Finite Group Databasebeta

← #25062871

Subgroups — #25062871

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×#14583577C211yesmaximal, characteristic
2#19143631C211yesmaximal, characteristic, complemented
3#19143626C211yesmaximal, characteristic, complemented
4#19132961C211yesmaximal, characteristic, complemented
5#19132961C211yesmaximal, characteristic, complemented
6#19132957C211yesmaximal, characteristic, complemented
7#19132957C211yesmaximal, characteristic, complemented
8#19132943C211yesmaximal, characteristic, complemented
9#19132931C211yesmaximal, characteristic, complemented
10#19132928C211yesmaximal, characteristic, complemented
11#19132920C211yesmaximal, characteristic, complemented
12#19132911C211yesmaximal, characteristic, complemented
13#19132908C211yesmaximal, characteristic, complemented
14#323×D43C211yesmaximal, characteristic, complemented
15C43×#1468C211yesmaximal, characteristic, complemented
16#14583577—21no—
17#14583577—21no—
18#14583577—21no—
19#14583577—21no—
20#14583577—21no—
21#14583577—21no—
22#14583577—21no—
23#14583577—21no—
24C2×#13063318C411yescharacteristic
25C2×#13063318C2211yescharacteristic
26C2×#13063312C411yescharacteristic
27C2×#13063307C411yescharacteristic
28C2×#13063307C411yescharacteristic
29C2×#13063303C411yescharacteristic
30C2×#13063303C2211yescharacteristic
31C2×#13063293C411yescharacteristic
32C2×C4×C22⋊D43C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×#13063283C411yescharacteristic
35C2×#13063283C2211yescharacteristic
36C2×C22⋊C4×D43C411yescharacteristic
37C2×C22⋊C4×D43C2211yescharacteristic
38#14582975—21no—
39#14582974—21no—
40#14582973—21no—
41#14582970—21no—
42#14582968—21no—
43#14582967—21no—
44C8×C22⋊D43—21no—
45(C22⋊D43)⋊C8—21no—
46#14582953C2211yescharacteristic, complemented
47#14582953C2211yescharacteristic, complemented
48#14582949C2211yescharacteristic, complemented
49#14582949C2211yescharacteristic, complemented
50#14582863C2211yescharacteristic, complemented
51#14582861C2211yescharacteristic
52#14582861C2211yescharacteristic
53C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
54C22⋊C8×D43C2211yescharacteristic
55C22⋊C8×D43C2211yescharacteristic
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×#123×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic, complemented
70C2×C22⋊C8×C43C2211yescharacteristic, complemented
71C43×#324C2211yescharacteristic, complemented
72C43×#324C2211yescharacteristic, complemented
73C43×#323C2211yescharacteristic
74C43×#323C2211yescharacteristic
75C24×D43C2×C411yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C22×C22⋊D43C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C22×C4×D43C2×C411yescharacteristic
80C22×C4×D43C2×C411yescharacteristic
81C22×C4×D43C2×C411yescharacteristic
82C22×C4×D43C2311yescharacteristic
83C2×#10621877—21no—
84C2×#10621872—21no—
85C2×#10621872—21no—
86C22×C43⋊C8—21no—
87C2×C8×D43—21no—
88C2×C8×D43—21no—
89#13063318—21no—
90#13063318—21no—
91#13063318—21no—
92#13063318—21no—
93#13063318—21no—
94#13063318—21no—
95#13063318—21no—
96#13063318—21no—
97#13063312—21no—
98#13063312—21no—
99#13063312—21no—
100#13063312—21no—
101#13063307—21no—
102#13063307—21no—
103#13063307—21no—
104#13063307—21no—
105#13063307—21no—
106#13063307—21no—
107#13063307—21no—
108#13063307—21no—
109#13063303—21no—
110#13063303—21no—
111#13063303—21no—
112#13063303—21no—
113#13063303—21no—
114#13063303—21no—
115#13063303—21no—
116#13063303—21no—
117#13063293—21no—
118#13063293—21no—
119#13063293—21no—
120#13063293—21no—
121C4×C22⋊D43—21no—
122C4×C22⋊D43—21no—
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43D411yescharacteristic
126C4×C22⋊D43D411yescharacteristic
127C4×C22⋊D43D411yescharacteristic
128C4×C22⋊D43D411yescharacteristic
129C4×C22⋊D43D411yescharacteristic
130C4×C22⋊D43D411yescharacteristic
131C4×C22⋊D43D411yescharacteristic
132C4×C22⋊D43D411yescharacteristic
133#13063283—21no—
134#13063283—21no—
135#13063283—21no—
136#13063283—21no—
137#13063283—21no—
138#13063283—21no—
139#13063283—21no—
140#13063283—21no—
141C2×C4⋊Dic43C2×C411yescharacteristic
142C2×C4⋊Dic43C2×C411yescharacteristic
143C2×Dic43⋊C4C2×C411yescharacteristic
144C2×Dic43⋊C4C2×C411yescharacteristic
145C2×Dic43⋊C4C2×C411yescharacteristic
146C2×Dic43⋊C4C2311yescharacteristic
147C2×C22⋊Dic43C2×C411yescharacteristic
148C2×C22⋊Dic43C2×C411yescharacteristic
149C2×C22⋊Dic43C2×C411yescharacteristic
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)⋊C4C2311yescharacteristic
158C22⋊C4×D43—21no—
159C22⋊C4×D43—21no—
160C22⋊C4×D43—21no—
161C22⋊C4×D43—21no—
162C22⋊C4×D43—21no—
163C22⋊C4×D43—21no—
164C22⋊C4×D43—21no—
165C22⋊C4×D43—21no—
166C2×C4×Dic43C2×C411yescharacteristic
167C2×C4×Dic43C2×C411yescharacteristic
168C2×C4×Dic43C2311yescharacteristic
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)—21no—
175C22⋊(C43⋊C8)C2311yescharacteristic
176C22⋊(C43⋊C8)C2311yescharacteristic
177C22⋊(C43⋊C8)C2311yescharacteristic
178C22⋊(C43⋊C8)C2311yescharacteristic
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181(C2×D43)⋊C8—21no—
182(C2×D43)⋊C8—21no—
183#13063235—21no—
184#13063235—21no—
185C8×Dic43—21no—
186C8×Dic43—21no—
187C22×D4×C43C2×C411yescharacteristic
188C23×C4×C43C2311yescharacteristic
189C2×M16×C43—21no—
190C22×C8×C43—21no—
191#123×C43—21no—
192#123×C43—21no—
193#123×C43—21no—
194#123×C43—21no—
195C2×C4⋊C4×C43C2×C411yescharacteristic
196C2×C4⋊C4×C43C2311yescharacteristic
197C2×C22⋊C4×C43C2×C411yescharacteristic
198C2×C22⋊C4×C43C2×C411yescharacteristic
199C2×C22⋊C4×C43C2311yescharacteristic
200C22⋊C8×C43—21no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204C22⋊C8×C43C2311yescharacteristic
205C22⋊C8×C43C2311yescharacteristic
206C24×C43C22×C411yescharacteristic
207C24×C43C22×C411yescharacteristic
208C23×D43—21no—
209C23×D43—21no—
210C23×D43—22no—
211C23×D43—41no—
212C23×D43—42no—
213C23×D43—81no—
214C23×D43C22×C411yescharacteristic
215C23×D43C22×C411yescharacteristic
216C2×D4×C43—21no—
217C2×D4×C43—21no—
218C2×D4×C43—81no—
219C22×C4×C43—81no—
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C22×C411yescharacteristic
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2411yescharacteristic
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—22no—
232C2×C22⋊D43—41no—
233C2×C22⋊D43—42no—
234C2×C22⋊D43C22⋊C411yescharacteristic
235C2×C22⋊D43C22⋊C411yescharacteristic
236C2×C22⋊D43C22⋊C411yescharacteristic
237C2×C22⋊D43C22⋊C411yescharacteristic
238C22×Dic43C22×C411yescharacteristic
239C22×Dic43C22×C411yescharacteristic
240C22×Dic43C22×C411yescharacteristic
241C22×Dic43C22×C411yescharacteristic
242C22×Dic43C22×C411yescharacteristic
243C22×Dic43C22×C411yescharacteristic
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—22no—
251C2×C4×D43—41no—
252C2×C4×D43—42no—
253C2×C4×D43—81no—
254C2×C4×D43—81no—
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—
262M16×C43—81no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—81no—
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—
278C22⋊Dic43—21no—
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43—21no—
285C22⋊Dic43—21no—
286C22⋊Dic43C22⋊C411yescharacteristic
287C22⋊Dic43C22⋊C411yescharacteristic
288C22⋊Dic43C22⋊C411yescharacteristic
289C22⋊Dic43C22⋊C411yescharacteristic
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
304C4⋊Dic43—21no—
305C4⋊Dic43—21no—
306C4⋊Dic43—21no—
307C4⋊Dic43—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4C22⋊C411yescharacteristic
315Dic43⋊C4C22⋊C411yescharacteristic
316Dic43⋊C4C22⋊C411yescharacteristic
317Dic43⋊C4C22⋊C411yescharacteristic
318C4×Dic43—21no—
319C4×Dic43—21no—
320C4×Dic43—21no—
321C4×Dic43—21no—
322C4×Dic43C2×D411yescharacteristic
323C4×Dic43C2×D411yescharacteristic
324C4×Dic43C2×D411yescharacteristic
325C4×Dic43C2×D411yescharacteristic
326#10621877—81no—
327C2×C43⋊C8—21no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—21no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—81no—
332#10621872—81no—
333#10621872—81no—
334C8×D43—81no—
335C8×D43—81no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—21no—
339C23×C43—21no—
340C23×C43—21no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43C2×C22⋊C411yescharacteristic
346C23×C43C2×C22⋊C411yescharacteristic
347C23×C43C23×C411yescharacteristic
348C22×D43—21no—
349C22×D43—21no—
350C22×D43—21no—
351C22×D43—21no—
352C22×D43—22no—
353C22×D43—41no—
354C22×D43—42no—
355C22×D43—42no—
356C22×D43—42no—
357C22×D43—41no—
358C22×D43—41no—
359C22×D43—42no—
360C22×D43—81no—
361C22×D43—81no—
362C22×D43—84no—
363C22×D43—84no—
364C22×D43C2×C22⋊C411yescharacteristic
365C22×D43C2×C22⋊C411yescharacteristic
366C22×D43#13112yes—
367D4×C43—81no—
368D4×C43—81no—
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×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43C2×C22⋊C411yescharacteristic
383C2×C4×C43C2×C22⋊C411yescharacteristic
384C2×C4×C43C22×D411yescharacteristic
385C2×C4×C43C22×D411yescharacteristic
386C22⋊D43—22no—
387C22⋊D43—22no—
388C22⋊D43—41no—
389C22⋊D43—41no—
390C22⋊D43—42no—
391C22⋊D43—42no—
392C2×Dic43—21no—
393C2×Dic43—21no—
394C2×Dic43—21no—
395C2×Dic43—21no—
396C2×Dic43—21no—
397C2×Dic43—21no—
398C2×Dic43—21no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—41no—
403C2×Dic43C2×C22⋊C411yescharacteristic
404C2×Dic43C2×C22⋊C411yescharacteristic
405C2×Dic43C2×C22⋊C411yescharacteristic
406C2×Dic43C2×C22⋊C411yescharacteristic
407C2×Dic43C2×C22⋊C411yescharacteristic
408C2×Dic43C2×C22⋊C411yescharacteristic
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—21no—
433C22×C43—21no—
434C22×C43—21no—
435C22×C43—21no—
436C22×C43—21no—
437C22×C43—21no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43—81no—
442C22×C43—81no—
443C22×C43—81no—
444C22×C43—81no—
445C22×C43C22×C22⋊C411yescharacteristic
446C22×C43C2×#13111yescharacteristic
447C22×C43#56811yescharacteristic
448C2×D43—21no—
449C2×D43—21no—
450C2×D43—21no—
451C2×D43—22no—
452C2×D43—21no—
453C2×D43—21no—
454C2×D43—42no—
455C2×D43—42no—
456C2×D43—42no—
457C2×D43—41no—
458C2×D43—41no—
459C2×D43—42no—
460C2×D43—84no—
461C2×D43—84no—
462C2×D43#41312yes—
463C4×C43—21no—
464C4×C43—21no—
465C4×C43—21no—
466C4×C43—21no—
467C4×C43—41no—
468C4×C43—41no—
469C4×C43—41no—
470Dic43—21no—
471Dic43—21no—
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#1473—431no—
484#1472—431no—
485#1472—431no—
486#1468—431no—
487#1468D4311yescharacteristic, complemented
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—41no—
497C2×C43—41no—
498C2×C43—81no—
499C2×C43#288011yescharacteristic
500C2×C43#288311yescharacteristic
501C2×C43C2×#41311yescharacteristic
502D43—22no—
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×#126—431no—
515C2×#124—431no—
516C2×#123—431no—
517C2×#123—431no—
518C2×#123C2×D4311yescharacteristic
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#432—431no—
538#431—431no—
539#431—431no—
540#407—431no—
541#407—431no—
542#407—431no—
543#407C2×D4311yescharacteristic, complemented
544C2×C22⋊C8—431no—
545C2×C22⋊C8—431no—
546C2×C22⋊C8—431no—
547C2×C22⋊C8C2×D4311yescharacteristic, complemented
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×D4C4×D4311yescharacteristic
570C23×C4—431no—
571C23×C4—431no—
572C23×C4—431no—
573C23×C4—431no—
574C23×C4C22×D4311yescharacteristic
575C2×M16—21no—
576C2×M16—861no—
577C2×M16—861no—
578C2×M16—861no—
579C22×C8—21no—
580C22×C8—861no—
581C22×C8—861no—
582C22×C8—861no—
583#126—861no—
584#126—861no—
585#126—861no—
586#126—861no—
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—21no—
596#123—21no—
597#123—21no—
598#123—21no—
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⋊C4—431no—
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×C42—431no—
672C4⋊C8—861no—
673C4⋊C8—861no—
674C4⋊C8—861no—
675C4⋊C8—861no—
676C22⋊C8—21no—
677C22⋊C8—21no—
678C22⋊C8—431no—
679C22⋊C8—431no—
680C22⋊C8—431no—
681C22⋊C8—431no—
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—861no—
693#97—861no—
694C4×C8—861no—
695C4×C8—861no—
696C24—431no—
697C24—431no—
698C24—862no—
699C24—861no—
700C24—861no—
701C24—3441no—
702C24—1721no—
703C24—1722no—
704C24C2×C4×D4311yescharacteristic
705C24C2×C4×D4311yescharacteristic
706C2×Q8—861no—
707C2×Q8—861no—
708C2×Q8—3441no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—81no—
712C2×D4—431no—
713C2×D4—431no—
714C2×D4—431no—
715C2×D4—431no—
716C2×D4—862no—
717C2×D4—861no—
718C2×D4—861no—
719C2×D4—1721no—
720C2×D4—1722no—
721C22×C4—81no—
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—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—862no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—3441no—
740C22×C4—3441no—
741C22×C4—1721no—
742C22×C4—1722no—
743C22×C4C2×C4×D4311yescharacteristic
744C22×C4C2×C4×D4311yescharacteristic
745C22×C4C2×C4×D4311yescharacteristic
746C22×C4C2×C4×D4311yescharacteristic
747C22×C4D4×D4311yescharacteristic
748C22×C4D4×D4311yescharacteristic
749C22×C4D4×D4311yescharacteristic
750C22×C4D4×D4311yescharacteristic
751C22×C4C23×D4311yescharacteristic
752M16—81no—
753M16—3441no—
754M16—3441no—
755M16—3441no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C2×C8—861no—
762C2×C8—861no—
763C2×C8—861no—
764C2×C8—861no—
765C2×C8—3441no—
766C2×C8—3441no—
767C2×C8—3441no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—431no—
773C4⋊C4—431no—
774C4⋊C4—431no—
775C4⋊C4—431no—
776C4⋊C4—861no—
777C4⋊C4—861no—
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—431no—
819C42—431no—
820C42—431no—
821C42—431no—
822C42—861no—
823C42—861no—
824C42—861no—
825C42—861no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—431no—
836C23—431no—
837C23—432no—
838C23—862no—
839C23—861no—
840C23—861no—
841C23—861no—
842C23—861no—
843C23—3441no—
844C23—3441no—
845C23—3444no—
846C23—3444no—
847C23—1721no—
848C23—1721no—
849C23—1721no—
850C23—1722no—
851C23—1722no—
852C23—1722no—
853C23—1722no—
854C23C22⋊C4×D4311yescharacteristic
855C23C22⋊C4×D4311yescharacteristic
856C23C22×C4×D4311yescharacteristic
857Q8—3441no—
858Q8—3441no—
859D4—81no—
860D4—81no—
861D4—862no—
862D4—862no—
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—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—431no—
881C2×C4—431no—
882C2×C4—431no—
883C2×C4—431no—
884C2×C4—431no—
885C2×C4—431no—
886C2×C4—861no—
887C2×C4—861no—
888C2×C4—861no—
889C2×C4—861no—
890C2×C4—861no—
891C2×C4—861no—
892C2×C4—861no—
893C2×C4—3441no—
894C2×C4—3441no—
895C2×C4—1721no—
896C2×C4—1721no—
897C2×C4—1721no—
898C2×C4—1721no—
899C2×C4—1722no—
900C2×C4—1722no—
901C2×C4—1722no—
902C2×C4—1722no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4—1721no—
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—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—432no—
935C22—861no—
936C22—861no—
937C22—862no—
938C22—861no—
939C22—861no—
940C22—861no—
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—41no—
957C4—41no—
958C4—41no—
959C4—861no—
960C4—861no—
961C4—861no—
962C4—861no—
963C4—861no—
964C4—861no—
965C4—1721no—
966C4—1721no—
967C4—1721no—
968C2—21no—
969C2—21no—
970C2—41no—
971C2—41no—
972C2—81no—
973C2—862no—
974C2—1721no—
975C2—1722no—
976C2#1914304311yescharacteristic
977C2#1914305311yescharacteristic
978C2#413×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1468C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063293C4
cosocleC22×C4×C43C24
hypercenter#1468D43
hypocenterC43#17422
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1468

Complements

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

NH ≅ G/Ntype
2. #19143631C2semidirect
3. #19143626C2semidirect
4. #19132961C2semidirect
5. #19132961C2semidirect
6. #19132957C2semidirect
7. #19132957C2semidirect
8. #19132943C2semidirect
9. #19132931C2semidirect
10. #19132928C2semidirect
11. #19132920C2semidirect
12. #19132911C2semidirect
13. #19132908C2semidirect
14. #323×D43C2semidirect
15. C43×#1468C2semidirect
46. #14582953C22semidirect
47. #14582953C22semidirect
48. #14582949C22semidirect
49. #14582949C22semidirect
50. #14582863C22semidirect
53. C2×C22⋊(C43⋊C8)C22semidirect
56. #14582625C22semidirect
57. #14582625C22semidirect
58. #14582624C22semidirect
59. #14582624C22semidirect
60. #14582624C22semidirect
61. #14582624C22semidirect
69. C43×#407C22semidirect
70. C2×C22⋊C8×C43C22semidirect
71. C43×#324C22semidirect
72. C43×#324C22semidirect
487. #1468D43semidirect
543. #407C2×D43semidirect
547. C2×C22⋊C8C2×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×#145835772
#191436312
#191436262
#191329612
#191329572
#191329432
#191329312
#191329282
#191329202
#191329112
#191329082
#323×D432
C43×#14682
#1742243