Finite Group Databasebeta

← #25150209

Subgroups — #25150209

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×#14583504C211yesmaximal, characteristic, complemented
2C2×#14583275C211yesmaximal, characteristic, complemented
3C2×#14583263C211yesmaximal, characteristic, complemented
4#19135591C214yesmaximal, complemented
5#19135559C211yesmaximal, characteristic, complemented
6#19135418C211yesmaximal, characteristic, complemented
7#19134946C214yesmaximal, complemented
8#19134361C211yesmaximal, characteristic, complemented
9C43×#2619C211yesmaximal, characteristic, complemented
10C22×#10621882C2214yes—
11#14583504—24no—
12#14583504—24no—
13C2×#13063322C2211yescharacteristic
14C2×#13063317C2211yescharacteristic
15C2×#13063310—22no—
16C2×#13063299C2212yes—
17C2×#13063298—22no—
18C2×C4×D172C2212yes—
19#14583275—24no—
20#14583263—24no—
21C2×#13063246C2214yes—
22C2×#13063245C2214yes—
23C2×C22⋊(C43⋊C8)C2212yes—
24C2×#13063236C2211yescharacteristic
25C2×C4×C43⋊C8C2211yescharacteristic
26#14582661C2214yes—
27#14582654C2212yes—
28C2×#127×C43C2211yescharacteristic
29C2×#121×C43C2212yes—
30C2×#117×C43C2211yescharacteristic
31C43×#394—22no—
32C43×#392—22no—
33C43×#390C2212yes—
34C43×#382C2211yescharacteristic
35C22×D172—22no—
36C22×D172C2312yes—
37C22×C22⋊D43—22no—
38C22×C4×D43—22no—
39C2×#10621882—28no—
40C2×#10621882—28no—
41C2×#10621882—44no—
42C22×C43⋊C8C2312yes—
43C22×C43⋊C8C2312yes—
44#13063322—22no—
45#13063322D414yescomplemented
46#13063317—22no—
47#13063317D414yescomplemented
48#13063310—216no—
49#13063299—24no—
50#13063299—24no—
51#13063298—216no—
52C4×D172—24no—
53C4×D172—24no—
54C2×C4⋊Dic43C2312yes—
55C2×Dic43⋊C4—22no—
56C2×(C2×D43)⋊C4—22no—
57C2×(C2×D43)⋊C4—22no—
58#13063246—28no—
59#13063245—44no—
60C22⋊(C43⋊C8)—24no—
61#13063236—22no—
62C4×C43⋊C8—22no—
63C22×D4×C43—22no—
64C22×D4×C43—22no—
65C22×D4×C43C2312yes—
66C23×C4×C43C2311yescharacteristic
67#127×C43—22no—
68#127×C43—22no—
69#121×C43—44no—
70#117×C43—22no—
71#117×C43—22no—
72C2×C4⋊C4×C43D412yes—
73C2×C4⋊C4×C43C2312yes—
74C2×C22⋊C4×C43—22no—
75C2×C22⋊C4×C43—24no—
76C2×C22⋊C4×C43D412yes—
77C2×C42×C43C2311yescharacteristic
78C2×C42×C43C2311yescharacteristic
79#95×C43—22no—
80C24×C43—22no—
81C24×C43C2×D411yescharacteristic
82C23×D43—22no—
83C2×D4×C43—22no—
84C2×D4×C43—22no—
85C2×D4×C43—24no—
86C2×D4×C43—24no—
87C2×D4×C43—44no—
88C2×D4×C43—44no—
89C2×D4×C43—84no—
90C2×D4×C43—84no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—22no—
94C22×C4×C43—22no—
95C22×C4×C43—22no—
96C22×C4×C43C2×D412yes—
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D412yes—
99C22×C4×C43C2411yescharacteristic
100C2×C22⋊D43—28no—
101C2×C22⋊D43—84no—
102C22×Dic43—22no—
103C2×D172—22no—
104C2×D172—28no—
105C2×D172—24no—
106C2×D172—24no—
107C2×D172—84no—
108C2×D172C2×D414yes—
109C2×C4×D43—28no—
110C2×C4×D43—84no—
111C4⋊C4×C43—24no—
112C4⋊C4×C43—24no—
113C22⋊C4×C43—24no—
114C22⋊C4×C43—44no—
115C22⋊C4×C43—84no—
116C42×C43—21no—
117C42×C43—21no—
118C42×C43C2×D412yes—
119C42×C43C2×D412yes—
120#10621882—416no—
121(C2×D43)⋊C4—28no—
122(C2×D43)⋊C4—28no—
123C4⋊Dic43—22no—
124C4⋊Dic43C2×D414yes—
125Dic43⋊C4—28no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—22no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8#4114yes—
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43—24no—
136C23×C43—42no—
137C23×C43—42no—
138C23×C43—42no—
139C23×C43—44no—
140C23×C43—44no—
141C23×C43C22×D411yescharacteristic
142C22×D43—24no—
143C22×D43—42no—
144C22×D43—42no—
145C22×D43—44no—
146C22×D43—44no—
147D4×C43—44no—
148D4×C43—44no—
149D4×C43—88no—
150D4×C43—88no—
151C2×C4×C43—24no—
152C2×C4×C43—21no—
153C2×C4×C43—22no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—24no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—42no—
160C2×C4×C43—44no—
161C2×C4×C43#12014yes—
162C2×C4×C43C22×D411yescharacteristic
163C2×C4×C43C22×D411yescharacteristic
164C2×C4×C43C2×#4112yes—
165C2×C4×C43H(5,𝔽2)12yes—
166C22⋊D43—88no—
167C2×Dic43—24no—
168C2×Dic43—44no—
169D172—28no—
170D172—44no—
171D172—88no—
172C4×D43—88no—
173C43⋊C8—24no—
174C43⋊C8—42no—
175#25608—431nomaximal, Sylow
176C22×C43—42no—
177C22×C43—41no—
178C22×C43—42no—
179C22×C43—42no—
180C22×C43—84no—
181C22×C43—82no—
182C22×C43—82no—
183C22×C43—82no—
184C22×C43—84no—
185C22×C43C2×#12011yescharacteristic
186C22×C43#53211yescharacteristic
187C22×C43#53511yescharacteristic
188C22×C43#57614yes—
189C2×D43—44no—
190C2×D43—44no—
191C2×D43—44no—
192C2×D43—84no—
193C2×D43—84no—
194C4×C43—24no—
195C4×C43—41no—
196C4×C43—42no—
197C4×C43—82no—
198C4×C43#54612yes—
199C4×C43#55012yes—
200Dic43—44no—
201C2×#540—431no—
202C2×#493—431no—
203C2×#490—431no—
204#2619D4311yescharacteristic, complemented
205#1999—434no—
206#1991—431no—
207#1961—431no—
208#1879—434no—
209#1750—431no—
210C2×C43—81no—
211C2×C43—162no—
212C2×C43#243111yescharacteristic
213C2×C43#300812yes—
214C2×C43#317612yes—
215C2×C43#322012yes—
216D43—84no—
217C22×D8—434no—
218#540—864no—
219#540—864no—
220C2×#127—431no—
221C2×#127C2×D4311yescharacteristic
222C2×#125—431no—
223C2×#123—862no—
224C2×#121—432no—
225C2×#121—862no—
226C2×#121C2×D4312yes—
227C2×C4×D4—432no—
228C2×#117C2×D4311yescharacteristic
229#493—864no—
230#490—864no—
231C2×#102—434no—
232C2×#102—434no—
233C2×C22⋊C8—432no—
234C2×#97—431no—
235C2×C4×C8—431no—
236#394—22no—
237#392—22no—
238#390C2×D4312yes—
239#382C2×D4311yescharacteristic
240#340—434no—
241#336—432no—
242C43#2560811yescharacteristic, complemented, Sylow
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—432no—
246C22×D4—862no—
247C22×D4—862no—
248C22×D4C22×D4312yes—
249C23×C4—862no—
250C23×C4C22×D4311yescharacteristic
251C2×D8—868no—
252C2×D8—868no—
253C2×D8—1724no—
254C22×C8—432no—
255C22×C8—432no—
256#127—22no—
257#127—22no—
258#127—434no—
259#127—862no—
260#125—434no—
261#125—862no—
262#123—8616no—
263#121—44no—
264#121—8616no—
265#121—864no—
266#121—864no—
267C4×D4—864no—
268C4×D4—864no—
269#117—22no—
270#117—22no—
271C2×C4⋊C4—432no—
272C2×C4⋊C4—862no—
273C2×C4⋊C4C22⋊D4312yes—
274C2×C4⋊C4C22×D4312yes—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—862no—
278C2×C22⋊C4—862no—
279C2×C22⋊C4C22⋊D4312yes—
280C2×C42C22×D4311yescharacteristic
281C2×C42C22×D4311yescharacteristic
282#102—868no—
283#102—1724no—
284C22⋊C8—864no—
285#97—862no—
286C4×C8—862no—
287#95—22no—
288C24—22no—
289C24—862no—
290C24C2×C22⋊D4311yescharacteristic
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—24no—
294C2×D4—24no—
295C2×D4—44no—
296C2×D4—44no—
297C2×D4—84no—
298C2×D4—84no—
299C2×D4—434no—
300C2×D4—868no—
301C2×D4—868no—
302C2×D4—862no—
303C2×D4—864no—
304C2×D4—864no—
305C2×D4—3444no—
306C2×D4—3444no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—868no—
313C22×C4—862no—
314C22×C4—3444no—
315C22×C4C2×C22⋊D4312yes—
316C22×C4C2×C22⋊D4311yescharacteristic
317C22×C4C2×C22⋊D4312yes—
318C22×C4C23×D4311yescharacteristic
319D8—17216no—
320C2×C8—434no—
321C2×C8—862no—
322C2×C8—862no—
323C2×C8—862no—
324C2×C8—862no—
325C2×C8—862no—
326C4⋊C4—24no—
327C4⋊C4—24no—
328C4⋊C4—434no—
329C4⋊C4—868no—
330C4⋊C4—862no—
331C22⋊C4—24no—
332C22⋊C4—44no—
333C22⋊C4—84no—
334C22⋊C4—868no—
335C22⋊C4—868no—
336C42—21no—
337C42—21no—
338C42D4×D4312yes—
339C42D4×D4312yes—
340C23—21no—
341C23—21no—
342C23—24no—
343C23—21no—
344C23—42no—
345C23—42no—
346C23—44no—
347C23—44no—
348C23—42no—
349C23—864no—
350C23—1722no—
351C23—1724no—
352C23—1724no—
353C23—1722no—
354C23C22×C22⋊D4311yescharacteristic
355D4—44no—
356D4—44no—
357D4—88no—
358D4—88no—
359D4—868no—
360D4—3448no—
361D4—3448no—
362D4—1724no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—24no—
368C2×C4—21no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—864no—
374C2×C4—3448no—
375C2×C4—1724no—
376C2×C4#1306329314yes—
377C2×C4C2×D4×D4311yescharacteristic
378C2×C4C2×D4×D4311yescharacteristic
379C2×C4#41×D4312yes—
380C2×C4#1306337012yes—
381C8—864no—
382C8—1722no—
383C22—42no—
384C22—41no—
385C22—42no—
386C22—42no—
387C22—84no—
388C22—82no—
389C22—82no—
390C22—82no—
391C22—84no—
392C22—3444no—
393C22—3444no—
394C22—1724no—
395C22—1724no—
396C22—1724no—
397C22C2×#1306329311yescharacteristic
398C22#1458344511yescharacteristic
399C22#1458346611yescharacteristic
400C22#1458370214yes—
401C4—24no—
402C4—41no—
403C4—42no—
404C4—82no—
405C4—1724no—
406C4#1458354612yes—
407C4#1458356712yes—
408C2—81no—
409C2—162no—
410C2—3444no—
411C2#1913821511yescharacteristic
412C2#1914386112yes—
413C2#1914523912yes—
414C2#1914564512yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2619C2
socleC23×C43C22×D4
hypercenter#2619D43
hypocenterC43#25608
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2619

Complements

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

NH ≅ G/Ntype
1. C2×#14583504C2semidirect
2. C2×#14583275C2semidirect
3. C2×#14583263C2semidirect
4. #19135591C2semidirect
5. #19135559C2semidirect
6. #19135418C2semidirect
7. #19134946C2semidirect
8. #19134361C2semidirect
9. C43×#2619C2semidirect
45. #13063322D4semidirect
47. #13063317D4semidirect
204. #2619D43semidirect
242. C43#25608semidirect

Maximal subgroups

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

subgroupindex
C2×#145835042
C2×#145832752
C2×#145832632
#191355912
#191355592
#191354182
#191349462
#191343612
C43×#26192
#2560843