Finite Group Databasebeta

← #25118892

Subgroups — #25118892

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×#14583121C211yesmaximal, characteristic
2C2×#14582991C211yesmaximal, characteristic, complemented
3C2×#14582984C211yesmaximal, characteristic
4#19137666C211yesmaximal, characteristic
5#19137516C211yesmaximal, characteristic, complemented
6#19135406C211yesmaximal, characteristic
7#19135363C211yesmaximal, characteristic, complemented
8#19135279C211yesmaximal, characteristic
9#19135272C211yesmaximal, characteristic, complemented
10#19134948C211yesmaximal, characteristic
11#19134934C211yesmaximal, characteristic, complemented
12#19134864C211yesmaximal, characteristic, complemented
13#19134843C211yesmaximal, characteristic
14C8×C4⋊Dic43C211yesmaximal, characteristic, complemented
15C4×#103×C43C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23#14583121C418yescomplemented
24#14582991—24no—
25#14582984—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582804C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582798—21no—
40#14582798—21no—
41#14582798C2211yescharacteristic
42#14582798C2211yescharacteristic
43#14582791—21no—
44#14582790—21no—
45#14582773—21no—
46#14582765—21no—
47#14582765C2211yescharacteristic
48C4×C4⋊Dic43—21no—
49C4×C4⋊Dic43C2211yescharacteristic
50C4×(C2×D43)⋊C4—21no—
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C2×#10621885—22no—
66C2×#10621885—22no—
67C2×#10621885C2×C414yescomplemented
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884C2×C414yes—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063313—22no—
74#13063313C2×C414yes—
75Q8×Dic43—22no—
76Q8×Dic43—22no—
77Q8×Dic43—41no—
78Q8×Dic43—41no—
79#13063290—22no—
80#13063290—41no—
81#13063287—22no—
82#13063287—41no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43D411yescharacteristic
88C2×C4⋊Dic43D411yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102#13063258—22no—
103#13063256—22no—
104C4⋊(C43⋊C8)C2×C414yescomplemented
105#13063250—22no—
106#13063250—41no—
107#13063248C2×C414yescomplemented
108#13063247—22no—
109#13063247—41no—
110#13063245C2×C414yes—
111C8×Dic43—22no—
112C8×Dic43—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95D411yescharacteristic
120C43⋊#95D411yescharacteristic
121C22×Q8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C4×Q8×C43—22no—
125C4×Q8×C43C2×C414yescomplemented
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C42×C43—21no—
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#103×C43—22no—
134#103×C43D414yes—
135C4×C8×C43—22no—
136#95×C43—21no—
137C23×D43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43C22×C412yes—
142C2×Q8×C43C2×D412yes—
143C2×Q8×C43#4112yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172C22×C412yes—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43—81no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86C22×C412yes—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D412yes—
179C4⋊C4×C43—24no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43C22×C412yes—
185C4⋊C4×C43C2×D412yes—
186C42×C43—24no—
187C42×C43—81no—
188C42×C43C22×C412yes—
189C42×C43#4112yes—
190#10621885—28no—
191#10621884—28no—
192(C2×D43)⋊C4—24no—
193(C2×D43)⋊C4—24no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—81no—
197C4⋊Dic43—22no—
198C4⋊Dic43—22no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—42no—
204C4⋊Dic43—42no—
205C4⋊Dic43—42no—
206C4⋊Dic43—42no—
207Dic43⋊C4—42no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—42no—
213C4×Dic43—42no—
214C4×Dic43—42no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C22×C412yes—
220C2×C43⋊C8C22×C412yes—
221C23×C43C22×D411yescharacteristic
222C22×D43—22no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229Q8×C43—22no—
230Q8×C43—22no—
231Q8×C43—22no—
232Q8×C43C4×D414yes—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43C4×D412yes—
250C2×C4×C43C4×D412yes—
251C2×C4×C43C23×C411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×C4×C432−1+411yescharacteristic
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
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—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43#13512yes—
277C2×Dic43#13512yes—
278D172—22no—
279D172—22no—
280D172—41no—
281D172—41no—
282C4×D43—84no—
283Dic86—22no—
284Dic86—22no—
285Dic86—41no—
286Dic86—41no—
287C8×C43—22no—
288C8×C43—41no—
289C43⋊C8—22no—
290C43⋊C8—22no—
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—24no—
307C4×C43—22no—
308C4×C43—22no—
309C4×C43—42no—
310C4×C43—42no—
311C4×C43—81no—
312C4×C43C2×C4×D411yescharacteristic
313C4×C43#52011yescharacteristic
314C4×C43#54711yescharacteristic
315C4×C43#55311yescharacteristic
316Dic43—22no—
317Dic43—22no—
318Dic43—42no—
319Dic43—41no—
320Dic43—41no—
321Dic43—81no—
322Dic43—81no—
323C2×#464—431no—
324C2×C4×Q16—431no—
325C2×C4×SD16—431no—
326#2367—431no—
327#2351—431no—
328#1958—431no—
329#1949—431no—
330#1934—431no—
331#1933—431no—
332#1880—431no—
333#1878—431no—
334#1865—431no—
335#1862—431no—
336C8×C4⋊C4—431no—
337C4×#103D4311yescharacteristic, complemented
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×Q8C2×D4311yescharacteristic
353C2×C4×D4—431no—
354#464—438no—
355C4×Q16—864no—
356C4×SD16—864no—
357C2×#107—431no—
358C2×#106—431no—
359C2×C4⋊C8—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103—431no—
363C2×#103C2×D4311yescharacteristic
364C2×#103C2×D4311yescharacteristic
365C2×#102—431no—
366C2×#102—431no—
367C2×#102—431no—
368C2×C4×C8—431no—
369C2×C4×C8—431no—
370C2×C4×C8C2×D4311yescharacteristic
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—431no—
381#382—861no—
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×Q8C22×D4311yescharacteristic
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—22no—
410C4×Q8—862no—
411C4×Q8—862no—
412C4×Q8—862no—
413C4×Q8—1721no—
414C4×Q8—1721no—
415C4×Q8—1721no—
416C4×Q8C4×D4314yescomplemented
417C4×D4—862no—
418C4×D4—1721no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
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—21no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—861no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42C22×D4311yescharacteristic
445#107—862no—
446#106—862no—
447C4⋊C8—434no—
448#103—22no—
449#103—434no—
450#103—862no—
451#103—1721no—
452#103D17214yes—
453#102—434no—
454#102—862no—
455#102—1721no—
456C4×C8—22no—
457C4×C8—862no—
458C4×C8—862no—
459#95—21no—
460#95—431no—
461#95—431no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468C24—861no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—432no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8C2×C4×D4312yes—
479C2×Q8C2×D17212yes—
480C2×Q8#1062189812yes—
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—21no—
511C2×C8—432no—
512C2×C8—432no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8C2×D17212yes—
518C4⋊C4—24no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—1722no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4C2×C4×D4312yes—
535C4⋊C4C2×D17212yes—
536C22⋊C4—864no—
537C22⋊C4—864no—
538C22⋊C4—3441no—
539C22⋊C4—1722no—
540C22⋊C4—1722no—
541C42—24no—
542C42—81no—
543C42—861no—
544C42—861no—
545C42—861no—
546C42—861no—
547C42—1722no—
548C42—1722no—
549C42—1722no—
550C42C2×C4×D4312yes—
551C42#1062190012yes—
552C23—862no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23C2×D4×D4311yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—22no—
563Q8—862no—
564Q8—862no—
565Q8—1721no—
566Q8—1721no—
567Q8C4×D17214yes—
568D4—862no—
569D4—862no—
570D4—1721no—
571D4—1721no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
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—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—862no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—3444no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4(C22⋊D43)⋊C412yes—
611C2×C4(C22⋊D43)⋊C412yes—
612C2×C4C22×C4×D4311yescharacteristic
613C2×C4C22×D17211yescharacteristic
614C2×C4C2×#1062190011yescharacteristic
615C2×C4C2×#1062189811yescharacteristic
616C2×C4#1306337111yescharacteristic
617C2×C4#1306337211yescharacteristic
618C8—22no—
619C8—41no—
620C8—862no—
621C8—862no—
622C22—3441no—
623C22—3441no—
624C22—3441no—
625C22—3441no—
626C22—1722no—
627C22—1722no—
628C22—1722no—
629C22C2×(C22⋊D43)⋊C411yescharacteristic
630C22D4×D17211yescharacteristic
631C22#1458355811yescharacteristic
632C22#135×D4311yescharacteristic
633C22#135×D4311yescharacteristic
634C22#1458370511yescharacteristic
635C22#1458371211yescharacteristic
636C4—22no—
637C4—24no—
638C4—22no—
639C4—42no—
640C4—42no—
641C4—81no—
642C4—862no—
643C4—862no—
644C4—3441no—
645C4—3441no—
646C4—1721no—
647C4—1722no—
648C4—1721no—
649C4C2×C4×D17211yescharacteristic
650C4#1458337911yescharacteristic
651C4#1458355311yescharacteristic
652C4#1458359511yescharacteristic
653C2—3442no—
654C2#1913760911yescharacteristic
655C2#1914336311yescharacteristic
656C2#1914343211yescharacteristic
657C2#1914630411yescharacteristic
658C2#1914633711yescharacteristic
659C2#1914728111yescharacteristic
660C2#1914729211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#103×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenterC4×#103D43
hypocenterC43#23000
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
2. C2×#14582991C2semidirect
5. #19137516C2semidirect
7. #19135363C2semidirect
9. #19135272C2semidirect
11. #19134934C2semidirect
12. #19134864C2semidirect
14. C8×C4⋊Dic43C2semidirect
15. C4×#103×C43C2semidirect
23. #14583121C4semidirect
67. C2×#10621885C2×C4semidirect
104. C4⋊(C43⋊C8)C2×C4semidirect
107. #13063248C2×C4semidirect
125. C4×Q8×C43C2×C4semidirect
337. C4×#103D43semidirect
392. C43#23000semidirect
416. C4×Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831212
C2×#145829912
C2×#145829842
#191376662
#191375162
#191354062
#191353632
#191352792
#191352722
#191349482
#191349342
#191348642
#191348432
C8×C4⋊Dic432
C4×#103×C432
#2300043