Finite Group Databasebeta

← #25112281

Subgroups — #25112281

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#19148081C211yesmaximal, characteristic
2#19143330C211yesmaximal, characteristic, complemented
3C2×#14582914C211yesmaximal, characteristic, complemented
4C2×#104×D43C211yesmaximal, characteristic, complemented
5#19137039C211yesmaximal, characteristic, complemented
6#19135515C211yesmaximal, characteristic, complemented
7#19135040C211yesmaximal, characteristic, complemented
8#19135035C211yesmaximal, characteristic, complemented
9#19134894C211yesmaximal, characteristic, complemented
10#19134894C211yesmaximal, characteristic, complemented
11#19134612C211yesmaximal, characteristic, complemented
12#19134537C211yesmaximal, characteristic, complemented
13#19134537C211yesmaximal, characteristic, complemented
14#19134406C211yesmaximal, characteristic, complemented
15C43×#1963C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#41×D43C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic, complemented
19C2×M16×D43C2211yescharacteristic, complemented
20#14583569C411yescharacteristic, complemented
21#14583564C411yescharacteristic, complemented
22#14583557C411yescharacteristic, complemented
23#14583557C411yescharacteristic, complemented
24#14583552C411yescharacteristic, complemented
25#14583549—21no—
26#14583542C411yescharacteristic, complemented
27#14583542C411yescharacteristic, complemented
28#14583538—21no—
29#14583538—21no—
30#14583534C411yescharacteristic, complemented
31#14583533—21no—
32#14583446—21no—
33#14583408—21no—
34#14583408—21no—
35#14583406C2211yescharacteristic
36#14583406C2211yescharacteristic
37C4×#10621898C2211yescharacteristic
38C2×C4×D172C2211yescharacteristic
39C4×D4×D43—21no—
40C2×#13063282C2211yescharacteristic, complemented
41C2×C42×D43C2211yescharacteristic, complemented
42#14582976—21no—
43#14582969—21no—
44#14582969—21no—
45#14582964—21no—
46#14582914—24no—
47C2×#13063253C2211yescharacteristic
48C2×#13063253C2211yescharacteristic
49C2×#13063252C2211yescharacteristic, complemented
50C2×#13063252C2211yescharacteristic, complemented
51C2×#13063252C2211yescharacteristic, complemented
52C2×#13063252C2211yescharacteristic, complemented
53C2×#13063251C2211yescharacteristic
54C2×#13063251C2211yescharacteristic
55#104×D43—24no—
56#14582862C2211yescharacteristic, complemented
57#14582862C2211yescharacteristic, complemented
58C4×#10621877C2211yescharacteristic, complemented
59#14582791—21no—
60#14582784—21no—
61#14582777—21no—
62#14582773—21no—
63C4×C4⋊Dic43C2211yescharacteristic, complemented
64C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
65C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
66#14582660C2211yescharacteristic, complemented
67#14582660C2211yescharacteristic, complemented
68#14582659C2211yescharacteristic, complemented
69#14582659C2211yescharacteristic, complemented
70C43×#532C2211yescharacteristic
71C43×#423C2211yescharacteristic, complemented
72C2×#104×C43C2211yescharacteristic, complemented
73C2×#104×C43C2211yescharacteristic, complemented
74C2×#104×C43C2211yescharacteristic, complemented
75C2×#104×C43C2211yescharacteristic, complemented
76C43×#376C2211yescharacteristic, complemented
77C2×#10621902C2×C411yescharacteristic
78C2×#10621902C2×C411yescharacteristic, complemented
79C2×#10621898—21no—
80C2×#10621898—21no—
81C2×#10621898C2311yescharacteristic
82C2×#10621900—21no—
83C2×#10621900—21no—
84C2×#10621900C2×C411yescharacteristic
85C2×#10621900C2×C411yescharacteristic, complemented
86#41×D43—22no—
87#41×D43—22no—
88#41×D43—22no—
89#41×D43—22no—
90#41×D43—41no—
91#41×D43—41no—
92#41×D43—41no—
93#41×D43—41no—
94C2×Q8×D43C2×C411yescharacteristic
95C2×Q8×D43C2×C411yescharacteristic, complemented
96C22×D172D411yescharacteristic
97C2×D4×D43—21no—
98C2×D4×D43—21no—
99C2×D4×D43—21no—
100C2×D4×D43C2×C411yescharacteristic
101C2×D4×D43C2×C411yescharacteristic, complemented
102C22×C4×D43—21no—
103C22×C4×D43—21no—
104C22×C4×D43—21no—
105C22×C4×D43C2311yescharacteristic
106C22×C4×D43C2311yescharacteristic
107C2×#10621877C2311yescharacteristic
108C2×#10621877C2311yescharacteristic
109C2×#10621872—21no—
110C2×#10621872—21no—
111M16×D43—22no—
112M16×D43—22no—
113M16×D43—41no—
114M16×D43—41no—
115C2×C8×D43—21no—
116C2×C8×D43—21no—
117#13063324—21no—
118#13063321—21no—
119#13063311—21no—
120#13063311—21no—
121#13063310—21no—
122#13063310—21no—
123#13063307—21no—
124#13063307—21no—
125#13063306—21no—
126#13063306—21no—
127#13063303—21no—
128#13063303—21no—
129#13063302—21no—
130#13063302—21no—
131#13063301C2×C411yescharacteristic
132#13063301C2×C411yescharacteristic
133#13063301C2×C411yescharacteristic, complemented
134#13063301C2×C411yescharacteristic, complemented
135#13063300—21no—
136#13063298—21no—
137#13063298—21no—
138#13063298—21no—
139#13063298—21no—
140#13063297—21no—
141#13063297—21no—
142#13063296—21no—
143#13063296C2×C411yescharacteristic
144#13063296C2×C411yescharacteristic
145#13063296C2×C411yescharacteristic, complemented
146#13063296C2×C411yescharacteristic, complemented
147#13063295—21no—
148#13063295—21no—
149#13063293—21no—
150#13063293—21no—
151#13063293—21no—
152#13063293—21no—
153C4×Dic86C2×C411yescharacteristic, complemented
154C4×Dic86C2×C411yescharacteristic, complemented
155C4×D172C2×C411yescharacteristic
156C4×D172C2×C411yescharacteristic
157C4×D172C2×C411yescharacteristic
158C4×D172C2×C411yescharacteristic
159C4×D172C2×C411yescharacteristic, complemented
160C4×D172C2×C411yescharacteristic, complemented
161C4×D172D411yescharacteristic
162C4×D172D411yescharacteristic
163C4×D172D411yescharacteristic
164C4×D172D411yescharacteristic
165D4×Dic43—21no—
166#13063287—21no—
167C4×C22⋊D43—21no—
168C4×C22⋊D43—21no—
169C4×C22⋊D43—21no—
170C4×C22⋊D43—21no—
171C4×C22⋊D43—21no—
172C4×C22⋊D43—21no—
173(C22⋊D43)⋊C4—21no—
174(C22⋊D43)⋊C4—21no—
175#13063284C2311yescharacteristic
176#13063282—21no—
177#13063282—22no—
178#13063282—41no—
179C2×C4⋊Dic43—21no—
180C2×C4⋊Dic43D411yescharacteristic
181C2×Dic43⋊C4—21no—
182C4⋊C4×D43—21no—
183C2×(C2×D43)⋊C4—21no—
184C2×(C2×D43)⋊C4—21no—
185C2×(C2×D43)⋊C4—21no—
186C2×(C2×D43)⋊C4D411yescharacteristic
187C2×(C2×D43)⋊C4D411yescharacteristic
188C22⋊C4×D43—21no—
189C22⋊C4×D43—21no—
190C2×C4×Dic43—21no—
191C2×C4×Dic43C2311yescharacteristic
192C2×C4×Dic43C2311yescharacteristic
193C42×D43—21no—
194C42×D43—22no—
195C42×D43—41no—
196#13063253—22no—
197#13063253D414yescomplemented
198#13063252—22no—
199#13063252—22no—
200#13063252—41no—
201#13063252—41no—
202#13063251—22no—
203#13063251—22no—
204(C2×D43)⋊C8—21no—
205(C2×D43)⋊C8—21no—
206(C2×D43)⋊C8—21no—
207(C2×D43)⋊C8—21no—
208#13063236—21no—
209C4×C43⋊C8—21no—
210C43⋊#95—21no—
211C43⋊#95—21no—
212C43⋊#95—21no—
213C2×#41×C43C2311yescharacteristic
214C2×#41×C43C2311yescharacteristic
215C2×M16×C43C2311yescharacteristic
216C2×M16×C43C2311yescharacteristic
217C4⋊Q8×C43C2×C411yescharacteristic, complemented
218#127×C43C2×C411yescharacteristic, complemented
219#124×C43C2×C411yescharacteristic, complemented
220#124×C43C2×C411yescharacteristic, complemented
221#121×C43—21no—
222#121×C43—21no—
223C4×D4×C43—21no—
224C4×D4×C43—21no—
225C2×C42×C43C2311yescharacteristic
226C2×C42×C43C2311yescharacteristic
227C2×C42×C43C2311yescharacteristic
228C4⋊C8×C43—21no—
229C4⋊C8×C43—21no—
230#104×C43—22no—
231#104×C43—22no—
232#104×C43—41no—
233#104×C43—41no—
234#95×C43—21no—
235#95×C43—21no—
236C23×D43—21no—
237C23×D43—21no—
238C23×D43C2×D411yescharacteristic
239C23×D43C2×D411yescharacteristic
240#41×C43—21no—
241#41×C43—21no—
242#41×C43—21no—
243#41×C43—21no—
244#41×C43—21no—
245#41×C43—21no—
246#41×C43—21no—
247#41×C43—21no—
248C2×Q8×C43C22×C411yescharacteristic
249C2×Q8×C43C22×C411yescharacteristic
250C2×D4×C43—21no—
251C2×D4×C43—21no—
252C2×D4×C43—21no—
253C2×D4×C43—21no—
254C2×D4×C43C22×C411yescharacteristic
255C2×D4×C43C22×C411yescharacteristic
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43C2×D411yescharacteristic
261C22×C4×C43C2×D411yescharacteristic
262C22×C4×C43C2411yescharacteristic
263C2×C22⋊D43—21no—
264C2×C22⋊D43—21no—
265C2×C22⋊D43—21no—
266C2×C22⋊D43—21no—
267C2×C22⋊D43—21no—
268C2×C22⋊D43—21no—
269C2×C22⋊D43—21no—
270C2×C22⋊D43—21no—
271C2×C22⋊D43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43C2×D411yescharacteristic
277C22×Dic43C2×D411yescharacteristic
278#10621902—22no—
279#10621902—22no—
280#10621902—41no—
281#10621902—41no—
282Q8×D43—22no—
283Q8×D43—22no—
284Q8×D43—41no—
285Q8×D43—41no—
286#10621900—22no—
287#10621900—22no—
288#10621900—41no—
289#10621900—41no—
290#10621900—42no—
291#10621900—42no—
292#10621900—42no—
293#10621900—42no—
294D4×D43—22no—
295D4×D43—22no—
296D4×D43—42no—
297D4×D43—42no—
298D4×D43—42no—
299D4×D43—42no—
300D4×D43—41no—
301D4×D43—41no—
302D4×D43—44no—
303#10621898—21no—
304#10621898—21no—
305#10621898—42no—
306#10621898—42no—
307#10621898—42no—
308#10621898—42no—
309#10621898C2×D412yes—
310#10621898#4112yes—
311C2×D172—21no—
312C2×D172—21no—
313C2×D172—42no—
314C2×D172C22⋊C411yescharacteristic
315C2×D172C22⋊C411yescharacteristic
316C2×D172C22⋊C411yescharacteristic
317C2×D172C22⋊C411yescharacteristic
318C2×D172C22×C411yescharacteristic
319C2×C4×D43—21no—
320C2×C4×D43—21no—
321C2×C4×D43—21no—
322C2×C4×D43—21no—
323C2×C4×D43—21no—
324C2×C4×D43—21no—
325C2×C4×D43—21no—
326C2×C4×D43—21no—
327C2×C4×D43—21no—
328C2×C4×D43—21no—
329C2×C4×D43—21no—
330C2×C4×D43—21no—
331C2×C4×D43—21no—
332C2×C4×D43—21no—
333C2×C4×D43—21no—
334C2×C4×D43—42no—
335C2×C4×D43—42no—
336C2×C4×D43—42no—
337C2×C4×D43—42no—
338C2×C4×D43—42no—
339C2×C4×D43—42no—
340C2×C4×D43—42no—
341C2×C4×D43C22×C411yescharacteristic
342C2×C4×D43C22×C411yescharacteristic
343C2×C4×D43C22×C411yescharacteristic
344C2×C4×D43C22×C411yescharacteristic
345C2×C4×D43C2×D411yescharacteristic
346C2×C4×D43C2×D411yescharacteristic
347C2×C4×D43C2×D411yescharacteristic
348C2×C4×D43C2×D411yescharacteristic
349C2×Dic86—21no—
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—
358C4⋊C4×C43—21no—
359C4⋊C4×C43—21no—
360C22⋊C4×C43—21no—
361C22⋊C4×C43—21no—
362C22⋊C4×C43—21no—
363C22⋊C4×C43—21no—
364C42×C43—21no—
365C42×C43—21no—
366C42×C43—21no—
367C42×C43C22×C411yescharacteristic
368C42×C43C22×C411yescharacteristic
369C42×C43C2×D411yescharacteristic
370C42×C43C2×D411yescharacteristic
371C42×C43C2×D412yescomplemented
372C22⋊Dic43—21no—
373C22⋊Dic43—21no—
374C22⋊Dic43—21no—
375C22⋊Dic43—21no—
376C22⋊Dic43—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—21no—
383(C2×D43)⋊C4—42no—
384(C2×D43)⋊C4—42no—
385(C2×D43)⋊C4—42no—
386(C2×D43)⋊C4C22⋊C411yescharacteristic
387(C2×D43)⋊C4C22⋊C411yescharacteristic
388(C2×D43)⋊C4C22⋊C411yescharacteristic
389(C2×D43)⋊C4C22⋊C411yescharacteristic
390(C2×D43)⋊C4C22⋊C411yescharacteristic
391(C2×D43)⋊C4C22⋊C411yescharacteristic
392(C2×D43)⋊C4C22⋊C411yescharacteristic
393(C2×D43)⋊C4C22⋊C411yescharacteristic
394C4⋊Dic43—42no—
395C4⋊Dic43C22⋊C411yescharacteristic
396C4⋊Dic43C22⋊C411yescharacteristic
397C4⋊Dic43C22⋊C411yescharacteristic
398C4⋊Dic43C22⋊C411yescharacteristic
399C4⋊Dic43C22×C411yescharacteristic
400C4⋊Dic43C22×C411yescharacteristic
401Dic43⋊C4—21no—
402Dic43⋊C4—21no—
403Dic43⋊C4—21no—
404Dic43⋊C4—21no—
405Dic43⋊C4—21no—
406Dic43⋊C4—21no—
407Dic43⋊C4—42no—
408C4×Dic43—21no—
409C4×Dic43—21no—
410C4×Dic43—21no—
411C4×Dic43—21no—
412C4×Dic43—21no—
413C4×Dic43—21no—
414C4×Dic43—21no—
415C4×Dic43—42no—
416#10621877—21no—
417#10621877—21no—
418#10621877—21no—
419#10621877C2×D412yescomplemented
420C2×C43⋊C8—21no—
421C2×C43⋊C8—21no—
422#10621872—42no—
423#10621872—42no—
424C8×D43—42no—
425C8×D43—42no—
426C23×C43—21no—
427C23×C43—21no—
428C23×C43C22×D411yescharacteristic
429C22×D43—21no—
430C22×D43—21no—
431C22×D43—21no—
432C22×D43—21no—
433C22×D43—21no—
434C22×D43—22no—
435C22×D43—41no—
436C22×D43—41no—
437C22×D43—41no—
438C22×D43—42no—
439C22×D43—42no—
440C22×D43—42no—
441C22×D43—42no—
442C22×D43—81no—
443C22×D43—81no—
444C22×D43C2×C22⋊C411yescharacteristic
445C22×D43C2×C22⋊C411yescharacteristic
446C22×D43C2×C22⋊C411yescharacteristic
447C22×D43C2×C22⋊C411yescharacteristic
448Q8×C43—21no—
449Q8×C43—21no—
450Q8×C43—21no—
451Q8×C43—21no—
452D4×C43—21no—
453D4×C43—21no—
454D4×C43—21no—
455D4×C43—21no—
456D4×C43—42no—
457D4×C43—41no—
458D4×C43—41no—
459D4×C43—41no—
460D4×C43—41no—
461D4×C43—81no—
462C2×C4×C43—21no—
463C2×C4×C43—21no—
464C2×C4×C43—22no—
465C2×C4×C43—41no—
466C2×C4×C43—41no—
467C2×C4×C43—41no—
468C2×C4×C43—41no—
469C2×C4×C43—41no—
470C2×C4×C43—41no—
471C2×C4×C43—41no—
472C2×C4×C43—41no—
473C2×C4×C43—41no—
474C2×C4×C43—41no—
475C2×C4×C43—41no—
476C2×C4×C43C2×C22⋊C411yescharacteristic
477C2×C4×C43C2×C22⋊C411yescharacteristic
478C2×C4×C43C2×C22⋊C411yescharacteristic
479C2×C4×C43C2×C22⋊C411yescharacteristic
480C2×C4×C43C23×C411yescharacteristic
481C2×C4×C43C22×D411yescharacteristic
482C2×C4×C43C22×D411yescharacteristic
483C2×C4×C43C2×#4111yescharacteristic
484C2×C4×C43H(5,𝔽2)11yescharacteristic
485C2×C4×C43H(5,𝔽2)11yescharacteristic
486C22⋊D43—22no—
487C22⋊D43—22no—
488C22⋊D43—42no—
489C22⋊D43—42no—
490C22⋊D43—42no—
491C22⋊D43—42no—
492C22⋊D43—42no—
493C22⋊D43—42no—
494C22⋊D43—81no—
495C22⋊D43—81no—
496C2×Dic43—21no—
497C2×Dic43—21no—
498C2×Dic43—21no—
499C2×Dic43—21no—
500C2×Dic43—21no—
501C2×Dic43—22no—
502C2×Dic43—21no—
503C2×Dic43—21no—
504C2×Dic43—42no—
505C2×Dic43—42no—
506C2×Dic43—41no—
507C2×Dic43—41no—
508C2×Dic43—41no—
509C2×Dic43—41no—
510C2×Dic43—41no—
511C2×Dic43C2×C22⋊C411yescharacteristic
512C2×Dic43C2×C22⋊C411yescharacteristic
513C2×Dic43C2×C22⋊C411yescharacteristic
514C2×Dic43C2×C22⋊C411yescharacteristic
515D172—22no—
516D172—22no—
517D172—21no—
518D172—41no—
519D172—41no—
520D172—42no—
521D172—42no—
522D172C4×D412yes—
523C4×D43—21no—
524C4×D43—21no—
525C4×D43—21no—
526C4×D43—21no—
527C4×D43—21no—
528C4×D43—21no—
529C4×D43—21no—
530C4×D43—21no—
531C4×D43—21no—
532C4×D43—21no—
533C4×D43—21no—
534C4×D43—21no—
535C4×D43—22no—
536C4×D43—21no—
537C4×D43—21no—
538C4×D43—21no—
539C4×D43—21no—
540C4×D43—22no—
541C4×D43—42no—
542C4×D43—42no—
543C4×D43—42no—
544C4×D43—42no—
545C4×D43—42no—
546C4×D43—48no—
547C4×D43—81no—
548Dic86—21no—
549Dic86—42no—
550Dic86—42no—
551Dic86C4×D412yes—
552C8×C43—41no—
553C8×C43—41no—
554C43⋊C8—22no—
555C43⋊C8—41no—
556#22434—431nomaximal, Sylow
557C22×C43—21no—
558C22×C43—21no—
559C22×C43—41no—
560C22×C43—41no—
561C22×C43—41no—
562C22×C43—41no—
563C22×C43—41no—
564C22×C43—41no—
565C22×C43C22×C22⋊C411yescharacteristic
566C22×C43D4211yescharacteristic
567C22×C43#54611yescharacteristic
568C2×D43—21no—
569C2×D43—21no—
570C2×D43—21no—
571C2×D43—21no—
572C2×D43—21no—
573C2×D43—22no—
574C2×D43—21no—
575C2×D43—21no—
576C2×D43—21no—
577C2×D43—21no—
578C2×D43—21no—
579C2×D43—21no—
580C2×D43—42no—
581C2×D43—42no—
582C2×D43—41no—
583C2×D43—41no—
584C2×D43—84no—
585C2×D43—81no—
586C2×D43—81no—
587C2×D43—84no—
588C2×D43#42112yescomplemented
589C4×C43—21no—
590C4×C43—21no—
591C4×C43—21no—
592C4×C43—21no—
593C4×C43—42no—
594C4×C43—41no—
595C4×C43—41no—
596C4×C43—81no—
597C4×C43C2×C4×D411yescharacteristic
598C4×C43#51811yescharacteristic
599C4×C43D4211yescharacteristic
600C4×C43#54611yescharacteristic
601Dic43—22no—
602Dic43—21no—
603Dic43—21no—
604Dic43—21no—
605Dic43—21no—
606Dic43—42no—
607Dic43—41no—
608Dic43—41no—
609Dic43—81no—
610D4×#41—431no—
611D4×M16—431no—
612C2×#421—431no—
613C22×#104—431no—
614#2290—431no—
615#1980—431no—
616#1963D4311yescharacteristic, complemented
617#1897—431no—
618#1896—431no—
619#1871—431no—
620#1871—431no—
621#1806—431no—
622#1789—431no—
623#1789—431no—
624#1759—431no—
625C2×C43—21no—
626C2×C43—21no—
627C2×C43—81no—
628C2×C43—81no—
629C2×C43D4×C22⋊C411yescharacteristic
630C2×C43C2×#42111yescharacteristic
631C2×C43#290111yescharacteristic
632D43—22no—
633D43—41no—
634D43—41no—
635D43—41no—
636D43—42no—
637C22×#41—431no—
638C22×#41—431no—
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—861no—
654#532C2×D4311yescharacteristic
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#423C2×D4311yescharacteristic, complemented
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, complemented
680C2×#104C2×D4311yescharacteristic, complemented
681C2×#104C2×D4311yescharacteristic, complemented
682C2×#104C2×D4311yescharacteristic, complemented
683#407—431no—
684#407—431no—
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⋊C4—431no—
693#376C2×D4311yescharacteristic, complemented
694#339—431no—
695#339—431no—
696#339—431no—
697#339—431no—
698C43#2243411yescharacteristic, complemented, Sylow
699C2×#41—431no—
700C2×#41—431no—
701C2×#41—431no—
702C2×#41—431no—
703C2×#41—431no—
704C2×#41—861no—
705C2×#41—861no—
706C2×#41—861no—
707C2×#41—861no—
708C2×#41—862no—
709C2×#41—862no—
710C2×#41—862no—
711C2×#41—862no—
712C2×#41—1721no—
713C2×#41—1721no—
714C2×#41—1721no—
715C2×#41—1721no—
716C2×#41C22×D4311yescharacteristic
717C2×#41C22×D4311yescharacteristic
718C22×Q8—431no—
719C22×Q8—431no—
720C22×D4—431no—
721C22×D4—431no—
722C22×D4—431no—
723C22×D4—861no—
724C22×D4—861no—
725C22×D4—861no—
726C23×C4—431no—
727C23×C4—431no—
728C23×C4—861no—
729C23×C4—861no—
730C23×C4—861no—
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—861no—
744C4⋊Q8C4×D4311yescharacteristic, complemented
745#127—861no—
746#127C4×D4311yescharacteristic, complemented
747#124—861no—
748#124—861no—
749#124C4×D4311yescharacteristic, complemented
750#124C4×D4311yescharacteristic, complemented
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—21no—
766#121—21no—
767#121—431no—
768#121—431no—
769#121—431no—
770#121—431no—
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—21no—
788C4×D4—21no—
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—431no—
798C4×D4—431no—
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—861no—
811#117—862no—
812#117—1721no—
813C2×C4⋊C4—431no—
814C2×C4⋊C4—861no—
815C2×C4⋊C4—861no—
816C2×C4⋊C4—861no—
817C2×C22⋊C4—431no—
818C2×C22⋊C4—431no—
819C2×C22⋊C4—861no—
820C2×C22⋊C4—861no—
821C2×C22⋊C4—861no—
822C2×C22⋊C4—861no—
823C2×C22⋊C4—861no—
824C2×C42—431no—
825C2×C42—431no—
826C2×C42—861no—
827C2×C42—862no—
828C2×C42—861no—
829C2×C42—1721no—
830C2×C42C22×D4311yescharacteristic
831C2×C42C22×D4311yescharacteristic
832C2×C42C22×D4311yescharacteristic
833C4⋊C8—21no—
834C4⋊C8—21no—
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—861no—
848C22⋊C8—861no—
849C22⋊C8—861no—
850C22⋊C8—861no—
851#97—861no—
852C4×C8—861no—
853#95—21no—
854#95—21no—
855#95—861no—
856#95—861no—
857#95—861no—
858C24—431no—
859C24—431no—
860C24—861no—
861C24—861no—
862#41—21no—
863#41—21no—
864#41—21no—
865#41—21no—
866#41—21no—
867#41—21no—
868#41—21no—
869#41—21no—
870#41—432no—
871#41—432no—
872#41—861no—
873#41—861no—
874#41—862no—
875#41—862no—
876#41—862no—
877#41—862no—
878#41—1722no—
879#41—1722no—
880#41—1722no—
881#41—1722no—
882#41—1721no—
883#41—1721no—
884#41—1722no—
885#41—1722no—
886#41—1722no—
887#41—1722no—
888#41—1721no—
889#41—1721no—
890C2×Q8—431no—
891C2×Q8—861no—
892C2×Q8—861no—
893C2×Q8—862no—
894C2×Q8—862no—
895C2×Q8—1721no—
896C2×Q8—1721no—
897C2×Q8C2×C4×D4311yescharacteristic
898C2×Q8C2×C4×D4311yescharacteristic
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—431no—
904C2×D4—431no—
905C2×D4—431no—
906C2×D4—431no—
907C2×D4—431no—
908C2×D4—861no—
909C2×D4—861no—
910C2×D4—861no—
911C2×D4—861no—
912C2×D4—862no—
913C2×D4—862no—
914C2×D4—861no—
915C2×D4—861no—
916C2×D4—861no—
917C2×D4—861no—
918C2×D4—861no—
919C2×D4—861no—
920C2×D4—861no—
921C2×D4—1722no—
922C2×D4—1721no—
923C2×D4—1721no—
924C2×D4—1722no—
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—431no—
936C22×C4—431no—
937C22×C4—431no—
938C22×C4—431no—
939C22×C4—431no—
940C22×C4—431no—
941C22×C4—431no—
942C22×C4—431no—
943C22×C4—431no—
944C22×C4—431no—
945C22×C4—861no—
946C22×C4—861no—
947C22×C4—861no—
948C22×C4—861no—
949C22×C4—861no—
950C22×C4—861no—
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—861no—
964C22×C4—1722no—
965C22×C4—1722no—
966C22×C4—1722no—
967C22×C4—1722no—
968C22×C4—1722no—
969C22×C4—1722no—
970C22×C4—1722no—
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—21no—
991C4⋊C4—21no—
992C4⋊C4—431no—
993C4⋊C4—431no—
994C4⋊C4—431no—
995C4⋊C4—431no—
996C4⋊C4—431no—
997C4⋊C4—431no—
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—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—431no—
1011C22⋊C4—431no—
1012C22⋊C4—431no—
1013C22⋊C4—431no—
1014C22⋊C4—431no—
1015C22⋊C4—431no—
1016C22⋊C4—431no—
1017C22⋊C4—431no—
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—1722no—
1030C22⋊C4—1722no—
1031C22⋊C4—1722no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—861no—
1036C42—861no—
1037C42—861no—
1038C42—861no—
1039C42—861no—
1040C42—861no—
1041C42—861no—
1042C42—1722no—
1043C42C2×C4×D4311yescharacteristic
1044C42C2×C4×D4311yescharacteristic
1045C42D4×D4311yescharacteristic
1046C42D4×D4311yescharacteristic
1047C42D4×D4312yescomplemented
1048C23—21no—
1049C23—21no—
1050C23—431no—
1051C23—431no—
1052C23—431no—
1053C23—431no—
1054C23—862no—
1055C23—861no—
1056C23—861no—
1057C23—861no—
1058C23—861no—
1059C23—861no—
1060C23—3441no—
1061C23—3441no—
1062C23—1721no—
1063C23—1721no—
1064C23—1721no—
1065C23—1722no—
1066C23—1722no—
1067C23—1722no—
1068C23—1722no—
1069C23C2×D4×D4311yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—21no—
1073Q8—21no—
1074Q8—432no—
1075Q8—861no—
1076Q8—1722no—
1077Q8—1722no—
1078D4—21no—
1079D4—21no—
1080D4—21no—
1081D4—21no—
1082D4—42no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—81no—
1088D4—432no—
1089D4—862no—
1090D4—862no—
1091D4—862no—
1092D4—862no—
1093D4—861no—
1094D4—3441no—
1095D4—3441no—
1096D4—1721no—
1097D4—1721no—
1098D4—1722no—
1099D4—1722no—
1100D4—1722no—
1101D4—1722no—
1102D4—1722no—
1103D4—1722no—
1104D4—1722no—
1105D4—1722no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—431no—
1121C2×C4—431no—
1122C2×C4—431no—
1123C2×C4—431no—
1124C2×C4—861no—
1125C2×C4—861no—
1126C2×C4—861no—
1127C2×C4—861no—
1128C2×C4—861no—
1129C2×C4—861no—
1130C2×C4—861no—
1131C2×C4—861no—
1132C2×C4—861no—
1133C2×C4—861no—
1134C2×C4—861no—
1135C2×C4—861no—
1136C2×C4—861no—
1137C2×C4—861no—
1138C2×C4—861no—
1139C2×C4—861no—
1140C2×C4—861no—
1141C2×C4—862no—
1142C2×C4—861no—
1143C2×C4—861no—
1144C2×C4—861no—
1145C2×C4—861no—
1146C2×C4—862no—
1147C2×C4—862no—
1148C2×C4—861no—
1149C2×C4—861no—
1150C2×C4—3441no—
1151C2×C4—1722no—
1152C2×C4—1722no—
1153C2×C4—1722no—
1154C2×C4—1722no—
1155C2×C4—1722no—
1156C2×C4—1728no—
1157C2×C4—1722no—
1158C2×C4—1722no—
1159C2×C4—1721no—
1160C2×C4—1721no—
1161C2×C4—1721no—
1162C2×C4—1721no—
1163C2×C4—1721no—
1164C2×C4C22⋊C4×D4311yescharacteristic
1165C2×C4C22⋊C4×D4311yescharacteristic
1166C2×C4C22⋊C4×D4311yescharacteristic
1167C2×C4C22⋊C4×D4311yescharacteristic
1168C2×C4C22×C4×D4311yescharacteristic
1169C2×C4C2×D4×D4311yescharacteristic
1170C2×C4C2×D4×D4311yescharacteristic
1171C2×C4#41×D4311yescharacteristic
1172C2×C4#1306337011yescharacteristic
1173C2×C4#1306337111yescharacteristic
1174C8—41no—
1175C8—41no—
1176C8—862no—
1177C8—1721no—
1178C22—21no—
1179C22—21no—
1180C22—41no—
1181C22—41no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—432no—
1187C22—861no—
1188C22—861no—
1189C22—861no—
1190C22—861no—
1191C22—861no—
1192C22—862no—
1193C22—861no—
1194C22—861no—
1195C22—861no—
1196C22—861no—
1197C22—861no—
1198C22—861no—
1199C22—3441no—
1200C22—3441no—
1201C22—3444no—
1202C22—3444no—
1203C22—1722no—
1204C22—1722no—
1205C22—1721no—
1206C22—1721no—
1207C22C2×C22⋊C4×D4311yescharacteristic
1208C22#1458353311yescharacteristic
1209C22#1458354611yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—42no—
1215C4—41no—
1216C4—41no—
1217C4—81no—
1218C4—861no—
1219C4—861no—
1220C4—861no—
1221C4—861no—
1222C4—862no—
1223C4—3441no—
1224C4—1722no—
1225C4—1721no—
1226C4—1721no—
1227C4C4×D4×D4311yescharacteristic
1228C4#1458337111yescharacteristic
1229C4#1458353411yescharacteristic
1230C4#1458354211yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—81no—
1234C2—81no—
1235C2—862no—
1236C2—1721no—
1237C2—1721no—
1238C2—1721no—
1239C2—1722no—
1240C2#1913741611yescharacteristic
1241C2#421×D4311yescharacteristic
1242C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1963C2
socleC22×C43C22×C22⋊C4
prime radical#19148081C2
cosocleC22×C4×C43C24
hypercenter#1963D43
hypocenterC43#22434
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
2. #19143330C2semidirect
3. C2×#14582914C2semidirect
4. C2×#104×D43C2semidirect
5. #19137039C2semidirect
6. #19135515C2semidirect
7. #19135040C2semidirect
8. #19135035C2semidirect
9. #19134894C2semidirect
10. #19134894C2semidirect
11. #19134612C2semidirect
12. #19134537C2semidirect
13. #19134537C2semidirect
14. #19134406C2semidirect
15. C43×#1963C2semidirect
18. C2×M16×D43C22semidirect
19. C2×M16×D43C22semidirect
20. #14583569C4semidirect
21. #14583564C4semidirect
22. #14583557C4semidirect
23. #14583557C4semidirect
24. #14583552C4semidirect
26. #14583542C4semidirect
27. #14583542C4semidirect
30. #14583534C4semidirect
40. C2×#13063282C22semidirect
41. C2×C42×D43C22semidirect
49. C2×#13063252C22semidirect
50. C2×#13063252C22semidirect
51. C2×#13063252C22semidirect
52. C2×#13063252C22semidirect
56. #14582862C22semidirect
57. #14582862C22semidirect
58. C4×#10621877C22semidirect
63. C4×C4⋊Dic43C22semidirect
64. C4×(C2×D43)⋊C4C22semidirect
65. C4×(C2×D43)⋊C4C22semidirect
66. #14582660C22semidirect
67. #14582660C22semidirect
68. #14582659C22semidirect
69. #14582659C22semidirect
71. C43×#423C22semidirect
72. C2×#104×C43C22semidirect
73. C2×#104×C43C22semidirect
74. C2×#104×C43C22semidirect
75. C2×#104×C43C22semidirect
76. C43×#376C22semidirect
78. C2×#10621902C2×C4semidirect
85. C2×#10621900C2×C4semidirect
95. C2×Q8×D43C2×C4semidirect
101. C2×D4×D43C2×C4semidirect
133. #13063301C2×C4semidirect
134. #13063301C2×C4semidirect
145. #13063296C2×C4semidirect
146. #13063296C2×C4semidirect
153. C4×Dic86C2×C4semidirect
154. C4×Dic86C2×C4semidirect
159. C4×D172C2×C4semidirect
160. C4×D172C2×C4semidirect
197. #13063253D4semidirect
217. C4⋊Q8×C43C2×C4semidirect
218. #127×C43C2×C4semidirect
219. #124×C43C2×C4semidirect
220. #124×C43C2×C4semidirect
371. C42×C43C2×D4semidirect
419. #10621877C2×D4semidirect
588. C2×D43#421semidirect
616. #1963D43semidirect
668. #423C2×D43semidirect
679. C2×#104C2×D43semidirect
680. C2×#104C2×D43semidirect
681. C2×#104C2×D43semidirect
682. C2×#104C2×D43semidirect
693. #376C2×D43semidirect
698. C43#22434semidirect
744. C4⋊Q8C4×D43semidirect
746. #127C4×D43semidirect
749. #124C4×D43semidirect
750. #124C4×D43semidirect
1047. C42D4×D43semidirect

Maximal subgroups

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

subgroupindex
#191480812
#191433302
C2×#145829142
C2×#104×D432
#191370392
#191355152
#191350402
#191350352
#191348942
#191346122
#191345372
#191344062
C43×#19632
#2243443