Finite Group Databasebeta

← #25008664

Subgroups — #25008664

Order 11008.

466 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 59 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#19141525C211yesmaximal, characteristic, complemented
2#19133598C212yesmaximal, complemented
3#19132600C212yesmaximal, complemented
4#19132527C211yesmaximal, characteristic, complemented
5C43×#2006C211yesmaximal, characteristic
6C2×#13063306—21no—
7#14583210—22no—
8#14582829C2212yes—
9#14582824—22no—
10#14582797—21no—
11#14582774—22no—
12#14582633—22no—
13#14582625C2212yes—
14C2×AGL(1,ℤ/8)×C43—21no—
15C43×#537C2211yescharacteristic
16C2×#104×C43—21no—
17C43×#390C2211yescharacteristic
18C43×#343C2211yescharacteristic
19C23×Dic43—21no—
20#13063306—42no—
21#13063306—42no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43D412yes—
25C2×Dic43⋊C4—22no—
26C2×C22⋊Dic43—21no—
27C2×C22⋊Dic43—22no—
28#13063258—42no—
29#13063246—42no—
30C22⋊(C43⋊C8)—22no—
31C43⋊#95—22no—
32C43⋊#95—22no—
33C43⋊#95D412yes—
34C2×#41×C43—21no—
35C22×D4×C43D411yescharacteristic
36AGL(1,ℤ/8)×C43—42no—
37AGL(1,ℤ/8)×C43—42no—
38C2×SD16×C43—41no—
39C2×D8×C43—41no—
40C2×M16×C43—21no—
41C22⋊Q8×C43—41no—
42#121×C43—22no—
43#121×C43—41no—
44C2×C4⋊C4×C43C2311yescharacteristic
45C2×C22⋊C4×C43—22no—
46C2×C42×C43D411yescharacteristic
47#104×C43—42no—
48C24×C43—21no—
49#41×C43—41no—
50#41×C43—41no—
51#41×C43—41no—
52#41×C43—41no—
53C2×Q8×C43—21no—
54C2×D4×C43—21no—
55C2×D4×C43—21no—
56C2×D4×C43—22no—
57C2×D4×C43—41no—
58C2×D4×C43—41no—
59C2×D4×C43—41no—
60C2×D4×C43D812yes—
61C22×C4×C43—21no—
62C22×C4×C43—41no—
63C22×C4×C43C2×D412yes—
64C22×C4×C43C2×D411yescharacteristic
65C22×Dic43—22no—
66C22×Dic43—22no—
67C22×Dic43—42no—
68C22×Dic43—81no—
69C22×Dic43—81no—
70SD16×C43—44no—
71D8×C43—44no—
72M16×C43—22no—
73M16×C43—41no—
74C2×C8×C43—41no—
75C4⋊C4×C43—22no—
76C4⋊C4×C43—41no—
77C22⋊C4×C43—44no—
78C22⋊C4×C43—42no—
79C42×C43—41no—
80C22⋊Dic43—42no—
81C22⋊Dic43—44no—
82C4⋊Dic43—42no—
83C4⋊Dic43—42no—
84C4⋊Dic43—81no—
85Dic43⋊C4—42no—
86Dic43⋊C4—42no—
87C2×C43⋊C8—42no—
88C23×C43—22no—
89C23×C43—42no—
90C23×C43—42no—
91C23×C43—41no—
92C23×C43—41no—
93C23×C43—41no—
94C23×C43#12011yescharacteristic
95Q8×C43—41no—
96Q8×C43—41no—
97D4×C43—42no—
98D4×C43—41no—
99D4×C43—41no—
100D4×C43—81no—
101D4×C43—82no—
102D4×C43—81no—
103D4×C43—81no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—22no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—42no—
111C2×C4×C43—41no—
112C2×C4×C43—81no—
113C2×C4×C43—81no—
114C2×C4×C43C2×D811yescharacteristic
115C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
116C2×Dic43—42no—
117C2×Dic43—42no—
118C2×Dic43—42no—
119C2×Dic43—42no—
120C2×Dic43—42no—
121C2×Dic43—42no—
122C2×Dic43—84no—
123C8×C43—42no—
124C43⋊C8—82no—
125#12097—431nomaximal, Sylow
126C22×C43—21no—
127C22×C43—21no—
128C22×C43—44no—
129C22×C43—42no—
130C22×C43—82no—
131C22×C43—81no—
132C22×C43—81no—
133C22×C43—81no—
134C22×C43—81no—
135C22×C43—81no—
136C22×C43#44711yescharacteristic
137C22×C43#45311yescharacteristic
138C22×C43B(4,𝔽2)11yescharacteristic
139C4×C43—21no—
140C4×C43—21no—
141C4×C43—42no—
142C4×C43—42no—
143C4×C43—81no—
144Dic43—82no—
145Dic43—82no—
146#2724—431no—
147#2006D4311yescharacteristic
148#1610—432no—
149#1346—432no—
150#1318—431no—
151C2×C43—21no—
152C2×C43—21no—
153C2×C43—82no—
154C2×C43—161no—
155C2×C43#159511yescharacteristic
156C2×C43#219811yescharacteristic
157C2×C43#220311yescharacteristic
158C2×AGL(1,ℤ/8)—21no—
159#537C2×D4311yescharacteristic
160C2×#123—861no—
161#480—862no—
162C2×#104—21no—
163#398—432no—
164#397—862no—
165#390C2×D4311yescharacteristic
166#389—861no—
167#385—862no—
168#343C2×D4311yescharacteristic
169#327—862no—
170#324—432no—
171C43#1209711yescharacteristic, complemented, Sylow
172C2×#41—21no—
173C22×D4C22⋊D4311yescharacteristic
174C23×C4—861no—
175AGL(1,ℤ/8)—42no—
176AGL(1,ℤ/8)—42no—
177C2×SD16—41no—
178C2×D8—41no—
179C2×M16—21no—
180#123—1722no—
181#123—1722no—
182C22⋊Q8—41no—
183#121—22no—
184#121—41no—
185C2×C4⋊C4—432no—
186C2×C4⋊C4—861no—
187C2×C4⋊C4—861no—
188C2×C4⋊C4—862no—
189C2×C4⋊C4C22×D4311yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—862no—
192C2×C22⋊C4—861no—
193C2×C42C22⋊D4311yescharacteristic
194#107—1722no—
195#104—42no—
196#102—1722no—
197C22⋊C8—862no—
198#95—432no—
199#95—862no—
200#95—862no—
201C24—21no—
202#41—41no—
203#41—41no—
204#41—41no—
205#41—41no—
206C2×Q8—21no—
207C2×D4—21no—
208C2×D4—22no—
209C2×D4—21no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4#1062188212yes—
214C22×C4—21no—
215C22×C4—41no—
216C22×C4—862no—
217C22×C4—862no—
218C22×C4—3441no—
219C22×C4—3441no—
220C22×C4—1722no—
221C22×C4D4×D4312yes—
222C22×C4C2×C22⋊D4311yescharacteristic
223SD16—44no—
224D8—44no—
225M16—22no—
226M16—41no—
227C2×C8—41no—
228C2×C8—1722no—
229C4⋊C4—22no—
230C4⋊C4—41no—
231C4⋊C4—3441no—
232C4⋊C4—1722no—
233C4⋊C4—1722no—
234C4⋊C4—1722no—
235C4⋊C4—1722no—
236C22⋊C4—44no—
237C22⋊C4—42no—
238C22⋊C4—1722no—
239C22⋊C4—1724no—
240C42—41no—
241C23—22no—
242C23—42no—
243C23—42no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23#1306329311yescharacteristic
248Q8—41no—
249Q8—41no—
250D4—42no—
251D4—41no—
252D4—41no—
253D4—81no—
254D4—82no—
255D4—81no—
256D4—81no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—3444no—
268C2×C4—1722no—
269C2×C4—1722no—
270C2×C4—1722no—
271C2×C4—1722no—
272C2×C4—1722no—
273C2×C4—1722no—
274C2×C4C2×#1062188211yescharacteristic
275C2×C4#1306335011yescharacteristic
276C8—42no—
277C8—3442no—
278C22—21no—
279C22—21no—
280C22—44no—
281C22—42no—
282C22—82no—
283C22—81no—
284C22—81no—
285C22—81no—
286C22—81no—
287C22—81no—
288C22#1458303211yescharacteristic
289C22#1458306611yescharacteristic
290C22#1458308511yescharacteristic
291C4—21no—
292C4—21no—
293C4—42no—
294C4—42no—
295C4—81no—
296C4—3442no—
297C4—3442no—
298C2—21no—
299C2—21no—
300C2—82no—
301C2—161no—
302C2#1913351211yescharacteristic
303C2#1913659011yescharacteristic
304C2#1913661511yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
Fitting, prime radicalC43×#2006C2
socleC22×C43B(4,𝔽2)
hypercenter#2006D43
hypocenterC43#12097
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2006

Complements

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

NH ≅ G/Ntype
1. #19141525C2semidirect
2. #19133598C2semidirect
3. #19132600C2semidirect
4. #19132527C2semidirect
171. C43#12097semidirect

Maximal subgroups

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

subgroupindex
#191415252
#191335982
#191326002
#191325272
C43×#20062
#1209743