Finite Group Databasebeta

← #24994865

Subgroups — #24994865

Order 11008.

398 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135532C211yesmaximal, characteristic
2#19135311C211yesmaximal, characteristic
3C4×#13063249C211yesmaximal, characteristic
4C2×#14582621C211yesmaximal, characteristic
5#19132435C211yesmaximal, characteristic
6#19132429C211yesmaximal, characteristic
7C2×C43×Q8⋊C8C211yesmaximal, characteristic
8C2×C4⋊(C43⋊C8)C2211yescharacteristic
9C2×Dic43⋊C8—21no—
10C2×#13063249C411yescharacteristic
11C2×#13063249C411yescharacteristic
12C2×C4×C43⋊C8C2211yescharacteristic
13C2×C4×C43⋊C8C2211yescharacteristic
14C4×C4⋊Dic43C2211yescharacteristic
15#14582661C411yescharacteristic
16#14582661C411yescharacteristic
17#14582654—21no—
18#14582654—21no—
19#14582653—21no—
20#14582621—22no—
21C2×C4×Q8×C43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4×C8×C43C2211yescharacteristic
24C43×Q8⋊C8—22no—
25C22×C43⋊C8—21no—
26C22×C43⋊C8C2×C411yescharacteristic
27C22×C43⋊C8C2×C411yescharacteristic
28C22×C43⋊C8D411yescharacteristic
29C22×C43⋊C8D411yescharacteristic
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×C4×Dic43—21no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35Dic43⋊C8—42no—
36#13063249—22no—
37#13063249C814yescomplemented
38C4×C43⋊C8—21no—
39C4×C43⋊C8—21no—
40C4×C43⋊C8—21no—
41C4×C43⋊C8—21no—
42C43⋊#95—21no—
43C22×Q8×C43C2×C411yescharacteristic
44C22×C8×C43—21no—
45C22×C8×C43—21no—
46C4×Q8×C43—21no—
47C4×Q8×C43—21no—
48C4×Q8×C43—21no—
49C4×Q8×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43C2×C411yescharacteristic
52C2×C42×C43—21no—
53C2×C42×C43C2311yescharacteristic
54C4⋊C8×C43—21no—
55C4⋊C8×C43—21no—
56C4×C8×C43—21no—
57C4×C8×C43D412yes—
58C2×Q8×C43—21no—
59C2×Q8×C43—21no—
60C2×Q8×C43—21no—
61C2×Q8×C43—21no—
62C2×Q8×C43—21no—
63C2×Q8×C43C2×C812yes—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43#4111yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C2×C8×C43—22no—
72C2×C8×C43—41no—
73C2×C8×C43—41no—
74C2×C8×C43—41no—
75C2×C8×C43—41no—
76C2×C8×C43—41no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C42×C43—41no—
82C42×C43—41no—
83C42×C43C2×D411yescharacteristic
84C42×C43#4111yescharacteristic
85C42×C43#4111yescharacteristic
86C42×C43#4111yescharacteristic
87C4⋊Dic43—21no—
88C4⋊Dic43—21no—
89C4⋊Dic43—21no—
90C4⋊Dic43C2×C812yes—
91C4×Dic43—41no—
92C4×Dic43—41no—
93C2×C43⋊C8—21no—
94C2×C43⋊C8—21no—
95C2×C43⋊C8—21no—
96C2×C43⋊C8—21no—
97C2×C43⋊C8—21no—
98C2×C43⋊C8—21no—
99C2×C43⋊C8—21no—
100C2×C43⋊C8—21no—
101C2×C43⋊C8—21no—
102C2×C43⋊C8—21no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8C2×C812yes—
107C2×C43⋊C8M1612yes—
108C23×C43C4×D411yescharacteristic
109Q8×C43—22no—
110Q8×C43—22no—
111Q8×C43—41no—
112Q8×C43—41no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—22no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43#11711yescharacteristic
122C2×C4×C43C4×D411yescharacteristic
123C2×C4×C43#12111yescharacteristic
124C2×C4×C43#12311yescharacteristic
125C2×C4×C43#12411yescharacteristic
126C2×C4×C43#12611yescharacteristic
127C2×C4×C43C22×C811yescharacteristic
128C2×C4×C43C2×M1611yescharacteristic
129C2×C4×C43#13111yescharacteristic
130C2×C4×C43#13111yescharacteristic
131C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C43#13711yescharacteristic
133C2×C4×C43#13711yescharacteristic
134C2×C4×C43#13711yescharacteristic
135C2×Dic43—22no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C8×C43—42no—
142C8×C43—81no—
143C43⋊C8—22no—
144C43⋊C8—22no—
145C43⋊C8—41no—
146C43⋊C8—41no—
147C43⋊C8—81no—
148#9555—431nomaximal, Sylow
149C22×C43#38811yescharacteristic
150C22×C43C8×D411yescharacteristic
151C22×C43#43611yescharacteristic
152C22×C43#44011yescharacteristic
153C22×C43#44111yescharacteristic
154C22×C43#44411yescharacteristic
155C22×C43#44411yescharacteristic
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—42no—
159C4×C43—81no—
160C4×C43#43111yescharacteristic
161C4×C43#43311yescharacteristic
162C4×C43C8×D411yescharacteristic
163C4×C43#43511yescharacteristic
164C4×C43#46811yescharacteristic
165C4×C43#47011yescharacteristic
166C4×C43#48911yescharacteristic
167C4×C43#49111yescharacteristic
168Dic43—42no—
169Dic43—81no—
170#1984—431no—
171#1939—431no—
172C4×#103—431no—
173C2×Q8⋊C8D4311yescharacteristic
174C2×#322—431no—
175#1279—431no—
176#1277—431no—
177C2×C43SD16⋊C811yescharacteristic
178C2×C43#157911yescharacteristic
179C2×C43#159211yescharacteristic
180C2×C43#159311yescharacteristic
181C2×C43#192311yescharacteristic
182C2×C43#193511yescharacteristic
183C2×C43#193811yescharacteristic
184C2×C4×Q8C2×D4311yescharacteristic
185C2×C4⋊C8—431no—
186C2×C4⋊C8—861no—
187C2×C4⋊C8C2×D4311yescharacteristic
188C2×#103—431no—
189C2×#103—431no—
190C2×C4×C8—431no—
191C2×C4×C8—431no—
192C2×C4×C8C2×D4311yescharacteristic
193C4×C4⋊C4—431no—
194#340—431no—
195#340—431no—
196#336—861no—
197#336—861no—
198#336—861no—
199Q8⋊C8—22no—
200#322—862no—
201C43#955511yescharacteristic, complemented, Sylow
202C22×Q8C4×D4311yescharacteristic
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—431no—
206C22×C8—431no—
207C22×C8—431no—
208C22×C8—431no—
209C22×C8—861no—
210C4×Q8—21no—
211C4×Q8—21no—
212C4×Q8—21no—
213C4×Q8—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—431no—
216C2×C4⋊C4—431no—
217C2×C4⋊C4C4×D4311yescharacteristic
218C2×C42—21no—
219C2×C42—861no—
220C2×C42C22×D4311yescharacteristic
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—861no—
224C4⋊C8—861no—
225C4⋊C8—1722no—
226#103—434no—
227#103—862no—
228C4×C8—21no—
229C4×C8—861no—
230C4×C8—861no—
231C4×C8—861no—
232C4×C8—861no—
233C4×C8C22⋊D4312yes—
234#95—861no—
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8C8×D4312yes—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4C2×C4×D4311yescharacteristic
246C22×C4D4×D4311yescharacteristic
247C22×C4#1062190011yescharacteristic
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—432no—
255C2×C8—432no—
256C2×C8—861no—
257C2×C8—861no—
258C2×C8—861no—
259C2×C8—861no—
260C2×C8—861no—
261C2×C8—861no—
262C2×C8—861no—
263C2×C8—861no—
264C2×C8—861no—
265C2×C8—861no—
266C2×C8—1721no—
267C2×C8—1721no—
268C2×C8—1721no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—432no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C42—41no—
278C42—41no—
279C42—1721no—
280C42—1721no—
281C42#1062189811yescharacteristic
282C42#1062190011yescharacteristic
283C42#1062190011yescharacteristic
284C42C2×C22⋊D4311yescharacteristic
285C23(C22⋊D43)⋊C411yescharacteristic
286Q8—22no—
287Q8—22no—
288Q8—41no—
289Q8—41no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—862no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4#1306328111yescharacteristic
305C2×C4C4×C22⋊D4311yescharacteristic
306C2×C4#1306329611yescharacteristic
307C2×C4#1306330611yescharacteristic
308C2×C4#1306331111yescharacteristic
309C2×C4#1306331811yescharacteristic
310C2×C4C2×C8×D4311yescharacteristic
311C2×C4M16×D4311yescharacteristic
312C2×C4#1306333111yescharacteristic
313C2×C4#1306333311yescharacteristic
314C2×C4#1306335211yescharacteristic
315C2×C4#1306335411yescharacteristic
316C2×C4#1306335711yescharacteristic
317C2×C4#1306335711yescharacteristic
318C8—42no—
319C8—81no—
320C8—862no—
321C8—862no—
322C8—3441no—
323C8—1721no—
324C8—1721no—
325C22#1458278711yescharacteristic
326C22(C22⋊D43)⋊C811yescharacteristic
327C22#1458297411yescharacteristic
328C22#1458300211yescharacteristic
329C22#1458300311yescharacteristic
330C22#1458301811yescharacteristic
331C22#1458301811yescharacteristic
332C4—21no—
333C4—21no—
334C4—42no—
335C4—81no—
336C4—3441no—
337C4—1722no—
338C4#1458294911yescharacteristic
339C4#1458295711yescharacteristic
340C4C8×C22⋊D4311yescharacteristic
341C4#1458296811yescharacteristic
342C4#1458314211yescharacteristic
343C4#1458315411yescharacteristic
344C4#1458326011yescharacteristic
345C4#1458326611yescharacteristic
346C2#1913341011yescharacteristic
347C2#1913341111yescharacteristic
348C2#1913350011yescharacteristic
349C2#1913350111yescharacteristic
350C2#1913519811yescharacteristic
351C2#1913528211yescharacteristic
352C2#1913530311yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC2×C43×Q8⋊C8C2
socle, prime radicalC23×C43C4×D4
cosocleC2×C42×C43C23
hypercenterC2×Q8⋊C8D43
hypocenterC43#9555
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
37. #13063249C8semidirect
201. C43#9555semidirect

Maximal subgroups

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

subgroupindex
#191355322
#191353112
C4×#130632492
C2×#145826212
#191324352
#191324292
C2×C43×Q8⋊C82
#955543