Finite Group Databasebeta

← #25252171

Subgroups — #25252171

Order 11008.

554 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145174C211yesmaximal, characteristic, complemented
2#19136882C211yesmaximal, characteristic, complemented
3#19136862C211yesmaximal, characteristic, complemented
4#19136838C211yesmaximal, characteristic, complemented
5#19136831C211yesmaximal, characteristic, complemented
6#19136710C212yesmaximal, complemented
7#19136696C212yesmaximal, complemented
8C4×#13063268C212yesmaximal, complemented
9C4×#13063266C212yesmaximal, complemented
10C4×#13063265C211yesmaximal, 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—
25#14582703C2212yes—
26#14582700C2212yes—
27#14582699C2212yes—
28#14582699C2212yes—
29#14582675C2211yescharacteristic
30#14582675C2211yescharacteristic
31C4×C43⋊C16C2212yes—
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—24no—
54#13063266—24no—
55#13063265—24no—
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—22no—
104SD16×C43—42no—
105D8×C43—22no—
106C2×C8×C43—22no—
107C2×C8×C43—22no—
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43C2411yescharacteristic
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—41no—
117C4⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C22⋊C4×C43—41no—
123C42×C43—41no—
124C42×C43D811yescharacteristic
125C42×C43D811yescharacteristic
126C42×C43C2×D411yescharacteristic
127C42×C43C2×D411yescharacteristic
128(C2×D43)⋊C4—42no—
129(C2×D43)⋊C4—42no—
130C4⋊Dic43—22no—
131C4⋊Dic43—41no—
132D344—22no—
133D344—22no—
134D344—42no—
135C43⋊C16—22no—
136C43⋊C16#4114yescomplemented
137C23×C43—41no—
138C23×C43C2×D811yescharacteristic
139C22×D43—42no—
140Q8×C43—41no—
141Q8×C43—41no—
142D4×C43—41no—
143D4×C43—41no—
144D4×C43—82no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—22no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—82no—
153C2×C4×C43C2×D811yescharacteristic
154C2×C4×C43C2×D811yescharacteristic
155C2×C4×C43C2×D811yescharacteristic
156C2×C4×C43C2×D811yescharacteristic
157C2×C4×C43C2×D811yescharacteristic
158C2×C4×C43C22×D411yescharacteristic
159C22⋊D43—84no—
160C2×Dic43—42no—
161D172—42no—
162D172—42no—
163D172—82no—
164D172—82no—
165C4×D43—84no—
166Dic86—82no—
167C8×C43—21no—
168C8×C43—21no—
169C8×C43#13512yes—
170C8×C43C2×#4112yes—
171#33737—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—81no—
176C22×C43—81no—
177C22×C43—81no—
178C22×C43C22×D811yescharacteristic
179C2×D43—82no—
180C2×D43—82no—
181C2×D43—82no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—81no—
187C4×C43—81no—
188C4×C43—81no—
189C4×C43#50912yes—
190C4×C43#53211yescharacteristic
191C4×C43C2×#13511yescharacteristic
192Dic43—82no—
193#3169—431no—
194#3168D4311yescharacteristic, complemented
195#2255—431no—
196#2250—431no—
197#2244—431no—
198#2243—431no—
199#2220—432no—
200#2218—432no—
201C4×SD32—432no—
202C4×D16—432no—
203C4×M32—431no—
204C2×C43—41no—
205C2×C43—161no—
206C2×C43#316911yescharacteristic
207C2×C43C2×#50911yescharacteristic
208C2×C43#341411yescharacteristic
209D43—162no—
210#532—861no—
211#529—21no—
212C2×SD32—432no—
213C2×D16—432no—
214C2×M32—432no—
215#500—431no—
216#499C2×D4311yescharacteristic
217#495C2×D4311yescharacteristic
218#493—431no—
219#488—21no—
220#486—861no—
221#467C2×D4311yescharacteristic
222#466—432no—
223#466—861no—
224#466C2×D4311yescharacteristic
225#465—21no—
226C4×Q16C2×D4311yescharacteristic
227C4×SD16—21no—
228C4×D8—432no—
229C4×D8—861no—
230C4×D8C2×D4311yescharacteristic
231C2×C4×C8C2×D4311yescharacteristic
232#367—432no—
233#366—432no—
234#358—432no—
235#357—432no—
236#357—432no—
237#357—432no—
238#346—431no—
239#346—431no—
240C4×C16—432no—
241C43#3373711yescharacteristic, complemented, Sylow
242C2×#41—1721no—
243C2×Q16C22×D4311yescharacteristic
244C2×SD16—21no—
245C2×D8—432no—
246C2×D8—861no—
247C2×D8C22×D4311yescharacteristic
248C22×C8C22⋊D4311yescharacteristic
249C22×C8C22×D4311yescharacteristic
250C4⋊Q8—861no—
251#127—861no—
252#126—41no—
253#125—21no—
254#124—21no—
255#124—1721no—
256#123—41no—
257C22⋊Q8—21no—
258#121—21no—
259#121—862no—
260#121—1721no—
261C4×Q8—21no—
262C4×D4—21no—
263C4×D4—41no—
264C4×D4—862no—
265C4×D4—1721no—
266#117—41no—
267C2×C42C22⋊D4311yescharacteristic
268SD32—864no—
269D16—864no—
270M32—864no—
271C2×C16—432no—
272C2×C16—432no—
273#107—432no—
274#107—861no—
275#107C22×D4311yescharacteristic
276#107C22×D4311yescharacteristic
277#106—21no—
278#103—21no—
279#103—21no—
280#102—21no—
281#102—21no—
282#102—862no—
283#102—862no—
284C4×C8C22⋊D4311yescharacteristic
285C4×C8C22⋊D4311yescharacteristic
286C4×C8C22×D4311yescharacteristic
287C4×C8C22×D4311yescharacteristic
288#41—3444no—
289C2×Q8—21no—
290C2×Q8—1721no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—862no—
294C2×D4—1722no—
295C2×D4—1721no—
296C2×D4—1721no—
297C22×C4—41no—
298C22×C4—1722no—
299C22×C4#1062188211yescharacteristic
300C22×C4#1062188211yescharacteristic
301C22×C4C2×C22⋊D4311yescharacteristic
302Q16—22no—
303SD16—42no—
304D8—22no—
305D8—862no—
306D8—862no—
307D8—1722no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8C2×C22⋊D4311yescharacteristic
311C2×C8C2×C22⋊D4311yescharacteristic
312C2×C8C2×C22⋊D4311yescharacteristic
313C2×C8C23×D4311yescharacteristic
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—862no—
321C4⋊C4—1721no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—1722no—
328C22⋊C4—1722no—
329C42—41no—
330C42#1062188211yescharacteristic
331C42#1062188211yescharacteristic
332C42C2×C22⋊D4311yescharacteristic
333C42C2×C22⋊D4311yescharacteristic
334C16—434no—
335C16—862no—
336C23—41no—
337C23—1722no—
338C23C2×#1062188211yescharacteristic
339Q8—41no—
340Q8—41no—
341Q8—3442no—
342D4—41no—
343D4—41no—
344D4—82no—
345D4—3442no—
346D4—3442no—
347D4—3444no—
348D4—1722no—
349D4—1722no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—82no—
358C2×C4—3444no—
359C2×C4—1722no—
360C2×C4C2×#1062188211yescharacteristic
361C2×C4C2×#1062188211yescharacteristic
362C2×C4C2×#1062188211yescharacteristic
363C2×C4C2×#1062188211yescharacteristic
364C2×C4C2×#1062188211yescharacteristic
365C2×C4C22×C22⋊D4311yescharacteristic
366C8—21no—
367C8—21no—
368C8#1306334512yes—
369C8#41×D4312yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—3442no—
377C22—3442no—
378C22—3442no—
379C22C22×#1062188211yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—3442no—
388C4#1458333412yes—
389C4#1458344511yescharacteristic
390C4C2×#1306334511yescharacteristic
391C2—41no—
392C2—161no—
393C2—6882no—
394C2#1914517011yescharacteristic
395C2C2×#1458333411yescharacteristic
396C2#1914772911yescharacteristic
subgroupG/H
centerC2×C4C2×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3168C2
socleC22×C43C22×D8
hypercenter#3168D43
hypocenterC43#33737
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #19145174C2semidirect
2. #19136882C2semidirect
3. #19136862C2semidirect
4. #19136838C2semidirect
5. #19136831C2semidirect
6. #19136710C2semidirect
7. #19136696C2semidirect
8. C4×#13063268C2semidirect
9. C4×#13063266C2semidirect
10. C4×#13063265C2semidirect
11. C43×#3168C2semidirect
136. C43⋊C16#41semidirect
194. #3168D43semidirect
241. C43#33737semidirect

Maximal subgroups

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

subgroupindex
#191451742
#191368822
#191368622
#191368382
#191368312
#191367102
#191366962
C4×#130632682
C4×#130632662
C4×#130632652
C43×#31682
#3373743