Finite Group Databasebeta

← #24993291

Subgroups — #24993291

Order 11008.

490 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143536C211yesmaximal, characteristic, complemented
2#19135420C211yesmaximal, characteristic
3#19133263C211yesmaximal, characteristic
4#19133159C211yesmaximal, characteristic, complemented
5#19132454C211yesmaximal, characteristic, complemented
6#19132425C211yesmaximal, characteristic, complemented
7C43×#3208C211yesmaximal, characteristic
8#14583030—22no—
9#14583030—22no—
10#14582952C2211yescharacteristic
11#14582926—21no—
12#14582923C2211yescharacteristic
13C2×#13063246—21no—
14C2×#13063246—21no—
15#14582855—21no—
16C2×#13063236C2211yescharacteristic
17#14582765C2211yescharacteristic
18#14582643—22no—
19#14582636—22no—
20C43×#533C2211yescharacteristic
21C2×#127×C43C2211yescharacteristic
22C43×#492C412yescomplemented
23C43×#486C412yescomplemented
24C43×#460—22no—
25C43×#450—22no—
26C43×#431C2211yescharacteristic
27C2×#10621877—21no—
28C22×C43⋊C8D411yescharacteristic
29C22×C43⋊C8D411yescharacteristic
30C2×C4⋊Dic43—21no—
31C4⋊(C43⋊C8)—24no—
32C4⋊(C43⋊C8)—21no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)D412yes—
35#13063246—42no—
36#13063246—42no—
37C22⋊(C43⋊C8)—21no—
38#13063236—22no—
39#13063236—21no—
40#13063236—21no—
41C4×C43⋊C8—22no—
42C4×C43⋊C8—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C22×D4×C43—21no—
46C22×D4×C43—21no—
47C22×D4×C43—21no—
48C2×SD16×C43—24no—
49C4⋊Q8×C43C2×C411yescharacteristic
50C4⋊Q8×C43C2×C411yescharacteristic
51#127×C43—21no—
52#127×C43—21no—
53#127×C43—21no—
54#127×C43C2×C412yes—
55#125×C43—21no—
56C22⋊Q8×C43—21no—
57C22⋊Q8×C43D412yes—
58C4×Q8×C43—21no—
59C4×Q8×C43D412yes—
60#117×C43—21no—
61C2×C42×C43C2311yescharacteristic
62C4⋊C8×C43—21no—
63#102×C43—24no—
64C22⋊C8×C43—21no—
65C4×C8×C43C2×C412yes—
66C24×C43—41no—
67C2×Q8×C43—21no—
68C2×Q8×C43C22⋊C412yes—
69C2×D4×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43—22no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43—41no—
78C2×D4×C43—41no—
79C2×D4×C43—82no—
80C2×D4×C43—82no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C22×Dic43—41no—
85SD16×C43—84no—
86C2×C8×C43—22no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—22no—
92C4⋊C4×C43C22⋊C412yes—
93C22⋊C4×C43—22no—
94C42×C43—22no—
95C42×C43C22×C411yescharacteristic
96C42×C43C2×D411yescharacteristic
97C42×C43C2×D411yescharacteristic
98C42×C43#4111yescharacteristic
99C4⋊Dic43—41no—
100C4⋊Dic43—41no—
101#10621877—41no—
102#10621877—41no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—22no—
106C2×C43⋊C8—21no—
107C2×C43⋊C8—21no—
108C2×C43⋊C8—21no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8SD1612yescomplemented
111C23×C43—42no—
112C23×C43—82no—
113C23×C43—82no—
114C23×C43—81no—
115C23×C43—81no—
116C23×C43#12111yescharacteristic
117Q8×C43—42no—
118Q8×C43—81no—
119D4×C43—44no—
120D4×C43—42no—
121D4×C43—42no—
122D4×C43—82no—
123D4×C43—82no—
124D4×C43—82no—
125D4×C43—81no—
126D4×C43—81no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43C2×C22⋊C411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12311yescharacteristic
137C2×C4×C43C2×SD1611yescharacteristic
138C2×C4×C43#13511yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C2×Dic43—81no—
142C2×Dic43—81no—
143C2×Dic43—81no—
144C8×C43—42no—
145C43⋊C8—22no—
146C43⋊C8—41no—
147C43⋊C8—42no—
148C43⋊C8—81no—
149#9294—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—82no—
153C22×C43—82no—
154C22×C43—82no—
155C22×C43—162no—
156C22×C43—162no—
157C22×C43#38611yescharacteristic
158C22×C43#46011yescharacteristic
159C22×C43#46411yescharacteristic
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—42no—
165C4×C43—42no—
166C4×C43C4×SD1611yescharacteristic
167C4×C43#44011yescharacteristic
168C4×C43#44811yescharacteristic
169C4×C43#44911yescharacteristic
170Dic43—161no—
171#3208D4311yescharacteristic
172#2961—431no—
173#1961—431no—
174#1545—431no—
175#1518—431no—
176#1286—431no—
177#1275—431no—
178C2×C43—21no—
179C2×C43—21no—
180C2×C43—162no—
181C2×C43#188011yescharacteristic
182C2×C43#190311yescharacteristic
183C2×C43#191011yescharacteristic
184#533C2×D4311yescharacteristic
185C2×#127C2×D4311yescharacteristic
186#492Dic4312yescomplemented
187#486Dic4312yescomplemented
188#460—22no—
189#450—22no—
190#446—862no—
191#446—862no—
192#431—431no—
193#431C2×D4311yescharacteristic
194#424—861no—
195#423—431no—
196C2×#102—861no—
197C2×#102—861no—
198#405—861no—
199C2×#97—431no—
200#382—431no—
201#331—862no—
202#328—862no—
203C43#929411yescharacteristic, complemented, Sylow
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C2×SD16—24no—
208C2×M16—861no—
209C22×C8—431no—
210C22×C8—431no—
211C4⋊Q8C2×Dic4311yescharacteristic
212C4⋊Q8C2×Dic4311yescharacteristic
213#127—21no—
214#127—21no—
215#127—21no—
216#127C2×Dic4312yes—
217#125—21no—
218C22⋊Q8—21no—
219C22⋊Q8C22⋊D4312yes—
220C4×Q8—21no—
221C4×Q8C22⋊D4312yes—
222#117—21no—
223C2×C4⋊C4—861no—
224C2×C42C22×D4311yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—432no—
227C4⋊C8—864no—
228C4⋊C8—861no—
229C4⋊C8—861no—
230#102—24no—
231#102—1722no—
232#102—1722no—
233C22⋊C8—21no—
234C22⋊C8—861no—
235#97—862no—
236#97—861no—
237#97—861no—
238C4×C8—862no—
239C4×C8—861no—
240C4×C8C2×Dic4312yes—
241#95—861no—
242#95—861no—
243C24—41no—
244C2×Q8—21no—
245C2×Q8C22⋊Dic4312yes—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—82no—
257C2×D4—82no—
258C22×C4—1721no—
259C22×C4D4×D4311yescharacteristic
260C22×C4#1062190011yescharacteristic
261C22×C4C2×C22⋊D4311yescharacteristic
262SD16—84no—
263M16—1721no—
264M16—1721no—
265C2×C8—22no—
266C2×C8—432no—
267C2×C8—861no—
268C2×C8—861no—
269C2×C8—862no—
270C2×C8—861no—
271C2×C8—861no—
272C2×C8—861no—
273C2×C8—1721no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C4⋊C4C22⋊Dic4312yes—
282C22⋊C4—22no—
283C42—22no—
284C42D4×D4311yescharacteristic
285C42#1062190011yescharacteristic
286C42C22×Dic4311yescharacteristic
287C42C2×C22⋊D4311yescharacteristic
288C23—42no—
289C23—82no—
290C23—82no—
291C23—81no—
292C23—81no—
293C23#1306329711yescharacteristic
294Q8—42no—
295Q8—81no—
296D4—44no—
297D4—42no—
298D4—42no—
299D4—82no—
300D4—82no—
301D4—82no—
302D4—81no—
303D4—81no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—3441no—
309C2×C4—3441no—
310C2×C4—3441no—
311C2×C4C2×C22⋊Dic4311yescharacteristic
312C2×C4D4×Dic4311yescharacteristic
313C2×C4D4×Dic4311yescharacteristic
314C2×C4#1306329311yescharacteristic
315C2×C4#1306329711yescharacteristic
316C2×C4#1306330611yescharacteristic
317C2×C4SD16×D4311yescharacteristic
318C2×C4#1306334611yescharacteristic
319C2×C4#1306335211yescharacteristic
320C2×C4#1306335411yescharacteristic
321C8—42no—
322C8—862no—
323C8—3441no—
324C8—1721no—
325C8—1722no—
326C22—21no—
327C22—21no—
328C22—82no—
329C22—82no—
330C22—82no—
331C22—162no—
332C22—162no—
333C22#1458277911yescharacteristic
334C22#1458309711yescharacteristic
335C22#1458311911yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—6881no—
343C4SD16×Dic4311yescharacteristic
344C4#1458300011yescharacteristic
345C4#1458303611yescharacteristic
346C4#1458304311yescharacteristic
347C2—21no—
348C2—21no—
349C2—162no—
350C2#1913495211yescharacteristic
351C2#1913507711yescharacteristic
352C2#1913512311yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3208C2
socleC22×C43#386
prime radicalC2×#127×C43C22
cosocleC2×C42×C43C23
hypercenter#3208D43
hypocenterC43#9294
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #19143536C2semidirect
4. #19133159C2semidirect
5. #19132454C2semidirect
6. #19132425C2semidirect
22. C43×#492C4semidirect
23. C43×#486C4semidirect
110. C2×C43⋊C8SD16semidirect
186. #492Dic43semidirect
187. #486Dic43semidirect
203. C43#9294semidirect

Maximal subgroups

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

subgroupindex
#191435362
#191354202
#191332632
#191331592
#191324542
#191324252
C43×#32082
#929443