Finite Group Databasebeta

← #24994734

Subgroups — #24994734

Order 11008.

372 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135311C211yesmaximal, characteristic
2C4×#13063259C211yesmaximal, characteristic
3#19134460C211yesmaximal, characteristic
4#19132434C211yesmaximal, characteristic
5#19132434C211yesmaximal, characteristic
6C43⋊#1273C211yesmaximal, characteristic
7C43×#1277C211yesmaximal, characteristic
8C2×#13063259C411yescharacteristic
9C2×#13063259C411yescharacteristic
10C2×Dic43⋊C8—21no—
11C2×C4×C43⋊C8C2211yescharacteristic
12C2×C4×C43⋊C8C2211yescharacteristic
13C2×C8×Dic43—21no—
14C4×C4⋊Dic43C2211yescharacteristic
15C4×C4⋊Dic43C2211yescharacteristic
16#14582662C411yescharacteristic
17#14582662C411yescharacteristic
18#14582653—21no—
19#14582653—21no—
20C2×C4⋊C8×C43C2211yescharacteristic
21C2×C4⋊C8×C43C2211yescharacteristic
22C2×C4×C8×C43C2211yescharacteristic
23C22×C43⋊C8—21no—
24C22×C43⋊C8D411yescharacteristic
25C22×C43⋊C8D411yescharacteristic
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×C4×Dic43—21no—
31C2×C4×Dic43—21no—
32#13063259—22no—
33#13063259C814yescomplemented
34Dic43⋊C8—42no—
35C4×C43⋊C8—21no—
36C4×C43⋊C8—21no—
37C4×C43⋊C8—21no—
38C4×C43⋊C8—21no—
39C8×Dic43—42no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C22×C8×C43—21no—
43C22×C8×C43—21no—
44C22×C8×C43C2×C411yescharacteristic
45C22×C8×C43C2×C411yescharacteristic
46C2×C42×C43C2311yescharacteristic
47C4⋊C8×C43—21no—
48C4⋊C8×C43—21no—
49C4⋊C8×C43—21no—
50C4⋊C8×C43Q812yes—
51C4×C8×C43—21no—
52C4×C8×C43—21no—
53C22×C4×C43C22×C411yescharacteristic
54C22×C4×C43C2×D411yescharacteristic
55C22×C4×C43#4111yescharacteristic
56C22×Dic43—21no—
57C22×Dic43—21no—
58C22×Dic43—21no—
59C22×Dic43—21no—
60C2×C8×C43—21no—
61C2×C8×C43—21no—
62C2×C8×C43—21no—
63C2×C8×C43—22no—
64C2×C8×C43—21no—
65C2×C8×C43—21no—
66C2×C8×C43—41no—
67C2×C8×C43—41no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C2×C8×C43C2×C812yes—
72C42×C43C2×Q811yescharacteristic
73C42×C43#4111yescharacteristic
74C42×C43#4111yescharacteristic
75C42×C43#4111yescharacteristic
76C4⋊Dic43—21no—
77C4⋊Dic43—21no—
78C4⋊Dic43—21no—
79C4⋊Dic43—21no—
80C4⋊Dic43—21no—
81C4⋊Dic43C2×C812yes—
82C4⋊Dic43C2×C812yes—
83C4⋊Dic43M1612yes—
84C4×Dic43—41no—
85C4×Dic43—41no—
86C4×Dic43—41no—
87C4×Dic43—41no—
88C2×C43⋊C8—21no—
89C2×C43⋊C8—21no—
90C2×C43⋊C8—22no—
91C2×C43⋊C8—21no—
92C2×C43⋊C8—21no—
93C2×C43⋊C8—21no—
94C2×C43⋊C8—41no—
95C2×C43⋊C8—41no—
96C2×C43⋊C8Q1612yes—
97C23×C43C4×D411yescharacteristic
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43#11711yescharacteristic
101C2×C4×C43C4×Q811yescharacteristic
102C2×C4×C43C22⋊Q811yescharacteristic
103C2×C4×C43#12311yescharacteristic
104C2×C4×C43#12511yescharacteristic
105C2×C4×C43#12611yescharacteristic
106C2×C4×C43C22×C811yescharacteristic
107C2×C4×C43C2×M1611yescharacteristic
108C2×C4×C43#13111yescharacteristic
109C2×C4×C43#13111yescharacteristic
110C2×C4×C43C2×Q1611yescharacteristic
111C2×C4×C43#13511yescharacteristic
112C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
113C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
114C2×Dic43—22no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C8×C43—22no—
127C8×C43—41no—
128C8×C43—42no—
129C8×C43—81no—
130C43⋊C8—22no—
131C43⋊C8—42no—
132C43⋊C8—41no—
133#9536—431nomaximal, Sylow
134C22×C43#38711yescharacteristic
135C22×C43C8×D411yescharacteristic
136C22×C43#43511yescharacteristic
137C22×C43C4×Q1611yescharacteristic
138C22×C43#44211yescharacteristic
139C22×C43#44311yescharacteristic
140C22×C43#44411yescharacteristic
141C4×C43—21no—
142C4×C43—21no—
143C4×C43#43111yescharacteristic
144C4×C43#43311yescharacteristic
145C4×C43C8×Q811yescharacteristic
146C4×C43#44611yescharacteristic
147C4×C43#47711yescharacteristic
148C4×C43#47811yescharacteristic
149C4×C43#48211yescharacteristic
150C4×C43#48411yescharacteristic
151Dic43—42no—
152Dic43—42no—
153Dic43—42no—
154Dic43—81no—
155#1939—431no—
156C4×#107—431no—
157C8×C4⋊C4—431no—
158#1279—431no—
159#1279—431no—
160#1277D4311yescharacteristic
161#1273—431no—
162C2×C43C8×Q1611yescharacteristic
163C2×C43#158011yescharacteristic
164C2×C43#158411yescharacteristic
165C2×C43#158611yescharacteristic
166C2×C43#191611yescharacteristic
167C2×C43#192111yescharacteristic
168C2×C43#192211yescharacteristic
169C2×#107—431no—
170C2×#107—431no—
171C2×C4⋊C8—861no—
172C2×C4⋊C8C2×D4311yescharacteristic
173C2×C4⋊C8C2×D4311yescharacteristic
174C2×C4×C8—431no—
175C2×C4×C8—431no—
176C2×C4×C8—861no—
177C2×C4×C8C2×D4311yescharacteristic
178C4×C4⋊C4—431no—
179C4×C4⋊C4—431no—
180#340—431no—
181#340—431no—
182#336—861no—
183#336—861no—
184C43#953611yescharacteristic, complemented, Sylow
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—431no—
188C22×C8—431no—
189C22×C8—861no—
190C22×C8C4×D4311yescharacteristic
191C22×C8C4×D4311yescharacteristic
192C2×C4⋊C4—431no—
193C2×C4⋊C4—431no—
194C2×C4⋊C4—431no—
195C2×C4⋊C4—431no—
196C2×C42—861no—
197C2×C42—861no—
198C2×C42C22×D4311yescharacteristic
199#107—434no—
200#107—862no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—1722no—
205C4⋊C8Dic8612yes—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—861no—
209C4×C8—861no—
210C4×C8—861no—
211C4×C8—861no—
212C4×C8—1722no—
213#95—861no—
214#95—861no—
215C22×C4—861no—
216C22×C4—861no—
217C22×C4—861no—
218C22×C4—861no—
219C22×C4C2×C4×D4311yescharacteristic
220C22×C4D4×D4311yescharacteristic
221C22×C4#1062190211yescharacteristic
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—22no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—432no—
234C2×C8—861no—
235C2×C8—861no—
236C2×C8—862no—
237C2×C8—861no—
238C2×C8—861no—
239C2×C8—861no—
240C2×C8—1721no—
241C2×C8—1721no—
242C2×C8C8×D4312yes—
243C4⋊C4—432no—
244C4⋊C4—432no—
245C4⋊C4—432no—
246C4⋊C4—861no—
247C4⋊C4—861no—
248C4⋊C4—861no—
249C4⋊C4—861no—
250C4⋊C4—861no—
251C42—1721no—
252C42—1721no—
253C42—1721no—
254C42—1721no—
255C42C2×Dic8611yescharacteristic
256C42#1062189811yescharacteristic
257C42#1062190011yescharacteristic
258C42#1062190011yescharacteristic
259C23#1306328711yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—862no—
263C2×C4—862no—
264C2×C4—862no—
265C2×C4—1721no—
266C2×C4—1721no—
267C2×C4—1721no—
268C2×C4—1721no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4—1721no—
272C2×C4—1721no—
273C2×C4—1721no—
274C2×C4#1306328111yescharacteristic
275C2×C4C4×Dic8611yescharacteristic
276C2×C4#1306330211yescharacteristic
277C2×C4#1306330711yescharacteristic
278C2×C4#1306331611yescharacteristic
279C2×C4#1306332011yescharacteristic
280C2×C4C2×C8×D4311yescharacteristic
281C2×C4M16×D4311yescharacteristic
282C2×C4#1306333111yescharacteristic
283C2×C4#1306333311yescharacteristic
284C2×C4Q16×D4311yescharacteristic
285C2×C4#1306334411yescharacteristic
286C2×C4#1306335211yescharacteristic
287C2×C4#1306335211yescharacteristic
288C8—22no—
289C8—42no—
290C8—41no—
291C8—81no—
292C8—862no—
293C8—1722no—
294C8—1721no—
295C22#1458278211yescharacteristic
296C22#1458296411yescharacteristic
297C22#1458296911yescharacteristic
298C22#1458299311yescharacteristic
299C22#1458301011yescharacteristic
300C22#1458301511yescharacteristic
301C22#1458302011yescharacteristic
302C4—21no—
303C4—21no—
304C4—3441no—
305C4—1722no—
306C4—1722no—
307C4—1722no—
308C4#1458294911yescharacteristic
309C4#1458295711yescharacteristic
310C4C8×Dic8611yescharacteristic
311C4#1458302711yescharacteristic
312C4#1458319211yescharacteristic
313C4#1458319711yescharacteristic
314C4#1458322111yescharacteristic
315C4#1458323311yescharacteristic
316C2#1913340111yescharacteristic
317C2#1913341811yescharacteristic
318C2#1913344411yescharacteristic
319C2#1913345811yescharacteristic
320C2#1913515111yescharacteristic
321C2#1913518611yescharacteristic
322C2#1913519311yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1277C2
socle, prime radicalC23×C43C4×D4
cosocleC2×C42×C43C23
hypercenter#1277D43
hypocenterC43#9536
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
33. #13063259C8semidirect
184. C43#9536semidirect

Maximal subgroups

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

subgroupindex
#191353112
C4×#130632592
#191344602
#191324342
C43⋊#12732
C43×#12772
#953643