Finite Group Databasebeta

← #25251511

Subgroups — #25251511

Order 11008.

546 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144253C211yesmaximal, characteristic
2#19143203C211yesmaximal, characteristic, complemented
3#19136813C214yesmaximal, complemented
4#19136808C214yesmaximal, complemented
5C2×#14582723C211yesmaximal, characteristic, complemented
6C2×#14582722C211yesmaximal, characteristic, complemented
7#19136344C211yesmaximal, characteristic, complemented
8#19136215C211yesmaximal, characteristic, complemented
9C43×#2148C211yesmaximal, characteristic, complemented
10#14583665—21no—
11C2×#13063331C2211yescharacteristic
12#14583477—21no—
13C2×#13063265C2211yescharacteristic
14#14583154C2212yes—
15#14583149C2212yes—
16#14583125—22no—
17#14582947—21no—
18#14582946C2214yes—
19C2×#13063261C2211yescharacteristic
20#108×D43—22no—
21C2×#13063257C2211yescharacteristic
22#14582900—21no—
23#14582723C2214yes—
24#14582722C2214yes—
25#14582715C2212yes—
26#14582712C2212yes—
27#14582680C2214yes—
28C2×#135×C43C2211yescharacteristic
29C2×M32×C43C2211yescharacteristic
30C2×#108×C43C2211yescharacteristic
31C43×#362C2212yes—
32C43×#361C2212yes—
33C2×#10621898D411yescharacteristic
34#13063333—42no—
35#13063331—21no—
36#13063331—21no—
37#13063331—21no—
38#13063331—21no—
39#13063331—42no—
40C2×#10621877—21no—
41C2×#10621877D411yescharacteristic
42C2×#10621872C2312yes—
43M16×D43—24no—
44C2×C8×D43D412yes—
45#13063304—41no—
46#13063301—22no—
47#13063299—41no—
48#13063297—42no—
49#13063296—22no—
50C2×C4⋊Dic43—21no—
51#13063265—21no—
52#13063265C2312yes—
53C2×C43⋊C16—21no—
54#13063261—21no—
55#13063261C2312yes—
56#13063260—24no—
57#13063257—21no—
58#13063257C2312yes—
59#13063249—22no—
60#13063246—22no—
61C2×#41×C43—21no—
62#135×C43—21no—
63#135×C43—21no—
64#135×C43—21no—
65#135×C43—21no—
66C2×Q16×C43C2311yescharacteristic
67C2×SD16×C43—21no—
68C2×D8×C43C2311yescharacteristic
69C2×M16×C43—21no—
70C22×C8×C43C2311yescharacteristic
71M32×C43—21no—
72M32×C43C2312yes—
73C2×C16×C43—21no—
74#108×C43—21no—
75#108×C43C2312yes—
76#41×C43—41no—
77#41×C43—41no—
78#41×C43—41no—
79#41×C43—41no—
80C2×Q8×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43C2×D411yescharacteristic
85C2×C22⋊D43—42no—
86C2×C22⋊D43SD1612yes—
87C22×Dic43—41no—
88#10621898—21no—
89#10621898—21no—
90#10621898—21no—
91#10621898—21no—
92C2×D172SD1611yescharacteristic
93C2×C4×D43C2×D412yes—
94C2×Dic86SD1611yescharacteristic
95Q16×C43—21no—
96Q16×C43—21no—
97SD16×C43—41no—
98SD16×C43—41no—
99D8×C43—21no—
100D8×C43—21no—
101M16×C43—22no—
102M16×C43—41no—
103C2×C8×C43—41no—
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43#4111yescharacteristic
106C2×C8×C43#4111yescharacteristic
107C2×C8×C43#4111yescharacteristic
108C2×C8×C43#4111yescharacteristic
109C2×C8×C43C2411yescharacteristic
110C22⋊Dic43—42no—
111(C2×D43)⋊C4—42no—
112C4⋊Dic43—22no—
113C4⋊Dic43—41no—
114Dic43⋊C4—42no—
115#10621877—21no—
116#10621877—21no—
117#10621877—22no—
118#10621877—41no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8C2×D412yes—
121#10621872—22no—
122#10621872—22no—
123#10621872—44no—
124C8×D43—22no—
125C8×D43—22no—
126C8×D43—44no—
127C16×C43—22no—
128C43⋊C16—22no—
129C23×C43—41no—
130C23×C43C2×SD1611yescharacteristic
131C22×D43C2×SD1612yes—
132Q8×C43—41no—
133Q8×C43—41no—
134D4×C43—41no—
135D4×C43—41no—
136D4×C43—81no—
137D4×C43—81no—
138C2×C4×C43—41no—
139C2×C4×C43—81no—
140C2×C4×C43—81no—
141C2×C4×C43#12311yescharacteristic
142C2×C4×C43#12311yescharacteristic
143C2×C4×C43C2×SD1611yescharacteristic
144C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C43C22×D411yescharacteristic
147C22⋊D43—22no—
148C22⋊D43—22no—
149C22⋊D43—162no—
150C2×Dic43—42no—
151C2×Dic43—161no—
152C2×Dic43C2×SD1612yes—
153D172—21no—
154D172—21no—
155C4×D43—22no—
156C4×D43—22no—
157Dic86—21no—
158Dic86—21no—
159C8×C43—42no—
160C8×C43#12311yescharacteristic
161C8×C43#12311yescharacteristic
162C8×C43C2×#4111yescharacteristic
163C8×C43C2×#4111yescharacteristic
164C43⋊C8—22no—
165C43⋊C8—42no—
166#33659—431nomaximal, Sylow
167C22×C43—41no—
168C22×C43—81no—
169C22×C43—81no—
170C22×C43—81no—
171C22×C43#48111yescharacteristic
172C22×C43#48111yescharacteristic
173C22×C43C22×SD1611yescharacteristic
174C2×D43—22no—
175C2×D43—42no—
176C4×C43—81no—
177C4×C43#48111yescharacteristic
178C4×C43#48111yescharacteristic
179C4×C43C2×#12311yescharacteristic
180C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
181Dic43—22no—
182Dic43—82no—
183#3060—431no—
184#2916—431no—
185#2239—434no—
186#2238—434no—
187C2×#365—431no—
188C2×#365—431no—
189#2148—431no—
190#2148D4311yescharacteristic, complemented
191#2115—431no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43—21no—
195C2×C43—161no—
196C2×C43C2×#48111yescharacteristic
197D43—42no—
198C2×#135C2×D4311yescharacteristic
199#568—861no—
200C2×#131—431no—
201#537—861no—
202C2×M32—431no—
203C2×M32C2×D4311yescharacteristic
204#470—432no—
205#469—432no—
206#465—862no—
207#430—434no—
208#430—861no—
209C2×#108—431no—
210C2×#108—862no—
211C2×#108C2×D4311yescharacteristic
212C2×#106—431no—
213#417—861no—
214#365—434no—
215#365—434no—
216#362—432no—
217#362C2×D4312yes—
218#361—432no—
219#361C2×D4312yes—
220#349—434no—
221C43#3365911yescharacteristic, complemented, Sylow
222C2×#41—21no—
223C2×#41—431no—
224#135—21no—
225#135—21no—
226#135—21no—
227#135—21no—
228C2×Q16C22×D4311yescharacteristic
229C2×SD16—21no—
230C2×D8C22×D4311yescharacteristic
231#131—861no—
232#131—861no—
233#131—861no—
234#131—861no—
235#131—1722no—
236#131—1722no—
237C2×M16—21no—
238C2×M16—431no—
239C2×M16—432no—
240C2×M16—864no—
241C2×M16—861no—
242C22×C8—432no—
243C22×C8C22×D4311yescharacteristic
244C22⋊Q8—862no—
245C22⋊Q8—1721no—
246#121—862no—
247#121—1721no—
248#121—1722no—
249C2×C4⋊C4—861no—
250M32—21no—
251M32—432no—
252M32—861no—
253M32C22×D4312yes—
254C2×C16—21no—
255C2×C16—861no—
256#108—21no—
257#108—432no—
258#108—864no—
259#108—861no—
260#108C22×D4312yes—
261#106—432no—
262#106—861no—
263#103—862no—
264#102—862no—
265#41—41no—
266#41—41no—
267#41—41no—
268#41—41no—
269#41—861no—
270#41—861no—
271#41—861no—
272#41—861no—
273C2×Q8—21no—
274C2×Q8—431no—
275C2×D4—21no—
276C2×D4—41no—
277C2×D4—432no—
278C2×D4—431no—
279C2×D4—1722no—
280C22×C4—41no—
281C22×C4—432no—
282C22×C4—1721no—
283C22×C4D4×D4311yescharacteristic
284Q16—21no—
285Q16—21no—
286SD16—41no—
287SD16—41no—
288D8—21no—
289D8—21no—
290M16—22no—
291M16—41no—
292M16—861no—
293M16—861no—
294M16—862no—
295M16—862no—
296M16—862no—
297M16—1724no—
298M16—1721no—
299C2×C8—41no—
300C2×C8—432no—
301C2×C8—862no—
302C2×C8—862no—
303C2×C8—1724no—
304C2×C8—1721no—
305C2×C8#1062189811yescharacteristic
306C2×C8#1062189811yescharacteristic
307C2×C8D4×D4311yescharacteristic
308C2×C8#1062190011yescharacteristic
309C2×C8#1062190011yescharacteristic
310C2×C8C23×D4311yescharacteristic
311C4⋊C4—862no—
312C4⋊C4—1722no—
313C4⋊C4—1721no—
314C22⋊C4—1722no—
315C22⋊C4—1722no—
316C16—22no—
317C16—862no—
318C23—41no—
319C23—432no—
320C23SD16×D4311yescharacteristic
321Q8—41no—
322Q8—41no—
323Q8—861no—
324Q8—861no—
325D4—41no—
326D4—41no—
327D4—81no—
328D4—81no—
329D4—862no—
330D4—862no—
331D4—861no—
332D4—861no—
333D4—6882no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—432no—
338C2×C4—862no—
339C2×C4—862no—
340C2×C4—1722no—
341C2×C4—6881no—
342C2×C4#1306330711yescharacteristic
343C2×C4#1306330711yescharacteristic
344C2×C4SD16×D4311yescharacteristic
345C2×C4#1306334911yescharacteristic
346C2×C4#1306334911yescharacteristic
347C2×C4C2×D4×D4311yescharacteristic
348C8—42no—
349C8—862no—
350C8—1722no—
351C8#1306330711yescharacteristic
352C8#1306330711yescharacteristic
353C8C2×#1062190011yescharacteristic
354C8C2×#1062189811yescharacteristic
355C22—41no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—862no—
360C22—1722no—
361C22#1458321611yescharacteristic
362C22#1458321611yescharacteristic
363C22C2×SD16×D4311yescharacteristic
364C4—81no—
365C4—862no—
366C4—3442no—
367C4#1458321611yescharacteristic
368C4#1458321611yescharacteristic
369C4C2×#1306330711yescharacteristic
370C4C2×#1306334911yescharacteristic
371C2—21no—
372C2—21no—
373C2—21no—
374C2—161no—
375C2—1722no—
376C2C2×#1458321611yescharacteristic
subgroupG/H
centerC2C2×#14583216
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2148C2
socleC2×C43C2×#481
prime radical#19144253C2
hypercenter#2148D43
hypocenterC43#33659
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #2148

Complements

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

NH ≅ G/Ntype
2. #19143203C2semidirect
3. #19136813C2semidirect
4. #19136808C2semidirect
5. C2×#14582723C2semidirect
6. C2×#14582722C2semidirect
7. #19136344C2semidirect
8. #19136215C2semidirect
9. C43×#2148C2semidirect
190. #2148D43semidirect
221. C43#33659semidirect

Maximal subgroups

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

subgroupindex
#191442532
#191432032
#191368132
#191368082
C2×#145827232
C2×#145827222
#191363442
#191362152
C43×#21482
#3365943