Finite Group Databasebeta

← #24995576

Subgroups — #24995576

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊(C43⋊C8)C211yesmaximal, characteristic
2C2×#14582636C214yesmaximal
3#19132825C211yesmaximal, characteristic
4C43×#2857C211yesmaximal, characteristic
5C22×C4⋊Dic43—21no—
6C2×C22⋊(C43⋊C8)C2212yes—
7C2×C4×C43⋊C8—21no—
8C2×C43⋊#95—21no—
9C2×C43⋊#95C2212yes—
10#14582654—21no—
11#14582636—28no—
12C2×C4⋊Q8×C43C411yescharacteristic, complemented
13C2×C22⋊Q8×C43C2212yes—
14C22×C42×C43C2211yescharacteristic
15C43×#391C412yescomplemented
16C43×#389—21no—
17C43×#389—21no—
18C43×#384C411yescharacteristic, complemented
19C43×#380—21no—
20C43×#380—21no—
21C23×Dic43—22no—
22C22×C43⋊C8—22no—
23C2×C4⋊Dic43—24no—
24C2×C4⋊Dic43—42no—
25C2×C4⋊Dic43—42no—
26C22⋊(C43⋊C8)—22no—
27C22⋊(C43⋊C8)D414yes—
28C4×C43⋊C8—42no—
29C43⋊#95—24no—
30C43⋊#95—42no—
31C22×Q8×C43C2×C412yes—
32C23×C4×C43D411yescharacteristic
33C23×C4×C43D411yescharacteristic
34C23×C4×C43C2311yescharacteristic
35C4⋊Q8×C43—42no—
36C22⋊Q8×C43—24no—
37C22⋊Q8×C43—24no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43—21no—
40C2×C4⋊C4×C43—21no—
41C2×C4⋊C4×C43—21no—
42C2×C4⋊C4×C43—22no—
43C2×C4⋊C4×C43C2×C412yes—
44C2×C22⋊C4×C43—22no—
45C2×C42×C43—42no—
46C2×C42×C43C2×C411yescharacteristic
47C2×C42×C43C2×C411yescharacteristic
48C2×C42×C43D411yescharacteristic
49C2×C42×C43D411yescharacteristic
50#95×C43—22no—
51#95×C43—22no—
52C24×C43C2×D411yescharacteristic
53C2×Q8×C43—24no—
54C2×Q8×C43—42no—
55C2×Q8×C43—42no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—22no—
60C22×C4×C43—41no—
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×C43SD1612yes—
69C22×C4×C43SD1612yes—
70C22×C4×C43Q1612yes—
71C22×C4×C43Q1612yes—
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D412yes—
75C22×C4×C43#4112yes—
76C22×Dic43—24no—
77C22×Dic43—42no—
78C22×Dic43—42no—
79C22×Dic43—42no—
80C22×Dic43—42no—
81C22×Dic43—42no—
82C22×Dic43—42no—
83C4⋊C4×C43—24no—
84C4⋊C4×C43—42no—
85C4⋊C4×C43—42no—
86C4⋊C4×C43—42no—
87C4⋊C4×C43—42no—
88C4⋊C4×C43—44no—
89C22⋊C4×C43—42no—
90C22⋊C4×C43—42no—
91C42×C43—22no—
92C42×C43—22no—
93C42×C43—41no—
94C42×C43—41no—
95C4⋊Dic43—48no—
96C2×C43⋊C8—24no—
97C2×C43⋊C8—42no—
98C2×C43⋊C8—42no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43C2×C22⋊C411yescharacteristic
104C23×C43#12411yescharacteristic
105C23×C43#12711yescharacteristic
106C23×C43C2×SD1611yescharacteristic
107C23×C43C2×SD1611yescharacteristic
108C23×C43C2×Q1611yescharacteristic
109C23×C43C2×Q1611yescharacteristic
110Q8×C43—84no—
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—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—24no—
122C2×C4×C43—24no—
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—42no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43#9912yes—
134C2×C4×C43#10312yes—
135C2×C4×C43#10312yes—
136C2×C4×C43#10312yes—
137C2×C4×C43#10312yes—
138C2×C4×C43#10412yes—
139C2×C4×C43C4×D412yes—
140C2×C4×C43#12112yes—
141C2×Dic43—44no—
142C2×Dic43—44no—
143C2×Dic43—44no—
144C2×Dic43—82no—
145C2×Dic43—82no—
146C2×Dic43—82no—
147C2×Dic43—82no—
148C43⋊C8—44no—
149#9679—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43#39011yescharacteristic
163C22×C43C2×#9911yescharacteristic
164C22×C43#41011yescharacteristic
165C22×C43C2×#10311yescharacteristic
166C22×C43C2×#10311yescharacteristic
167C22×C43C2×#10411yescharacteristic
168C22×C43#42111yescharacteristic
169C22×C43#48711yescharacteristic
170C22×C43#48711yescharacteristic
171C22×C43#49211yescharacteristic
172C22×C43#49411yescharacteristic
173C4×C43—22no—
174C4×C43—22no—
175C4×C43—22no—
176C4×C43—22no—
177C4×C43—22no—
178C4×C43—82no—
179C4×C43—82no—
180C4×C43#32814yescomplemented
181Dic43—84no—
182#2857D4311yescharacteristic
183C4×C22⋊C8—431no—
184C2×#328—434no—
185C4⋊#95—431no—
186C2×C43—21no—
187C2×C43—21no—
188C2×C43—21no—
189C2×C43—21no—
190C2×C43C2×#32811yescharacteristic
191C2×C43#150311yescharacteristic
192C2×C43#151811yescharacteristic
193C2×C43#152011yescharacteristic
194C2×C43#195611yescharacteristic
195C2×C43#196411yescharacteristic
196C2×C43#198011yescharacteristic
197C2×C4⋊Q8Dic4311yescharacteristic, complemented
198C2×C22⋊Q8C2×D4312yes—
199C22×C4⋊C4—861no—
200C22×C42C2×D4311yescharacteristic
201C2×C22⋊C8—432no—
202C2×C4×C8—861no—
203#391Dic4312yescomplemented
204#389—21no—
205#389—21no—
206#384Dic4311yescharacteristic, complemented
207#380—21no—
208#380—21no—
209C2×#95—432no—
210C2×#95—861no—
211#336—861no—
212#328—868no—
213C43#967911yescharacteristic, complemented, Sylow
214C22×Q8C2×Dic4312yes—
215C23×C4—862no—
216C23×C4C22⋊D4311yescharacteristic
217C23×C4C22⋊D4311yescharacteristic
218C23×C4C22×D4311yescharacteristic
219C22×C8—862no—
220C4⋊Q8—42no—
221C22⋊Q8—24no—
222C22⋊Q8—24no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—864no—
229C2×C4⋊C4—1722no—
230C2×C4⋊C4—1722no—
231C2×C4⋊C4C2×Dic4312yes—
232C2×C22⋊C4—22no—
233C2×C42—42no—
234C2×C42C2×Dic4311yescharacteristic
235C2×C42C2×Dic4311yescharacteristic
236C2×C42C22⋊D4311yescharacteristic
237C2×C42C22⋊D4311yescharacteristic
238C22⋊C8—434no—
239C22⋊C8—862no—
240C4×C8—1722no—
241#95—22no—
242#95—22no—
243#95—864no—
244#95—1722no—
245C24C2×C22⋊D4311yescharacteristic
246C2×Q8—24no—
247C2×Q8—42no—
248C2×Q8—42no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—864no—
258C22×C4—1722no—
259C22×C4—1722no—
260C22×C4—1722no—
261C22×C4—1722no—
262C22×C4—1722no—
263C22×C4—1722no—
264C22×C4#1062188412yes—
265C22×C4#1062188412yes—
266C22×C4#1062188512yes—
267C22×C4#1062188512yes—
268C22×C4C22⋊Dic4311yescharacteristic
269C22×C4C22⋊Dic4311yescharacteristic
270C22×C4C22⋊Dic4311yescharacteristic
271C22×C4C22⋊Dic4311yescharacteristic
272C22×C4D4×D4312yes—
273C22×C4#1062190012yes—
274C22×C4C22×Dic4311yescharacteristic
275C22×C4C2×C22⋊D4311yescharacteristic
276C2×C8—864no—
277C2×C8—1722no—
278C2×C8—1722no—
279C4⋊C4—24no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—44no—
285C4⋊C4—1728no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C42—22no—
289C42—22no—
290C42—41no—
291C42—41no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23C2×C22⋊Dic4311yescharacteristic
297C23#1306331211yescharacteristic
298C23#1306332111yescharacteristic
299C23C2×#1062188411yescharacteristic
300C23C2×#1062188411yescharacteristic
301C23C2×#1062188511yescharacteristic
302C23C2×#1062188511yescharacteristic
303Q8—84no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—3442no—
327C2×C4—3442no—
328C2×C4—3442no—
329C2×C4—3442no—
330C2×C4—1724no—
331C2×C4—1724no—
332C2×C4—1724no—
333C2×C4#1306324012yes—
334C2×C4#1306324912yes—
335C2×C4#1306324912yes—
336C2×C4#1306324912yes—
337C2×C4#1306324912yes—
338C2×C4#1306325212yes—
339C2×C4D4×Dic4312yes—
340C2×C4#1306329612yes—
341C8—1724no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22#1458280211yescharacteristic
355C22C2×#1306324011yescharacteristic
356C22#1458287311yescharacteristic
357C22C2×#1306324911yescharacteristic
358C22C2×#1306324911yescharacteristic
359C22C2×#1306325211yescharacteristic
360C22#1458291611yescharacteristic
361C22#1458324911yescharacteristic
362C22#1458324911yescharacteristic
363C22#1458327311yescharacteristic
364C22#1458327811yescharacteristic
365C4—22no—
366C4—22no—
367C4—22no—
368C4—22no—
369C4—22no—
370C4—82no—
371C4—82no—
372C4—3444no—
373C4#1458263614yescomplemented
374C2—21no—
375C2—21no—
376C2—21no—
377C2—21no—
378C2C2×#1458263611yescharacteristic
379C2#1913309411yescharacteristic
380C2#1913315911yescharacteristic
381C2#1913316711yescharacteristic
382C2#1913539811yescharacteristic
383C2#1913543211yescharacteristic
384C2#1913551511yescharacteristic
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#9679
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
12. C2×C4⋊Q8×C43C4semidirect
15. C43×#391C4semidirect
18. C43×#384C4semidirect
180. C4×C43#328semidirect
197. C2×C4⋊Q8Dic43semidirect
203. #391Dic43semidirect
206. #384Dic43semidirect
213. C43#9679semidirect
373. C4#14582636semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊(C43⋊C8)2
C2×#145826362
#191328252
C43×#28572
#967943