Finite Group Databasebeta

← #24995755

Subgroups — #24995755

Order 11008.

506 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145170C211yesmaximal, characteristic
2#19135515C211yesmaximal, characteristic, complemented
3#19135513C211yesmaximal, characteristic, complemented
4C4×#13063258C211yesmaximal, characteristic, complemented
5#19133091C211yesmaximal, characteristic, complemented
6#19132876C211yesmaximal, characteristic, complemented
7C43×#1502C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583302C411yescharacteristic, complemented
10#14583275C411yescharacteristic, complemented
11#14583247C411yescharacteristic, complemented
12#14583245C411yescharacteristic, complemented
13#14583133—21no—
14#14583133—21no—
15C4×#10621882—21no—
16C4×#10621882—21no—
17C2×#13063258—21no—
18C2×#13063253—22no—
19C2×#13063252—22no—
20C4×#10621877C2211yescharacteristic
21C2×C4×C43⋊C8C2211yescharacteristic
22C4×C4⋊Dic43C2211yescharacteristic
23#14582661—21no—
24#14582634—22no—
25#14582621—21no—
26C8×C43⋊C8—21no—
27C43×#532C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C4×C4⋊C4×C43C2211yescharacteristic
30C43×#327—22no—
31C2×#10621898—21no—
32C2×#10621882—21no—
33C2×#10621882—21no—
34C2×#10621877D412yes—
35C22×C43⋊C8D411yescharacteristic
36C22×C43⋊C8D411yescharacteristic
37#13063325C2×C411yescharacteristic
38#13063322C2×C411yescharacteristic
39#13063313—21no—
40#13063299—21no—
41#13063299—21no—
42C4×D172—21no—
43C4×D172—21no—
44C2×C4⋊Dic43—21no—
45C2×C4×Dic43—21no—
46#13063258—24no—
47#13063258—21no—
48#13063258—21no—
49#13063253—44no—
50#13063252—44no—
51#13063246—21no—
52#13063246—21no—
53#13063245—21no—
54#13063245—21no—
55#13063236—21no—
56C4×C43⋊C8—21no—
57C4×C43⋊C8C2×C411yescharacteristic
58C4×C43⋊C8C2×C411yescharacteristic
59C4×C43⋊C8D411yescharacteristic
60C4×C43⋊C8D411yescharacteristic
61C43⋊#95—21no—
62C2×#41×C43—21no—
63C4⋊Q8×C43C2×C411yescharacteristic
64#127×C43C2×C411yescharacteristic
65#124×C43—21no—
66#121×C43—21no—
67#121×C43—21no—
68C4×D4×C43—21no—
69C4×D4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C42×C43—21no—
72C2×C42×C43C2311yescharacteristic
73C4⋊C8×C43—21no—
74C22⋊C8×C43D412yes—
75C4×C8×C43—21no—
76#95×C43—21no—
77#41×C43—42no—
78#41×C43—42no—
79C2×Q8×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C2×C22⋊D43—41no—
90C22×Dic43—41no—
91#10621898—42no—
92#10621898—42no—
93C2×D172—21no—
94C2×D172—21no—
95C2×D172—21no—
96C2×C4×D43—41no—
97C2×Dic86—21no—
98C2×C8×C43—22no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—41no—
103C22⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C42×C43—42no—
106C42×C43C22×C411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43#4111yescharacteristic
109C42×C43#4111yescharacteristic
110#10621882—42no—
111#10621882—42no—
112(C2×D43)⋊C4—41no—
113(C2×D43)⋊C4—41no—
114C4⋊Dic43—22no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4⋊Dic43—41no—
118C4×Dic43—42no—
119#10621877—22no—
120#10621877D814yescomplemented
121C2×C43⋊C8—22no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—41no—
124C2×C43⋊C8C22⋊C411yescharacteristic
125C2×C43⋊C8C22⋊C411yescharacteristic
126C2×C43⋊C8C22⋊C411yescharacteristic
127C2×C43⋊C8C22⋊C411yescharacteristic
128C23×C43—41no—
129C23×C43#12711yescharacteristic
130C22×D43—41no—
131Q8×C43—42no—
132D4×C43—41no—
133D4×C43—41no—
134D4×C43—42no—
135D4×C43—81no—
136D4×C43—81no—
137D4×C43—81no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—41no—
143C2×C4×C43—81no—
144C2×C4×C43—81no—
145C2×C4×C43—82no—
146C2×C4×C43C2×C22⋊C411yescharacteristic
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12411yescharacteristic
152C2×C4×C43C2×D812yes—
153C2×C4×C43#13512yes—
154C22⋊D43—81no—
155C22⋊D43—81no—
156C2×Dic43—42no—
157C2×Dic43—41no—
158C2×Dic43—81no—
159C2×Dic43—81no—
160D172—41no—
161D172—41no—
162D172—42no—
163D172—81no—
164C4×D43—82no—
165Dic86—42no—
166C8×C43—42no—
167C43⋊C8—21no—
168C43⋊C8—21no—
169C43⋊C8—21no—
170C43⋊C8—24no—
171C43⋊C8#10412yescomplemented
172#9719—431nomaximal, Sylow
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—81no—
176C22×C43—81no—
177C22×C43—81no—
178C22×C43#39011yescharacteristic
179C22×C43#49311yescharacteristic
180C22×C43#49511yescharacteristic
181C2×D43—81no—
182C2×D43—81no—
183C2×D43—81no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—82no—
188C4×C43—81no—
189C4×C43C2×#10411yescharacteristic
190C4×C43#42111yescharacteristic
191C4×C43C4×D812yes—
192C4×C43#46612yes—
193Dic43—82no—
194Dic43—81no—
195#3169—431no—
196#1980—431no—
197#1980—431no—
198C4×#107—431no—
199#1502—431no—
200#1502D4311yescharacteristic, complemented
201C8×M16—431no—
202C2×C43—21no—
203C2×C43—21no—
204C2×C43—161no—
205C2×C43#197011yescharacteristic
206C2×C43#197611yescharacteristic
207C2×C43#198011yescharacteristic
208D43—161no—
209#532—431no—
210#532C2×D4311yescharacteristic
211#500—431no—
212#493—431no—
213#486—431no—
214#486—431no—
215#466—861no—
216#466—861no—
217C4×D8—861no—
218C4×D8—861no—
219#431C2×D4311yescharacteristic
220C2×#107—861no—
221C2×#104—862no—
222C2×#104—862no—
223C4×M16—431no—
224C2×C4×C8—431no—
225C4×C4⋊C4—431no—
226C4×C4⋊C4C2×D4311yescharacteristic
227#340—861no—
228#327—22no—
229#327—862no—
230#322—861no—
231C82—861no—
232C43#971911yescharacteristic, complemented, Sylow
233C2×#41—21no—
234C2×#41—861no—
235C2×D8—861no—
236C2×D8—861no—
237C2×M16—432no—
238C22×C8—431no—
239C22×C8—431no—
240C4⋊Q8—431no—
241C4⋊Q8C4×D4311yescharacteristic
242#127—431no—
243#127C4×D4311yescharacteristic
244#124—21no—
245#124—861no—
246#121—21no—
247#121—21no—
248#121—861no—
249#121—861no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—861no—
253C4×D4—861no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—861no—
256C2×C42—21no—
257C2×C42—861no—
258C2×C42C22×D4311yescharacteristic
259#107—861no—
260#107—861no—
261#107—864no—
262C4⋊C8—21no—
263#104—1724no—
264#104—1724no—
265#102—861no—
266#102—861no—
267#102—861no—
268#102—861no—
269C22⋊C8C22⋊D4312yes—
270#97—861no—
271C4×C8—21no—
272C4×C8—431no—
273C4×C8—431no—
274C4×C8—431no—
275C4×C8—431no—
276C4×C8—861no—
277#95—21no—
278#95—861no—
279#41—42no—
280#41—42no—
281#41—1722no—
282#41—1722no—
283C2×Q8—21no—
284C2×Q8—861no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—861no—
290C2×D4—861no—
291C2×D4—861no—
292C2×D4—1721no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—1721no—
296C22×C4—1721no—
297C22×C4D4×D4311yescharacteristic
298C22×C4D4×D4311yescharacteristic
299C22×C4C2×C22⋊D4311yescharacteristic
300D8—1722no—
301D8—1722no—
302M16—434no—
303M16—862no—
304C2×C8—22no—
305C2×C8—431no—
306C2×C8—431no—
307C2×C8—431no—
308C2×C8—431no—
309C2×C8—862no—
310C2×C8—862no—
311C2×C8—1721no—
312C4⋊C4—22no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—862no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C4⋊C4—1721no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—1721no—
323C22⋊C4—1721no—
324C42—42no—
325C42—1722no—
326C42C2×C4×D4311yescharacteristic
327C42#1062189811yescharacteristic
328C42D4×D4311yescharacteristic
329C42#1062190011yescharacteristic
330C23—41no—
331C23—1721no—
332C23#1306332111yescharacteristic
333Q8—42no—
334Q8—1722no—
335D4—41no—
336D4—41no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—3441no—
342D4—3441no—
343D4—3441no—
344D4—1721no—
345D4—1721no—
346D4—1722no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—82no—
355C2×C4—3441no—
356C2×C4—3441no—
357C2×C4—3442no—
358C2×C4—1722no—
359C2×C4—1721no—
360C2×C4C22⋊C4×D4311yescharacteristic
361C2×C4(C22⋊D43)⋊C411yescharacteristic
362C2×C4C4×C22⋊D4311yescharacteristic
363C2×C4#1306329711yescharacteristic
364C2×C4#1306329811yescharacteristic
365C2×C4#1306331111yescharacteristic
366C2×C4D8×D4312yes—
367C2×C4#1306334612yes—
368C8—42no—
369C8—432no—
370C8—864no—
371C8—861no—
372C8—861no—
373C8—861no—
374C22—21no—
375C22—21no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—3441no—
380C22—3441no—
381C22—3441no—
382C22#1458279911yescharacteristic
383C22#1458327411yescharacteristic
384C22#1458328011yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—82no—
389C4—81no—
390C4—3442no—
391C4—3441no—
392C4#104×D4311yescharacteristic
393C4#1458291411yescharacteristic
394C4#1458297912yes—
395C4#1458313412yes—
396C2—21no—
397C2—21no—
398C2—161no—
399C2—6881no—
400C2#1913545811yescharacteristic
401C2#1913549011yescharacteristic
402C2#1913551211yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1502C2
socleC22×C43#390
prime radical#19145170C2
cosocleC2×C42×C43C23
hypercenter#1502D43
hypocenterC43#9719
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #19135515C2semidirect
3. #19135513C2semidirect
4. C4×#13063258C2semidirect
5. #19133091C2semidirect
6. #19132876C2semidirect
7. C43×#1502C2semidirect
9. #14583302C4semidirect
10. #14583275C4semidirect
11. #14583247C4semidirect
12. #14583245C4semidirect
120. #10621877D8semidirect
171. C43⋊C8#104semidirect
200. #1502D43semidirect
232. C43#9719semidirect

Maximal subgroups

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

subgroupindex
#191451702
#191355152
#191355132
C4×#130632582
#191330912
#191328762
C43×#15022
#971943