Finite Group Databasebeta

← #25252995

Subgroups — #25252995

Order 11008.

476 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145234C211yesmaximal, characteristic
2#19136756C211yesmaximal, characteristic, complemented
3#19136749C211yesmaximal, characteristic, complemented
4#19136747C211yesmaximal, characteristic, complemented
5#19136737C211yesmaximal, characteristic, complemented
6#19136710C211yesmaximal, characteristic
7#19136701C211yesmaximal, characteristic, complemented
8#19136693C211yesmaximal, characteristic
9#19136684C211yesmaximal, characteristic, complemented
10#19136657C211yesmaximal, characteristic, complemented
11#19136657C211yesmaximal, characteristic, complemented
12#19136642C211yesmaximal, characteristic, complemented
13#19136637C211yesmaximal, characteristic, complemented
14#19136354C211yesmaximal, characteristic, complemented
15C43×#3177C211yesmaximal, characteristic, complemented
16#14583520—21no—
17C2×#13063271C2211yescharacteristic
18C2×#13063271C2211yescharacteristic
19C2×#13063268C2211yescharacteristic
20C2×#13063268C2211yescharacteristic
21C2×#13063265C2211yescharacteristic
22C22×C43⋊C16C2211yescharacteristic
23#14583304C2211yescharacteristic
24#14583283C2211yescharacteristic
25#14583259—21no—
26#14583145—21no—
27#14583140C2211yescharacteristic
28#14583135C2211yescharacteristic
29#14583001—21no—
30C4×Dic172C2211yescharacteristic
31C4×D344C2211yescharacteristic
32#14582726C2211yescharacteristic
33#14582726C2211yescharacteristic
34#14582724C2211yescharacteristic
35#14582724C2211yescharacteristic
36C4⋊(C43⋊C16)C2211yescharacteristic
37C4⋊(C43⋊C16)C2211yescharacteristic
38C4⋊(C43⋊C16)C2211yescharacteristic
39C4⋊(C43⋊C16)C2211yescharacteristic
40#14582703C2211yescharacteristic
41#14582703C2211yescharacteristic
42#14582703C2211yescharacteristic
43#14582703C2211yescharacteristic
44#14582702C2211yescharacteristic
45#14582702C2211yescharacteristic
46#14582699C2211yescharacteristic
47#14582699C2211yescharacteristic
48C43×#541—21no—
49C43×#499C2211yescharacteristic
50C43×#494C2211yescharacteristic
51C43×#491—21no—
52C43×#470—21no—
53C43×#467C2211yescharacteristic
54C43×#467C2211yescharacteristic
55C43×#441—21no—
56C4×Q16×C43C2211yescharacteristic
57C4×Q16×C43C2211yescharacteristic
58C43×#405C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621873—21no—
61C2×D344C2311yescharacteristic
62#13063325—21no—
63#13063320—41no—
64#13063313—21no—
65#13063311—41no—
66#13063307—41no—
67#13063304—21no—
68#13063303—41no—
69#13063299—21no—
70C4×Dic86—21no—
71C4×D172—21no—
72#13063271—41no—
73#13063271—41no—
74#13063268—41no—
75#13063268—41no—
76#13063265—41no—
77C2×C43⋊C16—41no—
78C2×C43⋊C16C2311yescharacteristic
79C2×C43⋊C16C2311yescharacteristic
80C2×C43⋊C16C2311yescharacteristic
81C2×C43⋊C16C2311yescharacteristic
82#13063259—21no—
83#13063259C2311yescharacteristic
84#13063259C2311yescharacteristic
85#13063250—21no—
86#13063250—21no—
87#13063247—21no—
88#13063247—21no—
89C2×Q16×C43—21no—
90C2×Q16×C43C2311yescharacteristic
91C2×Q16×C43C2311yescharacteristic
92C2×M16×C43D411yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C4⋊Q8×C43—21no—
95#126×C43—41no—
96#126×C43—41no—
97#125×C43—21no—
98#125×C43—41no—
99#125×C43—41no—
100C22⋊Q8×C43—21no—
101C22⋊Q8×C43—21no—
102C4×Q8×C43—21no—
103C4×Q8×C43—21no—
104#117×C43D411yescharacteristic
105#107×C43C2311yescharacteristic
106#107×C43C2311yescharacteristic
107#106×C43—21no—
108#103×C43—21no—
109#103×C43—21no—
110#103×C43—21no—
111#103×C43—21no—
112#97×C43D411yescharacteristic
113#97×C43D411yescharacteristic
114C4×C8×C43C2311yescharacteristic
115C4×C8×C43C2311yescharacteristic
116C2×Q8×C43—21no—
117C2×Q8×C43—21no—
118C22×C4×C43C2×D411yescharacteristic
119C2×C22⋊D43—41no—
120C2×D172—21no—
121C2×C4×D43—41no—
122C2×Dic86—21no—
123C2×Dic86—41no—
124Q16×C43—21no—
125Q16×C43—21no—
126Q16×C43—21no—
127Q16×C43—21no—
128Q16×C43—42no—
129M16×C43—41no—
130C2×C8×C43—21no—
131C2×C8×C43—21no—
132C2×C8×C43C2×D411yescharacteristic
133C2×C8×C43C2×D411yescharacteristic
134C2×C8×C43C2×D411yescharacteristic
135C2×C8×C43C2411yescharacteristic
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—41no—
139C4⋊C4×C43—41no—
140C4⋊C4×C43—41no—
141C4⋊C4×C43—41no—
142C4⋊C4×C43—41no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—41no—
145C4⋊C4×C43—41no—
146C4⋊C4×C43D811yescharacteristic
147C4⋊C4×C43D811yescharacteristic
148C22⋊C4×C43—41no—
149C22⋊C4×C43—41no—
150C22⋊C4×C43D811yescharacteristic
151C22⋊C4×C43D811yescharacteristic
152C42×C43—41no—
153C42×C43—41no—
154C42×C43C2×D411yescharacteristic
155C42×C43C2×D411yescharacteristic
156C22⋊Dic43—41no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163C4⋊Dic43—41no—
164Dic43⋊C4—41no—
165Dic43⋊C4—41no—
166C4×Dic43—41no—
167Dic172—21no—
168Dic172—21no—
169D344—21no—
170D344—21no—
171#10621873—42no—
172C43⋊C16—21no—
173C43⋊C16—21no—
174C43⋊C16—21no—
175C43⋊C16—21no—
176C23×C43C2×D811yescharacteristic
177C22×D43—41no—
178Q8×C43—41no—
179Q8×C43—41no—
180Q8×C43—41no—
181Q8×C43—41no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43C2×D811yescharacteristic
189C2×C4×C43C2×D811yescharacteristic
190C2×C4×C43C2×D811yescharacteristic
191C2×C4×C43C2×D811yescharacteristic
192C2×C4×C43C2×D811yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C22⋊D43—161no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198D172—41no—
199D172—41no—
200C4×D43—161no—
201Dic86—41no—
202Dic86—41no—
203Dic86—161no—
204C8×C43—21no—
205C8×C43—21no—
206C8×C43—21no—
207C8×C43H(5,𝔽2)11yescharacteristic
208C8×C432−1+411yescharacteristic
209#33824—431nomaximal, Sylow
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—21no—
213C22×C43C22×D811yescharacteristic
214C2×D43—81no—
215C2×D43—81no—
216C2×D43—81no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—21no—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—81no—
223C4×C43—81no—
224C4×C43—81no—
225C4×C43—81no—
226C4×C43#53711yescharacteristic
227C4×C43#57511yescharacteristic
228Dic43—81no—
229Dic43—81no—
230Dic43—81no—
231#3177D4311yescharacteristic, complemented
232#3175—431no—
233#2229—431no—
234#2228—431no—
235#2227—431no—
236#2225—431no—
237#2220—431no—
238#2219—431no—
239#2217—431no—
240#2216—431no—
241#2211—431no—
242#2211—431no—
243#2209—431no—
244#2208—431no—
245#2151—431no—
246C2×C43—41no—
247C2×C43#324511yescharacteristic
248C2×C43#341611yescharacteristic
249C2×C43#341711yescharacteristic
250D43—161no—
251#542—861no—
252#541—21no—
253C2×Q32—431no—
254C2×Q32—431no—
255C2×SD32—431no—
256C2×SD32—431no—
257C2×M32—431no—
258C22×C16—431no—
259#500—431no—
260#499C2×D4311yescharacteristic
261#495—431no—
262#494C2×D4311yescharacteristic
263#491—21no—
264#489—861no—
265#470—21no—
266#468—861no—
267#467—431no—
268#467C2×D4311yescharacteristic
269#467C2×D4311yescharacteristic
270#466—431no—
271#441—21no—
272#440—861no—
273C4×Q16—431no—
274C4×Q16C2×D4311yescharacteristic
275C4×Q16C2×D4311yescharacteristic
276C4×D8—431no—
277#405C2×D4311yescharacteristic
278#367—431no—
279#367—431no—
280#366—431no—
281#366—431no—
282C4⋊C16—431no—
283C4⋊C16—431no—
284C4⋊C16—431no—
285C4⋊C16—431no—
286#358—431no—
287#358—431no—
288#358—431no—
289#358—431no—
290#358—431no—
291#358—431no—
292#357—431no—
293#357—431no—
294C43#3382411yescharacteristic, complemented, Sylow
295C2×Q16—21no—
296C2×Q16—431no—
297C2×Q16C22×D4311yescharacteristic
298C2×Q16C22×D4311yescharacteristic
299C2×SD16—861no—
300C2×D8—431no—
301C2×M16C22⋊D4311yescharacteristic
302C22×C8C22×D4311yescharacteristic
303C4⋊Q8—21no—
304C4⋊Q8—861no—
305#126—41no—
306#126—41no—
307#126—1721no—
308#125—21no—
309#125—41no—
310#125—41no—
311#124—861no—
312#124—1721no—
313#123—1721no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—861no—
317C22⋊Q8—1721no—
318#121—861no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—861no—
322C4×D4—861no—
323#117C22⋊D4311yescharacteristic
324Q32—1721no—
325Q32—1721no—
326SD32—1721no—
327SD32—1721no—
328M32—1721no—
329C2×C16—431no—
330C2×C16—431no—
331C2×C16—431no—
332C2×C16—431no—
333C2×C16—1721no—
334#107—431no—
335#107—431no—
336#107—861no—
337#107C22×D4311yescharacteristic
338#107C22×D4311yescharacteristic
339#106—21no—
340#103—21no—
341#103—21no—
342#103—21no—
343#103—21no—
344#103—861no—
345#103—861no—
346#102—861no—
347#102—861no—
348#97C22⋊D4311yescharacteristic
349#97C22⋊D4311yescharacteristic
350C4×C8C22×D4311yescharacteristic
351C4×C8C22×D4311yescharacteristic
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—861no—
355C2×Q8—1721no—
356C2×D4—861no—
357C2×D4—1721no—
358C22×C4—1721no—
359C22×C4C2×C22⋊D4311yescharacteristic
360Q16—21no—
361Q16—21no—
362Q16—21no—
363Q16—21no—
364Q16—42no—
365Q16—861no—
366Q16—861no—
367SD16—1722no—
368D8—861no—
369D8—861no—
370M16—41no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8C2×C22⋊D4311yescharacteristic
374C2×C8C2×C22⋊D4311yescharacteristic
375C2×C8C2×C22⋊D4311yescharacteristic
376C2×C8C23×D4311yescharacteristic
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—861no—
388C4⋊C4—861no—
389C4⋊C4—1721no—
390C4⋊C4—1721no—
391C4⋊C4—1721no—
392C4⋊C4#1062188211yescharacteristic
393C4⋊C4#1062188211yescharacteristic
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—1721no—
397C22⋊C4—1721no—
398C22⋊C4—1721no—
399C22⋊C4—1721no—
400C22⋊C4—1721no—
401C22⋊C4#1062188211yescharacteristic
402C22⋊C4#1062188211yescharacteristic
403C42—41no—
404C42—41no—
405C42—1721no—
406C42C2×C22⋊D4311yescharacteristic
407C42C2×C22⋊D4311yescharacteristic
408C16—861no—
409C16—861no—
410C16—861no—
411C16—861no—
412C23—1721no—
413C23C2×#1062188211yescharacteristic
414Q8—41no—
415Q8—41no—
416Q8—41no—
417Q8—41no—
418Q8—1721no—
419Q8—1721no—
420Q8—6881no—
421D4—1721no—
422D4—1721no—
423D4—6881no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—1721no—
431C2×C4—1721no—
432C2×C4—1721no—
433C2×C4—6881no—
434C2×C4C2×#1062188211yescharacteristic
435C2×C4C2×#1062188211yescharacteristic
436C2×C4C2×#1062188211yescharacteristic
437C2×C4C2×#1062188211yescharacteristic
438C2×C4C2×#1062188211yescharacteristic
439C2×C4C22×C22⋊D4311yescharacteristic
440C8—21no—
441C8—21no—
442C8—21no—
443C8#1306337111yescharacteristic
444C8#1306337211yescharacteristic
445C22—21no—
446C22—21no—
447C22—21no—
448C22—3441no—
449C22—3441no—
450C22—3441no—
451C22C22×#1062188211yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—3441no—
462C4—3441no—
463C4—3441no—
464C4#1458347711yescharacteristic
465C4#1458369711yescharacteristic
466C2—41no—
467C2—6881no—
468C2#1914590211yescharacteristic
469C2#1914773911yescharacteristic
470C2#1914774611yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3177C2
socleC22×C43C22×D8
prime radical#14583135C22
hypercenter#3177D43
hypocenterC43#33824
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3177

Complements

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

NH ≅ G/Ntype
2. #19136756C2semidirect
3. #19136749C2semidirect
4. #19136747C2semidirect
5. #19136737C2semidirect
7. #19136701C2semidirect
9. #19136684C2semidirect
10. #19136657C2semidirect
11. #19136657C2semidirect
12. #19136642C2semidirect
13. #19136637C2semidirect
14. #19136354C2semidirect
15. C43×#3177C2semidirect
231. #3177D43semidirect
294. C43#33824semidirect

Maximal subgroups

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

subgroupindex
#191452342
#191367562
#191367492
#191367472
#191367372
#191367102
#191367012
#191366932
#191366842
#191366572
#191366422
#191366372
#191363542
C43×#31772
#3382443