Finite Group Databasebeta

← #24988985

Subgroups — #24988985

Order 11008.

820 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 820 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135420C211yesmaximal, characteristic, complemented
2#19133309C211yesmaximal, characteristic, complemented
3#19133215C212yesmaximal, complemented
4#19133133C212yesmaximal, complemented
5C43×#3543C211yesmaximal, characteristic
6#14582956C2212yescomplemented
7C2×#13063246—22no—
8C2×#13063236C2211yescharacteristic, complemented
9#14582765C2211yescharacteristic, complemented
10#14582643—22no—
11#14582641—22no—
12#14582639—22no—
13#14582636—22no—
14#14582633—22no—
15C43×#560—22no—
16C43×#559C411yescharacteristic, complemented
17C43×#550C412yescomplemented
18C43×#546—22no—
19D42×C43—22no—
20D42×C43C411yescharacteristic, complemented
21C43×#540—22no—
22C43×#535—22no—
23C43×#534—22no—
24C2×#127×C43C2211yescharacteristic
25C43×#529C2212yes—
26C22×C43⋊C8—21no—
27C2×C4⋊Dic43—21no—
28C4⋊(C43⋊C8)—22no—
29#13063246—44no—
30C22⋊(C43⋊C8)—22no—
31#13063236—22no—
32#13063236—22no—
33C43⋊#95—22no—
34C2×#41×C43—22no—
35C22×D4×C43—22no—
36C22×D4×C43—22no—
37C22×D4×C43—22no—
38C22×D4×C43D412yes—
39#127×C43—22no—
40#127×C43—22no—
41#127×C43C2×C411yescharacteristic
42#127×C43C2×C411yescharacteristic
43#127×C43D412yes—
44#126×C43—22no—
45#125×C43D412yes—
46#124×C43—22no—
47#124×C43D412yes—
48#123×C43—22no—
49#123×C43—24no—
50#123×C43—22no—
51#123×C43—22no—
52C22⋊Q8×C43D412yes—
53#121×C43—24no—
54#121×C43—24no—
55#121×C43—24no—
56#121×C43—24no—
57#121×C43—22no—
58#121×C43—22no—
59#121×C43D412yes—
60#120×C43—22no—
61#120×C43—24no—
62#120×C43—24no—
63#120×C43—22no—
64C4×Q8×C43C2×C412yes—
65C4×D4×C43—22no—
66C4×D4×C43—22no—
67C4×D4×C43—22no—
68C4×D4×C43C2×C412yes—
69#117×C43—22no—
70C2×C22⋊C4×C43—22no—
71C2×C42×C43C2311yescharacteristic
72C24×C43—22no—
73C24×C43—22no—
74#41×C43—84no—
75C2×Q8×C43C22⋊C412yes—
76C2×D4×C43—24no—
77C2×D4×C43—24no—
78C2×D4×C43—24no—
79C2×D4×C43—22no—
80C2×D4×C43—22no—
81C2×D4×C43—22no—
82C2×D4×C43—24no—
83C2×D4×C43—22no—
84C2×D4×C43—42no—
85C2×D4×C43—42no—
86C2×D4×C43—82no—
87C2×D4×C43—82no—
88C2×D4×C43—84no—
89C2×D4×C43—84no—
90C2×D4×C43C22⋊C412yes—
91C2×D4×C43C22⋊C412yes—
92C2×D4×C43C22⋊C412yes—
93C22×C4×C43—24no—
94C22×C4×C43—22no—
95C22×C4×C43—22no—
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D412yes—
98C22×Dic43—41no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43C22⋊C412yes—
104C4⋊C4×C43C22⋊C412yes—
105C22⋊C4×C43—22no—
106C22⋊C4×C43—22no—
107C22⋊C4×C43—24no—
108C22⋊C4×C43—24no—
109C22⋊C4×C43—22no—
110C22⋊C4×C43—22no—
111C22⋊C4×C43—22no—
112C22⋊C4×C43—22no—
113C22⋊C4×C43—22no—
114C42×C43—22no—
115C42×C43C22×C411yescharacteristic
116C42×C43C2×D412yes—
117C42×C43C2×D411yescharacteristic
118C4⋊Dic43—42no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—42no—
123C23×C43—22no—
124C23×C43—22no—
125C23×C43—22no—
126C23×C43—42no—
127C23×C43—42no—
128C23×C43—84no—
129C23×C43—82no—
130C23×C43—84no—
131C23×C43#12011yescharacteristic
132Q8×C43—42no—
133D4×C43—42no—
134D4×C43—42no—
135D4×C43—42no—
136D4×C43—44no—
137D4×C43—44no—
138D4×C43—42no—
139D4×C43—42no—
140D4×C43—82no—
141D4×C43—84no—
142D4×C43—84no—
143D4×C43—84no—
144D4×C43—84no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—22no—
150C2×C4×C43—42no—
151C2×C4×C43—44no—
152C2×C4×C43—82no—
153C2×C4×C43—84no—
154C2×C4×C43C2×C22⋊C412yes—
155C2×C4×C43C2×C22⋊C411yescharacteristic
156C2×C4×C43#12011yescharacteristic
157C2×C4×C43#12012yes—
158C2×Dic43—82no—
159C2×Dic43—81no—
160C43⋊C8—42no—
161C43⋊C8—82no—
162#8497—431nomaximal, Sylow
163C22×C43—22no—
164C22×C43—42no—
165C22×C43—42no—
166C22×C43—42no—
167C22×C43—42no—
168C22×C43—44no—
169C22×C43—42no—
170C22×C43—44no—
171C22×C43—162no—
172C22×C43—162no—
173C22×C43—164no—
174C22×C43#37911yescharacteristic
175C22×C43#45311yescharacteristic
176C22×C43#45511yescharacteristic
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—22no—
180C4×C43—22no—
181C4×C43—42no—
182C4×C43—42no—
183C4×C43—42no—
184Dic43—161no—
185#3543D4311yescharacteristic
186#1961—431no—
187#1555—431no—
188#1532—432no—
189#1512—432no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43—82no—
193C2×C43—82no—
194C2×C43—82no—
195C2×C43#179211yescharacteristic
196C2×C43#179512yes—
197#560—22no—
198#559Dic4311yescharacteristic, complemented
199#550Dic4312yescomplemented
200#546—22no—
201D42—22no—
202D42Dic4311yescharacteristic, complemented
203#540—22no—
204#535—22no—
205#534—22no—
206C2×#127C2×D4311yescharacteristic
207#529C2×D4312yes—
208#432—432no—
209C2×#102—862no—
210C2×#97—431no—
211#382—431no—
212#331—862no—
213#330—862no—
214#329—862no—
215#328—862no—
216#327—862no—
217C43#849711yescharacteristic, complemented, Sylow
218C2×#41—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4C22⋊D4312yes—
223C22×C8—861no—
224#127—22no—
225#127—22no—
226#127C2×Dic4311yescharacteristic
227#127C2×Dic4311yescharacteristic
228#127C22⋊D4312yes—
229#126—22no—
230#125C22⋊D4312yes—
231#124—22no—
232#124C22⋊D4312yes—
233#123—22no—
234#123—24no—
235#123—22no—
236#123—22no—
237C22⋊Q8C22⋊D4312yes—
238#121—24no—
239#121—24no—
240#121—24no—
241#121—24no—
242#121—22no—
243#121—22no—
244#121C22⋊D4312yes—
245#120—22no—
246#120—24no—
247#120—24no—
248#120—22no—
249C4×Q8C2×Dic4312yes—
250C4×D4—22no—
251C4×D4—22no—
252C4×D4—22no—
253C4×D4C2×Dic4312yes—
254#117—22no—
255C2×C4⋊C4—861no—
256C2×C22⋊C4—22no—
257C2×C42C22×D4311yescharacteristic
258C4⋊C8—862no—
259#102—1724no—
260C22⋊C8—862no—
261#97—862no—
262#97—862no—
263#95—862no—
264C24—22no—
265C24—22no—
266#41—84no—
267C2×Q8C22⋊Dic4312yes—
268C2×D4—22no—
269C2×D4—24no—
270C2×D4—24no—
271C2×D4—24no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—24no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—84no—
279C2×D4—84no—
280C2×D4—82no—
281C2×D4—82no—
282C2×D4C22⋊Dic4312yes—
283C2×D4C22⋊Dic4312yes—
284C2×D4C22⋊Dic4312yes—
285C22×C4—24no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—1721no—
289C22×C4C2×C22⋊D4311yescharacteristic
290C22×C4C2×C22⋊D4312yes—
291C2×C8—862no—
292C2×C8—1722no—
293C2×C8—1721no—
294C2×C8—1721no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—1722no—
300C4⋊C4C22⋊Dic4312yes—
301C4⋊C4C22⋊Dic4312yes—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—24no—
305C22⋊C4—24no—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C42—22no—
312C42C22×Dic4311yescharacteristic
313C42C2×C22⋊D4312yes—
314C42C2×C22⋊D4311yescharacteristic
315C23—22no—
316C23—22no—
317C23—22no—
318C23—42no—
319C23—42no—
320C23—84no—
321C23—82no—
322C23—84no—
323C23#1306329411yescharacteristic
324Q8—42no—
325D4—42no—
326D4—42no—
327D4—42no—
328D4—44no—
329D4—44no—
330D4—42no—
331D4—42no—
332D4—82no—
333D4—84no—
334D4—84no—
335D4—84no—
336D4—84no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—82no—
345C2×C4—84no—
346C2×C4—3442no—
347C2×C4—3441no—
348C2×C4C2×C22⋊Dic4312yes—
349C2×C4C2×C22⋊Dic4311yescharacteristic
350C2×C4#1306329411yescharacteristic
351C2×C4#1306329412yes—
352C8—3442no—
353C8—1722no—
354C22—22no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—44no—
360C22—44no—
361C22—42no—
362C22—162no—
363C22—162no—
364C22—164no—
365C22#1458275511yescharacteristic
366C22#1458306711yescharacteristic
367C22#1458307711yescharacteristic
368C4—21no—
369C4—21no—
370C4—22no—
371C4—22no—
372C4—42no—
373C4—42no—
374C4—42no—
375C4—6881no—
376C2—21no—
377C2—21no—
378C2—82no—
379C2—82no—
380C2—82no—
381C2#1913454911yescharacteristic
382C2#1913456512yes—
subgroupG/H
centerC22#14582755
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3543C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3543D43
hypocenterC43#8497
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3543

Complements

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

NH ≅ G/Ntype
1. #19135420C2semidirect
2. #19133309C2semidirect
3. #19133215C2semidirect
4. #19133133C2semidirect
6. #14582956C22semidirect
8. C2×#13063236C22semidirect
9. #14582765C22semidirect
16. C43×#559C4semidirect
17. C43×#550C4semidirect
20. D42×C43C4semidirect
198. #559Dic43semidirect
199. #550Dic43semidirect
202. D42Dic43semidirect
217. C43#8497semidirect

Maximal subgroups

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

subgroupindex
#191354202
#191333092
#191332152
#191331332
C43×#35432
#849743