Finite Group Databasebeta

← #25105725

Subgroups — #25105725

Order 11008.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D43C211yesmaximal, characteristic
2C2×#14582862C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D43C211yesmaximal, characteristic, complemented
4#19135037C212yesmaximal, complemented
5#19135035C212yesmaximal, complemented
6#19134898C211yesmaximal, characteristic, complemented
7#19134897C211yesmaximal, characteristic, complemented
8#19134895C211yesmaximal, characteristic, complemented
9#19134693C212yesmaximal, complemented
10#19134537C212yesmaximal, complemented
11C43×#1871C211yesmaximal, characteristic, complemented
12C2×#41×D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C22×#10621877C2211yescharacteristic, complemented
15#14583412C411yescharacteristic, complemented
16#14583412C411yescharacteristic, complemented
17#14583411C2211yescharacteristic
18#14583410C2211yescharacteristic
19#14583409C411yescharacteristic, complemented
20#14583409C411yescharacteristic, complemented
21#14583408—21no—
22#14583408—21no—
23#14583407—21no—
24#14583406C2211yescharacteristic
25#14583405—21no—
26#123×D43—21no—
27C22⋊Q8×D43C411yescharacteristic, complemented
28C22⋊Q8×D43C411yescharacteristic, complemented
29#121×D43C411yescharacteristic, complemented
30#121×D43C411yescharacteristic, complemented
31#120×D43—21no—
32C4×D4×D43—21no—
33C4×D4×D43—21no—
34#117×D43C2211yescharacteristic
35C2×C22⋊C4×D43—21no—
36C2×C42×D43C2212yescomplemented
37C2×#13063253C2212yescomplemented
38C2×#13063252C2212yescomplemented
39C2×#13063251C2212yescomplemented
40#14582862—21no—
41#14582862—21no—
42#14582862C2212yes—
43#14582862C2212yescomplemented
44C2×(C2×D43)⋊C8—21no—
45C2×(C2×D43)⋊C8—21no—
46C22⋊C4×Dic43—21no—
47C4×(C2×D43)⋊C4C2212yes—
48C4×C22⋊Dic43C2211yescharacteristic, complemented
49#14582746—21no—
50#95×D43—21no—
51#14582660C2212yescomplemented
52#14582659C2212yescomplemented
53#14582658C2212yescomplemented
54C22×M16×C43C2211yescharacteristic, complemented
55C43×#525C2211yescharacteristic
56C2×#104×C43C2212yescomplemented
57C4×C22⋊C4×C43C2211yescharacteristic, complemented
58C43×#339C2212yescomplemented
59C24×D43D411yescharacteristic
60C2×#10621902C2×C411yescharacteristic, complemented
61C2×#10621898—21no—
62C2×#10621898C2311yescharacteristic
63C2×#10621900—21no—
64C2×#10621900C2×C411yescharacteristic, complemented
65#41×D43—42no—
66#41×D43—42no—
67C2×Q8×D43C2×C411yescharacteristic, complemented
68C2×D4×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×D4×D43C2×C411yescharacteristic, complemented
72C23×Dic43D411yescharacteristic
73C22×C4×D43—22no—
74C22×C4×D43—21no—
75C22×C4×D43—42no—
76C22×C4×D43—42no—
77C22×C4×D43C2×C411yescharacteristic
78C22×C4×D43C2×C411yescharacteristic
79C22×C4×D43C2×C411yescharacteristic
80C22×C4×D43C2×C411yescharacteristic
81C22×C4×D43D411yescharacteristic
82C22×C4×D43D411yescharacteristic
83C22×C4×D43D411yescharacteristic
84C22×C4×D43D411yescharacteristic
85C22×C4×D43D411yescharacteristic
86C22×C4×D43D411yescharacteristic
87C22×C4×D43C2311yescharacteristic
88C22×C4×D43C2311yescharacteristic
89C2×#10621877—21no—
90C2×#10621877—42no—
91C2×#10621877C2312yes—
92C22×C43⋊C8—21no—
93#13063310—21no—
94#13063310—21no—
95#13063309—21no—
96#13063308—21no—
97#13063307—21no—
98#13063307—21no—
99#13063306—21no—
100#13063305C2×C411yescharacteristic
101#13063305C2×C411yescharacteristic
102#13063304C2×C411yescharacteristic, complemented
103#13063304C2×C411yescharacteristic, complemented
104#13063303—21no—
105#13063303—21no—
106#13063302—21no—
107#13063302—21no—
108#13063301C2×C411yescharacteristic
109#13063301C2×C411yescharacteristic
110#13063300C2×C411yescharacteristic
111#13063300C2×C411yescharacteristic
112#13063299C2×C411yescharacteristic, complemented
113#13063299C2×C411yescharacteristic, complemented
114#13063298—21no—
115#13063298—21no—
116#13063297—21no—
117#13063297—21no—
118#13063296C2×C411yescharacteristic
119#13063296C2×C411yescharacteristic
120#13063295—21no—
121#13063295—21no—
122#13063295—21no—
123#13063294—21no—
124#13063293—21no—
125#13063293—21no—
126#13063293—21no—
127C4×D172—21no—
128C4×D172—21no—
129D4×Dic43—21no—
130D4×Dic43—21no—
131#13063287—21no—
132#13063287—21no—
133C4×C22⋊D43—21no—
134C4×C22⋊D43—21no—
135C4×C22⋊D43—21no—
136C4×C22⋊D43—21no—
137(C22⋊D43)⋊C4—21no—
138(C22⋊D43)⋊C4—21no—
139(C22⋊D43)⋊C4—21no—
140(C22⋊D43)⋊C4—21no—
141#13063284C2311yescharacteristic
142#13063283C2×C411yescharacteristic, complemented
143#13063283C2×C411yescharacteristic, complemented
144#13063282—21no—
145#13063281—21no—
146C4⋊C4×D43—21no—
147C4⋊C4×D43—21no—
148C4⋊C4×D43C2×C411yescharacteristic, complemented
149C4⋊C4×D43C2×C411yescharacteristic, complemented
150C2×C22⋊Dic43—21no—
151C2×(C2×D43)⋊C4—22no—
152C22⋊C4×D43—28no—
153C22⋊C4×D43—21no—
154C22⋊C4×D43—21no—
155C22⋊C4×D43—21no—
156C22⋊C4×D43—21no—
157C22⋊C4×D43—21no—
158C2×C4×Dic43—22no—
159C2×C4×Dic43C2312yes—
160C42×D43—21no—
161C42×D43—42no—
162C42×D43—42no—
163#13063253—42no—
164#13063252—42no—
165#13063251—42no—
166(C2×D43)⋊C8—22no—
167(C2×D43)⋊C8—22no—
168(C2×D43)⋊C8—22no—
169(C2×D43)⋊C8—22no—
170C43⋊#95—21no—
171C43⋊#95—22no—
172C2×#41×C43C2311yescharacteristic
173C23×C4×C43C2311yescharacteristic
174C2×M16×C43—21no—
175C2×M16×C43—42no—
176C2×M16×C43C2312yes—
177C22×C8×C43—21no—
178#123×C43—21no—
179C22⋊Q8×C43C2×C411yescharacteristic, complemented
180C22⋊Q8×C43C2×C411yescharacteristic, complemented
181#121×C43C2×C411yescharacteristic, complemented
182#121×C43C2×C411yescharacteristic, complemented
183#120×C43—21no—
184C4×D4×C43—21no—
185C4×D4×C43—21no—
186#117×C43C2311yescharacteristic
187C2×C22⋊C4×C43—21no—
188C2×C42×C43C2312yes—
189#104×C43—42no—
190#95×C43—21no—
191C24×C43C2×D411yescharacteristic
192C23×D43—24no—
193C23×D43—21no—
194C23×D43—42no—
195C23×D43—42no—
196C23×D43C22⋊C411yescharacteristic
197C23×D43C22⋊C411yescharacteristic
198C23×D43C22⋊C411yescharacteristic
199C23×D43C22⋊C411yescharacteristic
200C23×D43C2×D411yescharacteristic
201C23×D43C2×D411yescharacteristic
202#41×C43—22no—
203#41×C43—22no—
204C2×Q8×C43C22×C411yescharacteristic
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43C22×C411yescharacteristic
209C22×C4×C43—22no—
210C22×C4×C43—22no—
211C22×C4×C43—21no—
212C22×C4×C43—22no—
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C22×C411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2411yescharacteristic
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C2×C22⋊D43—21no—
225C2×C22⋊D43—21no—
226C22×Dic43—21no—
227C22×Dic43—22no—
228C22×Dic43—42no—
229C22×Dic43C22⋊C411yescharacteristic
230C22×Dic43C22⋊C411yescharacteristic
231C22×Dic43C22⋊C411yescharacteristic
232C22×Dic43C22⋊C411yescharacteristic
233C22×Dic43C2×D411yescharacteristic
234C22×Dic43C2×D411yescharacteristic
235#10621902—42no—
236Q8×D43—42no—
237#10621900—42no—
238#10621900—44no—
239D4×D43—44no—
240D4×D43—44no—
241D4×D43—42no—
242D4×D43—44no—
243#10621898—22no—
244#10621898—22no—
245#10621898—42no—
246#10621898—42no—
247C2×D172—21no—
248C2×D172—21no—
249C2×D172—21no—
250C2×D172C22×C411yescharacteristic
251C2×C4×D43—22no—
252C2×C4×D43—22no—
253C2×C4×D43—22no—
254C2×C4×D43—22no—
255C2×C4×D43—28no—
256C2×C4×D43—21no—
257C2×C4×D43—21no—
258C2×C4×D43—21no—
259C2×C4×D43—21no—
260C2×C4×D43—21no—
261C2×C4×D43—42no—
262C2×C4×D43—42no—
263C2×C4×D43—44no—
264C2×C4×D43—44no—
265C2×C4×D43—42no—
266C2×C4×D43—42no—
267C2×C4×D43—42no—
268C2×C4×D43—42no—
269C2×C4×D43—41no—
270C2×C4×D43—41no—
271C2×C4×D43—41no—
272C2×C4×D43—41no—
273C2×C4×D43—41no—
274C2×C4×D43—41no—
275C2×C4×D43—41no—
276C2×C4×D43—41no—
277C2×C4×D43—42no—
278C2×C4×D43—42no—
279C2×C4×D43C22⋊C411yescharacteristic
280C2×C4×D43C22⋊C411yescharacteristic
281C2×C4×D43C22⋊C411yescharacteristic
282C2×C4×D43C22⋊C411yescharacteristic
283C2×C4×D43C22⋊C411yescharacteristic
284C2×C4×D43C22⋊C411yescharacteristic
285C2×C4×D43C22⋊C411yescharacteristic
286C2×C4×D43C22⋊C411yescharacteristic
287C2×C4×D43C22×C411yescharacteristic
288C2×C4×D43C22×C411yescharacteristic
289C2×C4×D43C22×C411yescharacteristic
290C2×C4×D43C22×C411yescharacteristic
291C2×C4×D43C2×D411yescharacteristic
292C2×C4×D43C2×D411yescharacteristic
293C2×C4×D43C2×D411yescharacteristic
294C2×C4×D43C2×D411yescharacteristic
295C2×Dic86—21no—
296C2×Dic86C22×C411yescharacteristic
297M16×C43—22no—
298M16×C43—22no—
299M16×C43—42no—
300C2×C8×C43—22no—
301C2×C8×C43—42no—
302C4⋊C4×C43—21no—
303C4⋊C4×C43—21no—
304C4⋊C4×C43C22×C411yescharacteristic
305C4⋊C4×C43C22×C411yescharacteristic
306C22⋊C4×C43—24no—
307C22⋊C4×C43—21no—
308C22⋊C4×C43—21no—
309C22⋊C4×C43—21no—
310C22⋊C4×C43—21no—
311C22⋊C4×C43—21no—
312C42×C43—21no—
313C42×C43—22no—
314C42×C43—22no—
315C22⋊Dic43—24no—
316C22⋊Dic43—21no—
317C22⋊Dic43—21no—
318C22⋊Dic43—21no—
319C22⋊Dic43—21no—
320C22⋊Dic43—21no—
321(C2×D43)⋊C4—28no—
322(C2×D43)⋊C4—21no—
323(C2×D43)⋊C4—21no—
324(C2×D43)⋊C4—21no—
325(C2×D43)⋊C4—21no—
326(C2×D43)⋊C4—21no—
327(C2×D43)⋊C4—21no—
328(C2×D43)⋊C4—21no—
329(C2×D43)⋊C4—21no—
330(C2×D43)⋊C4—21no—
331(C2×D43)⋊C4—21no—
332C4⋊Dic43—21no—
333C4⋊Dic43—21no—
334C4⋊Dic43C22×C411yescharacteristic
335C4⋊Dic43C22×C411yescharacteristic
336Dic43⋊C4—21no—
337Dic43⋊C4—21no—
338Dic43⋊C4—21no—
339Dic43⋊C4—21no—
340Dic43⋊C4—21no—
341Dic43⋊C4—21no—
342C4×Dic43—21no—
343C4×Dic43—21no—
344C4×Dic43—21no—
345C4×Dic43—22no—
346C4×Dic43—22no—
347C4×Dic43—44no—
348#10621877—22no—
349#10621877—22no—
350#10621877—42no—
351C2×C43⋊C8—22no—
352C2×C43⋊C8—42no—
353C23×C43—22no—
354C23×C43—22no—
355C23×C43—21no—
356C23×C43—41no—
357C23×C43C2×C22⋊C411yescharacteristic
358C23×C43C2×C22⋊C411yescharacteristic
359C23×C43C22×D411yescharacteristic
360C22×D43—22no—
361C22×D43—22no—
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—21no—
371C22×D43—41no—
372C22×D43—41no—
373C22×D43—41no—
374C22×D43—41no—
375C22×D43—41no—
376C22×D43—41no—
377C22×D43—41no—
378C22×D43—416no—
379C22×D43—42no—
380C22×D43—42no—
381C22×D43—42no—
382C22×D43#10414yescomplemented
383C22×D43C2×C22⋊C411yescharacteristic
384C22×D43C2×C22⋊C411yescharacteristic
385C22×D43C2×C22⋊C411yescharacteristic
386C22×D43C2×C22⋊C411yescharacteristic
387Q8×C43—22no—
388D4×C43—22no—
389D4×C43—42no—
390D4×C43—42no—
391D4×C43—42no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
394C2×C4×C43—22no—
395C2×C4×C43—21no—
396C2×C4×C43—21no—
397C2×C4×C43—21no—
398C2×C4×C43—21no—
399C2×C4×C43—24no—
400C2×C4×C43—21no—
401C2×C4×C43—21no—
402C2×C4×C43—21no—
403C2×C4×C43—42no—
404C2×C4×C43—42no—
405C2×C4×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43C2×C22⋊C411yescharacteristic
408C2×C4×C43C2×C22⋊C411yescharacteristic
409C2×C4×C43C23×C411yescharacteristic
410C2×C4×C43C22×D411yescharacteristic
411C2×C4×C43H(5,𝔽2)12yes—
412C2×C4×C43H(5,𝔽2)12yes—
413C22⋊D43—42no—
414C22⋊D43—42no—
415C22⋊D43—42no—
416C22⋊D43—42no—
417C22⋊D43—42no—
418C22⋊D43—42no—
419C22⋊D43—42no—
420C2×Dic43—22no—
421C2×Dic43—22no—
422C2×Dic43—24no—
423C2×Dic43—21no—
424C2×Dic43—21no—
425C2×Dic43—21no—
426C2×Dic43—41no—
427C2×Dic43—41no—
428C2×Dic43—41no—
429C2×Dic43—41no—
430C2×Dic43—42no—
431C2×Dic43—42no—
432C2×Dic43—42no—
433C2×Dic43C2×C22⋊C411yescharacteristic
434C2×Dic43C2×C22⋊C411yescharacteristic
435C2×Dic43C2×C22⋊C411yescharacteristic
436C2×Dic43C2×C22⋊C411yescharacteristic
437D172—22no—
438D172—42no—
439D172—42no—
440D172—42no—
441C4×D43—22no—
442C4×D43—22no—
443C4×D43—22no—
444C4×D43—22no—
445C4×D43—21no—
446C4×D43—21no—
447C4×D43—21no—
448C4×D43—21no—
449C4×D43—21no—
450C4×D43—21no—
451C4×D43—21no—
452C4×D43—21no—
453C4×D43—41no—
454C4×D43—41no—
455C4×D43—41no—
456C4×D43—41no—
457C4×D43—41no—
458C4×D43—41no—
459C4×D43—41no—
460C4×D43—41no—
461C4×D43—42no—
462C4×D43—416no—
463C4×D43—42no—
464C4×D43—42no—
465C4×D43—42no—
466C4×D43—41no—
467C4×D43—41no—
468Dic86—22no—
469Dic86—42no—
470C8×C43—42no—
471C43⋊C8—42no—
472#21773—431nomaximal, Sylow
473C22×C43—21no—
474C22×C43—21no—
475C22×C43—21no—
476C22×C43—21no—
477C22×C43—21no—
478C22×C43—21no—
479C22×C43—21no—
480C22×C43—44no—
481C22×C43—41no—
482C22×C43—41no—
483C22×C43—41no—
484C22×C43C2×#10412yes—
485C22×C43C22×C22⋊C411yescharacteristic
486C22×C43#53412yes—
487C2×D43—28no—
488C2×D43—21no—
489C2×D43—21no—
490C2×D43—21no—
491C2×D43—21no—
492C2×D43—21no—
493C2×D43—21no—
494C2×D43—21no—
495C2×D43—21no—
496C2×D43—21no—
497C2×D43—44no—
498C2×D43—44no—
499C2×D43—44no—
500C2×D43—44no—
501C2×D43—44no—
502C2×D43—41no—
503C2×D43—41no—
504C2×D43—41no—
505C2×D43—84no—
506C2×D43C2×#10412yes—
507C2×D43C2×#10412yes—
508C2×D43#42112yes—
509C4×C43—21no—
510C4×C43—21no—
511C4×C43—44no—
512C4×C43—41no—
513C4×C43—41no—
514C4×C43—41no—
515C4×C43#51812yes—
516C4×C43#53411yescharacteristic
517C4×C43#53411yescharacteristic
518Dic43—21no—
519Dic43—21no—
520Dic43—21no—
521Dic43—21no—
522Dic43—44no—
523Dic43—41no—
524Dic43—41no—
525Dic43—41no—
526C2×#525—431no—
527C2×#407—431no—
528C2×C4×C22⋊C4—431no—
529#1896—432no—
530#1896—432no—
531#1871—431no—
532#1871—431no—
533#1871—431no—
534#1871D4311yescharacteristic, complemented
535#1826—432no—
536#1789—432no—
537C2×C43—22no—
538C2×C43—22no—
539C2×C43—41no—
540C2×C43—81no—
541C2×C43#230811yescharacteristic
542C2×C43C22×#10411yescharacteristic
543C2×C43C2×#42111yescharacteristic
544D43—22no—
545D43—22no—
546D43—22no—
547D43—41no—
548D43—81no—
549C22×#41—431no—
550C24×C4—431no—
551C22×M16—431no—
552C22×M16C2×D4311yescharacteristic, complemented
553#525—431no—
554#525—431no—
555#525—431no—
556#525—431no—
557#525—431no—
558#525—431no—
559#525—431no—
560#525—861no—
561#525—861no—
562#525—861no—
563#525—861no—
564#525C2×D4311yescharacteristic
565C2×#123—861no—
566C2×C22⋊Q8—431no—
567C2×C22⋊Q8—431no—
568C2×#121—431no—
569C2×#121—431no—
570C2×#120—861no—
571C2×C4×D4—861no—
572C2×C4×D4—861no—
573C2×#117—431no—
574C22×C22⋊C4—861no—
575C22×C42—432no—
576C2×#104—432no—
577C2×#104—432no—
578C2×#104—432no—
579C2×#104C2×D4312yescomplemented
580#407—432no—
581#407—432no—
582#407—861no—
583#407—861no—
584C2×C22⋊C8—861no—
585C2×C22⋊C8—861no—
586C4×C22⋊C4—431no—
587C4×C22⋊C4—432no—
588C4×C22⋊C4—861no—
589C4×C22⋊C4—861no—
590C4×C22⋊C4C2×D4311yescharacteristic, complemented
591C2×#95—861no—
592#339—432no—
593#339—432no—
594#339—432no—
595#339C2×D4312yescomplemented
596C43#2177311yescharacteristic, complemented, Sylow
597C25—431no—
598C2×#41—431no—
599C2×#41—431no—
600C2×#41—431no—
601C2×#41—861no—
602C2×#41—861no—
603C2×#41—1722no—
604C2×#41—1722no—
605C2×#41C22×D4311yescharacteristic
606C22×Q8—431no—
607C22×D4—431no—
608C22×D4—861no—
609C22×D4—861no—
610C22×D4—861no—
611C23×C4—431no—
612C23×C4—431no—
613C23×C4—431no—
614C23×C4—431no—
615C23×C4—431no—
616C23×C4—431no—
617C23×C4—431no—
618C23×C4—431no—
619C23×C4—431no—
620C23×C4—431no—
621C23×C4—431no—
622C23×C4—431no—
623C23×C4—431no—
624C23×C4—861no—
625C23×C4—862no—
626C23×C4—1722no—
627C23×C4—1722no—
628C23×C4C22×D4311yescharacteristic
629C2×M16—21no—
630C2×M16—42no—
631C2×M16—432no—
632C2×M16—861no—
633C2×M16—1722no—
634C2×M16C22×D4312yes—
635C22×C8—21no—
636C22×C8—861no—
637#123—21no—
638#123—861no—
639#123—861no—
640#123—861no—
641#123—861no—
642#123—861no—
643#123—861no—
644#123—861no—
645C22⋊Q8—431no—
646C22⋊Q8—431no—
647C22⋊Q8—431no—
648C22⋊Q8—431no—
649C22⋊Q8—431no—
650C22⋊Q8—431no—
651C22⋊Q8—861no—
652C22⋊Q8—861no—
653C22⋊Q8—861no—
654C22⋊Q8—861no—
655C22⋊Q8C4×D4311yescharacteristic, complemented
656C22⋊Q8C4×D4311yescharacteristic, complemented
657#121—431no—
658#121—431no—
659#121—431no—
660#121—431no—
661#121—431no—
662#121—431no—
663#121—861no—
664#121—861no—
665#121—861no—
666#121—861no—
667#121C4×D4311yescharacteristic, complemented
668#121C4×D4311yescharacteristic, complemented
669#120—21no—
670#120—861no—
671#120—861no—
672#120—861no—
673#120—861no—
674#120—861no—
675#120—861no—
676#120—861no—
677C4×D4—21no—
678C4×D4—21no—
679C4×D4—861no—
680C4×D4—861no—
681C4×D4—861no—
682C4×D4—861no—
683C4×D4—861no—
684C4×D4—861no—
685C4×D4—861no—
686C4×D4—861no—
687C4×D4—861no—
688C4×D4—861no—
689C4×D4—861no—
690C4×D4—861no—
691C4×D4—861no—
692C4×D4—861no—
693#117—431no—
694#117—431no—
695#117—431no—
696#117—861no—
697#117—861no—
698#117C22×D4311yescharacteristic
699C2×C4⋊C4—431no—
700C2×C4⋊C4—431no—
701C2×C4⋊C4—861no—
702C2×C4⋊C4—861no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—861no—
705C2×C22⋊C4—861no—
706C2×C22⋊C4—861no—
707C2×C22⋊C4—861no—
708C2×C22⋊C4—861no—
709C2×C22⋊C4—868no—
710C2×C22⋊C4—862no—
711C2×C22⋊C4—861no—
712C2×C42—432no—
713C2×C42—861no—
714C2×C42—862no—
715C2×C42—1722no—
716C2×C42—1722no—
717C2×C42C22×D4312yes—
718#104—42no—
719#104—1722no—
720#104—1722no—
721#104—1722no—
722C22⋊C8—862no—
723C22⋊C8—862no—
724C22⋊C8—862no—
725C22⋊C8—862no—
726#95—21no—
727#95—862no—
728#95—861no—
729C24—431no—
730C24—431no—
731C24—431no—
732C24—431no—
733C24—431no—
734C24—431no—
735C24—864no—
736C24—861no—
737C24—1722no—
738C24—1722no—
739C24D4×D4311yescharacteristic
740#41—22no—
741#41—22no—
742#41—862no—
743#41—862no—
744#41—1722no—
745#41—1722no—
746#41—1722no—
747#41—1724no—
748#41—1722no—
749C2×Q8—431no—
750C2×Q8—861no—
751C2×Q8—1722no—
752C2×Q8C2×C4×D4311yescharacteristic
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—431no—
757C2×D4—861no—
758C2×D4—861no—
759C2×D4—861no—
760C2×D4—861no—
761C2×D4—861no—
762C2×D4—861no—
763C2×D4—861no—
764C2×D4—861no—
765C2×D4—861no—
766C2×D4—861no—
767C2×D4—1722no—
768C2×D4—1724no—
769C2×D4—1724no—
770C2×D4—1724no—
771C2×D4C2×C4×D4311yescharacteristic
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—431no—
777C22×C4—431no—
778C22×C4—431no—
779C22×C4—431no—
780C22×C4—431no—
781C22×C4—431no—
782C22×C4—431no—
783C22×C4—431no—
784C22×C4—431no—
785C22×C4—431no—
786C22×C4—431no—
787C22×C4—431no—
788C22×C4—431no—
789C22×C4—431no—
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—868no—
803C22×C4—861no—
804C22×C4—862no—
805C22×C4—862no—
806C22×C4—862no—
807C22×C4—862no—
808C22×C4—862no—
809C22×C4—861no—
810C22×C4—1722no—
811C22×C4—1722no—
812C22×C4—1722no—
813C22×C4—1722no—
814C22×C4—1721no—
815C22×C4—1721no—
816C22×C4—1721no—
817C22×C4—1721no—
818C22×C4—1721no—
819C22×C4—1721no—
820C22×C4—1721no—
821C22×C4—1721no—
822C22×C4—1722no—
823C22×C4—1722no—
824C22×C4—1722no—
825C22×C4—1722no—
826C22×C4—1724no—
827C22×C4—1724no—
828C22×C4—1722no—
829C22×C4C2×C4×D4311yescharacteristic
830C22×C4C2×C4×D4311yescharacteristic
831C22×C4D4×D4311yescharacteristic
832C22×C4D4×D4311yescharacteristic
833C22×C4D4×D4311yescharacteristic
834C22×C4C23×D4311yescharacteristic
835M16—22no—
836M16—22no—
837M16—42no—
838M16—862no—
839M16—862no—
840M16—1722no—
841C2×C8—22no—
842C2×C8—42no—
843C2×C8—862no—
844C2×C8—1722no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—431no—
848C4⋊C4—431no—
849C4⋊C4—861no—
850C4⋊C4—861no—
851C4⋊C4—861no—
852C4⋊C4—861no—
853C4⋊C4—861no—
854C4⋊C4—861no—
855C4⋊C4—861no—
856C4⋊C4—861no—
857C4⋊C4C2×C4×D4311yescharacteristic
858C4⋊C4C2×C4×D4311yescharacteristic
859C22⋊C4—24no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—861no—
866C22⋊C4—861no—
867C22⋊C4—861no—
868C22⋊C4—861no—
869C22⋊C4—861no—
870C22⋊C4—861no—
871C22⋊C4—861no—
872C22⋊C4—861no—
873C22⋊C4—868no—
874C22⋊C4—861no—
875C22⋊C4—861no—
876C22⋊C4—864no—
877C22⋊C4—861no—
878C22⋊C4—861no—
879C22⋊C4—861no—
880C22⋊C4—861no—
881C22⋊C4—861no—
882C42—21no—
883C42—22no—
884C42—22no—
885C42—861no—
886C42—861no—
887C42—861no—
888C42—862no—
889C42—862no—
890C42—1724no—
891C23—22no—
892C23—22no—
893C23—21no—
894C23—41no—
895C23—431no—
896C23—431no—
897C23—431no—
898C23—434no—
899C23—431no—
900C23—862no—
901C23—862no—
902C23—862no—
903C23—862no—
904C23—862no—
905C23—862no—
906C23—862no—
907C23—862no—
908C23—862no—
909C23—862no—
910C23—861no—
911C23—1721no—
912C23—1721no—
913C23—1721no—
914C23—1721no—
915C23—1721no—
916C23—1721no—
917C23—1721no—
918C23—1722no—
919C23—1722no—
920C23—1722no—
921C23—17216no—
922C23C22⋊C4×D4311yescharacteristic
923C23C22⋊C4×D4311yescharacteristic
924C23C2×D4×D4311yescharacteristic
925Q8—22no—
926Q8—862no—
927Q8—1722no—
928D4—22no—
929D4—42no—
930D4—42no—
931D4—42no—
932D4—862no—
933D4—1722no—
934D4—1722no—
935D4—1722no—
936D4—1722no—
937D4—1722no—
938D4—1722no—
939D4—1722no—
940D4—1722no—
941D4—1722no—
942D4—1722no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—24no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—431no—
959C2×C4—431no—
960C2×C4—431no—
961C2×C4—431no—
962C2×C4—862no—
963C2×C4—862no—
964C2×C4—862no—
965C2×C4—862no—
966C2×C4—862no—
967C2×C4—862no—
968C2×C4—861no—
969C2×C4—861no—
970C2×C4—861no—
971C2×C4—861no—
972C2×C4—861no—
973C2×C4—861no—
974C2×C4—861no—
975C2×C4—861no—
976C2×C4—864no—
977C2×C4—861no—
978C2×C4—861no—
979C2×C4—861no—
980C2×C4—1721no—
981C2×C4—1721no—
982C2×C4—1721no—
983C2×C4—1721no—
984C2×C4—1721no—
985C2×C4—1721no—
986C2×C4—1721no—
987C2×C4—1721no—
988C2×C4—1722no—
989C2×C4—1722no—
990C2×C4—1722no—
991C2×C4—17216no—
992C2×C4—1722no—
993C2×C4—1721no—
994C2×C4—1721no—
995C2×C4—1721no—
996C2×C4—1721no—
997C2×C4—1722no—
998C2×C4—1722no—
999C2×C4—1722no—
1000C2×C4—1721no—
1001C2×C4—1721no—
1002C2×C4C22⋊C4×D4311yescharacteristic
1003C2×C4C22⋊C4×D4311yescharacteristic
1004C2×C4C22×C4×D4311yescharacteristic
1005C2×C4C2×D4×D4311yescharacteristic
1006C2×C4#1306337012yes—
1007C2×C4#1306337112yes—
1008C8—42no—
1009C8—1722no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—44no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—432no—
1022C22—432no—
1023C22—432no—
1024C22—868no—
1025C22—861no—
1026C22—861no—
1027C22—861no—
1028C22—861no—
1029C22—861no—
1030C22—861no—
1031C22—861no—
1032C22—861no—
1033C22—861no—
1034C22—3444no—
1035C22—1724no—
1036C22—1724no—
1037C22—1724no—
1038C22—1724no—
1039C22—1724no—
1040C22—1721no—
1041C22—1721no—
1042C22—1721no—
1043C22#104×D4312yes—
1044C22C2×C22⋊C4×D4311yescharacteristic
1045C22#1458345712yes—
1046C4—21no—
1047C4—21no—
1048C4—44no—
1049C4—41no—
1050C4—41no—
1051C4—41no—
1052C4—861no—
1053C4—861no—
1054C4—861no—
1055C4—861no—
1056C4—1724no—
1057C4—1721no—
1058C4—1721no—
1059C4—1721no—
1060C4#1458337112yes—
1061C4#1458345911yescharacteristic
1062C4#1458346011yescharacteristic
1063C2—22no—
1064C2—22no—
1065C2—41no—
1066C2—81no—
1067C2—862no—
1068C2—862no—
1069C2—862no—
1070C2—3441no—
1071C2—1721no—
1072C2#1913716911yescharacteristic
1073C2C2×#104×D4311yescharacteristic
1074C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1871C2
socleC22×C43C22×C22⋊C4
prime radical#525×D43C2
cosocleC22×C4×C43C24
hypercenter#1871D43
hypocenterC43#21773
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. C2×#14582862C2semidirect
3. C4×C22⋊C4×D43C2semidirect
4. #19135037C2semidirect
5. #19135035C2semidirect
6. #19134898C2semidirect
7. #19134897C2semidirect
8. #19134895C2semidirect
9. #19134693C2semidirect
10. #19134537C2semidirect
11. C43×#1871C2semidirect
14. C22×#10621877C22semidirect
15. #14583412C4semidirect
16. #14583412C4semidirect
19. #14583409C4semidirect
20. #14583409C4semidirect
27. C22⋊Q8×D43C4semidirect
28. C22⋊Q8×D43C4semidirect
29. #121×D43C4semidirect
30. #121×D43C4semidirect
36. C2×C42×D43C22semidirect
37. C2×#13063253C22semidirect
38. C2×#13063252C22semidirect
39. C2×#13063251C22semidirect
43. #14582862C22semidirect
48. C4×C22⋊Dic43C22semidirect
51. #14582660C22semidirect
52. #14582659C22semidirect
53. #14582658C22semidirect
54. C22×M16×C43C22semidirect
56. C2×#104×C43C22semidirect
57. C4×C22⋊C4×C43C22semidirect
58. C43×#339C22semidirect
60. C2×#10621902C2×C4semidirect
64. C2×#10621900C2×C4semidirect
67. C2×Q8×D43C2×C4semidirect
71. C2×D4×D43C2×C4semidirect
102. #13063304C2×C4semidirect
103. #13063304C2×C4semidirect
112. #13063299C2×C4semidirect
113. #13063299C2×C4semidirect
142. #13063283C2×C4semidirect
143. #13063283C2×C4semidirect
148. C4⋊C4×D43C2×C4semidirect
149. C4⋊C4×D43C2×C4semidirect
179. C22⋊Q8×C43C2×C4semidirect
180. C22⋊Q8×C43C2×C4semidirect
181. #121×C43C2×C4semidirect
182. #121×C43C2×C4semidirect
382. C22×D43#104semidirect
534. #1871D43semidirect
552. C22×M16C2×D43semidirect
579. C2×#104C2×D43semidirect
590. C4×C22⋊C4C2×D43semidirect
595. #339C2×D43semidirect
596. C43#21773semidirect
655. C22⋊Q8C4×D43semidirect
656. C22⋊Q8C4×D43semidirect
667. #121C4×D43semidirect
668. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
#525×D432
C2×#145828622
C4×C22⋊C4×D432
#191350372
#191350352
#191348982
#191348972
#191348952
#191346932
#191345372
C43×#18712
#2177343