Finite Group Databasebeta

← #25010179

Subgroups — #25010179

Order 11008.

308 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147677C211yesmaximal, characteristic
2#19136642C211yesmaximal, characteristic, complemented
3#19134086C211yesmaximal, characteristic, complemented
4#19132638C211yesmaximal, characteristic
5#19132578C211yesmaximal, characteristic, complemented
6#19132566C211yesmaximal, characteristic, complemented
7C43×#2251C211yesmaximal, characteristic
8#14583618—21no—
9C2×#13063271—21no—
10#14583290—21no—
11#14583181—21no—
12#14583118—21no—
13#14583112—21no—
14#14583107—21no—
15#14583029C2211yescharacteristic
16#14583000—21no—
17C4×Dic172C2211yescharacteristic
18C4⋊(C43⋊C16)C2211yescharacteristic
19#14582703—21no—
20#14582650C2211yescharacteristic
21#14582645—21no—
22C2×Q32×C43—21no—
23C2×SD32×C43—21no—
24C43×#495C2211yescharacteristic
25C43×#494C2211yescharacteristic
26C43×#346C2211yescharacteristic
27C2×Dic172D411yescharacteristic
28C2×#10621885—21no—
29C2×#10621883—21no—
30#13063323—21no—
31#13063318—41no—
32#13063318—41no—
33#13063312—21no—
34#13063302—41no—
35Q8×Dic43—21no—
36C4×Dic86—21no—
37C4×Dic86D411yescharacteristic
38D4×Dic43—21no—
39#13063281—41no—
40#13063271—42no—
41C2×C43⋊C16—21no—
42#13063259D411yescharacteristic
43#13063256—41no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)D411yescharacteristic
46Dic43⋊C8—21no—
47#13063250—21no—
48#13063249—21no—
49#13063248—41no—
50#13063246—21no—
51#13063235—21no—
52C2×Q16×C43—21no—
53C2×Q16×C43—21no—
54C2×Q16×C43D411yescharacteristic
55C2×SD16×C43—21no—
56C2×D8×C43D411yescharacteristic
57C4⋊Q8×C43—21no—
58#124×C43—21no—
59Q32×C43—42no—
60SD32×C43—42no—
61C2×C16×C43—21no—
62C4×C8×C43C2311yescharacteristic
63C2×Q8×C43—21no—
64C2×Q8×C43—41no—
65C2×D4×C43—21no—
66C22×Dic43—41no—
67C2×Dic86—21no—
68C2×Dic86D811yescharacteristic
69Q16×C43—41no—
70Q16×C43—41no—
71Q16×C43—41no—
72Q16×C43—41no—
73Q16×C43—41no—
74SD16×C43—41no—
75SD16×C43—41no—
76D8×C43—41no—
77C2×C8×C43C2×D411yescharacteristic
78C2×C8×C43C2×D411yescharacteristic
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C22⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C42×C43C2×D411yescharacteristic
84C22⋊Dic43—41no—
85C22⋊Dic43—41no—
86C22⋊Dic43—41no—
87#10621885—81no—
88#10621883—81no—
89C4⋊Dic43—21no—
90C4⋊Dic43—41no—
91C4⋊Dic43D811yescharacteristic
92Dic43⋊C4—21no—
93Dic43⋊C4—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96C4×Dic43—21no—
97C4×Dic43—41no—
98C4×Dic43—41no—
99C2×C43⋊C8—21no—
100C2×C43⋊C8—41no—
101Dic172—21no—
102Dic172—21no—
103C16×C43—22no—
104C43⋊C16—41no—
105C23×C43—41no—
106Q8×C43—41no—
107Q8×C43—41no—
108Q8×C43—81no—
109Q8×C43—81no—
110D4×C43—41no—
111D4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—81no—
114C2×C4×C43#12011yescharacteristic
115C2×C4×C43C2×D811yescharacteristic
116C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—82no—
122Dic86—41no—
123Dic86—41no—
124Dic86—41no—
125C8×C43—21no—
126C8×C43#13511yescharacteristic
127C8×C43AGL(1,ℤ/8)11yescharacteristic
128C43⋊C8—41no—
129C43⋊C8—81no—
130#12339—431nomaximal, Sylow
131C22×C43—81no—
132C22×C43—81no—
133C22×C43—81no—
134C22×C43#44711yescharacteristic
135C4×C43—21no—
136C4×C43—21no—
137C4×C43—81no—
138C4×C43—161no—
139C4×C43#44911yescharacteristic
140C4×C43#45311yescharacteristic
141Dic43—41no—
142Dic43—41no—
143Dic43—81no—
144Dic43—81no—
145#3402—431no—
146#2251D4311yescharacteristic
147#2209—431no—
148#1690—431no—
149#1360—431no—
150#1338—431no—
151#1334—431no—
152C2×C43—161no—
153C2×C43#162111yescharacteristic
154C2×C43#219111yescharacteristic
155C2×C43#219511yescharacteristic
156#556—861no—
157C2×Q32—21no—
158C2×Q32—861no—
159C2×SD32—21no—
160#497—861no—
161#495C2×D4311yescharacteristic
162#494C2×D4311yescharacteristic
163#475—861no—
164#464—861no—
165#463—861no—
166#462—861no—
167#446—431no—
168#440—861no—
169C4×Q16—431no—
170C4⋊C16—431no—
171#358—861no—
172#346C2×D4311yescharacteristic
173#334—431no—
174#332—861no—
175C43#1233911yescharacteristic, complemented, Sylow
176C2×Q16—21no—
177C2×Q16—21no—
178C2×Q16—431no—
179C2×Q16—861no—
180C2×Q16C22⋊D4311yescharacteristic
181C2×SD16—21no—
182C2×SD16—861no—
183C2×D8C22⋊D4311yescharacteristic
184C4⋊Q8—21no—
185C4⋊Q8—861no—
186#126—1721no—
187#126—1721no—
188#124—21no—
189#124—861no—
190C22⋊Q8—1721no—
191C4×Q8—431no—
192C4×Q8—861no—
193C4×Q8—861no—
194C4×D4—861no—
195#117—1721no—
196Q32—42no—
197Q32—1722no—
198SD32—42no—
199C2×C16—21no—
200C2×C16—861no—
201#107—431no—
202#106—1721no—
203C4⋊C8—431no—
204C4⋊C8—861no—
205C4⋊C8—861no—
206#103—861no—
207#103—861no—
208#103—1721no—
209#102—861no—
210#97—861no—
211C4×C8C22×D4311yescharacteristic
212C2×Q8—21no—
213C2×Q8—41no—
214C2×Q8—431no—
215C2×Q8—861no—
216C2×D4—21no—
217C22×C4—1721no—
218Q16—41no—
219Q16—41no—
220Q16—41no—
221Q16—41no—
222Q16—41no—
223Q16—861no—
224Q16—861no—
225Q16—3441no—
226SD16—41no—
227SD16—41no—
228SD16—3441no—
229D8—41no—
230C2×C8—861no—
231C2×C8—1721no—
232C2×C8D4×D4311yescharacteristic
233C2×C8C2×C22⋊D4311yescharacteristic
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—431no—
237C4⋊C4—861no—
238C4⋊C4—861no—
239C4⋊C4—1721no—
240C4⋊C4—1721no—
241C4⋊C4—1721no—
242C4⋊C4—1721no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—1721no—
246C22⋊C4—1721no—
247C22⋊C4—1721no—
248C42—861no—
249C42—1721no—
250C42—1721no—
251C42D4×D4311yescharacteristic
252C16—22no—
253C16—1721no—
254C23—41no—
255Q8—41no—
256Q8—41no—
257Q8—81no—
258Q8—81no—
259Q8—1721no—
260Q8—1721no—
261Q8—1721no—
262D4—41no—
263D4—41no—
264C2×C4—41no—
265C2×C4—81no—
266C2×C4—861no—
267C2×C4—861no—
268C2×C4—3442no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4#1306329311yescharacteristic
272C2×C4D8×D4311yescharacteristic
273C2×C4#1306334911yescharacteristic
274C8—21no—
275C8—3441no—
276C8—1721no—
277C8#1306334411yescharacteristic
278C8#1306334911yescharacteristic
279C22—81no—
280C22—81no—
281C22—81no—
282C22#1458303111yescharacteristic
283C4—21no—
284C4—21no—
285C4—81no—
286C4—161no—
287C4—3441no—
288C4—3441no—
289C4—1721no—
290C4—1721no—
291C4#1458304111yescharacteristic
292C4#1458306611yescharacteristic
293C2—161no—
294C2#1913365711yescharacteristic
295C2#1913654411yescharacteristic
296C2#1913657011yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2251C2
socleC22×C43#447
prime radicalC2×D8×C43D4
hypercenter#2251D43
hypocenterC43#12339
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2251

Complements

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

NH ≅ G/Ntype
2. #19136642C2semidirect
3. #19134086C2semidirect
5. #19132578C2semidirect
6. #19132566C2semidirect
175. C43#12339semidirect

Maximal subgroups

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

subgroupindex
#191476772
#191366422
#191340862
#191326382
#191325782
#191325662
C43×#22512
#1233943