Finite Group Databasebeta

← #25112269

Subgroups — #25112269

Order 11008.

1608 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148078C211yesmaximal, characteristic
2M16×C22⋊D43C211yesmaximal, characteristic, complemented
3C22×#13063251C211yesmaximal, characteristic, complemented
4C2×#104×D43C211yesmaximal, characteristic, complemented
5C4×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
6#19135512C211yesmaximal, characteristic, complemented
7#19135421C211yesmaximal, characteristic, complemented
8#19135039C211yesmaximal, characteristic, complemented
9#19135037C211yesmaximal, characteristic, complemented
10#19134896C211yesmaximal, characteristic, complemented
11#19134614C211yesmaximal, characteristic, complemented
12#19134540C211yesmaximal, characteristic, complemented
13#19134537C211yesmaximal, characteristic, complemented
14#19134399C211yesmaximal, 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
38C2×(C22⋊D43)⋊C4—21no—
39C4×D4×D43—21no—
40C22×C4×Dic43C2211yescharacteristic, complemented
41C2×C42×D43C2211yescharacteristic, complemented
42#14582975—21no—
43#14582970—21no—
44#14582968—21no—
45C8×C22⋊D43—21no—
46#14582922C2211yescharacteristic, complemented
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#104×D43—24no—
59#14582863C2211yescharacteristic, complemented
60#14582862C2211yescharacteristic, complemented
61M16×Dic43C2211yescharacteristic, complemented
62C4×Dic43⋊C4C2211yescharacteristic, complemented
63#14582750—21no—
64C22⋊C4×Dic43—21no—
65C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
66#14582746—21no—
67C42×Dic43C2211yescharacteristic, 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, complemented
86C2×#10621898C2×C411yescharacteristic, complemented
87C2×#10621898C2311yescharacteristic
88C2×#10621898C2311yescharacteristic
89C2×#10621900—21no—
90C2×#10621900C2×C411yescharacteristic, complemented
91#41×D43—22no—
92#41×D43—22no—
93#41×D43—41no—
94#41×D43—41no—
95C22×Dic86C2×C411yescharacteristic, complemented
96C2×Q8×D43C2×C411yescharacteristic, complemented
97C22×D172C2×C411yescharacteristic, complemented
98C22×C22⋊D43—21no—
99C22×C22⋊D43D411yescharacteristic
100C2×D4×D43—21no—
101C2×D4×D43—21no—
102C2×D4×D43C2×C411yescharacteristic, complemented
103C23×Dic43—21no—
104C22×C4×D43—21no—
105C22×C4×D43—21no—
106C22×C4×D43—21no—
107C22×C4×D43C2311yescharacteristic
108C2×#10621877C2311yescharacteristic
109C2×#10621877C2311yescharacteristic
110C2×#10621872—21no—
111M16×D43—22no—
112M16×D43—41no—
113C2×C8×D43—21no—
114#13063324—21no—
115#13063323C2×C411yescharacteristic, complemented
116#13063321—21no—
117#13063321C2×C411yescharacteristic, complemented
118#13063314C2×C411yescharacteristic, complemented
119#13063312C2×C411yescharacteristic, complemented
120#13063311—21no—
121#13063311—21no—
122#13063310—21no—
123#13063310—21no—
124#13063309—21no—
125#13063307—21no—
126#13063307—21no—
127#13063305C2×C411yescharacteristic, complemented
128#13063305C2×C411yescharacteristic, complemented
129#13063303—21no—
130#13063303—21no—
131#13063302—21no—
132#13063302—21no—
133#13063300—21no—
134#13063300C2×C411yescharacteristic, complemented
135#13063300C2×C411yescharacteristic, complemented
136#13063298—21no—
137#13063298—21no—
138#13063298—21no—
139#13063298—21no—
140#13063297—21no—
141#13063297—21no—
142#13063297—21no—
143#13063297—21no—
144#13063296—21no—
145#13063295—21no—
146#13063295—21no—
147#13063295—21no—
148#13063293—21no—
149#13063293—21no—
150#13063290C2×C411yescharacteristic, complemented
151#13063290C2×C411yescharacteristic, complemented
152C4×D172—21no—
153C4×D172—21no—
154D4×Dic43—21no—
155#13063287—21no—
156#13063287C2×C411yescharacteristic, complemented
157#13063287C2×C411yescharacteristic, complemented
158C4×C22⋊D43—21no—
159C4×C22⋊D43—21no—
160C4×C22⋊D43C2×C411yescharacteristic
161C4×C22⋊D43C2×C411yescharacteristic
162C4×C22⋊D43C2×C411yescharacteristic
163C4×C22⋊D43C2×C411yescharacteristic
164C4×C22⋊D43D411yescharacteristic
165C4×C22⋊D43D411yescharacteristic
166C4×C22⋊D43D411yescharacteristic
167C4×C22⋊D43D411yescharacteristic
168(C22⋊D43)⋊C4—28no—
169(C22⋊D43)⋊C4—21no—
170(C22⋊D43)⋊C4—21no—
171(C22⋊D43)⋊C4—21no—
172(C22⋊D43)⋊C4—21no—
173#13063282—21no—
174C2×Dic43⋊C4—21no—
175C2×Dic43⋊C4D411yescharacteristic
176C4⋊C4×D43—21no—
177C2×C22⋊Dic43D411yescharacteristic
178C2×(C2×D43)⋊C4—21no—
179C2×(C2×D43)⋊C4D411yescharacteristic
180C22⋊C4×D43—21no—
181C22⋊C4×D43—21no—
182C2×C4×Dic43—21no—
183C2×C4×Dic43—22no—
184C2×C4×Dic43—21no—
185C2×C4×Dic43—21no—
186C2×C4×Dic43—21no—
187C2×C4×Dic43—41no—
188C2×C4×Dic43C2311yescharacteristic
189C2×C4×Dic43C2311yescharacteristic
190C2×C4×Dic43C2311yescharacteristic
191C42×D43—21no—
192C42×D43—22no—
193C42×D43—41no—
194Dic43⋊C8—21no—
195Dic43⋊C8—21no—
196#13063253—22no—
197#13063253—22no—
198#13063253—41no—
199#13063253—41no—
200#13063252—22no—
201#13063252—41no—
202#13063251—22no—
203#13063251—22no—
204#13063251—22no—
205#13063251D414yescomplemented
206C22⋊(C43⋊C8)—21no—
207C22⋊(C43⋊C8)—21no—
208(C2×D43)⋊C8—21no—
209(C2×D43)⋊C8—21no—
210#13063235—21no—
211C8×Dic43—21no—
212C43⋊#95—21no—
213C43⋊#95—21no—
214C2×#41×C43C2311yescharacteristic
215C23×C4×C43C2311yescharacteristic
216C2×M16×C43—21no—
217C2×M16×C43—22no—
218C2×M16×C43—41no—
219C2×M16×C43C2311yescharacteristic
220C2×M16×C43C2311yescharacteristic
221C22×C8×C43—21no—
222#123×C43—21no—
223C22⋊Q8×C43C2×C411yescharacteristic, complemented
224C22⋊Q8×C43C2×C411yescharacteristic, complemented
225#121×C43C2×C411yescharacteristic, complemented
226#121×C43C2×C411yescharacteristic, complemented
227#120×C43—21no—
228C4×D4×C43—21no—
229C4×D4×C43—21no—
230#117×C43C2311yescharacteristic
231C2×C22⋊C4×C43—21no—
232C2×C42×C43C2311yescharacteristic
233C2×C42×C43C2311yescharacteristic
234#104×C43—22no—
235#104×C43—41no—
236#95×C43—21no—
237C24×C43C2×D411yescharacteristic
238C23×D43—21no—
239C23×D43—21no—
240C23×D43C2×D411yescharacteristic
241#41×C43—21no—
242#41×C43—21no—
243#41×C43—21no—
244#41×C43—21no—
245C2×Q8×C43C22×C411yescharacteristic
246C2×D4×C43—21no—
247C2×D4×C43—21no—
248C2×D4×C43—21no—
249C2×D4×C43C22×C411yescharacteristic
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43C22×C411yescharacteristic
258C22×C4×C43C22×C411yescharacteristic
259C22×C4×C43C2×D411yescharacteristic
260C22×C4×C43C2×D411yescharacteristic
261C22×C4×C43C2×D411yescharacteristic
262C22×C4×C43C2411yescharacteristic
263C2×C22⋊D43—24no—
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—
272C2×C22⋊D43—42no—
273C2×C22⋊D43—42no—
274C2×C22⋊D43C22⋊C411yescharacteristic
275C2×C22⋊D43C22⋊C411yescharacteristic
276C2×C22⋊D43C22⋊C411yescharacteristic
277C2×C22⋊D43C22⋊C411yescharacteristic
278C22×Dic43—24no—
279C22×Dic43—21no—
280C22×Dic43—21no—
281C22×Dic43—21no—
282C22×Dic43—21no—
283C22×Dic43—42no—
284C22×Dic43—42no—
285C22×Dic43C2×D411yescharacteristic
286C22×Dic43C2×D411yescharacteristic
287C22×Dic43C2×D411yescharacteristic
288#10621902—22no—
289#10621902—41no—
290Q8×D43—22no—
291Q8×D43—41no—
292#10621900—22no—
293#10621900—41no—
294#10621900—42no—
295#10621900—42no—
296D4×D43—22no—
297D4×D43—42no—
298D4×D43—42no—
299D4×D43—41no—
300D4×D43—44no—
301#10621898—21no—
302#10621898—21no—
303#10621898—21no—
304#10621898—21no—
305#10621898—21no—
306#10621898—21no—
307#10621898—22no—
308#10621898—22no—
309#10621898—41no—
310#10621898—41no—
311#10621898—42no—
312#10621898—42no—
313#10621898—42no—
314#10621898—42no—
315#10621898—42no—
316#10621898—42no—
317#10621898C2×D412yes—
318#10621898#4112yes—
319C2×D172—21no—
320C2×D172—21no—
321C2×D172—21no—
322C2×D172—21no—
323C2×D172—22no—
324C2×D172—41no—
325C2×D172C22×C411yescharacteristic
326C2×D172C22×C411yescharacteristic
327C2×C4×D43—21no—
328C2×C4×D43—21no—
329C2×C4×D43—21no—
330C2×C4×D43—21no—
331C2×C4×D43—21no—
332C2×C4×D43—24no—
333C2×C4×D43—21no—
334C2×C4×D43—21no—
335C2×C4×D43—21no—
336C2×C4×D43—21no—
337C2×C4×D43—21no—
338C2×C4×D43—21no—
339C2×C4×D43—21no—
340C2×C4×D43—42no—
341C2×C4×D43—42no—
342C2×C4×D43—42no—
343C2×C4×D43—42no—
344C2×C4×D43—42no—
345C2×C4×D43—42no—
346C2×C4×D43C22×C411yescharacteristic
347C2×C4×D43C22×C411yescharacteristic
348C2×C4×D43C2×D411yescharacteristic
349C2×C4×D43C2×D411yescharacteristic
350C2×Dic86—22no—
351C2×Dic86—21no—
352C2×Dic86—21no—
353C2×Dic86—41no—
354C2×Dic86C22×C411yescharacteristic
355C2×Dic86C22×C411yescharacteristic
356M16×C43—21no—
357M16×C43—21no—
358M16×C43—21no—
359M16×C43—42no—
360M16×C43C2×D412yescomplemented
361C2×C8×C43—21no—
362C2×C8×C43—21no—
363C2×C8×C43—42no—
364C4⋊C4×C43—21no—
365C4⋊C4×C43—21no—
366C4⋊C4×C43C22×C411yescharacteristic
367C4⋊C4×C43C22×C411yescharacteristic
368C22⋊C4×C43—24no—
369C22⋊C4×C43—21no—
370C22⋊C4×C43—21no—
371C22⋊C4×C43—21no—
372C22⋊C4×C43—21no—
373C22⋊C4×C43—21no—
374C42×C43—21no—
375C42×C43—21no—
376C42×C43—21no—
377C42×C43—21no—
378C42×C43—21no—
379C22⋊Dic43—21no—
380C22⋊Dic43—21no—
381C22⋊Dic43C22⋊C411yescharacteristic
382C22⋊Dic43C22⋊C411yescharacteristic
383C22⋊Dic43C22⋊C411yescharacteristic
384C22⋊Dic43C22⋊C411yescharacteristic
385(C2×D43)⋊C4—24no—
386(C2×D43)⋊C4—21no—
387(C2×D43)⋊C4—21no—
388(C2×D43)⋊C4—21no—
389(C2×D43)⋊C4—21no—
390(C2×D43)⋊C4—21no—
391(C2×D43)⋊C4—21no—
392(C2×D43)⋊C4—21no—
393(C2×D43)⋊C4—21no—
394(C2×D43)⋊C4C22⋊C411yescharacteristic
395(C2×D43)⋊C4C22⋊C411yescharacteristic
396(C2×D43)⋊C4C22⋊C411yescharacteristic
397(C2×D43)⋊C4C22⋊C411yescharacteristic
398C4⋊Dic43—21no—
399C4⋊Dic43—21no—
400Dic43⋊C4—24no—
401Dic43⋊C4—21no—
402Dic43⋊C4—21no—
403Dic43⋊C4—21no—
404Dic43⋊C4—21no—
405Dic43⋊C4C22⋊C411yescharacteristic
406Dic43⋊C4C22⋊C411yescharacteristic
407Dic43⋊C4C22⋊C411yescharacteristic
408Dic43⋊C4C22⋊C411yescharacteristic
409C4×Dic43—24no—
410C4×Dic43—21no—
411C4×Dic43—21no—
412C4×Dic43—21no—
413C4×Dic43—21no—
414C4×Dic43—21no—
415C4×Dic43—42no—
416C4×Dic43—42no—
417C4×Dic43—42no—
418C4×Dic43C22×C411yescharacteristic
419C4×Dic43C22×C411yescharacteristic
420C4×Dic43C2×D411yescharacteristic
421C4×Dic43C2×D411yescharacteristic
422C4×Dic43C2×D412yescomplemented
423#10621877—21no—
424#10621877—21no—
425#10621877—21no—
426#10621877—21no—
427C2×C43⋊C8—21no—
428C2×C43⋊C8—21no—
429#10621872—42no—
430C8×D43—42no—
431C23×C43—21no—
432C23×C43—21no—
433C23×C43—22no—
434C23×C43—21no—
435C23×C43—41no—
436C23×C43C2×C22⋊C411yescharacteristic
437C23×C43C2×C22⋊C411yescharacteristic
438C23×C43C22×D411yescharacteristic
439C22×D43—21no—
440C22×D43—21no—
441C22×D43—21no—
442C22×D43—22no—
443C22×D43—21no—
444C22×D43—41no—
445C22×D43—42no—
446C22×D43—42no—
447C22×D43—42no—
448C22×D43—42no—
449C22×D43—81no—
450C22×D43—81no—
451C22×D43C2×C22⋊C411yescharacteristic
452C22×D43C2×C22⋊C411yescharacteristic
453Q8×C43—21no—
454Q8×C43—21no—
455D4×C43—21no—
456D4×C43—21no—
457D4×C43—41no—
458D4×C43—41no—
459D4×C43—42no—
460D4×C43—81no—
461C2×C4×C43—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—22no—
472C2×C4×C43—22no—
473C2×C4×C43—21no—
474C2×C4×C43—21no—
475C2×C4×C43—21no—
476C2×C4×C43—41no—
477C2×C4×C43—41no—
478C2×C4×C43—41no—
479C2×C4×C43—41no—
480C2×C4×C43—41no—
481C2×C4×C43—41no—
482C2×C4×C43C2×C22⋊C411yescharacteristic
483C2×C4×C43C2×C22⋊C411yescharacteristic
484C2×C4×C43C23×C411yescharacteristic
485C2×C4×C43C22×D411yescharacteristic
486C2×C4×C43C22×D411yescharacteristic
487C2×C4×C43C2×#4111yescharacteristic
488C2×C4×C43H(5,𝔽2)11yescharacteristic
489C2×C4×C43H(5,𝔽2)11yescharacteristic
490C22⋊D43—22no—
491C22⋊D43—22no—
492C22⋊D43—22no—
493C22⋊D43—22no—
494C22⋊D43—22no—
495C22⋊D43—42no—
496C22⋊D43—42no—
497C22⋊D43—42no—
498C22⋊D43—42no—
499C22⋊D43—41no—
500C22⋊D43—41no—
501C22⋊D43—42no—
502C22⋊D43—81no—
503C22⋊D43#10414yescomplemented
504C2×Dic43—22no—
505C2×Dic43—22no—
506C2×Dic43—21no—
507C2×Dic43—22no—
508C2×Dic43—21no—
509C2×Dic43—21no—
510C2×Dic43—22no—
511C2×Dic43—22no—
512C2×Dic43—21no—
513C2×Dic43—41no—
514C2×Dic43—42no—
515C2×Dic43—42no—
516C2×Dic43—48no—
517C2×Dic43—41no—
518C2×Dic43—41no—
519C2×Dic43C2×C22⋊C411yescharacteristic
520C2×Dic43C2×C22⋊C411yescharacteristic
521C2×Dic43C2×C22⋊C411yescharacteristic
522C2×Dic43C2×C22⋊C411yescharacteristic
523C2×Dic43C2×C22⋊C411yescharacteristic
524C2×Dic43C2×C22⋊C411yescharacteristic
525D172—21no—
526D172—21no—
527D172—21no—
528D172—42no—
529D172—42no—
530D172—42no—
531D172—81no—
532D172C4×D412yescomplemented
533C4×D43—21no—
534C4×D43—21no—
535C4×D43—21no—
536C4×D43—21no—
537C4×D43—21no—
538C4×D43—21no—
539C4×D43—22no—
540C4×D43—21no—
541C4×D43—21no—
542C4×D43—22no—
543C4×D43—42no—
544C4×D43—42no—
545C4×D43—42no—
546C4×D43—48no—
547C4×D43—42no—
548C4×D43—41no—
549C4×D43—41no—
550C4×D43—42no—
551C4×D43—81no—
552Dic86—21no—
553Dic86—21no—
554Dic86—21no—
555Dic86—42no—
556Dic86—42no—
557Dic86C4×D412yescomplemented
558C8×C43—22no—
559C8×C43—41no—
560C43⋊C8—41no—
561C43⋊C8—41no—
562D4×#104—431nomaximal, Sylow
563C22×C43—21no—
564C22×C43—21no—
565C22×C43—21no—
566C22×C43—21no—
567C22×C43—21no—
568C22×C43—21no—
569C22×C43—21no—
570C22×C43—42no—
571C22×C43—42no—
572C22×C43—41no—
573C22×C43—41no—
574C22×C43—41no—
575C22×C43C2×#10412yescomplemented
576C22×C43C22×C22⋊C411yescharacteristic
577C22×C43D4211yescharacteristic
578C22×C43#54611yescharacteristic
579C2×D43—21no—
580C2×D43—21no—
581C2×D43—21no—
582C2×D43—22no—
583C2×D43—21no—
584C2×D43—21no—
585C2×D43—42no—
586C2×D43—42no—
587C2×D43—41no—
588C2×D43—41no—
589C2×D43—41no—
590C2×D43—41no—
591C2×D43—41no—
592C2×D43—84no—
593C2×D43—84no—
594C2×D43C2×#10412yescomplemented
595C4×C43—21no—
596C4×C43—21no—
597C4×C43—42no—
598C4×C43—42no—
599C4×C43—41no—
600C4×C43—41no—
601C4×C43—41no—
602C4×C43C2×C4×D411yescharacteristic
603C4×C43#51811yescharacteristic
604C4×C43D4211yescharacteristic
605C4×C43#54611yescharacteristic
606Dic43—24no—
607Dic43—22no—
608Dic43—21no—
609Dic43—21no—
610Dic43—21no—
611Dic43—21no—
612Dic43—21no—
613Dic43—42no—
614Dic43—41no—
615Dic43C2×#10412yescomplemented
616D4×#41—431no—
617D4×M16—431no—
618C22×#104—431no—
619C22×#104—431no—
620C42×D4—431no—
621#1980—431no—
622#1962—431no—
623#1896—431no—
624#1896—431no—
625#1871—431no—
626#1871D4311yescharacteristic, complemented
627#1806—431no—
628#1789—431no—
629#1789—431no—
630C4×#104—431no—
631C2×C43—21no—
632C2×C43—21no—
633C2×C43—22no—
634C2×C43—41no—
635C2×C43—81no—
636C2×C43D4×C22⋊C411yescharacteristic
637C2×C43C22×#10411yescharacteristic
638C2×C43#290111yescharacteristic
639D43—22no—
640D43—41no—
641D43—42no—
642D43—81no—
643C22×#41—431no—
644C22×#41—431no—
645C22×M16—431no—
646C22×M16C2×D4311yescharacteristic, complemented
647#550—431no—
648D4×Q8—431no—
649#548—431no—
650#548—431no—
651#547—431no—
652#547—861no—
653#546—431no—
654#546—431no—
655#546—861no—
656#546—861no—
657D42—431no—
658D42—861no—
659#532—431no—
660#532—861no—
661#525—431no—
662#525—861no—
663#525—861no—
664#525C2×D4311yescharacteristic
665C4×#41—431no—
666C2×C4×D4—431no—
667C2×C4×D4—861no—
668C2×C4×D4—861no—
669C22×C42—431no—
670C22×C42—431no—
671#436—861no—
672#435—861no—
673#435—861no—
674C8×D4—861no—
675#423—431no—
676C2×#104—431no—
677C2×#104—431no—
678C2×#104—431no—
679C2×#104—431no—
680C2×#104—431no—
681C2×#104—431no—
682C2×#104—431no—
683C2×#104—431no—
684C2×#104—431no—
685C2×#104—431no—
686C2×#104—864no—
687C2×#104—864no—
688C2×#104C2×D4311yescharacteristic, complemented
689C2×#104C2×D4311yescharacteristic, complemented
690#407—431no—
691#407—431no—
692C4×M16—431no—
693C4×C4⋊C4—431no—
694C4×C4⋊C4—861no—
695C4×C22⋊C4—431no—
696C4×C22⋊C4—861no—
697C4×C22⋊C4—861no—
698C4×C22⋊C4C2×D4311yescharacteristic, complemented
699C43—431no—
700#339—431no—
701#339—431no—
702#339C2×D4311yescharacteristic, complemented
703#339C2×D4311yescharacteristic, complemented
704C43D4×#10411yescharacteristic, complemented, Sylow
705C2×#41—431no—
706C2×#41—431no—
707C2×#41—431no—
708C2×#41—431no—
709C2×#41—431no—
710C2×#41—431no—
711C2×#41—861no—
712C2×#41—862no—
713C2×#41—862no—
714C2×#41—861no—
715C2×#41—861no—
716C2×#41—861no—
717C2×#41—862no—
718C2×#41—862no—
719C2×#41—1721no—
720C2×#41—1721no—
721C2×#41—1721no—
722C2×#41—1721no—
723C2×#41C22×D4311yescharacteristic
724C22×Q8—431no—
725C22×Q8—431no—
726C22×D4—431no—
727C22×D4—431no—
728C22×D4—431no—
729C22×D4—861no—
730C22×D4—861no—
731C22×D4—861no—
732C23×C4—431no—
733C23×C4—861no—
734C23×C4—861no—
735C23×C4—861no—
736C23×C4—861no—
737C23×C4C22×D4311yescharacteristic
738C2×M16—21no—
739C2×M16—22no—
740C2×M16—41no—
741C2×M16—431no—
742C2×M16—431no—
743C2×M16—861no—
744C2×M16—862no—
745C2×M16—1721no—
746C2×M16C22×D4311yescharacteristic
747C2×M16C22×D4311yescharacteristic
748C22×C8—21no—
749C22×C8—861no—
750C4⋊Q8—431no—
751C4⋊Q8—861no—
752#127—431no—
753#127—861no—
754#124—431no—
755#124—431no—
756#124—861no—
757#124—861no—
758#123—21no—
759#123—861no—
760#123—861no—
761#123—861no—
762#123—861no—
763#123—861no—
764C22⋊Q8—431no—
765C22⋊Q8—431no—
766C22⋊Q8—861no—
767C22⋊Q8—861no—
768C22⋊Q8—861no—
769C22⋊Q8—861no—
770C22⋊Q8C4×D4311yescharacteristic, complemented
771C22⋊Q8C4×D4311yescharacteristic, complemented
772#121—431no—
773#121—431no—
774#121—861no—
775#121—861no—
776#121—861no—
777#121—861no—
778#121—861no—
779#121—861no—
780#121—861no—
781#121—861no—
782#121—861no—
783#121—861no—
784#121C4×D4311yescharacteristic, complemented
785#121C4×D4311yescharacteristic, complemented
786#120—21no—
787#120—861no—
788#120—861no—
789#120—861no—
790#120—861no—
791#120—861no—
792C4×Q8—431no—
793C4×Q8—431no—
794C4×D4—21no—
795C4×D4—21no—
796C4×D4—431no—
797C4×D4—431no—
798C4×D4—431no—
799C4×D4—431no—
800C4×D4—431no—
801C4×D4—431no—
802C4×D4—431no—
803C4×D4—431no—
804C4×D4—431no—
805C4×D4—431no—
806C4×D4—861no—
807C4×D4—861no—
808C4×D4—861no—
809C4×D4—861no—
810C4×D4—861no—
811C4×D4—861no—
812C4×D4—861no—
813C4×D4—861no—
814C4×D4—868no—
815C4×D4—861no—
816C4×D4—861no—
817#117—861no—
818#117C22×D4311yescharacteristic
819C2×C4⋊C4—431no—
820C2×C4⋊C4—861no—
821C2×C4⋊C4—861no—
822C2×C22⋊C4—21no—
823C2×C22⋊C4—431no—
824C2×C22⋊C4—431no—
825C2×C22⋊C4—861no—
826C2×C22⋊C4—861no—
827C2×C22⋊C4—861no—
828C2×C42—431no—
829C2×C42—431no—
830C2×C42—431no—
831C2×C42—861no—
832C2×C42—862no—
833C2×C42—862no—
834C2×C42—861no—
835C2×C42—861no—
836C2×C42—861no—
837C2×C42—861no—
838C2×C42—1721no—
839C2×C42—1721no—
840C2×C42C22×D4311yescharacteristic
841C2×C42C22×D4311yescharacteristic
842C4⋊C8—861no—
843C4⋊C8—861no—
844#104—22no—
845#104—41no—
846#104—434no—
847#104—862no—
848#104—862no—
849#104—862no—
850#104—862no—
851#104—862no—
852#104—862no—
853#104—1721no—
854#104—1721no—
855#104—1721no—
856C22⋊C8—861no—
857C22⋊C8—861no—
858C22⋊C8—861no—
859C22⋊C8—861no—
860#97—861no—
861C4×C8—861no—
862#95—21no—
863#95—861no—
864#95—861no—
865C24—431no—
866C24—861no—
867C24—861no—
868C24D4×D4311yescharacteristic
869#41—21no—
870#41—21no—
871#41—21no—
872#41—21no—
873#41—432no—
874#41—432no—
875#41—862no—
876#41—862no—
877#41—861no—
878#41—861no—
879#41—862no—
880#41—862no—
881#41—861no—
882#41—861no—
883#41—861no—
884#41—861no—
885#41—1722no—
886#41—1722no—
887#41—1721no—
888#41—1721no—
889#41—1722no—
890#41—1722no—
891#41—1722no—
892#41—1722no—
893#41—1721no—
894#41—1722no—
895#41—1722no—
896#41—1721no—
897C2×Q8—431no—
898C2×Q8—431no—
899C2×Q8—861no—
900C2×Q8—862no—
901C2×Q8—861no—
902C2×Q8—862no—
903C2×Q8—1721no—
904C2×Q8—1721no—
905C2×Q8C2×C4×D4311yescharacteristic
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—431no—
910C2×D4—431no—
911C2×D4—431no—
912C2×D4—431no—
913C2×D4—431no—
914C2×D4—431no—
915C2×D4—862no—
916C2×D4—861no—
917C2×D4—861no—
918C2×D4—861no—
919C2×D4—861no—
920C2×D4—861no—
921C2×D4—861no—
922C2×D4—862no—
923C2×D4—864no—
924C2×D4—861no—
925C2×D4—861no—
926C2×D4—861no—
927C2×D4—861no—
928C2×D4—861no—
929C2×D4—861no—
930C2×D4—1721no—
931C2×D4—1721no—
932C2×D4—1724no—
933C2×D4—1722no—
934C2×D4—1722no—
935C2×D4—1722no—
936C2×D4—1722no—
937C2×D4C2×C4×D4311yescharacteristic
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—431no—
946C22×C4—431no—
947C22×C4—431no—
948C22×C4—431no—
949C22×C4—431no—
950C22×C4—431no—
951C22×C4—431no—
952C22×C4—861no—
953C22×C4—861no—
954C22×C4—861no—
955C22×C4—861no—
956C22×C4—864no—
957C22×C4—861no—
958C22×C4—861no—
959C22×C4—861no—
960C22×C4—861no—
961C22×C4—861no—
962C22×C4—861no—
963C22×C4—861no—
964C22×C4—864no—
965C22×C4—861no—
966C22×C4—861no—
967C22×C4—861no—
968C22×C4—861no—
969C22×C4—861no—
970C22×C4—1722no—
971C22×C4—1722no—
972C22×C4—1722no—
973C22×C4—1722no—
974C22×C4—1722no—
975C22×C4—1722no—
976C22×C4—1722no—
977C22×C4—1722no—
978C22×C4C2×C4×D4311yescharacteristic
979C22×C4C2×C4×D4311yescharacteristic
980C22×C4D4×D4311yescharacteristic
981C22×C4D4×D4311yescharacteristic
982C22×C4D4×D4311yescharacteristic
983C22×C4C23×D4311yescharacteristic
984M16—21no—
985M16—21no—
986M16—21no—
987M16—42no—
988M16—861no—
989M16—861no—
990M16—861no—
991M16—861no—
992M16—1722no—
993M16D4×D4312yescomplemented
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—42no—
997C2×C8—861no—
998C2×C8—861no—
999C2×C8—1722no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—431no—
1003C4⋊C4—431no—
1004C4⋊C4—431no—
1005C4⋊C4—431no—
1006C4⋊C4—861no—
1007C4⋊C4—861no—
1008C4⋊C4—861no—
1009C4⋊C4—861no—
1010C4⋊C4—861no—
1011C4⋊C4—861no—
1012C4⋊C4—864no—
1013C4⋊C4C2×C4×D4311yescharacteristic
1014C4⋊C4C2×C4×D4311yescharacteristic
1015C22⋊C4—24no—
1016C22⋊C4—21no—
1017C22⋊C4—21no—
1018C22⋊C4—21no—
1019C22⋊C4—21no—
1020C22⋊C4—21no—
1021C22⋊C4—431no—
1022C22⋊C4—431no—
1023C22⋊C4—431no—
1024C22⋊C4—431no—
1025C22⋊C4—431no—
1026C22⋊C4—431no—
1027C22⋊C4—431no—
1028C22⋊C4—431no—
1029C22⋊C4—861no—
1030C22⋊C4—861no—
1031C22⋊C4—861no—
1032C22⋊C4—861no—
1033C22⋊C4—861no—
1034C22⋊C4—861no—
1035C22⋊C4—861no—
1036C22⋊C4—861no—
1037C22⋊C4—864no—
1038C22⋊C4—861no—
1039C22⋊C4—861no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—431no—
1046C42—431no—
1047C42—431no—
1048C42—431no—
1049C42—432no—
1050C42—861no—
1051C42—861no—
1052C42—864no—
1053C42—861no—
1054C42—861no—
1055C42—861no—
1056C42—1722no—
1057C42—1722no—
1058C42—1722no—
1059C23—22no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—41no—
1064C23—431no—
1065C23—431no—
1066C23—862no—
1067C23—861no—
1068C23—861no—
1069C23—861no—
1070C23—861no—
1071C23—3441no—
1072C23—3441no—
1073C23—1721no—
1074C23—1722no—
1075C23—1722no—
1076C23—1722no—
1077C23—1722no—
1078C23C22⋊C4×D4311yescharacteristic
1079C23C22⋊C4×D4311yescharacteristic
1080C23C2×D4×D4311yescharacteristic
1081Q8—21no—
1082Q8—21no—
1083Q8—432no—
1084Q8—861no—
1085Q8—861no—
1086Q8—861no—
1087Q8—1722no—
1088Q8—1722no—
1089D4—21no—
1090D4—21no—
1091D4—42no—
1092D4—41no—
1093D4—41no—
1094D4—81no—
1095D4—434no—
1096D4—432no—
1097D4—862no—
1098D4—862no—
1099D4—862no—
1100D4—862no—
1101D4—862no—
1102D4—861no—
1103D4—861no—
1104D4—861no—
1105D4—3441no—
1106D4—3441no—
1107D4—1722no—
1108D4—1722no—
1109D4—1722no—
1110D4—1722no—
1111D4—1722no—
1112D4—1722no—
1113D4—1722no—
1114D4—1722no—
1115D4—1721no—
1116D4—1721no—
1117C2×C4—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—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—431no—
1139C2×C4—431no—
1140C2×C4—431no—
1141C2×C4—431no—
1142C2×C4—431no—
1143C2×C4—431no—
1144C2×C4—862no—
1145C2×C4—862no—
1146C2×C4—862no—
1147C2×C4—861no—
1148C2×C4—862no—
1149C2×C4—861no—
1150C2×C4—861no—
1151C2×C4—861no—
1152C2×C4—861no—
1153C2×C4—861no—
1154C2×C4—861no—
1155C2×C4—861no—
1156C2×C4—861no—
1157C2×C4—862no—
1158C2×C4—861no—
1159C2×C4—861no—
1160C2×C4—862no—
1161C2×C4—862no—
1162C2×C4—861no—
1163C2×C4—3441no—
1164C2×C4—1722no—
1165C2×C4—1722no—
1166C2×C4—1722no—
1167C2×C4—1722no—
1168C2×C4—1722no—
1169C2×C4—1728no—
1170C2×C4—1721no—
1171C2×C4—1722no—
1172C2×C4—1722no—
1173C2×C4—1728no—
1174C2×C4—1721no—
1175C2×C4—1721no—
1176C2×C4—1721no—
1177C2×C4—1721no—
1178C2×C4C22⋊C4×D4311yescharacteristic
1179C2×C4C22⋊C4×D4311yescharacteristic
1180C2×C4C22×C4×D4311yescharacteristic
1181C2×C4C2×D4×D4311yescharacteristic
1182C2×C4C2×D4×D4311yescharacteristic
1183C2×C4#41×D4311yescharacteristic
1184C2×C4#1306337011yescharacteristic
1185C2×C4#1306337111yescharacteristic
1186C8—22no—
1187C8—41no—
1188C8—1721no—
1189C8—1721no—
1190C22—21no—
1191C22—21no—
1192C22—21no—
1193C22—21no—
1194C22—21no—
1195C22—21no—
1196C22—21no—
1197C22—42no—
1198C22—42no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—432no—
1203C22—861no—
1204C22—861no—
1205C22—861no—
1206C22—862no—
1207C22—861no—
1208C22—861no—
1209C22—3444no—
1210C22—3444no—
1211C22—1722no—
1212C22—1722no—
1213C22—1721no—
1214C22—1721no—
1215C22—1721no—
1216C22—1721no—
1217C22—1721no—
1218C22#104×D4312yescomplemented
1219C22C2×C22⋊C4×D4311yescharacteristic
1220C22#1458353311yescharacteristic
1221C22#1458353811yescharacteristic
1222C4—21no—
1223C4—21no—
1224C4—42no—
1225C4—42no—
1226C4—41no—
1227C4—41no—
1228C4—41no—
1229C4—432no—
1230C4—864no—
1231C4—861no—
1232C4—861no—
1233C4—862no—
1234C4—861no—
1235C4—861no—
1236C4—861no—
1237C4—1722no—
1238C4—1721no—
1239C4C4×D4×D4311yescharacteristic
1240C4#1458337111yescharacteristic
1241C4#1458353111yescharacteristic
1242C4#1458354111yescharacteristic
1243C2—21no—
1244C2—21no—
1245C2—22no—
1246C2—41no—
1247C2—81no—
1248C2—862no—
1249C2—3441no—
1250C2—1721no—
1251C2—1722no—
1252C2#1913741311yescharacteristic
1253C2C2×#104×D4311yescharacteristic
1254C2#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
hypocenterC43D4×#104
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. C22×#13063251C2semidirect
4. C2×#104×D43C2semidirect
5. C4×(C22⋊D43)⋊C4C2semidirect
6. #19135512C2semidirect
7. #19135421C2semidirect
8. #19135039C2semidirect
9. #19135037C2semidirect
10. #19134896C2semidirect
11. #19134614C2semidirect
12. #19134540C2semidirect
13. #19134537C2semidirect
14. #19134399C2semidirect
15. C43×#1871C2semidirect
18. C2×M16×D43C22semidirect
19. #14583567C4semidirect
20. #14583562C4semidirect
21. #14583559C4semidirect
22. #14583555C4semidirect
23. #14583551C4semidirect
25. #14583546C4semidirect
27. #14583540C4semidirect
29. #14583533C4semidirect
40. C22×C4×Dic43C22semidirect
41. C2×C42×D43C22semidirect
46. #14582922C22semidirect
49. C2×#13063253C22semidirect
50. C2×#13063253C22semidirect
51. C2×#13063252C22semidirect
52. C2×#13063252C22semidirect
56. C2×#13063251C22semidirect
57. C2×#13063251C22semidirect
59. #14582863C22semidirect
60. #14582862C22semidirect
61. M16×Dic43C22semidirect
62. C4×Dic43⋊C4C22semidirect
65. C4×(C2×D43)⋊C4C22semidirect
67. C42×Dic43C22semidirect
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
85. C2×#10621898C2×C4semidirect
86. C2×#10621898C2×C4semidirect
90. C2×#10621900C2×C4semidirect
95. C22×Dic86C2×C4semidirect
96. C2×Q8×D43C2×C4semidirect
97. C22×D172C2×C4semidirect
102. C2×D4×D43C2×C4semidirect
115. #13063323C2×C4semidirect
117. #13063321C2×C4semidirect
118. #13063314C2×C4semidirect
119. #13063312C2×C4semidirect
127. #13063305C2×C4semidirect
128. #13063305C2×C4semidirect
134. #13063300C2×C4semidirect
135. #13063300C2×C4semidirect
150. #13063290C2×C4semidirect
151. #13063290C2×C4semidirect
156. #13063287C2×C4semidirect
157. #13063287C2×C4semidirect
205. #13063251D4semidirect
223. C22⋊Q8×C43C2×C4semidirect
224. C22⋊Q8×C43C2×C4semidirect
225. #121×C43C2×C4semidirect
226. #121×C43C2×C4semidirect
360. M16×C43C2×D4semidirect
422. C4×Dic43C2×D4semidirect
503. C22⋊D43#104semidirect
532. D172C4×D4semidirect
557. Dic86C4×D4semidirect
575. C22×C43C2×#104semidirect
594. C2×D43C2×#104semidirect
615. Dic43C2×#104semidirect
626. #1871D43semidirect
646. C22×M16C2×D43semidirect
688. C2×#104C2×D43semidirect
689. C2×#104C2×D43semidirect
698. C4×C22⋊C4C2×D43semidirect
702. #339C2×D43semidirect
703. #339C2×D43semidirect
704. C43D4×#104semidirect
770. C22⋊Q8C4×D43semidirect
771. C22⋊Q8C4×D43semidirect
784. #121C4×D43semidirect
785. #121C4×D43semidirect
993. M16D4×D43semidirect
1218. C22#104×D43semidirect

Maximal subgroups

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

subgroupindex
#191480782
M16×C22⋊D432
C22×#130632512
C2×#104×D432
C4×(C22⋊D43)⋊C42
#191355122
#191354212
#191350392
#191350372
#191348962
#191346142
#191345402
#191345372
#191343992
C43×#18712
D4×#10443