Finite Group Databasebeta

← #24992677

Subgroups — #24992677

Order 11008.

478 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144377C211yesmaximal, characteristic
2#19143551C211yesmaximal, characteristic
3#19134616C211yesmaximal, characteristic
4#19133050C211yesmaximal, characteristic, complemented
5#19132491C211yesmaximal, characteristic, complemented
6#19132436C211yesmaximal, characteristic, complemented
7C43×#1503C211yesmaximal, characteristic, complemented
8C4×#10621898C2211yescharacteristic
9#14583203—21no—
10#14583196—21no—
11#14583191C411yescharacteristic, complemented
12#14583186C411yescharacteristic, complemented
13#14583181C411yescharacteristic, complemented
14#14583176C411yescharacteristic, complemented
15#14583023—21no—
16#14582964—21no—
17(C22⋊D43)⋊C8—22no—
18#14582950—21no—
19#14582935—21no—
20#14582923C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063253—21no—
23#14582893—21no—
24C2×C4×C43⋊C8C2211yescharacteristic
25C4×C8×D43—21no—
26#14582659—21no—
27Q8⋊(C43⋊C8)—21no—
28Q8⋊(C43⋊C8)—21no—
29C43×#533C2211yescharacteristic
30C43×#431C2211yescharacteristic
31C4×C4⋊C4×C43C2211yescharacteristic
32C43×#328—22no—
33C2×#10621898D411yescharacteristic
34C2×#10621877—21no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37C2×C8×D43—22no—
38C4×Dic86C2×C411yescharacteristic
39C4×Dic86D411yescharacteristic
40C4×D172C2×C411yescharacteristic
41C4×D172D411yescharacteristic
42C4×C22⋊D43—21no—
43C4×C22⋊D43—21no—
44#13063284D411yescharacteristic
45#13063282—21no—
46C42×D43—21no—
47#13063258—21no—
48#13063258—21no—
49#13063256—21no—
50#13063256—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)C2×C411yescharacteristic
55C4⋊(C43⋊C8)C2×C411yescharacteristic
56Dic43⋊C8—22no—
57#13063253—42no—
58#13063248—21no—
59#13063248—21no—
60#13063245—21no—
61#13063245—21no—
62(C2×D43)⋊C8—22no—
63C4×C43⋊C8—21no—
64C4×C43⋊C8D411yescharacteristic
65C4×C43⋊C8D411yescharacteristic
66C8×Dic43—22no—
67C4⋊Q8×C43C2×C411yescharacteristic
68C4⋊Q8×C43C2×C411yescharacteristic
69#125×C43—21no—
70C22⋊Q8×C43—21no—
71C22⋊Q8×C43—21no—
72C4×Q8×C43—21no—
73C4×Q8×C43—21no—
74#117×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C42×C43—21no—
77C2×C42×C43C2311yescharacteristic
78C4⋊C8×C43—21no—
79C22⋊C8×C43D412yes—
80C4×C8×C43—21no—
81#95×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C22×C4×C43—41no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C2×C22⋊D43—21no—
89#10621898—21no—
90#10621898—21no—
91#10621898SD1612yes—
92#10621898Q1612yes—
93C2×D172C22⋊C411yescharacteristic
94C2×C4×D43—21no—
95C2×C4×D43—21no—
96C2×C4×D43—21no—
97C2×Dic86C22⋊C411yescharacteristic
98C2×C8×C43—22no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C42×C43—41no—
109C42×C43—41no—
110C42×C43—41no—
111C42×C43C22×C411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115C22⋊Dic43—21no—
116(C2×D43)⋊C4—21no—
117(C2×D43)⋊C4—21no—
118C4⋊Dic43C22⋊C411yescharacteristic
119C4⋊Dic43C22⋊C411yescharacteristic
120Dic43⋊C4—21no—
121Dic43⋊C4—21no—
122C4×Dic43—21no—
123C4×Dic43—21no—
124C4×Dic43—21no—
125#10621877—41no—
126#10621877—41no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—21no—
130C2×C43⋊C8—21no—
131C2×C43⋊C8—42no—
132C2×C43⋊C8—41no—
133C2×C43⋊C8—41no—
134C2×C43⋊C8—41no—
135C8×D43—44no—
136C23×C43#12111yescharacteristic
137C22×D43—21no—
138Q8×C43—41no—
139Q8×C43—41no—
140Q8×C43—81no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—81no—
148C2×C4×C43—81no—
149C2×C4×C43C2×C22⋊C411yescharacteristic
150C2×C4×C43C4×D411yescharacteristic
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43#12011yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12311yescharacteristic
155C2×C4×C43C2×SD1611yescharacteristic
156C2×C4×C43C2×Q1611yescharacteristic
157C2×C4×C43#13511yescharacteristic
158C2×C4×C43#13511yescharacteristic
159C22⋊D43—22no—
160C22⋊D43—22no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164D172—21no—
165D172#10312yes—
166C4×D43—22no—
167C4×D43—22no—
168C4×D43—42no—
169C4×D43—41no—
170C4×D43—41no—
171Dic86—21no—
172Dic86#10312yes—
173C8×C43—42no—
174C43⋊C8—22no—
175C43⋊C8—41no—
176C43⋊C8—41no—
177C43⋊C8—41no—
178C43⋊C8—81no—
179#9207—431nomaximal, Sylow
180C22×C43—21no—
181C22×C43—21no—
182C22×C43#38611yescharacteristic
183C22×C43#46511yescharacteristic
184C22×C43#46711yescharacteristic
185C2×D43—22no—
186C2×D43—41no—
187C2×D43—41no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—82no—
192C4×C43—81no—
193C4×C43—81no—
194C4×C43C2×#10311yescharacteristic
195C4×C43#41611yescharacteristic
196C4×C43#44311yescharacteristic
197C4×C43#44411yescharacteristic
198C4×C43#46511yescharacteristic
199C4×C43#46711yescharacteristic
200Dic43—22no—
201Dic43—41no—
202Dic43—41no—
203#3076—431no—
204C8×#41—431no—
205#1806—431no—
206#1503D4311yescharacteristic, complemented
207#1493—431no—
208#1301—431no—
209#1279—431no—
210C2×C43—21no—
211C2×C43—21no—
212C2×C43#187611yescharacteristic
213C2×C43#189211yescharacteristic
214C2×C43#190611yescharacteristic
215D43—42no—
216#533C2×D4311yescharacteristic
217C4×#41—431no—
218#479—861no—
219#478—861no—
220#477—431no—
221#476—431no—
222#475—431no—
223#474—431no—
224C8×Q8—861no—
225C8×D4—861no—
226C8×D4—862no—
227#431—861no—
228#431C2×D4311yescharacteristic
229#427—861no—
230#423—431no—
231C2×C4⋊C8—431no—
232C2×#104—861no—
233#416—861no—
234C2×C4×C8—431no—
235C2×C4×C8—861no—
236C4×C4⋊C4C2×D4311yescharacteristic
237#339—861no—
238#328—22no—
239Q8⋊C8—861no—
240Q8⋊C8—861no—
241C43#920711yescharacteristic, complemented, Sylow
242C2×#41—431no—
243C2×M16—861no—
244C22×C8—862no—
245C22×C8—861no—
246C22×C8—861no—
247C4⋊Q8C4×D4311yescharacteristic
248C4⋊Q8C4×D4311yescharacteristic
249#125—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—431no—
255C4×Q8—431no—
256C4×D4—431no—
257C4×D4—431no—
258C4×D4—861no—
259C4×D4—861no—
260#117—21no—
261#117—431no—
262#117—861no—
263C2×C4⋊C4—21no—
264C2×C42—21no—
265C2×C42—861no—
266C2×C42C22×D4311yescharacteristic
267#107—861no—
268#107—861no—
269#106—861no—
270#106—861no—
271C4⋊C8—21no—
272C4⋊C8—431no—
273C4⋊C8—431no—
274C4⋊C8—862no—
275C4⋊C8—861no—
276C4⋊C8—861no—
277C4⋊C8—861no—
278#104—1722no—
279#103—861no—
280#103—861no—
281#102—861no—
282#102—861no—
283C22⋊C8—862no—
284C22⋊C8C22⋊D4312yes—
285C4×C8—21no—
286C4×C8—431no—
287C4×C8—431no—
288C4×C8—862no—
289C4×C8—861no—
290#95—21no—
291#41—432no—
292#41—432no—
293#41—861no—
294#41—861no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—431no—
298C2×D4—431no—
299C2×D4—861no—
300C22×C4—41no—
301C22×C4—861no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4D4×D4311yescharacteristic
305C22×C4#1062190011yescharacteristic
306C22×C4C2×C22⋊D4311yescharacteristic
307M16—1721no—
308M16—1721no—
309C2×C8—22no—
310C2×C8—861no—
311C2×C8—861no—
312C2×C8—861no—
313C2×C8—861no—
314C2×C8—1724no—
315C2×C8—1722no—
316C2×C8—1721no—
317C2×C8—1721no—
318C2×C8—1721no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—431no—
328C4⋊C4—431no—
329C4⋊C4—861no—
330C4⋊C4—861no—
331C22⋊C4—41no—
332C22⋊C4—861no—
333C22⋊C4—861no—
334C22⋊C4—861no—
335C42—41no—
336C42—41no—
337C42—41no—
338C42—861no—
339C42—861no—
340C42—861no—
341C42C2×C4×D4311yescharacteristic
342C42#1062189811yescharacteristic
343C42D4×D4311yescharacteristic
344C42D4×D4311yescharacteristic
345C23—861no—
346C23#1306329611yescharacteristic
347Q8—41no—
348Q8—41no—
349Q8—81no—
350Q8—432no—
351Q8—861no—
352D4—432no—
353D4—862no—
354D4—862no—
355D4—861no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—861no—
365C2×C4—862no—
366C2×C4—862no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—1722no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4C22⋊C4×D4311yescharacteristic
373C2×C4(C22⋊D43)⋊C411yescharacteristic
374C2×C4C4×C22⋊D4311yescharacteristic
375C2×C4#1306329311yescharacteristic
376C2×C4#1306329811yescharacteristic
377C2×C4#1306330711yescharacteristic
378C2×C4SD16×D4311yescharacteristic
379C2×C4Q16×D4311yescharacteristic
380C2×C4#1306334611yescharacteristic
381C2×C4#1306334811yescharacteristic
382C8—42no—
383C8—862no—
384C8—3441no—
385C8—1721no—
386C8—1721no—
387C8—1721no—
388C22—21no—
389C22—21no—
390C22—862no—
391C22—1721no—
392C22—1721no—
393C22#1458277511yescharacteristic
394C22#1458312511yescharacteristic
395C22#1458313711yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—82no—
400C4—81no—
401C4—81no—
402C4—862no—
403C4—1721no—
404C4—1721no—
405C4#103×D4311yescharacteristic
406C4#1458289411yescharacteristic
407C4#1458301311yescharacteristic
408C4#1458301811yescharacteristic
409C4#1458313111yescharacteristic
410C4#1458313911yescharacteristic
411C2—21no—
412C2—21no—
413C2—1722no—
414C2#1913491911yescharacteristic
415C2#1913501511yescharacteristic
416C2#1913509311yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1503C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1503D43
hypocenterC43#9207
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
4. #19133050C2semidirect
5. #19132491C2semidirect
6. #19132436C2semidirect
7. C43×#1503C2semidirect
11. #14583191C4semidirect
12. #14583186C4semidirect
13. #14583181C4semidirect
14. #14583176C4semidirect
206. #1503D43semidirect
241. C43#9207semidirect

Maximal subgroups

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

subgroupindex
#191443772
#191435512
#191346162
#191330502
#191324912
#191324362
C43×#15032
#920743