Finite Group Databasebeta

← #25252164

Subgroups — #25252164

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#19145165C211yesmaximal, characteristic, complemented
2#19136878C211yesmaximal, characteristic, complemented
3#19136859C211yesmaximal, characteristic, complemented
4#19136836C211yesmaximal, characteristic, complemented
5#19136834C211yesmaximal, characteristic, complemented
6#19136706C212yesmaximal, complemented
7#19136696C212yesmaximal, complemented
8C4×#13063269C212yesmaximal, complemented
9C4×#13063266C212yesmaximal, complemented
10C4×#13063265C211yesmaximal, characteristic, complemented
11C43×#3169C211yesmaximal, characteristic, complemented
12#14583433—21no—
13C2×#13063269C2212yes—
14C2×#13063266C2212yes—
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—
27#14582702C2212yes—
28#14582700C2212yes—
29#14582700C2212yes—
30#14582699C2212yes—
31#14582675C2211yescharacteristic
32#14582675C2211yescharacteristic
33C4×C43⋊C16C2212yes—
34C43×#532—21no—
35C43×#500C2211yescharacteristic
36C43×#493C2211yescharacteristic
37C43×#486—21no—
38C43×#466—21no—
39C43×#466C2212yes—
40C4×D8×C43—21no—
41C4×D8×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#13063269—24no—
57#13063266—24no—
58#13063265—24no—
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×#41×C43—41no—
69C2×D8×C43—21no—
70C2×D8×C43C2312yes—
71C22×C8×C43D411yescharacteristic
72C22×C8×C43C2311yescharacteristic
73C4⋊Q8×C43—21no—
74#127×C43—21no—
75#124×C43—41no—
76#121×C43—22no—
77#121×C43—41no—
78C4×D4×C43—22no—
79C4×D4×C43—41no—
80C2×C42×C43D411yescharacteristic
81#107×C43—21no—
82#107×C43C2312yes—
83#102×C43—22no—
84#102×C43—22no—
85C4×C8×C43D411yescharacteristic
86C4×C8×C43D411yescharacteristic
87C4×C8×C43C2311yescharacteristic
88C4×C8×C43C2311yescharacteristic
89#41×C43—84no—
90C2×Q8×C43—41no—
91C2×D4×C43—22no—
92C2×D4×C43—41no—
93C2×D4×C43—41no—
94C2×D4×C43—42no—
95C22×C4×C43—42no—
96C22×C4×C43D811yescharacteristic
97C22×C4×C43D811yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C2×C22⋊D43—41no—
100C2×D172—21no—
101C2×C4×D43—41no—
102C2×Dic86—21no—
103D8×C43—22no—
104D8×C43—22no—
105D8×C43—42no—
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—22no—
113C4⋊C4×C43—41no—
114C22⋊C4×C43—42no—
115C22⋊C4×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—22no—
133D344—22no—
134#10621873—42no—
135C43⋊C16—22no—
136C43⋊C16#4114yescomplemented
137C23×C43—42no—
138C23×C43C2×D811yescharacteristic
139C22×D43—41no—
140Q8×C43—82no—
141D4×C43—42no—
142D4×C43—42no—
143D4×C43—82no—
144D4×C43—82no—
145D4×C43—84no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—22no—
149C2×C4×C43—41no—
150C2×C4×C43—42no—
151C2×C4×C43—84no—
152C2×C4×C43C2×D811yescharacteristic
153C2×C4×C43C2×D811yescharacteristic
154C2×C4×C43C2×D811yescharacteristic
155C2×C4×C43C2×D811yescharacteristic
156C2×C4×C43C2×D811yescharacteristic
157C2×C4×C43C22×D411yescharacteristic
158C22⋊D43—82no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162D172—41no—
163D172—41no—
164C4×D43—82no—
165Dic86—41no—
166Dic86—41no—
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—82no—
176C22×C43—82no—
177C22×C43—82no—
178C22×C43C22×D811yescharacteristic
179C2×D43—81no—
180C2×D43—81no—
181C2×D43—81no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—82no—
187C4×C43#50912yes—
188C4×C43#53211yescharacteristic
189C4×C43C2×#13511yescharacteristic
190Dic43—81no—
191Dic43—81no—
192Dic43—81no—
193#3169D4311yescharacteristic, complemented
194#3168—431no—
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—162no—
206C2×C43#316911yescharacteristic
207C2×C43C2×#50911yescharacteristic
208C2×C43#341411yescharacteristic
209D43—161no—
210#532—21no—
211#529—861no—
212C2×SD32—432no—
213C2×D16—432no—
214C2×M32—432no—
215#500C2×D4311yescharacteristic
216#499—431no—
217#495—431no—
218#493C2×D4311yescharacteristic
219#488—861no—
220#486—21no—
221#467—431no—
222#466—21no—
223#466—431no—
224#466C2×D4312yes—
225#465—861no—
226C4×Q16—431no—
227C4×SD16—861no—
228C4×D8—21no—
229C4×D8—431no—
230C4×D8C2×D4312yes—
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—41no—
243C2×Q16—431no—
244C2×SD16—861no—
245C2×D8—21no—
246C2×D8—431no—
247C2×D8C22×D4312yes—
248C22×C8C22⋊D4311yescharacteristic
249C22×C8C22×D4311yescharacteristic
250C4⋊Q8—21no—
251#127—21no—
252#126—1721no—
253#125—861no—
254#124—41no—
255#124—861no—
256#123—1721no—
257C22⋊Q8—861no—
258#121—22no—
259#121—41no—
260#121—861no—
261C4×Q8—861no—
262C4×D4—22no—
263C4×D4—41no—
264C4×D4—861no—
265C4×D4—1721no—
266#117—1721no—
267C2×C42C22⋊D4311yescharacteristic
268SD32—864no—
269D16—864no—
270M32—864no—
271C2×C16—432no—
272C2×C16—432no—
273#107—21no—
274#107—431no—
275#107—431no—
276#107C22×D4312yes—
277#106—861no—
278#103—861no—
279#103—861no—
280#102—22no—
281#102—22no—
282#102—861no—
283#102—861no—
284C4×C8C22⋊D4311yescharacteristic
285C4×C8C22⋊D4311yescharacteristic
286C4×C8C22×D4311yescharacteristic
287C4×C8C22×D4311yescharacteristic
288#41—84no—
289C2×Q8—41no—
290C2×Q8—861no—
291C2×D4—22no—
292C2×D4—42no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—861no—
296C2×D4—1721no—
297C22×C4—42no—
298C22×C4—1721no—
299C22×C4#1062188211yescharacteristic
300C22×C4#1062188211yescharacteristic
301C22×C4C2×C22⋊D4311yescharacteristic
302Q16—862no—
303SD16—1722no—
304D8—22no—
305D8—22no—
306D8—42no—
307D8—862no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8C2×C22⋊D4311yescharacteristic
311C2×C8C2×C22⋊D4311yescharacteristic
312C2×C8C2×C22⋊D4311yescharacteristic
313C2×C8C23×D4311yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4—1721no—
319C4⋊C4—1721no—
320C4⋊C4—1721no—
321C4⋊C4—1721no—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C22⋊C4—1721no—
325C22⋊C4—1721no—
326C22⋊C4—1721no—
327C22⋊C4—1721no—
328C22⋊C4—1721no—
329C42—1721no—
330C42#1062188211yescharacteristic
331C42#1062188211yescharacteristic
332C42C2×C22⋊D4311yescharacteristic
333C42C2×C22⋊D4311yescharacteristic
334C16—434no—
335C16—862no—
336C23—42no—
337C23—1721no—
338C23C2×#1062188211yescharacteristic
339Q8—82no—
340Q8—1721no—
341Q8—1721no—
342D4—42no—
343D4—42no—
344D4—82no—
345D4—82no—
346D4—84no—
347D4—3442no—
348D4—1721no—
349D4—1721no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—84no—
356C2×C4—3442no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
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—82no—
374C22—82no—
375C22—82no—
376C22—3441no—
377C22—3441no—
378C22—3441no—
379C22C22×#1062188211yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—3441no—
386C4—3441no—
387C4—3441no—
388C4#1458333512yes—
389C4#1458344511yescharacteristic
390C4C2×#1306334511yescharacteristic
391C2—41no—
392C2—162no—
393C2—6881no—
394C2#1914517011yescharacteristic
395C2C2×#1458333511yescharacteristic
396C2#1914772911yescharacteristic
subgroupG/H
centerC2×C4C2×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3169C2
socleC22×C43C22×D8
hypercenter#3169D43
hypocenterC43#33737
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #19145165C2semidirect
2. #19136878C2semidirect
3. #19136859C2semidirect
4. #19136836C2semidirect
5. #19136834C2semidirect
6. #19136706C2semidirect
7. #19136696C2semidirect
8. C4×#13063269C2semidirect
9. C4×#13063266C2semidirect
10. C4×#13063265C2semidirect
11. C43×#3169C2semidirect
136. C43⋊C16#41semidirect
193. #3169D43semidirect
241. C43#33737semidirect

Maximal subgroups

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

subgroupindex
#191451652
#191368782
#191368592
#191368362
#191368342
#191367062
#191366962
C4×#130632692
C4×#130632662
C4×#130632652
C43×#31692
#3373743