Finite Group Databasebeta

← #25126281

Subgroups — #25126281

Order 11008.

752 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143419C212yesmaximal
2C2×#14582993C211yesmaximal, characteristic, complemented
3#19143235C211yesmaximal, characteristic
4#19136101C211yesmaximal, characteristic, complemented
5#19135963C212yesmaximal, complemented
6#19135892C212yesmaximal
7#19135864C211yesmaximal, characteristic, complemented
8#19135716C211yesmaximal, characteristic
9#19134496C211yesmaximal, characteristic, complemented
10#19134390C212yesmaximal, complemented
11C43×#2078C211yesmaximal, characteristic
12C2×#13063355C2212yes—
13C22×Dic172C2211yescharacteristic
14#41×Dic43C2211yescharacteristic
15C2×#13063290C2212yes—
16#14583003—22no—
17#14582996—22no—
18#14582993—22no—
19#14582993—22no—
20#14582991—22no—
21#14582990—22no—
22#14582957—22no—
23#14582949—22no—
24C2×#13063260C2212yes—
25#14582939C2212yes—
26#14582927C2211yescharacteristic
27#14582925C2211yescharacteristic
28#14582909C2212yes—
29C2×#13063248C2212yes—
30C2×#13063243C2212yes—
31C2×#13063243C2212yes—
32#14582866C2211yescharacteristic
33M16×Dic43C2212yes—
34M16×Dic43C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36#14582668C2212yes—
37#14582664C2211yescharacteristic
38C2×#107×C43C2211yescharacteristic
39C43×#417C2212yes—
40C43×#408C2211yescharacteristic
41C43×#343C2212yes—
42C43×#341C2211yescharacteristic
43C22×Dic86C2312yes—
44#13063355—24no—
45#13063355—24no—
46C2×Dic172—24no—
47C2×Dic172—22no—
48C2×#10621885—22no—
49C2×#10621883—22no—
50C2×#10621877C2311yescharacteristic
51C2×#10621877C2312yes—
52C22×C43⋊C8C2311yescharacteristic
53Q8×Dic43D411yescharacteristic
54Q8×Dic43D411yescharacteristic
55#13063290—22no—
56#13063290—22no—
57#13063290—22no—
58#13063290—22no—
59D4×Dic43—21no—
60D4×Dic43—21no—
61D4×Dic43D411yescharacteristic
62D4×Dic43D411yescharacteristic
63#13063284—21no—
64#13063284C2311yescharacteristic
65C2×Dic43⋊C4—22no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43—22no—
68C2×C4×Dic43C2311yescharacteristic
69#13063260—24no—
70#13063258—22no—
71#13063256—22no—
72Dic43⋊C8—22no—
73Dic43⋊C8—22no—
74#13063250—22no—
75#13063250—22no—
76#13063248—24no—
77#13063243—24no—
78#13063243—24no—
79C22⋊(C43⋊C8)—22no—
80#13063235—21no—
81#13063235—22no—
82C8×Dic43—21no—
83C8×Dic43—22no—
84C8×Dic43D412yes—
85C8×Dic43D412yes—
86C2×#41×C43C2311yescharacteristic
87C2×M16×C43C2311yescharacteristic
88C2×M16×C43C2312yes—
89C22×C8×C43C2311yescharacteristic
90C2×C4⋊C4×C43C2312yes—
91#107×C43—22no—
92#103×C43—22no—
93#102×C43—22no—
94C22⋊C8×C43—22no—
95#41×C43—22no—
96#41×C43—22no—
97C2×Q8×C43C2×D411yescharacteristic
98C2×D4×C43—21no—
99C2×D4×C43C2×D411yescharacteristic
100C22×C4×C43—21no—
101C22×C4×C43—22no—
102C22×C4×C43C2411yescharacteristic
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—22no—
106C22×Dic43#4111yescharacteristic
107C22×Dic43#4111yescharacteristic
108C2×Dic86—22no—
109C2×Dic86—22no—
110C2×Dic86—22no—
111C2×Dic86—22no—
112C2×Dic86—22no—
113C2×Dic86#4114yes—
114M16×C43—22no—
115M16×C43—22no—
116M16×C43—22no—
117C2×C8×C43—22no—
118C2×C8×C43—21no—
119C2×C8×C43—22no—
120C2×C8×C43C2×D412yes—
121C4⋊C4×C43—22no—
122C4⋊C4×C43—22no—
123C22⋊Dic43—21no—
124C22⋊Dic43—21no—
125C22⋊Dic43—21no—
126#10621885—28no—
127#10621883—28no—
128C4⋊Dic43—21no—
129C4⋊Dic43—21no—
130C4⋊Dic43C2×D411yescharacteristic
131C4⋊Dic43C2×D411yescharacteristic
132Dic43⋊C4—42no—
133Dic43⋊C4—42no—
134C4×Dic43—21no—
135C4×Dic43—21no—
136C4×Dic43—21no—
137C4×Dic43—42no—
138C4×Dic43—42no—
139C4×Dic43C2×D411yescharacteristic
140C4×Dic43C2×D411yescharacteristic
141C4×Dic43C2×D411yescharacteristic
142C4×Dic43C2×D411yescharacteristic
143#10621877—22no—
144#10621877—22no—
145#10621877#4114yes—
146C2×C43⋊C8—22no—
147C2×C43⋊C8—22no—
148C2×C43⋊C8—21no—
149C2×C43⋊C8C2×D412yes—
150Dic172—28no—
151C23×C43—21no—
152C23×C43C2×#4111yescharacteristic
153Q8×C43—22no—
154D4×C43—22no—
155D4×C43—42no—
156C2×C4×C43—21no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—42no—
160C2×C4×C43—82no—
161C2×C4×C43C22×D411yescharacteristic
162C2×C4×C43C22×D411yescharacteristic
163C2×C4×C43C2×#4112yes—
164C2×C4×C43C2×#4112yes—
165C2×Dic43—22no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—24no—
169C2×Dic43—41no—
170C2×Dic43—42no—
171C2×Dic43—42no—
172C2×Dic43—42no—
173C2×Dic43—42no—
174C2×Dic43#12111yescharacteristic
175C2×Dic43#12111yescharacteristic
176C2×Dic43#12111yescharacteristic
177C2×Dic43#12111yescharacteristic
178Dic86—24no—
179Dic86—24no—
180Dic86—42no—
181Dic86—42no—
182C8×C43—22no—
183C8×C43—42no—
184C8×C43—41no—
185C43⋊C8—24no—
186C43⋊C8—22no—
187C43⋊C8—41no—
188#23717—431nomaximal, Sylow
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—41no—
194C22×C43C2×#12111yescharacteristic
195C22×C43#52912yes—
196C4×C43—41no—
197C4×C43—82no—
198C4×C43#52512yes—
199C4×C43#52511yescharacteristic
200C4×C43#53211yescharacteristic
201Dic43—21no—
202Dic43—21no—
203Dic43—21no—
204Dic43—44no—
205Dic43—41no—
206Dic43—41no—
207Dic43#47312yes—
208C4×#137—432no—
209C2×C4×Q16—431no—
210#2922—431no—
211#2089—431no—
212#2078D4311yescharacteristic
213#2064—432no—
214#2052—432no—
215#2047—431no—
216#2020—431no—
217C4×#108—431no—
218C4×#101—432no—
219C2×C43—22no—
220C2×C43—81no—
221C2×C43#239211yescharacteristic
222C2×C43C2×#47311yescharacteristic
223C2×C43#306711yescharacteristic
224C2×#137—432no—
225C22×Q16—431no—
226C4×#41—431no—
227C2×C4×Q8—432no—
228#441—862no—
229#440—862no—
230C4×Q16—862no—
231C4×Q16—862no—
232C4×Q16—862no—
233C4×SD16—862no—
234#433—862no—
235#431—862no—
236C2×#108—432no—
237#428—432no—
238C2×#107C2×D4311yescharacteristic
239#424—431no—
240#424—431no—
241#419—432no—
242#417C2×D4312yes—
243C2×#103—432no—
244C2×#101—432no—
245C2×#101—432no—
246#408—431no—
247#408C2×D4311yescharacteristic
248C4×M16—431no—
249C4×M16—432no—
250C2×C4×C8—431no—
251#343—432no—
252#343C2×D4312yes—
253#341—431no—
254#341C2×D4311yescharacteristic
255C43#2371711yescharacteristic, complemented, Sylow
256C2×#41C22×D4311yescharacteristic
257C22×Q8—432no—
258#137—864no—
259#137—864no—
260C2×Q16—864no—
261C2×Q16—862no—
262C2×Q16—862no—
263C2×SD16—862no—
264C2×M16—432no—
265C2×M16—431no—
266C2×M16C22×D4312yes—
267C2×M16C22×D4311yescharacteristic
268C22×C8—431no—
269C22×C8C22×D4311yescharacteristic
270C4×Q8—431no—
271C4×Q8—431no—
272C4×Q8—862no—
273C4×Q8—862no—
274C4×Q8—862no—
275C4×Q8—862no—
276C4×D4—431no—
277C4×D4—431no—
278C4×D4—861no—
279C4×D4—861no—
280#117—431no—
281#117—861no—
282C2×C4⋊C4—862no—
283C2×C4⋊C4C22×D4312yes—
284C2×C42—431no—
285C2×C42—861no—
286C2×C42—862no—
287#108—864no—
288#107—22no—
289#107—862no—
290#106—862no—
291C4⋊C8—862no—
292C4⋊C8—862no—
293#103—22no—
294#103—864no—
295#103—862no—
296#103—862no—
297#102—22no—
298#101—864no—
299#101—864no—
300C22⋊C8—22no—
301C22⋊C8—862no—
302#97—861no—
303#97—862no—
304C4×C8—432no—
305C4×C8—432no—
306C4×C8—861no—
307C4×C8—862no—
308#41—22no—
309#41—22no—
310C2×Q8—434no—
311C2×Q8—862no—
312C2×Q8—862no—
313C2×Q8—862no—
314C2×Q8—862no—
315C2×Q8—862no—
316C2×Q8D4×D4311yescharacteristic
317C2×D4—21no—
318C2×D4D4×D4311yescharacteristic
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—431no—
322C22×C4—431no—
323C22×C4—861no—
324C22×C4—861no—
325C22×C4—862no—
326C22×C4C23×D4311yescharacteristic
327Q16—868no—
328Q16—868no—
329SD16—868no—
330M16—22no—
331M16—22no—
332M16—22no—
333M16—434no—
334M16—862no—
335M16—862no—
336C2×C8—22no—
337C2×C8—21no—
338C2×C8—22no—
339C2×C8—432no—
340C2×C8—862no—
341C2×C8—862no—
342C2×C8—861no—
343C2×C8D4×D4312yes—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—431no—
347C4⋊C4—431no—
348C4⋊C4—861no—
349C4⋊C4—861no—
350C4⋊C4—1722no—
351C4⋊C4—1722no—
352C22⋊C4—861no—
353C22⋊C4—861no—
354C22⋊C4—861no—
355C42—431no—
356C42—431no—
357C42—431no—
358C42—431no—
359C42—861no—
360C42—861no—
361C42—861no—
362C42—1722no—
363C42—1722no—
364C23—21no—
365C23#41×D4311yescharacteristic
366Q8—22no—
367Q8—864no—
368Q8—864no—
369Q8—1722no—
370Q8—1722no—
371D4—22no—
372D4—42no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—82no—
378C2×C4—431no—
379C2×C4—431no—
380C2×C4—431no—
381C2×C4—431no—
382C2×C4—862no—
383C2×C4—861no—
384C2×C4—861no—
385C2×C4—864no—
386C2×C4—1722no—
387C2×C4—1721no—
388C2×C4—1722no—
389C2×C4—1722no—
390C2×C4—1722no—
391C2×C4C2×D4×D4311yescharacteristic
392C2×C4C2×D4×D4311yescharacteristic
393C2×C4#41×D4312yes—
394C2×C4#41×D4312yes—
395C8—22no—
396C8—42no—
397C8—41no—
398C8—864no—
399C8—862no—
400C8—1721no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22#121×D4311yescharacteristic
407C22#1458343212yes—
408C4—41no—
409C4—82no—
410C4—432no—
411C4—861no—
412C4—861no—
413C4—861no—
414C4—1724no—
415C4—1721no—
416C4—1721no—
417C4#1458340711yescharacteristic
418C4#1458340712yes—
419C4#1458344811yescharacteristic
420C2—22no—
421C2—81no—
422C2#1913783211yescharacteristic
423C2#473×D4311yescharacteristic
424C2#1914431311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2078C2
socleC22×C43C2×#121
prime radicalC2×#41×C43C23
hypercenter#2078D43
hypocenterC43#23717
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2078

Complements

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

NH ≅ G/Ntype
2. C2×#14582993C2semidirect
4. #19136101C2semidirect
5. #19135963C2semidirect
7. #19135864C2semidirect
9. #19134496C2semidirect
10. #19134390C2semidirect
255. C43#23717semidirect

Maximal subgroups

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

subgroupindex
#191434192
C2×#145829932
#191432352
#191361012
#191359632
#191358922
#191358642
#191357162
#191344962
#191343902
C43×#20782
#2371743