Finite Group Databasebeta

← #25001319

Subgroups — #25001319

Order 11008.

418 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135389C211yesmaximal, characteristic
2#19134752C211yesmaximal, characteristic, complemented
3#19134596C211yesmaximal, characteristic
4#19134596C211yesmaximal, characteristic
5#19132479C211yesmaximal, characteristic, complemented
6#19132479C211yesmaximal, characteristic, complemented
7C43×#1277C211yesmaximal, characteristic, complemented
8C2×C4×D172C2211yescharacteristic
9C2×#13063257—21no—
10C2×#13063257—21no—
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063247—21no—
13C2×#13063247—21no—
14C2×(C2×D43)⋊C8—21no—
15C2×(C2×D43)⋊C8—21no—
16#14582769C2211yescharacteristic
17#14582769C2211yescharacteristic
18#14582662—21no—
19#14582662—21no—
20C2×C4⋊C8×C43C2211yescharacteristic
21C2×C4⋊C8×C43C2211yescharacteristic
22C2×C4×C8×C43C2211yescharacteristic
23C22×D172D411yescharacteristic
24C22×C4×D43—21no—
25C22×C43⋊C8—21no—
26C4×D172—21no—
27C4×D172—21no—
28C4×D172—21no—
29C4×D172—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43D411yescharacteristic
37C2×(C2×D43)⋊C4—21no—
38#13063257—42no—
39#13063257—42no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42#13063247—42no—
43#13063247—42no—
44(C2×D43)⋊C8—42no—
45(C2×D43)⋊C8—42no—
46C22×C8×C43—21no—
47C22×C8×C43—21no—
48C22×C8×C43D411yescharacteristic
49C22×C8×C43D411yescharacteristic
50C2×C42×C43C2311yescharacteristic
51C4⋊C8×C43—21no—
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43—21no—
55C4×C8×C43—21no—
56C4×C8×C43—21no—
57C23×D43—21no—
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43#4111yescharacteristic
61C22×Dic43—21no—
62C22×Dic43—41no—
63C22×Dic43—41no—
64C2×D172—21no—
65C2×D172—21no—
66C2×D172—21no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172SD1612yes—
70C2×C4×D43—41no—
71C2×C4×D43—41no—
72C2×C4×D43—41no—
73C2×C4×D43—41no—
74C2×C4×D43—41no—
75C2×C4×D43—41no—
76C2×C8×C43—21no—
77C2×C8×C43—21no—
78C2×C8×C43—21no—
79C2×C8×C43—21no—
80C2×C8×C43—41no—
81C2×C8×C43—41no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C2×C8×C43D812yes—
87C2×C8×C43SD1612yes—
88C42×C43#4111yescharacteristic
89C42×C43#4111yescharacteristic
90C42×C43#4111yescharacteristic
91C42×C43#4111yescharacteristic
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—41no—
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43—41no—
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99C4⋊Dic43—41no—
100C4⋊Dic43—41no—
101C4⋊Dic43—41no—
102C4⋊Dic43—41no—
103C4⋊Dic43—41no—
104C4⋊Dic43—81no—
105C4⋊Dic43—81no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C23×C43#12111yescharacteristic
110C22×D43—22no—
111C22×D43—41no—
112C22×D43—41no—
113C22×D43—41no—
114C22×D43—41no—
115C22×D43—41no—
116C22×D43—41no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43#12311yescharacteristic
120C2×C4×C43#12311yescharacteristic
121C2×C4×C43#12311yescharacteristic
122C2×C4×C43#12411yescharacteristic
123C2×C4×C43#12611yescharacteristic
124C2×C4×C43#12611yescharacteristic
125C2×C4×C43C2×D811yescharacteristic
126C2×C4×C43C2×SD1611yescharacteristic
127C2×C4×C43C2×SD1611yescharacteristic
128C2×C4×C43#13511yescharacteristic
129C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C43#13711yescharacteristic
132C2×C4×C43#13711yescharacteristic
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—81no—
137C2×Dic43—81no—
138C2×Dic43—81no—
139C2×Dic43—81no—
140C2×Dic43—81no—
141C2×Dic43—81no—
142D172—22no—
143D172—22no—
144D172—41no—
145D172—41no—
146C4×D43—81no—
147C4×D43—81no—
148C4×D43—81no—
149C4×D43—81no—
150C8×C43—22no—
151C8×C43—22no—
152C8×C43—81no—
153C8×C43—81no—
154C43⋊C8—81no—
155#10619—431nomaximal, Sylow
156C22×C43#39711yescharacteristic
157C22×C43#45911yescharacteristic
158C22×C43#46111yescharacteristic
159C22×C43#46511yescharacteristic
160C22×C43#46811yescharacteristic
161C22×C43#47111yescharacteristic
162C22×C43#47111yescharacteristic
163C2×D43—42no—
164C2×D43—42no—
165C2×D43—42no—
166C2×D43—81no—
167C2×D43—81no—
168C2×D43—81no—
169C2×D43—81no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43#48011yescharacteristic
173C4×C43#48111yescharacteristic
174C4×C43#48111yescharacteristic
175C4×C43#48211yescharacteristic
176C4×C43#48311yescharacteristic
177C4×C43#48511yescharacteristic
178C4×C43#48611yescharacteristic
179C4×C43#48911yescharacteristic
180Dic43—81no—
181Dic43—161no—
182Dic43—161no—
183#1954—431no—
184#1844—431no—
185#1802—431no—
186#1802—431no—
187#1296—431no—
188#1296—431no—
189#1277D4311yescharacteristic, complemented
190C2×C43#166511yescharacteristic
191C2×C43#167111yescharacteristic
192C2×C43#168511yescharacteristic
193C2×C43#169111yescharacteristic
194C2×C43#207111yescharacteristic
195C2×C43#207711yescharacteristic
196C2×C43#207911yescharacteristic
197D43—82no—
198C2×C4×D4—431no—
199C2×#106—861no—
200C2×#106—861no—
201C2×C4⋊C8—431no—
202C2×C4⋊C8C2×D4311yescharacteristic
203C2×C4⋊C8C2×D4311yescharacteristic
204C2×#102—861no—
205C2×#102—861no—
206C2×C22⋊C8—861no—
207C2×C22⋊C8—861no—
208C2×C4×C8C2×D4311yescharacteristic
209#384—431no—
210#384—431no—
211#340—861no—
212#340—861no—
213C43#1061911yescharacteristic, complemented, Sylow
214C22×D4—431no—
215C23×C4—861no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—861no—
219C22×C8D17211yescharacteristic
220C22×C8D17211yescharacteristic
221C4×D4—861no—
222C4×D4—861no—
223C4×D4—861no—
224C4×D4—861no—
225C2×C4⋊C4—431no—
226C2×C4⋊C4—861no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4—861no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—861no—
232C2×C22⋊C4—861no—
233C2×C42C22×D4311yescharacteristic
234#106—1722no—
235#106—1722no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—861no—
241C4⋊C8—861no—
242#102—1722no—
243#102—1722no—
244C22⋊C8—1722no—
245C22⋊C8—1722no—
246C4×C8—21no—
247C4×C8—21no—
248C24—861no—
249C2×D4—432no—
250C2×D4—861no—
251C2×D4—861no—
252C2×D4—861no—
253C2×D4—861no—
254C2×D4—861no—
255C22×C4—861no—
256C22×C4—1721no—
257C22×C4—1721no—
258C22×C4—1721no—
259C22×C4—1721no—
260C22×C4—1721no—
261C22×C4—1721no—
262C22×C4—1721no—
263C22×C4—1721no—
264C22×C4C2×D17211yescharacteristic
265C22×C4D4×D4311yescharacteristic
266C22×C4#1062190211yescharacteristic
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—1721no—
278C2×C8—1721no—
279C2×C8—1721no—
280C2×C8#1062187312yes—
281C2×C8D34412yes—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—3441no—
285C4⋊C4—3441no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C4⋊C4—1721no—
292C4⋊C4—1721no—
293C4⋊C4—1721no—
294C22⋊C4—1721no—
295C22⋊C4—1721no—
296C42#1062189811yescharacteristic
297C42#1062189811yescharacteristic
298C42#1062190011yescharacteristic
299C42#1062190011yescharacteristic
300C23—862no—
301C23—1721no—
302C23—1721no—
303C23—1721no—
304C23—1721no—
305C23—1721no—
306C23—1721no—
307C23#1306330011yescharacteristic
308D4—862no—
309D4—862no—
310D4—1721no—
311D4—1721no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—3441no—
315C2×C4—3441no—
316C2×C4—3441no—
317C2×C4—3441no—
318C2×C4—3441no—
319C2×C4—3441no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4—3441no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4#1306330711yescharacteristic
328C2×C4#1306330711yescharacteristic
329C2×C4#1306330911yescharacteristic
330C2×C4#1306331311yescharacteristic
331C2×C4#1306332011yescharacteristic
332C2×C4#1306332011yescharacteristic
333C2×C4C2×D34411yescharacteristic
334C2×C4SD16×D4311yescharacteristic
335C2×C4C2×#1062187311yescharacteristic
336C2×C4#1306334611yescharacteristic
337C2×C4#1306334911yescharacteristic
338C2×C4#1306335311yescharacteristic
339C2×C4#1306335711yescharacteristic
340C2×C4#1306335811yescharacteristic
341C8—22no—
342C8—22no—
343C8—81no—
344C8—81no—
345C8—3441no—
346C22—3441no—
347C22—3441no—
348C22—3441no—
349C22—3441no—
350C22—1722no—
351C22—1722no—
352C22—1722no—
353C22#1458282611yescharacteristic
354C22#1458309511yescharacteristic
355C22#1458310511yescharacteristic
356C22#1458312911yescharacteristic
357C22#1458314611yescharacteristic
358C22#1458316311yescharacteristic
359C22#1458316311yescharacteristic
360C4—21no—
361C4—21no—
362C4—3441no—
363C4—6881no—
364C4—6881no—
365C4#1458321311yescharacteristic
366C4#1458321611yescharacteristic
367C4#1458321811yescharacteristic
368C4#1458322211yescharacteristic
369C4#1458322811yescharacteristic
370C4#1458323811yescharacteristic
371C4#1458324611yescharacteristic
372C4#1458325911yescharacteristic
373C2—3442no—
374C2#1913393711yescharacteristic
375C2#1913397111yescharacteristic
376C2#1913406111yescharacteristic
377C2#1913409511yescharacteristic
378C2#1913600011yescharacteristic
379C2#1913603011yescharacteristic
380C2#1913604211yescharacteristic
subgroupG/H
centerC23#13063300
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1277C2
socleC23×C43#121
prime radicalC22×D172D4
hypercenter#1277D43
hypocenterC43#10619
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. #19134752C2semidirect
5. #19132479C2semidirect
6. #19132479C2semidirect
7. C43×#1277C2semidirect
189. #1277D43semidirect
213. C43#10619semidirect

Maximal subgroups

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

subgroupindex
#191353892
#191347522
#191345962
#191324792
C43×#12772
#1061943