Finite Group Databasebeta

← #25114738

Subgroups — #25114738

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic
2C2×#14582935C211yesmaximal, characteristic, complemented
3C2×#14582934C211yesmaximal, characteristic, complemented
4#19137545C211yesmaximal, characteristic
5#19137539C211yesmaximal, characteristic
6#19135357C211yesmaximal, characteristic, complemented
7#19135355C211yesmaximal, characteristic, complemented
8#19134797C211yesmaximal, characteristic, complemented
9#19134796C211yesmaximal, characteristic, complemented
10#19134791C211yesmaximal, characteristic, complemented
11#19134753C211yesmaximal, characteristic, complemented
12#19134623C211yesmaximal, characteristic, complemented
13#19134622C211yesmaximal, characteristic, complemented
14#19134487C211yesmaximal, characteristic, complemented
15C43×#1854C211yesmaximal, characteristic, complemented
16C23×C43⋊C8C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×C4×C22⋊D43C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22(C22⋊D43)⋊C8C418yescomplemented
23#14582935—24no—
24#14582934—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×#13063258C2211yescharacteristic
29C2×#13063258C2211yescharacteristic
30C2×#13063257C2211yescharacteristic
31C2×#13063256C2211yescharacteristic
32C2×#13063256C2211yescharacteristic
33C2×Dic43⋊C8C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36#14582799—21no—
37#14582799—21no—
38#14582793—21no—
39#14582790—21no—
40#14582788—21no—
41#14582787—21no—
42#14582768C2211yescharacteristic
43#14582768C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48C4⋊C4×Dic43C2211yescharacteristic
49C4×Dic43⋊C4—21no—
50#14582750—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C2×#107×C43C2211yescharacteristic
57C2×#106×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×C22⋊D43D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C22×C43⋊C8—22no—
65C22×C43⋊C8—22no—
66C22×C43⋊C8C2×C414yes—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C2×C8×D43—22no—
70C2×C8×D43—22no—
71C2×C8×D43C2×C414yes—
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⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4D411yescharacteristic
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43D411yescharacteristic
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4D411yescharacteristic
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43C2311yescharacteristic
103#13063259—41no—
104#13063258—22no—
105#13063258—22no—
106#13063258—22no—
107#13063258D414yescomplemented
108#13063257—22no—
109#13063256—22no—
110#13063256—22no—
111Dic43⋊C8C2×C414yes—
112(C2×D43)⋊C8C2×C414yes—
113C8×Dic43C2×C414yes—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C23×C4×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122#117×C43—22no—
123#117×C43—41no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C42×C43—21no—
131#107×C43—41no—
132#106×C43—22no—
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×C43C22×C412yes—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×Q812yes—
148C22×C4×C43C2411yescharacteristic
149C2×C22⋊D43—22no—
150C2×C22⋊D43—22no—
151C2×C22⋊D43C4⋊C414yes—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43C22×C412yes—
164C2×C4×D43C2×Q812yes—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C22×C412yes—
170C2×C8×C43C22×C412yes—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C2×D412yes—
179C22⋊C4×C43—42no—
180C22⋊C4×C43—81no—
181C42×C43—42no—
182C22⋊Dic43—42no—
183C22⋊Dic43—81no—
184C22⋊Dic43C4⋊C414yes—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—42no—
187(C2×D43)⋊C4—81no—
188(C2×D43)⋊C4—81no—
189(C2×D43)⋊C4C4⋊C414yes—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43C2×D412yes—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—81no—
201Dic43⋊C4—81no—
202Dic43⋊C4C4⋊C414yes—
203C4×Dic43—42no—
204C4×Dic43—42no—
205C4×Dic43—42no—
206C4×Dic43—42no—
207C4×Dic43—42no—
208C4×Dic43C22×C412yes—
209C4×Dic43C2×Q812yes—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—28no—
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×C43C2×C4⋊C412yes—
252C2×C4×C43C23×C411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×Q811yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×C4×C432−1+411yescharacteristic
258C22⋊D43—28no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
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×Dic43C2×C4⋊C412yes—
276C2×Dic43C2×C4⋊C412yes—
277C2×Dic43C2×C4⋊C412yes—
278C2×Dic43#13512yes—
279C2×Dic43#13512yes—
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—22no—
284C8×C43—22no—
285C8×C43—22no—
286C43⋊C8—22no—
287C43⋊C8C4×D414yes—
288#22658—431nomaximal, Sylow
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43C22×C4⋊C411yescharacteristic
297C22×C43D4211yescharacteristic
298C22×C43#54711yescharacteristic
299C22×C43C2×#13511yescharacteristic
300C22×C43C2×#13511yescharacteristic
301C22×C43#57611yescharacteristic
302C22×C43#57811yescharacteristic
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—41no—
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—41no—
310C4×C43—22no—
311C4×C43—42no—
312C4×C43—81no—
313C4×C43—81no—
314C4×C43—81no—
315C4×C43C2×C4×D411yescharacteristic
316C4×C43#52011yescharacteristic
317C4×C43D4×Q811yescharacteristic
318C4×C43#55411yescharacteristic
319Dic43—22no—
320Dic43—22no—
321Dic43—42no—
322Dic43—81no—
323Dic43—81no—
324Dic43—81no—
325Dic43#42714yescomplemented
326C2×C8×D4—431no—
327C2×#427—431no—
328C2×#427—431no—
329#2354—431no—
330#2354—431no—
331#1948—431no—
332#1948—431no—
333#1854—431no—
334#1854—431no—
335#1854—431no—
336#1854D4311yescharacteristic, complemented
337#1845—431no—
338#1808—431no—
339#1808—431no—
340C4×#107—431no—
341C2×C43—42no—
342C2×C43D4×C4⋊C411yescharacteristic
343C2×C43C2×#42711yescharacteristic
344C2×C43#291311yescharacteristic
345C2×C43#328311yescharacteristic
346C2×C43#328711yescharacteristic
347C2×C43#334111yescharacteristic
348C2×C43#334211yescharacteristic
349D43—42no—
350C23×C8—431no—
351C23×C8—431no—
352C2×C4×D4—431no—
353C2×#117—431no—
354C2×#117—431no—
355C2×#117—431no—
356C2×#117C2×D4311yescharacteristic
357C8×D4—438no—
358#427—864no—
359#427—864no—
360C2×#107—431no—
361C2×#107—431no—
362C2×#107—431no—
363C2×#107—431no—
364C2×#107—431no—
365C2×#107C2×D4311yescharacteristic
366C2×#106—431no—
367C2×#106—431no—
368C2×#106—431no—
369C2×#106C2×D4311yescharacteristic
370C2×C4⋊C8—431no—
371C2×C22⋊C8—431no—
372C2×C22⋊C8C2×D4311yescharacteristic
373C2×C4×C8—431no—
374#390—861no—
375#390—861no—
376#388—861no—
377#388—861no—
378#388—861no—
379#388—861no—
380#384—431no—
381#384—431no—
382#380—431no—
383#380—431no—
384#380—431no—
385#380C2×D4311yescharacteristic
386C4×C4⋊C4—431no—
387C4×C4⋊C4—431no—
388C4×C4⋊C4—861no—
389C4×C4⋊C4—861no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340C2×D4311yescharacteristic
395#340C2×D4311yescharacteristic
396C43#2265811yescharacteristic, complemented, Sylow
397C22×D4—431no—
398C23×C4—431no—
399C23×C4C22×D4311yescharacteristic
400C22×C8—431no—
401C22×C8—434no—
402C22×C8—431no—
403C22×C8—434no—
404C22×C8—862no—
405C22×C8—862no—
406C22×C8—862no—
407C22×C8—862no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410C4×D4—434no—
411C4×D4—434no—
412#117—22no—
413#117—41no—
414#117—862no—
415#117—862no—
416#117—862no—
417#117—1721no—
418#117—1721no—
419#117—1721no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
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×C4⋊C4C22×D4311yescharacteristic
433C2×C22⋊C4—21no—
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—21no—
444C2×C42—431no—
445C2×C42—861no—
446C2×C42—861no—
447C2×C42—861no—
448C2×C42—861no—
449C2×C42—861no—
450#107—41no—
451#107—434no—
452#107—862no—
453#107—862no—
454#107—862no—
455#107—1721no—
456#106—22no—
457#106—862no—
458#106—862no—
459#106—862no—
460C4⋊C8—434no—
461C22⋊C8—434no—
462C22⋊C8C4×D4314yes—
463C4×C8—434no—
464#95—21no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470C24—431no—
471C24D4×D4311yescharacteristic
472C2×D4—434no—
473C2×D4—862no—
474C2×D4—862no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—432no—
487C22×C4—432no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4C2×C4×D4312yes—
497C22×C4D4×D4311yescharacteristic
498C22×C4Q8×D4312yes—
499C22×C4C23×D4311yescharacteristic
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—432no—
505C2×C8—432no—
506C2×C8—432no—
507C2×C8—432no—
508C2×C8—868no—
509C2×C8—868no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8C2×C4×D4312yes—
513C2×C8C2×C4×D4312yes—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—434no—
522C4⋊C4—432no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—3441no—
531C4⋊C4—3441no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4D4×D4312yes—
535C22⋊C4—42no—
536C22⋊C4—81no—
537C22⋊C4—434no—
538C22⋊C4—434no—
539C22⋊C4—3441no—
540C22⋊C4—3441no—
541C22⋊C4—3441no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C42—42no—
546C42—432no—
547C42—432no—
548C42—1722no—
549C42—1722no—
550C42—1722no—
551C42—1722no—
552C42—1722no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—432no—
560C23—861no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23—861no—
566C23C4⋊C4×D4312yes—
567C23C2×D4×D4311yescharacteristic
568D4—868no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—41no—
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—432no—
588C2×C4—432no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—1721no—
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—1721no—
611C2×C4—1721no—
612C2×C4C4⋊C4×D4312yes—
613C2×C4C22×C4×D4311yescharacteristic
614C2×C4C2×D4×D4311yescharacteristic
615C2×C4C2×Q8×D4311yescharacteristic
616C2×C4#41×D4311yescharacteristic
617C2×C4#1306337011yescharacteristic
618C2×C4#1306337211yescharacteristic
619C8—22no—
620C8—22no—
621C8—434no—
622C8—862no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—862no—
631C22—862no—
632C22—862no—
633C22—1721no—
634C22—1721no—
635C22—1721no—
636C22—1721no—
637C22C2×C4⋊C4×D4311yescharacteristic
638C22#1458353111yescharacteristic
639C22#1458354711yescharacteristic
640C22#135×D4311yescharacteristic
641C22#135×D4311yescharacteristic
642C22#1458370311yescharacteristic
643C22#1458371511yescharacteristic
644C4—22no—
645C4—42no—
646C4—81no—
647C4—81no—
648C4—81no—
649C4—434no—
650C4—862no—
651C4—862no—
652C4—3441no—
653C4—3441no—
654C4—3441no—
655C4—1722no—
656C4C4×D4×D4311yescharacteristic
657C4#1458337811yescharacteristic
658C4#1458356211yescharacteristic
659C4#1458360311yescharacteristic
660C2—42no—
661C2—1722no—
662C2#1913749311yescharacteristic
663C2#427×D4311yescharacteristic
664C2#1914319411yescharacteristic
665C2#1914631011yescharacteristic
666C2#1914634811yescharacteristic
667C2#1914701211yescharacteristic
668C2#1914702011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
cosocleC22×C4×C43C24
hypercenter#1854D43
hypocenterC43#22658
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#14582935C2semidirect
3. C2×#14582934C2semidirect
6. #19135357C2semidirect
7. #19135355C2semidirect
8. #19134797C2semidirect
9. #19134796C2semidirect
10. #19134791C2semidirect
11. #19134753C2semidirect
12. #19134623C2semidirect
13. #19134622C2semidirect
14. #19134487C2semidirect
15. C43×#1854C2semidirect
22. (C22⋊D43)⋊C8C4semidirect
107. #13063258D4semidirect
325. Dic43#427semidirect
336. #1854D43semidirect
396. C43#22658semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D43)⋊C82
C2×#145829352
C2×#145829342
#191375452
#191375392
#191353572
#191353552
#191347972
#191347962
#191347912
#191347532
#191346232
#191346222
#191344872
C43×#18542
#2265843