Finite Group Databasebeta

← #25064082

Subgroups — #25064082

Order 11008.

1510 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D43C211yesmaximal, characteristic
2#407×D43C211yesmaximal, characteristic, complemented
3#380×D43C211yesmaximal, characteristic, complemented
4#19133165C212yesmaximal, complemented
5#19133161C212yesmaximal, complemented
6#19133139C211yesmaximal, characteristic, complemented
7#19133138C211yesmaximal, characteristic, complemented
8#19133136C211yesmaximal, characteristic, complemented
9#19133098C212yesmaximal, complemented
10#19133096C212yesmaximal, complemented
11C43×#1513C211yesmaximal, characteristic, complemented
12C2×#41×D43C411yescharacteristic, complemented
13C23×C4×D43C2211yescharacteristic
14C2×M16×D43—21no—
15#14583412C411yescharacteristic, complemented
16#14583412C2211yescharacteristic
17#14583411C411yescharacteristic, complemented
18#14583410C2211yescharacteristic
19#14583409C411yescharacteristic, complemented
20#14583409C2211yescharacteristic
21#14583408—21no—
22#14583408—21no—
23#14583407—21no—
24#14583406C411yescharacteristic, complemented
25#14583405—21no—
26#123×D43—21no—
27C22⋊Q8×D43C411yescharacteristic, complemented
28C22⋊Q8×D43C2211yescharacteristic
29#121×D43C411yescharacteristic, complemented
30#121×D43C2211yescharacteristic
31#120×D43—21no—
32C4×D4×D43—21no—
33C4×D4×D43—21no—
34#117×D43C411yescharacteristic, complemented
35C2×C4⋊C4×D43—21no—
36C2×C22⋊C4×D43—21no—
37#14582863C2211yescharacteristic, complemented
38#14582862—21no—
39#14582861—21no—
40#14582861C2212yescomplemented
41C22⋊C8×D43—21no—
42C22⋊C8×D43C2212yes—
43#14582759C2211yescharacteristic, complemented
44#14582758C2212yes—
45#14582757—21no—
46#14582756—21no—
47#95×D43C2212yescomplemented
48#14582637C2212yescomplemented
49#14582636C2212yescomplemented
50#14582635C2212yescomplemented
51#14582634C2212yescomplemented
52#14582633C2212yescomplemented
53#14582632C2212yescomplemented
54C43×#525C2211yescharacteristic
55C43×#407C2211yescharacteristic, complemented
56C43×#380C2211yescharacteristic, complemented
57C43×#328C2212yescomplemented
58C43×#327C2212yescomplemented
59C24×D43D411yescharacteristic
60C2×#10621902C2×C411yescharacteristic
61C2×#10621898—21no—
62C2×#10621898C2×C411yescharacteristic, complemented
63C2×#10621900—21no—
64C2×#10621900C2×C411yescharacteristic
65#41×D43—44no—
66C2×Q8×D43C2×C411yescharacteristic, complemented
67C2×D4×D43—21no—
68C2×D4×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43C2×C411yescharacteristic, complemented
71C23×Dic43D411yescharacteristic
72C22×C4×D43—21no—
73C22×C4×D43—22no—
74C22×C4×D43—44no—
75C22×C4×D43C2×C411yescharacteristic
76C22×C4×D43C2×C411yescharacteristic
77C22×C4×D43C2×C411yescharacteristic
78C22×C4×D43C2×C411yescharacteristic
79C22×C4×D43D411yescharacteristic
80C22×C4×D43D411yescharacteristic
81C22×C4×D43D411yescharacteristic
82C22×C4×D43D411yescharacteristic
83C22×C4×D43D411yescharacteristic
84C22×C4×D43D411yescharacteristic
85C22×C4×D43C2311yescharacteristic
86C22×C4×D43C2311yescharacteristic
87C2×#10621877—21no—
88C2×#10621872—22no—
89M16×D43—44no—
90C2×C8×D43—22no—
91#13063310—21no—
92#13063310—21no—
93#13063309—21no—
94#13063308—21no—
95#13063307—21no—
96#13063307—21no—
97#13063306—21no—
98#13063305C2×C411yescharacteristic
99#13063305C2×C411yescharacteristic, complemented
100#13063304C2×C411yescharacteristic, complemented
101#13063304C2311yescharacteristic
102#13063303—21no—
103#13063303—21no—
104#13063302—21no—
105#13063302—21no—
106#13063301C2×C411yescharacteristic
107#13063301C2×C411yescharacteristic, complemented
108#13063300C2×C411yescharacteristic
109#13063300C2×C411yescharacteristic, complemented
110#13063299C2×C411yescharacteristic, complemented
111#13063299C2311yescharacteristic
112#13063298—21no—
113#13063298—21no—
114#13063297—21no—
115#13063297—21no—
116#13063296C2×C411yescharacteristic
117#13063296C2×C411yescharacteristic, complemented
118#13063295—21no—
119#13063295—21no—
120#13063295—21no—
121#13063294—21no—
122#13063293—21no—
123#13063293—21no—
124#13063293—21no—
125C4×D172—21no—
126C4×D172—21no—
127D4×Dic43—21no—
128D4×Dic43—21no—
129#13063287—21no—
130#13063287—21no—
131C4×C22⋊D43—21no—
132C4×C22⋊D43—21no—
133C4×C22⋊D43—21no—
134C4×C22⋊D43—21no—
135(C22⋊D43)⋊C4—21no—
136(C22⋊D43)⋊C4—21no—
137(C22⋊D43)⋊C4—21no—
138(C22⋊D43)⋊C4—21no—
139#13063284C2×C411yescharacteristic, complemented
140#13063283C2×C411yescharacteristic
141#13063283C2×C411yescharacteristic
142#13063282—21no—
143#13063281—21no—
144C2×C4⋊Dic43—21no—
145C2×Dic43⋊C4—22no—
146C4⋊C4×D43—21no—
147C4⋊C4×D43—21no—
148C4⋊C4×D43—44no—
149C4⋊C4×D43C2×C411yescharacteristic, complemented
150C4⋊C4×D43C2×C411yescharacteristic, complemented
151C2×C22⋊Dic43—21no—
152C2×(C2×D43)⋊C4—22no—
153C22⋊C4×D43—21no—
154C22⋊C4×D43—21no—
155C22⋊C4×D43—21no—
156C22⋊C4×D43—21no—
157C22⋊C4×D43—21no—
158C22⋊C4×D43—44no—
159C42×D43—21no—
160C22⋊(C43⋊C8)—21no—
161C22⋊(C43⋊C8)C2312yes—
162(C2×D43)⋊C8—22no—
163(C2×D43)⋊C8—22no—
164C43⋊#95—22no—
165C43⋊#95C2312yes—
166C2×#41×C43C2×C411yescharacteristic, complemented
167C23×C4×C43C2311yescharacteristic
168C2×M16×C43—21no—
169#123×C43—21no—
170C22⋊Q8×C43C2×C411yescharacteristic, complemented
171C22⋊Q8×C43C2311yescharacteristic
172#121×C43C2×C411yescharacteristic, complemented
173#121×C43C2311yescharacteristic
174#120×C43—21no—
175C4×D4×C43—21no—
176C4×D4×C43—21no—
177#117×C43C2×C411yescharacteristic, complemented
178C2×C4⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C22⋊C8×C43—21no—
181C22⋊C8×C43C2312yes—
182#95×C43C2312yes—
183C24×C43C2×D411yescharacteristic
184C23×D43—22no—
185C23×D43—22no—
186C23×D43—21no—
187C23×D43—42no—
188C23×D43—42no—
189C23×D43C22⋊C411yescharacteristic
190C23×D43C22⋊C411yescharacteristic
191C23×D43C22⋊C411yescharacteristic
192C23×D43C22⋊C411yescharacteristic
193C23×D43C2×D411yescharacteristic
194C23×D43C2×D411yescharacteristic
195#41×C43—42no—
196C2×Q8×C43C22×C411yescharacteristic
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43C22×C411yescharacteristic
201C22×C4×C43—21no—
202C22×C4×C43—22no—
203C22×C4×C43—42no—
204C22×C4×C43C22×C411yescharacteristic
205C22×C4×C43C22×C411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2411yescharacteristic
210C2×C22⋊D43—21no—
211C2×C22⋊D43—21no—
212C2×C22⋊D43—21no—
213C2×C22⋊D43—21no—
214C2×C22⋊D43—21no—
215C2×C22⋊D43—21no—
216C2×C22⋊D43—21no—
217C22×Dic43—21no—
218C22×Dic43—22no—
219C22×Dic43—42no—
220C22×Dic43C22⋊C411yescharacteristic
221C22×Dic43C22⋊C411yescharacteristic
222C22×Dic43C22⋊C411yescharacteristic
223C22×Dic43C22⋊C411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225C22×Dic43C2×D411yescharacteristic
226#10621902—42no—
227Q8×D43—42no—
228#10621900—42no—
229#10621900—44no—
230D4×D43—44no—
231D4×D43—44no—
232D4×D43—42no—
233D4×D43—42no—
234D4×D43—42no—
235#10621898—44no—
236#10621898—42no—
237C2×D172—21no—
238C2×D172—21no—
239C2×D172—21no—
240C2×D172C22×C411yescharacteristic
241C2×C4×D43—24no—
242C2×C4×D43—24no—
243C2×C4×D43—24no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—42no—
250C2×C4×D43—42no—
251C2×C4×D43—42no—
252C2×C4×D43—44no—
253C2×C4×D43—44no—
254C2×C4×D43—44no—
255C2×C4×D43—42no—
256C2×C4×D43—42no—
257C2×C4×D43—42no—
258C2×C4×D43—42no—
259C2×C4×D43—42no—
260C2×C4×D43—42no—
261C2×C4×D43—44no—
262C2×C4×D43C22⋊C411yescharacteristic
263C2×C4×D43C22⋊C411yescharacteristic
264C2×C4×D43C22⋊C411yescharacteristic
265C2×C4×D43C22⋊C411yescharacteristic
266C2×C4×D43C22⋊C411yescharacteristic
267C2×C4×D43C22⋊C411yescharacteristic
268C2×C4×D43C22⋊C411yescharacteristic
269C2×C4×D43C22⋊C411yescharacteristic
270C2×C4×D43C22×C411yescharacteristic
271C2×C4×D43C22×C411yescharacteristic
272C2×C4×D43C22×C411yescharacteristic
273C2×C4×D43C22×C411yescharacteristic
274C2×C4×D43C2×D411yescharacteristic
275C2×C4×D43C2×D411yescharacteristic
276C2×C4×D43C2×D411yescharacteristic
277C2×C4×D43C2×D411yescharacteristic
278C2×Dic86—21no—
279C2×Dic86C22×C411yescharacteristic
280M16×C43—42no—
281C2×C8×C43—22no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43—42no—
285C4⋊C4×C43C22×C411yescharacteristic
286C4⋊C4×C43C22×C411yescharacteristic
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—21no—
291C22⋊C4×C43—21no—
292C22⋊C4×C43—42no—
293C42×C43—21no—
294C22⋊Dic43—21no—
295C22⋊Dic43—21no—
296C22⋊Dic43—21no—
297C22⋊Dic43—21no—
298C22⋊Dic43—21no—
299C22⋊Dic43—42no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4—21no—
306(C2×D43)⋊C4—21no—
307(C2×D43)⋊C4—21no—
308(C2×D43)⋊C4—21no—
309(C2×D43)⋊C4—21no—
310(C2×D43)⋊C4—44no—
311C4⋊Dic43—21no—
312C4⋊Dic43—21no—
313C4⋊Dic43—42no—
314C4⋊Dic43C22×C411yescharacteristic
315C4⋊Dic43C22×C411yescharacteristic
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—44no—
323C4×Dic43—21no—
324C4×Dic43—21no—
325C4×Dic43—21no—
326#10621877—42no—
327C2×C43⋊C8—22no—
328#10621872—44no—
329C8×D43—44no—
330C23×C43—21no—
331C23×C43—21no—
332C23×C43—21no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43C2×C22⋊C411yescharacteristic
336C23×C43C2×C22⋊C411yescharacteristic
337C23×C43C22×D411yescharacteristic
338C22×D43—21no—
339C22×D43—21no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—21no—
351C22×D43—41no—
352C22×D43—41no—
353C22×D43—41no—
354C22×D43—41no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—48no—
358C22×D43—48no—
359C22×D43—42no—
360C22×D43—42no—
361C22×D43—42no—
362C22×D43C2×C22⋊C411yescharacteristic
363C22×D43C2×C22⋊C411yescharacteristic
364C22×D43C2×C22⋊C411yescharacteristic
365C22×D43C2×C22⋊C411yescharacteristic
366C22×D43AGL(1,ℤ/8)12yes—
367C22×D43#13712yes—
368Q8×C43—41no—
369D4×C43—41no—
370D4×C43—42no—
371D4×C43—42no—
372D4×C43—41no—
373D4×C43—41no—
374C2×C4×C43—22no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—21no—
378C2×C4×C43—21no—
379C2×C4×C43—21no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—42no—
384C2×C4×C43—42no—
385C2×C4×C43—42no—
386C2×C4×C43—42no—
387C2×C4×C43C2×C22⋊C411yescharacteristic
388C2×C4×C43C2×C22⋊C411yescharacteristic
389C2×C4×C43C23×C411yescharacteristic
390C2×C4×C43C22×D411yescharacteristic
391C22⋊D43—42no—
392C22⋊D43—42no—
393C22⋊D43—41no—
394C22⋊D43—41no—
395C22⋊D43—42no—
396C22⋊D43—42no—
397C22⋊D43—42no—
398C22⋊D43—42no—
399C2×Dic43—22no—
400C2×Dic43—22no—
401C2×Dic43—22no—
402C2×Dic43—21no—
403C2×Dic43—21no—
404C2×Dic43—21no—
405C2×Dic43—41no—
406C2×Dic43—41no—
407C2×Dic43—41no—
408C2×Dic43—42no—
409C2×Dic43—42no—
410C2×Dic43—42no—
411C2×Dic43—42no—
412C2×Dic43C2×C22⋊C411yescharacteristic
413C2×Dic43C2×C22⋊C411yescharacteristic
414C2×Dic43C2×C22⋊C411yescharacteristic
415C2×Dic43C2×C22⋊C411yescharacteristic
416D172—41no—
417D172—42no—
418D172—42no—
419D172—42no—
420C4×D43—22no—
421C4×D43—22no—
422C4×D43—22no—
423C4×D43—22no—
424C4×D43—22no—
425C4×D43—22no—
426C4×D43—22no—
427C4×D43—22no—
428C4×D43—22no—
429C4×D43—41no—
430C4×D43—41no—
431C4×D43—41no—
432C4×D43—41no—
433C4×D43—41no—
434C4×D43—41no—
435C4×D43—42no—
436C4×D43—42no—
437C4×D43—42no—
438C4×D43—42no—
439C4×D43—42no—
440C4×D43—88no—
441C4×D43#9914yes—
442Dic86—42no—
443Dic86—41no—
444C8×C43—42no—
445C43⋊C8—42no—
446#17592—431nomaximal, Sylow
447C22×C43—21no—
448C22×C43—21no—
449C22×C43—21no—
450C22×C43—21no—
451C22×C43—21no—
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—42no—
456C22×C43—42no—
457C22×C43—41no—
458C22×C43—41no—
459C22×C43—41no—
460C22×C43C22×C22⋊C411yescharacteristic
461C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
462C22×C43C2×#13711yescharacteristic
463C2×D43—24no—
464C2×D43—24no—
465C2×D43—21no—
466C2×D43—21no—
467C2×D43—21no—
468C2×D43—21no—
469C2×D43—21no—
470C2×D43—21no—
471C2×D43—21no—
472C2×D43—21no—
473C2×D43—42no—
474C2×D43—42no—
475C2×D43—44no—
476C2×D43—44no—
477C2×D43—44no—
478C2×D43—44no—
479C2×D43—41no—
480C2×D43—41no—
481C2×D43—41no—
482C2×D43—84no—
483C2×D43C2×#9912yes—
484C2×D43#41712yes—
485C2×D43#41712yes—
486C2×D43#42112yes—
487C4×C43—21no—
488C4×C43—21no—
489C4×C43—21no—
490C4×C43—41no—
491C4×C43—41no—
492C4×C43—41no—
493C4×C43—82no—
494C4×C43C2×#9912yes—
495Dic43—21no—
496Dic43—21no—
497Dic43—21no—
498Dic43—41no—
499Dic43—41no—
500Dic43—41no—
501Dic43—82no—
502Dic43C2×#9912yes—
503C2×#525—431no—
504C2×#407—431no—
505C2×#380—431no—
506#1520—432no—
507#1519—432no—
508#1513—431no—
509#1513—431no—
510#1513—431no—
511#1513D4311yescharacteristic, complemented
512#1504—432no—
513#1504—432no—
514C2×C43—21no—
515C2×C43—21no—
516C2×C43—41no—
517C2×C43—41no—
518C2×C43—81no—
519C2×C43C22×#9911yescharacteristic
520C2×C43C2×#41711yescharacteristic
521C2×C43C2×#42111yescharacteristic
522D43—22no—
523D43—22no—
524D43—22no—
525D43—22no—
526D43—81no—
527C22×#41—431no—
528C24×C4—431no—
529C22×M16—861no—
530#525—431no—
531#525—431no—
532#525—431no—
533#525—431no—
534#525—431no—
535#525—431no—
536#525—431no—
537#525—861no—
538#525—861no—
539#525—861no—
540#525—861no—
541#525C2×D4311yescharacteristic
542C2×#123—861no—
543C2×C22⋊Q8—431no—
544C2×C22⋊Q8—431no—
545C2×#121—431no—
546C2×#121—431no—
547C2×#120—861no—
548C2×C4×D4—861no—
549C2×C4×D4—861no—
550C2×#117—431no—
551C22×C4⋊C4—861no—
552C22×C22⋊C4—861no—
553#407—431no—
554#407—432no—
555#407—861no—
556#407—861no—
557#407C2×D4311yescharacteristic, complemented
558C2×C22⋊C8—432no—
559C2×C22⋊C8—861no—
560#380—431no—
561#380—432no—
562#380—861no—
563#380—861no—
564#380C2×D4311yescharacteristic, complemented
565C2×#95—432no—
566#328—432no—
567#328—432no—
568#328—432no—
569#328C2×D4312yescomplemented
570#327—432no—
571#327—432no—
572#327—432no—
573#327C2×D4312yescomplemented
574C43#1759211yescharacteristic, complemented, Sylow
575C25—431no—
576C2×#41—431no—
577C2×#41—431no—
578C2×#41—431no—
579C2×#41—861no—
580C2×#41—861no—
581C2×#41—1724no—
582C2×#41C4×D4311yescharacteristic, complemented
583C22×Q8—431no—
584C22×D4—431no—
585C22×D4—861no—
586C22×D4—861no—
587C22×D4—861no—
588C23×C4—431no—
589C23×C4—431no—
590C23×C4—431no—
591C23×C4—431no—
592C23×C4—431no—
593C23×C4—431no—
594C23×C4—431no—
595C23×C4—431no—
596C23×C4—431no—
597C23×C4—431no—
598C23×C4—431no—
599C23×C4—431no—
600C23×C4—431no—
601C23×C4—861no—
602C23×C4—862no—
603C23×C4—1724no—
604C23×C4C22×D4311yescharacteristic
605C2×M16—21no—
606C2×M16—862no—
607C2×M16—861no—
608C2×M16—1724no—
609C22×C8—862no—
610#123—21no—
611#123—861no—
612#123—861no—
613#123—861no—
614#123—861no—
615#123—861no—
616#123—861no—
617#123—861no—
618C22⋊Q8—431no—
619C22⋊Q8—431no—
620C22⋊Q8—431no—
621C22⋊Q8—431no—
622C22⋊Q8—431no—
623C22⋊Q8—431no—
624C22⋊Q8—861no—
625C22⋊Q8—861no—
626C22⋊Q8—861no—
627C22⋊Q8—861no—
628C22⋊Q8C4×D4311yescharacteristic, complemented
629C22⋊Q8C22×D4311yescharacteristic
630#121—431no—
631#121—431no—
632#121—431no—
633#121—431no—
634#121—431no—
635#121—431no—
636#121—861no—
637#121—861no—
638#121—861no—
639#121—861no—
640#121C4×D4311yescharacteristic, complemented
641#121C22×D4311yescharacteristic
642#120—21no—
643#120—861no—
644#120—861no—
645#120—861no—
646#120—861no—
647#120—861no—
648#120—861no—
649#120—861no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—861no—
653C4×D4—861no—
654C4×D4—861no—
655C4×D4—861no—
656C4×D4—861no—
657C4×D4—861no—
658C4×D4—861no—
659C4×D4—861no—
660C4×D4—861no—
661C4×D4—861no—
662C4×D4—861no—
663C4×D4—861no—
664C4×D4—861no—
665C4×D4—861no—
666#117—431no—
667#117—431no—
668#117—431no—
669#117—861no—
670#117—861no—
671#117C4×D4311yescharacteristic, complemented
672C2×C4⋊C4—21no—
673C2×C4⋊C4—431no—
674C2×C4⋊C4—431no—
675C2×C4⋊C4—861no—
676C2×C4⋊C4—861no—
677C2×C4⋊C4—862no—
678C2×C4⋊C4—861no—
679C2×C4⋊C4—1724no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—861no—
682C2×C22⋊C4—861no—
683C2×C22⋊C4—861no—
684C2×C22⋊C4—861no—
685C2×C22⋊C4—861no—
686C2×C22⋊C4—862no—
687C2×C22⋊C4—861no—
688C2×C22⋊C4—1724no—
689C2×C42—861no—
690C22⋊C8—21no—
691C22⋊C8—432no—
692C22⋊C8—862no—
693C22⋊C8—862no—
694C22⋊C8—861no—
695C22⋊C8C22×D4312yes—
696#95—432no—
697#95—862no—
698#95C22×D4312yes—
699C24—431no—
700C24—431no—
701C24—431no—
702C24—431no—
703C24—431no—
704C24—431no—
705C24—862no—
706C24—862no—
707C24—861no—
708C24—1722no—
709C24—1722no—
710C24D4×D4311yescharacteristic
711#41—42no—
712#41—1722no—
713#41—1724no—
714#41—1724no—
715#41—1722no—
716#41—1722no—
717C2×Q8—431no—
718C2×Q8—861no—
719C2×Q8—1722no—
720C2×Q8C2×C4×D4311yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—431no—
725C2×D4—861no—
726C2×D4—861no—
727C2×D4—861no—
728C2×D4—861no—
729C2×D4—861no—
730C2×D4—861no—
731C2×D4—861no—
732C2×D4—861no—
733C2×D4—861no—
734C2×D4—861no—
735C2×D4—1722no—
736C2×D4—1722no—
737C2×D4—1722no—
738C2×D4—1724no—
739C2×D4—1724no—
740C2×D4C2×C4×D4311yescharacteristic
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—42no—
744C22×C4—431no—
745C22×C4—431no—
746C22×C4—431no—
747C22×C4—431no—
748C22×C4—431no—
749C22×C4—431no—
750C22×C4—431no—
751C22×C4—431no—
752C22×C4—431no—
753C22×C4—431no—
754C22×C4—431no—
755C22×C4—431no—
756C22×C4—431no—
757C22×C4—431no—
758C22×C4—431no—
759C22×C4—431no—
760C22×C4—431no—
761C22×C4—431no—
762C22×C4—431no—
763C22×C4—431no—
764C22×C4—431no—
765C22×C4—431no—
766C22×C4—864no—
767C22×C4—864no—
768C22×C4—864no—
769C22×C4—861no—
770C22×C4—861no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—861no—
774C22×C4—861no—
775C22×C4—862no—
776C22×C4—1722no—
777C22×C4—1722no—
778C22×C4—1722no—
779C22×C4—1722no—
780C22×C4—1722no—
781C22×C4—1722no—
782C22×C4—1722no—
783C22×C4—1722no—
784C22×C4—1722no—
785C22×C4—1724no—
786C22×C4—1724no—
787C22×C4—1724no—
788C22×C4—1724no—
789C22×C4—1722no—
790C22×C4C2×C4×D4311yescharacteristic
791C22×C4C2×C4×D4311yescharacteristic
792C22×C4D4×D4311yescharacteristic
793C22×C4D4×D4311yescharacteristic
794C22×C4D4×D4311yescharacteristic
795C22×C4C23×D4311yescharacteristic
796M16—42no—
797M16—1724no—
798M16—1722no—
799C2×C8—22no—
800C2×C8—862no—
801C2×C8—1724no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—42no—
805C4⋊C4—431no—
806C4⋊C4—431no—
807C4⋊C4—861no—
808C4⋊C4—861no—
809C4⋊C4—861no—
810C4⋊C4—861no—
811C4⋊C4—861no—
812C4⋊C4—861no—
813C4⋊C4—861no—
814C4⋊C4—861no—
815C4⋊C4—1722no—
816C4⋊C4—1724no—
817C4⋊C4C2×C4×D4311yescharacteristic
818C4⋊C4C2×C4×D4311yescharacteristic
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—42no—
825C22⋊C4—861no—
826C22⋊C4—861no—
827C22⋊C4—861no—
828C22⋊C4—861no—
829C22⋊C4—861no—
830C22⋊C4—861no—
831C22⋊C4—861no—
832C22⋊C4—861no—
833C22⋊C4—861no—
834C22⋊C4—861no—
835C22⋊C4—861no—
836C22⋊C4—861no—
837C22⋊C4—861no—
838C22⋊C4—861no—
839C22⋊C4—861no—
840C22⋊C4—1724no—
841C22⋊C4—1722no—
842C42—21no—
843C42—861no—
844C42—861no—
845C42—861no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—41no—
850C23—41no—
851C23—431no—
852C23—431no—
853C23—431no—
854C23—431no—
855C23—432no—
856C23—432no—
857C23—862no—
858C23—862no—
859C23—862no—
860C23—862no—
861C23—862no—
862C23—862no—
863C23—862no—
864C23—862no—
865C23—862no—
866C23—862no—
867C23—861no—
868C23—861no—
869C23—861no—
870C23—1721no—
871C23—1721no—
872C23—1721no—
873C23—1721no—
874C23—1721no—
875C23—1721no—
876C23—1722no—
877C23—1722no—
878C23—1722no—
879C23—1728no—
880C23—1728no—
881C23C22⋊C4×D4311yescharacteristic
882C23C22⋊C4×D4311yescharacteristic
883C23C2×D4×D4311yescharacteristic
884Q8—41no—
885Q8—1721no—
886Q8—1722no—
887D4—41no—
888D4—42no—
889D4—42no—
890D4—41no—
891D4—41no—
892D4—1721no—
893D4—1722no—
894D4—1722no—
895D4—1722no—
896D4—1722no—
897D4—1722no—
898D4—1722no—
899D4—1722no—
900D4—1722no—
901D4—1722no—
902D4—1721no—
903D4—1721no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—431no—
918C2×C4—434no—
919C2×C4—431no—
920C2×C4—431no—
921C2×C4—431no—
922C2×C4—862no—
923C2×C4—862no—
924C2×C4—862no—
925C2×C4—862no—
926C2×C4—862no—
927C2×C4—862no—
928C2×C4—862no—
929C2×C4—862no—
930C2×C4—862no—
931C2×C4—862no—
932C2×C4—862no—
933C2×C4—862no—
934C2×C4—861no—
935C2×C4—861no—
936C2×C4—861no—
937C2×C4—3448no—
938C2×C4—1721no—
939C2×C4—1721no—
940C2×C4—1721no—
941C2×C4—1721no—
942C2×C4—1721no—
943C2×C4—1721no—
944C2×C4—1722no—
945C2×C4—1722no—
946C2×C4—1722no—
947C2×C4—1722no—
948C2×C4—1721no—
949C2×C4—1721no—
950C2×C4—1721no—
951C2×C4—1722no—
952C2×C4—1722no—
953C2×C4—1722no—
954C2×C4—1722no—
955C2×C4—1722no—
956C2×C4C22⋊C4×D4311yescharacteristic
957C2×C4C22⋊C4×D4311yescharacteristic
958C2×C4C22×C4×D4311yescharacteristic
959C2×C4C2×D4×D4311yescharacteristic
960C8—42no—
961C8—1722no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—42no—
971C22—42no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—432no—
976C22—432no—
977C22—432no—
978C22—432no—
979C22—864no—
980C22—864no—
981C22—861no—
982C22—861no—
983C22—861no—
984C22—861no—
985C22—861no—
986C22—861no—
987C22—861no—
988C22—861no—
989C22—3444no—
990C22—1722no—
991C22—1722no—
992C22—1724no—
993C22—1724no—
994C22—1724no—
995C22—1724no—
996C22—1721no—
997C22—1721no—
998C22—1721no—
999C22C2×C22⋊C4×D4311yescharacteristic
1000C22AGL(1,ℤ/8)×D4311yescharacteristic
1001C22#137×D4311yescharacteristic
1002C4—21no—
1003C4—21no—
1004C4—21no—
1005C4—41no—
1006C4—41no—
1007C4—41no—
1008C4—82no—
1009C4—432no—
1010C4—861no—
1011C4—861no—
1012C4—861no—
1013C4—3442no—
1014C4—1721no—
1015C4—1721no—
1016C4—1721no—
1017C4#99×D4312yes—
1018C2—21no—
1019C2—21no—
1020C2—41no—
1021C2—41no—
1022C2—81no—
1023C2—862no—
1024C2—862no—
1025C2—862no—
1026C2—862no—
1027C2—3441no—
1028C2C2×#99×D4311yescharacteristic
1029C2#417×D4311yescharacteristic
1030C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1513C2
socleC22×C43C22×C22⋊C4
prime radical#525×D43C2
cosocleC22×C4×C43C24
hypercenter#1513D43
hypocenterC43#17592
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #407×D43C2semidirect
3. #380×D43C2semidirect
4. #19133165C2semidirect
5. #19133161C2semidirect
6. #19133139C2semidirect
7. #19133138C2semidirect
8. #19133136C2semidirect
9. #19133098C2semidirect
10. #19133096C2semidirect
11. C43×#1513C2semidirect
12. C2×#41×D43C4semidirect
15. #14583412C4semidirect
17. #14583411C4semidirect
19. #14583409C4semidirect
24. #14583406C4semidirect
27. C22⋊Q8×D43C4semidirect
29. #121×D43C4semidirect
34. #117×D43C4semidirect
37. #14582863C22semidirect
40. #14582861C22semidirect
43. #14582759C22semidirect
47. #95×D43C22semidirect
48. #14582637C22semidirect
49. #14582636C22semidirect
50. #14582635C22semidirect
51. #14582634C22semidirect
52. #14582633C22semidirect
53. #14582632C22semidirect
55. C43×#407C22semidirect
56. C43×#380C22semidirect
57. C43×#328C22semidirect
58. C43×#327C22semidirect
62. C2×#10621898C2×C4semidirect
66. C2×Q8×D43C2×C4semidirect
70. C2×D4×D43C2×C4semidirect
99. #13063305C2×C4semidirect
100. #13063304C2×C4semidirect
107. #13063301C2×C4semidirect
109. #13063300C2×C4semidirect
110. #13063299C2×C4semidirect
117. #13063296C2×C4semidirect
139. #13063284C2×C4semidirect
149. C4⋊C4×D43C2×C4semidirect
150. C4⋊C4×D43C2×C4semidirect
166. C2×#41×C43C2×C4semidirect
170. C22⋊Q8×C43C2×C4semidirect
172. #121×C43C2×C4semidirect
177. #117×C43C2×C4semidirect
511. #1513D43semidirect
557. #407C2×D43semidirect
564. #380C2×D43semidirect
569. #328C2×D43semidirect
573. #327C2×D43semidirect
574. C43#17592semidirect
582. C2×#41C4×D43semidirect
628. C22⋊Q8C4×D43semidirect
640. #121C4×D43semidirect
671. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#525×D432
#407×D432
#380×D432
#191331652
#191331612
#191331392
#191331382
#191331362
#191330982
#191330962
C43×#15132
#1759243