Finite Group Databasebeta

← #25254360

Subgroups — #25254360

Order 11008.

494 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147608C211yesmaximal, characteristic, complemented
2#19136838C211yesmaximal, characteristic, complemented
3#19136834C211yesmaximal, characteristic, complemented
4#19136829C211yesmaximal, characteristic, complemented
5#19136756C211yesmaximal, characteristic, complemented
6#19136749C211yesmaximal, characteristic, complemented
7#19136729C211yesmaximal, characteristic, complemented
8#19136650C211yesmaximal, characteristic, complemented
9#19136650C211yesmaximal, characteristic, complemented
10#19136630C211yesmaximal, characteristic
11#19136504C211yesmaximal, characteristic, complemented
12#19136469C211yesmaximal, characteristic, complemented
13#19136459C211yesmaximal, characteristic, complemented
14C4×#13063266C211yesmaximal, characteristic, complemented
15C43×#3380C211yesmaximal, characteristic, complemented
16#14583634—21no—
17C2×#13063269C2211yescharacteristic
18C2×#13063266C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20#14583283C2211yescharacteristic
21#14583283C2211yescharacteristic
22#14583276C2211yescharacteristic
23#14583115—21no—
24#14583115—21no—
25#14583100—21no—
26C4×Dic172C2211yescharacteristic
27C4×D344C2211yescharacteristic
28C4×D344C2211yescharacteristic
29#14582726C2211yescharacteristic
30#14582724C2211yescharacteristic
31#14582724C2211yescharacteristic
32C4⋊(C43⋊C16)C2211yescharacteristic
33C4⋊(C43⋊C16)C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35#14582702C2211yescharacteristic
36#14582702C2211yescharacteristic
37#14582702C2211yescharacteristic
38#14582700C2211yescharacteristic
39#14582699C2211yescharacteristic
40#14582699C2211yescharacteristic
41#14582699C2211yescharacteristic
42#14582699C2211yescharacteristic
43#14582699C2211yescharacteristic
44#14582699C2211yescharacteristic
45#14582675C2211yescharacteristic
46#14582675C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C43×#554—21no—
49C43×#500C2211yescharacteristic
50C43×#499C2211yescharacteristic
51C43×#499C2211yescharacteristic
52C43×#478—21no—
53C43×#478—21no—
54C43×#476—21no—
55C8×Q8×C43C2211yescharacteristic
56C4×D8×C43C2211yescharacteristic
57C4×D8×C43C2211yescharacteristic
58C4×D8×C43C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621873—21no—
61C2×#10621873—21no—
62C2×D344—21no—
63C2×D344C2311yescharacteristic
64C2×D344C2311yescharacteristic
65#13063322—21no—
66#13063314—41no—
67#13063313—21no—
68#13063313—21no—
69#13063310—41no—
70#13063310—41no—
71C4×Dic86—21no—
72C4×D172—21no—
73C4×D172—21no—
74#13063287—41no—
75#13063269—22no—
76#13063266—22no—
77#13063266—22no—
78C2×C43⋊C16C2311yescharacteristic
79C2×C43⋊C16C2311yescharacteristic
80C2×C43⋊C16C2311yescharacteristic
81C2×C43⋊C16C2311yescharacteristic
82#13063259C2311yescharacteristic
83#13063250—21no—
84#13063247—21no—
85#13063247—21no—
86C2×D8×C43C2311yescharacteristic
87C4⋊Q8×C43—21no—
88#125×C43—21no—
89#125×C43—21no—
90C22⋊Q8×C43—41no—
91C22⋊Q8×C43—41no—
92C22⋊Q8×C43—41no—
93C4×Q8×C43D411yescharacteristic
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C2×C4⋊C4×C43—41no—
98#107×C43—21no—
99#107×C43C2311yescharacteristic
100#107×C43C2311yescharacteristic
101#107×C43C2311yescharacteristic
102#106×C43—21no—
103#106×C43—21no—
104C4⋊C8×C43D411yescharacteristic
105C4⋊C8×C43D411yescharacteristic
106C4⋊C8×C43D411yescharacteristic
107#102×C43—21no—
108#102×C43—21no—
109#102×C43—21no—
110C4×C8×C43C2311yescharacteristic
111C4×C8×C43C2311yescharacteristic
112C4×C8×C43C2311yescharacteristic
113C2×Q8×C43—41no—
114C2×Q8×C43D811yescharacteristic
115C2×D4×C43—21no—
116C22×C4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C2×D172—21no—
120C2×D172—21no—
121C2×D172—41no—
122C2×D172—41no—
123C2×C4×D43—41no—
124C2×C4×D43—41no—
125C2×Dic86—21no—
126D8×C43—21no—
127D8×C43#4112yes—
128C2×C8×C43C2×D411yescharacteristic
129C2×C8×C43C2×D411yescharacteristic
130C2×C8×C43C2×D411yescharacteristic
131C2×C8×C43C2411yescharacteristic
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—41no—
136C4⋊C4×C43—41no—
137C4⋊C4×C43—41no—
138C4⋊C4×C43—41no—
139C4⋊C4×C43—41no—
140C4⋊C4×C43D811yescharacteristic
141C4⋊C4×C43D811yescharacteristic
142C4⋊C4×C43D811yescharacteristic
143C22⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43C2×D411yescharacteristic
149(C2×D43)⋊C4—41no—
150(C2×D43)⋊C4—41no—
151(C2×D43)⋊C4—41no—
152(C2×D43)⋊C4—41no—
153(C2×D43)⋊C4—41no—
154(C2×D43)⋊C4—41no—
155C4⋊Dic43—21no—
156Dic43⋊C4—41no—
157C4×Dic43—41no—
158Dic172—21no—
159Dic172—21no—
160D344—21no—
161D344—21no—
162D344—21no—
163D344—21no—
164D344—81no—
165#10621873—81no—
166#10621873—81no—
167C43⋊C16—21no—
168C43⋊C16—21no—
169C43⋊C16—21no—
170C43⋊C16—21no—
171C23×C43—41no—
172C22×D43—41no—
173C22×D43—41no—
174Q8×C43—41no—
175Q8×C43—161no—
176D4×C43—22no—
177D4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—82no—
182C2×C4×C43—161no—
183C2×C4×C43—161no—
184C2×C4×C43C2×D811yescharacteristic
185C2×C4×C43C2×D811yescharacteristic
186C2×C4×C43C2×D811yescharacteristic
187C2×C4×C43C2×D811yescharacteristic
188C2×C4×C43C2×D811yescharacteristic
189C2×C4×C43C2×D811yescharacteristic
190C2×C4×C43C22×D411yescharacteristic
191C2×Dic43—41no—
192C2×Dic43—41no—
193D172—41no—
194D172—41no—
195D172—41no—
196D172—41no—
197D172—82no—
198D172—161no—
199C4×D43—161no—
200C4×D43—161no—
201Dic86—41no—
202Dic86—41no—
203C8×C43—21no—
204C8×C43—21no—
205C8×C43—21no—
206C8×C43C2×#4111yescharacteristic
207C8×C432−1+411yescharacteristic
208#33937—431nomaximal, Sylow
209C22×C43—42no—
210C22×C43—81no—
211C22×C43—81no—
212C22×C43C22×D811yescharacteristic
213C2×D43—81no—
214C2×D43—81no—
215C2×D43—81no—
216C2×D43—81no—
217C2×D43—81no—
218C2×D43—81no—
219C4×C43—21no—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—81no—
226C4×C43—81no—
227C4×C43—81no—
228C4×C43#54811yescharacteristic
229C4×C43#57711yescharacteristic
230Dic43—81no—
231Dic43—81no—
232#3396—431no—
233#3380D4311yescharacteristic, complemented
234#2244—431no—
235#2243—431no—
236#2242—431no—
237#2229—431no—
238#2228—431no—
239#2224—431no—
240#2210—431no—
241#2210—431no—
242#2206—431no—
243#2183—431no—
244#2177—431no—
245#2175—431no—
246C4×D16—431no—
247C2×C43—82no—
248C2×C43#335811yescharacteristic
249C2×C43#341411yescharacteristic
250C2×C43#341511yescharacteristic
251D43—161no—
252D43—161no—
253#559—861no—
254#554—21no—
255C2×SD32—431no—
256C2×D16—431no—
257C2×D16—431no—
258#500C2×D4311yescharacteristic
259#499C2×D4311yescharacteristic
260#499C2×D4311yescharacteristic
261#495—431no—
262#495—431no—
263#493—431no—
264#478—21no—
265#478—21no—
266#476—21no—
267#463—861no—
268#463—861no—
269#460—861no—
270C8×Q8C2×D4311yescharacteristic
271C4×Q16—431no—
272C4×D8—431no—
273C4×D8—431no—
274C4×D8C2×D4311yescharacteristic
275C4×D8C2×D4311yescharacteristic
276C4×D8C2×D4311yescharacteristic
277#367—431no—
278#366—431no—
279#366—431no—
280C4⋊C16—431no—
281C4⋊C16—431no—
282C4⋊C16—431no—
283#358—431no—
284#358—431no—
285#358—431no—
286#357—431no—
287#357—431no—
288#357—431no—
289#357—431no—
290#357—431no—
291#357—431no—
292#357—431no—
293#346—431no—
294#346—431no—
295C4×C16—431no—
296C43#3393711yescharacteristic, complemented, Sylow
297C2×Q16—431no—
298C2×SD16—861no—
299C2×SD16—861no—
300C2×D8—431no—
301C2×D8—431no—
302C2×D8—861no—
303C2×D8C22×D4311yescharacteristic
304C4⋊Q8—21no—
305#127—861no—
306#125—21no—
307#125—21no—
308#124—861no—
309#124—861no—
310#124—1721no—
311#123—1721no—
312#123—1721no—
313C22⋊Q8—41no—
314C22⋊Q8—41no—
315C22⋊Q8—41no—
316C4×Q8—861no—
317C4×Q8C22⋊D4311yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—861no—
322C4×D4—861no—
323C4×D4—1721no—
324C2×C4⋊C4—41no—
325SD32—862no—
326D16—862no—
327D16—862no—
328C2×C16—431no—
329C2×C16—431no—
330C2×C16—431no—
331C2×C16—431no—
332#107—21no—
333#107—431no—
334#107C22×D4311yescharacteristic
335#107C22×D4311yescharacteristic
336#107C22×D4311yescharacteristic
337#106—21no—
338#106—21no—
339C4⋊C8C22⋊D4311yescharacteristic
340C4⋊C8C22⋊D4311yescharacteristic
341C4⋊C8C22⋊D4311yescharacteristic
342#103—861no—
343#102—21no—
344#102—21no—
345#102—21no—
346#102—861no—
347#102—861no—
348C4×C8C22×D4311yescharacteristic
349C4×C8C22×D4311yescharacteristic
350C4×C8C22×D4311yescharacteristic
351C2×Q8—41no—
352C2×Q8—861no—
353C2×Q8#1062188211yescharacteristic
354C2×D4—21no—
355C2×D4—861no—
356C2×D4—861no—
357C2×D4—1721no—
358C2×D4—1721no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—1721no—
363C22×C4—1721no—
364Q16—861no—
365Q16—861no—
366SD16—3441no—
367SD16—3441no—
368D8—21no—
369D8—861no—
370D8—861no—
371D8—861no—
372D8—861no—
373D8—3441no—
374D8#1062190212yes—
375C2×C8C2×C22⋊D4311yescharacteristic
376C2×C8C2×C22⋊D4311yescharacteristic
377C2×C8C2×C22⋊D4311yescharacteristic
378C2×C8C23×D4311yescharacteristic
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—861no—
388C4⋊C4—1721no—
389C4⋊C4#1062188211yescharacteristic
390C4⋊C4#1062188211yescharacteristic
391C4⋊C4#1062188211yescharacteristic
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—1721no—
396C22⋊C4—1721no—
397C22⋊C4—1721no—
398C22⋊C4—1721no—
399C22⋊C4—1721no—
400C22⋊C4—1721no—
401C42—1721no—
402C42C2×C22⋊D4311yescharacteristic
403C42C2×C22⋊D4311yescharacteristic
404C42C2×C22⋊D4311yescharacteristic
405C16—861no—
406C16—861no—
407C16—861no—
408C16—861no—
409C23—41no—
410C23—1721no—
411C23—1721no—
412Q8—41no—
413Q8—161no—
414Q8—1721no—
415Q8—1721no—
416D4—22no—
417D4—41no—
418D4—3442no—
419D4—1721no—
420D4—1721no—
421D4—1721no—
422D4—1721no—
423D4—6881no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—82no—
428C2×C4—161no—
429C2×C4—161no—
430C2×C4—1721no—
431C2×C4—1721no—
432C2×C4—6881no—
433C2×C4—6881no—
434C2×C4C2×#1062188211yescharacteristic
435C2×C4C2×#1062188211yescharacteristic
436C2×C4C2×#1062188211yescharacteristic
437C2×C4C2×#1062188211yescharacteristic
438C2×C4C2×#1062188211yescharacteristic
439C2×C4C2×#1062188211yescharacteristic
440C2×C4C22×C22⋊D4311yescharacteristic
441C8—21no—
442C8—21no—
443C8—21no—
444C8C2×#1062190211yescharacteristic
445C8#1306337311yescharacteristic
446C22—42no—
447C22—81no—
448C22—81no—
449C22—3441no—
450C22—3441no—
451C22—3441no—
452C22—3441no—
453C22—3441no—
454C22—3441no—
455C22C22×#1062188211yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—3441no—
466C4—3441no—
467C4#1458356011yescharacteristic
468C4#1458370711yescharacteristic
469C2—82no—
470C2—6881no—
471C2—6881no—
472C2#1914723011yescharacteristic
473C2#1914772911yescharacteristic
474C2#1914773411yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3380C2
socleC22×C43C22×D8
prime radical#19136630C2
hypercenter#3380D43
hypocenterC43#33937
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3380

Complements

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

NH ≅ G/Ntype
1. #19147608C2semidirect
2. #19136838C2semidirect
3. #19136834C2semidirect
4. #19136829C2semidirect
5. #19136756C2semidirect
6. #19136749C2semidirect
7. #19136729C2semidirect
8. #19136650C2semidirect
9. #19136650C2semidirect
11. #19136504C2semidirect
12. #19136469C2semidirect
13. #19136459C2semidirect
14. C4×#13063266C2semidirect
15. C43×#3380C2semidirect
233. #3380D43semidirect
296. C43#33937semidirect

Maximal subgroups

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

subgroupindex
#191476082
#191368382
#191368342
#191368292
#191367562
#191367492
#191367292
#191366502
#191366302
#191365042
#191364692
#191364592
C4×#130632662
C43×#33802
#3393743