Finite Group Databasebeta

← #25105930

Subgroups — #25105930

Order 11008.

1374 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583449C211yesmaximal, characteristic
2#19136993C211yesmaximal, characteristic, complemented
3#19135521C212yesmaximal, complemented
4#19135517C212yesmaximal, complemented
5#19135406C214yesmaximal, complemented
6#19134536C214yesmaximal, complemented
7C2×C43×#431C211yesmaximal, characteristic, complemented
8C22×#10621898C2212yes—
9#14583449—24no—
10#14583449C418yescomplemented
11C2×#13063325C2211yescharacteristic
12C2×#13063322C2211yescharacteristic
13C2×#13063313C2212yes—
14C2×#13063299—21no—
15C2×#13063299—21no—
16C2×C4×D172—21no—
17C2×C4×D172—21no—
18C2×#13063250C2218yes—
19C2×#13063247C2218yes—
20#14582767—21no—
21#14582765C2212yes—
22#14582762—21no—
23#14582759C2212yes—
24C4×C4⋊Dic43C2212yes—
25C4×C22⋊Dic43—21no—
26#14582745—21no—
27C22×C42×C43C2211yescharacteristic
28C43×#431—24no—
29C2×C4⋊C8×C43C2212yes—
30C2×C22⋊C8×C43C2212yes—
31C2×C4×C8×C43C2212yes—
32C2×#10621898—24no—
33C2×#10621898—48no—
34C2×#10621898C2×C418yes—
35C22×Dic86C2312yes—
36C22×D172—21no—
37C22×D172—21no—
38C22×D172C2312yes—
39C22×C22⋊D43—22no—
40C22×C4×D43—22no—
41#13063325—22no—
42#13063325C2×C414yes—
43#13063322—22no—
44#13063322C2×C414yes—
45#13063313—24no—
46#13063313C2×C418yes—
47#13063299—28no—
48#13063299—28no—
49C4×D172—28no—
50C4×D172—28no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43C2314yes—
54C2×C22⋊Dic43—22no—
55C2×(C2×D43)⋊C4—22no—
56C2×(C2×D43)⋊C4—22no—
57C2×C4×Dic43—22no—
58#13063250—48no—
59#13063247—48no—
60C43⋊#95—22no—
61C43⋊#95—22no—
62C43⋊#95—22no—
63C43⋊#95—22no—
64C23×C4×C43D411yescharacteristic
65C23×C4×C43D411yescharacteristic
66C23×C4×C43C2311yescharacteristic
67C22×C8×C43C2314yes—
68C2×C42×C43C2×C414yes—
69C2×C42×C43D411yescharacteristic
70C2×C42×C43D411yescharacteristic
71C2×C42×C43D414yes—
72C2×C42×C43C2311yescharacteristic
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43—24no—
75C22⋊C8×C43—24no—
76C4×C8×C43—24no—
77C24×C43C2×D411yescharacteristic
78C23×D43—22no—
79C22×C4×C43—24no—
80C22×C4×C43—24no—
81C22×C4×C43—42no—
82C22×C4×C43C22⋊C414yes—
83C22×C4×C43C22⋊C414yes—
84C22×C4×C43C22×C412yes—
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2411yescharacteristic
92C2×C22⋊D43—28no—
93C2×C22⋊D43—48no—
94C22×Dic43—22no—
95C22×Dic43—24no—
96#10621898—416no—
97#10621898—416no—
98C2×D172—24no—
99C2×D172—24no—
100C2×D172—22no—
101C2×D172—28no—
102C2×D172—44no—
103C2×D172—44no—
104C2×D172C22×C414yes—
105C2×C4×D43—28no—
106C2×C4×D43—48no—
107C2×Dic86—28no—
108C2×Dic86—22no—
109C2×Dic86C22×C414yes—
110C2×C8×C43—24no—
111C2×C8×C43—28no—
112C42×C43C22⋊C414yes—
113C42×C43C22⋊C414yes—
114C42×C43C22×C412yes—
115C42×C43C22×C412yes—
116C42×C43C2×D412yes—
117C42×C43C2×D412yes—
118C22⋊Dic43—44no—
119(C2×D43)⋊C4—28no—
120(C2×D43)⋊C4—28no—
121C4⋊Dic43—24no—
122C4⋊Dic43—24no—
123C4⋊Dic43—24no—
124C4⋊Dic43—24no—
125C4×Dic43—44no—
126C23×C43—22no—
127C23×C43—22no—
128C23×C43—22no—
129C23×C43C2×C22⋊C412yes—
130C23×C43C22×D411yescharacteristic
131C22×D43—24no—
132C22×D43—44no—
133C22×D43—44no—
134C22×D43—44no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—24no—
140C2×C4×C43—24no—
141C2×C4×C43—28no—
142C2×C4×C43—44no—
143C2×C4×C43C2×C22⋊C412yes—
144C2×C4×C43C2×C22⋊C412yes—
145C2×C4×C43C2×C22⋊C412yes—
146C2×C4×C43C2×C22⋊C412yes—
147C2×C4×C43C2×C22⋊C412yes—
148C2×C4×C43#13514yes—
149C2×C4×C43C23×C411yescharacteristic
150C2×C4×C43C22×D411yescharacteristic
151C2×C4×C43H(5,𝔽2)14yes—
152C22⋊D43—416no—
153C2×Dic43—24no—
154C2×Dic43—44no—
155C2×Dic43—44no—
156C2×Dic43—44no—
157C2×Dic43—44no—
158D172—28no—
159D172—48no—
160D172—44no—
161D172—48no—
162C4×D43—416no—
163Dic86—28no—
164Dic86—44no—
165C8×C43—44no—
166#21807—431nomaximal, Sylow
167C22×C43—22no—
168C22×C43—22no—
169C22×C43—22no—
170C22×C43—44no—
171C22×C43C22×C22⋊C411yescharacteristic
172C22×C43#53512yes—
173C22×C43C2×#13512yes—
174C22×C43#57512yes—
175C2×D43—44no—
176C2×D43—44no—
177C2×D43—44no—
178C2×D43—88no—
179C4×C43—22no—
180C4×C43—22no—
181C4×C43—22no—
182C4×C43—22no—
183C4×C43#41614yes—
184C4×C43#51812yes—
185C4×C43#53512yes—
186Dic43—44no—
187Dic43—84no—
188C2×#532—431no—
189C2×#431D4311yescharacteristic, complemented
190#2283—431no—
191#1982—432no—
192#1981—432no—
193#1958—434no—
194#1788—434no—
195C2×C43—42no—
196C2×C43#230911yescharacteristic
197C2×C43C2×#41611yescharacteristic
198C2×C43#289611yescharacteristic
199C2×C43#321214yes—
200D43—84no—
201C22×#41—432no—
202#532—438no—
203#532—864no—
204C2×C4⋊Q8—431no—
205C2×#127—431no—
206C2×#124—432no—
207C2×#121—861no—
208C2×#121—861no—
209C2×C4×D4—861no—
210C2×C4×D4—861no—
211C22×C42C2×D4311yescharacteristic
212#431—24no—
213C2×C4⋊C8C2×D4312yes—
214C2×#103—438no—
215C2×#102—438no—
216C2×C22⋊C8C2×D4312yes—
217C2×C4×C8C2×D4312yes—
218#383—861no—
219#382—432no—
220#381—861no—
221#380—432no—
222C4×C4⋊C4—432no—
223C4×C22⋊C4—861no—
224#376—861no—
225C43#2180711yescharacteristic, complemented, Sylow
226C2×#41—438no—
227C2×#41—864no—
228C2×#41—1728no—
229C22×Q8—432no—
230C22×D4—432no—
231C22×D4—862no—
232C22×D4—861no—
233C22×D4—861no—
234C23×C4—862no—
235C23×C4D17211yescharacteristic
236C23×C4D17211yescharacteristic
237C23×C4C22×D4311yescharacteristic
238C22×C8C22×D4314yes—
239C4⋊Q8—434no—
240C4⋊Q8—862no—
241#127—434no—
242#127—862no—
243#124—438no—
244#124—864no—
245#121—868no—
246#121—868no—
247C4×D4—868no—
248C4×D4—868no—
249C2×C4⋊C4—434no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4—861no—
252C2×C22⋊C4—862no—
253C2×C22⋊C4—862no—
254C2×C22⋊C4—862no—
255C2×C42—862no—
256C2×C42C4×D4314yes—
257C2×C42D17211yescharacteristic
258C2×C42D17211yescharacteristic
259C2×C42C22⋊D4314yes—
260C2×C42C22×D4311yescharacteristic
261C2×C42C22×D4311yescharacteristic
262C4⋊C8—24no—
263#103—1728no—
264#102—1728no—
265C22⋊C8—24no—
266C4×C8—24no—
267#95—862no—
268#95—862no—
269#95—862no—
270#95—862no—
271C24—862no—
272C24C2×D17211yescharacteristic
273#41—17216no—
274#41—17216no—
275C2×Q8—434no—
276C2×Q8—862no—
277C2×Q8—868no—
278C2×D4—434no—
279C2×D4—868no—
280C2×D4—864no—
281C2×D4—864no—
282C2×D4—862no—
283C2×D4—868no—
284C2×D4—1724no—
285C2×D4—1728no—
286C2×D4—1724no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—42no—
290C22×C4—862no—
291C22×C4—868no—
292C22×C4—864no—
293C22×C4—1728no—
294C22×C4(C2×D43)⋊C414yes—
295C22×C4(C2×D43)⋊C414yes—
296C22×C4C2×C4×D4312yes—
297C22×C4C2×D17211yescharacteristic
298C22×C4C2×D17211yescharacteristic
299C22×C4C2×D17211yescharacteristic
300C22×C4C2×D17211yescharacteristic
301C22×C4C2×D17211yescharacteristic
302C22×C4C2×C22⋊D4312yes—
303C22×C4C23×D4311yescharacteristic
304C2×C8—24no—
305C2×C8—28no—
306C4⋊C4—864no—
307C4⋊C4—864no—
308C4⋊C4—864no—
309C4⋊C4—864no—
310C22⋊C4—868no—
311C22⋊C4—868no—
312C22⋊C4—1724no—
313C42—1724no—
314C42(C2×D43)⋊C414yes—
315C42(C2×D43)⋊C414yes—
316C42C2×C4×D4312yes—
317C42C2×C4×D4312yes—
318C42C2×C22⋊D4312yes—
319C42C2×C22⋊D4312yes—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—864no—
324C23—1724no—
325C23—1724no—
326C23—1724no—
327C23C2×(C2×D43)⋊C412yes—
328C23C22×D17211yescharacteristic
329Q8—868no—
330Q8—1724no—
331D4—868no—
332D4—1728no—
333D4—17216no—
334D4—1728no—
335D4—1724no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—24no—
341C2×C4—28no—
342C2×C4—24no—
343C2×C4—44no—
344C2×C4—864no—
345C2×C4—17216no—
346C2×C4—1724no—
347C2×C4—1724no—
348C2×C4—1724no—
349C2×C4—1724no—
350C2×C4C2×(C2×D43)⋊C412yes—
351C2×C4C2×(C2×D43)⋊C412yes—
352C2×C4C2×(C2×D43)⋊C412yes—
353C2×C4C2×(C2×D43)⋊C412yes—
354C2×C4C2×(C2×D43)⋊C412yes—
355C2×C4#1306334714yes—
356C2×C4C22×C4×D4311yescharacteristic
357C2×C4C22×C22⋊D4311yescharacteristic
358C2×C4#1306337114yes—
359C8—44no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—44no—
364C22—3448no—
365C22—1724no—
366C22—1724no—
367C22—1724no—
368C22C22×(C2×D43)⋊C411yescharacteristic
369C22#1458346812yes—
370C22C2×#1306334712yes—
371C22#1458369912yes—
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—3444no—
377C4—1724no—
378C4#1458289614yes—
379C4#1458337312yes—
380C4#1458346312yes—
381C2—42no—
382C2—3444no—
383C2#1913717511yescharacteristic
384C2C2×#1458289611yescharacteristic
385C2#1914311511yescharacteristic
386C2#1914557314yes—
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#431C2
socleC23×C43C22×D4
prime radicalC2×#14583449C2
cosocleC22×C4×C43C24
hypercenterC2×#431D43
hypocenterC43#21807
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
2. #19136993C2semidirect
3. #19135521C2semidirect
4. #19135517C2semidirect
5. #19135406C2semidirect
6. #19134536C2semidirect
7. C2×C43×#431C2semidirect
10. #14583449C4semidirect
189. C2×#431D43semidirect
225. C43#21807semidirect

Maximal subgroups

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

subgroupindex
C2×#145834492
#191369932
#191355212
#191355172
#191354062
#191345362
C2×C43×#4312
#2180743