Finite Group Databasebeta

← #25112286

Subgroups — #25112286

Order 11008.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C22⋊D43C211yesmaximal, characteristic
2#19143327C211yesmaximal, characteristic, complemented
3C2×#14582914C211yesmaximal, characteristic, complemented
4C22×#13063252C211yesmaximal, characteristic, complemented
5#19137034C211yesmaximal, characteristic, complemented
6#19135512C211yesmaximal, characteristic, complemented
7#19135425C211yesmaximal, characteristic, complemented
8#19135040C211yesmaximal, characteristic, complemented
9#19135036C211yesmaximal, characteristic, complemented
10#19134895C211yesmaximal, characteristic, complemented
11#19134894C211yesmaximal, characteristic, complemented
12#19134613C211yesmaximal, characteristic, complemented
13#19134537C211yesmaximal, characteristic, complemented
14#19134407C211yesmaximal, characteristic, complemented
15C43×#1789C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C22×#10621877C2211yescharacteristic, complemented
18C2×M16×D43C2211yescharacteristic, complemented
19#14583568C411yescharacteristic, complemented
20Q8×C22⋊D43C411yescharacteristic, complemented
21#14583560C411yescharacteristic, complemented
22#14583556C411yescharacteristic, complemented
23#14583548—21no—
24#14583548C411yescharacteristic, complemented
25#14583543—21no—
26#14583543C411yescharacteristic, complemented
27#14583537—21no—
28#14583537C411yescharacteristic, complemented
29D4×C22⋊D43—21no—
30D4×C22⋊D43C411yescharacteristic, complemented
31#14583445—21no—
32#14583445C2211yescharacteristic
33#14583410—21no—
34#14583410C2211yescharacteristic
35#14583406—21no—
36#14583406C2211yescharacteristic
37#41×Dic43C2211yescharacteristic
38C2×C4×C22⋊D43—21no—
39C2×C4×C22⋊D43C2211yescharacteristic
40C2×#13063282C2211yescharacteristic, complemented
41C22×C4×Dic43C2211yescharacteristic, complemented
42#14582974—21no—
43#14582973—21no—
44#14582967—21no—
45(C22⋊D43)⋊C8—21no—
46#14582922C2211yescharacteristic, complemented
47#14582914—24no—
48C2×#13063253C2211yescharacteristic, complemented
49C2×#13063253C2211yescharacteristic, complemented
50C2×#13063252—24no—
51C2×#13063252C2211yescharacteristic
52C2×#13063252C2211yescharacteristic
53C2×#13063252C2211yescharacteristic, complemented
54C2×#13063252C2211yescharacteristic, complemented
55C2×#13063251C2211yescharacteristic, complemented
56C2×#13063251C2211yescharacteristic, complemented
57#14582862C2211yescharacteristic, complemented
58M16×Dic43C2211yescharacteristic, complemented
59#14582788—21no—
60#14582781—21no—
61#14582776—21no—
62#14582771—21no—
63C4×Dic43⋊C4C2211yescharacteristic, complemented
64C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
65#14582745C2211yescharacteristic, complemented
66#14582660C2211yescharacteristic, complemented
67#14582660C2211yescharacteristic, complemented
68#14582659C2211yescharacteristic, complemented
69#14582659C2211yescharacteristic, complemented
70C22×#41×C43C2211yescharacteristic
71C2×#104×C43C2211yescharacteristic
72C2×#104×C43C2211yescharacteristic
73C2×#104×C43C2211yescharacteristic, complemented
74C2×#104×C43C2211yescharacteristic, complemented
75C43×#407C2211yescharacteristic, complemented
76C4×C22⋊C4×C43C2211yescharacteristic, complemented
77C2×#10621902C2×C411yescharacteristic, complemented
78C2×#10621898—21no—
79C2×#10621898C2311yescharacteristic
80C2×#10621900—21no—
81C2×#10621900C2×C411yescharacteristic, complemented
82#41×D43—22no—
83#41×D43—22no—
84#41×D43—41no—
85#41×D43—41no—
86C2×Q8×D43C2×C411yescharacteristic, complemented
87C22×C22⋊D43—21no—
88C22×C22⋊D43D411yescharacteristic
89C2×D4×D43—21no—
90C2×D4×D43C2×C411yescharacteristic, complemented
91C23×Dic43—21no—
92C22×C4×D43—21no—
93C22×C4×D43C2311yescharacteristic
94C2×#10621877—21no—
95C2×#10621877—22no—
96C2×#10621877—41no—
97C2×#10621877C2311yescharacteristic
98C2×#10621877C2311yescharacteristic
99C2×#10621872—21no—
100M16×D43—22no—
101M16×D43—41no—
102C22×C43⋊C8—21no—
103C2×C8×D43—21no—
104#13063323—21no—
105#13063323C2×C411yescharacteristic, complemented
106#13063321—21no—
107#13063321C2×C411yescharacteristic, complemented
108#13063314—21no—
109#13063314C2×C411yescharacteristic, complemented
110#13063312—21no—
111#13063312C2×C411yescharacteristic, complemented
112#13063308—21no—
113#13063308—21no—
114#13063308—21no—
115#13063306—21no—
116#13063306—21no—
117#13063306—21no—
118#13063304—21no—
119#13063304—21no—
120#13063304C2×C411yescharacteristic
121#13063304C2×C411yescharacteristic
122#13063301—21no—
123#13063301—21no—
124#13063301C2×C411yescharacteristic, complemented
125#13063301C2×C411yescharacteristic, complemented
126#13063299—21no—
127#13063299—21no—
128#13063299C2×C411yescharacteristic
129#13063299C2×C411yescharacteristic
130#13063297—21no—
131#13063297—21no—
132#13063297—21no—
133#13063297—21no—
134#13063297—21no—
135#13063297—21no—
136#13063296—21no—
137#13063296—21no—
138#13063296C2×C411yescharacteristic, complemented
139#13063296C2×C411yescharacteristic, complemented
140#13063294—21no—
141#13063294—21no—
142#13063294—21no—
143#13063293—21no—
144#13063293—21no—
145#13063293—21no—
146Q8×Dic43C2×C411yescharacteristic, complemented
147Q8×Dic43C2×C411yescharacteristic, complemented
148D4×Dic43—21no—
149D4×Dic43—21no—
150D4×Dic43C2×C411yescharacteristic, complemented
151D4×Dic43C2×C411yescharacteristic, complemented
152C4×C22⋊D43—21no—
153C4×C22⋊D43—21no—
154C4×C22⋊D43—21no—
155C4×C22⋊D43—21no—
156C4×C22⋊D43—21no—
157C4×C22⋊D43—21no—
158C4×C22⋊D43—21no—
159C4×C22⋊D43—21no—
160C4×C22⋊D43—21no—
161C4×C22⋊D43—21no—
162C4×C22⋊D43C2×C411yescharacteristic
163C4×C22⋊D43C2×C411yescharacteristic
164C4×C22⋊D43C2×C411yescharacteristic
165C4×C22⋊D43C2×C411yescharacteristic
166C4×C22⋊D43D411yescharacteristic
167C4×C22⋊D43D411yescharacteristic
168C4×C22⋊D43D411yescharacteristic
169C4×C22⋊D43D411yescharacteristic
170#13063284—21no—
171#13063284C2311yescharacteristic
172#13063282—22no—
173#13063282—41no—
174C2×Dic43⋊C4—21no—
175C2×Dic43⋊C4—21no—
176C2×Dic43⋊C4—21no—
177C2×Dic43⋊C4D411yescharacteristic
178C2×C22⋊Dic43—21no—
179C2×C22⋊Dic43D411yescharacteristic
180C2×(C2×D43)⋊C4—21no—
181C2×(C2×D43)⋊C4—21no—
182C2×(C2×D43)⋊C4—21no—
183C2×(C2×D43)⋊C4D411yescharacteristic
184C2×C4×Dic43—21no—
185C2×C4×Dic43—22no—
186C2×C4×Dic43—21no—
187C2×C4×Dic43—41no—
188C2×C4×Dic43C2311yescharacteristic
189C2×C4×Dic43C2311yescharacteristic
190C2×C4×Dic43C2311yescharacteristic
191Dic43⋊C8—21no—
192Dic43⋊C8—21no—
193#13063253—22no—
194#13063253—41no—
195#13063252—22no—
196#13063252—22no—
197#13063252—22no—
198#13063252D414yescomplemented
199#13063251—22no—
200#13063251—41no—
201(C2×D43)⋊C8—21no—
202(C2×D43)⋊C8—21no—
203#13063235—21no—
204C8×Dic43—21no—
205C43⋊#95—21no—
206C43⋊#95—21no—
207C43⋊#95—21no—
208C43⋊#95—21no—
209C2×#41×C43—21no—
210C2×#41×C43—21no—
211C2×#41×C43—22no—
212C2×#41×C43—22no—
213C2×#41×C43—41no—
214C2×#41×C43—41no—
215C2×#41×C43C2×C411yescharacteristic
216C2×#41×C43C2×C411yescharacteristic
217C2×#41×C43C2311yescharacteristic
218C2×#41×C43C2311yescharacteristic
219C22×Q8×C43C2×C411yescharacteristic
220C22×D4×C43—21no—
221C22×D4×C43C2×C411yescharacteristic
222C23×C4×C43—21no—
223C23×C4×C43C2311yescharacteristic
224C2×M16×C43C2311yescharacteristic
225C2×M16×C43C2311yescharacteristic
226C2×C22⋊C4×C43—21no—
227C2×C42×C43C2311yescharacteristic
228C2×C42×C43C2311yescharacteristic
229#104×C43—22no—
230#104×C43—22no—
231#104×C43—41no—
232#104×C43—41no—
233C22⋊C8×C43—21no—
234C22⋊C8×C43—21no—
235#95×C43—21no—
236C24×C43—21no—
237C24×C43C2×D411yescharacteristic
238C23×D43—21no—
239C23×D43C2×D411yescharacteristic
240#41×C43—21no—
241#41×C43—21no—
242#41×C43—22no—
243#41×C43—22no—
244#41×C43—21no—
245#41×C43—21no—
246#41×C43—21no—
247#41×C43—21no—
248#41×C43—42no—
249#41×C43—42no—
250#41×C43—41no—
251#41×C43—41no—
252#41×C43—42no—
253#41×C43—42no—
254#41×C43C2×D412yes—
255#41×C43#4112yes—
256C2×Q8×C43—21no—
257C2×Q8×C43—22no—
258C2×Q8×C43—41no—
259C2×Q8×C43C22×C411yescharacteristic
260C2×Q8×C43C22×C411yescharacteristic
261C2×D4×C43—21no—
262C2×D4×C43—21no—
263C2×D4×C43—21no—
264C2×D4×C43—21no—
265C2×D4×C43—21no—
266C2×D4×C43—22no—
267C2×D4×C43—42no—
268C2×D4×C43—42no—
269C2×D4×C43—41no—
270C2×D4×C43C22×C411yescharacteristic
271C2×D4×C43C22×C411yescharacteristic
272C22×C4×C43—21no—
273C22×C4×C43—21no—
274C22×C4×C43—21no—
275C22×C4×C43—21no—
276C22×C4×C43—21no—
277C22×C4×C43—21no—
278C22×C4×C43—21no—
279C22×C4×C43—21no—
280C22×C4×C43—21no—
281C22×C4×C43—21no—
282C22×C4×C43—21no—
283C22×C4×C43—42no—
284C22×C4×C43—42no—
285C22×C4×C43C22×C411yescharacteristic
286C22×C4×C43C22×C411yescharacteristic
287C22×C4×C43C2×D411yescharacteristic
288C22×C4×C43C2×D411yescharacteristic
289C22×C4×C43C2×D411yescharacteristic
290C22×C4×C43C2411yescharacteristic
291C2×C22⋊D43—21no—
292C2×C22⋊D43—21no—
293C2×C22⋊D43—21no—
294C2×C22⋊D43—21no—
295C2×C22⋊D43—21no—
296C2×C22⋊D43—21no—
297C2×C22⋊D43—21no—
298C2×C22⋊D43—21no—
299C2×C22⋊D43—21no—
300C2×C22⋊D43—42no—
301C2×C22⋊D43—44no—
302C2×C22⋊D43C22⋊C411yescharacteristic
303C2×C22⋊D43C22⋊C411yescharacteristic
304C2×C22⋊D43C22⋊C411yescharacteristic
305C2×C22⋊D43C22⋊C411yescharacteristic
306C22×Dic43—21no—
307C22×Dic43—21no—
308C22×Dic43—21no—
309C22×Dic43—21no—
310C22×Dic43—21no—
311C22×Dic43—42no—
312C22×Dic43—42no—
313C22×Dic43—42no—
314C22×Dic43C2×D411yescharacteristic
315C22×Dic43C2×D411yescharacteristic
316C22×Dic43C2×D411yescharacteristic
317#10621902—22no—
318#10621902—41no—
319Q8×D43—22no—
320Q8×D43—41no—
321#10621900—22no—
322#10621900—41no—
323#10621900—42no—
324#10621900—42no—
325D4×D43—22no—
326D4×D43—42no—
327D4×D43—42no—
328D4×D43—41no—
329#10621898—21no—
330#10621898—21no—
331#10621898—21no—
332#10621898—21no—
333#10621898—42no—
334#10621898—42no—
335C2×D172—21no—
336C2×D172C22×C411yescharacteristic
337C2×C4×D43—21no—
338C2×C4×D43—21no—
339C2×C4×D43—21no—
340C2×C4×D43—21no—
341C2×C4×D43—21no—
342C2×C4×D43—21no—
343C2×C4×D43—21no—
344C2×C4×D43—42no—
345C2×C4×D43—42no—
346C2×C4×D43C22×C411yescharacteristic
347C2×C4×D43C22×C411yescharacteristic
348C2×C4×D43C2×D411yescharacteristic
349C2×C4×D43C2×D411yescharacteristic
350C2×Dic86—21no—
351C2×Dic86C22×C411yescharacteristic
352M16×C43—21no—
353M16×C43—21no—
354M16×C43—21no—
355M16×C43—21no—
356C2×C8×C43—21no—
357C2×C8×C43—21no—
358C22⋊C4×C43—42no—
359C42×C43—21no—
360C42×C43—21no—
361C42×C43—21no—
362C42×C43—21no—
363C22⋊Dic43—21no—
364C22⋊Dic43—21no—
365C22⋊Dic43—21no—
366C22⋊Dic43—21no—
367C22⋊Dic43—21no—
368C22⋊Dic43—21no—
369C22⋊Dic43—21no—
370C22⋊Dic43—21no—
371C22⋊Dic43—21no—
372C22⋊Dic43C22⋊C411yescharacteristic
373C22⋊Dic43C22⋊C411yescharacteristic
374C22⋊Dic43C22⋊C411yescharacteristic
375C22⋊Dic43C22⋊C411yescharacteristic
376(C2×D43)⋊C4—21no—
377(C2×D43)⋊C4—21no—
378(C2×D43)⋊C4—21no—
379(C2×D43)⋊C4—21no—
380(C2×D43)⋊C4—21no—
381(C2×D43)⋊C4—21no—
382(C2×D43)⋊C4—42no—
383(C2×D43)⋊C4—42no—
384(C2×D43)⋊C4C22⋊C411yescharacteristic
385(C2×D43)⋊C4C22⋊C411yescharacteristic
386(C2×D43)⋊C4C22⋊C411yescharacteristic
387(C2×D43)⋊C4C22⋊C411yescharacteristic
388C4⋊Dic43—21no—
389C4⋊Dic43—21no—
390C4⋊Dic43C22×C411yescharacteristic
391C4⋊Dic43C22×C411yescharacteristic
392Dic43⋊C4—21no—
393Dic43⋊C4—21no—
394Dic43⋊C4—21no—
395Dic43⋊C4—21no—
396Dic43⋊C4—21no—
397Dic43⋊C4—21no—
398Dic43⋊C4—42no—
399Dic43⋊C4—42no—
400Dic43⋊C4C22⋊C411yescharacteristic
401Dic43⋊C4C22⋊C411yescharacteristic
402Dic43⋊C4C22⋊C411yescharacteristic
403Dic43⋊C4C22⋊C411yescharacteristic
404C4×Dic43—21no—
405C4×Dic43—21no—
406C4×Dic43—21no—
407C4×Dic43—21no—
408C4×Dic43—21no—
409C4×Dic43—21no—
410C4×Dic43—42no—
411C4×Dic43C22×C411yescharacteristic
412C4×Dic43C22×C411yescharacteristic
413C4×Dic43C2×D411yescharacteristic
414C4×Dic43C2×D411yescharacteristic
415C4×Dic43C2×D412yescomplemented
416#10621877—21no—
417#10621877—21no—
418#10621877—21no—
419#10621877—42no—
420#10621877C2×D412yescomplemented
421C2×C43⋊C8—21no—
422C2×C43⋊C8—21no—
423C2×C43⋊C8—42no—
424#10621872—42no—
425C8×D43—42no—
426C23×C43—21no—
427C23×C43—21no—
428C23×C43—21no—
429C23×C43—22no—
430C23×C43—21no—
431C23×C43—41no—
432C23×C43—42no—
433C23×C43—42no—
434C23×C43—81no—
435C23×C43C2×C22⋊C411yescharacteristic
436C23×C43C2×C22⋊C411yescharacteristic
437C23×C43C22×D411yescharacteristic
438C22×D43—21no—
439C22×D43—21no—
440C22×D43—21no—
441C22×D43—41no—
442C22×D43—41no—
443C22×D43—42no—
444C22×D43—42no—
445C22×D43—81no—
446C22×D43C2×C22⋊C411yescharacteristic
447C22×D43C2×C22⋊C411yescharacteristic
448Q8×C43—21no—
449Q8×C43—21no—
450Q8×C43—21no—
451Q8×C43—42no—
452Q8×C43C4×D412yes—
453D4×C43—22no—
454D4×C43—22no—
455D4×C43—21no—
456D4×C43—21no—
457D4×C43—21no—
458D4×C43—42no—
459D4×C43—42no—
460D4×C43—42no—
461D4×C43—41no—
462D4×C43—41no—
463D4×C43C4×D412yes—
464C2×C4×C43—21no—
465C2×C4×C43—21no—
466C2×C4×C43—21no—
467C2×C4×C43—21no—
468C2×C4×C43—21no—
469C2×C4×C43—21no—
470C2×C4×C43—21no—
471C2×C4×C43—21no—
472C2×C4×C43—21no—
473C2×C4×C43—22no—
474C2×C4×C43—22no—
475C2×C4×C43—21no—
476C2×C4×C43—21no—
477C2×C4×C43—21no—
478C2×C4×C43—42no—
479C2×C4×C43—42no—
480C2×C4×C43—42no—
481C2×C4×C43—41no—
482C2×C4×C43—41no—
483C2×C4×C43—41no—
484C2×C4×C43—41no—
485C2×C4×C43—41no—
486C2×C4×C43—41no—
487C2×C4×C43—41no—
488C2×C4×C43—41no—
489C2×C4×C43C2×C22⋊C411yescharacteristic
490C2×C4×C43C2×C22⋊C411yescharacteristic
491C2×C4×C43C23×C411yescharacteristic
492C2×C4×C43C22×D411yescharacteristic
493C2×C4×C43C22×D411yescharacteristic
494C2×C4×C43C2×#4111yescharacteristic
495C2×C4×C43H(5,𝔽2)11yescharacteristic
496C2×C4×C43H(5,𝔽2)11yescharacteristic
497C22⋊D43—22no—
498C22⋊D43—22no—
499C22⋊D43—41no—
500C22⋊D43—41no—
501C22⋊D43—42no—
502C22⋊D43—42no—
503C22⋊D43—42no—
504C22⋊D43—42no—
505C22⋊D43—41no—
506C22⋊D43—41no—
507C22⋊D43—42no—
508C22⋊D43—81no—
509C22⋊D43—81no—
510C22⋊D43—81no—
511C2×Dic43—21no—
512C2×Dic43—21no—
513C2×Dic43—22no—
514C2×Dic43—21no—
515C2×Dic43—21no—
516C2×Dic43—21no—
517C2×Dic43—22no—
518C2×Dic43—41no—
519C2×Dic43—41no—
520C2×Dic43—42no—
521C2×Dic43—42no—
522C2×Dic43—41no—
523C2×Dic43—41no—
524C2×Dic43—41no—
525C2×Dic43—48no—
526C2×Dic43—41no—
527C2×Dic43—81no—
528C2×Dic43C2×C22⋊C411yescharacteristic
529C2×Dic43C2×C22⋊C411yescharacteristic
530C2×Dic43C2×C22⋊C411yescharacteristic
531C2×Dic43C2×C22⋊C411yescharacteristic
532C2×Dic43C2×C22⋊C411yescharacteristic
533C2×Dic43C2×C22⋊C411yescharacteristic
534D172—21no—
535D172—21no—
536D172—42no—
537C4×D43—21no—
538C4×D43—21no—
539C4×D43—21no—
540C4×D43—21no—
541C4×D43—21no—
542C4×D43—21no—
543C4×D43—21no—
544C4×D43—21no—
545C4×D43—42no—
546C4×D43—42no—
547C4×D43—41no—
548C4×D43—41no—
549Dic86—21no—
550Dic86—21no—
551Dic86—42no—
552C8×C43—41no—
553C8×C43—41no—
554C43⋊C8—22no—
555C43⋊C8—41no—
556#22434—431nomaximal, Sylow
557C22×C43—21no—
558C22×C43—21no—
559C22×C43—21no—
560C22×C43—21no—
561C22×C43—22no—
562C22×C43—21no—
563C22×C43—21no—
564C22×C43—21no—
565C22×C43—42no—
566C22×C43—42no—
567C22×C43—41no—
568C22×C43—41no—
569C22×C43—41no—
570C22×C43—41no—
571C22×C43—41no—
572C22×C43—84no—
573C22×C43#42112yescomplemented
574C22×C43C22×C22⋊C411yescharacteristic
575C22×C43D4211yescharacteristic
576C22×C43#54611yescharacteristic
577C2×D43—21no—
578C2×D43—21no—
579C2×D43—21no—
580C2×D43—21no—
581C2×D43—21no—
582C2×D43—21no—
583C2×D43—41no—
584C2×D43—41no—
585C2×D43—41no—
586C2×D43—81no—
587C2×D43—81no—
588C2×D43—84no—
589C4×C43—22no—
590C4×C43—21no—
591C4×C43—21no—
592C4×C43—41no—
593C4×C43—81no—
594C4×C43—81no—
595C4×C43C2×C4×D411yescharacteristic
596C4×C43#51811yescharacteristic
597C4×C43D4211yescharacteristic
598C4×C43#54611yescharacteristic
599Dic43—21no—
600Dic43—21no—
601Dic43—21no—
602Dic43—21no—
603Dic43—21no—
604Dic43—21no—
605Dic43—42no—
606Dic43—42no—
607Dic43—41no—
608Dic43—41no—
609Dic43—41no—
610D4×#41—431no—
611D4×M16—431no—
612C2×#421—431no—
613C22×#104—431no—
614#2290—431no—
615#1980—431no—
616#1963—431no—
617#1897—431no—
618#1896—431no—
619#1871—431no—
620#1871—431no—
621#1806—431no—
622#1789—431no—
623#1789D4311yescharacteristic, complemented
624#1759—431no—
625C2×C43—21no—
626C2×C43—21no—
627C2×C43—22no—
628C2×C43—42no—
629C2×C43—41no—
630C2×C43—81no—
631C2×C43D4×C22⋊C411yescharacteristic
632C2×C43C2×#42111yescharacteristic
633C2×C43#290111yescharacteristic
634D43—41no—
635D43—41no—
636D43—81no—
637C22×#41—431no—
638C22×#41C2×D4311yescharacteristic
639C22×M16—431no—
640C22×M16—431no—
641#550—431no—
642D4×Q8—431no—
643#548—431no—
644#548—431no—
645#547—431no—
646#547—861no—
647#546—431no—
648#546—431no—
649#546—861no—
650#546—861no—
651D42—431no—
652D42—861no—
653#532—431no—
654#532—861no—
655#525—431no—
656#525—431no—
657#525—861no—
658#525—861no—
659C4×#41—431no—
660C2×C4×D4—431no—
661C2×C4×D4—861no—
662C2×#117—431no—
663C22×C42—431no—
664#436—861no—
665#435—861no—
666#435—861no—
667C8×D4—861no—
668#423—431no—
669#421—864no—
670C2×#104—431no—
671C2×#104—431no—
672C2×#104—431no—
673C2×#104—431no—
674C2×#104—431no—
675C2×#104—431no—
676C2×#104—431no—
677C2×#104—431no—
678C2×#104—864no—
679C2×#104C2×D4311yescharacteristic
680C2×#104C2×D4311yescharacteristic
681C2×#104C2×D4311yescharacteristic, complemented
682C2×#104C2×D4311yescharacteristic, complemented
683#407—431no—
684#407C2×D4311yescharacteristic, complemented
685C4×M16—431no—
686#388—861no—
687#387—861no—
688#386—861no—
689#385—861no—
690C4×C4⋊C4—431no—
691C4×C22⋊C4—431no—
692C4×C22⋊C4C2×D4311yescharacteristic, complemented
693#376—431no—
694#339—431no—
695#339—431no—
696#339—431no—
697#339—431no—
698C43#2243411yescharacteristic, complemented, Sylow
699C2×#41—21no—
700C2×#41—21no—
701C2×#41—22no—
702C2×#41—22no—
703C2×#41—41no—
704C2×#41—41no—
705C2×#41—431no—
706C2×#41—431no—
707C2×#41—431no—
708C2×#41—861no—
709C2×#41—861no—
710C2×#41—862no—
711C2×#41—862no—
712C2×#41—1721no—
713C2×#41—1721no—
714C2×#41C4×D4311yescharacteristic
715C2×#41C4×D4311yescharacteristic
716C2×#41C22×D4311yescharacteristic
717C2×#41C22×D4311yescharacteristic
718C22×Q8—431no—
719C22×Q8C4×D4311yescharacteristic
720C22×D4—21no—
721C22×D4—431no—
722C22×D4—431no—
723C22×D4—861no—
724C22×D4—861no—
725C22×D4C4×D4311yescharacteristic
726C23×C4—21no—
727C23×C4—431no—
728C23×C4—861no—
729C23×C4—861no—
730C23×C4C22×D4311yescharacteristic
731C2×M16—431no—
732C2×M16—431no—
733C2×M16—861no—
734C2×M16—861no—
735C2×M16—862no—
736C2×M16—862no—
737C2×M16—1721no—
738C2×M16—1721no—
739C2×M16C22×D4311yescharacteristic
740C2×M16C22×D4311yescharacteristic
741C22×C8—861no—
742C22×C8—861no—
743C4⋊Q8—431no—
744C4⋊Q8—861no—
745#127—431no—
746#127—861no—
747#124—431no—
748#124—431no—
749#124—861no—
750#124—861no—
751#123—861no—
752#123—861no—
753#123—861no—
754#123—861no—
755#123—861no—
756#123—861no—
757C22⋊Q8—431no—
758C22⋊Q8—431no—
759C22⋊Q8—431no—
760C22⋊Q8—431no—
761C22⋊Q8—861no—
762C22⋊Q8—861no—
763C22⋊Q8—861no—
764C22⋊Q8—861no—
765#121—431no—
766#121—431no—
767#121—431no—
768#121—431no—
769#121—861no—
770#121—861no—
771#121—861no—
772#121—861no—
773#121—861no—
774#121—861no—
775#121—861no—
776#121—861no—
777#121—861no—
778#121—861no—
779#120—861no—
780#120—861no—
781#120—861no—
782#120—861no—
783#120—861no—
784#120—861no—
785C4×Q8—431no—
786C4×Q8—431no—
787C4×D4—431no—
788C4×D4—431no—
789C4×D4—431no—
790C4×D4—431no—
791C4×D4—431no—
792C4×D4—431no—
793C4×D4—431no—
794C4×D4—431no—
795C4×D4—431no—
796C4×D4—431no—
797C4×D4—861no—
798C4×D4—861no—
799C4×D4—861no—
800C4×D4—861no—
801C4×D4—861no—
802C4×D4—861no—
803C4×D4—861no—
804C4×D4—861no—
805C4×D4—861no—
806C4×D4—861no—
807C4×D4—861no—
808C4×D4—861no—
809#117—431no—
810#117—862no—
811#117—861no—
812#117—1721no—
813C2×C4⋊C4—431no—
814C2×C4⋊C4—861no—
815C2×C4⋊C4—861no—
816C2×C4⋊C4—861no—
817C2×C22⋊C4—21no—
818C2×C22⋊C4—431no—
819C2×C22⋊C4—431no—
820C2×C22⋊C4—861no—
821C2×C22⋊C4—861no—
822C2×C22⋊C4—861no—
823C2×C22⋊C4—861no—
824C2×C42—431no—
825C2×C42—431no—
826C2×C42—431no—
827C2×C42—861no—
828C2×C42—862no—
829C2×C42—861no—
830C2×C42—1721no—
831C2×C42C22×D4311yescharacteristic
832C2×C42C22×D4311yescharacteristic
833C4⋊C8—861no—
834C4⋊C8—861no—
835#104—22no—
836#104—22no—
837#104—41no—
838#104—41no—
839#104—434no—
840#104—862no—
841#104—862no—
842#104—862no—
843#104—862no—
844#104—862no—
845#104—1721no—
846#104—1721no—
847C22⋊C8—21no—
848C22⋊C8—21no—
849C22⋊C8—861no—
850C22⋊C8—861no—
851#97—861no—
852C4×C8—861no—
853#95—21no—
854#95—861no—
855#95—861no—
856#95—861no—
857#95—861no—
858C24—21no—
859C24—431no—
860C24—861no—
861C24D4×D4311yescharacteristic
862#41—21no—
863#41—21no—
864#41—22no—
865#41—22no—
866#41—21no—
867#41—21no—
868#41—21no—
869#41—21no—
870#41—42no—
871#41—42no—
872#41—41no—
873#41—41no—
874#41—42no—
875#41—42no—
876#41—862no—
877#41—862no—
878#41—861no—
879#41—861no—
880#41—861no—
881#41—861no—
882#41—1722no—
883#41—1722no—
884#41—1721no—
885#41—1722no—
886#41—1722no—
887#41—1721no—
888#41D4×D4312yes—
889#41#1062190012yes—
890C2×Q8—21no—
891C2×Q8—22no—
892C2×Q8—41no—
893C2×Q8—431no—
894C2×Q8—861no—
895C2×Q8—862no—
896C2×Q8—1721no—
897C2×Q8C2×C4×D4311yescharacteristic
898C2×Q8C2×C4×D4311yescharacteristic
899C2×D4—21no—
900C2×D4—22no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—41no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—431no—
909C2×D4—431no—
910C2×D4—431no—
911C2×D4—431no—
912C2×D4—431no—
913C2×D4—861no—
914C2×D4—861no—
915C2×D4—861no—
916C2×D4—861no—
917C2×D4—862no—
918C2×D4—861no—
919C2×D4—861no—
920C2×D4—861no—
921C2×D4—861no—
922C2×D4—861no—
923C2×D4—861no—
924C2×D4—1721no—
925C2×D4—1722no—
926C2×D4—1722no—
927C2×D4—1722no—
928C2×D4—1724no—
929C2×D4C2×C4×D4311yescharacteristic
930C2×D4C2×C4×D4311yescharacteristic
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—431no—
945C22×C4—431no—
946C22×C4—431no—
947C22×C4—431no—
948C22×C4—431no—
949C22×C4—431no—
950C22×C4—431no—
951C22×C4—861no—
952C22×C4—861no—
953C22×C4—861no—
954C22×C4—861no—
955C22×C4—861no—
956C22×C4—861no—
957C22×C4—861no—
958C22×C4—861no—
959C22×C4—861no—
960C22×C4—861no—
961C22×C4—861no—
962C22×C4—861no—
963C22×C4—1722no—
964C22×C4—1722no—
965C22×C4—1722no—
966C22×C4—1722no—
967C22×C4—1722no—
968C22×C4C2×C4×D4311yescharacteristic
969C22×C4C2×C4×D4311yescharacteristic
970C22×C4D4×D4311yescharacteristic
971C22×C4D4×D4311yescharacteristic
972C22×C4D4×D4311yescharacteristic
973C22×C4C23×D4311yescharacteristic
974M16—21no—
975M16—21no—
976M16—21no—
977M16—21no—
978M16—432no—
979M16—861no—
980M16—861no—
981M16—861no—
982M16—1722no—
983M16—1722no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—861no—
987C2×C8—861no—
988C2×C8—1722no—
989C2×C8—1722no—
990C4⋊C4—431no—
991C4⋊C4—431no—
992C4⋊C4—431no—
993C4⋊C4—431no—
994C4⋊C4—431no—
995C4⋊C4—431no—
996C4⋊C4—861no—
997C4⋊C4—861no—
998C4⋊C4—861no—
999C4⋊C4—861no—
1000C4⋊C4—861no—
1001C4⋊C4—861no—
1002C4⋊C4—861no—
1003C4⋊C4—861no—
1004C4⋊C4—1722no—
1005C4⋊C4—1722no—
1006C22⋊C4—42no—
1007C22⋊C4—431no—
1008C22⋊C4—431no—
1009C22⋊C4—431no—
1010C22⋊C4—431no—
1011C22⋊C4—431no—
1012C22⋊C4—431no—
1013C22⋊C4—431no—
1014C22⋊C4—431no—
1015C22⋊C4—861no—
1016C22⋊C4—861no—
1017C22⋊C4—861no—
1018C22⋊C4—861no—
1019C22⋊C4—861no—
1020C22⋊C4—861no—
1021C22⋊C4—861no—
1022C22⋊C4—861no—
1023C22⋊C4—861no—
1024C22⋊C4—861no—
1025C22⋊C4—861no—
1026C22⋊C4—861no—
1027C22⋊C4—861no—
1028C22⋊C4—861no—
1029C22⋊C4—861no—
1030C22⋊C4—1722no—
1031C22⋊C4—1722no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—431no—
1037C42—431no—
1038C42—431no—
1039C42—431no—
1040C42—432no—
1041C42—861no—
1042C42—861no—
1043C42—861no—
1044C42—861no—
1045C42—861no—
1046C42—861no—
1047C42—1722no—
1048C23—21no—
1049C23—22no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—41no—
1054C23—42no—
1055C23—42no—
1056C23—81no—
1057C23—431no—
1058C23—431no—
1059C23—861no—
1060C23—861no—
1061C23—861no—
1062C23—3441no—
1063C23—1721no—
1064C23—1721no—
1065C23—1722no—
1066C23—1722no—
1067C23C22⋊C4×D4311yescharacteristic
1068C23C22⋊C4×D4311yescharacteristic
1069C23C2×D4×D4311yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—21no—
1073Q8—42no—
1074Q8—861no—
1075Q8—861no—
1076Q8—1722no—
1077Q8(C22⋊D43)⋊C412yes—
1078D4—22no—
1079D4—22no—
1080D4—21no—
1081D4—21no—
1082D4—21no—
1083D4—42no—
1084D4—42no—
1085D4—42no—
1086D4—41no—
1087D4—41no—
1088D4—862no—
1089D4—862no—
1090D4—861no—
1091D4—861no—
1092D4—3441no—
1093D4—3441no—
1094D4—3441no—
1095D4—1722no—
1096D4—1721no—
1097D4—1721no—
1098D4—1722no—
1099D4—1722no—
1100D4—1722no—
1101D4—1722no—
1102D4—1722no—
1103D4—1721no—
1104D4—1721no—
1105D4(C22⋊D43)⋊C412yes—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—431no—
1132C2×C4—431no—
1133C2×C4—431no—
1134C2×C4—431no—
1135C2×C4—431no—
1136C2×C4—431no—
1137C2×C4—861no—
1138C2×C4—861no—
1139C2×C4—861no—
1140C2×C4—861no—
1141C2×C4—861no—
1142C2×C4—861no—
1143C2×C4—861no—
1144C2×C4—861no—
1145C2×C4—861no—
1146C2×C4—861no—
1147C2×C4—862no—
1148C2×C4—861no—
1149C2×C4—861no—
1150C2×C4—861no—
1151C2×C4—862no—
1152C2×C4—3441no—
1153C2×C4—1722no—
1154C2×C4—1722no—
1155C2×C4—1721no—
1156C2×C4—1721no—
1157C2×C4—1722no—
1158C2×C4—1722no—
1159C2×C4—1721no—
1160C2×C4—1721no—
1161C2×C4—1721no—
1162C2×C4—1728no—
1163C2×C4—1721no—
1164C2×C4—1721no—
1165C2×C4—1721no—
1166C2×C4C22⋊C4×D4311yescharacteristic
1167C2×C4C22⋊C4×D4311yescharacteristic
1168C2×C4C22×C4×D4311yescharacteristic
1169C2×C4C2×D4×D4311yescharacteristic
1170C2×C4C2×D4×D4311yescharacteristic
1171C2×C4C2×#1062190011yescharacteristic
1172C2×C4#1306337011yescharacteristic
1173C2×C4#1306337011yescharacteristic
1174C8—41no—
1175C8—41no—
1176C8—862no—
1177C8—1721no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—22no—
1184C22—21no—
1185C22—21no—
1186C22—42no—
1187C22—42no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—84no—
1194C22—861no—
1195C22—861no—
1196C22—861no—
1197C22—861no—
1198C22—861no—
1199C22—861no—
1200C22—3441no—
1201C22—3441no—
1202C22—3444no—
1203C22—1721no—
1204C22—1721no—
1205C22—1721no—
1206C22#1458291412yescomplemented
1207C22C2×C22⋊C4×D4311yescharacteristic
1208C22#1458353111yescharacteristic
1209C22#1458353611yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—22no—
1213C4—41no—
1214C4—81no—
1215C4—81no—
1216C4—861no—
1217C4—861no—
1218C4—861no—
1219C4—861no—
1220C4—861no—
1221C4—861no—
1222C4—1722no—
1223C4—1722no—
1224C4—1721no—
1225C4—1721no—
1226C4—1721no—
1227C4C2×(C22⋊D43)⋊C411yescharacteristic
1228C4#1458337211yescharacteristic
1229C4#1458353111yescharacteristic
1230C4#1458353611yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—22no—
1234C2—41no—
1235C2—42no—
1236C2—81no—
1237C2—3441no—
1238C2—1721no—
1239C2—1721no—
1240C2#1913741111yescharacteristic
1241C2C2×#1458291411yescharacteristic
1242C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1789C2
socleC22×C43C22×C22⋊C4
prime radical#41×C22⋊D43C2
cosocleC22×C4×C43C24
hypercenter#1789D43
hypocenterC43#22434
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #19143327C2semidirect
3. C2×#14582914C2semidirect
4. C22×#13063252C2semidirect
5. #19137034C2semidirect
6. #19135512C2semidirect
7. #19135425C2semidirect
8. #19135040C2semidirect
9. #19135036C2semidirect
10. #19134895C2semidirect
11. #19134894C2semidirect
12. #19134613C2semidirect
13. #19134537C2semidirect
14. #19134407C2semidirect
15. C43×#1789C2semidirect
17. C22×#10621877C22semidirect
18. C2×M16×D43C22semidirect
19. #14583568C4semidirect
20. Q8×C22⋊D43C4semidirect
21. #14583560C4semidirect
22. #14583556C4semidirect
24. #14583548C4semidirect
26. #14583543C4semidirect
28. #14583537C4semidirect
30. D4×C22⋊D43C4semidirect
40. C2×#13063282C22semidirect
41. C22×C4×Dic43C22semidirect
46. #14582922C22semidirect
48. C2×#13063253C22semidirect
49. C2×#13063253C22semidirect
53. C2×#13063252C22semidirect
54. C2×#13063252C22semidirect
55. C2×#13063251C22semidirect
56. C2×#13063251C22semidirect
57. #14582862C22semidirect
58. M16×Dic43C22semidirect
63. C4×Dic43⋊C4C22semidirect
64. C4×(C2×D43)⋊C4C22semidirect
65. #14582745C22semidirect
66. #14582660C22semidirect
67. #14582660C22semidirect
68. #14582659C22semidirect
69. #14582659C22semidirect
73. C2×#104×C43C22semidirect
74. C2×#104×C43C22semidirect
75. C43×#407C22semidirect
76. C4×C22⋊C4×C43C22semidirect
77. C2×#10621902C2×C4semidirect
81. C2×#10621900C2×C4semidirect
86. C2×Q8×D43C2×C4semidirect
90. C2×D4×D43C2×C4semidirect
105. #13063323C2×C4semidirect
107. #13063321C2×C4semidirect
109. #13063314C2×C4semidirect
111. #13063312C2×C4semidirect
124. #13063301C2×C4semidirect
125. #13063301C2×C4semidirect
138. #13063296C2×C4semidirect
139. #13063296C2×C4semidirect
146. Q8×Dic43C2×C4semidirect
147. Q8×Dic43C2×C4semidirect
150. D4×Dic43C2×C4semidirect
151. D4×Dic43C2×C4semidirect
198. #13063252D4semidirect
415. C4×Dic43C2×D4semidirect
420. #10621877C2×D4semidirect
573. C22×C43#421semidirect
623. #1789D43semidirect
681. C2×#104C2×D43semidirect
682. C2×#104C2×D43semidirect
684. #407C2×D43semidirect
692. C4×C22⋊C4C2×D43semidirect
698. C43#22434semidirect
1206. C22#14582914semidirect

Maximal subgroups

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

subgroupindex
#41×C22⋊D432
#191433272
C2×#145829142
C22×#130632522
#191370342
#191355122
#191354252
#191350402
#191350362
#191348952
#191348942
#191346132
#191345372
#191344072
C43×#17892
#2243443