Finite Group Databasebeta

← #24995998

Subgroups — #24995998

Order 11008.

440 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145154C211yesmaximal, characteristic
2#19133358C211yesmaximal, characteristic, complemented
3#19133209C211yesmaximal, characteristic, complemented
4#19133205C211yesmaximal, characteristic
5#19133106C211yesmaximal, characteristic, complemented
6#19133102C211yesmaximal, characteristic
7C43×#1726C211yesmaximal, characteristic, complemented
8#14583456C2211yescharacteristic
9#14583449C2211yescharacteristic
10#14583297C411yescharacteristic, complemented
11#14583272C411yescharacteristic, complemented
12#14583250C411yescharacteristic, complemented
13#14583246C411yescharacteristic, complemented
14#14583128—21no—
15#14583128—21no—
16C4×#10621873—21no—
17C4×#10621873—21no—
18#14582956C2211yescharacteristic
19#14582956C2211yescharacteristic
20#14582652—21no—
21#14582650—21no—
22#14582640—22no—
23#14582638—22no—
24#14582635—22no—
25#14582632—22no—
26C2×#97×C43—21no—
27C2×#97×C43C2211yescharacteristic
28C2×C4×C8×C43—21no—
29C2×C4×C8×C43C2211yescharacteristic
30C43×#376C2211yescharacteristic
31C2×#10621898—21no—
32C2×#10621873—21no—
33C2×#10621873—21no—
34#13063325C2×C411yescharacteristic
35#13063325C2×C411yescharacteristic
36#13063325C2×C411yescharacteristic
37#13063322C2×C411yescharacteristic
38#13063317—21no—
39#13063313—21no—
40#13063304—21no—
41#13063304—21no—
42#13063299—21no—
43#13063299—21no—
44C4×Dic86—21no—
45C4×Dic86—21no—
46C4×D172—21no—
47C4×D172—21no—
48#13063284—21no—
49#13063257—21no—
50#13063257—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)—21no—
53#13063250—21no—
54#13063250—21no—
55#13063247—21no—
56#13063247—21no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59#13063236—21no—
60#13063236—21no—
61C22×C8×C43—21no—
62C22×C8×C43D411yescharacteristic
63C22×C8×C43D411yescharacteristic
64C2×C42×C43—21no—
65C2×C42×C43C2311yescharacteristic
66#97×C43—24no—
67#97×C43—21no—
68#97×C43D412yes—
69C4×C8×C43—24no—
70C4×C8×C43C2×C411yescharacteristic
71C4×C8×C43C2×C411yescharacteristic
72C4×C8×C43D411yescharacteristic
73C4×C8×C43D411yescharacteristic
74#95×C43—21no—
75#95×C43D412yes—
76C22×C4×C43—22no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43#4111yescharacteristic
80C2×C22⋊D43—41no—
81#10621898—82no—
82C2×D172—21no—
83C2×D172—21no—
84C2×D172—21no—
85C2×C4×D43—41no—
86C2×Dic86—21no—
87C2×Dic86—21no—
88C2×Dic86—21no—
89C2×C8×C43—22no—
90C2×C8×C43—22no—
91C2×C8×C43—22no—
92C2×C8×C43—22no—
93C2×C8×C43—22no—
94C2×C8×C43C22⋊C411yescharacteristic
95C2×C8×C43C22⋊C411yescharacteristic
96C2×C8×C43C22⋊C411yescharacteristic
97C2×C8×C43C22⋊C411yescharacteristic
98C42×C43—22no—
99C42×C43—22no—
100C42×C43C22×C411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43#4111yescharacteristic
104C22⋊Dic43—41no—
105(C2×D43)⋊C4—41no—
106(C2×D43)⋊C4—41no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113Dic43⋊C4—41no—
114Dic43⋊C4—41no—
115C4×Dic43—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118#10621873—42no—
119#10621873—42no—
120C23×C43#12111yescharacteristic
121C22×D43—41no—
122C2×C4×C43—22no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—24no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43C2×C22⋊C411yescharacteristic
130C2×C4×C43C4×D411yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#12411yescharacteristic
134C2×C4×C43#12711yescharacteristic
135C22⋊D43—82no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139D172—41no—
140D172—41no—
141D172—81no—
142D172—81no—
143C4×D43—82no—
144Dic86—41no—
145Dic86—41no—
146Dic86—81no—
147Dic86—81no—
148C8×C43—24no—
149C8×C43—21no—
150C8×C43—21no—
151C8×C43#10412yes—
152C8×C43#10412yes—
153C43⋊C8—81no—
154C43⋊C8—81no—
155#9761—431nomaximal, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43#39011yescharacteristic
159C22×C43#47112yes—
160C2×D43—81no—
161C2×D43—81no—
162C2×D43—81no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—44no—
169C4×C43C2×#10411yescharacteristic
170C4×C43C2×#10411yescharacteristic
171Dic43—81no—
172Dic43—81no—
173Dic43—81no—
174#3167—431no—
175#1726D4311yescharacteristic, complemented
176#1568—431no—
177#1531—431no—
178#1530—431no—
179#1506—431no—
180#1505—431no—
181C2×C43—22no—
182C2×C43#196211yescharacteristic
183C2×C43#197611yescharacteristic
184C2×C43#197711yescharacteristic
185D43—161no—
186#533—431no—
187#532—431no—
188#498—431no—
189#492—431no—
190#487—431no—
191#486—431no—
192#465—861no—
193#465—861no—
194C4×SD16—861no—
195C4×SD16—861no—
196#432—431no—
197#432—431no—
198C2×#97—21no—
199C2×#97C2×D4311yescharacteristic
200C2×C4×C8—21no—
201C2×C4×C8C2×D4311yescharacteristic
202#376C2×D4311yescharacteristic
203#335—861no—
204#334—861no—
205#330—862no—
206#329—862no—
207#328—862no—
208#327—862no—
209C43#976111yescharacteristic, complemented, Sylow
210C2×#41—861no—
211C2×SD16—861no—
212C2×SD16—861no—
213C22×C8—21no—
214C22×C8C22⋊D4311yescharacteristic
215C22×C8C22⋊D4311yescharacteristic
216C4⋊Q8—431no—
217C4⋊Q8—431no—
218C4⋊Q8—431no—
219#127—431no—
220#125—861no—
221#124—861no—
222C22⋊Q8—861no—
223C22⋊Q8—861no—
224#121—861no—
225#121—861no—
226C4×Q8—861no—
227C4×Q8—861no—
228C4×D4—861no—
229C4×D4—861no—
230#117—861no—
231C2×C42—21no—
232C2×C42C22×D4311yescharacteristic
233#106—861no—
234#106—861no—
235C4⋊C8—861no—
236C4⋊C8—861no—
237#103—861no—
238#103—861no—
239#102—861no—
240#102—861no—
241C22⋊C8—861no—
242C22⋊C8—861no—
243#97—24no—
244#97—21no—
245#97—861no—
246#97—861no—
247#97D17212yes—
248C4×C8—24no—
249C4×C8C4×D4311yescharacteristic
250C4×C8C4×D4311yescharacteristic
251C4×C8D17211yescharacteristic
252C4×C8D17211yescharacteristic
253#95—21no—
254#95D17212yes—
255#41—3442no—
256C2×Q8—861no—
257C2×Q8—861no—
258C2×Q8—861no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—1721no—
263C22×C4—22no—
264C22×C4—1721no—
265C22×C4C2×D17211yescharacteristic
266C22×C4#1062189811yescharacteristic
267C22×C4C2×C22⋊D4311yescharacteristic
268SD16—1722no—
269SD16—1722no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—1721no—
276C2×C8—1721no—
277C2×C8(C2×D43)⋊C411yescharacteristic
278C2×C8(C2×D43)⋊C411yescharacteristic
279C2×C8(C2×D43)⋊C411yescharacteristic
280C2×C8(C2×D43)⋊C411yescharacteristic
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C22⋊C4—1721no—
290C22⋊C4—1721no—
291C22⋊C4—1721no—
292C42—22no—
293C42—22no—
294C42—1721no—
295C42C2×C4×D4311yescharacteristic
296C42C2×D17211yescharacteristic
297C42C2×D17211yescharacteristic
298C42#1062189811yescharacteristic
299C23—1721no—
300C23#1306329911yescharacteristic
301Q8—3441no—
302Q8—3441no—
303Q8—1721no—
304Q8—1721no—
305D4—3441no—
306D4—3441no—
307D4—3442no—
308D4—1721no—
309D4—1721no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—24no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—3442no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4C2×(C2×D43)⋊C411yescharacteristic
322C2×C4C4×D17211yescharacteristic
323C2×C4C4×D17211yescharacteristic
324C2×C4#1306329911yescharacteristic
325C2×C4#1306331311yescharacteristic
326C2×C4#1306332211yescharacteristic
327C8—24no—
328C8—21no—
329C8—21no—
330C8—3441no—
331C8—3441no—
332C8#1306325312yes—
333C8#1306325312yes—
334C22—21no—
335C22—21no—
336C22—3441no—
337C22—3441no—
338C22—3441no—
339C22#1458280111yescharacteristic
340C22#1458316212yes—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—44no—
347C4—3441no—
348C4—3441no—
349C4—3441no—
350C4C2×#1306325311yescharacteristic
351C4C2×#1306325311yescharacteristic
352C2—22no—
353C2—6881no—
354C2#1913542311yescharacteristic
355C2#1913549311yescharacteristic
356C2#1913549811yescharacteristic
subgroupG/H
centerC22#14582801
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1726C2
socleC22×C43#390
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1726D43
hypocenterC43#9761
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #19133358C2semidirect
3. #19133209C2semidirect
5. #19133106C2semidirect
7. C43×#1726C2semidirect
10. #14583297C4semidirect
11. #14583272C4semidirect
12. #14583250C4semidirect
13. #14583246C4semidirect
175. #1726D43semidirect
209. C43#9761semidirect

Maximal subgroups

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

subgroupindex
#191451542
#191333582
#191332092
#191332052
#191331062
#191331022
C43×#17262
#976143