Finite Group Databasebeta

← #25112264

Subgroups — #25112264

Order 11008.

1608 conjugacy classes of subgroups.

The subgroup lattice has 1256 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
3C22×#13063252C211yesmaximal, characteristic, complemented
4C2×#104×D43C211yesmaximal, characteristic, complemented
5C4×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
6#19135512C211yesmaximal, characteristic, complemented
7#19135421C211yesmaximal, characteristic, complemented
8#19135036C211yesmaximal, characteristic, complemented
9#19135035C211yesmaximal, characteristic, complemented
10#19134895C211yesmaximal, characteristic, complemented
11#19134894C211yesmaximal, characteristic, complemented
12#19134613C211yesmaximal, characteristic, complemented
13#19134537C211yesmaximal, characteristic, complemented
14#104×Dic43C211yesmaximal, 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×(C22⋊D43)⋊C4—21no—
41C22×C4×Dic43C2211yescharacteristic, complemented
42C2×C42×D43C2211yescharacteristic, complemented
43#14582974—21no—
44#14582973—21no—
45#14582967—21no—
46(C22⋊D43)⋊C8—21no—
47#14582922C2211yescharacteristic, complemented
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#104×D43—24no—
58#14582862C2211yescharacteristic, complemented
59M16×Dic43C2211yescharacteristic, complemented
60C4×Dic43⋊C4C2211yescharacteristic, complemented
61#14582750—21no—
62C22⋊C4×Dic43—21no—
63C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
64#14582746—21no—
65C42×Dic43C2211yescharacteristic, 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×D43—21no—
94C22×C4×D43C2311yescharacteristic
95C2×#10621877—21no—
96C2×#10621877—22no—
97C2×#10621877—41no—
98C2×#10621877C2311yescharacteristic
99C2×#10621877C2311yescharacteristic
100C2×#10621872—21no—
101M16×D43—22no—
102M16×D43—41no—
103C22×C43⋊C8—21no—
104C2×C8×D43—21no—
105#13063323—21no—
106#13063323C2×C411yescharacteristic, complemented
107#13063321—21no—
108#13063321C2×C411yescharacteristic, complemented
109#13063314—21no—
110#13063314C2×C411yescharacteristic, complemented
111#13063312—21no—
112#13063312C2×C411yescharacteristic, complemented
113#13063308—21no—
114#13063308—21no—
115#13063308—21no—
116#13063306—21no—
117#13063306—21no—
118#13063306—21no—
119#13063304—21no—
120#13063304—21no—
121#13063304C2×C411yescharacteristic, complemented
122#13063304C2×C411yescharacteristic, complemented
123#13063301—21no—
124#13063301—21no—
125#13063301C2×C411yescharacteristic, complemented
126#13063301C2×C411yescharacteristic, complemented
127#13063299—21no—
128#13063299—21no—
129#13063299C2×C411yescharacteristic, complemented
130#13063299C2×C411yescharacteristic, complemented
131#13063297—21no—
132#13063297—21no—
133#13063297—21no—
134#13063297—21no—
135#13063297—21no—
136#13063297—21no—
137#13063296—21no—
138#13063296—21no—
139#13063296C2×C411yescharacteristic, complemented
140#13063296C2×C411yescharacteristic, complemented
141#13063294—21no—
142#13063294—21no—
143#13063294—21no—
144#13063293—21no—
145#13063293—21no—
146#13063293—21no—
147Q8×Dic43C2×C411yescharacteristic, complemented
148Q8×Dic43C2×C411yescharacteristic, complemented
149D4×Dic43—21no—
150D4×Dic43—21no—
151D4×Dic43C2×C411yescharacteristic, complemented
152D4×Dic43C2×C411yescharacteristic, complemented
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⋊D43—21no—
163C4×C22⋊D43C2×C411yescharacteristic
164C4×C22⋊D43C2×C411yescharacteristic
165C4×C22⋊D43C2×C411yescharacteristic
166C4×C22⋊D43C2×C411yescharacteristic
167C4×C22⋊D43D411yescharacteristic
168C4×C22⋊D43D411yescharacteristic
169C4×C22⋊D43D411yescharacteristic
170C4×C22⋊D43D411yescharacteristic
171(C22⋊D43)⋊C4—28no—
172#13063284—21no—
173#13063284C2311yescharacteristic
174C2×Dic43⋊C4—21no—
175C2×Dic43⋊C4—21no—
176C2×Dic43⋊C4D411yescharacteristic
177C2×C22⋊Dic43—21no—
178C2×C22⋊Dic43D411yescharacteristic
179C2×(C2×D43)⋊C4—21no—
180C2×(C2×D43)⋊C4—21no—
181C2×(C2×D43)⋊C4D411yescharacteristic
182C2×C4×Dic43—21no—
183C2×C4×Dic43—21no—
184C2×C4×Dic43—22no—
185C2×C4×Dic43—21no—
186C2×C4×Dic43—21no—
187C2×C4×Dic43—21no—
188C2×C4×Dic43—41no—
189C2×C4×Dic43C2311yescharacteristic
190C2×C4×Dic43C2311yescharacteristic
191C2×C4×Dic43C2311yescharacteristic
192C42×D43—22no—
193C42×D43—41no—
194Dic43⋊C8—21no—
195Dic43⋊C8—21no—
196#13063253—22no—
197#13063253—41no—
198#13063252—22no—
199#13063252—22no—
200#13063252—22no—
201#13063252D414yescomplemented
202#13063251—22no—
203#13063251—41no—
204(C2×D43)⋊C8—21no—
205(C2×D43)⋊C8—21no—
206#13063235—21no—
207C8×Dic43—21no—
208C43⋊#95—21no—
209C43⋊#95—21no—
210C2×#41×C43—21no—
211C2×#41×C43—21no—
212C2×#41×C43—22no—
213C2×#41×C43—22no—
214C2×#41×C43—41no—
215C2×#41×C43—41no—
216C2×#41×C43C2×C411yescharacteristic, complemented
217C2×#41×C43C2×C411yescharacteristic, complemented
218C2×#41×C43C2311yescharacteristic
219C2×#41×C43C2311yescharacteristic
220C22×Q8×C43C2×C411yescharacteristic, complemented
221C22×D4×C43—21no—
222C22×D4×C43C2×C411yescharacteristic, complemented
223C23×C4×C43—21no—
224C23×C4×C43C2311yescharacteristic
225C2×M16×C43C2311yescharacteristic
226C2×M16×C43C2311yescharacteristic
227C2×C22⋊C4×C43—21no—
228C2×C42×C43C2311yescharacteristic
229C2×C42×C43C2311yescharacteristic
230#104×C43—22no—
231#104×C43—22no—
232#104×C43—41no—
233#104×C43—41no—
234C22⋊C8×C43—21no—
235C22⋊C8×C43—21no—
236#95×C43—21no—
237C24×C43—21no—
238C24×C43C2×D411yescharacteristic
239C23×D43—21no—
240C23×D43C2×D411yescharacteristic
241#41×C43—21no—
242#41×C43—21no—
243#41×C43—22no—
244#41×C43—22no—
245#41×C43—21no—
246#41×C43—21no—
247#41×C43—21no—
248#41×C43—21no—
249#41×C43—42no—
250#41×C43—42no—
251#41×C43—41no—
252#41×C43—41no—
253#41×C43—42no—
254#41×C43—42no—
255#41×C43C2×D412yes—
256#41×C43#4112yes—
257C2×Q8×C43—21no—
258C2×Q8×C43—22no—
259C2×Q8×C43—41no—
260C2×Q8×C43C22×C411yescharacteristic
261C2×Q8×C43C22×C411yescharacteristic
262C2×D4×C43—21no—
263C2×D4×C43—21no—
264C2×D4×C43—21no—
265C2×D4×C43—21no—
266C2×D4×C43—21no—
267C2×D4×C43—22no—
268C2×D4×C43—42no—
269C2×D4×C43—42no—
270C2×D4×C43—41no—
271C2×D4×C43C22×C411yescharacteristic
272C2×D4×C43C22×C411yescharacteristic
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—21no—
284C22×C4×C43—42no—
285C22×C4×C43—42no—
286C22×C4×C43C22×C411yescharacteristic
287C22×C4×C43C22×C411yescharacteristic
288C22×C4×C43C2×D411yescharacteristic
289C22×C4×C43C2×D411yescharacteristic
290C22×C4×C43C2×D411yescharacteristic
291C22×C4×C43C2411yescharacteristic
292C2×C22⋊D43—24no—
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—21no—
301C2×C22⋊D43—21no—
302C2×C22⋊D43—44no—
303C2×C22⋊D43C22⋊C411yescharacteristic
304C2×C22⋊D43C22⋊C411yescharacteristic
305C2×C22⋊D43C22⋊C411yescharacteristic
306C2×C22⋊D43C22⋊C411yescharacteristic
307C22×Dic43—24no—
308C22×Dic43—21no—
309C22×Dic43—21no—
310C22×Dic43—21no—
311C22×Dic43—21no—
312C22×Dic43—21no—
313C22×Dic43—42no—
314C22×Dic43—42no—
315C22×Dic43C2×D411yescharacteristic
316C22×Dic43C2×D411yescharacteristic
317C22×Dic43C2×D411yescharacteristic
318#10621902—22no—
319#10621902—41no—
320Q8×D43—22no—
321Q8×D43—41no—
322#10621900—22no—
323#10621900—41no—
324#10621900—42no—
325#10621900—42no—
326D4×D43—22no—
327D4×D43—42no—
328D4×D43—42no—
329D4×D43—41no—
330#10621898—21no—
331#10621898—21no—
332#10621898—21no—
333#10621898—21no—
334#10621898—42no—
335#10621898—42no—
336C2×D172—21no—
337C2×D172C22×C411yescharacteristic
338C2×C4×D43—21no—
339C2×C4×D43—21no—
340C2×C4×D43—21no—
341C2×C4×D43—21no—
342C2×C4×D43—24no—
343C2×C4×D43—21no—
344C2×C4×D43—21no—
345C2×C4×D43—21no—
346C2×C4×D43—42no—
347C2×C4×D43—42no—
348C2×C4×D43—42no—
349C2×C4×D43—42no—
350C2×C4×D43C22×C411yescharacteristic
351C2×C4×D43C22×C411yescharacteristic
352C2×C4×D43C2×D411yescharacteristic
353C2×C4×D43C2×D411yescharacteristic
354C2×Dic86—21no—
355C2×Dic86C22×C411yescharacteristic
356M16×C43—21no—
357M16×C43—21no—
358M16×C43—21no—
359M16×C43—21no—
360C2×C8×C43—21no—
361C2×C8×C43—21no—
362C22⋊C4×C43—24no—
363C42×C43—21no—
364C42×C43—21no—
365C42×C43—21no—
366C42×C43—21no—
367C22⋊Dic43—21no—
368C22⋊Dic43—21no—
369C22⋊Dic43—21no—
370C22⋊Dic43—21no—
371C22⋊Dic43—21no—
372C22⋊Dic43—21no—
373C22⋊Dic43—21no—
374C22⋊Dic43—21no—
375C22⋊Dic43—21no—
376C22⋊Dic43C22⋊C411yescharacteristic
377C22⋊Dic43C22⋊C411yescharacteristic
378C22⋊Dic43C22⋊C411yescharacteristic
379C22⋊Dic43C22⋊C411yescharacteristic
380(C2×D43)⋊C4—24no—
381(C2×D43)⋊C4—21no—
382(C2×D43)⋊C4—21no—
383(C2×D43)⋊C4—21no—
384(C2×D43)⋊C4—21no—
385(C2×D43)⋊C4—21no—
386(C2×D43)⋊C4—21no—
387(C2×D43)⋊C4C22⋊C411yescharacteristic
388(C2×D43)⋊C4C22⋊C411yescharacteristic
389(C2×D43)⋊C4C22⋊C411yescharacteristic
390(C2×D43)⋊C4C22⋊C411yescharacteristic
391C4⋊Dic43—21no—
392C4⋊Dic43—21no—
393C4⋊Dic43C22×C411yescharacteristic
394C4⋊Dic43C22×C411yescharacteristic
395Dic43⋊C4—24no—
396Dic43⋊C4—21no—
397Dic43⋊C4—21no—
398Dic43⋊C4—21no—
399Dic43⋊C4—21no—
400Dic43⋊C4—21no—
401Dic43⋊C4—21no—
402Dic43⋊C4C22⋊C411yescharacteristic
403Dic43⋊C4C22⋊C411yescharacteristic
404Dic43⋊C4C22⋊C411yescharacteristic
405Dic43⋊C4C22⋊C411yescharacteristic
406C4×Dic43—24no—
407C4×Dic43—21no—
408C4×Dic43—21no—
409C4×Dic43—21no—
410C4×Dic43—21no—
411C4×Dic43—21no—
412C4×Dic43—21no—
413C4×Dic43—42no—
414C4×Dic43—42no—
415C4×Dic43—42no—
416C4×Dic43C22×C411yescharacteristic
417C4×Dic43C22×C411yescharacteristic
418C4×Dic43C2×D411yescharacteristic
419C4×Dic43C2×D411yescharacteristic
420C4×Dic43C2×D412yescomplemented
421#10621877—21no—
422#10621877—21no—
423#10621877—21no—
424#10621877—42no—
425#10621877C2×D412yescomplemented
426C2×C43⋊C8—21no—
427C2×C43⋊C8—21no—
428C2×C43⋊C8—42no—
429#10621872—42no—
430C8×D43—42no—
431C23×C43—21no—
432C23×C43—21no—
433C23×C43—21no—
434C23×C43—22no—
435C23×C43—21no—
436C23×C43—41no—
437C23×C43—42no—
438C23×C43—42no—
439C23×C43—81no—
440C23×C43C2×C22⋊C411yescharacteristic
441C23×C43C2×C22⋊C411yescharacteristic
442C23×C43C22×D411yescharacteristic
443C22×D43—21no—
444C22×D43—21no—
445C22×D43—22no—
446C22×D43—21no—
447C22×D43—41no—
448C22×D43—42no—
449C22×D43—42no—
450C22×D43—81no—
451C22×D43C2×C22⋊C411yescharacteristic
452C22×D43C2×C22⋊C411yescharacteristic
453Q8×C43—21no—
454Q8×C43—21no—
455Q8×C43—21no—
456Q8×C43—42no—
457Q8×C43C4×D412yescomplemented
458D4×C43—22no—
459D4×C43—22no—
460D4×C43—21no—
461D4×C43—21no—
462D4×C43—21no—
463D4×C43—42no—
464D4×C43—42no—
465D4×C43—42no—
466D4×C43—41no—
467D4×C43—41no—
468D4×C43C4×D412yescomplemented
469C2×C4×C43—21no—
470C2×C4×C43—21no—
471C2×C4×C43—21no—
472C2×C4×C43—21no—
473C2×C4×C43—21no—
474C2×C4×C43—21no—
475C2×C4×C43—21no—
476C2×C4×C43—21no—
477C2×C4×C43—21no—
478C2×C4×C43—22no—
479C2×C4×C43—22no—
480C2×C4×C43—21no—
481C2×C4×C43—21no—
482C2×C4×C43—22no—
483C2×C4×C43—22no—
484C2×C4×C43—21no—
485C2×C4×C43—42no—
486C2×C4×C43—42no—
487C2×C4×C43—42no—
488C2×C4×C43—41no—
489C2×C4×C43—41no—
490C2×C4×C43—41no—
491C2×C4×C43—41no—
492C2×C4×C43—41no—
493C2×C4×C43—41no—
494C2×C4×C43C2×C22⋊C411yescharacteristic
495C2×C4×C43C2×C22⋊C411yescharacteristic
496C2×C4×C43C23×C411yescharacteristic
497C2×C4×C43C22×D411yescharacteristic
498C2×C4×C43C22×D411yescharacteristic
499C2×C4×C43C2×#4111yescharacteristic
500C2×C4×C43H(5,𝔽2)11yescharacteristic
501C2×C4×C43H(5,𝔽2)11yescharacteristic
502C22⋊D43—22no—
503C22⋊D43—22no—
504C22⋊D43—22no—
505C22⋊D43—42no—
506C22⋊D43—42no—
507C22⋊D43—41no—
508C22⋊D43—41no—
509C22⋊D43—42no—
510C22⋊D43—42no—
511C22⋊D43—42no—
512C22⋊D43—81no—
513C22⋊D43—81no—
514C22⋊D43—81no—
515C22⋊D43#10414yescomplemented
516C2×Dic43—22no—
517C2×Dic43—22no—
518C2×Dic43—22no—
519C2×Dic43—21no—
520C2×Dic43—21no—
521C2×Dic43—22no—
522C2×Dic43—22no—
523C2×Dic43—21no—
524C2×Dic43—21no—
525C2×Dic43—21no—
526C2×Dic43—41no—
527C2×Dic43—42no—
528C2×Dic43—48no—
529C2×Dic43—41no—
530C2×Dic43—41no—
531C2×Dic43—42no—
532C2×Dic43—81no—
533C2×Dic43C2×C22⋊C411yescharacteristic
534C2×Dic43C2×C22⋊C411yescharacteristic
535C2×Dic43C2×C22⋊C411yescharacteristic
536C2×Dic43C2×C22⋊C411yescharacteristic
537C2×Dic43C2×C22⋊C411yescharacteristic
538C2×Dic43C2×C22⋊C411yescharacteristic
539D172—21no—
540D172—21no—
541D172—42no—
542C4×D43—21no—
543C4×D43—21no—
544C4×D43—21no—
545C4×D43—21no—
546C4×D43—21no—
547C4×D43—21no—
548C4×D43—21no—
549C4×D43—21no—
550C4×D43—42no—
551C4×D43—48no—
552C4×D43—42no—
553C4×D43—41no—
554C4×D43—41no—
555Dic86—21no—
556Dic86—21no—
557Dic86—42no—
558C8×C43—41no—
559C8×C43—41no—
560C43⋊C8—22no—
561C43⋊C8—41no—
562D4×#104—431nomaximal, Sylow
563C22×C43—21no—
564C22×C43—21no—
565C22×C43—21no—
566C22×C43—21no—
567C22×C43—22no—
568C22×C43—21no—
569C22×C43—21no—
570C22×C43—21no—
571C22×C43—42no—
572C22×C43—42no—
573C22×C43—41no—
574C22×C43—41no—
575C22×C43—41no—
576C22×C43—41no—
577C22×C43—41no—
578C22×C43—84no—
579C22×C43C2×#10412yescomplemented
580C22×C43C22×C22⋊C411yescharacteristic
581C22×C43D4211yescharacteristic
582C22×C43#54611yescharacteristic
583C2×D43—21no—
584C2×D43—21no—
585C2×D43—21no—
586C2×D43—21no—
587C2×D43—21no—
588C2×D43—42no—
589C2×D43—42no—
590C2×D43—41no—
591C2×D43—41no—
592C2×D43—41no—
593C2×D43—84no—
594C2×D43C2×#10412yescomplemented
595C4×C43—22no—
596C4×C43—21no—
597C4×C43—21no—
598C4×C43—42no—
599C4×C43—42no—
600C4×C43—41no—
601C4×C43C2×C4×D411yescharacteristic
602C4×C43#51811yescharacteristic
603C4×C43D4211yescharacteristic
604C4×C43#54611yescharacteristic
605Dic43—24no—
606Dic43—21no—
607Dic43—21no—
608Dic43—21no—
609Dic43—21no—
610Dic43—21no—
611Dic43—42no—
612Dic43—41no—
613Dic43—41no—
614Dic43—41no—
615Dic43C2×#10412yescomplemented
616D4×#41—431no—
617D4×M16—431no—
618C22×#104—431no—
619C22×#104—431no—
620C42×D4—431no—
621#1980—431no—
622#1962—431no—
623#1896—431no—
624#1896—431no—
625#1871—431no—
626#1871—431no—
627#1806—431no—
628#1789—431no—
629#1789D4311yescharacteristic, complemented
630C4×#104—431no—
631C2×C43—21no—
632C2×C43—21no—
633C2×C43—22no—
634C2×C43—42no—
635C2×C43—41no—
636C2×C43—81no—
637C2×C43D4×C22⋊C411yescharacteristic
638C2×C43C22×#10411yescharacteristic
639C2×C43#290111yescharacteristic
640D43—22no—
641D43—41no—
642D43—81no—
643C22×#41—431no—
644C22×#41C2×D4311yescharacteristic
645C22×M16—431no—
646C22×M16—431no—
647#550—431no—
648D4×Q8—431no—
649#548—431no—
650#548—431no—
651#547—431no—
652#547—861no—
653#546—431no—
654#546—431no—
655#546—861no—
656#546—861no—
657D42—431no—
658D42—861no—
659#532—431no—
660#532—861no—
661#525—431no—
662#525—431no—
663#525—861no—
664#525—861no—
665C4×#41—431no—
666C2×C4×D4—431no—
667C2×C4×D4—861no—
668C2×C4×D4—861no—
669C22×C42—431no—
670C22×C42—431no—
671#436—861no—
672#435—861no—
673#435—861no—
674C8×D4—861no—
675#423—431no—
676C2×#104—431no—
677C2×#104—431no—
678C2×#104—431no—
679C2×#104—431no—
680C2×#104—431no—
681C2×#104—431no—
682C2×#104—431no—
683C2×#104—431no—
684C2×#104—864no—
685C2×#104—864no—
686C2×#104C2×D4311yescharacteristic
687C2×#104C2×D4311yescharacteristic
688C2×#104C2×D4311yescharacteristic, complemented
689C2×#104C2×D4311yescharacteristic, complemented
690#407—431no—
691#407C2×D4311yescharacteristic, complemented
692C4×M16—431no—
693C4×C4⋊C4—431no—
694C4×C4⋊C4—861no—
695C4×C22⋊C4—431no—
696C4×C22⋊C4—861no—
697C4×C22⋊C4—861no—
698C4×C22⋊C4C2×D4311yescharacteristic, complemented
699C43—431no—
700#339—431no—
701#339—431no—
702#339—431no—
703#339—431no—
704C43D4×#10411yescharacteristic, complemented, Sylow
705C2×#41—21no—
706C2×#41—21no—
707C2×#41—22no—
708C2×#41—22no—
709C2×#41—41no—
710C2×#41—41no—
711C2×#41—431no—
712C2×#41—431no—
713C2×#41—431no—
714C2×#41—861no—
715C2×#41—861no—
716C2×#41—862no—
717C2×#41—862no—
718C2×#41—1721no—
719C2×#41—1721no—
720C2×#41C4×D4311yescharacteristic, complemented
721C2×#41C4×D4311yescharacteristic, complemented
722C2×#41C22×D4311yescharacteristic
723C2×#41C22×D4311yescharacteristic
724C22×Q8—431no—
725C22×Q8C4×D4311yescharacteristic, complemented
726C22×D4—21no—
727C22×D4—431no—
728C22×D4—431no—
729C22×D4—861no—
730C22×D4—861no—
731C22×D4C4×D4311yescharacteristic, complemented
732C23×C4—21no—
733C23×C4—431no—
734C23×C4—861no—
735C23×C4—861no—
736C23×C4—861no—
737C23×C4C22×D4311yescharacteristic
738C2×M16—431no—
739C2×M16—431no—
740C2×M16—861no—
741C2×M16—861no—
742C2×M16—862no—
743C2×M16—862no—
744C2×M16—1721no—
745C2×M16—1721no—
746C2×M16C22×D4311yescharacteristic
747C2×M16C22×D4311yescharacteristic
748C22×C8—861no—
749C22×C8—861no—
750C4⋊Q8—431no—
751C4⋊Q8—861no—
752#127—431no—
753#127—861no—
754#124—431no—
755#124—431no—
756#124—861no—
757#124—861no—
758#123—861no—
759#123—861no—
760#123—861no—
761#123—861no—
762#123—861no—
763#123—861no—
764C22⋊Q8—431no—
765C22⋊Q8—431no—
766C22⋊Q8—431no—
767C22⋊Q8—431no—
768C22⋊Q8—861no—
769C22⋊Q8—861no—
770C22⋊Q8—861no—
771C22⋊Q8—861no—
772#121—431no—
773#121—431no—
774#121—431no—
775#121—431no—
776#121—861no—
777#121—861no—
778#121—861no—
779#121—861no—
780#121—861no—
781#121—861no—
782#121—861no—
783#121—861no—
784#121—861no—
785#121—861no—
786#120—861no—
787#120—861no—
788#120—861no—
789#120—861no—
790#120—861no—
791#120—861no—
792C4×Q8—431no—
793C4×Q8—431no—
794C4×D4—431no—
795C4×D4—431no—
796C4×D4—431no—
797C4×D4—431no—
798C4×D4—431no—
799C4×D4—431no—
800C4×D4—431no—
801C4×D4—431no—
802C4×D4—431no—
803C4×D4—431no—
804C4×D4—861no—
805C4×D4—861no—
806C4×D4—868no—
807C4×D4—861no—
808C4×D4—861no—
809C4×D4—861no—
810C4×D4—861no—
811C4×D4—861no—
812C4×D4—861no—
813C4×D4—861no—
814C4×D4—861no—
815C4×D4—861no—
816C4×D4—861no—
817#117—431no—
818#117—861no—
819C2×C4⋊C4—431no—
820C2×C4⋊C4—861no—
821C2×C4⋊C4—861no—
822C2×C22⋊C4—21no—
823C2×C22⋊C4—431no—
824C2×C22⋊C4—431no—
825C2×C22⋊C4—861no—
826C2×C22⋊C4—861no—
827C2×C22⋊C4—861no—
828C2×C42—431no—
829C2×C42—431no—
830C2×C42—431no—
831C2×C42—862no—
832C2×C42—861no—
833C2×C42—862no—
834C2×C42—861no—
835C2×C42—861no—
836C2×C42—861no—
837C2×C42—861no—
838C2×C42—1721no—
839C2×C42—1721no—
840C2×C42C22×D4311yescharacteristic
841C2×C42C22×D4311yescharacteristic
842C4⋊C8—861no—
843C4⋊C8—861no—
844#104—22no—
845#104—22no—
846#104—41no—
847#104—41no—
848#104—434no—
849#104—862no—
850#104—862no—
851#104—862no—
852#104—862no—
853#104—862no—
854#104—1721no—
855#104—1721no—
856C22⋊C8—21no—
857C22⋊C8—21no—
858C22⋊C8—861no—
859C22⋊C8—861no—
860#97—861no—
861C4×C8—861no—
862#95—21no—
863#95—861no—
864#95—861no—
865C24—21no—
866C24—431no—
867C24—861no—
868C24D4×D4311yescharacteristic
869#41—21no—
870#41—21no—
871#41—22no—
872#41—22no—
873#41—21no—
874#41—21no—
875#41—21no—
876#41—21no—
877#41—42no—
878#41—42no—
879#41—41no—
880#41—41no—
881#41—42no—
882#41—42no—
883#41—862no—
884#41—862no—
885#41—861no—
886#41—861no—
887#41—861no—
888#41—861no—
889#41—1722no—
890#41—1722no—
891#41—1721no—
892#41—1722no—
893#41—1722no—
894#41—1721no—
895#41D4×D4312yes—
896#41#1062190012yes—
897C2×Q8—21no—
898C2×Q8—22no—
899C2×Q8—41no—
900C2×Q8—431no—
901C2×Q8—861no—
902C2×Q8—862no—
903C2×Q8—1721no—
904C2×Q8C2×C4×D4311yescharacteristic
905C2×Q8C2×C4×D4311yescharacteristic
906C2×D4—21no—
907C2×D4—22no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—41no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—431no—
916C2×D4—431no—
917C2×D4—431no—
918C2×D4—431no—
919C2×D4—431no—
920C2×D4—861no—
921C2×D4—861no—
922C2×D4—861no—
923C2×D4—861no—
924C2×D4—864no—
925C2×D4—862no—
926C2×D4—861no—
927C2×D4—861no—
928C2×D4—861no—
929C2×D4—861no—
930C2×D4—861no—
931C2×D4—861no—
932C2×D4—1721no—
933C2×D4—1722no—
934C2×D4—1722no—
935C2×D4—1724no—
936C2×D4C2×C4×D4311yescharacteristic
937C2×D4C2×C4×D4311yescharacteristic
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—431no—
952C22×C4—431no—
953C22×C4—431no—
954C22×C4—431no—
955C22×C4—431no—
956C22×C4—431no—
957C22×C4—431no—
958C22×C4—861no—
959C22×C4—861no—
960C22×C4—864no—
961C22×C4—861no—
962C22×C4—861no—
963C22×C4—861no—
964C22×C4—861no—
965C22×C4—861no—
966C22×C4—861no—
967C22×C4—861no—
968C22×C4—861no—
969C22×C4—864no—
970C22×C4—861no—
971C22×C4—861no—
972C22×C4—1722no—
973C22×C4—1722no—
974C22×C4—1722no—
975C22×C4—1722no—
976C22×C4—1722no—
977C22×C4—1722no—
978C22×C4C2×C4×D4311yescharacteristic
979C22×C4C2×C4×D4311yescharacteristic
980C22×C4D4×D4311yescharacteristic
981C22×C4D4×D4311yescharacteristic
982C22×C4D4×D4311yescharacteristic
983C22×C4C23×D4311yescharacteristic
984M16—21no—
985M16—21no—
986M16—21no—
987M16—21no—
988M16—432no—
989M16—861no—
990M16—861no—
991M16—861no—
992M16—1722no—
993M16—1722no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—861no—
997C2×C8—861no—
998C2×C8—1722no—
999C2×C8—1722no—
1000C4⋊C4—431no—
1001C4⋊C4—431no—
1002C4⋊C4—431no—
1003C4⋊C4—431no—
1004C4⋊C4—431no—
1005C4⋊C4—431no—
1006C4⋊C4—861no—
1007C4⋊C4—861no—
1008C4⋊C4—861no—
1009C4⋊C4—861no—
1010C4⋊C4—861no—
1011C4⋊C4—861no—
1012C4⋊C4—864no—
1013C4⋊C4—861no—
1014C4⋊C4—861no—
1015C22⋊C4—24no—
1016C22⋊C4—431no—
1017C22⋊C4—431no—
1018C22⋊C4—431no—
1019C22⋊C4—431no—
1020C22⋊C4—431no—
1021C22⋊C4—431no—
1022C22⋊C4—431no—
1023C22⋊C4—431no—
1024C22⋊C4—861no—
1025C22⋊C4—861no—
1026C22⋊C4—861no—
1027C22⋊C4—861no—
1028C22⋊C4—864no—
1029C22⋊C4—861no—
1030C22⋊C4—861no—
1031C22⋊C4—861no—
1032C22⋊C4—861no—
1033C22⋊C4—861no—
1034C22⋊C4—861no—
1035C22⋊C4—861no—
1036C22⋊C4—861no—
1037C22⋊C4—861no—
1038C22⋊C4—861no—
1039C22⋊C4—861no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—431no—
1045C42—431no—
1046C42—431no—
1047C42—431no—
1048C42—432no—
1049C42—861no—
1050C42—861no—
1051C42—864no—
1052C42—861no—
1053C42—861no—
1054C42—861no—
1055C42—861no—
1056C42—1722no—
1057C42—1722no—
1058C42—1722no—
1059C23—21no—
1060C23—22no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—41no—
1065C23—42no—
1066C23—42no—
1067C23—81no—
1068C23—431no—
1069C23—431no—
1070C23—862no—
1071C23—861no—
1072C23—861no—
1073C23—861no—
1074C23—3441no—
1075C23—1721no—
1076C23—1722no—
1077C23—1722no—
1078C23C22⋊C4×D4311yescharacteristic
1079C23C22⋊C4×D4311yescharacteristic
1080C23C2×D4×D4311yescharacteristic
1081Q8—21no—
1082Q8—21no—
1083Q8—21no—
1084Q8—42no—
1085Q8—861no—
1086Q8—861no—
1087Q8—1722no—
1088Q8(C22⋊D43)⋊C412yescomplemented
1089D4—22no—
1090D4—22no—
1091D4—21no—
1092D4—21no—
1093D4—21no—
1094D4—42no—
1095D4—42no—
1096D4—42no—
1097D4—41no—
1098D4—41no—
1099D4—434no—
1100D4—862no—
1101D4—862no—
1102D4—862no—
1103D4—861no—
1104D4—861no—
1105D4—3441no—
1106D4—3441no—
1107D4—3441no—
1108D4—1722no—
1109D4—1722no—
1110D4—1722no—
1111D4—1722no—
1112D4—1722no—
1113D4—1722no—
1114D4—1721no—
1115D4—1721no—
1116D4(C22⋊D43)⋊C412yescomplemented
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—22no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—431no—
1143C2×C4—431no—
1144C2×C4—431no—
1145C2×C4—431no—
1146C2×C4—431no—
1147C2×C4—431no—
1148C2×C4—862no—
1149C2×C4—862no—
1150C2×C4—862no—
1151C2×C4—862no—
1152C2×C4—861no—
1153C2×C4—861no—
1154C2×C4—861no—
1155C2×C4—861no—
1156C2×C4—861no—
1157C2×C4—861no—
1158C2×C4—861no—
1159C2×C4—861no—
1160C2×C4—861no—
1161C2×C4—861no—
1162C2×C4—862no—
1163C2×C4—861no—
1164C2×C4—861no—
1165C2×C4—861no—
1166C2×C4—3441no—
1167C2×C4—1722no—
1168C2×C4—1722no—
1169C2×C4—1728no—
1170C2×C4—1722no—
1171C2×C4—1721no—
1172C2×C4—1722no—
1173C2×C4—1728no—
1174C2×C4—1721no—
1175C2×C4—1721no—
1176C2×C4—1721no—
1177C2×C4—1721no—
1178C2×C4C22⋊C4×D4311yescharacteristic
1179C2×C4C22⋊C4×D4311yescharacteristic
1180C2×C4C22×C4×D4311yescharacteristic
1181C2×C4C2×D4×D4311yescharacteristic
1182C2×C4C2×D4×D4311yescharacteristic
1183C2×C4C2×#1062190011yescharacteristic
1184C2×C4#1306337011yescharacteristic
1185C2×C4#1306337011yescharacteristic
1186C8—41no—
1187C8—41no—
1188C8—862no—
1189C8—1721no—
1190C22—21no—
1191C22—21no—
1192C22—21no—
1193C22—21no—
1194C22—21no—
1195C22—22no—
1196C22—21no—
1197C22—21no—
1198C22—42no—
1199C22—42no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—84no—
1206C22—432no—
1207C22—861no—
1208C22—861no—
1209C22—861no—
1210C22—861no—
1211C22—861no—
1212C22—3444no—
1213C22—1722no—
1214C22—1722no—
1215C22—1721no—
1216C22—1721no—
1217C22—1721no—
1218C22#104×D4312yescomplemented
1219C22C2×C22⋊C4×D4311yescharacteristic
1220C22#1458353111yescharacteristic
1221C22#1458353611yescharacteristic
1222C4—21no—
1223C4—21no—
1224C4—22no—
1225C4—42no—
1226C4—42no—
1227C4—41no—
1228C4—432no—
1229C4—864no—
1230C4—861no—
1231C4—861no—
1232C4—861no—
1233C4—861no—
1234C4—861no—
1235C4—1722no—
1236C4—1721no—
1237C4—1721no—
1238C4—1721no—
1239C4C2×(C22⋊D43)⋊C411yescharacteristic
1240C4#1458337211yescharacteristic
1241C4#1458353111yescharacteristic
1242C4#1458353611yescharacteristic
1243C2—21no—
1244C2—21no—
1245C2—22no—
1246C2—41no—
1247C2—42no—
1248C2—81no—
1249C2—862no—
1250C2—3441no—
1251C2—1721no—
1252C2#1913741111yescharacteristic
1253C2C2×#104×D4311yescharacteristic
1254C2#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
hypocenterC43D4×#104
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. C22×#13063252C2semidirect
4. C2×#104×D43C2semidirect
5. C4×(C22⋊D43)⋊C4C2semidirect
6. #19135512C2semidirect
7. #19135421C2semidirect
8. #19135036C2semidirect
9. #19135035C2semidirect
10. #19134895C2semidirect
11. #19134894C2semidirect
12. #19134613C2semidirect
13. #19134537C2semidirect
14. #104×Dic43C2semidirect
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
41. C22×C4×Dic43C22semidirect
42. C2×C42×D43C22semidirect
47. #14582922C22semidirect
48. C2×#13063253C22semidirect
49. C2×#13063253C22semidirect
53. C2×#13063252C22semidirect
54. C2×#13063252C22semidirect
55. C2×#13063251C22semidirect
56. C2×#13063251C22semidirect
58. #14582862C22semidirect
59. M16×Dic43C22semidirect
60. C4×Dic43⋊C4C22semidirect
63. C4×(C2×D43)⋊C4C22semidirect
65. C42×Dic43C22semidirect
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
106. #13063323C2×C4semidirect
108. #13063321C2×C4semidirect
110. #13063314C2×C4semidirect
112. #13063312C2×C4semidirect
121. #13063304C2×C4semidirect
122. #13063304C2×C4semidirect
125. #13063301C2×C4semidirect
126. #13063301C2×C4semidirect
129. #13063299C2×C4semidirect
130. #13063299C2×C4semidirect
139. #13063296C2×C4semidirect
140. #13063296C2×C4semidirect
147. Q8×Dic43C2×C4semidirect
148. Q8×Dic43C2×C4semidirect
151. D4×Dic43C2×C4semidirect
152. D4×Dic43C2×C4semidirect
201. #13063252D4semidirect
216. C2×#41×C43C2×C4semidirect
217. C2×#41×C43C2×C4semidirect
220. C22×Q8×C43C2×C4semidirect
222. C22×D4×C43C2×C4semidirect
420. C4×Dic43C2×D4semidirect
425. #10621877C2×D4semidirect
457. Q8×C43C4×D4semidirect
468. D4×C43C4×D4semidirect
515. C22⋊D43#104semidirect
579. C22×C43C2×#104semidirect
594. C2×D43C2×#104semidirect
615. Dic43C2×#104semidirect
629. #1789D43semidirect
688. C2×#104C2×D43semidirect
689. C2×#104C2×D43semidirect
691. #407C2×D43semidirect
698. C4×C22⋊C4C2×D43semidirect
704. C43D4×#104semidirect
720. C2×#41C4×D43semidirect
721. C2×#41C4×D43semidirect
725. C22×Q8C4×D43semidirect
731. C22×D4C4×D43semidirect
1088. Q8(C22⋊D43)⋊C4semidirect
1116. D4(C22⋊D43)⋊C4semidirect
1218. C22#104×D43semidirect

Maximal subgroups

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

subgroupindex
#41×C22⋊D432
#191433272
C22×#130632522
C2×#104×D432
C4×(C22⋊D43)⋊C42
#191355122
#191354212
#191350362
#191350352
#191348952
#191348942
#191346132
#191345372
#104×Dic432
C43×#17892
D4×#10443