Finite Group Databasebeta

← #24990262

Subgroups — #24990262

Order 11008.

378 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134746C211yesmaximal, characteristic
2#19134711C211yesmaximal, characteristic
3C4×#13063235C211yesmaximal, 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×#13063235C411yescharacteristic
13C2×#13063235C411yescharacteristic
14C2×#13063235C411yescharacteristic
15C2×#13063235C411yescharacteristic
16C2×C4×C43⋊C8C2211yescharacteristic
17C42×Dic43C2211yescharacteristic
18#14582653—21no—
19#14582653—21no—
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—
39#13063235—22no—
40#13063235—22no—
41#13063235—22no—
42#13063235C814yescomplemented
43C4×C43⋊C8—21no—
44C4×C43⋊C8—21no—
45C22×C8×C43—21no—
46C22×C8×C43—21no—
47C22×C8×C43C2×C411yescharacteristic
48C22×C8×C43C2×C411yescharacteristic
49C2×C42×C43C2311yescharacteristic
50C4⋊C8×C43—21no—
51C4⋊C8×C43—21no—
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54C4×C8×C43—21no—
55C4×C8×C43—21no—
56C22×C4×C43C22×C411yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43C2×Q811yescharacteristic
59C22×Dic43C4⋊C411yescharacteristic
60C22×Dic43C4⋊C411yescharacteristic
61C22×Dic43C4⋊C411yescharacteristic
62C22×Dic43C4⋊C411yescharacteristic
63C2×C8×C43—21no—
64C2×C8×C43—21no—
65C2×C8×C43—21no—
66C2×C8×C43—21no—
67C2×C8×C43—41no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C2×C8×C43C2×C812yes—
74C2×C8×C43M1612yes—
75C42×C43#4111yescharacteristic
76C42×C43#4111yescharacteristic
77C42×C43#4111yescharacteristic
78C42×C43#4111yescharacteristic
79C4×Dic43—21no—
80C4×Dic43—21no—
81C4×Dic43—21no—
82C4×Dic43—21no—
83C4×Dic43—21no—
84C4×Dic43—21no—
85C4×Dic43—41no—
86C4×Dic43—41no—
87C4×Dic43C2×C812yes—
88C4×Dic43M1612yes—
89C2×C43⋊C8—21no—
90C2×C43⋊C8—21no—
91C2×C43⋊C8—21no—
92C2×C43⋊C8—21no—
93C2×C43⋊C8—41no—
94C2×C43⋊C8—41no—
95C2×C43⋊C8—41no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8C2×C812yes—
100C2×C43⋊C8M1612yes—
101C23×C43C2×C4⋊C411yescharacteristic
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43#11711yescharacteristic
105C2×C4×C43#11711yescharacteristic
106C2×C4×C43#12411yescharacteristic
107C2×C4×C43#12411yescharacteristic
108C2×C4×C43#12511yescharacteristic
109C2×C4×C43#12511yescharacteristic
110C2×C4×C43C22×C811yescharacteristic
111C2×C4×C43C2×M1611yescharacteristic
112C2×C4×C43C2×M1611yescharacteristic
113C2×C4×C43C2×M1611yescharacteristic
114C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C43#13711yescharacteristic
117C2×C4×C43#13711yescharacteristic
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×Dic43C4⋊C812yes—
129C2×Dic43C4⋊C812yes—
130C8×C43—22no—
131C8×C43—22no—
132C8×C43—81no—
133C8×C43—81no—
134C43⋊C8—22no—
135C43⋊C8—22no—
136C43⋊C8—81no—
137C43⋊C8—81no—
138#8786—431nomaximal, Sylow
139C22×C43#38211yescharacteristic
140C22×C43C2×C4⋊C811yescharacteristic
141C22×C43#42311yescharacteristic
142C22×C43#42811yescharacteristic
143C22×C43#42811yescharacteristic
144C22×C43#43011yescharacteristic
145C22×C43#43011yescharacteristic
146C4×C43—21no—
147C4×C43—21no—
148C4×C43#43111yescharacteristic
149C4×C43#43111yescharacteristic
150C4×C43#43211yescharacteristic
151C4×C43#43211yescharacteristic
152C4×C43#48911yescharacteristic
153C4×C43#48911yescharacteristic
154C4×C43#49011yescharacteristic
155C4×C43#49111yescharacteristic
156Dic43—22no—
157Dic43—22no—
158Dic43—41no—
159Dic43—41no—
160#1842—431no—
161#1831—431no—
162C4×#97—431no—
163#1277—431no—
164#1277—431no—
165#1277—431no—
166#1277D4311yescharacteristic
167C2×C43#156511yescharacteristic
168C2×C43#156511yescharacteristic
169C2×C43#156911yescharacteristic
170C2×C43#156911yescharacteristic
171C2×C43#183111yescharacteristic
172C2×C43#183611yescharacteristic
173C2×C43#183811yescharacteristic
174C2×C4⋊C8—431no—
175C2×C4⋊C8—431no—
176C2×C4⋊C8—861no—
177C2×C4⋊C8—861no—
178C2×C4⋊C8C2×D4311yescharacteristic
179C2×C4⋊C8C2×D4311yescharacteristic
180C2×#97—431no—
181C2×#97—431no—
182C2×#97—431no—
183C2×#97—431no—
184C2×C4×C8—431no—
185C2×C4×C8C2×D4311yescharacteristic
186C43—431no—
187#336—861no—
188#336—861no—
189C43#878611yescharacteristic, complemented, Sylow
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—431no—
193C22×C8—431no—
194C22×C8—861no—
195C22×C8—861no—
196C22×C8C4×D4311yescharacteristic
197C22×C8C4×D4311yescharacteristic
198C2×C42—431no—
199C2×C42—431no—
200C2×C42—431no—
201C2×C42—431no—
202C2×C42—431no—
203C2×C42—431no—
204C2×C42C22×D4311yescharacteristic
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—861no—
210C4⋊C8—861no—
211C4⋊C8—861no—
212C4⋊C8—861no—
213C4⋊C8—1722no—
214C4⋊C8—1722no—
215#97—434no—
216#97—862no—
217#97—862no—
218#97—862no—
219C4×C8—21no—
220C4×C8—21no—
221C4×C8—861no—
222C4×C8—861no—
223C22×C4—431no—
224C22×C4—431no—
225C22×C4—431no—
226C22×C4—431no—
227C22×C4C2×C4×D4311yescharacteristic
228C22×C4D4×D4311yescharacteristic
229C22×C4Q8×D4311yescharacteristic
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—432no—
241C2×C8—432no—
242C2×C8—861no—
243C2×C8—861no—
244C2×C8—861no—
245C2×C8—861no—
246C2×C8—1721no—
247C2×C8—1721no—
248C2×C8—1721no—
249C2×C8—1721no—
250C2×C8—1721no—
251C2×C8—1721no—
252C2×C8C8×D4312yes—
253C2×C8#1062187212yes—
254C42—432no—
255C42—432no—
256C42—861no—
257C42—861no—
258C42—861no—
259C42—861no—
260C42—861no—
261C42—861no—
262C42—1721no—
263C42—1721no—
264C42#1062189811yescharacteristic
265C42#1062189811yescharacteristic
266C42#1062190011yescharacteristic
267C42#1062190011yescharacteristic
268C23C4⋊C4×D4311yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—432no—
272C2×C4—432no—
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—861no—
282C2×C4—861no—
283C2×C4#1306328111yescharacteristic
284C2×C4#1306328211yescharacteristic
285C2×C4#1306331111yescharacteristic
286C2×C4#1306331111yescharacteristic
287C2×C4#1306331511yescharacteristic
288C2×C4#1306331511yescharacteristic
289C2×C4C2×C8×D4311yescharacteristic
290C2×C4M16×D4311yescharacteristic
291C2×C4M16×D4311yescharacteristic
292C2×C4C2×#1062187211yescharacteristic
293C2×C4#1306334911yescharacteristic
294C2×C4#1306335211yescharacteristic
295C2×C4#1306335411yescharacteristic
296C2×C4#1306335711yescharacteristic
297C8—22no—
298C8—22no—
299C8—81no—
300C8—81no—
301C8—862no—
302C8—862no—
303C8—3441no—
304C8—3441no—
305C22#1458276311yescharacteristic
306C22C4⋊C8×D4311yescharacteristic
307C22#1458292111yescharacteristic
308C22#1458293811yescharacteristic
309C22#1458294011yescharacteristic
310C22#1458294611yescharacteristic
311C22#1458294611yescharacteristic
312C4—21no—
313C4—21no—
314C4—862no—
315C4—862no—
316C4—1721no—
317C4—1721no—
318C4#1458294911yescharacteristic
319C4#1458295011yescharacteristic
320C4#1458295311yescharacteristic
321C4#1458295411yescharacteristic
322C4#1458325711yescharacteristic
323C4#1458326011yescharacteristic
324C4#1458326211yescharacteristic
325C4#1458326611yescharacteristic
326C2#1913334411yescharacteristic
327C2#1913334611yescharacteristic
328C2#1913335911yescharacteristic
329C2#1913336111yescharacteristic
330C2#1913471011yescharacteristic
331C2#1913472711yescharacteristic
332C2#1913473411yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1277C2
socle, prime radicalC23×C43C2×C4⋊C4
cosocleC2×C42×C43C23
hypercenter#1277D43
hypocenterC43#8786
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
42. #13063235C8semidirect
189. C43#8786semidirect

Maximal subgroups

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

subgroupindex
#191347462
#191347112
C4×#130632352
#191324302
#191324292
C43×#12772
#878643