Finite Group Databasebeta

← #25254377

Subgroups — #25254377

Order 11008.

480 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147608C211yesmaximal, characteristic
2#19147487C211yesmaximal, characteristic, complemented
3#19136837C211yesmaximal, characteristic
4#19136832C211yesmaximal, characteristic, complemented
5#19136827C211yesmaximal, characteristic, complemented
6#19136760C211yesmaximal, characteristic, complemented
7#19136753C211yesmaximal, characteristic, complemented
8#19136743C211yesmaximal, characteristic, complemented
9#19136658C211yesmaximal, characteristic, complemented
10#19136658C211yesmaximal, characteristic, complemented
11#19136636C211yesmaximal, characteristic
12#19136467C211yesmaximal, characteristic, complemented
13#19136461C211yesmaximal, characteristic, complemented
14C4×#13063270C211yesmaximal, characteristic, complemented
15C43×#2183C211yesmaximal, characteristic, complemented
16#14583634—21no—
17#14583627—21no—
18C2×Dic344C2211yescharacteristic
19C2×#13063270C2211yescharacteristic
20C2×#13063270C2211yescharacteristic
21#14583304C2211yescharacteristic
22#14583301C2211yescharacteristic
23#14583301C2211yescharacteristic
24#14583283C2211yescharacteristic
25#14583283C2211yescharacteristic
26#14583276C2211yescharacteristic
27#14583207—21no—
28#14583207—21no—
29#14583185—21no—
30#14583115—21no—
31#14583115—21no—
32#14583100—21no—
33C4×Dic172C2211yescharacteristic
34C4×Dic172C2211yescharacteristic
35C4×Dic172C2211yescharacteristic
36C4×Dic172C2211yescharacteristic
37C4×D344C2211yescharacteristic
38C4×D344C2211yescharacteristic
39#14582727C2211yescharacteristic
40#14582727C2211yescharacteristic
41#14582725C2211yescharacteristic
42#14582704C2211yescharacteristic
43#14582704C2211yescharacteristic
44#14582704C2211yescharacteristic
45#14582704C2211yescharacteristic
46#14582701C2211yescharacteristic
47#14582701C2211yescharacteristic
48#14582701C2211yescharacteristic
49#14582701C2211yescharacteristic
50#14582701C2211yescharacteristic
51#14582701C2211yescharacteristic
52C8×Q8×C43C2211yescharacteristic
53C43×C4⋊C16C2211yescharacteristic
54C43×C4⋊C16C2211yescharacteristic
55C43×C4⋊C16C2211yescharacteristic
56C43×#346C2211yescharacteristic
57C43×#346C2211yescharacteristic
58C4×C16×C43C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×Dic172C2311yescharacteristic
61C2×#10621873—21no—
62C2×#10621873—21no—
63C2×D344—21no—
64C2×D344C2311yescharacteristic
65C2×D344C2311yescharacteristic
66#13063325—21no—
67#13063323—41no—
68#13063322—21no—
69#13063317—21no—
70#13063317—21no—
71#13063315—41no—
72#13063315—41no—
73#13063314—41no—
74#13063313—21no—
75#13063313—21no—
76#13063310—41no—
77#13063310—41no—
78C4×Dic86—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82#13063290—41no—
83C4×D172—21no—
84C4×D172—21no—
85#13063287—41no—
86Dic344—22no—
87#13063270—22no—
88#13063270—22no—
89#13063259—21no—
90#13063259C2311yescharacteristic
91#13063259C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063259C2311yescharacteristic
94#13063257—21no—
95#13063257—21no—
96#13063250—21no—
97#13063250—21no—
98#13063250—21no—
99#13063250—21no—
100#13063247—21no—
101#13063247—21no—
102C4×Q8×C43D411yescharacteristic
103C2×C16×C43C2311yescharacteristic
104C2×C16×C43C2311yescharacteristic
105C2×C16×C43C2311yescharacteristic
106C2×C16×C43C2311yescharacteristic
107C4⋊C8×C43D411yescharacteristic
108C4⋊C8×C43D411yescharacteristic
109C4⋊C8×C43D411yescharacteristic
110C4×C8×C43C2311yescharacteristic
111C4×C8×C43C2311yescharacteristic
112C4×C8×C43C2311yescharacteristic
113C2×Q8×C43D811yescharacteristic
114C2×D172—21no—
115C2×D172—21no—
116C2×D172—41no—
117C2×D172—41no—
118C2×C4×D43—41no—
119C2×C4×D43—41no—
120C2×Dic86—21no—
121C2×Dic86—21no—
122C2×Dic86—41no—
123C2×C8×C43C2×D411yescharacteristic
124C2×C8×C43C2×D411yescharacteristic
125C2×C8×C43C2×D411yescharacteristic
126C2×C8×C43C2411yescharacteristic
127C4⋊C4×C43D811yescharacteristic
128C4⋊C4×C43D811yescharacteristic
129C4⋊C4×C43D811yescharacteristic
130C42×C43C2×D411yescharacteristic
131C42×C43C2×D411yescharacteristic
132C42×C43C2×D411yescharacteristic
133(C2×D43)⋊C4—41no—
134(C2×D43)⋊C4—41no—
135(C2×D43)⋊C4—41no—
136(C2×D43)⋊C4—41no—
137(C2×D43)⋊C4—41no—
138(C2×D43)⋊C4—41no—
139C4⋊Dic43—21no—
140C4⋊Dic43—21no—
141C4⋊Dic43—21no—
142C4⋊Dic43—21no—
143C4⋊Dic43—41no—
144Dic43⋊C4—41no—
145Dic43⋊C4—41no—
146Dic43⋊C4—41no—
147Dic43⋊C4—41no—
148Dic43⋊C4—41no—
149Dic43⋊C4—41no—
150Dic43⋊C4—41no—
151Dic43⋊C4—41no—
152C4×Dic43—41no—
153C4×Dic43—41no—
154C4×Dic43—41no—
155C4×Dic43—41no—
156Dic172—21no—
157Dic172—21no—
158Dic172—21no—
159Dic172#4112yes—
160D344—21no—
161D344—21no—
162D344—21no—
163D344—21no—
164D344—81no—
165#10621873—81no—
166#10621873—81no—
167C16×C43—21no—
168C16×C43—21no—
169C16×C43—21no—
170C16×C43—21no—
171C22×D43—41no—
172C22×D43—41no—
173Q8×C43—41no—
174C2×C4×C43C2×D811yescharacteristic
175C2×C4×C43C2×D811yescharacteristic
176C2×C4×C43C2×D811yescharacteristic
177C2×C4×C43C2×D811yescharacteristic
178C2×C4×C43C2×D811yescharacteristic
179C2×C4×C43C2×D811yescharacteristic
180C2×C4×C43C22×D411yescharacteristic
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187D172—41no—
188D172—41no—
189D172—41no—
190D172—41no—
191D172—82no—
192D172—161no—
193C4×D43—161no—
194C4×D43—161no—
195Dic86—22no—
196Dic86—41no—
197Dic86—41no—
198Dic86—41no—
199Dic86—82no—
200C8×C43—21no—
201C8×C43—21no—
202C8×C43—21no—
203C8×C43C2×#4111yescharacteristic
204C8×C432−1+411yescharacteristic
205#33938—431nomaximal, Sylow
206C22×C43C22×D811yescharacteristic
207C2×D43—81no—
208C2×D43—81no—
209C2×D43—81no—
210C2×D43—81no—
211C2×D43—81no—
212C2×D43—81no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43#54811yescharacteristic
220C4×C43#57711yescharacteristic
221Dic43—42no—
222Dic43—81no—
223Dic43—81no—
224Dic43—81no—
225Dic43—81no—
226Dic43—81no—
227#3396—431no—
228#3383—431no—
229#2244—431no—
230#2243—431no—
231#2242—431no—
232#2229—431no—
233#2228—431no—
234#2226—431no—
235#2211—431no—
236#2211—431no—
237#2207—431no—
238#2183D4311yescharacteristic, complemented
239#2176—431no—
240#2175—431no—
241C4×SD32—431no—
242C2×C43#335811yescharacteristic
243C2×C43#341411yescharacteristic
244C2×C43#341611yescharacteristic
245D43—161no—
246D43—161no—
247#559—861no—
248#557—861no—
249C2×Q32—431no—
250C2×SD32—431no—
251C2×SD32—431no—
252#500—431no—
253#499—431no—
254#499—431no—
255#495—431no—
256#495—431no—
257#493—431no—
258#479—861no—
259#479—861no—
260#475—861no—
261#463—861no—
262#463—861no—
263#460—861no—
264C8×Q8C2×D4311yescharacteristic
265C4×Q16—431no—
266C4×Q16—431no—
267C4×Q16—431no—
268C4×Q16—431no—
269C4×D8—431no—
270C4×D8—431no—
271#367—431no—
272#367—431no—
273#366—431no—
274C4⋊C16C2×D4311yescharacteristic
275C4⋊C16C2×D4311yescharacteristic
276C4⋊C16C2×D4311yescharacteristic
277#358—431no—
278#358—431no—
279#358—431no—
280#358—431no—
281#357—431no—
282#357—431no—
283#357—431no—
284#357—431no—
285#357—431no—
286#357—431no—
287#346C2×D4311yescharacteristic
288#346C2×D4311yescharacteristic
289C4×C16C2×D4311yescharacteristic
290C43#3393811yescharacteristic, complemented, Sylow
291C2×Q16—431no—
292C2×Q16—431no—
293C2×SD16—861no—
294C2×SD16—861no—
295C2×D8—431no—
296C2×D8—431no—
297C2×D8—861no—
298C4⋊Q8—861no—
299C4⋊Q8—1721no—
300#127—861no—
301#125—861no—
302#125—861no—
303#125—1721no—
304#125—1721no—
305#124—861no—
306#124—861no—
307#124—1721no—
308#123—1721no—
309#123—1721no—
310C4×Q8—861no—
311C4×Q8—861no—
312C4×Q8—861no—
313C4×Q8—861no—
314C4×Q8—1721no—
315C4×Q8D17211yescharacteristic
316C4×D4—861no—
317C4×D4—861no—
318C4×D4—1721no—
319Q32—862no—
320SD32—862no—
321SD32—862no—
322C2×C16C22×D4311yescharacteristic
323C2×C16C22×D4311yescharacteristic
324C2×C16C22×D4311yescharacteristic
325C2×C16C22×D4311yescharacteristic
326#107—431no—
327#107—431no—
328#107—431no—
329#107—431no—
330#107—861no—
331#106—861no—
332#106—861no—
333C4⋊C8D17211yescharacteristic
334C4⋊C8D17211yescharacteristic
335C4⋊C8D17211yescharacteristic
336#103—861no—
337#103—861no—
338#103—861no—
339#103—861no—
340#102—861no—
341#102—861no—
342C4×C8C22×D4311yescharacteristic
343C4×C8C22×D4311yescharacteristic
344C4×C8C22×D4311yescharacteristic
345C2×Q8—861no—
346C2×Q8—861no—
347C2×Q8—1721no—
348C2×Q8D34411yescharacteristic
349C2×D4—861no—
350C2×D4—861no—
351C2×D4—1721no—
352C2×D4—1721no—
353C22×C4—1721no—
354C22×C4—1721no—
355Q16—432no—
356Q16—861no—
357Q16—861no—
358Q16—861no—
359SD16—3441no—
360SD16—3441no—
361D8—861no—
362D8—861no—
363D8—861no—
364D8—861no—
365D8—3441no—
366C2×C8C2×D17211yescharacteristic
367C2×C8C2×D17211yescharacteristic
368C2×C8C2×D17211yescharacteristic
369C2×C8C23×D4311yescharacteristic
370C4⋊C4—861no—
371C4⋊C4—861no—
372C4⋊C4—861no—
373C4⋊C4—861no—
374C4⋊C4—1721no—
375C4⋊C4—1721no—
376C4⋊C4—1721no—
377C4⋊C4—1721no—
378C4⋊C4—1721no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C4⋊C4D34411yescharacteristic
384C4⋊C4D34411yescharacteristic
385C4⋊C4D34411yescharacteristic
386C22⋊C4—1721no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C42—1721no—
393C42—1721no—
394C42—1721no—
395C42—1721no—
396C42C2×D17211yescharacteristic
397C42C2×D17211yescharacteristic
398C42C2×D17211yescharacteristic
399C16—21no—
400C16—21no—
401C16—21no—
402C16—21no—
403C23—1721no—
404C23—1721no—
405Q8—41no—
406Q8—862no—
407Q8—3442no—
408Q8—1721no—
409Q8—1721no—
410Q8—1721no—
411D4—3442no—
412D4—1721no—
413D4—1721no—
414D4—1721no—
415D4—1721no—
416D4—6881no—
417C2×C4—1721no—
418C2×C4—1721no—
419C2×C4—1721no—
420C2×C4—1721no—
421C2×C4—1721no—
422C2×C4—1721no—
423C2×C4—6881no—
424C2×C4—6881no—
425C2×C4C2×D34411yescharacteristic
426C2×C4C2×D34411yescharacteristic
427C2×C4C2×D34411yescharacteristic
428C2×C4C2×D34411yescharacteristic
429C2×C4C2×D34411yescharacteristic
430C2×C4C2×D34411yescharacteristic
431C2×C4C22×D17211yescharacteristic
432C8—21no—
433C8—21no—
434C8—21no—
435C8#41×D4311yescharacteristic
436C8#1306337311yescharacteristic
437C22—3441no—
438C22—3441no—
439C22—3441no—
440C22—3441no—
441C22—3441no—
442C22—3441no—
443C22C22×D34411yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—3441no—
451C4—3441no—
452C4—3441no—
453C4—3441no—
454C4—3441no—
455C4—1722no—
456C4#1458356111yescharacteristic
457C4#1458371111yescharacteristic
458C2—6881no—
459C2—6881no—
460C2#1914723111yescharacteristic
461C2#1914773111yescharacteristic
462C2#1914774311yescharacteristic
subgroupG/H
centerC22C22×D344
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2183C2
socleC22×C43C22×D8
prime radical#14583276C22
hypercenter#2183D43
hypocenterC43#33938
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #2183

Complements

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

NH ≅ G/Ntype
2. #19147487C2semidirect
4. #19136832C2semidirect
5. #19136827C2semidirect
6. #19136760C2semidirect
7. #19136753C2semidirect
8. #19136743C2semidirect
9. #19136658C2semidirect
10. #19136658C2semidirect
12. #19136467C2semidirect
13. #19136461C2semidirect
14. C4×#13063270C2semidirect
15. C43×#2183C2semidirect
238. #2183D43semidirect
290. C43#33938semidirect

Maximal subgroups

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

subgroupindex
#191476082
#191474872
#191368372
#191368322
#191368272
#191367602
#191367532
#191367432
#191366582
#191366362
#191364672
#191364612
C4×#130632702
C43×#21832
#3393843