Finite Group Databasebeta

← #25062869

Subgroups — #25062869

Order 11008.

1060 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583574C211yesmaximal, characteristic
2#19143632C211yesmaximal, characteristic, complemented
3#19143629C211yesmaximal, characteristic, complemented
4#19132964C211yesmaximal, characteristic, complemented
5#19132957C211yesmaximal, characteristic, complemented
6#19132957C211yesmaximal, characteristic, complemented
7#19132940C211yesmaximal, characteristic, complemented
8#19132940C211yesmaximal, characteristic, complemented
9#19132932C211yesmaximal, characteristic, complemented
10#19132927C211yesmaximal, characteristic, complemented
11#19132920C211yesmaximal, characteristic, complemented
12#19132912C211yesmaximal, characteristic, complemented
13#19132907C211yesmaximal, characteristic, complemented
14#323×D43C211yesmaximal, characteristic, complemented
15C43×#1473C211yesmaximal, characteristic, complemented
16#14583574—21no—
17#14583574—21no—
18#14583574—21no—
19#14583574—21no—
20#14583574—21no—
21#14583574—21no—
22#14583574—21no—
23#14583574—21no—
24C2×#13063318C411yescharacteristic
25C2×#13063311C411yescharacteristic
26C2×#13063310C411yescharacteristic
27C2×#13063310C411yescharacteristic
28C2×#13063307C2211yescharacteristic
29C2×#13063305C411yescharacteristic
30C2×#13063303C2211yescharacteristic
31C2×#13063295C411yescharacteristic
32C2×C4×D172C2211yescharacteristic
33C2×#13063287C2211yescharacteristic
34C2×#13063283C411yescharacteristic
35C2×#13063282C2211yescharacteristic
36C2×C22⋊C4×D43C411yescharacteristic
37C2×C22⋊C4×D43C2211yescharacteristic
38#14582978—21no—
39#14582976—21no—
40#14582972—21no—
41#14582972—21no—
42#14582969—21no—
43#14582969—21no—
44C8×D172—21no—
45#14582964—21no—
46#14582956C2211yescharacteristic, complemented
47#14582952C2211yescharacteristic, complemented
48#14582861C2211yescharacteristic
49#14582861C2211yescharacteristic
50#14582861C2211yescharacteristic, complemented
51#14582861C2211yescharacteristic, complemented
52C22⋊C8×D43C2211yescharacteristic
53C22⋊C8×D43C2211yescharacteristic
54C22⋊C8×D43C2211yescharacteristic, complemented
55C22⋊C8×D43C2211yescharacteristic, complemented
56#14582625C2211yescharacteristic, complemented
57#14582625C2211yescharacteristic, complemented
58#14582624C2211yescharacteristic, complemented
59#14582624C2211yescharacteristic, complemented
60#14582624C2211yescharacteristic, complemented
61#14582624C2211yescharacteristic, complemented
62#14582623C2211yescharacteristic
63#14582623C2211yescharacteristic
64#14582622C2211yescharacteristic
65#14582622C2211yescharacteristic
66#14582622C2211yescharacteristic
67#14582622C2211yescharacteristic
68C2×#126×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C43×#431C2211yescharacteristic, complemented
71C43×#324C2211yescharacteristic, complemented
72C43×#324C2211yescharacteristic, complemented
73C43×#323C2211yescharacteristic
74C43×#323C2211yescharacteristic
75C24×D43C2×C411yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C22×D172C2×C411yescharacteristic
78C22×D172C2×C411yescharacteristic
79C22×C22⋊D43C2×C411yescharacteristic
80C22×C4×D43C2×C411yescharacteristic
81C22×C4×D43C2×C411yescharacteristic
82C22×C4×D43C2×C411yescharacteristic
83C22×C4×D43C2311yescharacteristic
84C22×C4×D43C2311yescharacteristic
85C2×#10621872—21no—
86C2×#10621872—21no—
87C2×#10621872—21no—
88C2×#10621872—21no—
89C2×C8×D43—21no—
90C2×C8×D43—21no—
91C2×C8×D43—21no—
92C2×C8×D43—21no—
93#13063318—21no—
94#13063318—21no—
95#13063318—21no—
96#13063318—21no—
97#13063311—21no—
98#13063311—21no—
99#13063311—21no—
100#13063311—21no—
101#13063310—21no—
102#13063310—21no—
103#13063310—21no—
104#13063310—21no—
105#13063310—21no—
106#13063310—21no—
107#13063310—21no—
108#13063310—21no—
109#13063307—21no—
110#13063307—21no—
111#13063307—21no—
112#13063307—21no—
113#13063305—21no—
114#13063305—21no—
115#13063305—21no—
116#13063305—21no—
117#13063303—21no—
118#13063303—21no—
119#13063303—21no—
120#13063303—21no—
121#13063295—21no—
122#13063295—21no—
123#13063295—21no—
124#13063295—21no—
125C4×D172D411yescharacteristic
126C4×D172D411yescharacteristic
127C4×D172D411yescharacteristic
128C4×D172D411yescharacteristic
129C4×D172D411yescharacteristic
130C4×D172D411yescharacteristic
131C4×D172D411yescharacteristic
132C4×D172D411yescharacteristic
133#13063287—21no—
134#13063287—21no—
135#13063287—21no—
136#13063287—21no—
137#13063283—21no—
138#13063283—21no—
139#13063283—21no—
140#13063283—21no—
141#13063282—21no—
142#13063282—21no—
143#13063282—21no—
144#13063282—21no—
145C2×C4⋊Dic43C2×C411yescharacteristic
146C2×C4⋊Dic43C2×C411yescharacteristic
147C2×Dic43⋊C4C2×C411yescharacteristic
148C2×Dic43⋊C4C2×C411yescharacteristic
149C2×Dic43⋊C4C2311yescharacteristic
150C2×C22⋊Dic43C2×C411yescharacteristic
151C2×C22⋊Dic43C2×C411yescharacteristic
152C2×(C2×D43)⋊C4C2×C411yescharacteristic
153C2×(C2×D43)⋊C4C2×C411yescharacteristic
154C2×(C2×D43)⋊C4C2×C411yescharacteristic
155C2×(C2×D43)⋊C4C2×C411yescharacteristic
156C2×(C2×D43)⋊C4C2×C411yescharacteristic
157C2×(C2×D43)⋊C4C2×C411yescharacteristic
158C2×(C2×D43)⋊C4C2×C411yescharacteristic
159C2×(C2×D43)⋊C4C2×C411yescharacteristic
160C2×(C2×D43)⋊C4C2311yescharacteristic
161C22⋊C4×D43—21no—
162C22⋊C4×D43—21no—
163C22⋊C4×D43—21no—
164C22⋊C4×D43—21no—
165C22⋊C4×D43—21no—
166C22⋊C4×D43—21no—
167C22⋊C4×D43—21no—
168C22⋊C4×D43—21no—
169C2×C4×Dic43C2×C411yescharacteristic
170C2×C4×Dic43C2×C411yescharacteristic
171C4⋊(C43⋊C8)—21no—
172C4⋊(C43⋊C8)—21no—
173C22⋊(C43⋊C8)C2311yescharacteristic
174C22⋊(C43⋊C8)C2311yescharacteristic
175C22⋊(C43⋊C8)C2311yescharacteristic
176C22⋊(C43⋊C8)C2311yescharacteristic
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181(C2×D43)⋊C8—21no—
182(C2×D43)⋊C8—21no—
183(C2×D43)⋊C8—21no—
184(C2×D43)⋊C8—21no—
185#13063236—21no—
186C4×C43⋊C8—21no—
187#126×C43—21no—
188#126×C43—21no—
189#126×C43—21no—
190#126×C43—21no—
191C2×C4⋊C4×C43C2×C411yescharacteristic
192C2×C4⋊C4×C43C2×C411yescharacteristic
193C2×C4⋊C4×C43C2311yescharacteristic
194C2×C22⋊C4×C43C2×C411yescharacteristic
195C2×C22⋊C4×C43C2×C411yescharacteristic
196C2×C22⋊C4×C43C2311yescharacteristic
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C4⋊C8×C43—21no—
200C22⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204#97×C43—21no—
205C4×C8×C43—21no—
206C24×C43C22×C411yescharacteristic
207C23×D43—21no—
208C23×D43—21no—
209C23×D43—22no—
210C23×D43—41no—
211C23×D43—42no—
212C23×D43—81no—
213C23×D43C22×C411yescharacteristic
214C23×D43C22×C411yescharacteristic
215C23×D43C22×C411yescharacteristic
216C22×C4×C43C22×C411yescharacteristic
217C22×C4×C43C22×C411yescharacteristic
218C22×C4×C43C22×C411yescharacteristic
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C2411yescharacteristic
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C2×C22⋊D43—81no—
225C22×Dic43C22×C411yescharacteristic
226C22×Dic43C22×C411yescharacteristic
227C22×Dic43C22×C411yescharacteristic
228C22×Dic43C22×C411yescharacteristic
229C22×Dic43C22×C411yescharacteristic
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—22no—
233C2×D172—41no—
234C2×D172—42no—
235C2×D172C22⋊C411yescharacteristic
236C2×D172C22⋊C411yescharacteristic
237C2×D172C22⋊C411yescharacteristic
238C2×D172C22⋊C411yescharacteristic
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—22no—
246C2×C4×D43—41no—
247C2×C4×D43—42no—
248C2×C4×D43—81no—
249C2×C4×D43—81no—
250C2×C4×D43—81no—
251C2×C4×D43C2×D411yescharacteristic
252C2×C4×D43C2×D411yescharacteristic
253C2×C4×D43C2×D411yescharacteristic
254C2×C4×D43C2×D411yescharacteristic
255C2×C4×D43C2×D411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×C4×D43C2×D411yescharacteristic
259C2×Dic86—21no—
260C2×Dic86—21no—
261C2×Dic86—81no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C22⋊C4×C43—21no—
276C22⋊C4×C43—21no—
277C22⋊C4×C43—21no—
278C42×C43C2×D411yescharacteristic
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2×D411yescharacteristic
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43—21no—
285C22⋊Dic43—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4C22⋊C411yescharacteristic
301(C2×D43)⋊C4C22⋊C411yescharacteristic
302(C2×D43)⋊C4C22⋊C411yescharacteristic
303(C2×D43)⋊C4C22⋊C411yescharacteristic
304(C2×D43)⋊C4C22⋊C411yescharacteristic
305(C2×D43)⋊C4C22⋊C411yescharacteristic
306(C2×D43)⋊C4C22⋊C411yescharacteristic
307(C2×D43)⋊C4C22⋊C411yescharacteristic
308C4⋊Dic43—21no—
309C4⋊Dic43—21no—
310C4⋊Dic43C22⋊C411yescharacteristic
311C4⋊Dic43C22⋊C411yescharacteristic
312C4⋊Dic43C22⋊C411yescharacteristic
313C4⋊Dic43C22⋊C411yescharacteristic
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320C4×Dic43—21no—
321C4×Dic43—21no—
322C4×Dic43—21no—
323C4×Dic43—21no—
324C2×C43⋊C8—21no—
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327C2×C43⋊C8—21no—
328#10621872—81no—
329#10621872—81no—
330#10621872—81no—
331#10621872—81no—
332C8×D43—81no—
333C8×D43—81no—
334C8×D43—81no—
335C8×D43—81no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—21no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43C23×C411yescharacteristic
342C22×D43—21no—
343C22×D43—21no—
344C22×D43—21no—
345C22×D43—21no—
346C22×D43—21no—
347C22×D43—21no—
348C22×D43—22no—
349C22×D43—41no—
350C22×D43—41no—
351C22×D43—41no—
352C22×D43—42no—
353C22×D43—42no—
354C22×D43—42no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—42no—
358C22×D43—81no—
359C22×D43—81no—
360C22×D43—84no—
361C22×D43—84no—
362C22×D43C2×C22⋊C411yescharacteristic
363C22×D43C2×C22⋊C411yescharacteristic
364C22×D43C2×C22⋊C411yescharacteristic
365C22×D43C2×C22⋊C411yescharacteristic
366C22×D43#13112yes—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
371C2×C4×C43—21no—
372C2×C4×C43—21no—
373C2×C4×C43—21no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43C2×C22⋊C411yescharacteristic
379C2×C4×C43C2×C22⋊C411yescharacteristic
380C2×C4×C43C2×C22⋊C411yescharacteristic
381C2×C4×C43C2×C22⋊C411yescharacteristic
382C2×C4×C43C22×D411yescharacteristic
383C2×C4×C43C22×D411yescharacteristic
384C22⋊D43—81no—
385C22⋊D43—81no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—21no—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43C2×C22⋊C411yescharacteristic
396C2×Dic43C2×C22⋊C411yescharacteristic
397C2×Dic43C2×C22⋊C411yescharacteristic
398C2×Dic43C2×C22⋊C411yescharacteristic
399D172—22no—
400D172—22no—
401D172—41no—
402D172—41no—
403D172—42no—
404D172—42no—
405C4×D43—41no—
406C4×D43—41no—
407C4×D43—41no—
408C4×D43—41no—
409C4×D43—41no—
410C4×D43—41no—
411C4×D43—41no—
412C4×D43—41no—
413C4×D43—42no—
414C4×D43—42no—
415C4×D43—42no—
416C4×D43—42no—
417C4×D43—81no—
418C4×D43—81no—
419Dic86—81no—
420Dic86—81no—
421C8×C43—41no—
422C8×C43—41no—
423C8×C43—41no—
424C8×C43—41no—
425C43⋊C8—41no—
426C43⋊C8—41no—
427C43⋊C8—41no—
428C43⋊C8—41no—
429#17422—431nomaximal, Sylow
430C22×C43—21no—
431C22×C43—21no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—81no—
436C22×C43—81no—
437C22×C43C22×C22⋊C411yescharacteristic
438C22×C43C2×#13111yescharacteristic
439C22×C43#56811yescharacteristic
440C2×D43—21no—
441C2×D43—21no—
442C2×D43—21no—
443C2×D43—22no—
444C2×D43—21no—
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—21no—
450C2×D43—21no—
451C2×D43—21no—
452C2×D43—42no—
453C2×D43—42no—
454C2×D43—42no—
455C2×D43—41no—
456C2×D43—41no—
457C2×D43—42no—
458C2×D43—84no—
459C2×D43—81no—
460C2×D43—81no—
461C2×D43—84no—
462C2×D43#41312yes—
463C4×C43—21no—
464C4×C43—21no—
465C4×C43—21no—
466C4×C43—21no—
467C4×C43—21no—
468C4×C43—21no—
469C4×C43—41no—
470C4×C43—41no—
471C4×C43—41no—
472Dic43—21no—
473Dic43—21no—
474Dic43—21no—
475Dic43—21no—
476Dic43—41no—
477Dic43—41no—
478Dic43—41no—
479C2×#551—431no—
480#2974—431no—
481#2974—431no—
482#1473—431no—
483#1473D4311yescharacteristic, complemented
484#1472—431no—
485#1472—431no—
486#1468—431no—
487#1468—431no—
488#1465—431no—
489#1464—431no—
490#1462—431no—
491#1459—431no—
492#1458—431no—
493C2×#323—431no—
494C2×C43—21no—
495C2×C43—21no—
496C2×C43—81no—
497C2×C43#288011yescharacteristic
498C2×C43#288311yescharacteristic
499C2×C43C2×#41311yescharacteristic
500D43—22no—
501D43—41no—
502D43—41no—
503D43—41no—
504D43—42no—
505#551—861no—
506#551—861no—
507#551—861no—
508#551—861no—
509#551—861no—
510#551—861no—
511#551—861no—
512#551—861no—
513C2×#126—431no—
514C2×#126C2×D4311yescharacteristic
515C2×#124—431no—
516C2×#123—431no—
517C2×#123—431no—
518C2×#123—431no—
519C2×C22⋊Q8—431no—
520C2×C22⋊Q8—431no—
521C2×#120—431no—
522C2×C4×D4—431no—
523C2×C4×D4—431no—
524C2×#117—431no—
525C2×#117—431no—
526C22×C22⋊C4—431no—
527C22×C22⋊C4—431no—
528#436—861no—
529#436—861no—
530#435—861no—
531#435—861no—
532#435—861no—
533#435—861no—
534C8×D4—861no—
535C8×D4—861no—
536#432—431no—
537#432C2×D4311yescharacteristic, complemented
538#431—431no—
539#431C2×D4311yescharacteristic, complemented
540#407—431no—
541#407—431no—
542#407—431no—
543#407—431no—
544C2×C22⋊C8—431no—
545C2×C22⋊C8—431no—
546C2×C22⋊C8—431no—
547C2×C22⋊C8—431no—
548#324—431no—
549#324—431no—
550#324—431no—
551#324—431no—
552#324—431no—
553#324—431no—
554#324C2×D4311yescharacteristic, complemented
555#324C2×D4311yescharacteristic, complemented
556#323—431no—
557#323—431no—
558#323—431no—
559#323—431no—
560#323—431no—
561#323—431no—
562#323C2×D4311yescharacteristic
563#323C2×D4311yescharacteristic
564C43#1742211yescharacteristic, complemented, Sylow
565C25—431no—
566C22×Q8—431no—
567C22×D4—431no—
568C22×D4—431no—
569C22×D4—431no—
570C23×C4—431no—
571C23×C4—431no—
572C23×C4—431no—
573C23×C4—431no—
574C23×C4—431no—
575C2×M16—861no—
576C2×M16—861no—
577C2×M16—861no—
578C2×M16—861no—
579C22×C8—861no—
580C22×C8—861no—
581C22×C8—861no—
582C22×C8—861no—
583#126—21no—
584#126—21no—
585#126—21no—
586#126—21no—
587#126—861no—
588#126—861no—
589#126—861no—
590#126—861no—
591#124—861no—
592#124—861no—
593#124—861no—
594#124—861no—
595#123—861no—
596#123—861no—
597#123—861no—
598#123—861no—
599#123—861no—
600#123—861no—
601#123—861no—
602#123—861no—
603#123—861no—
604#123—861no—
605#123—861no—
606#123—861no—
607C22⋊Q8—861no—
608C22⋊Q8—861no—
609C22⋊Q8—861no—
610C22⋊Q8—861no—
611C22⋊Q8—861no—
612C22⋊Q8—861no—
613C22⋊Q8—861no—
614C22⋊Q8—861no—
615#120—861no—
616#120—861no—
617#120—861no—
618#120—861no—
619C4×D4—431no—
620C4×D4—431no—
621C4×D4—431no—
622C4×D4—431no—
623C4×D4—431no—
624C4×D4—431no—
625C4×D4—431no—
626C4×D4—431no—
627C4×D4—861no—
628C4×D4—861no—
629C4×D4—861no—
630C4×D4—861no—
631#117—861no—
632#117—861no—
633#117—861no—
634#117—861no—
635#117—861no—
636#117—861no—
637#117—861no—
638#117—861no—
639C2×C4⋊C4—431no—
640C2×C4⋊C4—431no—
641C2×C4⋊C4—431no—
642C2×C4⋊C4—431no—
643C2×C4⋊C4—431no—
644C2×C4⋊C4C4×D4311yescharacteristic
645C2×C4⋊C4C4×D4311yescharacteristic
646C2×C4⋊C4C22×D4311yescharacteristic
647C2×C22⋊C4—431no—
648C2×C22⋊C4—431no—
649C2×C22⋊C4—431no—
650C2×C22⋊C4—431no—
651C2×C22⋊C4—431no—
652C2×C22⋊C4—431no—
653C2×C22⋊C4—431no—
654C2×C22⋊C4—431no—
655C2×C22⋊C4—431no—
656C2×C22⋊C4—431no—
657C2×C22⋊C4—431no—
658C2×C22⋊C4—861no—
659C2×C22⋊C4—861no—
660C2×C22⋊C4—861no—
661C2×C22⋊C4—861no—
662C2×C22⋊C4—861no—
663C2×C22⋊C4—861no—
664C2×C22⋊C4—861no—
665C2×C22⋊C4—861no—
666C2×C22⋊C4C4×D4311yescharacteristic
667C2×C22⋊C4C4×D4311yescharacteristic
668C2×C22⋊C4C22×D4311yescharacteristic
669C2×C42—431no—
670C2×C42—431no—
671C2×C42C22×D4311yescharacteristic
672C4⋊C8—21no—
673C4⋊C8—21no—
674C4⋊C8—861no—
675C4⋊C8—861no—
676C22⋊C8—431no—
677C22⋊C8—431no—
678C22⋊C8—431no—
679C22⋊C8—431no—
680C22⋊C8—861no—
681C22⋊C8—861no—
682C22⋊C8—861no—
683C22⋊C8—861no—
684C22⋊C8—861no—
685C22⋊C8—861no—
686C22⋊C8—861no—
687C22⋊C8—861no—
688C22⋊C8C22×D4311yescharacteristic
689C22⋊C8C22×D4311yescharacteristic
690C22⋊C8C22×D4311yescharacteristic
691C22⋊C8C22×D4311yescharacteristic
692#97—21no—
693#97—861no—
694C4×C8—21no—
695C4×C8—861no—
696C24—431no—
697C24—431no—
698C24—431no—
699C24—862no—
700C24—861no—
701C24—861no—
702C24—3441no—
703C24—1721no—
704C24—1722no—
705C24C2×C4×D4311yescharacteristic
706C2×Q8—861no—
707C2×Q8—861no—
708C2×Q8—3441no—
709C2×D4—431no—
710C2×D4—431no—
711C2×D4—431no—
712C2×D4—431no—
713C2×D4—861no—
714C2×D4—861no—
715C2×D4—862no—
716C2×D4—861no—
717C2×D4—861no—
718C2×D4—3441no—
719C2×D4—1721no—
720C2×D4—1722no—
721C22×C4—431no—
722C22×C4—431no—
723C22×C4—431no—
724C22×C4—431no—
725C22×C4—431no—
726C22×C4—431no—
727C22×C4—431no—
728C22×C4—431no—
729C22×C4—431no—
730C22×C4—431no—
731C22×C4—431no—
732C22×C4—431no—
733C22×C4—431no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—862no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—3441no—
742C22×C4—3441no—
743C22×C4—3441no—
744C22×C4—1721no—
745C22×C4—1722no—
746C22×C4C2×C4×D4311yescharacteristic
747C22×C4C2×C4×D4311yescharacteristic
748C22×C4C2×C4×D4311yescharacteristic
749C22×C4C2×C4×D4311yescharacteristic
750C22×C4C2×C4×D4311yescharacteristic
751C22×C4C23×D4311yescharacteristic
752M16—3441no—
753M16—3441no—
754M16—3441no—
755M16—3441no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—861no—
761C2×C8—861no—
762C2×C8—861no—
763C2×C8—861no—
764C2×C8—3441no—
765C2×C8—3441no—
766C2×C8—3441no—
767C2×C8—3441no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—431no—
775C4⋊C4—431no—
776C4⋊C4—431no—
777C4⋊C4—431no—
778C4⋊C4—861no—
779C4⋊C4—861no—
780C4⋊C4—861no—
781C4⋊C4—861no—
782C4⋊C4—861no—
783C4⋊C4—861no—
784C4⋊C4—861no—
785C4⋊C4—861no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—431no—
793C22⋊C4—431no—
794C22⋊C4—431no—
795C22⋊C4—431no—
796C22⋊C4—431no—
797C22⋊C4—431no—
798C22⋊C4—431no—
799C22⋊C4—431no—
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⋊C4—861no—
811C22⋊C4—861no—
812C22⋊C4—861no—
813C22⋊C4—861no—
814C22⋊C4—861no—
815C22⋊C4—861no—
816C22⋊C4—861no—
817C22⋊C4—861no—
818C42—861no—
819C42—861no—
820C42—861no—
821C42—861no—
822C42D4×D4311yescharacteristic
823C42D4×D4311yescharacteristic
824C42D4×D4311yescharacteristic
825C42D4×D4311yescharacteristic
826C23—21no—
827C23—21no—
828C23—21no—
829C23—41no—
830C23—41no—
831C23—431no—
832C23—431no—
833C23—431no—
834C23—431no—
835C23—432no—
836C23—862no—
837C23—861no—
838C23—861no—
839C23—861no—
840C23—861no—
841C23—861no—
842C23—861no—
843C23—3441no—
844C23—3441no—
845C23—3444no—
846C23—3444no—
847C23—1721no—
848C23—1721no—
849C23—1721no—
850C23—1721no—
851C23—1721no—
852C23—1722no—
853C23—1722no—
854C23—1722no—
855C23—1722no—
856C23C22×C4×D4311yescharacteristic
857Q8—3441no—
858Q8—3441no—
859D4—862no—
860D4—862no—
861D4—3441no—
862D4—3441no—
863D4—1721no—
864D4—1721no—
865D4—1722no—
866D4—1722no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—431no—
879C2×C4—431no—
880C2×C4—431no—
881C2×C4—431no—
882C2×C4—861no—
883C2×C4—861no—
884C2×C4—861no—
885C2×C4—861no—
886C2×C4—861no—
887C2×C4—3441no—
888C2×C4—3441no—
889C2×C4—1721no—
890C2×C4—1721no—
891C2×C4—1721no—
892C2×C4—1721no—
893C2×C4—1721no—
894C2×C4—1721no—
895C2×C4—1721no—
896C2×C4—1721no—
897C2×C4—1722no—
898C2×C4—1722no—
899C2×C4—1722no—
900C2×C4—1722no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4C22⋊C4×D4311yescharacteristic
906C2×C4C22⋊C4×D4311yescharacteristic
907C2×C4C22⋊C4×D4311yescharacteristic
908C2×C4C22⋊C4×D4311yescharacteristic
909C2×C4C2×D4×D4311yescharacteristic
910C2×C4C2×D4×D4311yescharacteristic
911C8—41no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—1721no—
916C8—1721no—
917C8—1721no—
918C8—1721no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—81no—
925C22—81no—
926C22—432no—
927C22—861no—
928C22—861no—
929C22—862no—
930C22—861no—
931C22—861no—
932C22—861no—
933C22—861no—
934C22—861no—
935C22—861no—
936C22—861no—
937C22—861no—
938C22—861no—
939C22—3441no—
940C22—3441no—
941C22—3444no—
942C22—3444no—
943C22—1722no—
944C22—1722no—
945C22—1722no—
946C22—1722no—
947C22—1721no—
948C22—1721no—
949C22C2×C22⋊C4×D4311yescharacteristic
950C22#131×D4311yescharacteristic
951C22#1458366411yescharacteristic
952C4—21no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—21no—
957C4—21no—
958C4—41no—
959C4—41no—
960C4—41no—
961C4—861no—
962C4—861no—
963C4—861no—
964C4—861no—
965C4—1721no—
966C4—1721no—
967C4—1721no—
968C2—21no—
969C2—21no—
970C2—81no—
971C2—862no—
972C2—1721no—
973C2—1721no—
974C2—1721no—
975C2—1722no—
976C2#1914304311yescharacteristic
977C2#1914305411yescharacteristic
978C2#413×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1473C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063295C4
cosocleC22×C4×C43C24
hypercenter#1473D43
hypocenterC43#17422
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #19143632C2semidirect
3. #19143629C2semidirect
4. #19132964C2semidirect
5. #19132957C2semidirect
6. #19132957C2semidirect
7. #19132940C2semidirect
8. #19132940C2semidirect
9. #19132932C2semidirect
10. #19132927C2semidirect
11. #19132920C2semidirect
12. #19132912C2semidirect
13. #19132907C2semidirect
14. #323×D43C2semidirect
15. C43×#1473C2semidirect
46. #14582956C22semidirect
47. #14582952C22semidirect
50. #14582861C22semidirect
51. #14582861C22semidirect
54. C22⋊C8×D43C22semidirect
55. C22⋊C8×D43C22semidirect
56. #14582625C22semidirect
57. #14582625C22semidirect
58. #14582624C22semidirect
59. #14582624C22semidirect
60. #14582624C22semidirect
61. #14582624C22semidirect
69. C43×#432C22semidirect
70. C43×#431C22semidirect
71. C43×#324C22semidirect
72. C43×#324C22semidirect
483. #1473D43semidirect
537. #432C2×D43semidirect
539. #431C2×D43semidirect
554. #324C2×D43semidirect
555. #324C2×D43semidirect
564. C43#17422semidirect

Maximal subgroups

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

subgroupindex
C2×#145835742
#191436322
#191436292
#191329642
#191329572
#191329402
#191329322
#191329272
#191329202
#191329122
#191329072
#323×D432
C43×#14732
#1742243