Finite Group Databasebeta

← #24995982

Subgroups — #24995982

Order 11008.

408 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144920C211yesmaximal, characteristic
2#19134757C211yesmaximal, characteristic, complemented
3#19133159C211yesmaximal, characteristic, complemented
4#19133156C211yesmaximal, characteristic
5#19133154C211yesmaximal, characteristic
6#19132888C211yesmaximal, characteristic, complemented
7C43×#1518C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583256—21no—
10#14583256—21no—
11#14583251C411yescharacteristic, complemented
12#14583251C411yescharacteristic, complemented
13#14583247C411yescharacteristic, complemented
14#14583247C411yescharacteristic, complemented
15#14582952C2211yescharacteristic
16C2×#13063258—21no—
17C2×#13063256—21no—
18#14582893—21no—
19#14582893—21no—
20C2×C4×C43⋊C8C2211yescharacteristic
21#14582765C2211yescharacteristic
22#14582636—22no—
23#14582634—22no—
24#14582632—22no—
25#14582621—21no—
26#14582620—21no—
27C43×#533C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C43×#382C2211yescharacteristic
30C43×#328—22no—
31C2×#10621898—21no—
32C22×C43⋊C8D411yescharacteristic
33C22×C43⋊C8D411yescharacteristic
34#13063325C2×C411yescharacteristic
35#13063322C2×C411yescharacteristic
36#13063313—21no—
37#13063299—21no—
38#13063299—21no—
39C4×D172—21no—
40C4×D172—21no—
41C2×C4⋊Dic43—21no—
42#13063258—42no—
43#13063256—42no—
44C4⋊(C43⋊C8)—21no—
45#13063248—21no—
46#13063248—21no—
47#13063248—21no—
48#13063248—21no—
49#13063245—21no—
50#13063245—21no—
51#13063245—21no—
52#13063245—21no—
53C22⋊(C43⋊C8)D412yes—
54C4×C43⋊C8—21no—
55C4×C43⋊C8C2×C411yescharacteristic
56C4×C43⋊C8C2×C411yescharacteristic
57C4×C43⋊C8D411yescharacteristic
58C4×C43⋊C8D411yescharacteristic
59C43⋊#95—21no—
60C43⋊#95—21no—
61C4⋊Q8×C43C2×C411yescharacteristic
62C4⋊Q8×C43C2×C411yescharacteristic
63#125×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68#117×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43—21no—
72C22⋊C8×C43D412yes—
73C4×C8×C43—21no—
74#95×C43—21no—
75#95×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C22×C4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C2×C22⋊D43—41no—
83C22×Dic43—41no—
84#10621898—41no—
85#10621898—41no—
86#10621898—41no—
87#10621898—41no—
88C2×D172—21no—
89C2×D172—21no—
90C2×D172—21no—
91C2×C4×D43—41no—
92C2×Dic86—21no—
93C2×C8×C43—22no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C42×C43—41no—
104C42×C43C22×C411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43#4111yescharacteristic
107C42×C43#4111yescharacteristic
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—41no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—41no—
113C4⋊Dic43—41no—
114C2×C43⋊C8—21no—
115C2×C43⋊C8—21no—
116C2×C43⋊C8—21no—
117C2×C43⋊C8—21no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8C22⋊C411yescharacteristic
120C2×C43⋊C8C22⋊C411yescharacteristic
121C2×C43⋊C8C22⋊C411yescharacteristic
122C2×C43⋊C8C22⋊C411yescharacteristic
123C23×C43#12711yescharacteristic
124C22×D43—41no—
125Q8×C43—81no—
126Q8×C43—81no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43—81no—
134C2×C4×C43C2×C22⋊C411yescharacteristic
135C2×C4×C43C4×D411yescharacteristic
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×C4×C43#12411yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C2×C4×C43#13711yescharacteristic
144C22⋊D43—81no—
145C22⋊D43—81no—
146C2×Dic43—41no—
147C2×Dic43—81no—
148C2×Dic43—81no—
149C2×Dic43—81no—
150D172—41no—
151D172—41no—
152D172—81no—
153D172—81no—
154C4×D43—81no—
155C4×D43—81no—
156Dic86—41no—
157Dic86—41no—
158C8×C43—42no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C43⋊C8—21no—
162C43⋊C8—21no—
163C43⋊C8—42no—
164#9758—431nomaximal, Sylow
165C22×C43—21no—
166C22×C43—21no—
167C22×C43#39011yescharacteristic
168C22×C43#49611yescharacteristic
169C22×C43#49711yescharacteristic
170C2×D43—81no—
171C2×D43—81no—
172C2×D43—81no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—81no—
178C4×C43—81no—
179C4×C43—161no—
180C4×C43#41711yescharacteristic
181C4×C43#41711yescharacteristic
182C4×C43#48911yescharacteristic
183C4×C43#48911yescharacteristic
184Dic43—81no—
185Dic43—161no—
186#3131—431no—
187#1846—431no—
188#1518—431no—
189#1518D4311yescharacteristic, complemented
190#1517—431no—
191#1517—431no—
192#1452—431no—
193C2×C43—21no—
194C2×C43—21no—
195C2×C43#195911yescharacteristic
196C2×C43#197611yescharacteristic
197C2×C43#197611yescharacteristic
198D43—161no—
199#533C2×D4311yescharacteristic
200#532—431no—
201#488—861no—
202#488—861no—
203#487—431no—
204#487—431no—
205#486—431no—
206#486—431no—
207#431—431no—
208#431C2×D4311yescharacteristic
209C2×#107—861no—
210C2×#106—861no—
211#416—861no—
212#416—861no—
213C2×C4×C8—431no—
214#382—431no—
215#382C2×D4311yescharacteristic
216#328—22no—
217#328—862no—
218#327—862no—
219#327—862no—
220#322—861no—
221#322—861no—
222C43#975811yescharacteristic, complemented, Sylow
223C2×#41—861no—
224C22×C8—431no—
225C22×C8—431no—
226C4⋊Q8—431no—
227C4⋊Q8C4×D4311yescharacteristic
228C4⋊Q8C4×D4311yescharacteristic
229#127—431no—
230#125—21no—
231#124—861no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234#121—861no—
235#121—861no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×D4—861no—
239C4×D4—861no—
240#117—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—861no—
243C2×C42C22×D4311yescharacteristic
244#107—1722no—
245#106—1722no—
246C4⋊C8—21no—
247C4⋊C8—861no—
248#103—861no—
249#103—861no—
250#103—861no—
251#103—861no—
252#102—861no—
253#102—861no—
254#102—861no—
255#102—861no—
256C22⋊C8—432no—
257C22⋊C8C22⋊D4312yes—
258C4×C8—21no—
259C4×C8—431no—
260C4×C8—431no—
261C4×C8—431no—
262C4×C8—431no—
263C4×C8—861no—
264#95—21no—
265#95—21no—
266#95—861no—
267#95—861no—
268#41—1721no—
269#41—1721no—
270#41—1721no—
271#41—1721no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—861no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—1721no—
279C22×C4—41no—
280C22×C4—1721no—
281C22×C4—1721no—
282C22×C4D4×D4311yescharacteristic
283C22×C4D4×D4311yescharacteristic
284C22×C4C2×C22⋊D4311yescharacteristic
285C2×C8—22no—
286C2×C8—431no—
287C2×C8—431no—
288C2×C8—431no—
289C2×C8—431no—
290C2×C8—861no—
291C2×C8—861no—
292C2×C8—861no—
293C2×C8—861no—
294C2×C8—862no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4—1721no—
306C4⋊C4—1721no—
307C22⋊C4—41no—
308C22⋊C4—1721no—
309C22⋊C4—1721no—
310C42—41no—
311C42C2×C4×D4311yescharacteristic
312C42#1062189811yescharacteristic
313C42D4×D4311yescharacteristic
314C42#1062190011yescharacteristic
315C23—1721no—
316C23#1306332111yescharacteristic
317Q8—81no—
318Q8—81no—
319Q8—1721no—
320Q8—1721no—
321D4—3441no—
322D4—3441no—
323D4—3441no—
324D4—3441no—
325D4—1721no—
326D4—1721no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—3441no—
335C2×C4—3441no—
336C2×C4—3441no—
337C2×C4—3441no—
338C2×C4—3441no—
339C2×C4—1721no—
340C2×C4C22⋊C4×D4311yescharacteristic
341C2×C4(C22⋊D43)⋊C411yescharacteristic
342C2×C4C4×C22⋊D4311yescharacteristic
343C2×C4#1306329711yescharacteristic
344C2×C4#1306329811yescharacteristic
345C2×C4#1306331111yescharacteristic
346C2×C4#1306335211yescharacteristic
347C2×C4#1306335211yescharacteristic
348C2×C4#1306335711yescharacteristic
349C2×C4#1306335711yescharacteristic
350C8—42no—
351C8—861no—
352C8—861no—
353C8—861no—
354C8—861no—
355C8—1722no—
356C22—21no—
357C22—21no—
358C22—3441no—
359C22—3441no—
360C22—3441no—
361C22#1458279911yescharacteristic
362C22#1458328511yescharacteristic
363C22#1458329211yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—81no—
369C4—81no—
370C4—161no—
371C4—3441no—
372C4—6881no—
373C4#1458289911yescharacteristic
374C4#1458289911yescharacteristic
375C4#1458326011yescharacteristic
376C4#1458326011yescharacteristic
377C2—21no—
378C2—21no—
379C2—6881no—
380C2#1913540811yescharacteristic
381C2#1913549011yescharacteristic
382C2#1913549211yescharacteristic
subgroupG/H
centerC22#14582799
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1518C2
socleC22×C43#390
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1518D43
hypocenterC43#9758
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
2. #19134757C2semidirect
3. #19133159C2semidirect
6. #19132888C2semidirect
7. C43×#1518C2semidirect
11. #14583251C4semidirect
12. #14583251C4semidirect
13. #14583247C4semidirect
14. #14583247C4semidirect
189. #1518D43semidirect
222. C43#9758semidirect

Maximal subgroups

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

subgroupindex
#191449202
#191347572
#191331592
#191331562
#191331542
#191328882
C43×#15182
#975843