Finite Group Databasebeta

← #25098435

Subgroups — #25098435

Order 11008.

1866 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583463C211yesmaximal, characteristic
2C22×#13063241C212yesmaximal, complemented
3#19143040C211yesmaximal, characteristic, complemented
4#19135058C218yesmaximal, complemented
5#19134333C212yesmaximal, complemented
6C2×C43×#568C211yesmaximal, characteristic, complemented
7C23×D172C2211yescharacteristic
8C22×#10621877C2212yes—
9#14583463—24no—
10#14583463—24no—
11C2×#13063321C412yes—
12C2×#13063314C412yes—
13C2×#13063299C2214yes—
14C2×#13063293C414yes—
15C2×#13063284C2211yescharacteristic
16C2×#13063241—28no—
17C2×#13063241C2218yes—
18#14582866—24no—
19#14582863C2214yescomplemented
20#14582667C2218yescomplemented
21C22×#41×C43C2211yescharacteristic
22C43×#568—28no—
23C2×#131×C43—24no—
24C22×M16×C43C2212yes—
25C22×M16×C43C2214yescomplemented
26C24×D43C2×C412yes—
27C22×D172—24no—
28C22×D172—22no—
29C22×D172—22no—
30C22×D172—24no—
31C22×D172C2×C412yes—
32C22×D172C2312yes—
33C22×C22⋊D43C2×C418yes—
34C2×#10621877—22no—
35C2×#10621877—24no—
36C2×#10621877—24no—
37C2×#10621877C2314yes—
38C22×C43⋊C8—22no—
39#13063321—28no—
40#13063314—28no—
41#13063299—28no—
42#13063299—28no—
43#13063293—216no—
44#13063284—22no—
45#13063284—22no—
46C2×C4⋊Dic43C2312yes—
47C2×C22⋊Dic43C2×C412yes—
48C2×(C2×D43)⋊C4C2×C418yes—
49C2×C4×Dic43C2×C412yes—
50#13063241—216no—
51C22⋊(C43⋊C8)—28no—
52C2×#41×C43—24no—
53C2×#41×C43—24no—
54C2×#41×C43D414yes—
55C2×#41×C43D414yes—
56C22×Q8×C43C2×C411yescharacteristic
57C22×D4×C43C2×C412yes—
58C22×D4×C43C2×C411yescharacteristic
59C23×C4×C43C2312yes—
60C23×C4×C43C2311yescharacteristic
61#131×C43—232no—
62C2×M16×C43—22no—
63C2×M16×C43—24no—
64C2×M16×C43—24no—
65C2×M16×C43—216no—
66C2×M16×C43D418yescomplemented
67C2×M16×C43C2314yes—
68C22×C8×C43—22no—
69C22×C8×C43—24no—
70C24×C43C22×C412yes—
71C24×C43C22×C411yescharacteristic
72C23×D43—24no—
73C23×D43—28no—
74C23×D43—84no—
75C23×D43C22×C414yes—
76#41×C43—28no—
77#41×C43—28no—
78#41×C43—28no—
79#41×C43—28no—
80C2×Q8×C43—24no—
81C2×Q8×C43C22⋊C414yes—
82C2×D4×C43—24no—
83C2×D4×C43—28no—
84C2×D4×C43C22⋊C418yes—
85C2×D4×C43C22⋊C414yes—
86C22×C4×C43—24no—
87C22×C4×C43—24no—
88C22×C4×C43C22×C412yes—
89C22×C4×C43C22×C411yescharacteristic
90C22×C4×C43C2×D414yes—
91C22×C4×C43C2×D412yes—
92C22×C4×C43C2×D414yes—
93C22×C4×C43C2×D412yes—
94C22×C4×C43C2×D414yes—
95C22×C4×C43#4114yes—
96C22×C4×C43C2411yescharacteristic
97C2×C22⋊D43—216no—
98C2×C22⋊D43—88no—
99C22×Dic43C22×C414yes—
100C2×D172—24no—
101C2×D172—28no—
102C2×D172—24no—
103C2×D172—22no—
104C2×D172—22no—
105C2×D172—24no—
106C2×D172—44no—
107C2×D172—44no—
108C2×D172—44no—
109C2×D172—44no—
110M16×C43—216no—
111M16×C43—28no—
112M16×C43—24no—
113M16×C43C2×D418yes—
114C2×C8×C43—216no—
115C2×C8×C43—28no—
116C2×C8×C43—24no—
117C22⋊Dic43—24no—
118(C2×D43)⋊C4—216no—
119C4⋊Dic43—22no—
120C4⋊Dic43—22no—
121C4×Dic43—24no—
122#10621877—24no—
123#10621877—24no—
124#10621877—44no—
125C2×C43⋊C8—24no—
126C2×C43⋊C8—44no—
127C23×C43—24no—
128C23×C43—42no—
129C23×C43—44no—
130C23×C43C2×C22⋊C414yes—
131C23×C43C2×C22⋊C412yes—
132C23×C43C4×D414yes—
133C23×C43C23×C411yescharacteristic
134C22×D43—24no—
135C22×D43—28no—
136C22×D43—48no—
137C22×D43—48no—
138C22×D43—88no—
139C22×D43—816no—
140Q8×C43—28no—
141D4×C43—216no—
142D4×C43—28no—
143C2×C4×C43—24no—
144C2×C4×C43—24no—
145C2×C4×C43—28no—
146C2×C4×C43—24no—
147C2×C4×C43C2×C22⋊C414yes—
148C2×C4×C43C2×C22⋊C412yes—
149C2×C4×C43C4×D414yes—
150C2×C4×C43#12014yes—
151C2×C4×C43#12114yes—
152C2×C4×C43#12114yes—
153C2×C4×C43#12314yes—
154C2×C4×C43C22×D412yes—
155C2×C4×C43C22×D411yescharacteristic
156C2×C4×C43C22×D411yescharacteristic
157C2×C4×C43C2×#4112yes—
158C22⋊D43—816no—
159C2×Dic43—24no—
160C2×Dic43—44no—
161D172—42no—
162D172—44no—
163D172—42no—
164D172—48no—
165C8×C43—28no—
166C43⋊C8—44no—
167#20990—431nomaximal, Sylow
168C22×C43—22no—
169C22×C43—24no—
170C22×C43—28no—
171C22×C43—24no—
172C22×C43—44no—
173C22×C43—84no—
174C22×C43#38614yes—
175C22×C43C22×C22⋊C411yescharacteristic
176C22×C43C2×C4×D412yes—
177C2×D43—48no—
178C2×D43—44no—
179C2×D43—816no—
180C2×D43—88no—
181C4×C43—24no—
182C4×C43#38614yes—
183C4×C43C2×#12011yescharacteristic
184C4×C43C2×#12112yes—
185C4×C43C2×#12311yescharacteristic
186Dic43—44no—
187C2×#568D4311yescharacteristic, complemented
188C2×#535—431no—
189C22×#100—432no—
190#2879—431no—
191#1900—438no—
192#1742—432no—
193C2×C43—22no—
194C2×C43—24no—
195C2×C43—44no—
196C2×C43C2×#38611yescharacteristic
197C2×C43#288812yes—
198D43—84no—
199C22×#41C2×D4311yescharacteristic
200C23×D4—431no—
201#568—28no—
202C2×#131—24no—
203C22×M16—432no—
204C22×M16C2×D4312yes—
205C22×M16C2×D4314yescomplemented
206#535—864no—
207#535—864no—
208C2×#127—432no—
209C2×#124—432no—
210C2×#121—434no—
211C2×#120—434no—
212C2×#117—431no—
213C2×#100—438no—
214C2×#100—868no—
215#408—864no—
216#407—434no—
217#343—438no—
218C43#2099011yescharacteristic, complemented, Sylow
219C25—432no—
220C2×#41—24no—
221C2×#41—24no—
222C2×#41D17214yes—
223C2×#41C22⋊D4314yes—
224C22×Q8C4×D4311yescharacteristic
225C22×D4—438no—
226C22×D4—432no—
227C22×D4—432no—
228C22×D4—862no—
229C22×D4—864no—
230C22×D4—862no—
231C22×D4—864no—
232C22×D4C4×D4312yes—
233C22×D4C4×D4311yescharacteristic
234C23×C4C22×D4312yes—
235C23×C4C22×D4311yescharacteristic
236#131—232no—
237C2×M16—22no—
238C2×M16—24no—
239C2×M16—24no—
240C2×M16—216no—
241C2×M16—434no—
242C2×M16—862no—
243C2×M16—864no—
244C2×M16—864no—
245C2×M16C22⋊D4318yescomplemented
246C2×M16C22×D4314yes—
247C22×C8—22no—
248C22×C8—24no—
249C22×C8—862no—
250#127—868no—
251#124—868no—
252#121—868no—
253#121—868no—
254#120—8616no—
255#117—862no—
256#117—862no—
257C2×C4⋊C4—432no—
258C2×C22⋊C4—432no—
259C2×C22⋊C4—438no—
260C2×C42—432no—
261#100—8616no—
262C22⋊C8—868no—
263C24—434no—
264C24—864no—
265C24—868no—
266C24—3444no—
267C24C2×C4×D4312yes—
268C24C2×C4×D4311yescharacteristic
269#41—28no—
270#41—28no—
271#41—28no—
272#41—28no—
273C2×Q8—24no—
274C2×Q8(C2×D43)⋊C414yes—
275C2×D4—28no—
276C2×D4—24no—
277C2×D4—8616no—
278C2×D4—864no—
279C2×D4—868no—
280C2×D4—864no—
281C2×D4—862no—
282C2×D4—862no—
283C2×D4—864no—
284C2×D4—3448no—
285C2×D4—1724no—
286C2×D4—1724no—
287C2×D4—1724no—
288C2×D4—1724no—
289C2×D4(C2×D43)⋊C418yes—
290C2×D4(C2×D43)⋊C414yes—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—434no—
294C22×C4C2×C4×D4312yes—
295C22×C4C2×C4×D4311yescharacteristic
296C22×C4C2×D17214yes—
297C22×C4C2×D17212yes—
298C22×C4#1062189814yes—
299C22×C4C2×C22⋊D4314yes—
300C22×C4C2×C22⋊D4312yes—
301C22×C4C2×C22⋊D4314yes—
302C22×C4C23×D4311yescharacteristic
303M16—216no—
304M16—28no—
305M16—24no—
306M16—864no—
307M16—864no—
308M16—1724no—
309M16C2×C22⋊D4318yes—
310C2×C8—216no—
311C2×C8—28no—
312C2×C8—24no—
313C2×C8—864no—
314C2×C8—1724no—
315C4⋊C4—862no—
316C4⋊C4—862no—
317C22⋊C4—864no—
318C22⋊C4—8616no—
319C42—864no—
320C23—24no—
321C23—42no—
322C23—44no—
323C23—868no—
324C23—864no—
325C23—3448no—
326C23—34416no—
327C23—1728no—
328C23—1728no—
329C23C2×(C2×D43)⋊C414yes—
330C23C2×(C2×D43)⋊C412yes—
331C23C4×C22⋊D4314yes—
332C23C22×C4×D4311yescharacteristic
333Q8—28no—
334D4—216no—
335D4—28no—
336D4—34416no—
337D4—1722no—
338D4—1724no—
339D4—1722no—
340D4—1728no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—28no—
344C2×C4—24no—
345C2×C4—864no—
346C2×C4—1724no—
347C2×C4C2×(C2×D43)⋊C414yes—
348C2×C4C2×(C2×D43)⋊C412yes—
349C2×C4C4×C22⋊D4314yes—
350C2×C4#1306329414yes—
351C2×C4#1306329914yes—
352C2×C4#1306329914yes—
353C2×C4#1306330814yes—
354C2×C4C22×C22⋊D4312yes—
355C2×C4C22×C22⋊D4311yescharacteristic
356C2×C4C22×D17211yescharacteristic
357C2×C4C2×#1062189812yes—
358C8—28no—
359C8—1724no—
360C22—22no—
361C22—24no—
362C22—28no—
363C22—24no—
364C22—44no—
365C22—84no—
366C22—3448no—
367C22—34416no—
368C22—1728no—
369C22—1724no—
370C22#1458277814yes—
371C22C22×(C2×D43)⋊C411yescharacteristic
372C22C2×C4×C22⋊D4312yes—
373C4—24no—
374C4—1724no—
375C4#1458277814yes—
376C4C2×#1306329411yescharacteristic
377C4C2×#1306329912yes—
378C4C2×#1306330811yescharacteristic
379C2—22no—
380C2—24no—
381C2—44no—
382C2—3444no—
383C2C2×#1458277811yescharacteristic
384C2#1914307312yes—
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#568C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583463C2
cosocleC22×C4×C43C24
hypercenterC2×#568D43
hypocenterC43#20990
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×#41 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
2. C22×#13063241C2semidirect
3. #19143040C2semidirect
4. #19135058C2semidirect
5. #19134333C2semidirect
6. C2×C43×#568C2semidirect
19. #14582863C22semidirect
20. #14582667C22semidirect
25. C22×M16×C43C22semidirect
66. C2×M16×C43D4semidirect
187. C2×#568D43semidirect
205. C22×M16C2×D43semidirect
218. C43#20990semidirect
245. C2×M16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834632
C22×#130632412
#191430402
#191350582
#191343332
C2×C43×#5682
#2099043