Finite Group Databasebeta

← #25067443

Subgroups — #25067443

Order 11008.

584 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145155C211yesmaximal, characteristic
2#19143690C211yesmaximal, characteristic, complemented
3#19143673C211yesmaximal, characteristic
4#19133470C212yesmaximal, complemented
5#19133455C212yesmaximal, complemented
6#19133435C212yesmaximal, complemented
7#19133434C212yesmaximal, complemented
8#19133356C211yesmaximal, characteristic, complemented
9#19133065C211yesmaximal, characteristic
10#19132888C211yesmaximal, characteristic, complemented
11C43×#1497C211yesmaximal, characteristic, complemented
12#14583449C2211yescharacteristic
13#14583295C411yescharacteristic
14#14583273C411yescharacteristic
15#14583249C411yescharacteristic
16#14583247C411yescharacteristic
17#14583130C412yes—
18#14583130C412yes—
19#14583030—22no—
20#14583030C2212yes—
21Q8×C43⋊C8C2212yes—
22C4×#10621884C2212yes—
23C4×#10621884C2212yes—
24#14582976C2212yes—
25#14582972—22no—
26#14582964C2212yes—
27#14582960—22no—
28#14582956C2211yescharacteristic
29#14582952C2211yescharacteristic
30#14582864—22no—
31C2×C4×C43⋊C8C2211yescharacteristic
32#14582651C2212yes—
33#14582649C2212yes—
34#14582628C2212yes—
35#14582628C2212yes—
36#14582621C2211yescharacteristic
37#14582621C2211yescharacteristic
38#14582620C2211yescharacteristic
39#14582620C2211yescharacteristic
40C43×#533C2211yescharacteristic
41C43×#432C2211yescharacteristic
42C43×#431C2211yescharacteristic
43C43×Q8⋊C8C2212yes—
44C43×Q8⋊C8C2212yes—
45C2×#10621898—21no—
46C2×#10621884C2×C412yes—
47C2×#10621884C2×C412yes—
48C2×#10621872—22no—
49C22×C43⋊C8C2×C411yescharacteristic
50C22×C43⋊C8C2×C411yescharacteristic
51C2×C8×D43—22no—
52#13063325C2×C411yescharacteristic
53#13063322C2×C411yescharacteristic
54#13063313—21no—
55#13063299—21no—
56#13063299C2×C412yes—
57C4×D172—21no—
58C4×D172C2312yes—
59#13063256C2×C412yes—
60#13063256C2×C412yes—
61C4⋊(C43⋊C8)—22no—
62C4⋊(C43⋊C8)—22no—
63C4⋊(C43⋊C8)D412yes—
64C4⋊(C43⋊C8)C2312yes—
65#13063249C2×C412yes—
66#13063249C2×C412yes—
67#13063245C2×C412yes—
68#13063245C2×C412yes—
69C22⋊(C43⋊C8)—21no—
70C22⋊(C43⋊C8)D412yes—
71(C2×D43)⋊C8—22no—
72(C2×D43)⋊C8—22no—
73#13063236—21no—
74#13063236—22no—
75C4×C43⋊C8—22no—
76C4×C43⋊C8C2×C411yescharacteristic
77C4×C43⋊C8C2×C411yescharacteristic
78C4×C43⋊C8C2311yescharacteristic
79C4×C43⋊C8C2311yescharacteristic
80C4×C43⋊C8C2311yescharacteristic
81C4×C43⋊C8C2311yescharacteristic
82C4⋊Q8×C43C2×C411yescharacteristic
83C4⋊Q8×C43C2×C411yescharacteristic
84#125×C43—21no—
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43C2×C412yes—
87C4×Q8×C43—21no—
88C4×Q8×C43C2312yes—
89#117×C43—21no—
90C2×C42×C43C2311yescharacteristic
91C4⋊C8×C43—21no—
92C4⋊C8×C43C2312yes—
93C22⋊C8×C43—21no—
94C22⋊C8×C43—21no—
95#97×C43—21no—
96C4×C8×C43C2311yescharacteristic
97C4×C8×C43C2311yescharacteristic
98C2×Q8×C43—21no—
99C2×Q8×C43C22×C412yes—
100C22×C4×C43C22×C411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43#4111yescharacteristic
103C2×C22⋊D43—22no—
104#10621898—82no—
105C2×D172—21no—
106C2×D172—21no—
107C2×D172C22×C412yes—
108C2×C4×D43—22no—
109C2×Dic86—21no—
110C2×C8×C43—22no—
111C2×C8×C43—21no—
112C2×C8×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—22no—
117C4⋊C4×C43—22no—
118C4⋊C4×C43C22×C412yes—
119C22⋊C4×C43—22no—
120C42×C43—22no—
121C42×C43C22×C411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43#4111yescharacteristic
124C42×C43C2411yescharacteristic
125#10621884—42no—
126#10621884—42no—
127(C2×D43)⋊C4—22no—
128(C2×D43)⋊C4—22no—
129C4⋊Dic43—21no—
130C4⋊Dic43C22×C412yes—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—41no—
133C2×C43⋊C8—41no—
134C2×C43⋊C8C22×C411yescharacteristic
135C2×C43⋊C8C22×C411yescharacteristic
136C2×C43⋊C8C22×C411yescharacteristic
137C2×C43⋊C8C22×C411yescharacteristic
138C2×C43⋊C8C2×D412yes—
139C2×C43⋊C8C2×D412yes—
140#10621872—82no—
141C8×D43—82no—
142C23×C43C4×D411yescharacteristic
143C22×D43—22no—
144Q8×C43—22no—
145Q8×C43—22no—
146Q8×C43—81no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—22no—
150C2×C4×C43—22no—
151C2×C4×C43—22no—
152C2×C4×C43—41no—
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43C23×C411yescharacteristic
157C2×C4×C43C22×D411yescharacteristic
158C2×C4×C43C2×#4111yescharacteristic
159C22⋊D43—82no—
160C2×Dic43—22no—
161D172—22no—
162D172—22no—
163D172—81no—
164D172—81no—
165C4×D43—42no—
166C4×D43—42no—
167Dic86—81no—
168C8×C43—41no—
169C8×C43—41no—
170C8×C43—42no—
171C43⋊C8—21no—
172C43⋊C8—21no—
173C43⋊C8—21no—
174C43⋊C8—21no—
175C43⋊C8—22no—
176C43⋊C8—22no—
177C43⋊C8—42no—
178#17990—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43C2×C4×D411yescharacteristic
183C2×D43—42no—
184C2×D43—42no—
185C2×D43—42no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—42no—
191C4×C43—42no—
192C4×C43#56811yescharacteristic
193C4×C43#56811yescharacteristic
194C4×C43#57712yes—
195Dic43—42no—
196#3167—431no—
197#2985—431no—
198#2981—431no—
199#1588—432no—
200#1585—432no—
201#1583—432no—
202#1582—432no—
203#1568—431no—
204#1497D4311yescharacteristic, complemented
205#1496—431no—
206#1452—431no—
207C2×C43—41no—
208C2×C43#293211yescharacteristic
209C2×C43#294911yescharacteristic
210C2×C43#295711yescharacteristic
211D43—82no—
212#533C2×D4311yescharacteristic
213#532—431no—
214#498—431no—
215#492—431no—
216#487—431no—
217#486—431no—
218#465—432no—
219#465—432no—
220#446—432no—
221#446—862no—
222C8×Q8—432no—
223C4×SD16—432no—
224C4×SD16—432no—
225#436—432no—
226#435—862no—
227C8×D4—432no—
228#433—862no—
229#432—431no—
230#432C2×D4311yescharacteristic
231#431—431no—
232#431C2×D4311yescharacteristic
233#408—862no—
234C2×C4×C8—431no—
235#335—432no—
236#334—432no—
237Q8⋊C8C2×D4312yes—
238Q8⋊C8C2×D4312yes—
239D4⋊C8—432no—
240D4⋊C8—432no—
241#322—431no—
242#322—431no—
243#322—431no—
244#322—431no—
245C43#1799011yescharacteristic, complemented, Sylow
246C2×#41—861no—
247C2×SD16—432no—
248C2×SD16—432no—
249C2×M16—862no—
250C22×C8—431no—
251C22×C8—431no—
252C22×C8—862no—
253C4⋊Q8—431no—
254C4⋊Q8C4×D4311yescharacteristic
255C4⋊Q8C4×D4311yescharacteristic
256#127—431no—
257#125—21no—
258#124—861no—
259C22⋊Q8—21no—
260C22⋊Q8C4×D4312yes—
261#121—432no—
262#121—861no—
263C4×Q8—21no—
264C4×Q8C22×D4312yes—
265C4×D4—432no—
266C4×D4—861no—
267#117—21no—
268C2×C42C22×D4311yescharacteristic
269#106—432no—
270#106—432no—
271C4⋊C8—21no—
272C4⋊C8—432no—
273C4⋊C8—432no—
274C4⋊C8—862no—
275C4⋊C8—862no—
276C4⋊C8C22×D4312yes—
277#103—432no—
278#103—432no—
279#102—432no—
280#102—432no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—432no—
284C22⋊C8—862no—
285C22⋊C8—862no—
286C22⋊C8—861no—
287#97—21no—
288#97—862no—
289#97—861no—
290C4×C8—431no—
291C4×C8—431no—
292C4×C8—431no—
293C4×C8—431no—
294C4×C8—431no—
295C4×C8—431no—
296C4×C8—862no—
297C4×C8C22×D4311yescharacteristic
298C4×C8C22×D4311yescharacteristic
299#41—3442no—
300C2×Q8—21no—
301C2×Q8—861no—
302C2×Q8C2×C4×D4312yes—
303C2×D4—432no—
304C2×D4—862no—
305C2×D4—861no—
306C2×D4—861no—
307C22×C4—862no—
308C22×C4C2×C4×D4311yescharacteristic
309C22×C4D4×D4311yescharacteristic
310C22×C4#1062190011yescharacteristic
311SD16—1722no—
312SD16—1722no—
313M16—3442no—
314C2×C8—22no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—431no—
318C2×C8—431no—
319C2×C8—431no—
320C2×C8—431no—
321C2×C8—432no—
322C2×C8—432no—
323C2×C8—862no—
324C2×C8—3442no—
325C2×C8—1721no—
326C2×C8—1721no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—432no—
333C4⋊C4—861no—
334C4⋊C4C2×C4×D4312yes—
335C22⋊C4—22no—
336C22⋊C4—862no—
337C22⋊C4—862no—
338C42—22no—
339C42C2×C4×D4311yescharacteristic
340C42D4×D4311yescharacteristic
341C42#1062190011yescharacteristic
342C42C23×D4311yescharacteristic
343C23—862no—
344C23(C22⋊D43)⋊C411yescharacteristic
345Q8—22no—
346Q8—22no—
347Q8—81no—
348Q8—3441no—
349D4—862no—
350D4—862no—
351D4—3441no—
352D4—3441no—
353D4—3442no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—862no—
361C2×C4—1722no—
362C2×C4—1722no—
363C2×C4(C22⋊D43)⋊C411yescharacteristic
364C2×C4(C22⋊D43)⋊C411yescharacteristic
365C2×C4(C22⋊D43)⋊C411yescharacteristic
366C2×C4C22×C4×D4311yescharacteristic
367C2×C4C2×D4×D4311yescharacteristic
368C2×C4C2×#1062190011yescharacteristic
369C8—41no—
370C8—41no—
371C8—42no—
372C8—861no—
373C8—861no—
374C8—861no—
375C8—861no—
376C8—862no—
377C8—862no—
378C8—1722no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—1722no—
383C22—1722no—
384C22—1722no—
385C22C2×(C22⋊D43)⋊C411yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—42no—
392C4—1722no—
393C4#1458366411yescharacteristic
394C4#1458366411yescharacteristic
395C4#1458370812yes—
396C2—41no—
397C2—3442no—
398C2#1914331011yescharacteristic
399C2#1914345011yescharacteristic
400C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1497C2
socleC22×C43C2×C4×D4
prime radical#14583449C22
cosocleC42×C43C24
hypercenter#1497D43
hypocenterC43#17990
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
2. #19143690C2semidirect
4. #19133470C2semidirect
5. #19133455C2semidirect
6. #19133435C2semidirect
7. #19133434C2semidirect
8. #19133356C2semidirect
10. #19132888C2semidirect
11. C43×#1497C2semidirect
204. #1497D43semidirect
245. C43#17990semidirect

Maximal subgroups

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

subgroupindex
#191451552
#191436902
#191436732
#191334702
#191334552
#191334352
#191334342
#191333562
#191330652
#191328882
C43×#14972
#1799043