Finite Group Databasebeta

← #25251264

Subgroups — #25251264

Order 11008.

574 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063347C211yesmaximal, characteristic
2#19136744C212yesmaximal, complemented
3#19136739C212yesmaximal, complemented
4#19136734C212yesmaximal, complemented
5#19136729C212yesmaximal, complemented
6#19136381C212yesmaximal, complemented
7#19136351C211yesmaximal, characteristic, complemented
8#19136305C212yesmaximal
9C2×C43×#500C211yesmaximal, characteristic, complemented
10C2×#13063347C2211yescharacteristic
11C4×#10621898—21no—
12C2×#13063265C2212yes—
13C4×Dic172C2211yescharacteristic
14C4×Dic172C2211yescharacteristic
15C4×#10621873—21no—
16C4×#10621873—21no—
17C4×D344C2211yescharacteristic
18C4×D344C2211yescharacteristic
19#14582937C2211yescharacteristic
20#14582896—21no—
21#14582726C2214yes—
22#14582724C2214yes—
23C4⋊(C43⋊C16)C2212yes—
24C4⋊(C43⋊C16)C2212yes—
25#14582702C2214yes—
26#14582699C2214yes—
27C2×C4⋊Q8×C43—21no—
28C43×#500—21no—
29C43×#500—21no—
30C43×#500C2212yes—
31C43×#500C2212yes—
32C2×#107×C43—21no—
33C2×#107×C43C2212yes—
34C2×C4×C8×C43C2211yescharacteristic
35C2×#10621898—21no—
36#13063347—22no—
37#13063347Q814yescomplemented
38C2×Dic172C2311yescharacteristic
39C2×#10621873—21no—
40C2×D344C2311yescharacteristic
41C4×Dic86—21no—
42C4×Dic86—21no—
43C4×D172—21no—
44C4×D172—21no—
45C4×C22⋊D43—41no—
46C4×C22⋊D43—41no—
47#13063284—21no—
48#13063282—41no—
49C42×D43—41no—
50#13063265—24no—
51C2×C43⋊C16C2314yes—
52#13063259C2311yescharacteristic
53#13063259C2311yescharacteristic
54#13063257—21no—
55#13063250—21no—
56#13063250—21no—
57#13063247—21no—
58#13063247—21no—
59C22×Q8×C43—41no—
60C22×C8×C43D411yescharacteristic
61C22×C8×C43C2311yescharacteristic
62C4⋊Q8×C43—22no—
63C4⋊Q8×C43—22no—
64C4⋊Q8×C43—41no—
65C4⋊Q8×C43—41no—
66C2×C4⋊C4×C43—22no—
67C2×C4⋊C4×C43—41no—
68C2×C42×C43D411yescharacteristic
69#107×C43—22no—
70#107×C43—22no—
71#107×C43—22no—
72#107×C43C2314yes—
73C4×C8×C43D411yescharacteristic
74C4×C8×C43D411yescharacteristic
75C4×C8×C43C2311yescharacteristic
76C4×C8×C43C2311yescharacteristic
77C2×Q8×C43—42no—
78C2×Q8×C43—42no—
79C2×Q8×C43—84no—
80C22×C4×C43—42no—
81C22×C4×C43D811yescharacteristic
82C22×C4×C43D811yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C2×C22⋊D43—41no—
85#10621898—24no—
86#10621898—42no—
87C2×D172—21no—
88C2×C4×D43—41no—
89C2×C4×D43—41no—
90C2×C4×D43—41no—
91C2×Dic86—21no—
92C2×C8×C43—22no—
93C2×C8×C43C2×D411yescharacteristic
94C2×C8×C43C2×D411yescharacteristic
95C2×C8×C43C2×D411yescharacteristic
96C2×C8×C43C2×Q812yes—
97C2×C8×C43#4112yes—
98C2×C8×C43C2411yescharacteristic
99C4⋊C4×C43—24no—
100C4⋊C4×C43—42no—
101C4⋊C4×C43—42no—
102C4⋊C4×C43—42no—
103C42×C43D811yescharacteristic
104C42×C43D811yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C22⋊Dic43—41no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—41no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112Dic43⋊C4—41no—
113Dic43⋊C4—41no—
114C4×Dic43—41no—
115C4×Dic43—41no—
116C4×Dic43—41no—
117Dic172—21no—
118Dic172C2×Q812yescomplemented
119D344—21no—
120D344C2×Q812yescomplemented
121#10621873—24no—
122C43⋊C16—24no—
123C23×C43C2×D811yescharacteristic
124C22×D43—41no—
125Q8×C43—84no—
126Q8×C43—84no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—44no—
130C2×C4×C43—84no—
131C2×C4×C43C22⋊Q812yes—
132C2×C4×C43C2×D811yescharacteristic
133C2×C4×C43C2×D811yescharacteristic
134C2×C4×C43C2×D811yescharacteristic
135C2×C4×C43C2×D811yescharacteristic
136C2×C4×C43C2×D811yescharacteristic
137C2×C4×C43#13712yes—
138C2×C4×C43C22×D411yescharacteristic
139C22⋊D43—44no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143D172—22no—
144D172—41no—
145C4×D43—44no—
146C4×D43—82no—
147C4×D43—82no—
148Dic86—22no—
149Dic86—41no—
150C8×C43—21no—
151C8×C43—21no—
152C8×C43C22⋊Q812yes—
153C8×C43C22×Q811yescharacteristic
154C8×C43C2×#4111yescharacteristic
155#33629—431nomaximal, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43#47412yes—
159C22×C43C22×D811yescharacteristic
160C2×D43—42no—
161C2×D43—81no—
162C2×D43—81no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—84no—
166C4×C43#47412yes—
167C4×C43#50912yes—
168C4×C43#51012yes—
169C4×C43C2×C22⋊Q811yescharacteristic
170C4×C43C2×#13711yescharacteristic
171Dic43—42no—
172Dic43—81no—
173Dic43—81no—
174C2×#500D4311yescharacteristic, complemented
175C4×#135—431no—
176#2227—432no—
177#2226—432no—
178#2225—432no—
179#2224—432no—
180#2159—432no—
181#2150—431no—
182#2139—432no—
183C2×C43—22no—
184C2×C43C2×#47411yescharacteristic
185C2×C43C2×#50911yescharacteristic
186C2×C43C2×#51011yescharacteristic
187D43—82no—
188C2×#135—431no—
189C2×C4⋊Q8—21no—
190C4×#41—861no—
191C2×M32—432no—
192#500—21no—
193#500—21no—
194#500C2×D4312yes—
195#500C2×D4312yes—
196C4×Q16—431no—
197C4×Q16—431no—
198C4×SD16—861no—
199C4×SD16—861no—
200C4×D8—431no—
201C4×D8—431no—
202#427—431no—
203C2×#107—21no—
204C2×#107C2×D4312yes—
205#416—861no—
206C2×C4×C8C2×D4311yescharacteristic
207#367—434no—
208#366—434no—
209C4⋊C16—432no—
210C4⋊C16—432no—
211#358—434no—
212#357—434no—
213C43#3362911yescharacteristic, complemented, Sylow
214C2×#41—861no—
215C22×Q8—41no—
216#135—434no—
217#135—862no—
218C2×Q16—431no—
219C2×SD16—861no—
220C2×D8—431no—
221C22×C8C22⋊D4311yescharacteristic
222C22×C8C22×D4311yescharacteristic
223C4⋊Q8—22no—
224C4⋊Q8—22no—
225C4⋊Q8—41no—
226C4⋊Q8—41no—
227C4×Q8—861no—
228C4×Q8—861no—
229C4×D4—861no—
230C4×D4—861no—
231C4×D4—1721no—
232C4×D4—1721no—
233#117—861no—
234#117—1721no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—41no—
237C2×C42—1721no—
238C2×C42C22⋊D4311yescharacteristic
239M32—864no—
240C2×C16—434no—
241#107—22no—
242#107—22no—
243#107—22no—
244#107—431no—
245#107—431no—
246#107C22×D4314yes—
247#106—861no—
248#103—861no—
249#103—861no—
250#102—861no—
251#102—861no—
252C4×C8C22⋊D4311yescharacteristic
253C4×C8C22⋊D4311yescharacteristic
254C4×C8C22×D4311yescharacteristic
255C4×C8C22×D4311yescharacteristic
256#41—864no—
257#41—1722no—
258C2×Q8—42no—
259C2×Q8—42no—
260C2×Q8—84no—
261C2×Q8—861no—
262C2×D4—861no—
263C2×D4—1721no—
264C22×C4—42no—
265C22×C4—1721no—
266C22×C4—1721no—
267C22×C4—1721no—
268C22×C4#1062188211yescharacteristic
269C22×C4#1062188211yescharacteristic
270C22×C4C2×C22⋊D4311yescharacteristic
271Q16—432no—
272Q16—861no—
273SD16—864no—
274D8—432no—
275D8—861no—
276C2×C8—22no—
277C2×C8Q8×D4312yes—
278C2×C8#1062190212yes—
279C2×C8C2×C22⋊D4311yescharacteristic
280C2×C8C2×C22⋊D4311yescharacteristic
281C2×C8C2×C22⋊D4311yescharacteristic
282C2×C8C23×D4311yescharacteristic
283C4⋊C4—24no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C22⋊C4—1721no—
292C22⋊C4—1721no—
293C22⋊C4—1721no—
294C42—1721no—
295C42—1721no—
296C42—1721no—
297C42#1062188211yescharacteristic
298C42#1062188211yescharacteristic
299C42C2×C22⋊D4311yescharacteristic
300C42C2×C22⋊D4311yescharacteristic
301C16—864no—
302C23—1721no—
303C23C2×#1062188211yescharacteristic
304Q8—84no—
305Q8—84no—
306Q8—862no—
307Q8—1721no—
308D4—862no—
309D4—1724no—
310D4—1721no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—44no—
314C2×C4—84no—
315C2×C4—3442no—
316C2×C4—3442no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1724no—
321C2×C4#1306330112yes—
322C2×C4C2×#1062188211yescharacteristic
323C2×C4C2×#1062188211yescharacteristic
324C2×C4C2×#1062188211yescharacteristic
325C2×C4C2×#1062188211yescharacteristic
326C2×C4C2×#1062188211yescharacteristic
327C2×C4#1306335612yes—
328C2×C4C22×C22⋊D4311yescharacteristic
329C8—21no—
330C8—21no—
331C8#1306330112yes—
332C8C2×Q8×D4311yescharacteristic
333C8C2×#1062190211yescharacteristic
334C22—21no—
335C22—21no—
336C22—3441no—
337C22—3441no—
338C22—1722no—
339C22#1458317612yes—
340C22C22×#1062188211yescharacteristic
341C4—21no—
342C4—21no—
343C4—84no—
344C4—3441no—
345C4—3441no—
346C4—1722no—
347C4#1458317612yes—
348C4#1458333512yes—
349C4#1458334012yes—
350C4C2×#1306330111yescharacteristic
351C4C2×#1306335611yescharacteristic
352C2—22no—
353C2—3442no—
354C2C2×#1458317611yescharacteristic
355C2C2×#1458333511yescharacteristic
356C2C2×#1458334011yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#500C2
socleC22×C43C22×D8
prime radicalC2×#13063347C22
hypercenterC2×#500D43
hypocenterC43#33629
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
2. #19136744C2semidirect
3. #19136739C2semidirect
4. #19136734C2semidirect
5. #19136729C2semidirect
6. #19136381C2semidirect
7. #19136351C2semidirect
9. C2×C43×#500C2semidirect
37. #13063347Q8semidirect
118. Dic172C2×Q8semidirect
120. D344C2×Q8semidirect
174. C2×#500D43semidirect
213. C43#33629semidirect

Maximal subgroups

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

subgroupindex
C4×#130633472
#191367442
#191367392
#191367342
#191367292
#191363812
#191363512
#191363052
C2×C43×#5002
#3362943