Finite Group Databasebeta

← #24998139

Subgroups — #24998139

Order 11008.

470 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 89 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#19145746C211yesmaximal, characteristic
3#19135440C211yesmaximal, characteristic
4#19133189C211yesmaximal, characteristic
5#19133016C211yesmaximal, characteristic
6#19132485C211yesmaximal, characteristic
7C43×#3165C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583302—21no—
10#14583251—21no—
11#14583234—22no—
12#14583191—22no—
13#14583184—21no—
14#14583181—21no—
15#14583155—22no—
16#14583109—21no—
17#14583106—21no—
18#14582952C2211yescharacteristic
19#14582923C2211yescharacteristic
20C2×#13063244—22no—
21C4×#10621877C2211yescharacteristic
22#14582640—22no—
23Q8⋊(C43⋊C8)—22no—
24C43×#533C2211yescharacteristic
25C2×C4⋊Q8×C43C2211yescharacteristic
26C43×#501—22no—
27C43×#500—21no—
28C43×#498—21no—
29C43×#428—22no—
30C4×M16×C43C2211yescharacteristic
31C2×#10621885—22no—
32C2×#10621877—21no—
33C2×#10621877D412yes—
34#13063325D411yescharacteristic
35#13063325D411yescharacteristic
36#13063317—21no—
37#13063304—21no—
38#13063304—21no—
39C4×Dic86—21no—
40C4×Dic86—21no—
41#13063284—21no—
42#13063258—24no—
43#13063256—22no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)D412yes—
47#13063249—22no—
48#13063248—22no—
49#13063248—24no—
50#13063244—44no—
51C22⋊(C43⋊C8)—21no—
52#13063236—21no—
53C4×C43⋊C8—21no—
54C4×C43⋊C8—21no—
55C22×Q8×C43—21no—
56C2×M16×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43—21no—
59C4⋊Q8×C43—21no—
60C4⋊Q8×C43—21no—
61C4⋊Q8×C43D411yescharacteristic
62C4⋊Q8×C43D411yescharacteristic
63#125×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68#117×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43D412yes—
71C2×C42×C43C2311yescharacteristic
72#107×C43—24no—
73#106×C43—24no—
74#97×C43D412yes—
75C4×C8×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—42no—
79C2×Q8×C43—42no—
80C2×Q8×C43—41no—
81C2×Q8×C43—41no—
82C22×C4×C43—22no—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C2×Dic86—21no—
87C2×Dic86—21no—
88M16×C43—24no—
89C2×C8×C43—22no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—22no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C22⋊C4×C43—41no—
101C42×C43—41no—
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C22⋊Dic43—41no—
107#10621885—82no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112Dic43⋊C4—41no—
113Dic43⋊C4—41no—
114C4×Dic43—41no—
115#10621877—22no—
116#10621877—41no—
117#10621877—42no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—41no—
121C23×C43#12111yescharacteristic
122Q8×C43—41no—
123Q8×C43—41no—
124Q8×C43—42no—
125Q8×C43—82no—
126Q8×C43—81no—
127Q8×C43—81no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—44no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—42no—
136C2×C4×C43#12011yescharacteristic
137C2×C4×C43#12011yescharacteristic
138C2×C4×C43#12011yescharacteristic
139C2×C4×C43#12111yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43#12711yescharacteristic
142C2×Dic43—41no—
143C2×Dic43—41no—
144Dic86—41no—
145Dic86—41no—
146Dic86—42no—
147C8×C43—24no—
148C43⋊C8—42no—
149C43⋊C8—42no—
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—82no—
160C4×C43—81no—
161C4×C43—81no—
162C4×C43#45311yescharacteristic
163C4×C43#45411yescharacteristic
164C4×C43#45612yes—
165C4×C43#47312yes—
166Dic43—81no—
167Dic43—81no—
168#3255—431no—
169#3230—431no—
170#3165D4311yescharacteristic
171#1966—431no—
172#1526—431no—
173#1485—431no—
174#1299—431no—
175C2×C43—41no—
176C2×C43#200511yescharacteristic
177C2×C43#200611yescharacteristic
178C2×C43#202011yescharacteristic
179#533—431no—
180#533C2×D4311yescharacteristic
181C2×C4⋊Q8C2×D4311yescharacteristic
182#501—22no—
183#500—21no—
184#500—861no—
185#498—21no—
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#431—431no—
195#428—22no—
196#423—431no—
197C2×#101—862no—
198C4×M16—431no—
199C4×M16C2×D4311yescharacteristic
200#330—862no—
201Q8⋊C8—862no—
202C43#1011711yescharacteristic, complemented, Sylow
203C22×Q8—21no—
204C2×Q16—862no—
205C2×M16—21no—
206C2×M16—432no—
207C2×M16—861no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—431no—
213C4⋊Q8—431no—
214C4⋊Q8C22⋊D4311yescharacteristic
215C4⋊Q8C22⋊D4311yescharacteristic
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—21no—
229C2×C4⋊C4C22⋊D4312yes—
230C2×C42C22×D4311yescharacteristic
231#107—24no—
232#107—864no—
233#106—24no—
234#106—862no—
235C4⋊C8—432no—
236C4⋊C8—861no—
237C4⋊C8—861no—
238#103—862no—
239#103—864no—
240#103—862no—
241#101—1724no—
242C22⋊C8—861no—
243#97—861no—
244#97C22⋊D4312yes—
245C4×C8—21no—
246C4×C8—861no—
247C4×C8—861no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—861no—
255C2×Q8—861no—
256C22×C4—22no—
257C22×C4D4×D4311yescharacteristic
258C22×C4#1062190011yescharacteristic
259C22×C4C2×C22⋊D4311yescharacteristic
260Q16—3442no—
261M16—24no—
262M16—862no—
263M16—1721no—
264M16—1722no—
265C2×C8—22no—
266C2×C8—862no—
267C2×C8—862no—
268C2×C8—1721no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—22no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—1721no—
284C4⋊C4—1721no—
285C22⋊C4—41no—
286C22⋊C4—1721no—
287C42—41no—
288C42—1721no—
289C42D4×D4311yescharacteristic
290C42D4×D4311yescharacteristic
291C42C2×C22⋊D4311yescharacteristic
292C42C2×C22⋊D4311yescharacteristic
293C23#1306329711yescharacteristic
294Q8—41no—
295Q8—41no—
296Q8—42no—
297Q8—82no—
298Q8—81no—
299Q8—81no—
300Q8—1721no—
301Q8—1721no—
302Q8—1722no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—44no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4#1306329311yescharacteristic
314C2×C4#1306329311yescharacteristic
315C2×C4#1306329411yescharacteristic
316C2×C4#1306329611yescharacteristic
317C2×C4#1306329711yescharacteristic
318C2×C4#1306332111yescharacteristic
319C8—24no—
320C8—1722no—
321C8—1722no—
322C8—1722no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22#1458280711yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—82no—
331C4—81no—
332C4—81no—
333C4—3441no—
334C4—3441no—
335C4#1458306511yescharacteristic
336C4#1458307011yescharacteristic
337C4#1458308112yes—
338C4#1458317212yes—
339C2—41no—
340C2#1913563111yescharacteristic
341C2#1913563511yescharacteristic
342C2#1913571311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3165C2
socleC22×C43#392
prime radicalC23×C43#121
hypercenter#3165D43
hypocenterC43#10117
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

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
#191457462
#191354402
#191331892
#191330162
#191324852
C43×#31652
#1011743