Finite Group Databasebeta

← #25965924

Subgroups — #25965924

Order 11008.

2014 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583475C211yesmaximal, characteristic
2#19144984C214yesmaximal, complemented
3#19144977C214yesmaximal, complemented
4#19144965C2116yesmaximal, complemented
5#19143112C212yesmaximal
6C2×#14582907C212yesmaximal, complemented
7#19143014C211yesmaximal, characteristic, complemented
8C43×#3458C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C23×Dic86C2211yescharacteristic
11C22×#10621877C2212yes—
12#14583475—24no—
13#14583475C2218yes—
14C2×#13063325C2212yes—
15C2×#13063313C2212yes—
16C2×#13063309—22no—
17C2×#13063305—22no—
18#14583269C22116yescomplemented
19#14583261C22116yescomplemented
20#14583256C22116yescomplemented
21#14583251C22116yescomplemented
22#14582907C2214yes—
23#14582907C2218yes—
24#14582907C2218yescomplemented
25#14582903C2214yes—
26#14582898C2218yes—
27#14582893C2218yes—
28C2×#13063248C2218yescomplemented
29#14582855C2218yescomplemented
30C4×#10621877C2214yes—
31C43×#544—22no—
32C43×#544C2218yescomplemented
33C43×#543—22no—
34C43×#533—24no—
35C43×#533C2214yes—
36C2×#117×C43C2212yes—
37C2×#117×C43C2211yescharacteristic
38C2×#10621898—22no—
39C2×#10621898—28no—
40C2×#10621898C2314yes—
41C22×Dic86—28no—
42C22×Dic86—21no—
43C22×Dic86—22no—
44C22×Dic86C2314yes—
45C22×Dic86C2312yes—
46C22×Dic86C2311yescharacteristic
47C22×D172C2311yescharacteristic
48C22×C22⋊D43—21no—
49C23×Dic43—21no—
50C22×C4×D43—21no—
51C2×#10621877—28no—
52C2×#10621877C2314yes—
53C2×#10621877C2314yes—
54C22×C43⋊C8C2314yes—
55#13063325—24no—
56#13063325C2318yes—
57#13063313—24no—
58#13063313C2318yes—
59#13063309—216no—
60#13063305—216no—
61C2×C4⋊Dic43—24no—
62C2×(C2×D43)⋊C4—24no—
63#13063248C23132yes—
64#13063248C23116yes—
65#13063245C23116yes—
66#13063236C2318yes—
67C4×C43⋊C8C2318yes—
68C23×C4×C43C2311yescharacteristic
69C4⋊Q8×C43—28no—
70C4⋊Q8×C43C2318yes—
71#125×C43—28no—
72#125×C43C2318yes—
73C22⋊Q8×C43—28no—
74C22⋊Q8×C43—216no—
75C4×Q8×C43—28no—
76#117×C43—22no—
77#117×C43—22no—
78#117×C43D414yes—
79#117×C43C2314yes—
80#117×C43C2314yes—
81#117×C43C2314yes—
82C2×C4⋊C4×C43D412yes—
83C2×C4⋊C4×C43C2314yes—
84C2×C22⋊C4×C43—22no—
85C2×C22⋊C4×C43D412yes—
86C2×C42×C43—22no—
87C2×C42×C43C2312yes—
88C24×C43C2×D411yescharacteristic
89C23×D43—21no—
90C2×Q8×C43—28no—
91C22×C4×C43—24no—
92C22×C4×C43C2×D414yes—
93C22×C4×C43C2×D412yes—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43#4118yes—
96C22×C4×C43C2411yescharacteristic
97C22×C4×C43C2412yes—
98C2×C22⋊D43—24no—
99C2×C22⋊D43—44no—
100C22×Dic43—22no—
101C22×Dic43—21no—
102C22×Dic43—24no—
103C22×Dic43—44no—
104#10621898—28no—
105#10621898—28no—
106#10621898—48no—
107C2×D172—21no—
108C2×D172—24no—
109C2×D172C2412yes—
110C2×C4×D43—24no—
111C2×C4×D43—44no—
112C2×Dic86—28no—
113C2×Dic86—28no—
114C2×Dic86—28no—
115C2×Dic86—24no—
116C2×Dic86—24no—
117C2×Dic86—22no—
118C2×Dic86—21no—
119C2×Dic86—44no—
120C2×Dic86—48no—
121C2×Dic86C2414yes—
122C2×Dic86C2412yes—
123C4⋊C4×C43—24no—
124C4⋊C4×C43—28no—
125C4⋊C4×C43—216no—
126C4⋊C4×C43C2×D418yes—
127C4⋊C4×C43C2418yes—
128C22⋊C4×C43—24no—
129C22⋊C4×C43—24no—
130C22⋊C4×C43C2×D418yes—
131C42×C43—24no—
132C42×C43—24no—
133C42×C43C2×D414yes—
134C42×C43C2414yes—
135(C2×D43)⋊C4—216no—
136C4⋊Dic43—216no—
137#10621877—28no—
138#10621877—28no—
139C2×C43⋊C8—28no—
140C2×C43⋊C8C2418yes—
141C23×C43—42no—
142C23×C43#12414yes—
143C23×C43C22×D411yescharacteristic
144C23×C43C22×D412yes—
145C22×D43—22no—
146C22×D43—44no—
147C22×D43—42no—
148Q8×C43—88no—
149C2×C4×C43—28no—
150C2×C4×C43—44no—
151C2×C4×C43—84no—
152C2×C4×C43#12414yes—
153C2×C4×C43#12418yes—
154C2×C4×C43C22×D418yes—
155C2×C4×C43C22×D411yescharacteristic
156C2×C4×C43C22×D412yes—
157C2×C4×C43C2×#4114yes—
158C2×C4×C43C2×#4114yes—
159C2×C4×C43C2×#4114yes—
160C2×C4×C43C2511yescharacteristic
161C22⋊D43—48no—
162C2×Dic43—22no—
163C2×Dic43—24no—
164C2×Dic43—44no—
165C2×Dic43—48no—
166C2×Dic43—42no—
167D172—24no—
168D172—42no—
169C4×D43—48no—
170Dic86—28no—
171Dic86—24no—
172Dic86—44no—
173Dic86—48no—
174Dic86—42no—
175C43⋊C8—28no—
176#60620—431nomaximal, Sylow
177C22×C43—22no—
178C22×C43—24no—
179C22×C43—44no—
180C22×C43C2×#12412yes—
181C22×C43C2×#12414yes—
182C22×C43C23×D411yescharacteristic
183C2×D43—44no—
184C2×D43—42no—
185C2×D43—84no—
186C4×C43—28no—
187C4×C43—48no—
188C4×C43C2×#12412yes—
189C4×C43C2×#12414yes—
190C4×C43C22×#4112yes—
191Dic43—44no—
192Dic43—42no—
193#3458D4311yescharacteristic, complemented
194C2×#536—431no—
195#3140—434no—
196#3139—434no—
197#3137—4316no—
198#2896—432no—
199C2×#419—432no—
200#2873—431no—
201C2×C43—22no—
202C2×C43—24no—
203C2×C43C22×#12411yescharacteristic
204C2×C43#358612yes—
205D43—82no—
206C22×#41—431no—
207C23×Q8—431no—
208C22×M16—432no—
209#544—22no—
210#544C2×D4318yescomplemented
211#543—22no—
212#536—438no—
213#536—864no—
214#533—24no—
215#533C2×D4314yes—
216C2×C4⋊Q8—432no—
217C2×#124—432no—
218C2×#123—862no—
219C2×C22⋊Q8—862no—
220C2×#117C2×D4312yes—
221C2×#117C2×D4311yescharacteristic
222#491—4316no—
223#489—4316no—
224#488—4316no—
225#487—4316no—
226#419—438no—
227#419—434no—
228#419—438no—
229#418—434no—
230#417—438no—
231#416—438no—
232C2×#103—438no—
233#405—438no—
234C4×M16—434no—
235C43#6062011yescharacteristic, complemented, Sylow
236C2×#41—434no—
237C2×#41—862no—
238C2×#41—868no—
239C22×Q8—432no—
240C22×Q8—431no—
241C22×Q8—434no—
242C22×Q8—861no—
243C22×Q8—862no—
244C22×Q8—868no—
245C22×D4—431no—
246C22×D4—861no—
247C23×C4—861no—
248C23×C4—861no—
249C23×C4C22×D4311yescharacteristic
250C2×M16—434no—
251C2×M16—434no—
252C2×M16—868no—
253C22×C8—434no—
254C4⋊Q8—28no—
255C4⋊Q8—438no—
256C4⋊Q8—864no—
257C4⋊Q8C22×D4318yes—
258#125—28no—
259#125C22×D4318yes—
260#124—438no—
261#124—864no—
262#123—8616no—
263C22⋊Q8—28no—
264C22⋊Q8—216no—
265C22⋊Q8—8616no—
266C4×Q8—28no—
267#117—22no—
268#117—22no—
269#117C22⋊D4314yes—
270#117C22×D4314yes—
271#117C22×D4314yes—
272#117C22×D4314yes—
273C2×C4⋊C4—864no—
274C2×C4⋊C4C22⋊D4312yes—
275C2×C4⋊C4C22×D4314yes—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—864no—
278C2×C22⋊C4C22⋊D4312yes—
279C2×C42—22no—
280C2×C42C22×D4312yes—
281#103—4332no—
282#103—4316no—
283#102—4316no—
284#97—438no—
285C4×C8—438no—
286C24—861no—
287C24C2×C22⋊D4311yescharacteristic
288#41—868no—
289#41—868no—
290#41—1728no—
291C2×Q8—28no—
292C2×Q8—434no—
293C2×Q8—432no—
294C2×Q8—864no—
295C2×Q8—862no—
296C2×Q8—861no—
297C2×Q8—868no—
298C2×Q8—868no—
299C2×Q8—868no—
300C2×Q8—864no—
301C2×Q8—1724no—
302C2×Q8—1728no—
303C2×D4—432no—
304C2×D4—864no—
305C2×D4—861no—
306C2×D4—864no—
307C2×D4—1724no—
308C22×C4—24no—
309C22×C4—862no—
310C22×C4—861no—
311C22×C4—864no—
312C22×C4—864no—
313C22×C4—1724no—
314C22×C4—1724no—
315C22×C4#1062190218yes—
316C22×C4C2×C22⋊D4314yes—
317C22×C4C2×C22⋊D4312yes—
318C22×C4C2×C22⋊D4311yescharacteristic
319C22×C4C23×D4311yescharacteristic
320C22×C4C23×D4312yes—
321M16—868no—
322M16—868no—
323C2×C8—438no—
324C2×C8—868no—
325C4⋊C4—24no—
326C4⋊C4—28no—
327C4⋊C4—216no—
328C4⋊C4—8616no—
329C4⋊C4C2×C22⋊D4318yes—
330C4⋊C4C23×D4318yes—
331C22⋊C4—24no—
332C22⋊C4—24no—
333C22⋊C4—8616no—
334C22⋊C4C2×C22⋊D4318yes—
335C42—24no—
336C42—24no—
337C42C2×C22⋊D4314yes—
338C42C23×D4314yes—
339C23—42no—
340C23—862no—
341C23—1724no—
342C23—1722no—
343C23#1306331414yes—
344C23C22×C22⋊D4311yescharacteristic
345C23C22×C22⋊D4312yes—
346Q8—88no—
347Q8—868no—
348Q8—864no—
349Q8—1728no—
350Q8—1724no—
351Q8—1722no—
352D4—864no—
353D4—1728no—
354D4—1722no—
355C2×C4—28no—
356C2×C4—44no—
357C2×C4—84no—
358C2×C4—864no—
359C2×C4—862no—
360C2×C4—1722no—
361C2×C4—1724no—
362C2×C4—1728no—
363C2×C4—1728no—
364C2×C4#1306331414yes—
365C2×C4#1306331418yes—
366C2×C4C22×C22⋊D4318yes—
367C2×C4C22×C22⋊D4311yescharacteristic
368C2×C4C22×C22⋊D4312yes—
369C2×C4C2×#1062190214yes—
370C2×C4C2×#1062190214yes—
371C2×C4C2×#1062190214yes—
372C2×C4C24×D4311yescharacteristic
373C8—868no—
374C22—22no—
375C22—24no—
376C22—44no—
377C22—3444no—
378C22—1722no—
379C22—1724no—
380C22C2×#1306331412yes—
381C22C2×#1306331414yes—
382C22C23×C22⋊D4311yescharacteristic
383C4—28no—
384C4—48no—
385C4—1722no—
386C4—1724no—
387C4C2×#1306331414yes—
388C4C2×#1306331412yes—
389C4C22×#1062190212yes—
390C2—22no—
391C2—24no—
392C2—3442no—
393C2C22×#1306331411yescharacteristic
394C2#1914938112yes—
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3458C2
socleC22×C43C23×D4
prime radicalC22×#10621898C22
hypercenter#3458D43
hypocenterC43#60620
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3458

Complements

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

NH ≅ G/Ntype
2. #19144984C2semidirect
3. #19144977C2semidirect
4. #19144965C2semidirect
6. C2×#14582907C2semidirect
7. #19143014C2semidirect
8. C43×#3458C2semidirect
18. #14583269C22semidirect
19. #14583261C22semidirect
20. #14583256C22semidirect
21. #14583251C22semidirect
24. #14582907C22semidirect
28. C2×#13063248C22semidirect
29. #14582855C22semidirect
32. C43×#544C22semidirect
193. #3458D43semidirect
210. #544C2×D43semidirect
235. C43#60620semidirect

Maximal subgroups

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

subgroupindex
C2×#145834752
#191449842
#191449772
#191449652
#191431122
C2×#145829072
#191430142
C43×#34582
#6062043