Finite Group Databasebeta

← #25150205

Subgroups — #25150205

Order 11008.

1280 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
1C2×#14583503C211yesmaximal, characteristic, complemented
2C2×#14583263C211yesmaximal, characteristic, complemented
3#19140346C211yesmaximal, characteristic, complemented
4#19135590C214yesmaximal, complemented
5#19135560C211yesmaximal, characteristic, complemented
6#19135420C211yesmaximal, characteristic, complemented
7#19134945C214yesmaximal, complemented
8#19134362C211yesmaximal, characteristic, complemented
9C2×C43×#493C211yesmaximal, characteristic, complemented
10#14583503—24no—
11#14583503—24no—
12C2×#13063317C2211yescharacteristic
13C2×#13063306—22no—
14C2×#13063297—22no—
15C2×#13063296C2212yes—
16C2×#13063296C2212yes—
17C2×D4×Dic43C2212yes—
18C2×#13063282C2211yescharacteristic
19#14583263—24no—
20C2×#13063246C2214yes—
21C2×#13063246C2214yes—
22C2×(C2×D43)⋊C8C2212yes—
23C2×#13063236C2211yescharacteristic
24#14582813—22no—
25#14582807—22no—
26#14582802C2212yes—
27#14582765C2211yescharacteristic
28#14582662C2214yes—
29#14582653C2212yes—
30C22×D8×C43C2214yes—
31C2×#127×C43C2211yescharacteristic
32C2×#127×C43C2211yescharacteristic
33C43×#493—24no—
34C2×C4×C8×C43C2211yescharacteristic
35C22×C22⋊D43—22no—
36C22×C22⋊D43—22no—
37C23×Dic43—22no—
38C22×C4×D43C2311yescharacteristic
39C22×C43⋊C8C2312yes—
40#13063317—22no—
41#13063317D414yescomplemented
42#13063306—216no—
43#13063297—216no—
44#13063296—24no—
45#13063296—24no—
46#13063296—44no—
47D4×Dic43—24no—
48D4×Dic43—24no—
49#13063282—22no—
50#13063282—22no—
51C2×C4⋊Dic43C2312yes—
52C2×C4⋊Dic43C2312yes—
53C2×Dic43⋊C4—22no—
54C2×Dic43⋊C4D412yes—
55C2×C22⋊Dic43—22no—
56C2×C22⋊Dic43—22no—
57C2×C22⋊Dic43—22no—
58C2×C22⋊Dic43—24no—
59C2×(C2×D43)⋊C4D412yes—
60C2×C4×Dic43C2311yescharacteristic
61#13063246—28no—
62#13063246—44no—
63(C2×D43)⋊C8—24no—
64#13063236—22no—
65C43⋊#95—22no—
66C22×D4×C43—22no—
67C22×D4×C43—22no—
68C22×D4×C43C2312yes—
69C22×D4×C43C2312yes—
70C2×D8×C43—28no—
71C2×D8×C43—28no—
72C2×D8×C43—44no—
73C22×C8×C43C2312yes—
74#127×C43—22no—
75#127×C43—22no—
76#127×C43—22no—
77#127×C43D414yescomplemented
78C2×C42×C43C2311yescharacteristic
79C4×C8×C43—22no—
80C24×C43—22no—
81C24×C43—22no—
82C23×D43C2×D411yescharacteristic
83C2×D4×C43—28no—
84C2×D4×C43—22no—
85C2×D4×C43—22no—
86C2×D4×C43—22no—
87C2×D4×C43—24no—
88C2×D4×C43—24no—
89C2×D4×C43—24no—
90C2×D4×C43—24no—
91C2×D4×C43—44no—
92C2×D4×C43—84no—
93C2×D4×C43—84no—
94C2×D4×C43C2×D414yes—
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2411yescharacteristic
97C2×C22⋊D43—28no—
98C2×C22⋊D43—44no—
99C2×C22⋊D43—84no—
100C2×C22⋊D43—84no—
101C22×Dic43—28no—
102C22×Dic43—22no—
103C22×Dic43—22no—
104C22×Dic43—84no—
105C22×Dic43C2×D412yes—
106C22×Dic43C2×D411yescharacteristic
107C2×C4×D43—21no—
108C2×C4×D43—21no—
109C2×C4×D43—22no—
110C2×C4×D43—22no—
111D8×C43—416no—
112C2×C8×C43—22no—
113C2×C8×C43—22no—
114C2×C8×C43#4114yes—
115C42×C43C2×D412yes—
116C42×C43C2×D412yes—
117C22⋊Dic43—28no—
118C22⋊Dic43—28no—
119C22⋊Dic43—44no—
120C22⋊Dic43—84no—
121(C2×D43)⋊C4—24no—
122C4⋊Dic43—22no—
123C4⋊Dic43—24no—
124C4⋊Dic43C2×D414yes—
125Dic43⋊C4—28no—
126Dic43⋊C4—24no—
127C4×Dic43—21no—
128C4×Dic43—21no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—22no—
132C23×C43—24no—
133C23×C43—42no—
134C23×C43—42no—
135C23×C43—44no—
136C23×C43—44no—
137C23×C43—42no—
138C23×C43—42no—
139C23×C43—42no—
140C23×C43—44no—
141C23×C43—44no—
142C23×C43C22×D411yescharacteristic
143C22×D43—21no—
144C22×D43—21no—
145C22×D43—21no—
146C22×D43—24no—
147D4×C43—28no—
148D4×C43—44no—
149D4×C43—44no—
150D4×C43—44no—
151D4×C43—88no—
152D4×C43—88no—
153C2×C4×C43—24no—
154C2×C4×C43#12014yes—
155C2×C4×C43C22×D411yescharacteristic
156C2×C4×C43C22×D411yescharacteristic
157C2×C4×C43C2×#4112yes—
158C2×C4×C43H(5,𝔽2)12yes—
159C22⋊D43—88no—
160C22⋊D43—88no—
161C2×Dic43—22no—
162C2×Dic43—24no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—24no—
167C2×Dic43—44no—
168C2×Dic43—42no—
169C2×Dic43—44no—
170C2×Dic43—88no—
171C4×D43—42no—
172C4×D43—42no—
173C8×C43—24no—
174C43⋊C8—42no—
175#25608—431nomaximal, Sylow
176C22×C43—44no—
177C22×C43—44no—
178C22×C43—44no—
179C22×C43—84no—
180C22×C43—84no—
181C22×C43—84no—
182C22×C43—82no—
183C22×C43—82no—
184C22×C43—82no—
185C22×C43—84no—
186C22×C43C2×#12011yescharacteristic
187C22×C43#53211yescharacteristic
188C22×C43#53511yescharacteristic
189C22×C43#57614yes—
190C2×D43—42no—
191C2×D43—41no—
192C2×D43—42no—
193C2×D43—42no—
194C4×C43—24no—
195C4×C43#54612yes—
196C4×C43#55012yes—
197Dic43—41no—
198Dic43—42no—
199Dic43—44no—
200Dic43—82no—
201C2×#540—431no—
202C2×#493D4311yescharacteristic, complemented
203C2×#490—431no—
204#2619—431no—
205#1999—434no—
206#1991—431no—
207#1961—431no—
208#1879—434no—
209#1750—431no—
210C2×C43—84no—
211C2×C43—162no—
212C2×C43#243111yescharacteristic
213C2×C43#300812yes—
214C2×C43#317612yes—
215C2×C43#322012yes—
216D43—81no—
217C22×D8C2×D4314yes—
218#540—864no—
219#540—864no—
220C2×#127C2×D4311yescharacteristic
221C2×#127C2×D4311yescharacteristic
222C2×#125—431no—
223C2×#123—862no—
224C2×#121—432no—
225C2×#121—432no—
226C2×#121—862no—
227C2×C4×D4—432no—
228C2×#117—431no—
229#493—24no—
230#490—864no—
231C2×#102—434no—
232C2×#102—434no—
233C2×C22⋊C8—432no—
234C2×#97—431no—
235C2×C4×C8C2×D4311yescharacteristic
236#394—862no—
237#392—862no—
238#390—432no—
239#382—431no—
240#340—434no—
241#336—432no—
242C43#2560811yescharacteristic, complemented, Sylow
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—862no—
246C22×D4—862no—
247C22×D4C22×D4312yes—
248C22×D4C22×D4312yes—
249C23×C4—431no—
250C23×C4—862no—
251C2×D8—28no—
252C2×D8—28no—
253C2×D8—44no—
254C22×C8—432no—
255C22×C8C22×D4312yes—
256#127—22no—
257#127—22no—
258#127—22no—
259#127C22⋊D4314yescomplemented
260#125—434no—
261#125—862no—
262#123—8616no—
263#121—864no—
264#121—8616no—
265#121—864no—
266#121—1724no—
267C4×D4—864no—
268C4×D4—864no—
269#117—862no—
270#117—862no—
271C2×C4⋊C4—432no—
272C2×C4⋊C4—432no—
273C2×C4⋊C4—432no—
274C2×C4⋊C4—862no—
275C2×C22⋊C4—432no—
276C2×C22⋊C4—862no—
277C2×C22⋊C4—862no—
278C2×C22⋊C4—864no—
279C2×C22⋊C4—862no—
280C2×C42—431no—
281C2×C42C22×D4311yescharacteristic
282#102—868no—
283#102—1724no—
284C22⋊C8—864no—
285#97—862no—
286C4×C8—22no—
287#95—862no—
288C24—22no—
289C24—22no—
290C24—431no—
291C2×D4—28no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—24no—
296C2×D4—24no—
297C2×D4—24no—
298C2×D4—24no—
299C2×D4—44no—
300C2×D4—84no—
301C2×D4—84no—
302C2×D4—868no—
303C2×D4—3444no—
304C2×D4—3444no—
305C2×D4—1724no—
306C2×D4C2×C22⋊D4314yes—
307C22×C4—432no—
308C22×C4—431no—
309C22×C4—868no—
310C22×C4—862no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—862no—
314C22×C4—862no—
315C22×C4—862no—
316C22×C4—3444no—
317C22×C4D4×D4312yes—
318C22×C4C23×D4311yescharacteristic
319D8—416no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—862no—
323C2×C8—862no—
324C2×C8—862no—
325C2×C8#1062190014yes—
326C4⋊C4—434no—
327C4⋊C4—864no—
328C4⋊C4—868no—
329C4⋊C4—862no—
330C4⋊C4—864no—
331C22⋊C4—868no—
332C22⋊C4—868no—
333C22⋊C4—864no—
334C22⋊C4—3444no—
335C22⋊C4—1724no—
336C42—861no—
337C42—861no—
338C42D4×D4312yes—
339C42C2×C22⋊D4312yes—
340C23—24no—
341C23—44no—
342C23—44no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23—44no—
347C23—44no—
348C23—42no—
349C23—42no—
350C23—861no—
351C23—864no—
352C23—861no—
353C23—861no—
354C23C2×D4×D4311yescharacteristic
355D4—28no—
356D4—44no—
357D4—44no—
358D4—44no—
359D4—88no—
360D4—88no—
361D4—3448no—
362D4—3448no—
363C2×C4—24no—
364C2×C4—862no—
365C2×C4—861no—
366C2×C4—864no—
367C2×C4—864no—
368C2×C4—861no—
369C2×C4—861no—
370C2×C4—3448no—
371C2×C4—1724no—
372C2×C4—1722no—
373C2×C4—1724no—
374C2×C4—1722no—
375C2×C4—1722no—
376C2×C4#1306329314yes—
377C2×C4C2×D4×D4311yescharacteristic
378C2×C4C22×C22⋊D4311yescharacteristic
379C2×C4C2×#1062190012yes—
380C2×C4#1306337012yes—
381C8—24no—
382C8—1722no—
383C22—44no—
384C22—44no—
385C22—44no—
386C22—84no—
387C22—84no—
388C22—84no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—84no—
393C22—1722no—
394C22—1721no—
395C22—1722no—
396C22—1722no—
397C22C2×#1306329311yescharacteristic
398C22#1458344711yescharacteristic
399C22#1458346211yescharacteristic
400C22#1458370014yes—
401C4—24no—
402C4—3442no—
403C4—1721no—
404C4—1722no—
405C4—1724no—
406C4#1458354312yes—
407C4#1458356912yes—
408C2—84no—
409C2—162no—
410C2—3441no—
411C2#1913821111yescharacteristic
412C2#1914385912yes—
413C2#1914524212yes—
414C2#1914563812yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#493C2
socleC23×C43C22×D4
hypercenterC2×#493D43
hypocenterC43#25608
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#14583503C2semidirect
2. C2×#14583263C2semidirect
3. #19140346C2semidirect
4. #19135590C2semidirect
5. #19135560C2semidirect
6. #19135420C2semidirect
7. #19134945C2semidirect
8. #19134362C2semidirect
9. C2×C43×#493C2semidirect
41. #13063317D4semidirect
77. #127×C43D4semidirect
202. C2×#493D43semidirect
242. C43#25608semidirect
259. #127C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835032
C2×#145832632
#191403462
#191355902
#191355602
#191354202
#191349452
#191343622
C2×C43×#4932
#2560843