Finite Group Databasebeta

← #24999547

Subgroups — #24999547

Order 11008.

574 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 89 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#19145419C211yesmaximal, characteristic
2#19139080C211yesmaximal, characteristic
3#19139073C211yesmaximal, characteristic
4#19134673C211yesmaximal, characteristic
5#19133114C211yesmaximal, characteristic
6#19133114C211yesmaximal, characteristic
7C43×#1297C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C2×#13063304C2211yescharacteristic
10C22×C4⋊Dic43C2211yescharacteristic
11#14583230—21no—
12#14583230—21no—
13#14583157—22no—
14#14583057—21no—
15#14583057—21no—
16#14582863C2211yescharacteristic
17#14582839—22no—
18#14582831—22no—
19#14582805—21no—
20#14582805—21no—
21#14582774—22no—
22#14582769—21no—
23#14582765—21no—
24#14582760—22no—
25#14582667—22no—
26#14582635—22no—
27#14582635—22no—
28C43×#407C2211yescharacteristic
29C4×C22⋊C4×C43C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C22×Dic86D411yescharacteristic
33C23×Dic43D412yes—
34C2×Dic172—22no—
35C2×#10621877—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40#13063304—21no—
41#13063304—21no—
42#13063304—21no—
43#13063304—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43—24no—
51C2×C4⋊Dic43D411yescharacteristic
52C2×C4⋊Dic43D411yescharacteristic
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—21no—
55C2×C22⋊Dic43—21no—
56C2×C22⋊Dic43—21no—
57#13063257—22no—
58#13063250—22no—
59#13063250—22no—
60C22⋊(C43⋊C8)—21no—
61C22⋊(C43⋊C8)—21no—
62C43⋊#95—24no—
63C43⋊#95—24no—
64C43⋊#95—24no—
65C23×C4×C43C2311yescharacteristic
66C2×M16×C43D412yes—
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43—21no—
69C2×C42×C43—21no—
70C2×C42×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73#95×C43D412yes—
74#95×C43D412yes—
75C24×C43C2×D411yescharacteristic
76C22×C4×C43—22no—
77C22×C4×C43—22no—
78C22×C4×C43—42no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43#4111yescharacteristic
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—22no—
89C22×Dic43—22no—
90C22×Dic43—21no—
91C22×Dic43—22no—
92C22×Dic43—44no—
93C2×Dic86—21no—
94C2×Dic86—21no—
95C2×Dic86—21no—
96C2×Dic86—21no—
97C2×Dic86—42no—
98C2×Dic86—42no—
99M16×C43—42no—
100C2×C8×C43—22no—
101C22⋊C4×C43—24no—
102C22⋊C4×C43—42no—
103C42×C43—42no—
104C42×C43—42no—
105C22⋊Dic43—41no—
106C22⋊Dic43—41no—
107C22⋊Dic43—41no—
108C22⋊Dic43—41no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—41no—
114C4⋊Dic43—41no—
115C4⋊Dic43—41no—
116C4⋊Dic43—41no—
117C4⋊Dic43—84no—
118Dic43⋊C4—41no—
119Dic43⋊C4—41no—
120Dic43⋊C4—41no—
121Dic43⋊C4—41no—
122#10621877—42no—
123C2×C43⋊C8—41no—
124Dic172—82no—
125C23×C43—22no—
126C23×C43—22no—
127C23×C43—41no—
128C23×C43#12011yescharacteristic
129C23×C43#12011yescharacteristic
130C23×C43#12111yescharacteristic
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—24no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43#12011yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#12711yescharacteristic
147C2×Dic43—42no—
148C2×Dic43—42no—
149C2×Dic43—44no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—44no—
157C2×Dic43—42no—
158C2×Dic43—82no—
159Dic86—42no—
160Dic86—42no—
161Dic86—81no—
162Dic86—81no—
163C8×C43—42no—
164C43⋊C8—81no—
165#10335—431nomaximal, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—44no—
174C22×C43#39211yescharacteristic
175C22×C43#45512yes—
176C22×C43#45612yes—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—44no—
181C4×C43—82no—
182C4×C43#45812yes—
183Dic43—81no—
184Dic43—82no—
185Dic43—81no—
186Dic43—81no—
187Dic43—81no—
188#3195—431no—
189#2503—431no—
190#2502—431no—
191#1821—431no—
192#1508—431no—
193#1508—431no—
194#1297D4311yescharacteristic
195C2×C43—22no—
196C2×C43—22no—
197C2×C43—41no—
198C2×C43#200411yescharacteristic
199C2×C43#200511yescharacteristic
200C2×C43#202211yescharacteristic
201C2×C22⋊Q8—431no—
202C2×C22⋊Q8—431no—
203C22×C4⋊C4—431no—
204#483—861no—
205#483—861no—
206#470—862no—
207#451—861no—
208#451—861no—
209#407—431no—
210#407C2×D4311yescharacteristic
211#400—862no—
212#398—862no—
213#391—861no—
214#391—861no—
215#385—862no—
216#384—861no—
217#382—861no—
218#381—862no—
219C4×C22⋊C4C2×D4311yescharacteristic
220C4×C22⋊C4C2×D4311yescharacteristic
221#343—862no—
222#328—862no—
223#328—862no—
224C43#1033511yescharacteristic, complemented, Sylow
225C22×Q8—431no—
226C22×Q8—431no—
227C23×C4—432no—
228C23×C4C22×D4311yescharacteristic
229C2×Q16—862no—
230C2×M16—861no—
231C2×M16D17212yes—
232C22⋊Q8—861no—
233C22⋊Q8—861no—
234C22⋊Q8—861no—
235C22⋊Q8—861no—
236C22⋊Q8—861no—
237C22⋊Q8—861no—
238C22⋊Q8—861no—
239C22⋊Q8—861no—
240C2×C4⋊C4—431no—
241C2×C4⋊C4—431no—
242C2×C4⋊C4—864no—
243C2×C4⋊C4—861no—
244C2×C4⋊C4—861no—
245C2×C4⋊C4—861no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—861no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C42—21no—
256C2×C42—21no—
257#106—862no—
258#103—862no—
259#103—862no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—861no—
263C22⋊C8—861no—
264#95—864no—
265#95—864no—
266#95—864no—
267#95D17212yes—
268#95D17212yes—
269C24D4×D4311yescharacteristic
270C2×Q8—861no—
271C2×Q8—861no—
272C2×Q8—861no—
273C2×Q8—861no—
274C2×Q8—1722no—
275C2×Q8—1722no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—42no—
279C22×C4—862no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—862no—
284C22×C4—862no—
285C22×C4—861no—
286C22×C4—1724no—
287C22×C4C2×D17211yescharacteristic
288C22×C4C2×D17211yescharacteristic
289C22×C4C2×D17211yescharacteristic
290C22×C4D4×D4311yescharacteristic
291C22×C4D4×D4311yescharacteristic
292C22×C4#1062190211yescharacteristic
293Q16—3442no—
294M16—42no—
295M16—1722no—
296C2×C8—22no—
297C2×C8—1721no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4—3444no—
303C4⋊C4—1721no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C4⋊C4—1721no—
307C4⋊C4—1721no—
308C4⋊C4—1721no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C22⋊C4—24no—
312C22⋊C4—42no—
313C22⋊C4—1721no—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C42—42no—
318C42—42no—
319C23—22no—
320C23—22no—
321C23—41no—
322C23#1306329511yescharacteristic
323C23#1306329511yescharacteristic
324C23#1306330011yescharacteristic
325Q8—3441no—
326Q8—3441no—
327Q8—1722no—
328Q8—1722no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—3442no—
342C2×C4—1724no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1722no—
350C2×C4—1722no—
351C2×C4—1724no—
352C2×C4—1722no—
353C2×C4#1306329511yescharacteristic
354C2×C4#1306330011yescharacteristic
355C2×C4#1306330011yescharacteristic
356C2×C4#1306332211yescharacteristic
357C8—42no—
358C8—3441no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—44no—
367C22#1458280911yescharacteristic
368C22#1458307812yes—
369C22#1458308312yes—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—44no—
374C4—82no—
375C4—3442no—
376C4—3441no—
377C4—3441no—
378C4—3441no—
379C4—3441no—
380C4#1458309012yes—
381C2—22no—
382C2—22no—
383C2—41no—
384C2#1913562711yescharacteristic
385C2#1913563411yescharacteristic
386C2#1913572711yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1297C2
socleC22×C43#392
prime radicalC24×C43C2×D4
hypercenter#1297D43
hypocenterC43#10335
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
224. C43#10335semidirect

Maximal subgroups

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

subgroupindex
#191454192
#191390802
#191390732
#191346732
#191331142
C43×#12972
#1033543