Finite Group Databasebeta

← #24997433

Subgroups — #24997433

Order 11008.

496 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 83 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#19145803C211yesmaximal, characteristic
2#19144725C211yesmaximal, characteristic
3#19139983C211yesmaximal, characteristic
4#19135539C211yesmaximal, characteristic
5#19133196C211yesmaximal, characteristic
6#19132452C211yesmaximal, characteristic
7C43×#1491C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×#13063317C2211yescharacteristic
10#14583308—21no—
11#14583268—21no—
12#14583235—21no—
13#14583230—21no—
14#14583229—21no—
15#14583207—22no—
16#14583184—21no—
17#14583109—21no—
18#14583055—21no—
19#14583004—22no—
20#14582956C2211yescharacteristic
21#14582830—21no—
22#14582818—21no—
23#14582797—21no—
24#14582797—21no—
25#14582794—22no—
26C4×C4⋊Dic43C2211yescharacteristic
27#14582660—22no—
28#14582640—22no—
29C2×C4×Q8×C43C2211yescharacteristic
30C43×#432C2211yescharacteristic
31C4×M16×C43C2211yescharacteristic
32C43×Q8⋊C8—22no—
33C2×#10621885—22no—
34#13063325D411yescharacteristic
35#13063325D411yescharacteristic
36#13063317—21no—
37#13063317—21no—
38#13063317—21no—
39#13063317—21no—
40#13063317—21no—
41#13063304—21no—
42#13063304—21no—
43C4×Dic86—21no—
44C4×Dic86—21no—
45#13063284—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43D411yescharacteristic
48C2×C4⋊Dic43D411yescharacteristic
49C2×Dic43⋊C4—22no—
50C2×Dic43⋊C4—21no—
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—22no—
53C2×C4×Dic43D412yes—
54#13063259—22no—
55#13063257—22no—
56#13063256—22no—
57C4⋊(C43⋊C8)—21no—
58#13063250—22no—
59#13063250—22no—
60#13063249—22no—
61#13063248—22no—
62C22⋊(C43⋊C8)—21no—
63#13063236D412yes—
64C43⋊#95—22no—
65C43⋊#95—22no—
66C43⋊#95—21no—
67C22×Q8×C43D411yescharacteristic
68C2×M16×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71C4×Q8×C43—21no—
72C4×Q8×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C42×C43—21no—
76C2×C42×C43C2311yescharacteristic
77C4⋊C8×C43D412yes—
78C22⋊C8×C43—21no—
79#97×C43—21no—
80#97×C43—21no—
81C4×C8×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—42no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×Dic43—22no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C2×Dic86—21no—
94C2×Dic86—21no—
95M16×C43—22no—
96M16×C43—41no—
97C2×C8×C43—22no—
98C2×C8×C43—41no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C42×C43—41no—
104C42×C43—41no—
105C42×C43C2×D411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43#4111yescharacteristic
109C22⋊Dic43—41no—
110#10621885—44no—
111C4⋊Dic43—24no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120Dic43⋊C4—44no—
121Dic43⋊C4—41no—
122Dic43⋊C4—41no—
123Dic43⋊C4—41no—
124Dic43⋊C4—41no—
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127Dic43⋊C4—82no—
128C4×Dic43—41no—
129C4×Dic43—42no—
130C2×C43⋊C8—22no—
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—22no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43#12011yescharacteristic
147C2×C4×C43#12011yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12711yescharacteristic
152C2×Dic43—24no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162Dic86—42no—
163Dic86—42no—
164C8×C43—42no—
165C8×C43—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—42no—
179C4×C43—81no—
180C4×C43#45612yes—
181Dic43—44no—
182Dic43—81no—
183Dic43—81no—
184Dic43—81no—
185Dic43—81no—
186#3236—431no—
187#3113—431no—
188#2584—431no—
189#1986—431no—
190#1528—431no—
191#1491D4311yescharacteristic
192#1285—431no—
193C2×C43—21no—
194C2×C43—21no—
195C2×C43#200511yescharacteristic
196C2×C43#200711yescharacteristic
197C2×C43#201011yescharacteristic
198#533—431no—
199C2×#125—431no—
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#432C2×D4311yescharacteristic
213C4×M16C2×D4311yescharacteristic
214#398—861no—
215#395—861no—
216#389—861no—
217#389—861no—
218#389—862no—
219C4×C4⋊C4—431no—
220#339—862no—
221#330—862no—
222Q8⋊C8—22no—
223C43#1001111yescharacteristic, complemented, Sylow
224C22×Q8D17211yescharacteristic
225C2×Q16—862no—
226C2×M16—21no—
227C4⋊Q8—431no—
228C4⋊Q8—431no—
229#125—861no—
230#125—861no—
231#125—861no—
232#125—861no—
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—431no—
245C2×C4⋊C4—431no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4—862no—
248C2×C4⋊C4—862no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4D17211yescharacteristic
252C2×C42—21no—
253C2×C42—432no—
254C2×C42C22×D4311yescharacteristic
255#107—862no—
256#106—862no—
257#106—862no—
258C4⋊C8—861no—
259C4⋊C8C22⋊D4312yes—
260#103—862no—
261#103—862no—
262#103—862no—
263#103—862no—
264C22⋊C8—21no—
265C22⋊C8—861no—
266#97—21no—
267#97—21no—
268#97—432no—
269C4×C8—21no—
270#95—862no—
271#95—862no—
272#95—861no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—42no—
276C2×Q8—861no—
277C2×Q8—861no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—862no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4C2×D17211yescharacteristic
284C22×C4D4×D4311yescharacteristic
285C22×C4D4×D4311yescharacteristic
286Q16—1724no—
287M16—22no—
288M16—41no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—862no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—864no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4—861no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4—3442no—
306C4⋊C4—1724no—
307C4⋊C4—1721no—
308C4⋊C4—1721no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C22⋊C4—1721no—
314C42—41no—
315C42—41no—
316C42—1722no—
317C42—1721no—
318C42#1062189811yescharacteristic
319C42D4×D4311yescharacteristic
320C42D4×D4311yescharacteristic
321C42C2×C22⋊D4311yescharacteristic
322C23#1306329511yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—1722no—
328Q8—1722no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—864no—
340C2×C4—1722no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1722no—
348C2×C4—1722no—
349C2×C4#1306329311yescharacteristic
350C2×C4#1306329511yescharacteristic
351C2×C4#1306329811yescharacteristic
352C2×C4#1306329811yescharacteristic
353C2×C4#1306329911yescharacteristic
354C2×C4#1306332111yescharacteristic
355C8—42no—
356C8—42no—
357C8—1722no—
358C22—21no—
359C22—21no—
360C22#1458280811yescharacteristic
361C22#1458307811yescharacteristic
362C22#1458308311yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—42no—
369C4—81no—
370C4—3441no—
371C4—3441no—
372C4—3441no—
373C4—3441no—
374C4—1724no—
375C4#1458308012yes—
376C2—21no—
377C2—21no—
378C2#1913563211yescharacteristic
379C2#1913564311yescharacteristic
380C2#1913566211yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1491C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#1491D43
hypocenterC43#10011
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1491

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
#191458032
#191447252
#191399832
#191355392
#191331962
#191324522
C43×#14912
#1001143