Finite Group Databasebeta

← #24999319

Subgroups — #24999319

Order 11008.

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

normal subgroups only

This group has 504 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#19145743C211yesmaximal, characteristic
2#19142972C211yesmaximal, characteristic
3#19135573C211yesmaximal, characteristic
4#19133280C211yesmaximal, characteristic
5#19133279C211yesmaximal, characteristic
6#19132427C211yesmaximal, characteristic
7C43×#3230C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9#14583302—21no—
10#14583249—21no—
11#14583232—22no—
12#14583194—22no—
13#14582952C2211yescharacteristic
14#14582923C2211yescharacteristic
15#14582806—22no—
16#14582804—22no—
17#14582764—22no—
18C42×Dic43C2211yescharacteristic
19#14582658—22no—
20#14582646—22no—
21#14582645—22no—
22C43×#533C2211yescharacteristic
23C2×C4⋊Q8×C43C2211yescharacteristic
24C43×#500—21no—
25C43×#487—21no—
26C43×#484—22no—
27C43×#477—22no—
28C43×#431C2211yescharacteristic
29C22×Dic86—21no—
30C2×#10621877—21no—
31#13063325—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43D412yes—
37C2×C4×Dic43—21no—
38C2×C4×Dic43—21no—
39C2×C4×Dic43D412yes—
40#13063258—24no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)D412yes—
44#13063249—24no—
45C22⋊(C43⋊C8)—21no—
46C4×C43⋊C8—21no—
47C43⋊#95—28no—
48C22×Q8×C43—21no—
49C4⋊Q8×C43—21no—
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43D411yescharacteristic
54C4⋊Q8×C43D411yescharacteristic
55#125×C43—21no—
56C22⋊Q8×C43—21no—
57C22⋊Q8×C43—21no—
58C4×Q8×C43—21no—
59C4×Q8×C43—21no—
60#117×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43D412yes—
63C2×C42×C43C2311yescharacteristic
64#107×C43—24no—
65C4⋊C8×C43D412yes—
66#103×C43—24no—
67C22⋊C8×C43—21no—
68C4×C8×C43—21no—
69C2×Q8×C43—21no—
70C2×Q8×C43—21no—
71C2×Q8×C43—44no—
72C2×Q8×C43—41no—
73C2×Q8×C43—41no—
74C22×C4×C43—22no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×Dic43—22no—
79C22×Dic43—22no—
80C2×Dic86—44no—
81C2×Dic86—41no—
82C2×Dic86—41no—
83C2×C8×C43—22no—
84C4⋊C4×C43—22no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C42×C43—41no—
96C42×C43C2×D411yescharacteristic
97C42×C43C2×D411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C42×C43#4111yescharacteristic
100C4⋊Dic43—22no—
101C4⋊Dic43—22no—
102C4⋊Dic43—41no—
103C4⋊Dic43—41no—
104C4×Dic43—22no—
105C4×Dic43—42no—
106C4×Dic43—42no—
107C4×Dic43Q1614yes—
108#10621877—42no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8—41no—
111C23×C43#12011yescharacteristic
112Q8×C43—42no—
113Q8×C43—42no—
114Q8×C43—82no—
115Q8×C43—82no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—44no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—42no—
122C2×C4×C43#12011yescharacteristic
123C2×C4×C43#12011yescharacteristic
124C2×C4×C43#12111yescharacteristic
125C2×C4×C43#12111yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12711yescharacteristic
128C2×C4×C43C2×Q1612yes—
129C2×C4×C43#13712yes—
130C2×Dic43—24no—
131C2×Dic43—42no—
132C2×Dic43—42no—
133C2×Dic43—44no—
134C2×Dic43—42no—
135Dic86—82no—
136Dic86—82no—
137C8×C43—42no—
138C43⋊C8—42no—
139C43⋊C8—81no—
140#10295—431nomaximal, Sylow
141C22×C43—21no—
142C22×C43—21no—
143C22×C43#39211yescharacteristic
144C22×C43#45112yes—
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—82no—
148C4×C43—81no—
149C4×C43—81no—
150C4×C43#45412yes—
151C4×C43#45412yes—
152C4×C43#46212yes—
153C4×C43#49411yescharacteristic
154C4×C43#49711yescharacteristic
155Dic43—44no—
156Dic43—82no—
157#3230—431no—
158#3230D4311yescharacteristic
159#2862—431no—
160#1994—431no—
161#1549—431no—
162#1549—431no—
163#1276—431no—
164C2×C43—22no—
165C2×C43#200311yescharacteristic
166C2×C43#200311yescharacteristic
167C2×C43#201611yescharacteristic
168#533C2×D4311yescharacteristic
169C2×C4⋊Q8—431no—
170C2×C4⋊Q8C2×D4311yescharacteristic
171#500—21no—
172#500—861no—
173#487—21no—
174#487—861no—
175#484—22no—
176#484—862no—
177#477—22no—
178#477—862no—
179#431—431no—
180#431C2×D4311yescharacteristic
181#423—431no—
182#391—862no—
183#391—862no—
184#382—862no—
185C43—431no—
186#339—862no—
187#332—862no—
188#332—862no—
189C43#1029511yescharacteristic, complemented, Sylow
190C22×Q8—21no—
191C22×Q8—861no—
192C2×M16—861no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—861no—
198C4⋊Q8—861no—
199C4⋊Q8—861no—
200C4⋊Q8—861no—
201C4⋊Q8C22⋊D4311yescharacteristic
202C4⋊Q8C22⋊D4311yescharacteristic
203#125—21no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206C4×Q8—21no—
207C4×Q8—21no—
208#117—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—432no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4C22⋊D4312yes—
213C2×C42—432no—
214C2×C42—861no—
215C2×C42—861no—
216C2×C42C22×D4311yescharacteristic
217#107—24no—
218#107—864no—
219C4⋊C8—432no—
220C4⋊C8—861no—
221C4⋊C8—861no—
222C4⋊C8C22⋊D4312yes—
223#103—24no—
224#103—864no—
225C22⋊C8—21no—
226C22⋊C8—861no—
227C4×C8—21no—
228C4×C8—861no—
229#95—868no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—44no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—1724no—
236C2×Q8—1721no—
237C2×Q8—1721no—
238C22×C4—22no—
239C22×C4—862no—
240C22×C4—862no—
241C22×C4D4×D4311yescharacteristic
242C22×C4D4×D4311yescharacteristic
243C22×C4C2×C22⋊D4311yescharacteristic
244M16—1722no—
245C2×C8—22no—
246C2×C8—862no—
247C2×C8—1721no—
248C4⋊C4—21no—
249C4⋊C4—22no—
250C4⋊C4—21no—
251C4⋊C4—22no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—862no—
259C4⋊C4—862no—
260C4⋊C4—1721no—
261C4⋊C4—1721no—
262C22⋊C4—41no—
263C42—41no—
264C42—434no—
265C42—862no—
266C42—1722no—
267C42—1722no—
268C42D4×D4311yescharacteristic
269C42#1062190011yescharacteristic
270C42C2×C22⋊D4311yescharacteristic
271C42C2×C22⋊D4311yescharacteristic
272C23#1306329311yescharacteristic
273Q8—42no—
274Q8—42no—
275Q8—82no—
276Q8—82no—
277Q8—3442no—
278Q8—3442no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—44no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—864no—
286C2×C4—1724no—
287C2×C4—1722no—
288C2×C4—1722no—
289C2×C4—1722no—
290C2×C4#1306329311yescharacteristic
291C2×C4#1306329411yescharacteristic
292C2×C4#1306329611yescharacteristic
293C2×C4#1306329711yescharacteristic
294C2×C4#1306329711yescharacteristic
295C2×C4#1306332111yescharacteristic
296C2×C4Q16×D4312yes—
297C2×C4#1306335712yes—
298C8—42no—
299C8—3441no—
300C8—1722no—
301C22—21no—
302C22—21no—
303C22#1458280711yescharacteristic
304C22#1458305312yes—
305C4—21no—
306C4—21no—
307C4—82no—
308C4—81no—
309C4—81no—
310C4—3442no—
311C4—1724no—
312C4#1458307012yes—
313C4#1458307212yes—
314C4#1458310712yes—
315C4#1458327711yescharacteristic
316C4#1458329211yescharacteristic
317C2—22no—
318C2#1913561411yescharacteristic
319C2#1913561511yescharacteristic
320C2#1913569311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3230C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#3230D43
hypocenterC43#10295
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
189. C43#10295semidirect

Maximal subgroups

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

subgroupindex
#191457432
#191429722
#191355732
#191332802
#191332792
#191324272
C43×#32302
#1029543