Finite Group Databasebeta

← #25112749

Subgroups — #25112749

Order 11008.

1132 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic
2#19137462C212yesmaximal, complemented
3#19135580C212yesmaximal, complemented
4#19135050C214yesmaximal
5#19134671C212yesmaximal, complemented
6#19134583C211yesmaximal, characteristic
7#19134326C212yesmaximal, complemented
8C4×#99×C43C211yesmaximal, characteristic
9#14583589—24no—
10#14583589—22no—
11#14583589—22no—
12C2×#13063318C412yescomplemented
13C2×#13063317C411yescharacteristic, complemented
14C2×#13063315C412yescomplemented
15C2×#13063306C2212yes—
16C2×#13063304C411yescharacteristic, complemented
17C2×#13063304C2211yescharacteristic
18C2×C4×Dic86C411yescharacteristic, complemented
19C2×#13063284C411yescharacteristic, complemented
20C2×#13063281C2214yes—
21C2×#13063281C2212yes—
22C22×C4⋊Dic43C2211yescharacteristic
23C2×#13063240C2212yes—
24#14582797—22no—
25#14582784—24no—
26#14582760C2214yes—
27#14582759C2212yes—
28C4×C4⋊Dic43—22no—
29#14582666C2212yes—
30#14582665C2214yes—
31#14582665C2214yes—
32C2×C4×D4×C43C2211yescharacteristic
33C2×#99×C43C2212yes—
34C4×C22⋊C4×C43C2212yes—
35C43×#342C2211yescharacteristic
36C43×#342C2211yescharacteristic
37C22×Dic86C2×C411yescharacteristic
38C23×Dic43C2312yes—
39#13063318—24no—
40#13063318—24no—
41#13063317—22no—
42#13063317—22no—
43#13063315—24no—
44#13063315—24no—
45#13063306—24no—
46#13063306—24no—
47#13063304—22no—
48#13063304—22no—
49#13063304—22no—
50#13063304—22no—
51C4×Dic86—22no—
52C4×Dic86—21no—
53C4×Dic86—21no—
54#13063284—22no—
55#13063284—21no—
56#13063284—21no—
57#13063281—24no—
58#13063281—24no—
59#13063281—28no—
60#13063281—44no—
61C2×C4⋊Dic43—22no—
62C2×C4⋊Dic43C2×C411yescharacteristic
63C2×C4⋊Dic43C2×C411yescharacteristic
64C2×C4⋊Dic43C2×C411yescharacteristic
65C2×C4⋊Dic43C2×C412yes—
66C2×C4⋊Dic43D414yes—
67C2×C4⋊Dic43D412yes—
68C2×C4⋊Dic43D412yes—
69C2×Dic43⋊C4—24no—
70C2×Dic43⋊C4C2×C412yes—
71C2×Dic43⋊C4C2×C412yes—
72C2×Dic43⋊C4C2×C412yes—
73C2×Dic43⋊C4C2×C412yes—
74C2×Dic43⋊C4C2×C412yes—
75C2×C22⋊Dic43C2×C412yes—
76C2×C22⋊Dic43C2×C412yes—
77C2×C22⋊Dic43C2314yes—
78C2×C22⋊Dic43C2312yes—
79C2×C4×Dic43—24no—
80C2×C4×Dic43C2×C412yes—
81C2×C4×Dic43C2×C412yes—
82#13063240—42no—
83C43⋊#95—22no—
84C43⋊#95—24no—
85C43⋊#95—24no—
86C22×D4×C43C2311yescharacteristic
87C23×C4×C43C2×C411yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C4×D4×C43—22no—
90C4×D4×C43—22no—
91C2×C4⋊C4×C43C2×C411yescharacteristic
92C2×C22⋊C4×C43C2×C411yescharacteristic
93C2×C22⋊C4×C43C2312yes—
94C2×C22⋊C4×C43C2311yescharacteristic
95C2×C22⋊C4×C43C2312yes—
96C2×C42×C43—22no—
97C2×C42×C43C2×C411yescharacteristic
98#99×C43—24no—
99#95×C43—22no—
100C24×C43C22×C411yescharacteristic
101C24×C43C2411yescharacteristic
102C2×D4×C43—22no—
103C2×D4×C43—22no—
104C2×D4×C43—21no—
105C2×D4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—42no—
111C22×C4×C43—42no—
112C22×C4×C43C22×C411yescharacteristic
113C22×C4×C43C22×C411yescharacteristic
114C22×C4×C43C22×C411yescharacteristic
115C22×C4×C43C22×C411yescharacteristic
116C22×C4×C43C22×C411yescharacteristic
117C22×C4×C43C2×D412yes—
118C22×C4×C43C2×D412yes—
119C22×Dic43—24no—
120C22×Dic43—24no—
121C22×Dic43—22no—
122C22×Dic43—22no—
123C22×Dic43C22×C412yes—
124C22×Dic43C22×C412yes—
125C22×Dic43C22×C412yes—
126C22×Dic43C22×C412yes—
127C22×Dic43C2×D414yes—
128C22×Dic43C2×D414yes—
129C2×Dic86—21no—
130C2×Dic86—21no—
131C2×Dic86—42no—
132C4⋊C4×C43—22no—
133C22⋊C4×C43—22no—
134C22⋊C4×C43—22no—
135C22⋊C4×C43—22no—
136C22⋊C4×C43—22no—
137C22⋊C4×C43—22no—
138C22⋊C4×C43#4114yes—
139C42×C43—21no—
140C42×C43—21no—
141C42×C43—44no—
142C22⋊Dic43—22no—
143C22⋊Dic43—22no—
144C22⋊Dic43—24no—
145C22⋊Dic43—24no—
146C22⋊Dic43—24no—
147C22⋊Dic43—24no—
148C4⋊Dic43—21no—
149C4⋊Dic43—21no—
150C4⋊Dic43—44no—
151C4⋊Dic43C22⋊C412yes—
152C4⋊Dic43C22⋊C411yescharacteristic
153C4⋊Dic43C22⋊C411yescharacteristic
154C4⋊Dic43C22⋊C412yes—
155C4⋊Dic43C22⋊C412yes—
156C4⋊Dic43C22⋊C414yes—
157C4⋊Dic43C22⋊C414yes—
158Dic43⋊C4—24no—
159Dic43⋊C4—24no—
160Dic43⋊C4—24no—
161Dic43⋊C4—22no—
162Dic43⋊C4—22no—
163Dic43⋊C4—24no—
164Dic43⋊C4—48no—
165C4×Dic43—22no—
166C4×Dic43—22no—
167C4×Dic43—22no—
168C4×Dic43—22no—
169C4×Dic43—48no—
170C23×C43—21no—
171C23×C43—21no—
172C23×C43—21no—
173C23×C43—41no—
174C23×C43—41no—
175C23×C43—41no—
176C23×C43—41no—
177C23×C43C23×C411yescharacteristic
178C23×C43C22×D412yes—
179C23×C43C2×#4112yes—
180C23×C43H(5,𝔽2)11yescharacteristic
181C23×C432−1+411yescharacteristic
182D4×C43—42no—
183D4×C43—42no—
184C2×C4×C43—24no—
185C2×C4×C43—22no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—21no—
191C2×C4×C43—24no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43C2×C22⋊C412yes—
204C2×C4×C43C2×C22⋊C411yescharacteristic
205C2×C4×C43C2×C22⋊C411yescharacteristic
206C2×Dic43—22no—
207C2×Dic43—22no—
208C2×Dic43—22no—
209C2×Dic43—22no—
210C2×Dic43—24no—
211C2×Dic43—24no—
212C2×Dic43—24no—
213C2×Dic43—24no—
214C2×Dic43—22no—
215C2×Dic43—22no—
216C2×Dic43—42no—
217C2×Dic43—42no—
218C2×Dic43—44no—
219C2×Dic43—44no—
220C2×Dic43—44no—
221C2×Dic43C2×C22⋊C412yes—
222C2×Dic43C2×C22⋊C412yes—
223C2×Dic43C2×C22⋊C414yes—
224Dic86—42no—
225Dic86—42no—
226#22478—431nomaximal, Sylow
227C22×C43—21no—
228C22×C43—22no—
229C22×C43—21no—
230C22×C43—22no—
231C22×C43—42no—
232C22×C43—41no—
233C22×C43—41no—
234C22×C43—41no—
235C22×C43—41no—
236C22×C43—41no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43C22×C22⋊C411yescharacteristic
240C22×C43C4×#4111yescharacteristic
241C22×C43#52011yescharacteristic
242C22×C43#54612yes—
243C22×C43#54712yes—
244C4×C43—21no—
245C4×C43—22no—
246C4×C43—44no—
247C4×C43—41no—
248C4×C43—41no—
249C4×C43—41no—
250C4×C43—82no—
251C4×C43#41012yes—
252Dic43—22no—
253Dic43—24no—
254Dic43—22no—
255Dic43—42no—
256Dic43—42no—
257Dic43—84no—
258C2×#552—431no—
259#2344—432no—
260#1996—432no—
261#1899—434no—
262#1820—432no—
263#1799—431no—
264C4×#99D4311yescharacteristic
265#1740—432no—
266C2×C43—22no—
267C2×C43—22no—
268C2×C43—21no—
269C2×C43—21no—
270C2×C43—81no—
271C2×C43#233911yescharacteristic
272C2×C43C2×#41011yescharacteristic
273C2×C43#288411yescharacteristic
274#552—862no—
275#552—864no—
276#552—862no—
277C2×#126—432no—
278C2×#125—432no—
279C2×#125—431no—
280C2×#123—432no—
281C2×C22⋊Q8—431no—
282C2×C22⋊Q8—431no—
283C2×C4×Q8—431no—
284C2×C4×D4C2×D4311yescharacteristic
285C2×#117—431no—
286C2×#117—432no—
287C2×#117—434no—
288C22×C4⋊C4—431no—
289C2×#99—432no—
290C2×#99C2×D4312yes—
291#389—862no—
292#387—864no—
293#381—434no—
294#380—432no—
295C4×C4⋊C4—862no—
296C4×C22⋊C4C2×D4312yes—
297#342—432no—
298#342—434no—
299#342—434no—
300#342C2×D4311yescharacteristic
301#342C2×D4311yescharacteristic
302C43#2247811yescharacteristic, complemented, Sylow
303C22×Q8—431no—
304C22×D4C22×D4311yescharacteristic
305C23×C4—432no—
306C23×C4C4×D4311yescharacteristic
307C23×C4C22×D4311yescharacteristic
308#126—864no—
309#126—864no—
310#125—862no—
311#125—862no—
312#125—864no—
313#125—864no—
314#123—864no—
315#123—864no—
316C22⋊Q8—862no—
317C22⋊Q8—862no—
318C22⋊Q8—862no—
319C22⋊Q8—862no—
320C4×Q8—862no—
321C4×Q8—861no—
322C4×Q8—861no—
323C4×D4—22no—
324C4×D4—22no—
325#117—864no—
326#117—864no—
327#117—862no—
328#117—861no—
329#117—861no—
330#117—868no—
331#117—1724no—
332C2×C4⋊C4—431no—
333C2×C4⋊C4—431no—
334C2×C4⋊C4—432no—
335C2×C4⋊C4—432no—
336C2×C4⋊C4—434no—
337C2×C4⋊C4—432no—
338C2×C4⋊C4—432no—
339C2×C4⋊C4—431no—
340C2×C4⋊C4—432no—
341C2×C4⋊C4—432no—
342C2×C4⋊C4—432no—
343C2×C4⋊C4—432no—
344C2×C4⋊C4—864no—
345C2×C4⋊C4—862no—
346C2×C4⋊C4C4×D4311yescharacteristic
347C2×C22⋊C4—432no—
348C2×C22⋊C4—432no—
349C2×C22⋊C4—432no—
350C2×C22⋊C4—434no—
351C2×C22⋊C4C4×D4311yescharacteristic
352C2×C22⋊C4C22×D4312yes—
353C2×C22⋊C4C22×D4311yescharacteristic
354C2×C22⋊C4C22×D4312yes—
355C2×C42—22no—
356C2×C42—432no—
357C2×C42—432no—
358C2×C42—864no—
359C2×C42C4×D4311yescharacteristic
360#99—24no—
361#99—1722no—
362#95—22no—
363#95—864no—
364#95—864no—
365#95—862no—
366C24C2×C4×D4311yescharacteristic
367C24C23×D4311yescharacteristic
368C2×Q8—861no—
369C2×Q8—861no—
370C2×Q8—1722no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—21no—
374C2×D4—21no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—432no—
382C22×C4—432no—
383C22×C4—434no—
384C22×C4—434no—
385C22×C4—432no—
386C22×C4—432no—
387C22×C4—864no—
388C22×C4—862no—
389C22×C4—862no—
390C22×C4—864no—
391C22×C4C2×C4×D4311yescharacteristic
392C22×C4C2×C4×D4311yescharacteristic
393C22×C4C2×C4×D4311yescharacteristic
394C22×C4C2×C4×D4311yescharacteristic
395C22×C4C2×C4×D4311yescharacteristic
396C22×C4D4×D4312yes—
397C22×C4D4×D4312yes—
398C4⋊C4—22no—
399C4⋊C4—432no—
400C4⋊C4—431no—
401C4⋊C4—431no—
402C4⋊C4—432no—
403C4⋊C4—432no—
404C4⋊C4—434no—
405C4⋊C4—434no—
406C4⋊C4—864no—
407C4⋊C4—864no—
408C4⋊C4—862no—
409C4⋊C4—862no—
410C4⋊C4—864no—
411C4⋊C4—861no—
412C4⋊C4—861no—
413C4⋊C4—864no—
414C4⋊C4—1728no—
415C4⋊C4—1724no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—862no—
422C22⋊C4—862no—
423C22⋊C4—864no—
424C22⋊C4—864no—
425C22⋊C4—864no—
426C22⋊C4—864no—
427C22⋊C4#1062189814yes—
428C42—21no—
429C42—21no—
430C42—44no—
431C42—862no—
432C42—862no—
433C42—862no—
434C42—862no—
435C42—1728no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23C22×C4×D4311yescharacteristic
444C23C2×D4×D4312yes—
445C23C2×#1062189812yes—
446C23#1306337111yescharacteristic
447C23#1306337211yescharacteristic
448Q8—1722no—
449Q8—1722no—
450D4—42no—
451D4—42no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—24no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—432no—
472C2×C4—432no—
473C2×C4—434no—
474C2×C4—864no—
475C2×C4—864no—
476C2×C4—862no—
477C2×C4—862no—
478C2×C4—862no—
479C2×C4—862no—
480C2×C4—864no—
481C2×C4—864no—
482C2×C4—862no—
483C2×C4—862no—
484C2×C4—1724no—
485C2×C4—1724no—
486C2×C4—1724no—
487C2×C4—1722no—
488C2×C4—1722no—
489C2×C4C22⋊C4×D4311yescharacteristic
490C2×C4C22⋊C4×D4312yes—
491C2×C4C22⋊C4×D4311yescharacteristic
492C22—22no—
493C22—21no—
494C22—22no—
495C22—21no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—81no—
503C22—81no—
504C22C2×C22⋊C4×D4311yescharacteristic
505C22C4×#1062189811yescharacteristic
506C22#1458337911yescharacteristic
507C22#1458354512yes—
508C22#1458355412yes—
509C4—21no—
510C4—22no—
511C4—44no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—82no—
516C4—862no—
517C4—862no—
518C4—864no—
519C4—3444no—
520C4—1722no—
521C4—1722no—
522C4#1458287112yes—
523C2—22no—
524C2—22no—
525C2—21no—
526C2—21no—
527C2—81no—
528C2#1913742611yescharacteristic
529C2C2×#1458287111yescharacteristic
530C2#1914305711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC4×#99×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC22×D4×C43C23
cosocleC24×C43C24
hypercenterC4×#99D43
hypocenterC43#22478
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #19137462C2semidirect
3. #19135580C2semidirect
5. #19134671C2semidirect
7. #19134326C2semidirect
12. C2×#13063318C4semidirect
13. C2×#13063317C4semidirect
14. C2×#13063315C4semidirect
16. C2×#13063304C4semidirect
18. C2×C4×Dic86C4semidirect
19. C2×#13063284C4semidirect
302. C43#22478semidirect

Maximal subgroups

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

subgroupindex
C2×#145835892
#191374622
#191355802
#191350502
#191346712
#191345832
#191343262
C4×#99×C432
#2247843