Finite Group Databasebeta

← #25013598

Subgroups — #25013598

Order 11008.

508 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×#14583137C211yesmaximal, characteristic
2C2×#108×D43C211yesmaximal, characteristic
3C2×#14582715C211yesmaximal, characteristic, complemented
4#19136205C211yesmaximal, characteristic
5#19132705C211yesmaximal, characteristic, complemented
6#19132704C211yesmaximal, characteristic, complemented
7C2×C43×#362C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C22×C8×D43C2211yescharacteristic
10C2×#13063301—21no—
11C2×#13063265C2211yescharacteristic
12#14583137—21no—
13#14583137—21no—
14#14583137C412yes—
15#14583137C412yes—
16C2×#13063261C2211yescharacteristic
17C2×#13063260—21no—
18#108×D43—22no—
19#108×D43—22no—
20C2×#13063259C2211yescharacteristic
21C2×#13063249—21no—
22#14582715—22no—
23(C2×D43)⋊C16—21no—
24(C2×D43)⋊C16—21no—
25C22×Q16×C43C2211yescharacteristic
26C2×M32×C43C2211yescharacteristic
27C2×#108×C43C2211yescharacteristic
28C43×#362—22no—
29C22×C4×D43D411yescharacteristic
30C2×#10621877—21no—
31C2×#10621872—41no—
32M16×D43—24no—
33M16×D43—42no—
34C22×C43⋊C8D411yescharacteristic
35C2×C8×D43—21no—
36C2×C8×D43—21no—
37C2×C8×D43—21no—
38C2×C8×D43—21no—
39C2×C8×D43—41no—
40C2×C8×D43C2×C411yescharacteristic
41C2×C8×D43C2×C411yescharacteristic
42C2×C8×D43D411yescharacteristic
43C2×C8×D43D411yescharacteristic
44#13063301—22no—
45#13063301—22no—
46#13063301—41no—
47#13063301—41no—
48C2×C4⋊Dic43—21no—
49C2×Dic43⋊C4—41no—
50C2×(C2×D43)⋊C4—41no—
51#13063265—21no—
52#13063265—21no—
53C2×C43⋊C16—21no—
54#13063261—21no—
55#13063261D412yes—
56#13063260—24no—
57#13063259—21no—
58#13063259C2×C412yes—
59#13063249—22no—
60#13063249—22no—
61C22×Q8×C43—21no—
62C2×Q16×C43—21no—
63C2×Q16×C43—21no—
64C2×Q16×C43—21no—
65C2×Q16×C43—21no—
66C2×Q16×C43—21no—
67C2×Q16×C43C2×C412yes—
68C2×M16×C43—21no—
69C22×C8×C43C2311yescharacteristic
70M32×C43—21no—
71M32×C43—21no—
72C2×C16×C43—21no—
73#108×C43—21no—
74#108×C43D412yes—
75C23×D43SD1611yescharacteristic
76C2×Q8×C43—22no—
77C2×Q8×C43—41no—
78C2×Q8×C43—41no—
79C2×Q8×C43—41no—
80C2×Q8×C43—41no—
81C2×Q8×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43C2×D411yescharacteristic
84C22×Dic43—41no—
85C22×Dic43SD1611yescharacteristic
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×C4×D43C22⋊C411yescharacteristic
91C2×C4×D43C22⋊C411yescharacteristic
92C2×C4×D43D811yescharacteristic
93C2×C4×D43D811yescharacteristic
94Q16×C43—22no—
95Q16×C43—22no—
96Q16×C43—41no—
97Q16×C43—41no—
98M16×C43—22no—
99M16×C43—41no—
100C2×C8×C43—41no—
101C2×C8×C43C22×C411yescharacteristic
102C2×C8×C43C2×D411yescharacteristic
103C2×C8×C43C2×D411yescharacteristic
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43#4111yescharacteristic
106C2×C8×C43#4111yescharacteristic
107(C2×D43)⋊C4—42no—
108(C2×D43)⋊C4—42no—
109C4⋊Dic43—22no—
110C4⋊Dic43—41no—
111Dic43⋊C4—42no—
112Dic43⋊C4—42no—
113#10621877—22no—
114#10621877—41no—
115C2×C43⋊C8—21no—
116C2×C43⋊C8—21no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8C22⋊C411yescharacteristic
119C2×C43⋊C8C22⋊C411yescharacteristic
120#10621872—44no—
121C8×D43—21no—
122C8×D43—21no—
123C8×D43—21no—
124C8×D43—21no—
125C8×D43—21no—
126C8×D43—21no—
127C8×D43—21no—
128C8×D43—21no—
129C8×D43—44no—
130C16×C43—41no—
131C43⋊C16—41no—
132C23×C43C2×SD1611yescharacteristic
133C22×D43—21no—
134C22×D43—21no—
135C22×D43—22no—
136C22×D43—41no—
137C22×D43#10211yescharacteristic
138C22×D43#10211yescharacteristic
139Q8×C43—42no—
140Q8×C43—42no—
141Q8×C43—81no—
142Q8×C43—81no—
143C2×C4×C43—42no—
144C2×C4×C43—81no—
145C2×C4×C43—81no—
146C2×C4×C43C2×C22⋊C411yescharacteristic
147C2×C4×C43#12011yescharacteristic
148C2×C4×C43#12311yescharacteristic
149C2×C4×C43C2×D811yescharacteristic
150C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C43#13711yescharacteristic
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—42no—
155C2×Dic43—82no—
156C2×Dic43#10211yescharacteristic
157C2×Dic43#10211yescharacteristic
158C4×D43—21no—
159C4×D43—21no—
160C4×D43—21no—
161C4×D43—21no—
162C4×D43—21no—
163C4×D43—21no—
164C4×D43—21no—
165C4×D43—21no—
166C8×C43—42no—
167C8×C43C4×D411yescharacteristic
168C8×C43C4×D411yescharacteristic
169C8×C43#12111yescharacteristic
170C8×C43#12111yescharacteristic
171C43⋊C8—21no—
172C43⋊C8—21no—
173C43⋊C8—42no—
174#13003—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43C2×#10211yescharacteristic
178C22×C43#44811yescharacteristic
179C22×C43#48111yescharacteristic
180C2×D43—21no—
181C2×D43—21no—
182C2×D43—21no—
183C2×D43—21no—
184C2×D43—21no—
185C2×D43—42no—
186C2×D43—42no—
187C2×D43#36212yescomplemented
188C4×C43—82no—
189C4×C43#38611yescharacteristic
190C4×C43#41711yescharacteristic
191C4×C43#44711yescharacteristic
192C4×C43#48011yescharacteristic
193Dic43—21no—
194Dic43—21no—
195Dic43—82no—
196C2×#467—431no—
197C22×#108—431no—
198C2×#362—431no—
199C2×#362D4311yescharacteristic, complemented
200#2112—431no—
201#1387—431no—
202#1387—431no—
203C2×C43—21no—
204C2×C43—21no—
205C2×C43#187411yescharacteristic
206C2×C43C2×#36211yescharacteristic
207C2×C43#214811yescharacteristic
208D43—22no—
209D43—41no—
210C22×Q16C2×D4311yescharacteristic
211C22×M16—861no—
212C23×C8—431no—
213C2×C22⋊Q8—861no—
214C2×M32—431no—
215C2×M32C2×D4311yescharacteristic
216#467—432no—
217#467—432no—
218#467—861no—
219#467—861no—
220C2×#108—431no—
221C2×#108—862no—
222C2×#108—861no—
223C2×#108—862no—
224C2×#108C2×D4311yescharacteristic
225C2×#107—431no—
226C2×#103—861no—
227#362—22no—
228#362—862no—
229C22⋊C16—861no—
230C22⋊C16—861no—
231C43#1300311yescharacteristic, complemented, Sylow
232C22×Q8—21no—
233C23×C4—431no—
234C2×Q16—21no—
235C2×Q16—21no—
236C2×Q16—21no—
237C2×Q16—21no—
238C2×Q16—21no—
239C2×Q16C4×D4312yes—
240C2×M16—21no—
241C2×M16—864no—
242C2×M16—861no—
243C2×M16—1721no—
244C2×M16—1722no—
245C22×C8—431no—
246C22×C8—431no—
247C22×C8—431no—
248C22×C8—431no—
249C22×C8—431no—
250C22×C8—861no—
251C22×C8—861no—
252C22×C8—861no—
253C22×C8—861no—
254C22×C8—1721no—
255C22×C8C22×D4311yescharacteristic
256C22⋊Q8—862no—
257C22⋊Q8—862no—
258C22⋊Q8—1721no—
259C22⋊Q8—1721no—
260C2×C4⋊C4—861no—
261C2×C4⋊C4—1721no—
262C2×C22⋊C4—1721no—
263M32—21no—
264M32—21no—
265M32—861no—
266M32—861no—
267C2×C16—21no—
268C2×C16—861no—
269#108—21no—
270#108—432no—
271#108—864no—
272#108—861no—
273#108C22⋊D4312yes—
274#107—432no—
275#107—861no—
276#103—862no—
277#103—862no—
278C24—431no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C22×C4—41no—
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—431no—
290C22×C4—431no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—1721no—
296C22×C4D4×D4311yescharacteristic
297Q16—22no—
298Q16—22no—
299Q16—41no—
300Q16—41no—
301M16—22no—
302M16—41no—
303M16—862no—
304M16—1724no—
305M16—1721no—
306C2×C8—41no—
307C2×C8—431no—
308C2×C8—431no—
309C2×C8—861no—
310C2×C8—861no—
311C2×C8—861no—
312C2×C8—861no—
313C2×C8—861no—
314C2×C8—861no—
315C2×C8—861no—
316C2×C8—861no—
317C2×C8—861no—
318C2×C8—861no—
319C2×C8—1724no—
320C2×C8—1721no—
321C2×C8C2×C4×D4311yescharacteristic
322C2×C8#1062189811yescharacteristic
323C2×C8D4×D4311yescharacteristic
324C2×C8D4×D4311yescharacteristic
325C2×C8#1062190011yescharacteristic
326C2×C8C2×C22⋊D4311yescharacteristic
327C4⋊C4—862no—
328C4⋊C4—1722no—
329C4⋊C4—1722no—
330C4⋊C4—1721no—
331C22⋊C4—1722no—
332C22⋊C4—1722no—
333C16—41no—
334C16—1721no—
335C23—431no—
336C23—431no—
337C23—862no—
338C23—861no—
339C23—861no—
340C23—1721no—
341C23SD16×D4311yescharacteristic
342Q8—42no—
343Q8—42no—
344Q8—81no—
345Q8—81no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—431no—
350C2×C4—431no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—3442no—
362C2×C4—1722no—
363C2×C4C22⋊C4×D4311yescharacteristic
364C2×C4#1306329311yescharacteristic
365C2×C4#1306330711yescharacteristic
366C2×C4D8×D4311yescharacteristic
367C2×C4#1306334911yescharacteristic
368C2×C4#1306335411yescharacteristic
369C8—42no—
370C8—861no—
371C8—861no—
372C8—1722no—
373C8(C22⋊D43)⋊C411yescharacteristic
374C8C4×C22⋊D4311yescharacteristic
375C8#1306329611yescharacteristic
376C8#1306329811yescharacteristic
377C22—21no—
378C22—21no—
379C22—432no—
380C22—861no—
381C22—861no—
382C22—861no—
383C22—861no—
384C22—861no—
385C22—1722no—
386C22—1722no—
387C22#102×D4311yescharacteristic
388C22#1458303611yescharacteristic
389C22#1458321611yescharacteristic
390C4—82no—
391C4—861no—
392C4—861no—
393C4—3442no—
394C4#1458277511yescharacteristic
395C4#1458289711yescharacteristic
396C4#1458303111yescharacteristic
397C4#1458321111yescharacteristic
398C2—21no—
399C2—21no—
400C2—862no—
401C2—1721no—
402C2#1913490911yescharacteristic
403C2#362×D4311yescharacteristic
404C2#1913634311yescharacteristic
subgroupG/H
centerC22#102×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#362C2
socleC22×C43C2×#102
prime radicalC23×D43SD16
cosocleC22×C8×C43C23
hypercenterC2×#362D43
hypocenterC43#13003
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
3. C2×#14582715C2semidirect
5. #19132705C2semidirect
6. #19132704C2semidirect
7. C2×C43×#362C2semidirect
187. C2×D43#362semidirect
199. C2×#362D43semidirect
231. C43#13003semidirect

Maximal subgroups

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

subgroupindex
C2×#145831372
C2×#108×D432
C2×#145827152
#191362052
#191327052
#191327042
C2×C43×#3622
#1300343