Finite Group Databasebeta

← #26222043

Subgroups — #26222043

Order 12032.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689606C211yesmaximal, characteristic
2C2×#15689230C211yesmaximal, characteristic, complemented
3C2×SD16×Dic47C211yesmaximal, characteristic, complemented
4#20246072C211yesmaximal, characteristic, complemented
5#20243731C211yesmaximal, characteristic, complemented
6#20243724C211yesmaximal, characteristic, complemented
7#20243696C211yesmaximal, characteristic, complemented
8#20243658C211yesmaximal, characteristic, complemented
9#20243651C211yesmaximal, characteristic, complemented
10#20243583C211yesmaximal, characteristic, complemented
11#20243328C211yesmaximal, characteristic
12#20243215C211yesmaximal, characteristic, complemented
13#103×Dic47C211yesmaximal, characteristic, complemented
14#20243156C211yesmaximal, characteristic, complemented
15C2×C47×#452C211yesmaximal, characteristic
16#15689606—24no—
17#15689606—24no—
18C2×Q8×Dic47C2211yescharacteristic
19C2×Q8×Dic47C2211yescharacteristic
20C2×Q8×Dic47C2211yescharacteristic
21C2×D4×Dic47—21no—
22C2×D4×Dic47—21no—
23C2×D4×Dic47C2211yescharacteristic
24C2×D4×Dic47C2211yescharacteristic
25C2×#13093983—21no—
26C2×#13093983C2211yescharacteristic
27C22×C4⋊Dic47—21no—
28C22×C4⋊Dic47C2211yescharacteristic
29#15689230—24no—
30SD16×Dic47—24no—
31C2×#13093956C2211yescharacteristic
32C2×#13093956C2211yescharacteristic
33C2×#13093948C2211yescharacteristic
34C2×#13093948C2211yescharacteristic
35C2×#13093948C2211yescharacteristic
36C2×#13093948C2211yescharacteristic
37C2×#13093945C2211yescharacteristic
38C2×#13093945C2211yescharacteristic
39C2×C22⋊(C47⋊C8)C2211yescharacteristic
40C2×#13093934C2211yescharacteristic
41C2×C8×Dic47C2211yescharacteristic
42#15689030C2211yescharacteristic
43#15689022—21no—
44#15689022C2211yescharacteristic
45#15689016—21no—
46#15689016—21no—
47#15689009—21no—
48#15688983C2211yescharacteristic
49C4⋊C4×Dic47C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C22×#41×C47C2211yescharacteristic
57C22×Q16×C47C2211yescharacteristic
58C22×SD16×C47C2211yescharacteristic
59C2×C22⋊Q8×C47C2211yescharacteristic
60C47×#452C418yescomplemented
61C2×#103×C47C2211yescharacteristic
62C2×#102×C47C2211yescharacteristic
63C2×C22⋊C8×C47C2211yescharacteristic
64C23×Dic47—21no—
65C23×Dic47—21no—
66C23×Dic47—21no—
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69Q8×Dic47—22no—
70Q8×Dic47—22no—
71Q8×Dic47—22no—
72Q8×Dic47—22no—
73Q8×Dic47—22no—
74Q8×Dic47D414yes—
75D4×Dic47—28no—
76D4×Dic47—28no—
77D4×Dic47—22no—
78D4×Dic47—22no—
79D4×Dic47—22no—
80D4×Dic47D414yes—
81#13093983—28no—
82#13093983—22no—
83#13093983—22no—
84C2×C4⋊Dic47—28no—
85C2×C4⋊Dic47—21no—
86C2×C4⋊Dic47—21no—
87C2×C4⋊Dic47—21no—
88C2×C4⋊Dic47—22no—
89C2×C4⋊Dic47—22no—
90C2×C4⋊Dic47—21no—
91C2×C4⋊Dic47—21no—
92C2×C4⋊Dic47D411yescharacteristic
93C2×C4⋊Dic47D411yescharacteristic
94C2×C4⋊Dic47C2311yescharacteristic
95C2×C4⋊Dic47C2311yescharacteristic
96C2×C4⋊Dic47C2311yescharacteristic
97C2×C4⋊Dic47C2311yescharacteristic
98C2×C22⋊Dic47—21no—
99C2×C22⋊Dic47—21no—
100C2×C22⋊Dic47—21no—
101C2×C22⋊Dic47D411yescharacteristic
102C2×C22⋊Dic47D411yescharacteristic
103C2×C4×Dic47—21no—
104C2×C4×Dic47—21no—
105C2×C4×Dic47—21no—
106C2×C4×Dic47—21no—
107C2×C4×Dic47C2311yescharacteristic
108C2×C4×Dic47C2311yescharacteristic
109#13093956—22no—
110#13093956—22no—
111#13093948—22no—
112#13093948—22no—
113#13093948—22no—
114#13093948—22no—
115#13093945—22no—
116#13093945—22no—
117C22⋊(C47⋊C8)—22no—
118#13093934—22no—
119C8×Dic47—22no—
120C47⋊#95—21no—
121C47⋊#95—21no—
122C47⋊#95—21no—
123C47⋊#95—21no—
124C47⋊#95—21no—
125C2×#41×C47—22no—
126C2×#41×C47—22no—
127C2×#41×C47—22no—
128C2×#41×C47—22no—
129C2×#41×C47—22no—
130C2×#41×C47C2×C414yes—
131C22×Q8×C47C2311yescharacteristic
132C22×Q8×C47C2311yescharacteristic
133C22×D4×C47—21no—
134C22×D4×C47C2311yescharacteristic
135C23×C4×C47—21no—
136C23×C4×C47C2311yescharacteristic
137C2×Q16×C47—22no—
138C2×Q16×C47—22no—
139C2×Q16×C47C2×C414yescomplemented
140C2×SD16×C47—22no—
141C2×SD16×C47—22no—
142C2×SD16×C47C2×C414yescomplemented
143C22×C8×C47C2311yescharacteristic
144C22×C8×C47C2311yescharacteristic
145C22⋊Q8×C47—22no—
146C22⋊Q8×C47C2×C414yescomplemented
147C2×C4⋊C4×C47—21no—
148C2×C4⋊C4×C47C2311yescharacteristic
149C2×C22⋊C4×C47—21no—
150#103×C47C2×C414yescomplemented
151#102×C47C2×C414yescomplemented
152C22⋊C8×C47C2×C414yescomplemented
153C24×C47—21no—
154C24×C47C2×D411yescharacteristic
155#41×C47—28no—
156#41×C47—28no—
157#41×C47—28no—
158#41×C47—28no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47C22×C412yes—
168C2×Q8×C47C22×C412yes—
169C2×Q8×C47C2×D412yes—
170C2×Q8×C47#4112yes—
171C2×D4×C47—24no—
172C2×D4×C47—24no—
173C2×D4×C47—24no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47C22×C412yes—
178C2×D4×C47C2×D412yes—
179C2×D4×C47#4112yes—
180C22×C4×C47—24no—
181C22×C4×C47—24no—
182C22×C4×C47—21no—
183C22×C4×C47—24no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47C22×C412yes—
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47#4112yes—
193C22×C4×C47C2411yescharacteristic
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—24no—
197C22×Dic47—24no—
198C22×Dic47—24no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—81no—
202C22×Dic47—81no—
203C22×Dic47—81no—
204C22×Dic47—81no—
205C22×Dic47—81no—
206C22×Dic47—81no—
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211Q16×C47—28no—
212SD16×C47—28no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47C22×C412yes—
218C2×C8×C47C22×C412yes—
219C4⋊C4×C47—24no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47C22×C412yes—
222C22⋊C4×C47—24no—
223C22⋊Dic47—24no—
224C22⋊Dic47—24no—
225C22⋊Dic47—22no—
226C22⋊Dic47—22no—
227C22⋊Dic47—81no—
228C4⋊Dic47—24no—
229C4⋊Dic47—24no—
230C4⋊Dic47—21no—
231C4⋊Dic47—21no—
232C4⋊Dic47—22no—
233C4⋊Dic47—24no—
234C4⋊Dic47—22no—
235C4⋊Dic47—21no—
236C4⋊Dic47—21no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47—42no—
240C4⋊Dic47—81no—
241C4⋊Dic47C2×D412yes—
242C4⋊Dic47C2×D412yes—
243C4×Dic47—24no—
244C4×Dic47—21no—
245C4×Dic47—21no—
246C4×Dic47—24no—
247C4×Dic47—42no—
248C4×Dic47—81no—
249C4×Dic47C2×D412yes—
250C4×Dic47C2×D412yes—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257C23×C47—22no—
258C23×C47—21no—
259C23×C47—22no—
260C23×C47—21no—
261C23×C47—22no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47C4×D412yes—
271C23×C47C22×D411yescharacteristic
272Q8×C47—22no—
273Q8×C47—22no—
274Q8×C47—22no—
275Q8×C47—22no—
276Q8×C47—22no—
277Q8×C47—41no—
278Q8×C47—41no—
279Q8×C47C4×D414yes—
280D4×C47—216no—
281D4×C47—22no—
282D4×C47—22no—
283D4×C47—22no—
284D4×C47C4×D414yes—
285C2×C4×C47—216no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47C4×D412yes—
302C2×C4×C47C23×C411yescharacteristic
303C2×C4×C47C22×D411yescharacteristic
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C2×#4111yescharacteristic
306C2×C4×C47C2×#4111yescharacteristic
307C2×C4×C47C2×#4111yescharacteristic
308C2×Dic47—21no—
309C2×Dic47—21no—
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—21no—
317C2×Dic47—21no—
318C2×Dic47—21no—
319C2×Dic47—21no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—41no—
329C2×Dic47—41no—
330C2×Dic47—84no—
331C2×Dic47—84no—
332C2×Dic47—84no—
333C2×Dic47#12012yes—
334C2×Dic47#12012yes—
335C8×C47—22no—
336C8×C47—22no—
337C47⋊C8—41no—
338C47⋊C8—41no—
339#21461—471nomaximal, Sylow
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—24no—
344C22×C47—41no—
345C22×C47—42no—
346C22×C47—41no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—41no—
351C22×C47—42no—
352C22×C47—41no—
353C22×C47—42no—
354C22×C47C2×C4×D411yescharacteristic
355C22×C47C2×#12011yescharacteristic
356C22×C47#52511yescharacteristic
357C22×C47#57711yescharacteristic
358C22×C47#57711yescharacteristic
359C22×C47#57711yescharacteristic
360C22×C47#57811yescharacteristic
361C4×C47—22no—
362C4×C47—24no—
363C4×C47—42no—
364C4×C47—42no—
365C4×C47C2×C4×D411yescharacteristic
366C4×C47C2×C4×D411yescharacteristic
367C4×C47#52511yescharacteristic
368C4×C47#52511yescharacteristic
369Dic47—22no—
370Dic47—22no—
371Dic47—41no—
372Dic47—42no—
373Dic47—42no—
374Dic47—41no—
375Dic47—81no—
376Dic47—81no—
377C2×#520—471no—
378C2×#452D4711yescharacteristic
379C2×#441—471no—
380C2×C4×SD16—471no—
381#2323—471no—
382#1878—471no—
383#1877—471no—
384#1872—471no—
385#1865—471no—
386#1864—471no—
387#1853—471no—
388#1788—471no—
389#1762—471no—
390C4×#103—471no—
391#1750—471no—
392C2×C47—42no—
393C2×C47—44no—
394C2×C47C4×#12011yescharacteristic
395C2×C47#294711yescharacteristic
396C2×C47#295211yescharacteristic
397C2×C47#300911yescharacteristic
398C2×C47#301311yescharacteristic
399C2×C47#312011yescharacteristic
400C2×C47#312511yescharacteristic
401C22×#41C2×D4711yescharacteristic
402C22×Q16C2×D4711yescharacteristic
403C22×SD16C2×D4711yescharacteristic
404C2×C22⋊Q8C2×D4711yescharacteristic
405#520—944no—
406#520—944no—
407C2×C4×Q8—471no—
408C2×C4×Q8—471no—
409C2×C4×Q8—471no—
410C2×C4×D4—471no—
411C2×C4×D4—471no—
412C2×C4×D4—941no—
413C2×C4×D4—941no—
414C2×#117—471no—
415C2×#117—941no—
416C22×C4⋊C4—471no—
417C22×C4⋊C4—941no—
418#452Dic4718yescomplemented
419#441—944no—
420C4×SD16—944no—
421C2×#106—471no—
422C2×#106—471no—
423C2×#103—471no—
424C2×#103—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103C2×D4711yescharacteristic
428C2×#102—471no—
429C2×#102—471no—
430C2×#102C2×D4711yescharacteristic
431C2×C22⋊C8—471no—
432C2×C22⋊C8C2×D4711yescharacteristic
433C2×#97—471no—
434C2×C4×C8—471no—
435#391—471no—
436#389—471no—
437#389—941no—
438#388—941no—
439#388—941no—
440#387—941no—
441#380—471no—
442C4×C4⋊C4—471no—
443#340—471no—
444#340—471no—
445#340—471no—
446#340—471no—
447#336—471no—
448#336—471no—
449C47#2146111yescharacteristic, complemented, Sylow
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41C2×Dic4714yes—
456C22×Q8C22×D4711yescharacteristic
457C22×Q8C22×D4711yescharacteristic
458C22×D4—21no—
459C22×D4C22×D4711yescharacteristic
460C23×C4—21no—
461C23×C4—941no—
462C23×C4—941no—
463C23×C4—941no—
464C23×C4C22×D4711yescharacteristic
465C2×Q16—22no—
466C2×Q16—22no—
467C2×Q16C2×Dic4714yescomplemented
468C2×SD16—22no—
469C2×SD16—22no—
470C2×SD16C2×Dic4714yescomplemented
471C22×C8—471no—
472C22×C8—471no—
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475C22⋊Q8—22no—
476C22⋊Q8C2×Dic4714yescomplemented
477C4×Q8—474no—
478C4×Q8—942no—
479C4×Q8—942no—
480C4×Q8—942no—
481C4×Q8—942no—
482C4×Q8—942no—
483C4×D4—474no—
484C4×D4—942no—
485C4×D4—942no—
486C4×D4—948no—
487C4×D4—948no—
488C4×D4—942no—
489#117—942no—
490#117—942no—
491#117—948no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—471no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—942no—
500C2×C4⋊C4—942no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—948no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—471no—
510C2×C22⋊C4—471no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C42—471no—
515C2×C42—471no—
516C2×C42—941no—
517C2×C42—941no—
518C2×C42—941no—
519C2×C42—941no—
520#106—942no—
521#106—942no—
522#103—942no—
523#103—942no—
524#103—942no—
525#103—942no—
526#103C2×Dic4714yescomplemented
527#102—942no—
528#102—942no—
529#102C2×Dic4714yescomplemented
530C22⋊C8—942no—
531C22⋊C8C2×Dic4714yescomplemented
532#97—942no—
533C4×C8—942no—
534#95—941no—
535#95—941no—
536#95—941no—
537#95—941no—
538#95—941no—
539C24—21no—
540C24D4×D4711yescharacteristic
541#41—28no—
542#41—28no—
543#41—28no—
544#41—28no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8D4×D4712yes—
554C2×Q8#1062535212yes—
555C2×Q8C22×Dic4712yes—
556C2×Q8C22×Dic4712yes—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4D4×D4712yes—
564C2×D4#1062535212yes—
565C2×D4C22×Dic4712yes—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—471no—
577C22×C4—471no—
578C22×C4—471no—
579C22×C4—471no—
580C22×C4—944no—
581C22×C4—944no—
582C22×C4—944no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—941no—
587C22×C4—3761no—
588C22×C4—3761no—
589C22×C4—3761no—
590C22×C4—3761no—
591C22×C4—3761no—
592C22×C4—3761no—
593C22×C4D4×D4711yescharacteristic
594C22×C4#1062535212yes—
595C22×C4C22×Dic4712yes—
596C22×C4C23×D4711yescharacteristic
597Q16—28no—
598SD16—28no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—941no—
604C2×C8—941no—
605C2×C8—941no—
606C2×C8—941no—
607C2×C8—941no—
608C2×C8—941no—
609C2×C8C22×Dic4712yes—
610C2×C8C22×Dic4712yes—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—472no—
614C4⋊C4—472no—
615C4⋊C4—942no—
616C4⋊C4—942no—
617C4⋊C4—944no—
618C4⋊C4—944no—
619C4⋊C4—944no—
620C4⋊C4—941no—
621C4⋊C4—941no—
622C4⋊C4—941no—
623C4⋊C4—941no—
624C4⋊C4—941no—
625C4⋊C4—941no—
626C4⋊C4—3761no—
627C4⋊C4—1882no—
628C4⋊C4C22×Dic4712yes—
629C22⋊C4—24no—
630C22⋊C4—942no—
631C22⋊C4—942no—
632C22⋊C4—944no—
633C22⋊C4—944no—
634C22⋊C4—3761no—
635C42—472no—
636C42—472no—
637C42—944no—
638C42—944no—
639C42—941no—
640C42—941no—
641C42—3761no—
642C42—1882no—
643C23—22no—
644C23—21no—
645C23—22no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23D4×Dic4712yes—
657C23C2×D4×D4711yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665Q8D4×Dic4714yes—
666D4—216no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4D4×Dic4714yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—472no—
688C2×C4—472no—
689C2×C4—941no—
690C2×C4—941no—
691C2×C4—941no—
692C2×C4—941no—
693C2×C4—941no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—941no—
697C2×C4—941no—
698C2×C4—941no—
699C2×C4—941no—
700C2×C4—941no—
701C2×C4—3764no—
702C2×C4—3764no—
703C2×C4—3764no—
704C2×C4—1881no—
705C2×C4—1881no—
706C2×C4—1881no—
707C2×C4—1881no—
708C2×C4—1881no—
709C2×C4—1881no—
710C2×C4—1881no—
711C2×C4—1881no—
712C2×C4—1881no—
713C2×C4—1881no—
714C2×C4D4×Dic4712yes—
715C2×C4C23×Dic4711yescharacteristic
716C2×C4C2×D4×D4711yescharacteristic
717C2×C4C2×D4×D4711yescharacteristic
718C2×C4C2×#1062535211yescharacteristic
719C2×C4C2×#1062535211yescharacteristic
720C2×C4C2×#1062535211yescharacteristic
721C8—22no—
722C8—22no—
723C8—1881no—
724C8—1881no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—24no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22C2×D4×Dic4711yescharacteristic
740C22#120×D4711yescharacteristic
741C22#1568962911yescharacteristic
742C22#1568993011yescharacteristic
743C22#1568993011yescharacteristic
744C22#1568993211yescharacteristic
745C22#1568993911yescharacteristic
746C4—22no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—942no—
751C4—942no—
752C4—3761no—
753C4—3761no—
754C4—1881no—
755C4—1881no—
756C4—1882no—
757C4—1882no—
758C4C2×D4×Dic4711yescharacteristic
759C4C2×D4×Dic4711yescharacteristic
760C4#1568962911yescharacteristic
761C4#1568962911yescharacteristic
762C2—42no—
763C2—44no—
764C2#120×Dic4711yescharacteristic
765C2#2025223211yescharacteristic
766C2#2025227211yescharacteristic
767C2#2025266211yescharacteristic
768C2#2025270711yescharacteristic
769C2#2025359511yescharacteristic
770C2#2025365811yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#452C2
socleC23×C47C22×D4
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#452D47
hypocenterC47#21461
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#15689230C2semidirect
3. C2×SD16×Dic47C2semidirect
4. #20246072C2semidirect
5. #20243731C2semidirect
6. #20243724C2semidirect
7. #20243696C2semidirect
8. #20243658C2semidirect
9. #20243651C2semidirect
10. #20243583C2semidirect
12. #20243215C2semidirect
13. #103×Dic47C2semidirect
14. #20243156C2semidirect
60. C47×#452C4semidirect
139. C2×Q16×C47C2×C4semidirect
142. C2×SD16×C47C2×C4semidirect
146. C22⋊Q8×C47C2×C4semidirect
150. #103×C47C2×C4semidirect
151. #102×C47C2×C4semidirect
152. C22⋊C8×C47C2×C4semidirect
418. #452Dic47semidirect
449. C47#21461semidirect
467. C2×Q16C2×Dic47semidirect
470. C2×SD16C2×Dic47semidirect
476. C22⋊Q8C2×Dic47semidirect
526. #103C2×Dic47semidirect
529. #102C2×Dic47semidirect
531. C22⋊C8C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896062
C2×#156892302
C2×SD16×Dic472
#202460722
#202437312
#202437242
#202436962
#202436582
#202436512
#202435832
#202433282
#202432152
#103×Dic472
#202431562
C2×C47×#4522
#2146147