Finite Group Databasebeta

← #24997429

Subgroups — #24997429

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#19145797C211yesmaximal, characteristic
2#19139983C211yesmaximal, characteristic
3#19135540C211yesmaximal, characteristic
4#19133198C211yesmaximal, characteristic
5#19133042C211yesmaximal, characteristic
6#19132450C211yesmaximal, characteristic
7C43×#3113C211yesmaximal, characteristic
8C2×#13063317C2211yescharacteristic
9#14583305—21no—
10#14583267—21no—
11#14583232—21no—
12#14583227—21no—
13#14583206—22no—
14#14582956C2211yescharacteristic
15C4×#10621877C2211yescharacteristic
16#14582830—21no—
17#14582818—21no—
18#14582797—21no—
19#14582797—21no—
20#14582794—22no—
21C4×C4⋊Dic43C2211yescharacteristic
22#14582658—22no—
23#14582640—22no—
24Q8⋊(C43⋊C8)—22no—
25C43×#533C2211yescharacteristic
26C2×C4×Q8×C43C2211yescharacteristic
27C43×#483—21no—
28C43×#475—21no—
29C43×#462—21no—
30C43×#451—21no—
31C43×#441—22no—
32C43×#432C2211yescharacteristic
33C2×#10621877—21no—
34#13063317—21no—
35#13063317—21no—
36#13063317—21no—
37#13063317—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—22no—
45C2×C4×Dic43D412yes—
46#13063258—22no—
47#13063256—22no—
48C4⋊(C43⋊C8)D412yes—
49#13063249—22no—
50#13063249—22no—
51C22⋊(C43⋊C8)—21no—
52#13063236—21no—
53#13063236—21no—
54C4×C43⋊C8—21no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95—21no—
58C22×Q8×C43D411yescharacteristic
59C2×Q16×C43—22no—
60C4⋊Q8×C43D411yescharacteristic
61C4⋊Q8×C43D411yescharacteristic
62#125×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65C4×Q8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71#117×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C42×C43—21no—
75C2×C42×C43C2311yescharacteristic
76#106×C43—22no—
77C4⋊C8×C43—21no—
78#103×C43—22no—
79#103×C43—22no—
80C22⋊C8×C43—21no—
81#97×C43D412yes—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—42no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×Dic43—22no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95Q16×C43—44no—
96C2×C8×C43—22no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C42×C43—41no—
109C42×C43—41no—
110C42×C43—41no—
111C42×C43C2×D411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115C4⋊Dic43—24no—
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—82no—
126C4×Dic43—42no—
127#10621877—22no—
128#10621877—41no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—41no—
131C23×C43#12011yescharacteristic
132Q8×C43—22no—
133Q8×C43—22no—
134Q8×C43—41no—
135Q8×C43—41no—
136Q8×C43—42no—
137Q8×C43—42no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43#12011yescharacteristic
151C2×C4×C43#12011yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12711yescharacteristic
156C2×Dic43—24no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159C2×Dic43—42no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—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—42no—
179C4×C43—81no—
180C4×C43—81no—
181C4×C43—81no—
182C4×C43#45612yes—
183Dic43—44no—
184Dic43—81no—
185Dic43—81no—
186#3236—431no—
187#3113D4311yescharacteristic
188#2584—431no—
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#533C2×D4311yescharacteristic
199C2×#125—431no—
200C2×C4×Q8C2×D4311yescharacteristic
201#501—861no—
202#491—861no—
203#484—861no—
204#483—21no—
205#483—861no—
206#479—862no—
207#475—21no—
208#462—21no—
209#451—21no—
210#441—22no—
211#432—431no—
212#432C2×D4311yescharacteristic
213C4×M16—431no—
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—862no—
223C43#1001111yescharacteristic, complemented, Sylow
224C22×Q8C22⋊D4311yescharacteristic
225C2×Q16—22no—
226C2×M16—861no—
227C4⋊Q8C22⋊D4311yescharacteristic
228C4⋊Q8C22⋊D4311yescharacteristic
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—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242#117—21no—
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⋊C4C22⋊D4311yescharacteristic
252C2×C42—21no—
253C2×C42—432no—
254C2×C42C22×D4311yescharacteristic
255#107—862no—
256#106—22no—
257#106—862no—
258C4⋊C8—21no—
259C4⋊C8—432no—
260#103—22no—
261#103—22no—
262#103—862no—
263#103—862no—
264C22⋊C8—21no—
265C22⋊C8—861no—
266#97—861no—
267#97—861no—
268#97C22⋊D4312yes—
269C4×C8—861no—
270#95—862no—
271#95—862no—
272#95—861no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—42no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—862no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4D4×D4311yescharacteristic
284C22×C4D4×D4311yescharacteristic
285C22×C4C2×C22⋊D4311yescharacteristic
286Q16—44no—
287M16—862no—
288M16—1721no—
289C2×C8—22no—
290C2×C8—862no—
291C2×C8—1721no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—864no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4—861no—
306C4⋊C4—861no—
307C4⋊C4—3442no—
308C4⋊C4—1724no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C22⋊C4—41no—
314C42—41no—
315C42—41no—
316C42—41no—
317C42—1722no—
318C42D4×D4311yescharacteristic
319C42#1062190011yescharacteristic
320C42C2×C22⋊D4311yescharacteristic
321C42C2×C22⋊D4311yescharacteristic
322C23#1306329311yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—42no—
328Q8—42no—
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—41no—
340C2×C4—41no—
341C2×C4—864no—
342C2×C4—1722no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1722no—
348C2×C4—1722no—
349C2×C4#1306329311yescharacteristic
350C2×C4#1306329411yescharacteristic
351C2×C4#1306329611yescharacteristic
352C2×C4#1306329711yescharacteristic
353C2×C4#1306329711yescharacteristic
354C2×C4#1306332111yescharacteristic
355C8—42no—
356C8—1722no—
357C8—1722no—
358C22—21no—
359C22—21no—
360C22#1458280711yescharacteristic
361C22#1458307511yescharacteristic
362C22#1458308011yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—42no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4—3441no—
373C4—3441no—
374C4—1724no—
375C4#1458308012yes—
376C2—21no—
377C2—21no—
378C2#1913562811yescharacteristic
379C2#1913564011yescharacteristic
380C2#1913566011yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3113C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#3113D43
hypocenterC43#10011
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

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
#191399832
#191355402
#191331982
#191330422
#191324502
C43×#31132
#1001143