Finite Group Databasebeta

← #24993408

Subgroups — #24993408

Order 11008.

514 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144746C211yesmaximal, characteristic
2#19133205C211yesmaximal, characteristic, complemented
3#19133029C211yesmaximal, characteristic, complemented
4#19133013C211yesmaximal, characteristic, complemented
5#19132494C211yesmaximal, characteristic, complemented
6#19132467C211yesmaximal, characteristic, complemented
7C43×#2875C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583223—21no—
10#14583184C411yescharacteristic
11#14583179C411yescharacteristic
12#14583099C411yescharacteristic
13#14583094C411yescharacteristic
14#14583044—21no—
15#14583009—21no—
16#14582997—21no—
17#14582956C2211yescharacteristic
18#14582956C2211yescharacteristic
19#14582952C2211yescharacteristic
20#14582638—21no—
21#14582638—21no—
22Q8⋊(C43⋊C8)—21no—
23#14582628—22no—
24D4⋊(C43⋊C8)—21no—
25C2×#131×C43—21no—
26C4×#41×C43C2211yescharacteristic
27C43×#405—21no—
28C43×#405—22no—
29C4×M16×C43—21no—
30C4×M16×C43C2211yescharacteristic
31C2×#97×C43—21no—
32C2×#97×C43C2211yescharacteristic
33C2×#10621898—21no—
34C2×#10621884—21no—
35C2×#10621882—21no—
36#13063325C2×C411yescharacteristic
37#13063322C2×C411yescharacteristic
38#13063313—21no—
39#13063299—21no—
40#13063299—21no—
41C4×D172—21no—
42C4×D172—21no—
43#13063258—21no—
44#13063256—21no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)C2×C411yescharacteristic
48C4⋊(C43⋊C8)C2×C411yescharacteristic
49#13063249—21no—
50#13063246—21no—
51#13063245—21no—
52#13063245—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56#13063236—21no—
57#13063236—21no—
58C4×C43⋊C8—21no—
59C2×#41×C43D411yescharacteristic
60#131×C43—24no—
61#131×C43—24no—
62C2×M16×C43—22no—
63C2×M16×C43—21no—
64C22×C8×C43—22no—
65C22×C8×C43—21no—
66C4×Q8×C43C2×C411yescharacteristic
67C4×Q8×C43D411yescharacteristic
68C4×D4×C43—21no—
69C4×D4×C43—21no—
70C4×D4×C43C2×C411yescharacteristic
71C4×D4×C43D411yescharacteristic
72#117×C43—21no—
73#117×C43D411yescharacteristic
74C2×C42×C43—21no—
75C2×C42×C43C2311yescharacteristic
76#97×C43—22no—
77#97×C43—21no—
78#97×C43—21no—
79#97×C43D411yescharacteristic
80#97×C43D411yescharacteristic
81C4×C8×C43—22no—
82C4×C8×C43D412yes—
83#41×C43—22no—
84#41×C43—22no—
85C2×Q8×C43C22⋊C411yescharacteristic
86C2×D4×C43—21no—
87C2×D4×C43C22⋊C411yescharacteristic
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C2×C22⋊D43—41no—
95#10621898—82no—
96C2×D172—21no—
97C2×D172—21no—
98C2×D172—21no—
99C2×C4×D43—41no—
100C2×Dic86—21no—
101M16×C43—28no—
102M16×C43—22no—
103M16×C43—22no—
104C2×C8×C43—28no—
105C2×C8×C43—22no—
106C2×C8×C43—22no—
107C2×C8×C43—21no—
108C2×C8×C43—22no—
109C2×C8×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43C22⋊C411yescharacteristic
113C4⋊C4×C43C22⋊C411yescharacteristic
114C22⋊C4×C43—21no—
115C22⋊C4×C43—21no—
116C22⋊C4×C43—21no—
117C42×C43—21no—
118C42×C43—21no—
119C42×C43—21no—
120C42×C43C22×C411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43C2×D411yescharacteristic
124#10621884—42no—
125#10621882—42no—
126(C2×D43)⋊C4—41no—
127(C2×D43)⋊C4—41no—
128C4⋊Dic43—21no—
129C4⋊Dic43—21no—
130C2×C43⋊C8—21no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—41no—
133C2×C43⋊C8—41no—
134C23×C43—21no—
135C23×C43#12311yescharacteristic
136C22×D43—41no—
137Q8×C43—21no—
138Q8×C43#10412yes—
139D4×C43—24no—
140D4×C43—21no—
141D4×C43#10412yes—
142C2×C4×C43—24no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43C2×C22⋊C411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43#12011yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C22⋊D43—82no—
159C2×Dic43—41no—
160D172—42no—
161D172—41no—
162D172—41no—
163D172—81no—
164C4×D43—82no—
165Dic86—81no—
166C8×C43—22no—
167C8×C43—22no—
168C8×C43—24no—
169C43⋊C8—41no—
170C43⋊C8—41no—
171C43⋊C8—81no—
172C43⋊C8—81no—
173#9311—431nomaximal, Sylow
174C22×C43—21no—
175C22×C43—22no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43#38611yescharacteristic
181C2×D43—81no—
182C2×D43—81no—
183C2×D43—81no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—22no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—41no—
191C4×C43—41no—
192C4×C43C2×#10411yescharacteristic
193C4×C43C2×#10411yescharacteristic
194Dic43—81no—
195#3115—431no—
196#2875D4311yescharacteristic, complemented
197#1530—431no—
198#1488—431no—
199#1484—431no—
200#1302—431no—
201#1291—431no—
202C2×C43—41no—
203C2×C43—42no—
204C2×C43#188111yescharacteristic
205C2×C43#189611yescharacteristic
206C2×C43#190311yescharacteristic
207D43—161no—
208C2×#131—21no—
209#532—431no—
210C4×#41C2×D4311yescharacteristic
211#482—861no—
212#475—431no—
213#474—431no—
214#460—431no—
215#459—431no—
216#449—861no—
217#442—861no—
218#440—861no—
219#432—431no—
220#432—431no—
221#431—431no—
222#405—21no—
223#405—22no—
224C4×M16—21no—
225C4×M16C2×D4311yescharacteristic
226C2×#97—21no—
227C2×#97C2×D4311yescharacteristic
228#329—861no—
229#329—861no—
230Q8⋊C8—861no—
231D4⋊C8—861no—
232D4⋊C8—862no—
233C43#931111yescharacteristic, complemented, Sylow
234C2×#41—861no—
235C2×#41C22⋊D4311yescharacteristic
236C2×SD16—861no—
237C2×D8—861no—
238#131—24no—
239#131—24no—
240C2×M16—22no—
241C2×M16—21no—
242C22×C8—22no—
243C22×C8—21no—
244C4⋊Q8—431no—
245#127—431no—
246#124—861no—
247#121—861no—
248#121—861no—
249C4×Q8C4×D4311yescharacteristic
250C4×Q8D17211yescharacteristic
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—861no—
254C4×D4—861no—
255C4×D4C4×D4311yescharacteristic
256C4×D4D17211yescharacteristic
257#117—21no—
258#117C22⋊D4311yescharacteristic
259C2×C42—21no—
260C2×C42C22×D4311yescharacteristic
261#107—861no—
262#106—861no—
263C4⋊C8—431no—
264C4⋊C8—431no—
265C4⋊C8—861no—
266C4⋊C8—861no—
267#103—861no—
268#102—861no—
269#102—861no—
270#102—861no—
271C22⋊C8—861no—
272C22⋊C8—861no—
273C22⋊C8—861no—
274#97—22no—
275#97—21no—
276#97—21no—
277#97—861no—
278#97—861no—
279#97C22⋊D4311yescharacteristic
280#97C22⋊D4311yescharacteristic
281C4×C8—22no—
282C4×C8—861no—
283C4×C8C22⋊D4312yes—
284#41—22no—
285#41—22no—
286#41—3442no—
287C2×Q8—861no—
288C2×Q8(C2×D43)⋊C411yescharacteristic
289C2×D4—21no—
290C2×D4—861no—
291C2×D4—861no—
292C2×D4—861no—
293C2×D4—1721no—
294C2×D4(C2×D43)⋊C411yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—1721no—
299C22×C4#1062189811yescharacteristic
300C22×C4#1062189811yescharacteristic
301C22×C4C2×C22⋊D4311yescharacteristic
302SD16—1722no—
303D8—1722no—
304M16—28no—
305M16—22no—
306M16—22no—
307C2×C8—28no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—21no—
313C2×C8—861no—
314C2×C8—861no—
315C2×C8—1721no—
316C2×C8—1721no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—861no—
320C4⋊C4—861no—
321C4⋊C4(C2×D43)⋊C411yescharacteristic
322C4⋊C4(C2×D43)⋊C411yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—1721no—
327C22⋊C4—1721no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42C2×C4×D4311yescharacteristic
332C42C2×D17211yescharacteristic
333C42C2×C22⋊D4311yescharacteristic
334C42C2×C22⋊D4311yescharacteristic
335C23—21no—
336C23—1721no—
337C23#1306330811yescharacteristic
338Q8—21no—
339Q8—3441no—
340Q8#1306325312yes—
341D4—24no—
342D4—21no—
343D4—3441no—
344D4—3442no—
345D4—1722no—
346D4—1721no—
347D4—1721no—
348D4#1306325312yes—
349C2×C4—24no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—3442no—
360C2×C4—1721no—
361C2×C4C2×(C2×D43)⋊C411yescharacteristic
362C2×C4C4×C22⋊D4311yescharacteristic
363C2×C4C4×C22⋊D4311yescharacteristic
364C2×C4#1306329411yescharacteristic
365C2×C4#1306329911yescharacteristic
366C2×C4#1306329911yescharacteristic
367C8—22no—
368C8—22no—
369C8—24no—
370C8—3441no—
371C8—3441no—
372C8—1721no—
373C8—1721no—
374C22—21no—
375C22—22no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—3441no—
381C22—3441no—
382C22—3441no—
383C22#1458277811yescharacteristic
384C4—21no—
385C4—22no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—3441no—
393C4C2×#1306325311yescharacteristic
394C4C2×#1306325311yescharacteristic
395C2—41no—
396C2—42no—
397C2—6881no—
398C2#1913495711yescharacteristic
399C2#1913503811yescharacteristic
400C2#1913507511yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2875C2
socleC22×C43#386
prime radical#19144746C2
cosocleC2×C42×C43C23
hypercenter#2875D43
hypocenterC43#9311
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2875

Complements

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

NH ≅ G/Ntype
2. #19133205C2semidirect
3. #19133029C2semidirect
4. #19133013C2semidirect
5. #19132494C2semidirect
6. #19132467C2semidirect
7. C43×#2875C2semidirect
196. #2875D43semidirect
233. C43#9311semidirect

Maximal subgroups

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

subgroupindex
#191447462
#191332052
#191330292
#191330132
#191324942
#191324672
C43×#28752
#931143