Finite Group Databasebeta

← #25096733

Subgroups — #25096733

Order 11008.

1258 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147794C211yesmaximal, characteristic
2#19143232C211yesmaximal, characteristic, complemented
3#19137088C211yesmaximal, characteristic, complemented
4#19134693C211yesmaximal, characteristic, complemented
5#19134693C211yesmaximal, characteristic, complemented
6#19134616C211yesmaximal, characteristic, complemented
7#19134615C211yesmaximal, characteristic, complemented
8#19134612C211yesmaximal, characteristic, complemented
9#19134537C211yesmaximal, characteristic
10#19134537C211yesmaximal, characteristic
11#19134407C211yesmaximal, characteristic, complemented
12#19134404C211yesmaximal, characteristic, complemented
13#104×Dic43C211yesmaximal, characteristic, complemented
14#19134399C211yesmaximal, characteristic, complemented
15C43×#1806C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17#14583381C411yescharacteristic, complemented
18#14583381C411yescharacteristic, complemented
19#14583378—21no—
20#14583378—21no—
21#14583378C411yescharacteristic, complemented
22#14583378C411yescharacteristic, complemented
23#14583375C411yescharacteristic, complemented
24#14583375C411yescharacteristic, complemented
25#14583371—21no—
26#14583371—21no—
27#14583371C411yescharacteristic, complemented
28#14583371C411yescharacteristic, complemented
29#41×Dic43C2211yescharacteristic
30C4×#10621898—21no—
31C4×#10621898C2211yescharacteristic
32#14583367—21no—
33#14583367C2211yescharacteristic
34C2×#13063282—21no—
35C2×#13063282C2211yescharacteristic
36#117×D43—21no—
37#117×D43C2211yescharacteristic
38#14582959—21no—
39#14582959—21no—
40#14582959—21no—
41#14582959—21no—
42#14582923C2211yescharacteristic, complemented
43C2×#13063253C2211yescharacteristic
44C2×#13063253C2211yescharacteristic
45C2×#13063252C2211yescharacteristic
46C2×#13063252C2211yescharacteristic
47C2×#13063251C2211yescharacteristic
48C2×#13063251C2211yescharacteristic
49#14582862C2211yescharacteristic
50#14582862C2211yescharacteristic
51M16×Dic43C2211yescharacteristic, complemented
52M16×Dic43C2211yescharacteristic, complemented
53#14582791—21no—
54#14582789—21no—
55#14582786—21no—
56#14582780—21no—
57C4×C4⋊Dic43C2211yescharacteristic, complemented
58C4×(C2×D43)⋊C4C2211yescharacteristic
59C4×(C2×D43)⋊C4C2211yescharacteristic
60#14582745C2211yescharacteristic, complemented
61C42×Dic43C2211yescharacteristic, complemented
62#14582660C2211yescharacteristic, complemented
63#14582660C2211yescharacteristic, complemented
64#14582659C2211yescharacteristic, complemented
65#14582659C2211yescharacteristic, complemented
66#14582658C2211yescharacteristic, complemented
67#14582658C2211yescharacteristic, complemented
68C4×#41×C43C2211yescharacteristic
69C43×#423C2211yescharacteristic, complemented
70C2×#104×C43C2211yescharacteristic
71C2×#104×C43C2211yescharacteristic
72C4×C4⋊C4×C43C2211yescharacteristic, complemented
73C43×#339C2211yescharacteristic, complemented
74C43×#339C2211yescharacteristic, complemented
75C2×#10621902C2×C411yescharacteristic
76C2×#10621898—21no—
77C2×#10621898C2311yescharacteristic
78C2×#10621900—21no—
79C2×#10621900C2×C411yescharacteristic
80#41×D43—22no—
81#41×D43—22no—
82#41×D43—22no—
83#41×D43—22no—
84C2×Q8×D43C2×C411yescharacteristic
85C2×D4×D43—21no—
86C2×D4×D43C2×C411yescharacteristic
87C22×C4×D43—21no—
88C22×C4×D43C2311yescharacteristic
89C2×#10621877C2311yescharacteristic
90C2×#10621877C2311yescharacteristic
91Q8×Dic43C2×C411yescharacteristic
92Q8×Dic43C2×C411yescharacteristic
93C4×Dic86—21no—
94C4×Dic86—21no—
95C4×Dic86C2×C411yescharacteristic
96C4×Dic86C2×C411yescharacteristic
97#13063290—21no—
98#13063290—21no—
99#13063290C2×C411yescharacteristic
100#13063290C2×C411yescharacteristic
101C4×D172—21no—
102C4×D172—21no—
103C4×D172C2×C411yescharacteristic
104C4×D172C2×C411yescharacteristic
105D4×Dic43—21no—
106D4×Dic43—21no—
107D4×Dic43C2×C411yescharacteristic
108D4×Dic43C2×C411yescharacteristic
109#13063287—21no—
110#13063287—21no—
111#13063287C2×C411yescharacteristic
112#13063287C2×C411yescharacteristic
113C4×C22⋊D43—21no—
114C4×C22⋊D43—21no—
115C4×C22⋊D43—21no—
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119(C22⋊D43)⋊C4—21no—
120(C22⋊D43)⋊C4—21no—
121(C22⋊D43)⋊C4—21no—
122(C22⋊D43)⋊C4—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125#13063284—21no—
126#13063284C2311yescharacteristic
127#13063283—21no—
128#13063283—21no—
129#13063283C2×C411yescharacteristic
130#13063283C2×C411yescharacteristic
131#13063282—21no—
132#13063282—21no—
133#13063282—21no—
134#13063282—21no—
135#13063282—21no—
136#13063282—21no—
137#13063282—21no—
138#13063282C2×C411yescharacteristic
139#13063282C2×C411yescharacteristic
140#13063282C2×C411yescharacteristic
141#13063282C2×C411yescharacteristic
142#13063282D411yescharacteristic
143#13063282D411yescharacteristic
144#13063282D411yescharacteristic
145#13063282D411yescharacteristic
146#13063281—21no—
147#13063281—21no—
148#13063281—21no—
149C2×C4⋊Dic43—21no—
150C2×Dic43⋊C4—21no—
151C2×Dic43⋊C4—21no—
152C2×Dic43⋊C4D411yescharacteristic
153C2×Dic43⋊C4D411yescharacteristic
154C4⋊C4×D43—21no—
155C4⋊C4×D43—21no—
156C4⋊C4×D43C2×C411yescharacteristic
157C4⋊C4×D43C2×C411yescharacteristic
158C2×(C2×D43)⋊C4—21no—
159C2×(C2×D43)⋊C4—21no—
160C2×(C2×D43)⋊C4—21no—
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4D411yescharacteristic
163C2×(C2×D43)⋊C4D411yescharacteristic
164C22⋊C4×D43—21no—
165C22⋊C4×D43—21no—
166C22⋊C4×D43—21no—
167C2×C4×Dic43—21no—
168C2×C4×Dic43—21no—
169C2×C4×Dic43—21no—
170C2×C4×Dic43C2311yescharacteristic
171C2×C4×Dic43C2311yescharacteristic
172C2×C4×Dic43C2311yescharacteristic
173C42×D43—21no—
174C42×D43—21no—
175C42×D43—21no—
176C4⋊(C43⋊C8)—21no—
177C4⋊(C43⋊C8)—21no—
178#13063253—22no—
179#13063253—22no—
180#13063252—22no—
181#13063252—22no—
182#13063251—22no—
183#13063251—22no—
184(C2×D43)⋊C8—21no—
185(C2×D43)⋊C8—21no—
186(C2×D43)⋊C8—21no—
187(C2×D43)⋊C8—21no—
188#13063235—21no—
189#13063235—21no—
190C8×Dic43—21no—
191C8×Dic43—21no—
192C43⋊#95—21no—
193C43⋊#95—21no—
194C43⋊#95—21no—
195C43⋊#95—21no—
196C43⋊#95—21no—
197C2×#41×C43C2311yescharacteristic
198C2×M16×C43C2311yescharacteristic
199C2×M16×C43C2311yescharacteristic
200C4×Q8×C43C2×C411yescharacteristic
201C4×Q8×C43C2×C411yescharacteristic
202C4×D4×C43—21no—
203C4×D4×C43—21no—
204C4×D4×C43C2×C411yescharacteristic
205C4×D4×C43C2×C411yescharacteristic
206#117×C43—21no—
207#117×C43C2311yescharacteristic
208C2×C4⋊C4×C43—21no—
209C2×C42×C43—21no—
210C2×C42×C43C2311yescharacteristic
211C2×C42×C43C2311yescharacteristic
212C2×C42×C43C2311yescharacteristic
213C4⋊C8×C43—21no—
214C4⋊C8×C43—21no—
215#104×C43—22no—
216#104×C43—22no—
217#95×C43—21no—
218C23×D43—21no—
219C23×D43C2×D411yescharacteristic
220#41×C43—21no—
221#41×C43—21no—
222#41×C43#4112yes—
223#41×C43#4112yes—
224C2×Q8×C43C22×C411yescharacteristic
225C2×D4×C43—21no—
226C2×D4×C43C22×C411yescharacteristic
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2411yescharacteristic
235C2×C22⋊D43—21no—
236C2×C22⋊D43—21no—
237C2×C22⋊D43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43C2×D411yescharacteristic
244C22×Dic43C2×D411yescharacteristic
245C22×Dic43C2×D411yescharacteristic
246#10621902—22no—
247#10621902—22no—
248Q8×D43—22no—
249Q8×D43—22no—
250#10621900—24no—
251#10621900—24no—
252#10621900—22no—
253#10621900—22no—
254D4×D43—24no—
255D4×D43—24no—
256D4×D43—22no—
257D4×D43—22no—
258#10621898—24no—
259#10621898—24no—
260#10621898—21no—
261#10621898—21no—
262#10621898#4112yes—
263#10621898#4112yes—
264C2×D172—21no—
265C2×D172C22×C411yescharacteristic
266C2×C4×D43—24no—
267C2×C4×D43—24no—
268C2×C4×D43—21no—
269C2×C4×D43—21no—
270C2×C4×D43—21no—
271C2×C4×D43—21no—
272C2×C4×D43—21no—
273C2×C4×D43—21no—
274C2×C4×D43—21no—
275C2×C4×D43—21no—
276C2×C4×D43—21no—
277C2×C4×D43—21no—
278C2×C4×D43—21no—
279C2×C4×D43—21no—
280C2×C4×D43—21no—
281C2×C4×D43C22×C411yescharacteristic
282C2×C4×D43C22×C411yescharacteristic
283C2×C4×D43C2×D411yescharacteristic
284C2×C4×D43C2×D411yescharacteristic
285C2×Dic86—21no—
286C2×Dic86C22×C411yescharacteristic
287M16×C43—21no—
288M16×C43—21no—
289M16×C43—21no—
290M16×C43—21no—
291C2×C8×C43—21no—
292C2×C8×C43—21no—
293C4⋊C4×C43—21no—
294C4⋊C4×C43—21no—
295C4⋊C4×C43—42no—
296C4⋊C4×C43C22×C411yescharacteristic
297C4⋊C4×C43C22×C411yescharacteristic
298C22⋊C4×C43—21no—
299C22⋊C4×C43—21no—
300C22⋊C4×C43—21no—
301C42×C43—21no—
302C42×C43—21no—
303C42×C43—21no—
304C42×C43—21no—
305C42×C43—21no—
306C42×C43—21no—
307C42×C43—21no—
308C42×C43C22×C411yescharacteristic
309C42×C43C22×C411yescharacteristic
310C42×C43C2×D411yescharacteristic
311C42×C43C2×D411yescharacteristic
312C22⋊Dic43—21no—
313C22⋊Dic43—21no—
314C22⋊Dic43—21no—
315(C2×D43)⋊C4—21no—
316(C2×D43)⋊C4—21no—
317(C2×D43)⋊C4—21no—
318(C2×D43)⋊C4—21no—
319(C2×D43)⋊C4—21no—
320(C2×D43)⋊C4—21no—
321(C2×D43)⋊C4—42no—
322(C2×D43)⋊C4—42no—
323(C2×D43)⋊C4C22⋊C411yescharacteristic
324(C2×D43)⋊C4C22⋊C411yescharacteristic
325(C2×D43)⋊C4C22⋊C411yescharacteristic
326(C2×D43)⋊C4C22⋊C411yescharacteristic
327(C2×D43)⋊C4C22⋊C411yescharacteristic
328(C2×D43)⋊C4C22⋊C411yescharacteristic
329(C2×D43)⋊C4C22⋊C411yescharacteristic
330(C2×D43)⋊C4C22⋊C411yescharacteristic
331C4⋊Dic43—21no—
332C4⋊Dic43—21no—
333C4⋊Dic43—42no—
334C4⋊Dic43C22×C411yescharacteristic
335C4⋊Dic43C22×C411yescharacteristic
336Dic43⋊C4—21no—
337Dic43⋊C4—21no—
338Dic43⋊C4—21no—
339Dic43⋊C4—21no—
340Dic43⋊C4—21no—
341Dic43⋊C4—21no—
342Dic43⋊C4C22⋊C411yescharacteristic
343Dic43⋊C4C22⋊C411yescharacteristic
344Dic43⋊C4C22⋊C411yescharacteristic
345Dic43⋊C4C22⋊C411yescharacteristic
346Dic43⋊C4C22⋊C411yescharacteristic
347Dic43⋊C4C22⋊C411yescharacteristic
348Dic43⋊C4C22⋊C411yescharacteristic
349Dic43⋊C4C22⋊C411yescharacteristic
350C4×Dic43—21no—
351C4×Dic43—21no—
352C4×Dic43—21no—
353C4×Dic43—21no—
354C4×Dic43—21no—
355C4×Dic43—21no—
356C4×Dic43—21no—
357C4×Dic43—21no—
358C4×Dic43—21no—
359C4×Dic43—21no—
360C4×Dic43—21no—
361C4×Dic43—21no—
362C4×Dic43—21no—
363C4×Dic43—42no—
364C4×Dic43—42no—
365C4×Dic43C22×C411yescharacteristic
366C4×Dic43C22×C411yescharacteristic
367C4×Dic43C2×D411yescharacteristic
368C4×Dic43C2×D411yescharacteristic
369#10621877—21no—
370#10621877—21no—
371#10621877—21no—
372#10621877—21no—
373C2×C43⋊C8—21no—
374C2×C43⋊C8—21no—
375C23×C43—21no—
376C23×C43C22×D411yescharacteristic
377C22×D43—21no—
378C22×D43—24no—
379C22×D43—21no—
380C22×D43—21no—
381C22×D43—41no—
382C22×D43—41no—
383C22×D43—81no—
384C22×D43—81no—
385C22×D43C2×C22⋊C411yescharacteristic
386C22×D43C2×C22⋊C411yescharacteristic
387Q8×C43—21no—
388Q8×C43#11712yes—
389D4×C43—22no—
390D4×C43—22no—
391D4×C43—21no—
392D4×C43#11712yes—
393C2×C4×C43—21no—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—21no—
398C2×C4×C43—21no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43—41no—
406C2×C4×C43—81no—
407C2×C4×C43—81no—
408C2×C4×C43C2×C22⋊C411yescharacteristic
409C2×C4×C43C2×C22⋊C411yescharacteristic
410C2×C4×C43C2×C22⋊C411yescharacteristic
411C2×C4×C43C2×C22⋊C411yescharacteristic
412C2×C4×C43C23×C411yescharacteristic
413C2×C4×C43C22×D411yescharacteristic
414C2×C4×C43C2×#4111yescharacteristic
415C2×C4×C43C2×#4111yescharacteristic
416C2×C4×C43C2×#4111yescharacteristic
417C2×C4×C43C2×#4111yescharacteristic
418C22⋊D43—24no—
419C22⋊D43—24no—
420C22⋊D43—22no—
421C22⋊D43—22no—
422C2×Dic43—24no—
423C2×Dic43—21no—
424C2×Dic43—21no—
425C2×Dic43—21no—
426C2×Dic43—22no—
427C2×Dic43—21no—
428C2×Dic43—21no—
429C2×Dic43—41no—
430C2×Dic43—41no—
431C2×Dic43—41no—
432C2×Dic43—41no—
433C2×Dic43—41no—
434C2×Dic43—41no—
435C2×Dic43—41no—
436C2×Dic43—81no—
437C2×Dic43—81no—
438C2×Dic43C2×C22⋊C411yescharacteristic
439C2×Dic43C2×C22⋊C411yescharacteristic
440C2×Dic43C2×C22⋊C411yescharacteristic
441C2×Dic43C2×C22⋊C411yescharacteristic
442C2×Dic43C2×C22⋊C411yescharacteristic
443C2×Dic43C2×C22⋊C411yescharacteristic
444D172—24no—
445D172—21no—
446D172#11712yes—
447C4×D43—24no—
448C4×D43—24no—
449C4×D43—21no—
450C4×D43—21no—
451C4×D43—21no—
452C4×D43—21no—
453C4×D43—21no—
454C4×D43—21no—
455C4×D43—22no—
456C4×D43—22no—
457C4×D43—21no—
458C4×D43—21no—
459C4×D43—81no—
460C4×D43—81no—
461C4×D43—81no—
462C4×D43—81no—
463C4×D43—81no—
464C4×D43—81no—
465Dic86—24no—
466Dic86—21no—
467Dic86#11712yes—
468C8×C43—41no—
469C8×C43—41no—
470C43⋊C8—41no—
471C43⋊C8—41no—
472#20749—431nomaximal, Sylow
473C22×C43—21no—
474C22×C43—21no—
475C22×C43—22no—
476C22×C43—41no—
477C22×C43—41no—
478C22×C43C22×C22⋊C411yescharacteristic
479C22×C43#52511yescharacteristic
480C22×C43#52511yescharacteristic
481C2×D43—21no—
482C2×D43—21no—
483C2×D43—21no—
484C2×D43—21no—
485C2×D43—21no—
486C2×D43—22no—
487C2×D43—21no—
488C2×D43—41no—
489C2×D43—41no—
490C2×D43—81no—
491C2×D43—81no—
492C2×D43—84no—
493C4×C43—21no—
494C4×C43—21no—
495C4×C43—21no—
496C4×C43—21no—
497C4×C43—22no—
498C4×C43—42no—
499C4×C43—41no—
500C4×C43—41no—
501C4×C43—81no—
502C4×C43C2×#11711yescharacteristic
503C4×C43C2×#11711yescharacteristic
504C4×C43#52511yescharacteristic
505C4×C43#52511yescharacteristic
506Dic43—21no—
507Dic43—21no—
508Dic43—21no—
509Dic43—21no—
510Dic43—21no—
511Dic43—22no—
512Dic43—21no—
513Dic43—42no—
514Dic43—41no—
515Dic43—41no—
516Dic43—81no—
517#3428—431no—
518#2921—431no—
519#2298—431no—
520#1826—431no—
521#1826—431no—
522#1806—431no—
523#1806—431no—
524#1806—431no—
525#1806D4311yescharacteristic, complemented
526#1789—431no—
527#1789—431no—
528#1759—431no—
529#1759—431no—
530C4×#104—431no—
531C4×#104—431no—
532C2×C43—21no—
533C2×C43—21no—
534C2×C43—42no—
535C2×C43#228011yescharacteristic
536C2×C43#290111yescharacteristic
537C2×C43#290111yescharacteristic
538D43—41no—
539D43—41no—
540D43—42no—
541C22×#41—431no—
542#520—431no—
543#520—431no—
544#520—431no—
545#520—431no—
546#520—861no—
547#520—861no—
548#519—431no—
549#519—431no—
550#518—431no—
551#518—431no—
552#518—861no—
553#518—861no—
554C4×#41—431no—
555C4×#41—431no—
556C4×#41—431no—
557C4×#41—861no—
558C4×#41—861no—
559C4×#41C2×D4311yescharacteristic
560C2×#117—431no—
561C2×#117—431no—
562C2×#117—861no—
563C2×#117—861no—
564#433—861no—
565#433—861no—
566#433—861no—
567#433—861no—
568#423—431no—
569#423C2×D4311yescharacteristic, complemented
570C2×#104—431no—
571C2×#104—431no—
572C2×#104—431no—
573C2×#104—431no—
574C2×#104—431no—
575C2×#104—431no—
576C2×#104C2×D4311yescharacteristic
577C2×#104C2×D4311yescharacteristic
578#407—431no—
579#407—431no—
580C4×M16—431no—
581C4×M16—431no—
582#388—861no—
583#388—861no—
584#387—861no—
585#387—861no—
586C4×C4⋊C4—431no—
587C4×C4⋊C4C2×D4311yescharacteristic, complemented
588C4×C22⋊C4—431no—
589C4×C22⋊C4—431no—
590#376—431no—
591C43—431no—
592#339—431no—
593#339—431no—
594#339—431no—
595#339—431no—
596#339—431no—
597#339—431no—
598#339C2×D4311yescharacteristic, complemented
599#339C2×D4311yescharacteristic, complemented
600C43#2074911yescharacteristic, complemented, Sylow
601C2×#41—431no—
602C2×#41—431no—
603C2×#41—431no—
604C2×#41—861no—
605C2×#41—861no—
606C2×#41—862no—
607C2×#41—862no—
608C2×#41—862no—
609C2×#41—862no—
610C2×#41C22×D4311yescharacteristic
611C22×Q8—431no—
612C22×D4—431no—
613C22×D4—861no—
614C23×C4—431no—
615C23×C4—861no—
616C2×M16—431no—
617C2×M16—431no—
618C2×M16C22×D4311yescharacteristic
619C2×M16C22×D4311yescharacteristic
620C4×Q8—431no—
621C4×Q8—431no—
622C4×Q8—431no—
623C4×Q8—431no—
624C4×Q8—431no—
625C4×Q8—431no—
626C4×Q8—861no—
627C4×Q8—861no—
628C4×Q8—861no—
629C4×Q8—861no—
630C4×Q8C4×D4311yescharacteristic
631C4×Q8C4×D4311yescharacteristic
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—431no—
635C4×D4—431no—
636C4×D4—431no—
637C4×D4—431no—
638C4×D4—431no—
639C4×D4—431no—
640C4×D4—861no—
641C4×D4—861no—
642C4×D4—861no—
643C4×D4—861no—
644C4×D4—861no—
645C4×D4—861no—
646C4×D4—861no—
647C4×D4—861no—
648C4×D4—861no—
649C4×D4—861no—
650C4×D4—861no—
651C4×D4—861no—
652C4×D4—861no—
653C4×D4—861no—
654C4×D4—861no—
655C4×D4—861no—
656C4×D4—861no—
657C4×D4—861no—
658C4×D4C4×D4311yescharacteristic
659C4×D4C4×D4311yescharacteristic
660#117—21no—
661#117—431no—
662#117—431no—
663#117—431no—
664#117—431no—
665#117—431no—
666#117—431no—
667#117—431no—
668#117—431no—
669#117—431no—
670#117—431no—
671#117—431no—
672#117—861no—
673#117—861no—
674#117—861no—
675#117—861no—
676#117—861no—
677#117—861no—
678#117—861no—
679#117—861no—
680#117—861no—
681#117—861no—
682#117—861no—
683#117—861no—
684#117—861no—
685#117C22×D4311yescharacteristic
686C2×C4⋊C4—21no—
687C2×C4⋊C4—431no—
688C2×C4⋊C4—431no—
689C2×C4⋊C4—431no—
690C2×C4⋊C4—431no—
691C2×C4⋊C4—861no—
692C2×C4⋊C4—861no—
693C2×C4⋊C4—861no—
694C2×C4⋊C4—861no—
695C2×C4⋊C4—861no—
696C2×C22⋊C4—431no—
697C2×C22⋊C4—431no—
698C2×C22⋊C4—861no—
699C2×C22⋊C4—861no—
700C2×C22⋊C4—861no—
701C2×C22⋊C4—861no—
702C2×C22⋊C4—861no—
703C2×C22⋊C4—861no—
704C2×C22⋊C4—861no—
705C2×C42—21no—
706C2×C42—431no—
707C2×C42—431no—
708C2×C42—431no—
709C2×C42—861no—
710C2×C42—861no—
711C2×C42—861no—
712C2×C42—861no—
713C2×C42—861no—
714C2×C42—861no—
715C2×C42C22×D4311yescharacteristic
716C2×C42C22×D4311yescharacteristic
717C2×C42C22×D4311yescharacteristic
718C4⋊C8—21no—
719C4⋊C8—21no—
720C4⋊C8—861no—
721C4⋊C8—861no—
722#104—22no—
723#104—22no—
724#104—862no—
725#104—862no—
726#104—862no—
727#104—862no—
728#104—862no—
729#104—862no—
730C22⋊C8—861no—
731C22⋊C8—861no—
732C22⋊C8—861no—
733C22⋊C8—861no—
734#97—861no—
735#97—861no—
736C4×C8—861no—
737C4×C8—861no—
738#95—21no—
739#95—861no—
740#95—861no—
741#95—861no—
742#95—861no—
743#95—861no—
744C24—431no—
745C24—861no—
746#41—21no—
747#41—21no—
748#41—432no—
749#41—432no—
750#41—864no—
751#41—864no—
752#41—862no—
753#41—864no—
754#41—864no—
755#41—862no—
756#41—862no—
757#41—862no—
758#41—861no—
759#41—861no—
760#41#1062190012yes—
761#41#1062190212yes—
762C2×Q8—431no—
763C2×Q8—861no—
764C2×Q8—862no—
765C2×Q8—862no—
766C2×Q8C2×C4×D4311yescharacteristic
767C2×D4—21no—
768C2×D4—431no—
769C2×D4—861no—
770C2×D4—861no—
771C2×D4—862no—
772C2×D4—864no—
773C2×D4—864no—
774C2×D4—861no—
775C2×D4—861no—
776C2×D4—862no—
777C2×D4C2×C4×D4311yescharacteristic
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—431no—
784C22×C4—431no—
785C22×C4—431no—
786C22×C4—431no—
787C22×C4—431no—
788C22×C4—431no—
789C22×C4—431no—
790C22×C4—861no—
791C22×C4—861no—
792C22×C4—861no—
793C22×C4—861no—
794C22×C4—864no—
795C22×C4—864no—
796C22×C4—861no—
797C22×C4—861no—
798C22×C4—861no—
799C22×C4—861no—
800C22×C4—861no—
801C22×C4—861no—
802C22×C4—861no—
803C22×C4—861no—
804C22×C4—861no—
805C22×C4—861no—
806C22×C4—861no—
807C22×C4—861no—
808C22×C4—861no—
809C22×C4—861no—
810C22×C4D4×D4311yescharacteristic
811C22×C4D4×D4311yescharacteristic
812C22×C4C23×D4311yescharacteristic
813M16—21no—
814M16—21no—
815M16—21no—
816M16—21no—
817M16—861no—
818M16—861no—
819M16—861no—
820M16—861no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—861no—
824C2×C8—861no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—42no—
828C4⋊C4—431no—
829C4⋊C4—431no—
830C4⋊C4—431no—
831C4⋊C4—431no—
832C4⋊C4—431no—
833C4⋊C4—431no—
834C4⋊C4—431no—
835C4⋊C4—431no—
836C4⋊C4—431no—
837C4⋊C4—431no—
838C4⋊C4—861no—
839C4⋊C4—861no—
840C4⋊C4—861no—
841C4⋊C4—861no—
842C4⋊C4—861no—
843C4⋊C4—861no—
844C4⋊C4—861no—
845C4⋊C4—861no—
846C4⋊C4—1722no—
847C4⋊C4C2×C4×D4311yescharacteristic
848C4⋊C4C2×C4×D4311yescharacteristic
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—431no—
853C22⋊C4—431no—
854C22⋊C4—431no—
855C22⋊C4—431no—
856C22⋊C4—431no—
857C22⋊C4—431no—
858C22⋊C4—431no—
859C22⋊C4—431no—
860C22⋊C4—861no—
861C22⋊C4—861no—
862C22⋊C4—861no—
863C22⋊C4—861no—
864C22⋊C4—861no—
865C22⋊C4—861no—
866C22⋊C4—861no—
867C22⋊C4—861no—
868C22⋊C4—861no—
869C22⋊C4—1722no—
870C22⋊C4—1722no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—431no—
879C42—431no—
880C42—431no—
881C42—431no—
882C42—861no—
883C42—861no—
884C42—861no—
885C42—861no—
886C42—861no—
887C42—861no—
888C42—861no—
889C42—861no—
890C42—861no—
891C42—861no—
892C42—861no—
893C42—861no—
894C42—861no—
895C42—1722no—
896C42—1722no—
897C42C2×C4×D4311yescharacteristic
898C42C2×C4×D4311yescharacteristic
899C42D4×D4311yescharacteristic
900C42D4×D4311yescharacteristic
901C23—21no—
902C23—431no—
903C23—431no—
904C23—864no—
905C23—861no—
906C23—861no—
907C23—861no—
908C23—3441no—
909C23—3441no—
910C23—1721no—
911C23—1721no—
912C23C2×D4×D4311yescharacteristic
913Q8—21no—
914Q8—432no—
915Q8—864no—
916Q8—861no—
917Q8#1306328312yes—
918D4—22no—
919D4—22no—
920D4—21no—
921D4—432no—
922D4—864no—
923D4—864no—
924D4—864no—
925D4—862no—
926D4—862no—
927D4—861no—
928D4#1306328312yes—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—81no—
943C2×C4—81no—
944C2×C4—431no—
945C2×C4—431no—
946C2×C4—431no—
947C2×C4—431no—
948C2×C4—431no—
949C2×C4—431no—
950C2×C4—864no—
951C2×C4—864no—
952C2×C4—864no—
953C2×C4—861no—
954C2×C4—861no—
955C2×C4—861no—
956C2×C4—861no—
957C2×C4—861no—
958C2×C4—861no—
959C2×C4—861no—
960C2×C4—861no—
961C2×C4—861no—
962C2×C4—862no—
963C2×C4—861no—
964C2×C4—861no—
965C2×C4—862no—
966C2×C4—862no—
967C2×C4—861no—
968C2×C4—861no—
969C2×C4—3441no—
970C2×C4—3441no—
971C2×C4—3441no—
972C2×C4—3441no—
973C2×C4—3441no—
974C2×C4—3441no—
975C2×C4—3441no—
976C2×C4—3441no—
977C2×C4—1721no—
978C2×C4—1721no—
979C2×C4—1721no—
980C2×C4—1721no—
981C2×C4—1721no—
982C2×C4—1721no—
983C2×C4—1721no—
984C2×C4C22⋊C4×D4311yescharacteristic
985C2×C4C22⋊C4×D4311yescharacteristic
986C2×C4C22⋊C4×D4311yescharacteristic
987C2×C4C22⋊C4×D4311yescharacteristic
988C2×C4C22×C4×D4311yescharacteristic
989C2×C4C2×D4×D4311yescharacteristic
990C2×C4#41×D4311yescharacteristic
991C2×C4#41×D4311yescharacteristic
992C2×C4C2×#1062190011yescharacteristic
993C2×C4C2×#1062190211yescharacteristic
994C8—41no—
995C8—41no—
996C8—1721no—
997C8—1721no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—41no—
1002C22—41no—
1003C22—861no—
1004C22—862no—
1005C22—861no—
1006C22—861no—
1007C22—861no—
1008C22—861no—
1009C22—861no—
1010C22—3441no—
1011C22—3441no—
1012C22—3444no—
1013C22—1721no—
1014C22—1721no—
1015C22C2×C22⋊C4×D4311yescharacteristic
1016C22#1458340911yescharacteristic
1017C22#1458341211yescharacteristic
1018C4—22no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—21no—
1023C4—42no—
1024C4—41no—
1025C4—41no—
1026C4—81no—
1027C4—861no—
1028C4—861no—
1029C4—862no—
1030C4—861no—
1031C4—861no—
1032C4—861no—
1033C4—861no—
1034C4—3441no—
1035C4—1722no—
1036C4—1721no—
1037C4—1721no—
1038C4#117×D4311yescharacteristic
1039C4C2×#1306328311yescharacteristic
1040C4#1458340911yescharacteristic
1041C4#1458341211yescharacteristic
1042C2—21no—
1043C2—21no—
1044C2—42no—
1045C2—1721no—
1046C2—1721no—
1047C2—1722no—
1048C2#1913697711yescharacteristic
1049C2#1914313911yescharacteristic
1050C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1806C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1806D43
hypocenterC43#20749
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #19143232C2semidirect
3. #19137088C2semidirect
4. #19134693C2semidirect
5. #19134693C2semidirect
6. #19134616C2semidirect
7. #19134615C2semidirect
8. #19134612C2semidirect
11. #19134407C2semidirect
12. #19134404C2semidirect
13. #104×Dic43C2semidirect
14. #19134399C2semidirect
15. C43×#1806C2semidirect
17. #14583381C4semidirect
18. #14583381C4semidirect
21. #14583378C4semidirect
22. #14583378C4semidirect
23. #14583375C4semidirect
24. #14583375C4semidirect
27. #14583371C4semidirect
28. #14583371C4semidirect
42. #14582923C22semidirect
51. M16×Dic43C22semidirect
52. M16×Dic43C22semidirect
57. C4×C4⋊Dic43C22semidirect
60. #14582745C22semidirect
61. C42×Dic43C22semidirect
62. #14582660C22semidirect
63. #14582660C22semidirect
64. #14582659C22semidirect
65. #14582659C22semidirect
66. #14582658C22semidirect
67. #14582658C22semidirect
69. C43×#423C22semidirect
72. C4×C4⋊C4×C43C22semidirect
73. C43×#339C22semidirect
74. C43×#339C22semidirect
525. #1806D43semidirect
569. #423C2×D43semidirect
587. C4×C4⋊C4C2×D43semidirect
598. #339C2×D43semidirect
599. #339C2×D43semidirect
600. C43#20749semidirect

Maximal subgroups

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

subgroupindex
#191477942
#191432322
#191370882
#191346932
#191346162
#191346152
#191346122
#191345372
#191344072
#191344042
#104×Dic432
#191343992
C43×#18062
#2074943