Finite Group Databasebeta

← #24999625

Subgroups — #24999625

Order 11008.

500 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139834C211yesmaximal, characteristic, complemented
2#19135522C211yesmaximal, characteristic
3#19135521C211yesmaximal, characteristic
4#19135401C211yesmaximal, characteristic
5#19132479C211yesmaximal, characteristic, complemented
6#19132435C211yesmaximal, characteristic, complemented
7C43×#1279C211yesmaximal, characteristic, complemented
8C2×#13063322C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×#13063247—21no—
11C2×#13063247—21no—
12C2×#13063247—22no—
13C2×#13063245—21no—
14C2×#13063245—21no—
15#14582841—22no—
16#14582797—21no—
17#14582795—21no—
18#14582769C2211yescharacteristic
19#14582765—21no—
20#14582764—21no—
21C4×C4⋊Dic43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4×C8×C43C2211yescharacteristic
24C4×C4⋊C4×C43C2211yescharacteristic
25C22×D172—21no—
26C22×D172—21no—
27C22×D172—21no—
28C22×C43⋊C8—21no—
29#13063322—21no—
30#13063322—21no—
31#13063322—21no—
32#13063322Q812yes—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43D411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×C4⋊Dic43D412yes—
38C2×Dic43⋊C4—22no—
39C2×C4×Dic43—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42#13063247—42no—
43#13063247—42no—
44#13063247—44no—
45#13063245—42no—
46#13063245—42no—
47C43⋊#95—22no—
48C43⋊#95—22no—
49C43⋊#95—22no—
50C43⋊#95—21no—
51C22×C8×C43—21no—
52C22×C8×C43—21no—
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C42×C43—21no—
56C2×C42×C43C2311yescharacteristic
57C4⋊C8×C43—21no—
58C4⋊C8×C43—21no—
59C4×C8×C43—21no—
60C4×C8×C43—21no—
61#95×C43—21no—
62C23×D43—41no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—22no—
71C2×D172—22no—
72C2×D172—22no—
73C2×D172—22no—
74C2×D172—41no—
75C2×D172—41no—
76C2×D172—41no—
77C2×D172—42no—
78C2×D172—42no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172—41no—
85C2×D172—41no—
86C2×D172—41no—
87C2×C8×C43—22no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C42×C43—41no—
98C42×C43—41no—
99C42×C43C2×Q811yescharacteristic
100C42×C43#4111yescharacteristic
101C42×C43#4111yescharacteristic
102C42×C43#4111yescharacteristic
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109C4⋊Dic43—41no—
110C4⋊Dic43—41no—
111C4⋊Dic43—42no—
112Dic43⋊C4—82no—
113C4×Dic43—41no—
114C4×Dic43—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C23×C43#12011yescharacteristic
119C22×D43—42no—
120C22×D43—81no—
121C22×D43—81no—
122C22×D43—81no—
123C22×D43—81no—
124C22×D43—81no—
125C22×D43—81no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43C22⋊Q811yescharacteristic
135C2×C4×C43C22⋊Q811yescharacteristic
136C2×C4×C43C22⋊Q811yescharacteristic
137C2×C4×C43#12411yescharacteristic
138C2×C4×C43#12411yescharacteristic
139C2×C4×C43#12411yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C2×C4×C43#13511yescharacteristic
142C2×C4×C43#13511yescharacteristic
143C2×C4×C43#13511yescharacteristic
144C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—42no—
153C2×Dic43—42no—
154C2×Dic43—41no—
155C2×Dic43—42no—
156C2×Dic43—41no—
157D172—44no—
158D172—42no—
159D172—42no—
160D172—42no—
161D172—42no—
162D172—82no—
163D172—81no—
164D172—81no—
165D172—81no—
166D172—81no—
167C8×C43—42no—
168C8×C43—81no—
169C43⋊C8—81no—
170#10351—431nomaximal, Sylow
171C22×C43#39311yescharacteristic
172C22×C43#44911yescharacteristic
173C22×C43#44911yescharacteristic
174C22×C43#44911yescharacteristic
175C22×C43#44911yescharacteristic
176C22×C43#45311yescharacteristic
177C22×C43#45411yescharacteristic
178C2×D43—82no—
179C2×D43—82no—
180C2×D43—82no—
181C2×D43—161no—
182C2×D43—161no—
183C2×D43—161no—
184C2×D43—161no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—81no—
188C4×C43—81no—
189C4×C43#47811yescharacteristic
190C4×C43#47811yescharacteristic
191C4×C43#47811yescharacteristic
192C4×C43#47811yescharacteristic
193C4×C43#48811yescharacteristic
194C4×C43#48811yescharacteristic
195C4×C43#49011yescharacteristic
196C4×C43#49011yescharacteristic
197Dic43—82no—
198Dic43—81no—
199Dic43—81no—
200#2571—431no—
201#1982—431no—
202#1982—431no—
203#1957—431no—
204#1296—431no—
205#1279—431no—
206#1279D4311yescharacteristic, complemented
207C2×C43#162011yescharacteristic
208C2×C43#162411yescharacteristic
209C2×C43#162811yescharacteristic
210C2×C43#162811yescharacteristic
211C2×C43#202511yescharacteristic
212C2×C43#202511yescharacteristic
213C2×C43#202711yescharacteristic
214D43—162no—
215C2×#127—431no—
216C2×C4⋊C8—431no—
217C2×C4⋊C8C2×D4311yescharacteristic
218C2×#102—862no—
219C2×#102—861no—
220C2×#102—861no—
221C2×#102—861no—
222C2×#102—861no—
223C2×C4×C8C2×D4311yescharacteristic
224#400—862no—
225#389—861no—
226#389—861no—
227#384—431no—
228#382—861no—
229#382—861no—
230C4×C4⋊C4—431no—
231C4×C4⋊C4C2×D4311yescharacteristic
232C43#1035111yescharacteristic, complemented, Sylow
233C22×D4—861no—
234C22×D4—861no—
235C22×D4—861no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—861no—
239#127—432no—
240#127—861no—
241#127—861no—
242#127—861no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4—431no—
245C2×C4⋊C4—432no—
246C2×C4⋊C4—862no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4D17211yescharacteristic
250C2×C4⋊C4D17211yescharacteristic
251C2×C42—21no—
252C2×C42—861no—
253C2×C42C22×D4311yescharacteristic
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—861no—
257C4⋊C8—861no—
258#102—1722no—
259#102—1722no—
260#102—1722no—
261#102—1722no—
262#102—1724no—
263C4×C8—21no—
264C4×C8—21no—
265#95—21no—
266#95—862no—
267#95—862no—
268#95—862no—
269#95—861no—
270C24—1721no—
271C2×D4—862no—
272C2×D4—862no—
273C2×D4—862no—
274C2×D4—1722no—
275C2×D4—1722no—
276C2×D4—1721no—
277C2×D4—1721no—
278C2×D4—1721no—
279C2×D4—1721no—
280C2×D4—1721no—
281C2×D4—1721no—
282C2×D4—1721no—
283C2×D4—1721no—
284C2×D4—1721no—
285C2×D4—1721no—
286C2×D4—1721no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—862no—
292C22×C4C2×D17211yescharacteristic
293C22×C4D4×D4311yescharacteristic
294C22×C4D4×D4311yescharacteristic
295C2×C8—22no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—1721no—
302C2×C8—1721no—
303C2×C8—1721no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4—3442no—
313C4⋊C4—1722no—
314C4⋊C4—1721no—
315C4⋊C4—1721no—
316C4⋊C4—1721no—
317C4⋊C4—1721no—
318C42—41no—
319C42—41no—
320C42—1721no—
321C42—1721no—
322C42#1062189811yescharacteristic
323C42#1062189811yescharacteristic
324C42#1062190011yescharacteristic
325C42Q8×D4311yescharacteristic
326C23—3441no—
327C23—3441no—
328C23—3441no—
329C23—3441no—
330C23—3441no—
331C23—3441no—
332C23—1722no—
333C23#1306329511yescharacteristic
334D4—3442no—
335D4—3441no—
336D4—3441no—
337D4—3441no—
338D4—3441no—
339D4—1724no—
340D4—1722no—
341D4—1722no—
342D4—1722no—
343D4—1722no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1722no—
356C2×C4—1721no—
357C2×C4—1722no—
358C2×C4—1721no—
359C2×C4—1722no—
360C2×C4—1721no—
361C2×C4#1306330311yescharacteristic
362C2×C4#1306330311yescharacteristic
363C2×C4#1306330511yescharacteristic
364C2×C4#1306331111yescharacteristic
365C2×C4#1306331111yescharacteristic
366C2×C4#1306331311yescharacteristic
367C2×C4#1306334611yescharacteristic
368C2×C4#1306334711yescharacteristic
369C2×C4#1306334711yescharacteristic
370C2×C4#1306334811yescharacteristic
371C2×C4#1306334911yescharacteristic
372C2×C4#1306335211yescharacteristic
373C2×C4#1306335311yescharacteristic
374C2×C4#1306335311yescharacteristic
375C8—42no—
376C8—81no—
377C8—3441no—
378C22—3442no—
379C22—3442no—
380C22—3442no—
381C22—6881no—
382C22—6881no—
383C22—6881no—
384C22—6881no—
385C22#1458281211yescharacteristic
386C22#1458304511yescharacteristic
387C22#1458304611yescharacteristic
388C22#1458304611yescharacteristic
389C22#1458304711yescharacteristic
390C22#1458306811yescharacteristic
391C22#1458307311yescharacteristic
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—3441no—
397C4—3442no—
398C4—3441no—
399C4#1458319811yescharacteristic
400C4#1458320011yescharacteristic
401C4#1458320011yescharacteristic
402C4#1458320211yescharacteristic
403C4#1458325411yescharacteristic
404C4#1458325511yescharacteristic
405C4#1458326211yescharacteristic
406C4#1458326411yescharacteristic
407C2—6882no—
408C2#1913365611yescharacteristic
409C2#1913368011yescharacteristic
410C2#1913370711yescharacteristic
411C2#1913370811yescharacteristic
412C2#1913574011yescharacteristic
413C2#1913574211yescharacteristic
414C2#1913575011yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1279C2
socleC23×C43#120
prime radicalC2×#13063322C22
hypercenter#1279D43
hypocenterC43#10351
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
1. #19139834C2semidirect
5. #19132479C2semidirect
6. #19132435C2semidirect
7. C43×#1279C2semidirect
206. #1279D43semidirect
232. C43#10351semidirect

Maximal subgroups

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

subgroupindex
#191398342
#191355222
#191355212
#191354012
#191324792
#191324352
C43×#12792
#1035143