Finite Group Databasebeta

← #25169713

Subgroups — #25169713

Order 11008.

672 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138995C211yesmaximal, characteristic
2#19136013C211yesmaximal, characteristic, complemented
3#19135976C211yesmaximal, characteristic, complemented
4#19135795C211yesmaximal, characteristic
5#19135788C211yesmaximal, characteristic
6#19135363C211yesmaximal, characteristic, complemented
7#19135330C211yesmaximal, characteristic, complemented
8#19135210C211yesmaximal, characteristic
9#19135187C211yesmaximal, characteristic, complemented
10#19135177C211yesmaximal, characteristic, complemented
11#19134849C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic
13#19134690C211yesmaximal, characteristic
14#19134425C211yesmaximal, characteristic, complemented
15C43×#2362C211yesmaximal, characteristic
16C2×#13063258C2211yescharacteristic
17C2×#13063258C2211yescharacteristic
18C2×#13063256C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063236C2211yescharacteristic
28C43⋊#401—21no—
29#14582827—21no—
30#14582797C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582793—21no—
33#14582781—21no—
34#14582765C2211yescharacteristic
35#14582759C2211yescharacteristic
36#14582759C2211yescharacteristic
37C4×C4⋊Dic43C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C22⋊Q8×C43C2211yescharacteristic
49C2×C4×Q8×C43C2211yescharacteristic
50C2×#117×C43C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#388—21no—
54C43×#388—21no—
55C43×#387—21no—
56C4×C4⋊C4×C43—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C2×C4⋊Dic43C2311yescharacteristic
64C2×C4⋊Dic43C2311yescharacteristic
65C2×C4⋊Dic43C2311yescharacteristic
66C2×C4⋊Dic43C2311yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×C22⋊Dic43—21no—
70C2×C22⋊Dic43—21no—
71C2×C4×Dic43—21no—
72#13063258—22no—
73#13063258—22no—
74#13063256—22no—
75#13063256—41no—
76C4⋊(C43⋊C8)—22no—
77#13063249—22no—
78#13063249—22no—
79#13063249—22no—
80#13063249—41no—
81C22⋊(C43⋊C8)—22no—
82C22⋊(C43⋊C8)—41no—
83#13063236—41no—
84C43⋊#95—21no—
85C43⋊#95—21no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C22×Q8×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C22⋊Q8×C43—22no—
94C22⋊Q8×C43—22no—
95C4×Q8×C43—22no—
96C4×Q8×C43—41no—
97#117×C43—22no—
98#117×C43—41no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43D411yescharacteristic
108C2×C22⋊C4×C43D411yescharacteristic
109C2×C42×C43—21no—
110C2×C42×C43—21no—
111C2×C42×C43—21no—
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114#95×C43—21no—
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43D411yescharacteristic
119#95×C43D411yescharacteristic
120C24×C43C2×D411yescharacteristic
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43#4112yes—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C4⋊C4×C43—24no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—42no—
153C4⋊C4×C43—42no—
154C4⋊C4×C43#4112yes—
155C4⋊C4×C43#4112yes—
156C22⋊C4×C43—24no—
157C22⋊C4×C43—41no—
158C22⋊C4×C43—41no—
159C22⋊C4×C43—42no—
160C42×C43—21no—
161C42×C43—21no—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43—42no—
165C42×C43—42no—
166C42×C43—42no—
167C22⋊Dic43—42no—
168C22⋊Dic43—81no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177Dic43⋊C4—42no—
178Dic43⋊C4—81no—
179C4×Dic43—81no—
180C2×C43⋊C8—21no—
181C2×C43⋊C8—21no—
182C2×C43⋊C8—21no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8#4112yes—
192C23×C43—21no—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43C22×D411yescharacteristic
200Q8×C43—22no—
201Q8×C43—22no—
202Q8×C43—41no—
203Q8×C43—41no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—22no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C2×C4×C432−1+411yescharacteristic
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C43⋊C8—22no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#27061—431nomaximal, Sylow
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43#52511yescharacteristic
266C22×C43#54611yescharacteristic
267C22×C43#54711yescharacteristic
268C22×C43#57511yescharacteristic
269C22×C43#57511yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57811yescharacteristic
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—42no—
275C4×C43—41no—
276C4×C43—42no—
277C4×C43—41no—
278C4×C43—42no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43#52911yescharacteristic
282C4×C43#53911yescharacteristic
283C4×C43#55311yescharacteristic
284C4×C43#55611yescharacteristic
285Dic43—81no—
286Dic43—81no—
287Dic43—81no—
288Dic43—81no—
289#2494—431no—
290#2362D4311yescharacteristic
291#2074—431no—
292#2066—431no—
293#2036—431no—
294#2035—431no—
295#1949—431no—
296#1943—431no—
297#1924—431no—
298#1921—431no—
299#1920—431no—
300#1863—431no—
301#1854—431no—
302#1825—431no—
303#1763—431no—
304C2×C43—81no—
305C2×C43#246611yescharacteristic
306C2×C43#311111yescharacteristic
307C2×C43#312111yescharacteristic
308C2×C43#330711yescharacteristic
309C2×C43#332711yescharacteristic
310C2×C43#334911yescharacteristic
311C2×C43#335011yescharacteristic
312C2×C22⋊Q8C2×D4311yescharacteristic
313C2×C4×Q8C2×D4311yescharacteristic
314C2×#117C2×D4311yescharacteristic
315C2×#107—431no—
316C2×#107—431no—
317C2×#106—431no—
318C2×#106—431no—
319C2×C4⋊C8—431no—
320C2×#103—431no—
321C2×#103—431no—
322C2×#103—431no—
323C2×#103—431no—
324C2×C22⋊C8—431no—
325C2×C22⋊C8—431no—
326C2×#97—431no—
327#401—861no—
328#397—861no—
329#391C2×D4311yescharacteristic
330#389—431no—
331#389—431no—
332#389C2×D4311yescharacteristic
333#388—21no—
334#388—21no—
335#388—861no—
336#387—21no—
337#387—861no—
338#382—431no—
339#380—431no—
340#380—431no—
341C4×C4⋊C4—21no—
342C4×C4⋊C4—431no—
343C4×C4⋊C4C2×D4311yescharacteristic
344C4×C22⋊C4C2×D4311yescharacteristic
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#336—431no—
354#336—431no—
355C43#2706111yescharacteristic, complemented, Sylow
356C22×Q8C22×D4311yescharacteristic
357C23×C4C22×D4311yescharacteristic
358C22×C8—431no—
359C22×C8—431no—
360C22×C8—431no—
361C22×C8—431no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C4×Q8—22no—
365C4×Q8—41no—
366#117—22no—
367#117—41no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4C22⋊D4311yescharacteristic
385C2×C22⋊C4C22⋊D4311yescharacteristic
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—861no—
390C2×C42C22×D4311yescharacteristic
391C2×C42C22×D4311yescharacteristic
392#107—862no—
393#107—862no—
394#106—862no—
395#106—1721no—
396C4⋊C8—862no—
397#103—862no—
398#103—862no—
399#103—862no—
400#103—1721no—
401C22⋊C8—862no—
402C22⋊C8—1721no—
403#97—1721no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95C22⋊D4311yescharacteristic
416#95C22⋊D4311yescharacteristic
417C24C2×C22⋊D4311yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8#1062189812yes—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4C2×C22⋊D4311yescharacteristic
439C22×C4C2×C22⋊D4311yescharacteristic
440C22×C4C2×C22⋊D4311yescharacteristic
441C22×C4C2×C22⋊D4311yescharacteristic
442C22×C4C2×C22⋊D4311yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—432no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C4⋊C4—24no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—3441no—
472C4⋊C4—1722no—
473C4⋊C4#1062189812yes—
474C4⋊C4#1062190012yes—
475C22⋊C4—24no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—42no—
479C22⋊C4—3441no—
480C22⋊C4—1722no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—42no—
486C42—42no—
487C42—42no—
488C42—3441no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23C22×C22⋊D4311yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4#41×D4311yescharacteristic
545C2×C4C2×#1062190011yescharacteristic
546C2×C4C2×#1062189811yescharacteristic
547C2×C4C2×#1062189811yescharacteristic
548C2×C4#1306337011yescharacteristic
549C2×C4#1306337211yescharacteristic
550C8—862no—
551C8—1721no—
552C8—1721no—
553C8—1721no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22#1458341011yescharacteristic
562C22#1458354311yescharacteristic
563C22#1458354811yescharacteristic
564C22#1458369711yescharacteristic
565C22#1458369711yescharacteristic
566C22#1458370711yescharacteristic
567C22#1458371411yescharacteristic
568C4—42no—
569C4—41no—
570C4—42no—
571C4—41no—
572C4—42no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—3441no—
578C4—3441no—
579C4—3441no—
580C4—3441no—
581C4#1458342911yescharacteristic
582C4#1458349111yescharacteristic
583C4#1458359911yescharacteristic
584C4#1458361911yescharacteristic
585C2—81no—
586C2#1913862511yescharacteristic
587C2#1914470411yescharacteristic
588C2#1914482411yescharacteristic
589C2#1914657111yescharacteristic
590C2#1914686311yescharacteristic
591C2#1914712511yescharacteristic
592C2#1914714011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2362C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2362D43
hypocenterC43#27061
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. #19136013C2semidirect
3. #19135976C2semidirect
6. #19135363C2semidirect
7. #19135330C2semidirect
9. #19135187C2semidirect
10. #19135177C2semidirect
11. #19134849C2semidirect
14. #19134425C2semidirect
355. C43#27061semidirect

Maximal subgroups

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

subgroupindex
#191389952
#191360132
#191359762
#191357952
#191357882
#191353632
#191353302
#191352102
#191351872
#191351772
#191348492
#191347942
#191346902
#191344252
C43×#23622
#2706143