Finite Group Databasebeta

← #24992297

Subgroups — #24992297

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142947C211yesmaximal, characteristic
2#19134575C211yesmaximal, characteristic
3C2×#14582646C212yesmaximal, complemented
4#19132479C212yesmaximal, complemented
5C2×C43×#432C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7C2×#13063304—21no—
8C2×C4⋊(C43⋊C8)C2212yes—
9C2×C22⋊(C43⋊C8)—21no—
10#14582805—21no—
11#14582797—21no—
12#14582797C412yes—
13#14582769C2211yescharacteristic
14#14582759—21no—
15#14582759C412yes—
16#14582654—21no—
17#14582646—24no—
18C22×C42×C43C2211yescharacteristic
19C43×#432—24no—
20C2×C4⋊C8×C43C2212yes—
21C2×C22⋊C8×C43—21no—
22C2×#97×C43—21no—
23C22×Dic86—21no—
24C22×C43⋊C8—22no—
25#13063325—22no—
26#13063325—22no—
27#13063304—44no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43C2×C412yes—
32C2×C4⋊Dic43C2×C412yes—
33C2×Dic43⋊C4—22no—
34C2×C22⋊Dic43—22no—
35C4⋊(C43⋊C8)—22no—
36C4⋊(C43⋊C8)—22no—
37C22⋊(C43⋊C8)—42no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C23×C4×C43C2×C411yescharacteristic
41C23×C4×C43D411yescharacteristic
42C23×C4×C43D411yescharacteristic
43C22×C8×C43—22no—
44C2×C42×C43—22no—
45C2×C42×C43—22no—
46C2×C42×C43C2×C411yescharacteristic
47C2×C42×C43D411yescharacteristic
48C2×C42×C43D411yescharacteristic
49C2×C42×C43C2311yescharacteristic
50C4⋊C8×C43—22no—
51C4⋊C8×C43D414yes—
52C22⋊C8×C43—24no—
53#97×C43—24no—
54C24×C43C22⋊C411yescharacteristic
55C22×C4×C43—22no—
56C22×C4×C43—21no—
57C22×C4×C43—22no—
58C22×C4×C43—21no—
59C22×C4×C43—22no—
60C22×C4×C43—21no—
61C22×C4×C43—22no—
62C22×C4×C43—21no—
63C22×C4×C43—22no—
64C22×C4×C43—22no—
65C22×C4×C43—41no—
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—22no—
73C22×Dic43—22no—
74C2×Dic86—41no—
75C2×Dic86—41no—
76C2×Dic86—42no—
77C2×Dic86—42no—
78C2×C8×C43—24no—
79C2×C8×C43—42no—
80C2×C8×C43—42no—
81C42×C43—22no—
82C42×C43—21no—
83C42×C43—22no—
84C42×C43—21no—
85C42×C43C2×D412yes—
86C42×C43#4112yes—
87C22⋊Dic43—44no—
88C4⋊Dic43—24no—
89C4⋊Dic43—42no—
90C4⋊Dic43—41no—
91C4⋊Dic43—42no—
92C4⋊Dic43—41no—
93C4⋊Dic43—42no—
94Dic43⋊C4—44no—
95C2×C43⋊C8—42no—
96C2×C43⋊C8—42no—
97C2×C43⋊C8—42no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43#10112yes—
105C23×C43C2×C22⋊C411yescharacteristic
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
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—21no—
116C2×C4×C43—21no—
117C2×C4×C43—44no—
118C2×C4×C43—42no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43C4×D412yes—
123C2×C4×C43#12011yescharacteristic
124C2×C4×C43#12112yes—
125C2×C4×C43#12311yescharacteristic
126C2×C4×C43#13512yes—
127C2×C4×C43AGL(1,ℤ/8)12yes—
128C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C43#13712yes—
130C2×C4×C43#13711yescharacteristic
131C2×Dic43—42no—
132C2×Dic43—42no—
133C2×Dic43—42no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137Dic86—82no—
138Dic86—82no—
139C8×C43—44no—
140C43⋊C8—82no—
141#9140—431nomaximal, Sylow
142C22×C43—22no—
143C22×C43—22no—
144C22×C43—22no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43#38611yescharacteristic
150C22×C43C2×#10111yescharacteristic
151C22×C43#41311yescharacteristic
152C22×C43#41611yescharacteristic
153C22×C43#41711yescharacteristic
154C22×C43#41811yescharacteristic
155C22×C43#41911yescharacteristic
156C4×C43—22no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43#44912yes—
161C4×C43#46812yes—
162C4×C43#47012yes—
163C4×C43#48212yes—
164Dic43—82no—
165Dic43—82no—
166C2×#432D4311yescharacteristic
167#2857—431no—
168#1797—431no—
169C2×#332—432no—
170#1296—432no—
171C2×C43—42no—
172C2×C43#155211yescharacteristic
173C2×C43#155411yescharacteristic
174C2×C43#155611yescharacteristic
175C2×C43#155711yescharacteristic
176C2×C43#187511yescharacteristic
177C2×C43#189411yescharacteristic
178C2×C43#190111yescharacteristic
179C2×C4⋊Q8—431no—
180C2×C22⋊Q8—861no—
181C22×C42C2×D4311yescharacteristic
182#432—24no—
183C2×C4⋊C8—432no—
184C2×C4⋊C8C2×D4312yes—
185C2×C22⋊C8—21no—
186C2×C22⋊C8—861no—
187C2×#97—21no—
188#391—861no—
189#389—432no—
190#389—861no—
191#384—431no—
192#380—432no—
193#380—861no—
194#336—861no—
195#332—864no—
196C43#914011yescharacteristic, complemented, Sylow
197C22×Q8—861no—
198C23×C4C4×D4311yescharacteristic
199C23×C4D17211yescharacteristic
200C23×C4C22⋊D4311yescharacteristic
201C22×C8—22no—
202C22×C8—862no—
203C4⋊Q8—862no—
204C4⋊Q8—862no—
205C22⋊Q8—1724no—
206C2×C4⋊C4—432no—
207C2×C4⋊C4—432no—
208C2×C4⋊C4—862no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4—861no—
212C2×C22⋊C4—862no—
213C2×C42—22no—
214C2×C42—22no—
215C2×C42C4×D4311yescharacteristic
216C2×C42D17211yescharacteristic
217C2×C42C22⋊D4311yescharacteristic
218C2×C42C22×D4311yescharacteristic
219C4⋊C8—22no—
220C4⋊C8—862no—
221C4⋊C8—862no—
222C4⋊C8C22⋊D4314yes—
223C22⋊C8—24no—
224C22⋊C8—1722no—
225#97—24no—
226#95—862no—
227#95—862no—
228C24(C2×D43)⋊C411yescharacteristic
229C2×Q8—1721no—
230C2×Q8—1721no—
231C2×Q8—1722no—
232C2×Q8—1722no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—862no—
245C22×C4—862no—
246C22×C4(C2×D43)⋊C411yescharacteristic
247C22×C4(C2×D43)⋊C411yescharacteristic
248C22×C4(C2×D43)⋊C411yescharacteristic
249C22×C4C2×C4×D4311yescharacteristic
250C22×C4C2×D17211yescharacteristic
251C22×C4C2×C22⋊D4311yescharacteristic
252C2×C8—24no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—1722no—
256C2×C8—1722no—
257C2×C8—1722no—
258C4⋊C4—864no—
259C4⋊C4—1722no—
260C4⋊C4—1724no—
261C4⋊C4—1722no—
262C4⋊C4—1722no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C22⋊C4—1724no—
266C42—22no—
267C42—21no—
268C42—22no—
269C42—21no—
270C42#1062189812yes—
271C42C2×C22⋊D4312yes—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23#1306324312yes—
279C23C2×(C2×D43)⋊C411yescharacteristic
280Q8—3442no—
281Q8—3442no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—44no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—1722no—
299C2×C4—1722no—
300C2×C4—1722no—
301C2×C4—1722no—
302C2×C4—1722no—
303C2×C4—1722no—
304C2×C4C4×C22⋊D4312yes—
305C2×C4#1306329411yescharacteristic
306C2×C4#1306329912yes—
307C2×C4#1306330811yescharacteristic
308C2×C4#1306334512yes—
309C2×C4#1306335012yes—
310C2×C4#1306335311yescharacteristic
311C2×C4#1306335812yes—
312C2×C4#1306335811yescharacteristic
313C8—44no—
314C8—3442no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22#1458277811yescharacteristic
323C22C2×#1306324311yescharacteristic
324C22#1458288111yescharacteristic
325C22#1458289311yescharacteristic
326C22#1458290111yescharacteristic
327C22#1458290311yescharacteristic
328C22#1458290911yescharacteristic
329C4—22no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—3442no—
334C4—3442no—
335C4#1458304412yes—
336C4#1458314512yes—
337C4#1458315712yes—
338C4#1458322312yes—
339C2—42no—
340C2#1913329611yescharacteristic
341C2#1913330611yescharacteristic
342C2#1913331311yescharacteristic
343C2#1913331811yescharacteristic
344C2#1913491711yescharacteristic
345C2#1913502811yescharacteristic
346C2#1913506311yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#432C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenterC2×#432D43
hypocenterC43#9140
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
3. C2×#14582646C2semidirect
4. #19132479C2semidirect
196. C43#9140semidirect

Maximal subgroups

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

subgroupindex
#191429472
#191345752
C2×#145826462
#191324792
C2×C43×#4322
#914043