Finite Group Databasebeta

← #24995200

Subgroups — #24995200

Order 11008.

368 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134711C211yesmaximal, characteristic
2#19134450C211yesmaximal, characteristic
3C4×Dic43⋊C8C211yesmaximal, characteristic
4C2×#14582651C211yesmaximal, characteristic
5C2×#14582650C211yesmaximal, characteristic
6#19132429C211yesmaximal, characteristic
7C43×#1277C211yesmaximal, characteristic
8C2×C4⋊(C43⋊C8)C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×Dic43⋊C8C411yescharacteristic
11C2×Dic43⋊C8C411yescharacteristic
12C2×#13063235—21no—
13C2×C4×C43⋊C8C2211yescharacteristic
14C42×Dic43C2211yescharacteristic
15#14582653—21no—
16#14582653—21no—
17#14582653—21no—
18#14582653C411yescharacteristic
19#14582653C411yescharacteristic
20#14582651—22no—
21#14582650—22no—
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4×C8×C43C2211yescharacteristic
25C22×C43⋊C8—21no—
26C22×C43⋊C8—21no—
27C22×C43⋊C8C2×C411yescharacteristic
28C22×C43⋊C8C2×C411yescharacteristic
29C2×C4×Dic43C2×C411yescharacteristic
30C2×C4×Dic43C2×C411yescharacteristic
31C2×C4×Dic43D411yescharacteristic
32C2×C4×Dic43D411yescharacteristic
33C2×C4×Dic43Q811yescharacteristic
34C2×C4×Dic43Q811yescharacteristic
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)D412yes—
39Dic43⋊C8—22no—
40Dic43⋊C8—22no—
41#13063235—42no—
42C4×C43⋊C8—21no—
43C4×C43⋊C8—21no—
44C22×C8×C43—21no—
45C22×C8×C43—21no—
46C22×C8×C43C2×C411yescharacteristic
47C22×C8×C43C2×C411yescharacteristic
48C2×C42×C43C2311yescharacteristic
49C4⋊C8×C43—21no—
50C4⋊C8×C43—21no—
51C4⋊C8×C43—21no—
52C4⋊C8×C43Q812yes—
53C4×C8×C43—21no—
54C4×C8×C43—21no—
55C22×C4×C43C22×C411yescharacteristic
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43C2×Q811yescharacteristic
58C22×Dic43C4⋊C411yescharacteristic
59C22×Dic43C4⋊C411yescharacteristic
60C22×Dic43C4⋊C411yescharacteristic
61C22×Dic43C4⋊C411yescharacteristic
62C2×C8×C43—21no—
63C2×C8×C43—21no—
64C2×C8×C43—21no—
65C2×C8×C43—22no—
66C2×C8×C43—21no—
67C2×C8×C43—21no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C2×C8×C43M1612yes—
74C42×C43C2×D411yescharacteristic
75C42×C43C2×Q811yescharacteristic
76C42×C43#4111yescharacteristic
77C42×C43#4111yescharacteristic
78C4×Dic43—21no—
79C4×Dic43—21no—
80C4×Dic43—21no—
81C4×Dic43—21no—
82C4×Dic43—21no—
83C4×Dic43—21no—
84C4×Dic43—21no—
85C4×Dic43—21no—
86C4×Dic43—22no—
87C4×Dic43—41no—
88C2×C43⋊C8—21no—
89C2×C43⋊C8—21no—
90C2×C43⋊C8—21no—
91C2×C43⋊C8—22no—
92C2×C43⋊C8—21no—
93C2×C43⋊C8—21no—
94C2×C43⋊C8—41no—
95C2×C43⋊C8—41no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8M1612yes—
100C23×C43C2×C4⋊C411yescharacteristic
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43C4×D411yescharacteristic
104C2×C4×C43C4×Q811yescharacteristic
105C2×C4×C43#12111yescharacteristic
106C2×C4×C43C22⋊Q811yescharacteristic
107C2×C4×C43#12511yescharacteristic
108C2×C4×C43C4⋊Q811yescharacteristic
109C2×C4×C43C2×M1611yescharacteristic
110C2×C4×C43C2×M1611yescharacteristic
111C2×C4×C43#13111yescharacteristic
112C2×C4×C43#13111yescharacteristic
113C2×C4×C43#13511yescharacteristic
114C2×C4×C43#13511yescharacteristic
115C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C43#13711yescharacteristic
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—21no—
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43#10812yes—
129C8×C43—22no—
130C8×C43—41no—
131C8×C43—42no—
132C8×C43—81no—
133C43⋊C8—22no—
134C43⋊C8—41no—
135C43⋊C8—42no—
136C43⋊C8—81no—
137#9606—431nomaximal, Sylow
138C22×C43#38911yescharacteristic
139C22×C43#42311yescharacteristic
140C22×C43#42411yescharacteristic
141C22×C43#42711yescharacteristic
142C22×C43#42811yescharacteristic
143C22×C43C2×#10811yescharacteristic
144C22×C43#43011yescharacteristic
145C4×C43—21no—
146C4×C43—21no—
147C4×C43#43511yescharacteristic
148C4×C43#43511yescharacteristic
149C4×C43#44611yescharacteristic
150C4×C43#44611yescharacteristic
151C4×C43#46311yescharacteristic
152C4×C43#46411yescharacteristic
153C4×C43#47811yescharacteristic
154C4×C43#47911yescharacteristic
155Dic43—22no—
156Dic43—41no—
157Dic43—41no—
158Dic43—41no—
159#1831—431no—
160#1767—431no—
161C4×C4⋊C8—431no—
162C2×#335—431no—
163C2×#334—431no—
164#1277—431no—
165#1277D4311yescharacteristic
166C2×C43#156811yescharacteristic
167C2×C43#156911yescharacteristic
168C2×C43#157211yescharacteristic
169C2×C43#157411yescharacteristic
170C2×C43#194011yescharacteristic
171C2×C43#194911yescharacteristic
172C2×C43#195011yescharacteristic
173C2×C4⋊C8—431no—
174C2×C4⋊C8—431no—
175C2×C4⋊C8—431no—
176C2×C4⋊C8—431no—
177C2×C4⋊C8C2×D4311yescharacteristic
178C2×C4⋊C8C2×D4311yescharacteristic
179C2×#97—861no—
180C2×C4×C8—431no—
181C2×C4×C8C2×D4311yescharacteristic
182C43—431no—
183#336—431no—
184#336—431no—
185#336—861no—
186#336—861no—
187#336—861no—
188#335—862no—
189#334—862no—
190C43#960611yescharacteristic, complemented, Sylow
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—431no—
194C22×C8—431no—
195C22×C8—861no—
196C22×C8—861no—
197C22×C8C4×D4311yescharacteristic
198C22×C8C4×D4311yescharacteristic
199C2×C42—431no—
200C2×C42—431no—
201C2×C42—431no—
202C2×C42—431no—
203C2×C42—431no—
204C2×C42—431no—
205C2×C42C22×D4311yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—432no—
210C4⋊C8—862no—
211C4⋊C8—862no—
212C4⋊C8—861no—
213C4⋊C8—861no—
214C4⋊C8—861no—
215C4⋊C8Dic8612yes—
216#97—1722no—
217C4×C8—21no—
218C4×C8—21no—
219C4×C8—861no—
220C4×C8—861no—
221C22×C4—431no—
222C22×C4—431no—
223C22×C4—431no—
224C22×C4—431no—
225C22×C4C2×C4×D4311yescharacteristic
226C22×C4D4×D4311yescharacteristic
227C22×C4Q8×D4311yescharacteristic
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—22no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—432no—
240C2×C8—861no—
241C2×C8—861no—
242C2×C8—861no—
243C2×C8—862no—
244C2×C8—861no—
245C2×C8—861no—
246C2×C8—1721no—
247C2×C8—1721no—
248C2×C8—1721no—
249C2×C8—1721no—
250C2×C8—1721no—
251C2×C8#1062187212yes—
252C42—862no—
253C42—861no—
254C42—861no—
255C42—861no—
256C42—861no—
257C42—861no—
258C42—861no—
259C42—861no—
260C42—861no—
261C42—1721no—
262C42C2×Dic8611yescharacteristic
263C42#1062189811yescharacteristic
264C42D4×D4311yescharacteristic
265C42#1062190011yescharacteristic
266C23C4⋊C4×D4311yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—432no—
270C2×C4—861no—
271C2×C4—861no—
272C2×C4—861no—
273C2×C4—861no—
274C2×C4—861no—
275C2×C4—861no—
276C2×C4—861no—
277C2×C4—861no—
278C2×C4—861no—
279C2×C4—861no—
280C2×C4—861no—
281C2×C4(C22⋊D43)⋊C411yescharacteristic
282C2×C4C4×Dic8611yescharacteristic
283C2×C4#1306329811yescharacteristic
284C2×C4#1306330211yescharacteristic
285C2×C4#1306331511yescharacteristic
286C2×C4#1306332411yescharacteristic
287C2×C4M16×D4311yescharacteristic
288C2×C4C2×#1062187211yescharacteristic
289C2×C4#1306333111yescharacteristic
290C2×C4#1306333311yescharacteristic
291C2×C4#1306334611yescharacteristic
292C2×C4#1306334611yescharacteristic
293C2×C4#1306334911yescharacteristic
294C2×C4#1306335711yescharacteristic
295C8—22no—
296C8—42no—
297C8—41no—
298C8—81no—
299C8—862no—
300C8—3441no—
301C8—1722no—
302C8—1721no—
303C22#1458279611yescharacteristic
304C22#1458292111yescharacteristic
305C22#1458292411yescharacteristic
306C22#1458293411yescharacteristic
307C22#1458294011yescharacteristic
308C22#108×D4311yescharacteristic
309C22#1458294611yescharacteristic
310C4—21no—
311C4—21no—
312C4—862no—
313C4—1721no—
314C4—1721no—
315C4—1721no—
316C4#1458296711yescharacteristic
317C4#1458297311yescharacteristic
318C4#1458302711yescharacteristic
319C4#1458302911yescharacteristic
320C4#1458311311yescharacteristic
321C4#1458312411yescharacteristic
322C4#1458320111yescharacteristic
323C4#1458320411yescharacteristic
324C2#1913335511yescharacteristic
325C2#1913336111yescharacteristic
326C2#1913337211yescharacteristic
327C2#1913338511yescharacteristic
328C2#1913531711yescharacteristic
329C2#1913536211yescharacteristic
330C2#1913536911yescharacteristic
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#9606
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
190. C43#9606semidirect

Maximal subgroups

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

subgroupindex
#191347112
#191344502
C4×Dic43⋊C82
C2×#145826512
C2×#145826502
#191324292
C43×#12772
#960643