Finite Group Databasebeta

← #25013655

Subgroups — #25013655

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D688C211yesmaximal, characteristic
2C2×#14582981C211yesmaximal, characteristic, complemented
3C2×#14582699C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic, complemented
5#19135459C211yesmaximal, characteristic, complemented
6#19132672C211yesmaximal, characteristic, complemented
7C43×#1380C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C22×D344C2211yescharacteristic
10C2×#13063287—21no—
11C2×D688—22no—
12C2×D688—22no—
13C2×D688C414yescomplemented
14C22×C43⋊C16C2211yescharacteristic
15#14582981—22no—
16#14582981—22no—
17C2×#13063245—21no—
18C2×#13063245—21no—
19C2×C8×Dic43C2211yescharacteristic
20#14582800—21no—
21#14582699—22no—
22#14582699—22no—
23C22×C16×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C2×#107×C43C2211yescharacteristic
26C22×D172—21no—
27C22×D172—21no—
28C22×C4×D43—41no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344—21no—
33C2×D344—21no—
34C2×D344—21no—
35C2×D344—21no—
36C2×D344—21no—
37C2×D344C2×C412yes—
38C2×D344C2×C412yescomplemented
39C2×D344D412yes—
40C2×D344D412yes—
41C22×C43⋊C8D411yescharacteristic
42#13063287—24no—
43#13063287—42no—
44C2×(C2×D43)⋊C4—41no—
45C2×(C2×D43)⋊C4—41no—
46C2×(C2×D43)⋊C4—41no—
47C2×C4×Dic43D411yescharacteristic
48D688—28no—
49C2×C43⋊C16—21no—
50C2×C43⋊C16—21no—
51C2×C43⋊C16—21no—
52#13063245—24no—
53#13063245—42no—
54C8×Dic43—21no—
55C8×Dic43—21no—
56C22×C8×C43C2311yescharacteristic
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C16×C43—21no—
60C2×C16×C43—21no—
61C2×C16×C43C2×C412yescomplemented
62#107×C43—21no—
63#107×C43—21no—
64#107×C43—21no—
65#107×C43D412yes—
66C23×D43—41no—
67C23×D43—41no—
68C22×C4×C43—41no—
69C22×C4×C43—41no—
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43D811yescharacteristic
72C22×Dic43D811yescharacteristic
73C2×D172—22no—
74C2×D172—22no—
75C2×D172—22no—
76C2×D172—22no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172—41no—
85C2×C4×D43—44no—
86C2×C4×D43—82no—
87C2×C4×D43—82no—
88C2×C8×C43C22×C411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43C2×D411yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C4⋊C4×C43—22no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98(C2×D43)⋊C4—44no—
99(C2×D43)⋊C4—82no—
100(C2×D43)⋊C4—82no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—21no—
106D344—22no—
107D344—22no—
108D344—22no—
109D344—22no—
110D344—22no—
111D344—41no—
112D344—41no—
113D344C22⋊C414yescomplemented
114C16×C43—22no—
115C43⋊C16—41no—
116C23×C43C2×D811yescharacteristic
117C22×D43—42no—
118C22×D43—42no—
119C22×D43—42no—
120C22×D43—42no—
121C22×D43—81no—
122C22×D43—81no—
123C22×D43—81no—
124C22×D43—81no—
125C22×D43—81no—
126C22×D43—81no—
127C22×D43—81no—
128C22×D43—81no—
129C22×D43—81no—
130C22×D43—81no—
131C2×C4×C43—42no—
132C2×C4×C43—81no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43#12011yescharacteristic
139C2×C4×C43#12111yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43D1612yescomplemented
149D172—24no—
150D172—42no—
151D172—42no—
152D172—42no—
153D172—42no—
154D172—42no—
155D172—81no—
156D172—81no—
157C4×D43—88no—
158C8×C43C2×C22⋊C411yescharacteristic
159C8×C43C4×D411yescharacteristic
160C8×C43#12111yescharacteristic
161C8×C43#12311yescharacteristic
162C43⋊C8—41no—
163#13012—431nomaximal, Sylow
164C22×C43C4×D811yescharacteristic
165C22×C43#44711yescharacteristic
166C22×C43#45911yescharacteristic
167C22×C43C2×D1611yescharacteristic
168C22×C43#50811yescharacteristic
169C22×C43#50911yescharacteristic
170C22×C43#50911yescharacteristic
171C2×D43—44no—
172C2×D43—82no—
173C2×D43—82no—
174C2×D43—82no—
175C2×D43—82no—
176C2×D43—82no—
177C2×D43—82no—
178C2×D43—82no—
179C2×D43—82no—
180C2×D43—82no—
181C2×D43—161no—
182C2×D43—161no—
183C2×D43—161no—
184C2×D43—161no—
185C4×C43—82no—
186C4×C43—161no—
187C4×C43#38611yescharacteristic
188C4×C43#44211yescharacteristic
189C4×C43#44911yescharacteristic
190C4×C43#46311yescharacteristic
191Dic43—22no—
192Dic43—41no—
193C22×D16—431no—
194C2×C4×D8—431no—
195C2×#357—431no—
196C2×#357—431no—
197#1970—431no—
198#1380D4311yescharacteristic, complemented
199#1374—431no—
200C2×C43#187911yescharacteristic
201C2×C43C4×D1611yescharacteristic
202C2×C43#217711yescharacteristic
203C2×C43#218411yescharacteristic
204C2×C43#218611yescharacteristic
205C2×C43#220611yescharacteristic
206C2×C43#221011yescharacteristic
207D43—84no—
208D43—162no—
209C22×D8—431no—
210C22×D8—431no—
211C2×C4×D4—861no—
212C2×D16—434no—
213C2×D16—862no—
214C2×D16—862no—
215C22×C16—431no—
216C22×C16C2×D4311yescharacteristic
217C4×D8—862no—
218C4×D8—862no—
219C2×#107C2×D4311yescharacteristic
220C2×#107C2×D4311yescharacteristic
221C2×#102—861no—
222C2×#102—861no—
223C2×C4×C8—431no—
224#390—861no—
225#357—862no—
226#357—862no—
227C43#1301211yescharacteristic, complemented, Sylow
228C22×D4—861no—
229C22×D4—861no—
230C23×C4—1721no—
231C2×D8—432no—
232C2×D8—432no—
233C2×D8—432no—
234C2×D8—432no—
235C2×D8—861no—
236C2×D8—861no—
237C2×D8—861no—
238C2×D8—861no—
239C2×D8—861no—
240C2×D8—861no—
241C2×D8—861no—
242C2×D8—861no—
243C22×C8—431no—
244C22×C8C22×D4311yescharacteristic
245C4×D4—864no—
246C4×D4—1722no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C22⋊C4—1721no—
250C2×C22⋊C4—1721no—
251C2×C22⋊C4—1721no—
252C2×C42—431no—
253D16—868no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16—861no—
257C2×C16—861no—
258C2×C16—861no—
259C2×C16C4×D4312yescomplemented
260#107—21no—
261#107—21no—
262#107—21no—
263#107D17212yes—
264#102—864no—
265#102—1722no—
266C4×C8—861no—
267C4×C8—861no—
268C24—1721no—
269C24—1721no—
270C2×D4—862no—
271C2×D4—862no—
272C2×D4—862no—
273C2×D4—862no—
274C2×D4—1721no—
275C2×D4—1721no—
276C2×D4—1721no—
277C2×D4—1721no—
278C2×D4—1721no—
279C2×D4—1721no—
280C2×D4—1721no—
281C2×D4—1721no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—431no—
285C22×C4—431no—
286C22×C4—3442no—
287C22×C4—3442no—
288C22×C4—1724no—
289C22×C4D4×D4311yescharacteristic
290D8—434no—
291D8—862no—
292D8—862no—
293D8—862no—
294D8—862no—
295D8—862no—
296D8—1721no—
297D8—1721no—
298C2×C8—861no—
299C2×C8—861no—
300C2×C8—861no—
301C2×C8C2×C4×D4311yescharacteristic
302C2×C8C2×D17211yescharacteristic
303C2×C8#1062189811yescharacteristic
304C2×C8D4×D4311yescharacteristic
305C2×C8D4×D4311yescharacteristic
306C2×C8#1062190211yescharacteristic
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C22⋊C4—3442no—
312C22⋊C4—3442no—
313C22⋊C4—1724no—
314C42—861no—
315C42—861no—
316C16—22no—
317C16—1721no—
318C23—3441no—
319C23—3441no—
320C23—3441no—
321C23—3441no—
322C23—3441no—
323C23—3441no—
324C23—3441no—
325C23—3441no—
326C23—3441no—
327C23—3441no—
328C23—1722no—
329C23—1722no—
330C23—1722no—
331C23—1722no—
332C23D8×D4311yescharacteristic
333D4—864no—
334D4—3441no—
335D4—3441no—
336D4—1722no—
337D4—1722no—
338D4—1722no—
339D4—1722no—
340D4—1722no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—432no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—3448no—
354C2×C4#1306328711yescharacteristic
355C2×C4#1306329511yescharacteristic
356C2×C4#1306329811yescharacteristic
357C2×C4#1306334811yescharacteristic
358C2×C4#1306335211yescharacteristic
359C2×C4#1306335211yescharacteristic
360C8—1721no—
361C8C22⋊C4×D4311yescharacteristic
362C8C4×D17211yescharacteristic
363C8#1306330011yescharacteristic
364C8#1306331011yescharacteristic
365C22—3442no—
366C22—3442no—
367C22—3442no—
368C22—3442no—
369C22—3442no—
370C22—3442no—
371C22—3442no—
372C22—3442no—
373C22—3442no—
374C22—1724no—
375C22—6881no—
376C22—6881no—
377C22—6881no—
378C22—6881no—
379C22#1458298111yescharacteristic
380C22#1458303411yescharacteristic
381C22#1458309311yescharacteristic
382C22D16×D4311yescharacteristic
383C22#1458333211yescharacteristic
384C22#1458333611yescharacteristic
385C22#1458333611yescharacteristic
386C4—82no—
387C4—161no—
388C4—862no—
389C4—1721no—
390C4#1458277711yescharacteristic
391C4#1458301011yescharacteristic
392C4#1458304711yescharacteristic
393C4#1458311711yescharacteristic
394C2—3444no—
395C2—6882no—
396C2#1913494411yescharacteristic
397C2#1913644111yescharacteristic
398C2#1913647011yescharacteristic
399C2#1913650811yescharacteristic
400C2#1913652111yescharacteristic
401C2#1913662911yescharacteristic
402C2#1913665311yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1380C2
socleC23×C43C2×D8
prime radicalC22×D688C2
cosocleC22×C8×C43C23
hypercenter#1380D43
hypocenterC43#13012
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×#14582981C2semidirect
3. C2×#14582699C2semidirect
4. C2×#14582699C2semidirect
5. #19135459C2semidirect
6. #19132672C2semidirect
7. C43×#1380C2semidirect
13. C2×D688C4semidirect
38. C2×D344C2×C4semidirect
61. C2×C16×C43C2×C4semidirect
113. D344C22⋊C4semidirect
148. C2×Dic43D16semidirect
198. #1380D43semidirect
227. C43#13012semidirect
259. C2×C16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×D6882
C2×#145829812
C2×#145826992
#191354592
#191326722
C43×#13802
#1301243