Finite Group Databasebeta

← #24999331

Subgroups — #24999331

Order 11008.

528 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 109 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#19145540C211yesmaximal, characteristic
2#19142972C211yesmaximal, characteristic
3#19135573C211yesmaximal, characteristic
4#19133276C211yesmaximal, characteristic
5#19133275C211yesmaximal, characteristic
6#19132427C211yesmaximal, characteristic
7C43×#3209C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9#14583278—21no—
10#14583251—21no—
11#14583109—22no—
12#14583054—22no—
13#14582952C2211yescharacteristic
14#14582923C2211yescharacteristic
15#14582806—22no—
16#14582804—22no—
17#14582764—22no—
18C42×Dic43C2211yescharacteristic
19#14582658—22no—
20#14582648—22no—
21#14582647—22no—
22C43×#533C2211yescharacteristic
23C2×C4⋊Q8×C43C2211yescharacteristic
24C43×#494—21no—
25C43×#487—21no—
26C43×#462—22no—
27C43×#451—22no—
28C43×#431C2211yescharacteristic
29C22×Dic86D412yes—
30C2×#10621885—24no—
31C2×#10621877—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325—21no—
35#13063325—21no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—21no—
38C2×C4×Dic43—21no—
39C2×C4×Dic43—21no—
40C2×C4×Dic43D412yes—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)D412yes—
44#13063248—24no—
45C22⋊(C43⋊C8)—21no—
46C4×C43⋊C8—21no—
47C43⋊#95—28no—
48C22×Q8×C43D412yes—
49C2×Q16×C43—24no—
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43D411yescharacteristic
55C4⋊Q8×C43D411yescharacteristic
56#125×C43—21no—
57C22⋊Q8×C43—21no—
58C22⋊Q8×C43—21no—
59C4×Q8×C43—21no—
60C4×Q8×C43—21no—
61#117×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C42×C43C2311yescharacteristic
65C4⋊C8×C43D412yes—
66#103×C43—24no—
67C22⋊C8×C43—21no—
68C4×C8×C43—21no—
69C2×Q8×C43—22no—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C2×Q8×C43—22no—
73C2×Q8×C43—44no—
74C22×C4×C43—22no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×Dic43—22no—
79C22×Dic43—22no—
80C2×Dic86—22no—
81C2×Dic86—22no—
82C2×Dic86—44no—
83Q16×C43—84no—
84C2×C8×C43—22no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C22⋊C4×C43—41no—
96C42×C43—41no—
97C42×C43C2×D411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43#4111yescharacteristic
101#10621885—84no—
102C4⋊Dic43—41no—
103C4⋊Dic43—41no—
104C4⋊Dic43—41no—
105C4⋊Dic43—41no—
106C4×Dic43—22no—
107C4×Dic43—42no—
108C4×Dic43—42no—
109C4×Dic43Q1614yescomplemented
110#10621877—42no—
111C2×C43⋊C8—22no—
112C2×C43⋊C8—41no—
113C23×C43#12011yescharacteristic
114Q8×C43—42no—
115Q8×C43—42no—
116Q8×C43—44no—
117Q8×C43—82no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—44no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—42no—
124C2×C4×C43#12011yescharacteristic
125C2×C4×C43#12011yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12711yescharacteristic
130C2×C4×C43C2×Q1612yes—
131C2×C4×C43#13712yes—
132C2×Dic43—24no—
133C2×Dic43—42no—
134C2×Dic43—42no—
135C2×Dic43—44no—
136C2×Dic43—42no—
137Dic86—44no—
138Dic86—82no—
139C8×C43—42no—
140C43⋊C8—42no—
141C43⋊C8—81no—
142#10297—431nomaximal, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43#39211yescharacteristic
146C22×C43#45112yes—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—82no—
150C4×C43—81no—
151C4×C43—81no—
152C4×C43#45512yes—
153C4×C43#45512yes—
154C4×C43#46212yes—
155C4×C43#49411yescharacteristic
156C4×C43#49711yescharacteristic
157Dic43—44no—
158Dic43—82no—
159#3209—431no—
160#3209D4311yescharacteristic
161#2862—431no—
162#1994—431no—
163#1548—431no—
164#1548—431no—
165#1276—431no—
166C2×C43—22no—
167C2×C43#200411yescharacteristic
168C2×C43#200411yescharacteristic
169C2×C43#201611yescharacteristic
170#533C2×D4311yescharacteristic
171C2×C4⋊Q8—431no—
172C2×C4⋊Q8C2×D4311yescharacteristic
173#494—21no—
174#494—861no—
175#487—21no—
176#487—861no—
177#462—22no—
178#462—862no—
179#451—22no—
180#451—862no—
181#431—431no—
182#431C2×D4311yescharacteristic
183#423—431no—
184#391—862no—
185#391—862no—
186#382—862no—
187C43—431no—
188#339—862no—
189#333—862no—
190#333—862no—
191C43#1029711yescharacteristic, complemented, Sylow
192C22×Q8—432no—
193C22×Q8C22⋊D4312yes—
194C2×Q16—24no—
195C2×Q16—864no—
196C2×M16—861no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—861no—
202C4⋊Q8—861no—
203C4⋊Q8—861no—
204C4⋊Q8—861no—
205C4⋊Q8C22⋊D4311yescharacteristic
206C4⋊Q8C22⋊D4311yescharacteristic
207#125—21no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C4×Q8—21no—
211C4×Q8—21no—
212#117—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C42—432no—
218C2×C42—861no—
219C2×C42—861no—
220C2×C42C22×D4311yescharacteristic
221C4⋊C8—432no—
222C4⋊C8—861no—
223C4⋊C8—861no—
224C4⋊C8C22⋊D4312yes—
225#103—24no—
226#103—864no—
227C22⋊C8—21no—
228C22⋊C8—861no—
229C4×C8—21no—
230C4×C8—861no—
231#95—868no—
232C2×Q8—21no—
233C2×Q8—22no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—44no—
237C2×Q8—862no—
238C2×Q8—862no—
239C2×Q8—1724no—
240C22×C4—22no—
241C22×C4—862no—
242C22×C4—862no—
243C22×C4D4×D4311yescharacteristic
244C22×C4D4×D4311yescharacteristic
245C22×C4C2×C22⋊D4311yescharacteristic
246Q16—84no—
247Q16—3444no—
248M16—1722no—
249C2×C8—22no—
250C2×C8—862no—
251C2×C8—1721no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C22⋊C4—41no—
267C42—41no—
268C42—434no—
269C42—862no—
270C42—1722no—
271C42—1722no—
272C42D4×D4311yescharacteristic
273C42#1062190011yescharacteristic
274C42C2×C22⋊D4311yescharacteristic
275C42C2×C22⋊D4311yescharacteristic
276C23#1306329311yescharacteristic
277Q8—42no—
278Q8—42no—
279Q8—44no—
280Q8—82no—
281Q8—3442no—
282Q8—1724no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—44no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—864no—
290C2×C4—1724no—
291C2×C4—1722no—
292C2×C4—1722no—
293C2×C4—1722no—
294C2×C4#1306329311yescharacteristic
295C2×C4#1306329411yescharacteristic
296C2×C4#1306329611yescharacteristic
297C2×C4#1306329711yescharacteristic
298C2×C4#1306329711yescharacteristic
299C2×C4#1306332111yescharacteristic
300C2×C4Q16×D4312yes—
301C2×C4#1306335712yes—
302C8—42no—
303C8—3441no—
304C8—1722no—
305C22—21no—
306C22—21no—
307C22#1458280711yescharacteristic
308C22#1458305312yes—
309C4—21no—
310C4—21no—
311C4—81no—
312C4—82no—
313C4—81no—
314C4—3442no—
315C4—1724no—
316C4#1458307512yes—
317C4#1458307712yes—
318C4#1458310712yes—
319C4#1458327711yescharacteristic
320C4#1458329211yescharacteristic
321C2—22no—
322C2#1913562111yescharacteristic
323C2#1913562211yescharacteristic
324C2#1913569311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3209C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#3209D43
hypocenterC43#10297
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
109. C4×Dic43Q16semidirect
191. C43#10297semidirect

Maximal subgroups

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

subgroupindex
#191455402
#191429722
#191355732
#191332762
#191332752
#191324272
C43×#32092
#1029743