Finite Group Databasebeta

← #24999546

Subgroups — #24999546

Order 11008.

574 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 87 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#19139076C211yesmaximal, characteristic
3#19139069C211yesmaximal, characteristic
4#19133116C211yesmaximal, characteristic
5#19133116C211yesmaximal, characteristic
6#19132480C211yesmaximal, characteristic
7C43×#1821C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C2×#13063304C2211yescharacteristic
10#14583230—21no—
11#14583230—21no—
12#14583157—22no—
13#14583057—21no—
14#14583057—21no—
15#14582837—22no—
16#14582830—22no—
17#14582804—21no—
18#14582804—21no—
19#14582772—22no—
20#14582768—21no—
21#14582764—21no—
22#14582762—22no—
23C4×C22⋊Dic43C2211yescharacteristic
24C4×C22⋊Dic43C2211yescharacteristic
25#14582637—22no—
26#14582637—22no—
27C22×C4⋊C4×C43C2211yescharacteristic
28C43×#407C2211yescharacteristic
29C43×#407C2211yescharacteristic
30C43×#343—22no—
31C22×Dic86D411yescharacteristic
32C22×Dic86D411yescharacteristic
33C2×Dic172—22no—
34#13063304—21no—
35#13063304—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40#13063304—21no—
41#13063304—21no—
42C2×C4⋊Dic43D411yescharacteristic
43C2×C4⋊Dic43D411yescharacteristic
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4—24no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C4×Dic43—21no—
52C2×C4×Dic43—21no—
53#13063257—22no—
54#13063250—22no—
55#13063250—22no—
56C43⋊#95—24no—
57C43⋊#95—24no—
58C43⋊#95—24no—
59C43⋊#95D412yes—
60C43⋊#95D412yes—
61C23×C4×C43D412yes—
62C23×C4×C43C2311yescharacteristic
63C2×M16×C43—21no—
64C2×M16×C43D412yes—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75C24×C43C2×D411yescharacteristic
76C22×C4×C43—22no—
77C22×C4×C43—22no—
78C22×C4×C43—22no—
79C22×C4×C43—44no—
80C22×C4×C43—42no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C22×Dic43—22no—
88C22×Dic43—22no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C2×Dic86—21no—
94C2×Dic86—21no—
95C2×Dic86—21no—
96C2×Dic86—21no—
97C2×Dic86—42no—
98C2×Dic86—42no—
99M16×C43—42no—
100M16×C43—42no—
101C2×C8×C43—22no—
102C2×C8×C43—41no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C22⋊Dic43—24no—
108C22⋊Dic43—42no—
109C22⋊Dic43—41no—
110C22⋊Dic43—41no—
111C22⋊Dic43—41no—
112C22⋊Dic43—41no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117Dic43⋊C4—41no—
118Dic43⋊C4—41no—
119Dic43⋊C4—41no—
120Dic43⋊C4—41no—
121Dic43⋊C4—84no—
122C4×Dic43—42no—
123C4×Dic43—42no—
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—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—44no—
138C2×C4×C43—42no—
139C2×C4×C43—44no—
140C2×C4×C43—82no—
141C2×C4×C43#12011yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12711yescharacteristic
145C2×Dic43—24no—
146C2×Dic43—42no—
147C2×Dic43—42no—
148C2×Dic43—42no—
149C2×Dic43—42no—
150C2×Dic43—42no—
151C2×Dic43—42no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159Dic86—42no—
160Dic86—42no—
161Dic86—81no—
162Dic86—81no—
163C8×C43—42no—
164C8×C43—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#45812yes—
182Dic43—44no—
183Dic43—82no—
184Dic43—81no—
185Dic43—81no—
186Dic43—81no—
187Dic43—81no—
188#3195—431no—
189#2503—431no—
190#2502—431no—
191#1821D4311yescharacteristic
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⋊Q8—431no—
203C22×C4⋊C4C2×D4311yescharacteristic
204#483—861no—
205#483—861no—
206#470—862no—
207#451—861no—
208#451—861no—
209#407C2×D4311yescharacteristic
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⋊C4—431no—
220C4×C22⋊C4—431no—
221#343—22no—
222#328—862no—
223#328—862no—
224C43#1033511yescharacteristic, complemented, Sylow
225C22×Q8—431no—
226C22×Q8—431no—
227C23×C4D17212yes—
228C23×C4C22×D4311yescharacteristic
229C2×Q16—862no—
230C2×M16—21no—
231C2×M16C22⋊D4312yes—
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—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—431no—
248C2×C4⋊C4—864no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—861no—
251C2×C22⋊C4—861no—
252C2×C22⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C42—861no—
256C2×C42—861no—
257#106—862no—
258#103—862no—
259#103—862no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264#95—432no—
265#95—432no—
266#95—864no—
267#95—864no—
268#95—864no—
269C24C2×D17211yescharacteristic
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—22no—
279C22×C4—42no—
280C22×C4—44no—
281C22×C4—862no—
282C22×C4—862no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4#1062189811yescharacteristic
288C22×C4D4×D4311yescharacteristic
289C22×C4D4×D4311yescharacteristic
290C22×C4D4×D4311yescharacteristic
291C22×C4D4×D4311yescharacteristic
292C22×C4C2×C22⋊D4311yescharacteristic
293Q16—3442no—
294M16—42no—
295M16—42no—
296C2×C8—22no—
297C2×C8—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—861no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4—861no—
306C4⋊C4—3444no—
307C4⋊C4—1721no—
308C4⋊C4—1721no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C22⋊C4—864no—
312C22⋊C4—1722no—
313C22⋊C4—1721no—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C42—1722no—
318C42—1722no—
319C23—22no—
320C23—22no—
321C23—41no—
322C23#1306329511yescharacteristic
323C23#1306329511yescharacteristic
324C23#1306329911yescharacteristic
325Q8—3441no—
326Q8—3441no—
327Q8—1722no—
328Q8—1722no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—44no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—82no—
339C2×C4—864no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4—1722no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4—1722no—
349C2×C4—1722no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4—1722no—
353C2×C4#1306329311yescharacteristic
354C2×C4#1306329811yescharacteristic
355C2×C4#1306329811yescharacteristic
356C2×C4#1306332111yescharacteristic
357C8—42no—
358C8—81no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—44no—
367C22#1458280811yescharacteristic
368C22#1458307912yes—
369C22#1458308412yes—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—3442no—
375C4—3441no—
376C4—3441no—
377C4—3441no—
378C4—3441no—
379C4—1724no—
380C4#1458308812yes—
381C2—22no—
382C2—22no—
383C2—41no—
384C2#1913562611yescharacteristic
385C2#1913563311yescharacteristic
386C2#1913572611yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1821C2
socleC22×C43#392
prime radicalC24×C43C2×D4
hypercenter#1821D43
hypocenterC43#10335
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

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
#191390762
#191390692
#191331162
#191324802
C43×#18212
#1033543