Finite Group Databasebeta

← #25253003

Subgroups — #25253003

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#19145254C211yesmaximal, characteristic, complemented
2#19145234C211yesmaximal, characteristic
3#19136760C211yesmaximal, characteristic, complemented
4#19136753C211yesmaximal, characteristic, complemented
5#19136748C211yesmaximal, characteristic, complemented
6#19136738C211yesmaximal, characteristic, complemented
7#19136708C211yesmaximal, characteristic
8#19136703C211yesmaximal, characteristic, complemented
9#19136691C211yesmaximal, characteristic
10#19136686C211yesmaximal, characteristic, complemented
11#19136658C211yesmaximal, characteristic, complemented
12#19136658C211yesmaximal, characteristic, complemented
13#19136646C211yesmaximal, characteristic, complemented
14#19136641C211yesmaximal, characteristic, complemented
15C43×#2151C211yesmaximal, characteristic, complemented
16#14583520—21no—
17#14583511—21no—
18C2×Dic344C2211yescharacteristic
19C2×Dic344C2211yescharacteristic
20C2×#13063270C2211yescharacteristic
21C2×#13063270C2211yescharacteristic
22#14583304C2211yescharacteristic
23#14583301C2211yescharacteristic
24#14583283C2211yescharacteristic
25#14583279C2211yescharacteristic
26#14583268—21no—
27#14583259—21no—
28#14583157—21no—
29#14583145—21no—
30#14583140C2211yescharacteristic
31#14583140C2211yescharacteristic
32#14583140C2211yescharacteristic
33#14583135C2211yescharacteristic
34#14583007—21no—
35#14583001—21no—
36C4×Dic172C2211yescharacteristic
37C4×Dic172C2211yescharacteristic
38C4×Dic172C2211yescharacteristic
39C4×D344C2211yescharacteristic
40#14582727C2211yescharacteristic
41#14582727C2211yescharacteristic
42#14582725C2211yescharacteristic
43#14582725C2211yescharacteristic
44#14582704C2211yescharacteristic
45#14582704C2211yescharacteristic
46#14582704C2211yescharacteristic
47#14582704C2211yescharacteristic
48#14582704C2211yescharacteristic
49#14582704C2211yescharacteristic
50#14582701C2211yescharacteristic
51#14582701C2211yescharacteristic
52C2×M32×C43C2211yescharacteristic
53C22×C16×C43C2211yescharacteristic
54C43×#405C2211yescharacteristic
55C43×C4⋊C16C2211yescharacteristic
56C43×C4⋊C16C2211yescharacteristic
57C43×C4⋊C16C2211yescharacteristic
58C43×C4⋊C16C2211yescharacteristic
59C2×Dic172—21no—
60C2×Dic172C2311yescharacteristic
61C2×Dic172C2311yescharacteristic
62C2×Dic172C2311yescharacteristic
63C2×#10621873—21no—
64C2×D344C2311yescharacteristic
65#13063325—21no—
66#13063325—21no—
67#13063320—41no—
68#13063318—41no—
69#13063318—41no—
70#13063317—21no—
71#13063315—41no—
72#13063315—41no—
73#13063313—21no—
74#13063311—41no—
75#13063307—41no—
76#13063304—21no—
77#13063304—21no—
78#13063304—21no—
79#13063303—41no—
80#13063299—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×D172—21no—
85Dic344—41no—
86Dic344—41no—
87#13063270—41no—
88#13063270—41no—
89#13063259—21no—
90#13063259C2311yescharacteristic
91#13063259C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063259C2311yescharacteristic
94#13063257—21no—
95#13063250—21no—
96#13063250—21no—
97#13063250—21no—
98#13063250—21no—
99#13063250—21no—
100#13063250—21no—
101#13063247—21no—
102#13063247—21no—
103C2×M16×C43D411yescharacteristic
104C22×C8×C43C2311yescharacteristic
105#117×C43D411yescharacteristic
106M32×C43—41no—
107C2×C16×C43—41no—
108C2×C16×C43C2311yescharacteristic
109C2×C16×C43C2311yescharacteristic
110C2×C16×C43C2311yescharacteristic
111C2×C16×C43C2311yescharacteristic
112#97×C43D411yescharacteristic
113#97×C43D411yescharacteristic
114C4×C8×C43C2311yescharacteristic
115C4×C8×C43C2311yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C2×C22⋊D43—41no—
118C2×D172—21no—
119C2×C4×D43—41no—
120C2×Dic86—21no—
121C2×Dic86—21no—
122C2×Dic86—21no—
123C2×Dic86—41no—
124M16×C43—41no—
125C2×C8×C43—21no—
126C2×C8×C43—21no—
127C2×C8×C43C2×D411yescharacteristic
128C2×C8×C43C2×D411yescharacteristic
129C2×C8×C43C2×D411yescharacteristic
130C2×C8×C43C2411yescharacteristic
131C4⋊C4×C43D811yescharacteristic
132C4⋊C4×C43D811yescharacteristic
133C22⋊C4×C43D811yescharacteristic
134C22⋊C4×C43D811yescharacteristic
135C42×C43C2×D411yescharacteristic
136C42×C43C2×D411yescharacteristic
137C22⋊Dic43—41no—
138C22⋊Dic43—41no—
139C22⋊Dic43—41no—
140(C2×D43)⋊C4—41no—
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4—41no—
143(C2×D43)⋊C4—41no—
144C4⋊Dic43—21no—
145C4⋊Dic43—21no—
146C4⋊Dic43—21no—
147C4⋊Dic43—21no—
148C4⋊Dic43—41no—
149C4⋊Dic43—41no—
150C4⋊Dic43—41no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154Dic43⋊C4—41no—
155Dic43⋊C4—41no—
156Dic43⋊C4—41no—
157Dic43⋊C4—41no—
158Dic43⋊C4—41no—
159C4×Dic43—41no—
160C4×Dic43—41no—
161C4×Dic43—41no—
162Dic172—21no—
163Dic172—21no—
164Dic172—21no—
165Dic172—21no—
166Dic172—21no—
167Dic172—21no—
168Dic172—42no—
169D344—21no—
170D344—21no—
171#10621873—42no—
172C16×C43—21no—
173C16×C43—21no—
174C16×C43—21no—
175C16×C43—21no—
176C23×C43C2×D811yescharacteristic
177C22×D43—41no—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43C2×D811yescharacteristic
181C2×C4×C43C2×D811yescharacteristic
182C2×C4×C43C2×D811yescharacteristic
183C2×C4×C43C2×D811yescharacteristic
184C2×C4×C43C2×D811yescharacteristic
185C2×C4×C43C22×D411yescharacteristic
186C22⋊D43—161no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—41no—
193C2×Dic43—41no—
194D172—41no—
195D172—41no—
196C4×D43—161no—
197Dic86—41no—
198Dic86—41no—
199Dic86—41no—
200Dic86—41no—
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#53711yescharacteristic
223C4×C43#57511yescharacteristic
224Dic43—81no—
225Dic43—81no—
226Dic43—81no—
227Dic43—81no—
228Dic43—81no—
229Dic43—81no—
230Dic43—81no—
231#3177—431no—
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#2151D4311yescharacteristic, complemented
246C2×C43—41no—
247C2×C43#324511yescharacteristic
248C2×C43#341611yescharacteristic
249C2×C43#341711yescharacteristic
250D43—161no—
251#542—861no—
252#541—861no—
253C2×Q32—431no—
254C2×Q32—431no—
255C2×SD32—431no—
256C2×SD32—431no—
257C2×M32C2×D4311yescharacteristic
258C22×C16C2×D4311yescharacteristic
259#500—431no—
260#499—431no—
261#495—431no—
262#494—431no—
263#491—861no—
264#489—861no—
265#470—861no—
266#468—861no—
267#467—431no—
268#467—431no—
269#467—431no—
270#466—431no—
271#441—861no—
272#440—861no—
273C4×Q16—431no—
274C4×Q16—431no—
275C4×Q16—431no—
276C4×D8—431no—
277#405C2×D4311yescharacteristic
278#367—431no—
279#367—431no—
280#366—431no—
281#366—431no—
282C4⋊C16C2×D4311yescharacteristic
283C4⋊C16C2×D4311yescharacteristic
284C4⋊C16C2×D4311yescharacteristic
285C4⋊C16C2×D4311yescharacteristic
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—431no—
296C2×Q16—431no—
297C2×Q16—431no—
298C2×Q16—861no—
299C2×SD16—861no—
300C2×D8—431no—
301C2×M16D17211yescharacteristic
302C22×C8C22×D4311yescharacteristic
303C4⋊Q8—861no—
304C4⋊Q8—861no—
305#126—1721no—
306#126—1721no—
307#126—1721no—
308#125—861no—
309#125—1721no—
310#125—1721no—
311#124—861no—
312#124—1721no—
313#123—1721no—
314C22⋊Q8—861no—
315C22⋊Q8—861no—
316C22⋊Q8—861no—
317C22⋊Q8—1721no—
318#121—861no—
319C4×Q8—861no—
320C4×Q8—861no—
321C4×Q8—861no—
322C4×D4—861no—
323#117D17211yescharacteristic
324Q32—1721no—
325Q32—1721no—
326SD32—1721no—
327SD32—1721no—
328M32—41no—
329C2×C16—41no—
330C2×C16C22×D4311yescharacteristic
331C2×C16C22×D4311yescharacteristic
332C2×C16C22×D4311yescharacteristic
333C2×C16C22×D4311yescharacteristic
334#107—431no—
335#107—431no—
336#107—431no—
337#107—431no—
338#107—861no—
339#106—861no—
340#103—861no—
341#103—861no—
342#103—861no—
343#103—861no—
344#103—861no—
345#103—861no—
346#102—861no—
347#102—861no—
348#97D17211yescharacteristic
349#97D17211yescharacteristic
350C4×C8C22×D4311yescharacteristic
351C4×C8C22×D4311yescharacteristic
352C2×Q8—861no—
353C2×Q8—861no—
354C2×Q8—861no—
355C2×Q8—1721no—
356C2×D4—861no—
357C2×D4—1721no—
358C22×C4—1721no—
359C22×C4C2×D17211yescharacteristic
360Q16—861no—
361Q16—861no—
362Q16—861no—
363Q16—861no—
364Q16—861no—
365Q16—861no—
366Q16—1722no—
367SD16—1722no—
368D8—861no—
369D8—861no—
370M16—41no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8C2×D17211yescharacteristic
374C2×C8C2×D17211yescharacteristic
375C2×C8C2×D17211yescharacteristic
376C2×C8C23×D4311yescharacteristic
377C4⋊C4—861no—
378C4⋊C4—861no—
379C4⋊C4—861no—
380C4⋊C4—861no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C4⋊C4—1721no—
384C4⋊C4—1721no—
385C4⋊C4—1721no—
386C4⋊C4—1721no—
387C4⋊C4—1721no—
388C4⋊C4—1721no—
389C4⋊C4—1721no—
390C4⋊C4—1721no—
391C4⋊C4—1721no—
392C4⋊C4D34411yescharacteristic
393C4⋊C4D34411yescharacteristic
394C22⋊C4—1721no—
395C22⋊C4—1721no—
396C22⋊C4—1721no—
397C22⋊C4—1721no—
398C22⋊C4—1721no—
399C22⋊C4—1721no—
400C22⋊C4—1721no—
401C22⋊C4D34411yescharacteristic
402C22⋊C4D34411yescharacteristic
403C42—1721no—
404C42—1721no—
405C42—1721no—
406C42C2×D17211yescharacteristic
407C42C2×D17211yescharacteristic
408C16—21no—
409C16—21no—
410C16—21no—
411C16—21no—
412C23—1721no—
413C23C2×D34411yescharacteristic
414Q8—1721no—
415Q8—1721no—
416Q8—1721no—
417Q8—1721no—
418Q8—1721no—
419Q8—1721no—
420Q8—6881no—
421D4—1721no—
422D4—1721no—
423D4—6881no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—1721no—
427C2×C4—1721no—
428C2×C4—1721no—
429C2×C4—1721no—
430C2×C4—1721no—
431C2×C4—1721no—
432C2×C4—1721no—
433C2×C4—6881no—
434C2×C4C2×D34411yescharacteristic
435C2×C4C2×D34411yescharacteristic
436C2×C4C2×D34411yescharacteristic
437C2×C4C2×D34411yescharacteristic
438C2×C4C2×D34411yescharacteristic
439C2×C4C22×D17211yescharacteristic
440C8—21no—
441C8—21no—
442C8—21no—
443C8#1306337011yescharacteristic
444C8#1306337311yescharacteristic
445C22—21no—
446C22—21no—
447C22—21no—
448C22—3441no—
449C22—3441no—
450C22—3441no—
451C22C22×D34411yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—3441no—
458C4—3441no—
459C4—3441no—
460C4—3441no—
461C4—3441no—
462C4—3441no—
463C4—3441no—
464C4#1458348011yescharacteristic
465C4#1458369911yescharacteristic
466C2—41no—
467C2—6881no—
468C2#1914590511yescharacteristic
469C2#1914774311yescharacteristic
470C2#1914774811yescharacteristic
subgroupG/H
centerC22C22×D344
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2151C2
socleC22×C43C22×D8
prime radical#14583135C22
hypercenter#2151D43
hypocenterC43#33824
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2151

Complements

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

NH ≅ G/Ntype
1. #19145254C2semidirect
3. #19136760C2semidirect
4. #19136753C2semidirect
5. #19136748C2semidirect
6. #19136738C2semidirect
8. #19136703C2semidirect
10. #19136686C2semidirect
11. #19136658C2semidirect
12. #19136658C2semidirect
13. #19136646C2semidirect
14. #19136641C2semidirect
15. C43×#2151C2semidirect
245. #2151D43semidirect
294. C43#33824semidirect

Maximal subgroups

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

subgroupindex
#191452542
#191452342
#191367602
#191367532
#191367482
#191367382
#191367082
#191367032
#191366912
#191366862
#191366582
#191366462
#191366412
C43×#21512
#3382443