Finite Group Databasebeta

← #25107197

Subgroups — #25107197

Order 11008.

762 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137218C211yesmaximal, characteristic
2#19137204C211yesmaximal, characteristic
3#19135365C212yesmaximal, complemented
4#19135354C212yesmaximal, complemented
5#19134796C212yesmaximal
6#19134785C212yesmaximal
7#19134763C211yesmaximal, characteristic, complemented
8#19134755C211yesmaximal, characteristic, complemented
9#19134729C211yesmaximal, characteristic, complemented
10#19134726C211yesmaximal, characteristic, complemented
11C2×C43×#433C211yesmaximal, characteristic
12C2×#13063284C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C2×#13063259C2212yes—
15C2×#13063259C2212yes—
16C2×#13063259C2212yes—
17C2×#13063257C2212yes—
18#14582798—22no—
19#14582792—22no—
20#14582785—22no—
21#14582774—22no—
22#14582769C2211yescharacteristic
23#14582769C2211yescharacteristic
24#14582769C2211yescharacteristic
25#14582765C2211yescharacteristic
26#14582765C2211yescharacteristic
27#14582765C2211yescharacteristic
28#14582759C2212yes—
29C4×C4⋊Dic43C2212yes—
30#14582662C2212yes—
31#14582662C2212yes—
32#14582662C2212yes—
33#14582662C2212yes—
34C2×#117×C43C2211yescharacteristic
35C43×#433C418yescomplemented
36C2×C4⋊C8×C43C2212yes—
37C2×C22⋊C8×C43C2212yes—
38C2×#97×C43C2211yescharacteristic
39C2×C4×C8×C43C2211yescharacteristic
40C23×Dic43—21no—
41#13063284—42no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—22no—
44C2×C4⋊Dic43—22no—
45C2×C4⋊Dic43—22no—
46C2×C4⋊Dic43—42no—
47C2×C4⋊Dic43C2311yescharacteristic
48C2×C4⋊Dic43C2311yescharacteristic
49C2×C4⋊Dic43C2311yescharacteristic
50C2×C4⋊Dic43C2311yescharacteristic
51C2×C4⋊Dic43C2312yes—
52C2×C4⋊Dic43C2312yes—
53C2×C22⋊Dic43—21no—
54C2×C22⋊Dic43—22no—
55C2×C4×Dic43—21no—
56C2×C4×Dic43—22no—
57#13063259—42no—
58#13063259—42no—
59#13063259—42no—
60#13063257—42no—
61C43⋊#95—22no—
62C43⋊#95—22no—
63C43⋊#95—22no—
64C43⋊#95—22no—
65C43⋊#95—22no—
66C23×C4×C43C2311yescharacteristic
67C22×C8×C43C2312yes—
68C22×C8×C43C2312yes—
69#117×C43C2×C414yes—
70#117×C43Q814yes—
71C2×C4⋊C4×C43D412yes—
72C2×C22⋊C4×C43D412yes—
73C2×C42×C43C2311yescharacteristic
74C2×C42×C43C2311yescharacteristic
75C4⋊C8×C43C2×C418yescomplemented
76C22⋊C8×C43C2×C418yes—
77#97×C43C2×C414yescomplemented
78C4×C8×C43C2×C414yescomplemented
79C24×C43C2×D411yescharacteristic
80C22×C4×C43—22no—
81C22×C4×C43—22no—
82C22×C4×C43C22×C412yes—
83C22×C4×C43C2×D412yes—
84C22×C4×C43C2×D412yes—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×Q812yes—
87C22×C4×C43C2411yescharacteristic
88C22×Dic43—21no—
89C22×Dic43—22no—
90C22×Dic43—22no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—42no—
95C22×Dic43—82no—
96C2×C8×C43—22no—
97C2×C8×C43—22no—
98C2×C8×C43—22no—
99C2×C8×C43—22no—
100C2×C8×C43C22×C414yes—
101C2×C8×C43C22×C414yes—
102C4⋊C4×C43C4⋊C418yes—
103C22⋊C4×C43C4⋊C418yes—
104C42×C43C22×C412yes—
105C42×C43C22×C412yes—
106C42×C43C2×Q812yes—
107C42×C43C2×Q812yes—
108C22⋊Dic43—42no—
109C22⋊Dic43—82no—
110C4⋊Dic43—22no—
111C4⋊Dic43—22no—
112C4⋊Dic43—22no—
113C4⋊Dic43—22no—
114C4⋊Dic43—22no—
115C4⋊Dic43—22no—
116C4⋊Dic43—24no—
117C4⋊Dic43—42no—
118C4⋊Dic43—82no—
119C4⋊Dic43—82no—
120C4⋊Dic43—82no—
121C4×Dic43—42no—
122C4×Dic43—82no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—22no—
126C23×C43—22no—
127C23×C43C2×C4⋊C412yes—
128C23×C43C22×D411yescharacteristic
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43—24no—
136C2×C4×C43—24no—
137C2×C4×C43C2×C4⋊C414yes—
138C2×C4×C43C2×C4⋊C414yes—
139C2×C4×C43C2×C4⋊C412yes—
140C2×C4×C43C23×C411yescharacteristic
141C2×C4×C43C22×Q811yescharacteristic
142C2×C4×C43H(5,𝔽2)12yes—
143C2×C4×C432−1+412yes—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—42no—
149C2×Dic43—42no—
150C2×Dic43—42no—
151C2×Dic43—42no—
152C2×Dic43—42no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—84no—
159C8×C43—24no—
160C8×C43—24no—
161#21991—431nomaximal, Sylow
162C22×C43—22no—
163C22×C43—24no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—42no—
167C22×C43C22×C4⋊C411yescharacteristic
168C22×C43#53511yescharacteristic
169C22×C43#53611yescharacteristic
170C22×C43#57612yes—
171C22×C43#57812yes—
172C4×C43—22no—
173C4×C43—24no—
174C4×C43—24no—
175C4×C43#52012yes—
176C4×C43#54412yes—
177Dic43—81no—
178Dic43—82no—
179Dic43—81no—
180Dic43—81no—
181Dic43—81no—
182Dic43—82no—
183C2×#433D4311yescharacteristic
184#2317—431no—
185#2314—431no—
186#1949—432no—
187#1947—432no—
188#1854—432no—
189#1852—432no—
190#1847—431no—
191#1845—431no—
192#1836—431no—
193#1835—431no—
194C2×C43—42no—
195C2×C43#231711yescharacteristic
196C2×C43#291312yes—
197C2×C43#322011yescharacteristic
198C2×C43#322311yescharacteristic
199C2×C43#324312yes—
200C2×#117—431no—
201C2×#117C2×D4311yescharacteristic
202C22×C4⋊C4—431no—
203#433Dic4318yescomplemented
204C2×#107—432no—
205C2×#107—432no—
206C2×#107—432no—
207C2×#106—432no—
208C2×C4⋊C8C2×D4312yes—
209C2×C22⋊C8C2×D4312yes—
210C2×#97C2×D4311yescharacteristic
211C2×C4×C8C2×D4311yescharacteristic
212#389—862no—
213#388—862no—
214#387—862no—
215#385—862no—
216#384—431no—
217#384—431no—
218#384—431no—
219#382—431no—
220#382—431no—
221#382—431no—
222#380—432no—
223C4×C4⋊C4—432no—
224#340—432no—
225#340—432no—
226#340—432no—
227#340—432no—
228C43#2199111yescharacteristic, complemented, Sylow
229C23×C4—861no—
230C23×C4C22×D4311yescharacteristic
231C22×C8C22×D4312yes—
232C22×C8C22×D4312yes—
233#117—1722no—
234#117Dic8614yes—
235#117C2×Dic4314yes—
236C2×C4⋊C4—431no—
237C2×C4⋊C4—431no—
238C2×C4⋊C4—431no—
239C2×C4⋊C4—431no—
240C2×C4⋊C4—432no—
241C2×C4⋊C4—432no—
242C2×C4⋊C4—862no—
243C2×C4⋊C4—862no—
244C2×C4⋊C4—862no—
245C2×C4⋊C4—861no—
246C2×C4⋊C4—1722no—
247C2×C4⋊C4D17212yes—
248C2×C22⋊C4—862no—
249C2×C22⋊C4—861no—
250C2×C22⋊C4D17212yes—
251C2×C42—862no—
252C2×C42—861no—
253C2×C42C22×D4311yescharacteristic
254C2×C42C22×D4311yescharacteristic
255#107—1722no—
256#107—1722no—
257#107—1722no—
258#106—1722no—
259C4⋊C8C2×Dic4318yescomplemented
260C22⋊C8C2×Dic4318yes—
261#97C2×Dic4314yescomplemented
262C4×C8C2×Dic4314yescomplemented
263#95—862no—
264#95—862no—
265#95—862no—
266#95—862no—
267#95—862no—
268C24C2×D17211yescharacteristic
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—862no—
272C22×C4—861no—
273C22×C4—862no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—3442no—
278C22×C4—1722no—
279C22×C4C2×Dic8612yes—
280C22×C4C2×D17212yes—
281C22×C4C2×D17211yescharacteristic
282C22×C4C2×D17212yes—
283C22×C4C22×Dic4312yes—
284C22×C4C23×D4311yescharacteristic
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8C22×Dic4314yes—
290C2×C8C22×Dic4314yes—
291C4⋊C4—862no—
292C4⋊C4—862no—
293C4⋊C4—862no—
294C4⋊C4—862no—
295C4⋊C4—862no—
296C4⋊C4—862no—
297C4⋊C4—864no—
298C4⋊C4—3442no—
299C4⋊C4—3442no—
300C4⋊C4—3442no—
301C4⋊C4—1722no—
302C4⋊C4C4⋊Dic4318yes—
303C22⋊C4—3442no—
304C22⋊C4—1722no—
305C22⋊C4C4⋊Dic4318yes—
306C42—3442no—
307C42—1722no—
308C42C2×Dic8612yes—
309C42C2×Dic8612yes—
310C42C22×Dic4312yes—
311C42C22×Dic4312yes—
312C23—22no—
313C23—22no—
314C23—21no—
315C23—21no—
316C23C2×C4⋊Dic4312yes—
317C23C22×D17211yescharacteristic
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—3444no—
327C2×C4—1722no—
328C2×C4—1722no—
329C2×C4—1722no—
330C2×C4—1722no—
331C2×C4—1722no—
332C2×C4—1722no—
333C2×C4—1722no—
334C2×C4—1722no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4C2×C4⋊Dic4314yes—
342C2×C4C2×C4⋊Dic4314yes—
343C2×C4C2×C4⋊Dic4312yes—
344C2×C4C23×Dic4311yescharacteristic
345C2×C4C22×Dic8611yescharacteristic
346C2×C4#1306337112yes—
347C2×C4#1306337212yes—
348C8—24no—
349C8—24no—
350C22—24no—
351C22—22no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22C22×C4⋊Dic4311yescharacteristic
356C22#1458346811yescharacteristic
357C22#1458347511yescharacteristic
358C22#1458370412yes—
359C22#1458371612yes—
360C4—24no—
361C4—24no—
362C4—22no—
363C4—3442no—
364C4—3441no—
365C4—3441no—
366C4—3442no—
367C4—3441no—
368C4—3441no—
369C4#1458338212yes—
370C4#1458352712yes—
371C2—42no—
372C2#1913721811yescharacteristic
373C2#1914319512yes—
374C2#1914564711yescharacteristic
375C2#1914568011yescharacteristic
376C2#1914588012yes—
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#433C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterC2×#433D43
hypocenterC43#21991
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
3. #19135365C2semidirect
4. #19135354C2semidirect
7. #19134763C2semidirect
8. #19134755C2semidirect
9. #19134729C2semidirect
10. #19134726C2semidirect
35. C43×#433C4semidirect
75. C4⋊C8×C43C2×C4semidirect
77. #97×C43C2×C4semidirect
78. C4×C8×C43C2×C4semidirect
203. #433Dic43semidirect
228. C43#21991semidirect
259. C4⋊C8C2×Dic43semidirect
261. #97C2×Dic43semidirect
262. C4×C8C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191372182
#191372042
#191353652
#191353542
#191347962
#191347852
#191347632
#191347552
#191347292
#191347262
C2×C43×#4332
#2199143