Finite Group Databasebeta

← #25068346

Subgroups — #25068346

Order 11008.

652 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143721C212yesmaximal, complemented
2C4×#13063347C211yesmaximal, characteristic
3#19133503C212yesmaximal, complemented
4#19133430C214yesmaximal, complemented
5#19133418C212yesmaximal, complemented
6#19133032C212yesmaximal, complemented
7#19132884C211yesmaximal, characteristic, complemented
8C43×#1566C211yesmaximal, characteristic, complemented
9C2×#13063347C411yescharacteristic
10C4×#10621898C2212yes—
11#14583026C2214yes—
12C4×Dic172C411yescharacteristic
13C4×Dic172C2211yescharacteristic
14C4×#10621873C412yes—
15C4×#10621873C2212yes—
16C4×D344C411yescharacteristic
17C4×D344C2211yescharacteristic
18#14582968—24no—
19#14582964C2214yes—
20#14582955—22no—
21#14582952C2211yescharacteristic
22#14582937C411yescharacteristic
23C4⋊C8×D43—22no—
24#14582896C412yes—
25C4×#10621877C2211yescharacteristic
26#14582629C2214yes—
27#14582626C2214yes—
28#14582621C2212yes—
29#14582620C2212yes—
30C43×#423C2212yes—
31C2×C4×C8×C43C2211yescharacteristic
32C43×#334C2212yes—
33C43×#334C2212yes—
34C2×#10621898C2×C412yes—
35#13063347—24no—
36C2×Dic172C2×C411yescharacteristic
37C2×#10621873C2×C412yes—
38C2×D344C2×C411yescharacteristic
39C2×#10621877—21no—
40C2×C8×D43—24no—
41C4×Dic86C2×C412yes—
42C4×Dic86C2312yes—
43C4×D172C2×C412yes—
44C4×D172C2312yes—
45C4×C22⋊D43—22no—
46C4×C22⋊D43—22no—
47#13063284C2×C412yes—
48#13063282—22no—
49C42×D43—22no—
50#13063259C2×C411yescharacteristic
51#13063259C2×C411yescharacteristic
52#13063257C2×C412yes—
53C4⋊(C43⋊C8)D412yes—
54Dic43⋊C8—24no—
55#13063250C2×C412yes—
56#13063250C2×C412yes—
57#13063247C2×C412yes—
58#13063247C2×C412yes—
59C22⋊(C43⋊C8)D412yes—
60(C2×D43)⋊C8—24no—
61#13063236—21no—
62#13063235—24no—
63C4×C43⋊C8C2312yes—
64C4×C43⋊C8C2312yes—
65C2×M16×C43—22no—
66C22×C8×C43C2×C411yescharacteristic
67C22×C8×C43C2×C411yescharacteristic
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—22no—
70C4⋊C8×C43C2314yes—
71C4×C8×C43C2×C411yescharacteristic
72C4×C8×C43C2×C411yescharacteristic
73C4×C8×C43C2311yescharacteristic
74C4×C8×C43C2311yescharacteristic
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C2×C22⋊D43—22no—
79#10621898—24no—
80#10621898—42no—
81C2×D172C22×C412yes—
82C2×C4×D43—22no—
83C2×C4×D43—22no—
84C2×C4×D43—22no—
85C2×Dic86C22×C412yes—
86M16×C43—82no—
87C2×C8×C43—22no—
88C2×C8×C43—24no—
89C2×C8×C43—41no—
90C2×C8×C43C22×C411yescharacteristic
91C2×C8×C43C22×C411yescharacteristic
92C2×C8×C43C22×C411yescharacteristic
93C2×C8×C43C22×C411yescharacteristic
94C42×C43C22×C411yescharacteristic
95C42×C43C2×D411yescharacteristic
96C42×C43#4111yescharacteristic
97C42×C43C2411yescharacteristic
98C22⋊Dic43—22no—
99(C2×D43)⋊C4—22no—
100(C2×D43)⋊C4—22no—
101C4⋊Dic43C22×C412yes—
102C4⋊Dic43C22×C412yes—
103Dic43⋊C4—22no—
104Dic43⋊C4—22no—
105C4×Dic43—22no—
106C4×Dic43—22no—
107C4×Dic43—22no—
108#10621877—42no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8C2×D414yes—
111Dic172—22no—
112D344M1614yescomplemented
113#10621873—24no—
114C8×D43—84no—
115C23×C43C4×D411yescharacteristic
116C22×D43—22no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43C4×D411yescharacteristic
122C2×C4×C43C4×D411yescharacteristic
123C2×C4×C43C4×D411yescharacteristic
124C2×C4×C43C23×C411yescharacteristic
125C2×C4×C43C22×D411yescharacteristic
126C2×C4×C43C2×#4111yescharacteristic
127C22⋊D43—44no—
128C2×Dic43—22no—
129C2×Dic43—22no—
130C2×Dic43—22no—
131D172—22no—
132D172C2×M1614yes—
133C4×D43—44no—
134C4×D43—42no—
135C4×D43—42no—
136C4×D43—44no—
137Dic86—22no—
138Dic86—22no—
139C8×C43—21no—
140C8×C43—21no—
141C8×C43—21no—
142C8×C43—44no—
143C8×C43C2×M1612yes—
144C43⋊C8—24no—
145C43⋊C8—42no—
146#18065—431nomaximal, Sylow
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43C2×C4×D411yescharacteristic
151C2×D43—24no—
152C2×D43—42no—
153C2×D43—42no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43#44412yes—
158C4×C43C22×M1611yescharacteristic
159C4×C43#56811yescharacteristic
160C4×C43#57712yes—
161Dic43—42no—
162Dic43—42no—
163Dic43—42no—
164#2990—432no—
165C4×#135—431no—
166#1593—432no—
167#1582—434no—
168#1580—432no—
169#1566D4311yescharacteristic, complemented
170#1489—432no—
171#1451—431no—
172C2×C43—41no—
173C2×C43D4×M1611yescharacteristic
174C2×C43#295211yescharacteristic
175C2×C43C2×#44411yescharacteristic
176D43—44no—
177C2×#135—431no—
178C4×#41—432no—
179#446—434no—
180C4×Q16—431no—
181C4×Q16—431no—
182C4×SD16—432no—
183C4×SD16—432no—
184C4×D8—431no—
185C4×D8—431no—
186#435—864no—
187C8×D4—434no—
188#432—862no—
189#431—431no—
190#427—431no—
191#423C2×D4312yes—
192C2×C4⋊C8—862no—
193#416—432no—
194C4×M16—431no—
195C2×C4×C8C2×D4311yescharacteristic
196#334C2×D4312yes—
197#334C2×D4312yes—
198Q8⋊C8—434no—
199D4⋊C8—434no—
200#322—432no—
201#322—432no—
202C43#1806511yescharacteristic, complemented, Sylow
203C2×#41—432no—
204#135—864no—
205C2×Q16—431no—
206C2×SD16—432no—
207C2×D8—431no—
208C2×M16—22no—
209C2×M16—861no—
210C22×C8—864no—
211C22×C8C4×D4311yescharacteristic
212C22×C8C4×D4311yescharacteristic
213C4×Q8—432no—
214C4×Q8—432no—
215C4×D4—432no—
216C4×D4—432no—
217C4×D4—862no—
218C4×D4—862no—
219#117—432no—
220#117—862no—
221C2×C42—862no—
222C2×C42C22×D4311yescharacteristic
223#107—431no—
224#107—431no—
225#106—432no—
226C4⋊C8—22no—
227C4⋊C8—432no—
228C4⋊C8—864no—
229C4⋊C8C22×D4314yes—
230#103—432no—
231#103—432no—
232#102—432no—
233#102—432no—
234C22⋊C8—432no—
235C22⋊C8—864no—
236#97—864no—
237#97—861no—
238C4×C8—432no—
239C4×C8—432no—
240C4×C8C4×D4311yescharacteristic
241C4×C8C4×D4311yescharacteristic
242C4×C8C22×D4311yescharacteristic
243C4×C8C22×D4311yescharacteristic
244#41—864no—
245#41—1722no—
246C2×Q8—432no—
247C2×D4—432no—
248C2×D4—862no—
249C22×C4—862no—
250C22×C4—862no—
251C22×C4—862no—
252C22×C4C2×C4×D4311yescharacteristic
253C22×C4D4×D4311yescharacteristic
254C22×C4#1062190211yescharacteristic
255Q16—862no—
256SD16—864no—
257D8—434no—
258M16—82no—
259M16—1722no—
260C2×C8—22no—
261C2×C8—24no—
262C2×C8—41no—
263C2×C8—434no—
264C2×C8—862no—
265C2×C8—3444no—
266C2×C8C2×C4×D4311yescharacteristic
267C2×C8C2×C4×D4311yescharacteristic
268C2×C8C2×C4×D4311yescharacteristic
269C2×C8C2×C4×D4311yescharacteristic
270C4⋊C4—432no—
271C4⋊C4—432no—
272C4⋊C4—862no—
273C4⋊C4—862no—
274C22⋊C4—862no—
275C22⋊C4—862no—
276C22⋊C4—862no—
277C42—862no—
278C42—862no—
279C42—862no—
280C42C2×C4×D4311yescharacteristic
281C42D4×D4311yescharacteristic
282C42#1062190211yescharacteristic
283C42C23×D4311yescharacteristic
284C23—862no—
285C23#1306328711yescharacteristic
286Q8—862no—
287Q8—862no—
288D4—434no—
289D4—862no—
290D4—1724no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—862no—
296C2×C4—862no—
297C2×C4—862no—
298C2×C4—1724no—
299C2×C4—1722no—
300C2×C4—1722no—
301C2×C4—1724no—
302C2×C4#1306328711yescharacteristic
303C2×C4#1306328711yescharacteristic
304C2×C4#1306328711yescharacteristic
305C2×C4C22×C4×D4311yescharacteristic
306C2×C4C2×D4×D4311yescharacteristic
307C2×C4C2×#1062190211yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—44no—
312C8—864no—
313C8—1722no—
314C8M16×D4312yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—864no—
319C22—1722no—
320C22—1722no—
321C22C2×#1306328711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—1722no—
326C4—1722no—
327C4—1722no—
328C4#1458302012yes—
329C4C2×M16×D4311yescharacteristic
330C4#1458366511yescharacteristic
331C4#1458370512yes—
332C2—41no—
333C2—1724no—
334C2#1914333011yescharacteristic
335C2#1914347811yescharacteristic
336C2C2×#1458302011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1566C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063347C4
cosocleC42×C43C24
hypercenter#1566D43
hypocenterC43#18065
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
1. #19143721C2semidirect
3. #19133503C2semidirect
4. #19133430C2semidirect
5. #19133418C2semidirect
6. #19133032C2semidirect
7. #19132884C2semidirect
8. C43×#1566C2semidirect
112. D344M16semidirect
169. #1566D43semidirect
202. C43#18065semidirect

Maximal subgroups

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

subgroupindex
#191437212
C4×#130633472
#191335032
#191334302
#191334182
#191330322
#191328842
C43×#15662
#1806543