Finite Group Databasebeta

← #25252948

Subgroups — #25252948

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#19145181C211yesmaximal, characteristic, complemented
2#19136756C212yesmaximal, complemented
3#19136747C211yesmaximal, characteristic, complemented
4#19136742C211yesmaximal, characteristic, complemented
5#19136706C212yesmaximal
6#19136701C212yesmaximal, complemented
7#19136654C212yesmaximal, complemented
8#19136645C211yesmaximal, characteristic, complemented
9#19136640C211yesmaximal, characteristic, complemented
10#19136351C211yesmaximal, characteristic, complemented
11C43×#3168C211yesmaximal, characteristic
12#14583456—21no—
13C2×#13063271C2212yes—
14C2×#13063269C2212yes—
15C2×#13063265C2212yes—
16#14583304C2211yescharacteristic
17#14583279C2211yescharacteristic
18#14583250—21no—
19#14583140—21no—
20#14583140C2212yes—
21C4×Dic172—21no—
22C4×Dic172C2212yes—
23#14582726C2212yes—
24#14582724C2212yes—
25C4⋊(C43⋊C16)C2211yescharacteristic
26C4⋊(C43⋊C16)C2211yescharacteristic
27C4⋊(C43⋊C16)C2212yes—
28#14582703C2212yes—
29#14582702C2212yes—
30#14582702C2212yes—
31#14582700C2212yes—
32C43×#529—21no—
33C43×#499C2211yescharacteristic
34C43×#495C2211yescharacteristic
35C43×#488—21no—
36C43×#467C2211yescharacteristic
37C43×#466C2211yescharacteristic
38C43×#465—21no—
39C4×Q16×C43C2211yescharacteristic
40C4×SD16×C43—21no—
41C4×D8×C43C2211yescharacteristic
42C2×C4×C8×C43C2211yescharacteristic
43C2×Dic172—21no—
44C2×Dic172C2312yes—
45#13063325—21no—
46#13063325—21no—
47#13063317—41no—
48#13063304—22no—
49#13063304—41no—
50C4×Dic86—22no—
51C4×Dic86—41no—
52#13063284—41no—
53#13063271—42no—
54#13063269—42no—
55#13063265—42no—
56C2×C43⋊C16C2312yes—
57C2×C43⋊C16C2312yes—
58#13063259—21no—
59#13063259C2312yes—
60#13063250—22no—
61#13063250—22no—
62C2×Q16×C43C2311yescharacteristic
63C2×SD16×C43—21no—
64C2×D8×C43C2311yescharacteristic
65C22×C8×C43D411yescharacteristic
66C22×C8×C43C2311yescharacteristic
67#126×C43—41no—
68#125×C43—21no—
69#124×C43—21no—
70#123×C43—41no—
71C22⋊Q8×C43—21no—
72#121×C43—21no—
73C4×Q8×C43—21no—
74C4×D4×C43—21no—
75C4×D4×C43—41no—
76#117×C43—41no—
77C2×C42×C43D411yescharacteristic
78#107×C43C2311yescharacteristic
79#107×C43C2311yescharacteristic
80#106×C43—21no—
81#103×C43—21no—
82#103×C43—21no—
83#102×C43—21no—
84#102×C43—21no—
85C4×C8×C43D411yescharacteristic
86C4×C8×C43D411yescharacteristic
87C4×C8×C43C2311yescharacteristic
88C4×C8×C43C2311yescharacteristic
89C2×Q8×C43—21no—
90C2×D4×C43—21no—
91C2×D4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43D811yescharacteristic
94C22×C4×C43D811yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C2×Dic86—22no—
97C2×Dic86—41no—
98Q16×C43—21no—
99Q16×C43—21no—
100SD16×C43—42no—
101D8×C43—21no—
102D8×C43—21no—
103C2×C8×C43—21no—
104C2×C8×C43—21no—
105C2×C8×C43—41no—
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43C2411yescharacteristic
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C42×C43—41no—
122C42×C43D811yescharacteristic
123C42×C43D811yescharacteristic
124C42×C43C2×D411yescharacteristic
125C42×C43C2×D411yescharacteristic
126C22⋊Dic43—42no—
127C4⋊Dic43—22no—
128C4⋊Dic43—41no—
129C4⋊Dic43—41no—
130C4⋊Dic43—41no—
131Dic43⋊C4—42no—
132Dic43⋊C4—42no—
133C4×Dic43—42no—
134Dic172—22no—
135Dic172—22no—
136Dic172—42no—
137C43⋊C16—22no—
138C43⋊C16—22no—
139C23×C43—41no—
140C23×C43C2×D811yescharacteristic
141Q8×C43—41no—
142Q8×C43—41no—
143D4×C43—41no—
144D4×C43—41no—
145D4×C43—82no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—22no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—82no—
154C2×C4×C43C2×D811yescharacteristic
155C2×C4×C43C2×D811yescharacteristic
156C2×C4×C43C2×D811yescharacteristic
157C2×C4×C43C2×D811yescharacteristic
158C2×C4×C43C2×D811yescharacteristic
159C2×C4×C43C22×D411yescharacteristic
160C2×Dic43—42no—
161C2×Dic43—42no—
162Dic86—42no—
163Dic86—42no—
164Dic86—82no—
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×C43—81no—
175C22×C43—81no—
176C22×C43—81no—
177C22×C43C22×D811yescharacteristic
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—81no—
183C4×C43—81no—
184C4×C43—81no—
185C4×C43#51012yes—
186C4×C43#53711yescharacteristic
187C4×C43#57511yescharacteristic
188Dic43—82no—
189Dic43—82no—
190#3170—431no—
191#3168D4311yescharacteristic
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—161no—
203C2×C43#324511yescharacteristic
204C2×C43C2×#51011yescharacteristic
205C2×C43#341411yescharacteristic
206#533—861no—
207#529—21no—
208C2×Q32—432no—
209C2×SD32—432no—
210C2×M32—432no—
211#500—431no—
212#499C2×D4311yescharacteristic
213#495C2×D4311yescharacteristic
214#494—431no—
215#488—21no—
216#487—861no—
217#467—432no—
218#467—861no—
219#467C2×D4311yescharacteristic
220#466C2×D4311yescharacteristic
221#465—21no—
222C4×Q16—432no—
223C4×Q16—861no—
224C4×Q16C2×D4311yescharacteristic
225C4×SD16—21no—
226C4×D8C2×D4311yescharacteristic
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—432no—
239C2×Q16—861no—
240C2×Q16C22×D4311yescharacteristic
241C2×SD16—21no—
242C2×D8C22×D4311yescharacteristic
243C22×C8C22⋊D4311yescharacteristic
244C22×C8C22×D4311yescharacteristic
245C4⋊Q8—861no—
246C4⋊Q8—861no—
247#126—41no—
248#125—21no—
249#125—1721no—
250#124—21no—
251#123—41no—
252C22⋊Q8—21no—
253C22⋊Q8—862no—
254C22⋊Q8—1721no—
255#121—21no—
256C4×Q8—21no—
257C4×Q8—862no—
258C4×Q8—1721no—
259C4×D4—21no—
260C4×D4—41no—
261#117—41no—
262#117—1721no—
263C2×C42C22⋊D4311yescharacteristic
264Q32—1722no—
265SD32—1722no—
266M32—1722no—
267C2×C16—432no—
268C2×C16—432no—
269#107—432no—
270#107—861no—
271#107C22×D4311yescharacteristic
272#107C22×D4311yescharacteristic
273#106—21no—
274#103—21no—
275#103—21no—
276#103—862no—
277#103—862no—
278#102—21no—
279#102—21no—
280C4×C8C22⋊D4311yescharacteristic
281C4×C8C22⋊D4311yescharacteristic
282C4×C8C22×D4311yescharacteristic
283C4×C8C22×D4311yescharacteristic
284C2×Q8—21no—
285C2×Q8—862no—
286C2×Q8—1721no—
287C2×D4—21no—
288C2×D4—41no—
289C22×C4—41no—
290C22×C4#1062188211yescharacteristic
291C22×C4#1062188211yescharacteristic
292C22×C4C2×C22⋊D4311yescharacteristic
293Q16—21no—
294Q16—21no—
295Q16—862no—
296Q16—862no—
297Q16—1722no—
298SD16—42no—
299D8—21no—
300D8—21no—
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—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—862no—
315C4⋊C4—1721no—
316C4⋊C4—1721no—
317C4⋊C4—1722no—
318C4⋊C4—1722no—
319C4⋊C4—1721no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—1722no—
326C42—41no—
327C42—1722no—
328C42#1062188211yescharacteristic
329C42#1062188211yescharacteristic
330C42C2×C22⋊D4311yescharacteristic
331C42C2×C22⋊D4311yescharacteristic
332C16—862no—
333C16—862no—
334C23—41no—
335C23C2×#1062188211yescharacteristic
336Q8—41no—
337Q8—41no—
338Q8—3442no—
339Q8—1722no—
340Q8—1722no—
341D4—41no—
342D4—41no—
343D4—82no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—82no—
352C2×C4—1722no—
353C2×C4—1722no—
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—81no—
369C22—81no—
370C22—81no—
371C22C22×#1062188211yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—3442no—
380C4—3442no—
381C4#1458333912yes—
382C4#1458347711yescharacteristic
383C4#1458369711yescharacteristic
384C2—41no—
385C2—161no—
386C2#1914590211yescharacteristic
387C2C2×#1458333911yescharacteristic
388C2#1914772911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3168C2
socleC22×C43C22×D8
prime radicalC43×#466C22
hypercenter#3168D43
hypocenterC43#33818
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #19145181C2semidirect
2. #19136756C2semidirect
3. #19136747C2semidirect
4. #19136742C2semidirect
6. #19136701C2semidirect
7. #19136654C2semidirect
8. #19136645C2semidirect
9. #19136640C2semidirect
10. #19136351C2semidirect
237. C43#33818semidirect

Maximal subgroups

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

subgroupindex
#191451812
#191367562
#191367472
#191367422
#191367062
#191367012
#191366542
#191366452
#191366402
#191363512
C43×#31682
#3381843