Finite Group Databasebeta

← #25114769

Subgroups — #25114769

Order 11008.

970 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582973C211yesmaximal, characteristic
2C2×#14582939C211yesmaximal, characteristic, complemented
3C2×#14582936C211yesmaximal, characteristic, complemented
4#19137539C211yesmaximal, characteristic
5#19137520C211yesmaximal, characteristic
6#19135366C211yesmaximal, characteristic, complemented
7#19135350C211yesmaximal, characteristic, complemented
8#19134796C211yesmaximal, characteristic, complemented
9#19134795C211yesmaximal, characteristic, complemented
10#19134791C211yesmaximal, characteristic, complemented
11#19134762C211yesmaximal, characteristic, complemented
12#19134626C211yesmaximal, characteristic, complemented
13#19134623C211yesmaximal, characteristic, complemented
14#19134491C211yesmaximal, characteristic, complemented
15C43×#1852C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×C4×C22⋊D43C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22#14582973C418yescomplemented
23#14582939—24no—
24#14582936—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×#13063258C2211yescharacteristic
29C2×#13063257C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×#13063256C2211yescharacteristic
32C2×#13063256C2211yescharacteristic
33C2×Dic43⋊C8C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36#14582799—21no—
37#14582793—21no—
38#14582789—21no—
39#14582788—21no—
40#14582780—21no—
41#14582778—21no—
42#14582768C2211yescharacteristic
43#14582764C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48C4⋊C4×Dic43C2211yescharacteristic
49#14582750—21no—
50C4×C22⋊Dic43—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C2×#107×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×C22⋊D43D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C2×#10621877—22no—
65C2×#10621877—22no—
66C2×#10621877C2×C414yes—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C2×C8×D43—22no—
70C2×C8×D43—22no—
71C2×C8×D43C2×C414yescomplemented
72C4×C22⋊D43C2×C414yes—
73C4×C22⋊D43Q814yes—
74#13063284—22no—
75#13063284—41no—
76#13063283—22no—
77#13063283—22no—
78#13063283—41no—
79#13063283—41no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4D411yescharacteristic
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43D411yescharacteristic
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101#13063259—22no—
102#13063258—22no—
103#13063258—22no—
104#13063258—22no—
105#13063257—41no—
106#13063256—22no—
107#13063256—22no—
108#13063256D414yescomplemented
109Dic43⋊C8C2×C414yescomplemented
110(C2×D43)⋊C8C2×C414yescomplemented
111#13063235C2×C414yescomplemented
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C23×C4×C43—21no—
120C23×C4×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C2×C4⋊C4×C43—22no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—41no—
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131#107×C43—22no—
132#107×C43—41no—
133C22⋊C8×C43C2×C414yes—
134#95×C43—21no—
135C24×C43C2×D411yescharacteristic
136C23×D43C2×D411yescharacteristic
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43—81no—
148C22×C4×C43C22×C412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×Q812yes—
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—41no—
153C2×C22⋊D43—41no—
154C2×C22⋊D43C4⋊C414yes—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43C22×C412yes—
167C2×C4×D43C2×Q812yes—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43C22×C412yes—
173C2×C8×C43C22×C412yes—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43C2×D412yes—
183C22⋊C4×C43—81no—
184C22⋊Dic43—42no—
185C22⋊Dic43—42no—
186C22⋊Dic43C4⋊C414yes—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—81no—
190(C2×D43)⋊C4—81no—
191(C2×D43)⋊C4C4⋊C414yes—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43C2×D412yes—
200Dic43⋊C4—42no—
201Dic43⋊C4—81no—
202Dic43⋊C4C4⋊C414yes—
203C4×Dic43—42no—
204C4×Dic43—42no—
205C4×Dic43—42no—
206C4×Dic43—42no—
207C4×Dic43—81no—
208C4×Dic43C22×C412yes—
209C4×Dic43C2×Q812yes—
210#10621877—28no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8C22×C412yes—
214C2×C43⋊C8C22×C412yes—
215C2×C43⋊C8C2×D412yes—
216C2×C43⋊C8#4112yes—
217C8×D43—28no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43C2×C4⋊C412yes—
225C23×C43C22×D411yescharacteristic
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43C2×C4⋊C412yes—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
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×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—84no—
252C2×C4×C43C2×C4⋊C412yes—
253C2×C4×C43C23×C411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×Q811yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C22⋊D43—44no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—41no—
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—41no—
277C2×Dic43—41no—
278C2×Dic43C2×C4⋊C412yes—
279C2×Dic43C2×C4⋊C412yes—
280C2×Dic43C2×C4⋊C412yes—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—22no—
285C8×C43—22no—
286C8×C43—22no—
287C43⋊C8—22no—
288C43⋊C8C4×D414yes—
289#22660—431nomaximal, Sylow
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43C22×C4⋊C411yescharacteristic
298C22×C43D4211yescharacteristic
299C22×C43#54711yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57511yescharacteristic
302C22×C43#57611yescharacteristic
303C22×C43#57811yescharacteristic
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—41no—
311C4×C43—22no—
312C4×C43—42no—
313C4×C43—81no—
314C4×C43—81no—
315C4×C43—81no—
316C4×C43C2×C4×D411yescharacteristic
317C4×C43#52011yescharacteristic
318C4×C43D4×Q811yescharacteristic
319C4×C43#55411yescharacteristic
320Dic43—22no—
321Dic43—22no—
322Dic43—22no—
323Dic43—42no—
324Dic43—81no—
325Dic43—81no—
326Dic43—81no—
327C2×#435—431no—
328C2×#428—431no—
329C2×#427—431no—
330#2354—431no—
331#2352—431no—
332#1949—431no—
333#1947—431no—
334#1854—431no—
335#1854—431no—
336#1854—431no—
337#1852D4311yescharacteristic, complemented
338#1847—431no—
339#1809—431no—
340#1808—431no—
341#1776—431no—
342C2×C43—42no—
343C2×C43D4×C4⋊C411yescharacteristic
344C2×C43#291111yescharacteristic
345C2×C43#291311yescharacteristic
346C2×C43#326811yescharacteristic
347C2×C43#326911yescharacteristic
348C2×C43#334711yescharacteristic
349C2×C43#334911yescharacteristic
350D43—42no—
351C22×M16—431no—
352C23×C8—431no—
353C2×C4×D4—431no—
354C2×#117—431no—
355C2×#117—431no—
356C2×#117—431no—
357C22×C4⋊C4C2×D4311yescharacteristic
358#435—438no—
359#428—864no—
360#427—864no—
361C2×#107—431no—
362C2×#107—431no—
363C2×#107—431no—
364C2×#107—431no—
365C2×#107C2×D4311yescharacteristic
366C2×#107C2×D4311yescharacteristic
367C2×#106—431no—
368C2×#106—431no—
369C2×#106—431no—
370C2×#106—431no—
371C2×C4⋊C8—431no—
372C2×C22⋊C8—431no—
373C2×C22⋊C8C2×D4311yescharacteristic
374C2×#97—431no—
375#390—861no—
376#388—861no—
377#388—861no—
378#388—861no—
379#387—861no—
380#386—861no—
381#384—431no—
382#382—431no—
383#380—431no—
384#380—431no—
385#380—431no—
386#380C2×D4311yescharacteristic
387C4×C4⋊C4—431no—
388C4×C4⋊C4—431no—
389C4×C4⋊C4—861no—
390C4×C22⋊C4—861no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#340C2×D4311yescharacteristic
396#340C2×D4311yescharacteristic
397C43#2266011yescharacteristic, complemented, Sylow
398C22×D4—431no—
399C23×C4—21no—
400C23×C4—431no—
401C23×C4C22×D4311yescharacteristic
402C2×M16—434no—
403C2×M16—862no—
404C2×M16—862no—
405C22×C8—431no—
406C22×C8—431no—
407C22×C8—434no—
408C22×C8—862no—
409C22×C8—862no—
410C22×C8C22×D4311yescharacteristic
411C22×C8C22×D4311yescharacteristic
412C4×D4—434no—
413C4×D4—434no—
414#117—862no—
415#117—862no—
416#117—862no—
417#117—1721no—
418#117—1721no—
419#117—1721no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—431no—
436C2×C22⋊C4—431no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42—861no—
447C2×C42—861no—
448C2×C42—861no—
449#107—22no—
450#107—41no—
451#107—862no—
452#107—862no—
453#107—862no—
454#107—862no—
455#106—434no—
456#106—862no—
457#106—862no—
458#106—1721no—
459C4⋊C8—434no—
460C22⋊C8—434no—
461C22⋊C8C4×D4314yes—
462#97—434no—
463#95—21no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471C24—431no—
472C24D4×D4311yescharacteristic
473C2×D4—434no—
474C2×D4—1721no—
475C2×D4—1721no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—81no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—432no—
491C22×C4—432no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4C2×C4×D4312yes—
501C22×C4D4×D4311yescharacteristic
502C22×C4Q8×D4312yes—
503C22×C4C23×D4311yescharacteristic
504M16—868no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—432no—
510C2×C8—432no—
511C2×C8—432no—
512C2×C8—432no—
513C2×C8—868no—
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—42no—
526C4⋊C4—434no—
527C4⋊C4—432no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—3441no—
536C4⋊C4—1722no—
537C4⋊C4D4×D4312yes—
538C22⋊C4—81no—
539C22⋊C4—434no—
540C22⋊C4—434no—
541C22⋊C4—3441no—
542C22⋊C4—3441no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C42—432no—
548C42—432no—
549C42—3441no—
550C42—1722no—
551C42—1722no—
552C42—1722no—
553C42—1722no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—432no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23—861no—
566C23—861no—
567C23C4⋊C4×D4312yes—
568C23C2×D4×D4311yescharacteristic
569D4—1724no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
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—84no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4C4⋊C4×D4312yes—
615C2×C4C22×C4×D4311yescharacteristic
616C2×C4C2×D4×D4311yescharacteristic
617C2×C4C2×Q8×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4#1306337011yescharacteristic
620C2×C4#1306337211yescharacteristic
621C8—22no—
622C8—22no—
623C8—434no—
624C8—862no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—862no—
633C22—862no—
634C22—862no—
635C22—1721no—
636C22—1721no—
637C22—1721no—
638C22—1721no—
639C22C2×C4⋊C4×D4311yescharacteristic
640C22#1458353111yescharacteristic
641C22#1458354711yescharacteristic
642C22#1458369511yescharacteristic
643C22#1458369811yescharacteristic
644C22#1458370011yescharacteristic
645C22#1458371211yescharacteristic
646C4—22no—
647C4—42no—
648C4—81no—
649C4—81no—
650C4—81no—
651C4—862no—
652C4—862no—
653C4—862no—
654C4—3441no—
655C4—3441no—
656C4—3441no—
657C4—1722no—
658C4C4×D4×D4311yescharacteristic
659C4#1458337811yescharacteristic
660C4#1458356211yescharacteristic
661C4#1458360311yescharacteristic
662C2—42no—
663C2—1722no—
664C2#1913749311yescharacteristic
665C2#1914318211yescharacteristic
666C2#1914319111yescharacteristic
667C2#1914613311yescharacteristic
668C2#1914615311yescharacteristic
669C2#1914709811yescharacteristic
670C2#1914711811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1852C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
cosocleC22×C4×C43C24
hypercenter#1852D43
hypocenterC43#22660
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. C2×#14582939C2semidirect
3. C2×#14582936C2semidirect
6. #19135366C2semidirect
7. #19135350C2semidirect
8. #19134796C2semidirect
9. #19134795C2semidirect
10. #19134791C2semidirect
11. #19134762C2semidirect
12. #19134626C2semidirect
13. #19134623C2semidirect
14. #19134491C2semidirect
15. C43×#1852C2semidirect
22. #14582973C4semidirect
71. C2×C8×D43C2×C4semidirect
108. #13063256D4semidirect
109. Dic43⋊C8C2×C4semidirect
110. (C2×D43)⋊C8C2×C4semidirect
111. #13063235C2×C4semidirect
337. #1852D43semidirect
397. C43#22660semidirect

Maximal subgroups

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

subgroupindex
C2×#145829732
C2×#145829392
C2×#145829362
#191375392
#191375202
#191353662
#191353502
#191347962
#191347952
#191347912
#191347622
#191346262
#191346232
#191344912
C43×#18522
#2266043