Finite Group Databasebeta

← #24990272

Subgroups — #24990272

Order 11008.

342 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134746C211yesmaximal, characteristic
2#19134711C211yesmaximal, characteristic
3#19134340C211yesmaximal, characteristic
4#19132430C211yesmaximal, characteristic
5#19132429C211yesmaximal, characteristic
6#19132429C211yesmaximal, characteristic
7C43×#1277C211yesmaximal, characteristic
8C2×C4⋊(C43⋊C8)C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×Dic43⋊C8—21no—
11C2×Dic43⋊C8—21no—
12C2×C4×C43⋊C8C2211yescharacteristic
13C42×Dic43C2211yescharacteristic
14#14582653—21no—
15#14582653—21no—
16#14582653C411yescharacteristic
17#14582653C411yescharacteristic
18#14582653C411yescharacteristic
19#14582653C411yescharacteristic
20C2×C4⋊C8×C43C2211yescharacteristic
21C2×C4⋊C8×C43C2211yescharacteristic
22C2×C4×C8×C43C2211yescharacteristic
23C22×C43⋊C8—21no—
24C22×C43⋊C8—21no—
25C22×C43⋊C8C2×C411yescharacteristic
26C22×C43⋊C8C2×C411yescharacteristic
27C2×C4×Dic43C2×C411yescharacteristic
28C2×C4×Dic43C2×C411yescharacteristic
29C2×C4×Dic43D411yescharacteristic
30C2×C4×Dic43D411yescharacteristic
31C2×C4×Dic43Q811yescharacteristic
32C2×C4×Dic43Q811yescharacteristic
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37Dic43⋊C8—42no—
38Dic43⋊C8—42no—
39C4×C43⋊C8—21no—
40C4×C43⋊C8—21no—
41C22×C8×C43—21no—
42C22×C8×C43—21no—
43C22×C8×C43C2×C411yescharacteristic
44C22×C8×C43C2×C411yescharacteristic
45C2×C42×C43C2311yescharacteristic
46C4⋊C8×C43—21no—
47C4⋊C8×C43—21no—
48C4⋊C8×C43—21no—
49C4⋊C8×C43—21no—
50C4×C8×C43—21no—
51C4×C8×C43—21no—
52C22×C4×C43C22×C411yescharacteristic
53C22×C4×C43C2×D411yescharacteristic
54C22×C4×C43C2×Q811yescharacteristic
55C22×Dic43C4⋊C411yescharacteristic
56C22×Dic43C4⋊C411yescharacteristic
57C22×Dic43C4⋊C411yescharacteristic
58C22×Dic43C4⋊C411yescharacteristic
59C2×C8×C43—21no—
60C2×C8×C43—21no—
61C2×C8×C43—21no—
62C2×C8×C43—21no—
63C2×C8×C43—21no—
64C2×C8×C43—21no—
65C2×C8×C43—41no—
66C2×C8×C43—41no—
67C2×C8×C43—41no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C42×C43#4111yescharacteristic
72C42×C43#4111yescharacteristic
73C42×C43#4111yescharacteristic
74C42×C43#4111yescharacteristic
75C4×Dic43—21no—
76C4×Dic43—21no—
77C4×Dic43—21no—
78C4×Dic43—21no—
79C4×Dic43—21no—
80C4×Dic43—21no—
81C4×Dic43—21no—
82C4×Dic43—21no—
83C4×Dic43—22no—
84C4×Dic43—22no—
85C2×C43⋊C8—21no—
86C2×C43⋊C8—21no—
87C2×C43⋊C8—21no—
88C2×C43⋊C8—21no—
89C2×C43⋊C8—21no—
90C2×C43⋊C8—21no—
91C2×C43⋊C8—41no—
92C2×C43⋊C8—41no—
93C2×C43⋊C8—41no—
94C2×C43⋊C8—41no—
95C2×C43⋊C8—41no—
96C2×C43⋊C8—41no—
97C23×C43C2×C4⋊C411yescharacteristic
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43#11711yescharacteristic
101C2×C4×C43#11711yescharacteristic
102C2×C4×C43#12411yescharacteristic
103C2×C4×C43#12411yescharacteristic
104C2×C4×C43#12511yescharacteristic
105C2×C4×C43#12511yescharacteristic
106C2×C4×C43#13111yescharacteristic
107C2×C4×C43#13111yescharacteristic
108C2×C4×C43#13111yescharacteristic
109C2×C4×C43#13111yescharacteristic
110C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C43#13711yescharacteristic
113C2×C4×C43#13711yescharacteristic
114C2×Dic43—21no—
115C2×Dic43—21no—
116C2×Dic43—21no—
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—21no—
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43#10812yes—
125C2×Dic43#10812yes—
126C8×C43—41no—
127C8×C43—41no—
128C8×C43—81no—
129C8×C43—81no—
130C43⋊C8—41no—
131C43⋊C8—41no—
132C43⋊C8—81no—
133C43⋊C8—81no—
134#8789—431nomaximal, Sylow
135C22×C43#38211yescharacteristic
136C22×C43#42411yescharacteristic
137C22×C43#42411yescharacteristic
138C22×C43#42811yescharacteristic
139C22×C43#42811yescharacteristic
140C22×C43C2×#10811yescharacteristic
141C22×C43C2×#10811yescharacteristic
142C4×C43—21no—
143C4×C43—21no—
144C4×C43#43311yescharacteristic
145C4×C43#43311yescharacteristic
146C4×C43#43311yescharacteristic
147C4×C43#43311yescharacteristic
148C4×C43#48911yescharacteristic
149C4×C43#48911yescharacteristic
150C4×C43#49011yescharacteristic
151C4×C43#49111yescharacteristic
152Dic43—22no—
153Dic43—22no—
154Dic43—41no—
155Dic43—41no—
156#1842—431no—
157#1831—431no—
158#1744—431no—
159#1277—431no—
160#1277—431no—
161#1277—431no—
162#1277D4311yescharacteristic
163C2×C43#157311yescharacteristic
164C2×C43#157311yescharacteristic
165C2×C43#157411yescharacteristic
166C2×C43#157411yescharacteristic
167C2×C43#183211yescharacteristic
168C2×C43#183611yescharacteristic
169C2×C43#183711yescharacteristic
170C2×C4⋊C8—431no—
171C2×C4⋊C8—431no—
172C2×C4⋊C8—861no—
173C2×C4⋊C8—861no—
174C2×C4⋊C8C2×D4311yescharacteristic
175C2×C4⋊C8C2×D4311yescharacteristic
176C2×C4×C8—431no—
177C2×C4×C8C2×D4311yescharacteristic
178C43—431no—
179#336—431no—
180#336—431no—
181#336—431no—
182#336—431no—
183#336—861no—
184#336—861no—
185C43#878911yescharacteristic, complemented, Sylow
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—431no—
189C22×C8—431no—
190C22×C8—861no—
191C22×C8—861no—
192C22×C8C4×D4311yescharacteristic
193C22×C8C4×D4311yescharacteristic
194C2×C42—431no—
195C2×C42—431no—
196C2×C42—431no—
197C2×C42—431no—
198C2×C42—431no—
199C2×C42—431no—
200C2×C42C22×D4311yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—861no—
206C4⋊C8—861no—
207C4⋊C8—861no—
208C4⋊C8—861no—
209C4⋊C8—1722no—
210C4⋊C8—1722no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—861no—
214C4×C8—861no—
215C22×C4—431no—
216C22×C4—431no—
217C22×C4—431no—
218C22×C4—431no—
219C22×C4C2×C4×D4311yescharacteristic
220C22×C4D4×D4311yescharacteristic
221C22×C4Q8×D4311yescharacteristic
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—861no—
235C2×C8—861no—
236C2×C8—861no—
237C2×C8—861no—
238C2×C8—861no—
239C2×C8—861no—
240C2×C8—1721no—
241C2×C8—1721no—
242C2×C8—1721no—
243C2×C8—1721no—
244C2×C8—1721no—
245C2×C8—1721no—
246C42—862no—
247C42—862no—
248C42—861no—
249C42—861no—
250C42—861no—
251C42—861no—
252C42—861no—
253C42—861no—
254C42—861no—
255C42—861no—
256C42#1062189811yescharacteristic
257C42#1062189811yescharacteristic
258C42#1062190011yescharacteristic
259C42#1062190011yescharacteristic
260C23C4⋊C4×D4311yescharacteristic
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—432no—
264C2×C4—432no—
265C2×C4—861no—
266C2×C4—861no—
267C2×C4—861no—
268C2×C4—861no—
269C2×C4—861no—
270C2×C4—861no—
271C2×C4—861no—
272C2×C4—861no—
273C2×C4—861no—
274C2×C4—861no—
275C2×C4#1306328111yescharacteristic
276C2×C4#1306328211yescharacteristic
277C2×C4#1306331111yescharacteristic
278C2×C4#1306331111yescharacteristic
279C2×C4#1306331511yescharacteristic
280C2×C4#1306331511yescharacteristic
281C2×C4#1306333111yescharacteristic
282C2×C4#1306333111yescharacteristic
283C2×C4#1306333311yescharacteristic
284C2×C4#1306333311yescharacteristic
285C2×C4#1306334911yescharacteristic
286C2×C4#1306335211yescharacteristic
287C2×C4#1306335411yescharacteristic
288C2×C4#1306335711yescharacteristic
289C8—41no—
290C8—41no—
291C8—81no—
292C8—81no—
293C8—3441no—
294C8—3441no—
295C8—1721no—
296C8—1721no—
297C22#1458276311yescharacteristic
298C22#1458292411yescharacteristic
299C22#1458292411yescharacteristic
300C22#1458293811yescharacteristic
301C22#1458294011yescharacteristic
302C22#108×D4311yescharacteristic
303C22#108×D4311yescharacteristic
304C4—21no—
305C4—21no—
306C4—862no—
307C4—862no—
308C4—1721no—
309C4—1721no—
310C4#1458295711yescharacteristic
311C4#1458295711yescharacteristic
312C4#1458295811yescharacteristic
313C4#1458296111yescharacteristic
314C4#1458325711yescharacteristic
315C4#1458326011yescharacteristic
316C4#1458326211yescharacteristic
317C4#1458326611yescharacteristic
318C2#1913337711yescharacteristic
319C2#1913337911yescharacteristic
320C2#1913338211yescharacteristic
321C2#1913338511yescharacteristic
322C2#1913471311yescharacteristic
323C2#1913472711yescharacteristic
324C2#1913473111yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1277C2
socle, prime radicalC23×C43C2×C4⋊C4
cosocleC2×C42×C43C23
hypercenter#1277D43
hypocenterC43#8789
LCSG ▷ C22×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
185. C43#8789semidirect

Maximal subgroups

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

subgroupindex
#191347462
#191347112
#191343402
#191324302
#191324292
C43×#12772
#878943