Finite Group Databasebeta

← #25113072

Subgroups — #25113072

Order 11008.

1262 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148149C211yesmaximal, characteristic
2#19143327C211yesmaximal, characteristic, complemented
3C4×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
4#19135570C211yesmaximal, characteristic, complemented
5#19135537C211yesmaximal, characteristic, complemented
6#19135037C211yesmaximal, characteristic, complemented
7#19135036C211yesmaximal, characteristic, complemented
8#19134896C211yesmaximal, characteristic, complemented
9#19134895C211yesmaximal, characteristic, complemented
10#19134693C211yesmaximal, characteristic, complemented
11#19134614C211yesmaximal, characteristic, complemented
12#19134399C211yesmaximal, characteristic, complemented
13C2×#14582658C211yesmaximal, characteristic, complemented
14#339×D43C211yesmaximal, characteristic, complemented
15C43×#1826C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic
18#14583617C411yescharacteristic, complemented
19#14583612C411yescharacteristic, complemented
20#14583604C411yescharacteristic, complemented
21#14583597C411yescharacteristic, complemented
22#14583593C411yescharacteristic, complemented
23#14583588C411yescharacteristic, complemented
24#14583584C411yescharacteristic, complemented
25#14583582—21no—
26#14583575—21no—
27#14583573—21no—
28#14583550C411yescharacteristic, complemented
29#14583539—21no—
30#14583452C2211yescharacteristic
31#14583433—21no—
32#14583427—21no—
33#14583427—21no—
34#14583411C2211yescharacteristic
35#14583410C2211yescharacteristic
36C4×#10621898—21no—
37#14583367C2211yescharacteristic
38C2×C4×C22⋊D43C2211yescharacteristic
39C2×(C22⋊D43)⋊C4—21no—
40#117×D43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C2×C42×D43C2211yescharacteristic
43#14582974—21no—
44#14582973—21no—
45#14582967—21no—
46(C22⋊D43)⋊C8—21no—
47#14582922C2211yescharacteristic
48C2×#13063253C2211yescharacteristic
49C2×#13063253C2211yescharacteristic
50C2×#13063251C2211yescharacteristic
51C2×#13063251C2211yescharacteristic
52#14582862C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54C4×Dic43⋊C4C2211yescharacteristic
55#14582750—21no—
56C22⋊C4×Dic43—21no—
57C4×(C2×D43)⋊C4C2211yescharacteristic
58#14582746—21no—
59C42×Dic43C2211yescharacteristic
60#14582660C2211yescharacteristic
61#14582660C2211yescharacteristic
62#14582659C2211yescharacteristic
63#14582659C2211yescharacteristic
64#14582658C2211yescharacteristic
65#14582658C2211yescharacteristic
66#14582658C2211yescharacteristic
67#14582658C2211yescharacteristic
68C2×#117×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic
70C4×C22⋊C4×C43C2211yescharacteristic
71C43×#339C2211yescharacteristic
72C43×#339C2211yescharacteristic
73C43×#339C2211yescharacteristic
74C43×#339C2211yescharacteristic
75C2×#10621898—21no—
76C2×#10621898C2311yescharacteristic
77C22×C22⋊D43D411yescharacteristic
78C23×Dic43—21no—
79C22×C4×D43—21no—
80C22×C4×D43C2311yescharacteristic
81C2×#10621877—21no—
82C2×#10621877—22no—
83C2×#10621877—41no—
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C2×#10621872—21no—
87M16×D43—22no—
88M16×D43—41no—
89C22×C43⋊C8—21no—
90C2×C8×D43—21no—
91#13063324C2×C411yescharacteristic, complemented
92#13063324C2×C411yescharacteristic, complemented
93#13063320—21no—
94#13063320—21no—
95#13063319—21no—
96#13063319—21no—
97#13063318—21no—
98#13063318—21no—
99#13063317—21no—
100#13063316C2×C411yescharacteristic, complemented
101#13063316C2×C411yescharacteristic, complemented
102#13063315—21no—
103#13063315—21no—
104#13063313—21no—
105#13063311—21no—
106#13063311—21no—
107#13063310—21no—
108#13063310—21no—
109#13063309—21no—
110#13063308—21no—
111#13063308—21no—
112#13063308—21no—
113#13063307—21no—
114#13063307—21no—
115#13063305C2×C411yescharacteristic, complemented
116#13063305C2×C411yescharacteristic, complemented
117#13063304—21no—
118#13063304C2×C411yescharacteristic, complemented
119#13063304C2×C411yescharacteristic, complemented
120#13063303—21no—
121#13063303—21no—
122#13063302—21no—
123#13063302—21no—
124#13063300C2×C411yescharacteristic, complemented
125#13063300C2×C411yescharacteristic, complemented
126#13063299—21no—
127#13063299C2×C411yescharacteristic, complemented
128#13063299C2×C411yescharacteristic, complemented
129#13063298—21no—
130#13063298—21no—
131#13063295—21no—
132#13063294—21no—
133C4×Dic86—21no—
134C4×Dic86—21no—
135C4×Dic86—21no—
136#13063290C2×C411yescharacteristic, complemented
137#13063290C2×C411yescharacteristic, complemented
138C4×D172—21no—
139C4×D172—21no—
140C4×D172—21no—
141#13063287C2×C411yescharacteristic, complemented
142#13063287C2×C411yescharacteristic, complemented
143C4×C22⋊D43—21no—
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146C4×C22⋊D43—21no—
147C4×C22⋊D43C2×C411yescharacteristic
148C4×C22⋊D43C2×C411yescharacteristic
149C4×C22⋊D43C2×C411yescharacteristic
150C4×C22⋊D43C2×C411yescharacteristic
151C4×C22⋊D43D411yescharacteristic
152C4×C22⋊D43D411yescharacteristic
153C4×C22⋊D43D411yescharacteristic
154C4×C22⋊D43D411yescharacteristic
155(C22⋊D43)⋊C4—28no—
156(C22⋊D43)⋊C4—21no—
157(C22⋊D43)⋊C4—21no—
158#13063284—21no—
159#13063284C2311yescharacteristic
160#13063283C2×C411yescharacteristic, complemented
161#13063283C2×C411yescharacteristic, complemented
162#13063282—21no—
163#13063282—21no—
164#13063282—21no—
165#13063282—21no—
166#13063281—21no—
167C2×Dic43⋊C4—21no—
168C2×Dic43⋊C4D411yescharacteristic
169C4⋊C4×D43C2×C411yescharacteristic, complemented
170C4⋊C4×D43C2×C411yescharacteristic, complemented
171C2×C22⋊Dic43D411yescharacteristic
172C2×(C2×D43)⋊C4—21no—
173C2×(C2×D43)⋊C4D411yescharacteristic
174C22⋊C4×D43—21no—
175C2×C4×Dic43—21no—
176C2×C4×Dic43—22no—
177C2×C4×Dic43—21no—
178C2×C4×Dic43—21no—
179C2×C4×Dic43—21no—
180C2×C4×Dic43—41no—
181C2×C4×Dic43C2311yescharacteristic
182C2×C4×Dic43C2311yescharacteristic
183C2×C4×Dic43C2311yescharacteristic
184C42×D43—21no—
185C42×D43—21no—
186C42×D43—22no—
187C42×D43—41no—
188Dic43⋊C8—21no—
189Dic43⋊C8—21no—
190#13063253—22no—
191#13063253—41no—
192#13063251—22no—
193#13063251—41no—
194(C2×D43)⋊C8—21no—
195(C2×D43)⋊C8—21no—
196#13063235—21no—
197C8×Dic43—21no—
198C43⋊#95—21no—
199C43⋊#95—21no—
200C23×C4×C43C2311yescharacteristic
201C2×M16×C43C2311yescharacteristic
202C2×M16×C43C2311yescharacteristic
203#117×C43—21no—
204#117×C43—21no—
205#117×C43C2×C411yescharacteristic, complemented
206#117×C43C2×C411yescharacteristic, complemented
207#117×C43C2311yescharacteristic
208#117×C43C2311yescharacteristic
209C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
210C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
211C2×C22⋊C4×C43—21no—
212C2×C22⋊C4×C43—21no—
213C2×C42×C43—21no—
214C2×C42×C43C2311yescharacteristic
215C2×C42×C43C2311yescharacteristic
216C22⋊C8×C43—21no—
217C22⋊C8×C43—21no—
218#95×C43—21no—
219C24×C43C2×D411yescharacteristic
220C23×D43C2×D411yescharacteristic
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43C22×C411yescharacteristic
230C22×C4×C43C22×C411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2411yescharacteristic
235C2×C22⋊D43—24no—
236C2×C22⋊D43—21no—
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C2×C22⋊D43C22⋊C411yescharacteristic
240C2×C22⋊D43C22⋊C411yescharacteristic
241C2×C22⋊D43C22⋊C411yescharacteristic
242C2×C22⋊D43C22⋊C411yescharacteristic
243C22×Dic43—24no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—42no—
247C22×Dic43—42no—
248C22×Dic43C2×D411yescharacteristic
249C22×Dic43C2×D411yescharacteristic
250C22×Dic43C2×D411yescharacteristic
251#10621898—21no—
252#10621898—21no—
253#10621898—21no—
254#10621898—21no—
255#10621898—44no—
256C2×D172—21no—
257C2×D172—21no—
258C2×D172C22×C411yescharacteristic
259C2×C4×D43—21no—
260C2×C4×D43—21no—
261C2×C4×D43—21no—
262C2×C4×D43—21no—
263C2×C4×D43—24no—
264C2×C4×D43—21no—
265C2×C4×D43—21no—
266C2×C4×D43—21no—
267C2×C4×D43—21no—
268C2×C4×D43—21no—
269C2×C4×D43—42no—
270C2×C4×D43—42no—
271C2×C4×D43C22×C411yescharacteristic
272C2×C4×D43C22×C411yescharacteristic
273C2×C4×D43C2×D411yescharacteristic
274C2×C4×D43C2×D411yescharacteristic
275C2×Dic86—21no—
276C2×Dic86—21no—
277C2×Dic86C22×C411yescharacteristic
278M16×C43—21no—
279M16×C43—21no—
280M16×C43—21no—
281M16×C43—21no—
282C2×C8×C43—21no—
283C2×C8×C43—21no—
284C4⋊C4×C43—21no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43C22×C411yescharacteristic
287C4⋊C4×C43C22×C411yescharacteristic
288C4⋊C4×C43C22×C411yescharacteristic
289C4⋊C4×C43C22×C411yescharacteristic
290C22⋊C4×C43—24no—
291C22⋊C4×C43—21no—
292C22⋊C4×C43—21no—
293C22⋊C4×C43—21no—
294C22⋊C4×C43—21no—
295C42×C43—21no—
296C42×C43—21no—
297C42×C43—21no—
298C42×C43—21no—
299C42×C43—21no—
300C42×C43—21no—
301C42×C43—21no—
302C42×C43—21no—
303C22⋊Dic43—21no—
304C22⋊Dic43—21no—
305C22⋊Dic43—21no—
306C22⋊Dic43C22⋊C411yescharacteristic
307C22⋊Dic43C22⋊C411yescharacteristic
308C22⋊Dic43C22⋊C411yescharacteristic
309C22⋊Dic43C22⋊C411yescharacteristic
310(C2×D43)⋊C4—24no—
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—
316(C2×D43)⋊C4—21no—
317(C2×D43)⋊C4—21no—
318(C2×D43)⋊C4—21no—
319(C2×D43)⋊C4—21no—
320(C2×D43)⋊C4—21no—
321(C2×D43)⋊C4C22⋊C411yescharacteristic
322(C2×D43)⋊C4C22⋊C411yescharacteristic
323(C2×D43)⋊C4C22⋊C411yescharacteristic
324(C2×D43)⋊C4C22⋊C411yescharacteristic
325C4⋊Dic43—21no—
326C4⋊Dic43—21no—
327C4⋊Dic43—21no—
328C4⋊Dic43—21no—
329C4⋊Dic43C22×C411yescharacteristic
330C4⋊Dic43C22×C411yescharacteristic
331Dic43⋊C4—24no—
332Dic43⋊C4—21no—
333Dic43⋊C4—21no—
334Dic43⋊C4—21no—
335Dic43⋊C4—21no—
336Dic43⋊C4—21no—
337Dic43⋊C4—21no—
338Dic43⋊C4—21no—
339Dic43⋊C4—21no—
340Dic43⋊C4—21no—
341Dic43⋊C4—21no—
342Dic43⋊C4C22⋊C411yescharacteristic
343Dic43⋊C4C22⋊C411yescharacteristic
344Dic43⋊C4C22⋊C411yescharacteristic
345Dic43⋊C4C22⋊C411yescharacteristic
346C4×Dic43—24no—
347C4×Dic43—21no—
348C4×Dic43—21no—
349C4×Dic43—21no—
350C4×Dic43—21no—
351C4×Dic43—21no—
352C4×Dic43—21no—
353C4×Dic43—21no—
354C4×Dic43—21no—
355C4×Dic43—42no—
356C4×Dic43—42no—
357C4×Dic43—42no—
358C4×Dic43C22×C411yescharacteristic
359C4×Dic43C22×C411yescharacteristic
360C4×Dic43C2×D411yescharacteristic
361C4×Dic43C2×D411yescharacteristic
362C4×Dic43#4112yescomplemented
363#10621877—21no—
364#10621877—21no—
365#10621877—21no—
366#10621877—42no—
367#10621877#4112yescomplemented
368C2×C43⋊C8—21no—
369C2×C43⋊C8—21no—
370C2×C43⋊C8—42no—
371#10621872—42no—
372C8×D43—42no—
373C23×C43—21no—
374C23×C43—21no—
375C23×C43—22no—
376C23×C43—41no—
377C23×C43C2×C22⋊C411yescharacteristic
378C23×C43C2×C22⋊C411yescharacteristic
379C23×C43C22×D411yescharacteristic
380C22×D43—21no—
381C22×D43—21no—
382C22×D43—22no—
383C22×D43—21no—
384C22×D43—41no—
385C22×D43C2×C22⋊C411yescharacteristic
386C22×D43C2×C22⋊C411yescharacteristic
387C2×C4×C43—21no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—21no—
392C2×C4×C43—21no—
393C2×C4×C43—21no—
394C2×C4×C43—21no—
395C2×C4×C43—21no—
396C2×C4×C43—21no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—21no—
400C2×C4×C43—21no—
401C2×C4×C43—21no—
402C2×C4×C43—21no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43—42no—
408C2×C4×C43—81no—
409C2×C4×C43C2×C22⋊C411yescharacteristic
410C2×C4×C43C2×C22⋊C411yescharacteristic
411C2×C4×C43C23×C411yescharacteristic
412C2×C4×C43C22×D411yescharacteristic
413C2×C4×C43C2×#4111yescharacteristic
414C2×C4×C43C2×#4111yescharacteristic
415C2×C4×C43H(5,𝔽2)11yescharacteristic
416C2×C4×C432−1+411yescharacteristic
417C22⋊D43—22no—
418C22⋊D43—22no—
419C22⋊D43—22no—
420C22⋊D43—41no—
421C22⋊D43—41no—
422C22⋊D43—42no—
423C22⋊D43—81no—
424C22⋊D43#10414yescomplemented
425C2×Dic43—22no—
426C2×Dic43—22no—
427C2×Dic43—22no—
428C2×Dic43—21no—
429C2×Dic43—21no—
430C2×Dic43—22no—
431C2×Dic43—22no—
432C2×Dic43—21no—
433C2×Dic43—21no—
434C2×Dic43—21no—
435C2×Dic43—41no—
436C2×Dic43—48no—
437C2×Dic43—41no—
438C2×Dic43—41no—
439C2×Dic43C2×C22⋊C411yescharacteristic
440C2×Dic43C2×C22⋊C411yescharacteristic
441C2×Dic43C2×C22⋊C411yescharacteristic
442C2×Dic43C2×C22⋊C411yescharacteristic
443C2×Dic43C2×C22⋊C411yescharacteristic
444C2×Dic43C2×C22⋊C411yescharacteristic
445D172—21no—
446D172—21no—
447D172—42no—
448D172—81no—
449C4×D43—21no—
450C4×D43—21no—
451C4×D43—21no—
452C4×D43—21no—
453C4×D43—21no—
454C4×D43—21no—
455C4×D43—21no—
456C4×D43—21no—
457C4×D43—48no—
458C4×D43—42no—
459C4×D43—41no—
460C4×D43—41no—
461C4×D43—42no—
462C4×D43—81no—
463C4×D43—81no—
464Dic86—21no—
465Dic86—21no—
466Dic86—42no—
467Dic86—81no—
468C8×C43—41no—
469C8×C43—41no—
470C43⋊C8—22no—
471C43⋊C8—41no—
472#22505—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—42no—
481C22×C43—42no—
482C22×C43C2×#10412yes—
483C22×C43C22×C22⋊C411yescharacteristic
484C22×C43#54611yescharacteristic
485C22×C43#54711yescharacteristic
486C2×D43—21no—
487C2×D43—21no—
488C2×D43—21no—
489C2×D43—21no—
490C2×D43—21no—
491C2×D43—42no—
492C2×D43—42no—
493C2×D43—41no—
494C2×D43—41no—
495C2×D43—41no—
496C2×D43C2×#10412yes—
497C4×C43—21no—
498C4×C43—21no—
499C4×C43—42no—
500C4×C43—42no—
501C4×C43—41no—
502C4×C43—41no—
503C4×C43—41no—
504C4×C43—41no—
505C4×C43C4×#4111yescharacteristic
506C4×C43#52011yescharacteristic
507C4×C43#54611yescharacteristic
508C4×C43#54711yescharacteristic
509Dic43—24no—
510Dic43—21no—
511Dic43—21no—
512Dic43—21no—
513Dic43—21no—
514Dic43—21no—
515Dic43—42no—
516Dic43—41no—
517Dic43—41no—
518Dic43—41no—
519Dic43C2×#10412yes—
520#3475—431no—
521D4×M16—431no—
522C42×D4—431no—
523#1994—431no—
524#1986—431no—
525#1896—431no—
526#1896—431no—
527#1871—431no—
528#1871—431no—
529#1826—431no—
530#1826D4311yescharacteristic, complemented
531#1806—431no—
532C4×#104—431no—
533C2×#339—431no—
534C2×#339—431no—
535C2×C43—21no—
536C2×C43—21no—
537C2×C43—22no—
538C2×C43—41no—
539C2×C43#233911yescharacteristic
540C2×C43C22×#10411yescharacteristic
541C2×C43#290111yescharacteristic
542D43—22no—
543D43—41no—
544D43—81no—
545C22×M16—431no—
546C22×M16—431no—
547#556—431no—
548#555—431no—
549#554—431no—
550#553—431no—
551#553—431no—
552#552—431no—
553#552—431no—
554#552—861no—
555#551—861no—
556#551—861no—
557#547—431no—
558#546—861no—
559#533—431no—
560#529—861no—
561#529—861no—
562#529—861no—
563#525—431no—
564#525—431no—
565C4×#41—431no—
566C4×#41—861no—
567C2×C4×D4—431no—
568C2×C4×D4—861no—
569C2×#117—431no—
570C2×#117C2×D4311yescharacteristic
571C22×C42—431no—
572C22×C42—431no—
573#436—861no—
574#435—861no—
575#435—861no—
576C8×D4—861no—
577#423—431no—
578C2×#104—431no—
579C2×#104—431no—
580C2×#104—431no—
581C2×#104—431no—
582#407—431no—
583#407C2×D4311yescharacteristic
584C4×M16—431no—
585C4×C4⋊C4—431no—
586C4×C4⋊C4—861no—
587C4×C22⋊C4—431no—
588C4×C22⋊C4—861no—
589C4×C22⋊C4—861no—
590C4×C22⋊C4C2×D4311yescharacteristic
591C43—431no—
592#339—431no—
593#339—431no—
594#339—431no—
595#339—431no—
596#339—431no—
597#339—431no—
598#339—431no—
599#339—431no—
600#339C2×D4311yescharacteristic
601#339C2×D4311yescharacteristic
602#339C2×D4311yescharacteristic
603#339C2×D4311yescharacteristic
604C43#2250511yescharacteristic, complemented, Sylow
605C2×#41—431no—
606C2×#41—861no—
607C22×D4—431no—
608C23×C4—431no—
609C23×C4—861no—
610C23×C4—861no—
611C23×C4C22×D4311yescharacteristic
612C2×M16—431no—
613C2×M16—431no—
614C2×M16—861no—
615C2×M16—861no—
616C2×M16—862no—
617C2×M16—862no—
618C2×M16—1721no—
619C2×M16—1721no—
620C2×M16C22×D4311yescharacteristic
621C2×M16C22×D4311yescharacteristic
622C22×C8—861no—
623C22×C8—861no—
624C4⋊Q8—431no—
625C4⋊Q8—431no—
626#126—861no—
627#126—861no—
628#126—861no—
629#126—861no—
630#126—861no—
631#126—861no—
632#125—431no—
633#125—431no—
634#125—861no—
635#125—861no—
636#125—861no—
637#124—861no—
638#124—861no—
639#124—861no—
640#123—861no—
641#123—861no—
642#123—861no—
643#123—861no—
644#123—861no—
645#123—861no—
646#123—861no—
647#123—861no—
648C22⋊Q8—431no—
649C22⋊Q8—431no—
650C22⋊Q8—431no—
651C22⋊Q8—431no—
652C22⋊Q8—861no—
653C22⋊Q8—861no—
654C22⋊Q8—861no—
655C22⋊Q8—861no—
656C22⋊Q8—861no—
657#121—431no—
658#121—431no—
659#121—431no—
660#121—431no—
661#121—861no—
662#121—861no—
663#121—861no—
664#120—861no—
665#120—861no—
666C4×Q8—431no—
667C4×Q8—431no—
668C4×Q8—861no—
669C4×Q8—861no—
670C4×Q8—861no—
671C4×D4—431no—
672C4×D4—431no—
673C4×D4—431no—
674C4×D4—431no—
675C4×D4—431no—
676C4×D4—431no—
677C4×D4—431no—
678C4×D4—431no—
679C4×D4—431no—
680C4×D4—431no—
681C4×D4—861no—
682C4×D4—861no—
683C4×D4—861no—
684C4×D4—861no—
685C4×D4—861no—
686C4×D4—868no—
687C4×D4—861no—
688C4×D4—861no—
689C4×D4—861no—
690C4×D4—861no—
691#117—21no—
692#117—21no—
693#117—431no—
694#117—431no—
695#117—431no—
696#117—861no—
697#117—861no—
698#117—861no—
699#117—861no—
700#117—861no—
701#117—861no—
702#117C4×D4311yescharacteristic, complemented
703#117C4×D4311yescharacteristic, complemented
704#117C22×D4311yescharacteristic
705#117C22×D4311yescharacteristic
706C2×C4⋊C4—431no—
707C2×C4⋊C4—431no—
708C2×C4⋊C4—431no—
709C2×C4⋊C4—861no—
710C2×C4⋊C4C4×D4311yescharacteristic, complemented
711C2×C4⋊C4C4×D4311yescharacteristic, complemented
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—431no—
715C2×C22⋊C4—431no—
716C2×C22⋊C4—861no—
717C2×C22⋊C4—861no—
718C2×C42—21no—
719C2×C42—431no—
720C2×C42—431no—
721C2×C42—431no—
722C2×C42—861no—
723C2×C42—862no—
724C2×C42—861no—
725C2×C42—862no—
726C2×C42—861no—
727C2×C42—861no—
728C2×C42—861no—
729C2×C42—861no—
730C2×C42—1721no—
731C2×C42—1721no—
732C2×C42C22×D4311yescharacteristic
733C2×C42C22×D4311yescharacteristic
734C4⋊C8—861no—
735C4⋊C8—861no—
736#104—862no—
737#104—862no—
738#104—1721no—
739#104—1721no—
740C22⋊C8—21no—
741C22⋊C8—21no—
742C22⋊C8—861no—
743C22⋊C8—861no—
744#97—861no—
745C4×C8—861no—
746#95—21no—
747#95—861no—
748#95—861no—
749C24—431no—
750C24D4×D4311yescharacteristic
751#41—861no—
752#41—861no—
753#41—861no—
754#41—861no—
755#41—1724no—
756C2×Q8—431no—
757C2×Q8—861no—
758C2×Q8—861no—
759C2×D4—431no—
760C2×D4—431no—
761C2×D4—431no—
762C2×D4—431no—
763C2×D4—431no—
764C2×D4—861no—
765C2×D4—861no—
766C2×D4—864no—
767C2×D4—861no—
768C2×D4—861no—
769C2×D4—861no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—431no—
779C22×C4—431no—
780C22×C4—431no—
781C22×C4—431no—
782C22×C4—431no—
783C22×C4—431no—
784C22×C4—431no—
785C22×C4—861no—
786C22×C4—861no—
787C22×C4—861no—
788C22×C4—861no—
789C22×C4—864no—
790C22×C4—861no—
791C22×C4—861no—
792C22×C4—861no—
793C22×C4—861no—
794C22×C4—861no—
795C22×C4—864no—
796C22×C4—861no—
797C22×C4—861no—
798C22×C4—1722no—
799C22×C4—1722no—
800C22×C4—1722no—
801C22×C4—1722no—
802C22×C4C2×C4×D4311yescharacteristic
803C22×C4C2×C4×D4311yescharacteristic
804C22×C4D4×D4311yescharacteristic
805C22×C4D4×D4311yescharacteristic
806C22×C4D4×D4311yescharacteristic
807C22×C4C23×D4311yescharacteristic
808M16—21no—
809M16—21no—
810M16—21no—
811M16—21no—
812M16—432no—
813M16—861no—
814M16—861no—
815M16—861no—
816M16—1722no—
817M16—1722no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—861no—
821C2×C8—861no—
822C2×C8—1722no—
823C2×C8—1722no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—431no—
827C4⋊C4—431no—
828C4⋊C4—431no—
829C4⋊C4—431no—
830C4⋊C4—431no—
831C4⋊C4—431no—
832C4⋊C4—861no—
833C4⋊C4—861no—
834C4⋊C4—861no—
835C4⋊C4—861no—
836C4⋊C4—861no—
837C4⋊C4—861no—
838C4⋊C4—861no—
839C4⋊C4—861no—
840C4⋊C4—861no—
841C4⋊C4—861no—
842C4⋊C4—861no—
843C4⋊C4—861no—
844C4⋊C4—864no—
845C4⋊C4—861no—
846C4⋊C4—861no—
847C4⋊C4C2×C4×D4311yescharacteristic
848C4⋊C4C2×C4×D4311yescharacteristic
849C4⋊C4C2×C4×D4311yescharacteristic
850C4⋊C4C2×C4×D4311yescharacteristic
851C22⋊C4—24no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—431no—
857C22⋊C4—431no—
858C22⋊C4—431no—
859C22⋊C4—431no—
860C22⋊C4—431no—
861C22⋊C4—431no—
862C22⋊C4—431no—
863C22⋊C4—431no—
864C22⋊C4—861no—
865C22⋊C4—861no—
866C22⋊C4—861no—
867C22⋊C4—861no—
868C22⋊C4—861no—
869C22⋊C4—861no—
870C22⋊C4—861no—
871C22⋊C4—861no—
872C22⋊C4—864no—
873C22⋊C4—861no—
874C22⋊C4—861no—
875C22⋊C4—861no—
876C22⋊C4—861no—
877C22⋊C4—861no—
878C42—21no—
879C42—21no—
880C42—21no—
881C42—21no—
882C42—21no—
883C42—21no—
884C42—21no—
885C42—21no—
886C42—431no—
887C42—431no—
888C42—431no—
889C42—431no—
890C42—432no—
891C42—861no—
892C42—861no—
893C42—861no—
894C42—861no—
895C42—864no—
896C42—861no—
897C42—861no—
898C42—861no—
899C42—861no—
900C42—1722no—
901C42—1722no—
902C42—1722no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—41no—
907C23—431no—
908C23—431no—
909C23—862no—
910C23—861no—
911C23—861no—
912C23—861no—
913C23—1721no—
914C23C22⋊C4×D4311yescharacteristic
915C23C22⋊C4×D4311yescharacteristic
916C23C2×D4×D4311yescharacteristic
917Q8—861no—
918Q8—861no—
919Q8—3441no—
920Q8—1722no—
921D4—434no—
922D4—862no—
923D4—862no—
924D4—862no—
925D4—861no—
926D4—861no—
927D4—3441no—
928D4—3441no—
929D4—1722no—
930D4—1722no—
931D4—1721no—
932D4—1721no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—42no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—81no—
955C2×C4—431no—
956C2×C4—431no—
957C2×C4—431no—
958C2×C4—431no—
959C2×C4—431no—
960C2×C4—431no—
961C2×C4—862no—
962C2×C4—862no—
963C2×C4—862no—
964C2×C4—862no—
965C2×C4—861no—
966C2×C4—861no—
967C2×C4—861no—
968C2×C4—861no—
969C2×C4—861no—
970C2×C4—861no—
971C2×C4—861no—
972C2×C4—861no—
973C2×C4—861no—
974C2×C4—861no—
975C2×C4—862no—
976C2×C4—861no—
977C2×C4—861no—
978C2×C4—861no—
979C2×C4—3441no—
980C2×C4—3441no—
981C2×C4—1722no—
982C2×C4—1728no—
983C2×C4—1722no—
984C2×C4—1721no—
985C2×C4—1728no—
986C2×C4—1721no—
987C2×C4—1721no—
988C2×C4—1721no—
989C2×C4—1721no—
990C2×C4C22⋊C4×D4311yescharacteristic
991C2×C4C22⋊C4×D4311yescharacteristic
992C2×C4C22×C4×D4311yescharacteristic
993C2×C4C2×D4×D4311yescharacteristic
994C2×C4#41×D4311yescharacteristic
995C2×C4#41×D4311yescharacteristic
996C2×C4#1306337111yescharacteristic
997C2×C4#1306337211yescharacteristic
998C8—41no—
999C8—41no—
1000C8—862no—
1001C8—1721no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—42no—
1010C22—42no—
1011C22—432no—
1012C22—861no—
1013C22—861no—
1014C22—861no—
1015C22—861no—
1016C22—861no—
1017C22—1722no—
1018C22—1722no—
1019C22—1721no—
1020C22—1721no—
1021C22—1721no—
1022C22#104×D4312yes—
1023C22C2×C22⋊C4×D4311yescharacteristic
1024C22#1458354111yescharacteristic
1025C22#1458354711yescharacteristic
1026C4—21no—
1027C4—21no—
1028C4—42no—
1029C4—42no—
1030C4—41no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—432no—
1035C4—864no—
1036C4—861no—
1037C4—861no—
1038C4—861no—
1039C4—861no—
1040C4—861no—
1041C4—1722no—
1042C4—1721no—
1043C4—1721no—
1044C4—1721no—
1045C4#1458336711yescharacteristic
1046C4#1458337911yescharacteristic
1047C4#1458354111yescharacteristic
1048C4#1458354711yescharacteristic
1049C2—21no—
1050C2—21no—
1051C2—22no—
1052C2—41no—
1053C2—862no—
1054C2—3441no—
1055C2—1721no—
1056C2#1913741911yescharacteristic
1057C2C2×#104×D4311yescharacteristic
1058C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1826C2
socleC22×C43C22×C22⋊C4
prime radical#19148149C2
cosocleC22×C4×C43C24
hypercenter#1826D43
hypocenterC43#22505
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
2. #19143327C2semidirect
3. C4×(C22⋊D43)⋊C4C2semidirect
4. #19135570C2semidirect
5. #19135537C2semidirect
6. #19135037C2semidirect
7. #19135036C2semidirect
8. #19134896C2semidirect
9. #19134895C2semidirect
10. #19134693C2semidirect
11. #19134614C2semidirect
12. #19134399C2semidirect
13. C2×#14582658C2semidirect
14. #339×D43C2semidirect
15. C43×#1826C2semidirect
18. #14583617C4semidirect
19. #14583612C4semidirect
20. #14583604C4semidirect
21. #14583597C4semidirect
22. #14583593C4semidirect
23. #14583588C4semidirect
24. #14583584C4semidirect
28. #14583550C4semidirect
91. #13063324C2×C4semidirect
92. #13063324C2×C4semidirect
100. #13063316C2×C4semidirect
101. #13063316C2×C4semidirect
115. #13063305C2×C4semidirect
116. #13063305C2×C4semidirect
118. #13063304C2×C4semidirect
119. #13063304C2×C4semidirect
124. #13063300C2×C4semidirect
125. #13063300C2×C4semidirect
127. #13063299C2×C4semidirect
128. #13063299C2×C4semidirect
136. #13063290C2×C4semidirect
137. #13063290C2×C4semidirect
141. #13063287C2×C4semidirect
142. #13063287C2×C4semidirect
160. #13063283C2×C4semidirect
161. #13063283C2×C4semidirect
169. C4⋊C4×D43C2×C4semidirect
170. C4⋊C4×D43C2×C4semidirect
205. #117×C43C2×C4semidirect
206. #117×C43C2×C4semidirect
209. C2×C4⋊C4×C43C2×C4semidirect
210. C2×C4⋊C4×C43C2×C4semidirect
362. C4×Dic43#41semidirect
367. #10621877#41semidirect
424. C22⋊D43#104semidirect
530. #1826D43semidirect
604. C43#22505semidirect
702. #117C4×D43semidirect
703. #117C4×D43semidirect
710. C2×C4⋊C4C4×D43semidirect
711. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191481492
#191433272
C4×(C22⋊D43)⋊C42
#191355702
#191355372
#191350372
#191350362
#191348962
#191348952
#191346932
#191346142
#191343992
C2×#145826582
#339×D432
C43×#18262
#2250543