Finite Group Databasebeta

← #24996771

Subgroups — #24996771

Order 11008.

684 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134575C211yesmaximal, characteristic
2C4×C43⋊#95C211yesmaximal, characteristic
3#19132473C214yesmaximal
4C43×#2857C211yesmaximal, characteristic
5C22×C4×Dic43—21no—
6C2×C4⋊(C43⋊C8)—21no—
7C2×C22⋊(C43⋊C8)C2212yes—
8C2×C43⋊#95—21no—
9C2×C43⋊#95C2212yes—
10#14582654—21no—
11C2×C4⋊Q8×C43C411yescharacteristic, complemented
12C2×C22⋊Q8×C43—21no—
13C22×C42×C43C2211yescharacteristic
14C43×#391—21no—
15C43×#389—21no—
16C43×#389C412yescomplemented
17C43×#384C411yescharacteristic, complemented
18C43×#380—21no—
19C43×#380C2212yes—
20C23×Dic43—22no—
21C22×C43⋊C8—22no—
22C2×C4×Dic43—24no—
23C2×C4×Dic43—42no—
24C2×C4×Dic43—42no—
25C4⋊(C43⋊C8)—42no—
26C22⋊(C43⋊C8)—24no—
27C43⋊#95—24no—
28C43⋊#95—22no—
29C43⋊#95Q814yescomplemented
30C22×Q8×C43—21no—
31C23×C4×C43D411yescharacteristic
32C23×C4×C43D411yescharacteristic
33C23×C4×C43C2311yescharacteristic
34C4⋊Q8×C43—42no—
35C22⋊Q8×C43—42no—
36C22⋊Q8×C43—42no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—22no—
39C2×C4⋊C4×C43—21no—
40C2×C4⋊C4×C43—21no—
41C2×C4⋊C4×C43C2×C412yes—
42C2×C4⋊C4×C43C2×C412yes—
43C2×C22⋊C4×C43—22no—
44C2×C42×C43—42no—
45C2×C42×C43C2×C411yescharacteristic
46C2×C42×C43C2×C411yescharacteristic
47C2×C42×C43D411yescharacteristic
48C2×C42×C43D411yescharacteristic
49#95×C43—22no—
50#95×C43—22no—
51C24×C43C2×D411yescharacteristic
52C2×Q8×C43—42no—
53C2×Q8×C43—42no—
54C2×Q8×C43—42no—
55C22×C4×C43—22no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—22no—
60C22×C4×C43—22no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43—41no—
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43D812yes—
69C22×C4×C43SD1612yes—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×Q812yes—
73C22×C4×C43#4112yes—
74C22×Dic43—24no—
75C22×Dic43—24no—
76C22×Dic43—24no—
77C22×Dic43—42no—
78C22×Dic43—42no—
79C22×Dic43—42no—
80C22×Dic43—42no—
81C4⋊C4×C43—42no—
82C4⋊C4×C43—42no—
83C4⋊C4×C43—42no—
84C4⋊C4×C43—42no—
85C4⋊C4×C43—44no—
86C4⋊C4×C43—42no—
87C22⋊C4×C43—42no—
88C22⋊C4×C43—42no—
89C42×C43—22no—
90C42×C43—22no—
91C42×C43—41no—
92C42×C43—41no—
93C4×Dic43—48no—
94C2×C43⋊C8—42no—
95C2×C43⋊C8—42no—
96C2×C43⋊C8—42no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43C2×C22⋊C411yescharacteristic
102C23×C43C22⋊Q812yes—
103C23×C43C2×D811yescharacteristic
104C23×C43C2×SD1611yescharacteristic
105C23×C43#13712yes—
106Q8×C43—84no—
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—24no—
116C2×C4×C43—24no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—44no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43#9912yes—
130C2×C4×C43#10212yes—
131C2×C4×C43#10212yes—
132C2×C4×C43#10412yes—
133C2×C4×C43#10412yes—
134C2×C4×C43C4×Q812yes—
135C2×C4×C43#12411yescharacteristic
136C2×C4×C43C4⋊Q811yescharacteristic
137C2×Dic43—28no—
138C2×Dic43—44no—
139C2×Dic43—44no—
140C2×Dic43—44no—
141C2×Dic43—44no—
142C2×Dic43—44no—
143C2×Dic43—44no—
144C43⋊C8—82no—
145#9909—431nomaximal, Sylow
146C22×C43—22no—
147C22×C43—22no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—22no—
153C22×C43—22no—
154C22×C43#39111yescharacteristic
155C22×C43C2×#9911yescharacteristic
156C22×C43#41011yescharacteristic
157C22×C43C2×#10211yescharacteristic
158C22×C43#41911yescharacteristic
159C22×C43C2×#10411yescharacteristic
160C22×C43C2×#10411yescharacteristic
161C22×C43#47412yes—
162C22×C43#47512yes—
163C4×C43—21no—
164C4×C43—22no—
165C4×C43—21no—
166C4×C43—22no—
167C4×C43—22no—
168C4×C43—41no—
169C4×C43—82no—
170C4×C43—82no—
171C4×C43#32714yes—
172Dic43—48no—
173#2857D4311yescharacteristic
174#1797—431no—
175C4×#95—431no—
176#1294—434no—
177C2×C43—22no—
178C2×C43—22no—
179C2×C43C2×#32711yescharacteristic
180C2×C43#150211yescharacteristic
181C2×C43#150611yescharacteristic
182C2×C43#150811yescharacteristic
183C2×C43#198811yescharacteristic
184C2×C43#199411yescharacteristic
185C2×C43#199611yescharacteristic
186C2×C4⋊Q8Dic4311yescharacteristic, complemented
187C2×C22⋊Q8—21no—
188C22×C42—861no—
189C22×C42C2×D4311yescharacteristic
190C2×C4⋊C8—861no—
191C2×C22⋊C8—432no—
192#391—21no—
193#389—21no—
194#389Dic4312yescomplemented
195#384Dic4311yescharacteristic, complemented
196#380—21no—
197#380C2×D4312yes—
198C2×#95—432no—
199C2×#95—861no—
200#336—861no—
201C43#990911yescharacteristic, complemented, Sylow
202C22×Q8—21no—
203C23×C4—862no—
204C23×C4C22⋊D4311yescharacteristic
205C23×C4C22⋊D4311yescharacteristic
206C23×C4C22×D4311yescharacteristic
207C22×C8—862no—
208C4⋊Q8—42no—
209C22⋊Q8—42no—
210C22⋊Q8—42no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×Dic4312yes—
216C2×C4⋊C4C2×Dic4312yes—
217C2×C22⋊C4—22no—
218C2×C42—42no—
219C2×C42—864no—
220C2×C42—1722no—
221C2×C42—1722no—
222C2×C42C2×Dic4311yescharacteristic
223C2×C42C2×Dic4311yescharacteristic
224C2×C42C22⋊D4311yescharacteristic
225C2×C42C22⋊D4311yescharacteristic
226C4⋊C8—1722no—
227C22⋊C8—864no—
228#95—22no—
229#95—22no—
230#95—434no—
231#95—864no—
232#95—862no—
233C24C2×C22⋊D4311yescharacteristic
234C2×Q8—42no—
235C2×Q8—42no—
236C2×Q8—42no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—864no—
247C22×C4—864no—
248C22×C4—864no—
249C22×C4—1722no—
250C22×C4—1722no—
251C22×C4—1722no—
252C22×C4—1722no—
253C22×C4#1062188212yes—
254C22×C4#1062188312yes—
255C22×C4C22⋊Dic4311yescharacteristic
256C22×C4C22⋊Dic4311yescharacteristic
257C22×C4C22⋊Dic4311yescharacteristic
258C22×C4C22⋊Dic4311yescharacteristic
259C22×C4Q8×D4312yes—
260C22×C4#1062190212yes—
261C22×C4C22×Dic4311yescharacteristic
262C22×C4C2×C22⋊D4311yescharacteristic
263C2×C8—1722no—
264C2×C8—1722no—
265C2×C8—1722no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—44no—
271C4⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C42—22no—
275C42—22no—
276C42—41no—
277C42—41no—
278C42—1728no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23C2×C22⋊Dic4311yescharacteristic
284C23#1306330112yes—
285C23C2×#1062188211yescharacteristic
286C23C2×#1062188311yescharacteristic
287C23#1306335612yes—
288Q8—84no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—44no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—868no—
312C2×C4—1724no—
313C2×C4—1724no—
314C2×C4—1724no—
315C2×C4—1724no—
316C2×C4—1724no—
317C2×C4—1724no—
318C2×C4#1306324012yes—
319C2×C4#1306324612yes—
320C2×C4#1306324612yes—
321C2×C4#1306325212yes—
322C2×C4#1306325212yes—
323C2×C4Q8×Dic4312yes—
324C2×C4#1306331411yescharacteristic
325C2×C4#1306332311yescharacteristic
326C8—3442no—
327C22—22no—
328C22—22no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22#1458280611yescharacteristic
336C22C2×#1306324011yescharacteristic
337C22#1458287311yescharacteristic
338C22C2×#1306324611yescharacteristic
339C22#1458290811yescharacteristic
340C22C2×#1306325211yescharacteristic
341C22C2×#1306325211yescharacteristic
342C22#1458317612yes—
343C22#1458318112yes—
344C4—21no—
345C4—22no—
346C4—21no—
347C4—22no—
348C4—22no—
349C4—41no—
350C4—82no—
351C4—82no—
352C4—1728no—
353C4#1458263314yes—
354C2—22no—
355C2—22no—
356C2C2×#1458263311yescharacteristic
357C2#1913309011yescharacteristic
358C2#1913310711yescharacteristic
359C2#1913311511yescharacteristic
360C2#1913554811yescharacteristic
361C2#1913557311yescharacteristic
362C2#1913558111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2857C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#2857D43
hypocenterC43#9909
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
11. C2×C4⋊Q8×C43C4semidirect
16. C43×#389C4semidirect
17. C43×#384C4semidirect
29. C43⋊#95Q8semidirect
186. C2×C4⋊Q8Dic43semidirect
194. #389Dic43semidirect
195. #384Dic43semidirect
201. C43#9909semidirect

Maximal subgroups

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

subgroupindex
#191345752
C4×C43⋊#952
#191324732
C43×#28572
#990943