Finite Group Databasebeta

← #25066347

Subgroups — #25066347

Order 11008.

682 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143562C212yesmaximal, complemented
2#19133492C212yesmaximal, complemented
3#19133486C214yesmaximal, complemented
4#19133480C212yesmaximal, complemented
5#19133343C211yesmaximal, characteristic, complemented
6#19132977C212yesmaximal, complemented
7C2×C8×C43⋊C8C211yesmaximal, characteristic, complemented
8C4×#135×C43C211yesmaximal, characteristic
9#14583030C2214yes—
10#14582977C2214yes—
11#14582971—24no—
12#14582952—22no—
13#14582952C2212yes—
14C4×#10621877—22no—
15C2×C4×C43⋊C8C2211yescharacteristic
16C2×C4×C43⋊C8C2211yescharacteristic
17#14582652C2212yes—
18#14582650C2212yes—
19Q8⋊(C43⋊C8)C2214yes—
20D4⋊(C43⋊C8)C2214yes—
21C8×C43⋊C8C2212yes—
22C8×C43⋊C8C2212yes—
23C2×#135×C43C411yescharacteristic
24C4×#41×C43C2212yes—
25C4×Q16×C43C411yescharacteristic
26C4×Q16×C43C2211yescharacteristic
27C4×SD16×C43C412yes—
28C4×SD16×C43C2212yes—
29C4×D8×C43C411yescharacteristic
30C4×D8×C43C2211yescharacteristic
31C43×#427C411yescharacteristic
32C43×#416C412yes—
33C2×C4×C8×C43C2211yescharacteristic
34C2×#10621877—24no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8D412yes—
37C4⋊(C43⋊C8)—24no—
38C4⋊(C43⋊C8)C2314yes—
39C22⋊(C43⋊C8)—22no—
40C22⋊(C43⋊C8)—24no—
41#13063236—24no—
42C4×C43⋊C8—22no—
43C4×C43⋊C8—21no—
44C4×C43⋊C8D411yescharacteristic
45C4×C43⋊C8D411yescharacteristic
46C4×C43⋊C8C2312yes—
47C4×C43⋊C8C2312yes—
48C2×#41×C43C2×C412yes—
49#135×C43—24no—
50C2×Q16×C43C2×C411yescharacteristic
51C2×SD16×C43C2×C412yes—
52C2×D8×C43C2×C411yescharacteristic
53C22×C8×C43C2×C411yescharacteristic
54C22×C8×C43C2×C411yescharacteristic
55C4×Q8×C43C2×C412yes—
56C4×Q8×C43C2312yes—
57C4×D4×C43—22no—
58C4×D4×C43—22no—
59C4×D4×C43C2×C412yes—
60C4×D4×C43C2312yes—
61#117×C43—22no—
62#117×C43C2×C412yes—
63C2×C42×C43—22no—
64C2×C42×C43C2311yescharacteristic
65#107×C43C2×C411yescharacteristic
66#107×C43C2×C411yescharacteristic
67#106×C43C2×C412yes—
68#103×C43C2×C412yes—
69#103×C43C2×C412yes—
70#102×C43C2×C412yes—
71#102×C43C2×C412yes—
72C4×C8×C43C2×C411yescharacteristic
73C4×C8×C43C2×C411yescharacteristic
74C4×C8×C43C2311yescharacteristic
75C4×C8×C43C2311yescharacteristic
76#41×C43—24no—
77#41×C43—24no—
78C2×Q8×C43C22×C412yes—
79C2×D4×C43—22no—
80C2×D4×C43C22×C412yes—
81C22×C4×C43—22no—
82C22×C4×C43—22no—
83C22×C4×C43—22no—
84C22×C4×C43C22×C411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87Q16×C43—22no—
88SD16×C43—24no—
89D8×C43—22no—
90C2×C8×C43—22no—
91C2×C8×C43M1614yescomplemented
92C2×C8×C43C22×C411yescharacteristic
93C2×C8×C43C22×C411yescharacteristic
94C2×C8×C43C22×C411yescharacteristic
95C2×C8×C43C22×C411yescharacteristic
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43C22×C412yes—
99C4⋊C4×C43C22×C412yes—
100C22⋊C4×C43—22no—
101C22⋊C4×C43—22no—
102C22⋊C4×C43—22no—
103C42×C43—22no—
104C42×C43—22no—
105C42×C43—22no—
106C42×C43C22×C411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43#4111yescharacteristic
109C42×C43C2411yescharacteristic
110#10621877—48no—
111C2×C43⋊C8—24no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—24no—
114C2×C43⋊C8—24no—
115C2×C43⋊C8C2×D412yes—
116C2×C43⋊C8C2×D412yes—
117C23×C43—22no—
118C23×C43C4×D411yescharacteristic
119Q8×C43—22no—
120Q8×C43—22no—
121D4×C43—22no—
122D4×C43—22no—
123D4×C43—44no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—44no—
130C2×C4×C43—44no—
131C2×C4×C43—44no—
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43C2×M1612yes—
136C2×C4×C43#13112yes—
137C2×C4×C43C23×C411yescharacteristic
138C2×C4×C43C22×D411yescharacteristic
139C2×C4×C43C2×#4111yescharacteristic
140C8×C43—21no—
141C8×C43—21no—
142C8×C43C2×M1612yes—
143C8×C43C2×M1612yes—
144C43⋊C8—24no—
145C43⋊C8—22no—
146C43⋊C8—44no—
147C43⋊C8#13514yescomplemented
148#17886—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—42no—
152C22×C43—42no—
153C22×C43—42no—
154C22×C43#43612yes—
155C22×C43C2×C4×D411yescharacteristic
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—42no—
159C4×C43—42no—
160C4×C43—42no—
161C4×C43#43612yes—
162C4×C43#44312yes—
163C4×C43C22×M1611yescharacteristic
164C4×C43C2×#13111yescharacteristic
165C4×C43C2×#13512yes—
166#2965—432no—
167C4×#135D4311yescharacteristic
168#1591—432no—
169#1590—434no—
170#1589—432no—
171#1564—431no—
172#1476—432no—
173C2×C82—431no—
174C2×C43—22no—
175C2×C43—82no—
176C2×C43C2×#43611yescharacteristic
177C2×C43C4×#13511yescharacteristic
178C2×C43C2×#44311yescharacteristic
179C2×#135Dic4311yescharacteristic
180C4×#41C2×D4312yes—
181#446—434no—
182C4×Q16Dic4311yescharacteristic
183C4×Q16C2×D4311yescharacteristic
184C4×SD16Dic4312yes—
185C4×SD16C2×D4312yes—
186C4×D8Dic4311yescharacteristic
187C4×D8C2×D4311yescharacteristic
188#436—434no—
189#435—864no—
190#431—432no—
191#431—862no—
192#427Dic4311yescharacteristic
193#416Dic4312yes—
194C4×M16—862no—
195C2×C4×C8—431no—
196C2×C4×C8—431no—
197C2×C4×C8C2×D4311yescharacteristic
198#335—432no—
199#334—432no—
200Q8⋊C8—434no—
201D4⋊C8—434no—
202C82—432no—
203C82—432no—
204C43#1788611yescharacteristic, complemented, Sylow
205C2×#41C2×Dic4312yes—
206#135—24no—
207C2×Q16C2×Dic4311yescharacteristic
208C2×SD16C2×Dic4312yes—
209C2×D8C2×Dic4311yescharacteristic
210C2×M16—864no—
211C22×C8—432no—
212C22×C8—861no—
213C22×C8C2×Dic4311yescharacteristic
214C22×C8C2×Dic4311yescharacteristic
215C4×Q8C2×Dic4312yes—
216C4×Q8C22×D4312yes—
217C4×D4—22no—
218C4×D4—22no—
219C4×D4C2×Dic4312yes—
220C4×D4C22×D4312yes—
221#117—22no—
222#117C2×Dic4312yes—
223C2×C42—22no—
224C2×C42C22×D4311yescharacteristic
225#107C2×Dic4311yescharacteristic
226#107C2×Dic4311yescharacteristic
227#106C2×Dic4312yes—
228C4⋊C8—434no—
229C4⋊C8—864no—
230#103C2×Dic4312yes—
231#103C2×Dic4312yes—
232#102C2×Dic4312yes—
233#102C2×Dic4312yes—
234C22⋊C8—864no—
235C22⋊C8—862no—
236#97—864no—
237C4×C8—431no—
238C4×C8—431no—
239C4×C8—432no—
240C4×C8—432no—
241C4×C8—862no—
242C4×C8—861no—
243C4×C8C2×Dic4311yescharacteristic
244C4×C8C2×Dic4311yescharacteristic
245C4×C8C22×D4311yescharacteristic
246C4×C8C22×D4311yescharacteristic
247#41—24no—
248#41—24no—
249C2×Q8C22×Dic4312yes—
250C2×D4—22no—
251C2×D4C22×Dic4312yes—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4D4×D4311yescharacteristic
256C22×C4#1062190011yescharacteristic
257C22×C4C22×Dic4311yescharacteristic
258Q16—22no—
259SD16—24no—
260D8—22no—
261M16—1728no—
262C2×C8—22no—
263C2×C8—432no—
264C2×C8—432no—
265C2×C8—864no—
266C2×C8—864no—
267C2×C8—862no—
268C2×C8—864no—
269C2×C8#1062187714yescomplemented
270C2×C8C22×Dic4311yescharacteristic
271C2×C8C22×Dic4311yescharacteristic
272C2×C8C22×Dic4311yescharacteristic
273C2×C8C22×Dic4311yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4C22×Dic4312yes—
277C4⋊C4C22×Dic4312yes—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C42—22no—
282C42—22no—
283C42—22no—
284C42D4×D4311yescharacteristic
285C42#1062190011yescharacteristic
286C42C22×Dic4311yescharacteristic
287C42C23×D4311yescharacteristic
288C23—22no—
289C23D4×Dic4311yescharacteristic
290Q8—22no—
291Q8—22no—
292D4—22no—
293D4—22no—
294D4—44no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4D4×Dic4311yescharacteristic
304C2×C4D4×Dic4311yescharacteristic
305C2×C4D4×Dic4311yescharacteristic
306C2×C4C2×#1062187712yes—
307C2×C4#1306333212yes—
308C2×C4C23×Dic4311yescharacteristic
309C2×C4C2×D4×D4311yescharacteristic
310C2×C4C2×#1062190011yescharacteristic
311C8—21no—
312C8—21no—
313C8—434no—
314C8—864no—
315C8—862no—
316C8—1724no—
317C8C2×#1062187712yes—
318C8C2×#1062187712yes—
319C22—21no—
320C22—21no—
321C22—42no—
322C22—42no—
323C22—42no—
324C22#1458297712yes—
325C22C2×D4×Dic4311yescharacteristic
326C4—21no—
327C4—21no—
328C4—42no—
329C4—42no—
330C4—42no—
331C4#1458297712yes—
332C4#1458301612yes—
333C4C22×#1062187711yescharacteristic
334C4C2×#1306333211yescharacteristic
335C4#135×D4312yes—
336C2—22no—
337C2—82no—
338C2C2×#1458297711yescharacteristic
339C2#135×Dic4311yescharacteristic
340C2C2×#1458301611yescharacteristic
subgroupG/H
centerC42D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC4×#135×C43C2
socleC22×C43C2×C4×D4
prime radicalC2×#135×C43C4
cosocleC42×C43C24
hypercenterC4×#135D43
hypocenterC43#17886
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #19143562C2semidirect
2. #19133492C2semidirect
3. #19133486C2semidirect
4. #19133480C2semidirect
5. #19133343C2semidirect
6. #19132977C2semidirect
7. C2×C8×C43⋊C8C2semidirect
91. C2×C8×C43M16semidirect
147. C43⋊C8#135semidirect
204. C43#17886semidirect
269. C2×C8#10621877semidirect

Maximal subgroups

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

subgroupindex
#191435622
#191334922
#191334862
#191334802
#191333432
#191329772
C2×C8×C43⋊C82
C4×#135×C432
#1788643