Finite Group Databasebeta

← #24994036

Subgroups — #24994036

Order 11008.

618 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 97 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#19139970C211yesmaximal, characteristic
2#19136950C211yesmaximal, characteristic
3#19133116C211yesmaximal, characteristic
4#19133114C211yesmaximal, characteristic
5#19132924C211yesmaximal, characteristic
6#19132481C211yesmaximal, characteristic
7C43×#1297C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C2×#13063281—21no—
10C22×Dic43⋊C4C2211yescharacteristic
11#14582863C2211yescharacteristic
12#14582831C412yescomplemented
13#14582820C412yescomplemented
14#14582797—22no—
15#14582774—21no—
16#14582774—21no—
17C4×Dic43⋊C4—22no—
18#14582750—22no—
19C22⋊C4×Dic43—21no—
20C4×C22⋊Dic43C2211yescharacteristic
21#14582637—22no—
22#14582635—22no—
23#14582624—22no—
24C43×#407C2211yescharacteristic
25C4×C22⋊C4×C43C2211yescharacteristic
26C4×C22⋊C4×C43C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28C23×Dic43D411yescharacteristic
29C23×Dic43D411yescharacteristic
30C2×#10621877—21no—
31#13063304—21no—
32#13063304—21no—
33#13063304—21no—
34#13063304—21no—
35#13063281—28no—
36C2×C4⋊Dic43—22no—
37C2×C4⋊Dic43—22no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×Dic43⋊C4—22no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4C2×C412yes—
46C2×Dic43⋊C4D412yes—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C4×Dic43—22no—
50C2×C4×Dic43—22no—
51C2×C4×Dic43—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C43⋊#95—22no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95D412yes—
58C23×C4×C43C2311yescharacteristic
59C2×M16×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—21no—
62C2×C42×C43—21no—
63C2×C42×C43—21no—
64C22⋊C8×C43—21no—
65C22⋊C8×C43—21no—
66#95×C43C2×C412yes—
67#95×C43D412yes—
68C24×C43C2×D411yescharacteristic
69C22×C4×C43—22no—
70C22×C4×C43—22no—
71C22×C4×C43—81no—
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43#4111yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×Dic43—24no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—22no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—81no—
87C22×Dic43C22⋊C412yes—
88C22×Dic43C22⋊C412yes—
89C2×Dic86—21no—
90C2×Dic86—21no—
91C2×Dic86—81no—
92M16×C43—81no—
93C2×C8×C43—41no—
94C22⋊C4×C43—24no—
95C22⋊C4×C43—24no—
96C42×C43—81no—
97C42×C43—81no—
98C22⋊Dic43—24no—
99C22⋊Dic43—41no—
100C22⋊Dic43—41no—
101C4⋊Dic43—21no—
102C4⋊Dic43—21no—
103C4⋊Dic43—44no—
104C4⋊Dic43—82no—
105Dic43⋊C4—28no—
106Dic43⋊C4—22no—
107Dic43⋊C4—22no—
108Dic43⋊C4—22no—
109Dic43⋊C4—22no—
110Dic43⋊C4—41no—
111Dic43⋊C4—41no—
112C4×Dic43—28no—
113C4×Dic43—81no—
114C4×Dic43—82no—
115#10621877—81no—
116C2×C43⋊C8—41no—
117C23×C43—22no—
118C23×C43—22no—
119C23×C43—41no—
120C23×C43C2×C22⋊C411yescharacteristic
121C23×C43#12011yescharacteristic
122C23×C43#12311yescharacteristic
123C2×C4×C43—24no—
124C2×C4×C43—24no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43C4×D411yescharacteristic
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×Dic43—22no—
140C2×Dic43—22no—
141C2×Dic43—24no—
142C2×Dic43—22no—
143C2×Dic43—22no—
144C2×Dic43—24no—
145C2×Dic43—22no—
146C2×Dic43—42no—
147C2×Dic43—42no—
148C2×Dic43—42no—
149C2×Dic43—42no—
150C2×Dic43—42no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—42no—
154C2×Dic43—81no—
155C2×Dic43#10414yes—
156Dic86—81no—
157Dic86—81no—
158C8×C43—81no—
159C43⋊C8—81no—
160#9408—431nomaximal, Sylow
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—44no—
169C22×C43#38611yescharacteristic
170C22×C43C2×#10412yes—
171C22×C43#45612yes—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—44no—
177C4×C43—44no—
178Dic43—24no—
179Dic43—44no—
180Dic43—42no—
181Dic43—81no—
182Dic43—81no—
183#2583—431no—
184#2274—431no—
185#1508—431no—
186#1508—431no—
187#1463—431no—
188#1297—431no—
189#1297D4311yescharacteristic
190C2×C43—22no—
191C2×C43—22no—
192C2×C43—41no—
193C2×C43#188611yescharacteristic
194C2×C43#189611yescharacteristic
195C2×C43#191311yescharacteristic
196C2×C22⋊Q8—431no—
197C2×#117—861no—
198C22×C4⋊C4—431no—
199#407—431no—
200#407C2×D4311yescharacteristic
201#398—432no—
202#395—432no—
203#389—862no—
204#385—861no—
205#385—861no—
206C4×C4⋊C4—862no—
207C4×C4⋊C4—862no—
208C4×C22⋊C4—431no—
209C4×C22⋊C4—861no—
210C4×C22⋊C4C2×D4311yescharacteristic
211C4×C22⋊C4C2×D4311yescharacteristic
212#328—862no—
213#328—862no—
214#324—862no—
215C43#940811yescharacteristic, complemented, Sylow
216C22×Q8—431no—
217C23×C4—431no—
218C23×C4—431no—
219C23×C4C22×D4311yescharacteristic
220C2×M16—21no—
221C2×M16—861no—
222C22⋊Q8—861no—
223C22⋊Q8—861no—
224C22⋊Q8—861no—
225C22⋊Q8—861no—
226#117—868no—
227C2×C4⋊C4—432no—
228C2×C4⋊C4—432no—
229C2×C4⋊C4—431no—
230C2×C4⋊C4—862no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—862no—
236C2×C4⋊C4—862no—
237C2×C4⋊C4—861no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—861no—
241C2×C22⋊C4—861no—
242C2×C42—21no—
243C2×C42—21no—
244C2×C42—862no—
245C2×C42—862no—
246C2×C42—861no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—861no—
250C22⋊C8—861no—
251#95—432no—
252#95—862no—
253#95—862no—
254#95—862no—
255#95C4×D4312yes—
256#95D17212yes—
257C24D4×D4311yescharacteristic
258C2×Q8—861no—
259C2×Q8—861no—
260C2×Q8—3441no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—81no—
264C22×C4—432no—
265C22×C4—432no—
266C22×C4—864no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—862no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—3441no—
275C22×C4C2×C4×D4311yescharacteristic
276C22×C4C2×D17211yescharacteristic
277C22×C4#1062189811yescharacteristic
278C22×C4D4×D4311yescharacteristic
279C22×C4D4×D4311yescharacteristic
280C22×C4#1062190211yescharacteristic
281M16—81no—
282M16—3441no—
283C2×C8—41no—
284C2×C8—1721no—
285C4⋊C4—868no—
286C4⋊C4—862no—
287C4⋊C4—862no—
288C4⋊C4—862no—
289C4⋊C4—862no—
290C4⋊C4—861no—
291C4⋊C4—861no—
292C4⋊C4—3442no—
293C4⋊C4—1724no—
294C4⋊C4—1721no—
295C4⋊C4—1721no—
296C22⋊C4—24no—
297C22⋊C4—24no—
298C22⋊C4—864no—
299C22⋊C4—1721no—
300C22⋊C4—1721no—
301C42—81no—
302C42—81no—
303C42—868no—
304C42—3441no—
305C42—3442no—
306C23—22no—
307C23—22no—
308C23—41no—
309C23C22⋊C4×D4311yescharacteristic
310C23#1306329511yescharacteristic
311C23#1306331011yescharacteristic
312Q8—3441no—
313Q8—3441no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—434no—
327C2×C4—862no—
328C2×C4—862no—
329C2×C4—864no—
330C2×C4—862no—
331C2×C4—862no—
332C2×C4—864no—
333C2×C4—862no—
334C2×C4—3441no—
335C2×C4—1722no—
336C2×C4—1722no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4#1306328711yescharacteristic
344C2×C4C4×D17211yescharacteristic
345C2×C4#1306329811yescharacteristic
346C2×C4#1306330011yescharacteristic
347C8—81no—
348C8—3441no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—44no—
357C22#1458277711yescharacteristic
358C22#104×D4312yes—
359C22#1458308312yes—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—44no—
365C4—44no—
366C4—864no—
367C4—3441no—
368C4—3441no—
369C4—1724no—
370C4—1722no—
371C2—22no—
372C2—22no—
373C2—41no—
374C2#1913498711yescharacteristic
375C2#1913503711yescharacteristic
376C2#1913513611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1297C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1297D43
hypocenterC43#9408
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
12. #14582831C4semidirect
13. #14582820C4semidirect
215. C43#9408semidirect

Maximal subgroups

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

subgroupindex
#191399702
#191369502
#191331162
#191331142
#191329242
#191324812
C43×#12972
#940843