Finite Group Databasebeta

← #25112266

Subgroups — #25112266

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#19148078C211yesmaximal, characteristic
2#19143327C211yesmaximal, characteristic, complemented
3C22×#13063253C211yesmaximal, characteristic, complemented
4C2×#104×D43C211yesmaximal, characteristic, complemented
5C42×C22⋊D43C211yesmaximal, characteristic, complemented
6#19135512C211yesmaximal, characteristic, complemented
7#19135421C211yesmaximal, characteristic, complemented
8#19135037C211yesmaximal, characteristic, complemented
9#19134898C211yesmaximal, characteristic, complemented
10#19134896C211yesmaximal, characteristic, complemented
11#19134614C211yesmaximal, characteristic, complemented
12#19134538C211yesmaximal, characteristic, complemented
13#19134537C211yesmaximal, characteristic, complemented
14#19134399C211yesmaximal, characteristic, complemented
15C43×#1896C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#41×D43C2211yescharacteristic
18C22×#10621877C2211yescharacteristic, complemented
19C2×M16×D43C2211yescharacteristic, complemented
20#14583567C411yescharacteristic, complemented
21#14583562C411yescharacteristic, complemented
22#14583559C411yescharacteristic, complemented
23#14583555C411yescharacteristic, complemented
24#14583551C411yescharacteristic, complemented
25#14583547—21no—
26#14583546C411yescharacteristic, complemented
27#14583541—21no—
28#14583540C411yescharacteristic, complemented
29#14583536—21no—
30#14583533C411yescharacteristic, complemented
31#14583531—21no—
32#14583446—21no—
33#14583445C2211yescharacteristic
34#14583411C2211yescharacteristic
35#14583408—21no—
36#14583408—21no—
37#14583367C2211yescharacteristic
38C2×C4×C22⋊D43—21no—
39C2×C4×C22⋊D43C2211yescharacteristic
40C4×D4×D43—21no—
41C2×C42×D43C2211yescharacteristic, complemented
42#14582974—21no—
43#14582973—21no—
44#14582967—21no—
45(C22⋊D43)⋊C8—21no—
46#14582922C2211yescharacteristic, complemented
47C2×#13063253—24no—
48C2×#13063253C2211yescharacteristic
49C2×#13063253C2211yescharacteristic
50C2×#13063253C2211yescharacteristic, complemented
51C2×#13063253C2211yescharacteristic, complemented
52C2×#13063252C2211yescharacteristic, complemented
53C2×#13063252C2211yescharacteristic, complemented
54C2×#13063251C2211yescharacteristic
55C2×#13063251C2211yescharacteristic
56C2×#13063251C2211yescharacteristic, complemented
57C2×#13063251C2211yescharacteristic, complemented
58#104×D43—24no—
59#14582862C2211yescharacteristic, complemented
60M16×Dic43C2211yescharacteristic, complemented
61C4×Dic43⋊C4—21no—
62C4×Dic43⋊C4C2211yescharacteristic, complemented
63C4×(C2×D43)⋊C4—21no—
64C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
65C4×C22⋊Dic43—21no—
66C4×C22⋊Dic43C2211yescharacteristic, complemented
67C42×Dic43C2211yescharacteristic, complemented
68#14582658C2211yescharacteristic, complemented
69#14582658C2211yescharacteristic, complemented
70C43×#525C2211yescharacteristic
71C22×C42×C43C2211yescharacteristic, complemented
72C2×#104×C43C2211yescharacteristic, complemented
73C2×#104×C43C2211yescharacteristic, complemented
74C43×#407C2211yescharacteristic, complemented
75C43×#339C2211yescharacteristic, complemented
76C43×#339C2211yescharacteristic, complemented
77C2×#10621902C2×C411yescharacteristic, complemented
78C2×#10621898—21no—
79C2×#10621898—21no—
80C2×#10621898—21no—
81C2×#10621898—22no—
82C2×#10621898—22no—
83C2×#10621898—41no—
84C2×#10621898—41no—
85C2×#10621898C2×C411yescharacteristic, complemented
86C2×#10621898C2×C411yescharacteristic, complemented
87C2×#10621898C2311yescharacteristic
88C2×#10621898C2311yescharacteristic
89C2×#10621900—21no—
90C2×#10621900C2×C411yescharacteristic, complemented
91#41×D43—22no—
92#41×D43—22no—
93#41×D43—41no—
94#41×D43—41no—
95C22×Dic86C2×C411yescharacteristic, complemented
96C2×Q8×D43C2×C411yescharacteristic, complemented
97C22×D172C2×C411yescharacteristic, complemented
98C22×C22⋊D43—21no—
99C22×C22⋊D43D411yescharacteristic
100C2×D4×D43—21no—
101C2×D4×D43—21no—
102C2×D4×D43C2×C411yescharacteristic, complemented
103C22×C4×D43—21no—
104C22×C4×D43—21no—
105C22×C4×D43—21no—
106C22×C4×D43C2311yescharacteristic
107C2×#10621877—21no—
108C2×#10621877—22no—
109C2×#10621877—41no—
110C2×#10621877C2311yescharacteristic
111C2×#10621877C2311yescharacteristic
112C2×#10621872—21no—
113M16×D43—22no—
114M16×D43—41no—
115C22×C43⋊C8—21no—
116C2×C8×D43—21no—
117#13063324—21no—
118#13063323C2×C411yescharacteristic, complemented
119#13063321—21no—
120#13063321C2×C411yescharacteristic, complemented
121#13063314C2×C411yescharacteristic, complemented
122#13063312C2×C411yescharacteristic, complemented
123#13063311—21no—
124#13063311—21no—
125#13063310—21no—
126#13063310—21no—
127#13063309—21no—
128#13063307—21no—
129#13063307—21no—
130#13063305C2×C411yescharacteristic, complemented
131#13063305C2×C411yescharacteristic, complemented
132#13063303—21no—
133#13063303—21no—
134#13063302—21no—
135#13063302—21no—
136#13063300—21no—
137#13063300C2×C411yescharacteristic, complemented
138#13063300C2×C411yescharacteristic, complemented
139#13063298—21no—
140#13063298—21no—
141#13063298—21no—
142#13063298—21no—
143#13063297—21no—
144#13063297—21no—
145#13063297—21no—
146#13063297—21no—
147#13063296—21no—
148#13063295—21no—
149#13063295—21no—
150#13063295—21no—
151#13063293—21no—
152#13063293—21no—
153#13063290C2×C411yescharacteristic, complemented
154#13063290C2×C411yescharacteristic, complemented
155C4×D172—21no—
156C4×D172—21no—
157D4×Dic43—21no—
158#13063287—21no—
159#13063287C2×C411yescharacteristic, complemented
160#13063287C2×C411yescharacteristic, complemented
161C4×C22⋊D43—28no—
162C4×C22⋊D43—21no—
163C4×C22⋊D43—21no—
164C4×C22⋊D43C2×C411yescharacteristic
165C4×C22⋊D43C2×C411yescharacteristic
166C4×C22⋊D43C2×C411yescharacteristic
167C4×C22⋊D43C2×C411yescharacteristic
168C4×C22⋊D43D411yescharacteristic
169C4×C22⋊D43D411yescharacteristic
170C4×C22⋊D43D411yescharacteristic
171C4×C22⋊D43D411yescharacteristic
172(C22⋊D43)⋊C4—21no—
173(C22⋊D43)⋊C4—21no—
174(C22⋊D43)⋊C4—21no—
175(C22⋊D43)⋊C4—21no—
176#13063282—21no—
177C2×Dic43⋊C4—21no—
178C2×Dic43⋊C4D411yescharacteristic
179C4⋊C4×D43—21no—
180C2×C22⋊Dic43—21no—
181C2×C22⋊Dic43D411yescharacteristic
182C2×(C2×D43)⋊C4—21no—
183C2×(C2×D43)⋊C4D411yescharacteristic
184C22⋊C4×D43—21no—
185C22⋊C4×D43—21no—
186C2×C4×Dic43—21no—
187C2×C4×Dic43—21no—
188C2×C4×Dic43—21no—
189C2×C4×Dic43C2311yescharacteristic
190C2×C4×Dic43C2311yescharacteristic
191C2×C4×Dic43C2311yescharacteristic
192C42×D43—21no—
193C42×D43—22no—
194C42×D43—41no—
195Dic43⋊C8—21no—
196Dic43⋊C8—21no—
197#13063253—22no—
198#13063253—22no—
199#13063253—22no—
200#13063253D414yescomplemented
201#13063252—22no—
202#13063252—41no—
203#13063251—22no—
204#13063251—22no—
205#13063251—41no—
206#13063251—41no—
207(C2×D43)⋊C8—21no—
208(C2×D43)⋊C8—21no—
209#13063235—21no—
210C8×Dic43—21no—
211C43⋊#95—21no—
212C43⋊#95—21no—
213C43⋊#95—21no—
214C2×#41×C43C2311yescharacteristic
215C23×C4×C43—21no—
216C23×C4×C43C2311yescharacteristic
217C2×M16×C43C2311yescharacteristic
218C2×M16×C43C2311yescharacteristic
219#123×C43—21no—
220C22⋊Q8×C43C2×C411yescharacteristic, complemented
221C22⋊Q8×C43C2×C411yescharacteristic, complemented
222#121×C43C2×C411yescharacteristic, complemented
223#121×C43C2×C411yescharacteristic, complemented
224#120×C43—21no—
225C4×D4×C43—21no—
226C4×D4×C43—21no—
227#117×C43C2311yescharacteristic
228C2×C42×C43—22no—
229C2×C42×C43—21no—
230C2×C42×C43—41no—
231C2×C42×C43C2311yescharacteristic
232C2×C42×C43C2311yescharacteristic
233#104×C43—22no—
234#104×C43—41no—
235C22⋊C8×C43—21no—
236C22⋊C8×C43—21no—
237C24×C43C2×D411yescharacteristic
238C23×D43—21no—
239C23×D43—21no—
240C23×D43C2×D411yescharacteristic
241#41×C43—21no—
242#41×C43—21no—
243#41×C43—21no—
244#41×C43—21no—
245C2×Q8×C43C22×C411yescharacteristic
246C2×D4×C43—21no—
247C2×D4×C43—21no—
248C2×D4×C43—21no—
249C2×D4×C43C22×C411yescharacteristic
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—24no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—42no—
259C22×C4×C43—42no—
260C22×C4×C43C22×C411yescharacteristic
261C22×C4×C43C22×C411yescharacteristic
262C22×C4×C43C2×D411yescharacteristic
263C22×C4×C43C2×D411yescharacteristic
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2411yescharacteristic
266C2×C22⋊D43—24no—
267C2×C22⋊D43—21no—
268C2×C22⋊D43—21no—
269C2×C22⋊D43—21no—
270C2×C22⋊D43—21no—
271C2×C22⋊D43—21no—
272C2×C22⋊D43—21no—
273C2×C22⋊D43—21no—
274C2×C22⋊D43—21no—
275C2×C22⋊D43—42no—
276C2×C22⋊D43—42no—
277C2×C22⋊D43C22⋊C411yescharacteristic
278C2×C22⋊D43C22⋊C411yescharacteristic
279C2×C22⋊D43C22⋊C411yescharacteristic
280C2×C22⋊D43C22⋊C411yescharacteristic
281C22×Dic43—21no—
282C22×Dic43—21no—
283C22×Dic43—21no—
284C22×Dic43—21no—
285C22×Dic43C2×D411yescharacteristic
286C22×Dic43C2×D411yescharacteristic
287C22×Dic43C2×D411yescharacteristic
288#10621902—22no—
289#10621902—41no—
290Q8×D43—22no—
291Q8×D43—41no—
292#10621900—22no—
293#10621900—41no—
294#10621900—42no—
295#10621900—42no—
296D4×D43—22no—
297D4×D43—42no—
298D4×D43—42no—
299D4×D43—41no—
300D4×D43—44no—
301#10621898—21no—
302#10621898—21no—
303#10621898—21no—
304#10621898—21no—
305#10621898—21no—
306#10621898—21no—
307#10621898—22no—
308#10621898—22no—
309#10621898—41no—
310#10621898—41no—
311#10621898—42no—
312#10621898—42no—
313#10621898—42no—
314#10621898—42no—
315#10621898—42no—
316#10621898—42no—
317#10621898C2×D412yes—
318#10621898#4112yes—
319C2×D172—21no—
320C2×D172—21no—
321C2×D172—21no—
322C2×D172—21no—
323C2×D172—22no—
324C2×D172—41no—
325C2×D172C22×C411yescharacteristic
326C2×D172C22×C411yescharacteristic
327C2×C4×D43—21no—
328C2×C4×D43—21no—
329C2×C4×D43—21no—
330C2×C4×D43—21no—
331C2×C4×D43—21no—
332C2×C4×D43—24no—
333C2×C4×D43—21no—
334C2×C4×D43—21no—
335C2×C4×D43—21no—
336C2×C4×D43—21no—
337C2×C4×D43—21no—
338C2×C4×D43—21no—
339C2×C4×D43—21no—
340C2×C4×D43—42no—
341C2×C4×D43—42no—
342C2×C4×D43—42no—
343C2×C4×D43—42no—
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—22no—
351C2×Dic86—21no—
352C2×Dic86—21no—
353C2×Dic86—41no—
354C2×Dic86C22×C411yescharacteristic
355C2×Dic86C22×C411yescharacteristic
356M16×C43—21no—
357M16×C43—21no—
358M16×C43—21no—
359M16×C43—21no—
360C2×C8×C43—21no—
361C2×C8×C43—21no—
362C4⋊C4×C43—21no—
363C4⋊C4×C43—21no—
364C4⋊C4×C43C22×C411yescharacteristic
365C4⋊C4×C43C22×C411yescharacteristic
366C22⋊C4×C43—21no—
367C22⋊C4×C43—21no—
368C22⋊C4×C43—21no—
369C22⋊C4×C43—21no—
370C22⋊C4×C43—21no—
371C42×C43—21no—
372C42×C43—21no—
373C42×C43—21no—
374C42×C43—21no—
375C42×C43—42no—
376C42×C43C2×D412yescomplemented
377C22⋊Dic43—24no—
378C22⋊Dic43—21no—
379C22⋊Dic43—21no—
380C22⋊Dic43C22⋊C411yescharacteristic
381C22⋊Dic43C22⋊C411yescharacteristic
382C22⋊Dic43C22⋊C411yescharacteristic
383C22⋊Dic43C22⋊C411yescharacteristic
384(C2×D43)⋊C4—24no—
385(C2×D43)⋊C4—21no—
386(C2×D43)⋊C4—21no—
387(C2×D43)⋊C4—21no—
388(C2×D43)⋊C4—21no—
389(C2×D43)⋊C4—21no—
390(C2×D43)⋊C4—21no—
391(C2×D43)⋊C4—21no—
392(C2×D43)⋊C4—21no—
393(C2×D43)⋊C4C22⋊C411yescharacteristic
394(C2×D43)⋊C4C22⋊C411yescharacteristic
395(C2×D43)⋊C4C22⋊C411yescharacteristic
396(C2×D43)⋊C4C22⋊C411yescharacteristic
397C4⋊Dic43—21no—
398C4⋊Dic43—21no—
399Dic43⋊C4—24no—
400Dic43⋊C4—21no—
401Dic43⋊C4—21no—
402Dic43⋊C4—21no—
403Dic43⋊C4—21no—
404Dic43⋊C4C22⋊C411yescharacteristic
405Dic43⋊C4C22⋊C411yescharacteristic
406Dic43⋊C4C22⋊C411yescharacteristic
407Dic43⋊C4C22⋊C411yescharacteristic
408C4×Dic43—24no—
409C4×Dic43—21no—
410C4×Dic43—21no—
411C4×Dic43—21no—
412C4×Dic43—21no—
413C4×Dic43—21no—
414C4×Dic43—21no—
415C4×Dic43—42no—
416C4×Dic43—42no—
417C4×Dic43C22×C411yescharacteristic
418C4×Dic43C22×C411yescharacteristic
419C4×Dic43C2×D411yescharacteristic
420C4×Dic43C2×D411yescharacteristic
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—22no—
434C23×C43—21no—
435C23×C43—41no—
436C23×C43C2×C22⋊C411yescharacteristic
437C23×C43C2×C22⋊C411yescharacteristic
438C23×C43C22×D411yescharacteristic
439C22×D43—21no—
440C22×D43—21no—
441C22×D43—21no—
442C22×D43—22no—
443C22×D43—21no—
444C22×D43—41no—
445C22×D43—42no—
446C22×D43—42no—
447C22×D43—42no—
448C22×D43—42no—
449C22×D43—81no—
450C22×D43—81no—
451C22×D43C2×C22⋊C411yescharacteristic
452C22×D43C2×C22⋊C411yescharacteristic
453Q8×C43—21no—
454Q8×C43—21no—
455D4×C43—21no—
456D4×C43—21no—
457D4×C43—41no—
458D4×C43—41no—
459D4×C43—42no—
460D4×C43—81no—
461C2×C4×C43—22no—
462C2×C4×C43—22no—
463C2×C4×C43—22no—
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—21no—
474C2×C4×C43—22no—
475C2×C4×C43—21no—
476C2×C4×C43—21no—
477C2×C4×C43—21no—
478C2×C4×C43—48no—
479C2×C4×C43—41no—
480C2×C4×C43—41no—
481C2×C4×C43—41no—
482C2×C4×C43—41no—
483C2×C4×C43C2×C22⋊C411yescharacteristic
484C2×C4×C43C2×C22⋊C411yescharacteristic
485C2×C4×C43C23×C411yescharacteristic
486C2×C4×C43C22×D411yescharacteristic
487C2×C4×C43C22×D411yescharacteristic
488C2×C4×C43C2×#4111yescharacteristic
489C2×C4×C43H(5,𝔽2)11yescharacteristic
490C2×C4×C43H(5,𝔽2)11yescharacteristic
491C22⋊D43—22no—
492C22⋊D43—22no—
493C22⋊D43—22no—
494C22⋊D43—22no—
495C22⋊D43—22no—
496C22⋊D43—42no—
497C22⋊D43—42no—
498C22⋊D43—42no—
499C22⋊D43—42no—
500C22⋊D43—41no—
501C22⋊D43—41no—
502C22⋊D43—42no—
503C22⋊D43—81no—
504C22⋊D43#10414yescomplemented
505C2×Dic43—21no—
506C2×Dic43—21no—
507C2×Dic43—21no—
508C2×Dic43—22no—
509C2×Dic43—22no—
510C2×Dic43—22no—
511C2×Dic43—21no—
512C2×Dic43—41no—
513C2×Dic43—42no—
514C2×Dic43—42no—
515C2×Dic43—41no—
516C2×Dic43—41no—
517C2×Dic43—41no—
518C2×Dic43—41no—
519C2×Dic43C2×C22⋊C411yescharacteristic
520C2×Dic43C2×C22⋊C411yescharacteristic
521C2×Dic43C2×C22⋊C411yescharacteristic
522C2×Dic43C2×C22⋊C411yescharacteristic
523C2×Dic43C2×C22⋊C411yescharacteristic
524C2×Dic43C2×C22⋊C411yescharacteristic
525D172—21no—
526D172—21no—
527D172—21no—
528D172—42no—
529D172—42no—
530D172—42no—
531D172—81no—
532D172C4×D412yescomplemented
533C4×D43—21no—
534C4×D43—21no—
535C4×D43—21no—
536C4×D43—21no—
537C4×D43—21no—
538C4×D43—21no—
539C4×D43—22no—
540C4×D43—21no—
541C4×D43—21no—
542C4×D43—22no—
543C4×D43—42no—
544C4×D43—42no—
545C4×D43—42no—
546C4×D43—42no—
547C4×D43—48no—
548C4×D43—41no—
549C4×D43—41no—
550C4×D43—42no—
551C4×D43—81no—
552Dic86—21no—
553Dic86—21no—
554Dic86—21no—
555Dic86—42no—
556Dic86—42no—
557Dic86C4×D412yescomplemented
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—21no—
568C22×C43—21no—
569C22×C43—21no—
570C22×C43—42no—
571C22×C43—42no—
572C22×C43—41no—
573C22×C43—41no—
574C22×C43—41no—
575C22×C43C2×#10412yescomplemented
576C22×C43C22×C22⋊C411yescharacteristic
577C22×C43D4211yescharacteristic
578C22×C43#54611yescharacteristic
579C2×D43—21no—
580C2×D43—21no—
581C2×D43—21no—
582C2×D43—22no—
583C2×D43—21no—
584C2×D43—21no—
585C2×D43—42no—
586C2×D43—42no—
587C2×D43—41no—
588C2×D43—41no—
589C2×D43—41no—
590C2×D43—41no—
591C2×D43—41no—
592C2×D43—84no—
593C2×D43—84no—
594C2×D43C2×#10412yescomplemented
595C4×C43—24no—
596C4×C43—21no—
597C4×C43—21no—
598C4×C43—42no—
599C4×C43—41no—
600C4×C43—41no—
601C4×C43—41no—
602C4×C43C2×C4×D411yescharacteristic
603C4×C43#51811yescharacteristic
604C4×C43D4211yescharacteristic
605C4×C43#54611yescharacteristic
606Dic43—22no—
607Dic43—21no—
608Dic43—21no—
609Dic43—21no—
610Dic43—21no—
611Dic43—21no—
612Dic43—42no—
613Dic43—42no—
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#1896D4311yescharacteristic, complemented
625#1871—431no—
626#1871—431no—
627#1806—431no—
628#1789—431no—
629#1789—431no—
630C4×#104—431no—
631C2×C43—21no—
632C2×C43—21no—
633C2×C43—22no—
634C2×C43—41no—
635C2×C43—81no—
636C2×C43D4×C22⋊C411yescharacteristic
637C2×C43C22×#10411yescharacteristic
638C2×C43#290111yescharacteristic
639D43—22no—
640D43—41no—
641D43—42no—
642D43—81no—
643C22×#41—431no—
644C22×#41—431no—
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—861no—
663#525—861no—
664#525C2×D4311yescharacteristic
665C4×#41—431no—
666C2×C4×D4—431no—
667C2×C4×D4—861no—
668C2×C4×D4—861no—
669C22×C42—431no—
670C22×C42C2×D4311yescharacteristic, complemented
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—431no—
685C2×#104—431no—
686C2×#104—864no—
687C2×#104—864no—
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—431no—
697C4×C22⋊C4—861no—
698C4×C22⋊C4—861no—
699C43—431no—
700#339—431no—
701#339—431no—
702#339C2×D4311yescharacteristic, complemented
703#339C2×D4311yescharacteristic, complemented
704C43D4×#10411yescharacteristic, complemented, Sylow
705C2×#41—431no—
706C2×#41—431no—
707C2×#41—431no—
708C2×#41—431no—
709C2×#41—431no—
710C2×#41—431no—
711C2×#41—861no—
712C2×#41—862no—
713C2×#41—862no—
714C2×#41—861no—
715C2×#41—861no—
716C2×#41—861no—
717C2×#41—862no—
718C2×#41—862no—
719C2×#41—1721no—
720C2×#41—1721no—
721C2×#41—1721no—
722C2×#41—1721no—
723C2×#41C22×D4311yescharacteristic
724C22×Q8—431no—
725C22×Q8—431no—
726C22×D4—431no—
727C22×D4—431no—
728C22×D4—431no—
729C22×D4—861no—
730C22×D4—861no—
731C22×D4—861no—
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—21no—
759#123—861no—
760#123—861no—
761#123—861no—
762#123—861no—
763#123—861no—
764C22⋊Q8—431no—
765C22⋊Q8—431no—
766C22⋊Q8—861no—
767C22⋊Q8—861no—
768C22⋊Q8—861no—
769C22⋊Q8—861no—
770C22⋊Q8C4×D4311yescharacteristic, complemented
771C22⋊Q8C4×D4311yescharacteristic, complemented
772#121—431no—
773#121—431no—
774#121—861no—
775#121—861no—
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#121C4×D4311yescharacteristic, complemented
785#121C4×D4311yescharacteristic, complemented
786#120—21no—
787#120—861no—
788#120—861no—
789#120—861no—
790#120—861no—
791#120—861no—
792C4×Q8—431no—
793C4×Q8—431no—
794C4×D4—21no—
795C4×D4—21no—
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—431no—
805C4×D4—431no—
806C4×D4—861no—
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—868no—
817#117—861no—
818#117C22×D4311yescharacteristic
819C2×C4⋊C4—431no—
820C2×C4⋊C4—861no—
821C2×C4⋊C4—861no—
822C2×C22⋊C4—431no—
823C2×C22⋊C4—431no—
824C2×C22⋊C4—861no—
825C2×C22⋊C4—861no—
826C2×C22⋊C4—861no—
827C2×C22⋊C4—861no—
828C2×C42—22no—
829C2×C42—21no—
830C2×C42—41no—
831C2×C42—431no—
832C2×C42—431no—
833C2×C42—431no—
834C2×C42—861no—
835C2×C42—861no—
836C2×C42—862no—
837C2×C42—861no—
838C2×C42—861no—
839C2×C42—1721no—
840C2×C42C22×D4311yescharacteristic
841C2×C42C22×D4311yescharacteristic
842C4⋊C8—861no—
843C4⋊C8—861no—
844#104—22no—
845#104—41no—
846#104—434no—
847#104—862no—
848#104—862no—
849#104—862no—
850#104—862no—
851#104—862no—
852#104—862no—
853#104—1721no—
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—861no—
863#95—861no—
864#95—861no—
865C24—431no—
866C24—861no—
867C24—861no—
868C24D4×D4311yescharacteristic
869#41—21no—
870#41—21no—
871#41—21no—
872#41—21no—
873#41—432no—
874#41—432no—
875#41—862no—
876#41—862no—
877#41—861no—
878#41—861no—
879#41—862no—
880#41—862no—
881#41—861no—
882#41—861no—
883#41—861no—
884#41—861no—
885#41—1722no—
886#41—1722no—
887#41—1721no—
888#41—1721no—
889#41—1722no—
890#41—1722no—
891#41—1722no—
892#41—1722no—
893#41—1721no—
894#41—1722no—
895#41—1722no—
896#41—1721no—
897C2×Q8—431no—
898C2×Q8—431no—
899C2×Q8—861no—
900C2×Q8—862no—
901C2×Q8—861no—
902C2×Q8—862no—
903C2×Q8—1721no—
904C2×Q8—1721no—
905C2×Q8C2×C4×D4311yescharacteristic
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—431no—
910C2×D4—431no—
911C2×D4—431no—
912C2×D4—431no—
913C2×D4—431no—
914C2×D4—431no—
915C2×D4—862no—
916C2×D4—861no—
917C2×D4—861no—
918C2×D4—861no—
919C2×D4—861no—
920C2×D4—861no—
921C2×D4—861no—
922C2×D4—862no—
923C2×D4—864no—
924C2×D4—861no—
925C2×D4—861no—
926C2×D4—861no—
927C2×D4—861no—
928C2×D4—861no—
929C2×D4—861no—
930C2×D4—1721no—
931C2×D4—1721no—
932C2×D4—1724no—
933C2×D4—1722no—
934C2×D4—1722no—
935C2×D4—1722no—
936C2×D4—1722no—
937C2×D4C2×C4×D4311yescharacteristic
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—24no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—431no—
949C22×C4—431no—
950C22×C4—431no—
951C22×C4—431no—
952C22×C4—431no—
953C22×C4—431no—
954C22×C4—431no—
955C22×C4—861no—
956C22×C4—861no—
957C22×C4—861no—
958C22×C4—861no—
959C22×C4—864no—
960C22×C4—861no—
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—861no—
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—21no—
1001C4⋊C4—21no—
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⋊C4C2×C4×D4311yescharacteristic
1014C4⋊C4C2×C4×D4311yescharacteristic
1015C22⋊C4—21no—
1016C22⋊C4—21no—
1017C22⋊C4—21no—
1018C22⋊C4—21no—
1019C22⋊C4—21no—
1020C22⋊C4—431no—
1021C22⋊C4—431no—
1022C22⋊C4—431no—
1023C22⋊C4—431no—
1024C22⋊C4—431no—
1025C22⋊C4—431no—
1026C22⋊C4—431no—
1027C22⋊C4—431no—
1028C22⋊C4—861no—
1029C22⋊C4—861no—
1030C22⋊C4—861no—
1031C22⋊C4—861no—
1032C22⋊C4—861no—
1033C22⋊C4—861no—
1034C22⋊C4—861no—
1035C22⋊C4—861no—
1036C22⋊C4—864no—
1037C22⋊C4—861no—
1038C22⋊C4—861no—
1039C22⋊C4—864no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—42no—
1045C42—431no—
1046C42—431no—
1047C42—431no—
1048C42—431no—
1049C42—861no—
1050C42—861no—
1051C42—864no—
1052C42—861no—
1053C42—861no—
1054C42—861no—
1055C42—861no—
1056C42—1722no—
1057C42—1722no—
1058C42D4×D4312yescomplemented
1059C23—22no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—41no—
1064C23—431no—
1065C23—431no—
1066C23—862no—
1067C23—861no—
1068C23—861no—
1069C23—861no—
1070C23—861no—
1071C23—3441no—
1072C23—3441no—
1073C23—1721no—
1074C23—1722no—
1075C23—1722no—
1076C23—1722no—
1077C23—1722no—
1078C23C22⋊C4×D4311yescharacteristic
1079C23C22⋊C4×D4311yescharacteristic
1080C23C2×D4×D4311yescharacteristic
1081Q8—21no—
1082Q8—21no—
1083Q8—432no—
1084Q8—861no—
1085Q8—861no—
1086Q8—861no—
1087Q8—1722no—
1088Q8—1722no—
1089D4—21no—
1090D4—21no—
1091D4—42no—
1092D4—41no—
1093D4—41no—
1094D4—81no—
1095D4—434no—
1096D4—432no—
1097D4—862no—
1098D4—862no—
1099D4—862no—
1100D4—862no—
1101D4—862no—
1102D4—861no—
1103D4—861no—
1104D4—861no—
1105D4—3441no—
1106D4—3441no—
1107D4—1722no—
1108D4—1722no—
1109D4—1722no—
1110D4—1722no—
1111D4—1722no—
1112D4—1722no—
1113D4—1722no—
1114D4—1722no—
1115D4—1721no—
1116D4—1721no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—48no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—431no—
1140C2×C4—431no—
1141C2×C4—431no—
1142C2×C4—431no—
1143C2×C4—431no—
1144C2×C4—431no—
1145C2×C4—862no—
1146C2×C4—861no—
1147C2×C4—861no—
1148C2×C4—861no—
1149C2×C4—861no—
1150C2×C4—861no—
1151C2×C4—861no—
1152C2×C4—861no—
1153C2×C4—861no—
1154C2×C4—861no—
1155C2×C4—862no—
1156C2×C4—861no—
1157C2×C4—861no—
1158C2×C4—862no—
1159C2×C4—862no—
1160C2×C4—862no—
1161C2×C4—861no—
1162C2×C4—3441no—
1163C2×C4—1722no—
1164C2×C4—1722no—
1165C2×C4—1728no—
1166C2×C4—1722no—
1167C2×C4—1722no—
1168C2×C4—1722no—
1169C2×C4—1721no—
1170C2×C4—1722no—
1171C2×C4—1722no—
1172C2×C4—1721no—
1173C2×C4—1721no—
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×C4#41×D4311yescharacteristic
1184C2×C4#1306337011yescharacteristic
1185C2×C4#1306337111yescharacteristic
1186C8—41no—
1187C8—41no—
1188C8—862no—
1189C8—1721no—
1190C22—21no—
1191C22—21no—
1192C22—21no—
1193C22—21no—
1194C22—21no—
1195C22—21no—
1196C22—21no—
1197C22—42no—
1198C22—42no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—432no—
1203C22—861no—
1204C22—861no—
1205C22—861no—
1206C22—862no—
1207C22—861no—
1208C22—861no—
1209C22—3444no—
1210C22—3444no—
1211C22—1722no—
1212C22—1722no—
1213C22—1721no—
1214C22—1721no—
1215C22—1721no—
1216C22—1721no—
1217C22—1721no—
1218C22#104×D4312yescomplemented
1219C22C2×C22⋊C4×D4311yescharacteristic
1220C22#1458353111yescharacteristic
1221C22#1458354111yescharacteristic
1222C4—24no—
1223C4—21no—
1224C4—21no—
1225C4—42no—
1226C4—41no—
1227C4—41no—
1228C4—41no—
1229C4—432no—
1230C4—861no—
1231C4—861no—
1232C4—862no—
1233C4—861no—
1234C4—861no—
1235C4—861no—
1236C4—1722no—
1237C4—1722no—
1238C4—1721no—
1239C4C4×D4×D4311yescharacteristic
1240C4#1458337111yescharacteristic
1241C4#1458353311yescharacteristic
1242C4#1458353811yescharacteristic
1243C2—21no—
1244C2—21no—
1245C2—22no—
1246C2—41no—
1247C2—81no—
1248C2—862no—
1249C2—3441no—
1250C2—1721no—
1251C2—1722no—
1252C2#1913741311yescharacteristic
1253C2C2×#104×D4311yescharacteristic
1254C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1896C2
socleC22×C43C22×C22⋊C4
prime radical#19148078C2
cosocleC22×C4×C43C24
hypercenter#1896D43
hypocenterC43D4×#104
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. #19143327C2semidirect
3. C22×#13063253C2semidirect
4. C2×#104×D43C2semidirect
5. C42×C22⋊D43C2semidirect
6. #19135512C2semidirect
7. #19135421C2semidirect
8. #19135037C2semidirect
9. #19134898C2semidirect
10. #19134896C2semidirect
11. #19134614C2semidirect
12. #19134538C2semidirect
13. #19134537C2semidirect
14. #19134399C2semidirect
15. C43×#1896C2semidirect
18. C22×#10621877C22semidirect
19. C2×M16×D43C22semidirect
20. #14583567C4semidirect
21. #14583562C4semidirect
22. #14583559C4semidirect
23. #14583555C4semidirect
24. #14583551C4semidirect
26. #14583546C4semidirect
28. #14583540C4semidirect
30. #14583533C4semidirect
41. C2×C42×D43C22semidirect
46. #14582922C22semidirect
50. C2×#13063253C22semidirect
51. C2×#13063253C22semidirect
52. C2×#13063252C22semidirect
53. C2×#13063252C22semidirect
56. C2×#13063251C22semidirect
57. C2×#13063251C22semidirect
59. #14582862C22semidirect
60. M16×Dic43C22semidirect
62. C4×Dic43⋊C4C22semidirect
64. C4×(C2×D43)⋊C4C22semidirect
66. C4×C22⋊Dic43C22semidirect
67. C42×Dic43C22semidirect
68. #14582658C22semidirect
69. #14582658C22semidirect
71. C22×C42×C43C22semidirect
72. C2×#104×C43C22semidirect
73. C2×#104×C43C22semidirect
74. C43×#407C22semidirect
75. C43×#339C22semidirect
76. C43×#339C22semidirect
77. C2×#10621902C2×C4semidirect
85. C2×#10621898C2×C4semidirect
86. C2×#10621898C2×C4semidirect
90. C2×#10621900C2×C4semidirect
95. C22×Dic86C2×C4semidirect
96. C2×Q8×D43C2×C4semidirect
97. C22×D172C2×C4semidirect
102. C2×D4×D43C2×C4semidirect
118. #13063323C2×C4semidirect
120. #13063321C2×C4semidirect
121. #13063314C2×C4semidirect
122. #13063312C2×C4semidirect
130. #13063305C2×C4semidirect
131. #13063305C2×C4semidirect
137. #13063300C2×C4semidirect
138. #13063300C2×C4semidirect
153. #13063290C2×C4semidirect
154. #13063290C2×C4semidirect
159. #13063287C2×C4semidirect
160. #13063287C2×C4semidirect
200. #13063253D4semidirect
220. C22⋊Q8×C43C2×C4semidirect
221. C22⋊Q8×C43C2×C4semidirect
222. #121×C43C2×C4semidirect
223. #121×C43C2×C4semidirect
376. C42×C43C2×D4semidirect
425. #10621877C2×D4semidirect
504. C22⋊D43#104semidirect
532. D172C4×D4semidirect
557. Dic86C4×D4semidirect
575. C22×C43C2×#104semidirect
594. C2×D43C2×#104semidirect
615. Dic43C2×#104semidirect
624. #1896D43semidirect
670. C22×C42C2×D43semidirect
688. C2×#104C2×D43semidirect
689. C2×#104C2×D43semidirect
691. #407C2×D43semidirect
702. #339C2×D43semidirect
703. #339C2×D43semidirect
704. C43D4×#104semidirect
770. C22⋊Q8C4×D43semidirect
771. C22⋊Q8C4×D43semidirect
784. #121C4×D43semidirect
785. #121C4×D43semidirect
1058. C42D4×D43semidirect
1218. C22#104×D43semidirect

Maximal subgroups

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

subgroupindex
#191480782
#191433272
C22×#130632532
C2×#104×D432
C42×C22⋊D432
#191355122
#191354212
#191350372
#191348982
#191348962
#191346142
#191345382
#191345372
#191343992
C43×#18962
D4×#10443