Finite Group Databasebeta

← #25112280

Subgroups — #25112280

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#19148078C211yesmaximal, characteristic
2M16×C22⋊D43C211yesmaximal, characteristic, complemented
3C2×#14582914C211yesmaximal, characteristic, complemented
4C22×#13063251C211yesmaximal, characteristic, complemented
5#19137034C211yesmaximal, characteristic, complemented
6#19135512C211yesmaximal, characteristic, complemented
7#19135425C211yesmaximal, characteristic, complemented
8#19135042C211yesmaximal, characteristic, complemented
9#19135039C211yesmaximal, characteristic, complemented
10#19134896C211yesmaximal, characteristic, complemented
11#19134614C211yesmaximal, characteristic, complemented
12#19134540C211yesmaximal, characteristic, complemented
13#19134537C211yesmaximal, characteristic, complemented
14#19134404C211yesmaximal, characteristic, complemented
15C43×#1871C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#41×D43C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic, complemented
19#14583567C411yescharacteristic, complemented
20#14583562C411yescharacteristic, complemented
21#14583559C411yescharacteristic, complemented
22#14583555C411yescharacteristic, complemented
23#14583551C411yescharacteristic, complemented
24#14583547—21no—
25#14583546C411yescharacteristic, complemented
26#14583541—21no—
27#14583540C411yescharacteristic, complemented
28#14583536—21no—
29#14583533C411yescharacteristic, complemented
30#14583531—21no—
31#14583446—21no—
32#14583445C2211yescharacteristic
33#14583411C2211yescharacteristic
34#14583408—21no—
35#14583408—21no—
36#14583367C2211yescharacteristic
37C2×C4×C22⋊D43C2211yescharacteristic
38C4×D4×D43—21no—
39C2×#13063282C2211yescharacteristic, complemented
40C22×C4×Dic43C2211yescharacteristic, complemented
41#14582975—21no—
42#14582970—21no—
43#14582968—21no—
44C8×C22⋊D43—21no—
45#14582922C2211yescharacteristic, complemented
46#14582914—24no—
47C2×#13063253C2211yescharacteristic
48C2×#13063253C2211yescharacteristic
49C2×#13063253C2211yescharacteristic, complemented
50C2×#13063253C2211yescharacteristic, complemented
51C2×#13063252C2211yescharacteristic, complemented
52C2×#13063252C2211yescharacteristic, complemented
53C2×#13063251—24no—
54C2×#13063251C2211yescharacteristic
55C2×#13063251C2211yescharacteristic
56C2×#13063251C2211yescharacteristic, complemented
57C2×#13063251C2211yescharacteristic, complemented
58#14582863C2211yescharacteristic, complemented
59#14582862C2211yescharacteristic, complemented
60M16×Dic43C2211yescharacteristic, complemented
61#14582788—21no—
62#14582781—21no—
63#14582776—21no—
64#14582771—21no—
65C4×Dic43⋊C4C2211yescharacteristic, complemented
66C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
67#14582745C2211yescharacteristic, complemented
68#14582658C2211yescharacteristic, complemented
69#14582658C2211yescharacteristic, complemented
70C22×M16×C43C2211yescharacteristic, complemented
71C43×#525C2211yescharacteristic
72C2×#104×C43C2211yescharacteristic, complemented
73C2×#104×C43C2211yescharacteristic, complemented
74C4×C22⋊C4×C43C2211yescharacteristic, 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
86C2×#10621898C2×C411yescharacteristic
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
96C2×Q8×D43C2×C411yescharacteristic, complemented
97C22×D172C2×C411yescharacteristic
98C22×C22⋊D43—21no—
99C22×C22⋊D43D411yescharacteristic
100C2×D4×D43—21no—
101C2×D4×D43—21no—
102C2×D4×D43C2×C411yescharacteristic, complemented
103C23×Dic43—21no—
104C22×C4×D43—21no—
105C22×C4×D43—21no—
106C22×C4×D43C2311yescharacteristic
107C2×#10621877C2311yescharacteristic
108C2×#10621877C2311yescharacteristic
109C2×#10621872—21no—
110M16×D43—22no—
111M16×D43—41no—
112C2×C8×D43—21no—
113#13063324—21no—
114#13063323C2×C411yescharacteristic, complemented
115#13063321—21no—
116#13063321C2×C411yescharacteristic, complemented
117#13063314C2×C411yescharacteristic, complemented
118#13063312C2×C411yescharacteristic, complemented
119#13063311—21no—
120#13063311—21no—
121#13063310—21no—
122#13063310—21no—
123#13063309—21no—
124#13063307—21no—
125#13063307—21no—
126#13063305C2×C411yescharacteristic, complemented
127#13063305C2×C411yescharacteristic, complemented
128#13063303—21no—
129#13063303—21no—
130#13063302—21no—
131#13063302—21no—
132#13063300—21no—
133#13063300C2×C411yescharacteristic, complemented
134#13063300C2×C411yescharacteristic, complemented
135#13063298—21no—
136#13063298—21no—
137#13063298—21no—
138#13063298—21no—
139#13063297—21no—
140#13063297—21no—
141#13063297—21no—
142#13063297—21no—
143#13063296—21no—
144#13063295—21no—
145#13063295—21no—
146#13063295—21no—
147#13063293—21no—
148#13063293—21no—
149#13063290C2×C411yescharacteristic, complemented
150#13063290C2×C411yescharacteristic, complemented
151C4×D172—21no—
152C4×D172—21no—
153D4×Dic43—21no—
154#13063287—21no—
155#13063287C2×C411yescharacteristic, complemented
156#13063287C2×C411yescharacteristic, complemented
157C4×C22⋊D43—21no—
158C4×C22⋊D43—21no—
159C4×C22⋊D43C2×C411yescharacteristic
160C4×C22⋊D43C2×C411yescharacteristic
161C4×C22⋊D43C2×C411yescharacteristic
162C4×C22⋊D43C2×C411yescharacteristic
163C4×C22⋊D43D411yescharacteristic
164C4×C22⋊D43D411yescharacteristic
165C4×C22⋊D43D411yescharacteristic
166C4×C22⋊D43D411yescharacteristic
167(C22⋊D43)⋊C4—21no—
168(C22⋊D43)⋊C4—21no—
169(C22⋊D43)⋊C4—21no—
170(C22⋊D43)⋊C4—21no—
171#13063282—21no—
172#13063282—22no—
173#13063282—41no—
174C2×Dic43⋊C4—21no—
175C2×Dic43⋊C4—21no—
176C2×Dic43⋊C4D411yescharacteristic
177C4⋊C4×D43—21no—
178C2×C22⋊Dic43D411yescharacteristic
179C2×(C2×D43)⋊C4—21no—
180C2×(C2×D43)⋊C4—21no—
181C2×(C2×D43)⋊C4D411yescharacteristic
182C22⋊C4×D43—21no—
183C22⋊C4×D43—21no—
184C2×C4×Dic43—22no—
185C2×C4×Dic43—21no—
186C2×C4×Dic43—41no—
187C2×C4×Dic43C2311yescharacteristic
188C2×C4×Dic43C2311yescharacteristic
189C2×C4×Dic43C2311yescharacteristic
190C42×D43—21no—
191Dic43⋊C8—21no—
192Dic43⋊C8—21no—
193#13063253—22no—
194#13063253—22no—
195#13063253—41no—
196#13063253—41no—
197#13063252—22no—
198#13063252—41no—
199#13063251—22no—
200#13063251—22no—
201#13063251—22no—
202#13063251D414yescomplemented
203C22⋊(C43⋊C8)—21no—
204C22⋊(C43⋊C8)—21no—
205(C2×D43)⋊C8—21no—
206(C2×D43)⋊C8—21no—
207#13063235—21no—
208C8×Dic43—21no—
209C43⋊#95—21no—
210C43⋊#95—21no—
211C43⋊#95—21no—
212C43⋊#95—21no—
213C2×#41×C43C2311yescharacteristic
214C23×C4×C43C2311yescharacteristic
215C2×M16×C43—21no—
216C2×M16×C43—22no—
217C2×M16×C43—41no—
218C2×M16×C43C2311yescharacteristic
219C2×M16×C43C2311yescharacteristic
220C22×C8×C43—21no—
221#123×C43—21no—
222C22⋊Q8×C43C2×C411yescharacteristic
223C22⋊Q8×C43C2×C411yescharacteristic
224#121×C43C2×C411yescharacteristic
225#121×C43C2×C411yescharacteristic
226#120×C43—21no—
227C4×D4×C43—21no—
228C4×D4×C43—21no—
229#117×C43C2311yescharacteristic
230C2×C22⋊C4×C43—21no—
231C2×C42×C43C2311yescharacteristic
232C2×C42×C43C2311yescharacteristic
233#104×C43—22no—
234#104×C43—41no—
235#95×C43—21no—
236C24×C43C2×D411yescharacteristic
237C23×D43—21no—
238C23×D43—21no—
239C23×D43C2×D411yescharacteristic
240#41×C43—21no—
241#41×C43—21no—
242#41×C43—21no—
243#41×C43—21no—
244C2×Q8×C43C22×C411yescharacteristic
245C2×D4×C43—21no—
246C2×D4×C43—21no—
247C2×D4×C43—21no—
248C2×D4×C43C22×C411yescharacteristic
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43C22×C411yescharacteristic
257C22×C4×C43C22×C411yescharacteristic
258C22×C4×C43C2×D411yescharacteristic
259C22×C4×C43C2×D411yescharacteristic
260C22×C4×C43C2×D411yescharacteristic
261C22×C4×C43C2411yescharacteristic
262C2×C22⋊D43—21no—
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—42no—
271C2×C22⋊D43—42no—
272C2×C22⋊D43—42no—
273C2×C22⋊D43C22⋊C411yescharacteristic
274C2×C22⋊D43C22⋊C411yescharacteristic
275C2×C22⋊D43C22⋊C411yescharacteristic
276C2×C22⋊D43C22⋊C411yescharacteristic
277C22×Dic43—21no—
278C22×Dic43—21no—
279C22×Dic43—21no—
280C22×Dic43—21no—
281C22×Dic43—42no—
282C22×Dic43—42no—
283C22×Dic43—42no—
284C22×Dic43C2×D411yescharacteristic
285C22×Dic43C2×D411yescharacteristic
286C22×Dic43C2×D411yescharacteristic
287#10621902—22no—
288#10621902—41no—
289Q8×D43—22no—
290Q8×D43—41no—
291#10621900—22no—
292#10621900—41no—
293#10621900—42no—
294#10621900—42no—
295D4×D43—22no—
296D4×D43—42no—
297D4×D43—42no—
298D4×D43—41no—
299D4×D43—44no—
300#10621898—21no—
301#10621898—21no—
302#10621898—21no—
303#10621898—21no—
304#10621898—21no—
305#10621898—21no—
306#10621898—22no—
307#10621898—22no—
308#10621898—41no—
309#10621898—41no—
310#10621898—42no—
311#10621898—42no—
312#10621898—42no—
313#10621898—42no—
314#10621898—42no—
315#10621898—42no—
316#10621898C2×D412yes—
317#10621898#4112yes—
318C2×D172—21no—
319C2×D172—21no—
320C2×D172—21no—
321C2×D172—21no—
322C2×D172—22no—
323C2×D172—41no—
324C2×D172C22×C411yescharacteristic
325C2×D172C22×C411yescharacteristic
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—21no—
335C2×C4×D43—21no—
336C2×C4×D43—21no—
337C2×C4×D43—21no—
338C2×C4×D43—42no—
339C2×C4×D43—42no—
340C2×C4×D43—42no—
341C2×C4×D43—42no—
342C2×C4×D43C22×C411yescharacteristic
343C2×C4×D43C22×C411yescharacteristic
344C2×C4×D43C2×D411yescharacteristic
345C2×C4×D43C2×D411yescharacteristic
346C2×Dic86—22no—
347C2×Dic86—21no—
348C2×Dic86—21no—
349C2×Dic86—41no—
350C2×Dic86C22×C411yescharacteristic
351C2×Dic86C22×C411yescharacteristic
352M16×C43—21no—
353M16×C43—21no—
354M16×C43—21no—
355M16×C43—42no—
356M16×C43C2×D412yescomplemented
357C2×C8×C43—21no—
358C2×C8×C43—21no—
359C2×C8×C43—42no—
360C4⋊C4×C43—21no—
361C4⋊C4×C43—21no—
362C4⋊C4×C43C22×C411yescharacteristic
363C4⋊C4×C43C22×C411yescharacteristic
364C22⋊C4×C43—21no—
365C22⋊C4×C43—21no—
366C22⋊C4×C43—21no—
367C22⋊C4×C43—21no—
368C22⋊C4×C43—21no—
369C22⋊C4×C43—42no—
370C42×C43—21no—
371C42×C43—21no—
372C42×C43—21no—
373C42×C43—21no—
374C42×C43—21no—
375C22⋊Dic43—21no—
376C22⋊Dic43—21no—
377C22⋊Dic43C22⋊C411yescharacteristic
378C22⋊Dic43C22⋊C411yescharacteristic
379C22⋊Dic43C22⋊C411yescharacteristic
380C22⋊Dic43C22⋊C411yescharacteristic
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)⋊C4—21no—
388(C2×D43)⋊C4—21no—
389(C2×D43)⋊C4—42no—
390(C2×D43)⋊C4—42no—
391(C2×D43)⋊C4C22⋊C411yescharacteristic
392(C2×D43)⋊C4C22⋊C411yescharacteristic
393(C2×D43)⋊C4C22⋊C411yescharacteristic
394(C2×D43)⋊C4C22⋊C411yescharacteristic
395C4⋊Dic43—21no—
396C4⋊Dic43—21no—
397Dic43⋊C4—21no—
398Dic43⋊C4—21no—
399Dic43⋊C4—21no—
400Dic43⋊C4—21no—
401Dic43⋊C4—42no—
402Dic43⋊C4—42no—
403Dic43⋊C4C22⋊C411yescharacteristic
404Dic43⋊C4C22⋊C411yescharacteristic
405Dic43⋊C4C22⋊C411yescharacteristic
406Dic43⋊C4C22⋊C411yescharacteristic
407C4×Dic43—21no—
408C4×Dic43—21no—
409C4×Dic43—21no—
410C4×Dic43—21no—
411C4×Dic43—21no—
412C4×Dic43—42no—
413C4×Dic43C22×C411yescharacteristic
414C4×Dic43C22×C411yescharacteristic
415C4×Dic43C2×D411yescharacteristic
416C4×Dic43C2×D411yescharacteristic
417C4×Dic43C2×D412yescomplemented
418#10621877—21no—
419#10621877—21no—
420#10621877—21no—
421#10621877—21no—
422C2×C43⋊C8—21no—
423C2×C43⋊C8—21no—
424#10621872—42no—
425C8×D43—42no—
426C23×C43—21no—
427C23×C43—21no—
428C23×C43—22no—
429C23×C43—21no—
430C23×C43—41no—
431C23×C43C2×C22⋊C411yescharacteristic
432C23×C43C2×C22⋊C411yescharacteristic
433C23×C43C22×D411yescharacteristic
434C22×D43—21no—
435C22×D43—21no—
436C22×D43—21no—
437C22×D43—21no—
438C22×D43—41no—
439C22×D43—41no—
440C22×D43—42no—
441C22×D43—42no—
442C22×D43—42no—
443C22×D43—42no—
444C22×D43—81no—
445C22×D43—81no—
446C22×D43C2×C22⋊C411yescharacteristic
447C22×D43C2×C22⋊C411yescharacteristic
448Q8×C43—21no—
449Q8×C43—21no—
450D4×C43—21no—
451D4×C43—21no—
452D4×C43—41no—
453D4×C43—41no—
454D4×C43—42no—
455D4×C43—81no—
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—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×C43—41no—
477C2×C4×C43C2×C22⋊C411yescharacteristic
478C2×C4×C43C2×C22⋊C411yescharacteristic
479C2×C4×C43C23×C411yescharacteristic
480C2×C4×C43C22×D411yescharacteristic
481C2×C4×C43C22×D411yescharacteristic
482C2×C4×C43C2×#4111yescharacteristic
483C2×C4×C43H(5,𝔽2)11yescharacteristic
484C2×C4×C43H(5,𝔽2)11yescharacteristic
485C22⋊D43—22no—
486C22⋊D43—22no—
487C22⋊D43—22no—
488C22⋊D43—22no—
489C22⋊D43—41no—
490C22⋊D43—41no—
491C22⋊D43—42no—
492C22⋊D43—42no—
493C22⋊D43—42no—
494C22⋊D43—42no—
495C22⋊D43—42no—
496C22⋊D43—41no—
497C22⋊D43—41no—
498C22⋊D43—81no—
499C2×Dic43—21no—
500C2×Dic43—21no—
501C2×Dic43—21no—
502C2×Dic43—22no—
503C2×Dic43—21no—
504C2×Dic43—22no—
505C2×Dic43—41no—
506C2×Dic43—41no—
507C2×Dic43—42no—
508C2×Dic43—42no—
509C2×Dic43—41no—
510C2×Dic43—41no—
511C2×Dic43—41no—
512C2×Dic43—48no—
513C2×Dic43—41no—
514C2×Dic43C2×C22⋊C411yescharacteristic
515C2×Dic43C2×C22⋊C411yescharacteristic
516C2×Dic43C2×C22⋊C411yescharacteristic
517C2×Dic43C2×C22⋊C411yescharacteristic
518C2×Dic43C2×C22⋊C411yescharacteristic
519C2×Dic43C2×C22⋊C411yescharacteristic
520D172—21no—
521D172—21no—
522D172—21no—
523D172—42no—
524D172—42no—
525D172—42no—
526D172—81no—
527D172C4×D412yes—
528C4×D43—21no—
529C4×D43—21no—
530C4×D43—21no—
531C4×D43—21no—
532C4×D43—21no—
533C4×D43—21no—
534C4×D43—22no—
535C4×D43—21no—
536C4×D43—21no—
537C4×D43—22no—
538C4×D43—42no—
539C4×D43—42no—
540C4×D43—42no—
541C4×D43—42no—
542C4×D43—42no—
543C4×D43—41no—
544C4×D43—41no—
545C4×D43—81no—
546Dic86—21no—
547Dic86—21no—
548Dic86—21no—
549Dic86—42no—
550Dic86—42no—
551Dic86C4×D412yes—
552C8×C43—22no—
553C8×C43—41no—
554C43⋊C8—41no—
555C43⋊C8—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—42no—
565C22×C43—42no—
566C22×C43—41no—
567C22×C43—41no—
568C22×C43—41no—
569C22×C43#42112yescomplemented
570C22×C43C22×C22⋊C411yescharacteristic
571C22×C43D4211yescharacteristic
572C22×C43#54611yescharacteristic
573C2×D43—21no—
574C2×D43—21no—
575C2×D43—22no—
576C2×D43—21no—
577C2×D43—21no—
578C2×D43—21no—
579C2×D43—21no—
580C2×D43—41no—
581C2×D43—41no—
582C2×D43—41no—
583C2×D43—41no—
584C2×D43—41no—
585C2×D43—81no—
586C2×D43—81no—
587C2×D43—84no—
588C2×D43—84no—
589C4×C43—21no—
590C4×C43—21no—
591C4×C43—41no—
592C4×C43—41no—
593C4×C43—41no—
594C4×C43—81no—
595C4×C43—81no—
596C4×C43C2×C4×D411yescharacteristic
597C4×C43#51811yescharacteristic
598C4×C43D4211yescharacteristic
599C4×C43#54611yescharacteristic
600Dic43—22no—
601Dic43—21no—
602Dic43—21no—
603Dic43—21no—
604Dic43—21no—
605Dic43—21no—
606Dic43—21no—
607Dic43—42no—
608Dic43—42no—
609Dic43—41no—
610D4×#41—431no—
611D4×M16—431no—
612C2×#421—431no—
613C22×#104—431no—
614#2290—431no—
615#1980—431no—
616#1963—431no—
617#1897—431no—
618#1896—431no—
619#1871—431no—
620#1871D4311yescharacteristic, complemented
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—81no—
630C2×C43D4×C22⋊C411yescharacteristic
631C2×C43C2×#42111yescharacteristic
632C2×C43#290111yescharacteristic
633D43—41no—
634D43—41no—
635D43—42no—
636D43—81no—
637C22×#41—431no—
638C22×#41—431no—
639C22×M16—431no—
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—861no—
657#525—861no—
658#525C2×D4311yescharacteristic
659C4×#41—431no—
660C2×C4×D4—431no—
661C2×C4×D4—861no—
662C2×#117—431no—
663C22×C42—431no—
664#436—861no—
665#435—861no—
666#435—861no—
667C8×D4—861no—
668#423—431no—
669#421—864no—
670C2×#104—431no—
671C2×#104—431no—
672C2×#104—431no—
673C2×#104—431no—
674C2×#104—431no—
675C2×#104—431no—
676C2×#104—431no—
677C2×#104—431no—
678C2×#104—431no—
679C2×#104—431no—
680C2×#104—864no—
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⋊C4C2×D4311yescharacteristic, complemented
693#376—431no—
694#339—431no—
695#339—431no—
696#339C2×D4311yescharacteristic, complemented
697#339C2×D4311yescharacteristic, complemented
698C43#2243411yescharacteristic, complemented, Sylow
699C2×#41—431no—
700C2×#41—431no—
701C2×#41—431no—
702C2×#41—431no—
703C2×#41—431no—
704C2×#41—431no—
705C2×#41—861no—
706C2×#41—862no—
707C2×#41—862no—
708C2×#41—861no—
709C2×#41—861no—
710C2×#41—861no—
711C2×#41—862no—
712C2×#41—862no—
713C2×#41—1721no—
714C2×#41—1721no—
715C2×#41—1721no—
716C2×#41—1721no—
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—861no—
728C23×C4—861no—
729C23×C4—861no—
730C23×C4C22×D4311yescharacteristic
731C2×M16—21no—
732C2×M16—22no—
733C2×M16—41no—
734C2×M16—431no—
735C2×M16—431no—
736C2×M16—861no—
737C2×M16—862no—
738C2×M16—1721no—
739C2×M16C22×D4311yescharacteristic
740C2×M16C22×D4311yescharacteristic
741C22×C8—21no—
742C22×C8—861no—
743C4⋊Q8—431no—
744C4⋊Q8—861no—
745#127—431no—
746#127—861no—
747#124—431no—
748#124—431no—
749#124—861no—
750#124—861no—
751#123—21no—
752#123—861no—
753#123—861no—
754#123—861no—
755#123—861no—
756#123—861no—
757C22⋊Q8—431no—
758C22⋊Q8—431no—
759C22⋊Q8—861no—
760C22⋊Q8—861no—
761C22⋊Q8—861no—
762C22⋊Q8—861no—
763C22⋊Q8C4×D4311yescharacteristic
764C22⋊Q8C4×D4311yescharacteristic
765#121—431no—
766#121—431no—
767#121—861no—
768#121—861no—
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#121C4×D4311yescharacteristic
778#121C4×D4311yescharacteristic
779#120—21no—
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—861no—
810#117—862no—
811#117—1721no—
812#117C22×D4311yescharacteristic
813C2×C4⋊C4—431no—
814C2×C4⋊C4—861no—
815C2×C4⋊C4—861no—
816C2×C4⋊C4—861no—
817C2×C22⋊C4—21no—
818C2×C22⋊C4—431no—
819C2×C22⋊C4—431no—
820C2×C22⋊C4—861no—
821C2×C22⋊C4—861no—
822C2×C22⋊C4—861no—
823C2×C22⋊C4—861no—
824C2×C42—431no—
825C2×C42—431no—
826C2×C42—431no—
827C2×C42—861no—
828C2×C42—862no—
829C2×C42—861no—
830C2×C42—1721no—
831C2×C42C22×D4311yescharacteristic
832C2×C42C22×D4311yescharacteristic
833C4⋊C8—861no—
834C4⋊C8—861no—
835#104—22no—
836#104—41no—
837#104—434no—
838#104—862no—
839#104—862no—
840#104—862no—
841#104—862no—
842#104—862no—
843#104—862no—
844#104—1721no—
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—861no—
855#95—861no—
856#95—861no—
857#95—861no—
858C24—431no—
859C24—861no—
860C24—861no—
861C24D4×D4311yescharacteristic
862#41—21no—
863#41—21no—
864#41—21no—
865#41—21no—
866#41—432no—
867#41—432no—
868#41—862no—
869#41—862no—
870#41—861no—
871#41—861no—
872#41—862no—
873#41—862no—
874#41—861no—
875#41—861no—
876#41—861no—
877#41—861no—
878#41—1722no—
879#41—1722no—
880#41—1721no—
881#41—1721no—
882#41—1722no—
883#41—1722no—
884#41—1722no—
885#41—1722no—
886#41—1721no—
887#41—1722no—
888#41—1722no—
889#41—1721no—
890C2×Q8—431no—
891C2×Q8—431no—
892C2×Q8—861no—
893C2×Q8—862no—
894C2×Q8—861no—
895C2×Q8—862no—
896C2×Q8—1721no—
897C2×Q8—1721no—
898C2×Q8C2×C4×D4311yescharacteristic
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—431no—
903C2×D4—431no—
904C2×D4—431no—
905C2×D4—431no—
906C2×D4—431no—
907C2×D4—431no—
908C2×D4—862no—
909C2×D4—861no—
910C2×D4—861no—
911C2×D4—861no—
912C2×D4—861no—
913C2×D4—861no—
914C2×D4—861no—
915C2×D4—862no—
916C2×D4—861no—
917C2×D4—861no—
918C2×D4—861no—
919C2×D4—861no—
920C2×D4—861no—
921C2×D4—861no—
922C2×D4—1721no—
923C2×D4—1721no—
924C2×D4—1722no—
925C2×D4—1722no—
926C2×D4—1724no—
927C2×D4—1722no—
928C2×D4—1722no—
929C2×D4—1722no—
930C2×D4C2×C4×D4311yescharacteristic
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—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—1722no—
962C22×C4—1722no—
963C22×C4—1722no—
964C22×C4—1722no—
965C22×C4—1722no—
966C22×C4—1722no—
967C22×C4—1722no—
968C22×C4C2×C4×D4311yescharacteristic
969C22×C4C2×C4×D4311yescharacteristic
970C22×C4D4×D4311yescharacteristic
971C22×C4D4×D4311yescharacteristic
972C22×C4D4×D4311yescharacteristic
973C22×C4C23×D4311yescharacteristic
974M16—21no—
975M16—21no—
976M16—21no—
977M16—42no—
978M16—861no—
979M16—861no—
980M16—861no—
981M16—861no—
982M16—1722no—
983M16D4×D4312yescomplemented
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—42no—
987C2×C8—861no—
988C2×C8—861no—
989C2×C8—1722no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—431no—
993C4⋊C4—431no—
994C4⋊C4—431no—
995C4⋊C4—431no—
996C4⋊C4—861no—
997C4⋊C4—861no—
998C4⋊C4—861no—
999C4⋊C4—861no—
1000C4⋊C4—861no—
1001C4⋊C4—861no—
1002C4⋊C4—1722no—
1003C4⋊C4—1722no—
1004C4⋊C4C2×C4×D4311yescharacteristic
1005C4⋊C4C2×C4×D4311yescharacteristic
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—21no—
1011C22⋊C4—42no—
1012C22⋊C4—431no—
1013C22⋊C4—431no—
1014C22⋊C4—431no—
1015C22⋊C4—431no—
1016C22⋊C4—431no—
1017C22⋊C4—431no—
1018C22⋊C4—431no—
1019C22⋊C4—431no—
1020C22⋊C4—861no—
1021C22⋊C4—861no—
1022C22⋊C4—861no—
1023C22⋊C4—861no—
1024C22⋊C4—861no—
1025C22⋊C4—861no—
1026C22⋊C4—861no—
1027C22⋊C4—861no—
1028C22⋊C4—861no—
1029C22⋊C4—861no—
1030C22⋊C4—1722no—
1031C22⋊C4—1722no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—431no—
1038C42—431no—
1039C42—431no—
1040C42—431no—
1041C42—432no—
1042C42—861no—
1043C42—861no—
1044C42—861no—
1045C42—861no—
1046C42—861no—
1047C42—1722no—
1048C23—22no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—41no—
1053C23—431no—
1054C23—431no—
1055C23—861no—
1056C23—861no—
1057C23—861no—
1058C23—861no—
1059C23—3441no—
1060C23—3441no—
1061C23—1721no—
1062C23—1721no—
1063C23—1722no—
1064C23—1722no—
1065C23—1722no—
1066C23—1722no—
1067C23C22⋊C4×D4311yescharacteristic
1068C23C22⋊C4×D4311yescharacteristic
1069C23C2×D4×D4311yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—432no—
1073Q8—861no—
1074Q8—861no—
1075Q8—861no—
1076Q8—1722no—
1077Q8—1722no—
1078D4—21no—
1079D4—21no—
1080D4—42no—
1081D4—41no—
1082D4—41no—
1083D4—81no—
1084D4—432no—
1085D4—862no—
1086D4—862no—
1087D4—862no—
1088D4—862no—
1089D4—861no—
1090D4—861no—
1091D4—861no—
1092D4—3441no—
1093D4—3441no—
1094D4—1722no—
1095D4—1722no—
1096D4—1722no—
1097D4—1721no—
1098D4—1721no—
1099D4—1722no—
1100D4—1722no—
1101D4—1722no—
1102D4—1722no—
1103D4—1722no—
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—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—431no—
1128C2×C4—431no—
1129C2×C4—431no—
1130C2×C4—431no—
1131C2×C4—431no—
1132C2×C4—431no—
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—861no—
1142C2×C4—862no—
1143C2×C4—861no—
1144C2×C4—861no—
1145C2×C4—862no—
1146C2×C4—862no—
1147C2×C4—861no—
1148C2×C4—862no—
1149C2×C4—3441no—
1150C2×C4—1722no—
1151C2×C4—1722no—
1152C2×C4—1722no—
1153C2×C4—1722no—
1154C2×C4—1722no—
1155C2×C4—1721no—
1156C2×C4—1721no—
1157C2×C4—1722no—
1158C2×C4—1722no—
1159C2×C4—1721no—
1160C2×C4—1721no—
1161C2×C4—1721no—
1162C2×C4—1728no—
1163C2×C4—1721no—
1164C2×C4—1721no—
1165C2×C4—1721no—
1166C2×C4C22⋊C4×D4311yescharacteristic
1167C2×C4C22⋊C4×D4311yescharacteristic
1168C2×C4C22×C4×D4311yescharacteristic
1169C2×C4C2×D4×D4311yescharacteristic
1170C2×C4C2×D4×D4311yescharacteristic
1171C2×C4#41×D4311yescharacteristic
1172C2×C4#1306337011yescharacteristic
1173C2×C4#1306337111yescharacteristic
1174C8—22no—
1175C8—41no—
1176C8—1721no—
1177C8—1721no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—42no—
1186C22—42no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—861no—
1191C22—861no—
1192C22—862no—
1193C22—861no—
1194C22—861no—
1195C22—861no—
1196C22—861no—
1197C22—3444no—
1198C22—3441no—
1199C22—3441no—
1200C22—3444no—
1201C22—1721no—
1202C22—1721no—
1203C22—1721no—
1204C22—1721no—
1205C22—1721no—
1206C22#1458291412yescomplemented
1207C22C2×C22⋊C4×D4311yescharacteristic
1208C22#1458353311yescharacteristic
1209C22#1458353811yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—81no—
1216C4—81no—
1217C4—861no—
1218C4—861no—
1219C4—862no—
1220C4—861no—
1221C4—861no—
1222C4—861no—
1223C4—861no—
1224C4—1722no—
1225C4—1722no—
1226C4—1721no—
1227C4C4×D4×D4311yescharacteristic
1228C4#1458337111yescharacteristic
1229C4#1458353111yescharacteristic
1230C4#1458354111yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—22no—
1234C2—41no—
1235C2—81no—
1236C2—3441no—
1237C2—1721no—
1238C2—1721no—
1239C2—1722no—
1240C2#1913741311yescharacteristic
1241C2C2×#1458291411yescharacteristic
1242C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1871C2
socleC22×C43C22×C22⋊C4
prime radical#19148078C2
cosocleC22×C4×C43C24
hypercenter#1871D43
hypocenterC43#22434
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D43C2semidirect
3. C2×#14582914C2semidirect
4. C22×#13063251C2semidirect
5. #19137034C2semidirect
6. #19135512C2semidirect
7. #19135425C2semidirect
8. #19135042C2semidirect
9. #19135039C2semidirect
10. #19134896C2semidirect
11. #19134614C2semidirect
12. #19134540C2semidirect
13. #19134537C2semidirect
14. #19134404C2semidirect
15. C43×#1871C2semidirect
18. C2×M16×D43C22semidirect
19. #14583567C4semidirect
20. #14583562C4semidirect
21. #14583559C4semidirect
22. #14583555C4semidirect
23. #14583551C4semidirect
25. #14583546C4semidirect
27. #14583540C4semidirect
29. #14583533C4semidirect
39. C2×#13063282C22semidirect
40. C22×C4×Dic43C22semidirect
45. #14582922C22semidirect
49. C2×#13063253C22semidirect
50. C2×#13063253C22semidirect
51. C2×#13063252C22semidirect
52. C2×#13063252C22semidirect
56. C2×#13063251C22semidirect
57. C2×#13063251C22semidirect
58. #14582863C22semidirect
59. #14582862C22semidirect
60. M16×Dic43C22semidirect
65. C4×Dic43⋊C4C22semidirect
66. C4×(C2×D43)⋊C4C22semidirect
67. #14582745C22semidirect
68. #14582658C22semidirect
69. #14582658C22semidirect
70. C22×M16×C43C22semidirect
72. C2×#104×C43C22semidirect
73. C2×#104×C43C22semidirect
74. C4×C22⋊C4×C43C22semidirect
75. C43×#339C22semidirect
76. C43×#339C22semidirect
77. C2×#10621902C2×C4semidirect
90. C2×#10621900C2×C4semidirect
96. C2×Q8×D43C2×C4semidirect
102. C2×D4×D43C2×C4semidirect
114. #13063323C2×C4semidirect
116. #13063321C2×C4semidirect
117. #13063314C2×C4semidirect
118. #13063312C2×C4semidirect
126. #13063305C2×C4semidirect
127. #13063305C2×C4semidirect
133. #13063300C2×C4semidirect
134. #13063300C2×C4semidirect
149. #13063290C2×C4semidirect
150. #13063290C2×C4semidirect
155. #13063287C2×C4semidirect
156. #13063287C2×C4semidirect
202. #13063251D4semidirect
356. M16×C43C2×D4semidirect
417. C4×Dic43C2×D4semidirect
569. C22×C43#421semidirect
620. #1871D43semidirect
640. C22×M16C2×D43semidirect
681. C2×#104C2×D43semidirect
682. C2×#104C2×D43semidirect
692. C4×C22⋊C4C2×D43semidirect
696. #339C2×D43semidirect
697. #339C2×D43semidirect
698. C43#22434semidirect
983. M16D4×D43semidirect
1206. C22#14582914semidirect

Maximal subgroups

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

subgroupindex
#191480782
M16×C22⋊D432
C2×#145829142
C22×#130632512
#191370342
#191355122
#191354252
#191350422
#191350392
#191348962
#191346142
#191345402
#191345372
#191344042
C43×#18712
#2243443