Finite Group Databasebeta

← #25000477

Subgroups — #25000477

Order 11008.

490 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583176C211yesmaximal, characteristic
2#19135389C211yesmaximal, characteristic
3#19134592C211yesmaximal, characteristic
4C2×#14582652C211yesmaximal, characteristic, complemented
5C2×#14582645C211yesmaximal, characteristic, complemented
6#19132478C211yesmaximal, characteristic, complemented
7C43×#1956C211yesmaximal, characteristic, complemented
8C2×C4×D172C2211yescharacteristic
9#14583176—22no—
10#14583176—22no—
11C2×#13063258—21no—
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×C4⋊(C43⋊C8)C2211yescharacteristic
15C2×#13063245—21no—
16C2×#13063245—21no—
17C2×(C2×D43)⋊C8—21no—
18C2×(C2×D43)⋊C8—21no—
19#14582661—21no—
20#14582652—22no—
21#14582645—22no—
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×#103×C43—21no—
24C2×#103×C43—21no—
25C2×C4×C8×C43C2211yescharacteristic
26C43×#384C2211yescharacteristic
27C22×D172D411yescharacteristic
28C22×C4×D43—21no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32C4×D172—21no—
33C4×D172—21no—
34C4×D172—21no—
35C4×D172—21no—
36C2×C4⋊Dic43D411yescharacteristic
37C2×(C2×D43)⋊C4—21no—
38#13063258—24no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)D412yes—
45#13063245—24no—
46#13063245—42no—
47(C2×D43)⋊C8—42no—
48(C2×D43)⋊C8—42no—
49C22×Q8×C43—21no—
50C22×C8×C43D411yescharacteristic
51C22×C8×C43D411yescharacteristic
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43—21no—
55C4⋊Q8×C43D412yes—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C42×C43C2311yescharacteristic
62#103×C43—42no—
63#103×C43—42no—
64C4×C8×C43—21no—
65C4×C8×C43—21no—
66C23×D43—21no—
67C2×Q8×C43—22no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43—41no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×Dic43—21no—
79C2×D172—21no—
80C2×D172—21no—
81C2×D172—21no—
82C2×D172—21no—
83C2×D172—21no—
84C2×D172Q1612yes—
85C2×C4×D43—41no—
86C2×C4×D43—41no—
87C2×C4×D43—41no—
88C2×C4×D43—41no—
89C2×C4×D43—41no—
90C2×C4×D43—41no—
91C2×C8×C43—21no—
92C2×C8×C43—21no—
93C2×C8×C43—21no—
94C2×C8×C43—21no—
95C2×C8×C43—21no—
96C2×C8×C43D812yes—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—81no—
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43#4111yescharacteristic
109C42×C43#4111yescharacteristic
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—41no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C2×C43⋊C8—22no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C23×C43#12111yescharacteristic
124C22×D43—22no—
125C22×D43—41no—
126C22×D43—41no—
127C22×D43—41no—
128C22×D43—41no—
129C22×D43—41no—
130C22×D43—41no—
131Q8×C43—42no—
132Q8×C43—42no—
133Q8×C43—81no—
134Q8×C43—81no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—42no—
138C2×C4×C43—81no—
139C2×C4×C43—81no—
140C2×C4×C43—81no—
141C2×C4×C43—81no—
142C2×C4×C43—81no—
143C2×C4×C43#12011yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#12311yescharacteristic
147C2×C4×C43#12311yescharacteristic
148C2×C4×C43#12411yescharacteristic
149C2×C4×C43C2×D811yescharacteristic
150C2×C4×C43C2×Q1611yescharacteristic
151C2×C4×C43#13511yescharacteristic
152C2×C4×C43#13511yescharacteristic
153C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C43#13711yescharacteristic
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160D172—22no—
161D172—22no—
162D172—41no—
163D172—41no—
164C4×D43—81no—
165C4×D43—81no—
166C4×D43—81no—
167C4×D43—81no—
168C8×C43—22no—
169C8×C43—41no—
170C43⋊C8—42no—
171C43⋊C8—81no—
172C43⋊C8—81no—
173#10485—431nomaximal, Sylow
174C22×C43#39411yescharacteristic
175C22×C43#45911yescharacteristic
176C22×C43#46311yescharacteristic
177C22×C43#46711yescharacteristic
178C22×C43#46811yescharacteristic
179C22×C43#47111yescharacteristic
180C22×C43#47311yescharacteristic
181C2×D43—42no—
182C2×D43—42no—
183C2×D43—42no—
184C2×D43—81no—
185C2×D43—81no—
186C2×D43—81no—
187C2×D43—81no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—82no—
191C4×C43—161no—
192C4×C43#44911yescharacteristic
193C4×C43#45111yescharacteristic
194C4×C43#45911yescharacteristic
195C4×C43#46311yescharacteristic
196C4×C43#46611yescharacteristic
197C4×C43#46911yescharacteristic
198C4×C43#48411yescharacteristic
199C4×C43#48511yescharacteristic
200Dic43—81no—
201C2×#474—431no—
202#1956D4311yescharacteristic, complemented
203#1954—431no—
204#1802—431no—
205C2×#335—431no—
206C2×#332—431no—
207#1296—431no—
208C2×C43#166911yescharacteristic
209C2×C43#168311yescharacteristic
210C2×C43#168511yescharacteristic
211C2×C43#169911yescharacteristic
212C2×C43#203611yescharacteristic
213C2×C43#205211yescharacteristic
214C2×C43#205411yescharacteristic
215D43—82no—
216C2×C4⋊Q8C2×D4311yescharacteristic
217C2×C4×D4—431no—
218#474—862no—
219#474—862no—
220C2×#107—861no—
221C2×C4⋊C8—431no—
222C2×C4⋊C8—431no—
223C2×C4⋊C8—431no—
224C2×#103—21no—
225C2×#103—21no—
226C2×#102—861no—
227C2×#102—861no—
228C2×C22⋊C8—861no—
229C2×C22⋊C8—861no—
230C2×C4×C8C2×D4311yescharacteristic
231#384C2×D4311yescharacteristic
232#340—861no—
233#335—862no—
234#332—862no—
235C43#1048511yescharacteristic, complemented, Sylow
236C22×Q8—21no—
237C22×D4—431no—
238C23×C4—861no—
239C22×C8—861no—
240C22×C8—861no—
241C22×C8—861no—
242C22×C8C22⋊D4311yescharacteristic
243C22×C8C22⋊D4311yescharacteristic
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8D17212yes—
248C4×D4—861no—
249C4×D4—861no—
250C4×D4—861no—
251C4×D4—861no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—431no—
258C2×C22⋊C4—861no—
259C2×C42C22×D4311yescharacteristic
260#107—864no—
261C4⋊C8—432no—
262C4⋊C8—861no—
263C4⋊C8—861no—
264C4⋊C8—861no—
265C4⋊C8—861no—
266C4⋊C8—861no—
267#103—42no—
268#103—42no—
269#102—864no—
270#102—1722no—
271C22⋊C8—1722no—
272C22⋊C8—1722no—
273C4×C8—21no—
274C4×C8—21no—
275C24—861no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×D4—432no—
283C2×D4—861no—
284C2×D4—861no—
285C2×D4—861no—
286C2×D4—861no—
287C2×D4—861no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—861no—
291C22×C4—1721no—
292C22×C4—1721no—
293C22×C4—1721no—
294C22×C4—1721no—
295C22×C4—1721no—
296C22×C4—1721no—
297C22×C4D4×D4311yescharacteristic
298C22×C4#1062190011yescharacteristic
299C22×C4C2×C22⋊D4311yescharacteristic
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—862no—
306C2×C8—1721no—
307C2×C8—1721no—
308C2×C8—1721no—
309C2×C8—1721no—
310C2×C8—1721no—
311C2×C8—1721no—
312C2×C8—1721no—
313C2×C8—1721no—
314C2×C8#1062188212yes—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—81no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C22⋊C4—1721no—
327C22⋊C4—1721no—
328C42C2×D17211yescharacteristic
329C42#1062189811yescharacteristic
330C42D4×D4311yescharacteristic
331C42#1062190011yescharacteristic
332C23—862no—
333C23—1721no—
334C23—1721no—
335C23—1721no—
336C23—1721no—
337C23—1721no—
338C23—1721no—
339C23#1306329611yescharacteristic
340Q8—42no—
341Q8—42no—
342Q8—81no—
343Q8—81no—
344D4—862no—
345D4—862no—
346D4—1721no—
347D4—1721no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—3441no—
357C2×C4—3441no—
358C2×C4—3441no—
359C2×C4—3441no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4#1306329511yescharacteristic
364C2×C4#1306329711yescharacteristic
365C2×C4#1306329911yescharacteristic
366C2×C4#1306330711yescharacteristic
367C2×C4#1306330911yescharacteristic
368C2×C4#1306331111yescharacteristic
369C2×C4C2×#1062188211yescharacteristic
370C2×C4Q16×D4311yescharacteristic
371C2×C4#1306334511yescharacteristic
372C2×C4#1306334811yescharacteristic
373C2×C4#1306335011yescharacteristic
374C2×C4#1306335111yescharacteristic
375C2×C4#1306335211yescharacteristic
376C2×C4#1306335411yescharacteristic
377C8—22no—
378C8—41no—
379C8—3441no—
380C8—3441no—
381C8—1722no—
382C22—3441no—
383C22—3441no—
384C22—3441no—
385C22—3441no—
386C22—1722no—
387C22—1722no—
388C22—1722no—
389C22#1458281511yescharacteristic
390C22#1458309111yescharacteristic
391C22#1458311111yescharacteristic
392C22#1458313711yescharacteristic
393C22#1458314211yescharacteristic
394C22#1458315911yescharacteristic
395C22#1458317111yescharacteristic
396C4—21no—
397C4—21no—
398C4—82no—
399C4—161no—
400C4—3441no—
401C4#1458304711yescharacteristic
402C4#1458305611yescharacteristic
403C4#1458309411yescharacteristic
404C4#1458311411yescharacteristic
405C4#1458313311yescharacteristic
406C4#1458315011yescharacteristic
407C4#1458323311yescharacteristic
408C4#1458323911yescharacteristic
409C2—3442no—
410C2#1913395711yescharacteristic
411C2#1913404311yescharacteristic
412C2#1913405711yescharacteristic
413C2#1913413911yescharacteristic
414C2#1913579711yescharacteristic
415C2#1913589511yescharacteristic
416C2#1913590511yescharacteristic
subgroupG/H
centerC23#13063296
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1956C2
socleC23×C43#121
prime radicalC22×D172D4
hypercenter#1956D43
hypocenterC43#10485
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
4. C2×#14582652C2semidirect
5. C2×#14582645C2semidirect
6. #19132478C2semidirect
7. C43×#1956C2semidirect
202. #1956D43semidirect
235. C43#10485semidirect

Maximal subgroups

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

subgroupindex
C2×#145831762
#191353892
#191345922
C2×#145826522
C2×#145826452
#191324782
C43×#19562
#1048543