Finite Group Databasebeta

← #25112277

Subgroups — #25112277

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
2#19143327C211yesmaximal, characteristic, complemented
3C2×#14582917C211yesmaximal, characteristic, complemented
4C2×#104×D43C211yesmaximal, characteristic, complemented
5#19137032C211yesmaximal, characteristic, complemented
6#19135512C211yesmaximal, characteristic, complemented
7#19135425C211yesmaximal, 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#19134404C211yesmaximal, characteristic, complemented
15C43×#1897C211yesmaximal, 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⋊D43C2211yescharacteristic
39C4×D4×D43—21no—
40C2×C42×D43C2211yescharacteristic, complemented
41#14582974—21no—
42#14582973—21no—
43#14582967—21no—
44(C22⋊D43)⋊C8—21no—
45#14582922C2211yescharacteristic, complemented
46#14582917—24no—
47C2×#13063253C2211yescharacteristic
48C2×#13063253C2211yescharacteristic
49C2×#13063253C2211yescharacteristic, complemented
50C2×#13063253C2211yescharacteristic, complemented
51C2×#13063252C2211yescharacteristic, complemented
52C2×#13063252C2211yescharacteristic, complemented
53C2×#13063251C2211yescharacteristic
54C2×#13063251C2211yescharacteristic
55C2×#13063251C2211yescharacteristic, complemented
56C2×#13063251C2211yescharacteristic, complemented
57#104×D43—24no—
58#14582862C2211yescharacteristic, complemented
59M16×Dic43C2211yescharacteristic, complemented
60#14582787—21no—
61#14582780—21no—
62#14582775—21no—
63#14582770—21no—
64C4×Dic43⋊C4C2211yescharacteristic, complemented
65C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
66C4×C22⋊Dic43C2211yescharacteristic, complemented
67#14582745C2211yescharacteristic, complemented
68#14582658C2211yescharacteristic, complemented
69#14582658C2211yescharacteristic, complemented
70C43×#525C2211yescharacteristic
71C2×#117×C43C2211yescharacteristic, complemented
72C2×#104×C43C2211yescharacteristic, complemented
73C2×#104×C43C2211yescharacteristic, complemented
74C43×#407C2211yescharacteristic, complemented
75C43×#339C2211yescharacteristic, complemented
76C43×#339C2211yescharacteristic, complemented
77C2×#10621902C2×C411yescharacteristic
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
91#41×D43—22no—
92#41×D43—22no—
93#41×D43—41no—
94#41×D43—41no—
95C22×Dic86C2×C411yescharacteristic, complemented
96C2×Q8×D43C2×C411yescharacteristic
97C22×D172C2×C411yescharacteristic, complemented
98C22×C22⋊D43—21no—
99C22×C22⋊D43D411yescharacteristic
100C2×D4×D43—21no—
101C2×D4×D43—21no—
102C2×D4×D43C2×C411yescharacteristic
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
131#13063305C2×C411yescharacteristic
132#13063303—21no—
133#13063303—21no—
134#13063302—21no—
135#13063302—21no—
136#13063300—21no—
137#13063300C2×C411yescharacteristic
138#13063300C2×C411yescharacteristic
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—21no—
162C4×C22⋊D43—21no—
163C4×C22⋊D43C2×C411yescharacteristic
164C4×C22⋊D43C2×C411yescharacteristic
165C4×C22⋊D43C2×C411yescharacteristic
166C4×C22⋊D43C2×C411yescharacteristic
167C4×C22⋊D43D411yescharacteristic
168C4×C22⋊D43D411yescharacteristic
169C4×C22⋊D43D411yescharacteristic
170C4×C22⋊D43D411yescharacteristic
171(C22⋊D43)⋊C4—21no—
172(C22⋊D43)⋊C4—21no—
173(C22⋊D43)⋊C4—21no—
174(C22⋊D43)⋊C4—21no—
175#13063282—21no—
176C2×Dic43⋊C4—21no—
177C2×Dic43⋊C4D411yescharacteristic
178C4⋊C4×D43—21no—
179C2×C22⋊Dic43—21no—
180C2×C22⋊Dic43D411yescharacteristic
181C2×(C2×D43)⋊C4—21no—
182C2×(C2×D43)⋊C4D411yescharacteristic
183C22⋊C4×D43—21no—
184C22⋊C4×D43—21no—
185C2×C4×Dic43—21no—
186C2×C4×Dic43C2311yescharacteristic
187C2×C4×Dic43C2311yescharacteristic
188C2×C4×Dic43C2311yescharacteristic
189C42×D43—21no—
190C42×D43—22no—
191C42×D43—41no—
192Dic43⋊C8—21no—
193Dic43⋊C8—21no—
194#13063253—22no—
195#13063253—22no—
196#13063253—22no—
197#13063253D414yescomplemented
198#13063252—22no—
199#13063252—41no—
200#13063251—22no—
201#13063251—22no—
202#13063251—41no—
203#13063251—41no—
204(C2×D43)⋊C8—21no—
205(C2×D43)⋊C8—21no—
206#13063235—21no—
207C8×Dic43—21no—
208C43⋊#95—21no—
209C43⋊#95—21no—
210C43⋊#95—21no—
211C43⋊#95—21no—
212C43⋊#95—21no—
213C2×#41×C43C2311yescharacteristic
214C23×C4×C43C2311yescharacteristic
215C2×M16×C43C2311yescharacteristic
216C2×M16×C43C2311yescharacteristic
217#123×C43—21no—
218C22⋊Q8×C43C2×C411yescharacteristic, complemented
219C22⋊Q8×C43C2×C411yescharacteristic, complemented
220#121×C43C2×C411yescharacteristic, complemented
221#121×C43C2×C411yescharacteristic, complemented
222#120×C43—21no—
223C4×D4×C43—21no—
224C4×D4×C43—21no—
225#117×C43—22no—
226#117×C43—41no—
227#117×C43C2311yescharacteristic
228C2×C4⋊C4×C43—21no—
229C2×C22⋊C4×C43—21no—
230C2×C42×C43C2311yescharacteristic
231C2×C42×C43C2311yescharacteristic
232#104×C43—22no—
233#104×C43—41no—
234C22⋊C8×C43—21no—
235C22⋊C8×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×Dic43C2×D411yescharacteristic
282C22×Dic43C2×D411yescharacteristic
283C22×Dic43C2×D411yescharacteristic
284#10621902—22no—
285#10621902—41no—
286Q8×D43—22no—
287Q8×D43—41no—
288#10621900—22no—
289#10621900—41no—
290#10621900—42no—
291#10621900—42no—
292D4×D43—22no—
293D4×D43—42no—
294D4×D43—42no—
295D4×D43—41no—
296D4×D43—44no—
297#10621898—21no—
298#10621898—21no—
299#10621898—21no—
300#10621898—21no—
301#10621898—21no—
302#10621898—21no—
303#10621898—22no—
304#10621898—22no—
305#10621898—41no—
306#10621898—41no—
307#10621898—42no—
308#10621898—42no—
309#10621898—42no—
310#10621898—42no—
311#10621898—42no—
312#10621898—42no—
313#10621898C2×D412yes—
314#10621898#4112yes—
315C2×D172—21no—
316C2×D172—21no—
317C2×D172—21no—
318C2×D172—21no—
319C2×D172—22no—
320C2×D172—41no—
321C2×D172C22×C411yescharacteristic
322C2×D172C22×C411yescharacteristic
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—21no—
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×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—21no—
356C2×C8×C43—21no—
357C2×C8×C43—21no—
358C4⋊C4×C43—21no—
359C4⋊C4×C43—21no—
360C4⋊C4×C43—42no—
361C4⋊C4×C43C22×C411yescharacteristic
362C4⋊C4×C43C22×C411yescharacteristic
363C22⋊C4×C43—21no—
364C22⋊C4×C43—21no—
365C22⋊C4×C43—21no—
366C22⋊C4×C43—21no—
367C22⋊C4×C43—21no—
368C22⋊C4×C43—42no—
369C42×C43—21no—
370C42×C43—21no—
371C42×C43—21no—
372C42×C43—21no—
373C42×C43C2×D412yescomplemented
374C22⋊Dic43—21no—
375C22⋊Dic43—21no—
376C22⋊Dic43—42no—
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)⋊C4C22⋊C411yescharacteristic
391(C2×D43)⋊C4C22⋊C411yescharacteristic
392(C2×D43)⋊C4C22⋊C411yescharacteristic
393(C2×D43)⋊C4C22⋊C411yescharacteristic
394C4⋊Dic43—21no—
395C4⋊Dic43—21no—
396Dic43⋊C4—21no—
397Dic43⋊C4—21no—
398Dic43⋊C4—21no—
399Dic43⋊C4—21no—
400Dic43⋊C4—42no—
401Dic43⋊C4C22⋊C411yescharacteristic
402Dic43⋊C4C22⋊C411yescharacteristic
403Dic43⋊C4C22⋊C411yescharacteristic
404Dic43⋊C4C22⋊C411yescharacteristic
405C4×Dic43—21no—
406C4×Dic43—21no—
407C4×Dic43—21no—
408C4×Dic43—21no—
409C4×Dic43—21no—
410C4×Dic43—21no—
411C4×Dic43—42no—
412C4×Dic43C22×C411yescharacteristic
413C4×Dic43C22×C411yescharacteristic
414C4×Dic43C2×D411yescharacteristic
415C4×Dic43C2×D411yescharacteristic
416#10621877—21no—
417#10621877—21no—
418#10621877—21no—
419#10621877—42no—
420#10621877C2×D412yescomplemented
421C2×C43⋊C8—21no—
422C2×C43⋊C8—21no—
423C2×C43⋊C8—42no—
424#10621872—42no—
425C8×D43—42no—
426C23×C43—21no—
427C23×C43—21no—
428C23×C43—21no—
429C23×C43—41no—
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—22no—
438C22×D43—21no—
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—42no—
453D4×C43—41no—
454D4×C43—41no—
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—22no—
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—41no—
505C2×Dic43—41no—
506C2×Dic43—42no—
507C2×Dic43—42no—
508C2×Dic43—41no—
509C2×Dic43—41no—
510C2×Dic43—41no—
511C2×Dic43—41no—
512C2×Dic43—41no—
513C2×Dic43C2×C22⋊C411yescharacteristic
514C2×Dic43C2×C22⋊C411yescharacteristic
515C2×Dic43C2×C22⋊C411yescharacteristic
516C2×Dic43C2×C22⋊C411yescharacteristic
517C2×Dic43C2×C22⋊C411yescharacteristic
518C2×Dic43C2×C22⋊C411yescharacteristic
519D172—21no—
520D172—21no—
521D172—21no—
522D172—42no—
523D172—42no—
524D172—42no—
525D172—81no—
526D172C4×D412yes—
527C4×D43—21no—
528C4×D43—21no—
529C4×D43—21no—
530C4×D43—21no—
531C4×D43—21no—
532C4×D43—21no—
533C4×D43—22no—
534C4×D43—21no—
535C4×D43—21no—
536C4×D43—22no—
537C4×D43—42no—
538C4×D43—42no—
539C4×D43—42no—
540C4×D43—42no—
541C4×D43—42no—
542C4×D43—48no—
543C4×D43—41no—
544C4×D43—41no—
545C4×D43—81no—
546Dic86—21no—
547Dic86—21no—
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—21no—
560C22×C43—21no—
561C22×C43—21no—
562C22×C43—21no—
563C22×C43—21no—
564C22×C43—21no—
565C22×C43—41no—
566C22×C43—41no—
567C22×C43—41no—
568C22×C43—81no—
569C22×C43—81no—
570C22×C43C22×C22⋊C411yescharacteristic
571C22×C43D4211yescharacteristic
572C22×C43#54611yescharacteristic
573C2×D43—21no—
574C2×D43—21no—
575C2×D43—21no—
576C2×D43—22no—
577C2×D43—21no—
578C2×D43—21no—
579C2×D43—42no—
580C2×D43—42no—
581C2×D43—41no—
582C2×D43—41no—
583C2×D43—41no—
584C2×D43—41no—
585C2×D43—41no—
586C2×D43—84no—
587C2×D43—84no—
588C2×D43#42112yescomplemented
589C4×C43—21no—
590C4×C43—21no—
591C4×C43—42no—
592C4×C43—41no—
593C4×C43—41no—
594C4×C43—41no—
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—41no—
609Dic43—81no—
610D4×#41—431no—
611D4×M16—431no—
612C2×#421—431no—
613C22×#104—431no—
614#2290—431no—
615#1980—431no—
616#1963—431no—
617#1897D4311yescharacteristic, complemented
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—41no—
628C2×C43—41no—
629C2×C43—81no—
630C2×C43D4×C22⋊C411yescharacteristic
631C2×C43C2×#42111yescharacteristic
632C2×C43#290111yescharacteristic
633D43—22no—
634D43—41no—
635D43—42no—
636D43—81no—
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—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×#117C2×D4311yescharacteristic, complemented
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#407C2×D4311yescharacteristic, complemented
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#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—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—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, complemented
764C22⋊Q8C4×D4311yescharacteristic, complemented
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, complemented
778#121C4×D4311yescharacteristic, complemented
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—22no—
810#117—41no—
811#117—861no—
812#117C22×D4311yescharacteristic
813C2×C4⋊C4—21no—
814C2×C4⋊C4—431no—
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—21no—
848C22⋊C8—21no—
849C22⋊C8—861no—
850C22⋊C8—861no—
851#97—861no—
852C4×C8—861no—
853#95—861no—
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—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—42no—
993C4⋊C4—431no—
994C4⋊C4—431no—
995C4⋊C4—431no—
996C4⋊C4—431no—
997C4⋊C4—861no—
998C4⋊C4—861no—
999C4⋊C4—861no—
1000C4⋊C4—861no—
1001C4⋊C4—861no—
1002C4⋊C4—861no—
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—431no—
1037C42—431no—
1038C42—431no—
1039C42—431no—
1040C42—861no—
1041C42—861no—
1042C42—861no—
1043C42—861no—
1044C42—861no—
1045C42—861no—
1046C42—1722no—
1047C42D4×D4312yescomplemented
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—41no—
1052C23—41no—
1053C23—431no—
1054C23—431no—
1055C23—862no—
1056C23—861no—
1057C23—861no—
1058C23—861no—
1059C23—861no—
1060C23—3441no—
1061C23—3441no—
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—22no—
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—3441no—
1149C2×C4—1722no—
1150C2×C4—1722no—
1151C2×C4—1722no—
1152C2×C4—1722no—
1153C2×C4—1722no—
1154C2×C4—1728no—
1155C2×C4—1721no—
1156C2×C4—1721no—
1157C2×C4—1722no—
1158C2×C4—1722no—
1159C2×C4—1721no—
1160C2×C4—1721no—
1161C2×C4—1721no—
1162C2×C4—1721no—
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—41no—
1175C8—41no—
1176C8—862no—
1177C8—1721no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—81no—
1190C22—81no—
1191C22—432no—
1192C22—861no—
1193C22—861no—
1194C22—861no—
1195C22—862no—
1196C22—861no—
1197C22—861no—
1198C22—3444no—
1199C22—3444no—
1200C22—1722no—
1201C22—1722no—
1202C22—1721no—
1203C22—1721no—
1204C22—1721no—
1205C22—1721no—
1206C22—1721no—
1207C22C2×C22⋊C4×D4311yescharacteristic
1208C22#1458353111yescharacteristic
1209C22#1458354111yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—42no—
1213C4—41no—
1214C4—41no—
1215C4—41no—
1216C4—81no—
1217C4—861no—
1218C4—861no—
1219C4—862no—
1220C4—861no—
1221C4—861no—
1222C4—861no—
1223C4—861no—
1224C4—3441no—
1225C4—1722no—
1226C4—1721no—
1227C4C4×D4×D4311yescharacteristic
1228C4#1458337111yescharacteristic
1229C4#1458353311yescharacteristic
1230C4#1458353811yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—41no—
1234C2—41no—
1235C2—81no—
1236C2—862no—
1237C2—3441no—
1238C2—1721no—
1239C2—1722no—
1240C2#1913741311yescharacteristic
1241C2#421×D4311yescharacteristic
1242C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1897C2
socleC22×C43C22×C22⋊C4
prime radical#19148078C2
cosocleC22×C4×C43C24
hypercenter#1897D43
hypocenterC43#22434
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1897

Complements

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

NH ≅ G/Ntype
2. #19143327C2semidirect
3. C2×#14582917C2semidirect
4. C2×#104×D43C2semidirect
5. #19137032C2semidirect
6. #19135512C2semidirect
7. #19135425C2semidirect
8. #19135037C2semidirect
9. #19134898C2semidirect
10. #19134896C2semidirect
11. #19134614C2semidirect
12. #19134538C2semidirect
13. #19134537C2semidirect
14. #19134404C2semidirect
15. C43×#1897C2semidirect
18. C22×#10621877C22semidirect
19. C2×M16×D43C22semidirect
20. #14583567C4semidirect
21. #14583562C4semidirect
22. #14583559C4semidirect
23. #14583555C4semidirect
24. #14583551C4semidirect
26. #14583546C4semidirect
28. #14583540C4semidirect
30. #14583533C4semidirect
40. C2×C42×D43C22semidirect
45. #14582922C22semidirect
49. C2×#13063253C22semidirect
50. C2×#13063253C22semidirect
51. C2×#13063252C22semidirect
52. C2×#13063252C22semidirect
55. C2×#13063251C22semidirect
56. C2×#13063251C22semidirect
58. #14582862C22semidirect
59. M16×Dic43C22semidirect
64. C4×Dic43⋊C4C22semidirect
65. C4×(C2×D43)⋊C4C22semidirect
66. C4×C22⋊Dic43C22semidirect
67. #14582745C22semidirect
68. #14582658C22semidirect
69. #14582658C22semidirect
71. C2×#117×C43C22semidirect
72. C2×#104×C43C22semidirect
73. C2×#104×C43C22semidirect
74. C43×#407C22semidirect
75. C43×#339C22semidirect
76. C43×#339C22semidirect
85. C2×#10621898C2×C4semidirect
86. C2×#10621898C2×C4semidirect
95. C22×Dic86C2×C4semidirect
97. C22×D172C2×C4semidirect
118. #13063323C2×C4semidirect
120. #13063321C2×C4semidirect
121. #13063314C2×C4semidirect
122. #13063312C2×C4semidirect
153. #13063290C2×C4semidirect
154. #13063290C2×C4semidirect
159. #13063287C2×C4semidirect
160. #13063287C2×C4semidirect
197. #13063253D4semidirect
218. C22⋊Q8×C43C2×C4semidirect
219. C22⋊Q8×C43C2×C4semidirect
220. #121×C43C2×C4semidirect
221. #121×C43C2×C4semidirect
373. C42×C43C2×D4semidirect
420. #10621877C2×D4semidirect
588. C2×D43#421semidirect
617. #1897D43semidirect
662. C2×#117C2×D43semidirect
681. C2×#104C2×D43semidirect
682. C2×#104C2×D43semidirect
684. #407C2×D43semidirect
696. #339C2×D43semidirect
697. #339C2×D43semidirect
698. C43#22434semidirect
763. C22⋊Q8C4×D43semidirect
764. C22⋊Q8C4×D43semidirect
777. #121C4×D43semidirect
778. #121C4×D43semidirect
1047. C42D4×D43semidirect

Maximal subgroups

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

subgroupindex
#191480782
#191433272
C2×#145829172
C2×#104×D432
#191370322
#191355122
#191354252
#191350372
#191348982
#191348962
#191346142
#191345382
#191345372
#191344042
C43×#18972
#2243443