Finite Group Databasebeta

← #25252937

Subgroups — #25252937

Order 11008.

534 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145174C211yesmaximal, characteristic, complemented
2#19136749C212yesmaximal, complemented
3#19136737C211yesmaximal, characteristic, complemented
4#19136732C211yesmaximal, characteristic, complemented
5#19136710C212yesmaximal, complemented
6#19136696C212yesmaximal, complemented
7#19136647C212yesmaximal, complemented
8#19136635C211yesmaximal, characteristic, complemented
9#19136630C211yesmaximal, characteristic, complemented
10#19136351C211yesmaximal, characteristic, complemented
11C43×#3168C211yesmaximal, characteristic, complemented
12#14583449—21no—
13C2×#13063268C2212yes—
14C2×#13063266C2212yes—
15C2×#13063265C2212yes—
16#14583304C2211yescharacteristic
17#14583276C2211yescharacteristic
18#14583246—21no—
19#14583135—21no—
20#14583135C2212yes—
21C4×D344—21no—
22C4×D344C2212yes—
23#14582726C2212yes—
24#14582724C2212yes—
25C4⋊(C43⋊C16)C2211yescharacteristic
26C4⋊(C43⋊C16)C2211yescharacteristic
27C4⋊(C43⋊C16)C2212yes—
28#14582703C2212yes—
29#14582700C2212yes—
30#14582699C2212yes—
31#14582699C2212yes—
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×#10621898—41no—
44C2×D344—21no—
45C2×D344C2312yes—
46#13063325—21no—
47#13063322—21no—
48#13063313—41no—
49#13063299—22no—
50#13063299—41no—
51C4×D172—22no—
52C4×D172—41no—
53#13063268—42no—
54#13063266—42no—
55#13063265—42no—
56C2×C43⋊C16C2312yes—
57C2×C43⋊C16C2312yes—
58#13063259—21no—
59#13063259C2312yes—
60#13063247—22no—
61#13063247—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×C22⋊D43—42no—
97#10621898—84no—
98C2×D172—22no—
99C2×D172—41no—
100C2×D172—41no—
101C2×C4×D43—42no—
102C2×Dic86—41no—
103Q16×C43—21no—
104Q16×C43—21no—
105SD16×C43—42no—
106D8×C43—21no—
107D8×C43—21no—
108C2×C8×C43—21no—
109C2×C8×C43—21no—
110C2×C8×C43—41no—
111C2×C8×C43C2×D411yescharacteristic
112C2×C8×C43C2×D411yescharacteristic
113C2×C8×C43C2×D411yescharacteristic
114C2×C8×C43C2411yescharacteristic
115C4⋊C4×C43—21no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—41no—
118C4⋊C4×C43—41no—
119C4⋊C4×C43—41no—
120C4⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C22⋊C4×C43—41no—
123C22⋊C4×C43—41no—
124C22⋊C4×C43—41no—
125C22⋊C4×C43—41no—
126C42×C43—41no—
127C42×C43D811yescharacteristic
128C42×C43D811yescharacteristic
129C42×C43C2×D411yescharacteristic
130C42×C43C2×D411yescharacteristic
131(C2×D43)⋊C4—42no—
132(C2×D43)⋊C4—42no—
133C4⋊Dic43—22no—
134C4⋊Dic43—41no—
135D344—22no—
136D344—22no—
137D344—42no—
138C43⋊C16—22no—
139C43⋊C16—22no—
140C23×C43—41no—
141C23×C43C2×D811yescharacteristic
142C22×D43—42no—
143Q8×C43—41no—
144Q8×C43—41no—
145D4×C43—41no—
146D4×C43—41no—
147D4×C43—82no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—22no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—82no—
156C2×C4×C43C2×D811yescharacteristic
157C2×C4×C43C2×D811yescharacteristic
158C2×C4×C43C2×D811yescharacteristic
159C2×C4×C43C2×D811yescharacteristic
160C2×C4×C43C2×D811yescharacteristic
161C2×C4×C43C22×D411yescharacteristic
162C22⋊D43—84no—
163C2×Dic43—42no—
164D172—42no—
165D172—42no—
166D172—82no—
167D172—82no—
168C4×D43—84no—
169Dic86—82no—
170C8×C43—21no—
171C8×C43—21no—
172C8×C43—21no—
173C8×C43H(5,𝔽2)11yescharacteristic
174C8×C432−1+411yescharacteristic
175#33817—431nomaximal, Sylow
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43C22×D811yescharacteristic
183C2×D43—82no—
184C2×D43—82no—
185C2×D43—82no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—81no—
191C4×C43—81no—
192C4×C43—81no—
193C4×C43#50912yes—
194C4×C43#53711yescharacteristic
195C4×C43#57511yescharacteristic
196Dic43—82no—
197#3169—431no—
198#3168D4311yescharacteristic, complemented
199#2228—432no—
200#2225—431no—
201#2224—431no—
202#2220—432no—
203#2218—432no—
204#2210—432no—
205#2207—431no—
206#2206—431no—
207#2150—431no—
208C2×C43—41no—
209C2×C43—161no—
210C2×C43#324511yescharacteristic
211C2×C43C2×#50911yescharacteristic
212C2×C43#341411yescharacteristic
213D43—162no—
214#532—861no—
215#529—21no—
216C2×SD32—432no—
217C2×D16—432no—
218C2×M32—432no—
219#500—431no—
220#499C2×D4311yescharacteristic
221#495C2×D4311yescharacteristic
222#493—431no—
223#488—21no—
224#486—861no—
225#467C2×D4311yescharacteristic
226#466—432no—
227#466—861no—
228#466C2×D4311yescharacteristic
229#465—21no—
230C4×Q16C2×D4311yescharacteristic
231C4×SD16—21no—
232C4×D8—432no—
233C4×D8—861no—
234C4×D8C2×D4311yescharacteristic
235C2×C4×C8C2×D4311yescharacteristic
236#367—432no—
237#366—432no—
238C4⋊C16—431no—
239C4⋊C16—431no—
240C4⋊C16—432no—
241#358—432no—
242#357—432no—
243#357—432no—
244#357—432no—
245C43#3381711yescharacteristic, complemented, Sylow
246C2×#41—1721no—
247C2×Q16C22×D4311yescharacteristic
248C2×SD16—21no—
249C2×D8—432no—
250C2×D8—861no—
251C2×D8C22×D4311yescharacteristic
252C22×C8C22⋊D4311yescharacteristic
253C22×C8C22×D4311yescharacteristic
254C4⋊Q8—861no—
255#127—861no—
256#126—41no—
257#125—21no—
258#124—21no—
259#124—1721no—
260#123—41no—
261C22⋊Q8—21no—
262#121—21no—
263#121—862no—
264#121—1721no—
265C4×Q8—21no—
266C4×D4—21no—
267C4×D4—41no—
268C4×D4—862no—
269C4×D4—1721no—
270#117—41no—
271C2×C42C22⋊D4311yescharacteristic
272SD32—1722no—
273D16—1722no—
274M32—1722no—
275C2×C16—432no—
276C2×C16—432no—
277#107—432no—
278#107—861no—
279#107C22×D4311yescharacteristic
280#107C22×D4311yescharacteristic
281#106—21no—
282#103—21no—
283#103—21no—
284#102—21no—
285#102—21no—
286#102—862no—
287#102—862no—
288C4×C8C22⋊D4311yescharacteristic
289C4×C8C22⋊D4311yescharacteristic
290C4×C8C22×D4311yescharacteristic
291C4×C8C22×D4311yescharacteristic
292#41—3444no—
293C2×Q8—21no—
294C2×Q8—1721no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—862no—
298C2×D4—1722no—
299C2×D4—1721no—
300C2×D4—1721no—
301C22×C4—41no—
302C22×C4—1722no—
303C22×C4#1062188211yescharacteristic
304C22×C4#1062188211yescharacteristic
305C22×C4C2×C22⋊D4311yescharacteristic
306Q16—21no—
307Q16—21no—
308SD16—42no—
309D8—21no—
310D8—21no—
311D8—862no—
312D8—862no—
313D8—1722no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—41no—
317C2×C8C2×C22⋊D4311yescharacteristic
318C2×C8C2×C22⋊D4311yescharacteristic
319C2×C8C2×C22⋊D4311yescharacteristic
320C2×C8C23×D4311yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—862no—
328C4⋊C4—1721no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—1722no—
335C22⋊C4—1722no—
336C42—41no—
337C42#1062188211yescharacteristic
338C42#1062188211yescharacteristic
339C42C2×C22⋊D4311yescharacteristic
340C42C2×C22⋊D4311yescharacteristic
341C16—862no—
342C16—862no—
343C23—41no—
344C23—1722no—
345C23C2×#1062188211yescharacteristic
346Q8—41no—
347Q8—41no—
348Q8—3442no—
349D4—41no—
350D4—41no—
351D4—82no—
352D4—3442no—
353D4—3444no—
354D4—3442no—
355D4—1722no—
356D4—1722no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—82no—
365C2×C4—3444no—
366C2×C4—1722no—
367C2×C4C2×#1062188211yescharacteristic
368C2×C4C2×#1062188211yescharacteristic
369C2×C4C2×#1062188211yescharacteristic
370C2×C4C2×#1062188211yescharacteristic
371C2×C4C2×#1062188211yescharacteristic
372C2×C4C22×C22⋊D4311yescharacteristic
373C8—21no—
374C8—21no—
375C8—21no—
376C8#1306337111yescharacteristic
377C8#1306337211yescharacteristic
378C22—21no—
379C22—21no—
380C22—21no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—3442no—
385C22—3442no—
386C22—3442no—
387C22C22×#1062188211yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—81no—
393C4—81no—
394C4—81no—
395C4—3442no—
396C4#1458333412yes—
397C4#1458347711yescharacteristic
398C4#1458369711yescharacteristic
399C2—41no—
400C2—161no—
401C2—6882no—
402C2#1914590211yescharacteristic
403C2C2×#1458333411yescharacteristic
404C2#1914772911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3168C2
socleC22×C43C22×D8
hypercenter#3168D43
hypocenterC43#33817
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. #19145174C2semidirect
2. #19136749C2semidirect
3. #19136737C2semidirect
4. #19136732C2semidirect
5. #19136710C2semidirect
6. #19136696C2semidirect
7. #19136647C2semidirect
8. #19136635C2semidirect
9. #19136630C2semidirect
10. #19136351C2semidirect
11. C43×#3168C2semidirect
198. #3168D43semidirect
245. C43#33817semidirect

Maximal subgroups

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

subgroupindex
#191451742
#191367492
#191367372
#191367322
#191367102
#191366962
#191366472
#191366352
#191366302
#191363512
C43×#31682
#3381743