Finite Group Databasebeta

← #24986139

Subgroups — #24986139

Order 11008.

614 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
1C2×#14582951C211yesmaximal, characteristic
2C2×#14582950C211yesmaximal, characteristic
3#19136991C211yesmaximal, characteristic
4#19132436C211yesmaximal, characteristic, complemented
5#19132435C211yesmaximal, characteristic, complemented
6#19132434C211yesmaximal, characteristic, complemented
7C43×#1279C211yesmaximal, characteristic, complemented
8C2×C42×D43C2211yescharacteristic
9#14582951—22no—
10#14582951C414yescomplemented
11#14582950—22no—
12#14582950C414yescomplemented
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×Dic43⋊C8—21no—
15C2×(C2×D43)⋊C8—21no—
16C2×(C2×D43)⋊C8—21no—
17C2×C4×C43⋊C8C2211yescharacteristic
18C2×C8×Dic43—21no—
19#14582766—21no—
20#14582764C412yes—
21#14582761—21no—
22#14582756C412yes—
23C4×C4⋊Dic43C2211yescharacteristic
24C4×(C2×D43)⋊C4—21no—
25#14582745—21no—
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×C4×C8×C43C2211yescharacteristic
28C4×C4⋊C4×C43C2211yescharacteristic
29C22×C4×D43C2×C411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C22×C4×D43D411yescharacteristic
32C22×C43⋊C8—21no—
33C22×C43⋊C8—21no—
34C2×C4⋊Dic43C2×C412yes—
35C2×(C2×D43)⋊C4—22no—
36C2×C4×Dic43—21no—
37C2×C4×Dic43C2×C411yescharacteristic
38C2×C4×Dic43D411yescharacteristic
39C2×C4×Dic43D411yescharacteristic
40C42×D43C2×C412yes—
41C42×D43C2×C412yes—
42C42×D43D412yes—
43C42×D43Q812yes—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)C2×C412yes—
46Dic43⋊C8—24no—
47(C2×D43)⋊C8—24no—
48(C2×D43)⋊C8—24no—
49C4×C43⋊C8—21no—
50C4×C43⋊C8C2×C412yes—
51C8×Dic43—24no—
52C43⋊#95—21no—
53C43⋊#95—22no—
54C43⋊#95—22no—
55C43⋊#95—22no—
56C22×C8×C43—21no—
57C22×C8×C43—21no—
58C2×C4⋊C4×C43C2×C412yes—
59C2×C42×C43—21no—
60C2×C42×C43C2311yescharacteristic
61C4⋊C8×C43—21no—
62C4⋊C8×C43C2×C412yes—
63C4×C8×C43—21no—
64C4×C8×C43C2×C412yes—
65#95×C43—21no—
66C23×D43C22⋊C411yescharacteristic
67C22×C4×C43—22no—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—22no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C2×C4×D43—22no—
76C2×C4×D43—22no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—42no—
82C2×C4×D43C4212yes—
83C2×C4×D43C22⋊C412yes—
84C2×C4×D43C22⋊C412yes—
85C2×C4×D43C4⋊C412yes—
86C2×C4×D43C4⋊C412yes—
87C2×C4×D43C4⋊C412yes—
88C2×C8×C43—22no—
89C2×C8×C43—22no—
90C2×C8×C43—42no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—22no—
95C42×C43—41no—
96C42×C43—41no—
97C42×C43C22×C411yescharacteristic
98C42×C43C22×C411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43C2×Q811yescharacteristic
101(C2×D43)⋊C4—44no—
102C4⋊Dic43—22no—
103C4⋊Dic43—22no—
104C4×Dic43—41no—
105C4×Dic43—41no—
106C4×Dic43C4212yes—
107C4×Dic43C22⋊C412yes—
108C4×Dic43C22⋊C412yes—
109C4×Dic43C4⋊C412yes—
110C4×Dic43C4⋊C412yes—
111C4×Dic43C4⋊C412yes—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—22no—
114C2×C43⋊C8—42no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C23×C43C2×C22⋊C411yescharacteristic
118C22×D43—22no—
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—22no—
122C22×D43#9512yes—
123C2×C4×C43—22no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43C2×C4211yescharacteristic
128C2×C4×C43C2×C22⋊C411yescharacteristic
129C2×C4×C43C2×C22⋊C411yescharacteristic
130C2×C4×C43C2×C4⋊C411yescharacteristic
131C2×C4×C43C2×C4⋊C411yescharacteristic
132C2×C4×C43C2×C4⋊C411yescharacteristic
133C2×C4×C43#13112yes—
134C2×C4×C43#13112yes—
135C2×C4×C43#13511yescharacteristic
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43#13511yescharacteristic
139C2×Dic43—22no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—22no—
143C2×Dic43—42no—
144C2×Dic43—42no—
145C2×Dic43—42no—
146C2×Dic43#9512yes—
147C2×Dic43#9512yes—
148C2×Dic43#9512yes—
149C4×D43—22no—
150C4×D43—22no—
151C4×D43—22no—
152C4×D43—22no—
153C4×D43—24no—
154C4×D43—22no—
155C4×D43—22no—
156C4×D43—42no—
157C4×D43—42no—
158C8×C43—42no—
159C8×C43—42no—
160C43⋊C8—42no—
161C43⋊C8—42no—
162#7894—431nomaximal, Sylow
163C22×C43C2×#9511yescharacteristic
164C22×C43#40812yes—
165C22×C43#41611yescharacteristic
166C22×C43#41611yescharacteristic
167C22×C43#42112yes—
168C2×D43—22no—
169C2×D43—22no—
170C2×D43—22no—
171C2×D43—42no—
172C2×D43—42no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—82no—
176C4×C43#40511yescharacteristic
177C4×C43#40511yescharacteristic
178C4×C43#41611yescharacteristic
179C4×C43#41611yescharacteristic
180C4×C43#42412yes—
181C4×C43#42711yescharacteristic
182C4×C43#42711yescharacteristic
183Dic43—22no—
184Dic43—22no—
185Dic43—22no—
186Dic43—82no—
187C2×#431—431no—
188C2×#431—431no—
189#2283—431no—
190#1279—431no—
191#1279—431no—
192#1279—431no—
193#1279D4311yescharacteristic, complemented
194C2×C43#148212yes—
195C2×C43#148212yes—
196C2×C43#172911yescharacteristic
197C2×C43#173311yescharacteristic
198C2×C43#173511yescharacteristic
199D43—42no—
200C22×C42—431no—
201#431—434no—
202#431—434no—
203#431—862no—
204#431—862no—
205C2×C4⋊C8—431no—
206C2×C4⋊C8—861no—
207C2×C4⋊C8C2×D4311yescharacteristic
208C2×C22⋊C8—861no—
209C2×C22⋊C8—861no—
210C2×C4×C8—431no—
211C2×C4×C8—861no—
212C2×C4×C8C2×D4311yescharacteristic
213#383—861no—
214#382—432no—
215#381—861no—
216#380—432no—
217C4×C4⋊C4—431no—
218C4×C4⋊C4C2×D4311yescharacteristic
219C4×C22⋊C4—861no—
220#376—861no—
221C43#789411yescharacteristic, complemented, Sylow
222C23×C4—431no—
223C23×C4—431no—
224C23×C4—431no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—861no—
228C22×C8—861no—
229C2×C4⋊C4—432no—
230C2×C4⋊C4C4×D4312yes—
231C2×C22⋊C4—862no—
232C2×C42—21no—
233C2×C42—431no—
234C2×C42—431no—
235C2×C42—431no—
236C2×C42—432no—
237C2×C42—432no—
238C2×C42—432no—
239C2×C42—432no—
240C2×C42—861no—
241C2×C42C22×D4311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—432no—
244C4⋊C8—864no—
245C4⋊C8—861no—
246C4⋊C8C4×D4312yes—
247C22⋊C8—864no—
248C22⋊C8—864no—
249C4×C8—21no—
250C4×C8—432no—
251C4×C8—864no—
252C4×C8—861no—
253C4×C8C4×D4312yes—
254#95—21no—
255#95—862no—
256#95—862no—
257#95—862no—
258#95—861no—
259C24—431no—
260C22×C4—22no—
261C22×C4—431no—
262C22×C4—431no—
263C22×C4—431no—
264C22×C4—432no—
265C22×C4—432no—
266C22×C4—432no—
267C22×C4—432no—
268C22×C4—432no—
269C22×C4—432no—
270C22×C4—862no—
271C22×C4—862no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—862no—
277C22×C4—1722no—
278C22×C4C2×C4×D4311yescharacteristic
279C22×C4D4×D4311yescharacteristic
280C22×C4D4×D4311yescharacteristic
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—42no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—862no—
287C2×C8—862no—
288C2×C8—1722no—
289C2×C8—1721no—
290C2×C8—1721no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—862no—
294C4⋊C4—862no—
295C22⋊C4—1724no—
296C42—41no—
297C42—41no—
298C42—432no—
299C42—432no—
300C42—432no—
301C42—432no—
302C42—432no—
303C42—432no—
304C42—1721no—
305C42—1721no—
306C42C2×C4×D4311yescharacteristic
307C42C2×C4×D4311yescharacteristic
308C42D4×D4311yescharacteristic
309C42Q8×D4311yescharacteristic
310C23—432no—
311C23—862no—
312C23—861no—
313C23—861no—
314C23—862no—
315C23C22⋊C4×D4311yescharacteristic
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—432no—
321C2×C4—432no—
322C2×C4—432no—
323C2×C4—862no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—862no—
327C2×C4—862no—
328C2×C4—862no—
329C2×C4—862no—
330C2×C4—862no—
331C2×C4—864no—
332C2×C4—862no—
333C2×C4—862no—
334C2×C4—1722no—
335C2×C4—1722no—
336C2×C4—1722no—
337C2×C4—1722no—
338C2×C4—1722no—
339C2×C4C42×D4311yescharacteristic
340C2×C4C22⋊C4×D4311yescharacteristic
341C2×C4C22⋊C4×D4311yescharacteristic
342C2×C4C4⋊C4×D4311yescharacteristic
343C2×C4C4⋊C4×D4311yescharacteristic
344C2×C4C4⋊C4×D4311yescharacteristic
345C2×C4#1306333112yes—
346C2×C4#1306333312yes—
347C2×C4#1306334411yescharacteristic
348C2×C4#1306334611yescharacteristic
349C2×C4#1306334611yescharacteristic
350C2×C4#1306334811yescharacteristic
351C8—42no—
352C8—42no—
353C8—1722no—
354C8—1722no—
355C22—862no—
356C22—862no—
357C22—862no—
358C22—1722no—
359C22—1722no—
360C22#95×D4311yescharacteristic
361C22#1458286412yes—
362C22#1458289211yescharacteristic
363C22#1458289411yescharacteristic
364C22#1458291412yes—
365C4—21no—
366C4—21no—
367C4—82no—
368C4—862no—
369C4—862no—
370C4—862no—
371C4—3442no—
372C4#1458285311yescharacteristic
373C4#1458285611yescharacteristic
374C4#1458289211yescharacteristic
375C4#1458289411yescharacteristic
376C4#1458292412yes—
377C4#1458293411yescharacteristic
378C4#1458293611yescharacteristic
379C2—1722no—
380C2#1913300012yes—
381C2#1913300212yes—
382C2#1913429011yescharacteristic
383C2#1913430311yescharacteristic
384C2#1913431011yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC43×#1279C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1279D43
hypocenterC43#7894
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #19132436C2semidirect
5. #19132435C2semidirect
6. #19132434C2semidirect
7. C43×#1279C2semidirect
10. #14582951C4semidirect
12. #14582950C4semidirect
193. #1279D43semidirect
221. C43#7894semidirect

Maximal subgroups

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

subgroupindex
C2×#145829512
C2×#145829502
#191369912
#191324362
#191324352
#191324342
C43×#12792
#789443