Finite Group Databasebeta

← #25105543

Subgroups — #25105543

Order 11008.

1554 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583406C211yesmaximal, characteristic
2#19136975C211yesmaximal, characteristic, complemented
3#381×D43C211yesmaximal, characteristic, complemented
4#19135050C214yesmaximal, complemented
5#19135045C214yesmaximal, complemented
6#19134670C211yesmaximal, characteristic, complemented
7#19134670C211yesmaximal, characteristic, complemented
8#19134513C211yesmaximal, characteristic, complemented
9C43×#1782C211yesmaximal, characteristic, complemented
10C23×C4×D43C2211yescharacteristic
11#14583406—22no—
12#14583406—22no—
13#14583406—22no—
14#14583406—22no—
15C2×#13063306C2212yes—
16C2×#13063301C412yescomplemented
17C2×#13063296C412yescomplemented
18C2×#13063293C2212yes—
19C2×C4×C22⋊D43C414yescomplemented
20C2×#13063284C2211yescharacteristic
21C2×#13063281C2212yes—
22C2×C22⋊C4×D43C2212yes—
23C2×#13063240C2214yes—
24#14582762C2211yescharacteristic
25#14582762C2211yescharacteristic
26#14582761—22no—
27#14582760C2212yes—
28#14582758—22no—
29#14582754C2212yes—
30#14582746—22no—
31#95×D43—22no—
32#14582665C2214yes—
33#14582665C2214yes—
34C22×#41×C43C2211yescharacteristic
35C2×#99×C43C2214yes—
36C43×#381C2211yescharacteristic
37C43×#381C2211yescharacteristic
38C24×D43C2311yescharacteristic
39C22×C22⋊D43C2×C414yes—
40C23×Dic43C2311yescharacteristic
41C22×C4×D43—22no—
42C22×C4×D43—44no—
43C22×C4×D43C2×C412yes—
44C22×C4×D43C2×C412yes—
45C22×C4×D43D412yes—
46C22×C4×D43D412yes—
47C22×C4×D43D412yes—
48C22×C4×D43D412yes—
49#13063306—24no—
50#13063306—22no—
51#13063306—22no—
52#13063301—22no—
53#13063301—22no—
54#13063301—22no—
55#13063301—22no—
56#13063296—22no—
57#13063296—22no—
58#13063296—22no—
59#13063296—22no—
60#13063293—22no—
61#13063293—24no—
62#13063293—22no—
63C4×C22⋊D43—24no—
64C4×C22⋊D43—24no—
65C4×C22⋊D43—24no—
66C4×C22⋊D43—24no—
67#13063284—22no—
68#13063284—22no—
69#13063281—44no—
70C2×C4⋊Dic43C2×C412yescomplemented
71C2×Dic43⋊C4—22no—
72C2×Dic43⋊C4C2×C414yescomplemented
73C2×C22⋊Dic43C2×C414yescomplemented
74C2×C22⋊Dic43C2312yes—
75C2×C22⋊Dic43C2312yes—
76C2×C22⋊Dic43C2312yes—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—24no—
79C2×(C2×D43)⋊C4C2×C414yes—
80C22⋊C4×D43—44no—
81C2×C4×Dic43—22no—
82C2×C4×Dic43C2×C412yescomplemented
83#13063240—44no—
84C43⋊#95—22no—
85C43⋊#95—22no—
86C43⋊#95—24no—
87C2×#41×C43—22no—
88C2×#41×C43—22no—
89C2×#41×C43—44no—
90C22×Q8×C43C2×C411yescharacteristic, complemented
91C22×D4×C43C2×C411yescharacteristic, complemented
92C22×D4×C43C2312yes—
93C23×C4×C43C2×C412yescomplemented
94C23×C4×C43C2311yescharacteristic
95C2×C22⋊C4×C43C2312yes—
96C2×C22⋊C4×C43C2312yes—
97#99×C43—44no—
98#95×C43—22no—
99#95×C43—22no—
100C24×C43C22×C412yes—
101C24×C43C2411yescharacteristic
102C23×D43—24no—
103C23×D43—44no—
104C23×D43C22×C412yes—
105C23×D43C2×D411yescharacteristic
106C23×D43C2×D412yes—
107C23×D43C2×D411yescharacteristic
108#41×C43—48no—
109#41×C43—48no—
110C2×Q8×C43—22no—
111C2×Q8×C43—42no—
112C2×D4×C43—22no—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43—24no—
116C2×D4×C43—24no—
117C2×D4×C43—42no—
118C22×C4×C43—24no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—24no—
122C22×C4×C43—42no—
123C22×C4×C43—42no—
124C22×C4×C43C22×C412yes—
125C22×C4×C43C22×C411yescharacteristic
126C22×C4×C43C22×C411yescharacteristic
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D412yes—
129C2×C22⋊D43—24no—
130C2×C22⋊D43—24no—
131C2×C22⋊D43—48no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—24no—
135C22×Dic43C22×C412yes—
136C22×Dic43C22×C414yes—
137C22×Dic43C2×D412yes—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C2×C4×D43—44no—
141C2×C4×D43—44no—
142C2×C4×D43—44no—
143C2×C4×D43—44no—
144C2×C4×D43—44no—
145C2×C4×D43—44no—
146C2×C4×D43—44no—
147C2×C4×D43—48no—
148C2×C4×D43C22⋊C412yes—
149C2×C4×D43C22⋊C412yes—
150C2×C4×D43C22⋊C412yes—
151C2×C4×D43C22⋊C412yes—
152C2×C4×D43C22⋊C412yes—
153C2×C4×D43C22⋊C412yes—
154C2×C4×D43C22⋊C412yes—
155C2×C4×D43C22⋊C412yes—
156C22⋊C4×C43—24no—
157C22⋊C4×C43—24no—
158C22⋊Dic43—24no—
159C22⋊Dic43—24no—
160C22⋊Dic43—22no—
161C22⋊Dic43—22no—
162C22⋊Dic43—24no—
163C22⋊Dic43—24no—
164(C2×D43)⋊C4—24no—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—44no—
167(C2×D43)⋊C4—48no—
168C4⋊Dic43—22no—
169C4⋊Dic43—22no—
170Dic43⋊C4—24no—
171Dic43⋊C4—24no—
172Dic43⋊C4—44no—
173C4×Dic43—24no—
174C4×Dic43—44no—
175C23×C43—22no—
176C23×C43—22no—
177C23×C43—22no—
178C23×C43—42no—
179C23×C43—44no—
180C23×C43C23×C411yescharacteristic
181C23×C43C22×D411yescharacteristic
182C23×C43C22×D411yescharacteristic
183C23×C43H(5,𝔽2)14yes—
184C22×D43—22no—
185C22×D43—24no—
186C22×D43—24no—
187C22×D43—22no—
188C22×D43—24no—
189C22×D43—24no—
190C22×D43—24no—
191C22×D43—42no—
192C22×D43—42no—
193C22×D43—42no—
194C22×D43—416no—
195C22×D43C2×C22⋊C412yes—
196C22×D43C2×C22⋊C412yes—
197Q8×C43—44no—
198D4×C43—44no—
199D4×C43—44no—
200D4×C43—44no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—24no—
204C2×C4×C43—24no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—48no—
209C2×C4×C43—44no—
210C2×C4×C43—44no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43C2×C22⋊C412yes—
214C2×C4×C43C2×C22⋊C412yes—
215C22⋊D43—48no—
216C22⋊D43—48no—
217C2×Dic43—24no—
218C2×Dic43—22no—
219C2×Dic43—22no—
220C2×Dic43—24no—
221C2×Dic43—24no—
222C2×Dic43—44no—
223C2×Dic43—44no—
224C2×Dic43—44no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43C2×C22⋊C412yes—
228C2×Dic43C2×C22⋊C412yes—
229C4×D43—42no—
230C4×D43—42no—
231C4×D43—42no—
232C4×D43—42no—
233C4×D43—42no—
234C4×D43—42no—
235C4×D43—42no—
236C4×D43—42no—
237C4×D43—88no—
238#21748—431nomaximal, Sylow
239C22×C43—22no—
240C22×C43—22no—
241C22×C43—22no—
242C22×C43—44no—
243C22×C43—42no—
244C22×C43—44no—
245C22×C43—82no—
246C22×C43—82no—
247C22×C43C22×C22⋊C411yescharacteristic
248C22×C43#51812yes—
249C22×C43#53412yes—
250C22×C43#53412yes—
251C2×D43—28no—
252C2×D43—22no—
253C2×D43—22no—
254C2×D43—22no—
255C2×D43—22no—
256C2×D43—22no—
257C2×D43—48no—
258C2×D43—48no—
259C2×D43—44no—
260C2×D43#41014yes—
261C4×C43—22no—
262C4×C43—22no—
263C4×C43—42no—
264C4×C43—82no—
265C4×C43—82no—
266Dic43—22no—
267Dic43—22no—
268Dic43—44no—
269Dic43—82no—
270Dic43—82no—
271C2×#525—431no—
272#2280—431no—
273C2×#381—431no—
274#1899—434no—
275#1898—434no—
276#1820—431no—
277#1820—431no—
278#1782—431no—
279#1782D4311yescharacteristic, complemented
280C2×C43—22no—
281C2×C43—22no—
282C2×C43—22no—
283C2×C43—82no—
284C2×C43#230811yescharacteristic
285C2×C43C2×#41012yes—
286D43—24no—
287D43—42no—
288C22×#41C2×D4311yescharacteristic
289C24×C4—431no—
290#525—862no—
291#525—862no—
292#525—862no—
293#525—862no—
294C2×#123—432no—
295C2×C22⋊Q8—432no—
296C2×#121—432no—
297C2×#120—432no—
298C2×C4×D4—434no—
299C2×#117—431no—
300C2×#117—432no—
301C22×C22⋊C4—432no—
302C2×#99—434no—
303C2×#99C2×D4314yes—
304#381—431no—
305#381—431no—
306#381—432no—
307#381—862no—
308#381C2×D4311yescharacteristic
309#381C2×D4311yescharacteristic
310#380—862no—
311#379—432no—
312C4×C22⋊C4—862no—
313C2×#95—862no—
314#342—434no—
315#342—434no—
316C43#2174811yescharacteristic, complemented, Sylow
317C25—431no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41—44no—
321C22×Q8C4×D4311yescharacteristic, complemented
322C22×D4—434no—
323C22×D4C4×D4311yescharacteristic, complemented
324C22×D4C22×D4312yes—
325C23×C4—431no—
326C23×C4—432no—
327C23×C4—432no—
328C23×C4—432no—
329C23×C4—432no—
330C23×C4—432no—
331C23×C4—432no—
332C23×C4—862no—
333C23×C4—1724no—
334C23×C4C4×D4312yescomplemented
335C23×C4C22×D4311yescharacteristic
336#123—864no—
337#123—862no—
338#123—862no—
339C22⋊Q8—862no—
340C22⋊Q8—862no—
341C22⋊Q8—862no—
342C22⋊Q8—862no—
343#121—862no—
344#121—862no—
345#121—862no—
346#121—862no—
347#120—862no—
348#120—864no—
349#120—862no—
350C4×D4—864no—
351C4×D4—864no—
352C4×D4—864no—
353C4×D4—864no—
354#117—862no—
355#117—862no—
356#117—1724no—
357C2×C4⋊C4—432no—
358C2×C4⋊C4—434no—
359C2×C4⋊C4—862no—
360C2×C22⋊C4—434no—
361C2×C22⋊C4—432no—
362C2×C22⋊C4—434no—
363C2×C22⋊C4—432no—
364C2×C22⋊C4—432no—
365C2×C22⋊C4—862no—
366C2×C22⋊C4—864no—
367C2×C22⋊C4—1724no—
368C2×C22⋊C4C22×D4312yes—
369C2×C22⋊C4C22×D4312yes—
370C2×C42—432no—
371C2×C42—862no—
372#99—44no—
373#99—1724no—
374#95—22no—
375#95—22no—
376#95—864no—
377#95—862no—
378#95—862no—
379C24—431no—
380C24—432no—
381C24—432no—
382C24—431no—
383C24—864no—
384C24—1724no—
385C24C2×C4×D4312yes—
386C24C23×D4311yescharacteristic
387#41—48no—
388#41—48no—
389C2×Q8—22no—
390C2×Q8—42no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—22no—
396C2×D4—42no—
397C2×D4—864no—
398C2×D4—864no—
399C2×D4—1728no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—432no—
407C22×C4—432no—
408C22×C4—431no—
409C22×C4—431no—
410C22×C4—432no—
411C22×C4—432no—
412C22×C4—432no—
413C22×C4—432no—
414C22×C4—432no—
415C22×C4—432no—
416C22×C4—432no—
417C22×C4—432no—
418C22×C4—434no—
419C22×C4—864no—
420C22×C4—862no—
421C22×C4—862no—
422C22×C4—1724no—
423C22×C4—1724no—
424C22×C4—1724no—
425C22×C4—1724no—
426C22×C4—1724no—
427C22×C4—1724no—
428C22×C4—1724no—
429C22×C4—1728no—
430C22×C4C2×C4×D4312yes—
431C22×C4C2×C4×D4311yescharacteristic
432C22×C4C2×C4×D4311yescharacteristic
433C22×C4D4×D4312yes—
434C22×C4D4×D4312yes—
435C4⋊C4—864no—
436C4⋊C4—864no—
437C4⋊C4—862no—
438C4⋊C4—862no—
439C4⋊C4—1724no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—864no—
443C22⋊C4—864no—
444C22⋊C4—864no—
445C22⋊C4—864no—
446C22⋊C4—862no—
447C22⋊C4—862no—
448C22⋊C4—864no—
449C22⋊C4—864no—
450C22⋊C4—1724no—
451C22⋊C4—1728no—
452C42—864no—
453C42—1724no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—42no—
458C23—44no—
459C23—432no—
460C23—432no—
461C23—864no—
462C23—864no—
463C23—864no—
464C23—862no—
465C23—864no—
466C23—862no—
467C23—864no—
468C23—1722no—
469C23—1722no—
470C23—1722no—
471C23—17216no—
472C23C22×C4×D4311yescharacteristic
473C23C2×D4×D4311yescharacteristic
474C23C2×D4×D4311yescharacteristic
475C23#1306337014yes—
476Q8—44no—
477D4—44no—
478D4—44no—
479D4—44no—
480D4—1728no—
481D4—1728no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—48no—
490C2×C4—44no—
491C2×C4—44no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—432no—
495C2×C4—432no—
496C2×C4—864no—
497C2×C4—862no—
498C2×C4—862no—
499C2×C4—864no—
500C2×C4—864no—
501C2×C4—3448no—
502C2×C4—1722no—
503C2×C4—1722no—
504C2×C4—1722no—
505C2×C4—1722no—
506C2×C4—1722no—
507C2×C4—1722no—
508C2×C4—1722no—
509C2×C4—1722no—
510C2×C4—1724no—
511C2×C4—1724no—
512C2×C4—1722no—
513C2×C4—1722no—
514C2×C4—1724no—
515C2×C4C22⋊C4×D4312yes—
516C2×C4C22⋊C4×D4312yes—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—44no—
521C22—44no—
522C22—42no—
523C22—82no—
524C22—82no—
525C22—434no—
526C22—868no—
527C22—862no—
528C22—862no—
529C22—862no—
530C22—862no—
531C22—862no—
532C22—1728no—
533C22—1728no—
534C22—1724no—
535C22C2×C22⋊C4×D4311yescharacteristic
536C22#1458337212yes—
537C22#1458345912yes—
538C22#1458345912yes—
539C4—22no—
540C4—22no—
541C4—42no—
542C4—82no—
543C4—82no—
544C4—862no—
545C4—862no—
546C4—3442no—
547C4—3442no—
548C4—1724no—
549C2—22no—
550C2—22no—
551C2—22no—
552C2—82no—
553C2—864no—
554C2—1722no—
555C2#1913717111yescharacteristic
556C2#410×D4312yes—
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1782C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583406C2
cosocleC24×C43C24
hypercenter#1782D43
hypocenterC43#21748
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. #19136975C2semidirect
3. #381×D43C2semidirect
4. #19135050C2semidirect
5. #19135045C2semidirect
6. #19134670C2semidirect
7. #19134670C2semidirect
8. #19134513C2semidirect
9. C43×#1782C2semidirect
16. C2×#13063301C4semidirect
17. C2×#13063296C4semidirect
19. C2×C4×C22⋊D43C4semidirect
70. C2×C4⋊Dic43C2×C4semidirect
72. C2×Dic43⋊C4C2×C4semidirect
73. C2×C22⋊Dic43C2×C4semidirect
82. C2×C4×Dic43C2×C4semidirect
90. C22×Q8×C43C2×C4semidirect
91. C22×D4×C43C2×C4semidirect
93. C23×C4×C43C2×C4semidirect
279. #1782D43semidirect
316. C43#21748semidirect
321. C22×Q8C4×D43semidirect
323. C22×D4C4×D43semidirect
334. C23×C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834062
#191369752
#381×D432
#191350502
#191350452
#191346702
#191345132
C43×#17822
#2174843