Finite Group Databasebeta

← #25063792

Subgroups — #25063792

Order 11008.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148615C211yesmaximal, characteristic
2#19143631C211yesmaximal, characteristic, complemented
3#19136953C211yesmaximal, characteristic, complemented
4#19133119C211yesmaximal, characteristic, complemented
5#19133112C211yesmaximal, characteristic, complemented
6#19133109C211yesmaximal, characteristic, complemented
7#19133101C211yesmaximal, characteristic, complemented
8#19133098C211yesmaximal, characteristic, complemented
9#19133088C211yesmaximal, characteristic, complemented
10#19133086C211yesmaximal, characteristic, complemented
11#19133085C211yesmaximal, characteristic, complemented
12#19133080C211yesmaximal, characteristic, complemented
13C2×#14582632C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C43×#1504C211yesmaximal, characteristic, complemented
16#14583612C411yescharacteristic, complemented
17#14583607C411yescharacteristic, complemented
18#14583601C411yescharacteristic, complemented
19#14583598—21no—
20#14583593C411yescharacteristic, complemented
21#14583568C411yescharacteristic, complemented
22#14583544—21no—
23#14583540C411yescharacteristic, complemented
24#14583537C411yescharacteristic, complemented
25#14583536—21no—
26#14583533C411yescharacteristic, complemented
27#14583531—21no—
28#14583501—21no—
29#14583485—21no—
30#14583482—21no—
31#14583444C2211yescharacteristic
32#14583435C2211yescharacteristic
33#14583412C2211yescharacteristic
34C2×#13063299C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583371—21no—
37C2×C4×C22⋊D43—21no—
38C2×C4×C22⋊D43C2211yescharacteristic
39#14582975—21no—
40#14582968—21no—
41#14582967—21no—
42(C22⋊D43)⋊C8—21no—
43#14582953C2211yescharacteristic, complemented
44#14582949C2211yescharacteristic, complemented
45#14582861C2211yescharacteristic, complemented
46C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47C22⋊C8×D43C2211yescharacteristic, complemented
48#14582750—21no—
49#14582750C2211yescharacteristic, complemented
50C4×C22⋊Dic43—21no—
51C4×C22⋊Dic43C2211yescharacteristic, complemented
52#14582746—21no—
53#14582746C2211yescharacteristic, complemented
54#14582744C2211yescharacteristic, complemented
55#95×D43C2211yescharacteristic, complemented
56#14582636C2211yescharacteristic, complemented
57#14582636C2211yescharacteristic, complemented
58#14582634C2211yescharacteristic
59#14582634C2211yescharacteristic
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582633C2211yescharacteristic, complemented
63#14582633C2211yescharacteristic, complemented
64#14582632C2211yescharacteristic
65#14582632C2211yescharacteristic
66#14582632C2211yescharacteristic, complemented
67#14582632C2211yescharacteristic, complemented
68C43×#525C2211yescharacteristic
69C43×#407C2211yescharacteristic, complemented
70C2×#95×C43C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic, complemented
74C43×#327C2211yescharacteristic, complemented
75C2×#10621902C2×C411yescharacteristic, complemented
76C2×#10621900—21no—
77C22×D172C2×C411yescharacteristic, complemented
78C22×C22⋊D43—21no—
79C22×C22⋊D43D411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43—21no—
82C2×D4×D43C2×C411yescharacteristic, complemented
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C2×#10621872—21no—
86C22×C43⋊C8—21no—
87C2×C8×D43—21no—
88#13063324C2×C411yescharacteristic, complemented
89#13063321—21no—
90#13063321C2×C411yescharacteristic, complemented
91#13063320—21no—
92#13063319—21no—
93#13063318—21no—
94#13063316C2×C411yescharacteristic, complemented
95#13063315—21no—
96#13063314C2×C411yescharacteristic, complemented
97#13063313—21no—
98#13063311—21no—
99#13063311—21no—
100#13063310—21no—
101#13063310—21no—
102#13063309—21no—
103#13063309—21no—
104#13063308—21no—
105#13063307—21no—
106#13063305—21no—
107#13063302—21no—
108#13063301C2×C411yescharacteristic, complemented
109#13063300—21no—
110#13063300C2×C411yescharacteristic, complemented
111#13063300C2×C411yescharacteristic, complemented
112#13063299—21no—
113#13063299—21no—
114#13063299—21no—
115#13063299C2×C411yescharacteristic, complemented
116#13063299C2×C411yescharacteristic, complemented
117#13063299C2311yescharacteristic
118#13063299C2311yescharacteristic
119#13063298—21no—
120#13063298—21no—
121#13063298—21no—
122#13063298—21no—
123#13063297—21no—
124#13063297—21no—
125#13063297—21no—
126#13063297—21no—
127#13063296—21no—
128#13063296C2×C411yescharacteristic, complemented
129#13063295—21no—
130#13063295—21no—
131#13063295—21no—
132#13063293—21no—
133#13063293—21no—
134Q8×Dic43C2×C411yescharacteristic, complemented
135C4×D172—21no—
136D4×Dic43—21no—
137D4×Dic43C2×C411yescharacteristic, complemented
138#13063287—21no—
139#13063287C2×C411yescharacteristic, complemented
140#13063287C2×C411yescharacteristic, complemented
141C4×C22⋊D43—28no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43C2×C411yescharacteristic
146C4×C22⋊D43C2×C411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149C4×C22⋊D43D411yescharacteristic
150C4×C22⋊D43D411yescharacteristic
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153(C22⋊D43)⋊C4—21no—
154(C22⋊D43)⋊C4—21no—
155#13063283—21no—
156#13063283C2×C411yescharacteristic, complemented
157#13063282—21no—
158C2×C4⋊Dic43C2×C411yescharacteristic, complemented
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4D411yescharacteristic
161C4⋊C4×D43C2×C411yescharacteristic, complemented
162C2×C22⋊Dic43—21no—
163C2×C22⋊Dic43D411yescharacteristic
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4D411yescharacteristic
168C22⋊C4×D43—21no—
169C22⋊C4×D43—21no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43—21no—
174C2×C4×Dic43C2311yescharacteristic
175Dic43⋊C8—21no—
176Dic43⋊C8—21no—
177C22⋊(C43⋊C8)—21no—
178C22⋊(C43⋊C8)C2311yescharacteristic
179C22⋊(C43⋊C8)C2311yescharacteristic
180(C2×D43)⋊C8—21no—
181(C2×D43)⋊C8—21no—
182#13063235—21no—
183C8×Dic43—21no—
184C43⋊#95—21no—
185C43⋊#95—21no—
186C43⋊#95C2311yescharacteristic
187C43⋊#95C2311yescharacteristic
188C2×#41×C43C2×C411yescharacteristic, complemented
189C23×C4×C43—21no—
190C23×C4×C43C2311yescharacteristic
191C2×M16×C43—21no—
192#123×C43—21no—
193C22⋊Q8×C43C2×C411yescharacteristic, complemented
194C22⋊Q8×C43C2311yescharacteristic
195#121×C43C2×C411yescharacteristic, complemented
196#121×C43C2311yescharacteristic
197#120×C43—21no—
198C4×D4×C43—21no—
199C4×D4×C43—21no—
200#117×C43C2×C411yescharacteristic, complemented
201C22⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204#95×C43—21no—
205#95×C43C2311yescharacteristic
206#95×C43C2311yescharacteristic
207C24×C43C2×D411yescharacteristic
208C23×D43—21no—
209C23×D43—21no—
210C23×D43C2×D411yescharacteristic
211#41×C43—81no—
212C2×Q8×C43C22×C411yescharacteristic
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—21no—
216C2×D4×C43C22×C411yescharacteristic
217C22×C4×C43—24no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—81no—
222C22×C4×C43—81no—
223C22×C4×C43—81no—
224C22×C4×C43C22×C411yescharacteristic
225C22×C4×C43C22×C411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C2×C22⋊D43—24no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43—21no—
235C2×C22⋊D43—21no—
236C2×C22⋊D43—21no—
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C2×C22⋊D43—81no—
240C2×C22⋊D43—81no—
241C2×C22⋊D43C22⋊C411yescharacteristic
242C2×C22⋊D43C22⋊C411yescharacteristic
243C2×C22⋊D43C22⋊C411yescharacteristic
244C2×C22⋊D43C22⋊C411yescharacteristic
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43C2×D411yescharacteristic
250C22×Dic43C2×D411yescharacteristic
251C22×Dic43C2×D411yescharacteristic
252#10621902—81no—
253#10621900—81no—
254#10621900—81no—
255D4×D43—44no—
256D4×D43—81no—
257D4×D43—81no—
258D4×D43—81no—
259C2×D172—21no—
260C2×D172—21no—
261C2×D172—21no—
262C2×D172—21no—
263C2×D172—81no—
264C2×D172C22×C411yescharacteristic
265C2×D172C22×C411yescharacteristic
266C2×C4×D43—21no—
267C2×C4×D43—24no—
268C2×C4×D43—21no—
269C2×C4×D43—21no—
270C2×C4×D43—21no—
271C2×C4×D43—81no—
272C2×C4×D43—81no—
273C2×C4×D43—81no—
274C2×C4×D43C22×C411yescharacteristic
275C2×C4×D43C22×C411yescharacteristic
276C2×C4×D43C2×D411yescharacteristic
277C2×C4×D43C2×D411yescharacteristic
278C2×Dic86—21no—
279M16×C43—81no—
280C2×C8×C43—21no—
281C2×C8×C43—21no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43C22×C411yescharacteristic
285C4⋊C4×C43C22×C411yescharacteristic
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—21no—
291C42×C43—21no—
292C22⋊Dic43—24no—
293C22⋊Dic43—21no—
294C22⋊Dic43—21no—
295C22⋊Dic43C22⋊C411yescharacteristic
296C22⋊Dic43C22⋊C411yescharacteristic
297C22⋊Dic43C22⋊C411yescharacteristic
298C22⋊Dic43C22⋊C411yescharacteristic
299(C2×D43)⋊C4—24no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4—21no—
306(C2×D43)⋊C4—21no—
307(C2×D43)⋊C4—21no—
308(C2×D43)⋊C4—21no—
309(C2×D43)⋊C4—21no—
310(C2×D43)⋊C4—21no—
311(C2×D43)⋊C4—21no—
312(C2×D43)⋊C4C22⋊C411yescharacteristic
313(C2×D43)⋊C4C22⋊C411yescharacteristic
314(C2×D43)⋊C4C22⋊C411yescharacteristic
315(C2×D43)⋊C4C22⋊C411yescharacteristic
316C4⋊Dic43—21no—
317C4⋊Dic43—21no—
318C4⋊Dic43—21no—
319C4⋊Dic43C22×C411yescharacteristic
320C4⋊Dic43C22×C411yescharacteristic
321Dic43⋊C4—24no—
322Dic43⋊C4—21no—
323Dic43⋊C4—21no—
324Dic43⋊C4—21no—
325Dic43⋊C4—21no—
326Dic43⋊C4C22⋊C411yescharacteristic
327Dic43⋊C4C22⋊C411yescharacteristic
328Dic43⋊C4C22⋊C411yescharacteristic
329Dic43⋊C4C22⋊C411yescharacteristic
330C4×Dic43—24no—
331C4×Dic43—21no—
332C4×Dic43—21no—
333C4×Dic43—81no—
334C4×Dic43—81no—
335C4×Dic43—81no—
336C4×Dic43C22×C411yescharacteristic
337C4×Dic43C22×C411yescharacteristic
338C4×Dic43C2×D411yescharacteristic
339C4×Dic43C2×D411yescharacteristic
340C2×C43⋊C8—21no—
341C2×C43⋊C8—21no—
342C2×C43⋊C8—81no—
343#10621872—81no—
344C8×D43—81no—
345C23×C43—21no—
346C23×C43—21no—
347C23×C43—22no—
348C23×C43—21no—
349C23×C43—41no—
350C23×C43C2×C22⋊C411yescharacteristic
351C23×C43C2×C22⋊C411yescharacteristic
352C23×C43C22×D411yescharacteristic
353C22×D43—21no—
354C22×D43—21no—
355C22×D43—22no—
356C22×D43—21no—
357C22×D43—21no—
358C22×D43—41no—
359C22×D43—42no—
360C22×D43—42no—
361C22×D43—81no—
362C22×D43—81no—
363C22×D43—81no—
364C22×D43—81no—
365C22×D43C2×C22⋊C411yescharacteristic
366C22×D43C2×C22⋊C411yescharacteristic
367Q8×C43—41no—
368D4×C43—41no—
369D4×C43—41no—
370D4×C43—41no—
371D4×C43—42no—
372D4×C43—81no—
373C2×C4×C43—22no—
374C2×C4×C43—22no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
377C2×C4×C43—21no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—81no—
389C2×C4×C43—84no—
390C2×C4×C43C2×C22⋊C411yescharacteristic
391C2×C4×C43C2×C22⋊C411yescharacteristic
392C2×C4×C43C23×C411yescharacteristic
393C2×C4×C43C22×D411yescharacteristic
394C22⋊D43—22no—
395C22⋊D43—22no—
396C22⋊D43—22no—
397C22⋊D43—41no—
398C22⋊D43—41no—
399C22⋊D43—41no—
400C22⋊D43—41no—
401C22⋊D43—42no—
402C22⋊D43—81no—
403C22⋊D43—81no—
404C22⋊D43—81no—
405C22⋊D43—81no—
406C22⋊D43—81no—
407C22⋊D43#10414yes—
408C2×Dic43—21no—
409C2×Dic43—21no—
410C2×Dic43—22no—
411C2×Dic43—22no—
412C2×Dic43—22no—
413C2×Dic43—21no—
414C2×Dic43—21no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43—81no—
421C2×Dic43—81no—
422C2×Dic43C2×C22⋊C411yescharacteristic
423C2×Dic43C2×C22⋊C411yescharacteristic
424C2×Dic43C2×C22⋊C411yescharacteristic
425C2×Dic43C2×C22⋊C411yescharacteristic
426C2×Dic43C2×C22⋊C411yescharacteristic
427C2×Dic43C2×C22⋊C411yescharacteristic
428D172—41no—
429D172—41no—
430D172—42no—
431D172—81no—
432D172—81no—
433D172—81no—
434C4×D43—41no—
435C4×D43—41no—
436C4×D43—41no—
437C4×D43—41no—
438C4×D43—42no—
439C4×D43—81no—
440C4×D43—81no—
441C4×D43—81no—
442C4×D43—84no—
443Dic86—81no—
444C8×C43—41no—
445C8×C43—41no—
446C43⋊C8—41no—
447C43⋊C8—41no—
448#17547—431nomaximal, Sylow
449C22×C43—21no—
450C22×C43—21no—
451C22×C43—21no—
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—21no—
456C22×C43—42no—
457C22×C43—42no—
458C22×C43—41no—
459C22×C43—41no—
460C22×C43—41no—
461C22×C43C2×#10412yes—
462C22×C43C22×C22⋊C411yescharacteristic
463C22×C43#57611yescharacteristic
464C22×C43#57711yescharacteristic
465C2×D43—21no—
466C2×D43—21no—
467C2×D43—21no—
468C2×D43—21no—
469C2×D43—21no—
470C2×D43—42no—
471C2×D43—42no—
472C2×D43—41no—
473C2×D43—41no—
474C2×D43—41no—
475C2×D43—41no—
476C2×D43—41no—
477C2×D43—41no—
478C2×D43—162no—
479C2×D43—162no—
480C2×D43C2×#10412yes—
481C4×C43—21no—
482C4×C43—21no—
483C4×C43—21no—
484C4×C43—21no—
485C4×C43—42no—
486C4×C43—42no—
487C4×C43—41no—
488C4×C43—41no—
489C4×C43—41no—
490Dic43—21no—
491Dic43—21no—
492Dic43—21no—
493Dic43—21no—
494Dic43—21no—
495Dic43—42no—
496Dic43—42no—
497Dic43—41no—
498Dic43—41no—
499Dic43C2×#10412yes—
500#3519—431no—
501#2974—431no—
502#2275—431no—
503#1509—431no—
504#1507—431no—
505#1507—431no—
506#1505—431no—
507#1504—431no—
508#1504D4311yescharacteristic, complemented
509#1502—431no—
510#1501—431no—
511#1501—431no—
512#1500—431no—
513C2×#327—431no—
514C2×#327—431no—
515C2×C43—21no—
516C2×C43—21no—
517C2×C43—22no—
518C2×C43—41no—
519C2×C43—81no—
520C2×C43#288311yescharacteristic
521C2×C43#289711yescharacteristic
522C2×C43C22×#10411yescharacteristic
523D43—22no—
524D43—41no—
525D43—81no—
526D43—81no—
527#555—431no—
528#554—431no—
529#553—431no—
530#553—431no—
531#553—861no—
532#550—431no—
533#546—431no—
534#546—431no—
535#546—861no—
536#546—861no—
537D42—431no—
538D42—861no—
539#540—861no—
540#538—861no—
541#538—861no—
542#532—431no—
543#529—431no—
544#525—431no—
545#525C2×D4311yescharacteristic
546C2×#121—431no—
547C2×#121—431no—
548#518—861no—
549C2×C4×D4—431no—
550C2×C4×D4—861no—
551#436—861no—
552#435—861no—
553#435—861no—
554C8×D4—861no—
555#432—431no—
556#431—431no—
557#407—431no—
558#407C2×D4311yescharacteristic, complemented
559C2×C22⋊C8—431no—
560C2×C22⋊C8—431no—
561C4×C4⋊C4—431no—
562C4×C4⋊C4—861no—
563C4×C22⋊C4—431no—
564C4×C22⋊C4—431no—
565C4×C22⋊C4—861no—
566C4×C22⋊C4—861no—
567#376—431no—
568C2×#95—431no—
569C2×#95C2×D4311yescharacteristic, complemented
570#328—431no—
571#328—431no—
572#328C2×D4311yescharacteristic, complemented
573#328C2×D4311yescharacteristic, complemented
574#327—431no—
575#327—431no—
576#327—431no—
577#327—431no—
578#327—431no—
579#327—431no—
580#327—431no—
581#327—431no—
582#327—431no—
583#327—431no—
584#327C2×D4311yescharacteristic, complemented
585#327C2×D4311yescharacteristic, complemented
586C43#1754711yescharacteristic, complemented, Sylow
587C2×#41—431no—
588C2×#41—861no—
589C2×#41C4×D4311yescharacteristic, complemented
590C22×D4—431no—
591C22×D4—431no—
592C22×D4—431no—
593C22×D4—861no—
594C22×D4—861no—
595C22×D4—861no—
596C23×C4—21no—
597C23×C4—431no—
598C23×C4—861no—
599C23×C4C22×D4311yescharacteristic
600C2×M16—21no—
601C2×M16—861no—
602C22×C8—861no—
603C22×C8—861no—
604C4⋊Q8—431no—
605#127—431no—
606#127—861no—
607#126—861no—
608#126—861no—
609#126—861no—
610#125—431no—
611#125—861no—
612#124—431no—
613#124—861no—
614#124—861no—
615#124—861no—
616#123—21no—
617#123—861no—
618#123—861no—
619#123—861no—
620#123—861no—
621#123—861no—
622#123—861no—
623C22⋊Q8—431no—
624C22⋊Q8—861no—
625C22⋊Q8—861no—
626C22⋊Q8C4×D4311yescharacteristic, complemented
627C22⋊Q8C22×D4311yescharacteristic
628#121—431no—
629#121—431no—
630#121—431no—
631#121—431no—
632#121—431no—
633#121—431no—
634#121—431no—
635#121—861no—
636#121—861no—
637#121—861no—
638#121—861no—
639#121—861no—
640#121—861no—
641#121—861no—
642#121—861no—
643#121—861no—
644#121—861no—
645#121—861no—
646#121—861no—
647#121—861no—
648#121C4×D4311yescharacteristic, complemented
649#121C22×D4311yescharacteristic
650#120—21no—
651#120—861no—
652#120—861no—
653#120—861no—
654#120—861no—
655#120—861no—
656C4×Q8—431no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—431no—
660C4×D4—431no—
661C4×D4—431no—
662C4×D4—431no—
663C4×D4—431no—
664C4×D4—431no—
665C4×D4—431no—
666C4×D4—431no—
667C4×D4—431no—
668C4×D4—431no—
669C4×D4—431no—
670C4×D4—861no—
671C4×D4—861no—
672C4×D4—861no—
673C4×D4—861no—
674C4×D4—861no—
675C4×D4—861no—
676C4×D4—861no—
677C4×D4—861no—
678C4×D4—868no—
679#117—431no—
680#117—861no—
681#117—861no—
682#117C4×D4311yescharacteristic, complemented
683C2×C4⋊C4—431no—
684C2×C4⋊C4—431no—
685C2×C4⋊C4—431no—
686C2×C4⋊C4—861no—
687C2×C22⋊C4—431no—
688C2×C22⋊C4—431no—
689C2×C22⋊C4—861no—
690C2×C22⋊C4—861no—
691C2×C22⋊C4—861no—
692C2×C22⋊C4—861no—
693C2×C22⋊C4—861no—
694C2×C22⋊C4—861no—
695C2×C42—431no—
696C2×C42—861no—
697C2×C42—861no—
698C2×C42—861no—
699C2×C42—861no—
700C4⋊C8—861no—
701C4⋊C8—861no—
702C22⋊C8—21no—
703C22⋊C8—431no—
704C22⋊C8—431no—
705C22⋊C8—861no—
706C22⋊C8—861no—
707C22⋊C8—861no—
708C22⋊C8C22×D4311yescharacteristic
709C22⋊C8C22×D4311yescharacteristic
710#97—861no—
711C4×C8—861no—
712#95—21no—
713#95—431no—
714#95—431no—
715#95—861no—
716#95—861no—
717#95C22×D4311yescharacteristic
718#95C22×D4311yescharacteristic
719C24—431no—
720C24—861no—
721C24—861no—
722C24D4×D4311yescharacteristic
723#41—81no—
724#41—3441no—
725#41—3441no—
726#41—3441no—
727C2×Q8—861no—
728C2×Q8C2×C4×D4311yescharacteristic
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—431no—
733C2×D4—431no—
734C2×D4—431no—
735C2×D4—431no—
736C2×D4—431no—
737C2×D4—431no—
738C2×D4—861no—
739C2×D4—861no—
740C2×D4—861no—
741C2×D4—861no—
742C2×D4—861no—
743C2×D4—861no—
744C2×D4—864no—
745C2×D4—861no—
746C2×D4—861no—
747C2×D4—861no—
748C2×D4—861no—
749C2×D4—861no—
750C2×D4—861no—
751C2×D4—3441no—
752C2×D4—3441no—
753C2×D4—3441no—
754C2×D4—3441no—
755C2×D4—3441no—
756C2×D4—3441no—
757C2×D4—1724no—
758C2×D4C2×C4×D4311yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—24no—
762C22×C4—21no—
763C22×C4—81no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—431no—
767C22×C4—431no—
768C22×C4—431no—
769C22×C4—431no—
770C22×C4—431no—
771C22×C4—431no—
772C22×C4—431no—
773C22×C4—861no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—861no—
777C22×C4—864no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—3441no—
783C22×C4—3441no—
784C22×C4—3441no—
785C22×C4C2×C4×D4311yescharacteristic
786C22×C4C2×C4×D4311yescharacteristic
787C22×C4D4×D4311yescharacteristic
788C22×C4D4×D4311yescharacteristic
789C22×C4D4×D4311yescharacteristic
790C22×C4C23×D4311yescharacteristic
791M16—81no—
792M16—3441no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—861no—
796C2×C8—861no—
797C2×C8—3441no—
798C2×C8—3441no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—431no—
802C4⋊C4—431no—
803C4⋊C4—431no—
804C4⋊C4—431no—
805C4⋊C4—431no—
806C4⋊C4—431no—
807C4⋊C4—861no—
808C4⋊C4—861no—
809C4⋊C4—861no—
810C4⋊C4—861no—
811C4⋊C4—861no—
812C4⋊C4—861no—
813C4⋊C4—864no—
814C4⋊C4—861no—
815C4⋊C4C2×C4×D4311yescharacteristic
816C4⋊C4C2×C4×D4311yescharacteristic
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—431no—
823C22⋊C4—431no—
824C22⋊C4—431no—
825C22⋊C4—431no—
826C22⋊C4—431no—
827C22⋊C4—431no—
828C22⋊C4—431no—
829C22⋊C4—431no—
830C22⋊C4—861no—
831C22⋊C4—861no—
832C22⋊C4—861no—
833C22⋊C4—861no—
834C22⋊C4—861no—
835C22⋊C4—861no—
836C22⋊C4—861no—
837C22⋊C4—861no—
838C22⋊C4—864no—
839C22⋊C4—861no—
840C22⋊C4—861no—
841C22⋊C4—864no—
842C22⋊C4—861no—
843C22⋊C4—861no—
844C22⋊C4—861no—
845C22⋊C4—861no—
846C42—21no—
847C42—431no—
848C42—431no—
849C42—431no—
850C42—431no—
851C42—861no—
852C42—861no—
853C42—864no—
854C42—3441no—
855C42—3441no—
856C42—3441no—
857C23—22no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—41no—
862C23—431no—
863C23—431no—
864C23—862no—
865C23—861no—
866C23—861no—
867C23—861no—
868C23—861no—
869C23—3441no—
870C23—3441no—
871C23—3441no—
872C23—3441no—
873C23—1721no—
874C23—1722no—
875C23—1722no—
876C23C22⋊C4×D4311yescharacteristic
877C23C22⋊C4×D4311yescharacteristic
878C23C2×D4×D4311yescharacteristic
879Q8—41no—
880Q8—3441no—
881D4—41no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—81no—
886D4—434no—
887D4—862no—
888D4—862no—
889D4—862no—
890D4—3441no—
891D4—3441no—
892D4—3441no—
893D4—3441no—
894D4—3441no—
895D4—3441no—
896D4—3441no—
897D4—3441no—
898D4—1721no—
899D4—1721no—
900D4—1722no—
901D4—1722no—
902D4—1721no—
903D4—1721no—
904D4—1721no—
905D4—1721no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—81no—
922C2×C4—84no—
923C2×C4—431no—
924C2×C4—431no—
925C2×C4—431no—
926C2×C4—431no—
927C2×C4—431no—
928C2×C4—431no—
929C2×C4—862no—
930C2×C4—861no—
931C2×C4—861no—
932C2×C4—862no—
933C2×C4—862no—
934C2×C4—861no—
935C2×C4—861no—
936C2×C4—3441no—
937C2×C4—3441no—
938C2×C4—3441no—
939C2×C4—3444no—
940C2×C4—3441no—
941C2×C4—3441no—
942C2×C4—1721no—
943C2×C4—1721no—
944C2×C4—1721no—
945C2×C4—1721no—
946C2×C4—1722no—
947C2×C4—1721no—
948C2×C4—1721no—
949C2×C4—1721no—
950C2×C4—1721no—
951C2×C4—1721no—
952C2×C4C22⋊C4×D4311yescharacteristic
953C2×C4C22⋊C4×D4311yescharacteristic
954C2×C4C22×C4×D4311yescharacteristic
955C2×C4C2×D4×D4311yescharacteristic
956C8—41no—
957C8—41no—
958C8—1721no—
959C8—1721no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—42no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—432no—
973C22—861no—
974C22—861no—
975C22—861no—
976C22—861no—
977C22—861no—
978C22—1722no—
979C22—1722no—
980C22—1721no—
981C22—1721no—
982C22—1721no—
983C22—1721no—
984C22—1721no—
985C22—1721no—
986C22—6882no—
987C22—6882no—
988C22#104×D4312yes—
989C22C2×C22⋊C4×D4311yescharacteristic
990C22#1458370311yescharacteristic
991C22#1458370811yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—41no—
1001C4—432no—
1002C4—861no—
1003C4—861no—
1004C4—861no—
1005C4—861no—
1006C4—861no—
1007C4—1722no—
1008C4—1722no—
1009C4—1721no—
1010C4—1721no—
1011C2—21no—
1012C2—21no—
1013C2—22no—
1014C2—41no—
1015C2—81no—
1016C2—862no—
1017C2—3441no—
1018C2—3441no—
1019C2—1721no—
1020C2#1914305311yescharacteristic
1021C2#1914311911yescharacteristic
1022C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1504C2
socleC22×C43C22×C22⋊C4
prime radical#19148615C2
cosocleC22×C4×C43C24
hypercenter#1504D43
hypocenterC43#17547
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #19143631C2semidirect
3. #19136953C2semidirect
4. #19133119C2semidirect
5. #19133112C2semidirect
6. #19133109C2semidirect
7. #19133101C2semidirect
8. #19133098C2semidirect
9. #19133088C2semidirect
10. #19133086C2semidirect
11. #19133085C2semidirect
12. #19133080C2semidirect
13. C2×#14582632C2semidirect
14. #327×D43C2semidirect
15. C43×#1504C2semidirect
16. #14583612C4semidirect
17. #14583607C4semidirect
18. #14583601C4semidirect
20. #14583593C4semidirect
21. #14583568C4semidirect
23. #14583540C4semidirect
24. #14583537C4semidirect
26. #14583533C4semidirect
43. #14582953C22semidirect
44. #14582949C22semidirect
45. #14582861C22semidirect
46. C2×C22⋊(C43⋊C8)C22semidirect
47. C22⋊C8×D43C22semidirect
49. #14582750C22semidirect
51. C4×C22⋊Dic43C22semidirect
53. #14582746C22semidirect
54. #14582744C22semidirect
55. #95×D43C22semidirect
56. #14582636C22semidirect
57. #14582636C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
62. #14582633C22semidirect
63. #14582633C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
69. C43×#407C22semidirect
70. C2×#95×C43C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
73. C43×#327C22semidirect
74. C43×#327C22semidirect
75. C2×#10621902C2×C4semidirect
77. C22×D172C2×C4semidirect
82. C2×D4×D43C2×C4semidirect
88. #13063324C2×C4semidirect
90. #13063321C2×C4semidirect
94. #13063316C2×C4semidirect
96. #13063314C2×C4semidirect
108. #13063301C2×C4semidirect
110. #13063300C2×C4semidirect
111. #13063300C2×C4semidirect
115. #13063299C2×C4semidirect
116. #13063299C2×C4semidirect
128. #13063296C2×C4semidirect
134. Q8×Dic43C2×C4semidirect
137. D4×Dic43C2×C4semidirect
139. #13063287C2×C4semidirect
140. #13063287C2×C4semidirect
156. #13063283C2×C4semidirect
158. C2×C4⋊Dic43C2×C4semidirect
161. C4⋊C4×D43C2×C4semidirect
188. C2×#41×C43C2×C4semidirect
193. C22⋊Q8×C43C2×C4semidirect
195. #121×C43C2×C4semidirect
200. #117×C43C2×C4semidirect
508. #1504D43semidirect
558. #407C2×D43semidirect
569. C2×#95C2×D43semidirect
572. #328C2×D43semidirect
573. #328C2×D43semidirect
584. #327C2×D43semidirect
585. #327C2×D43semidirect
586. C43#17547semidirect
589. C2×#41C4×D43semidirect
626. C22⋊Q8C4×D43semidirect
648. #121C4×D43semidirect
682. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191486152
#191436312
#191369532
#191331192
#191331122
#191331092
#191331012
#191330982
#191330882
#191330862
#191330852
#191330802
C2×#145826322
#327×D432
C43×#15042
#1754743