Finite Group Databasebeta

← #25062870

Subgroups — #25062870

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×#14583576C211yesmaximal, characteristic
2#19143631C211yesmaximal, characteristic, complemented
3#19143626C211yesmaximal, characteristic, complemented
4#19132963C211yesmaximal, characteristic, complemented
5#19132963C211yesmaximal, characteristic, complemented
6#19132959C211yesmaximal, characteristic, complemented
7#19132942C211yesmaximal, characteristic, complemented
8#19132942C211yesmaximal, characteristic, complemented
9#19132932C211yesmaximal, characteristic, complemented
10#19132928C211yesmaximal, characteristic, complemented
11#19132921C211yesmaximal, characteristic, complemented
12#19132912C211yesmaximal, characteristic, complemented
13#19132908C211yesmaximal, characteristic, complemented
14C2×#14582622C211yesmaximal, characteristic, complemented
15C43×#1472C211yesmaximal, characteristic, complemented
16#14583576—21no—
17#14583576—21no—
18#14583576—21no—
19#14583576—21no—
20#14583576—21no—
21#14583576—21no—
22#14583576—21no—
23#14583576—21no—
24C2×#13063320C411yescharacteristic
25C2×#13063320C2211yescharacteristic
26C2×#13063314C411yescharacteristic
27C2×#13063310C411yescharacteristic
28C2×#13063310C2211yescharacteristic
29C2×#13063309C411yescharacteristic
30C2×#13063301C411yescharacteristic
31C2×#13063295C411yescharacteristic
32C2×#13063287C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×#13063283C2211yescharacteristic
35C2×#13063281C411yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C2×C22⋊C4×D43C411yescharacteristic
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
51#14582861C2211yescharacteristic, complemented
52#14582861C2211yescharacteristic, complemented
53C2×C22⋊(C43⋊C8)C2211yescharacteristic
54C22⋊C8×D43C2211yescharacteristic, complemented
55C22⋊C8×D43C2211yescharacteristic, complemented
56#14582625C2211yescharacteristic, complemented
57#14582625C2211yescharacteristic, complemented
58#14582625C2211yescharacteristic, complemented
59#14582625C2211yescharacteristic, complemented
60#14582622C2211yescharacteristic
61#14582622C2211yescharacteristic
62#14582622C2211yescharacteristic
63#14582622C2211yescharacteristic
64#14582622C2211yescharacteristic
65#14582622C2211yescharacteristic
66#14582622C2211yescharacteristic
67#14582622C2211yescharacteristic
68C2×C22⋊Q8×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic
70C2×C22⋊C8×C43C2211yescharacteristic
71C43×#324C2211yescharacteristic, complemented
72C43×#324C2211yescharacteristic, complemented
73C43×#324C2211yescharacteristic, complemented
74C43×#324C2211yescharacteristic, complemented
75C24×D43C2×C411yescharacteristic
76C22×D172C2×C411yescharacteristic
77C22×D172C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C23×Dic43C2×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#13063320—21no—
90#13063320—21no—
91#13063320—21no—
92#13063320—21no—
93#13063320—21no—
94#13063320—21no—
95#13063320—21no—
96#13063320—21no—
97#13063314—21no—
98#13063314—21no—
99#13063314—21no—
100#13063314—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#13063309—21no—
110#13063309—21no—
111#13063309—21no—
112#13063309—21no—
113#13063301—21no—
114#13063301—21no—
115#13063301—21no—
116#13063301—21no—
117#13063295—21no—
118#13063295—21no—
119#13063295—21no—
120#13063295—21no—
121#13063287—21no—
122#13063287—21no—
123#13063287—21no—
124#13063287—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#13063281—21no—
138#13063281—21no—
139#13063281—21no—
140#13063281—21no—
141C2×C4⋊Dic43C2×C411yescharacteristic
142C2×C4⋊Dic43C2×C411yescharacteristic
143C2×Dic43⋊C4C2×C411yescharacteristic
144C2×Dic43⋊C4C2×C411yescharacteristic
145C2×Dic43⋊C4C2×C411yescharacteristic
146C2×C22⋊Dic43C2×C411yescharacteristic
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4C2×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
161C2×(C2×D43)⋊C4C2311yescharacteristic
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×Q8×C43C2×C411yescharacteristic
188C23×C4×C43C2311yescharacteristic
189C2×M16×C43—21no—
190C22×C8×C43—21no—
191C22⋊Q8×C43—21no—
192C22⋊Q8×C43—21no—
193C22⋊Q8×C43—21no—
194C22⋊Q8×C43—21no—
195C2×C4⋊C4×C43C2×C411yescharacteristic
196C2×C4⋊C4×C43C2311yescharacteristic
197C2×C4⋊C4×C43C2311yescharacteristic
198C2×C22⋊C4×C43C2×C411yescharacteristic
199C2×C22⋊C4×C43C2×C411yescharacteristic
200C22⋊C8×C43—21no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204C22⋊C8×C43C2311yescharacteristic
205C22⋊C8×C43C2311yescharacteristic
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
216C2×Q8×C43—21no—
217C2×Q8×C43—21no—
218C2×Q8×C43—81no—
219C22×C4×C43—81no—
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C22×C411yescharacteristic
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C22×C411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C2×C22⋊D43—42no—
231C2×C22⋊D43C22⋊C411yescharacteristic
232C2×C22⋊D43C22⋊C411yescharacteristic
233C2×C22⋊D43C22⋊C411yescharacteristic
234C2×C22⋊D43C22⋊C411yescharacteristic
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—42no—
238C22×Dic43C22×C411yescharacteristic
239C22×Dic43C22×C411yescharacteristic
240C22×Dic43C22×C411yescharacteristic
241C22×Dic43C22×C411yescharacteristic
242C22×Dic43C22×C411yescharacteristic
243C2×D172—21no—
244C2×D172—21no—
245C2×D172—21no—
246C2×D172—21no—
247C2×D172—22no—
248C2×D172—41no—
249C2×D172—81no—
250C2×C4×D43—21no—
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—21no—
254C2×C4×D43—22no—
255C2×C4×D43—41no—
256C2×C4×D43—81no—
257C2×C4×D43—81no—
258C2×C4×D43C2×D411yescharacteristic
259C2×C4×D43C2×D411yescharacteristic
260C2×C4×D43C2×D411yescharacteristic
261C2×C4×D43C2×D411yescharacteristic
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—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C22⋊C4×C43—21no—
276C22⋊C4×C43—21no—
277C22⋊C4×C43—21no—
278C22⋊Dic43C22⋊C411yescharacteristic
279C22⋊Dic43C22⋊C411yescharacteristic
280C22⋊Dic43C22⋊C411yescharacteristic
281C22⋊Dic43C22⋊C411yescharacteristic
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—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)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4C22⋊C411yescharacteristic
303(C2×D43)⋊C4C22⋊C411yescharacteristic
304(C2×D43)⋊C4C22⋊C411yescharacteristic
305(C2×D43)⋊C4C22⋊C411yescharacteristic
306C4⋊Dic43—21no—
307C4⋊Dic43—21no—
308C4⋊Dic43—21no—
309C4⋊Dic43—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—22no—
339C23×C43—41no—
340C23×C43C2×C22⋊C411yescharacteristic
341C23×C43C2×C22⋊C411yescharacteristic
342C23×C43C23×C411yescharacteristic
343C22×D43—21no—
344C22×D43—21no—
345C22×D43—21no—
346C22×D43—21no—
347C22×D43—21no—
348C22×D43—21no—
349C22×D43—21no—
350C22×D43—41no—
351C22×D43—41no—
352C22×D43—42no—
353C22×D43—42no—
354C22×D43—41no—
355C22×D43—41no—
356C22×D43—42no—
357C22×D43—42no—
358C22×D43—41no—
359C22×D43—41no—
360C22×D43—81no—
361C22×D43—81no—
362C22×D43—84no—
363C22×D43—84no—
364C22×D43C2×C22⋊C411yescharacteristic
365C22×D43C2×C22⋊C411yescharacteristic
366C22×D43#13112yes—
367Q8×C43—81no—
368Q8×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—21no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
377C2×C4×C43—41no—
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×C43C2×C22⋊C411yescharacteristic
386C2×C4×C43C2×C22⋊C411yescharacteristic
387C2×C4×C43C22×D411yescharacteristic
388C2×C4×C43C22×D411yescharacteristic
389C22⋊D43—22no—
390C22⋊D43—22no—
391C22⋊D43—41no—
392C22⋊D43—41no—
393C2×Dic43—21no—
394C2×Dic43—21no—
395C2×Dic43—21no—
396C2×Dic43—21no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—42no—
400C2×Dic43—42no—
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
409D172—42no—
410D172—42no—
411D172—81no—
412D172—81no—
413C4×D43—41no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—41no—
417C4×D43—42no—
418C4×D43—42no—
419C4×D43—81no—
420C4×D43—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—42no—
438C22×C43—42no—
439C22×C43#41312yes—
440C22×C43C22×C22⋊C411yescharacteristic
441C22×C43C2×#13111yescharacteristic
442C22×C43#56811yescharacteristic
443C2×D43—22no—
444C2×D43—21no—
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—21no—
450C2×D43—42no—
451C2×D43—41no—
452C2×D43—41no—
453C2×D43—42no—
454C2×D43—41no—
455C2×D43—41no—
456C2×D43—41no—
457C2×D43—81no—
458C2×D43—81no—
459C2×D43—84no—
460C2×D43—84no—
461C2×D43—81no—
462C2×D43—81no—
463C4×C43—21no—
464C4×C43—21no—
465C4×C43—21no—
466C4×C43—21no—
467C4×C43—41no—
468C4×C43—41no—
469C4×C43—41no—
470C4×C43—41no—
471Dic43—21no—
472Dic43—21no—
473Dic43—21no—
474Dic43—21no—
475Dic43—21no—
476Dic43—21no—
477Dic43—41no—
478Dic43—41no—
479C2×#551—431no—
480#2974—431no—
481#2974—431no—
482#1473—431no—
483#1473—431no—
484#1472—431no—
485#1472D4311yescharacteristic, complemented
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—22no—
497C2×C43—41no—
498C2×C43#288011yescharacteristic
499C2×C43#288311yescharacteristic
500C2×C43C2×#41311yescharacteristic
501D43—41no—
502D43—41no—
503D43—42no—
504D43—81no—
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×#123—431no—
519C2×C22⋊Q8—431no—
520C2×C22⋊Q8C2×D4311yescharacteristic
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
544C2×C22⋊C8—431no—
545C2×C22⋊C8—431no—
546C2×C22⋊C8—431no—
547C2×C22⋊C8C2×D4311yescharacteristic
548#324—431no—
549#324—431no—
550#324—431no—
551#324—431no—
552#324C2×D4311yescharacteristic, complemented
553#324C2×D4311yescharacteristic, complemented
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#323—431no—
563#323—431no—
564C43#1742211yescharacteristic, complemented, Sylow
565C25—431no—
566C22×Q8C4×D4311yescharacteristic
567C22×D4—431no—
568C22×D4—431no—
569C22×D4—431no—
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—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—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
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⋊C4C22×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—431no—
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⋊C4—861no—
667C2×C22⋊C4C4×D4311yescharacteristic
668C2×C22⋊C4C4×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—431no—
699C24—862no—
700C24—861no—
701C24—861no—
702C24—3441no—
703C24—1721no—
704C24—1722no—
705C24C2×C4×D4311yescharacteristic
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—81no—
709C2×D4—431no—
710C2×D4—431no—
711C2×D4—431no—
712C2×D4—431no—
713C2×D4—861no—
714C2×D4—861no—
715C2×D4—861no—
716C2×D4—861no—
717C2×D4—862no—
718C2×D4—3441no—
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—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—862no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—3441no—
739C22×C4—3441no—
740C22×C4—1721no—
741C22×C4—1722no—
742C22×C4C2×C4×D4311yescharacteristic
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—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—431no—
791C22⋊C4—431no—
792C22⋊C4—431no—
793C22⋊C4—431no—
794C22⋊C4—431no—
795C22⋊C4—431no—
796C22⋊C4—431no—
797C22⋊C4—431no—
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⋊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—22no—
827C23—21no—
828C23—21no—
829C23—41no—
830C23—431no—
831C23—431no—
832C23—432no—
833C23—861no—
834C23—861no—
835C23—861no—
836C23—861no—
837C23—861no—
838C23—861no—
839C23—861no—
840C23—3441no—
841C23—3441no—
842C23—3444no—
843C23—3444no—
844C23—1721no—
845C23—1721no—
846C23—1722no—
847C23—1722no—
848C23—1721no—
849C23—1721no—
850C23—1722no—
851C23—1721no—
852C23—1721no—
853C23—1722no—
854C23C22⋊C4×D4311yescharacteristic
855C23C22⋊C4×D4311yescharacteristic
856C23C22×C4×D4311yescharacteristic
857Q8—81no—
858Q8—81no—
859D4—862no—
860D4—862no—
861D4—3441no—
862D4—3441no—
863D4—1722no—
864D4—1722no—
865D4—1721no—
866D4—1721no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—431no—
884C2×C4—431no—
885C2×C4—431no—
886C2×C4—431no—
887C2×C4—431no—
888C2×C4—431no—
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—1721no—
902C2×C4—1721no—
903C2×C4—1722no—
904C2×C4—1722no—
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—42no—
927C22—42no—
928C22—862no—
929C22—861no—
930C22—861no—
931C22—861no—
932C22—861no—
933C22—861no—
934C22—861no—
935C22—3441no—
936C22—3441no—
937C22—3444no—
938C22—3441no—
939C22—3441no—
940C22—3444no—
941C22—1722no—
942C22—1722no—
943C22—1721no—
944C22—1721no—
945C22—1721no—
946C22—1721no—
947C22—1721no—
948C22#1458288212yes—
949C22C2×C22⋊C4×D4311yescharacteristic
950C22#131×D4311yescharacteristic
951C22#1458366411yescharacteristic
952C4—21no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—41no—
957C4—41no—
958C4—41no—
959C4—41no—
960C4—861no—
961C4—861no—
962C4—861no—
963C4—861no—
964C4—861no—
965C4—861no—
966C4—1721no—
967C4—1721no—
968C2—21no—
969C2—21no—
970C2—22no—
971C2—41no—
972C2—3441no—
973C2—1721no—
974C2—1721no—
975C2—1722no—
976C2#1914304311yescharacteristic
977C2#1914305311yescharacteristic
978C2C2×#1458288211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1472C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063295C4
cosocleC22×C4×C43C24
hypercenter#1472D43
hypocenterC43#17422
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
2. #19143631C2semidirect
3. #19143626C2semidirect
4. #19132963C2semidirect
5. #19132963C2semidirect
6. #19132959C2semidirect
7. #19132942C2semidirect
8. #19132942C2semidirect
9. #19132932C2semidirect
10. #19132928C2semidirect
11. #19132921C2semidirect
12. #19132912C2semidirect
13. #19132908C2semidirect
14. C2×#14582622C2semidirect
15. C43×#1472C2semidirect
46. #14582953C22semidirect
47. #14582953C22semidirect
48. #14582949C22semidirect
49. #14582949C22semidirect
51. #14582861C22semidirect
52. #14582861C22semidirect
54. C22⋊C8×D43C22semidirect
55. C22⋊C8×D43C22semidirect
56. #14582625C22semidirect
57. #14582625C22semidirect
58. #14582625C22semidirect
59. #14582625C22semidirect
71. C43×#324C22semidirect
72. C43×#324C22semidirect
73. C43×#324C22semidirect
74. C43×#324C22semidirect
485. #1472D43semidirect
552. #324C2×D43semidirect
553. #324C2×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×#145835762
#191436312
#191436262
#191329632
#191329592
#191329422
#191329322
#191329282
#191329212
#191329122
#191329082
C2×#145826222
C43×#14722
#1742243