Finite Group Databasebeta

← #25002400

Subgroups — #25002400

Order 11008.

842 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×Dic43C211yesmaximal, characteristic
2#19136998C212yesmaximal
3C2×#14582656C211yesmaximal, characteristic
4C2×#14582655C212yesmaximal
5C2×C43×H(3,ℤ/4)C211yesmaximal, characteristic
6C22×#10621877C2211yescharacteristic
7C2×#13063284C2212yes—
8C22×C4×Dic43C2211yescharacteristic
9M16×Dic43—22no—
10M16×Dic43—22no—
11C2×#13063235C412yescomplemented
12C2×C8×Dic43C412yescomplemented
13#14582768—22no—
14#14582764—22no—
15#14582757—24no—
16C4×Dic43⋊C4C418yescomplemented
17#14582656—22no—
18#14582655—24no—
19C22×M16×C43C2211yescharacteristic
20C2×#117×C43C2212yes—
21C43×H(3,ℤ/4)—22no—
22C23×Dic43D412yes—
23C2×#10621877—22no—
24C2×#10621877—22no—
25C2×#10621877D412yes—
26C2×#10621877Q812yes—
27C22×C43⋊C8C2×C412yes—
28#13063284—22no—
29#13063284—22no—
30#13063284—22no—
31#13063284—22no—
32C2×C4⋊Dic43—22no—
33C2×Dic43⋊C4—28no—
34C2×C22⋊Dic43—22no—
35C2×C4×Dic43C2×C414yes—
36C2×C4×Dic43C2×C411yescharacteristic
37C2×C4×Dic43C2×C411yescharacteristic
38C2×C4×Dic43C2×C414yes—
39C2×C4×Dic43D412yes—
40C2×C4×Dic43D412yes—
41C2×C4×Dic43Q812yes—
42#13063235—24no—
43C8×Dic43—22no—
44C8×Dic43—22no—
45C43⋊#95—28no—
46C23×C4×C43C2311yescharacteristic
47C2×M16×C43—22no—
48C2×M16×C43—22no—
49C2×M16×C43D412yes—
50C2×M16×C43Q812yes—
51C22×C8×C43C2×C412yes—
52#117×C43—22no—
53#117×C43—22no—
54#117×C43—22no—
55#117×C43—22no—
56C2×C4⋊C4×C43—22no—
57C2×C22⋊C4×C43—22no—
58C2×C42×C43C2×C414yes—
59C24×C43C2×D411yescharacteristic
60C22×C4×C43—24no—
61C22×C4×C43C22×C412yes—
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D412yes—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×Q811yescharacteristic
67C22×C4×C43C2×Q811yescharacteristic
68C22×C4×C43C2×Q811yescharacteristic
69C22×C4×C43#4112yes—
70C22×C4×C43#4112yes—
71C22×Dic43—24no—
72C22×Dic43—44no—
73C22×Dic43C22⋊C414yes—
74C22×Dic43C22⋊C414yes—
75C22×Dic43C4⋊C412yes—
76C22×Dic43C4⋊C412yes—
77M16×C43—24no—
78M16×C43—24no—
79C2×C8×C43—22no—
80C2×C8×C43—22no—
81C2×C8×C43C4⋊C414yescomplemented
82C4⋊C4×C43—42no—
83C4⋊C4×C43—42no—
84C22⋊C4×C43—42no—
85C22⋊C4×C43—42no—
86C42×C43—24no—
87C42×C43—24no—
88C22⋊Dic43—42no—
89C22⋊Dic43—42no—
90C4⋊Dic43—42no—
91C4⋊Dic43—42no—
92Dic43⋊C4—416no—
93C4×Dic43—24no—
94C4×Dic43—24no—
95C4×Dic43C4212yes—
96C4×Dic43C4212yes—
97C4×Dic43C22⋊C411yescharacteristic
98C4×Dic43C22⋊C411yescharacteristic
99C4×Dic43C22⋊C412yes—
100C4×Dic43C4⋊C414yes—
101C4×Dic43C4⋊C414yes—
102#10621877—24no—
103#10621877—24no—
104C2×C43⋊C8—22no—
105C2×C43⋊C8—22no—
106C2×C43⋊C8C4⋊C414yescomplemented
107C23×C43—42no—
108C23×C43C2×C22⋊C412yes—
109C23×C43C2×C4⋊C411yescharacteristic
110C23×C43#12412yes—
111C23×C43#12711yescharacteristic
112C23×C43C4⋊Q811yescharacteristic
113C2×C4×C43—48no—
114C2×C4×C43—44no—
115C2×C4×C43C2×C4211yescharacteristic
116C2×C4×C43C2×C22⋊C411yescharacteristic
117C2×C4×C43C2×C4⋊C411yescharacteristic
118C2×C4×C43C2×C4⋊C412yes—
119C2×C4×C43C2×C4⋊C411yescharacteristic
120C2×C4×C43#11711yescharacteristic
121C2×C4×C43#11711yescharacteristic
122C2×C4×C43C4×D412yes—
123C2×C4×C43C4×D412yes—
124C2×C4×C43C4×Q812yes—
125C2×C4×C43C4×Q812yes—
126C2×C4×C43#12112yes—
127C2×C4×C43#12112yes—
128C2×C4×C43C22⋊Q812yes—
129C2×C4×C43C22⋊Q812yes—
130C2×C4×C43#12512yes—
131C2×C4×C43C4⋊Q811yescharacteristic
132C2×C4×C43C4⋊Q811yescharacteristic
133C2×Dic43—28no—
134C2×Dic43—24no—
135C2×Dic43—44no—
136C2×Dic43—42no—
137C2×Dic43—48no—
138C2×Dic43—44no—
139C2×Dic43#9512yes—
140C2×Dic43#9514yes—
141C2×Dic43#9512yes—
142C8×C43—24no—
143C43⋊C8—24no—
144#10837—431nomaximal, Sylow
145C22×C43—24no—
146C22×C43—22no—
147C22×C43—42no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43C2×#9511yescharacteristic
151C22×C43#38211yescharacteristic
152C22×C43#38411yescharacteristic
153C22×C43#39012yes—
154C22×C43#39112yes—
155C4×C43—84no—
156C4×C43C4×C4⋊C411yescharacteristic
157C4×C43C4×C4⋊C411yescharacteristic
158C4×C43#38011yescharacteristic
159C4×C43#38011yescharacteristic
160C4×C43#38912yes—
161C4×C43#38912yes—
162Dic43—24no—
163Dic43—22no—
164Dic43—84no—
165Dic43H(3,ℤ/4)14yescomplemented
166C2×C4×M16—431no—
167#2285—432no—
168C2×H(3,ℤ/4)—431no—
169C2×H(3,ℤ/4)—432no—
170C2×H(3,ℤ/4)D4311yescharacteristic
171C2×C43—22no—
172C2×C43—21no—
173C2×C43—21no—
174C2×C43—22no—
175C2×C43C4⋊#9511yescharacteristic
176C2×C43C2×H(3,ℤ/4)12yes—
177C22×M16—431no—
178C22×M16C2×D4311yescharacteristic
179C2×#117—432no—
180C2×#117C2×D4312yes—
181C22×C42—431no—
182C4×M16—862no—
183C4×M16—862no—
184C2×#97—432no—
185C2×C4×C8—432no—
186#384—862no—
187#382—862no—
188#380—864no—
189C4×C4⋊C4—438no—
190H(3,ℤ/4)—22no—
191H(3,ℤ/4)—864no—
192H(3,ℤ/4)—862no—
193C43#1083711yescharacteristic, complemented, Sylow
194C23×C4—432no—
195C23×C4C22×D4311yescharacteristic
196C2×M16—22no—
197C2×M16—22no—
198C2×M16—432no—
199C2×M16—432no—
200C2×M16—862no—
201C2×M16—862no—
202C2×M16Dic8612yes—
203C2×M16C22⋊D4312yes—
204C22×C8—432no—
205C22×C8C4×D4312yes—
206#117—22no—
207#117—22no—
208#117—22no—
209#117—22no—
210#117—862no—
211#117—862no—
212#117—862no—
213#117—862no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—868no—
216C2×C4⋊C4—862no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—862no—
219C2×C42—434no—
220C2×C42—431no—
221C2×C42—431no—
222C2×C42—432no—
223C2×C42—432no—
224C2×C42—432no—
225C2×C42—434no—
226C2×C42C4×D4314yes—
227#97—864no—
228C4×C8—862no—
229C4×C8—862no—
230#95—868no—
231C24D4×D4311yescharacteristic
232C22×C4—24no—
233C22×C4—434no—
234C22×C4—432no—
235C22×C4—434no—
236C22×C4—432no—
237C22×C4—864no—
238C22×C4—1724no—
239C22×C4C2×Dic8611yescharacteristic
240C22×C4C2×C4×D4311yescharacteristic
241C22×C4C2×C4×D4312yes—
242C22×C4#1062189812yes—
243C22×C4D4×D4312yes—
244C22×C4D4×D4311yescharacteristic
245C22×C4#1062190012yes—
246C22×C4Q8×D4311yescharacteristic
247C22×C4Q8×D4311yescharacteristic
248C22×C4C2×C22⋊D4311yescharacteristic
249M16—24no—
250M16—24no—
251M16—864no—
252M16—864no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—434no—
256C2×C8—862no—
257C2×C8—862no—
258C2×C8Dic43⋊C414yescomplemented
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—17216no—
262C4⋊C4—1722no—
263C4⋊C4—1722no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C22⋊C4—1722no—
267C22⋊C4—1722no—
268C42—24no—
269C42—24no—
270C42—432no—
271C42—432no—
272C42—431no—
273C42—431no—
274C42—432no—
275C42—434no—
276C42—434no—
277C42—864no—
278C42—864no—
279C23—42no—
280C23C22⋊C4×D4312yes—
281C23C4⋊C4×D4311yescharacteristic
282C23#1306331112yes—
283C23#1306332111yescharacteristic
284C23#1306332411yescharacteristic
285C2×C4—48no—
286C2×C4—44no—
287C2×C4—432no—
288C2×C4—432no—
289C2×C4—434no—
290C2×C4—868no—
291C2×C4—864no—
292C2×C4—1724no—
293C2×C4—1722no—
294C2×C4—1728no—
295C2×C4—1724no—
296C2×C4C42×D4311yescharacteristic
297C2×C4C22⋊C4×D4311yescharacteristic
298C2×C4C4⋊C4×D4312yes—
299C2×C4C4⋊C4×D4311yescharacteristic
300C2×C4C2×Dic43⋊C411yescharacteristic
301C2×C4#1306328111yescharacteristic
302C2×C4#1306328211yescharacteristic
303C2×C4(C22⋊D43)⋊C412yes—
304C2×C4C4×C22⋊D4312yes—
305C2×C4#1306329012yes—
306C2×C4C4×Dic8612yes—
307C2×C4#1306329712yes—
308C2×C4#1306329812yes—
309C2×C4#1306330212yes—
310C2×C4#1306330312yes—
311C2×C4#1306331512yes—
312C2×C4#1306332311yescharacteristic
313C2×C4#1306332411yescharacteristic
314C8—24no—
315C8—864no—
316C22—24no—
317C22—22no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22#95×D4311yescharacteristic
322C22#1458276311yescharacteristic
323C22#1458276811yescharacteristic
324C22#1458279912yes—
325C22#1458280312yes—
326C4—84no—
327C4—434no—
328C4—864no—
329C4—862no—
330C4—3444no—
331C4#1458275011yescharacteristic
332C4C4×Dic43⋊C411yescharacteristic
333C4#1458275711yescharacteristic
334C4#1458275811yescharacteristic
335C4#1458279412yes—
336C4#1458279612yes—
337C2—22no—
338C2—22no—
339C2—21no—
340C2—21no—
341C2Dic43⋊#9511yescharacteristic
342C2H(3,ℤ/4)×D4312yes—
subgroupG/H
centerC2×C4C42×D43
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC2×C43×H(3,ℤ/4)C2
socleC22×C43C2×#95
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC2×H(3,ℤ/4)D43
hypocenterC43#10837
LCSG ▷ C2×C4×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
11. C2×#13063235C4semidirect
12. C2×C8×Dic43C4semidirect
16. C4×Dic43⋊C4C4semidirect
81. C2×C8×C43C4⋊C4semidirect
106. C2×C43⋊C8C4⋊C4semidirect
165. Dic43H(3,ℤ/4)semidirect
193. C43#10837semidirect
258. C2×C8Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×M16×Dic432
#191369982
C2×#145826562
C2×#145826552
C2×C43×H(3,ℤ/4)2
#1083743