Finite Group Databasebeta

← #24999544

Subgroups — #24999544

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#19145416C211yesmaximal, characteristic
2#19139069C211yesmaximal, characteristic
3#19134675C211yesmaximal, characteristic
4#19133115C211yesmaximal, characteristic
5#19133114C211yesmaximal, characteristic
6#19132481C211yesmaximal, characteristic
7C43×#2503C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9#14583229—21no—
10#14583227—21no—
11#14583155—22no—
12#14583055—21no—
13#14583054—21no—
14#14582863C2211yescharacteristic
15#14582863C2211yescharacteristic
16#14582830—22no—
17#14582804—21no—
18#14582772—22no—
19#14582768—21no—
20C4×C22⋊Dic43C2211yescharacteristic
21#14582668—22no—
22#14582636—22no—
23#14582635—22no—
24C2×C22⋊Q8×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C43×#400—22no—
27C43×#391—21no—
28C43×#382—21no—
29C43×#381—22no—
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C2×#10621885—22no—
33C2×#10621877—21no—
34C2×#10621877D412yes—
35#13063304—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—24no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C4×Dic43—21no—
45#13063256—22no—
46#13063249—22no—
47#13063248—22no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C43⋊#95—24no—
53C43⋊#95D412yes—
54C22×Q8×C43D411yescharacteristic
55C23×C4×C43D412yes—
56C23×C4×C43C2311yescharacteristic
57C22⋊Q8×C43—21no—
58C22⋊Q8×C43—21no—
59C22⋊Q8×C43—21no—
60C22⋊Q8×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C42×C43—21no—
72#95×C43—24no—
73#95×C43—24no—
74#95×C43D412yes—
75C24×C43C2×D411yescharacteristic
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—42no—
79C22×C4×C43—22no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—22no—
83C22×C4×C43—22no—
84C22×C4×C43—22no—
85C22×C4×C43—44no—
86C22×C4×C43—42no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×Dic43—22no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C2×Dic86—21no—
97C2×Dic86—21no—
98C2×Dic86—42no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C22⋊C4×C43—42no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—41no—
110C42×C43—42no—
111C22⋊Dic43—24no—
112C22⋊Dic43—41no—
113C22⋊Dic43—41no—
114#10621885—82no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117Dic43⋊C4—41no—
118Dic43⋊C4—41no—
119Dic43⋊C4—84no—
120C4×Dic43—42no—
121#10621877—42no—
122#10621877—42no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—41no—
125C23×C43—22no—
126C23×C43—22no—
127C23×C43—41no—
128C23×C43#12011yescharacteristic
129C23×C43#12011yescharacteristic
130C23×C43#12111yescharacteristic
131Q8×C43—42no—
132Q8×C43—81no—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—44no—
142C2×C4×C43—42no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—44no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—82no—
150C2×C4×C43#12011yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12711yescharacteristic
154C2×Dic43—24no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—42no—
161Dic86—42no—
162Dic86—81no—
163C43⋊C8—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—82no—
181C4×C43—82no—
182C4×C43—81no—
183C4×C43—81no—
184C4×C43#45812yes—
185Dic43—44no—
186Dic43—81no—
187Dic43—81no—
188#3195—431no—
189#2503D4311yescharacteristic
190#2502—431no—
191#1821—431no—
192#1508—431no—
193#1508—431no—
194#1297—431no—
195C2×C43—22no—
196C2×C43—22no—
197C2×C43—41no—
198C2×C43#200411yescharacteristic
199C2×C43#200511yescharacteristic
200C2×C43#202211yescharacteristic
201C2×C22⋊Q8—431no—
202C2×C22⋊Q8C2×D4311yescharacteristic
203C22×C4⋊C4C2×D4311yescharacteristic
204#483—861no—
205#483—861no—
206#470—862no—
207#451—861no—
208#451—861no—
209#407—431no—
210#407—431no—
211#400—22no—
212#398—862no—
213#391—21no—
214#391—861no—
215#385—862no—
216#384—861no—
217#382—21no—
218#381—22no—
219C4×C22⋊C4—431no—
220C4×C22⋊C4C2×D4311yescharacteristic
221#343—862no—
222#328—862no—
223#328—862no—
224C43#1033511yescharacteristic, complemented, Sylow
225C22×Q8—431no—
226C22×Q8C22⋊D4311yescharacteristic
227C23×C4C22⋊D4312yes—
228C23×C4C22×D4311yescharacteristic
229C2×Q16—862no—
230C2×M16—432no—
231C2×M16—861no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—861no—
237C22⋊Q8—861no—
238C22⋊Q8—861no—
239C22⋊Q8—861no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—431no—
248C2×C4⋊C4—864no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4C22⋊D4311yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C42—21no—
256C2×C42—861no—
257#106—862no—
258#103—862no—
259#103—862no—
260C22⋊C8—861no—
261C22⋊C8—861no—
262C22⋊C8—861no—
263C22⋊C8—861no—
264#95—24no—
265#95—24no—
266#95—432no—
267#95—864no—
268#95C22⋊D4312yes—
269C24C2×C22⋊D4311yescharacteristic
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—42no—
273C2×Q8—861no—
274C2×Q8—861no—
275C2×Q8—1722no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—44no—
284C22×C4—862no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4D4×D4311yescharacteristic
288C22×C4D4×D4311yescharacteristic
289C22×C4D4×D4311yescharacteristic
290C22×C4#1062190011yescharacteristic
291C22×C4C2×C22⋊D4311yescharacteristic
292C22×C4C2×C22⋊D4311yescharacteristic
293Q16—3442no—
294M16—1722no—
295M16—1722no—
296C2×C8—862no—
297C2×C8—1721no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C4⋊C4—3444no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C22⋊C4—42no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—864no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C42—42no—
318C42—1722no—
319C23—22no—
320C23—22no—
321C23—41no—
322C23#1306329311yescharacteristic
323C23#1306329411yescharacteristic
324C23#1306329711yescharacteristic
325Q8—42no—
326Q8—81no—
327Q8—3441no—
328Q8—1722no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—44no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—82no—
346C2×C4—864no—
347C2×C4—1722no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4—1722no—
353C2×C4#1306329311yescharacteristic
354C2×C4#1306329611yescharacteristic
355C2×C4#1306329711yescharacteristic
356C2×C4#1306332111yescharacteristic
357C8—3441no—
358C8—1722no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—44no—
367C22#1458280711yescharacteristic
368C22#1458307612yes—
369C22#1458308212yes—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—82no—
375C4—81no—
376C4—81no—
377C4—3441no—
378C4—3441no—
379C4—1724no—
380C4#1458308812yes—
381C2—22no—
382C2—22no—
383C2—41no—
384C2#1913562411yescharacteristic
385C2#1913562911yescharacteristic
386C2#1913572311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2503C2
socleC22×C43#392
prime radicalC24×C43C2×D4
hypercenter#2503D43
hypocenterC43#10335
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2503

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
#191454162
#191390692
#191346752
#191331152
#191331142
#191324812
C43×#25032
#1033543