Finite Group Databasebeta

← #24988060

Subgroups — #24988060

Order 11008.

876 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134663C211yesmaximal, characteristic
2C2×#14582636C214yesmaximal
3#19132822C211yesmaximal, characteristic
4C2×C43×#533C211yesmaximal, characteristic
5C2×C22⋊(C43⋊C8)C2212yes—
6C2×C43⋊#95—21no—
7C2×C43⋊#95—21no—
8C2×C43⋊#95C2212yes—
9#14582654—21no—
10#14582654—21no—
11#14582636—28no—
12C43×#533—28no—
13C2×C4⋊Q8×C43C411yescharacteristic, complemented
14C2×C4⋊Q8×C43C411yescharacteristic, complemented
15C2×#125×C43—21no—
16C2×C22⋊Q8×C43—21no—
17C2×C22⋊Q8×C43C2212yes—
18C2×C4×Q8×C43—21no—
19C2×C4×Q8×C43C412yescomplemented
20C2×#117×C43—21no—
21C22×C42×C43C2211yescharacteristic
22C23×Dic43—22no—
23C22×C43⋊C8—22no—
24C22⋊(C43⋊C8)—24no—
25C43⋊#95—24no—
26C43⋊#95—24no—
27C43⋊#95—42no—
28C22×Q8×C43—21no—
29C22×Q8×C43C2×C412yes—
30C23×C4×C43D411yescharacteristic
31C23×C4×C43D411yescharacteristic
32C23×C4×C43C2311yescharacteristic
33C4⋊Q8×C43—24no—
34C4⋊Q8×C43—24no—
35#125×C43—28no—
36C22⋊Q8×C43—28no—
37C22⋊Q8×C43—24no—
38C22⋊Q8×C43D418yes—
39C4×Q8×C43—28no—
40C4×Q8×C43—24no—
41C4×Q8×C43—24no—
42#117×C43—28no—
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—22no—
47C2×C4⋊C4×C43—22no—
48C2×C4⋊C4×C43C2×C412yes—
49C2×C22⋊C4×C43—22no—
50C2×C42×C43—22no—
51C2×C42×C43—24no—
52C2×C42×C43C2×C411yescharacteristic
53C2×C42×C43C2×C411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C2×C42×C43D411yescharacteristic
56C24×C43C2×D411yescharacteristic
57C2×Q8×C43—24no—
58C2×Q8×C43—22no—
59C2×Q8×C43—42no—
60C2×Q8×C43—42no—
61C2×Q8×C43—42no—
62C2×Q8×C43—42no—
63C2×Q8×C43C22⋊C414yes—
64C22×C4×C43—22no—
65C22×C4×C43—22no—
66C22×C4×C43—22no—
67C22×C4×C43—22no—
68C22×C4×C43—22no—
69C22×C4×C43—22no—
70C22×C4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43SD1612yes—
78C22×C4×C43Q1612yes—
79C22×C4×C43C22×C411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D414yes—
82C22×Dic43—24no—
83C22×Dic43—42no—
84C22×Dic43—42no—
85C22×Dic43—42no—
86C22×Dic43—42no—
87C22×Dic43—42no—
88C22×Dic43—42no—
89C4⋊C4×C43—24no—
90C4⋊C4×C43—24no—
91C4⋊C4×C43—28no—
92C4⋊C4×C43—24no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—28no—
95C4⋊C4×C43C22⋊C414yes—
96C22⋊C4×C43—28no—
97C42×C43—28no—
98C42×C43—22no—
99C42×C43—22no—
100C42×C43—22no—
101C42×C43—22no—
102C2×C43⋊C8—42no—
103C2×C43⋊C8—42no—
104C2×C43⋊C8—42no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43C2×C22⋊C411yescharacteristic
110C23×C43#12012yes—
111C23×C43C2×SD1611yescharacteristic
112C23×C43C2×Q1611yescharacteristic
113C23×C43#13712yes—
114Q8×C43—44no—
115Q8×C43—44no—
116Q8×C43—48no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—24no—
128C2×C4×C43—24no—
129C2×C4×C43—21no—
130C2×C4×C43—24no—
131C2×C4×C43—24no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—44no—
135C2×C4×C43—44no—
136C2×C4×C43—42no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43#10312yes—
141C2×C4×C43#10312yes—
142C2×C4×C43#10412yes—
143C2×C4×C43C2×C22⋊C412yes—
144C2×C4×C43#12012yes—
145C2×Dic43—44no—
146C2×Dic43—44no—
147C2×Dic43—44no—
148C2×Dic43—82no—
149C2×Dic43—82no—
150C2×Dic43—82no—
151C2×Dic43—82no—
152C43⋊C8—82no—
153#8333—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—22no—
157C22×C43—22no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—22no—
161C22×C43—22no—
162C22×C43#37911yescharacteristic
163C22×C43#41011yescharacteristic
164C22×C43#41011yescharacteristic
165C22×C43C2×#10311yescharacteristic
166C22×C43#41911yescharacteristic
167C22×C43C2×#10411yescharacteristic
168C22×C43#42111yescharacteristic
169C22×C43#44812yes—
170C22×C43#45112yes—
171C4×C43—22no—
172C4×C43—22no—
173C4×C43—22no—
174C4×C43—22no—
175C4×C43—22no—
176C4×C43—44no—
177C4×C43—41no—
178C4×C43—44no—
179Dic43—84no—
180C2×#533D4311yescharacteristic
181#1817—431no—
182C2×#328—434no—
183#1434—431no—
184C2×C43—22no—
185C2×C43—22no—
186C2×C43#150311yescharacteristic
187C2×C43#150611yescharacteristic
188C2×C43#151511yescharacteristic
189C2×C43#151811yescharacteristic
190C2×C43#178211yescharacteristic
191C2×C43#178711yescharacteristic
192C2×C43#178911yescharacteristic
193#533—28no—
194C2×C4⋊Q8Dic4311yescharacteristic, complemented
195C2×C4⋊Q8Dic4311yescharacteristic, complemented
196C2×#125—21no—
197C2×C22⋊Q8—21no—
198C2×C22⋊Q8C2×D4312yes—
199C2×C4×Q8—21no—
200C2×C4×Q8Dic4312yescomplemented
201C2×#117—21no—
202C22×C42C2×D4311yescharacteristic
203C2×C22⋊C8—432no—
204C2×#95—432no—
205C2×#95—861no—
206C2×#95—861no—
207#336—861no—
208#336—861no—
209#328—868no—
210C43#833311yescharacteristic, complemented, Sylow
211C22×Q8—21no—
212C22×Q8C2×Dic4312yes—
213C23×C4—862no—
214C23×C4C22⋊D4311yescharacteristic
215C23×C4C22⋊D4311yescharacteristic
216C23×C4C22×D4311yescharacteristic
217C22×C8—862no—
218C4⋊Q8—24no—
219C4⋊Q8—24no—
220#125—28no—
221C22⋊Q8—28no—
222C22⋊Q8—24no—
223C22⋊Q8C22⋊D4318yes—
224C4×Q8—28no—
225C4×Q8—24no—
226C4×Q8—24no—
227#117—28no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4C2×Dic4312yes—
234C2×C22⋊C4—22no—
235C2×C42—22no—
236C2×C42—24no—
237C2×C42C2×Dic4311yescharacteristic
238C2×C42C2×Dic4311yescharacteristic
239C2×C42C22⋊D4311yescharacteristic
240C2×C42C22⋊D4311yescharacteristic
241C22⋊C8—864no—
242#95—864no—
243#95—864no—
244#95—1722no—
245C24C2×C22⋊D4311yescharacteristic
246C2×Q8—24no—
247C2×Q8—22no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8C22⋊Dic4314yes—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—864no—
263C22×C4—1722no—
264C22×C4—1722no—
265C22×C4—1722no—
266C22×C4—1722no—
267C22×C4—1722no—
268C22×C4—1722no—
269C22×C4#1062188412yes—
270C22×C4#1062188512yes—
271C22×C4C22⋊Dic4311yescharacteristic
272C22×C4C22⋊Dic4311yescharacteristic
273C22×C4C22⋊Dic4311yescharacteristic
274C22×C4C22⋊Dic4311yescharacteristic
275C22×C4C22×Dic4311yescharacteristic
276C22×C4C2×C22⋊D4311yescharacteristic
277C22×C4C2×C22⋊D4314yes—
278C2×C8—1722no—
279C2×C8—1722no—
280C2×C8—1722no—
281C4⋊C4—24no—
282C4⋊C4—24no—
283C4⋊C4—28no—
284C4⋊C4—24no—
285C4⋊C4—22no—
286C4⋊C4—28no—
287C4⋊C4C22⋊Dic4314yes—
288C22⋊C4—28no—
289C42—28no—
290C42—22no—
291C42—22no—
292C42—22no—
293C42—22no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23C2×C22⋊Dic4311yescharacteristic
299C23#1306329412yes—
300C23C2×#1062188411yescharacteristic
301C23C2×#1062188511yescharacteristic
302C23#1306335612yes—
303Q8—44no—
304Q8—44no—
305Q8—48no—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—3442no—
330C2×C4—3442no—
331C2×C4—3442no—
332C2×C4—3442no—
333C2×C4—1724no—
334C2×C4—1724no—
335C2×C4—1724no—
336C2×C4#1306324912yes—
337C2×C4#1306324912yes—
338C2×C4#1306325212yes—
339C2×C4C2×C22⋊Dic4312yes—
340C2×C4#1306329412yes—
341C8—3442no—
342C22—22no—
343C22—22no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—21no—
349C22—21no—
350C22#1458275511yescharacteristic
351C22#1458287311yescharacteristic
352C22#1458287311yescharacteristic
353C22C2×#1306324911yescharacteristic
354C22#1458290811yescharacteristic
355C22C2×#1306325211yescharacteristic
356C22#1458291611yescharacteristic
357C22#1458303812yes—
358C22#1458305512yes—
359C4—22no—
360C4—22no—
361C4—22no—
362C4—22no—
363C4—22no—
364C4—44no—
365C4—41no—
366C4—44no—
367C4—3444no—
368C2—22no—
369C2—22no—
370C2#1913309411yescharacteristic
371C2#1913310711yescharacteristic
372C2#1913314611yescharacteristic
373C2#1913315911yescharacteristic
374C2#1913451311yescharacteristic
375C2#1913453011yescharacteristic
376C2#1913453911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#533C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC2×#533D43
hypocenterC43#8333
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
13. C2×C4⋊Q8×C43C4semidirect
14. C2×C4⋊Q8×C43C4semidirect
19. C2×C4×Q8×C43C4semidirect
194. C2×C4⋊Q8Dic43semidirect
195. C2×C4⋊Q8Dic43semidirect
200. C2×C4×Q8Dic43semidirect
210. C43#8333semidirect

Maximal subgroups

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

subgroupindex
#191346632
C2×#145826362
#191328222
C2×C43×#5332
#833343