Finite Group Databasebeta

← #24997435

Subgroups — #24997435

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#19145803C211yesmaximal, characteristic
2#19144726C211yesmaximal, characteristic
3#19139978C211yesmaximal, characteristic
4#19135538C211yesmaximal, characteristic
5#19133198C211yesmaximal, characteristic
6#19133041C211yesmaximal, characteristic
7C43×#1285C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×#13063317C2211yescharacteristic
10C2×C4×Dic86C2211yescharacteristic
11#14583308—21no—
12#14583268—21no—
13#14583235—21no—
14#14583230—21no—
15#14583230—21no—
16#14583207—22no—
17#14583185—21no—
18#14583110—21no—
19#14583057—21no—
20#14583007—22no—
21C4×#10621877C2211yescharacteristic
22#14582831—21no—
23#14582820—21no—
24#14582798—21no—
25#14582798—21no—
26#14582797—22no—
27#14582659—22no—
28#14582640—22no—
29#14582629—22no—
30C43×#432C2211yescharacteristic
31C43×#432C2211yescharacteristic
32C4×C4⋊C4×C43C2211yescharacteristic
33C22×Dic86D411yescharacteristic
34C2×Dic172—22no—
35C2×#10621877—21no—
36#13063325D411yescharacteristic
37#13063325D411yescharacteristic
38#13063317—21no—
39#13063317—21no—
40#13063317—21no—
41#13063317—21no—
42#13063317—21no—
43#13063304—21no—
44#13063304—21no—
45C4×Dic86—21no—
46C4×Dic86—21no—
47C4×Dic86—21no—
48C4×Dic86—21no—
49C4×Dic86—21no—
50C4×Dic86—21no—
51#13063284—21no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43D411yescharacteristic
55C2×C4⋊Dic43D411yescharacteristic
56C2×C4⋊Dic43D411yescharacteristic
57C2×Dic43⋊C4—21no—
58C2×Dic43⋊C4—21no—
59C2×Dic43⋊C4—21no—
60C2×C4×Dic43—21no—
61#13063259—22no—
62#13063257—22no—
63#13063257—22no—
64#13063250—22no—
65#13063250—22no—
66#13063250—22no—
67#13063250—22no—
68#13063236—21no—
69C4×C43⋊C8—21no—
70C43⋊#95—22no—
71C43⋊#95—22no—
72C2×C4⋊C4×C43—21no—
73C2×C42×C43D412yes—
74C2×C42×C43C2311yescharacteristic
75C4⋊C8×C43—21no—
76C4⋊C8×C43D412yes—
77C22⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79#97×C43—21no—
80#97×C43D412yes—
81#95×C43—21no—
82C22×C4×C43—22no—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C2×Dic86—21no—
91C2×Dic86—21no—
92C2×Dic86—21no—
93C2×Dic86—21no—
94C2×Dic86—42no—
95C2×C8×C43—22no—
96C2×C8×C43—22no—
97C4⋊C4×C43—24no—
98C42×C43—42no—
99C42×C43C2×D411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43#4111yescharacteristic
103C22⋊Dic43—41no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—44no—
115C4⋊Dic43—82no—
116Dic43⋊C4—41no—
117Dic43⋊C4—41no—
118Dic43⋊C4—41no—
119Dic43⋊C4—41no—
120Dic43⋊C4—41no—
121Dic43⋊C4—41no—
122Dic43⋊C4—41no—
123Dic43⋊C4—41no—
124C4×Dic43—41no—
125C4×Dic43—41no—
126C4×Dic43—41no—
127#10621877—22no—
128#10621877—41no—
129C2×C43⋊C8—41no—
130Dic172—44no—
131C23×C43#12011yescharacteristic
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—22no—
135C2×C4×C43—24no—
136C2×C4×C43—41no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43#12011yescharacteristic
140C2×C4×C43#12011yescharacteristic
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12711yescharacteristic
145C2×Dic43—22no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—42no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158Dic86—22no—
159Dic86—22no—
160Dic86—41no—
161Dic86—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—44no—
179C4×C43#45612yes—
180Dic43—42no—
181Dic43—81no—
182Dic43—81no—
183Dic43—81no—
184Dic43—81no—
185Dic43—81no—
186#3236—431no—
187#3113—431no—
188#2584—431no—
189#1986—431no—
190#1528—431no—
191#1491—431no—
192#1285D4311yescharacteristic
193C2×C43—21no—
194C2×C43—21no—
195C2×C43#200511yescharacteristic
196C2×C43#200711yescharacteristic
197C2×C43#201011yescharacteristic
198#533—431no—
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#432C2×D4311yescharacteristic
212#432C2×D4311yescharacteristic
213C4×M16—431no—
214#398—861no—
215#395—861no—
216#389—861no—
217#389—861no—
218#389—862no—
219C4×C4⋊C4C2×D4311yescharacteristic
220#339—862no—
221#330—862no—
222Q8⋊C8—862no—
223C43#1001111yescharacteristic, complemented, Sylow
224C22×Q8—431no—
225C2×Q16—862no—
226C2×M16—861no—
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—861no—
237C4×Q8—861no—
238C4×Q8—861no—
239C4×Q8—861no—
240C4×Q8—861no—
241C4×Q8—861no—
242#117—861no—
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×C42D17212yes—
254C2×C42C22×D4311yescharacteristic
255#107—862no—
256#106—862no—
257#106—862no—
258C4⋊C8—21no—
259C4⋊C8D17212yes—
260#103—862no—
261#103—862no—
262#103—862no—
263#103—862no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266#97—21no—
267#97—861no—
268#97D17212yes—
269C4×C8—861no—
270#95—21no—
271#95—862no—
272#95—862no—
273C2×Q8—861no—
274C2×Q8—861no—
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×C4C2×D17211yescharacteristic
284C22×C4D4×D4311yescharacteristic
285C22×C4D4×D4311yescharacteristic
286Q16—1724no—
287M16—862no—
288M16—1721no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—1721no—
292C4⋊C4—24no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4—861no—
303C4⋊C4—3442no—
304C4⋊C4—1724no—
305C4⋊C4—1721no—
306C4⋊C4—1721no—
307C4⋊C4—1721no—
308C4⋊C4—1721no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C22⋊C4—1721no—
314C42—42no—
315C42—1721no—
316C42—1721no—
317C42—1721no—
318C42C2×D17211yescharacteristic
319C42C2×D17211yescharacteristic
320C42D4×D4311yescharacteristic
321C42#1062190211yescharacteristic
322C23#1306329511yescharacteristic
323Q8—862no—
324Q8—862no—
325Q8—1722no—
326Q8—1721no—
327Q8—1721no—
328Q8—1722no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—862no—
337C2×C4—1722no—
338C2×C4—1721no—
339C2×C4—1721no—
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#1306330011yescharacteristic
352C2×C4#1306330011yescharacteristic
353C2×C4#1306330011yescharacteristic
354C2×C4#1306332211yescharacteristic
355C8—42no—
356C8—42no—
357C8—1722no—
358C22—21no—
359C22—21no—
360C22#1458280911yescharacteristic
361C22#1458307911yescharacteristic
362C22#1458308411yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—44no—
369C4—3441no—
370C4—3441no—
371C4—3441no—
372C4—3441no—
373C4—3441no—
374C4—1722no—
375C4#1458308312yes—
376C2—21no—
377C2—21no—
378C2#1913563411yescharacteristic
379C2#1913564411yescharacteristic
380C2#1913566311yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1285C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#1285D43
hypocenterC43#10011
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

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
#191447262
#191399782
#191355382
#191331982
#191330412
C43×#12852
#1001143