Finite Group Databasebeta

← #25079809

Subgroups — #25079809

Order 11008.

646 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145738C212yesmaximal
2#494×D43C211yesmaximal, characteristic
3#19143526C211yesmaximal, characteristic
4#19134090C211yesmaximal, characteristic, complemented
5#19134089C211yesmaximal, characteristic, complemented
6#19134086C211yesmaximal, characteristic, complemented
7#19133964C212yesmaximal, complemented
8#19133963C212yesmaximal, complemented
9#19133340C211yesmaximal, characteristic
10#19133265C212yesmaximal
11C43×#1690C211yesmaximal, characteristic, complemented
12C2×Q16×D43—21no—
13C2×Q16×D43—21no—
14#14583453C2211yescharacteristic
15C4⋊Q8×D43C2212yes—
16#14583296—22no—
17#14583279C2211yescharacteristic
18#14583278C2212yes—
19#14583277—21no—
20#14583277—21no—
21#14583248—22no—
22#14583231—22no—
23#14583228—22no—
24#14583185C2212yes—
25#14583184C2212yes—
26#14583181C2212yes—
27#14583029C2211yescharacteristic
28#14583027—21no—
29Q8×C43⋊C8C2211yescharacteristic
30#14583023—21no—
31#14583023C2211yescharacteristic
32#14582951C2212yes—
33#14582924—21no—
34#14582921C2211yescharacteristic
35#14582856—21no—
36C4×C8×D43C2211yescharacteristic
37#14582651C2212yes—
38#14582650C2211yescharacteristic
39#14582646C2212yes—
40#14582645C2212yes—
41#14582644C2212yes—
42C43×#494C2211yescharacteristic
43C43×#475C2212yes—
44C43×#446C2211yescharacteristic
45C43×#334C2211yescharacteristic
46C43×#332C2212yes—
47C2×Q8×D43—22no—
48C2×Dic172—21no—
49C2×Dic172—21no—
50C2×#10621885—22no—
51C2×#10621885—22no—
52Q16×D43—44no—
53Q16×D43—44no—
54C2×#10621872—21no—
55C2×C8×D43D411yescharacteristic
56C2×C8×D43D411yescharacteristic
57#13063325C2312yes—
58#13063324—22no—
59#13063324—22no—
60#13063324D411yescharacteristic
61#13063323—22no—
62#13063323D411yescharacteristic
63#13063315—21no—
64#13063305D411yescharacteristic
65#13063303—21no—
66#13063301D411yescharacteristic
67C4×Dic86—21no—
68C4×Dic86C2311yescharacteristic
69#13063282—21no—
70C4⋊C4×D43—22no—
71C4⋊C4×D43—22no—
72C42×D43C2311yescharacteristic
73#13063257—22no—
74#13063256—22no—
75#13063256—22no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)C2311yescharacteristic
78C4⋊(C43⋊C8)C2312yes—
79Dic43⋊C8—21no—
80Dic43⋊C8—21no—
81Dic43⋊C8—21no—
82#13063250—22no—
83#13063249—22no—
84#13063248—22no—
85(C2×D43)⋊C8—22no—
86#13063235—21no—
87C4×C43⋊C8—21no—
88C4×C43⋊C8C2311yescharacteristic
89C8×Dic43—22no—
90C8×Dic43—21no—
91C8×Dic43D411yescharacteristic
92C8×Dic43D411yescharacteristic
93C2×Q16×C43—21no—
94C2×Q16×C43—21no—
95C4⋊Q8×C43C2312yes—
96C4×Q8×C43C2311yescharacteristic
97#106×C43—22no—
98C4⋊C8×C43—21no—
99C4⋊C8×C43C2311yescharacteristic
100C4⋊C8×C43C2312yes—
101#103×C43—22no—
102#97×C43—21no—
103C4×C8×C43C2311yescharacteristic
104C2×Q8×C43—22no—
105C2×Q8×C43C2×D411yescharacteristic
106Q8×D43—44no—
107Q8×D43—44no—
108C2×C4×D43—42no—
109C2×C4×D43C2×D411yescharacteristic
110C2×C4×D43C2×D411yescharacteristic
111C2×C4×D43#4111yescharacteristic
112C2×Dic86—21no—
113C2×Dic86—22no—
114C2×Dic86—42no—
115C2×Dic86C2×D411yescharacteristic
116Q16×C43—42no—
117Q16×C43—42no—
118C2×C8×C43—21no—
119C2×C8×C43—22no—
120C2×C8×C43C2×D411yescharacteristic
121C2×C8×C43C2×D411yescharacteristic
122C4⋊C4×C43—21no—
123C4⋊C4×C43—22no—
124C4⋊C4×C43—22no—
125C4⋊C4×C43C2×D411yescharacteristic
126C42×C43—21no—
127C42×C43C2411yescharacteristic
128#10621885—44no—
129#10621885—44no—
130(C2×D43)⋊C4—21no—
131(C2×D43)⋊C4—21no—
132C4⋊Dic43—21no—
133C4⋊Dic43—22no—
134C4⋊Dic43—22no—
135C4⋊Dic43C2×D411yescharacteristic
136Dic43⋊C4—21no—
137Dic43⋊C4—21no—
138Dic43⋊C4—21no—
139Dic43⋊C4—21no—
140Dic43⋊C4—21no—
141Dic43⋊C4—42no—
142Dic43⋊C4—42no—
143C4×Dic43—21no—
144C4×Dic43C2×D411yescharacteristic
145C4×Dic43C2×D411yescharacteristic
146C4×Dic43#4111yescharacteristic
147C2×C43⋊C8—22no—
148C2×C43⋊C8—21no—
149C2×C43⋊C8C2×D411yescharacteristic
150C2×C43⋊C8C2×D411yescharacteristic
151Dic172—42no—
152Dic172—42no—
153#10621872—42no—
154C8×D43—22no—
155C8×D43SD1614yes—
156C22×D43#12111yescharacteristic
157Q8×C43—22no—
158Q8×C43—42no—
159Q8×C43—42no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—42no—
163C2×C4×C43C22×D411yescharacteristic
164C2×C4×C43C22×D411yescharacteristic
165C2×C4×C43C2×#4111yescharacteristic
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—42no—
169C2×Dic43#12111yescharacteristic
170C2×Dic43#12111yescharacteristic
171C2×Dic43#12111yescharacteristic
172C4×D43—22no—
173C4×D43—22no—
174C4×D43—84no—
175C4×D43C2×SD1612yes—
176C4×D43AGL(1,ℤ/8)12yes—
177Dic86—22no—
178Dic86—42no—
179Dic86—42no—
180Dic86—42no—
181Dic86—84no—
182C8×C43—21no—
183C8×C43—41no—
184C8×C43—42no—
185C8×C43C2×SD1612yes—
186C43⋊C8—21no—
187C43⋊C8—41no—
188C43⋊C8—42no—
189C43⋊C8C2×SD1612yes—
190#19204—431nomaximal, Sylow
191C22×C43C2×#12111yescharacteristic
192C2×D43—21no—
193C2×D43—21no—
194C2×D43#46012yes—
195C4×C43—21no—
196C4×C43—41no—
197C4×C43—41no—
198C4×C43—82no—
199C4×C43C22×SD1611yescharacteristic
200C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
201C4×C43#57812yes—
202Dic43—21no—
203Dic43—41no—
204Dic43—41no—
205Dic43—82no—
206Dic43#46012yes—
207Dic43#47312yes—
208#3229—432no—
209C2×#494—431no—
210#2960—431no—
211#1690—431no—
212#1690—431no—
213#1690—431no—
214#1690D4311yescharacteristic, complemented
215#1670—432no—
216#1670—432no—
217#1564—431no—
218#1546—432no—
219C2×C43C2×#46011yescharacteristic
220C2×C43#305911yescharacteristic
221C2×C43C2×#47311yescharacteristic
222D43—22no—
223C22×Q16—861no—
224C22×Q16—861no—
225#533—431no—
226C2×C4⋊Q8—432no—
227#498—862no—
228#494—432no—
229#494—431no—
230#494—861no—
231#494—861no—
232#494C2×D4311yescharacteristic
233#487—862no—
234#483—862no—
235#483—862no—
236#475—432no—
237#475—432no—
238#475—432no—
239#475C2×D4312yes—
240#446—431no—
241#446—861no—
242#446C2×D4311yescharacteristic
243C8×Q8—431no—
244C8×Q8—431no—
245C8×Q8—861no—
246#431—432no—
247#424—861no—
248#423—431no—
249#405—861no—
250C2×C4×C8—431no—
251#335—432no—
252#334—431no—
253#334C2×D4311yescharacteristic
254#332—432no—
255#332—432no—
256#332—432no—
257#332C2×D4312yes—
258C43#1920411yescharacteristic, complemented, Sylow
259C22×Q8—862no—
260C2×Q16—21no—
261C2×Q16—21no—
262C2×Q16—862no—
263C2×Q16—862no—
264C2×Q16—861no—
265C2×Q16—861no—
266C2×Q16—1724no—
267C2×Q16—1724no—
268C2×M16—861no—
269C22×C8—431no—
270C22×C8—431no—
271C4⋊Q8—431no—
272C4⋊Q8—431no—
273C4⋊Q8—432no—
274C4⋊Q8—862no—
275C4⋊Q8—862no—
276C4⋊Q8—862no—
277C4⋊Q8C22×D4312yes—
278#125—861no—
279C22⋊Q8—431no—
280C22⋊Q8—431no—
281C22⋊Q8—861no—
282C4×Q8—431no—
283C4×Q8—861no—
284C4×Q8C22×D4311yescharacteristic
285#117—861no—
286C2×C4⋊C4—862no—
287C2×C4⋊C4—862no—
288C2×C42—431no—
289#106—22no—
290#106—862no—
291#106—862no—
292#106—862no—
293C4⋊C8—21no—
294C4⋊C8—431no—
295C4⋊C8—432no—
296C4⋊C8—861no—
297C4⋊C8—861no—
298C4⋊C8—861no—
299C4⋊C8—861no—
300C4⋊C8C22×D4311yescharacteristic
301C4⋊C8C22×D4312yes—
302#103—22no—
303#103—862no—
304#103—862no—
305#103—862no—
306C22⋊C8—862no—
307#97—21no—
308#97—861no—
309C4×C8—431no—
310C4×C8—431no—
311C4×C8—431no—
312C4×C8—861no—
313C4×C8—862no—
314C4×C8—861no—
315C4×C8C22×D4311yescharacteristic
316C2×Q8—22no—
317C2×Q8—431no—
318C2×Q8—861no—
319C2×Q8—862no—
320C2×Q8—1722no—
321C2×Q8—1724no—
322C2×Q8—1724no—
323C2×Q8D4×D4311yescharacteristic
324C22×C4—431no—
325C22×C4—431no—
326C22×C4—431no—
327C22×C4—1722no—
328Q16—42no—
329Q16—42no—
330Q16—1722no—
331Q16—1724no—
332Q16—1724no—
333Q16—1722no—
334M16—1722no—
335C2×C8—21no—
336C2×C8—22no—
337C2×C8—431no—
338C2×C8—434no—
339C2×C8—431no—
340C2×C8—862no—
341C2×C8—861no—
342C2×C8—862no—
343C2×C8D4×D4311yescharacteristic
344C2×C8D4×D4311yescharacteristic
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—431no—
349C4⋊C4—861no—
350C4⋊C4—861no—
351C4⋊C4—861no—
352C4⋊C4—861no—
353C4⋊C4—861no—
354C4⋊C4—861no—
355C4⋊C4—862no—
356C4⋊C4—862no—
357C4⋊C4—1722no—
358C4⋊C4—1722no—
359C4⋊C4D4×D4311yescharacteristic
360C22⋊C4—861no—
361C22⋊C4—861no—
362C42—21no—
363C42—431no—
364C42—431no—
365C42—431no—
366C42—861no—
367C42C23×D4311yescharacteristic
368C23—431no—
369Q8—22no—
370Q8—42no—
371Q8—42no—
372Q8—862no—
373Q8—3444no—
374Q8—1722no—
375Q8—1722no—
376Q8—1722no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—431no—
381C2×C4—431no—
382C2×C4—432no—
383C2×C4—432no—
384C2×C4—431no—
385C2×C4—862no—
386C2×C4—862no—
387C2×C4—861no—
388C2×C4—861no—
389C2×C4—3444no—
390C2×C4—1722no—
391C2×C4C2×D4×D4311yescharacteristic
392C2×C4C2×D4×D4311yescharacteristic
393C2×C4#41×D4311yescharacteristic
394C8—21no—
395C8—41no—
396C8—42no—
397C8—432no—
398C8—861no—
399C8—1721no—
400C8—1722no—
401C8SD16×D4312yes—
402C22—432no—
403C22—861no—
404C22—861no—
405C22#121×D4311yescharacteristic
406C4—21no—
407C4—41no—
408C4—41no—
409C4—82no—
410C4—432no—
411C4—432no—
412C4—861no—
413C4—3442no—
414C4—1721no—
415C4—1721no—
416C4C2×SD16×D4311yescharacteristic
417C4AGL(1,ℤ/8)×D4311yescharacteristic
418C4#1458371512yes—
419C2—862no—
420C2#460×D4311yescharacteristic
421C2#1914424811yescharacteristic
422C2#473×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1690C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1690D43
hypocenterC43#19204
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1690

Complements

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

NH ≅ G/Ntype
4. #19134090C2semidirect
5. #19134089C2semidirect
6. #19134086C2semidirect
7. #19133964C2semidirect
8. #19133963C2semidirect
11. C43×#1690C2semidirect
214. #1690D43semidirect
258. C43#19204semidirect

Maximal subgroups

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

subgroupindex
#191457382
#494×D432
#191435262
#191340902
#191340892
#191340862
#191339642
#191339632
#191333402
#191332652
C43×#16902
#1920443