Finite Group Databasebeta

← #24993289

Subgroups — #24993289

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#19145533C211yesmaximal, characteristic
2#19135419C211yesmaximal, characteristic
3#19133264C211yesmaximal, characteristic
4#19133159C211yesmaximal, characteristic, complemented
5#19132455C211yesmaximal, characteristic, complemented
6#19132426C211yesmaximal, characteristic, complemented
7C43×#2961C211yesmaximal, characteristic, complemented
8C2×#13063322C2211yescharacteristic
9#14583273C412yescomplemented
10#14583247C412yescomplemented
11#14583099—22no—
12#14583049—22no—
13#14582952C2211yescharacteristic
14#14582952C2211yescharacteristic
15C2×#13063247—21no—
16C2×#13063247—21no—
17#14582765C2211yescharacteristic
18#14582642—22no—
19#14582636—22no—
20C43×#533C2211yescharacteristic
21C43×#446—22no—
22C43×#446—22no—
23C43×#424—21no—
24C43×#423C2211yescharacteristic
25C43×#405—21no—
26C2×#97×C43C2211yescharacteristic
27C22×D172—21no—
28C22×D172—21no—
29C22×D172—21no—
30C2×#10621884—24no—
31#13063322—21no—
32#13063322—21no—
33#13063322—21no—
34#13063322C2×C412yes—
35C2×C4⋊Dic43—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38#13063247—42no—
39#13063247—42no—
40#13063245—24no—
41C22⋊(C43⋊C8)—21no—
42C22⋊(C43⋊C8)—21no—
43C4×C43⋊C8—21no—
44C4×C43⋊C8C2×C412yes—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C2×M16×C43—21no—
48C22×C8×C43D411yescharacteristic
49C22×C8×C43D411yescharacteristic
50C4⋊Q8×C43C2×C411yescharacteristic
51C4⋊Q8×C43C2×C411yescharacteristic
52#125×C43—21no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43D412yes—
55C4×Q8×C43—21no—
56C4×Q8×C43D412yes—
57#117×C43—21no—
58C2×C42×C43C2311yescharacteristic
59C4⋊C8×C43—24no—
60C4⋊C8×C43—21no—
61C4⋊C8×C43D412yes—
62#97×C43—22no—
63#97×C43—21no—
64#97×C43—21no—
65C4×C8×C43—22no—
66C23×D43—41no—
67C2×Q8×C43—21no—
68C2×Q8×C43C22⋊C412yes—
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43#4111yescharacteristic
72C22×Dic43—41no—
73C2×D172—22no—
74C2×D172—22no—
75C2×D172—22no—
76C2×D172—41no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172—41no—
83C2×D172—82no—
84C2×D172—82no—
85M16×C43—41no—
86M16×C43—41no—
87C2×C8×C43—21no—
88C2×C8×C43—21no—
89C2×C8×C43—22no—
90C2×C8×C43—21no—
91C2×C8×C43—21no—
92C2×C8×C43—21no—
93C2×C8×C43SD1612yescomplemented
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43C22⋊C412yes—
100C22⋊C4×C43—22no—
101C42×C43—22no—
102C42×C43C22×C411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43#4111yescharacteristic
106#10621884—84no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8—41no—
111C23×C43#12111yescharacteristic
112C22×D43—42no—
113C22×D43—82no—
114C22×D43—82no—
115C22×D43—81no—
116C22×D43—81no—
117Q8×C43—42no—
118Q8×C43—81no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43C2×C22⋊C411yescharacteristic
124C2×C4×C43C4×D411yescharacteristic
125C2×C4×C43C4×D411yescharacteristic
126C2×C4×C43#12011yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12311yescharacteristic
129C2×C4×C43C2×SD1611yescharacteristic
130C2×C4×C43#13511yescharacteristic
131C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C43#13711yescharacteristic
133C2×Dic43—81no—
134C2×Dic43—81no—
135C2×Dic43—81no—
136D172—44no—
137D172—42no—
138D172—42no—
139D172—82no—
140D172—82no—
141D172—82no—
142D172—81no—
143D172—81no—
144C8×C43—22no—
145C8×C43—41no—
146C8×C43—42no—
147C43⋊C8—42no—
148C43⋊C8—81no—
149#9294—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43#38611yescharacteristic
153C22×C43#46011yescharacteristic
154C22×C43#46411yescharacteristic
155C2×D43—82no—
156C2×D43—82no—
157C2×D43—82no—
158C2×D43—162no—
159C2×D43—162no—
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#3208—431no—
172#2961D4311yescharacteristic, complemented
173#1961—431no—
174#1545—431no—
175#1518—431no—
176#1286—431no—
177#1275—431no—
178C2×C43—21no—
179C2×C43—21no—
180C2×C43#188011yescharacteristic
181C2×C43#190311yescharacteristic
182C2×C43#191011yescharacteristic
183D43—162no—
184#533C2×D4311yescharacteristic
185C2×#127—431no—
186#492—432no—
187#486—432no—
188#460—862no—
189#450—862no—
190#446—22no—
191#446—22no—
192#431—431no—
193#431—431no—
194#424—21no—
195#423C2×D4311yescharacteristic
196C2×#102—861no—
197C2×#102—861no—
198#405—21no—
199C2×#97C2×D4311yescharacteristic
200#382—431no—
201#331—862no—
202#328—862no—
203C43#929411yescharacteristic, complemented, Sylow
204C22×D4—861no—
205C22×D4—861no—
206C22×D4—861no—
207C2×SD16—864no—
208C2×M16—21no—
209C22×C8C22⋊D4311yescharacteristic
210C22×C8C22⋊D4311yescharacteristic
211C4⋊Q8C4×D4311yescharacteristic
212C4⋊Q8C4×D4311yescharacteristic
213#127—432no—
214#127—861no—
215#127—861no—
216#127—861no—
217#125—21no—
218C22⋊Q8—21no—
219C22⋊Q8D17212yes—
220C4×Q8—21no—
221C4×Q8C22⋊D4312yes—
222#117—21no—
223C2×C4⋊C4—861no—
224C2×C42C22×D4311yescharacteristic
225C4⋊C8—24no—
226C4⋊C8—21no—
227C4⋊C8—861no—
228C4⋊C8—861no—
229C4⋊C8C22⋊D4312yes—
230#102—864no—
231#102—1722no—
232#102—1722no—
233C22⋊C8—861no—
234C22⋊C8—861no—
235#97—22no—
236#97—21no—
237#97—21no—
238C4×C8—22no—
239C4×C8—432no—
240C4×C8—861no—
241#95—861no—
242#95—861no—
243C24—1721no—
244C2×Q8—21no—
245C2×Q8(C2×D43)⋊C412yes—
246C2×D4—862no—
247C2×D4—862no—
248C2×D4—862no—
249C2×D4—3442no—
250C2×D4—3442no—
251C2×D4—1721no—
252C2×D4—1721no—
253C2×D4—1721no—
254C2×D4—1721no—
255C2×D4—1721no—
256C2×D4—1721no—
257C2×D4—1721no—
258C22×C4—1721no—
259C22×C4C2×D17211yescharacteristic
260C22×C4#1062189811yescharacteristic
261C22×C4C2×C22⋊D4311yescharacteristic
262SD16—3444no—
263M16—41no—
264M16—41no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—22no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—862no—
272C2×C8—1721no—
273C2×C8#1062188412yescomplemented
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C4⋊C4(C2×D43)⋊C412yes—
282C22⋊C4—22no—
283C42—22no—
284C42C2×C4×D4311yescharacteristic
285C42#1062189811yescharacteristic
286C42C2×C22⋊D4311yescharacteristic
287C42C2×C22⋊D4311yescharacteristic
288C23—3442no—
289C23—3442no—
290C23—3441no—
291C23—3441no—
292C23—1722no—
293C23#1306329911yescharacteristic
294Q8—42no—
295Q8—81no—
296D4—3442no—
297D4—3442no—
298D4—3442no—
299D4—3441no—
300D4—3441no—
301D4—1724no—
302D4—1722no—
303D4—1722no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—3441no—
309C2×C4—3441no—
310C2×C4—3441no—
311C2×C4C2×(C2×D43)⋊C411yescharacteristic
312C2×C4C4×C22⋊D4311yescharacteristic
313C2×C4C4×C22⋊D4311yescharacteristic
314C2×C4#1306329411yescharacteristic
315C2×C4#1306329911yescharacteristic
316C2×C4#1306330811yescharacteristic
317C2×C4C2×#1062188411yescharacteristic
318C2×C4#1306334511yescharacteristic
319C2×C4#1306335011yescharacteristic
320C2×C4#1306335611yescharacteristic
321C8—22no—
322C8—41no—
323C8—42no—
324C8—3441no—
325C8—1722no—
326C22—21no—
327C22—21no—
328C22—3442no—
329C22—3442no—
330C22—3442no—
331C22—6882no—
332C22—6882no—
333C22#1458277811yescharacteristic
334C22#1458309911yescharacteristic
335C22#1458312111yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—6881no—
343C4C4×#1062188411yescharacteristic
344C4#1458299711yescharacteristic
345C4#1458303811yescharacteristic
346C4#1458304411yescharacteristic
347C2—21no—
348C2—21no—
349C2—6882no—
350C2#1913495011yescharacteristic
351C2#1913507511yescharacteristic
352C2#1913512211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2961C2
socleC22×C43#386
prime radicalC2×#13063322C22
cosocleC2×C42×C43C23
hypercenter#2961D43
hypocenterC43#9294
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2961

Complements

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

NH ≅ G/Ntype
4. #19133159C2semidirect
5. #19132455C2semidirect
6. #19132426C2semidirect
7. C43×#2961C2semidirect
9. #14583273C4semidirect
10. #14583247C4semidirect
93. C2×C8×C43SD16semidirect
172. #2961D43semidirect
203. C43#9294semidirect
273. C2×C8#10621884semidirect

Maximal subgroups

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

subgroupindex
#191455332
#191354192
#191332642
#191331592
#191324552
#191324262
C43×#29612
#929443