Finite Group Databasebeta

← #25014966

Subgroups — #25014966

Order 11008.

510 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063266C211yesmaximal, characteristic
2C2×#14582724C211yesmaximal, characteristic, complemented
3C2×#14582700C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic, complemented
5C2×C4×C43⋊C16C211yesmaximal, characteristic, complemented
6#19135461C211yesmaximal, characteristic, complemented
7C43×#1970C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C2×#13063266—22no—
10C2×#13063266—22no—
11C2×#13063266C414yescomplemented
12C22×C43⋊C16C2211yescharacteristic
13C22×C43⋊C16C2211yescharacteristic
14C2×#13063259C2211yescharacteristic
15C2×#13063247—21no—
16#14582801—21no—
17#14582724—22no—
18#14582700—22no—
19#14582699—22no—
20C4×C43⋊C16—22no—
21C22×D8×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C2×#102×C43—21no—
24C2×C4×C8×C43C2211yescharacteristic
25C43×#390—21no—
26C22×D172—21no—
27C2×D344—21no—
28C2×D344—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344C2×C412yes—
33C2×C4⋊Dic43—21no—
34C2×(C2×D43)⋊C4—42no—
35#13063266—28no—
36C2×C43⋊C16—21no—
37C2×C43⋊C16—21no—
38C2×C43⋊C16C2×C412yes—
39C2×C43⋊C16D412yes—
40C2×C43⋊C16D412yes—
41C2×C43⋊C16D412yes—
42#13063259—21no—
43#13063259—21no—
44#13063247—42no—
45C22×D4×C43—21no—
46C2×D8×C43—21no—
47C2×D8×C43—21no—
48C2×D8×C43—21no—
49C2×D8×C43—21no—
50C2×D8×C43—21no—
51C2×D8×C43C2×C412yes—
52C22×C8×C43D411yescharacteristic
53C22×C8×C43C2311yescharacteristic
54C2×C4⋊C4×C43—21no—
55C2×C22⋊C4×C43—42no—
56C2×C42×C43D411yescharacteristic
57#107×C43—21no—
58#107×C43—21no—
59#102×C43—42no—
60C4×C8×C43—21no—
61C4×C8×C43—21no—
62C24×C43—41no—
63C23×D43—41no—
64C2×D4×C43—22no—
65C2×D4×C43—41no—
66C2×D4×C43—41no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C2×D4×C43—41no—
70C22×C4×C43—41no—
71C22×C4×C43D812yes—
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—41no—
74C2×D172—22no—
75C2×D172—41no—
76C2×D172—41no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172—41no—
80D8×C43—22no—
81D8×C43—22no—
82D8×C43—41no—
83D8×C43—41no—
84C2×C8×C43—21no—
85C2×C8×C43—21no—
86C2×C8×C43D812yes—
87C2×C8×C43C22×C411yescharacteristic
88C2×C8×C43C2×D411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43#4111yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C22⋊C4×C43—84no—
96C42×C43—21no—
97C42×C43—21no—
98(C2×D43)⋊C4—84no—
99C4⋊Dic43—41no—
100C4⋊Dic43—41no—
101D344—22no—
102D344—22no—
103D344—41no—
104D344—41no—
105C43⋊C16—22no—
106C43⋊C16C22⋊C414yescomplemented
107C23×C43—42no—
108C23×C43—81no—
109C23×C43—81no—
110C23×C43—82no—
111C23×C43—82no—
112C23×C43C2×D811yescharacteristic
113C22×D43—42no—
114C22×D43—81no—
115C22×D43—81no—
116C22×D43—82no—
117C22×D43—82no—
118D4×C43—42no—
119D4×C43—42no—
120D4×C43—81no—
121D4×C43—81no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—81no—
125C2×C4×C43—82no—
126C2×C4×C43D1614yescomplemented
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12711yescharacteristic
130C2×C4×C43C2×D811yescharacteristic
131C2×C4×C43#13511yescharacteristic
132C2×C4×C43#13511yescharacteristic
133C2×Dic43—81no—
134C2×Dic43—82no—
135D172—42no—
136D172—42no—
137D172—81no—
138D172—81no—
139C8×C43—22no—
140C8×C43C2×C22⋊C411yescharacteristic
141C8×C43C4×D411yescharacteristic
142C8×C43#12111yescharacteristic
143C8×C43#12411yescharacteristic
144#13235—431nomaximal, Sylow
145C22×C43—84no—
146C22×C43—82no—
147C22×C43—162no—
148C22×C43—161no—
149C22×C43—161no—
150C22×C43C4×D811yescharacteristic
151C22×C43#46611yescharacteristic
152C22×C43#49311yescharacteristic
153C22×C43C2×D1612yes—
154C22×C43#50812yes—
155C2×D43—84no—
156C2×D43—82no—
157C2×D43—162no—
158C2×D43—161no—
159C2×D43—161no—
160C4×C43—24no—
161C4×C43—161no—
162C4×C43#39011yescharacteristic
163C4×C43C4×D811yescharacteristic
164C4×C43#46611yescharacteristic
165C4×C43#49511yescharacteristic
166Dic43—161no—
167C22×D16—431no—
168C2×#366—431no—
169C2×#357—431no—
170C2×#357—431no—
171C2×C4×C16—431no—
172#1970—431no—
173#1970D4311yescharacteristic, complemented
174C2×C43—162no—
175C2×C43#197011yescharacteristic
176C2×C43C4×D1612yes—
177C2×C43#221512yes—
178C2×C43#224611yescharacteristic
179C2×C43#224911yescharacteristic
180D43—162no—
181C22×D8—431no—
182C22×D8C2×D4311yescharacteristic
183C2×D16—434no—
184C2×D16—862no—
185C2×D16—862no—
186C22×C16—431no—
187C22×C16—431no—
188C2×#107—431no—
189C2×#107C2×D4311yescharacteristic
190C2×#102—21no—
191C2×#102—861no—
192C2×C4×C8C2×D4311yescharacteristic
193#390—21no—
194#390—861no—
195#366—862no—
196#357—862no—
197#357—862no—
198C4×C16—862no—
199C43#1323511yescharacteristic, complemented, Sylow
200C22×D4—21no—
201C22×D4—861no—
202C2×D8—21no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8—21no—
206C2×D8—21no—
207C2×D8—432no—
208C2×D8—861no—
209C2×D8—861no—
210C2×D8—861no—
211C2×D8—861no—
212C2×D8—861no—
213C2×D8C4×D4312yes—
214C22×C8C22⋊D4311yescharacteristic
215C22×C8C22×D4311yescharacteristic
216C2×C4⋊C4—21no—
217C2×C4⋊C4—861no—
218C2×C22⋊C4—42no—
219C2×C22⋊C4—1722no—
220C2×C42C22⋊D4311yescharacteristic
221D16—868no—
222C2×C16—432no—
223C2×C16—432no—
224C2×C16—432no—
225C2×C16—432no—
226C2×C16—861no—
227C2×C16—861no—
228#107—21no—
229#107—21no—
230#107—861no—
231#107—861no—
232#102—42no—
233#102—1722no—
234C4×C8—21no—
235C4×C8—21no—
236C24—41no—
237C24—1721no—
238C2×D4—22no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—862no—
245C2×D4—1721no—
246C2×D4—1721no—
247C2×D4—1721no—
248C2×D4—1721no—
249C2×D4—1721no—
250C22×C4—41no—
251C22×C4—1721no—
252C22×C4#1062188212yes—
253C22×C4C2×C22⋊D4311yescharacteristic
254D8—22no—
255D8—22no—
256D8—41no—
257D8—41no—
258D8—862no—
259D8—862no—
260D8—1721no—
261D8—1721no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8#1062188212yes—
265C2×C8C2×C4×D4311yescharacteristic
266C2×C8#1062189811yescharacteristic
267C2×C8D4×D4311yescharacteristic
268C2×C8D4×D4311yescharacteristic
269C2×C8D4×D4311yescharacteristic
270C2×C8#1062190011yescharacteristic
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C22⋊C4—84no—
276C22⋊C4—3444no—
277C42—21no—
278C42—21no—
279C16—434no—
280C16—862no—
281C23—42no—
282C23—82no—
283C23—82no—
284C23—81no—
285C23—81no—
286C23—3442no—
287C23—3442no—
288C23—3441no—
289C23—3441no—
290C23—1722no—
291C23C2×#1062188211yescharacteristic
292D4—42no—
293D4—42no—
294D4—81no—
295D4—81no—
296D4—3441no—
297D4—3441no—
298D4—1722no—
299D4—1722no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—3442no—
305C2×C4—3441no—
306C2×C4#1306326614yescomplemented
307C2×C4C4×C22⋊D4311yescharacteristic
308C2×C4#1306329711yescharacteristic
309C2×C4#1306332111yescharacteristic
310C2×C4C2×#1062188211yescharacteristic
311C2×C4#1306334511yescharacteristic
312C2×C4#1306334511yescharacteristic
313C8—22no—
314C8C22⋊C4×D4311yescharacteristic
315C8(C22⋊D43)⋊C411yescharacteristic
316C8#1306329811yescharacteristic
317C8#1306331111yescharacteristic
318C22—84no—
319C22—82no—
320C22—161no—
321C22—161no—
322C22—162no—
323C22—3444no—
324C22—3442no—
325C22—6881no—
326C22—6881no—
327C22—6882no—
328C22C4×#1062188211yescharacteristic
329C22#1458313311yescharacteristic
330C22#1458327511yescharacteristic
331C22C2×#1306326612yes—
332C22#1458332912yes—
333C4—24no—
334C4—161no—
335C4—6881no—
336C4#1458279911yescharacteristic
337C4C4×#1062188211yescharacteristic
338C4#1458313311yescharacteristic
339C4#1458328111yescharacteristic
340C2—162no—
341C2—6882no—
342C2#1913546011yescharacteristic
343C2C4×#1306326612yes—
344C2#1913667912yes—
345C2#1913684411yescharacteristic
346C2#1913685411yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1970C2
socleC23×C43C2×D8
prime radicalC22×#13063266C2
cosocleC22×C8×C43C23
hypercenter#1970D43
hypocenterC43#13235
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. C2×#14582724C2semidirect
3. C2×#14582700C2semidirect
4. C2×#14582699C2semidirect
5. C2×C4×C43⋊C16C2semidirect
6. #19135461C2semidirect
7. C43×#1970C2semidirect
11. C2×#13063266C4semidirect
106. C43⋊C16C22⋊C4semidirect
126. C2×C4×C43D16semidirect
173. #1970D43semidirect
199. C43#13235semidirect
306. C2×C4#13063266semidirect

Maximal subgroups

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

subgroupindex
C22×#130632662
C2×#145827242
C2×#145827002
C2×#145826992
C2×C4×C43⋊C162
#191354612
C43×#19702
#1323543