Finite Group Databasebeta

← #25015062

Subgroups — #25015062

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583274C211yesmaximal, characteristic
2C2×Dic43⋊C16C211yesmaximal, characteristic, complemented
3C2×#14582701C211yesmaximal, characteristic, complemented
4C2×#14582700C211yesmaximal, characteristic, complemented
5C2×#14582699C211yesmaximal, characteristic, complemented
6#107×Dic43C211yesmaximal, characteristic, complemented
7C2×C43×#357C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C22×#10621882—21no—
10C2×#13063321—21no—
11C22×C43⋊C16C2211yescharacteristic
12#14583274—22no—
13#14583274C414yescomplemented
14C2×#13063259C2211yescharacteristic
15C2×C8×Dic43C2211yescharacteristic
16C4⋊C4×Dic43—21no—
17Dic43⋊C16—22no—
18#14582701—22no—
19#14582700—22no—
20#14582699—22no—
21#14582661—21no—
22C22×D8×C43C2211yescharacteristic
23C22×C16×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C43×#357—22no—
26C22×D172—21no—
27C22×C22⋊D43—41no—
28C22×C22⋊D43—41no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344—21no—
33C2×D344—21no—
34C2×D344C2×C412yes—
35C2×#10621882—24no—
36C2×#10621882—42no—
37C2×#10621882—42no—
38C22×C43⋊C8D411yescharacteristic
39#13063321—24no—
40#13063321—42no—
41C2×C4⋊Dic43—21no—
42C2×C4×Dic43—41no—
43C2×C4×Dic43D411yescharacteristic
44C2×C43⋊C16—21no—
45C2×C43⋊C16—21no—
46C2×C43⋊C16—21no—
47#13063259—21no—
48#13063259D412yescomplemented
49C8×Dic43C2×C412yes—
50C8×Dic43D412yes—
51C43⋊#95—41no—
52C22×D4×C43—21no—
53C2×D8×C43—21no—
54C2×D8×C43—21no—
55C2×D8×C43—21no—
56C2×D8×C43—21no—
57C2×D8×C43—21no—
58C2×D8×C43C2×C412yes—
59C22×C8×C43C2311yescharacteristic
60C2×C4⋊C4×C43—21no—
61C2×C16×C43—21no—
62C2×C16×C43—21no—
63C2×C16×C43—21no—
64#107×C43—21no—
65#107×C43D412yescomplemented
66C24×C43—41no—
67C23×D43—41no—
68C2×D4×C43—22no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C22×C4×C43—41no—
75C22×C4×C43C2×D411yescharacteristic
76C2×C22⋊D43—44no—
77C2×C22⋊D43—44no—
78C2×C22⋊D43—82no—
79C2×C22⋊D43—82no—
80C2×C22⋊D43—82no—
81C2×C22⋊D43—82no—
82C22×Dic43—41no—
83C22×Dic43D811yescharacteristic
84C22×Dic43D811yescharacteristic
85C2×D172—22no—
86C2×D172—41no—
87C2×D172—41no—
88C2×D172—41no—
89C2×D172—41no—
90C2×D172—41no—
91D8×C43—22no—
92D8×C43—22no—
93D8×C43—41no—
94D8×C43—41no—
95C2×C8×C43C22×C411yescharacteristic
96C2×C8×C43C2×D411yescharacteristic
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43#4111yescharacteristic
100C2×C8×C43#4111yescharacteristic
101C4⋊C4×C43—22no—
102C4⋊C4×C43—41no—
103#10621882—48no—
104C4⋊Dic43—22no—
105C4⋊Dic43—41no—
106C4×Dic43—82no—
107C4×Dic43C22⋊C412yes—
108C4×Dic43SD1612yes—
109C2×C43⋊C8—21no—
110C2×C43⋊C8—21no—
111C2×C43⋊C8C22⋊C412yes—
112D344—22no—
113D344—22no—
114D344—41no—
115D344—41no—
116C16×C43—41no—
117C43⋊C16—41no—
118C23×C43—42no—
119C23×C43—81no—
120C23×C43—81no—
121C23×C43—81no—
122C23×C43—81no—
123C23×C43—81no—
124C23×C43—81no—
125C23×C43C2×D811yescharacteristic
126C22×D43—42no—
127C22×D43—81no—
128C22×D43—81no—
129C22×D43—81no—
130C22×D43—81no—
131C22×D43—81no—
132C22×D43—81no—
133D4×C43—42no—
134D4×C43—42no—
135D4×C43—81no—
136D4×C43—81no—
137C2×C4×C43—42no—
138C2×C4×C43—81no—
139C2×C4×C43—81no—
140C2×C4×C43C2×C22⋊C411yescharacteristic
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43C2×SD1611yescharacteristic
144C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
146C22⋊D43—88no—
147C22⋊D43—88no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—42no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153C2×Dic43#10212yes—
154C2×Dic43#10212yes—
155C2×Dic43D1612yes—
156C2×Dic43SD3212yes—
157D172—42no—
158D172—42no—
159D172—81no—
160D172—81no—
161C8×C43C4×D411yescharacteristic
162C8×C43C4×D411yescharacteristic
163C8×C43#12411yescharacteristic
164C8×C43#12711yescharacteristic
165C43⋊C8—22no—
166#13252—431nomaximal, Sylow
167C22×C43—82no—
168C22×C43—82no—
169C22×C43—82no—
170C22×C43—161no—
171C22×C43—161no—
172C22×C43—161no—
173C22×C43—161no—
174C22×C43C2×#10211yescharacteristic
175C22×C43#45911yescharacteristic
176C22×C43#45911yescharacteristic
177C22×C43C2×D1611yescharacteristic
178C22×C43C2×SD3211yescharacteristic
179C22×C43#50911yescharacteristic
180C22×C43#50911yescharacteristic
181C2×D43—82no—
182C2×D43—82no—
183C2×D43—82no—
184C2×D43—161no—
185C2×D43—161no—
186C2×D43—161no—
187C2×D43—161no—
188C4×C43—82no—
189C4×C43#39011yescharacteristic
190C4×C43#41811yescharacteristic
191C4×C43#46011yescharacteristic
192C4×C43#46011yescharacteristic
193Dic43—22no—
194Dic43—82no—
195Dic43#35714yescomplemented
196C2×#493—431no—
197C2×C4⋊C16—431no—
198C2×#357—431no—
199C2×#357—431no—
200C2×#357—431no—
201C2×#357D4311yescharacteristic, complemented
202C4×#107—431no—
203C2×C43—162no—
204C2×C43#198211yescharacteristic
205C2×C43C2×#35711yescharacteristic
206C2×C43#214011yescharacteristic
207C2×C43#220611yescharacteristic
208C2×C43#220611yescharacteristic
209C2×C43#220711yescharacteristic
210C2×C43#220711yescharacteristic
211D43—162no—
212C22×D8—431no—
213C22×D8—861no—
214C22×D8C2×D4311yescharacteristic
215C2×#127—861no—
216C22×C16—431no—
217C22×C16C2×D4311yescharacteristic
218#493—434no—
219#493—862no—
220C2×#107—431no—
221C2×#107C2×D4311yescharacteristic
222C2×C4×C8—431no—
223C4×C4⋊C4—861no—
224C4⋊C16—862no—
225#357—22no—
226#357—862no—
227#357—862no—
228#357—862no—
229#340—861no—
230C43#1325211yescharacteristic, complemented, Sylow
231C22×D4—21no—
232C22×D4—861no—
233C22×D4—1721no—
234C22×D4—1721no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—21no—
239C2×D8—21no—
240C2×D8—432no—
241C2×D8—864no—
242C2×D8—861no—
243C2×D8—861no—
244C2×D8—861no—
245C2×D8—861no—
246C2×D8—861no—
247C2×D8—1722no—
248C2×D8—1722no—
249C2×D8C4×D4312yes—
250C22×C8—431no—
251C22×C8C22×D4311yescharacteristic
252#127—864no—
253#127—1722no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—861no—
256C2×C42—431no—
257C2×C42—1721no—
258C2×C16—21no—
259C2×C16—21no—
260C2×C16—21no—
261C2×C16—861no—
262C2×C16—861no—
263C2×C16—861no—
264#107—21no—
265#107—432no—
266#107—861no—
267#107C22⋊D4312yescomplemented
268C4×C8—432no—
269C4×C8—432no—
270#95—1721no—
271C24—41no—
272C24—1721no—
273C2×D4—22no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—862no—
280C2×D4—3442no—
281C2×D4—3442no—
282C2×D4—3442no—
283C2×D4—3442no—
284C2×D4—1724no—
285C2×D4—1724no—
286C2×D4—1721no—
287C2×D4—1721no—
288C2×D4—1721no—
289C2×D4—1721no—
290C2×D4—1721no—
291C22×C4—41no—
292C22×C4—431no—
293C22×C4—431no—
294C22×C4—1721no—
295C22×C4D4×D4311yescharacteristic
296D8—22no—
297D8—22no—
298D8—41no—
299D8—41no—
300D8—862no—
301D8—862no—
302D8—1728no—
303D8—1721no—
304D8—1721no—
305C2×C8—432no—
306C2×C8—861no—
307C2×C8—861no—
308C2×C8C2×C4×D4311yescharacteristic
309C2×C8#1062189811yescharacteristic
310C2×C8D4×D4311yescharacteristic
311C2×C8D4×D4311yescharacteristic
312C2×C8#1062190011yescharacteristic
313C2×C8C2×C22⋊D4311yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—862no—
317C4⋊C4—1721no—
318C42—432no—
319C42—432no—
320C42—3442no—
321C16—41no—
322C16—1721no—
323C23—42no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—3441no—
331C23—3441no—
332C23—3441no—
333C23—3441no—
334C23—3441no—
335C23—3441no—
336C23—1722no—
337C23D8×D4311yescharacteristic
338D4—42no—
339D4—42no—
340D4—81no—
341D4—81no—
342D4—3448no—
343D4—3448no—
344D4—3441no—
345D4—3441no—
346D4—1722no—
347D4—1722no—
348C2×C4—42no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—432no—
352C2×C4—432no—
353C2×C4—432no—
354C2×C4—432no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—3441no—
358C2×C4—3441no—
359C2×C4—1722no—
360C2×C4C22⋊C4×D4311yescharacteristic
361C2×C4#1306329711yescharacteristic
362C2×C4#1306329811yescharacteristic
363C2×C4SD16×D4311yescharacteristic
364C2×C4#1306334911yescharacteristic
365C2×C4#1306335211yescharacteristic
366C8—862no—
367C8(C22⋊D43)⋊C411yescharacteristic
368C8C4×C22⋊D4311yescharacteristic
369C8#1306331111yescharacteristic
370C8#1306332111yescharacteristic
371C22—82no—
372C22—82no—
373C22—82no—
374C22—161no—
375C22—161no—
376C22—161no—
377C22—161no—
378C22—3442no—
379C22—3442no—
380C22—3442no—
381C22—6881no—
382C22—6881no—
383C22—6881no—
384C22—6881no—
385C22#102×D4311yescharacteristic
386C22#1458309211yescharacteristic
387C22#1458309311yescharacteristic
388C22D16×D4311yescharacteristic
389C22SD32×D4311yescharacteristic
390C22#1458333311yescharacteristic
391C22#1458333611yescharacteristic
392C4—82no—
393C4—434no—
394C4—862no—
395C4—3442no—
396C4#1458279911yescharacteristic
397C4#1458290211yescharacteristic
398C4#1458309711yescharacteristic
399C4#1458309811yescharacteristic
400C2—162no—
401C2—6882no—
402C2#1913552011yescharacteristic
403C2#357×D4311yescharacteristic
404C2#1913630911yescharacteristic
405C2#1913662811yescharacteristic
406C2#1913662911yescharacteristic
407C2#1913663311yescharacteristic
408C2#1913663411yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#357C2
socleC23×C43C2×D8
prime radicalC2×#14583274C2
cosocleC22×C8×C43C23
hypercenterC2×#357D43
hypocenterC43#13252
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×Dic43⋊C16C2semidirect
3. C2×#14582701C2semidirect
4. C2×#14582700C2semidirect
5. C2×#14582699C2semidirect
6. #107×Dic43C2semidirect
7. C2×C43×#357C2semidirect
13. #14583274C4semidirect
48. #13063259D4semidirect
65. #107×C43D4semidirect
195. Dic43#357semidirect
201. C2×#357D43semidirect
230. C43#13252semidirect
267. #107C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832742
C2×Dic43⋊C162
C2×#145827012
C2×#145827002
C2×#145826992
#107×Dic432
C2×C43×#3572
#1325243