Finite Group Databasebeta

← #24995979

Subgroups — #24995979

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#19144917C211yesmaximal, characteristic
2#19134725C211yesmaximal, characteristic, complemented
3#19133160C211yesmaximal, characteristic, complemented
4#19133158C211yesmaximal, characteristic, complemented
5#19133155C211yesmaximal, characteristic
6#19132879C211yesmaximal, characteristic, complemented
7C43×#1517C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583253—21no—
10#14583253—21no—
11#14583249C411yescharacteristic, complemented
12#14583249C411yescharacteristic, complemented
13#14583245C411yescharacteristic, complemented
14#14583245C411yescharacteristic, complemented
15#14582952C2211yescharacteristic
16#14582895—21no—
17#14582895—21no—
18C2×C4×C43⋊C8C2211yescharacteristic
19#14582765C2211yescharacteristic
20#14582661—21no—
21#14582661—21no—
22#14582637—22no—
23#14582635—22no—
24#14582633—22no—
25#14582621—21no—
26C8×C43⋊C8—21no—
27C43×#532C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C43×#382C2211yescharacteristic
30C43×#327—22no—
31C22×C43⋊C8D411yescharacteristic
32C22×C43⋊C8D411yescharacteristic
33#13063325C2×C411yescharacteristic
34#13063325C2×C411yescharacteristic
35#13063317—21no—
36#13063304—21no—
37#13063304—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40#13063284—21no—
41C2×C4⋊Dic43—21no—
42C4⋊(C43⋊C8)—21no—
43#13063249—21no—
44#13063249—21no—
45#13063249—21no—
46#13063249—21no—
47#13063246—21no—
48#13063246—21no—
49#13063246—21no—
50#13063246—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—
59C2×#41×C43—21no—
60C4⋊Q8×C43C2×C411yescharacteristic
61#127×C43C2×C411yescharacteristic
62#124×C43—21no—
63#121×C43—21no—
64#121×C43—21no—
65C4×D4×C43—21no—
66C4×D4×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—
74#41×C43—41no—
75#41×C43—41no—
76#41×C43—41no—
77#41×C43—41no—
78C2×Q8×C43—21no—
79C2×D4×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×Dic43—41no—
89C2×Dic86—21no—
90C2×Dic86—21no—
91C2×C8×C43—22no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—41no—
95C4⋊C4×C43—41no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C42×C43C22×C411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43#4111yescharacteristic
101C42×C43#4111yescharacteristic
102C22⋊Dic43—41no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109Dic43⋊C4—41no—
110Dic43⋊C4—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—41no—
122C23×C43#12711yescharacteristic
123Q8×C43—41no—
124Q8×C43—41no—
125D4×C43—41no—
126D4×C43—41no—
127D4×C43—81no—
128D4×C43—81no—
129D4×C43—81no—
130D4×C43—81no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C2×C4×C43—81no—
138C2×C4×C43—81no—
139C2×C4×C43C2×C22⋊C411yescharacteristic
140C2×C4×C43C4×D411yescharacteristic
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12411yescharacteristic
145C2×C4×C43#13511yescharacteristic
146C2×C4×C43#13511yescharacteristic
147C2×C4×C43#13511yescharacteristic
148C2×C4×C43#13511yescharacteristic
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153C2×Dic43—81no—
154Dic86—81no—
155Dic86—81no—
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—81no—
166C22×C43—81no—
167C22×C43—81no—
168C22×C43#39011yescharacteristic
169C22×C43#49511yescharacteristic
170C22×C43#49511yescharacteristic
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—81no—
176C4×C43—161no—
177C4×C43#41611yescharacteristic
178C4×C43#41611yescharacteristic
179C4×C43#48811yescharacteristic
180C4×C43#48811yescharacteristic
181Dic43—81no—
182Dic43—81no—
183Dic43—161no—
184#3131—431no—
185#1835—431no—
186#1518—431no—
187#1518—431no—
188#1517—431no—
189#1517D4311yescharacteristic
190#1450—431no—
191C2×C43—21no—
192C2×C43—21no—
193C2×C43—161no—
194C2×C43#195811yescharacteristic
195C2×C43#197611yescharacteristic
196C2×C43#197611yescharacteristic
197#533—431no—
198#532C2×D4311yescharacteristic
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—862no—
215#328—862no—
216#327—22no—
217#327—862no—
218#322—861no—
219C82—861no—
220C43#975711yescharacteristic, complemented, Sylow
221C2×#41—21no—
222C22×C8—431no—
223C22×C8—431no—
224C4⋊Q8—431no—
225C4⋊Q8—431no—
226C4⋊Q8C4×D4311yescharacteristic
227#127C4×D4311yescharacteristic
228#125—861no—
229#124—21no—
230C22⋊Q8—861no—
231C22⋊Q8—861no—
232#121—21no—
233#121—21no—
234C4×Q8—861no—
235C4×Q8—861no—
236C4×D4—21no—
237C4×D4—21no—
238#117—861no—
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—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×Q8—861no—
270C2×Q8—861no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—41no—
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—41no—
294C4⋊C4—41no—
295C4⋊C4—861no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4—1721no—
300C4⋊C4—1721no—
301C4⋊C4—1721no—
302C4⋊C4—1721no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—1721no—
306C42—1721no—
307C42C2×C4×D4311yescharacteristic
308C42#1062189811yescharacteristic
309C42D4×D4311yescharacteristic
310C42#1062190011yescharacteristic
311C23—41no—
312C23#1306332111yescharacteristic
313Q8—41no—
314Q8—41no—
315Q8—3441no—
316Q8—3441no—
317D4—41no—
318D4—41no—
319D4—81no—
320D4—81no—
321D4—81no—
322D4—81no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—3441no—
332C2×C4—3441no—
333C2×C4—3441no—
334C2×C4—1721no—
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#1306334411yescharacteristic
343C2×C4#1306334411yescharacteristic
344C2×C4#1306334611yescharacteristic
345C2×C4#1306334611yescharacteristic
346C8—42no—
347C8—861no—
348C8—861no—
349C8—861no—
350C8—861no—
351C8—1722no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22#1458279911yescharacteristic
358C22#1458328011yescharacteristic
359C22#1458328211yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—161no—
366C4—3441no—
367C4—3441no—
368C4—6881no—
369C4#1458289211yescharacteristic
370C4#1458289211yescharacteristic
371C4#1458325211yescharacteristic
372C4#1458325211yescharacteristic
373C2—21no—
374C2—21no—
375C2—161no—
376C2#1913540511yescharacteristic
377C2#1913549011yescharacteristic
378C2#1913549211yescharacteristic
subgroupG/H
centerC22#14582799
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1517C2
socleC22×C43#390
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#1517D43
hypocenterC43#9757
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #19134725C2semidirect
3. #19133160C2semidirect
4. #19133158C2semidirect
6. #19132879C2semidirect
11. #14583249C4semidirect
12. #14583249C4semidirect
13. #14583245C4semidirect
14. #14583245C4semidirect
220. C43#9757semidirect

Maximal subgroups

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

subgroupindex
#191449172
#191347252
#191331602
#191331582
#191331552
#191328792
C43×#15172
#975743