Finite Group Databasebeta

← #25000445

Subgroups — #25000445

Order 11008.

474 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583190C211yesmaximal, characteristic
2#19135556C211yesmaximal, characteristic, complemented
3#19135389C211yesmaximal, characteristic
4#19134596C211yesmaximal, characteristic
5C2×#14582647C211yesmaximal, characteristic, complemented
6#19132479C211yesmaximal, characteristic, complemented
7C2×C43×#334C211yesmaximal, characteristic, complemented
8C2×#13063325C2211yescharacteristic
9C2×C4×D172C2211yescharacteristic
10#14583190—22no—
11#14583190—22no—
12C2×#13063257—21no—
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×#13063247—21no—
15C2×#13063247—21no—
16C2×(C2×D43)⋊C8—21no—
17C2×(C2×D43)⋊C8—21no—
18#14582769C2211yescharacteristic
19#14582662—21no—
20#14582662—21no—
21#14582662—21no—
22#14582647—22no—
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×C4×C8×C43C2211yescharacteristic
26C43×#334—22no—
27C22×Dic86—21no—
28C22×D172D411yescharacteristic
29C22×C4×D43—21no—
30C22×C43⋊C8—21no—
31#13063325—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325D412yes—
35C4×D172—21no—
36C4×D172—21no—
37C4×D172—21no—
38C4×D172—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43D411yescharacteristic
45C2×(C2×D43)⋊C4—21no—
46#13063257—24no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49#13063247—24no—
50#13063247—42no—
51(C2×D43)⋊C8—42no—
52(C2×D43)⋊C8—42no—
53C22×C8×C43—21no—
54C22×C8×C43—21no—
55C22×C8×C43D411yescharacteristic
56C22×C8×C43D411yescharacteristic
57C2×C42×C43C2311yescharacteristic
58C4⋊C8×C43—21no—
59C4⋊C8×C43—21no—
60C4⋊C8×C43—21no—
61C4⋊C8×C43D412yes—
62C4×C8×C43—21no—
63C4×C8×C43—21no—
64C23×D43—21no—
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43#4111yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—41no—
70C22×Dic43—41no—
71C2×D172—21no—
72C2×D172—21no—
73C2×D172—21no—
74C2×D172—21no—
75C2×D172—21no—
76C2×D172SD1612yes—
77C2×C4×D43—41no—
78C2×C4×D43—41no—
79C2×C4×D43—41no—
80C2×C4×D43—41no—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83C2×Dic86—22no—
84C2×Dic86—41no—
85C2×Dic86—81no—
86C2×Dic86—81no—
87C2×C8×C43—21no—
88C2×C8×C43—21no—
89C2×C8×C43—22no—
90C2×C8×C43—21no—
91C2×C8×C43—21no—
92C2×C8×C43—21no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43SD1612yes—
99C42×C43C2×D411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43#4111yescharacteristic
102C42×C43#4111yescharacteristic
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—41no—
105C4⋊Dic43—22no—
106C4⋊Dic43—21no—
107C4⋊Dic43—22no—
108C4⋊Dic43—21no—
109C4⋊Dic43—41no—
110C4⋊Dic43—41no—
111C4⋊Dic43—41no—
112C4⋊Dic43—41no—
113C4⋊Dic43—41no—
114C4⋊Dic43—41no—
115C4⋊Dic43—81no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8—41no—
119C23×C43#12111yescharacteristic
120C22×D43—22no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—41no—
126C22×D43—41no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12311yescharacteristic
133C2×C4×C43#12311yescharacteristic
134C2×C4×C43#12411yescharacteristic
135C2×C4×C43C2×SD1611yescharacteristic
136C2×C4×C43C2×SD1611yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43#13511yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C2×C4×C43#13711yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C2×Dic43—42no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—81no—
148C2×Dic43—81no—
149C2×Dic43—81no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152D172—22no—
153D172—22no—
154D172—41no—
155D172—41no—
156C4×D43—81no—
157C4×D43—81no—
158C4×D43—81no—
159C4×D43—81no—
160Dic86—82no—
161Dic86—82no—
162C8×C43—22no—
163C8×C43—42no—
164C8×C43—41no—
165C8×C43—81no—
166C43⋊C8—81no—
167#10480—431nomaximal, Sylow
168C22×C43#39411yescharacteristic
169C22×C43#46111yescharacteristic
170C22×C43#46311yescharacteristic
171C22×C43#46511yescharacteristic
172C22×C43#47011yescharacteristic
173C22×C43#47111yescharacteristic
174C22×C43#47211yescharacteristic
175C2×D43—42no—
176C2×D43—42no—
177C2×D43—42no—
178C2×D43—81no—
179C2×D43—81no—
180C2×D43—81no—
181C2×D43—81no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43#44811yescharacteristic
185C4×C43#45211yescharacteristic
186C4×C43#46011yescharacteristic
187C4×C43#46411yescharacteristic
188C4×C43#46511yescharacteristic
189C4×C43#46811yescharacteristic
190C4×C43#48311yescharacteristic
191C4×C43#48511yescharacteristic
192Dic43—82no—
193Dic43—81no—
194Dic43—161no—
195C2×#476—431no—
196#1990—431no—
197#1954—431no—
198#1802—431no—
199C2×#334D4311yescharacteristic, complemented
200C2×#333—431no—
201#1296—431no—
202C2×C43#167111yescharacteristic
203C2×C43#167711yescharacteristic
204C2×C43#169511yescharacteristic
205C2×C43#170311yescharacteristic
206C2×C43#203511yescharacteristic
207C2×C43#205111yescharacteristic
208C2×C43#205511yescharacteristic
209D43—82no—
210C2×C4⋊Q8—431no—
211C2×C4×D4—431no—
212#476—862no—
213#476—862no—
214C2×#106—861no—
215C2×C4⋊C8—431no—
216C2×C4⋊C8C2×D4311yescharacteristic
217C2×C4⋊C8C2×D4311yescharacteristic
218C2×#102—861no—
219C2×#102—861no—
220C2×C22⋊C8—861no—
221C2×C22⋊C8—861no—
222C2×C4×C8C2×D4311yescharacteristic
223#384—431no—
224#340—861no—
225#340—861no—
226#340—861no—
227#334—22no—
228#333—862no—
229C43#1048011yescharacteristic, complemented, Sylow
230C22×Q8—861no—
231C22×D4—431no—
232C23×C4—861no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—861no—
236C22×C8D17211yescharacteristic
237C22×C8D17211yescharacteristic
238C4⋊Q8—432no—
239C4⋊Q8—861no—
240C4⋊Q8—861no—
241C4⋊Q8—861no—
242C4×D4—861no—
243C4×D4—861no—
244C4×D4—861no—
245C4×D4—861no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4—861no—
252C2×C22⋊C4—861no—
253C2×C42C22×D4311yescharacteristic
254#106—864no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—861no—
259C4⋊C8—861no—
260C4⋊C8C22⋊D4312yes—
261#102—864no—
262#102—1722no—
263C22⋊C8—1722no—
264C22⋊C8—1722no—
265C4×C8—21no—
266C4×C8—21no—
267C24—861no—
268C2×Q8—862no—
269C2×Q8—3441no—
270C2×Q8—3441no—
271C2×Q8—1721no—
272C2×D4—432no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—861no—
278C22×C4—861no—
279C22×C4—1721no—
280C22×C4—1721no—
281C22×C4—1721no—
282C22×C4—1721no—
283C22×C4—1721no—
284C22×C4—1721no—
285C22×C4—1721no—
286C22×C4—1721no—
287C22×C4C2×D17211yescharacteristic
288C22×C4D4×D4311yescharacteristic
289C22×C4#1062190211yescharacteristic
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—22no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—1721no—
302C2×C8—1721no—
303C2×C8—1721no—
304C2×C8#1062187312yes—
305C4⋊C4—862no—
306C4⋊C4—861no—
307C4⋊C4—862no—
308C4⋊C4—861no—
309C4⋊C4—3441no—
310C4⋊C4—1721no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C4⋊C4—1721no—
316C22⋊C4—1721no—
317C22⋊C4—1721no—
318C42#1062189811yescharacteristic
319C42D4×D4311yescharacteristic
320C42#1062190211yescharacteristic
321C42C2×C22⋊D4311yescharacteristic
322C23—862no—
323C23—1721no—
324C23—1721no—
325C23—1721no—
326C23—1721no—
327C23—1721no—
328C23—1721no—
329C23#1306330011yescharacteristic
330Q8—3442no—
331Q8—3442no—
332D4—862no—
333D4—862no—
334D4—1721no—
335D4—1721no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—3441no—
339C2×C4—3441no—
340C2×C4—3441no—
341C2×C4—3441no—
342C2×C4—3441no—
343C2×C4—3441no—
344C2×C4—3441no—
345C2×C4—3441no—
346C2×C4—3441no—
347C2×C4—1721no—
348C2×C4—1722no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4#1306329311yescharacteristic
352C2×C4#1306329911yescharacteristic
353C2×C4#1306330011yescharacteristic
354C2×C4#1306331011yescharacteristic
355C2×C4#1306331011yescharacteristic
356C2×C4#1306331411yescharacteristic
357C2×C4SD16×D4311yescharacteristic
358C2×C4C2×#1062187311yescharacteristic
359C2×C4#1306334611yescharacteristic
360C2×C4#1306334711yescharacteristic
361C2×C4#1306335311yescharacteristic
362C2×C4#1306335411yescharacteristic
363C2×C4#1306335411yescharacteristic
364C2×C4#1306335811yescharacteristic
365C8—22no—
366C8—42no—
367C8—41no—
368C8—81no—
369C8—3441no—
370C22—3441no—
371C22—3441no—
372C22—3441no—
373C22—3441no—
374C22—1722no—
375C22—1722no—
376C22—1722no—
377C22#1458281611yescharacteristic
378C22#1458310511yescharacteristic
379C22#1458311511yescharacteristic
380C22#1458312911yescharacteristic
381C22#1458315811yescharacteristic
382C22#1458316311yescharacteristic
383C22#1458317011yescharacteristic
384C4—21no—
385C4—21no—
386C4—3442no—
387C4—3441no—
388C4—6881no—
389C4#1458303611yescharacteristic
390C4#1458305811yescharacteristic
391C4#1458310011yescharacteristic
392C4#1458312211yescharacteristic
393C4#1458312811yescharacteristic
394C4#1458314511yescharacteristic
395C4#1458323111yescharacteristic
396C4#1458324311yescharacteristic
397C2—3442no—
398C2#1913397111yescharacteristic
399C2#1913400511yescharacteristic
400C2#1913411911yescharacteristic
401C2#1913417111yescharacteristic
402C2#1913579311yescharacteristic
403C2#1913588911yescharacteristic
404C2#1913591311yescharacteristic
subgroupG/H
centerC23#13063300
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#334C2
socleC23×C43#121
prime radicalC22×D172D4
hypercenterC2×#334D43
hypocenterC43#10480
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. #19135556C2semidirect
5. C2×#14582647C2semidirect
6. #19132479C2semidirect
7. C2×C43×#334C2semidirect
199. C2×#334D43semidirect
229. C43#10480semidirect

Maximal subgroups

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

subgroupindex
C2×#145831902
#191355562
#191353892
#191345962
C2×#145826472
#191324792
C2×C43×#3342
#1048043