacteristic
525#103C2×Dic4711yescharacteristic
526#103C2×Dic4711yescharacteristic
527#103C2×Dic4711yescharacteristic
528#102C2×Dic4711yescharacteristic
529#102C2×Dic4711yescharacteristic
530#102C2×Dic4711yescharacteristic
531#102C2×Dic4711yescharacteristic
532C22⋊C8—941no—
533C22⋊C8—941no—
534C22⋊C8—941no—
535C22⋊C8—941no—
536#97—942no—
537#97—941no—
538C4×C8—942no—
539C4×C8—941no—
540#95—941no—
541#95—941no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41D4×D4712yes—
553#41#1062535212yes—
554C2×Q8C22×Dic4711yescharacteristic
555C2×Q8C22×Dic4711yescharacteristic
556C2×Q8C22×Dic4711yescharacteristic
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4C22×Dic4711yescharacteristic
563C2×D4C22×Dic4711yescharacteristic
564C2×D4C22×Dic4711yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—941no—
571C22×C4—941no—
572C22×C4#1062535211yescharacteristic
573C22×C4#1062535211yescharacteristic
574C22×C4C23×D4711yescharacteristic
575Q16—22no—
576Q16—22no—
577SD16—22no—
578SD16—22no—
579SD16—22no—
580SD16—22no—
581D8—22no—
582D8—22no—
583M16—472no—
584M16—941no—
585M16—941no—
586M16—941no—
587M16—941no—
588M16—941no—
589M16—941no—
590M16—941no—
591M16—1882no—
592M16—1882no—
593M16—1882no—
594M16—1882no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—471no—
600C2×C8—471no—
601C2×C8—471no—
602C2×C8—471no—
603C2×C8—941no—
604C2×C8—941no—
605C2×C8—941no—
606C2×C8—941no—
607C2×C8—941no—
608C2×C8—941no—
609C2×C8—941no—
610C2×C8—941no—
611C2×C8—1882no—
612C2×C8—1882no—
613C2×C8—1882no—
614C2×C8—1882no—
615C2×C8C22×Dic4711yescharacteristic
616C2×C8C22×Dic4711yescharacteristic
617C2×C8C22×Dic4711yescharacteristic
618C2×C8C22×Dic4711yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C22×Dic4711yescharacteristic
624C4⋊C4C22×Dic4711yescharacteristic
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—472no—
636C42—941no—
637C42—941no—
638C42—941no—
639C42D4×D4711yescharacteristic
640C42D4×D4711yescharacteristic
641C42C22×Dic4711yescharacteristic
642C42C22×Dic4711yescharacteristic
643C23—21no—
644C23—21no—
645C23—21no—
646C23C2×#1062535211yescharacteristic
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8D4×Dic4712yes—
653D4—22no—
654D4—22no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—42no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4D4×Dic4712yes—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—81no—
682C2×C4—942no—
683C2×C4—1881no—
684C2×C4—1881no—
685C2×C4—1881no—
686C2×C4—1881no—
687C2×C4—1881no—
688C2×C4D4×Dic4711yescharacteristic
689C2×C4D4×Dic4711yescharacteristic
690C2×C4D4×Dic4711yescharacteristic
691C2×C4D4×Dic4711yescharacteristic
692C2×C4C23×Dic4711yescharacteristic
693C2×C4C2×D4×D4711yescharacteristic
694C2×C4C2×D4×D4711yescharacteristic
695C2×C4C2×#1062535211yescharacteristic
696C2×C4#1309407011yescharacteristic
697C2×C4#1309407111yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—941no—
703C8—941no—
704C8—941no—
705C8—941no—
706C8—942no—
707C8—1881no—
708C8—1881no—
709C8—1881no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22C2×D4×Dic4711yescharacteristic
722C22#1568977311yescharacteristic
723C22#1568982511yescharacteristic
724C4—21no—
725C4—21no—
726C4—22no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—3761no—
734C4—1882no—
735C4C2×D4×Dic4711yescharacteristic
736C4#1568960611yescharacteristic
737C4#1568975711yescharacteristic
738C4#1568977911yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—81no—
743C2—81no—
744C2#2024640811yescharacteristic
745C2#2025229111yescharacteristic
746C2#2025230511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC47×#3035C2
socleC22×C47C2×C4×D4
cosocleC22×C4×C47C24
hypercenter#3035D47
hypocenterC47#23017
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. C2×#15689245C2semidirect
2. C2×#15689240C2semidirect
3. #20252132C2semidirect
4. #20251956C2semidirect
5. #20244221C2semidirect
6. #20244164C2semidirect
7. #20244101C2semidirect
8. #20244094C2semidirect
9. #20243717C2semidirect
10. #20243717C2semidirect
11. #20243665C2semidirect
12. #20243665C2semidirect
13. #20243247C2semidirect
14. #20243198C2semidirect
58. C47×#464C4semidirect
59. C47×#464C4semidirect
60. C47×#463C4semidirect
61. C47×#463C4semidirect
62. C47×#462C4semidirect
63. C47×#461C4semidirect
64. C47×#460C4semidirect
65. C47×#459C4semidirect
110. #13093951D4semidirect
397. #464Dic47semidirect
398. #464Dic47semidirect
399. #463Dic47semidirect
400. #463Dic47semidirect
401. #462Dic47semidirect
402. #461Dic47semidirect
403. #460Dic47semidirect
404. #459Dic47semidirect
442. C47#23017semidirect

Maximal subgroups

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

subgroupindex
C2×#156892452
C2×#156892402
#202521322
#202519562
#202442212
#202441642
#202441012
#202440942
#202437172
#202436652
#202432472
#202431982
C47×#30352
#2301747