Finite Group Databasebeta

← #24994031

Subgroups — #24994031

Order 11008.

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

normal subgroups only

This group has 726 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#19139748C211yesmaximal, characteristic
2#19136947C211yesmaximal, characteristic
3#19133116C211yesmaximal, characteristic, complemented
4#19133114C211yesmaximal, characteristic, complemented
5#19132921C211yesmaximal, characteristic
6#19132481C211yesmaximal, characteristic, complemented
7C43×#1297C211yesmaximal, characteristic, complemented
8C2×#13063304C2211yescharacteristic
9C22×(C2×D43)⋊C4C2211yescharacteristic
10C2×C22⋊C4×D43—21no—
11#14582863C2211yescharacteristic
12#14582826C412yescomplemented
13#14582812C412yescomplemented
14#14582790—22no—
15#14582760—21no—
16#14582754—21no—
17C22⋊C4×Dic43—21no—
18C4×(C2×D43)⋊C4—22no—
19C4×C22⋊Dic43C2211yescharacteristic
20#14582746—22no—
21#14582637—22no—
22#14582635—22no—
23#14582622—22no—
24C43×#407C2211yescharacteristic
25C4×C22⋊C4×C43C2211yescharacteristic
26C4×C22⋊C4×C43C2211yescharacteristic
27C24×D43D411yescharacteristic
28C22×Dic86C2×C411yescharacteristic, complemented
29C23×Dic43D411yescharacteristic
30C22×C4×D43—22no—
31C2×#10621877—21no—
32#13063304—21no—
33#13063304—21no—
34#13063304—21no—
35#13063304—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic, complemented
37C2×Dic43⋊C4—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×(C2×D43)⋊C4—22no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4—22no—
47C2×(C2×D43)⋊C4C2×C412yes—
48C2×(C2×D43)⋊C4D412yes—
49C22⋊C4×D43—28no—
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×C412yescomplemented
67#95×C43D412yes—
68C24×C43C2×D411yescharacteristic
69C23×D43—21no—
70C23×D43—21no—
71C23×D43—24no—
72C23×D43—42no—
73C23×D43—81no—
74C23×D43C22⋊C412yes—
75C22×C4×C43—22no—
76C22×C4×C43—22no—
77C22×C4×C43—81no—
78C22×C4×C43C22×C411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—22no—
88C22×Dic43—21no—
89C22×Dic43—42no—
90C22×Dic43C22⋊C412yes—
91C2×C4×D43—28no—
92C2×C4×D43—82no—
93C2×C4×D43—82no—
94C2×Dic86—21no—
95C2×Dic86—21no—
96C2×Dic86—81no—
97M16×C43—81no—
98C2×C8×C43—41no—
99C22⋊C4×C43—24no—
100C22⋊C4×C43—42no—
101C42×C43—81no—
102C42×C43—81no—
103C22⋊Dic43—24no—
104C22⋊Dic43—41no—
105C22⋊Dic43—41no—
106(C2×D43)⋊C4—28no—
107(C2×D43)⋊C4—22no—
108(C2×D43)⋊C4—22no—
109(C2×D43)⋊C4—22no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4—44no—
112(C2×D43)⋊C4—82no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115Dic43⋊C4—41no—
116Dic43⋊C4—41no—
117C4×Dic43—81no—
118C4×Dic43—82no—
119#10621877—81no—
120C2×C43⋊C8—41no—
121C23×C43—22no—
122C23×C43—22no—
123C23×C43—41no—
124C23×C43C2×C22⋊C411yescharacteristic
125C23×C43#12011yescharacteristic
126C23×C43#12311yescharacteristic
127C22×D43—22no—
128C22×D43—22no—
129C22×D43—22no—
130C22×D43—24no—
131C22×D43—22no—
132C22×D43—42no—
133C22×D43—42no—
134C22×D43—42no—
135C22×D43—42no—
136C22×D43—88no—
137C22×D43—81no—
138C22×D43—81no—
139C22×D43#10414yes—
140C2×C4×C43—24no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×Dic43—24no—
157C2×Dic43—22no—
158C2×Dic43—42no—
159C2×Dic43—42no—
160C2×Dic43—42no—
161C2×Dic43—42no—
162C2×Dic43—42no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—42no—
166C2×Dic43—81no—
167C4×D43—88no—
168Dic86—81no—
169Dic86—81no—
170C8×C43—81no—
171C43⋊C8—81no—
172#9407—431nomaximal, Sylow
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—44no—
181C22×C43#38611yescharacteristic
182C22×C43C2×#10412yes—
183C22×C43#45512yes—
184C2×D43—24no—
185C2×D43—44no—
186C2×D43—44no—
187C2×D43—42no—
188C2×D43—42no—
189C2×D43—44no—
190C2×D43—82no—
191C2×D43—84no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—44no—
197C4×C43—82no—
198Dic43—44no—
199Dic43—42no—
200Dic43—81no—
201Dic43—81no—
202#2561—431no—
203#2273—431no—
204#1508—431no—
205#1508—431no—
206#1462—431no—
207#1297—431no—
208#1297D4311yescharacteristic, complemented
209C2×C43—22no—
210C2×C43—22no—
211C2×C43—41no—
212C2×C43#188511yescharacteristic
213C2×C43#189611yescharacteristic
214C2×C43#191311yescharacteristic
215D43—44no—
216C2×C22⋊Q8—431no—
217C22×C22⋊C4—431no—
218C22×C22⋊C4—861no—
219#407—431no—
220#407C2×D4311yescharacteristic
221#397—432no—
222#393—432no—
223#388—862no—
224#381—861no—
225#379—861no—
226C4×C22⋊C4—431no—
227C4×C22⋊C4—862no—
228C4×C22⋊C4—861no—
229C4×C22⋊C4—862no—
230C4×C22⋊C4C2×D4311yescharacteristic
231C4×C22⋊C4C2×D4311yescharacteristic
232#328—862no—
233#328—862no—
234#323—862no—
235C43#940711yescharacteristic, complemented, Sylow
236C25—431no—
237C22×Q8—431no—
238C23×C4—431no—
239C23×C4—862no—
240C23×C4C22×D4311yescharacteristic
241C2×M16—21no—
242C2×M16—861no—
243C22⋊Q8—861no—
244C22⋊Q8—861no—
245C22⋊Q8—861no—
246C22⋊Q8—861no—
247C2×C4⋊C4—431no—
248C2×C4⋊C4—861no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—432no—
252C2×C22⋊C4—432no—
253C2×C22⋊C4—868no—
254C2×C22⋊C4—862no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C22⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4—862no—
261C2×C22⋊C4—862no—
262C2×C22⋊C4—861no—
263C2×C42—21no—
264C2×C42—21no—
265C2×C42—862no—
266C2×C42—861no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C22⋊C8—861no—
270C22⋊C8—861no—
271#95—432no—
272#95—862no—
273#95—862no—
274#95—862no—
275#95C4×D4312yescomplemented
276#95D17212yes—
277C24—432no—
278C24—864no—
279C24—861no—
280C24—861no—
281C24—3441no—
282C24—1722no—
283C24D4×D4311yescharacteristic
284C2×Q8—861no—
285C2×Q8—861no—
286C2×Q8—3441no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—81no—
290C22×C4—432no—
291C22×C4—868no—
292C22×C4—861no—
293C22×C4—862no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—3442no—
298C22×C4—3442no—
299C22×C4—1722no—
300C22×C4C2×C4×D4311yescharacteristic
301C22×C4C2×D17211yescharacteristic
302C22×C4#1062189811yescharacteristic
303C22×C4D4×D4311yescharacteristic
304C22×C4D4×D4311yescharacteristic
305C22×C4#1062190211yescharacteristic
306M16—81no—
307M16—3441no—
308C2×C8—41no—
309C2×C8—1721no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4—1721no—
313C4⋊C4—1721no—
314C22⋊C4—24no—
315C22⋊C4—42no—
316C22⋊C4—868no—
317C22⋊C4—864no—
318C22⋊C4—862no—
319C22⋊C4—862no—
320C22⋊C4—862no—
321C22⋊C4—862no—
322C22⋊C4—3442no—
323C22⋊C4—1724no—
324C22⋊C4—1721no—
325C22⋊C4—1721no—
326C42—81no—
327C42—81no—
328C42—3441no—
329C42—3442no—
330C23—22no—
331C23—22no—
332C23—41no—
333C23—434no—
334C23—864no—
335C23—862no—
336C23—862no—
337C23—862no—
338C23—862no—
339C23—3441no—
340C23—3441no—
341C23—3448no—
342C23—1722no—
343C23—1722no—
344C23—1722no—
345C23—1722no—
346C23C22⋊C4×D4311yescharacteristic
347C23#1306329511yescharacteristic
348C23#1306331011yescharacteristic
349Q8—3441no—
350Q8—3441no—
351C2×C4—24no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—864no—
364C2×C4—862no—
365C2×C4—3448no—
366C2×C4—3441no—
367C2×C4—1722no—
368C2×C4—1722no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1722no—
372C2×C4—1722no—
373C2×C4—1722no—
374C2×C4—1722no—
375C2×C4#1306328711yescharacteristic
376C2×C4C4×D17211yescharacteristic
377C2×C4#1306329811yescharacteristic
378C2×C4#1306330011yescharacteristic
379C8—81no—
380C8—3441no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—44no—
389C22—864no—
390C22—3442no—
391C22—3444no—
392C22—1724no—
393C22—1724no—
394C22—1724no—
395C22—1722no—
396C22—1722no—
397C22#1458277711yescharacteristic
398C22#104×D4312yes—
399C22#1458307812yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—44no—
405C4—82no—
406C4—3441no—
407C4—3441no—
408C4—1724no—
409C4—1722no—
410C2—22no—
411C2—22no—
412C2—41no—
413C2—1724no—
414C2#1913498211yescharacteristic
415C2#1913503711yescharacteristic
416C2#1913513611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1297C2
socleC22×C43#386
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1297D43
hypocenterC43#9407
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
3. #19133116C2semidirect
4. #19133114C2semidirect
6. #19132481C2semidirect
7. C43×#1297C2semidirect
12. #14582826C4semidirect
13. #14582812C4semidirect
28. C22×Dic86C2×C4semidirect
36. C2×C4⋊Dic43C2×C4semidirect
66. #95×C43C2×C4semidirect
208. #1297D43semidirect
235. C43#9407semidirect
275. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191397482
#191369472
#191331162
#191331142
#191329212
#191324812
C43×#12972
#940743