Finite Group Databasebeta

← #25251515

Subgroups — #25251515

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#19144258C211yesmaximal, characteristic
2#19143203C211yesmaximal, characteristic, complemented
3#19136816C214yesmaximal, complemented
4#19136811C214yesmaximal, complemented
5C2×#14582721C211yesmaximal, characteristic, complemented
6#19136345C211yesmaximal, characteristic, complemented
7#19136342C211yesmaximal, characteristic, complemented
8#19136215C211yesmaximal, characteristic, complemented
9C2×C43×#365C211yesmaximal, characteristic, complemented
10C2×#13063347C2211yescharacteristic
11#14583665—21no—
12C2×#13063331C2211yescharacteristic
13#14583480—21no—
14C2×#13063265C2211yescharacteristic
15#14583158C2212yes—
16#14583153C2212yes—
17#14583129—22no—
18#14582947—21no—
19#14582946C2214yes—
20C2×#13063261C2211yescharacteristic
21#108×D43—22no—
22#14582898—21no—
23#14582721C2214yes—
24#14582716C2212yes—
25#14582714C2212yes—
26#14582713C2212yes—
27#14582711C2212yes—
28#14582680C2214yes—
29C2×M32×C43C2211yescharacteristic
30C2×#108×C43C2211yescharacteristic
31C2×#106×C43C2211yescharacteristic
32C43×#365C2214yes—
33C2×#10621898—21no—
34C2×#10621898D411yescharacteristic
35#13063347—21no—
36#13063347—21no—
37#13063347—21no—
38#13063347—21no—
39C2×Dic172C2311yescharacteristic
40C2×#10621873—21no—
41C2×D344C2311yescharacteristic
42#13063333—42no—
43#13063331—21no—
44#13063331—21no—
45#13063331—21no—
46#13063331—21no—
47#13063331—42no—
48C2×#10621877—21no—
49C2×#10621877D411yescharacteristic
50C2×#10621872C2312yes—
51M16×D43—24no—
52C2×C8×D43D412yes—
53#13063305—22no—
54#13063305—41no—
55#13063300—22no—
56#13063300—41no—
57#13063299—42no—
58#13063265—21no—
59#13063265C2312yes—
60C2×C43⋊C16—21no—
61#13063261—21no—
62#13063261C2312yes—
63#13063260—24no—
64#13063248—22no—
65#13063245—22no—
66C2×M16×C43—21no—
67C22×C8×C43C2311yescharacteristic
68C2×C4⋊C4×C43—21no—
69M32×C43—21no—
70M32×C43C2312yes—
71C2×C16×C43—21no—
72#108×C43—21no—
73#108×C43C2312yes—
74#106×C43—21no—
75#106×C43C2312yes—
76C22×C4×C43—41no—
77C22×C4×C43C2×D411yescharacteristic
78C2×C22⋊D43—41no—
79C2×C22⋊D43SD1612yes—
80#10621898—21no—
81#10621898—21no—
82#10621898—21no—
83#10621898—21no—
84#10621898—41no—
85#10621898—41no—
86#10621898—41no—
87#10621898—41no—
88C2×D172—21no—
89C2×D172—42no—
90C2×D172SD1611yescharacteristic
91C2×C4×D43—41no—
92C2×C4×D43C2×D412yes—
93C2×Dic86—21no—
94C2×Dic86SD1611yescharacteristic
95M16×C43—22no—
96M16×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43#4111yescharacteristic
100C2×C8×C43#4111yescharacteristic
101C2×C8×C43#4111yescharacteristic
102C2×C8×C43#4111yescharacteristic
103C2×C8×C43C2411yescharacteristic
104C4⋊C4×C43—22no—
105C4⋊C4×C43—41no—
106(C2×D43)⋊C4—42no—
107(C2×D43)⋊C4—42no—
108C4⋊Dic43—42no—
109#10621877—21no—
110#10621877—21no—
111#10621877—22no—
112#10621877—41no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8C2×D412yes—
115Dic172—21no—
116Dic172—21no—
117D344—21no—
118D344—21no—
119#10621873—41no—
120#10621873—41no—
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×C43C2×SD1611yescharacteristic
130C22×D43—41no—
131C22×D43C2×SD1612yes—
132C2×C4×C43—42no—
133C2×C4×C43—161no—
134C2×C4×C43#12311yescharacteristic
135C2×C4×C43#12311yescharacteristic
136C2×C4×C43C2×SD1611yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C43C22×D411yescharacteristic
140C22⋊D43—22no—
141C22⋊D43—22no—
142C22⋊D43—81no—
143C22⋊D43—81no—
144C2×Dic43—41no—
145C2×Dic43C2×SD1612yes—
146D172—21no—
147D172—21no—
148D172—41no—
149D172—41no—
150D172—162no—
151C4×D43—22no—
152C4×D43—22no—
153C4×D43—81no—
154C4×D43—81no—
155Dic86—21no—
156Dic86—21no—
157Dic86—41no—
158Dic86—41no—
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#48111yescharacteristic
169C22×C43#48111yescharacteristic
170C22×C43C22×SD1611yescharacteristic
171C2×D43—22no—
172C2×D43—42no—
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C4×C43—82no—
177C4×C43#48111yescharacteristic
178C4×C43#48111yescharacteristic
179C4×C43C2×#12311yescharacteristic
180C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
181Dic43—22no—
182Dic43—81no—
183#3060—431no—
184#2916—431no—
185#2239—434no—
186#2238—434no—
187C2×#365—431no—
188C2×#365D4311yescharacteristic, complemented
189#2148—431no—
190#2148—431no—
191#2115—431no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43—21no—
195C2×C43C2×#48111yescharacteristic
196D43—42no—
197D43—161no—
198C2×#135—431no—
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×#106C2×D4311yescharacteristic
213#417—861no—
214#365—434no—
215#365C2×D4314yes—
216#362—432no—
217#362—432no—
218#361—432no—
219#361—432no—
220#349—434no—
221C43#3365911yescharacteristic, complemented, Sylow
222C2×#41—431no—
223C2×#41—861no—
224#135—861no—
225#135—861no—
226#135—861no—
227#135—861no—
228C2×Q16—431no—
229C2×SD16—861no—
230C2×D8—431no—
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—21no—
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—21no—
262#106C22×D4312yes—
263#103—862no—
264#102—862no—
265#41—861no—
266#41—861no—
267#41—861no—
268#41—861no—
269#41—1721no—
270#41—1721no—
271#41—1721no—
272#41—1721no—
273C2×Q8—431no—
274C2×Q8—861no—
275C2×D4—432no—
276C2×D4—431no—
277C2×D4—861no—
278C2×D4—1722no—
279C2×D4—1721no—
280C22×C4—41no—
281C22×C4—432no—
282C22×C4—1721no—
283C22×C4D4×D4311yescharacteristic
284Q16—861no—
285Q16—861no—
286SD16—1721no—
287SD16—1721no—
288D8—861no—
289D8—861no—
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#1062190211yescharacteristic
309C2×C8#1062190211yescharacteristic
310C2×C8C23×D4311yescharacteristic
311C4⋊C4—22no—
312C4⋊C4—41no—
313C4⋊C4—1722no—
314C22⋊C4—1722no—
315C22⋊C4—1722no—
316C16—22no—
317C16—862no—
318C23—432no—
319C23—1721no—
320C23SD16×D4311yescharacteristic
321Q8—861no—
322Q8—861no—
323Q8—1721no—
324Q8—1721no—
325D4—862no—
326D4—862no—
327D4—861no—
328D4—861no—
329D4—3441no—
330D4—3441no—
331D4—1721no—
332D4—1721no—
333D4—6882no—
334C2×C4—42no—
335C2×C4—161no—
336C2×C4—432no—
337C2×C4—862no—
338C2×C4—862no—
339C2×C4—3441no—
340C2×C4—3441no—
341C2×C4—1721no—
342C2×C4#1306331011yescharacteristic
343C2×C4#1306331011yescharacteristic
344C2×C4SD16×D4311yescharacteristic
345C2×C4#1306335211yescharacteristic
346C2×C4#1306335211yescharacteristic
347C2×C4C2×D4×D4311yescharacteristic
348C8—42no—
349C8—862no—
350C8—1722no—
351C8#1306331011yescharacteristic
352C8#1306331011yescharacteristic
353C8C2×#1062189811yescharacteristic
354C8C2×#1062190211yescharacteristic
355C22—41no—
356C22—862no—
357C22—3441no—
358C22—3441no—
359C22—3441no—
360C22—1722no—
361C22#1458321911yescharacteristic
362C22#1458321911yescharacteristic
363C22C2×SD16×D4311yescharacteristic
364C4—82no—
365C4—862no—
366C4—3441no—
367C4#1458321911yescharacteristic
368C4#1458321911yescharacteristic
369C4C2×#1306331011yescharacteristic
370C4C2×#1306335211yescharacteristic
371C2—21no—
372C2—21no—
373C2—21no—
374C2—1722no—
375C2—6881no—
376C2C2×#1458321911yescharacteristic
subgroupG/H
centerC2C2×#14583219
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#365C2
socleC2×C43C2×#481
prime radical#19144258C2
hypercenterC2×#365D43
hypocenterC43#33659
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

Complements

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

NH ≅ G/Ntype
2. #19143203C2semidirect
3. #19136816C2semidirect
4. #19136811C2semidirect
5. C2×#14582721C2semidirect
6. #19136345C2semidirect
7. #19136342C2semidirect
8. #19136215C2semidirect
9. C2×C43×#365C2semidirect
188. C2×#365D43semidirect
221. C43#33659semidirect

Maximal subgroups

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

subgroupindex
#191442582
#191432032
#191368162
#191368112
C2×#145827212
#191363452
#191363422
#191362152
C2×C43×#3652
#3365943