Finite Group Databasebeta

← #26215860

Subgroups — #26215860

Order 12032.

1590 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D47C211yesmaximal, characteristic
2C2×#15689164C211yesmaximal, characteristic, complemented
3C2×#15689162C211yesmaximal, characteristic, complemented
4#20245770C211yesmaximal, characteristic
5#380×D47C211yesmaximal, characteristic
6#20243421C211yesmaximal, characteristic, complemented
7#20243419C211yesmaximal, characteristic, complemented
8#20243419C211yesmaximal, characteristic, complemented
9#20243416C211yesmaximal, characteristic, complemented
10#20243414C211yesmaximal, characteristic, complemented
11#20243412C211yesmaximal, characteristic, complemented
12#20243410C211yesmaximal, characteristic, complemented
13#20243106C211yesmaximal, characteristic, complemented
14#20243106C211yesmaximal, characteristic, complemented
15C47×#1809C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C2×M16×D47—24no—
21C2×M16×D47—24no—
22C2×M16×D47C418yescomplemented
23C22×C8×D47C2211yescharacteristic
24C22×C8×D47C2211yescharacteristic
25C2×#13093982C2211yescharacteristic
26C2×#13093982C2211yescharacteristic
27C2×C4⋊C4×D47C2211yescharacteristic
28C2×C4⋊C4×D47C2211yescharacteristic
29C2×C22⋊C4×D47—21no—
30#15689164—24no—
31#15689162—24no—
32C2×#13093958C2211yescharacteristic, complemented
33C2×#13093957C2211yescharacteristic, complemented
34C2×#13093957C2211yescharacteristic, complemented
35C2×#13093956C2211yescharacteristic, complemented
36C2×#13093955C2211yescharacteristic, complemented
37C2×#13093955C2211yescharacteristic, complemented
38#15688985—21no—
39#15688983C2211yescharacteristic
40#15688983C2211yescharacteristic
41#15688982—21no—
42#15688981—21no—
43#15688980C2211yescharacteristic
44#15688980C2211yescharacteristic
45#15688980C2211yescharacteristic
46#15688980C2211yescharacteristic
47#15688978—21no—
48C22⋊C4×Dic47—21no—
49#15688970—21no—
50#95×D47—21no—
51#15688886C2211yescharacteristic, complemented
52#15688886C2211yescharacteristic, complemented
53#15688885C2211yescharacteristic, complemented
54#15688885C2211yescharacteristic, complemented
55#15688885C2211yescharacteristic, complemented
56#15688885C2211yescharacteristic, complemented
57C22×M16×C47C2211yescharacteristic
58C2×#107×C47C2211yescharacteristic, complemented
59C2×#106×C47C2211yescharacteristic, complemented
60C47×#380C2211yescharacteristic
61C47×#380C2211yescharacteristic
62C47×#340C2211yescharacteristic, complemented
63C47×#340C2211yescharacteristic, complemented
64C24×D47D411yescharacteristic
65C23×Dic47D411yescharacteristic
66C22×C4×D47—22no—
67C22×C4×D47—22no—
68C22×C4×D47—22no—
69C22×C4×D47—22no—
70C22×C4×D47—21no—
71C22×C4×D47—21no—
72C22×C4×D47C2×C414yes—
73C22×C4×D47D411yescharacteristic
74C22×C4×D47D411yescharacteristic
75C22×C4×D47Q814yes—
76C22×C4×D47C2311yescharacteristic
77C22×C4×D47C2311yescharacteristic
78C2×#10625329—22no—
79C2×#10625329—22no—
80C2×#10625329C2×C414yescomplemented
81C2×#10625324—22no—
82C2×#10625324—22no—
83C2×#10625324C2×C414yes—
84C2×#10625324C2×C414yes—
85C2×#10625324D414yes—
86C2×#10625324D414yes—
87M16×D47—232no—
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90C2×C8×D47—22no—
91C2×C8×D47—22no—
92C2×C8×D47—22no—
93C2×C8×D47—22no—
94C2×C8×D47C2×C414yescomplemented
95C2×C8×D47C2×C414yescomplemented
96#13093982—22no—
97#13093982—22no—
98#13093982—22no—
99#13093982—22no—
100C2×C4⋊Dic47C2311yescharacteristic
101C2×C4⋊Dic47C2311yescharacteristic
102C2×C4⋊Dic47C2311yescharacteristic
103C2×C4⋊Dic47C2311yescharacteristic
104C2×Dic47⋊C4—21no—
105C2×Dic47⋊C4—21no—
106C4⋊C4×D47—22no—
107C4⋊C4×D47—22no—
108C4⋊C4×D47—22no—
109C4⋊C4×D47—22no—
110C2×C22⋊Dic47—21no—
111C2×C22⋊Dic47—21no—
112C2×(C2×D47)⋊C4—21no—
113C2×(C2×D47)⋊C4—21no—
114C2×(C2×D47)⋊C4—21no—
115C2×(C2×D47)⋊C4—21no—
116C2×(C2×D47)⋊C4—21no—
117C2×(C2×D47)⋊C4—21no—
118C22⋊C4×D47—44no—
119C2×C4×Dic47—21no—
120C2×C4×Dic47—21no—
121#13093958—22no—
122#13093957—22no—
123#13093957—22no—
124#13093956—22no—
125#13093955—22no—
126#13093955—22no—
127C47⋊#95—21no—
128C47⋊#95—21no—
129C47⋊#95—21no—
130C47⋊#95—21no—
131C47⋊#95—21no—
132C47⋊#95—21no—
133C23×C4×C47C2311yescharacteristic
134C2×M16×C47—22no—
135C2×M16×C47—22no—
136C2×M16×C47C2×C414yescomplemented
137C22×C8×C47C2311yescharacteristic
138C22×C8×C47C2311yescharacteristic
139C2×C4⋊C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47C2311yescharacteristic
141C2×C4⋊C4×C47C2311yescharacteristic
142C2×C4⋊C4×C47C2311yescharacteristic
143C2×C22⋊C4×C47—21no—
144C2×C22⋊C4×C47—21no—
145#107×C47—22no—
146#106×C47—22no—
147#95×C47—21no—
148#95×C47—21no—
149C24×C47C2×D411yescharacteristic
150C23×D47—22no—
151C23×D47—22no—
152C23×D47—22no—
153C23×D47—22no—
154C23×D47—41no—
155C23×D47—41no—
156C23×D47C4⋊C414yes—
157C23×D47C2×D411yescharacteristic
158C23×D47C2×D411yescharacteristic
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47C22×C412yes—
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47C2×Q812yes—
170C22×C4×C47C2411yescharacteristic
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47C4⋊C414yes—
178C22×Dic47C2×D411yescharacteristic
179C22×Dic47C2×D411yescharacteristic
180C2×C4×D47—22no—
181C2×C4×D47—22no—
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—22no—
187C2×C4×D47—22no—
188C2×C4×D47—28no—
189C2×C4×D47—28no—
190C2×C4×D47—28no—
191C2×C4×D47—28no—
192C2×C4×D47—42no—
193C2×C4×D47—42no—
194C2×C4×D47—42no—
195C2×C4×D47—42no—
196C2×C4×D47—42no—
197C2×C4×D47—42no—
198C2×C4×D47C4⋊C414yes—
199C2×C4×D47C4⋊C414yes—
200C2×C4×D47C22×C412yes—
201C2×C4×D47C22×C412yes—
202C2×C4×D47C2×D412yes—
203C2×C4×D47C2×D412yes—
204C2×C4×D47C2×Q812yes—
205C2×C4×D47C2×Q812yes—
206C2×C4×D47#4112yes—
207C2×C4×D47#4112yes—
208M16×C47—28no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47C22×C412yes—
212C2×C8×C47C22×C412yes—
213C2×C8×C47C2×D412yes—
214C2×C8×C47C2×D412yes—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C22⋊C4×C47—42no—
224C22⋊C4×C47—42no—
225C22⋊Dic47—42no—
226C22⋊Dic47—42no—
227(C2×D47)⋊C4—42no—
228(C2×D47)⋊C4—42no—
229(C2×D47)⋊C4—42no—
230(C2×D47)⋊C4—42no—
231(C2×D47)⋊C4—42no—
232(C2×D47)⋊C4—42no—
233C4⋊Dic47—21no—
234C4⋊Dic47—21no—
235C4⋊Dic47—21no—
236C4⋊Dic47—21no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47—21no—
241Dic47⋊C4—42no—
242Dic47⋊C4—42no—
243C4×Dic47—42no—
244C4×Dic47—42no—
245#10625329—28no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8C22×C412yes—
249C2×C47⋊C8C22×C412yes—
250C2×C47⋊C8C2×D412yes—
251C2×C47⋊C8C2×D412yes—
252#10625324—28no—
253#10625324C22⋊C4116yescomplemented
254C8×D47—28no—
255C8×D47—28no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47C2×C4⋊C412yes—
263C23×C47C22×D411yescharacteristic
264C22×D47—21no—
265C22×D47—21no—
266C22×D47—21no—
267C22×D47—21no—
268C22×D47—21no—
269C22×D47—21no—
270C22×D47—21no—
271C22×D47—21no—
272C22×D47—28no—
273C22×D47—28no—
274C22×D47—44no—
275C22×D47—44no—
276C22×D47—44no—
277C22×D47—44no—
278C22×D47—44no—
279C22×D47C2×C4⋊C412yes—
280C22×D47C2×C4⋊C412yes—
281C22×D47#12112yes—
282C22×D47#12112yes—
283C22×D47AGL(1,ℤ/8)12yes—
284C22×D47#13712yes—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47C2×C4⋊C412yes—
304C2×C4×C47C23×C411yescharacteristic
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47C22×D411yescharacteristic
307C2×C4×C47C22×Q811yescharacteristic
308C2×C4×C47C2×#4111yescharacteristic
309C2×C4×C47C2×#4111yescharacteristic
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—28no—
313C2×Dic47—41no—
314C2×Dic47—41no—
315C2×Dic47—41no—
316C2×Dic47—41no—
317C2×Dic47—41no—
318C2×Dic47—41no—
319C2×Dic47—41no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47C2×C4⋊C412yes—
326C2×Dic47C2×C4⋊C412yes—
327C2×Dic47#12112yes—
328C2×Dic47#12112yes—
329C4×D47—28no—
330C4×D47—22no—
331C4×D47—22no—
332C4×D47—22no—
333C4×D47—22no—
334C4×D47—28no—
335C4×D47—84no—
336C4×D47—84no—
337C4×D47C2×C22⋊C414yes—
338C4×D47#11714yes—
339C4×D47C22⋊Q814yes—
340C4×D47C22⋊Q814yes—
341C8×C47—22no—
342C8×C47C2×C22⋊C414yescomplemented
343C47⋊C8—22no—
344C47⋊C8C2×C22⋊C414yescomplemented
345#20661—471nomaximal, Sylow
346C22×C47—22no—
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47C22×C4⋊C411yescharacteristic
354C22×C47C2×#12111yescharacteristic
355C22×C47C2×#12111yescharacteristic
356C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C47C2×#13711yescharacteristic
358C22×C47#57511yescharacteristic
359C22×C47#57511yescharacteristic
360C2×D47—22no—
361C2×D47—22no—
362C2×D47—22no—
363C2×D47—22no—
364C2×D47—22no—
365C2×D47—22no—
366C2×D47—22no—
367C2×D47—22no—
368C2×D47—22no—
369C2×D47—22no—
370C2×D47—22no—
371C2×D47—22no—
372C2×D47—416no—
373C2×D47#38014yes—
374C2×D47#42814yescomplemented
375C4×C47—22no—
376C4×C47—81no—
377C4×C47—81no—
378C4×C47—81no—
379C4×C47—81no—
380C4×C47C22×C22⋊C411yescharacteristic
381C4×C47C2×#11711yescharacteristic
382C4×C47C2×C22⋊Q811yescharacteristic
383C4×C47C2×C22⋊Q811yescharacteristic
384Dic47—22no—
385Dic47—81no—
386Dic47—81no—
387Dic47—81no—
388Dic47—81no—
389Dic47#38014yes—
390C23×M16—471no—
391C2×#428—471no—
392C2×#428—471no—
393#2280—471no—
394C2×#380—471no—
395#1809—471no—
396#1809—471no—
397#1809—471no—
398#1809D4711yescharacteristic, complemented
399#1808—471no—
400#1808—471no—
401#1807—471no—
402#1807—471no—
403#1736—471no—
404#1736—471no—
405C2×C47—42no—
406C2×C47C2×#38011yescharacteristic
407C2×C47C2×#42811yescharacteristic
408C2×C47#291111yescharacteristic
409C2×C47#305511yescharacteristic
410C2×C47#305511yescharacteristic
411C2×C47#305611yescharacteristic
412C2×C47#305611yescharacteristic
413D47—24no—
414D47—24no—
415C24×C4—471no—
416C22×M16—471no—
417C22×M16—478no—
418C22×M16—471no—
419C22×M16—471no—
420C22×M16—944no—
421C22×M16—944no—
422C22×M16C2×D4711yescharacteristic
423C23×C8—471no—
424C23×C8—471no—
425C2×#117—471no—
426C2×#117—471no—
427C22×C4⋊C4—471no—
428C22×C4⋊C4—471no—
429C22×C22⋊C4—941no—
430#428—944no—
431#428—944no—
432C2×#107—471no—
433C2×#107—471no—
434C2×#107—471no—
435C2×#107C2×D4711yescharacteristic, complemented
436C2×#106—471no—
437C2×#106—471no—
438C2×#106—471no—
439C2×#106C2×D4711yescharacteristic, complemented
440#381—941no—
441#380—471no—
442#380—471no—
443#380—471no—
444#380—471no—
445#380—471no—
446#380—471no—
447#380—941no—
448#380—941no—
449#380C2×D4711yescharacteristic
450#380C2×D4711yescharacteristic
451#379—941no—
452C4×C22⋊C4—941no—
453C4×C22⋊C4—941no—
454C2×#95—941no—
455#340—471no—
456#340—471no—
457#340—471no—
458#340—471no—
459#340—471no—
460#340—471no—
461#340C2×D4711yescharacteristic, complemented
462#340C2×D4711yescharacteristic, complemented
463C47#2066111yescharacteristic, complemented, Sylow
464C25—471no—
465C23×C4—471no—
466C23×C4—471no—
467C23×C4—474no—
468C23×C4—471no—
469C23×C4—471no—
470C23×C4—474no—
471C23×C4—471no—
472C23×C4—942no—
473C23×C4—942no—
474C23×C4—942no—
475C23×C4—942no—
476C23×C4—941no—
477C23×C4—941no—
478C23×C4C22×D4711yescharacteristic
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—474no—
482C2×M16—474no—
483C2×M16—474no—
484C2×M16—474no—
485C2×M16—474no—
486C2×M16—942no—
487C2×M16—942no—
488C2×M16—942no—
489C2×M16—942no—
490C2×M16—9432no—
491C2×M16C4×D4714yescomplemented
492C22×C8—471no—
493C22×C8—471no—
494C22×C8—474no—
495C22×C8—474no—
496C22×C8—942no—
497C22×C8—942no—
498C22×C8—942no—
499C22×C8—942no—
500C22×C8C22×D4711yescharacteristic
501C22×C8C22×D4711yescharacteristic
502#117—942no—
503#117—942no—
504#117—942no—
505#117—942no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—942no—
511C2×C4⋊C4—942no—
512C2×C4⋊C4—942no—
513C2×C4⋊C4—942no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4C22×D4711yescharacteristic
517C2×C4⋊C4C22×D4711yescharacteristic
518C2×C4⋊C4C22×D4711yescharacteristic
519C2×C4⋊C4C22×D4711yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—941no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4—941no—
529C2×C22⋊C4—941no—
530C2×C22⋊C4—1884no—
531C2×C42—941no—
532C2×C42—941no—
533#107—22no—
534#107—942no—
535#107—942no—
536#107—942no—
537#106—22no—
538#106—942no—
539#106—942no—
540#106—942no—
541#95—21no—
542#95—21no—
543#95—941no—
544#95—941no—
545#95—941no—
546#95—941no—
547#95—941no—
548#95—941no—
549C24—471no—
550C24—471no—
551C24—474no—
552C24—942no—
553C24—942no—
554C24—942no—
555C24—942no—
556C24—1881no—
557C24—1881no—
558C24D4×D4711yescharacteristic
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—471no—
568C22×C4—472no—
569C22×C4—472no—
570C22×C4—472no—
571C22×C4—472no—
572C22×C4—472no—
573C22×C4—472no—
574C22×C4—474no—
575C22×C4—471no—
576C22×C4—474no—
577C22×C4—474no—
578C22×C4—472no—
579C22×C4—472no—
580C22×C4—948no—
581C22×C4—942no—
582C22×C4—942no—
583C22×C4—948no—
584C22×C4—948no—
585C22×C4—948no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—1882no—
599C22×C4—1882no—
600C22×C4—1882no—
601C22×C4—1882no—
602C22×C4—1882no—
603C22×C4—1882no—
604C22×C4C2×C4×D4712yes—
605C22×C4D4×D4711yescharacteristic
606C22×C4Q8×D4712yes—
607C22×C4C23×D4711yescharacteristic
608M16—28no—
609M16—4716no—
610M16—948no—
611M16—948no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—472no—
615C2×C8—472no—
616C2×C8—472no—
617C2×C8—472no—
618C2×C8—948no—
619C2×C8—941no—
620C2×C8—941no—
621C2×C8—948no—
622C2×C8C2×C4×D4712yes—
623C2×C8C2×C4×D4712yes—
624C2×C8D4×D4712yes—
625C2×C8D4×D4712yes—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—941no—
635C4⋊C4—941no—
636C4⋊C4—941no—
637C4⋊C4—941no—
638C4⋊C4—941no—
639C4⋊C4—941no—
640C4⋊C4—941no—
641C4⋊C4—941no—
642C4⋊C4—1882no—
643C4⋊C4—1882no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—1882no—
647C22⋊C4—1882no—
648C22⋊C4—1882no—
649C22⋊C4—1882no—
650C22⋊C4—1882no—
651C22⋊C4—1882no—
652C22⋊C4—1882no—
653C22⋊C4—1882no—
654C42—1882no—
655C42—1882no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—472no—
663C23—472no—
664C23—472no—
665C23—472no—
666C23—472no—
667C23—472no—
668C23—948no—
669C23—948no—
670C23—941no—
671C23—941no—
672C23—941no—
673C23—941no—
674C23—941no—
675C23—941no—
676C23—941no—
677C23—941no—
678C23—1884no—
679C23—1884no—
680C23—1884no—
681C23—1884no—
682C23—1884no—
683C23C4⋊C4×D4712yes—
684C23C2×D4×D4711yescharacteristic
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—472no—
704C2×C4—472no—
705C2×C4—472no—
706C2×C4—474no—
707C2×C4—474no—
708C2×C4—474no—
709C2×C4—474no—
710C2×C4—472no—
711C2×C4—948no—
712C2×C4—948no—
713C2×C4—948no—
714C2×C4—941no—
715C2×C4—941no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—3764no—
721C2×C4—3764no—
722C2×C4—1881no—
723C2×C4—1881no—
724C2×C4—1881no—
725C2×C4—1881no—
726C2×C4—1881no—
727C2×C4—1881no—
728C2×C4—1881no—
729C2×C4—1881no—
730C2×C4—1881no—
731C2×C4—1881no—
732C2×C4—1881no—
733C2×C4—1881no—
734C2×C4C4⋊C4×D4712yes—
735C2×C4C22×C4×D4711yescharacteristic
736C2×C4C2×D4×D4711yescharacteristic
737C2×C4C2×D4×D4711yescharacteristic
738C2×C4C2×Q8×D4711yescharacteristic
739C2×C4#41×D4711yescharacteristic
740C2×C4#41×D4711yescharacteristic
741C8—22no—
742C8—474no—
743C8—942no—
744C8C22⋊C4×D4714yescomplemented
745C22—22no—
746C22—22no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—474no—
753C22—474no—
754C22—942no—
755C22—942no—
756C22—942no—
757C22—942no—
758C22—942no—
759C22—942no—
760C22—942no—
761C22—942no—
762C22—942no—
763C22—942no—
764C22—942no—
765C22—942no—
766C22—18816no—
767C22C2×C4⋊C4×D4711yescharacteristic
768C22#121×D4711yescharacteristic
769C22#121×D4711yescharacteristic
770C22AGL(1,ℤ/8)×D4711yescharacteristic
771C22#137×D4711yescharacteristic
772C22#1568991911yescharacteristic
773C22#1568992211yescharacteristic
774C4—22no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—474no—
780C4—942no—
781C4—3761no—
782C4—3761no—
783C4—3761no—
784C4—3761no—
785C4C2×C22⋊C4×D4711yescharacteristic
786C4#117×D4711yescharacteristic
787C4C22⋊Q8×D4711yescharacteristic
788C4C22⋊Q8×D4711yescharacteristic
789C2—42no—
790C2—944no—
791C2—944no—
792C2#380×D4711yescharacteristic
793C2#428×D4711yescharacteristic
794C2#2025197511yescharacteristic
795C2#2025300211yescharacteristic
796C2#2025300611yescharacteristic
797C2#2025301311yescharacteristic
798C2#2025301711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1809C2
socleC23×C47C22×D4
prime radicalC24×D47D4
cosocleC22×C4×C47C24
hypercenter#1809D47
hypocenterC47#20661
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#15689164C2semidirect
3. C2×#15689162C2semidirect
6. #20243421C2semidirect
7. #20243419C2semidirect
8. #20243419C2semidirect
9. #20243416C2semidirect
10. #20243414C2semidirect
11. #20243412C2semidirect
12. #20243410C2semidirect
13. #20243106C2semidirect
14. #20243106C2semidirect
15. C47×#1809C2semidirect
22. C2×M16×D47C4semidirect
32. C2×#13093958C22semidirect
33. C2×#13093957C22semidirect
34. C2×#13093957C22semidirect
35. C2×#13093956C22semidirect
36. C2×#13093955C22semidirect
37. C2×#13093955C22semidirect
51. #15688886C22semidirect
52. #15688886C22semidirect
53. #15688885C22semidirect
54. #15688885C22semidirect
55. #15688885C22semidirect
56. #15688885C22semidirect
58. C2×#107×C47C22semidirect
59. C2×#106×C47C22semidirect
62. C47×#340C22semidirect
63. C47×#340C22semidirect
80. C2×#10625329C2×C4semidirect
94. C2×C8×D47C2×C4semidirect
95. C2×C8×D47C2×C4semidirect
136. C2×M16×C47C2×C4semidirect
253. #10625324C22⋊C4semidirect
342. C8×C47C2×C22⋊C4semidirect
344. C47⋊C8C2×C22⋊C4semidirect
374. C2×D47#428semidirect
398. #1809D47semidirect
435. C2×#107C2×D47semidirect
439. C2×#106C2×D47semidirect
461. #340C2×D47semidirect
462. #340C2×D47semidirect
463. C47#20661semidirect
491. C2×M16C4×D47semidirect
744. C8C22⋊C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D472
C2×#156891642
C2×#156891622
#202457702
#380×D472
#202434212
#202434192
#202434162
#202434142
#202434122
#202434102
#202431062
C47×#18092
#2066147