Finite Group Databasebeta

← #25015755

Subgroups — #25015755

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×#14583136C211yesmaximal, characteristic
2C2×#14582724C211yesmaximal, characteristic, complemented
3C2×#14582701C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic, complemented
5C2×(C2×D43)⋊C16C211yesmaximal, characteristic, complemented
6#19134621C211yesmaximal, characteristic, complemented
7C43×#1380C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C22×C8×D43C2211yescharacteristic
10C2×#13063300—21no—
11C22×C43⋊C16C2211yescharacteristic
12#14583136—22no—
13#14583136—22no—
14C2×#13063259C2211yescharacteristic
15C2×#13063245—21no—
16#14582756—21no—
17#14582724—22no—
18#14582701—22no—
19#14582699—22no—
20(C2×D43)⋊C16—22no—
21#14582661—21no—
22C22×C16×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C22×D172—21no—
26C22×D172—41no—
27C22×C4×D43D411yescharacteristic
28C2×D344—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344—21no—
33C2×D344D412yes—
34C22×C43⋊C8D411yescharacteristic
35C2×C8×D43—21no—
36C2×C8×D43—21no—
37C2×C8×D43—21no—
38C2×C8×D43—21no—
39C2×C8×D43—21no—
40C2×C8×D43—21no—
41#13063300—24no—
42#13063300—42no—
43C2×C4⋊Dic43—21no—
44C2×(C2×D43)⋊C4—41no—
45C2×(C2×D43)⋊C4—41no—
46C2×C43⋊C16—21no—
47C2×C43⋊C16—21no—
48C2×C43⋊C16D412yescomplemented
49#13063259—21no—
50#13063259—21no—
51#13063245—24no—
52C43⋊#95—41no—
53C22×C8×C43C2311yescharacteristic
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C16×C43—21no—
57C2×C16×C43—21no—
58C2×C16×C43—21no—
59#107×C43—21no—
60#107×C43—21no—
61#107×C43—21no—
62#107×C43D412yes—
63C23×D43—41no—
64C23×D43D811yescharacteristic
65C22×C4×C43—41no—
66C22×C4×C43—41no—
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—41no—
69C22×Dic43D811yescharacteristic
70C2×D172—22no—
71C2×D172—44no—
72C2×D172—41no—
73C2×D172—41no—
74C2×D172—41no—
75C2×D172—41no—
76C2×D172—41no—
77C2×D172—82no—
78C2×D172—82no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C8×C43C2×D411yescharacteristic
86C2×C8×C43C2×D411yescharacteristic
87C2×C8×C43C2×D411yescharacteristic
88C2×C8×C43#4111yescharacteristic
89C2×C8×C43#4111yescharacteristic
90C2×C8×C43#4111yescharacteristic
91C4⋊C4×C43—22no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95(C2×D43)⋊C4—44no—
96(C2×D43)⋊C4—82no—
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99C2×C43⋊C8—21no—
100C2×C43⋊C8—21no—
101C2×C43⋊C8—21no—
102D344—22no—
103D344—22no—
104D344—41no—
105D344—41no—
106C8×D43—41no—
107C8×D43—41no—
108C8×D43—41no—
109C8×D43—41no—
110C16×C43—41no—
111C43⋊C16—22no—
112C23×C43C2×D811yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—42no—
120C22×D43—81no—
121C22×D43—81no—
122C22×D43—81no—
123C22×D43—81no—
124C22×D43—81no—
125C22×D43—81no—
126C22×D43D1612yes—
127C2×C4×C43—42no—
128C2×C4×C43—81no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43#12011yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12311yescharacteristic
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—81no—
143C2×Dic43—81no—
144C2×Dic43—81no—
145D172—42no—
146D172—42no—
147D172—88no—
148D172—81no—
149D172—81no—
150C4×D43—41no—
151C4×D43—41no—
152C4×D43—41no—
153C4×D43—41no—
154C8×C43#12111yescharacteristic
155C8×C43#12111yescharacteristic
156C8×C43#12311yescharacteristic
157C8×C43#12411yescharacteristic
158C43⋊C8—41no—
159#13380—431nomaximal, Sylow
160C22×C43#44711yescharacteristic
161C22×C43#46611yescharacteristic
162C22×C43#48011yescharacteristic
163C22×C43C2×D1611yescharacteristic
164C22×C43#50811yescharacteristic
165C22×C43#50911yescharacteristic
166C22×C43#51011yescharacteristic
167C2×D43—22no—
168C2×D43—22no—
169C2×D43—22no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—82no—
175C2×D43—82no—
176C2×D43—82no—
177C2×D43—161no—
178C2×D43—161no—
179C2×D43—161no—
180C2×D43—161no—
181C4×C43—82no—
182C4×C43—161no—
183C4×C43#39411yescharacteristic
184C4×C43#45211yescharacteristic
185C4×C43#46811yescharacteristic
186C4×C43#48211yescharacteristic
187Dic43—41no—
188Dic43—161no—
189C2×#466—431no—
190C2×#366—431no—
191C2×#357—431no—
192C2×#357—431no—
193C2×C22⋊C16—431no—
194#1808—431no—
195#1380D4311yescharacteristic, complemented
196C2×C43#203311yescharacteristic
197C2×C43#218411yescharacteristic
198C2×C43#218911yescharacteristic
199C2×C43#221511yescharacteristic
200C2×C43#222011yescharacteristic
201C2×C43#223211yescharacteristic
202C2×C43#223411yescharacteristic
203D43—42no—
204D43—162no—
205C22×D8—431no—
206C23×C8—431no—
207C2×#121—861no—
208C22×C16—431no—
209C22×C16C2×D4311yescharacteristic
210#466—862no—
211#466—862no—
212C2×#107—431no—
213C2×#107C2×D4311yescharacteristic
214C2×#107C2×D4311yescharacteristic
215C2×#102—861no—
216#380—861no—
217#366—862no—
218#357—862no—
219#357—862no—
220C22⋊C16—862no—
221#340—861no—
222C43#1338011yescharacteristic, complemented, Sylow
223C22×D4—861no—
224C22×D4—1721no—
225C23×C4—431no—
226C2×D8—432no—
227C2×D8—861no—
228C2×D8—861no—
229C2×D8—861no—
230C2×D8—861no—
231C2×D8—861no—
232C22×C8—431no—
233C22×C8—861no—
234C22×C8—861no—
235C22×C8—861no—
236C22×C8—861no—
237C22×C8—861no—
238C22×C8—861no—
239C22×C8C22×D4311yescharacteristic
240#121—864no—
241#121—1722no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—861no—
245C2×C22⋊C4—1721no—
246C2×C22⋊C4—1721no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—432no—
251C2×C16—861no—
252C2×C16—861no—
253#107—21no—
254#107—21no—
255#107—21no—
256#107—861no—
257#107—861no—
258#107D17212yes—
259#102—864no—
260#95—1721no—
261C24—431no—
262C24—1721no—
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—41no—
273C22×C4—41no—
274C22×C4—431no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—1721no—
282C22×C4D4×D4311yescharacteristic
283D8—862no—
284D8—862no—
285D8—1721no—
286D8—1721no—
287C2×C8—861no—
288C2×C8—861no—
289C2×C8—861no—
290C2×C8—1721no—
291C2×C8—1721no—
292C2×C8—1721no—
293C2×C8—1721no—
294C2×C8C2×D17211yescharacteristic
295C2×C8#1062189811yescharacteristic
296C2×C8#1062189811yescharacteristic
297C2×C8D4×D4311yescharacteristic
298C2×C8D4×D4311yescharacteristic
299C2×C8#1062190211yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C22⋊C4—3442no—
307C22⋊C4—1724no—
308C16—41no—
309C16—862no—
310C23—432no—
311C23—861no—
312C23—861no—
313C23—861no—
314C23—861no—
315C23—861no—
316C23—861no—
317C23—3441no—
318C23—3441no—
319C23—3441no—
320C23—3441no—
321C23—3441no—
322C23—3441no—
323C23—1722no—
324C23D8×D4311yescharacteristic
325D4—3448no—
326D4—3441no—
327D4—3441no—
328D4—1722no—
329D4—1722no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—3441no—
340C2×C4—3441no—
341C2×C4—3441no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4#1306329511yescharacteristic
347C2×C4#1306329811yescharacteristic
348C2×C4#1306331011yescharacteristic
349C2×C4#1306334611yescharacteristic
350C2×C4#1306335211yescharacteristic
351C2×C4#1306335711yescharacteristic
352C8—1721no—
353C8#1306329811yescharacteristic
354C8#1306330011yescharacteristic
355C8#1306331011yescharacteristic
356C8#1306331311yescharacteristic
357C22—862no—
358C22—862no—
359C22—862no—
360C22—3442no—
361C22—3442no—
362C22—3442no—
363C22—1721no—
364C22—1721no—
365C22—1721no—
366C22—1721no—
367C22—6881no—
368C22—6881no—
369C22—6881no—
370C22—6881no—
371C22#1458303411yescharacteristic
372C22#1458313411yescharacteristic
373C22#1458321411yescharacteristic
374C22D16×D4311yescharacteristic
375C22#1458333011yescharacteristic
376C22#1458333611yescharacteristic
377C22#1458334111yescharacteristic
378C4—82no—
379C4—161no—
380C4—1721no—
381C4—6881no—
382C4#1458281711yescharacteristic
383C4#1458306411yescharacteristic
384C4#1458314811yescharacteristic
385C4#1458322511yescharacteristic
386C2—1722no—
387C2—6882no—
388C2#1913578011yescharacteristic
389C2#1913650811yescharacteristic
390C2#1913653811yescharacteristic
391C2#1913668011yescharacteristic
392C2#1913671111yescharacteristic
393C2#1913677711yescharacteristic
394C2#1913678811yescharacteristic
subgroupG/H
centerC23D8×D43
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1380C2
socleC23×C43C2×D8
prime radicalC2×#14583136C2
hypercenter#1380D43
hypocenterC43#13380
LCSG ▷ C22×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×#14582724C2semidirect
3. C2×#14582701C2semidirect
4. C2×#14582699C2semidirect
5. C2×(C2×D43)⋊C16C2semidirect
6. #19134621C2semidirect
7. C43×#1380C2semidirect
48. C2×C43⋊C16D4semidirect
195. #1380D43semidirect
222. C43#13380semidirect

Maximal subgroups

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

subgroupindex
C2×#145831362
C2×#145827242
C2×#145827012
C2×#145826992
C2×(C2×D43)⋊C162
#191346212
C43×#13802
#1338043