Finite Group Databasebeta

← #452×Dic47 #26221909

Subgroups — #452×Dic47 #26221909

Order 12032.

1480 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic47C211yesmaximal, characteristic
2C2×Q16×Dic47C211yesmaximal, characteristic, complemented
3C2×SD16×Dic47C211yesmaximal, characteristic, complemented
4C22⋊Q8×Dic47C211yesmaximal, characteristic, complemented
5#20243731C211yesmaximal, characteristic, complemented
6#20243724C211yesmaximal, characteristic, complemented
7#20243701C211yesmaximal, characteristic, complemented
8#20243658C211yesmaximal, characteristic, complemented
9#20243637C211yesmaximal, characteristic, complemented
10#20243589C211yesmaximal, characteristic, complemented
11#20243328C211yesmaximal, characteristic
12#103×Dic47C211yesmaximal, characteristic, complemented
13#102×Dic47C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic47C211yesmaximal, characteristic, complemented
15C2×C47×#452C211yesmaximal, characteristic
16#41×Dic47—24no—
17#41×Dic47—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
29Q16×Dic47—24no—
30SD16×Dic47—24no—
31C2×#13093958C2211yescharacteristic
32C2×#13093956C2211yescharacteristic
33C2×#13093948C2211yescharacteristic
34C2×#13093948C2211yescharacteristic
35C2×#13093948C2211yescharacteristic
36C2×#13093948C2211yescharacteristic
37C2×#13093945C2211yescharacteristic
38C2×#13093945C2211yescharacteristic
39C2×C22⋊(C47⋊C8)C2211yescharacteristic
40C2×C8×Dic47C2211yescharacteristic
41C2×C8×Dic47C2211yescharacteristic
42#15689030C2211yescharacteristic
43#15689022C2211yescharacteristic
44#15689009—21no—
45#15688998—21no—
46#15688983C2211yescharacteristic
47C4⋊C4×Dic47—21no—
48C4⋊C4×Dic47C2211yescharacteristic
49C22⋊C4×Dic47—21no—
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×Dic47D411yescharacteristic
67C23×Dic47D411yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70Q8×Dic47—22no—
71Q8×Dic47—22no—
72Q8×Dic47—22no—
73Q8×Dic47—22no—
74Q8×Dic47—22no—
75Q8×Dic47D414yes—
76D4×Dic47—28no—
77D4×Dic47—28no—
78D4×Dic47—22no—
79D4×Dic47—22no—
80D4×Dic47—22no—
81D4×Dic47D414yes—
82#13093983—28no—
83#13093983—22no—
84#13093983—22no—
85C2×C4⋊Dic47—21no—
86C2×C4⋊Dic47—21no—
87C2×C4⋊Dic47—21no—
88C2×C4⋊Dic47—21no—
89C2×C4⋊Dic47C2311yescharacteristic
90C2×C4⋊Dic47C2311yescharacteristic
91C2×C4⋊Dic47C2311yescharacteristic
92C2×C4⋊Dic47C2311yescharacteristic
93C2×C22⋊Dic47—21no—
94C2×C22⋊Dic47—21no—
95C2×C22⋊Dic47—21no—
96C2×C22⋊Dic47—21no—
97C2×C4×Dic47—28no—
98C2×C4×Dic47—21no—
99C2×C4×Dic47—21no—
100C2×C4×Dic47—21no—
101C2×C4×Dic47—22no—
102C2×C4×Dic47—22no—
103C2×C4×Dic47—21no—
104C2×C4×Dic47—21no—
105C2×C4×Dic47D411yescharacteristic
106C2×C4×Dic47D411yescharacteristic
107C2×C4×Dic47C2311yescharacteristic
108C2×C4×Dic47C2311yescharacteristic
109#13093958—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—
118C8×Dic47—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—24no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—24no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—41no—
206C22×Dic47—42no—
207C22×Dic47—42no—
208C22×Dic47—42no—
209C22×Dic47—42no—
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213C22×Dic47C2×D411yescharacteristic
214Q16×C47—28no—
215SD16×C47—28no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—21no—
220C2×C8×C47C22×C412yes—
221C2×C8×C47C22×C412yes—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47C22×C412yes—
225C22⋊C4×C47—24no—
226C22⋊Dic47—24no—
227C22⋊Dic47—24no—
228C22⋊Dic47—24no—
229C22⋊Dic47—42no—
230C4⋊Dic47—24no—
231C4⋊Dic47—21no—
232C4⋊Dic47—21no—
233C4⋊Dic47—24no—
234C4⋊Dic47—21no—
235C4⋊Dic47—21no—
236C4⋊Dic47—21no—
237C4⋊Dic47—21no—
238C4⋊Dic47—42no—
239C4⋊Dic47—42no—
240C4⋊Dic47C2×D412yes—
241C4⋊Dic47C2×D412yes—
242C4×Dic47—24no—
243C4×Dic47—24no—
244C4×Dic47—21no—
245C4×Dic47—21no—
246C4×Dic47—22no—
247C4×Dic47—24no—
248C4×Dic47—22no—
249C4×Dic47—42no—
250C4×Dic47—42no—
251C4×Dic47C2×D412yes—
252C4×Dic47C2×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—
259C23×C47—22no—
260C23×C47—21no—
261C23×C47—22no—
262C23×C47—21no—
263C23×C47—22no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47C4×D412yes—
273C23×C47C22×D411yescharacteristic
274Q8×C47—22no—
275Q8×C47—22no—
276Q8×C47—22no—
277Q8×C47—22no—
278Q8×C47—22no—
279Q8×C47—41no—
280Q8×C47—41no—
281Q8×C47C4×D414yes—
282D4×C47—216no—
283D4×C47—22no—
284D4×C47—22no—
285D4×C47—22no—
286D4×C47C4×D414yes—
287C2×C4×C47—216no—
288C2×C4×C47—22no—
289C2×C4×C47—21no—
290C2×C4×C47—22no—
291C2×C4×C47—21no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47C4×D412yes—
304C2×C4×C47C23×C411yescharacteristic
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47C22×D411yescharacteristic
307C2×C4×C47C2×#4111yescharacteristic
308C2×C4×C47C2×#4111yescharacteristic
309C2×C4×C47C2×#4111yescharacteristic
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47—21no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—21no—
318C2×Dic47—21no—
319C2×Dic47—44no—
320C2×Dic47—48no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—44no—
326C2×Dic47—48no—
327C2×Dic47—41no—
328C2×Dic47—41no—
329C2×Dic47—41no—
330C2×Dic47—41no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47#12012yes—
334C2×Dic47#12012yes—
335C2×Dic47#13512yes—
336C2×Dic47#13512yes—
337C2×Dic47#13712yes—
338C8×C47—22no—
339C8×C47—22no—
340C47⋊C8—41no—
341C47⋊C8—41no—
342C4×#452—471nomaximal, Sylow
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—24no—
347C22×C47—41no—
348C22×C47—42no—
349C22×C47—41no—
350C22×C47—42no—
351C22×C47—42no—
352C22×C47—42no—
353C22×C47—41no—
354C22×C47—42no—
355C22×C47—41no—
356C22×C47—42no—
357C22×C47C2×C4×D411yescharacteristic
358C22×C47C2×#12011yescharacteristic
359C22×C47#52511yescharacteristic
360C22×C47C2×#13511yescharacteristic
361C22×C47C2×#13511yescharacteristic
362C22×C47C2×#13711yescharacteristic
363C22×C47#57511yescharacteristic
364C4×C47—22no—
365C4×C47—24no—
366C4×C47—42no—
367C4×C47—42no—
368C4×C47C2×C4×D411yescharacteristic
369C4×C47C2×C4×D411yescharacteristic
370C4×C47#52511yescharacteristic
371C4×C47#52511yescharacteristic
372Dic47—22no—
373Dic47—22no—
374Dic47—41no—
375Dic47—42no—
376Dic47—42no—
377Dic47—81no—
378Dic47—81no—
379Dic47#45214yesdirect product factor
380C2×C4×#41—471no—
381C2×#452D4711yescharacteristic
382C2×C4×Q16—471no—
383C2×C4×SD16—471no—
384C4×C22⋊Q8—471no—
385#1878—471no—
386#1877—471no—
387#1873—471no—
388#1865—471no—
389#1862—471no—
390#1854—471no—
391#1788—471no—
392C4×#103—471no—
393C4×#102—471no—
394C4×C22⋊C8—471no—
395C2×C47—42no—
396C2×C47—44no—
397C2×C47C4×#12011yescharacteristic
398C2×C47C4×#13511yescharacteristic
399C2×C47C4×#13711yescharacteristic
400C2×C47C2×#45211yescharacteristic
401C2×C47#300211yescharacteristic
402C2×C47#310211yescharacteristic
403C2×C47#310711yescharacteristic
404C22×#41C2×D4711yescharacteristic
405C22×Q16C2×D4711yescharacteristic
406C22×SD16C2×D4711yescharacteristic
407C2×C22⋊Q8C2×D4711yescharacteristic
408C4×#41—944no—
409C4×#41—944no—
410C2×C4×Q8—471no—
411C2×C4×Q8—471no—
412C2×C4×Q8—471no—
413C2×C4×D4—471no—
414C2×C4×D4—471no—
415C2×C4×D4—941no—
416C2×C4×D4—941no—
417C2×#117—471no—
418C2×#117—941no—
419C22×C42—471no—
420C22×C42—941no—
421#452Dic4718yesdirect product factor
422C4×Q16—944no—
423C4×SD16—944no—
424C2×#107—471no—
425C2×#106—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#103—471no—
430C2×#103C2×D4711yescharacteristic
431C2×#102—471no—
432C2×#102—471no—
433C2×#102C2×D4711yescharacteristic
434C2×C22⋊C8—471no—
435C2×C22⋊C8C2×D4711yescharacteristic
436C2×C4×C8—471no—
437C2×C4×C8—471no—
438#391—471no—
439#389—471no—
440#387—941no—
441#385—941no—
442#380—471no—
443C4×C4⋊C4—471no—
444C4×C4⋊C4—941no—
445C4×C22⋊C4—941no—
446#340—471no—
447#340—471no—
448#340—471no—
449#340—471no—
450#336—471no—
451#336—471no—
452C47C4×#45211yescharacteristic, complemented, Sylow
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41C2×Dic4714yes—
459C22×Q8C22×D4711yescharacteristic
460C22×Q8C22×D4711yescharacteristic
461C22×D4—21no—
462C22×D4C22×D4711yescharacteristic
463C23×C4—21no—
464C23×C4—471no—
465C23×C4—471no—
466C23×C4—941no—
467C23×C4—941no—
468C23×C4C22×D4711yescharacteristic
469C2×Q16—22no—
470C2×Q16—22no—
471C2×Q16C2×Dic4714yescomplemented
472C2×SD16—22no—
473C2×SD16—22no—
474C2×SD16C2×Dic4714yescomplemented
475C22×C8—471no—
476C22×C8—471no—
477C22×C8C22×D4711yescharacteristic
478C22×C8C22×D4711yescharacteristic
479C22⋊Q8—22no—
480C22⋊Q8C2×Dic4714yescomplemented
481C4×Q8—474no—
482C4×Q8—942no—
483C4×Q8—942no—
484C4×Q8—942no—
485C4×Q8—942no—
486C4×Q8—942no—
487C4×D4—474no—
488C4×D4—942no—
489C4×D4—942no—
490C4×D4—948no—
491C4×D4—948no—
492C4×D4—942no—
493#117—942no—
494#117—942no—
495#117—948no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C42—471no—
512C2×C42—471no—
513C2×C42—471no—
514C2×C42—471no—
515C2×C42—942no—
516C2×C42—942no—
517C2×C42—941no—
518C2×C42—941no—
519C2×C42—948no—
520C2×C42—941no—
521C2×C42—941no—
522C2×C42—941no—
523#107—942no—
524#106—942no—
525#103—942no—
526#103—942no—
527#103—942no—
528#103—942no—
529#103C2×Dic4714yescomplemented
530#102—942no—
531#102—942no—
532#102C2×Dic4714yescomplemented
533C22⋊C8—942no—
534C22⋊C8C2×Dic4714yescomplemented
535C4×C8—942no—
536C4×C8—942no—
537#95—941no—
538#95—941no—
539#95—941no—
540#95—941no—
541#95—941no—
542C24—21no—
543C24D4×D4711yescharacteristic
544#41—28no—
545#41—28no—
546#41—28no—
547#41—28no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8D4×D4712yes—
557C2×Q8#1062535212yes—
558C2×Q8C22×Dic4712yes—
559C2×Q8C22×Dic4712yes—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4D4×D4712yes—
567C2×D4#1062535212yes—
568C2×D4C22×Dic4712yes—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—471no—
580C22×C4—471no—
581C22×C4—471no—
582C22×C4—471no—
583C22×C4—944no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—944no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—1882no—
595C22×C4—1882no—
596C22×C4—1882no—
597C22×C4—1881no—
598C22×C4—1882no—
599C22×C4D4×D4711yescharacteristic
600C22×C4#1062535212yes—
601C22×C4C22×Dic4712yes—
602C22×C4C23×D4711yescharacteristic
603Q16—28no—
604SD16—28no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—941no—
610C2×C8—941no—
611C2×C8—941no—
612C2×C8—941no—
613C2×C8—941no—
614C2×C8—941no—
615C2×C8C22×Dic4712yes—
616C2×C8C22×Dic4712yes—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—472no—
620C4⋊C4—472no—
621C4⋊C4—944no—
622C4⋊C4—944no—
623C4⋊C4—941no—
624C4⋊C4—941no—
625C4⋊C4—941no—
626C4⋊C4—941no—
627C4⋊C4—941no—
628C4⋊C4—941no—
629C4⋊C4—1882no—
630C4⋊C4—1882no—
631C4⋊C4C22×Dic4712yes—
632C22⋊C4—24no—
633C22⋊C4—944no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—1882no—
637C42—472no—
638C42—472no—
639C42—942no—
640C42—942no—
641C42—944no—
642C42—944no—
643C42—944no—
644C42—941no—
645C42—941no—
646C42—1882no—
647C42—1882no—
648C23—22no—
649C23—21no—
650C23—22no—
651C23—21no—
652C23—22no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23D4×Dic4712yes—
662C23C2×D4×D4711yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—41no—
669Q8—41no—
670Q8D4×Dic4714yes—
671D4—216no—
672D4—22no—
673D4—22no—
674D4—22no—
675D4D4×Dic4714yes—
676C2×C4—216no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—472no—
693C2×C4—472no—
694C2×C4—472no—
695C2×C4—472no—
696C2×C4—472no—
697C2×C4—941no—
698C2×C4—941no—
699C2×C4—941no—
700C2×C4—941no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—941no—
704C2×C4—941no—
705C2×C4—941no—
706C2×C4—1884no—
707C2×C4—1888no—
708C2×C4—1884no—
709C2×C4—1888no—
710C2×C4—1881no—
711C2×C4—1881no—
712C2×C4—1881no—
713C2×C4—1881no—
714C2×C4—1881no—
715C2×C4—1881no—
716C2×C4—1881no—
717C2×C4—1881no—
718C2×C4—1881no—
719C2×C4—1881no—
720C2×C4D4×Dic4712yes—
721C2×C4C23×Dic4711yescharacteristic
722C2×C4C2×D4×D4711yescharacteristic
723C2×C4C2×D4×D4711yescharacteristic
724C2×C4C2×#1062535211yescharacteristic
725C2×C4C2×#1062535211yescharacteristic
726C2×C4C2×#1062535211yescharacteristic
727C8—22no—
728C8—22no—
729C8—1881no—
730C8—1881no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—24no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—41no—
740C22—42no—
741C22—41no—
742C22—42no—
743C22—41no—
744C22—42no—
745C22C2×D4×Dic4711yescharacteristic
746C22#120×D4711yescharacteristic
747C22#1568962911yescharacteristic
748C22#135×D4711yescharacteristic
749C22#135×D4711yescharacteristic
750C22#137×D4711yescharacteristic
751C22#1568992211yescharacteristic
752C4—22no—
753C4—24no—
754C4—42no—
755C4—42no—
756C4—474no—
757C4—942no—
758C4—942no—
759C4—3761no—
760C4—3761no—
761C4—1881no—
762C4—1882no—
763C4—1882no—
764C4C2×D4×Dic4711yescharacteristic
765C4C2×D4×Dic4711yescharacteristic
766C4#1568962911yescharacteristic
767C4#1568962911yescharacteristic
768C2—42no—
769C2—44no—
770C2#120×Dic4711yescharacteristic
771C2#135×Dic4711yescharacteristic
772C2#137×Dic4711yescharacteristic
773C2#452×D4711yescharacteristic
774C2#2025260911yescharacteristic
775C2#2025340711yescharacteristic
776C2#2025345211yescharacteristic
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
hypocenterC47C4×#452
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×Q16×Dic47C2semidirect
3. C2×SD16×Dic47C2semidirect
4. C22⋊Q8×Dic47C2semidirect
5. #20243731C2semidirect
6. #20243724C2semidirect
7. #20243701C2semidirect
8. #20243658C2semidirect
9. #20243637C2semidirect
10. #20243589C2semidirect
12. #103×Dic47C2semidirect
13. #102×Dic47C2semidirect
14. C22⋊C8×Dic47C2semidirect
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
379. Dic47#452direct (N × H)
421. #452Dic47direct (N × H)
452. C47C4×#452semidirect
471. C2×Q16C2×Dic47semidirect
474. C2×SD16C2×Dic47semidirect
480. C22⋊Q8C2×Dic47semidirect
529. #103C2×Dic47semidirect
532. #102C2×Dic47semidirect
534. C22⋊C8C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic472
C2×Q16×Dic472
C2×SD16×Dic472
C22⋊Q8×Dic472
#202437312
#202437242
#202437012
#202436582
#202436372
#202435892
#202433282
#103×Dic472
#102×Dic472
C22⋊C8×Dic472
C2×C47×#4522
C4×#45247