Finite Group Databasebeta

← #25001318

Subgroups — #25001318

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#19134592C211yesmaximal, characteristic
3#19134592C211yesmaximal, characteristic
4#19132478C211yesmaximal, characteristic, complemented
5#19132478C211yesmaximal, characteristic, complemented
6#19132430C211yesmaximal, characteristic, complemented
7C43×#1844C211yesmaximal, characteristic, complemented
8C2×C4×D172C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063245—21no—
13C2×#13063245—21no—
14C2×(C2×D43)⋊C8—21no—
15C2×(C2×D43)⋊C8—21no—
16#14582661—21no—
17#14582661—21no—
18C2×#106×C43—21no—
19C2×#106×C43—21no—
20C2×C4×C8×C43C2211yescharacteristic
21C43×#384C2211yescharacteristic
22C43×#384C2211yescharacteristic
23C22×D172D411yescharacteristic
24C22×C4×D43—21no—
25C22×C43⋊C8—21no—
26C22×C43⋊C8—21no—
27C22×C43⋊C8—21no—
28C4×D172—21no—
29C4×D172—21no—
30C4×D172—21no—
31C4×D172—21no—
32C2×C4⋊Dic43D411yescharacteristic
33C2×(C2×D43)⋊C4—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40#13063245—42no—
41#13063245—42no—
42(C2×D43)⋊C8—42no—
43(C2×D43)⋊C8—42no—
44C22×C8×C43D411yescharacteristic
45C22×C8×C43D411yescharacteristic
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C42×C43C2311yescharacteristic
53#106×C43—42no—
54#106×C43—42no—
55C4×C8×C43—21no—
56C4×C8×C43—21no—
57C23×D43—21no—
58C22×C4×C43—41no—
59C22×C4×C43—41no—
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43#4111yescharacteristic
63C22×Dic43—21no—
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×C43D812yes—
81C2×C8×C43SD1612yes—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—81no—
91C4⋊C4×C43—81no—
92C42×C43#4111yescharacteristic
93C42×C43#4111yescharacteristic
94C42×C43#4111yescharacteristic
95C42×C43#4111yescharacteristic
96(C2×D43)⋊C4—41no—
97(C2×D43)⋊C4—41no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
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—81no—
120C2×C4×C43—81no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×C4×C43—81no—
124C2×C4×C43—81no—
125C2×C4×C43#12311yescharacteristic
126C2×C4×C43#12311yescharacteristic
127C2×C4×C43#12311yescharacteristic
128C2×C4×C43#12411yescharacteristic
129C2×C4×C43#12611yescharacteristic
130C2×C4×C43#12611yescharacteristic
131C2×C4×C43C2×D811yescharacteristic
132C2×C4×C43C2×SD1611yescharacteristic
133C2×C4×C43C2×SD1611yescharacteristic
134C2×C4×C43#13511yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43#13711yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
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—
152C43⋊C8—81no—
153C43⋊C8—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—161no—
173C4×C43—161no—
174C4×C43#48011yescharacteristic
175C4×C43#48111yescharacteristic
176C4×C43#48111yescharacteristic
177C4×C43#48211yescharacteristic
178C4×C43#48311yescharacteristic
179C4×C43#48511yescharacteristic
180C4×C43#48611yescharacteristic
181C4×C43#48911yescharacteristic
182Dic43—81no—
183#1954—431no—
184#1844D4311yescharacteristic, complemented
185#1802—431no—
186#1802—431no—
187#1296—431no—
188#1296—431no—
189#1277—431no—
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—21no—
200C2×#106—21no—
201C2×C4⋊C8—431no—
202C2×C4⋊C8—431no—
203C2×C4⋊C8—431no—
204C2×#102—861no—
205C2×#102—861no—
206C2×C22⋊C8—861no—
207C2×C22⋊C8—861no—
208C2×C4×C8C2×D4311yescharacteristic
209#384C2×D4311yescharacteristic
210#384C2×D4311yescharacteristic
211#340—861no—
212#340—861no—
213C43#1061911yescharacteristic, complemented, Sylow
214C22×D4—431no—
215C23×C4—861no—
216C22×C8—861no—
217C22×C8—861no—
218C22×C8—861no—
219C22×C8C22⋊D4311yescharacteristic
220C22×C8C22⋊D4311yescharacteristic
221C4×D4—861no—
222C4×D4—861no—
223C4×D4—861no—
224C4×D4—861no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—431no—
232C2×C22⋊C4—861no—
233C2×C42C22×D4311yescharacteristic
234#106—42no—
235#106—42no—
236C4⋊C8—861no—
237C4⋊C8—861no—
238C4⋊C8—861no—
239C4⋊C8—861no—
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—41no—
256C22×C4—41no—
257C22×C4—861no—
258C22×C4—1721no—
259C22×C4—1721no—
260C22×C4—1721no—
261C22×C4—1721no—
262C22×C4—1721no—
263C22×C4—1721no—
264C22×C4D4×D4311yescharacteristic
265C22×C4#1062190011yescharacteristic
266C22×C4C2×C22⋊D4311yescharacteristic
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—1721no—
272C2×C8—1721no—
273C2×C8—1721no—
274C2×C8—1721no—
275C2×C8—1721no—
276C2×C8—1721no—
277C2×C8—1721no—
278C2×C8—1721no—
279C2×C8—1721no—
280C2×C8#1062188212yes—
281C2×C8#1062188412yes—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—81no—
291C4⋊C4—81no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C22⋊C4—1721no—
295C22⋊C4—1721no—
296C42#1062189811yescharacteristic
297C42#1062189811yescharacteristic
298C42#1062190211yescharacteristic
299C42#1062190211yescharacteristic
300C23—862no—
301C23—1721no—
302C23—1721no—
303C23—1721no—
304C23—1721no—
305C23—1721no—
306C23—1721no—
307C23#1306329611yescharacteristic
308D4—862no—
309D4—862no—
310D4—1721no—
311D4—1721no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4—3441no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4#1306330811yescharacteristic
328C2×C4#1306331011yescharacteristic
329C2×C4#1306331011yescharacteristic
330C2×C4#1306331411yescharacteristic
331C2×C4#1306332011yescharacteristic
332C2×C4#1306332011yescharacteristic
333C2×C4C2×#1062188211yescharacteristic
334C2×C4SD16×D4311yescharacteristic
335C2×C4C2×#1062188411yescharacteristic
336C2×C4#1306334611yescharacteristic
337C2×C4#1306335111yescharacteristic
338C2×C4#1306335211yescharacteristic
339C2×C4#1306335411yescharacteristic
340C2×C4#1306335611yescharacteristic
341C8—22no—
342C8—22no—
343C8—3441no—
344C8—3441no—
345C8—3441no—
346C22—3441no—
347C22—3441no—
348C22—3441no—
349C22—3441no—
350C22—1722no—
351C22—1722no—
352C22—1722no—
353C22#1458282511yescharacteristic
354C22#1458309111yescharacteristic
355C22#1458310111yescharacteristic
356C22#1458312511yescharacteristic
357C22#1458314211yescharacteristic
358C22#1458315911yescharacteristic
359C22#1458315911yescharacteristic
360C4—21no—
361C4—21no—
362C4—161no—
363C4—161no—
364C4—3441no—
365C4#1458321211yescharacteristic
366C4#1458321711yescharacteristic
367C4#1458321911yescharacteristic
368C4#1458322511yescharacteristic
369C4#1458323111yescharacteristic
370C4#1458324311yescharacteristic
371C4#1458324711yescharacteristic
372C4#1458326111yescharacteristic
373C2—3442no—
374C2#1913393311yescharacteristic
375C2#1913396711yescharacteristic
376C2#1913405711yescharacteristic
377C2#1913409111yescharacteristic
378C2#1913599911yescharacteristic
379C2#1913602911yescharacteristic
380C2#1913604111yescharacteristic
subgroupG/H
centerC23#13063296
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1844C2
socleC23×C43#121
prime radicalC22×D172D4
hypercenter#1844D43
hypocenterC43#10619
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1844

Complements

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

NH ≅ G/Ntype
4. #19132478C2semidirect
5. #19132478C2semidirect
6. #19132430C2semidirect
7. C43×#1844C2semidirect
184. #1844D43semidirect
213. C43#10619semidirect

Maximal subgroups

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

subgroupindex
#191353892
#191345922
#191324782
#191324302
C43×#18442
#1061943