Finite Group Databasebeta

← #25007665

Subgroups — #25007665

Order 11008.

422 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊(C43⋊C16)C211yesmaximal, characteristic, complemented
2#19134620C211yesmaximal, characteristic, complemented
3#19132607C212yesmaximal, complemented
4#19132604C212yesmaximal, complemented
5C43×#3050C211yesmaximal, characteristic
6C22×C43⋊C16—21no—
7C2×#13063257—21no—
8#14582759—21no—
9C22⋊(C43⋊C16)—21no—
10C22⋊(C43⋊C16)C2212yes—
11#14582662C2212yes—
12C2×#135×C43C411yescharacteristic, complemented
13C23×C8×C43C2211yescharacteristic
14C43×#525—21no—
15C43×#467C411yescharacteristic, complemented
16C43×#467C2211yescharacteristic
17C43×#466C411yescharacteristic, complemented
18C43×#466C2211yescharacteristic
19C43×#465—21no—
20C43×#465—21no—
21C43×#427C411yescharacteristic, complemented
22C43×#416—21no—
23C2×C4⋊Dic43—22no—
24C2×C22⋊Dic43—41no—
25C2×C43⋊C16—22no—
26C2×C43⋊C16—42no—
27#13063257—42no—
28C43⋊#95—41no—
29C2×#41×C43—21no—
30C23×C4×C43D411yescharacteristic
31#135×C43—42no—
32C2×Q16×C43C2×C411yescharacteristic
33C2×SD16×C43—21no—
34C2×D8×C43C2×C411yescharacteristic
35C22×C8×C43—42no—
36C22×C8×C43C2×C411yescharacteristic
37C22×C8×C43C2×C411yescharacteristic
38C22×C8×C43D411yescharacteristic
39C22×C8×C43D411yescharacteristic
40C22×C8×C43D411yescharacteristic
41C22×C8×C43C2311yescharacteristic
42#123×C43—41no—
43C22⋊Q8×C43—21no—
44C22⋊Q8×C43—21no—
45#121×C43—21no—
46#121×C43—21no—
47#120×C43—41no—
48C4×D4×C43—41no—
49C4×D4×C43—41no—
50#117×C43—21no—
51#107×C43C2×C411yescharacteristic
52#107×C43C2×C411yescharacteristic
53#106×C43—21no—
54#103×C43—21no—
55#103×C43—21no—
56#102×C43—21no—
57#102×C43—21no—
58C24×C43D811yescharacteristic
59#41×C43—42no—
60#41×C43—42no—
61C2×Q8×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43—41no—
64C2×D4×C43—41no—
65C2×D4×C43—41no—
66C22×C4×C43—41no—
67C22×C4×C43—41no—
68C22×C4×C43—41no—
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43D811yescharacteristic
72C22×C4×C43SD1611yescharacteristic
73C22×C4×C43SD1611yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—42no—
76Q16×C43—41no—
77SD16×C43—42no—
78D8×C43—41no—
79C2×C8×C43—22no—
80C2×C8×C43—22no—
81C2×C8×C43—22no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43C22⋊C411yescharacteristic
86C2×C8×C43C22⋊C411yescharacteristic
87C2×C8×C43C22×C411yescharacteristic
88C2×C8×C43C2×D411yescharacteristic
89C4⋊C4×C43—21no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—41no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C42×C43—41no—
99C22⋊Dic43—82no—
100C4⋊Dic43—42no—
101C4⋊Dic43—42no—
102C43⋊C16—42no—
103C23×C43—22no—
104C23×C43—22no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43#10211yescharacteristic
108C23×C43#10211yescharacteristic
109C23×C43C2×D811yescharacteristic
110Q8×C43—41no—
111Q8×C43—41no—
112D4×C43—41no—
113D4×C43—41no—
114D4×C43—82no—
115D4×C43—82no—
116D4×C43—82no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—82no—
130C2×C4×C43#10211yescharacteristic
131C2×C4×C43#10211yescharacteristic
132C2×C4×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43C2×SD1611yescharacteristic
134C2×Dic43—82no—
135C2×Dic43—82no—
136C2×Dic43—82no—
137C8×C43—21no—
138C8×C43—21no—
139C8×C43—21no—
140C8×C43#9912yes—
141#11885—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—44no—
150C22×C43—81no—
151C22×C43—81no—
152C22×C43—81no—
153C22×C43#36012yes—
154C22×C43C2×#10211yescharacteristic
155C22×C43#50812yes—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—81no—
160C4×C43—81no—
161C4×C43—81no—
162C4×C43C2×#9911yescharacteristic
163C4×C43#42111yescharacteristic
164Dic43—162no—
165#3050D4311yescharacteristic
166C2×C22⋊C16—431no—
167#1807—431no—
168#1348—432no—
169#1347—432no—
170C2×C43—22no—
171C2×C43—22no—
172C2×C43—41no—
173C2×C43—161no—
174C2×C43#151911yescharacteristic
175C2×C43#213811yescharacteristic
176C2×C43C2×#36011yescharacteristic
177C2×#135Dic4311yescharacteristic, complemented
178C23×C8C2×D4311yescharacteristic
179#525—21no—
180C22×C16—861no—
181#467Dic4311yescharacteristic, complemented
182#467C2×D4311yescharacteristic
183#466Dic4311yescharacteristic, complemented
184#466C2×D4311yescharacteristic
185#465—21no—
186#465—21no—
187#427Dic4311yescharacteristic, complemented
188C2×#106—861no—
189#416—21no—
190#380—861no—
191C22⋊C16—432no—
192C22⋊C16—861no—
193#340—432no—
194C43#1188511yescharacteristic, complemented, Sylow
195C2×#41—21no—
196C23×C4C22⋊D4311yescharacteristic
197#135—42no—
198C2×Q16C2×Dic4311yescharacteristic
199C2×SD16—21no—
200C2×D8C2×Dic4311yescharacteristic
201C22×C8—42no—
202C22×C8C2×Dic4311yescharacteristic
203C22×C8C2×Dic4311yescharacteristic
204C22×C8C22⋊D4311yescharacteristic
205C22×C8C22⋊D4311yescharacteristic
206C22×C8C22⋊D4311yescharacteristic
207C22×C8C22×D4311yescharacteristic
208#123—41no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211#121—21no—
212#121—21no—
213#120—41no—
214C4×D4—41no—
215C4×D4—41no—
216#117—21no—
217C2×C4⋊C4—862no—
218C2×C22⋊C4—1721no—
219C2×C16—862no—
220C2×C16—1722no—
221#107C2×Dic4311yescharacteristic
222#107C2×Dic4311yescharacteristic
223#106—21no—
224#106—1722no—
225#103—21no—
226#103—21no—
227#102—21no—
228#102—21no—
229#95—1721no—
230C24#1062188211yescharacteristic
231#41—42no—
232#41—42no—
233C2×Q8—21no—
234C2×D4—21no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—1722no—
242C22×C4#1062188211yescharacteristic
243C22×C4#1062188311yescharacteristic
244C22×C4#1062188311yescharacteristic
245C22×C4C22⋊Dic4311yescharacteristic
246C22×C4C22⋊Dic4311yescharacteristic
247C22×C4C2×C22⋊D4311yescharacteristic
248Q16—41no—
249SD16—42no—
250D8—41no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8C22⋊Dic4311yescharacteristic
258C2×C8C22⋊Dic4311yescharacteristic
259C2×C8C22×Dic4311yescharacteristic
260C2×C8C2×C22⋊D4311yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—1722no—
266C4⋊C4—1722no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—3442no—
273C42—41no—
274C16—1722no—
275C23—22no—
276C23—22no—
277C23—41no—
278C23—41no—
279C23#1306324611yescharacteristic
280C23#1306324611yescharacteristic
281C23C2×#1062188211yescharacteristic
282Q8—41no—
283Q8—41no—
284D4—41no—
285D4—41no—
286D4—82no—
287D4—82no—
288D4—82no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—82no—
302C2×C4—3442no—
303C2×C4—3442no—
304C2×C4—3442no—
305C2×C4#1306324611yescharacteristic
306C2×C4#1306324611yescharacteristic
307C2×C4C2×C22⋊Dic4311yescharacteristic
308C2×C4C2×#1062188311yescharacteristic
309C8—21no—
310C8—21no—
311C8—21no—
312C8#1306324012yes—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—44no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22#1458270912yes—
325C22C2×#1306324611yescharacteristic
326C22#1458332912yes—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4—6882no—
334C4C2×#1306324011yescharacteristic
335C4#1458291611yescharacteristic
336C2—22no—
337C2—22no—
338C2—41no—
339C2—161no—
340C2#1913316311yescharacteristic
341C2#1913630211yescharacteristic
342C2C2×#1458270911yescharacteristic
subgroupG/H
centerC22C2×#13063246
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
Fitting, prime radicalC43×#3050C2
socleC22×C43C2×#102
cosocleC22×C8×C43C23
hypercenter#3050D43
hypocenterC43#11885
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊(C43⋊C16)C2semidirect
2. #19134620C2semidirect
3. #19132607C2semidirect
4. #19132604C2semidirect
12. C2×#135×C43C4semidirect
15. C43×#467C4semidirect
17. C43×#466C4semidirect
21. C43×#427C4semidirect
177. C2×#135Dic43semidirect
181. #467Dic43semidirect
183. #466Dic43semidirect
187. #427Dic43semidirect
194. C43#11885semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊(C43⋊C16)2
#191346202
#191326072
#191326042
C43×#30502
#1188543