Finite Group Databasebeta

← #25064118

Subgroups — #25064118

Order 11008.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148627C211yesmaximal, characteristic
2#19143630C211yesmaximal, characteristic, complemented
3#19133170C211yesmaximal, characteristic, complemented
4#19133162C211yesmaximal, characteristic, complemented
5#19133154C211yesmaximal, characteristic, complemented
6#19133149C211yesmaximal, characteristic, complemented
7#19133141C211yesmaximal, characteristic, complemented
8#19133136C211yesmaximal, characteristic, complemented
9#19133131C211yesmaximal, characteristic, complemented
10#19133123C211yesmaximal, characteristic, complemented
11#19133110C211yesmaximal, characteristic, complemented
12#19133097C211yesmaximal, characteristic, complemented
13#19133084C211yesmaximal, characteristic, complemented
14C2×#14582632C211yesmaximal, characteristic, complemented
15C43×#2318C211yesmaximal, characteristic, complemented
16#14583614C411yescharacteristic, complemented
17#14583606C411yescharacteristic, complemented
18#14583597—21no—
19#14583595C411yescharacteristic, complemented
20#14583595C411yescharacteristic, complemented
21#14583570C411yescharacteristic, complemented
22#14583545C411yescharacteristic, complemented
23#14583545C411yescharacteristic, complemented
24#14583539—21no—
25#14583539—21no—
26D4×D172C411yescharacteristic, complemented
27D4×C22⋊D43—21no—
28#14583500—21no—
29#14583482—21no—
30#14583482—21no—
31#14583449C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583410C2211yescharacteristic
34#14583410C2211yescharacteristic
35C2×#13063299C2211yescharacteristic
36C2×#13063299C2211yescharacteristic
37#14583371—21no—
38#14582977—21no—
39#14582971—21no—
40#14582971—21no—
41D4×C43⋊C8—21no—
42#14582956C2211yescharacteristic, complemented
43#14582952C2211yescharacteristic, complemented
44#14582863C2211yescharacteristic, complemented
45#14582863C2211yescharacteristic, complemented
46C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
48#14582635C2211yescharacteristic, complemented
49#14582635C2211yescharacteristic, complemented
50#14582635C2211yescharacteristic, complemented
51#14582635C2211yescharacteristic, complemented
52#14582632C2211yescharacteristic
53#14582632C2211yescharacteristic
54#14582632C2211yescharacteristic
55#14582632C2211yescharacteristic
56#14582632C2211yescharacteristic, complemented
57#14582632C2211yescharacteristic, complemented
58#14582632C2211yescharacteristic, complemented
59#14582632C2211yescharacteristic, complemented
60#14582632C2211yescharacteristic, complemented
61#14582632C2211yescharacteristic, complemented
62#14582632C2211yescharacteristic, complemented
63#14582632C2211yescharacteristic, complemented
64C2×C4×D4×C43C2211yescharacteristic
65C43×#388—21no—
66C43×#387—21no—
67C43×#386—21no—
68C43×#385—21no—
69C43×#383C2211yescharacteristic, complemented
70C43×#382C2211yescharacteristic, complemented
71C43×#381C2211yescharacteristic, complemented
72C43×#380C2211yescharacteristic, complemented
73C4×C22⋊C4×C43C2211yescharacteristic, complemented
74C2×#95×C43C2211yescharacteristic, complemented
75C2×#10621898—21no—
76C2×#10621898C2×C411yescharacteristic
77C2×#10621898C2×C411yescharacteristic, complemented
78C22×D172C2×C411yescharacteristic
79C22×D172C2×C411yescharacteristic, complemented
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C2×D4×D43—21no—
83C2×#10621877—21no—
84C2×#10621877—21no—
85C22×C43⋊C8—21no—
86C22×C43⋊C8—21no—
87#13063325C2×C411yescharacteristic, complemented
88#13063322C2×C411yescharacteristic, complemented
89#13063321—21no—
90#13063320—21no—
91#13063320—21no—
92#13063319—21no—
93#13063317C2×C411yescharacteristic, complemented
94#13063316—21no—
95#13063313—21no—
96#13063313C2×C411yescharacteristic, complemented
97#13063311—21no—
98#13063311—21no—
99#13063310—21no—
100#13063310—21no—
101#13063308—21no—
102#13063308—21no—
103#13063308—21no—
104#13063307—21no—
105#13063307—21no—
106#13063304C2×C411yescharacteristic
107#13063304C2×C411yescharacteristic, complemented
108#13063304C2311yescharacteristic
109#13063302—21no—
110#13063302—21no—
111#13063300—21no—
112#13063299—21no—
113#13063299—21no—
114#13063299—21no—
115#13063299—21no—
116#13063299—21no—
117#13063299C2×C411yescharacteristic
118#13063299C2×C411yescharacteristic
119#13063299C2×C411yescharacteristic
120#13063299C2×C411yescharacteristic, complemented
121#13063299C2×C411yescharacteristic, complemented
122#13063299C2×C411yescharacteristic, complemented
123#13063299C2311yescharacteristic
124#13063299C2311yescharacteristic
125#13063299C2311yescharacteristic
126#13063298—21no—
127#13063298—21no—
128#13063298—21no—
129#13063298—21no—
130#13063297—21no—
131#13063297—21no—
132#13063296—21no—
133#13063295—21no—
134#13063295—21no—
135#13063294—21no—
136#13063294—21no—
137#13063293—21no—
138#13063293—21no—
139C4×Dic86C2×C411yescharacteristic, complemented
140C4×D172—21no—
141C4×D172C2×C411yescharacteristic, complemented
142C4×D172C2×C411yescharacteristic, complemented
143C4×D172C2×C411yescharacteristic, complemented
144D4×Dic43—21no—
145#13063287—21no—
146C4×C22⋊D43—21no—
147C4×C22⋊D43—21no—
148C4×C22⋊D43—21no—
149C4×C22⋊D43—21no—
150C4×C22⋊D43—21no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153#13063284C2×C411yescharacteristic
154#13063284C2×C411yescharacteristic, complemented
155#13063283—21no—
156#13063282—21no—
157C2×C4⋊Dic43C2×C411yescharacteristic
158C2×C4⋊Dic43C2×C411yescharacteristic, complemented
159C2×(C2×D43)⋊C4—21no—
160C2×(C2×D43)⋊C4—21no—
161C22⋊C4×D43—21no—
162C22⋊C4×D43—21no—
163C4⋊(C43⋊C8)—21no—
164C4⋊(C43⋊C8)—21no—
165C22⋊(C43⋊C8)—21no—
166C22⋊(C43⋊C8)—21no—
167C22⋊(C43⋊C8)—21no—
168C22⋊(C43⋊C8)—21no—
169C22⋊(C43⋊C8)C2311yescharacteristic
170C22⋊(C43⋊C8)C2311yescharacteristic
171C22⋊(C43⋊C8)C2311yescharacteristic
172C22⋊(C43⋊C8)C2311yescharacteristic
173#13063236—21no—
174C4×C43⋊C8—21no—
175C22×D4×C43D411yescharacteristic
176C23×C4×C43—21no—
177C23×C4×C43C2311yescharacteristic
178C23×C4×C43C2311yescharacteristic
179C4×D4×C43C2×C411yescharacteristic
180C4×D4×C43C2×C411yescharacteristic
181C4×D4×C43C2×C411yescharacteristic
182C4×D4×C43C2×C411yescharacteristic
183C4×D4×C43D411yescharacteristic
184C4×D4×C43D411yescharacteristic
185C4×D4×C43D411yescharacteristic
186C4×D4×C43D411yescharacteristic
187C2×C4⋊C4×C43—21no—
188C2×C4⋊C4×C43—21no—
189C2×C4⋊C4×C43D411yescharacteristic
190C2×C22⋊C4×C43—21no—
191C2×C22⋊C4×C43—21no—
192C2×C22⋊C4×C43—21no—
193C2×C22⋊C4×C43D411yescharacteristic
194C2×C22⋊C4×C43D411yescharacteristic
195C2×C42×C43—21no—
196C2×C42×C43C2311yescharacteristic
197#95×C43—21no—
198#95×C43—21no—
199#95×C43—21no—
200#95×C43—21no—
201#95×C43—21no—
202#95×C43C2311yescharacteristic
203#95×C43C2311yescharacteristic
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43C2×D411yescharacteristic
207C24×C43C2×D411yescharacteristic
208C23×D43—21no—
209C23×D43—21no—
210C2×D4×C43—42no—
211C2×D4×C43C22⋊C411yescharacteristic
212C2×D4×C43C22⋊C411yescharacteristic
213C2×D4×C43C22⋊C411yescharacteristic
214C2×D4×C43C22⋊C411yescharacteristic
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—42no—
220C22×C4×C43—81no—
221C22×C4×C43—81no—
222C22×C4×C43—81no—
223C22×C4×C43—81no—
224C22×C4×C43C22×C411yescharacteristic
225C22×C4×C43C22×C411yescharacteristic
226C22×C4×C43C22×C411yescharacteristic
227C22×C4×C43C22×C411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D411yescharacteristic
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2411yescharacteristic
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C2×C22⋊D43—21no—
240C2×C22⋊D43—21no—
241C2×C22⋊D43—21no—
242C2×C22⋊D43—21no—
243C2×C22⋊D43—21no—
244C2×C22⋊D43—21no—
245C2×C22⋊D43—21no—
246C2×C22⋊D43—21no—
247C2×C22⋊D43—21no—
248C2×C22⋊D43—81no—
249C2×C22⋊D43—81no—
250C2×C22⋊D43—81no—
251C2×C22⋊D43—81no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254D4×D43—44no—
255#10621898—81no—
256#10621898—81no—
257#10621898—81no—
258#10621898—81no—
259C2×D172—21no—
260C2×D172—21no—
261C2×D172—21no—
262C2×D172—21no—
263C2×D172—81no—
264C2×D172—81no—
265C2×D172C22×C411yescharacteristic
266C2×D172C22×C411yescharacteristic
267C2×D172C22×C411yescharacteristic
268C2×C4×D43—21no—
269C2×C4×D43—21no—
270C2×C4×D43—21no—
271C2×C4×D43—21no—
272C2×C4×D43—21no—
273C2×Dic86—21no—
274C2×Dic86C22×C411yescharacteristic
275C4⋊C4×C43—81no—
276C4⋊C4×C43—81no—
277C4⋊C4×C43C22⋊C411yescharacteristic
278C4⋊C4×C43C22⋊C411yescharacteristic
279C4⋊C4×C43C22⋊C411yescharacteristic
280C4⋊C4×C43C22⋊C411yescharacteristic
281C22⋊C4×C43—42no—
282C22⋊C4×C43—81no—
283C22⋊C4×C43—81no—
284C22⋊C4×C43C22⋊C411yescharacteristic
285C22⋊C4×C43C22⋊C411yescharacteristic
286C22⋊C4×C43C22⋊C411yescharacteristic
287C22⋊C4×C43C22⋊C411yescharacteristic
288C22⋊C4×C43C22⋊C411yescharacteristic
289C22⋊C4×C43C22⋊C411yescharacteristic
290C22⋊C4×C43C22⋊C411yescharacteristic
291C22⋊C4×C43C22⋊C411yescharacteristic
292C42×C43—81no—
293C42×C43C22×C411yescharacteristic
294C42×C43C22×C411yescharacteristic
295C42×C43C2×D411yescharacteristic
296C42×C43C2×D411yescharacteristic
297C22⋊Dic43—21no—
298C22⋊Dic43—21no—
299C22⋊Dic43—21no—
300C22⋊Dic43—21no—
301C22⋊Dic43—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4—21no—
306(C2×D43)⋊C4—21no—
307(C2×D43)⋊C4—21no—
308(C2×D43)⋊C4—21no—
309(C2×D43)⋊C4—21no—
310(C2×D43)⋊C4—21no—
311(C2×D43)⋊C4—21no—
312(C2×D43)⋊C4—21no—
313(C2×D43)⋊C4—21no—
314(C2×D43)⋊C4—21no—
315(C2×D43)⋊C4—21no—
316C4⋊Dic43—21no—
317C4⋊Dic43—21no—
318C4⋊Dic43—21no—
319C4⋊Dic43C22×C411yescharacteristic
320C4⋊Dic43C22×C411yescharacteristic
321C4⋊Dic43C22×C411yescharacteristic
322C4⋊Dic43C22×C411yescharacteristic
323Dic43⋊C4—21no—
324Dic43⋊C4—21no—
325Dic43⋊C4—21no—
326Dic43⋊C4—21no—
327Dic43⋊C4—21no—
328Dic43⋊C4—21no—
329C4×Dic43—21no—
330C4×Dic43—21no—
331C4×Dic43—21no—
332#10621877—81no—
333#10621877—81no—
334C2×C43⋊C8—21no—
335C2×C43⋊C8—21no—
336C2×C43⋊C8—21no—
337C2×C43⋊C8—21no—
338C2×C43⋊C8—81no—
339C2×C43⋊C8—81no—
340C23×C43—21no—
341C23×C43—21no—
342C23×C43—22no—
343C23×C43—21no—
344C23×C43—21no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43C2×C22⋊C411yescharacteristic
349C23×C43C2×C22⋊C411yescharacteristic
350C23×C43C2×C22⋊C411yescharacteristic
351C23×C43C2×C22⋊C411yescharacteristic
352C23×C43C22×D411yescharacteristic
353C22×D43—21no—
354C22×D43—21no—
355C22×D43—21no—
356C22×D43—42no—
357C22×D43—42no—
358C22×D43—81no—
359C22×D43—81no—
360C22×D43—81no—
361C22×D43—81no—
362D4×C43—22no—
363D4×C43—22no—
364D4×C43—41no—
365D4×C43—41no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
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×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—84no—
393C2×C4×C43C2×C22⋊C411yescharacteristic
394C2×C4×C43C2×C22⋊C411yescharacteristic
395C2×C4×C43C2×C22⋊C411yescharacteristic
396C2×C4×C43C2×C22⋊C411yescharacteristic
397C2×C4×C43C2×C22⋊C411yescharacteristic
398C2×C4×C43C2×C22⋊C411yescharacteristic
399C2×C4×C43C2×C22⋊C411yescharacteristic
400C2×C4×C43C2×C22⋊C411yescharacteristic
401C2×C4×C43C23×C411yescharacteristic
402C2×C4×C43C22×D411yescharacteristic
403C22⋊D43—42no—
404C22⋊D43—41no—
405C22⋊D43—41no—
406C22⋊D43—41no—
407C22⋊D43—41no—
408C22⋊D43—41no—
409C22⋊D43—41no—
410C22⋊D43—42no—
411C22⋊D43—81no—
412C22⋊D43—81no—
413C22⋊D43—81no—
414C22⋊D43—81no—
415C22⋊D43—81no—
416C22⋊D43—81no—
417C2×Dic43—21no—
418C2×Dic43—21no—
419C2×Dic43—21no—
420C2×Dic43—21no—
421C2×Dic43—21no—
422C2×Dic43—81no—
423C2×Dic43—81no—
424D172—41no—
425D172—41no—
426D172—41no—
427D172—42no—
428D172—81no—
429D172—81no—
430D172—81no—
431C4×D43—42no—
432C4×D43—81no—
433C4×D43—81no—
434C4×D43—81no—
435C4×D43—81no—
436Dic86—41no—
437Dic86—81no—
438C43⋊C8—41no—
439C43⋊C8—41no—
440C43⋊C8—41no—
441C43⋊C8—41no—
442#17597—431nomaximal, Sylow
443C22×C43—21no—
444C22×C43—21no—
445C22×C43—21no—
446C22×C43—21no—
447C22×C43—21no—
448C22×C43—21no—
449C22×C43—21no—
450C22×C43—21no—
451C22×C43—21no—
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—21no—
456C22×C43—42no—
457C22×C43—42no—
458C22×C43—81no—
459C22×C43—81no—
460C22×C43#42112yes—
461C22×C43C22×C22⋊C411yescharacteristic
462C22×C43#57611yescharacteristic
463C22×C43#57711yescharacteristic
464C2×D43—41no—
465C2×D43—41no—
466C2×D43—41no—
467C2×D43—41no—
468C2×D43—41no—
469C2×D43—41no—
470C2×D43—41no—
471C2×D43—41no—
472C2×D43—41no—
473C2×D43—162no—
474C2×D43—162no—
475C4×C43—21no—
476C4×C43—21no—
477C4×C43—21no—
478C4×C43—21no—
479C4×C43—21no—
480C4×C43—21no—
481C4×C43—21no—
482C4×C43—21no—
483C4×C43—21no—
484C4×C43—21no—
485C4×C43—81no—
486C4×C43—81no—
487C4×C43—81no—
488C4×C43—81no—
489Dic43—41no—
490Dic43—41no—
491Dic43—41no—
492Dic43—41no—
493Dic43—41no—
494#3519—431no—
495#2974—431no—
496#2318D4311yescharacteristic, complemented
497#1521—431no—
498#1519—431no—
499#1517—431no—
500#1516—431no—
501#1514—431no—
502#1513—431no—
503#1512—431no—
504#1510—431no—
505#1507—431no—
506#1504—431no—
507#1501—431no—
508C2×#327—431no—
509C2×C43—21no—
510C2×C43—21no—
511C2×C43—22no—
512C2×C43—41no—
513C2×C43—41no—
514C2×C43—41no—
515C2×C43#288311yescharacteristic
516C2×C43#289711yescharacteristic
517C2×C43C2×#42111yescharacteristic
518D43—81no—
519D43—81no—
520D43—81no—
521#555—431no—
522#554—431no—
523#553—431no—
524#553—431no—
525#553—861no—
526#550—431no—
527#546—431no—
528#546—431no—
529#546—861no—
530#546—861no—
531D42—431no—
532D42—861no—
533#540—861no—
534#538—861no—
535#538—861no—
536#532—431no—
537#529—431no—
538#525—431no—
539#525—431no—
540C2×#121—431no—
541C2×#121—431no—
542#518—861no—
543C2×C4×D4C2×D4311yescharacteristic
544#436—861no—
545#435—861no—
546#435—861no—
547C8×D4—861no—
548#432—431no—
549#431—431no—
550#407—431no—
551#407—431no—
552C2×C22⋊C8—431no—
553C2×C22⋊C8—431no—
554#388—21no—
555#387—21no—
556#386—21no—
557#385—21no—
558#383C2×D4311yescharacteristic, complemented
559#382C2×D4311yescharacteristic, complemented
560#381C2×D4311yescharacteristic, complemented
561#380C2×D4311yescharacteristic, complemented
562C4×C22⋊C4C2×D4311yescharacteristic, complemented
563C2×#95C2×D4311yescharacteristic, complemented
564#328—431no—
565#328—431no—
566#328—431no—
567#328—431no—
568#327—431no—
569#327—431no—
570#327—431no—
571#327—431no—
572#327—431no—
573#327—431no—
574#327—431no—
575#327—431no—
576#327—431no—
577#327—431no—
578#327—431no—
579#327—431no—
580C43#1759711yescharacteristic, complemented, Sylow
581C2×#41—431no—
582C2×#41—431no—
583C2×#41—861no—
584C22×D4—431no—
585C22×D4—431no—
586C22×D4—861no—
587C22×D4—861no—
588C22×D4—861no—
589C22×D4C22⋊D4311yescharacteristic
590C23×C4—21no—
591C23×C4C22×D4311yescharacteristic
592C23×C4C22×D4311yescharacteristic
593C2×M16—861no—
594C2×M16—861no—
595C22×C8—861no—
596C22×C8—861no—
597C4⋊Q8—431no—
598#127—431no—
599#127—861no—
600#126—861no—
601#126—861no—
602#126—861no—
603#125—431no—
604#125—861no—
605#124—431no—
606#124—861no—
607#124—861no—
608#124—861no—
609#123—861no—
610#123—861no—
611#123—861no—
612#123—861no—
613#123—861no—
614#123—861no—
615#123—861no—
616C22⋊Q8—431no—
617C22⋊Q8—431no—
618C22⋊Q8—431no—
619C22⋊Q8—861no—
620C22⋊Q8—861no—
621#121—431no—
622#121—431no—
623#121—431no—
624#121—431no—
625#121—431no—
626#121—431no—
627#121—431no—
628#121—431no—
629#121—431no—
630#121—861no—
631#121—861no—
632#121—861no—
633#121—861no—
634#121—861no—
635#121—861no—
636#121—861no—
637#121—861no—
638#121—861no—
639#121—861no—
640#121—861no—
641#121—861no—
642#121—861no—
643#120—861no—
644#120—861no—
645#120—861no—
646#120—861no—
647#120—861no—
648#120—861no—
649C4×Q8—431no—
650C4×D4—431no—
651C4×D4—431no—
652C4×D4—431no—
653C4×D4—861no—
654C4×D4—861no—
655C4×D4—861no—
656C4×D4—861no—
657C4×D4—861no—
658C4×D4—861no—
659C4×D4—861no—
660C4×D4—861no—
661C4×D4—861no—
662C4×D4—861no—
663C4×D4C4×D4311yescharacteristic
664C4×D4C4×D4311yescharacteristic
665C4×D4C4×D4311yescharacteristic
666C4×D4C4×D4311yescharacteristic
667C4×D4D17211yescharacteristic
668C4×D4D17211yescharacteristic
669C4×D4D17211yescharacteristic
670C4×D4D17211yescharacteristic
671#117—431no—
672#117—431no—
673#117—861no—
674#117—861no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—431no—
678C2×C4⋊C4—431no—
679C2×C4⋊C4C22⋊D4311yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—861no—
684C2×C22⋊C4—861no—
685C2×C22⋊C4—861no—
686C2×C22⋊C4—861no—
687C2×C22⋊C4C22⋊D4311yescharacteristic
688C2×C22⋊C4C22⋊D4311yescharacteristic
689C2×C42—21no—
690C2×C42C22×D4311yescharacteristic
691C4⋊C8—861no—
692C4⋊C8—861no—
693C22⋊C8—431no—
694C22⋊C8—431no—
695C22⋊C8—431no—
696C22⋊C8—431no—
697C22⋊C8—861no—
698C22⋊C8—861no—
699C22⋊C8—861no—
700C22⋊C8—861no—
701#97—861no—
702C4×C8—861no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95C22×D4311yescharacteristic
709#95C22×D4311yescharacteristic
710#95C22×D4311yescharacteristic
711#95C22×D4311yescharacteristic
712C24—861no—
713C24—861no—
714C24C2×C22⋊D4311yescharacteristic
715C24C2×C22⋊D4311yescharacteristic
716#41—3441no—
717#41—3441no—
718#41—3441no—
719#41—3441no—
720C2×Q8—431no—
721C2×Q8—861no—
722C2×D4—42no—
723C2×D4—431no—
724C2×D4—431no—
725C2×D4—431no—
726C2×D4—861no—
727C2×D4—861no—
728C2×D4—861no—
729C2×D4—861no—
730C2×D4—861no—
731C2×D4—861no—
732C2×D4—861no—
733C2×D4—861no—
734C2×D4—861no—
735C2×D4—861no—
736C2×D4—861no—
737C2×D4—861no—
738C2×D4—861no—
739C2×D4—861no—
740C2×D4—861no—
741C2×D4—3441no—
742C2×D4—3441no—
743C2×D4—3441no—
744C2×D4—3441no—
745C2×D4—3441no—
746C2×D4—3441no—
747C2×D4—1724no—
748C2×D4(C2×D43)⋊C411yescharacteristic
749C2×D4(C2×D43)⋊C411yescharacteristic
750C2×D4(C2×D43)⋊C411yescharacteristic
751C2×D4(C2×D43)⋊C411yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—42no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4—81no—
760C22×C4—81no—
761C22×C4—861no—
762C22×C4—861no—
763C22×C4—861no—
764C22×C4—861no—
765C22×C4—861no—
766C22×C4—861no—
767C22×C4—861no—
768C22×C4C2×C4×D4311yescharacteristic
769C22×C4C2×C4×D4311yescharacteristic
770C22×C4C2×C4×D4311yescharacteristic
771C22×C4C2×C4×D4311yescharacteristic
772C22×C4C2×D17211yescharacteristic
773C22×C4C2×D17211yescharacteristic
774C22×C4C2×D17211yescharacteristic
775C22×C4C2×D17211yescharacteristic
776C22×C4C2×C22⋊D4311yescharacteristic
777C22×C4C2×C22⋊D4311yescharacteristic
778C22×C4C2×C22⋊D4311yescharacteristic
779C22×C4C2×C22⋊D4311yescharacteristic
780C22×C4C23×D4311yescharacteristic
781M16—3441no—
782M16—3441no—
783C2×C8—861no—
784C2×C8—861no—
785C2×C8—861no—
786C2×C8—861no—
787C2×C8—3441no—
788C2×C8—3441no—
789C4⋊C4—81no—
790C4⋊C4—81no—
791C4⋊C4—431no—
792C4⋊C4—431no—
793C4⋊C4—431no—
794C4⋊C4—431no—
795C4⋊C4—861no—
796C4⋊C4—861no—
797C4⋊C4—861no—
798C4⋊C4—861no—
799C4⋊C4—861no—
800C4⋊C4—861no—
801C4⋊C4—861no—
802C4⋊C4—861no—
803C4⋊C4—861no—
804C4⋊C4(C2×D43)⋊C411yescharacteristic
805C4⋊C4(C2×D43)⋊C411yescharacteristic
806C4⋊C4(C2×D43)⋊C411yescharacteristic
807C4⋊C4(C2×D43)⋊C411yescharacteristic
808C22⋊C4—42no—
809C22⋊C4—81no—
810C22⋊C4—81no—
811C22⋊C4—861no—
812C22⋊C4—861no—
813C22⋊C4—861no—
814C22⋊C4—861no—
815C22⋊C4—861no—
816C22⋊C4—861no—
817C22⋊C4—861no—
818C22⋊C4—861no—
819C22⋊C4—861no—
820C22⋊C4—861no—
821C22⋊C4—861no—
822C22⋊C4—861no—
823C22⋊C4—861no—
824C22⋊C4—861no—
825C22⋊C4—861no—
826C22⋊C4—861no—
827C22⋊C4—861no—
828C22⋊C4—861no—
829C22⋊C4—861no—
830C22⋊C4(C2×D43)⋊C411yescharacteristic
831C22⋊C4(C2×D43)⋊C411yescharacteristic
832C22⋊C4(C2×D43)⋊C411yescharacteristic
833C22⋊C4(C2×D43)⋊C411yescharacteristic
834C22⋊C4(C2×D43)⋊C411yescharacteristic
835C22⋊C4(C2×D43)⋊C411yescharacteristic
836C22⋊C4(C2×D43)⋊C411yescharacteristic
837C22⋊C4(C2×D43)⋊C411yescharacteristic
838C42—81no—
839C42—861no—
840C42—861no—
841C42—861no—
842C42C2×C4×D4311yescharacteristic
843C42C2×C4×D4311yescharacteristic
844C42C2×D17211yescharacteristic
845C42C2×D17211yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—861no—
855C23—861no—
856C23—861no—
857C23—3441no—
858C23—3441no—
859C23—3441no—
860C23—3441no—
861C23—1722no—
862C23—1722no—
863C23C2×(C2×D43)⋊C411yescharacteristic
864C23C2×(C2×D43)⋊C411yescharacteristic
865C23C2×(C2×D43)⋊C411yescharacteristic
866C23C2×(C2×D43)⋊C411yescharacteristic
867C23C22×C22⋊D4311yescharacteristic
868Q8—3441no—
869Q8—1721no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—3441no—
875D4—3441no—
876D4—3441no—
877D4—3441no—
878D4—3441no—
879D4—3441no—
880D4—3441no—
881D4—3441no—
882D4—3441no—
883D4—1721no—
884D4—1721no—
885D4—1721no—
886D4—1722no—
887D4—1722no—
888D4—1722no—
889D4—1721no—
890D4—1721no—
891D4—1721no—
892D4—1721no—
893D4—1721no—
894D4—1721no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—84no—
922C2×C4—861no—
923C2×C4—861no—
924C2×C4—861no—
925C2×C4—861no—
926C2×C4—861no—
927C2×C4—3441no—
928C2×C4—3441no—
929C2×C4—3441no—
930C2×C4—3441no—
931C2×C4—3441no—
932C2×C4—3441no—
933C2×C4—1722no—
934C2×C4C2×(C2×D43)⋊C411yescharacteristic
935C2×C4C2×(C2×D43)⋊C411yescharacteristic
936C2×C4C2×(C2×D43)⋊C411yescharacteristic
937C2×C4C2×(C2×D43)⋊C411yescharacteristic
938C2×C4C2×(C2×D43)⋊C411yescharacteristic
939C2×C4C2×(C2×D43)⋊C411yescharacteristic
940C2×C4C2×(C2×D43)⋊C411yescharacteristic
941C2×C4C2×(C2×D43)⋊C411yescharacteristic
942C2×C4C22×C4×D4311yescharacteristic
943C2×C4C22×D17211yescharacteristic
944C8—1721no—
945C8—1721no—
946C8—1721no—
947C8—1721no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—81no—
964C22—81no—
965C22—1721no—
966C22—1721no—
967C22—1721no—
968C22—1721no—
969C22—1721no—
970C22—1721no—
971C22—1721no—
972C22—1721no—
973C22—1721no—
974C22—6882no—
975C22—6882no—
976C22#1458291712yes—
977C22C22×(C2×D43)⋊C411yescharacteristic
978C22#1458370211yescharacteristic
979C22#1458370711yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—81no—
991C4—81no—
992C4—81no—
993C4—81no—
994C4—1721no—
995C4—1721no—
996C4—1721no—
997C4—1721no—
998C4—1721no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—3441no—
1006C2—3441no—
1007C2—3441no—
1008C2#1914305511yescharacteristic
1009C2#1914311811yescharacteristic
1010C2C2×#1458291711yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2318C2
socleC22×C43C22×C22⋊C4
prime radical#19148627C2
cosocleC22×C4×C43C24
hypercenter#2318D43
hypocenterC43#17597
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #19143630C2semidirect
3. #19133170C2semidirect
4. #19133162C2semidirect
5. #19133154C2semidirect
6. #19133149C2semidirect
7. #19133141C2semidirect
8. #19133136C2semidirect
9. #19133131C2semidirect
10. #19133123C2semidirect
11. #19133110C2semidirect
12. #19133097C2semidirect
13. #19133084C2semidirect
14. C2×#14582632C2semidirect
15. C43×#2318C2semidirect
16. #14583614C4semidirect
17. #14583606C4semidirect
19. #14583595C4semidirect
20. #14583595C4semidirect
21. #14583570C4semidirect
22. #14583545C4semidirect
23. #14583545C4semidirect
26. D4×D172C4semidirect
42. #14582956C22semidirect
43. #14582952C22semidirect
44. #14582863C22semidirect
45. #14582863C22semidirect
46. C2×C22⋊(C43⋊C8)C22semidirect
47. C2×C22⋊(C43⋊C8)C22semidirect
48. #14582635C22semidirect
49. #14582635C22semidirect
50. #14582635C22semidirect
51. #14582635C22semidirect
56. #14582632C22semidirect
57. #14582632C22semidirect
58. #14582632C22semidirect
59. #14582632C22semidirect
60. #14582632C22semidirect
61. #14582632C22semidirect
62. #14582632C22semidirect
63. #14582632C22semidirect
69. C43×#383C22semidirect
70. C43×#382C22semidirect
71. C43×#381C22semidirect
72. C43×#380C22semidirect
73. C4×C22⋊C4×C43C22semidirect
74. C2×#95×C43C22semidirect
77. C2×#10621898C2×C4semidirect
79. C22×D172C2×C4semidirect
87. #13063325C2×C4semidirect
88. #13063322C2×C4semidirect
93. #13063317C2×C4semidirect
96. #13063313C2×C4semidirect
107. #13063304C2×C4semidirect
120. #13063299C2×C4semidirect
121. #13063299C2×C4semidirect
122. #13063299C2×C4semidirect
139. C4×Dic86C2×C4semidirect
141. C4×D172C2×C4semidirect
142. C4×D172C2×C4semidirect
143. C4×D172C2×C4semidirect
154. #13063284C2×C4semidirect
158. C2×C4⋊Dic43C2×C4semidirect
496. #2318D43semidirect
558. #383C2×D43semidirect
559. #382C2×D43semidirect
560. #381C2×D43semidirect
561. #380C2×D43semidirect
562. C4×C22⋊C4C2×D43semidirect
563. C2×#95C2×D43semidirect
580. C43#17597semidirect

Maximal subgroups

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

subgroupindex
#191486272
#191436302
#191331702
#191331622
#191331542
#191331492
#191331412
#191331362
#191331312
#191331232
#191331102
#191330972
#191330842
C2×#145826322
C43×#23182
#1759743