Finite Group Databasebeta

← #26222028

Subgroups — #26222028

Order 12032.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689606C211yesmaximal, characteristic, complemented
2C2×#15689224C211yesmaximal, characteristic, complemented
3C2×D8×Dic47C211yesmaximal, characteristic, complemented
4#20246083C211yesmaximal, characteristic, complemented
5#20243745C211yesmaximal, characteristic, complemented
6#20243738C211yesmaximal, characteristic, complemented
7#20243706C211yesmaximal, characteristic, complemented
8#20243644C211yesmaximal, characteristic, complemented
9#20243637C211yesmaximal, characteristic, complemented
10#20243578C211yesmaximal, characteristic, complemented
11#20243328C211yesmaximal, characteristic, complemented
12#20243215C211yesmaximal, characteristic, complemented
13#103×Dic47C211yesmaximal, characteristic, complemented
14#20243156C211yesmaximal, characteristic, complemented
15C2×C47×#449C211yesmaximal, characteristic
16#15689606—24no—
17#15689606—24no—
18C2×Q8×Dic47C2211yescharacteristic
19C2×Q8×Dic47C2211yescharacteristic
20C2×D4×Dic47—21no—
21C2×D4×Dic47—21no—
22C2×D4×Dic47C2211yescharacteristic
23C2×D4×Dic47C2211yescharacteristic
24C2×D4×Dic47C2211yescharacteristic
25C2×#13093983—21no—
26C2×#13093983C2211yescharacteristic
27C22×C4⋊Dic47—21no—
28C22×C4⋊Dic47C2211yescharacteristic
29#15689224—24no—
30D8×Dic47—24no—
31C2×#13093958C2211yescharacteristic
32C2×#13093958C2211yescharacteristic
33C2×#13093948C2211yescharacteristic
34C2×#13093948C2211yescharacteristic
35C2×#13093945C2211yescharacteristic
36C2×#13093945C2211yescharacteristic
37C2×#13093945C2211yescharacteristic
38C2×#13093945C2211yescharacteristic
39C2×C22⋊(C47⋊C8)C2211yescharacteristic
40C2×#13093934C2211yescharacteristic
41C2×C8×Dic47C2211yescharacteristic
42#15689026—21no—
43#15689026C2211yescharacteristic
44#15689022C2211yescharacteristic
45#15689016—21no—
46#15689003—21no—
47#15688998—21no—
48#15688983C2211yescharacteristic
49C4⋊C4×Dic47C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C22×#41×C47C2211yescharacteristic
57C22×SD16×C47C2211yescharacteristic
58C22×D8×C47C2211yescharacteristic
59C2×#121×C47C2211yescharacteristic
60C47×#449C418yescomplemented
61C2×#103×C47C2211yescharacteristic
62C2×#102×C47C2211yescharacteristic
63C2×C22⋊C8×C47C2211yescharacteristic
64C23×Dic47—21no—
65C23×Dic47—21no—
66C23×Dic47—21no—
67C23×Dic47—21no—
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70Q8×Dic47—22no—
71Q8×Dic47—22no—
72Q8×Dic47—22no—
73Q8×Dic47D414yescomplemented
74D4×Dic47—28no—
75D4×Dic47—28no—
76D4×Dic47—22no—
77D4×Dic47—22no—
78D4×Dic47—22no—
79D4×Dic47—22no—
80D4×Dic47—22no—
81D4×Dic47D414yescomplemented
82#13093983—28no—
83#13093983—22no—
84#13093983—22no—
85C2×C4⋊Dic47—28no—
86C2×C4⋊Dic47—21no—
87C2×C4⋊Dic47—21no—
88C2×C4⋊Dic47—21no—
89C2×C4⋊Dic47—22no—
90C2×C4⋊Dic47—22no—
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⋊Dic47—21no—
102C2×C22⋊Dic47—21no—
103C2×C22⋊Dic47—21no—
104C2×C22⋊Dic47D411yescharacteristic
105C2×C22⋊Dic47D411yescharacteristic
106C2×C4×Dic47—21no—
107C2×C4×Dic47—21no—
108C2×C4×Dic47—21no—
109C2×C4×Dic47C2311yescharacteristic
110C2×C4×Dic47C2311yescharacteristic
111#13093958—22no—
112#13093958—22no—
113#13093948—22no—
114#13093948—22no—
115#13093945—22no—
116#13093945—22no—
117#13093945—22no—
118#13093945—22no—
119C22⋊(C47⋊C8)—22no—
120#13093934—22no—
121C8×Dic47—22no—
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×C414yescomplemented
131C22×Q8×C47C2311yescharacteristic
132C22×D4×C47—21no—
133C22×D4×C47—21no—
134C22×D4×C47C2311yescharacteristic
135C22×D4×C47C2311yescharacteristic
136C23×C4×C47—21no—
137C23×C4×C47C2311yescharacteristic
138C2×SD16×C47—22no—
139C2×SD16×C47—22no—
140C2×SD16×C47C2×C414yescomplemented
141C2×D8×C47—22no—
142C2×D8×C47—22no—
143C2×D8×C47C2×C414yescomplemented
144C22×C8×C47C2311yescharacteristic
145C22×C8×C47C2311yescharacteristic
146#121×C47—22no—
147#121×C47C2×C414yescomplemented
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×C47—21no—
155C24×C47C2×D411yescharacteristic
156#41×C47—28no—
157#41×C47—28no—
158#41×C47—28no—
159#41×C47—28no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47C22×C412yes—
164C2×Q8×C47C2×D412yes—
165C2×Q8×C47#4112yes—
166C2×D4×C47—24no—
167C2×D4×C47—24no—
168C2×D4×C47—24no—
169C2×D4×C47—24no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47—81no—
179C2×D4×C47—81no—
180C2×D4×C47C22×C412yes—
181C2×D4×C47C22×C412yes—
182C2×D4×C47C2×D412yes—
183C2×D4×C47#4112yes—
184C22×C4×C47—24no—
185C22×C4×C47—24no—
186C22×C4×C47—21no—
187C22×C4×C47—24no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47C22×C412yes—
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47#4112yes—
196C22×C4×C47C2411yescharacteristic
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—24no—
200C22×Dic47—24no—
201C22×Dic47—24no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—42no—
205C22×Dic47—81no—
206C22×Dic47—81no—
207C22×Dic47—81no—
208C22×Dic47—81no—
209C22×Dic47—81no—
210C22×Dic47—81no—
211C22×Dic47—81no—
212C22×Dic47—81no—
213C22×Dic47C2×D411yescharacteristic
214C22×Dic47C2×D411yescharacteristic
215C22×Dic47C2×D411yescharacteristic
216C22×Dic47C2×D411yescharacteristic
217SD16×C47—28no—
218D8×C47—28no—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47C22×C412yes—
224C2×C8×C47C22×C412yes—
225C4⋊C4×C47—21no—
226C4⋊C4×C47C22×C412yes—
227C22⋊C4×C47—24no—
228C22⋊Dic47—24no—
229C22⋊Dic47—24no—
230C22⋊Dic47—22no—
231C22⋊Dic47—22no—
232C22⋊Dic47—42no—
233C22⋊Dic47—81no—
234C22⋊Dic47—81no—
235C22⋊Dic47—81no—
236C4⋊Dic47—24no—
237C4⋊Dic47—24no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47—22no—
241C4⋊Dic47—24no—
242C4⋊Dic47—22no—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47—21no—
246C4⋊Dic47—21no—
247C4⋊Dic47—81no—
248C4⋊Dic47C2×D412yes—
249C4⋊Dic47C2×D412yes—
250C4×Dic47—24no—
251C4×Dic47—21no—
252C4×Dic47—21no—
253C4×Dic47—24no—
254C4×Dic47—81no—
255C4×Dic47C2×D412yes—
256C4×Dic47C2×D412yes—
257C2×C47⋊C8—21no—
258C2×C47⋊C8—21no—
259C2×C47⋊C8—21no—
260C2×C47⋊C8—21no—
261C2×C47⋊C8—21no—
262C2×C47⋊C8—21no—
263C23×C47—22no—
264C23×C47—21no—
265C23×C47—22no—
266C23×C47—21no—
267C23×C47—22no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—22no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47C4×D412yes—
284C23×C47C22×D411yescharacteristic
285Q8×C47—22no—
286Q8×C47—22no—
287Q8×C47—22no—
288Q8×C47C4×D414yes—
289D4×C47—216no—
290D4×C47—22no—
291D4×C47—22no—
292D4×C47—22no—
293D4×C47—22no—
294D4×C47—22no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—84no—
298D4×C47C4×D414yes—
299C2×C4×C47—216no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47C4×D412yes—
313C2×C4×C47C23×C411yescharacteristic
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C2×#4111yescharacteristic
317C2×C4×C47C2×#4111yescharacteristic
318C2×C4×C47C2×#4111yescharacteristic
319C2×Dic47—21no—
320C2×Dic47—21no—
321C2×Dic47—21no—
322C2×Dic47—21no—
323C2×Dic47—21no—
324C2×Dic47—21no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—21no—
328C2×Dic47—21no—
329C2×Dic47—21no—
330C2×Dic47—21no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47—41no—
334C2×Dic47—41no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—41no—
341C2×Dic47—84no—
342C2×Dic47—84no—
343C2×Dic47—84no—
344C2×Dic47—84no—
345C2×Dic47#12012yes—
346C2×Dic47#12012yes—
347C8×C47—22no—
348C8×C47—22no—
349C47⋊C8—41no—
350C47⋊C8—41no—
351#21460—471nomaximal, Sylow
352C22×C47—22no—
353C22×C47—22no—
354C22×C47—22no—
355C22×C47—24no—
356C22×C47—41no—
357C22×C47—42no—
358C22×C47—41no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47—42no—
362C22×C47—41no—
363C22×C47—42no—
364C22×C47—41no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47—81no—
370C22×C47—81no—
371C22×C47—81no—
372C22×C47—81no—
373C22×C47C2×C4×D411yescharacteristic
374C22×C47C2×#12011yescharacteristic
375C22×C47#52511yescharacteristic
376C22×C47#57611yescharacteristic
377C22×C47#57611yescharacteristic
378C22×C47#57711yescharacteristic
379C22×C47#57811yescharacteristic
380C4×C47—22no—
381C4×C47—24no—
382C4×C47—42no—
383C4×C47C2×C4×D411yescharacteristic
384C4×C47C2×C4×D411yescharacteristic
385C4×C47#52511yescharacteristic
386C4×C47#52511yescharacteristic
387Dic47—22no—
388Dic47—22no—
389Dic47—41no—
390Dic47—42no—
391Dic47—42no—
392Dic47—41no—
393Dic47—81no—
394Dic47—81no—
395C2×#520—471no—
396C2×#449D4711yescharacteristic
397C2×#440—471no—
398C2×C4×D8—471no—
399#2324—471no—
400#1880—471no—
401#1879—471no—
402#1874—471no—
403#1863—471no—
404#1862—471no—
405#1852—471no—
406#1788—471no—
407#1762—471no—
408C4×#103—471no—
409#1750—471no—
410C2×C47—42no—
411C2×C47—44no—
412C2×C47—82no—
413C2×C47C4×#12011yescharacteristic
414C2×C47#294611yescharacteristic
415C2×C47#295111yescharacteristic
416C2×C47#300811yescharacteristic
417C2×C47#301311yescharacteristic
418C2×C47#311911yescharacteristic
419C2×C47#312411yescharacteristic
420C22×#41C2×D4711yescharacteristic
421C22×SD16C2×D4711yescharacteristic
422C22×D8C2×D4711yescharacteristic
423C2×#121C2×D4711yescharacteristic
424#520—944no—
425#520—944no—
426C2×C4×Q8—471no—
427C2×C4×Q8—471no—
428C2×C4×D4—471no—
429C2×C4×D4—471no—
430C2×C4×D4—471no—
431C2×C4×D4—941no—
432C2×C4×D4—941no—
433C2×#117—471no—
434C2×#117—941no—
435C22×C4⋊C4—471no—
436C22×C4⋊C4—941no—
437#449Dic4718yescomplemented
438#440—944no—
439C4×D8—944no—
440C2×#107—471no—
441C2×#107—471no—
442C2×#103—471no—
443C2×#103—471no—
444C2×#103C2×D4711yescharacteristic
445C2×#102—471no—
446C2×#102—471no—
447C2×#102—471no—
448C2×#102—471no—
449C2×#102C2×D4711yescharacteristic
450C2×C22⋊C8—471no—
451C2×C22⋊C8C2×D4711yescharacteristic
452C2×#97—471no—
453C2×C4×C8—471no—
454#390—471no—
455#390—941no—
456#389—471no—
457#388—941no—
458#386—941no—
459#385—941no—
460#380—471no—
461C4×C4⋊C4—471no—
462#340—471no—
463#340—471no—
464#340—471no—
465#340—471no—
466#336—471no—
467#336—471no—
468C47#2146011yescharacteristic, complemented, Sylow
469C2×#41—22no—
470C2×#41—22no—
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—22no—
474C2×#41C2×Dic4714yescomplemented
475C22×Q8C22×D4711yescharacteristic
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C22×D4711yescharacteristic
479C22×D4C22×D4711yescharacteristic
480C23×C4—21no—
481C23×C4—941no—
482C23×C4—941no—
483C23×C4—941no—
484C23×C4—941no—
485C23×C4C22×D4711yescharacteristic
486C2×SD16—22no—
487C2×SD16—22no—
488C2×SD16C2×Dic4714yescomplemented
489C2×D8—22no—
490C2×D8—22no—
491C2×D8C2×Dic4714yescomplemented
492C22×C8—471no—
493C22×C8—471no—
494C22×C8C22×D4711yescharacteristic
495C22×C8C22×D4711yescharacteristic
496#121—22no—
497#121C2×Dic4714yescomplemented
498C4×Q8—474no—
499C4×Q8—942no—
500C4×Q8—942no—
501C4×Q8—942no—
502C4×D4—474no—
503C4×D4—942no—
504C4×D4—942no—
505C4×D4—942no—
506C4×D4—942no—
507C4×D4—948no—
508C4×D4—948no—
509C4×D4—942no—
510#117—942no—
511#117—942no—
512#117—948no—
513C2×C4⋊C4—471no—
514C2×C4⋊C4—471no—
515C2×C4⋊C4—471no—
516C2×C4⋊C4—471no—
517C2×C4⋊C4—471no—
518C2×C4⋊C4—471no—
519C2×C4⋊C4—942no—
520C2×C4⋊C4—942no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—948no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4C22×D4711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—471no—
529C2×C22⋊C4—471no—
530C2×C22⋊C4—941no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C42—471no—
537C2×C42—471no—
538C2×C42—941no—
539C2×C42—941no—
540C2×C42—941no—
541#107—942no—
542#107—942no—
543#103—942no—
544#103—942no—
545#103C2×Dic4714yescomplemented
546#102—942no—
547#102—942no—
548#102—942no—
549#102—942no—
550#102C2×Dic4714yescomplemented
551C22⋊C8—942no—
552C22⋊C8C2×Dic4714yescomplemented
553#97—942no—
554C4×C8—942no—
555#95—941no—
556#95—941no—
557#95—941no—
558C24—21no—
559C24—21no—
560C24D4×D4711yescharacteristic
561#41—28no—
562#41—28no—
563#41—28no—
564#41—28no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8D4×D4712yes—
569C2×Q8#1062535212yes—
570C2×Q8C22×Dic4712yes—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4D4×D4712yes—
586C2×D4#1062535212yes—
587C2×D4C22×Dic4712yes—
588C2×D4C22×Dic4712yes—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—471no—
599C22×C4—471no—
600C22×C4—471no—
601C22×C4—471no—
602C22×C4—944no—
603C22×C4—944no—
604C22×C4—944no—
605C22×C4—941no—
606C22×C4—941no—
607C22×C4—941no—
608C22×C4—941no—
609C22×C4—3761no—
610C22×C4—3761no—
611C22×C4—3761no—
612C22×C4—3761no—
613C22×C4—3761no—
614C22×C4—3761no—
615C22×C4—3761no—
616C22×C4—3761no—
617C22×C4—1882no—
618C22×C4D4×D4711yescharacteristic
619C22×C4#1062535212yes—
620C22×C4C22×Dic4712yes—
621C22×C4C23×D4711yescharacteristic
622SD16—28no—
623D8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—941no—
629C2×C8—941no—
630C2×C8—941no—
631C2×C8—941no—
632C2×C8—941no—
633C2×C8—941no—
634C2×C8C22×Dic4712yes—
635C2×C8C22×Dic4712yes—
636C4⋊C4—21no—
637C4⋊C4—472no—
638C4⋊C4—472no—
639C4⋊C4—942no—
640C4⋊C4—942no—
641C4⋊C4—944no—
642C4⋊C4—944no—
643C4⋊C4—944no—
644C4⋊C4—941no—
645C4⋊C4—941no—
646C4⋊C4—941no—
647C4⋊C4—941no—
648C4⋊C4—941no—
649C4⋊C4—941no—
650C4⋊C4—3761no—
651C4⋊C4C22×Dic4712yes—
652C22⋊C4—24no—
653C22⋊C4—942no—
654C22⋊C4—942no—
655C22⋊C4—944no—
656C22⋊C4—944no—
657C22⋊C4—3761no—
658C22⋊C4—3761no—
659C22⋊C4—3761no—
660C22⋊C4—1882no—
661C42—472no—
662C42—472no—
663C42—944no—
664C42—944no—
665C42—941no—
666C42—941no—
667C42—3761no—
668C23—22no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23D4×Dic4712yes—
689C23C2×D4×D4711yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8D4×Dic4714yes—
694D4—216no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4D4×Dic4714yes—
704C2×C4—216no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—472no—
718C2×C4—472no—
719C2×C4—941no—
720C2×C4—941no—
721C2×C4—941no—
722C2×C4—941no—
723C2×C4—941no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—941no—
727C2×C4—941no—
728C2×C4—941no—
729C2×C4—941no—
730C2×C4—941no—
731C2×C4—3764no—
732C2×C4—3764no—
733C2×C4—3764no—
734C2×C4—3764no—
735C2×C4—1881no—
736C2×C4—1881no—
737C2×C4—1881no—
738C2×C4—1881no—
739C2×C4—1881no—
740C2×C4—1881no—
741C2×C4—1881no—
742C2×C4—1881no—
743C2×C4—1881no—
744C2×C4—1881no—
745C2×C4D4×Dic4712yes—
746C2×C4C23×Dic4711yescharacteristic
747C2×C4C2×D4×D4711yescharacteristic
748C2×C4C2×D4×D4711yescharacteristic
749C2×C4C2×#1062535211yescharacteristic
750C2×C4C2×#1062535211yescharacteristic
751C2×C4C2×#1062535211yescharacteristic
752C8—22no—
753C8—22no—
754C8—1881no—
755C8—1881no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×D4×Dic4711yescharacteristic
778C22#120×D4711yescharacteristic
779C22#1568962911yescharacteristic
780C22#1568992511yescharacteristic
781C22#1568992711yescharacteristic
782C22#1568993311yescharacteristic
783C22#1568993711yescharacteristic
784C4—22no—
785C4—24no—
786C4—42no—
787C4—942no—
788C4—942no—
789C4—3761no—
790C4—3761no—
791C4—1881no—
792C4—1881no—
793C4—1882no—
794C4—1882no—
795C4C2×D4×Dic4711yescharacteristic
796C4C2×D4×Dic4711yescharacteristic
797C4#1568962911yescharacteristic
798C4#1568962911yescharacteristic
799C2—42no—
800C2—44no—
801C2—82no—
802C2#120×Dic4711yescharacteristic
803C2#2025222111yescharacteristic
804C2#2025226411yescharacteristic
805C2#2025265311yescharacteristic
806C2#2025270111yescharacteristic
807C2#2025358011yescharacteristic
808C2#2025364311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#449C2
socleC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenterC2×#449D47
hypocenterC47#21460
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#15689606C2semidirect
2. C2×#15689224C2semidirect
3. C2×D8×Dic47C2semidirect
4. #20246083C2semidirect
5. #20243745C2semidirect
6. #20243738C2semidirect
7. #20243706C2semidirect
8. #20243644C2semidirect
9. #20243637C2semidirect
10. #20243578C2semidirect
11. #20243328C2semidirect
12. #20243215C2semidirect
13. #103×Dic47C2semidirect
14. #20243156C2semidirect
60. C47×#449C4semidirect
73. Q8×Dic47D4semidirect
81. D4×Dic47D4semidirect
130. C2×#41×C47C2×C4semidirect
140. C2×SD16×C47C2×C4semidirect
143. C2×D8×C47C2×C4semidirect
147. #121×C47C2×C4semidirect
150. #103×C47C2×C4semidirect
151. #102×C47C2×C4semidirect
152. C22⋊C8×C47C2×C4semidirect
437. #449Dic47semidirect
468. C47#21460semidirect
474. C2×#41C2×Dic47semidirect
488. C2×SD16C2×Dic47semidirect
491. C2×D8C2×Dic47semidirect
497. #121C2×Dic47semidirect
545. #103C2×Dic47semidirect
550. #102C2×Dic47semidirect
552. 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×#156892242
C2×D8×Dic472
#202460832
#202437452
#202437382
#202437062
#202436442
#202436372
#202435782
#202433282
#202432152
#103×Dic472
#202431562
C2×C47×#4492
#2146047