Finite Group Databasebeta

← #25015751

Subgroups — #25015751

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×#14583132C211yesmaximal, characteristic
2C2×#14582725C211yesmaximal, characteristic, complemented
3C2×#14582700C211yesmaximal, characteristic, complemented
4C2×(C2×D43)⋊C16C211yesmaximal, characteristic, complemented
5#19134621C211yesmaximal, characteristic, complemented
6#19132686C211yesmaximal, characteristic, complemented
7C2×C43×#357C211yesmaximal, characteristic, complemented
8C22×C8×D43C2211yescharacteristic
9C2×#13063296—21no—
10C22×C43⋊C16C2211yescharacteristic
11#14583132—22no—
12#14583132—22no—
13C2×#13063259C2211yescharacteristic
14C2×#13063259C2211yescharacteristic
15C2×#13063246—21no—
16#14582756—21no—
17#14582725—22no—
18#14582700—22no—
19(C2×D43)⋊C16—22no—
20#14582661—21no—
21C22×D8×C43C2211yescharacteristic
22C22×C16×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C43×#357—22no—
25C22×C22⋊D43—41no—
26C22×C4×D43D411yescharacteristic
27C22×C43⋊C8D411yescharacteristic
28C2×C8×D43—21no—
29C2×C8×D43—21no—
30C2×C8×D43—21no—
31C2×C8×D43—21no—
32C2×C8×D43—21no—
33C2×C8×D43—21no—
34#13063296—24no—
35#13063296—42no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—21no—
38C2×C22⋊Dic43—41no—
39C2×(C2×D43)⋊C4—41no—
40C2×C43⋊C16—21no—
41C2×C43⋊C16—21no—
42C2×C43⋊C16—21no—
43#13063259—21no—
44#13063259—21no—
45#13063259—21no—
46#13063259D412yes—
47#13063246—24no—
48C43⋊#95—41no—
49C22×D4×C43—21no—
50C2×D8×C43—21no—
51C2×D8×C43—21no—
52C2×D8×C43—21no—
53C2×D8×C43—21no—
54C2×D8×C43—21no—
55C2×D8×C43D412yes—
56C22×C8×C43C2311yescharacteristic
57C2×C4⋊C4×C43—21no—
58C2×C16×C43—21no—
59C2×C16×C43—21no—
60C2×C16×C43D412yescomplemented
61#107×C43—21no—
62#107×C43—21no—
63C24×C43—41no—
64C23×D43D811yescharacteristic
65C2×D4×C43—22no—
66C2×D4×C43—41no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43C2×D411yescharacteristic
73C2×C22⋊D43—44no—
74C2×C22⋊D43—82no—
75C2×C22⋊D43—82no—
76C22×Dic43—41no—
77C22×Dic43—41no—
78C22×Dic43D811yescharacteristic
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85D8×C43—22no—
86D8×C43—22no—
87D8×C43—41no—
88D8×C43—41no—
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43C2×D411yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C2×C8×C43#4111yescharacteristic
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C22⋊Dic43—44no—
98(C2×D43)⋊C4—82no—
99C4⋊Dic43—22no—
100C4⋊Dic43—41no—
101C4⋊Dic43—41no—
102C4⋊Dic43—41no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—21no—
106C8×D43—41no—
107C8×D43—41no—
108C8×D43—41no—
109C8×D43—41no—
110C16×C43—22no—
111C43⋊C16—41no—
112C23×C43—42no—
113C23×C43—81no—
114C23×C43—81no—
115C23×C43—81no—
116C23×C43—81no—
117C23×C43—81no—
118C23×C43—81no—
119C23×C43C2×D811yescharacteristic
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—21no—
125C22×D43—21no—
126C22×D43D1612yes—
127D4×C43—42no—
128D4×C43—42no—
129D4×C43—81no—
130D4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43—81no—
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12311yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C43#13711yescharacteristic
140C22⋊D43—88no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—42no—
145C2×Dic43—81no—
146C2×Dic43—81no—
147C2×Dic43—81no—
148C2×Dic43—81no—
149C2×Dic43—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—82no—
161C22×C43—82no—
162C22×C43—82no—
163C22×C43—161no—
164C22×C43—161no—
165C22×C43—161no—
166C22×C43—161no—
167C22×C43#44711yescharacteristic
168C22×C43#46611yescharacteristic
169C22×C43#48011yescharacteristic
170C22×C43C2×D1611yescharacteristic
171C22×C43#50811yescharacteristic
172C22×C43#50911yescharacteristic
173C22×C43#51011yescharacteristic
174C2×D43—22no—
175C2×D43—22no—
176C2×D43—22no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—41no—
181C4×C43—161no—
182C4×C43#39411yescharacteristic
183C4×C43#45211yescharacteristic
184C4×C43#46811yescharacteristic
185C4×C43#48211yescharacteristic
186Dic43—41no—
187Dic43—82no—
188Dic43—161no—
189C2×#466—431no—
190C2×#366—431no—
191C2×#357—431no—
192C2×#357D4311yescharacteristic, complemented
193C2×C22⋊C16—431no—
194#1808—431no—
195#1380—431no—
196C2×C43—162no—
197C2×C43#203311yescharacteristic
198C2×C43#218411yescharacteristic
199C2×C43#218911yescharacteristic
200C2×C43#221511yescharacteristic
201C2×C43#222011yescharacteristic
202C2×C43#223211yescharacteristic
203C2×C43#223411yescharacteristic
204D43—42no—
205C22×D8C2×D4311yescharacteristic
206C23×C8—431no—
207C2×#121—861no—
208C22×C16—431no—
209C22×C16C2×D4311yescharacteristic
210#466—862no—
211#466—862no—
212C2×#107—431no—
213C2×#107—431no—
214C2×#107C2×D4311yescharacteristic
215C2×#102—861no—
216#380—861no—
217#366—862no—
218#357—22no—
219#357—862no—
220C22⋊C16—862no—
221#340—861no—
222C43#1338011yescharacteristic, complemented, Sylow
223C22×D4—21no—
224C22×D4—1721no—
225C23×C4—431no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—21no—
229C2×D8—21no—
230C2×D8—21no—
231C2×D8D17212yes—
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—861no—
244C2×C4⋊C4—861no—
245C2×C22⋊C4—1721no—
246C2×C22⋊C4—1721no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—861no—
250C2×C16—861no—
251C2×C16—861no—
252C2×C16C22⋊D4312yescomplemented
253#107—21no—
254#107—21no—
255#107—432no—
256#107—861no—
257#107—861no—
258#107—861no—
259#102—864no—
260#95—1721no—
261C24—41no—
262C24—431no—
263C2×D4—22no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—3442no—
270C2×D4—3442no—
271C2×D4—1724no—
272C22×C4—41no—
273C22×C4—431no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—1721no—
281C22×C4—1721no—
282C22×C4D4×D4311yescharacteristic
283D8—22no—
284D8—22no—
285D8—41no—
286D8—41no—
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×C8D4×D4311yescharacteristic
297C2×C8#1062190011yescharacteristic
298C2×C8#1062190011yescharacteristic
299C2×C8C2×C22⋊D4311yescharacteristic
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—862no—
303C4⋊C4—1721no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C22⋊C4—3442no—
307C22⋊C4—1724no—
308C16—22no—
309C16—1721no—
310C23—42no—
311C23—81no—
312C23—81no—
313C23—81no—
314C23—81no—
315C23—81no—
316C23—81no—
317C23—432no—
318C23—861no—
319C23—861no—
320C23—861no—
321C23—861no—
322C23—861no—
323C23—861no—
324C23D8×D4311yescharacteristic
325D4—42no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—3448no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—3441no—
337C2×C4—3441no—
338C2×C4—3441no—
339C2×C4—3441no—
340C2×C4—3441no—
341C2×C4—1722no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4#1306329511yescharacteristic
347C2×C4#1306329611yescharacteristic
348C2×C4#1306330711yescharacteristic
349C2×C4#1306334411yescharacteristic
350C2×C4#1306335211yescharacteristic
351C2×C4#1306335411yescharacteristic
352C8—1721no—
353C8#1306329711yescharacteristic
354C8#1306329911yescharacteristic
355C8#1306330911yescharacteristic
356C8#1306331111yescharacteristic
357C22—82no—
358C22—82no—
359C22—82no—
360C22—161no—
361C22—161no—
362C22—161no—
363C22—161no—
364C22—862no—
365C22—862no—
366C22—862no—
367C22—1721no—
368C22—1721no—
369C22—1721no—
370C22—1721no—
371C22#1458303411yescharacteristic
372C22#1458313211yescharacteristic
373C22#1458321111yescharacteristic
374C22D16×D4311yescharacteristic
375C22#1458332811yescharacteristic
376C22#1458333611yescharacteristic
377C22#1458333811yescharacteristic
378C4—161no—
379C4—3442no—
380C4—1721no—
381C4—6881no—
382C4#1458281511yescharacteristic
383C4#1458306211yescharacteristic
384C4#1458314211yescharacteristic
385C4#1458322111yescharacteristic
386C2—162no—
387C2—1722no—
388C2#1913577611yescharacteristic
389C2#1913650811yescharacteristic
390C2#1913653611yescharacteristic
391C2#1913667811yescharacteristic
392C2#1913670511yescharacteristic
393C2#1913677411yescharacteristic
394C2#1913678411yescharacteristic
subgroupG/H
centerC23D8×D43
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC2×C43×#357C2
socleC23×C43C2×D8
prime radicalC2×#14583132C2
hypercenterC2×#357D43
hypocenterC43#13380
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#14582725C2semidirect
3. C2×#14582700C2semidirect
4. C2×(C2×D43)⋊C16C2semidirect
5. #19134621C2semidirect
6. #19132686C2semidirect
7. C2×C43×#357C2semidirect
60. C2×C16×C43D4semidirect
192. C2×#357D43semidirect
222. C43#13380semidirect
252. C2×C16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831322
C2×#145827252
C2×#145827002
C2×(C2×D43)⋊C162
#191346212
#191326862
C2×C43×#3572
#1338043