Finite Group Databasebeta

← #25113083

Subgroups — #25113083

Order 11008.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148149C211yesmaximal, characteristic
2#19143327C211yesmaximal, characteristic, complemented
3#19137041C211yesmaximal, characteristic, complemented
4#19135574C211yesmaximal, characteristic, complemented
5#19135537C211yesmaximal, characteristic, complemented
6#19135041C211yesmaximal, characteristic, complemented
7#19135037C211yesmaximal, characteristic, complemented
8#19134896C211yesmaximal, characteristic, complemented
9#19134895C211yesmaximal, characteristic, complemented
10#19134693C211yesmaximal, characteristic, complemented
11#19134614C211yesmaximal, characteristic, complemented
12#19134404C211yesmaximal, characteristic, complemented
13#19134304C211yesmaximal, 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×#13063284C2211yescharacteristic
40#117×D43C2211yescharacteristic
41C2×C42×D43C2211yescharacteristic
42#14582974—21no—
43#14582973—21no—
44#14582967—21no—
45(C22⋊D43)⋊C8—21no—
46#14582922C2211yescharacteristic
47C2×#13063253C2211yescharacteristic
48C2×#13063253C2211yescharacteristic
49C2×#13063251C2211yescharacteristic
50C2×#13063251C2211yescharacteristic
51#14582862C2211yescharacteristic
52M16×Dic43C2211yescharacteristic
53#14582793—21no—
54#14582786—21no—
55#14582775—21no—
56#14582773—21no—
57C4×Dic43⋊C4C2211yescharacteristic
58C4×(C2×D43)⋊C4C2211yescharacteristic
59#14582745C2211yescharacteristic
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
78C22×C4×D43—21no—
79C22×C4×D43C2311yescharacteristic
80C2×#10621877—21no—
81C2×#10621877—22no—
82C2×#10621877—41no—
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85C2×#10621872—21no—
86M16×D43—22no—
87M16×D43—41no—
88C22×C43⋊C8—21no—
89C2×C8×D43—21no—
90#13063324C2×C411yescharacteristic, complemented
91#13063324C2×C411yescharacteristic, complemented
92#13063320—21no—
93#13063320—21no—
94#13063319—21no—
95#13063319—21no—
96#13063318—21no—
97#13063318—21no—
98#13063317—21no—
99#13063316C2×C411yescharacteristic, complemented
100#13063316C2×C411yescharacteristic, complemented
101#13063315—21no—
102#13063315—21no—
103#13063313—21no—
104#13063311—21no—
105#13063311—21no—
106#13063310—21no—
107#13063310—21no—
108#13063309—21no—
109#13063308—21no—
110#13063308—21no—
111#13063308—21no—
112#13063307—21no—
113#13063307—21no—
114#13063305C2×C411yescharacteristic
115#13063305C2×C411yescharacteristic
116#13063304—21no—
117#13063304C2×C411yescharacteristic, complemented
118#13063304C2×C411yescharacteristic, complemented
119#13063303—21no—
120#13063303—21no—
121#13063302—21no—
122#13063302—21no—
123#13063300C2×C411yescharacteristic
124#13063300C2×C411yescharacteristic
125#13063299—21no—
126#13063299C2×C411yescharacteristic, complemented
127#13063299C2×C411yescharacteristic, complemented
128#13063298—21no—
129#13063298—21no—
130#13063295—21no—
131#13063294—21no—
132C4×Dic86—21no—
133C4×Dic86—21no—
134C4×Dic86—21no—
135#13063290C2×C411yescharacteristic, complemented
136#13063290C2×C411yescharacteristic, complemented
137C4×D172—21no—
138C4×D172—21no—
139C4×D172—21no—
140#13063287C2×C411yescharacteristic, complemented
141#13063287C2×C411yescharacteristic, complemented
142C4×C22⋊D43—21no—
143C4×C22⋊D43—21no—
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146C4×C22⋊D43C2×C411yescharacteristic
147C4×C22⋊D43C2×C411yescharacteristic
148C4×C22⋊D43C2×C411yescharacteristic
149C4×C22⋊D43C2×C411yescharacteristic
150C4×C22⋊D43D411yescharacteristic
151C4×C22⋊D43D411yescharacteristic
152C4×C22⋊D43D411yescharacteristic
153C4×C22⋊D43D411yescharacteristic
154(C22⋊D43)⋊C4—21no—
155(C22⋊D43)⋊C4—21no—
156#13063284—21no—
157#13063284—22no—
158#13063284—41no—
159#13063284C2311yescharacteristic
160#13063283C2×C411yescharacteristic
161#13063283C2×C411yescharacteristic
162#13063282—21no—
163#13063282—21no—
164#13063282—21no—
165#13063282—21no—
166#13063281—21no—
167C2×C4⋊Dic43—21no—
168C2×Dic43⋊C4—21no—
169C2×Dic43⋊C4D411yescharacteristic
170C4⋊C4×D43C2×C411yescharacteristic
171C4⋊C4×D43C2×C411yescharacteristic
172C2×C22⋊Dic43—21no—
173C2×C22⋊Dic43D411yescharacteristic
174C2×(C2×D43)⋊C4—21no—
175C2×(C2×D43)⋊C4D411yescharacteristic
176C22⋊C4×D43—21no—
177C2×C4×Dic43—21no—
178C2×C4×Dic43C2311yescharacteristic
179C2×C4×Dic43C2311yescharacteristic
180C2×C4×Dic43C2311yescharacteristic
181C42×D43—21no—
182C42×D43—21no—
183C42×D43—22no—
184C42×D43—41no—
185Dic43⋊C8—21no—
186Dic43⋊C8—21no—
187#13063253—22no—
188#13063253—41no—
189#13063251—22no—
190#13063251—41no—
191(C2×D43)⋊C8—21no—
192(C2×D43)⋊C8—21no—
193#13063235—21no—
194C8×Dic43—21no—
195C43⋊#95—21no—
196C43⋊#95—21no—
197C43⋊#95—21no—
198C43⋊#95—21no—
199C23×C4×C43C2311yescharacteristic
200C2×M16×C43C2311yescharacteristic
201C2×M16×C43C2311yescharacteristic
202#117×C43—21no—
203#117×C43—21no—
204#117×C43C2×C411yescharacteristic, complemented
205#117×C43C2×C411yescharacteristic, complemented
206#117×C43C2311yescharacteristic
207#117×C43C2311yescharacteristic
208C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
209C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
210C2×C22⋊C4×C43—21no—
211C2×C22⋊C4×C43—21no—
212C2×C42×C43—21no—
213C2×C42×C43C2311yescharacteristic
214C2×C42×C43C2311yescharacteristic
215C22⋊C8×C43—21no—
216C22⋊C8×C43—21no—
217#95×C43—21no—
218C24×C43C2×D411yescharacteristic
219C23×D43C2×D411yescharacteristic
220C22×C4×C43—21no—
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×C43C22×C411yescharacteristic
229C22×C4×C43C22×C411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2411yescharacteristic
234C2×C22⋊D43—21no—
235C2×C22⋊D43—21no—
236C2×C22⋊D43—21no—
237C2×C22⋊D43—42no—
238C2×C22⋊D43C22⋊C411yescharacteristic
239C2×C22⋊D43C22⋊C411yescharacteristic
240C2×C22⋊D43C22⋊C411yescharacteristic
241C2×C22⋊D43C22⋊C411yescharacteristic
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43C2×D411yescharacteristic
245C22×Dic43C2×D411yescharacteristic
246C22×Dic43C2×D411yescharacteristic
247#10621898—21no—
248#10621898—21no—
249#10621898—21no—
250#10621898—21no—
251#10621898—44no—
252C2×D172—21no—
253C2×D172—21no—
254C2×D172C22×C411yescharacteristic
255C2×C4×D43—21no—
256C2×C4×D43—21no—
257C2×C4×D43—21no—
258C2×C4×D43—21no—
259C2×C4×D43—21no—
260C2×C4×D43—21no—
261C2×C4×D43—21no—
262C2×C4×D43—21no—
263C2×C4×D43—21no—
264C2×C4×D43—42no—
265C2×C4×D43—42no—
266C2×C4×D43—42no—
267C2×C4×D43C22×C411yescharacteristic
268C2×C4×D43C22×C411yescharacteristic
269C2×C4×D43C2×D411yescharacteristic
270C2×C4×D43C2×D411yescharacteristic
271C2×Dic86—21no—
272C2×Dic86—21no—
273C2×Dic86C22×C411yescharacteristic
274M16×C43—21no—
275M16×C43—21no—
276M16×C43—21no—
277M16×C43—21no—
278C2×C8×C43—21no—
279C2×C8×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43C22×C411yescharacteristic
283C4⋊C4×C43C22×C411yescharacteristic
284C4⋊C4×C43C22×C411yescharacteristic
285C4⋊C4×C43C22×C411yescharacteristic
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—42no—
291C42×C43—21no—
292C42×C43—21no—
293C42×C43—21no—
294C42×C43—21no—
295C42×C43—21no—
296C42×C43—21no—
297C42×C43—21no—
298C42×C43—21no—
299C22⋊Dic43—21no—
300C22⋊Dic43—21no—
301C22⋊Dic43—21no—
302C22⋊Dic43—42no—
303C22⋊Dic43C22⋊C411yescharacteristic
304C22⋊Dic43C22⋊C411yescharacteristic
305C22⋊Dic43C22⋊C411yescharacteristic
306C22⋊Dic43C22⋊C411yescharacteristic
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—
316(C2×D43)⋊C4—21no—
317(C2×D43)⋊C4—42no—
318(C2×D43)⋊C4C22⋊C411yescharacteristic
319(C2×D43)⋊C4C22⋊C411yescharacteristic
320(C2×D43)⋊C4C22⋊C411yescharacteristic
321(C2×D43)⋊C4C22⋊C411yescharacteristic
322C4⋊Dic43—21no—
323C4⋊Dic43—21no—
324C4⋊Dic43—21no—
325C4⋊Dic43—21no—
326C4⋊Dic43—42no—
327C4⋊Dic43C22×C411yescharacteristic
328C4⋊Dic43C22×C411yescharacteristic
329Dic43⋊C4—21no—
330Dic43⋊C4—21no—
331Dic43⋊C4—21no—
332Dic43⋊C4—21no—
333Dic43⋊C4—21no—
334Dic43⋊C4—21no—
335Dic43⋊C4—21no—
336Dic43⋊C4—21no—
337Dic43⋊C4—21no—
338Dic43⋊C4—21no—
339Dic43⋊C4—42no—
340Dic43⋊C4C22⋊C411yescharacteristic
341Dic43⋊C4C22⋊C411yescharacteristic
342Dic43⋊C4C22⋊C411yescharacteristic
343Dic43⋊C4C22⋊C411yescharacteristic
344C4×Dic43—21no—
345C4×Dic43—21no—
346C4×Dic43—21no—
347C4×Dic43—21no—
348C4×Dic43—21no—
349C4×Dic43—21no—
350C4×Dic43—21no—
351C4×Dic43—21no—
352C4×Dic43—42no—
353C4×Dic43C22×C411yescharacteristic
354C4×Dic43C22×C411yescharacteristic
355C4×Dic43C2×D411yescharacteristic
356C4×Dic43C2×D411yescharacteristic
357C4×Dic43#4112yescomplemented
358#10621877—21no—
359#10621877—21no—
360#10621877—21no—
361#10621877—42no—
362#10621877#4112yescomplemented
363C2×C43⋊C8—21no—
364C2×C43⋊C8—21no—
365C2×C43⋊C8—42no—
366#10621872—42no—
367C8×D43—42no—
368C23×C43—21no—
369C23×C43—21no—
370C23×C43—41no—
371C23×C43—41no—
372C23×C43C2×C22⋊C411yescharacteristic
373C23×C43C2×C22⋊C411yescharacteristic
374C23×C43C22×D411yescharacteristic
375C22×D43—21no—
376C22×D43—21no—
377C22×D43—22no—
378C22×D43—21no—
379C22×D43—41no—
380C22×D43C2×C22⋊C411yescharacteristic
381C22×D43C2×C22⋊C411yescharacteristic
382C2×C4×C43—21no—
383C2×C4×C43—21no—
384C2×C4×C43—21no—
385C2×C4×C43—21no—
386C2×C4×C43—21no—
387C2×C4×C43—21no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—21no—
392C2×C4×C43—22no—
393C2×C4×C43—21no—
394C2×C4×C43—21no—
395C2×C4×C43—21no—
396C2×C4×C43—21no—
397C2×C4×C43—41no—
398C2×C4×C43—42no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—81no—
404C2×C4×C43C2×C22⋊C411yescharacteristic
405C2×C4×C43C2×C22⋊C411yescharacteristic
406C2×C4×C43C23×C411yescharacteristic
407C2×C4×C43C22×D411yescharacteristic
408C2×C4×C43C2×#4111yescharacteristic
409C2×C4×C43C2×#4111yescharacteristic
410C2×C4×C43H(5,𝔽2)11yescharacteristic
411C2×C4×C432−1+411yescharacteristic
412C22⋊D43—22no—
413C22⋊D43—22no—
414C22⋊D43—41no—
415C22⋊D43—41no—
416C22⋊D43—42no—
417C22⋊D43—41no—
418C22⋊D43—41no—
419C22⋊D43—81no—
420C2×Dic43—21no—
421C2×Dic43—21no—
422C2×Dic43—21no—
423C2×Dic43—21no—
424C2×Dic43—21no—
425C2×Dic43—22no—
426C2×Dic43—41no—
427C2×Dic43—41no—
428C2×Dic43—41no—
429C2×Dic43—41no—
430C2×Dic43—41no—
431C2×Dic43—41no—
432C2×Dic43—41no—
433C2×Dic43C2×C22⋊C411yescharacteristic
434C2×Dic43C2×C22⋊C411yescharacteristic
435C2×Dic43C2×C22⋊C411yescharacteristic
436C2×Dic43C2×C22⋊C411yescharacteristic
437C2×Dic43C2×C22⋊C411yescharacteristic
438C2×Dic43C2×C22⋊C411yescharacteristic
439D172—21no—
440D172—21no—
441D172—42no—
442D172—81no—
443C4×D43—21no—
444C4×D43—21no—
445C4×D43—21no—
446C4×D43—21no—
447C4×D43—21no—
448C4×D43—21no—
449C4×D43—21no—
450C4×D43—21no—
451C4×D43—42no—
452C4×D43—48no—
453C4×D43—42no—
454C4×D43—41no—
455C4×D43—41no—
456C4×D43—81no—
457C4×D43—81no—
458Dic86—21no—
459Dic86—21no—
460Dic86—42no—
461Dic86—81no—
462C8×C43—41no—
463C8×C43—41no—
464C43⋊C8—22no—
465C43⋊C8—41no—
466#22506—431nomaximal, Sylow
467C22×C43—21no—
468C22×C43—21no—
469C22×C43—21no—
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—21no—
474C22×C43—21no—
475C22×C43—81no—
476C22×C43—81no—
477C22×C43C22×C22⋊C411yescharacteristic
478C22×C43#54611yescharacteristic
479C22×C43#54711yescharacteristic
480C2×D43—21no—
481C2×D43—21no—
482C2×D43—21no—
483C2×D43—21no—
484C2×D43—21no—
485C2×D43—42no—
486C2×D43—42no—
487C2×D43—41no—
488C2×D43—41no—
489C2×D43—41no—
490C2×D43#42112yes—
491C4×C43—21no—
492C4×C43—21no—
493C4×C43—42no—
494C4×C43—41no—
495C4×C43—41no—
496C4×C43—41no—
497C4×C43—41no—
498C4×C43—81no—
499C4×C43C4×#4111yescharacteristic
500C4×C43#52011yescharacteristic
501C4×C43#54611yescharacteristic
502C4×C43#54711yescharacteristic
503Dic43—21no—
504Dic43—21no—
505Dic43—21no—
506Dic43—21no—
507Dic43—21no—
508Dic43—21no—
509Dic43—42no—
510Dic43—41no—
511Dic43—41no—
512Dic43—41no—
513Dic43—81no—
514#3475—431no—
515D4×M16—431no—
516#2290—431no—
517#1995—431no—
518#1986—431no—
519#1897—431no—
520#1896—431no—
521#1871—431no—
522#1871—431no—
523#1826—431no—
524#1826D4311yescharacteristic, complemented
525#1806—431no—
526#1759—431no—
527#1733—431no—
528C2×#339—431no—
529C2×C43—21no—
530C2×C43—21no—
531C2×C43—41no—
532C2×C43—41no—
533C2×C43#233911yescharacteristic
534C2×C43C2×#42111yescharacteristic
535C2×C43#290111yescharacteristic
536D43—22no—
537D43—41no—
538D43—81no—
539C22×M16—431no—
540C22×M16—431no—
541#556—431no—
542#555—431no—
543#554—431no—
544#553—431no—
545#553—431no—
546#552—431no—
547#552—431no—
548#552—861no—
549#551—861no—
550#551—861no—
551#547—431no—
552#546—861no—
553#533—431no—
554#529—861no—
555#529—861no—
556#529—861no—
557#525—431no—
558#525—431no—
559C4×#41—431no—
560C4×#41—861no—
561C2×C4×D4—431no—
562C2×#117—431no—
563C2×#117—431no—
564C2×#117C2×D4311yescharacteristic
565C22×C42—431no—
566#436—861no—
567#435—861no—
568#435—861no—
569C8×D4—861no—
570#423—431no—
571C2×#104—431no—
572C2×#104—431no—
573C2×#104—431no—
574C2×#104—431no—
575#407—431no—
576#407C2×D4311yescharacteristic
577C4×M16—431no—
578#388—861no—
579#387—861no—
580#386—861no—
581#385—861no—
582C4×C4⋊C4—431no—
583C4×C22⋊C4—431no—
584C4×C22⋊C4C2×D4311yescharacteristic
585#376—431no—
586#339—431no—
587#339—431no—
588#339—431no—
589#339—431no—
590#339—431no—
591#339—431no—
592#339—431no—
593#339—431no—
594#339C2×D4311yescharacteristic
595#339C2×D4311yescharacteristic
596#339C2×D4311yescharacteristic
597#339C2×D4311yescharacteristic
598C43#2250611yescharacteristic, complemented, Sylow
599C2×#41—431no—
600C2×#41—861no—
601C22×D4—431no—
602C23×C4—431no—
603C23×C4—861no—
604C23×C4C22×D4311yescharacteristic
605C2×M16—431no—
606C2×M16—431no—
607C2×M16—861no—
608C2×M16—861no—
609C2×M16—862no—
610C2×M16—862no—
611C2×M16—1721no—
612C2×M16—1721no—
613C2×M16C22×D4311yescharacteristic
614C2×M16C22×D4311yescharacteristic
615C22×C8—861no—
616C22×C8—861no—
617C4⋊Q8—431no—
618C4⋊Q8—431no—
619#126—861no—
620#126—861no—
621#126—861no—
622#126—861no—
623#126—861no—
624#126—861no—
625#125—431no—
626#125—431no—
627#125—861no—
628#125—861no—
629#125—861no—
630#124—861no—
631#124—861no—
632#124—861no—
633#123—861no—
634#123—861no—
635#123—861no—
636#123—861no—
637#123—861no—
638#123—861no—
639#123—861no—
640#123—861no—
641C22⋊Q8—431no—
642C22⋊Q8—431no—
643C22⋊Q8—431no—
644C22⋊Q8—431no—
645C22⋊Q8—861no—
646C22⋊Q8—861no—
647C22⋊Q8—861no—
648C22⋊Q8—861no—
649C22⋊Q8—861no—
650#121—431no—
651#121—431no—
652#121—431no—
653#121—431no—
654#121—861no—
655#121—861no—
656#121—861no—
657#120—861no—
658#120—861no—
659C4×Q8—431no—
660C4×Q8—431no—
661C4×Q8—861no—
662C4×Q8—861no—
663C4×Q8—861no—
664C4×D4—431no—
665C4×D4—431no—
666C4×D4—431no—
667C4×D4—431no—
668C4×D4—431no—
669C4×D4—431no—
670C4×D4—431no—
671C4×D4—431no—
672C4×D4—431no—
673C4×D4—431no—
674C4×D4—861no—
675C4×D4—861no—
676C4×D4—861no—
677C4×D4—861no—
678C4×D4—861no—
679C4×D4—861no—
680C4×D4—861no—
681C4×D4—861no—
682C4×D4—861no—
683#117—21no—
684#117—21no—
685#117—431no—
686#117—431no—
687#117—431no—
688#117—861no—
689#117—861no—
690#117—861no—
691#117—861no—
692#117—862no—
693#117—861no—
694#117—861no—
695#117—1721no—
696#117C4×D4311yescharacteristic, complemented
697#117C4×D4311yescharacteristic, complemented
698#117C22×D4311yescharacteristic
699#117C22×D4311yescharacteristic
700C2×C4⋊C4—431no—
701C2×C4⋊C4—431no—
702C2×C4⋊C4—431no—
703C2×C4⋊C4—861no—
704C2×C4⋊C4—861no—
705C2×C4⋊C4C4×D4311yescharacteristic, complemented
706C2×C4⋊C4C4×D4311yescharacteristic, complemented
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—431no—
710C2×C22⋊C4—431no—
711C2×C22⋊C4—861no—
712C2×C22⋊C4—861no—
713C2×C22⋊C4—861no—
714C2×C42—21no—
715C2×C42—431no—
716C2×C42—431no—
717C2×C42—431no—
718C2×C42—861no—
719C2×C42—862no—
720C2×C42—861no—
721C2×C42—861no—
722C2×C42—1721no—
723C2×C42C22×D4311yescharacteristic
724C2×C42C22×D4311yescharacteristic
725C4⋊C8—861no—
726C4⋊C8—861no—
727#104—862no—
728#104—862no—
729#104—1721no—
730#104—1721no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8—861no—
734C22⋊C8—861no—
735#97—861no—
736C4×C8—861no—
737#95—21no—
738#95—861no—
739#95—861no—
740#95—861no—
741#95—861no—
742C24—431no—
743C24D4×D4311yescharacteristic
744#41—861no—
745#41—861no—
746#41—861no—
747#41—861no—
748#41—1724no—
749C2×Q8—431no—
750C2×Q8—861no—
751C2×Q8—861no—
752C2×D4—431no—
753C2×D4—431no—
754C2×D4—431no—
755C2×D4—431no—
756C2×D4—431no—
757C2×D4—861no—
758C2×D4—861no—
759C2×D4—861no—
760C2×D4—861no—
761C2×D4—861no—
762C2×D4—1722no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—431no—
772C22×C4—431no—
773C22×C4—431no—
774C22×C4—431no—
775C22×C4—431no—
776C22×C4—431no—
777C22×C4—431no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—861no—
783C22×C4—861no—
784C22×C4—861no—
785C22×C4—861no—
786C22×C4—861no—
787C22×C4—861no—
788C22×C4—861no—
789C22×C4—1722no—
790C22×C4—1722no—
791C22×C4—1722no—
792C22×C4C2×C4×D4311yescharacteristic
793C22×C4C2×C4×D4311yescharacteristic
794C22×C4D4×D4311yescharacteristic
795C22×C4D4×D4311yescharacteristic
796C22×C4D4×D4311yescharacteristic
797C22×C4C23×D4311yescharacteristic
798M16—21no—
799M16—21no—
800M16—21no—
801M16—21no—
802M16—432no—
803M16—861no—
804M16—861no—
805M16—861no—
806M16—1722no—
807M16—1722no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—861no—
811C2×C8—861no—
812C2×C8—1722no—
813C2×C8—1722no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—431no—
817C4⋊C4—431no—
818C4⋊C4—431no—
819C4⋊C4—431no—
820C4⋊C4—431no—
821C4⋊C4—431no—
822C4⋊C4—861no—
823C4⋊C4—861no—
824C4⋊C4—861no—
825C4⋊C4—861no—
826C4⋊C4—861no—
827C4⋊C4—861no—
828C4⋊C4—861no—
829C4⋊C4—861no—
830C4⋊C4—861no—
831C4⋊C4—861no—
832C4⋊C4—861no—
833C4⋊C4—861no—
834C4⋊C4—861no—
835C4⋊C4—861no—
836C4⋊C4—1722no—
837C4⋊C4—1722no—
838C4⋊C4C2×C4×D4311yescharacteristic
839C4⋊C4C2×C4×D4311yescharacteristic
840C4⋊C4C2×C4×D4311yescharacteristic
841C4⋊C4C2×C4×D4311yescharacteristic
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—42no—
847C22⋊C4—431no—
848C22⋊C4—431no—
849C22⋊C4—431no—
850C22⋊C4—431no—
851C22⋊C4—431no—
852C22⋊C4—431no—
853C22⋊C4—431no—
854C22⋊C4—431no—
855C22⋊C4—861no—
856C22⋊C4—861no—
857C22⋊C4—861no—
858C22⋊C4—861no—
859C22⋊C4—861no—
860C22⋊C4—861no—
861C22⋊C4—861no—
862C22⋊C4—861no—
863C22⋊C4—861no—
864C22⋊C4—861no—
865C22⋊C4—861no—
866C22⋊C4—861no—
867C22⋊C4—861no—
868C22⋊C4—1722no—
869C22⋊C4—1722no—
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—431no—
879C42—431no—
880C42—431no—
881C42—431no—
882C42—432no—
883C42—861no—
884C42—861no—
885C42—861no—
886C42—861no—
887C42—861no—
888C42—861no—
889C42—861no—
890C42—861no—
891C42—1722no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—431no—
897C23—431no—
898C23—862no—
899C23—861no—
900C23—861no—
901C23—861no—
902C23—1721no—
903C23C22⋊C4×D4311yescharacteristic
904C23C22⋊C4×D4311yescharacteristic
905C23C2×D4×D4311yescharacteristic
906Q8—861no—
907Q8—861no—
908Q8—3441no—
909Q8—1722no—
910D4—862no—
911D4—862no—
912D4—861no—
913D4—861no—
914D4—3441no—
915D4—3441no—
916D4—1722no—
917D4—1721no—
918D4—1721no—
919D4—1722no—
920D4—1721no—
921D4—1721no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—81no—
944C2×C4—431no—
945C2×C4—431no—
946C2×C4—431no—
947C2×C4—431no—
948C2×C4—431no—
949C2×C4—431no—
950C2×C4—861no—
951C2×C4—861no—
952C2×C4—861no—
953C2×C4—861no—
954C2×C4—861no—
955C2×C4—861no—
956C2×C4—861no—
957C2×C4—861no—
958C2×C4—861no—
959C2×C4—861no—
960C2×C4—861no—
961C2×C4—861no—
962C2×C4—861no—
963C2×C4—862no—
964C2×C4—3441no—
965C2×C4—3441no—
966C2×C4—1722no—
967C2×C4—1722no—
968C2×C4—1728no—
969C2×C4—1721no—
970C2×C4—1721no—
971C2×C4—1721no—
972C2×C4—1721no—
973C2×C4—1721no—
974C2×C4—1721no—
975C2×C4—1721no—
976C2×C4—1721no—
977C2×C4—1721no—
978C2×C4C22⋊C4×D4311yescharacteristic
979C2×C4C22⋊C4×D4311yescharacteristic
980C2×C4C22×C4×D4311yescharacteristic
981C2×C4C2×D4×D4311yescharacteristic
982C2×C4#41×D4311yescharacteristic
983C2×C4#41×D4311yescharacteristic
984C2×C4#1306337111yescharacteristic
985C2×C4#1306337211yescharacteristic
986C8—41no—
987C8—41no—
988C8—862no—
989C8—1721no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—81no—
999C22—81no—
1000C22—432no—
1001C22—861no—
1002C22—861no—
1003C22—861no—
1004C22—861no—
1005C22—861no—
1006C22—1722no—
1007C22—1722no—
1008C22—1721no—
1009C22—1721no—
1010C22—1721no—
1011C22C2×C22⋊C4×D4311yescharacteristic
1012C22#1458354111yescharacteristic
1013C22#1458354711yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—42no—
1017C4—41no—
1018C4—41no—
1019C4—41no—
1020C4—41no—
1021C4—81no—
1022C4—861no—
1023C4—861no—
1024C4—861no—
1025C4—861no—
1026C4—861no—
1027C4—861no—
1028C4—3441no—
1029C4—1722no—
1030C4—1721no—
1031C4—1721no—
1032C4—1721no—
1033C4#1458336711yescharacteristic
1034C4#1458337911yescharacteristic
1035C4#1458354111yescharacteristic
1036C4#1458354711yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—41no—
1040C2—41no—
1041C2—862no—
1042C2—3441no—
1043C2—1721no—
1044C2#1913741911yescharacteristic
1045C2#421×D4311yescharacteristic
1046C2#1914313911yescharacteristic
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#22506
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. #19137041C2semidirect
4. #19135574C2semidirect
5. #19135537C2semidirect
6. #19135041C2semidirect
7. #19135037C2semidirect
8. #19134896C2semidirect
9. #19134895C2semidirect
10. #19134693C2semidirect
11. #19134614C2semidirect
12. #19134404C2semidirect
13. #19134304C2semidirect
14. #339×D43C2semidirect
15. C43×#1826C2semidirect
18. #14583617C4semidirect
19. #14583612C4semidirect
20. #14583604C4semidirect
21. #14583597C4semidirect
22. #14583593C4semidirect
23. #14583588C4semidirect
24. #14583584C4semidirect
28. #14583550C4semidirect
90. #13063324C2×C4semidirect
91. #13063324C2×C4semidirect
99. #13063316C2×C4semidirect
100. #13063316C2×C4semidirect
117. #13063304C2×C4semidirect
118. #13063304C2×C4semidirect
126. #13063299C2×C4semidirect
127. #13063299C2×C4semidirect
135. #13063290C2×C4semidirect
136. #13063290C2×C4semidirect
140. #13063287C2×C4semidirect
141. #13063287C2×C4semidirect
204. #117×C43C2×C4semidirect
205. #117×C43C2×C4semidirect
208. C2×C4⋊C4×C43C2×C4semidirect
209. C2×C4⋊C4×C43C2×C4semidirect
357. C4×Dic43#41semidirect
362. #10621877#41semidirect
524. #1826D43semidirect
598. C43#22506semidirect
696. #117C4×D43semidirect
697. #117C4×D43semidirect
705. C2×C4⋊C4C4×D43semidirect
706. 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
#191370412
#191355742
#191355372
#191350412
#191350372
#191348962
#191348952
#191346932
#191346142
#191344042
#191343042
#339×D432
C43×#18262
#2250643