Finite Group Databasebeta

← #25100271

Subgroups — #25100271

Order 11008.

1638 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583447C211yesmaximal, characteristic
2C2×#14582897C214yesmaximal, complemented
3C2×#14582851C211yesmaximal, characteristic, complemented
4#382×D43C211yesmaximal, characteristic, complemented
5#19135420C211yesmaximal, characteristic, complemented
6#19135415C211yesmaximal, characteristic, complemented
7#19135414C211yesmaximal, characteristic, complemented
8#19135405C214yesmaximal, complemented
9C43×#1961C211yesmaximal, characteristic, complemented
10C22×#10621900C2212yes—
11C22×#10621872C2212yes—
12#14583447—24no—
13#14583447C418yescomplemented
14C2×#13063325C2211yescharacteristic
15C2×#13063312C2212yes—
16C2×#13063296—22no—
17C2×D4×Dic43—22no—
18C2×C4⋊C4×D43C2212yes—
19C2×C42×D43C2211yescharacteristic
20#14582897—216no—
21C2×#13063250C2214yes—
22C2×#13063248C2214yes—
23C2×#13063246C2214yes—
24#14582851—24no—
25C2×#13063236C2211yescharacteristic
26C2×C8×Dic43C2212yes—
27#14582765C2211yescharacteristic
28#14582764C2212yes—
29#14582763—22no—
30#95×D43—22no—
31C2×#127×C43C2211yescharacteristic
32C2×#102×C43C2214yes—
33C2×#97×C43C2211yescharacteristic
34C43×#382C2211yescharacteristic
35C2×#10621900—28no—
36C2×#10621900—24no—
37C2×#10621900—28no—
38C2×#10621900C2×C418yes—
39C22×Dic86C2312yes—
40C22×C22⋊D43—22no—
41C23×Dic43—22no—
42C22×C4×D43—22no—
43C22×C4×D43D412yes—
44C22×C4×D43C2311yescharacteristic
45C2×#10621872—24no—
46C2×#10621872—24no—
47C2×#10621872D418yescomplemented
48C22×C43⋊C8C2312yes—
49#13063325—22no—
50#13063325C2×C414yescomplemented
51#13063312—24no—
52#13063312C2×C418yescomplemented
53#13063296—216no—
54D4×Dic43—216no—
55C2×C4⋊Dic43—22no—
56C2×C4⋊Dic43C2312yes—
57C2×Dic43⋊C4—22no—
58C4⋊C4×D43—28no—
59C2×C22⋊Dic43—24no—
60C2×C4×Dic43D412yes—
61C2×C4×Dic43C2311yescharacteristic
62C42×D43C2×C414yes—
63C42×D43D414yes—
64#13063250—28no—
65#13063248—28no—
66#13063246—28no—
67#13063236—22no—
68C8×Dic43—24no—
69C43⋊#95—22no—
70C43⋊#95—24no—
71C22×D4×C43—22no—
72C22×D4×C43C2312yes—
73C22×C8×C43C2312yes—
74#127×C43—22no—
75#127×C43C2×C414yescomplemented
76C2×C4⋊C4×C43C2312yes—
77C2×C42×C43C2311yescharacteristic
78#102×C43—28no—
79#97×C43—22no—
80#95×C43—22no—
81C24×C43—22no—
82C23×D43C2×D411yescharacteristic
83C2×D4×C43—28no—
84C2×D4×C43—22no—
85C2×D4×C43—24no—
86C2×D4×C43—24no—
87C2×D4×C43—48no—
88C2×D4×C43C22×C414yes—
89C22×C4×C43—22no—
90C22×C4×C43C2×D412yes—
91C22×C4×C43C2411yescharacteristic
92C2×C22⋊D43—28no—
93C2×C22⋊D43—44no—
94C2×C22⋊D43—44no—
95C22×Dic43—28no—
96C22×Dic43—22no—
97C22×Dic43—22no—
98C22×Dic43—44no—
99C22×Dic43—44no—
100C22×Dic43C2×D412yes—
101C22×Dic43C2×D411yescharacteristic
102#10621900—232no—
103#10621900—416no—
104C2×C4×D43—44no—
105C2×C4×D43—48no—
106C2×C4×D43—44no—
107C2×C4×D43C22⋊C418yes—
108C2×C4×D43C22×C412yes—
109C2×C4×D43C2×D412yes—
110C2×C4×D43C2×D414yes—
111C2×C4×D43#4114yes—
112C2×Dic86—24no—
113C2×Dic86—24no—
114C2×Dic86—22no—
115C2×Dic86C22×C414yes—
116C2×C8×C43—22no—
117C2×C8×C43—22no—
118C2×C8×C43C2×D414yes—
119C4⋊C4×C43—24no—
120C42×C43C22×C412yes—
121C42×C43C2×D412yes—
122C22⋊Dic43—216no—
123C4⋊Dic43—28no—
124C4⋊Dic43—24no—
125Dic43⋊C4—44no—
126C4×Dic43C22⋊C418yes—
127C4×Dic43C22×C412yes—
128C4×Dic43C2×D412yes—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8C2×D414yes—
132#10621872—216no—
133C23×C43—24no—
134C23×C43—42no—
135C23×C43—42no—
136C23×C43—48no—
137C23×C43C22×D411yescharacteristic
138C22×D43—24no—
139C22×D43C2×C22⋊C412yes—
140C22×D43#12412yes—
141C22×D43#12712yes—
142D4×C43—28no—
143D4×C43—416no—
144D4×C43—44no—
145C2×C4×C43—24no—
146C2×C4×C43—42no—
147C2×C4×C43—44no—
148C2×C4×C43C2×C22⋊C414yes—
149C2×C4×C43C23×C411yescharacteristic
150C2×C4×C43C22×D412yes—
151C2×C4×C43C22×D411yescharacteristic
152C2×C4×C43C2×#4112yes—
153C22⋊D43—416no—
154C2×Dic43—24no—
155C2×Dic43—24no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—416no—
159C2×Dic43—42no—
160C2×Dic43—44no—
161C2×Dic43C2×C22⋊C414yes—
162C2×Dic43C2×C22⋊C412yes—
163C2×Dic43#12412yes—
164C2×Dic43#12712yes—
165C4×D43—48no—
166C4×D43—88no—
167C4×D43C4×D418yes—
168C4×D43#12118yes—
169Dic86—28no—
170Dic86—44no—
171C8×C43—24no—
172C43⋊C8—24no—
173#21201—431nomaximal, Sylow
174C22×C43—48no—
175C22×C43—44no—
176C22×C43—84no—
177C22×C43—84no—
178C22×C43C22×C22⋊C411yescharacteristic
179C22×C43C2×#12411yescharacteristic
180C22×C43C2×#12711yescharacteristic
181C22×C43#57514yes—
182C2×D43—24no—
183C2×D43—24no—
184C2×D43—24no—
185C2×D43#39014yes—
186C4×C43—24no—
187C4×C43—82no—
188C4×C43C2×C4×D412yes—
189C4×C43C2×#12112yes—
190Dic43—24no—
191Dic43—44no—
192Dic43—82no—
193Dic43#39014yes—
194C2×#532—431no—
195C2×#417—434no—
196C2×C4×M16—431no—
197C2×#382—431no—
198#1961—431no—
199#1961D4311yescharacteristic, complemented
200#1960—431no—
201#1960—431no—
202#1958—434no—
203C2×C43—84no—
204C2×C43C2×#39011yescharacteristic
205C2×C43#289612yes—
206C2×C43#314212yes—
207C2×C43#315312yes—
208D43—24no—
209C22×#41—432no—
210C22×M16—432no—
211#532—438no—
212#532—864no—
213C2×C4⋊Q8—431no—
214C2×#127C2×D4311yescharacteristic
215C2×#124—432no—
216C2×#121—862no—
217C2×C4×D4—862no—
218C22×C4⋊C4—432no—
219C22×C42—431no—
220#417—8616no—
221C2×#103—434no—
222C2×#103—434no—
223C2×#102—434no—
224C2×#102C2×D4314yes—
225C4×M16—864no—
226C2×#97—431no—
227C2×#97C2×D4311yescharacteristic
228C2×C4×C8—432no—
229#382—432no—
230#382—431no—
231#382—862no—
232#382C2×D4311yescharacteristic
233C2×#95—862no—
234C43#2120111yescharacteristic, complemented, Sylow
235C2×#41—438no—
236C2×#41—864no—
237C2×#41—868no—
238C2×#41—868no—
239C22×Q8—432no—
240C22×D4—22no—
241C22×D4—862no—
242C22×D4C22×D4312yes—
243C23×C4—431no—
244C23×C4—432no—
245C23×C4—862no—
246C23×C4—862no—
247C2×M16—438no—
248C2×M16—864no—
249C2×M16—864no—
250C22×C8—432no—
251C22×C8C22×D4312yes—
252C4⋊Q8—434no—
253C4⋊Q8—862no—
254#127—22no—
255#127C4×D4314yescomplemented
256#124—438no—
257#124—864no—
258#121—8616no—
259C4×D4—8616no—
260C2×C4⋊C4—432no—
261C2×C4⋊C4—868no—
262C2×C4⋊C4—862no—
263C2×C4⋊C4—862no—
264C2×C4⋊C4C22×D4312yes—
265C2×C22⋊C4—864no—
266C2×C42—432no—
267C2×C42—431no—
268C2×C42—434no—
269C2×C42—434no—
270C2×C42C22×D4311yescharacteristic
271#103—868no—
272#103—868no—
273#102—28no—
274#102—868no—
275#97—22no—
276#97—862no—
277C4×C8—864no—
278#95—22no—
279#95—864no—
280#95—862no—
281C24—22no—
282C24—431no—
283#41—8632no—
284#41—17216no—
285C2×Q8—434no—
286C2×Q8—862no—
287C2×Q8—864no—
288C2×Q8—864no—
289C2×D4—28no—
290C2×D4—24no—
291C2×D4—22no—
292C2×D4—24no—
293C2×D4—48no—
294C2×D4—868no—
295C2×D4—1724no—
296C2×D4—1724no—
297C2×D4C2×C4×D4314yes—
298C22×C4—22no—
299C22×C4—431no—
300C22×C4—432no—
301C22×C4—432no—
302C22×C4—434no—
303C22×C4—434no—
304C22×C4—432no—
305C22×C4—438no—
306C22×C4—868no—
307C22×C4—862no—
308C22×C4—862no—
309C22×C4—1724no—
310C22×C4—1724no—
311C22×C4—1728no—
312C22×C4—1724no—
313C22×C4—1724no—
314C22×C4D4×D4312yes—
315C22×C4C23×D4311yescharacteristic
316M16—8616no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—434no—
320C2×C8—862no—
321C2×C8—862no—
322C2×C8D4×D4314yes—
323C4⋊C4—24no—
324C4⋊C4—868no—
325C4⋊C4—864no—
326C4⋊C4—1724no—
327C22⋊C4—8616no—
328C42—438no—
329C42—432no—
330C42—432no—
331C42C2×C4×D4312yes—
332C42D4×D4312yes—
333C23—24no—
334C23—42no—
335C23—42no—
336C23—48no—
337C23—432no—
338C23—432no—
339C23—432no—
340C23—864no—
341C23C2×D4×D4311yescharacteristic
342Q8—868no—
343Q8—1724no—
344D4—28no—
345D4—416no—
346D4—44no—
347D4—17216no—
348C2×C4—24no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—432no—
352C2×C4—432no—
353C2×C4—432no—
354C2×C4—438no—
355C2×C4—438no—
356C2×C4—434no—
357C2×C4—864no—
358C2×C4—864no—
359C2×C4—3448no—
360C2×C4—1728no—
361C2×C4—17216no—
362C2×C4—1722no—
363C2×C4—1724no—
364C2×C4—1722no—
365C2×C4—1722no—
366C2×C4C22⋊C4×D4314yes—
367C2×C4C22×C4×D4311yescharacteristic
368C2×C4C2×D4×D4312yes—
369C2×C4C2×D4×D4311yescharacteristic
370C2×C4#41×D4312yes—
371C8—24no—
372C8—864no—
373C22—44no—
374C22—48no—
375C22—84no—
376C22—84no—
377C22—434no—
378C22—864no—
379C22—864no—
380C22—864no—
381C22C2×C22⋊C4×D4311yescharacteristic
382C22#124×D4311yescharacteristic
383C22#127×D4311yescharacteristic
384C22#1458369514yes—
385C4—24no—
386C4—82no—
387C4—434no—
388C4—864no—
389C4—3442no—
390C4—1724no—
391C4C4×D4×D4312yes—
392C4#121×D4312yes—
393C2—84no—
394C2—864no—
395C2#390×D4311yescharacteristic
396C2#1914310912yes—
397C2#1914499412yes—
398C2#1914506012yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1961C2
socleC23×C43C22×D4
prime radicalC2×#14583447C2
cosocleC22×C4×C43C24
hypercenter#1961D43
hypocenterC43#21201
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
2. C2×#14582897C2semidirect
3. C2×#14582851C2semidirect
4. #382×D43C2semidirect
5. #19135420C2semidirect
6. #19135415C2semidirect
7. #19135414C2semidirect
8. #19135405C2semidirect
9. C43×#1961C2semidirect
13. #14583447C4semidirect
47. C2×#10621872D4semidirect
50. #13063325C2×C4semidirect
52. #13063312C2×C4semidirect
75. #127×C43C2×C4semidirect
199. #1961D43semidirect
234. C43#21201semidirect
255. #127C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834472
C2×#145828972
C2×#145828512
#382×D432
#191354202
#191354152
#191354142
#191354052
C43×#19612
#2120143