Finite Group Databasebeta

← #25105864

Subgroups — #25105864

Order 11008.

1334 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583477C211yesmaximal, characteristic
2#19137196C212yesmaximal, complemented
3#19135429C218yesmaximal, complemented
4#19134513C211yesmaximal, characteristic, complemented
5#19134512C212yesmaximal, complemented
6C43×#1782C211yesmaximal, characteristic, complemented
7C22×#10621898C2211yescharacteristic
8#14583477—24no—
9#14583477—24no—
10C2×#13063304C412yescomplemented
11C2×#13063301C412yescomplemented
12C2×#13063299C412yescomplemented
13C2×#13063297C2214yes—
14C2×#13063296C412yescomplemented
15C22×C4⋊Dic43C2211yescharacteristic
16C2×#13063240C2214yes—
17C2×#13063239C2218yes—
18#14582784—24no—
19#14582782—24no—
20#14582762C2212yes—
21#14582757C2214yes—
22C22⋊C4×Dic43C2214yes—
23C22×#41×C43C2211yescharacteristic
24C2×#99×C43C2214yes—
25C43×#381C2212yes—
26C2×#10621898—22no—
27C2×#10621898—22no—
28C2×#10621898—44no—
29C22×Dic86C2×C411yescharacteristic
30C22×D172C2×C411yescharacteristic
31C22×C22⋊D43C2×C414yes—
32C22×C22⋊D43C2312yes—
33C23×Dic43C2312yes—
34C22×C4×D43C2×C412yes—
35#13063304—24no—
36#13063304—24no—
37#13063301—28no—
38#13063299—24no—
39#13063299—24no—
40#13063297—28no—
41#13063297—28no—
42#13063296—28no—
43C2×C4⋊Dic43C2×C412yes—
44C2×C4⋊Dic43C2×C412yes—
45C2×C4⋊Dic43D414yes—
46C2×C4⋊Dic43D414yes—
47C2×Dic43⋊C4—24no—
48C2×Dic43⋊C4C2×C414yes—
49C2×C22⋊Dic43C2×C414yes—
50C2×C22⋊Dic43C2314yes—
51C2×(C2×D43)⋊C4C2×C414yes—
52C2×C4×Dic43—24no—
53#13063240—44no—
54#13063239—48no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95—24no—
58C43⋊#95—24no—
59C2×#41×C43—22no—
60C2×#41×C43—22no—
61C2×#41×C43—44no—
62C22×Q8×C43C2×C411yescharacteristic
63C22×D4×C43C2×C411yescharacteristic
64C22×D4×C43C2312yes—
65C23×C4×C43C2×C412yes—
66C23×C4×C43C2311yescharacteristic
67C2×C22⋊C4×C43C2314yes—
68#99×C43—44no—
69#95×C43—22no—
70#95×C43—22no—
71C24×C43C22×C412yes—
72C24×C43C2411yescharacteristic
73C23×D43C22×C412yes—
74#41×C43—48no—
75#41×C43—48no—
76C2×Q8×C43—22no—
77C2×Q8×C43—42no—
78C2×D4×C43—22no—
79C2×D4×C43—24no—
80C2×D4×C43—24no—
81C2×D4×C43—24no—
82C2×D4×C43—42no—
83C22×C4×C43—22no—
84C22×C4×C43—22no—
85C22×C4×C43—24no—
86C22×C4×C43—24no—
87C22×C4×C43—42no—
88C22×C4×C43—42no—
89C22×C4×C43C22×C412yes—
90C22×C4×C43C22×C411yescharacteristic
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C2×D412yes—
93C22×C4×C43C2×D412yes—
94C2×C22⋊D43—28no—
95C2×C22⋊D43—24no—
96C2×C22⋊D43—28no—
97C2×C22⋊D43—84no—
98C22×Dic43—24no—
99C22×Dic43—82no—
100C22×Dic43C22×C412yes—
101C22×Dic43C22×C414yes—
102C22×Dic43C2×D414yes—
103C22×Dic43C2×D414yes—
104#10621898—48no—
105#10621898—48no—
106C2×D172—21no—
107C2×D172—21no—
108C2×D172—42no—
109C2×C4×D43—24no—
110C2×C4×D43—44no—
111C2×Dic86—21no—
112C2×Dic86—21no—
113C2×Dic86—42no—
114C22⋊C4×C43—28no—
115C22⋊Dic43—28no—
116C22⋊Dic43—28no—
117(C2×D43)⋊C4—28no—
118C4⋊Dic43C22⋊C418yes—
119C4⋊Dic43C22⋊C414yes—
120C4⋊Dic43C22⋊C414yes—
121Dic43⋊C4—28no—
122Dic43⋊C4—84no—
123C4×Dic43—84no—
124C23×C43—22no—
125C23×C43—22no—
126C23×C43—22no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43—42no—
130C23×C43—42no—
131C23×C43C23×C411yescharacteristic
132C23×C43C22×D412yes—
133C23×C43H(5,𝔽2)14yes—
134C22×D43—22no—
135C22×D43—24no—
136C22×D43—42no—
137C22×D43—42no—
138Q8×C43—44no—
139D4×C43—44no—
140D4×C43—48no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—24no—
144C2×C4×C43—24no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—44no—
149C2×C4×C43—44no—
150C2×C4×C43—44no—
151C2×C4×C43—44no—
152C2×C4×C43—44no—
153C2×C4×C43C2×C22⋊C411yescharacteristic
154C2×C4×C43C2×C22⋊C411yescharacteristic
155C2×C4×C43C2×C22⋊C412yes—
156C22⋊D43—48no—
157C22⋊D43—88no—
158C2×Dic43—22no—
159C2×Dic43—24no—
160C2×Dic43—44no—
161C2×Dic43—44no—
162C2×Dic43—44no—
163C2×Dic43—44no—
164C2×Dic43—44no—
165C2×Dic43—44no—
166C2×Dic43C2×C22⋊C418yes—
167D172—42no—
168D172—42no—
169C4×D43—48no—
170Dic86—42no—
171Dic86—42no—
172#21796—431nomaximal, Sylow
173C22×C43—21no—
174C22×C43—22no—
175C22×C43—21no—
176C22×C43—22no—
177C22×C43—44no—
178C22×C43—42no—
179C22×C43—42no—
180C22×C43—42no—
181C22×C43—82no—
182C22×C43—82no—
183C22×C43C22×C22⋊C411yescharacteristic
184C22×C43#51812yes—
185C22×C43#53514yes—
186C2×D43—42no—
187C2×D43—42no—
188C2×D43—42no—
189C2×D43—84no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—22no—
193C4×C43—42no—
194C4×C43—84no—
195Dic43—28no—
196Dic43—42no—
197Dic43—84no—
198C2×#537—431no—
199#2313—432no—
200#1964—438no—
201#1782—432no—
202#1782—431no—
203#1782D4311yescharacteristic, complemented
204C2×C43—24no—
205C2×C43—22no—
206C2×C43—82no—
207C2×C43#230911yescharacteristic
208C2×C43#288311yescharacteristic
209C2×C43#288411yescharacteristic
210D43—82no—
211C22×#41—431no—
212C22×#41C2×D4311yescharacteristic
213#537—864no—
214#537—864no—
215C2×C22⋊Q8—432no—
216C2×C22⋊Q8—432no—
217C2×#121—434no—
218C2×#121—432no—
219C2×#121—432no—
220C22×C4⋊C4—431no—
221C2×#99—434no—
222C2×#99—438no—
223C2×#99C2×D4314yes—
224#387—864no—
225#387—864no—
226#381—432no—
227#381C2×D4312yes—
228#380—434no—
229C4×C22⋊C4—434no—
230C43#2179611yescharacteristic, complemented, Sylow
231C2×#41—22no—
232C2×#41—22no—
233C2×#41—44no—
234C2×#41—862no—
235C2×#41—862no—
236C2×#41—1724no—
237C22×Q8—431no—
238C22×Q8C4×D4311yescharacteristic
239C22×D4—432no—
240C22×D4—434no—
241C22×D4—431no—
242C22×D4C4×D4311yescharacteristic
243C22×D4C22×D4312yes—
244C23×C4—432no—
245C23×C4—432no—
246C23×C4C4×D4312yes—
247C23×C4C22×D4311yescharacteristic
248C22⋊Q8—864no—
249C22⋊Q8—864no—
250C22⋊Q8—868no—
251#121—864no—
252#121—864no—
253#121—868no—
254#121—868no—
255#121—868no—
256C2×C4⋊C4—432no—
257C2×C4⋊C4—432no—
258C2×C4⋊C4—434no—
259C2×C4⋊C4—434no—
260C2×C4⋊C4—434no—
261C2×C4⋊C4—864no—
262C2×C22⋊C4—434no—
263C2×C22⋊C4—434no—
264C2×C22⋊C4—434no—
265C2×C22⋊C4C22×D4314yes—
266C2×C42—864no—
267#99—44no—
268#99—1728no—
269#99—1724no—
270#95—22no—
271#95—22no—
272#95—864no—
273#95—864no—
274#95—862no—
275#95—862no—
276C24—432no—
277C24C2×C4×D4312yes—
278C24C23×D4311yescharacteristic
279#41—48no—
280#41—48no—
281#41—1728no—
282#41—1728no—
283C2×Q8—22no—
284C2×Q8—42no—
285C2×Q8—861no—
286C2×Q8—861no—
287C2×Q8—1722no—
288C2×D4—24no—
289C2×D4—24no—
290C2×D4—24no—
291C2×D4—22no—
292C2×D4—42no—
293C2×D4—868no—
294C2×D4—864no—
295C2×D4—868no—
296C2×D4—861no—
297C2×D4—861no—
298C2×D4—3444no—
299C2×D4—1722no—
300C22×C4—24no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—434no—
307C22×C4—434no—
308C22×C4—434no—
309C22×C4—432no—
310C22×C4—864no—
311C22×C4—864no—
312C22×C4—3442no—
313C22×C4—1724no—
314C22×C4C2×C4×D4312yes—
315C22×C4C2×C4×D4311yescharacteristic
316C22×C4C2×C4×D4311yescharacteristic
317C22×C4D4×D4312yes—
318C22×C4D4×D4312yes—
319C4⋊C4—434no—
320C4⋊C4—434no—
321C4⋊C4—438no—
322C4⋊C4—868no—
323C4⋊C4—3444no—
324C22⋊C4—28no—
325C22⋊C4—868no—
326C22⋊C4—868no—
327C22⋊C4—868no—
328C42—3444no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—41no—
333C23—41no—
334C23—42no—
335C23—42no—
336C23—864no—
337C23—862no—
338C23—1722no—
339C23—1722no—
340C23C22×C4×D4311yescharacteristic
341C23C2×D4×D4312yes—
342C23#1306337014yes—
343Q8—44no—
344Q8—1722no—
345Q8—1722no—
346D4—44no—
347D4—48no—
348D4—3448no—
349D4—1722no—
350D4—1722no—
351D4—1728no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—438no—
365C2×C4—862no—
366C2×C4—864no—
367C2×C4—1728no—
368C2×C4—1724no—
369C2×C4—1724no—
370C2×C4—1724no—
371C2×C4—1724no—
372C2×C4—1724no—
373C2×C4—1724no—
374C2×C4C22⋊C4×D4311yescharacteristic
375C2×C4C22⋊C4×D4311yescharacteristic
376C2×C4C22⋊C4×D4312yes—
377C22—22no—
378C22—21no—
379C22—22no—
380C22—21no—
381C22—44no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—82no—
386C22—82no—
387C22—3444no—
388C22—1722no—
389C22—1722no—
390C22—1722no—
391C22C2×C22⋊C4×D4311yescharacteristic
392C22#1458337212yes—
393C22#1458346414yes—
394C4—21no—
395C4—21no—
396C4—22no—
397C4—42no—
398C4—84no—
399C4—868no—
400C4—3444no—
401C4—1722no—
402C2—24no—
403C2—22no—
404C2—82no—
405C2—3442no—
406C2#1913717611yescharacteristic
407C2#1914305411yescharacteristic
408C2#1914305711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1782C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583477C2
cosocleC24×C43C24
hypercenter#1782D43
hypocenterC43#21796
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. #19137196C2semidirect
3. #19135429C2semidirect
4. #19134513C2semidirect
5. #19134512C2semidirect
6. C43×#1782C2semidirect
10. C2×#13063304C4semidirect
11. C2×#13063301C4semidirect
12. C2×#13063299C4semidirect
14. C2×#13063296C4semidirect
203. #1782D43semidirect
230. C43#21796semidirect

Maximal subgroups

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

subgroupindex
C2×#145834772
#191371962
#191354292
#191345132
#191345122
C43×#17822
#2179643