Finite Group Databasebeta

← #25015752

Subgroups — #25015752

Order 11008.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583135C211yesmaximal, characteristic
2C2×#14582724C211yesmaximal, characteristic, complemented
3C2×#14582699C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic, complemented
5C2×C22⋊(C43⋊C16)C211yesmaximal, characteristic, complemented
6#19132686C211yesmaximal, characteristic, complemented
7C43×#1808C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C2×#13063299—21no—
10C22×C43⋊C16C2211yescharacteristic
11C22×C43⋊C16C2211yescharacteristic
12#14583135—22no—
13#14583135—22no—
14C2×#13063259C2211yescharacteristic
15C2×#13063247—21no—
16#14582724—22no—
17#14582699—22no—
18#14582699—22no—
19C22⋊(C43⋊C16)—22no—
20C23×C8×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C43×#380—21no—
24C43×#340—21no—
25C22×D172—21no—
26C22×C22⋊D43—41no—
27C2×D344—21no—
28C2×D344—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344D412yes—
33#13063299—24no—
34#13063299—42no—
35C2×C4⋊Dic43—21no—
36C2×(C2×D43)⋊C4—41no—
37C2×C43⋊C16—21no—
38C2×C43⋊C16—21no—
39C2×C43⋊C16—21no—
40C2×C43⋊C16—21no—
41C2×C43⋊C16—21no—
42C2×C43⋊C16D412yescomplemented
43#13063259—21no—
44#13063259D412yes—
45#13063247—24no—
46C23×C4×C43D411yescharacteristic
47C22×C8×C43—21no—
48C22×C8×C43—21no—
49C22×C8×C43—21no—
50C22×C8×C43—21no—
51C22×C8×C43—21no—
52C22×C8×C43—21no—
53C22×C8×C43D411yescharacteristic
54C22×C8×C43C2311yescharacteristic
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C22⋊C4×C43—41no—
58#107×C43—21no—
59#107×C43—21no—
60#107×C43—21no—
61#107×C43—21no—
62#95×C43—41no—
63C24×C43D811yescharacteristic
64C23×D43—41no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43D811yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C2×C22⋊D43—44no—
76C2×C22⋊D43—82no—
77C2×C22⋊D43—82no—
78C22×Dic43—41no—
79C2×D172—22no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172—41no—
85C2×C8×C43—21no—
86C2×C8×C43—21no—
87C2×C8×C43—21no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C2×C8×C43C2×D411yescharacteristic
93C2×C8×C43C2×D411yescharacteristic
94C2×C8×C43C2×D411yescharacteristic
95C2×C8×C43#4111yescharacteristic
96C2×C8×C43#4111yescharacteristic
97C2×C8×C43#4111yescharacteristic
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C22⋊C4×C43—82no—
103(C2×D43)⋊C4—44no—
104C4⋊Dic43—22no—
105C4⋊Dic43—41no—
106D344—22no—
107D344—22no—
108D344—41no—
109D344—41no—
110C43⋊C16—22no—
111C43⋊C16—41no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43D1612yes—
119C23×C43C2×D811yescharacteristic
120C22×D43—42no—
121C22×D43—81no—
122C22×D43—81no—
123C22×D43—81no—
124C22×D43—81no—
125C22×D43—81no—
126C22×D43—81no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C2×C4×C43—81no—
138C2×C4×C43—81no—
139C2×C4×C43—81no—
140C2×C4×C43#12011yescharacteristic
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#12311yescharacteristic
143C2×C4×C43#13511yescharacteristic
144C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C43#13711yescharacteristic
146C22⋊D43—88no—
147C2×Dic43—42no—
148C2×Dic43—81no—
149C2×Dic43—81no—
150D172—42no—
151D172—42no—
152D172—81no—
153D172—81no—
154C8×C43—41no—
155C8×C43#12111yescharacteristic
156C8×C43#12111yescharacteristic
157C8×C43#12311yescharacteristic
158C8×C43#12411yescharacteristic
159#13380—431nomaximal, Sylow
160C22×C43—22no—
161C22×C43—22no—
162C22×C43—22no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43#44711yescharacteristic
168C22×C43#46611yescharacteristic
169C22×C43#48011yescharacteristic
170C22×C43C2×D1611yescharacteristic
171C22×C43#50811yescharacteristic
172C22×C43#50911yescharacteristic
173C22×C43#51011yescharacteristic
174C2×D43—82no—
175C2×D43—82no—
176C2×D43—82no—
177C2×D43—161no—
178C2×D43—161no—
179C2×D43—161no—
180C2×D43—161no—
181C4×C43—41no—
182C4×C43—161no—
183C4×C43—161no—
184C4×C43#39411yescharacteristic
185C4×C43#45211yescharacteristic
186C4×C43#46811yescharacteristic
187C4×C43#48211yescharacteristic
188Dic43—82no—
189C2×#466—431no—
190C2×#366—431no—
191C2×#357—431no—
192C2×#357—431no—
193C2×C22⋊C16—431no—
194#1808D4311yescharacteristic, complemented
195#1380—431no—
196C2×C43—42no—
197C2×C43#203311yescharacteristic
198C2×C43#218411yescharacteristic
199C2×C43#218911yescharacteristic
200C2×C43#221511yescharacteristic
201C2×C43#222011yescharacteristic
202C2×C43#223211yescharacteristic
203C2×C43#223411yescharacteristic
204D43—162no—
205C22×D8—431no—
206C23×C8C2×D4311yescharacteristic
207C2×#121—861no—
208C22×C16—431no—
209C22×C16—431no—
210#466—862no—
211#466—862no—
212C2×#107—431no—
213C2×#107C2×D4311yescharacteristic
214C2×#107C2×D4311yescharacteristic
215C2×#102—861no—
216#380—21no—
217#366—862no—
218#357—862no—
219#357—862no—
220C22⋊C16—862no—
221#340—21no—
222C43#1338011yescharacteristic, complemented, Sylow
223C22×D4—861no—
224C22×D4—1721no—
225C23×C4C22⋊D4311yescharacteristic
226C2×D8—432no—
227C2×D8—861no—
228C2×D8—861no—
229C2×D8—861no—
230C2×D8—861no—
231C2×D8—861no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8C22⋊D4311yescharacteristic
239C22×C8C22×D4311yescharacteristic
240#121—864no—
241#121—1722no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—861no—
245C2×C22⋊C4—41no—
246C2×C22⋊C4—1721no—
247C2×C16—432no—
248C2×C16—861no—
249C2×C16—861no—
250C2×C16—861no—
251C2×C16—861no—
252C2×C16—861no—
253#107—21no—
254#107—21no—
255#107—21no—
256#107—21no—
257#107—432no—
258#107—861no—
259#102—864no—
260#95—41no—
261C24—1721no—
262C24#1062188211yescharacteristic
263C2×D4—862no—
264C2×D4—3442no—
265C2×D4—3442no—
266C2×D4—1724no—
267C2×D4—1721no—
268C2×D4—1721no—
269C2×D4—1721no—
270C2×D4—1721no—
271C2×D4—1721no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—1721no—
281C22×C4#1062188211yescharacteristic
282C22×C4C2×C22⋊D4311yescharacteristic
283D8—862no—
284D8—862no—
285D8—1721no—
286D8—1721no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8#1062189811yescharacteristic
295C2×C8#1062189811yescharacteristic
296C2×C8D4×D4311yescharacteristic
297C2×C8D4×D4311yescharacteristic
298C2×C8D4×D4311yescharacteristic
299C2×C8#1062190011yescharacteristic
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—862no—
305C4⋊C4—1721no—
306C22⋊C4—82no—
307C22⋊C4—1724no—
308C16—862no—
309C16—1721no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—3441no—
317C23—3441no—
318C23—3441no—
319C23—3441no—
320C23—3441no—
321C23—3441no—
322C23—1722no—
323C23#1306326612yes—
324C23C2×#1062188211yescharacteristic
325D4—3448no—
326D4—3441no—
327D4—3441no—
328D4—1722no—
329D4—1722no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—3441no—
344C2×C4—3441no—
345C2×C4—1722no—
346C2×C4#1306329311yescharacteristic
347C2×C4#1306329711yescharacteristic
348C2×C4#1306330811yescharacteristic
349C2×C4#1306334511yescharacteristic
350C2×C4#1306335011yescharacteristic
351C2×C4#1306335611yescharacteristic
352C8—41no—
353C8#1306329811yescharacteristic
354C8#1306329811yescharacteristic
355C8#1306330711yescharacteristic
356C8#1306331111yescharacteristic
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—3442no—
365C22—3442no—
366C22—3442no—
367C22—6881no—
368C22—6881no—
369C22—6881no—
370C22—6881no—
371C22#1458303211yescharacteristic
372C22#1458313311yescharacteristic
373C22#1458321211yescharacteristic
374C22C2×#1306326611yescharacteristic
375C22#1458332911yescharacteristic
376C22#1458333411yescharacteristic
377C22#1458334011yescharacteristic
378C4—41no—
379C4—161no—
380C4—161no—
381C4—3442no—
382C4#1458281411yescharacteristic
383C4#1458305911yescharacteristic
384C4#1458314711yescharacteristic
385C4#1458322311yescharacteristic
386C2—42no—
387C2—6882no—
388C2#1913577711yescharacteristic
389C2#1913650611yescharacteristic
390C2#1913653311yescharacteristic
391C2#1913667911yescharacteristic
392C2#1913671011yescharacteristic
393C2#1913677511yescharacteristic
394C2#1913678611yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1808C2
socleC23×C43C2×D8
prime radicalC2×#14583135C2
hypercenter#1808D43
hypocenterC43#13380
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. C2×#14582724C2semidirect
3. C2×#14582699C2semidirect
4. C2×#14582699C2semidirect
5. C2×C22⋊(C43⋊C16)C2semidirect
6. #19132686C2semidirect
7. C43×#1808C2semidirect
42. C2×C43⋊C16D4semidirect
194. #1808D43semidirect
222. C43#13380semidirect

Maximal subgroups

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

subgroupindex
C2×#145831352
C2×#145827242
C2×#145826992
C2×C22⋊(C43⋊C16)2
#191326862
C43×#18082
#1338043