Finite Group Databasebeta

← #25118894

Subgroups — #25118894

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583122C211yesmaximal, characteristic
2C2×#14582993C211yesmaximal, characteristic, complemented
3C2×#14582986C211yesmaximal, characteristic
4#19137666C211yesmaximal, characteristic
5#19137512C211yesmaximal, characteristic, complemented
6#19135404C211yesmaximal, characteristic
7#19135276C211yesmaximal, characteristic
8#19135269C211yesmaximal, characteristic, complemented
9#19134951C211yesmaximal, characteristic
10#19134937C211yesmaximal, characteristic, complemented
11#19134860C211yesmaximal, characteristic, complemented
12#19134839C211yesmaximal, characteristic
13#19134460C211yesmaximal, characteristic, complemented
14C4×#13063248C211yesmaximal, characteristic, complemented
15C43×#1949C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24#14583122C418yescomplemented
25#14582993—24no—
26#14582986—24no—
27C2×#13063250C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582800C2211yescharacteristic
40#14582796—21no—
41#14582796—21no—
42#14582795C2211yescharacteristic
43#14582795C2211yescharacteristic
44#14582791—21no—
45#14582790—21no—
46#14582773—21no—
47#14582763—21no—
48C4×C4⋊Dic43C2211yescharacteristic
49#14582750—21no—
50C4×(C2×D43)⋊C4—21no—
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C43×#382C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C4×D43—21no—
66C2×Dic172—22no—
67C2×Dic172—22no—
68C2×Dic172C2×C414yescomplemented
69C2×#10621873—22no—
70C2×#10621873—22no—
71C2×#10621873C2×C414yes—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063313—22no—
75#13063313C2×C414yes—
76C4×Dic86—22no—
77C4×Dic86C2×C414yescomplemented
78#13063290—22no—
79#13063290—22no—
80#13063290—22no—
81#13063290—41no—
82#13063290—41no—
83#13063290—41no—
84#13063287—22no—
85#13063287—41no—
86C2×C4⋊Dic43D411yescharacteristic
87C2×C4⋊Dic43D411yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106#13063250C2×C414yescomplemented
107#13063248—22no—
108#13063248—22no—
109#13063248—41no—
110#13063248D414yes—
111#13063247C2×C414yes—
112#13063245—22no—
113#13063245—41no—
114C4×C43⋊C8—22no—
115C8×Dic43—22no—
116C8×Dic43—22no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95D411yescharacteristic
122C43⋊#95D411yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131#107×C43—22no—
132#106×C43—22no—
133C4⋊C8×C43C2×C414yescomplemented
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137C23×D43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172C22×C412yes—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—81no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86C22×C412yes—
170C2×Dic86C22×C412yes—
171C2×Dic86C2×D412yes—
172C2×Dic86#4112yes—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C22×C412yes—
178C2×C8×C43C22×C412yes—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43C2×D412yes—
187C42×C43—81no—
188C42×C43C22×C412yes—
189C42×C43#4112yes—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—81no—
195C4⋊Dic43—21no—
196C4⋊Dic43—22no—
197C4⋊Dic43—22no—
198C4⋊Dic43C22×C412yes—
199Dic43⋊C4—24no—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205C4×Dic43—24no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—42no—
211C4×Dic43—42no—
212C4×Dic43—42no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8C2×D412yes—
219Dic172—28no—
220#10621873—28no—
221C23×C43C22×D411yescharacteristic
222C22×D43—22no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43C4×D412yes—
246C2×C4×C43C4×D412yes—
247C2×C4×C43C23×C411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C2×C4×C432−1+411yescharacteristic
253C2×Dic43—22no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43#13512yes—
273C2×Dic43#13512yes—
274D172—22no—
275D172—22no—
276D172—41no—
277D172—41no—
278C4×D43—84no—
279Dic86—22no—
280Dic86—22no—
281Dic86—22no—
282Dic86—22no—
283Dic86—22no—
284Dic86—41no—
285Dic86—41no—
286Dic86C4×D414yes—
287C8×C43—22no—
288C8×C43—22no—
289C43⋊C8—22no—
290C43⋊C8—41no—
291#23000—431nomaximal, Sylow
292C22×C43C2×C4×D411yescharacteristic
293C22×C43D4211yescharacteristic
294C22×C43#54811yescharacteristic
295C22×C43C2×#13511yescharacteristic
296C22×C43C2×#13511yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57811yescharacteristic
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C4×C43—22no—
307C4×C43—22no—
308C4×C43—42no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43C2×C4×D411yescharacteristic
313C4×C43#52011yescharacteristic
314C4×C43#54711yescharacteristic
315C4×C43#55311yescharacteristic
316Dic43—24no—
317Dic43—22no—
318Dic43—22no—
319Dic43—42no—
320Dic43—42no—
321Dic43—41no—
322Dic43—41no—
323C2×#464—431no—
324C2×C4×Q16—431no—
325C2×C4×SD16—431no—
326#2367—431no—
327#2351—431no—
328#1958—431no—
329#1949D4311yescharacteristic, complemented
330#1934—431no—
331#1933—431no—
332#1880—431no—
333#1878—431no—
334#1865—431no—
335#1862—431no—
336C8×C4⋊C4—431no—
337C4×#103—431no—
338C2×C43#236111yescharacteristic
339C2×C43C4×#13511yescharacteristic
340C2×C43#294711yescharacteristic
341C2×C43#328211yescharacteristic
342C2×C43#328511yescharacteristic
343C2×C43#336411yescharacteristic
344C2×C43#336511yescharacteristic
345D43—82no—
346C22×Q16—431no—
347C22×SD16—431no—
348C2×#124—431no—
349C2×C4×Q8—431no—
350C2×C4×Q8—431no—
351C2×C4×Q8—431no—
352C2×C4×Q8—431no—
353C2×C4×D4—431no—
354#464—438no—
355C4×Q16—864no—
356C4×SD16—864no—
357C2×#107C2×D4311yescharacteristic
358C2×#106C2×D4311yescharacteristic
359C2×C4⋊C8C2×D4311yescharacteristic
360C2×#103—431no—
361C2×#103—431no—
362C2×#103—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#102—431no—
366C2×#102—431no—
367C2×#102—431no—
368C2×C4×C8—431no—
369C2×C4×C8—431no—
370C2×C4×C8—431no—
371#391—431no—
372#390—431no—
373#389—431no—
374#389—431no—
375#389—861no—
376#389—861no—
377#388—861no—
378#388—861no—
379#385—861no—
380#382—861no—
381#382C2×D4311yescharacteristic
382C4×C4⋊C4—431no—
383C4×C4⋊C4—861no—
384C4×C4⋊C4C2×D4311yescharacteristic
385C4×C22⋊C4—861no—
386#340—431no—
387#340—431no—
388#340C2×D4311yescharacteristic
389#340C2×D4311yescharacteristic
390#336—431no—
391#336—431no—
392C43#2300011yescharacteristic, complemented, Sylow
393C22×Q8—431no—
394C22×Q8—431no—
395C22×D4—431no—
396C23×C4—861no—
397C2×Q16—434no—
398C2×Q16—862no—
399C2×Q16—862no—
400C2×SD16—434no—
401C2×SD16—862no—
402C2×SD16—862no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407#124—434no—
408#124—862no—
409C4×Q8—434no—
410C4×Q8—862no—
411C4×Q8—862no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8—1721no—
415C4×Q8—1721no—
416C4×Q8—1721no—
417C4×D4—862no—
418C4×D4—1721no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C42—21no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42C22×D4311yescharacteristic
445#107—22no—
446#106—22no—
447C4⋊C8C4×D4314yescomplemented
448#103—434no—
449#103—434no—
450#103—862no—
451#103—862no—
452#103—1721no—
453#102—434no—
454#102—862no—
455#102—1721no—
456C4×C8—862no—
457C4×C8—862no—
458C4×C8—862no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—431no—
463#95—431no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468C24—861no—
469C2×Q8—432no—
470C2×Q8—432no—
471C2×Q8—432no—
472C2×Q8—432no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×D4—432no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—3441no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4D4×D4311yescharacteristic
502C22×C4D4×D4311yescharacteristic
503C22×C4C23×D4311yescharacteristic
504Q16—868no—
505SD16—868no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—432no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8C2×C4×D4312yes—
517C2×C8C2×C4×D4312yes—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—432no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—864no—
529C4⋊C4—861no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4D4×D4312yes—
536C22⋊C4—864no—
537C22⋊C4—864no—
538C22⋊C4—3441no—
539C22⋊C4—1722no—
540C22⋊C4—1722no—
541C42—81no—
542C42—864no—
543C42—861no—
544C42—861no—
545C42—861no—
546C42—861no—
547C42—1722no—
548C42—1722no—
549C42—1722no—
550C42C2×C4×D4312yes—
551C42#1062190212yes—
552C23—862no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23C2×D4×D4311yescharacteristic
560Q8—434no—
561Q8—862no—
562Q8—862no—
563Q8—862no—
564Q8—862no—
565Q8—862no—
566Q8—1721no—
567Q8—1721no—
568D4—862no—
569D4—862no—
570D4—1721no—
571D4—1721no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—432no—
589C2×C4—432no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—3444no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4#1306328712yes—
611C2×C4#1306328712yes—
612C2×C4C22×C4×D4311yescharacteristic
613C2×C4C2×D4×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4C2×#1062190211yescharacteristic
616C2×C4#1306337111yescharacteristic
617C2×C4#1306337311yescharacteristic
618C8—22no—
619C8—22no—
620C8—862no—
621C8—1721no—
622C22—3441no—
623C22—3441no—
624C22—3441no—
625C22—3441no—
626C22—1722no—
627C22—1722no—
628C22—1722no—
629C22C2×#1306328711yescharacteristic
630C22#1458353311yescharacteristic
631C22#1458355911yescharacteristic
632C22#135×D4311yescharacteristic
633C22#135×D4311yescharacteristic
634C22#1458370911yescharacteristic
635C22#1458371511yescharacteristic
636C4—22no—
637C4—22no—
638C4—42no—
639C4—81no—
640C4—81no—
641C4—81no—
642C4—862no—
643C4—864no—
644C4—862no—
645C4—1721no—
646C4—1722no—
647C4—1721no—
648C4—1722no—
649C4C4×D4×D4311yescharacteristic
650C4#1458338111yescharacteristic
651C4#1458355211yescharacteristic
652C4#1458360211yescharacteristic
653C2—3442no—
654C2#1913761011yescharacteristic
655C2#1914336611yescharacteristic
656C2#1914343611yescharacteristic
657C2#1914630811yescharacteristic
658C2#1914633111yescharacteristic
659C2#1914728311yescharacteristic
660C2#1914729411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1949C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1949D43
hypocenterC43#23000
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
2. C2×#14582993C2semidirect
5. #19137512C2semidirect
8. #19135269C2semidirect
10. #19134937C2semidirect
11. #19134860C2semidirect
13. #19134460C2semidirect
14. C4×#13063248C2semidirect
15. C43×#1949C2semidirect
24. #14583122C4semidirect
68. C2×Dic172C2×C4semidirect
77. C4×Dic86C2×C4semidirect
106. #13063250C2×C4semidirect
133. C4⋊C8×C43C2×C4semidirect
329. #1949D43semidirect
392. C43#23000semidirect
447. C4⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831222
C2×#145829932
C2×#145829862
#191376662
#191375122
#191354042
#191352762
#191352692
#191349512
#191349372
#191348602
#191348392
#191344602
C4×#130632482
C43×#19492
#2300043