Finite Group Databasebeta

← #24997431

Subgroups — #24997431

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#19145797C211yesmaximal, characteristic
2#19144721C211yesmaximal, characteristic
3#19139978C211yesmaximal, characteristic
4#19133196C211yesmaximal, characteristic
5#19133043C211yesmaximal, characteristic
6#19132451C211yesmaximal, characteristic
7C43×#1986C211yesmaximal, characteristic
8C2×#13063317C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10#14583305—21no—
11#14583267—21no—
12#14583232—21no—
13#14583227—21no—
14#14583227—21no—
15#14583206—22no—
16#14583181—21no—
17#14583106—21no—
18#14583054—21no—
19#14583004—22no—
20#14582956C2211yescharacteristic
21#14582956C2211yescharacteristic
22#14582831—21no—
23#14582820—21no—
24#14582798—21no—
25#14582798—21no—
26#14582797—22no—
27#14582640—22no—
28#14582631—22no—
29C43×#533C2211yescharacteristic
30C4×M16×C43C2211yescharacteristic
31C4×C4⋊C4×C43C2211yescharacteristic
32C43×#339—22no—
33C22×Dic86D411yescharacteristic
34C2×#10621885—22no—
35#13063317—21no—
36#13063317—21no—
37#13063317—21no—
38#13063317—21no—
39C4×Dic86—21no—
40C4×Dic86—21no—
41C4×Dic86—21no—
42C4×Dic86—21no—
43C2×C4⋊Dic43—22no—
44C2×C4⋊Dic43—22no—
45C2×C4⋊Dic43D411yescharacteristic
46C2×C4⋊Dic43D411yescharacteristic
47C2×C4⋊Dic43D411yescharacteristic
48C2×Dic43⋊C4—21no—
49C2×Dic43⋊C4—21no—
50C2×Dic43⋊C4—21no—
51C2×C4×Dic43—21no—
52#13063258—22no—
53#13063256—22no—
54#13063256—22no—
55C4⋊(C43⋊C8)—21no—
56C4⋊(C43⋊C8)D412yes—
57#13063249—22no—
58#13063249—22no—
59#13063249—22no—
60#13063248—22no—
61C22⋊(C43⋊C8)—21no—
62C22⋊(C43⋊C8)—21no—
63#13063236—21no—
64#13063236D412yes—
65C43⋊#95—22no—
66C43⋊#95—22no—
67C2×M16×C43—21no—
68C4⋊Q8×C43D411yescharacteristic
69C4⋊Q8×C43D411yescharacteristic
70#125×C43—21no—
71C22⋊Q8×C43—21no—
72C22⋊Q8×C43—21no—
73C4×Q8×C43—21no—
74C4×Q8×C43—21no—
75#117×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C42×C43D412yes—
78C2×C42×C43C2311yescharacteristic
79#97×C43—21no—
80C4×C8×C43—21no—
81#95×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C22×C4×C43—22no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C2×Dic86—21no—
93C2×Dic86—21no—
94C2×Dic86—42no—
95M16×C43—22no—
96M16×C43—41no—
97C2×C8×C43—41no—
98C4⋊C4×C43—24no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C42×C43—42no—
107C42×C43—41no—
108C42×C43C2×D411yescharacteristic
109C42×C43C2×D411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43#4111yescharacteristic
112#10621885—44no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—44no—
120C4⋊Dic43—82no—
121Dic43⋊C4—41no—
122Dic43⋊C4—41no—
123Dic43⋊C4—41no—
124Dic43⋊C4—41no—
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127C4×Dic43—41no—
128C4×Dic43—41no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—22no—
131C23×C43#12011yescharacteristic
132Q8×C43—42no—
133Q8×C43—42no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—22no—
137C2×C4×C43—24no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43#12011yescharacteristic
144C2×C4×C43#12011yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12711yescharacteristic
149C2×Dic43—22no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—42no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160Dic86—22no—
161Dic86—22no—
162Dic86—41no—
163Dic86—41no—
164C8×C43—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—81no—
180C4×C43—81no—
181C4×C43#45612yes—
182Dic43—42no—
183Dic43—81no—
184Dic43—81no—
185Dic43—81no—
186#3236—431no—
187#3113—431no—
188#2584—431no—
189#1986D4311yescharacteristic
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#533C2×D4311yescharacteristic
199C2×#125—431no—
200C2×C4×Q8—431no—
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×M16C2×D4311yescharacteristic
214#398—861no—
215#395—861no—
216#389—861no—
217#389—861no—
218#389—862no—
219C4×C4⋊C4C2×D4311yescharacteristic
220#339—22no—
221#330—862no—
222Q8⋊C8—862no—
223C43#1001111yescharacteristic, complemented, Sylow
224C22×Q8—431no—
225C2×Q16—862no—
226C2×M16—21no—
227C4⋊Q8D17211yescharacteristic
228C4⋊Q8D17211yescharacteristic
229#125—21no—
230#125—861no—
231#125—861no—
232#125—861no—
233#125—861no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—861no—
239C4×Q8—861no—
240C4×Q8—861no—
241C4×Q8—861no—
242#117—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—431no—
245C2×C4⋊C4—431no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—862no—
248C2×C4⋊C4—862no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4—861no—
252C2×C42—861no—
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—21no—
267#97—432no—
268#97—861no—
269C4×C8—21no—
270#95—21no—
271#95—862no—
272#95—862no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—861no—
276C2×Q8—861no—
277C2×Q8—1722no—
278C22×C4—22no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4D4×D4311yescharacteristic
284C22×C4D4×D4311yescharacteristic
285C22×C4C2×C22⋊D4311yescharacteristic
286Q16—1724no—
287M16—22no—
288M16—41no—
289C2×C8—41no—
290C2×C8—862no—
291C2×C8—862no—
292C4⋊C4—24no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
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—41no—
314C42—42no—
315C42—41no—
316C42—1721no—
317C42—1721no—
318C42C2×D17211yescharacteristic
319C42#1062189811yescharacteristic
320C42D4×D4311yescharacteristic
321C42D4×D4311yescharacteristic
322C23#1306329311yescharacteristic
323Q8—42no—
324Q8—42no—
325Q8—862no—
326Q8—862no—
327Q8—1721no—
328Q8—1721no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—862no—
339C2×C4—1722no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4#1306329511yescharacteristic
350C2×C4#1306329511yescharacteristic
351C2×C4#1306329811yescharacteristic
352C2×C4#1306329811yescharacteristic
353C2×C4#1306329911yescharacteristic
354C2×C4#1306332111yescharacteristic
355C8—42no—
356C8—1722no—
357C8—1722no—
358C22—21no—
359C22—21no—
360C22#1458280811yescharacteristic
361C22#1458307611yescharacteristic
362C22#1458308111yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—44no—
369C4—81no—
370C4—81no—
371C4—3441no—
372C4—3441no—
373C4—3441no—
374C4—1722no—
375C4#1458308312yes—
376C2—21no—
377C2—21no—
378C2#1913563011yescharacteristic
379C2#1913564111yescharacteristic
380C2#1913566111yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1986C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#1986D43
hypocenterC43#10011
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1986

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
#191457972
#191447212
#191399782
#191331962
#191330432
#191324512
C43×#19862
#1001143