Finite Group Databasebeta

← #25112276

Subgroups — #25112276

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
1D4×#10621898C211yesmaximal, characteristic
2C2×#14582915C211yesmaximal, characteristic, complemented
3C22×#13063251C211yesmaximal, characteristic, complemented
4#19137040C211yesmaximal, characteristic, complemented
5#19135514C211yesmaximal, characteristic, complemented
6#19135426C211yesmaximal, characteristic, complemented
7#19135041C211yesmaximal, characteristic, complemented
8#19135036C211yesmaximal, characteristic, complemented
9#19134897C211yesmaximal, characteristic, complemented
10#19134897C211yesmaximal, characteristic, complemented
11#19134612C211yesmaximal, characteristic, complemented
12#19134538C211yesmaximal, characteristic, complemented
13#19134538C211yesmaximal, characteristic, complemented
14#19134408C211yesmaximal, characteristic, complemented
15D4×M16×C43C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621898C2211yescharacteristic
18#14583570C411yescharacteristic, complemented
19D4×Dic86C411yescharacteristic, complemented
20#14583558C411yescharacteristic, complemented
21#14583558C411yescharacteristic, complemented
22#14583554C411yescharacteristic, complemented
23#14583550—21no—
24#14583545C411yescharacteristic, complemented
25#14583545C411yescharacteristic, complemented
26#14583539—21no—
27#14583539—21no—
28D4×D172C411yescharacteristic, complemented
29D4×C22⋊D43—21no—
30#14583449C2211yescharacteristic
31#14583446—21no—
32#14583410C2211yescharacteristic
33#14583410C2211yescharacteristic
34#14583408—21no—
35#14583408—21no—
36C4×#10621898C2211yescharacteristic
37C4×D4×D43—21no—
38C2×#13063284C2211yescharacteristic, complemented
39C22×C4×Dic43C2211yescharacteristic, complemented
40#14582915—24no—
41C2×#13063251—24no—
42C2×#13063251C2211yescharacteristic
43C2×#13063251C2211yescharacteristic
44C2×#13063251C2211yescharacteristic
45C2×#13063251C2211yescharacteristic
46C2×#13063251C2211yescharacteristic, complemented
47C2×#13063251C2211yescharacteristic, complemented
48C2×#13063251C2211yescharacteristic, complemented
49C2×#13063251C2211yescharacteristic, complemented
50C2×#13063251C2211yescharacteristic, complemented
51C2×#13063251C2211yescharacteristic, complemented
52C2×#13063251C2211yescharacteristic, complemented
53C2×#13063251C2211yescharacteristic, complemented
54#14582792—21no—
55#14582785—21no—
56#14582779—21no—
57#14582774—21no—
58C4×C4⋊Dic43C2211yescharacteristic, complemented
59C4×C22⋊Dic43C2211yescharacteristic, complemented
60C4×C22⋊Dic43C2211yescharacteristic, complemented
61#14582745C2211yescharacteristic, complemented
62#14582660C2211yescharacteristic, complemented
63#14582660C2211yescharacteristic, complemented
64#14582660C2211yescharacteristic, complemented
65#14582660C2211yescharacteristic, complemented
66C22×M16×C43C2211yescharacteristic, complemented
67C22×M16×C43C2211yescharacteristic, complemented
68C2×C4×D4×C43C2211yescharacteristic
69C43×#436—21no—
70C43×#435—21no—
71C43×#435—21no—
72C8×D4×C43—21no—
73C43×#423C2211yescharacteristic, complemented
74C43×#407C2211yescharacteristic, complemented
75C43×#407C2211yescharacteristic, complemented
76C4×M16×C43C2211yescharacteristic, complemented
77C2×#10621898—21no—
78C2×#10621898—21no—
79C2×#10621898—21no—
80C2×#10621898—21no—
81C2×#10621898—22no—
82C2×#10621898—22no—
83C2×#10621898—22no—
84C2×#10621898—22no—
85C2×#10621898—41no—
86C2×#10621898—41no—
87C2×#10621898—41no—
88C2×#10621898—41no—
89C2×#10621898C2×C411yescharacteristic
90C2×#10621898C2×C411yescharacteristic
91C2×#10621898C2×C411yescharacteristic, complemented
92C2×#10621898C2×C411yescharacteristic, complemented
93C2×#10621898C2311yescharacteristic
94C2×#10621898C2311yescharacteristic
95C2×#10621898C2311yescharacteristic
96C22×Dic86C2×C411yescharacteristic
97C22×Dic86C2×C411yescharacteristic, complemented
98C22×D172C2×C411yescharacteristic
99C22×D172C2×C411yescharacteristic, complemented
100C22×C22⋊D43—21no—
101C22×C22⋊D43—21no—
102C2×D4×D43—21no—
103C23×Dic43—21no—
104C22×C4×D43—21no—
105C22×C4×D43—21no—
106#13063325C2×C411yescharacteristic, complemented
107#13063324—21no—
108#13063322C2×C411yescharacteristic, complemented
109#13063321—21no—
110#13063313C2×C411yescharacteristic, complemented
111#13063313C2×C411yescharacteristic, complemented
112#13063311—21no—
113#13063311—21no—
114#13063310—21no—
115#13063310—21no—
116#13063308—21no—
117#13063308—21no—
118#13063307—21no—
119#13063307—21no—
120#13063304C2×C411yescharacteristic
121#13063304C2×C411yescharacteristic
122#13063304C2×C411yescharacteristic, complemented
123#13063304C2×C411yescharacteristic, complemented
124#13063303—21no—
125#13063303—21no—
126#13063302—21no—
127#13063302—21no—
128#13063300—21no—
129#13063299—21no—
130#13063299—21no—
131#13063299C2×C411yescharacteristic
132#13063299C2×C411yescharacteristic
133#13063299C2×C411yescharacteristic, complemented
134#13063299C2×C411yescharacteristic, complemented
135#13063298—21no—
136#13063298—21no—
137#13063298—21no—
138#13063298—21no—
139#13063297—21no—
140#13063297—21no—
141#13063296—21no—
142#13063295—21no—
143#13063295—21no—
144#13063294—21no—
145#13063294—21no—
146#13063293—21no—
147#13063293—21no—
148C4×Dic86C2×C411yescharacteristic, complemented
149C4×Dic86C2×C411yescharacteristic, complemented
150C4×D172—21no—
151C4×D172—21no—
152C4×D172C2×C411yescharacteristic, complemented
153C4×D172C2×C411yescharacteristic, complemented
154D4×Dic43—21no—
155#13063287—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—
162(C22⋊D43)⋊C4—21no—
163(C22⋊D43)⋊C4—21no—
164#13063284—22no—
165#13063284—41no—
166#13063284C2311yescharacteristic
167#13063282—21no—
168C2×C4⋊Dic43—21no—
169C2×C4⋊Dic43—21no—
170C4⋊C4×D43—21no—
171C2×C22⋊Dic43—21no—
172C2×C22⋊Dic43—21no—
173C2×C22⋊Dic43—21no—
174C22⋊C4×D43—21no—
175C22⋊C4×D43—21no—
176C2×C4×Dic43—22no—
177C2×C4×Dic43—21no—
178C2×C4×Dic43—41no—
179C2×C4×Dic43C2311yescharacteristic
180C2×C4×Dic43C2311yescharacteristic
181C2×C4×Dic43C2311yescharacteristic
182C2×C4×Dic43C2311yescharacteristic
183C42×D43—21no—
184#13063251—22no—
185#13063251—22no—
186#13063251—22no—
187#13063251—22no—
188#13063251—22no—
189#13063251—22no—
190#13063251—22no—
191#13063251—41no—
192#13063251—41no—
193#13063251—41no—
194#13063251—41no—
195#13063251D414yescomplemented
196C43⋊#95—21no—
197C43⋊#95—21no—
198C43⋊#95—21no—
199C43⋊#95—21no—
200C43⋊#95—21no—
201C22×D4×C43D411yescharacteristic
202C23×C4×C43C2311yescharacteristic
203C23×C4×C43C2311yescharacteristic
204C2×M16×C43—21no—
205C2×M16×C43—21no—
206C2×M16×C43—22no—
207C2×M16×C43—22no—
208C2×M16×C43—41no—
209C2×M16×C43—41no—
210C2×M16×C43C2311yescharacteristic
211C2×M16×C43C2311yescharacteristic
212C2×M16×C43C2311yescharacteristic
213C2×M16×C43C2311yescharacteristic
214C22×C8×C43—21no—
215C22×C8×C43—21no—
216C4×D4×C43C2×C411yescharacteristic
217C4×D4×C43C2×C411yescharacteristic
218C4×D4×C43C2×C411yescharacteristic
219C4×D4×C43C2×C411yescharacteristic
220C4×D4×C43D411yescharacteristic
221C4×D4×C43D411yescharacteristic
222C4×D4×C43D411yescharacteristic
223C4×D4×C43D411yescharacteristic
224C2×C4⋊C4×C43D411yescharacteristic
225C2×C22⋊C4×C43D411yescharacteristic
226C2×C22⋊C4×C43D411yescharacteristic
227C2×C42×C43C2311yescharacteristic
228C4⋊C8×C43—21no—
229C4⋊C8×C43—21no—
230C22⋊C8×C43—21no—
231C22⋊C8×C43—21no—
232C22⋊C8×C43—21no—
233C22⋊C8×C43—21no—
234#97×C43—21no—
235C4×C8×C43—21no—
236C24×C43C2×D411yescharacteristic
237C24×C43C2×D411yescharacteristic
238C23×D43—21no—
239C23×D43—21no—
240C2×D4×C43—42no—
241C2×D4×C43C22⋊C411yescharacteristic
242C2×D4×C43C22⋊C411yescharacteristic
243C2×D4×C43C22⋊C411yescharacteristic
244C2×D4×C43C22⋊C411yescharacteristic
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43C22×C411yescharacteristic
254C22×C4×C43C22×C411yescharacteristic
255C22×C4×C43C22×C411yescharacteristic
256C22×C4×C43C22×C411yescharacteristic
257C22×C4×C43C2×D411yescharacteristic
258C22×C4×C43C2×D411yescharacteristic
259C22×C4×C43C2×D411yescharacteristic
260C22×C4×C43C2×D411yescharacteristic
261C22×C4×C43C2×D411yescharacteristic
262C22×C4×C43C2×D411yescharacteristic
263C22×C4×C43C2×D411yescharacteristic
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2411yescharacteristic
266C2×C22⋊D43—21no—
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—21no—
276C2×C22⋊D43—21no—
277C2×C22⋊D43—42no—
278C2×C22⋊D43—42no—
279C2×C22⋊D43—42no—
280C2×C22⋊D43—42no—
281C22×Dic43—21no—
282C22×Dic43—21no—
283C22×Dic43—21no—
284C22×Dic43—21no—
285C22×Dic43—21no—
286C22×Dic43—21no—
287C22×Dic43—42no—
288C22×Dic43—42no—
289C22×Dic43—42no—
290D4×D43—44no—
291#10621898—21no—
292#10621898—21no—
293#10621898—21no—
294#10621898—21no—
295#10621898—21no—
296#10621898—21no—
297#10621898—21no—
298#10621898—21no—
299#10621898—21no—
300#10621898—21no—
301#10621898—22no—
302#10621898—22no—
303#10621898—22no—
304#10621898—22no—
305#10621898—41no—
306#10621898—41no—
307#10621898—41no—
308#10621898—41no—
309#10621898—42no—
310#10621898—42no—
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—22no—
325C2×D172—41no—
326C2×D172—41no—
327C2×D172C22×C411yescharacteristic
328C2×D172C22×C411yescharacteristic
329C2×D172C22×C411yescharacteristic
330C2×C4×D43—21no—
331C2×C4×D43—21no—
332C2×C4×D43—21no—
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—42no—
340C2×C4×D43—42no—
341C2×C4×D43—42no—
342C2×C4×D43—42no—
343C2×Dic86—22no—
344C2×Dic86—22no—
345C2×Dic86—21no—
346C2×Dic86—21no—
347C2×Dic86—41no—
348C2×Dic86—41no—
349C2×Dic86C22×C411yescharacteristic
350C2×Dic86C22×C411yescharacteristic
351C2×Dic86C22×C411yescharacteristic
352M16×C43—21no—
353M16×C43—21no—
354M16×C43—21no—
355M16×C43—21no—
356M16×C43—21no—
357M16×C43—21no—
358M16×C43—21no—
359M16×C43—42no—
360M16×C43—42no—
361M16×C43C2×D412yescomplemented
362C2×C8×C43—21no—
363C2×C8×C43—21no—
364C2×C8×C43—21no—
365C2×C8×C43—21no—
366C2×C8×C43—42no—
367C2×C8×C43—42no—
368C4⋊C4×C43C22⋊C411yescharacteristic
369C4⋊C4×C43C22⋊C411yescharacteristic
370C4⋊C4×C43C22⋊C411yescharacteristic
371C4⋊C4×C43C22⋊C411yescharacteristic
372C22⋊C4×C43C22⋊C411yescharacteristic
373C22⋊C4×C43C22⋊C411yescharacteristic
374C22⋊C4×C43C22⋊C411yescharacteristic
375C22⋊C4×C43C22⋊C411yescharacteristic
376C22⋊C4×C43C22⋊C411yescharacteristic
377C22⋊C4×C43C22⋊C411yescharacteristic
378C22⋊C4×C43C22⋊C411yescharacteristic
379C22⋊C4×C43C22⋊C411yescharacteristic
380C42×C43C22×C411yescharacteristic
381C42×C43C22×C411yescharacteristic
382C42×C43C2×D411yescharacteristic
383C42×C43C2×D411yescharacteristic
384C22⋊Dic43—21no—
385C22⋊Dic43—21no—
386C22⋊Dic43—21no—
387C22⋊Dic43—21no—
388C22⋊Dic43—21no—
389C22⋊Dic43—42no—
390C22⋊Dic43—42no—
391C22⋊Dic43—42no—
392(C2×D43)⋊C4—21no—
393(C2×D43)⋊C4—21no—
394(C2×D43)⋊C4—21no—
395(C2×D43)⋊C4—21no—
396(C2×D43)⋊C4—21no—
397(C2×D43)⋊C4—21no—
398(C2×D43)⋊C4—21no—
399(C2×D43)⋊C4—21no—
400(C2×D43)⋊C4—21no—
401(C2×D43)⋊C4—21no—
402C4⋊Dic43—21no—
403C4⋊Dic43—21no—
404C4⋊Dic43—42no—
405C4⋊Dic43—42no—
406C4⋊Dic43C22×C411yescharacteristic
407C4⋊Dic43C22×C411yescharacteristic
408Dic43⋊C4—21no—
409Dic43⋊C4—21no—
410Dic43⋊C4—21no—
411Dic43⋊C4—21no—
412Dic43⋊C4—21no—
413Dic43⋊C4—21no—
414C4×Dic43—21no—
415C4×Dic43—21no—
416C4×Dic43—21no—
417C4×Dic43—21no—
418C4×Dic43—21no—
419C4×Dic43—21no—
420C4×Dic43—21no—
421C4×Dic43—21no—
422C4×Dic43—21no—
423C4×Dic43—21no—
424C4×Dic43—42no—
425C4×Dic43C2×D412yescomplemented
426C23×C43—21no—
427C23×C43—21no—
428C23×C43—22no—
429C23×C43—21no—
430C23×C43—21no—
431C23×C43—41no—
432C23×C43—41no—
433C23×C43—41no—
434C23×C43C2×C22⋊C411yescharacteristic
435C23×C43C2×C22⋊C411yescharacteristic
436C23×C43C2×C22⋊C411yescharacteristic
437C23×C43C2×C22⋊C411yescharacteristic
438C23×C43C22×D411yescharacteristic
439C22×D43—21no—
440C22×D43—21no—
441C22×D43—21no—
442C22×D43—42no—
443C22×D43—42no—
444C22×D43—42no—
445C22×D43—42no—
446C22×D43—81no—
447C22×D43—81no—
448D4×C43—22no—
449D4×C43—22no—
450D4×C43—41no—
451D4×C43—41no—
452C2×C4×C43—21no—
453C2×C4×C43—21no—
454C2×C4×C43—21no—
455C2×C4×C43—21no—
456C2×C4×C43—21no—
457C2×C4×C43—21no—
458C2×C4×C43—21no—
459C2×C4×C43—21no—
460C2×C4×C43—21no—
461C2×C4×C43—21no—
462C2×C4×C43—21no—
463C2×C4×C43—21no—
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—41no—
473C2×C4×C43—41no—
474C2×C4×C43C2×C22⋊C411yescharacteristic
475C2×C4×C43C2×C22⋊C411yescharacteristic
476C2×C4×C43C2×C22⋊C411yescharacteristic
477C2×C4×C43C2×C22⋊C411yescharacteristic
478C2×C4×C43C2×C22⋊C411yescharacteristic
479C2×C4×C43C2×C22⋊C411yescharacteristic
480C2×C4×C43C2×C22⋊C411yescharacteristic
481C2×C4×C43C2×C22⋊C411yescharacteristic
482C2×C4×C43C23×C411yescharacteristic
483C2×C4×C43C22×D411yescharacteristic
484C2×C4×C43C22×D411yescharacteristic
485C2×C4×C43C2×#4111yescharacteristic
486C2×C4×C43H(5,𝔽2)11yescharacteristic
487C2×C4×C43H(5,𝔽2)11yescharacteristic
488C22⋊D43—22no—
489C22⋊D43—22no—
490C22⋊D43—42no—
491C22⋊D43—42no—
492C22⋊D43—42no—
493C22⋊D43—42no—
494C22⋊D43—42no—
495C22⋊D43—41no—
496C22⋊D43—41no—
497C22⋊D43—41no—
498C22⋊D43—41no—
499C22⋊D43—42no—
500C22⋊D43—81no—
501C22⋊D43—81no—
502C2×Dic43—21no—
503C2×Dic43—22no—
504C2×Dic43—21no—
505C2×Dic43—21no—
506C2×Dic43—21no—
507C2×Dic43—21no—
508C2×Dic43—22no—
509C2×Dic43—42no—
510C2×Dic43—42no—
511C2×Dic43—41no—
512C2×Dic43—41no—
513C2×Dic43—41no—
514C2×Dic43—48no—
515C2×Dic43—41no—
516C2×Dic43—41no—
517C2×Dic43—41no—
518C2×Dic43—41no—
519C2×Dic43—41no—
520C2×Dic43—41no—
521C2×Dic43—41no—
522D172—21no—
523D172—21no—
524D172—21no—
525D172—21no—
526D172—21no—
527D172—42no—
528D172—42no—
529D172—42no—
530D172—81no—
531D172C4×D412yes—
532C4×D43—22no—
533C4×D43—22no—
534C4×D43—42no—
535C4×D43—42no—
536C4×D43—42no—
537C4×D43—42no—
538C4×D43—42no—
539C4×D43—41no—
540C4×D43—41no—
541C4×D43—41no—
542C4×D43—41no—
543C4×D43—81no—
544Dic86—21no—
545Dic86—21no—
546Dic86—21no—
547Dic86—21no—
548Dic86—21no—
549Dic86—42no—
550Dic86—42no—
551Dic86C4×D412yes—
552C8×C43—22no—
553C8×C43—41no—
554C8×C43—41no—
555C8×C43—41no—
556#22434—431nomaximal, Sylow
557C22×C43—21no—
558C22×C43—21no—
559C22×C43—21no—
560C22×C43—21no—
561C22×C43—21no—
562C22×C43—21no—
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—81no—
573C22×C43—81no—
574C22×C43#42112yescomplemented
575C22×C43C22×C22⋊C411yescharacteristic
576C22×C43D4211yescharacteristic
577C22×C43#54611yescharacteristic
578C2×D43—22no—
579C2×D43—41no—
580C2×D43—41no—
581C2×D43—41no—
582C2×D43—41no—
583C2×D43—41no—
584C2×D43—41no—
585C2×D43—41no—
586C2×D43—41no—
587C2×D43—84no—
588C2×D43—84no—
589C4×C43—21no—
590C4×C43—21no—
591C4×C43—21no—
592C4×C43—21no—
593C4×C43—21no—
594C4×C43—21no—
595C4×C43—21no—
596C4×C43—21no—
597C4×C43C2×C4×D411yescharacteristic
598C4×C43#51811yescharacteristic
599C4×C43D4211yescharacteristic
600C4×C43#54611yescharacteristic
601Dic43—22no—
602Dic43—42no—
603Dic43—42no—
604Dic43—41no—
605Dic43—41no—
606Dic43—41no—
607Dic43—41no—
608Dic43—81no—
609Dic43—81no—
610D4×#41—431no—
611D4×M16D4311yescharacteristic, complemented
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#1789—431no—
624#1759—431no—
625C2×C43—21no—
626C2×C43—21no—
627C2×C43—22no—
628C2×C43—41no—
629C2×C43—41no—
630C2×C43—41no—
631C2×C43D4×C22⋊C411yescharacteristic
632C2×C43C2×#42111yescharacteristic
633C2×C43#290111yescharacteristic
634D43—42no—
635D43—81no—
636D43—81no—
637C22×#41—431no—
638C22×#41—431no—
639C22×M16C2×D4311yescharacteristic, complemented
640C22×M16C2×D4311yescharacteristic, complemented
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—861no—
661C2×C4×D4C2×D4311yescharacteristic
662C2×#117—431no—
663C22×C42—431no—
664#436—21no—
665#435—21no—
666#435—21no—
667C8×D4—21no—
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—431no—
679C2×#104—431no—
680C2×#104—431no—
681C2×#104—431no—
682C2×#104—864no—
683#407C2×D4311yescharacteristic, complemented
684#407C2×D4311yescharacteristic, complemented
685C4×M16C2×D4311yescharacteristic, complemented
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#376—431no—
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—431no—
705C2×#41—431no—
706C2×#41—862no—
707C2×#41—862no—
708C2×#41—862no—
709C2×#41—862no—
710C2×#41—861no—
711C2×#41—861no—
712C2×#41—861no—
713C2×#41—861no—
714C2×#41—1721no—
715C2×#41—1721no—
716C2×#41—1721no—
717C2×#41—1721no—
718C22×Q8—431no—
719C22×Q8—431no—
720C22×D4—431no—
721C22×D4—431no—
722C22×D4—861no—
723C22×D4—861no—
724C22×D4—861no—
725C22×D4D17211yescharacteristic
726C23×C4—861no—
727C23×C4—861no—
728C23×C4—861no—
729C23×C4C22×D4311yescharacteristic
730C23×C4C22×D4311yescharacteristic
731C2×M16—21no—
732C2×M16—21no—
733C2×M16—22no—
734C2×M16—22no—
735C2×M16—41no—
736C2×M16—41no—
737C2×M16C22×D4311yescharacteristic
738C2×M16C22×D4311yescharacteristic
739C2×M16C22×D4311yescharacteristic
740C2×M16C22×D4311yescharacteristic
741C22×C8—21no—
742C22×C8—21no—
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—861no—
790C4×D4—861no—
791C4×D4—861no—
792C4×D4—861no—
793C4×D4—861no—
794C4×D4—861no—
795C4×D4—861no—
796C4×D4—861no—
797C4×D4—861no—
798C4×D4—861no—
799C4×D4—861no—
800C4×D4—861no—
801C4×D4C4×D4311yescharacteristic
802C4×D4C4×D4311yescharacteristic
803C4×D4C4×D4311yescharacteristic
804C4×D4C4×D4311yescharacteristic
805C4×D4C22⋊D4311yescharacteristic
806C4×D4C22⋊D4311yescharacteristic
807C4×D4C22⋊D4311yescharacteristic
808C4×D4C22⋊D4311yescharacteristic
809#117—431no—
810#117—862no—
811#117—861no—
812#117—1721no—
813C2×C4⋊C4—861no—
814C2×C4⋊C4—861no—
815C2×C4⋊C4—861no—
816C2×C4⋊C4D17211yescharacteristic
817C2×C22⋊C4—861no—
818C2×C22⋊C4—861no—
819C2×C22⋊C4—861no—
820C2×C22⋊C4—861no—
821C2×C22⋊C4—861no—
822C2×C22⋊C4D17211yescharacteristic
823C2×C22⋊C4D17211yescharacteristic
824C2×C42—431no—
825C2×C42—431no—
826C2×C42—431no—
827C2×C42—431no—
828C2×C42—862no—
829C2×C42—861no—
830C2×C42—861no—
831C2×C42—1721no—
832C2×C42C22×D4311yescharacteristic
833C4⋊C8—21no—
834C4⋊C8—21no—
835#104—434no—
836#104—862no—
837#104—862no—
838#104—862no—
839#104—862no—
840#104—862no—
841#104—862no—
842#104—862no—
843#104—1721no—
844#104—1721no—
845#104—1721no—
846#104—1721no—
847C22⋊C8—21no—
848C22⋊C8—21no—
849C22⋊C8—21no—
850C22⋊C8—21no—
851#97—21no—
852C4×C8—21no—
853#95—861no—
854#95—861no—
855#95—861no—
856#95—861no—
857#95—861no—
858C24—861no—
859C24—861no—
860C24C2×D17211yescharacteristic
861C24C2×D17211yescharacteristic
862#41—432no—
863#41—432no—
864#41—862no—
865#41—862no—
866#41—862no—
867#41—862no—
868#41—861no—
869#41—861no—
870#41—861no—
871#41—861no—
872#41—861no—
873#41—861no—
874#41—861no—
875#41—861no—
876#41—861no—
877#41—861no—
878#41—1722no—
879#41—1722no—
880#41—1722no—
881#41—1722no—
882#41—1721no—
883#41—1721no—
884#41—1721no—
885#41—1721no—
886#41—1722no—
887#41—1722no—
888#41—1722no—
889#41—1722no—
890C2×Q8—431no—
891C2×Q8—431no—
892C2×Q8—431no—
893C2×Q8—862no—
894C2×Q8—862no—
895C2×Q8—861no—
896C2×Q8—861no—
897C2×Q8—1721no—
898C2×Q8—1721no—
899C2×D4—42no—
900C2×D4—431no—
901C2×D4—431no—
902C2×D4—431no—
903C2×D4—862no—
904C2×D4—862no—
905C2×D4—861no—
906C2×D4—861no—
907C2×D4—861no—
908C2×D4—861no—
909C2×D4—861no—
910C2×D4—861no—
911C2×D4—861no—
912C2×D4—861no—
913C2×D4—861no—
914C2×D4—861no—
915C2×D4—861no—
916C2×D4—861no—
917C2×D4—861no—
918C2×D4—861no—
919C2×D4—861no—
920C2×D4—1721no—
921C2×D4—1721no—
922C2×D4—1724no—
923C2×D4—1722no—
924C2×D4—1722no—
925C2×D4—1722no—
926C2×D4—1722no—
927C2×D4(C2×D43)⋊C411yescharacteristic
928C2×D4(C2×D43)⋊C411yescharacteristic
929C2×D4(C2×D43)⋊C411yescharacteristic
930C2×D4(C2×D43)⋊C411yescharacteristic
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—861no—
940C22×C4—861no—
941C22×C4—861no—
942C22×C4—861no—
943C22×C4—861no—
944C22×C4—861no—
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—1722no—
955C22×C4—1722no—
956C22×C4—1722no—
957C22×C4—1722no—
958C22×C4—1722no—
959C22×C4—1722no—
960C22×C4—1722no—
961C22×C4C2×C4×D4311yescharacteristic
962C22×C4C2×C4×D4311yescharacteristic
963C22×C4C2×C4×D4311yescharacteristic
964C22×C4C2×C4×D4311yescharacteristic
965C22×C4C2×D17211yescharacteristic
966C22×C4C2×D17211yescharacteristic
967C22×C4C2×D17211yescharacteristic
968C22×C4C2×D17211yescharacteristic
969C22×C4C2×C22⋊D4311yescharacteristic
970C22×C4C2×C22⋊D4311yescharacteristic
971C22×C4C2×C22⋊D4311yescharacteristic
972C22×C4C2×C22⋊D4311yescharacteristic
973C22×C4C23×D4311yescharacteristic
974M16—21no—
975M16—21no—
976M16—21no—
977M16—21no—
978M16—21no—
979M16—21no—
980M16—21no—
981M16—42no—
982M16—42no—
983M16D4×D4312yescomplemented
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—42no—
989C2×C8—42no—
990C4⋊C4—431no—
991C4⋊C4—431no—
992C4⋊C4—861no—
993C4⋊C4—861no—
994C4⋊C4—861no—
995C4⋊C4—861no—
996C4⋊C4—861no—
997C4⋊C4—861no—
998C4⋊C4—861no—
999C4⋊C4—861no—
1000C4⋊C4—1722no—
1001C4⋊C4—1722no—
1002C4⋊C4(C2×D43)⋊C411yescharacteristic
1003C4⋊C4(C2×D43)⋊C411yescharacteristic
1004C4⋊C4(C2×D43)⋊C411yescharacteristic
1005C4⋊C4(C2×D43)⋊C411yescharacteristic
1006C22⋊C4—861no—
1007C22⋊C4—861no—
1008C22⋊C4—861no—
1009C22⋊C4—861no—
1010C22⋊C4—861no—
1011C22⋊C4—861no—
1012C22⋊C4—861no—
1013C22⋊C4—861no—
1014C22⋊C4—861no—
1015C22⋊C4—861no—
1016C22⋊C4—861no—
1017C22⋊C4—861no—
1018C22⋊C4—861no—
1019C22⋊C4—861no—
1020C22⋊C4—861no—
1021C22⋊C4—1722no—
1022C22⋊C4—1722no—
1023C22⋊C4—1722no—
1024C22⋊C4(C2×D43)⋊C411yescharacteristic
1025C22⋊C4(C2×D43)⋊C411yescharacteristic
1026C22⋊C4(C2×D43)⋊C411yescharacteristic
1027C22⋊C4(C2×D43)⋊C411yescharacteristic
1028C22⋊C4(C2×D43)⋊C411yescharacteristic
1029C22⋊C4(C2×D43)⋊C411yescharacteristic
1030C22⋊C4(C2×D43)⋊C411yescharacteristic
1031C22⋊C4(C2×D43)⋊C411yescharacteristic
1032C42—432no—
1033C42—861no—
1034C42—861no—
1035C42—861no—
1036C42—861no—
1037C42—861no—
1038C42—861no—
1039C42—861no—
1040C42—861no—
1041C42—861no—
1042C42—861no—
1043C42—1722no—
1044C42C2×C4×D4311yescharacteristic
1045C42C2×C4×D4311yescharacteristic
1046C42C2×C22⋊D4311yescharacteristic
1047C42C2×C22⋊D4311yescharacteristic
1048C23—22no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—861no—
1057C23—861no—
1058C23—861no—
1059C23—3441no—
1060C23—3441no—
1061C23—1722no—
1062C23—1722no—
1063C23—1722no—
1064C23—1722no—
1065C23C2×(C2×D43)⋊C411yescharacteristic
1066C23C2×(C2×D43)⋊C411yescharacteristic
1067C23C2×(C2×D43)⋊C411yescharacteristic
1068C23C2×(C2×D43)⋊C411yescharacteristic
1069C23C22×D17211yescharacteristic
1070Q8—432no—
1071Q8—861no—
1072Q8—861no—
1073Q8—861no—
1074Q8—861no—
1075Q8—861no—
1076Q8—1722no—
1077Q8—1722no—
1078D4—22no—
1079D4—22no—
1080D4—41no—
1081D4—41no—
1082D4—432no—
1083D4—862no—
1084D4—862no—
1085D4—861no—
1086D4—861no—
1087D4—861no—
1088D4—861no—
1089D4—861no—
1090D4—3441no—
1091D4—3441no—
1092D4—3441no—
1093D4—1722no—
1094D4—1722no—
1095D4—1722no—
1096D4—1722no—
1097D4—1722no—
1098D4—1722no—
1099D4—1722no—
1100D4—1722no—
1101D4—1722no—
1102D4—1721no—
1103D4—1721no—
1104D4—1721no—
1105D4—1721no—
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—21no—
1116C2×C4—21no—
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—41no—
1127C2×C4—41no—
1128C2×C4—861no—
1129C2×C4—862no—
1130C2×C4—862no—
1131C2×C4—862no—
1132C2×C4—861no—
1133C2×C4—861no—
1134C2×C4—861no—
1135C2×C4—861no—
1136C2×C4—862no—
1137C2×C4—3441no—
1138C2×C4—1722no—
1139C2×C4—1722no—
1140C2×C4—1722no—
1141C2×C4—1722no—
1142C2×C4—1722no—
1143C2×C4—1722no—
1144C2×C4—1722no—
1145C2×C4—1721no—
1146C2×C4—1721no—
1147C2×C4—1721no—
1148C2×C4—1721no—
1149C2×C4—1721no—
1150C2×C4—1721no—
1151C2×C4—1721no—
1152C2×C4—1721no—
1153C2×C4—1721no—
1154C2×C4—1728no—
1155C2×C4—1721no—
1156C2×C4—1721no—
1157C2×C4—1721no—
1158C2×C4—1721no—
1159C2×C4—1721no—
1160C2×C4C2×(C2×D43)⋊C411yescharacteristic
1161C2×C4C2×(C2×D43)⋊C411yescharacteristic
1162C2×C4C2×(C2×D43)⋊C411yescharacteristic
1163C2×C4C2×(C2×D43)⋊C411yescharacteristic
1164C2×C4C2×(C2×D43)⋊C411yescharacteristic
1165C2×C4C2×(C2×D43)⋊C411yescharacteristic
1166C2×C4C2×(C2×D43)⋊C411yescharacteristic
1167C2×C4C2×(C2×D43)⋊C411yescharacteristic
1168C2×C4C22×C4×D4311yescharacteristic
1169C2×C4C2×D4×D4311yescharacteristic
1170C2×C4C22×C22⋊D4311yescharacteristic
1171C2×C4#41×D4311yescharacteristic
1172C2×C4#1306337011yescharacteristic
1173C2×C4#1306337111yescharacteristic
1174C8—22no—
1175C8—41no—
1176C8—41no—
1177C8—41no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—21no—
1191C22—42no—
1192C22—42no—
1193C22—81no—
1194C22—81no—
1195C22—862no—
1196C22—3444no—
1197C22—3444no—
1198C22—1721no—
1199C22—1721no—
1200C22—1721no—
1201C22—1721no—
1202C22—1721no—
1203C22—1721no—
1204C22—1721no—
1205C22—1721no—
1206C22#1458291512yescomplemented
1207C22C22×(C2×D43)⋊C411yescharacteristic
1208C22D4×D17211yescharacteristic
1209C22#1458354411yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—21no—
1215C4—21no—
1216C4—21no—
1217C4—21no—
1218C4—862no—
1219C4—3441no—
1220C4—3441no—
1221C4—1722no—
1222C4—1722no—
1223C4—1721no—
1224C4—1721no—
1225C4—1721no—
1226C4—1721no—
1227C4C4×D4×D4311yescharacteristic
1228C4#1458337111yescharacteristic
1229C4D4×C22⋊D4311yescharacteristic
1230C4#1458353711yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—22no—
1234C2—41no—
1235C2—41no—
1236C2—41no—
1237C2—3441no—
1238C2—3441no—
1239C2—1722no—
1240C2D4×(C2×D43)⋊C411yescharacteristic
1241C2C2×#1458291511yescharacteristic
1242C2#1914314011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×M16×C43C2
socleC22×C43C22×C22⋊C4
prime radicalD4×#10621898C2
cosocleC22×C4×C43C24
hypercenterD4×M16D43
hypocenterC43#22434
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. C2×#14582915C2semidirect
3. C22×#13063251C2semidirect
4. #19137040C2semidirect
5. #19135514C2semidirect
6. #19135426C2semidirect
7. #19135041C2semidirect
8. #19135036C2semidirect
9. #19134897C2semidirect
10. #19134897C2semidirect
11. #19134612C2semidirect
12. #19134538C2semidirect
13. #19134538C2semidirect
14. #19134408C2semidirect
15. D4×M16×C43C2semidirect
18. #14583570C4semidirect
19. D4×Dic86C4semidirect
20. #14583558C4semidirect
21. #14583558C4semidirect
22. #14583554C4semidirect
24. #14583545C4semidirect
25. #14583545C4semidirect
28. D4×D172C4semidirect
38. C2×#13063284C22semidirect
39. C22×C4×Dic43C22semidirect
46. C2×#13063251C22semidirect
47. C2×#13063251C22semidirect
48. C2×#13063251C22semidirect
49. C2×#13063251C22semidirect
50. C2×#13063251C22semidirect
51. C2×#13063251C22semidirect
52. C2×#13063251C22semidirect
53. C2×#13063251C22semidirect
58. C4×C4⋊Dic43C22semidirect
59. C4×C22⋊Dic43C22semidirect
60. C4×C22⋊Dic43C22semidirect
61. #14582745C22semidirect
62. #14582660C22semidirect
63. #14582660C22semidirect
64. #14582660C22semidirect
65. #14582660C22semidirect
66. C22×M16×C43C22semidirect
67. C22×M16×C43C22semidirect
73. C43×#423C22semidirect
74. C43×#407C22semidirect
75. C43×#407C22semidirect
76. C4×M16×C43C22semidirect
91. C2×#10621898C2×C4semidirect
92. C2×#10621898C2×C4semidirect
97. C22×Dic86C2×C4semidirect
99. C22×D172C2×C4semidirect
106. #13063325C2×C4semidirect
108. #13063322C2×C4semidirect
110. #13063313C2×C4semidirect
111. #13063313C2×C4semidirect
122. #13063304C2×C4semidirect
123. #13063304C2×C4semidirect
133. #13063299C2×C4semidirect
134. #13063299C2×C4semidirect
148. C4×Dic86C2×C4semidirect
149. C4×Dic86C2×C4semidirect
152. C4×D172C2×C4semidirect
153. C4×D172C2×C4semidirect
195. #13063251D4semidirect
361. M16×C43C2×D4semidirect
425. C4×Dic43C2×D4semidirect
574. C22×C43#421semidirect
611. D4×M16D43semidirect
639. C22×M16C2×D43semidirect
640. C22×M16C2×D43semidirect
668. #423C2×D43semidirect
683. #407C2×D43semidirect
684. #407C2×D43semidirect
685. C4×M16C2×D43semidirect
698. C43#22434semidirect
983. M16D4×D43semidirect
1206. C22#14582915semidirect

Maximal subgroups

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

subgroupindex
D4×#106218982
C2×#145829152
C22×#130632512
#191370402
#191355142
#191354262
#191350412
#191350362
#191348972
#191346122
#191345382
#191344082
D4×M16×C432
#2243443