Finite Group Databasebeta

← #25100021

Subgroups — #25100021

Order 11008.

890 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582946C211yesmaximal, characteristic
2#19143183C211yesmaximal, characteristic
3#424×D43C212yesmaximal
4C2×#14582853C211yesmaximal, characteristic
5#19135349C211yesmaximal, characteristic, complemented
6#19135347C212yesmaximal, complemented
7#19135346C211yesmaximal, characteristic, complemented
8#19135343C211yesmaximal, characteristic, complemented
9#19135340C212yesmaximal, complemented
10#19134303C212yesmaximal
11C43×#1945C211yesmaximal, characteristic, complemented
12C22×#10621872C2211yescharacteristic
13C2×M16×D43C2212yes—
14C22×C8×D43C2211yescharacteristic
15C2×#13063282C2211yescharacteristic
16#117×D43C2212yes—
17#14582946—24no—
18C2×#13063261C2211yescharacteristic
19C2×#13063260C2212yes—
20#14582940C414yescomplemented
21#14582938C414yescomplemented
22#14582937C2211yescharacteristic
23#14582935C2212yes—
24#14582927C2212yes—
25#14582926C2212yes—
26#14582925C2212yes—
27#14582924—24no—
28C4⋊C8×D43—24no—
29#14582853—24no—
30C2×#13063236C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582660C2212yes—
34#14582659C2212yes—
35#14582658C2212yes—
36C2×#108×C43C2211yescharacteristic
37C43×#427C2211yescharacteristic
38C43×#424C2212yes—
39C2×C4×C8×C43C2211yescharacteristic
40C43×#339C2212yes—
41C22×C4×D43C2311yescharacteristic
42C2×#10621877C2312yes—
43C2×#10621872—22no—
44C2×#10621872C2×C412yes—
45C2×#10621872C2×C412yes—
46C2×#10621872D414yes—
47C2×#10621872Q814yes—
48M16×D43—24no—
49M16×D43—24no—
50C22×C43⋊C8C2311yescharacteristic
51C22×C43⋊C8C2311yescharacteristic
52C2×C8×D43—22no—
53C2×C8×D43—22no—
54C2×C8×D43—22no—
55C2×C8×D43D414yes—
56#13063284C2312yes—
57#13063283C2×C414yes—
58#13063282—22no—
59#13063282—22no—
60#13063282Q814yes—
61#13063281—22no—
62C2×Dic43⋊C4—21no—
63C4⋊C4×D43C2×C414yes—
64C2×(C2×D43)⋊C4—21no—
65C22⋊C4×D43—22no—
66C2×C4×Dic43C2311yescharacteristic
67C42×D43—22no—
68#13063261—22no—
69#13063260—24no—
70#13063259C2×C412yes—
71#13063258C2×C414yes—
72#13063257C2×C412yes—
73#13063256C2×C414yes—
74C4⋊(C43⋊C8)—24no—
75Dic43⋊C8—24no—
76Dic43⋊C8—24no—
77#13063236—22no—
78#13063235—22no—
79C8×Dic43—22no—
80C2×M16×C43C2312yes—
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83#117×C43C2312yes—
84C2×C42×C43C2311yescharacteristic
85#108×C43—22no—
86#107×C43C2×C412yes—
87#106×C43C2×C412yes—
88C4⋊C8×C43—24no—
89C4×C8×C43—22no—
90C23×D43#4111yescharacteristic
91C22×C4×C43—21no—
92C22×C4×C43C2411yescharacteristic
93C22×Dic43—21no—
94C22×Dic43#4111yescharacteristic
95C2×C4×D43—24no—
96C2×C4×D43C22×C412yes—
97C2×C4×D43C2×D412yes—
98C2×C4×D43C2×D412yes—
99C2×C4×D43C2×Q812yes—
100C2×C4×D43C2×Q812yes—
101C2×C4×D43#4112yes—
102M16×C43—22no—
103M16×C43—22no—
104C2×C8×C43—21no—
105C2×C8×C43—21no—
106C2×C8×C43—22no—
107C2×C8×C43C22×C411yescharacteristic
108C2×C8×C43C22×C411yescharacteristic
109C2×C8×C43C2×D412yes—
110C2×C8×C43C2×D412yes—
111C2×C8×C43C2×Q812yes—
112C4⋊C4×C43C22×C414yes—
113C22⋊C4×C43—22no—
114C42×C43—21no—
115C42×C43—22no—
116C42×C43C2×Q812yes—
117C22⋊Dic43—22no—
118(C2×D43)⋊C4—24no—
119(C2×D43)⋊C4—24no—
120C4⋊Dic43C22×C414yes—
121Dic43⋊C4—24no—
122Dic43⋊C4—24no—
123C4×Dic43—21no—
124C4×Dic43—22no—
125C4×Dic43—24no—
126C4×Dic43C2×Q812yes—
127#10621877—22no—
128#10621877—22no—
129C2×C43⋊C8—21no—
130C2×C43⋊C8—21no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8C22×C412yes—
133C2×C43⋊C8C2×D412yes—
134C2×C43⋊C8C2×D412yes—
135C2×C43⋊C8C2×Q812yes—
136#10621872—44no—
137#10621872C4⋊C418yes—
138#10621872C4⋊C418yes—
139C8×D43—28no—
140C8×D43—44no—
141C23×C43C2×#4111yescharacteristic
142C22×D43—42no—
143C22×D43C4×D412yes—
144C22×D43C22⋊Q812yes—
145C22×D43#12512yes—
146C2×C4×C43—24no—
147C2×C4×C43—22no—
148C2×C4×C43—42no—
149C2×C4×C43C23×C411yescharacteristic
150C2×C4×C43C22×D411yescharacteristic
151C2×C4×C43C22×D411yescharacteristic
152C2×C4×C43C22×Q811yescharacteristic
153C2×C4×C43C22×Q811yescharacteristic
154C2×C4×C43C2×#4111yescharacteristic
155C2×Dic43—24no—
156C2×Dic43—22no—
157C2×Dic43—42no—
158C2×Dic43C4×D412yes—
159C2×Dic43C22⋊Q812yes—
160C2×Dic43#12512yes—
161C4×D43—48no—
162C4×D43C2×C4⋊C414yes—
163C4×D43C4×Q814yes—
164C4×D43#12114yes—
165C4×D43C4⋊Q814yes—
166C8×C43—22no—
167C8×C43—42no—
168C8×C43C2×C4⋊C412yes—
169C8×C43C2×C4⋊C412yes—
170C43⋊C8—22no—
171C43⋊C8—42no—
172C43⋊C8C2×C4⋊C414yes—
173#21164—431nomaximal, Sylow
174C22×C43—22no—
175C22×C43C2×C4×D411yescharacteristic
176C22×C43C2×C22⋊Q811yescharacteristic
177C22×C43C2×#12511yescharacteristic
178C2×D43—24no—
179C2×D43—42no—
180C2×D43—42no—
181C2×D43#38914yes—
182C4×C43—42no—
183C4×C43—44no—
184C4×C43C22×C4⋊C411yescharacteristic
185C4×C43C2×C4×Q811yescharacteristic
186C4×C43C2×#12111yescharacteristic
187C4×C43C2×C4⋊Q811yescharacteristic
188Dic43—42no—
189Dic43—44no—
190Dic43#38914yes—
191C2×#430—431no—
192#2911—431no—
193C2×#424—432no—
194C2×#405—431no—
195#1946—431no—
196#1946—431no—
197#1946—432no—
198#1945—432no—
199#1945—431no—
200#1945D4311yescharacteristic, complemented
201#1733—432no—
202C2×C43—21no—
203C2×C43—21no—
204C2×C43C2×#38911yescharacteristic
205C2×C43#295512yes—
206D43—24no—
207C22×M16—431no—
208C22×M16—432no—
209C23×C8—431no—
210C2×#117—431no—
211C2×#117—432no—
212#430—864no—
213C2×#108—432no—
214C2×#108—431no—
215C2×#108C2×D4311yescharacteristic
216#428—434no—
217#428—434no—
218#427—431no—
219#427—432no—
220#427C2×D4311yescharacteristic
221#424—432no—
222#424—432no—
223#424—432no—
224#424—864no—
225#424C2×D4312yes—
226C2×C4⋊C8—864no—
227#405—864no—
228C2×#97—431no—
229C2×#97—431no—
230C2×C4×C8—431no—
231C2×C4×C8C2×D4311yescharacteristic
232#339—432no—
233#339—432no—
234#339—432no—
235#339C2×D4312yes—
236C43#2116411yescharacteristic, complemented, Sylow
237C23×C4—431no—
238C2×M16—432no—
239C2×M16—432no—
240C2×M16—434no—
241C2×M16—434no—
242C2×M16—432no—
243C2×M16—862no—
244C2×M16—864no—
245C2×M16—864no—
246C2×M16C22×D4312yes—
247C22×C8—431no—
248C22×C8—431no—
249C22×C8—434no—
250C22×C8—862no—
251C22×C8—862no—
252C22×C8—862no—
253C22×C8C22×D4311yescharacteristic
254C22×C8C22×D4311yescharacteristic
255#117—434no—
256#117—432no—
257#117—434no—
258#117—862no—
259#117—862no—
260#117—862no—
261#117C22×D4312yes—
262C2×C4⋊C4—434no—
263C2×C4⋊C4—861no—
264C2×C22⋊C4—862no—
265C2×C22⋊C4—861no—
266C2×C42—431no—
267C2×C42—862no—
268C2×C42C22×D4311yescharacteristic
269#108—22no—
270#108—864no—
271#108—862no—
272#107—432no—
273#107—434no—
274#107C4×D4312yes—
275#106—432no—
276#106—434no—
277#106C4×D4312yes—
278C4⋊C8—24no—
279C4⋊C8—864no—
280C4⋊C8—864no—
281C4⋊C8—864no—
282#97—862no—
283#97—862no—
284C4×C8—22no—
285C4×C8—862no—
286C24—431no—
287C22×C4—21no—
288C22×C4—431no—
289C22×C4—432no—
290C22×C4—432no—
291C22×C4—432no—
292C22×C4—432no—
293C22×C4—432no—
294C22×C4—432no—
295C22×C4—864no—
296C22×C4—861no—
297C22×C4C23×D4311yescharacteristic
298M16—22no—
299M16—22no—
300M16—438no—
301M16—438no—
302M16—862no—
303M16—862no—
304M16—1724no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—22no—
308C2×C8—432no—
309C2×C8—432no—
310C2×C8—432no—
311C2×C8—432no—
312C2×C8—868no—
313C2×C8—861no—
314C2×C8—861no—
315C2×C8—862no—
316C2×C8—1724no—
317C2×C8C2×C4×D4311yescharacteristic
318C2×C8C2×C4×D4311yescharacteristic
319C2×C8D4×D4312yes—
320C2×C8D4×D4312yes—
321C2×C8Q8×D4312yes—
322C4⋊C4—434no—
323C4⋊C4—864no—
324C4⋊C4—864no—
325C4⋊C4C2×C4×D4314yes—
326C22⋊C4—22no—
327C22⋊C4—864no—
328C22⋊C4—864no—
329C22⋊C4—862no—
330C42—21no—
331C42—22no—
332C42—432no—
333C42—864no—
334C42—861no—
335C42—862no—
336C42Q8×D4312yes—
337C23—432no—
338C23—432no—
339C23—432no—
340C23—1722no—
341C23#41×D4311yescharacteristic
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—42no—
345C2×C4—432no—
346C2×C4—432no—
347C2×C4—432no—
348C2×C4—434no—
349C2×C4—434no—
350C2×C4—434no—
351C2×C4—434no—
352C2×C4—864no—
353C2×C4—862no—
354C2×C4—1728no—
355C2×C4—1722no—
356C2×C4C22×C4×D4311yescharacteristic
357C2×C4C2×D4×D4311yescharacteristic
358C2×C4C2×D4×D4311yescharacteristic
359C2×C4C2×Q8×D4311yescharacteristic
360C2×C4C2×Q8×D4311yescharacteristic
361C2×C4#41×D4311yescharacteristic
362C8—22no—
363C8—42no—
364C8—434no—
365C8—862no—
366C8—1722no—
367C8C4⋊C4×D4312yes—
368C8C4⋊C4×D4312yes—
369C22—22no—
370C22—434no—
371C22—864no—
372C22—1722no—
373C22—1722no—
374C22C4×D4×D4311yescharacteristic
375C22C22⋊Q8×D4311yescharacteristic
376C22#125×D4311yescharacteristic
377C4—42no—
378C4—44no—
379C4—434no—
380C4—1722no—
381C4—1724no—
382C4C2×C4⋊C4×D4311yescharacteristic
383C4C4×Q8×D4311yescharacteristic
384C4#121×D4311yescharacteristic
385C4C4⋊Q8×D4311yescharacteristic
386C2—21no—
387C2—21no—
388C2—864no—
389C2#389×D4311yescharacteristic
390C2#1914349312yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1945C2
socleC22×C43C2×C4×D4
prime radicalC23×D43#41
cosocleC22×C4×C43C24
hypercenter#1945D43
hypocenterC43#21164
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1945

Complements

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

NH ≅ G/Ntype
5. #19135349C2semidirect
6. #19135347C2semidirect
7. #19135346C2semidirect
8. #19135343C2semidirect
9. #19135340C2semidirect
11. C43×#1945C2semidirect
20. #14582940C4semidirect
21. #14582938C4semidirect
200. #1945D43semidirect
236. C43#21164semidirect

Maximal subgroups

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

subgroupindex
C2×#145829462
#191431832
#424×D432
C2×#145828532
#191353492
#191353472
#191353462
#191353432
#191353402
#191343032
C43×#19452
#2116443