Finite Group Databasebeta

← #25251428

Subgroups — #25251428

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#467×D43C211yesmaximal, characteristic
2C2×#14582936C211yesmaximal, characteristic
3#19136805C212yesmaximal, complemented
4#19136801C212yesmaximal, complemented
5#19136797C211yesmaximal, characteristic, complemented
6#19136793C211yesmaximal, characteristic, complemented
7#19136790C211yesmaximal, characteristic, complemented
8#19136380C212yesmaximal, complemented
9#19136313C212yesmaximal, complemented
10#19136204C211yesmaximal, characteristic
11C43×#2236C211yesmaximal, characteristic, complemented
12C2×Q16×D43C2211yescharacteristic
13C22×C8×D43C2211yescharacteristic
14C22⋊Q8×D43—21no—
15C2×#13063283—21no—
16C2×#13063264C2212yes—
17#14583141C2211yescharacteristic
18#14583140C2211yescharacteristic
19#14583139—21no—
20#14583138—21no—
21#14583137C2211yescharacteristic
22#14582936—21no—
23#14582936—21no—
24#14582936C2212yes—
25#14582936C2212yes—
26C2×#13063259C2211yescharacteristic
27#107×D43C2211yescharacteristic
28C2×#13063256—21no—
29#103×D43—21no—
30#14582727C2212yescomplemented
31#14582726C2212yescomplemented
32#14582724C2212yescomplemented
33#14582704C2212yescomplemented
34#14582703C2212yescomplemented
35#14582702C2212yescomplemented
36C22⋊(C43⋊C16)C2211yescharacteristic
37(C2×D43)⋊C16C2212yes—
38C43×#467C2211yescharacteristic
39C2×#107×C43C2211yescharacteristic
40C43×#366C2212yescomplemented
41C43×#358C2212yescomplemented
42C43×C22⋊C16C2211yescharacteristic
43C2×Q8×D43—21no—
44C22×C4×D43D411yescharacteristic
45C2×Dic172C2311yescharacteristic
46C2×#10621885—21no—
47Q16×D43—24no—
48C22×C43⋊C8D411yescharacteristic
49C2×C8×D43—24no—
50C2×C8×D43D411yescharacteristic
51C2×C8×D43D411yescharacteristic
52C2×C8×D43C2311yescharacteristic
53C2×C8×D43C2311yescharacteristic
54#13063305—21no—
55#13063304—21no—
56#13063303—41no—
57#13063302—41no—
58#13063301—21no—
59#13063283—22no—
60#13063283—22no—
61#13063283—41no—
62#13063283—41no—
63C2×C4⋊Dic43—21no—
64C4⋊C4×D43—21no—
65C4⋊C4×D43—41no—
66C2×(C2×D43)⋊C4—41no—
67C22⋊C4×D43—41no—
68C2×C4×Dic43—41no—
69#13063264—24no—
70C2×C43⋊C16C2312yes—
71#13063259—21no—
72#13063259C2311yescharacteristic
73#13063259C2312yes—
74#13063258—21no—
75#13063256—22no—
76#13063256—22no—
77#13063250—21no—
78#13063249—21no—
79#13063248—21no—
80C2×Q16×C43C2311yescharacteristic
81C22×C8×C43C2311yescharacteristic
82C22⋊Q8×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C16×C43C2312yes—
85#107×C43—21no—
86#107×C43C2311yescharacteristic
87#107×C43C2312yes—
88#103×C43—21no—
89C23×D43D811yescharacteristic
90C2×Q8×C43—21no—
91C22×C4×C43—41no—
92C22×C4×C43C2×D411yescharacteristic
93C22×Dic43—41no—
94C22×Dic43D811yescharacteristic
95Q8×D43—42no—
96Q8×D43—42no—
97C2×C4×D43—22no—
98C2×C4×D43—22no—
99C2×C4×D43—41no—
100C2×C4×D43—41no—
101C2×C4×D43D811yescharacteristic
102C2×C4×D43D811yescharacteristic
103C2×C4×D43C2×D411yescharacteristic
104C2×C4×D43C2×D411yescharacteristic
105C2×Dic86—21no—
106C2×Dic86—41no—
107Q16×C43—22no—
108C2×C8×C43—22no—
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43C2411yescharacteristic
111C4⋊C4×C43—21no—
112C4⋊C4×C43—22no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊Dic43—41no—
117#10621885—42no—
118(C2×D43)⋊C4—41no—
119(C2×D43)⋊C4—41no—
120(C2×D43)⋊C4—42no—
121(C2×D43)⋊C4—42no—
122C4⋊Dic43—21no—
123C4⋊Dic43—22no—
124C4⋊Dic43—41no—
125C4⋊Dic43—41no—
126Dic43⋊C4—41no—
127Dic43⋊C4—41no—
128Dic43⋊C4—41no—
129C4×Dic43—42no—
130C4×Dic43—42no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8C2×D411yescharacteristic
133C2×C43⋊C8C2×D411yescharacteristic
134Dic172—22no—
135C8×D43—22no—
136C8×D43—22no—
137C8×D43—22no—
138C8×D43#4114yes—
139C16×C43—22no—
140C43⋊C16—22no—
141C23×C43C2×D811yescharacteristic
142C22×D43—22no—
143C22×D43—22no—
144C22×D43—41no—
145C22×D43C2×D811yescharacteristic
146C22×D43C2×D811yescharacteristic
147Q8×C43—41no—
148Q8×C43—41no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—42no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—82no—
155C2×C4×C43C2×D811yescharacteristic
156C2×C4×C43C22×D411yescharacteristic
157C2×Dic43—22no—
158C2×Dic43—42no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—82no—
162C2×Dic43C2×D811yescharacteristic
163C2×Dic43C2×D811yescharacteristic
164C4×D43—22no—
165C4×D43—21no—
166C4×D43—21no—
167C4×D43—22no—
168C4×D43—82no—
169C4×D43—82no—
170C4×D43#12312yes—
171C4×D43#13712yes—
172Dic86—41no—
173Dic86—41no—
174Dic86—82no—
175C8×C43—21no—
176C8×C43C2×#4112yes—
177C43⋊C8—21no—
178C43⋊C8#12312yes—
179#33649—431nomaximal, Sylow
180C22×C43—21no—
181C22×C43—21no—
182C22×C43#51012yes—
183C22×C43C22×D811yescharacteristic
184C2×D43—21no—
185C2×D43—21no—
186C2×D43—21no—
187C2×D43—21no—
188C2×D43—21no—
189C2×D43—44no—
190C2×D43#48012yes—
191C4×C43—21no—
192C4×C43—81no—
193C4×C43—81no—
194C4×C43—82no—
195C4×C43C2×#12311yescharacteristic
196C4×C43C2×#13711yescharacteristic
197Dic43—21no—
198Dic43—81no—
199Dic43—82no—
200Dic43—81no—
201Dic43#48012yes—
202C2×#467—431no—
203C2×#427—431no—
204#2237—432no—
205#2237—432no—
206#2236—431no—
207#2236D4311yescharacteristic, complemented
208#2235—431no—
209#2235—431no—
210#2159—432no—
211#2141—432no—
212#2112—431no—
213C2×C43—22no—
214C2×C43C2×#48011yescharacteristic
215C2×C43C2×#51011yescharacteristic
216C2×C43#341411yescharacteristic
217D43—22no—
218D43—41no—
219C22×Q16—431no—
220C23×C8—431no—
221C2×C22⋊Q8—861no—
222C2×#117—861no—
223C2×M32—432no—
224#467—431no—
225#467—431no—
226#467—431no—
227#467—861no—
228#467—861no—
229#467C2×D4311yescharacteristic
230#427—432no—
231#427—432no—
232#427—861no—
233#427—861no—
234C2×#107—431no—
235C2×#107—431no—
236C2×#107C2×D4311yescharacteristic
237C2×#106—861no—
238C2×#103—861no—
239#367—432no—
240#367—432no—
241#366—432no—
242#366C2×D4312yescomplemented
243#358—432no—
244#358—432no—
245#358—432no—
246#358C2×D4312yescomplemented
247C22⋊C16—431no—
248C22⋊C16—432no—
249C22⋊C16C2×D4311yescharacteristic
250C43#3364911yescharacteristic, complemented, Sylow
251C22×Q8—861no—
252C23×C4—431no—
253C2×Q16—431no—
254C2×Q16—864no—
255C2×Q16—861no—
256C2×Q16C22×D4311yescharacteristic
257C22×C8—431no—
258C22×C8—431no—
259C22×C8—431no—
260C22×C8—431no—
261C22×C8—431no—
262C22×C8—864no—
263C22×C8C22×D4311yescharacteristic
264C22⋊Q8—21no—
265C22⋊Q8—861no—
266C22⋊Q8—861no—
267C22⋊Q8—861no—
268C22⋊Q8—1721no—
269C22⋊Q8—1721no—
270#117—862no—
271#117—862no—
272#117—1721no—
273#117—1721no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—861no—
276C2×C4⋊C4—861no—
277C2×C4⋊C4—1721no—
278C2×C22⋊C4—1721no—
279C2×C22⋊C4—1721no—
280C2×C42—1721no—
281M32—864no—
282C2×C16—432no—
283C2×C16C22×D4312yes—
284#107—21no—
285#107—432no—
286#107—431no—
287#107—861no—
288#107—861no—
289#107C22×D4312yes—
290#107C22×D4311yescharacteristic
291#106—862no—
292#106—862no—
293#103—21no—
294#103—861no—
295#103—861no—
296#103—861no—
297C24—431no—
298C2×Q8—21no—
299C2×Q8—861no—
300C2×Q8—1721no—
301C2×Q8—1722no—
302C2×Q8—1722no—
303C22×C4—41no—
304C22×C4—431no—
305C22×C4—431no—
306C22×C4—431no—
307C22×C4—431no—
308C22×C4—431no—
309C22×C4—862no—
310C22×C4—862no—
311C22×C4—1721no—
312C22×C4—1721no—
313C22×C4—1721no—
314C22×C4D4×D4311yescharacteristic
315Q16—22no—
316Q16—862no—
317Q16—1722no—
318C2×C8—22no—
319C2×C8—431no—
320C2×C8—434no—
321C2×C8—431no—
322C2×C8—862no—
323C2×C8—862no—
324C2×C8—862no—
325C2×C8—862no—
326C2×C8D4×D4311yescharacteristic
327C2×C8C23×D4311yescharacteristic
328C4⋊C4—21no—
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—861no—
333C4⋊C4—862no—
334C4⋊C4—1721no—
335C4⋊C4—1721no—
336C4⋊C4—1721no—
337C4⋊C4—1721no—
338C4⋊C4—1721no—
339C22⋊C4—41no—
340C22⋊C4—1722no—
341C22⋊C4—1722no—
342C22⋊C4—1721no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C42—1722no—
346C42—1722no—
347C16—22no—
348C16—862no—
349C23—431no—
350C23—431no—
351C23—862no—
352C23—862no—
353C23—1721no—
354C23D8×D4311yescharacteristic
355Q8—41no—
356Q8—41no—
357Q8—3442no—
358Q8—1721no—
359Q8—1721no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—431no—
367C2×C4—432no—
368C2×C4—432no—
369C2×C4—431no—
370C2×C4—862no—
371C2×C4—862no—
372C2×C4—862no—
373C2×C4—861no—
374C2×C4—861no—
375C2×C4—3442no—
376C2×C4—3442no—
377C2×C4—3442no—
378C2×C4—1722no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4D8×D4311yescharacteristic
382C2×C4C2×D4×D4311yescharacteristic
383C8—21no—
384C8—432no—
385C8—861no—
386C8#41×D4312yes—
387C22—21no—
388C22—21no—
389C22—432no—
390C22—861no—
391C22—861no—
392C22—861no—
393C22—861no—
394C22—861no—
395C22—1724no—
396C22#1458334112yes—
397C22C2×D8×D4311yescharacteristic
398C4—21no—
399C4—81no—
400C4—82no—
401C4—81no—
402C4—432no—
403C4—861no—
404C4—3441no—
405C4—3442no—
406C4—3441no—
407C4#123×D4311yescharacteristic
408C4#137×D4311yescharacteristic
409C2—22no—
410C2—862no—
411C2—1721no—
412C2#480×D4311yescharacteristic
413C2C2×#1458334111yescharacteristic
414C2#1914772711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2236C2
socleC22×C43C22×D8
prime radicalC23×D43D8
hypercenter#2236D43
hypocenterC43#33649
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
3. #19136805C2semidirect
4. #19136801C2semidirect
5. #19136797C2semidirect
6. #19136793C2semidirect
7. #19136790C2semidirect
8. #19136380C2semidirect
9. #19136313C2semidirect
11. C43×#2236C2semidirect
30. #14582727C22semidirect
31. #14582726C22semidirect
32. #14582724C22semidirect
33. #14582704C22semidirect
34. #14582703C22semidirect
35. #14582702C22semidirect
40. C43×#366C22semidirect
41. C43×#358C22semidirect
207. #2236D43semidirect
242. #366C2×D43semidirect
246. #358C2×D43semidirect
250. C43#33649semidirect

Maximal subgroups

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

subgroupindex
#467×D432
C2×#145829362
#191368052
#191368012
#191367972
#191367932
#191367902
#191363802
#191363132
#191362042
C43×#22362
#3364943