Finite Group Databasebeta

← #25252942

Subgroups — #25252942

Order 11008.

490 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145165C211yesmaximal, characteristic
2#19136759C212yesmaximal, complemented
3#19136744C211yesmaximal, characteristic, complemented
4#19136739C211yesmaximal, characteristic, complemented
5#19136710C212yesmaximal
6#19136701C212yesmaximal, complemented
7#19136657C212yesmaximal, complemented
8#19136642C211yesmaximal, characteristic, complemented
9#19136637C211yesmaximal, characteristic, complemented
10#19136351C211yesmaximal, characteristic, complemented
11C43×#3170C211yesmaximal, characteristic, complemented
12#14583433—21no—
13C2×#13063271C2212yes—
14C2×#13063268C2212yes—
15C2×#13063265C2212yes—
16#14583301C2211yescharacteristic
17#14583283C2211yescharacteristic
18#14583254—21no—
19#14583140C2211yescharacteristic
20#14583135C2211yescharacteristic
21#14583128—21no—
22C4×Dic172C2211yescharacteristic
23C4×#10621873—21no—
24C4×D344C2211yescharacteristic
25#14582726C2212yes—
26#14582724C2212yes—
27C4⋊(C43⋊C16)C2211yescharacteristic
28C4⋊(C43⋊C16)C2211yescharacteristic
29C4⋊(C43⋊C16)C2212yes—
30#14582703C2212yes—
31#14582703C2212yes—
32#14582702C2212yes—
33#14582699C2212yes—
34C43×#533—21no—
35C43×#500C2211yescharacteristic
36C43×#494C2211yescharacteristic
37C43×#487—21no—
38C43×#467—21no—
39C43×#467C2212yes—
40C4×Q16×C43—21no—
41C4×Q16×C43C2212yes—
42C2×C4×C8×C43C2211yescharacteristic
43C2×Dic172C2311yescharacteristic
44C2×#10621873—21no—
45C2×D344C2311yescharacteristic
46#13063319—41no—
47#13063317—21no—
48#13063313—21no—
49#13063308—41no—
50#13063304—21no—
51#13063299—21no—
52C4×Dic86—21no—
53C4×D172—21no—
54C4×C22⋊D43—41no—
55#13063282—41no—
56#13063271—42no—
57#13063268—42no—
58#13063265—42no—
59C2×C43⋊C16C2312yes—
60C2×C43⋊C16C2312yes—
61#13063259C2311yescharacteristic
62#13063259C2311yescharacteristic
63#13063257—21no—
64#13063250—21no—
65#13063250—21no—
66#13063247—21no—
67#13063247—21no—
68C2×Q16×C43—21no—
69C2×Q16×C43C2312yes—
70C22×C8×C43D411yescharacteristic
71C22×C8×C43C2311yescharacteristic
72C4⋊Q8×C43—21no—
73C4⋊Q8×C43—21no—
74#125×C43—41no—
75C22⋊Q8×C43—22no—
76C22⋊Q8×C43—41no—
77C4×Q8×C43—22no—
78C4×Q8×C43—41no—
79#117×C43—41no—
80C2×C42×C43D411yescharacteristic
81#107×C43—21no—
82#107×C43C2312yes—
83#103×C43—22no—
84#103×C43—22no—
85C4×C8×C43D411yescharacteristic
86C4×C8×C43D411yescharacteristic
87C4×C8×C43C2311yescharacteristic
88C4×C8×C43C2311yescharacteristic
89C2×Q8×C43—22no—
90C2×Q8×C43—41no—
91C22×C4×C43D811yescharacteristic
92C22×C4×C43D811yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C2×C22⋊D43—41no—
95C2×D172—21no—
96C2×C4×D43—41no—
97C2×Dic86—21no—
98Q16×C43—22no—
99Q16×C43—22no—
100Q16×C43—42no—
101C2×C8×C43—21no—
102C2×C8×C43—21no—
103C2×C8×C43—41no—
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43C2411yescharacteristic
108C4⋊C4×C43—22no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—42no—
112C4⋊C4×C43—42no—
113C4⋊C4×C43—41no—
114C22⋊C4×C43—42no—
115C42×C43—42no—
116C42×C43D811yescharacteristic
117C42×C43D811yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C22⋊Dic43—41no—
121(C2×D43)⋊C4—41no—
122(C2×D43)⋊C4—41no—
123(C2×D43)⋊C4—41no—
124(C2×D43)⋊C4—41no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127Dic43⋊C4—41no—
128Dic43⋊C4—41no—
129Dic43⋊C4—41no—
130Dic43⋊C4—41no—
131C4×Dic43—41no—
132Dic172—21no—
133Dic172—21no—
134D344—21no—
135D344—21no—
136#10621873—42no—
137C43⋊C16—22no—
138C43⋊C16—22no—
139C23×C43C2×D811yescharacteristic
140C22×D43—41no—
141Q8×C43—42no—
142Q8×C43—42no—
143Q8×C43—82no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—22no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43C2×D811yescharacteristic
151C2×C4×C43C2×D811yescharacteristic
152C2×C4×C43C2×D811yescharacteristic
153C2×C4×C43C2×D811yescharacteristic
154C2×C4×C43C2×D811yescharacteristic
155C2×C4×C43C22×D411yescharacteristic
156C22⋊D43—82no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160D172—41no—
161D172—41no—
162C4×D43—82no—
163Dic86—41no—
164Dic86—41no—
165C8×C43—21no—
166C8×C43—21no—
167C8×C43—21no—
168C8×C43H(5,𝔽2)11yescharacteristic
169C8×C432−1+411yescharacteristic
170#33818—431nomaximal, Sylow
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43C22×D811yescharacteristic
175C2×D43—81no—
176C2×D43—81no—
177C2×D43—81no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—82no—
183C4×C43—82no—
184C4×C43#51012yes—
185C4×C43#53711yescharacteristic
186C4×C43#57511yescharacteristic
187Dic43—81no—
188Dic43—81no—
189Dic43—81no—
190#3170D4311yescharacteristic, complemented
191#3168—431no—
192#2229—432no—
193#2227—431no—
194#2226—431no—
195#2220—432no—
196#2219—432no—
197#2211—432no—
198#2209—431no—
199#2208—431no—
200#2150—431no—
201C2×C43—41no—
202C2×C43#324511yescharacteristic
203C2×C43C2×#51011yescharacteristic
204C2×C43#341411yescharacteristic
205D43—161no—
206#533—21no—
207#529—861no—
208C2×Q32—432no—
209C2×SD32—432no—
210C2×M32—432no—
211#500C2×D4311yescharacteristic
212#499—431no—
213#495—431no—
214#494C2×D4311yescharacteristic
215#488—861no—
216#487—21no—
217#467—21no—
218#467—431no—
219#467C2×D4312yes—
220#466—431no—
221#465—861no—
222C4×Q16—21no—
223C4×Q16—431no—
224C4×Q16C2×D4312yes—
225C4×SD16—861no—
226C4×D8—431no—
227C2×C4×C8C2×D4311yescharacteristic
228#367—432no—
229#366—432no—
230C4⋊C16—431no—
231C4⋊C16—431no—
232C4⋊C16—432no—
233#358—432no—
234#358—432no—
235#358—432no—
236#357—432no—
237C43#3381811yescharacteristic, complemented, Sylow
238C2×Q16—21no—
239C2×Q16—431no—
240C2×Q16C22×D4312yes—
241C2×SD16—861no—
242C2×D8—431no—
243C22×C8C22⋊D4311yescharacteristic
244C22×C8C22×D4311yescharacteristic
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247#126—1721no—
248#125—41no—
249#125—861no—
250#124—861no—
251#123—1721no—
252C22⋊Q8—22no—
253C22⋊Q8—41no—
254C22⋊Q8—861no—
255#121—861no—
256C4×Q8—22no—
257C4×Q8—41no—
258C4×Q8—861no—
259C4×D4—861no—
260C4×D4—1721no—
261#117—41no—
262#117—1721no—
263C2×C42C22⋊D4311yescharacteristic
264Q32—1722no—
265SD32—1722no—
266M32—1722no—
267C2×C16—432no—
268C2×C16—432no—
269#107—21no—
270#107—431no—
271#107—431no—
272#107C22×D4312yes—
273#106—861no—
274#103—22no—
275#103—22no—
276#103—861no—
277#103—861no—
278#102—861no—
279#102—861no—
280C4×C8C22⋊D4311yescharacteristic
281C4×C8C22⋊D4311yescharacteristic
282C4×C8C22×D4311yescharacteristic
283C4×C8C22×D4311yescharacteristic
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—861no—
287C2×D4—861no—
288C2×D4—1721no—
289C22×C4—1721no—
290C22×C4#1062188211yescharacteristic
291C22×C4#1062188211yescharacteristic
292C22×C4C2×C22⋊D4311yescharacteristic
293Q16—22no—
294Q16—22no—
295Q16—42no—
296Q16—861no—
297Q16—861no—
298SD16—1722no—
299D8—861no—
300D8—861no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8C2×C22⋊D4311yescharacteristic
305C2×C8C2×C22⋊D4311yescharacteristic
306C2×C8C2×C22⋊D4311yescharacteristic
307C2×C8C23×D4311yescharacteristic
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—41no—
314C4⋊C4—861no—
315C4⋊C4—861no—
316C4⋊C4—1721no—
317C4⋊C4—1721no—
318C4⋊C4—1721no—
319C4⋊C4—1721no—
320C22⋊C4—42no—
321C22⋊C4—1721no—
322C22⋊C4—1721no—
323C22⋊C4—1721no—
324C22⋊C4—1721no—
325C22⋊C4—1721no—
326C42—42no—
327C42—1721no—
328C42#1062188211yescharacteristic
329C42#1062188211yescharacteristic
330C42C2×C22⋊D4311yescharacteristic
331C42C2×C22⋊D4311yescharacteristic
332C16—862no—
333C16—862no—
334C23—1721no—
335C23C2×#1062188211yescharacteristic
336Q8—42no—
337Q8—42no—
338Q8—82no—
339Q8—1721no—
340Q8—1721no—
341D4—3442no—
342D4—1721no—
343D4—1721no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—3442no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4C2×#1062188211yescharacteristic
355C2×C4C2×#1062188211yescharacteristic
356C2×C4C2×#1062188211yescharacteristic
357C2×C4C2×#1062188211yescharacteristic
358C2×C4C2×#1062188211yescharacteristic
359C2×C4C22×C22⋊D4311yescharacteristic
360C8—21no—
361C8—21no—
362C8—21no—
363C8#1306337111yescharacteristic
364C8#1306337211yescharacteristic
365C22—21no—
366C22—21no—
367C22—21no—
368C22—3441no—
369C22—3441no—
370C22—3441no—
371C22C22×#1062188211yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—82no—
377C4—82no—
378C4—3441no—
379C4—3441no—
380C4—3441no—
381C4#1458334012yes—
382C4#1458347711yescharacteristic
383C4#1458369711yescharacteristic
384C2—41no—
385C2—6881no—
386C2#1914590211yescharacteristic
387C2C2×#1458334011yescharacteristic
388C2#1914772911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3170C2
socleC22×C43C22×D8
prime radical#14583135C22
hypercenter#3170D43
hypocenterC43#33818
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3170

Complements

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

NH ≅ G/Ntype
2. #19136759C2semidirect
3. #19136744C2semidirect
4. #19136739C2semidirect
6. #19136701C2semidirect
7. #19136657C2semidirect
8. #19136642C2semidirect
9. #19136637C2semidirect
10. #19136351C2semidirect
11. C43×#3170C2semidirect
190. #3170D43semidirect
237. C43#33818semidirect

Maximal subgroups

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

subgroupindex
#191451652
#191367592
#191367442
#191367392
#191367102
#191367012
#191366572
#191366422
#191366372
#191363512
C43×#31702
#3381843