Finite Group Databasebeta

← #24984618

Subgroups — #24984618

Order 11008.

500 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137053C211yesmaximal, characteristic
2#19134737C211yesmaximal, characteristic, complemented
3#19134339C211yesmaximal, characteristic, complemented
4#19132418C211yesmaximal, characteristic, complemented
5#19132415C211yesmaximal, characteristic
6#19132415C211yesmaximal, characteristic
7C43×#1271C211yesmaximal, characteristic, complemented
8C2×#13063287C411yescharacteristic
9C2×#13063283—21no—
10C2×C8×Dic43—21no—
11#14582801C2211yescharacteristic
12#14582800C411yescharacteristic
13#14582798C411yescharacteristic
14#14582791—21no—
15#14582789—21no—
16C4⋊C4×Dic43C411yescharacteristic
17#14582746—21no—
18C42×Dic43C2211yescharacteristic
19#14582654C2211yescharacteristic
20#14582654C2211yescharacteristic
21#14582653—21no—
22#14582653—21no—
23#14582653—21no—
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×D172C2×C411yescharacteristic
28C22×C4×D43—21no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—21no—
31#13063287—22no—
32#13063287C814yescomplemented
33#13063283—42no—
34#13063283—42no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×C4×Dic43—21no—
43C2×C4×Dic43C2×C411yescharacteristic
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47C2×C4×Dic43D411yescharacteristic
48C2×C4×Dic43D411yescharacteristic
49C8×Dic43—24no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C22×C8×C43—21no—
53C22×C8×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C42×C43C2311yescharacteristic
58#95×C43—21no—
59C23×D43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×Dic43—21no—
66C22×Dic43C22⋊C411yescharacteristic
67C22×Dic43C22⋊C411yescharacteristic
68C22×Dic43C22⋊C411yescharacteristic
69C22×Dic43C22⋊C411yescharacteristic
70C2×D172—21no—
71C2×D172—41no—
72C2×D172—41no—
73C2×D172C2×C812yes—
74C2×C4×D43—24no—
75C2×C4×D43—42no—
76C2×C4×D43—42no—
77C2×C8×C43—22no—
78C2×C8×C43—41no—
79C2×C8×C43—41no—
80C2×C8×C43—41no—
81C2×C8×C43—41no—
82C2×C8×C43—41no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43C2×C812yes—
88C42×C43—41no—
89(C2×D43)⋊C4—24no—
90(C2×D43)⋊C4—42no—
91(C2×D43)⋊C4—41no—
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—42no—
96C4⋊Dic43—42no—
97C4⋊Dic43—41no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—22no—
103C4×Dic43—41no—
104C4×Dic43—41no—
105C4×Dic43—42no—
106C4×Dic43C2×C812yes—
107C4×Dic43M1612yes—
108C2×C43⋊C8—22no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C23×C43C2×C22⋊C411yescharacteristic
115C22×D43—22no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—22no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43C22×C811yescharacteristic
135C2×C4×C43C2×M1611yescharacteristic
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43C22⋊C812yes—
153C2×Dic43C22⋊C812yes—
154C2×Dic43#10412yes—
155D172—42no—
156D172—42no—
157C4×D43—48no—
158C8×C43—42no—
159C8×C43—81no—
160C43⋊C8—42no—
161C43⋊C8—81no—
162#7580—431nomaximal, Sylow
163C22×C43C2×C22⋊C811yescharacteristic
164C22×C43#41011yescharacteristic
165C22×C43#41311yescharacteristic
166C22×C43#41611yescharacteristic
167C22×C43#41811yescharacteristic
168C22×C43C2×#10411yescharacteristic
169C22×C43#42111yescharacteristic
170C2×D43—42no—
171C2×D43—42no—
172C2×D43—42no—
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C2×D43—81no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—42no—
184C4×C43—81no—
185Dic43—22no—
186Dic43—22no—
187Dic43—22no—
188Dic43—41no—
189Dic43—81no—
190#2293—431no—
191#1839—431no—
192#1744—431no—
193#1271—431no—
194#1271D4311yescharacteristic, complemented
195#1270—431no—
196#1270—431no—
197C2×C43#145811yescharacteristic
198C2×C43#147611yescharacteristic
199C2×C43#147811yescharacteristic
200C2×C43#150511yescharacteristic
201C2×C43#152111yescharacteristic
202C2×C43#153211yescharacteristic
203C2×C43#155311yescharacteristic
204D43—82no—
205C2×C4×D4—431no—
206C2×#117—861no—
207C2×C4×C8—861no—
208#390—431no—
209#390—431no—
210#389—431no—
211#389C2×D4311yescharacteristic
212#388—861no—
213#388—861no—
214C4×C4⋊C4—431no—
215C4×C22⋊C4—861no—
216C43—431no—
217#336—431no—
218#336—431no—
219#336—861no—
220#336—861no—
221#336—861no—
222#336C2×D4311yescharacteristic
223#336C2×D4311yescharacteristic
224C43#758011yescharacteristic, complemented, Sylow
225C22×D4—431no—
226C23×C4—861no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—861no—
230C22×C8—861no—
231C4×D4—434no—
232C4×D4—862no—
233#117—1722no—
234#117—1722no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—431no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4C4×D4311yescharacteristic
239C2×C4⋊C4C4×D4311yescharacteristic
240C2×C22⋊C4—861no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4—861no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C42—431no—
246C2×C42—431no—
247C2×C42—431no—
248C2×C42—431no—
249C2×C42—431no—
250C2×C42—431no—
251C2×C42—861no—
252C2×C42C22×D4311yescharacteristic
253C4×C8—864no—
254#95—21no—
255#95—861no—
256#95—861no—
257C24—861no—
258C2×D4—432no—
259C2×D4—861no—
260C2×D4—1721no—
261C2×D4—1721no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—431no—
265C22×C4—431no—
266C22×C4—431no—
267C22×C4—431no—
268C22×C4—864no—
269C22×C4—861no—
270C22×C4—1722no—
271C22×C4—1722no—
272C22×C4C2×C4×D4311yescharacteristic
273C22×C4D4×D4311yescharacteristic
274C22×C4D4×D4311yescharacteristic
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—862no—
282C2×C8—1721no—
283C2×C8—1721no—
284C2×C8—1721no—
285C2×C8—1721no—
286C2×C8—1721no—
287C4⋊C4—21no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—1721no—
292C4⋊C4—1722no—
293C4⋊C4C8×D4312yes—
294C22⋊C4—864no—
295C22⋊C4—1722no—
296C22⋊C4—1722no—
297C22⋊C4—1721no—
298C22⋊C4—1721no—
299C22⋊C4—1721no—
300C22⋊C4—1721no—
301C42—41no—
302C42—432no—
303C42—432no—
304C42—862no—
305C42—861no—
306C42—861no—
307C42—861no—
308C42—861no—
309C42—1721no—
310C42—1721no—
311C42—1722no—
312C23—862no—
313C23—1721no—
314C23—1721no—
315C23—1721no—
316C23—1721no—
317C23—1721no—
318C23—1721no—
319C23C22⋊C4×D4311yescharacteristic
320D4—1722no—
321D4—1722no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—432no—
335C2×C4—432no—
336C2×C4—432no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—1728no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4C2×C8×D4311yescharacteristic
351C2×C4M16×D4311yescharacteristic
352C2×C4#1306334611yescharacteristic
353C2×C4#1306334811yescharacteristic
354C2×C4#1306334911yescharacteristic
355C2×C4#1306335211yescharacteristic
356C8—42no—
357C8—81no—
358C8—3441no—
359C8—1722no—
360C22—3441no—
361C22—3441no—
362C22—3441no—
363C22—3441no—
364C22—1722no—
365C22—1722no—
366C22—1722no—
367C22C22⋊C8×D4311yescharacteristic
368C22#1458287111yescharacteristic
369C22#1458288211yescharacteristic
370C22#1458289411yescharacteristic
371C22#1458290211yescharacteristic
372C22#104×D4311yescharacteristic
373C22#1458291411yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—42no—
381C4—81no—
382C4—862no—
383C4—862no—
384C4—862no—
385C4—3441no—
386C4—1721no—
387C2—3442no—
388C2#1913290811yescharacteristic
389C2#1913297611yescharacteristic
390C2#1913298411yescharacteristic
391C2#1913310111yescharacteristic
392C2#1913317111yescharacteristic
393C2#1913321411yescharacteristic
394C2#1913329911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1271D43
hypocenterC43#7580
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
2. #19134737C2semidirect
3. #19134339C2semidirect
4. #19132418C2semidirect
7. C43×#1271C2semidirect
32. #13063287C8semidirect
194. #1271D43semidirect
224. C43#7580semidirect

Maximal subgroups

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

subgroupindex
#191370532
#191347372
#191343392
#191324182
#191324152
C43×#12712
#758043