Finite Group Databasebeta

← #24984541

Subgroups — #24984541

Order 11008.

462 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137070C211yesmaximal, characteristic
2#19134443C211yesmaximal, characteristic
3#19134339C211yesmaximal, characteristic
4#19132421C211yesmaximal, characteristic
5#19132419C211yesmaximal, characteristic
6#19132417C211yesmaximal, characteristic
7C43×#1272C211yesmaximal, characteristic
8C2×Q8×Dic43C411yescharacteristic
9C2×Dic43⋊C8—21no—
10C2×C8×Dic43—21no—
11C2×C8×Dic43—21no—
12#14582806C411yescharacteristic
13#14582797C2211yescharacteristic
14#14582795C411yescharacteristic
15#14582784—21no—
16#14582782—21no—
17C4⋊C4×Dic43C411yescharacteristic
18#14582750—21no—
19#14582744—21no—
20C42×Dic43C2211yescharacteristic
21#14582654C2211yescharacteristic
22#14582654C2211yescharacteristic
23#14582653—21no—
24C43×#391C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29Q8×Dic43—22no—
30Q8×Dic43C814yescomplemented
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×C4×Dic43—21no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43C2×C411yescharacteristic
39C2×C4×Dic43C2×C411yescharacteristic
40C2×C4×Dic43D411yescharacteristic
41C2×C4×Dic43D411yescharacteristic
42C2×C4×Dic43D411yescharacteristic
43C2×C4×Dic43D411yescharacteristic
44Dic43⋊C8—24no—
45C8×Dic43—24no—
46C8×Dic43—42no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C22×Q8×C43C2×C411yescharacteristic
53C22×C8×C43—21no—
54C22×C8×C43—21no—
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C42×C43C2311yescharacteristic
57#95×C43—21no—
58#95×C43—21no—
59C2×Q8×C43—21no—
60C2×Q8×C43—41no—
61C2×Q8×C43—41no—
62C2×Q8×C43C2×C812yes—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43C22⋊C411yescharacteristic
71C22×Dic43C22⋊C411yescharacteristic
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C2×C8×C43—22no—
75C2×C8×C43—22no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43—41no—
80C4⋊C4×C43—41no—
81C42×C43—41no—
82C4⋊Dic43—21no—
83C4⋊Dic43—24no—
84C4⋊Dic43—41no—
85C4⋊Dic43C2×C812yes—
86Dic43⋊C4—41no—
87Dic43⋊C4—41no—
88Dic43⋊C4—42no—
89C4×Dic43—21no—
90C4×Dic43—21no—
91C4×Dic43—24no—
92C4×Dic43—22no—
93C4×Dic43—22no—
94C4×Dic43—41no—
95C4×Dic43—42no—
96C4×Dic43C2×C812yes—
97C4×Dic43M1612yes—
98C4×Dic43SD1612yes—
99C4×Dic43Q1612yes—
100C2×C43⋊C8—22no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C23×C43C2×C22⋊C411yescharacteristic
107Q8×C43—42no—
108Q8×C43—42no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—22no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43C22×C811yescharacteristic
122C2×C4×C43C2×M1611yescharacteristic
123C2×C4×C43C2×SD1611yescharacteristic
124C2×C4×C43C2×Q1611yescharacteristic
125C2×C4×C43#13511yescharacteristic
126C2×C4×C43#13511yescharacteristic
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—22no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43C22⋊C812yes—
140C2×Dic43C22⋊C812yes—
141C2×Dic43#10312yes—
142C2×Dic43#10312yes—
143C2×Dic43#10412yes—
144C2×Dic43#10412yes—
145C8×C43—42no—
146C8×C43—42no—
147C43⋊C8—42no—
148C43⋊C8—42no—
149#7562—431nomaximal, Sylow
150C22×C43C2×C22⋊C811yescharacteristic
151C22×C43#41011yescharacteristic
152C22×C43#41311yescharacteristic
153C22×C43C2×#10311yescharacteristic
154C22×C43#41611yescharacteristic
155C22×C43C2×#10411yescharacteristic
156C22×C43C2×#10411yescharacteristic
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—42no—
164C4×C43—81no—
165Dic43—22no—
166Dic43—22no—
167Dic43—22no—
168Dic43—42no—
169Dic43—81no—
170Dic43Q8⋊C814yes—
171#2295—431no—
172C4×C4⋊C8—431no—
173#1744—431no—
174#1272—431no—
175#1272D4311yescharacteristic
176#1271—431no—
177#1271—431no—
178C2×C43#145811yescharacteristic
179C2×C43C2×Q8⋊C811yescharacteristic
180C2×C43#147611yescharacteristic
181C2×C43#150011yescharacteristic
182C2×C43#150311yescharacteristic
183C2×C43#152411yescharacteristic
184C2×C43#154211yescharacteristic
185C2×C4×Q8—431no—
186C2×C4⋊C8—861no—
187C2×C4×C8—861no—
188C2×C4×C8—861no—
189#391—431no—
190#391C2×D4311yescharacteristic
191#389—431no—
192#389—431no—
193#387—861no—
194#387—861no—
195C4×C4⋊C4—431no—
196C4×C4⋊C4—861no—
197#376—861no—
198C43—431no—
199#336—431no—
200#336—431no—
201#336—861no—
202#336C2×D4311yescharacteristic
203#336C2×D4311yescharacteristic
204C43#756211yescharacteristic, complemented, Sylow
205C22×Q8C4×D4311yescharacteristic
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—861no—
209C22×C8—861no—
210C4×Q8—434no—
211C4×Q8—862no—
212C2×C4⋊C4—431no—
213C2×C4⋊C4—431no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4C4×D4311yescharacteristic
218C2×C42—431no—
219C2×C42—431no—
220C2×C42—431no—
221C2×C42—431no—
222C2×C42—431no—
223C2×C42—431no—
224C2×C42—861no—
225C2×C42—861no—
226C2×C42C22×D4311yescharacteristic
227C4⋊C8—864no—
228C4×C8—864no—
229C4×C8—1722no—
230#95—21no—
231#95—21no—
232#95—861no—
233#95—861no—
234#95—861no—
235#95—861no—
236#95—861no—
237C2×Q8—21no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8C8×D4312yes—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—431no—
244C22×C4—431no—
245C22×C4—431no—
246C22×C4—431no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4C2×C4×D4311yescharacteristic
250C22×C4D4×D4311yescharacteristic
251C22×C4D4×D4311yescharacteristic
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—862no—
259C2×C8—862no—
260C2×C8—1721no—
261C2×C8—1721no—
262C2×C8—1721no—
263C2×C8—1721no—
264C4⋊C4—41no—
265C4⋊C4—432no—
266C4⋊C4—864no—
267C4⋊C4—861no—
268C4⋊C4—1721no—
269C4⋊C4—1722no—
270C4⋊C4—1721no—
271C4⋊C4—1721no—
272C42—41no—
273C42—432no—
274C42—432no—
275C42—432no—
276C42—432no—
277C42—862no—
278C42—862no—
279C42—864no—
280C42—861no—
281C42—861no—
282C42—1721no—
283C42—1722no—
284C23C22⋊C4×D4311yescharacteristic
285Q8—42no—
286Q8—42no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—432no—
300C2×C4—432no—
301C2×C4—432no—
302C2×C4—432no—
303C2×C4—432no—
304C2×C4—432no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—862no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4C2×C8×D4311yescharacteristic
318C2×C4M16×D4311yescharacteristic
319C2×C4SD16×D4311yescharacteristic
320C2×C4Q16×D4311yescharacteristic
321C2×C4#1306334611yescharacteristic
322C2×C4#1306334811yescharacteristic
323C8—42no—
324C8—42no—
325C8—1722no—
326C8—1722no—
327C22C22⋊C8×D4311yescharacteristic
328C22#1458287111yescharacteristic
329C22#1458288011yescharacteristic
330C22#103×D4311yescharacteristic
331C22#1458289411yescharacteristic
332C22#104×D4311yescharacteristic
333C22#104×D4311yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—81no—
342C4—434no—
343C4—862no—
344C4—862no—
345C4—862no—
346C4—3441no—
347C4—1722no—
348C2#1913290611yescharacteristic
349C2Q8⋊C8×D4311yescharacteristic
350C2#1913297611yescharacteristic
351C2#1913308011yescharacteristic
352C2#1913309211yescharacteristic
353C2#1913318011yescharacteristic
354C2#1913324911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socle, prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1272D43
hypocenterC43#7562
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
30. Q8×Dic43C8semidirect
204. C43#7562semidirect

Maximal subgroups

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

subgroupindex
#191370702
#191344432
#191343392
#191324212
#191324192
#191324172
C43×#12722
#756243