Finite Group Databasebeta

← #24997432

Subgroups — #24997432

Order 11008.

496 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 85 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#19145801C211yesmaximal, characteristic
2#19144725C211yesmaximal, characteristic
3#19135538C211yesmaximal, characteristic
4#19133197C211yesmaximal, characteristic
5#19133042C211yesmaximal, characteristic
6#19132451C211yesmaximal, characteristic
7C43×#2584C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583309—21no—
10#14583269—21no—
11#14583234—21no—
12#14583229—21no—
13#14583229—21no—
14#14583203—22no—
15#14583184—21no—
16#14583109—21no—
17#14583055—21no—
18#14583004—22no—
19#14582956C2211yescharacteristic
20#14582956C2211yescharacteristic
21C4×#10621877C2211yescharacteristic
22#14582659—22no—
23#14582641—22no—
24Q8⋊(C43⋊C8)—22no—
25C2×#125×C43C2211yescharacteristic
26C2×C4×Q8×C43C2211yescharacteristic
27C43×#398—21no—
28C43×#395—21no—
29C43×#389—21no—
30C43×#389—21no—
31C43×#389—22no—
32C4×C4⋊C4×C43C2211yescharacteristic
33C2×#10621885—22no—
34C2×#10621877—21no—
35#13063325D411yescharacteristic
36#13063325D411yescharacteristic
37#13063317—21no—
38#13063304—21no—
39#13063304—21no—
40C4×Dic86—21no—
41C4×Dic86—21no—
42#13063284—21no—
43#13063258—22no—
44#13063256—22no—
45#13063256—22no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)D412yes—
48#13063249—22no—
49#13063248—22no—
50#13063248—22no—
51#13063248—22no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54#13063236—21no—
55#13063236—21no—
56#13063236D412yes—
57C4×C43⋊C8—21no—
58C22×Q8×C43D411yescharacteristic
59#125×C43—21no—
60#125×C43—21no—
61#125×C43—21no—
62#125×C43—21no—
63C4×Q8×C43—21no—
64C4×Q8×C43—21no—
65C4×Q8×C43—21no—
66C4×Q8×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—22no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—22no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C4⋊C4×C43D411yescharacteristic
76C2×C42×C43—21no—
77C2×C42×C43D412yes—
78C2×C42×C43C2311yescharacteristic
79#95×C43—22no—
80#95×C43—22no—
81#95×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—42no—
85C22×C4×C43—22no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C2×Dic86—21no—
94C2×Dic86—21no—
95C4⋊C4×C43—24no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—44no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—82no—
110C42×C43—42no—
111C42×C43—41no—
112C42×C43—41no—
113C42×C43C2×D411yescharacteristic
114C42×C43C2×D411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43#4111yescharacteristic
117C22⋊Dic43—41no—
118#10621885—44no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123Dic43⋊C4—41no—
124Dic43⋊C4—41no—
125C4×Dic43—41no—
126#10621877—22no—
127#10621877—41no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—41no—
131C23×C43#12011yescharacteristic
132Q8×C43—22no—
133Q8×C43—22no—
134Q8×C43—41no—
135Q8×C43—41no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—22no—
139C2×C4×C43—24no—
140C2×C4×C43—22no—
141C2×C4×C43—41no—
142C2×C4×C43—42no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43#12011yescharacteristic
155C2×C4×C43#12011yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12711yescharacteristic
160C2×Dic43—41no—
161C2×Dic43—41no—
162Dic86—42no—
163Dic86—42no—
164C43⋊C8—42no—
165C43⋊C8—42no—
166C43⋊C8—42no—
167#10011—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43#39211yescharacteristic
171C22×C43#45511yescharacteristic
172C22×C43#45611yescharacteristic
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—44no—
179C4×C43—42no—
180C4×C43—81no—
181C4×C43—81no—
182C4×C43—81no—
183C4×C43#45612yes—
184Dic43—81no—
185Dic43—81no—
186#3236—431no—
187#3113—431no—
188#2584D4311yescharacteristic
189#1986—431no—
190#1528—431no—
191#1491—431no—
192#1285—431no—
193C2×C43—21no—
194C2×C43—21no—
195C2×C43#200511yescharacteristic
196C2×C43#200711yescharacteristic
197C2×C43#201011yescharacteristic
198#533—431no—
199C2×#125C2×D4311yescharacteristic
200C2×C4×Q8C2×D4311yescharacteristic
201#501—861no—
202#491—861no—
203#484—861no—
204#483—861no—
205#483—861no—
206#479—862no—
207#475—861no—
208#462—861no—
209#451—861no—
210#441—862no—
211#432—431no—
212#432—431no—
213C4×M16—431no—
214#398—21no—
215#395—21no—
216#389—21no—
217#389—21no—
218#389—22no—
219C4×C4⋊C4C2×D4311yescharacteristic
220#339—862no—
221#330—862no—
222Q8⋊C8—862no—
223C43#1001111yescharacteristic, complemented, Sylow
224C22×Q8C22⋊D4311yescharacteristic
225C2×Q16—862no—
226C2×M16—861no—
227C4⋊Q8—431no—
228C4⋊Q8—431no—
229#125—21no—
230#125—21no—
231#125—21no—
232#125—21no—
233#125—861no—
234C22⋊Q8—861no—
235C22⋊Q8—861no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—861no—
241C4×Q8—861no—
242#117—861no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4C22⋊D4311yescharacteristic
250C2×C4⋊C4C22⋊D4311yescharacteristic
251C2×C4⋊C4C22⋊D4311yescharacteristic
252C2×C42—21no—
253C2×C42C22⋊D4312yes—
254C2×C42C22×D4311yescharacteristic
255#107—862no—
256#106—862no—
257#106—862no—
258C4⋊C8—432no—
259C4⋊C8—861no—
260#103—862no—
261#103—862no—
262#103—862no—
263#103—862no—
264C22⋊C8—861no—
265C22⋊C8—861no—
266#97—432no—
267#97—861no—
268#97—861no—
269C4×C8—861no—
270#95—22no—
271#95—22no—
272#95—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—42no—
276C2×Q8—861no—
277C2×Q8—861no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4C2×C22⋊D4311yescharacteristic
284C22×C4C2×C22⋊D4311yescharacteristic
285C22×C4C2×C22⋊D4311yescharacteristic
286Q16—1724no—
287M16—862no—
288M16—1721no—
289C2×C8—862no—
290C2×C8—862no—
291C2×C8—1721no—
292C4⋊C4—24no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—44no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—82no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C22⋊C4—1721no—
314C42—42no—
315C42—41no—
316C42—41no—
317C42—1721no—
318C42D4×D4311yescharacteristic
319C42D4×D4311yescharacteristic
320C42D4×D4311yescharacteristic
321C42#1062190011yescharacteristic
322C23#1306329411yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—1722no—
328Q8—1722no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4#1306329311yescharacteristic
350C2×C4#1306329311yescharacteristic
351C2×C4#1306329611yescharacteristic
352C2×C4#1306329711yescharacteristic
353C2×C4#1306329711yescharacteristic
354C2×C4#1306332111yescharacteristic
355C8—1722no—
356C8—1722no—
357C8—1722no—
358C22—21no—
359C22—21no—
360C22#1458280711yescharacteristic
361C22#1458307711yescharacteristic
362C22#1458308211yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—44no—
369C4—42no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—3441no—
374C4—3441no—
375C4#1458308112yes—
376C2—21no—
377C2—21no—
378C2#1913563111yescharacteristic
379C2#1913564211yescharacteristic
380C2#1913566011yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2584C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#2584D43
hypocenterC43#10011
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2584

Complements

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

NH ≅ G/Ntype
223. C43#10011semidirect

Maximal subgroups

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

subgroupindex
#191458012
#191447252
#191355382
#191331972
#191330422
#191324512
C43×#25842
#1001143