Finite Group Databasebeta

← #24995977

Subgroups — #24995977

Order 11008.

400 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144920C211yesmaximal, characteristic
2#19134725C211yesmaximal, characteristic, complemented
3#19133159C211yesmaximal, characteristic, complemented
4#19133156C211yesmaximal, characteristic
5#19133154C211yesmaximal, characteristic
6#19132879C211yesmaximal, 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
16#14582893—21no—
17#14582893—21no—
18C2×C4×C43⋊C8C2211yescharacteristic
19#14582765C2211yescharacteristic
20#14582661—21no—
21#14582661—21no—
22#14582636—22no—
23#14582634—22no—
24#14582632—22no—
25#14582621—21no—
26C8×C43⋊C8—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—
42C4⋊(C43⋊C8)—21no—
43#13063248—21no—
44#13063248—21no—
45#13063248—21no—
46#13063248—21no—
47#13063245—21no—
48#13063245—21no—
49#13063245—21no—
50#13063245—21no—
51C22⋊(C43⋊C8)D412yes—
52C4×C43⋊C8—21no—
53C4×C43⋊C8C2×C411yescharacteristic
54C4×C43⋊C8C2×C411yescharacteristic
55C4×C43⋊C8D411yescharacteristic
56C4×C43⋊C8D411yescharacteristic
57C43⋊#95—21no—
58C43⋊#95—21no—
59C4⋊Q8×C43C2×C411yescharacteristic
60C4⋊Q8×C43C2×C411yescharacteristic
61#125×C43—21no—
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—21no—
64C4×Q8×C43—21no—
65C4×Q8×C43—21no—
66#117×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C22⋊C8×C43D412yes—
71C4×C8×C43—21no—
72#95×C43—21no—
73#95×C43—21no—
74C2×Q8×C43—21no—
75C2×Q8×C43—21no—
76C22×C4×C43—41no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C2×C22⋊D43—41no—
81C22×Dic43—41no—
82#10621898—41no—
83#10621898—41no—
84#10621898—41no—
85#10621898—41no—
86C2×D172—21no—
87C2×D172—21no—
88C2×D172—21no—
89C2×C4×D43—41no—
90C2×Dic86—21no—
91C2×C8×C43—22no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C22⋊C4×C43—41no—
101C42×C43—41no—
102C42×C43C22×C411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43#4111yescharacteristic
105C42×C43#4111yescharacteristic
106(C2×D43)⋊C4—41no—
107(C2×D43)⋊C4—41no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43—41no—
111C4⋊Dic43—41no—
112C2×C43⋊C8—21no—
113C2×C43⋊C8—21no—
114C2×C43⋊C8—21no—
115C2×C43⋊C8—21no—
116C2×C43⋊C8—22no—
117C2×C43⋊C8C22⋊C411yescharacteristic
118C2×C43⋊C8C22⋊C411yescharacteristic
119C2×C43⋊C8C22⋊C411yescharacteristic
120C2×C43⋊C8C22⋊C411yescharacteristic
121C23×C43#12711yescharacteristic
122C22×D43—41no—
123Q8×C43—81no—
124Q8×C43—81no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12411yescharacteristic
138C2×C4×C43#13511yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C2×C4×C43#13511yescharacteristic
142C22⋊D43—81no—
143C22⋊D43—81no—
144C2×Dic43—41no—
145C2×Dic43—81no—
146C2×Dic43—81no—
147C2×Dic43—81no—
148D172—41no—
149D172—41no—
150D172—81no—
151D172—81no—
152C4×D43—81no—
153C4×D43—81no—
154Dic86—41no—
155Dic86—41no—
156C8×C43—42no—
157C43⋊C8—21no—
158C43⋊C8—21no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C43⋊C8—42no—
162#9757—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43#39011yescharacteristic
166C22×C43#49511yescharacteristic
167C22×C43#49511yescharacteristic
168C2×D43—81no—
169C2×D43—81no—
170C2×D43—81no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—81no—
176C4×C43—81no—
177C4×C43—161no—
178C4×C43#41611yescharacteristic
179C4×C43#41611yescharacteristic
180C4×C43#48811yescharacteristic
181C4×C43#48811yescharacteristic
182Dic43—81no—
183Dic43—161no—
184#3131—431no—
185#1835—431no—
186#1518—431no—
187#1518D4311yescharacteristic, complemented
188#1517—431no—
189#1517—431no—
190#1450—431no—
191C2×C43—21no—
192C2×C43—21no—
193C2×C43#195811yescharacteristic
194C2×C43#197611yescharacteristic
195C2×C43#197611yescharacteristic
196D43—161no—
197#533C2×D4311yescharacteristic
198#532—431no—
199#488—861no—
200#488—861no—
201#487—431no—
202#487—431no—
203#486—431no—
204#486—431no—
205#431—431no—
206#431C2×D4311yescharacteristic
207#416—861no—
208#416—861no—
209C2×C4×C8—431no—
210#382—431no—
211#382C2×D4311yescharacteristic
212#340—861no—
213#340—861no—
214#328—22no—
215#328—862no—
216#327—862no—
217#327—862no—
218#322—861no—
219C82—861no—
220C43#975711yescharacteristic, complemented, Sylow
221C2×#41—861no—
222C22×C8—431no—
223C22×C8—431no—
224C4⋊Q8—431no—
225C4⋊Q8C4×D4311yescharacteristic
226C4⋊Q8C4×D4311yescharacteristic
227#127—431no—
228#125—21no—
229#124—861no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232#121—861no—
233#121—861no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—861no—
237C4×D4—861no—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—861no—
241C2×C42C22×D4311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—861no—
244#103—861no—
245#103—861no—
246#103—861no—
247#103—861no—
248#102—861no—
249#102—861no—
250#102—861no—
251#102—861no—
252C22⋊C8—432no—
253C22⋊C8C22⋊D4312yes—
254C4×C8—21no—
255C4×C8—431no—
256C4×C8—431no—
257C4×C8—431no—
258C4×C8—431no—
259C4×C8—861no—
260#95—21no—
261#95—21no—
262#95—861no—
263#95—861no—
264#41—1721no—
265#41—1721no—
266#41—1721no—
267#41—1721no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—861no—
271C2×D4—861no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—1721no—
275C22×C4—41no—
276C22×C4—1721no—
277C22×C4—1721no—
278C22×C4D4×D4311yescharacteristic
279C22×C4D4×D4311yescharacteristic
280C22×C4C2×C22⋊D4311yescharacteristic
281C2×C8—22no—
282C2×C8—431no—
283C2×C8—431no—
284C2×C8—431no—
285C2×C8—431no—
286C2×C8—861no—
287C2×C8—861no—
288C2×C8—861no—
289C2×C8—861no—
290C2×C8—862no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4—1721no—
302C4⋊C4—1721no—
303C22⋊C4—41no—
304C22⋊C4—1721no—
305C22⋊C4—1721no—
306C42—41no—
307C42C2×C4×D4311yescharacteristic
308C42#1062189811yescharacteristic
309C42D4×D4311yescharacteristic
310C42#1062190011yescharacteristic
311C23—1721no—
312C23#1306332111yescharacteristic
313Q8—81no—
314Q8—81no—
315Q8—1721no—
316Q8—1721no—
317D4—3441no—
318D4—3441no—
319D4—3441no—
320D4—3441no—
321D4—1721no—
322D4—1721no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—3441no—
331C2×C4—3441no—
332C2×C4—3441no—
333C2×C4—3441no—
334C2×C4—3441no—
335C2×C4—1721no—
336C2×C4C22⋊C4×D4311yescharacteristic
337C2×C4(C22⋊D43)⋊C411yescharacteristic
338C2×C4C4×C22⋊D4311yescharacteristic
339C2×C4#1306329711yescharacteristic
340C2×C4#1306329811yescharacteristic
341C2×C4#1306331111yescharacteristic
342C2×C4#1306334611yescharacteristic
343C2×C4#1306334611yescharacteristic
344C2×C4#1306334811yescharacteristic
345C2×C4#1306334811yescharacteristic
346C8—42no—
347C8—861no—
348C8—861no—
349C8—861no—
350C8—861no—
351C8—1722no—
352C22—21no—
353C22—21no—
354C22—3441no—
355C22—3441no—
356C22—3441no—
357C22#1458279911yescharacteristic
358C22#1458328011yescharacteristic
359C22#1458328411yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—81no—
366C4—161no—
367C4—3441no—
368C4—6881no—
369C4#1458289411yescharacteristic
370C4#1458289411yescharacteristic
371C4#1458325511yescharacteristic
372C4#1458325511yescharacteristic
373C2—21no—
374C2—21no—
375C2—6881no—
376C2#1913540311yescharacteristic
377C2#1913549011yescharacteristic
378C2#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#9757
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. #19134725C2semidirect
3. #19133159C2semidirect
6. #19132879C2semidirect
7. C43×#1518C2semidirect
11. #14583251C4semidirect
12. #14583251C4semidirect
13. #14583247C4semidirect
14. #14583247C4semidirect
187. #1518D43semidirect
220. C43#9757semidirect

Maximal subgroups

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

subgroupindex
#191449202
#191347252
#191331592
#191331562
#191331542
#191328792
C43×#15182
#975743