Finite Group Databasebeta

← #25013532

Subgroups — #25013532

Order 11008.

626 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583132C211yesmaximal, characteristic
2C2×#107×D43C211yesmaximal, characteristic, complemented
3C2×#14582700C211yesmaximal, characteristic, complemented
4C2×(C2×D43)⋊C16C211yesmaximal, characteristic, complemented
5#19132687C211yesmaximal, characteristic, complemented
6#19132686C211yesmaximal, characteristic, complemented
7C2×C43×#357C211yesmaximal, characteristic, complemented
8C22×C8×D43C2211yescharacteristic
9C2×#13063296—21no—
10C2×C4⋊C4×D43—21no—
11C22×C43⋊C16C2211yescharacteristic
12#14583132—22no—
13#14583132C414yescomplemented
14C2×#13063259C2211yescharacteristic
15C2×#13063259C2211yescharacteristic
16C2×#13063258—21no—
17#107×D43—22no—
18#107×D43—22no—
19C2×#13063246—21no—
20#14582700—22no—
21(C2×D43)⋊C16—22no—
22C22×D8×C43C2211yescharacteristic
23C22×C16×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C43×#357—22no—
26C22×C22⋊D43—41no—
27C22×C4×D43—41no—
28C22×C4×D43D411yescharacteristic
29C22×C43⋊C8D411yescharacteristic
30C2×C8×D43—21no—
31C2×C8×D43—21no—
32C2×C8×D43—21no—
33C2×C8×D43—21no—
34C2×C8×D43C2×C412yes—
35C2×C8×D43D412yes—
36#13063296—24no—
37#13063296—42no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—21no—
40C2×Dic43⋊C4—41no—
41C4⋊C4×D43—24no—
42C4⋊C4×D43—42no—
43C2×C22⋊Dic43—41no—
44C2×C43⋊C16—21no—
45C2×C43⋊C16—21no—
46C2×C43⋊C16—21no—
47#13063259—21no—
48#13063259—21no—
49#13063259C2×C412yescomplemented
50#13063259D412yescomplemented
51#13063258—24no—
52#13063246—24no—
53C22×D4×C43—21no—
54C2×D8×C43—21no—
55C2×D8×C43—21no—
56C2×D8×C43—21no—
57C2×D8×C43—21no—
58C2×D8×C43—21no—
59C2×D8×C43C2×C412yescomplemented
60C22×C8×C43C2311yescharacteristic
61C2×C4⋊C4×C43—21no—
62C2×C16×C43—21no—
63C2×C16×C43—21no—
64C2×C16×C43—21no—
65#107×C43—21no—
66#107×C43D412yescomplemented
67C24×C43—41no—
68C23×D43D811yescharacteristic
69C2×D4×C43—22no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C22×C4×C43—41no—
76C22×C4×C43C2×D411yescharacteristic
77C2×C22⋊D43—44no—
78C2×C22⋊D43—82no—
79C2×C22⋊D43—82no—
80C22×Dic43—41no—
81C22×Dic43—41no—
82C22×Dic43D811yescharacteristic
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—44no—
88C2×C4×D43—82no—
89C2×C4×D43—82no—
90C2×C4×D43C22⋊C412yes—
91C2×C4×D43SD1612yes—
92D8×C43—22no—
93D8×C43—22no—
94D8×C43—41no—
95D8×C43—41no—
96C2×C8×C43C22×C411yescharacteristic
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43#4111yescharacteristic
101C2×C8×C43#4111yescharacteristic
102C4⋊C4×C43—22no—
103C4⋊C4×C43—41no—
104C22⋊Dic43—44no—
105C4⋊Dic43—22no—
106C4⋊Dic43—22no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109Dic43⋊C4—44no—
110C2×C43⋊C8—21no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8C22⋊C412yes—
113C8×D43—22no—
114C8×D43—22no—
115C8×D43—22no—
116C8×D43—22no—
117C16×C43—41no—
118C43⋊C16—41no—
119C23×C43—42no—
120C23×C43—81no—
121C23×C43—81no—
122C23×C43—81no—
123C23×C43—81no—
124C23×C43—81no—
125C23×C43—81no—
126C23×C43C2×D811yescharacteristic
127C22×D43—21no—
128C22×D43—21no—
129C22×D43—21no—
130C22×D43—21no—
131C22×D43#10212yes—
132C22×D43D1612yes—
133C22×D43SD3212yes—
134D4×C43—42no—
135D4×C43—42no—
136D4×C43—81no—
137D4×C43—81no—
138C2×C4×C43—42no—
139C2×C4×C43—81no—
140C2×C4×C43—81no—
141C2×C4×C43C2×C22⋊C411yescharacteristic
142C2×C4×C43#12011yescharacteristic
143C2×C4×C43#12311yescharacteristic
144C2×C4×C43C2×SD1611yescharacteristic
145C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C43#13711yescharacteristic
147C22⋊D43—88no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—42no—
151C2×Dic43—42no—
152C2×Dic43—81no—
153C2×Dic43—81no—
154C2×Dic43—81no—
155C2×Dic43—81no—
156C2×Dic43#10212yes—
157C4×D43—22no—
158C4×D43—22no—
159C4×D43—22no—
160C4×D43—22no—
161C4×D43—88no—
162C8×C43C4×D411yescharacteristic
163C8×C43C4×D411yescharacteristic
164C8×C43#12111yescharacteristic
165C8×C43#12111yescharacteristic
166C43⋊C8—22no—
167#12991—431nomaximal, Sylow
168C22×C43—82no—
169C22×C43—82no—
170C22×C43—82no—
171C22×C43—161no—
172C22×C43—161no—
173C22×C43—161no—
174C22×C43—161no—
175C22×C43C2×#10211yescharacteristic
176C22×C43#44711yescharacteristic
177C22×C43#48011yescharacteristic
178C22×C43C2×D1611yescharacteristic
179C22×C43C2×SD3211yescharacteristic
180C22×C43#50911yescharacteristic
181C22×C43#51011yescharacteristic
182C2×D43—22no—
183C2×D43—22no—
184C2×D43—22no—
185C2×D43—22no—
186C2×D43—22no—
187C2×D43—22no—
188C2×D43#35714yescomplemented
189C4×C43—82no—
190C4×C43#38611yescharacteristic
191C4×C43#41711yescharacteristic
192C4×C43#44811yescharacteristic
193C4×C43#48111yescharacteristic
194Dic43—22no—
195Dic43—82no—
196Dic43—82no—
197C2×#466—431no—
198C22×#107—431no—
199C2×#357—431no—
200C2×#357D4311yescharacteristic, complemented
201C2×C22⋊C16—431no—
202#1380—431no—
203#1380—431no—
204C2×C43—162no—
205C2×C43#187411yescharacteristic
206C2×C43C2×#35711yescharacteristic
207C2×C43#213911yescharacteristic
208C2×C43#218411yescharacteristic
209C2×C43#218511yescharacteristic
210C2×C43#223211yescharacteristic
211C2×C43#223311yescharacteristic
212D43—24no—
213C22×D8C2×D4311yescharacteristic
214C23×C8—431no—
215C2×#121—861no—
216C22×C4⋊C4—861no—
217C22×C16—431no—
218C22×C16C2×D4311yescharacteristic
219#466—434no—
220#466—862no—
221C2×#107—431no—
222C2×#107—431no—
223C2×#107—862no—
224C2×#107—861no—
225C2×#107—862no—
226C2×#107C2×D4311yescharacteristic
227C2×#102—861no—
228#357—22no—
229#357—862no—
230C22⋊C16—862no—
231C43#1299111yescharacteristic, complemented, Sylow
232C22×D4—21no—
233C22×D4—1721no—
234C23×C4—431no—
235C23×C4—1721no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—21no—
239C2×D8—21no—
240C2×D8—21no—
241C2×D8C4×D4312yescomplemented
242C22×C8—431no—
243C22×C8—432no—
244C22×C8—432no—
245C22×C8—861no—
246C22×C8—861no—
247C22×C8—861no—
248C22×C8—861no—
249C22×C8C22×D4311yescharacteristic
250#121—864no—
251#121—1722no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—864no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4—1722no—
257C2×C4⋊C4—1721no—
258C2×C22⋊C4—1721no—
259C2×C16—21no—
260C2×C16—21no—
261C2×C16—21no—
262C2×C16—861no—
263C2×C16—861no—
264C2×C16—861no—
265#107—21no—
266#107—432no—
267#107—432no—
268#107—864no—
269#107—861no—
270#107—861no—
271#107C22⋊D4312yescomplemented
272#102—864no—
273C24—41no—
274C24—431no—
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—3442no—
282C2×D4—3442no—
283C2×D4—1724no—
284C22×C4—41no—
285C22×C4—431no—
286C22×C4—432no—
287C22×C4—432no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—3442no—
293C22×C4—3442no—
294C22×C4—1724no—
295C22×C4—1721no—
296C22×C4—1721no—
297C22×C4D4×D4311yescharacteristic
298D8—22no—
299D8—22no—
300D8—41no—
301D8—41no—
302C2×C8—432no—
303C2×C8—861no—
304C2×C8—861no—
305C2×C8—862no—
306C2×C8—862no—
307C2×C8—862no—
308C2×C8—862no—
309C2×C8C2×C4×D4311yescharacteristic
310C2×C8#1062189811yescharacteristic
311C2×C8D4×D4311yescharacteristic
312C2×C8D4×D4311yescharacteristic
313C2×C8#1062190011yescharacteristic
314C2×C8C2×C22⋊D4311yescharacteristic
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—862no—
318C4⋊C4—862no—
319C4⋊C4—1724no—
320C4⋊C4—1721no—
321C4⋊C4—1721no—
322C22⋊C4—1724no—
323C16—41no—
324C16—1721no—
325C23—42no—
326C23—81no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23—432no—
333C23—432no—
334C23—432no—
335C23—861no—
336C23—861no—
337C23—861no—
338C23—861no—
339C23D8×D4311yescharacteristic
340D4—42no—
341D4—42no—
342D4—81no—
343D4—81no—
344D4—3448no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—432no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—862no—
352C2×C4—862no—
353C2×C4—862no—
354C2×C4—862no—
355C2×C4—3448no—
356C2×C4—3441no—
357C2×C4—3441no—
358C2×C4—3441no—
359C2×C4—3441no—
360C2×C4—1722no—
361C2×C4—1722no—
362C2×C4C22⋊C4×D4311yescharacteristic
363C2×C4#1306329311yescharacteristic
364C2×C4#1306330711yescharacteristic
365C2×C4SD16×D4311yescharacteristic
366C2×C4#1306334911yescharacteristic
367C2×C4#1306335411yescharacteristic
368C8—862no—
369C8(C22⋊D43)⋊C411yescharacteristic
370C8C4×C22⋊D4311yescharacteristic
371C8#1306329611yescharacteristic
372C8#1306329811yescharacteristic
373C22—82no—
374C22—82no—
375C22—82no—
376C22—161no—
377C22—161no—
378C22—161no—
379C22—161no—
380C22—434no—
381C22—862no—
382C22—862no—
383C22—862no—
384C22—862no—
385C22—862no—
386C22—862no—
387C22#102×D4311yescharacteristic
388C22#1458303111yescharacteristic
389C22#1458321111yescharacteristic
390C22D16×D4311yescharacteristic
391C22SD32×D4311yescharacteristic
392C22#1458333311yescharacteristic
393C22#1458333811yescharacteristic
394C4—82no—
395C4—862no—
396C4—3442no—
397C4—3442no—
398C4#1458277511yescharacteristic
399C4#1458289711yescharacteristic
400C4#1458303611yescharacteristic
401C4#1458321611yescharacteristic
402C2—162no—
403C2—864no—
404C2#1913490911yescharacteristic
405C2#357×D4311yescharacteristic
406C2#1913630411yescharacteristic
407C2#1913650511yescharacteristic
408C2#1913651011yescharacteristic
409C2#1913677411yescharacteristic
410C2#1913677911yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#357C2
socleC23×C43C2×D8
prime radicalC2×#14583132C2
cosocleC22×C8×C43C23
hypercenterC2×#357D43
hypocenterC43#12991
LCSG ▷ C2×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×#107×D43C2semidirect
3. C2×#14582700C2semidirect
4. C2×(C2×D43)⋊C16C2semidirect
5. #19132687C2semidirect
6. #19132686C2semidirect
7. C2×C43×#357C2semidirect
13. #14583132C4semidirect
49. #13063259C2×C4semidirect
50. #13063259D4semidirect
59. C2×D8×C43C2×C4semidirect
66. #107×C43D4semidirect
188. C2×D43#357semidirect
200. C2×#357D43semidirect
231. C43#12991semidirect
241. C2×D8C4×D43semidirect
271. #107C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831322
C2×#107×D432
C2×#145827002
C2×(C2×D43)⋊C162
#191326872
#191326862
C2×C43×#3572
#1299143