Finite Group Databasebeta

← #25256704

Subgroups — #25256704

Order 11008.

3006 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583382C211yesmaximal, characteristic
2C2×#41×Dic43C211yesmaximal, characteristic
3#19137513C214yesmaximal, complemented
4#19137500C2112yesmaximal, complemented
5#19137219C213yesmaximal, complemented
6#19137215C213yesmaximal, complemented
7#19136998C213yesmaximal, complemented
8C2×#14582764C213yesmaximal, complemented
9C2×C43×#520C211yesmaximal, characteristic
10#14583382—28no—
11#41×Dic43C4116yescomplemented
12C2×Q8×Dic43C2212yes—
13C2×Q8×Dic43C2212yes—
14C2×D4×Dic43C2216yes—
15C2×D4×Dic43C2216yes—
16C2×#13063284C2213yes—
17C2×#13063284C2213yes—
18C22×C4⋊Dic43C2213yes—
19C22×C4×Dic43C2213yes—
20#14582797C22112yes—
21#14582795C22112yes—
22#14582772C22112yes—
23#14582771C22112yes—
24#14582768C2213yes—
25#14582768C2213yes—
26#14582764C2216yes—
27#14582764C2213yes—
28#14582764C22112yes—
29#14582764C2211yescharacteristic
30#14582757C22112yes—
31C4×Dic43⋊C4C22112yes—
32C2×C43⋊#95C22112yes—
33C22×#41×C43C2211yescharacteristic
34C43×#520—28no—
35C2×C4×Q8×C43C2212yes—
36C2×C4×D4×C43C2216yes—
37C2×#117×C43C2213yes—
38C22×C4⋊C4×C43C2213yes—
39C23×Dic43C2316yes—
40C23×Dic43C2316yes—
41Q8×Dic43—28no—
42Q8×Dic43C2×C4116yescomplemented
43D4×Dic43—224no—
44D4×Dic43C2×C4148yescomplemented
45#13063284—212no—
46#13063284C2×C4124yescomplemented
47C2×C4⋊Dic43—212no—
48C2×C4⋊Dic43C2316yes—
49C2×C4⋊Dic43C2313yes—
50C2×C4⋊Dic43C2311yescharacteristic
51C2×C4⋊Dic43C2316yes—
52C2×Dic43⋊C4C23112yes—
53C2×Dic43⋊C4C23112yes—
54C2×C22⋊Dic43C2316yes—
55C2×C22⋊Dic43C2316yes—
56C2×C4×Dic43C2×C4124yescomplemented
57C2×C4×Dic43C2316yes—
58C2×C4×Dic43C2311yescharacteristic
59C2×C4×Dic43C2313yes—
60C2×C4×Dic43C2316yes—
61C43⋊#95C23124yes—
62C43⋊#95C23112yes—
63C43⋊#95C2314yes—
64C2×#41×C43C2×C418yes—
65C2×#41×C43D418yes—
66C2×#41×C43Q818yes—
67C22×Q8×C43C2311yescharacteristic
68C22×D4×C43C2313yes—
69C23×C4×C43C2316yes—
70C23×C4×C43C2313yes—
71C4×Q8×C43—28no—
72C4×D4×C43—224no—
73#117×C43—212no—
74C2×C4⋊C4×C43—212no—
75C2×C4⋊C4×C43C2316yes—
76C2×C4⋊C4×C43C2313yes—
77C2×C4⋊C4×C43C2311yescharacteristic
78C2×C22⋊C4×C43C2316yes—
79C2×C42×C43C2316yes—
80C24×C43C2413yes—
81#41×C43C4⋊C4164yescomplemented
82C2×Q8×C43C22×C414yes—
83C2×Q8×C43C2×D414yes—
84C2×Q8×C43C2×Q814yes—
85C2×D4×C43C22×C4112yes—
86C2×D4×C43C2×D4112yes—
87C2×D4×C43C2×Q8112yes—
88C22×C4×C43—212no—
89C22×C4×C43—412no—
90C22×C4×C43C22×C4112yes—
91C22×C4×C43C2×D4112yes—
92C22×C4×C43C2×Q8112yes—
93C22×C4×C43C2412yes—
94C22×C4×C43C2416yes—
95C22×C4×C43C2413yes—
96C22×C4×C43C2411yescharacteristic
97C22×Dic43—212no—
98C22×Dic43—46no—
99C22×Dic43—46no—
100C22×Dic43—412no—
101C22×Dic43C22×C4124yes—
102C22×Dic43C2416yes—
103C22×Dic43C2412yes—
104C22×Dic43C2412yes—
105C22×Dic43C2416yes—
106C4⋊C4×C43—26no—
107C4⋊C4×C43—212no—
108C4⋊C4×C43—22no—
109C22⋊C4×C43—212no—
110C42×C43—212no—
111C22⋊Dic43—212no—
112C22⋊Dic43C22×C4124yes—
113C4⋊Dic43—26no—
114C4⋊Dic43—212no—
115C4⋊Dic43—22no—
116C4⋊Dic43C22×C4124yes—
117Dic43⋊C4—412no—
118Dic43⋊C4—412no—
119C4×Dic43—212no—
120C4×Dic43C22×C414yes—
121C4×Dic43C22×C4112yes—
122C4×Dic43C22×C4124yes—
123C23×C43—26no—
124C23×C43—26no—
125C23×C43C23×C416yes—
126C23×C43C22×D416yes—
127C23×C43C22×Q816yes—
128C23×C43C2511yescharacteristic
129Q8×C43C2×C4⋊C4116yes—
130D4×C43C2×C4⋊C4148yes—
131C2×C4×C43—22no—
132C2×C4×C43—26no—
133C2×C4×C43—24no—
134C2×C4×C43—212no—
135C2×C4×C43—812no—
136C2×C4×C43C2×C4⋊C4148yes—
137C2×C4×C43C23×C412yes—
138C2×C4×C43C23×C416yes—
139C2×C4×C43C22×D416yes—
140C2×C4×C43C22×D412yes—
141C2×C4×C43C22×Q812yes—
142C2×C4×C43C22×Q816yes—
143C2×Dic43—26no—
144C2×Dic43—26no—
145C2×Dic43—22no—
146C2×Dic43—22no—
147C2×Dic43—22no—
148C2×Dic43—26no—
149C2×Dic43—24no—
150C2×Dic43—212no—
151C2×Dic43—424no—
152C2×Dic43—812no—
153C2×Dic43C23×C414yes—
154C2×Dic43C23×C4112yes—
155#34184—431nomaximal, Sylow
156C22×C43—212no—
157C22×C43—26no—
158C22×C43—26no—
159C22×C43—212no—
160C22×C43C22×C4⋊C4112yes—
161C22×C43C24×C411yescharacteristic
162C22×C43C23×D411yescharacteristic
163C22×C43C23×Q811yescharacteristic
164C22×C43#58512yes—
165C22×C43#58512yes—
166C4×C43—42no—
167C4×C43—46no—
168C4×C43C22×C4⋊C414yes—
169C4×C43C22×C4⋊C4112yes—
170Dic43—24no—
171Dic43—212no—
172Dic43—42no—
173Dic43—46no—
174C2×#520—431no—
175C2×#520D4311yescharacteristic
176C2×C4×#41—431no—
177#2351—434no—
178#2349—4312no—
179#2317—433no—
180#2317—433no—
181#2285—433no—
182C2×#382—433no—
183C2×C43—212no—
184C2×C43C23×C4⋊C411yescharacteristic
185C2×C43#342812yes—
186C2×C43#350011yescharacteristic
187C2×C43#350011yescharacteristic
188C2×C43#350412yes—
189C22×#41C2×D4311yescharacteristic
190#520—28no—
191#520—868no—
192C4×#41—4316no—
193C2×C4×Q8—432no—
194C2×C4×Q8—432no—
195C2×C4×Q8C2×D4312yes—
196C2×C4×D4—436no—
197C2×C4×D4—436no—
198C2×C4×D4C2×D4316yes—
199C2×#117—433no—
200C2×#117—433no—
201C2×#117C2×D4313yes—
202C22×C4⋊C4—433no—
203C22×C4⋊C4C2×D4313yes—
204C22×C42—433no—
205#389—4312no—
206#389—4312no—
207#385—4312no—
208#385—4312no—
209#384—433no—
210#384—433no—
211#382—436no—
212#382—4312no—
213#382—433no—
214#382—431no—
215#380—4312no—
216C4×C4⋊C4—4312no—
217C2×#95—4312no—
218C43#3418411yescharacteristic, complemented, Sylow
219C2×#41Dic8618yes—
220C2×#41C4×D4318yes—
221C2×#41C22⋊D4318yes—
222C22×Q8C22×D4311yescharacteristic
223C22×D4C22×D4313yes—
224C23×C4—436no—
225C23×C4—436no—
226C23×C4C22×D4316yes—
227C23×C4C22×D4313yes—
228C4×Q8—28no—
229C4×Q8—4316no—
230C4×Q8—868no—
231C4×D4—224no—
232C4×D4—4348no—
233C4×D4—8624no—
234#117—212no—
235#117—4324no—
236#117—8612no—
237C2×C4⋊C4—212no—
238C2×C4⋊C4—436no—
239C2×C4⋊C4—433no—
240C2×C4⋊C4—436no—
241C2×C4⋊C4—431no—
242C2×C4⋊C4—4312no—
243C2×C4⋊C4—4312no—
244C2×C4⋊C4—8612no—
245C2×C4⋊C4C22×D4313yes—
246C2×C4⋊C4C22×D4316yes—
247C2×C4⋊C4C22×D4311yescharacteristic
248C2×C22⋊C4—436no—
249C2×C22⋊C4—436no—
250C2×C22⋊C4C22×D4316yes—
251C2×C42—4324no—
252C2×C42—433no—
253C2×C42—436no—
254C2×C42—431no—
255C2×C42—436no—
256C2×C42C22×D4316yes—
257#95—4312no—
258#95—4324no—
259#95—434no—
260C24C23×D4313yes—
261#41Dic43⋊C4164yescomplemented
262C2×Q8C2×Dic8614yes—
263C2×Q8C2×C4×D4314yes—
264C2×Q8C2×C22⋊D4314yes—
265C2×D4C2×Dic86112yes—
266C2×D4C2×C4×D43112yes—
267C2×D4C2×C22⋊D43112yes—
268C22×C4—212no—
269C22×C4—412no—
270C22×C4—432no—
271C22×C4—436no—
272C22×C4—4324no—
273C22×C4—436no—
274C22×C4—432no—
275C22×C4—8612no—
276C22×C4—17212no—
277C22×C4—1726no—
278C22×C4—1726no—
279C22×C4C2×Dic86112yes—
280C22×C4C2×C4×D43112yes—
281C22×C4C2×C22⋊D43112yes—
282C22×C4C23×D4316yes—
283C22×C4C23×D4312yes—
284C22×C4C23×D4313yes—
285C22×C4C23×D4311yescharacteristic
286C4⋊C4—26no—
287C4⋊C4—212no—
288C4⋊C4—22no—
289C4⋊C4—4324no—
290C4⋊C4—866no—
291C4⋊C4—8612no—
292C4⋊C4—862no—
293C4⋊C4—17212no—
294C4⋊C4—17212no—
295C22⋊C4—212no—
296C22⋊C4—4324no—
297C22⋊C4—8612no—
298C42—212no—
299C42—434no—
300C42—4312no—
301C42—4324no—
302C42—8612no—
303C23—26no—
304C23—26no—
305C23C22×C4×D4316yes—
306C23C22×C22⋊D4316yes—
307C23C22×Dic8616yes—
308C23C24×D4311yescharacteristic
309Q8C2×Dic43⋊C4116yes—
310D4C2×Dic43⋊C4148yes—
311C2×C4—22no—
312C2×C4—26no—
313C2×C4—212no—
314C2×C4—24no—
315C2×C4—812no—
316C2×C4—434no—
317C2×C4—4312no—
318C2×C4—866no—
319C2×C4—862no—
320C2×C4—866no—
321C2×C4—862no—
322C2×C4—862no—
323C2×C4—866no—
324C2×C4—864no—
325C2×C4—8612no—
326C2×C4—34412no—
327C2×C4—17224no—
328C2×C4C2×Dic43⋊C4148yes—
329C2×C4C22×C4×D4312yes—
330C2×C4C22×C4×D4316yes—
331C2×C4C22×C22⋊D4316yes—
332C2×C4C22×C22⋊D4312yes—
333C2×C4C22×Dic8612yes—
334C2×C4C22×Dic8616yes—
335C22—212no—
336C22—26no—
337C22—26no—
338C22—212no—
339C22C22×Dic43⋊C4112yes—
340C22C23×C4×D4311yescharacteristic
341C22C23×C22⋊D4311yescharacteristic
342C22C23×Dic8611yescharacteristic
343C22#1458373412yes—
344C22#1458373612yes—
345C4—46no—
346C4—42no—
347C4—864no—
348C4—8612no—
349C4—1722no—
350C4—1726no—
351C4C22×Dic43⋊C414yes—
352C4C22×Dic43⋊C4112yes—
353C2—212no—
354C2C23×Dic43⋊C411yescharacteristic
355C2#1914779512yes—
356C2#1914838311yescharacteristic
357C2#1914838911yescharacteristic
358C2#1914841712yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC2×C43×#520C2
socle, cosocleC23×C43C25
prime radicalC22×#41×C43C22
hypercenterC2×#520D43
hypocenterC43#34184
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
3. #19137513C2semidirect
4. #19137500C2semidirect
5. #19137219C2semidirect
6. #19137215C2semidirect
7. #19136998C2semidirect
8. C2×#14582764C2semidirect
11. #41×Dic43C4semidirect
42. Q8×Dic43C2×C4semidirect
44. D4×Dic43C2×C4semidirect
46. #13063284C2×C4semidirect
56. C2×C4×Dic43C2×C4semidirect
81. #41×C43C4⋊C4semidirect
218. C43#34184semidirect
261. #41Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145833822
C2×#41×Dic432
#191375132
#191375002
#191372192
#191372152
#191369982
C2×#145827642
C2×C43×#5202
#3418443