Finite Group Databasebeta

← #24998141

Subgroups — #24998141

Order 11008.

470 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 87 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#19145986C211yesmaximal, characteristic
2#19145748C211yesmaximal, characteristic
3#19145142C211yesmaximal, characteristic
4#19135439C211yesmaximal, characteristic
5#19133189C211yesmaximal, characteristic
6#19132486C211yesmaximal, characteristic
7C43×#1485C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×#13063325C2211yescharacteristic
10#14583309—22no—
11#14583304—21no—
12#14583302—21no—
13#14583295—21no—
14#14583250—21no—
15#14583235—22no—
16#14583195—22no—
17#14583184—21no—
18#14583181—21no—
19#14583155—22no—
20#14583109—21no—
21#14583106—21no—
22#14582942—22no—
23#14582923C2211yescharacteristic
24C2×#13063243—22no—
25C4×#10621877C2211yescharacteristic
26#14582640—22no—
27C43×#533C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C4×M16×C43C2211yescharacteristic
30C43×Q8⋊C8—22no—
31C22×Dic86—21no—
32C2×#10621885—22no—
33C2×#10621877—21no—
34C2×#10621877D412yes—
35#13063325—21no—
36#13063325—21no—
37#13063325—21no—
38#13063325—21no—
39#13063325D411yescharacteristic
40#13063325D411yescharacteristic
41#13063317—21no—
42#13063304—21no—
43#13063304—21no—
44C4×Dic86—21no—
45C4×Dic86—21no—
46#13063284—21no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43D412yes—
49#13063259—24no—
50#13063258—24no—
51#13063256—24no—
52#13063256—22no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)—21no—
55#13063250—24no—
56#13063249—22no—
57#13063248—22no—
58#13063243—44no—
59#13063236D412yes—
60C4×C43⋊C8—21no—
61C2×M16×C43—21no—
62C4⋊Q8×C43D411yescharacteristic
63C4⋊Q8×C43D411yescharacteristic
64#125×C43—21no—
65C22⋊Q8×C43—21no—
66C22⋊Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69#117×C43—21no—
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43D412yes—
72C22⋊C8×C43—21no—
73#97×C43—21no—
74C4×C8×C43—21no—
75C4×C8×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C22×Dic43—22no—
82C2×Dic86—21no—
83C2×Dic86—21no—
84C2×Dic86—42no—
85C2×Dic86—42no—
86C2×Dic86—41no—
87C2×Dic86—41no—
88M16×C43—22no—
89M16×C43—41no—
90C2×C8×C43—22no—
91C2×C8×C43—41no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C42×C43—41no—
100C42×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C22⋊Dic43—41no—
105#10621885—82no—
106C4⋊Dic43—21no—
107C4⋊Dic43—22no—
108C4⋊Dic43—22no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—41no—
113C4⋊Dic43—41no—
114Dic43⋊C4—41no—
115Dic43⋊C4—41no—
116C4×Dic43—41no—
117#10621877—24no—
118#10621877—42no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—22no—
121C23×C43#12111yescharacteristic
122Q8×C43—41no—
123Q8×C43—41no—
124Q8×C43—42no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43#12011yescharacteristic
132C2×C4×C43#12011yescharacteristic
133C2×C4×C43#12011yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12711yescharacteristic
137C2×Dic43—44no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—42no—
141Dic86—41no—
142Dic86—41no—
143Dic86—42no—
144Dic86—82no—
145Dic86—81no—
146Dic86—81no—
147C8×C43—42no—
148C8×C43—42no—
149C43⋊C8—24no—
150C43⋊C8—42no—
151#10117—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43#39211yescharacteristic
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—81no—
160C4×C43—81no—
161C4×C43#45311yescharacteristic
162C4×C43#45411yescharacteristic
163C4×C43#45612yes—
164C4×C43#47312yes—
165Dic43—81no—
166Dic43—81no—
167Dic43—82no—
168#3255—431no—
169#3230—431no—
170#3165—431no—
171#1966—431no—
172#1526—431no—
173#1485D4311yescharacteristic
174#1299—431no—
175C2×C43—41no—
176C2×C43#200511yescharacteristic
177C2×C43#200611yescharacteristic
178C2×C43#202011yescharacteristic
179#533—431no—
180#533C2×D4311yescharacteristic
181C2×C4⋊Q8—431no—
182#501—862no—
183#500—861no—
184#500—861no—
185#498—861no—
186#487—861no—
187#484—862no—
188#477—862no—
189#475—861no—
190#475—861no—
191#470—862no—
192#462—861no—
193#462—861no—
194#431C2×D4311yescharacteristic
195#428—862no—
196#423—431no—
197C2×#101—862no—
198C4×M16—431no—
199C4×M16C2×D4311yescharacteristic
200#330—862no—
201Q8⋊C8—22no—
202C43#1011711yescharacteristic, complemented, Sylow
203C22×Q8—861no—
204C2×Q16—862no—
205C2×M16—21no—
206C2×M16—432no—
207C2×M16—861no—
208C4⋊Q8—431no—
209C4⋊Q8—431no—
210C4⋊Q8—861no—
211C4⋊Q8—861no—
212C4⋊Q8—861no—
213C4⋊Q8—861no—
214C4⋊Q8D17211yescharacteristic
215C4⋊Q8D17211yescharacteristic
216#125—21no—
217#125—861no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C22⋊Q8—861no—
221C22⋊Q8—861no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—861no—
225C4×Q8—861no—
226#117—21no—
227#117—861no—
228C2×C4⋊C4—432no—
229C2×C4⋊C4—861no—
230C2×C42C22×D4311yescharacteristic
231#107—864no—
232#107—864no—
233#106—864no—
234#106—862no—
235C4⋊C8—861no—
236C4⋊C8—861no—
237C4⋊C8C22⋊D4312yes—
238#103—862no—
239#103—864no—
240#103—862no—
241#101—1724no—
242C22⋊C8—21no—
243#97—21no—
244#97—432no—
245C4×C8—21no—
246C4×C8—21no—
247C4×C8—861no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—861no—
251C2×Q8—861no—
252C2×Q8—1722no—
253C2×Q8—1722no—
254C2×Q8—1721no—
255C2×Q8—1721no—
256C22×C4—862no—
257C22×C4#1062189811yescharacteristic
258C22×C4D4×D4311yescharacteristic
259C22×C4D4×D4311yescharacteristic
260Q16—3442no—
261M16—22no—
262M16—41no—
263M16—864no—
264M16—1722no—
265C2×C8—22no—
266C2×C8—41no—
267C2×C8—862no—
268C2×C8—862no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—862no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—862no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—1721no—
282C4⋊C4—1721no—
283C4⋊C4—1721no—
284C4⋊C4—1721no—
285C22⋊C4—41no—
286C22⋊C4—1721no—
287C42—41no—
288C42—1721no—
289C42C2×D17211yescharacteristic
290C42D4×D4311yescharacteristic
291C42D4×D4311yescharacteristic
292C42C2×C22⋊D4311yescharacteristic
293C23#1306329811yescharacteristic
294Q8—41no—
295Q8—41no—
296Q8—42no—
297Q8—3442no—
298Q8—3441no—
299Q8—3441no—
300Q8—1721no—
301Q8—1721no—
302Q8—1722no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—1724no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1722no—
313C2×C4#1306329311yescharacteristic
314C2×C4#1306329511yescharacteristic
315C2×C4#1306329511yescharacteristic
316C2×C4#1306329811yescharacteristic
317C2×C4#1306329911yescharacteristic
318C2×C4#1306332111yescharacteristic
319C8—42no—
320C8—42no—
321C8—864no—
322C8—1722no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22#1458280811yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—3441no—
333C4—3442no—
334C4—3441no—
335C4#1458306811yescharacteristic
336C4#1458307311yescharacteristic
337C4#1458308012yes—
338C4#1458317412yes—
339C2—41no—
340C2#1913563211yescharacteristic
341C2#1913563811yescharacteristic
342C2#1913571611yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1485C2
socleC22×C43#392
prime radicalC23×C43#121
hypercenter#1485D43
hypocenterC43#10117
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
202. C43#10117semidirect

Maximal subgroups

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

subgroupindex
#191459862
#191457482
#191451422
#191354392
#191331892
#191324862
C43×#14852
#1011743