Finite Group Databasebeta

← #25014843

Subgroups — #25014843

Order 11008.

510 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145019C211yesmaximal, characteristic
2C2×#14582710C211yesmaximal, characteristic, complemented
3C2×#14582709C211yesmaximal, characteristic, complemented
4C2×#14582708C211yesmaximal, characteristic, complemented
5M32×Dic43C211yesmaximal, characteristic, complemented
6#19134750C211yesmaximal, characteristic, complemented
7C2×C43×#360C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9C2×#13063345—21no—
10#14583445—21no—
11C2×#13063265C2211yescharacteristic
12#14583284C411yescharacteristic, complemented
13#14583282C411yescharacteristic, complemented
14#14583280—21no—
15#14583277C411yescharacteristic, complemented
16#14583274C411yescharacteristic, complemented
17#14583270—21no—
18C2×#13063257C2211yescharacteristic
19C2×#13063256—21no—
20C2×C8×Dic43C2211yescharacteristic
21#14582768—21no—
22#14582710—22no—
23#14582709—22no—
24#14582708—22no—
25#14582674—21no—
26C16×Dic43—21no—
27C2×#135×C43C2211yescharacteristic
28C2×M32×C43C2211yescharacteristic
29C2×#106×C43C2211yescharacteristic
30C43×#360—22no—
31C2×#10621898—21no—
32#13063347—21no—
33#13063347—21no—
34#13063347—21no—
35#13063347—21no—
36#13063345—42no—
37#13063345—42no—
38C2×Dic172C2×C411yescharacteristic
39C2×#10621885—21no—
40C2×#10621873—21no—
41C2×#10621883—21no—
42C2×#10621884—21no—
43C2×D344C2×C411yescharacteristic
44C2×#10621882—21no—
45C22×C43⋊C8D411yescharacteristic
46#13063323—21no—
47#13063321—21no—
48#13063314—21no—
49#13063312—21no—
50#13063297—42no—
51C4×C22⋊D43—42no—
52C2×C4⋊Dic43—21no—
53C2×Dic43⋊C4—42no—
54C2×C4×Dic43D411yescharacteristic
55#13063265—21no—
56#13063265D412yescomplemented
57C2×C43⋊C16—21no—
58#13063257—21no—
59#13063257—21no—
60#13063256—42no—
61C8×Dic43C2×C411yescharacteristic
62C8×Dic43C2×C411yescharacteristic
63C8×Dic43D411yescharacteristic
64C8×Dic43D411yescharacteristic
65C2×#41×C43—21no—
66#135×C43—21no—
67#135×C43—21no—
68#135×C43—21no—
69#135×C43—21no—
70C2×Q16×C43C2×C411yescharacteristic
71C2×SD16×C43—21no—
72C2×D8×C43C2×C411yescharacteristic
73C22×C8×C43C2311yescharacteristic
74C2×C4⋊C4×C43—21no—
75M32×C43—21no—
76M32×C43D412yescomplemented
77C2×C16×C43—21no—
78#106×C43—21no—
79#106×C43—21no—
80#41×C43—41no—
81#41×C43—41no—
82#41×C43—41no—
83#41×C43—41no—
84C2×Q8×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43C2×D411yescharacteristic
90C2×C22⋊D43—42no—
91C2×C22⋊D43—41no—
92C22×Dic43—41no—
93C22×Dic43D812yes—
94#10621898—41no—
95#10621898—41no—
96#10621898—41no—
97#10621898—41no—
98C2×D172—21no—
99C2×C4×D43—41no—
100C2×Dic86—21no—
101Q16×C43—21no—
102Q16×C43—21no—
103SD16×C43—41no—
104SD16×C43—41no—
105D8×C43—21no—
106D8×C43—21no—
107C2×C8×C43C22×C411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43#4111yescharacteristic
112C2×C8×C43#4111yescharacteristic
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C22⋊Dic43—42no—
116#10621885—42no—
117#10621884—42no—
118#10621883—42no—
119#10621882—42no—
120(C2×D43)⋊C4—42no—
121C4⋊Dic43—41no—
122C4⋊Dic43—41no—
123Dic43⋊C4—42no—
124Dic43⋊C4—84no—
125C4×Dic43C22⋊C411yescharacteristic
126C4×Dic43C22⋊C411yescharacteristic
127C4×Dic43SD1612yes—
128C2×C43⋊C8C22⋊C411yescharacteristic
129C2×C43⋊C8C22⋊C411yescharacteristic
130C2×C43⋊C8D812yes—
131C2×C43⋊C8SD1612yes—
132Dic172—21no—
133Dic172—21no—
134D344—21no—
135D344—21no—
136#10621873—41no—
137#10621873—41no—
138C16×C43—22no—
139C43⋊C16—22no—
140C23×C43—41no—
141C23×C43C2×D811yescharacteristic
142C22×D43—41no—
143Q8×C43—41no—
144Q8×C43—41no—
145D4×C43—41no—
146D4×C43—41no—
147D4×C43—81no—
148D4×C43—81no—
149C2×C4×C43—41no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43—82no—
153C2×C4×C43—81no—
154C2×C4×C43C2×C22⋊C411yescharacteristic
155C2×C4×C43#12411yescharacteristic
156C2×C4×C43#12711yescharacteristic
157C2×C4×C43C2×D811yescharacteristic
158C2×C4×C43C2×SD1611yescharacteristic
159C2×C4×C43C2×SD1611yescharacteristic
160C22⋊D43—81no—
161C22⋊D43—81no—
162C22⋊D43—84no—
163C2×Dic43—24no—
164C2×Dic43—41no—
165C2×Dic43—82no—
166C2×Dic43—81no—
167C2×Dic43#10212yes—
168C2×Dic43#10212yes—
169D172—41no—
170D172—41no—
171C4×D43—81no—
172C4×D43—81no—
173Dic86—41no—
174Dic86—41no—
175C8×C43C4×D411yescharacteristic
176C8×C43C4×D411yescharacteristic
177C8×C43#12111yescharacteristic
178C8×C43#12111yescharacteristic
179C43⋊C8#10212yes—
180C43⋊C8#10212yes—
181#13210—431nomaximal, Sylow
182C22×C43—22no—
183C22×C43—82no—
184C22×C43—81no—
185C22×C43C2×#10211yescharacteristic
186C22×C43#48611yescharacteristic
187C22×C43#49311yescharacteristic
188C2×D43—82no—
189C2×D43—81no—
190C4×C43—81no—
191C4×C43—161no—
192C4×C43#39011yescharacteristic
193C4×C43C2×#10211yescharacteristic
194C4×C43#48611yescharacteristic
195C4×C43#49211yescharacteristic
196Dic43—22no—
197Dic43—81no—
198Dic43—161no—
199Dic43#36014yescomplemented
200#3147—431no—
201C2×#360—431no—
202C2×#360—431no—
203C2×#360—431no—
204C2×#360D4311yescharacteristic, complemented
205C4×M32—431no—
206#1844—431no—
207C2×C43—21no—
208C2×C43—21no—
209C2×C43—161no—
210C2×C43#195711yescharacteristic
211C2×C43C2×#36012yes—
212D43—161no—
213C2×#135—431no—
214C2×#135—861no—
215C2×#135C2×D4311yescharacteristic
216#532—861no—
217C2×M32—431no—
218C2×M32C2×D4311yescharacteristic
219#495—431no—
220#495—431no—
221#495—861no—
222#494—431no—
223#493—431no—
224#492—861no—
225C2×#106—431no—
226C2×#106—861no—
227C2×#106C2×D4311yescharacteristic
228C2×C4×C8—431no—
229#384—861no—
230#360—22no—
231#360—862no—
232#360—862no—
233#360—862no—
234#346—861no—
235C4×C16—861no—
236C43#1321011yescharacteristic, complemented, Sylow
237C2×#41—21no—
238C2×#41—861no—
239#135—21no—
240#135—21no—
241#135—21no—
242#135—21no—
243#135—861no—
244#135—861no—
245#135—861no—
246#135—861no—
247#135—1722no—
248#135—1722no—
249C2×Q16—431no—
250C2×Q16—861no—
251C2×Q16C4×D4311yescharacteristic
252C2×SD16—21no—
253C2×SD16—861no—
254C2×SD16—861no—
255C2×SD16—861no—
256C2×D8—431no—
257C2×D8—861no—
258C2×D8C4×D4311yescharacteristic
259C22×C8—431no—
260C22×C8C22×D4311yescharacteristic
261C4⋊Q8—861no—
262#127—861no—
263#124—861no—
264#124—861no—
265#121—1722no—
266C4×D4—1722no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4—1722no—
270C2×C42—431no—
271M32—21no—
272M32—432no—
273M32—861no—
274M32C22⋊D4312yescomplemented
275C2×C16—21no—
276C2×C16—861no—
277#106—21no—
278#106—21no—
279#106—861no—
280#106—861no—
281#106—1722no—
282C4×C8—431no—
283C4×C8—431no—
284C4×C8—431no—
285C4×C8—431no—
286#41—41no—
287#41—41no—
288#41—41no—
289#41—41no—
290#41—1721no—
291#41—1721no—
292#41—1721no—
293#41—1721no—
294C2×Q8—21no—
295C2×Q8—861no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—861no—
299C2×D4—1722no—
300C2×D4—1721no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—432no—
304C22×C4—1721no—
305C22×C4—1721no—
306C22×C4D4×D4311yescharacteristic
307Q16—21no—
308Q16—21no—
309Q16—861no—
310Q16—861no—
311Q16—1722no—
312SD16—41no—
313SD16—41no—
314SD16—1722no—
315SD16—1722no—
316SD16—1721no—
317SD16—1721no—
318D8—21no—
319D8—21no—
320D8—861no—
321D8—861no—
322D8—1722no—
323C2×C8—431no—
324C2×C8—431no—
325C2×C8—432no—
326C2×C8—432no—
327C2×C8C2×C4×D4311yescharacteristic
328C2×C8#1062189811yescharacteristic
329C2×C8D4×D4311yescharacteristic
330C2×C8D4×D4311yescharacteristic
331C2×C8#1062190011yescharacteristic
332C2×C8C2×C22⋊D4311yescharacteristic
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—3444no—
336C4⋊C4—1722no—
337C4⋊C4—1721no—
338C4⋊C4—1721no—
339C22⋊C4—1722no—
340C22⋊C4—1722no—
341C42—431no—
342C42—431no—
343C42—432no—
344C16—22no—
345C16—862no—
346C23—41no—
347C23—1721no—
348C23D8×D4311yescharacteristic
349Q8—41no—
350Q8—41no—
351Q8—1721no—
352Q8—1721no—
353D4—41no—
354D4—41no—
355D4—81no—
356D4—81no—
357D4—3444no—
358D4—3441no—
359D4—3441no—
360D4—1721no—
361D4—1721no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—432no—
368C2×C4—432no—
369C2×C4—864no—
370C2×C4—3441no—
371C2×C4—3441no—
372C2×C4—3442no—
373C2×C4—3441no—
374C2×C4—1721no—
375C2×C4C22⋊C4×D4311yescharacteristic
376C2×C4#1306331111yescharacteristic
377C2×C4#1306332111yescharacteristic
378C2×C4D8×D4311yescharacteristic
379C2×C4SD16×D4311yescharacteristic
380C2×C4SD16×D4311yescharacteristic
381C8—432no—
382C8—432no—
383C8(C22⋊D43)⋊C411yescharacteristic
384C8C4×C22⋊D4311yescharacteristic
385C8#1306329711yescharacteristic
386C8#1306329811yescharacteristic
387C22—22no—
388C22—82no—
389C22—81no—
390C22—3442no—
391C22—3441no—
392C22#102×D4311yescharacteristic
393C22#1458324411yescharacteristic
394C22#1458327411yescharacteristic
395C4—81no—
396C4—161no—
397C4—434no—
398C4—862no—
399C4—3441no—
400C4—6881no—
401C4#1458279911yescharacteristic
402C4#102×D4311yescharacteristic
403C4#1458324411yescharacteristic
404C4#1458327011yescharacteristic
405C2—21no—
406C2—21no—
407C2—161no—
408C2—6881no—
409C2#1913539911yescharacteristic
410C2#360×D4312yes—
subgroupG/H
centerC22#102×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#360C2
socleC22×C43C2×#102
prime radical#19145019C2
cosocleC22×C8×C43C23
hypercenterC2×#360D43
hypocenterC43#13210
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

Complements

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

NH ≅ G/Ntype
2. C2×#14582710C2semidirect
3. C2×#14582709C2semidirect
4. C2×#14582708C2semidirect
5. M32×Dic43C2semidirect
6. #19134750C2semidirect
7. C2×C43×#360C2semidirect
12. #14583284C4semidirect
13. #14583282C4semidirect
15. #14583277C4semidirect
16. #14583274C4semidirect
56. #13063265D4semidirect
76. M32×C43D4semidirect
199. Dic43#360semidirect
204. C2×#360D43semidirect
236. C43#13210semidirect
274. M32C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191450192
C2×#145827102
C2×#145827092
C2×#145827082
M32×Dic432
#191347502
C2×C43×#3602
#1321043