Finite Group Databasebeta

← #25065166

Subgroups — #25065166

Order 11008.

1230 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583447C211yesmaximal, characteristic
2#19143225C212yesmaximal, complemented
3#19133327C214yesmaximal, complemented
4#19133320C212yesmaximal, complemented
5#19133309C211yesmaximal, characteristic, complemented
6#19133254C214yesmaximal, complemented
7C43×#1555C211yesmaximal, characteristic, complemented
8C22×#10621900C412yes—
9#14583447—22no—
10#14583447—22no—
11#14583447C412yes—
12#14583447C412yes—
13#14583447C2212yes—
14#14583447C2212yes—
15C2×#13063325C2211yescharacteristic
16C2×#13063312C412yes—
17C2×#13063296—22no—
18C2×D4×Dic43—22no—
19C2×C42×D43C2211yescharacteristic
20#14582956C2212yes—
21#14582954—22no—
22#14582951C2214yescomplemented
23#14582949—22no—
24#14582921C2214yescomplemented
25#14582861—22no—
26#14582851—22no—
27#14582647C2218yescomplemented
28#14582643C2214yescomplemented
29C2×#127×C43C2211yescharacteristic
30C43×#432C2212yes—
31C43×#331C2214yescomplemented
32C2×#10621900—22no—
33C2×#10621900—22no—
34C2×#10621900—48no—
35C2×#10621900C2×C414yes—
36C2×#10621900C2×C414yes—
37C22×Dic86C2×C412yes—
38C22×C22⋊D43—22no—
39C23×Dic43—22no—
40C22×C4×D43C2×C411yescharacteristic
41C22×C4×D43D412yes—
42C2×#10621872—24no—
43#13063325—22no—
44#13063325C2×C412yes—
45#13063325C2312yes—
46#13063312—24no—
47#13063312C2×C414yes—
48#13063312C2×C414yes—
49#13063296—24no—
50#13063296—24no—
51#13063296—24no—
52#13063296—24no—
53D4×Dic43—24no—
54D4×Dic43—24no—
55D4×Dic43—24no—
56D4×Dic43—24no—
57C2×C4⋊Dic43—22no—
58C2×C22⋊Dic43—24no—
59C2×C4×Dic43C2×C411yescharacteristic
60C2×C4×Dic43D412yes—
61C42×D43C2×C411yescharacteristic
62C42×D43C2×C411yescharacteristic
63C42×D43D412yes—
64C42×D43D412yes—
65C42×D43C2311yescharacteristic
66C42×D43C2311yescharacteristic
67C4⋊(C43⋊C8)C2314yes—
68Dic43⋊C8—24no—
69C22⋊(C43⋊C8)—22no—
70(C2×D43)⋊C8—24no—
71#13063236—22no—
72C8×Dic43—24no—
73C22×D4×C43—22no—
74C22×D4×C43C2×C412yes—
75#127×C43—22no—
76#127×C43C2×C412yes—
77#127×C43C2312yes—
78C2×C42×C43C2311yescharacteristic
79C4⋊C8×C43C2314yes—
80C22⋊C8×C43—22no—
81#97×C43—22no—
82C24×C43—22no—
83C23×D43C22⋊C411yescharacteristic
84C2×D4×C43—22no—
85C2×D4×C43—24no—
86C2×D4×C43—24no—
87C2×D4×C43—48no—
88C2×D4×C43—44no—
89C2×D4×C43C22×C414yes—
90C22×C4×C43C22×C411yescharacteristic
91C22×C4×C43C2×D412yes—
92C2×C22⋊D43—24no—
93C2×C22⋊D43—24no—
94C2×C22⋊D43—48no—
95C22×Dic43—24no—
96C22×Dic43—24no—
97C22×Dic43—22no—
98C22×Dic43—48no—
99C22×Dic43C22⋊C412yes—
100C22×Dic43C22⋊C411yescharacteristic
101#10621900—48no—
102#10621900—48no—
103#10621900—48no—
104#10621900—48no—
105C2×C4×D43—24no—
106C2×C4×D43—44no—
107C2×C4×D43C22⋊C411yescharacteristic
108C2×C4×D43C22⋊C411yescharacteristic
109C2×C4×D43C22⋊C412yes—
110C2×C4×D43C22⋊C412yes—
111C2×C4×D43C22×C411yescharacteristic
112C2×C4×D43C22×C411yescharacteristic
113C2×C4×D43C2×D412yes—
114C2×C4×D43C2×D412yes—
115C2×Dic86—22no—
116C2×Dic86—44no—
117C2×Dic86C22×C414yes—
118C2×C8×C43—24no—
119C42×C43C22×C411yescharacteristic
120C42×C43C2×D412yes—
121C42×C43C2411yescharacteristic
122C22⋊Dic43—28no—
123C22⋊Dic43—28no—
124C4⋊Dic43—24no—
125C4⋊Dic43—24no—
126C4×Dic43C22⋊C412yes—
127C4×Dic43C22⋊C412yes—
128C4×Dic43C22⋊C412yes—
129C4×Dic43C22×C411yescharacteristic
130C4×Dic43C22×C411yescharacteristic
131C4×Dic43C2×D412yes—
132C4×Dic43C2×D412yes—
133C2×C43⋊C8—24no—
134#10621872—48no—
135C23×C43—24no—
136C23×C43—48no—
137C23×C43—44no—
138C23×C43C2×C22⋊C411yescharacteristic
139C22×D43—22no—
140C22×D43—42no—
141C22×D43C2×C22⋊C411yescharacteristic
142C22×D43C2×C22⋊C411yescharacteristic
143D4×C43—44no—
144D4×C43—44no—
145D4×C43—48no—
146D4×C43—48no—
147C2×C4×C43—22no—
148C2×C4×C43—24no—
149C2×C4×C43C2×C22⋊C412yes—
150C2×C4×C43C2×C22⋊C411yescharacteristic
151C2×C4×C43C23×C411yescharacteristic
152C2×C4×C43C22×D412yes—
153C22⋊D43—48no—
154C22⋊D43—48no—
155C2×Dic43—24no—
156C2×Dic43—42no—
157C2×Dic43—44no—
158C2×Dic43—48no—
159C2×Dic43—48no—
160C2×Dic43#10014yes—
161C2×Dic43C2×C22⋊C412yes—
162C2×Dic43C2×C22⋊C412yes—
163C2×Dic43C2×C22⋊C411yescharacteristic
164C2×Dic43C2×C22⋊C411yescharacteristic
165C4×D43—24no—
166C4×D43—24no—
167C4×D43—22no—
168C4×D43—22no—
169C4×D43—22no—
170C4×D43—22no—
171C4×D43—42no—
172C4×D43—42no—
173Dic86—44no—
174Dic86—44no—
175C8×C43—44no—
176C43⋊C8—44no—
177#17738—431nomaximal, Sylow
178C22×C43—22no—
179C22×C43—44no—
180C22×C43—48no—
181C22×C43—88no—
182C22×C43C2×#10012yes—
183C22×C43C22×C22⋊C411yescharacteristic
184C2×D43—21no—
185C2×D43—21no—
186C2×D43—22no—
187C2×D43—22no—
188C2×D43—44no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—22no—
192C4×C43#57514yes—
193Dic43—22no—
194Dic43—22no—
195Dic43—44no—
196Dic43C2×#10012yes—
197Dic43C2×#10012yes—
198C2×#532—431no—
199#2920—432no—
200#1560—434no—
201#1558—432no—
202#1555—431no—
203#1555D4311yescharacteristic, complemented
204#1543—434no—
205C2×C43—22no—
206C2×C43—84no—
207C2×C43C22×#10011yescharacteristic
208C2×C43#289612yes—
209D43—41no—
210D43—41no—
211C22×#41—432no—
212#532—432no—
213#532—432no—
214#532—432no—
215#532—432no—
216#532—862no—
217#532—862no—
218C2×C4⋊Q8—431no—
219C2×#127C2×D4311yescharacteristic
220C2×#124—432no—
221C2×#121—862no—
222C2×C4×D4—862no—
223C22×C42—431no—
224#432—432no—
225#432—862no—
226#432C2×D4312yes—
227#431—434no—
228#431—862no—
229#423—434no—
230#407—862no—
231C4×M16—862no—
232#333—438no—
233#331—434no—
234#331C2×D4314yescomplemented
235C43#1773811yescharacteristic, complemented, Sylow
236C2×#41—434no—
237C2×#41—434no—
238C2×#41—862no—
239C2×#41—862no—
240C2×#41—1728no—
241C22×Q8—432no—
242C22×D4—22no—
243C22×D4—862no—
244C22×D4C4×D4312yes—
245C23×C4—431no—
246C23×C4—432no—
247C23×C4—862no—
248C2×M16—864no—
249C4⋊Q8—432no—
250C4⋊Q8—432no—
251C4⋊Q8—862no—
252#127—22no—
253#127C4×D4312yes—
254#127C22×D4312yes—
255#124—434no—
256#124—434no—
257#124—864no—
258#121—864no—
259#121—864no—
260#121—864no—
261#121—864no—
262C4×D4—864no—
263C4×D4—864no—
264C4×D4—864no—
265C4×D4—864no—
266C2×C4⋊C4—862no—
267C2×C22⋊C4—864no—
268C2×C42—431no—
269C2×C42—432no—
270C2×C42—431no—
271C2×C42—431no—
272C2×C42—432no—
273C2×C42—432no—
274C2×C42—431no—
275C2×C42—431no—
276C2×C42C22×D4311yescharacteristic
277C4⋊C8—434no—
278C4⋊C8—864no—
279C4⋊C8C22×D4314yes—
280C22⋊C8—22no—
281C22⋊C8—864no—
282C22⋊C8—862no—
283#97—22no—
284#97—862no—
285C4×C8—864no—
286C24—22no—
287C24—431no—
288#41—1728no—
289#41—1728no—
290#41—1728no—
291#41—1728no—
292C2×Q8—434no—
293C2×Q8—862no—
294C2×Q8—1724no—
295C2×D4—24no—
296C2×D4—22no—
297C2×D4—24no—
298C2×D4—44no—
299C2×D4—48no—
300C2×D4—864no—
301C2×D4—864no—
302C2×D4—1728no—
303C2×D4C2×C4×D4314yes—
304C22×C4—431no—
305C22×C4—432no—
306C22×C4—431no—
307C22×C4—431no—
308C22×C4—431no—
309C22×C4—431no—
310C22×C4—432no—
311C22×C4—432no—
312C22×C4—432no—
313C22×C4—432no—
314C22×C4—864no—
315C22×C4—864no—
316C22×C4—864no—
317C22×C4—862no—
318C22×C4—1724no—
319C22×C4—1728no—
320C22×C4C2×C4×D4311yescharacteristic
321C22×C4D4×D4312yes—
322M16—1728no—
323C2×C8—24no—
324C2×C8—864no—
325C4⋊C4—864no—
326C4⋊C4—864no—
327C22⋊C4—868no—
328C22⋊C4—868no—
329C42—432no—
330C42—432no—
331C42—432no—
332C42—431no—
333C42—431no—
334C42—432no—
335C42—432no—
336C42C2×C4×D4311yescharacteristic
337C42D4×D4312yes—
338C42C23×D4311yescharacteristic
339C23—24no—
340C23—48no—
341C23—44no—
342C23—431no—
343C23—431no—
344C23—862no—
345C23—1722no—
346C23C22⋊C4×D4311yescharacteristic
347Q8—1724no—
348Q8—1724no—
349D4—44no—
350D4—44no—
351D4—48no—
352D4—48no—
353D4—1728no—
354D4—1728no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—431no—
358C2×C4—431no—
359C2×C4—434no—
360C2×C4—432no—
361C2×C4—432no—
362C2×C4—862no—
363C2×C4—862no—
364C2×C4—862no—
365C2×C4—862no—
366C2×C4—864no—
367C2×C4—864no—
368C2×C4—864no—
369C2×C4—1722no—
370C2×C4—1722no—
371C2×C4—1728no—
372C2×C4—1728no—
373C2×C4—1722no—
374C2×C4—1724no—
375C2×C4C22⋊C4×D4312yes—
376C2×C4C22⋊C4×D4311yescharacteristic
377C2×C4C22×C4×D4311yescharacteristic
378C2×C4C2×D4×D4312yes—
379C8—44no—
380C8—1724no—
381C22—22no—
382C22—44no—
383C22—48no—
384C22—88no—
385C22—861no—
386C22—861no—
387C22—862no—
388C22—862no—
389C22—1724no—
390C22#100×D4312yes—
391C22C2×C22⋊C4×D4311yescharacteristic
392C4—21no—
393C4—21no—
394C4—22no—
395C4—432no—
396C4—432no—
397C4—862no—
398C4—862no—
399C4—1724no—
400C4#1458369514yes—
401C2—22no—
402C2—84no—
403C2—1721no—
404C2—1721no—
405C2C2×#100×D4311yescharacteristic
406C2#1914310912yes—
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1555C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583447C2
cosocleC42×C43C24
hypercenter#1555D43
hypocenterC43#17738
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

Complements

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

NH ≅ G/Ntype
2. #19143225C2semidirect
3. #19133327C2semidirect
4. #19133320C2semidirect
5. #19133309C2semidirect
6. #19133254C2semidirect
7. C43×#1555C2semidirect
22. #14582951C22semidirect
24. #14582921C22semidirect
27. #14582647C22semidirect
28. #14582643C22semidirect
31. C43×#331C22semidirect
203. #1555D43semidirect
234. #331C2×D43semidirect
235. C43#17738semidirect

Maximal subgroups

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

subgroupindex
C2×#145834472
#191432252
#191333272
#191333202
#191333092
#191332542
C43×#15552
#1773843