Finite Group Databasebeta

← #25069722

Subgroups — #25069722

Order 11008.

958 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 187 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#19148405C211yesmaximal, characteristic, complemented
2#19144603C212yesmaximal
3#19133602C214yesmaximal, complemented
4#19133534C214yesmaximal
5#19133158C212yesmaximal, complemented
6#19132919C211yesmaximal, characteristic, complemented
7C43×#2536C211yesmaximal, characteristic
8Q8×Dic86—22no—
9#14583628—22no—
10#14583625—24no—
11#14583530—21no—
12#14583530C2214yes—
13#14583456—22no—
14#14583456C2212yes—
15#14583377—21no—
16#14583229C2214yes—
17#14583189—22no—
18#14583104—22no—
19#14583050C2214yes—
20C4×#10621883—24no—
21#14582952C2212yes—
22#14582635C2218yes—
23#14582625C2214yes—
24C2×C22⋊Q8×C43—21no—
25C2×C4×Q8×C43C2211yescharacteristic
26C2×C4×D4×C43C2211yescharacteristic
27C43×#398C2212yes—
28C43×#394C2212yes—
29C43×#388—22no—
30C43×#382C2211yescharacteristic
31C43×#380—21no—
32C2×#10621883—24no—
33#13063325—22no—
34#13063325—22no—
35#13063325D412yes—
36#13063325D412yes—
37#13063324—24no—
38#13063324—28no—
39#13063317—24no—
40#13063317—22no—
41#13063316—24no—
42#13063316—28no—
43#13063304—22no—
44#13063304—24no—
45#13063304C2314yes—
46Q8×Dic43—24no—
47Q8×Dic43—24no—
48C4×Dic86—24no—
49C4×Dic86—24no—
50C4×Dic86—22no—
51C4×Dic86D414yes—
52#13063284—24no—
53#13063284—22no—
54#13063256—24no—
55C4⋊(C43⋊C8)—22no—
56#13063248—24no—
57#13063246—24no—
58C22⋊(C43⋊C8)C2314yes—
59C4×C43⋊C8—22no—
60C22×Q8×C43D411yescharacteristic
61C22×D4×C43C2311yescharacteristic
62C23×C4×C43—21no—
63C22⋊Q8×C43—44no—
64C4×Q8×C43—22no—
65C4×Q8×C43—22no—
66C4×D4×C43—22no—
67C4×D4×C43—22no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—22no—
70C2×C4⋊C4×C43D411yescharacteristic
71C2×C4⋊C4×C43C2311yescharacteristic
72C2×C4⋊C4×C43C2312yes—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—22no—
75C2×C22⋊C4×C43—22no—
76C2×C42×C43D412yes—
77C2×C42×C43C2311yescharacteristic
78#95×C43—22no—
79#95×C43—21no—
80#95×C43C2312yes—
81C24×C43—21no—
82C2×Q8×C43—22no—
83C2×Q8×C43—22no—
84C2×Q8×C43SD1614yescomplemented
85C2×D4×C43—22no—
86C2×D4×C43—42no—
87C22×C4×C43—22no—
88C22×C4×C43—21no—
89C22×C4×C43—42no—
90C22×C4×C43—42no—
91C22×C4×C43—42no—
92C22×C4×C43C2×D412yes—
93C22×C4×C43C2×D412yes—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2411yescharacteristic
97C2×Dic86—22no—
98C2×Dic86—24no—
99C2×Dic86C2×D414yes—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—24no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—42no—
104C4⋊C4×C43—44no—
105C22⋊C4×C43—44no—
106C22⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—44no—
109C42×C43—22no—
110C42×C43—22no—
111C42×C43C2×D412yes—
112C42×C43C2×D412yes—
113C22⋊Dic43—24no—
114#10621883—48no—
115C4⋊Dic43—24no—
116C4⋊Dic43—24no—
117C4⋊Dic43—24no—
118C4⋊Dic43—22no—
119C4⋊Dic43—22no—
120C4⋊Dic43—22no—
121C4⋊Dic43C2×D414yes—
122Dic43⋊C4—28no—
123Dic43⋊C4—24no—
124Dic43⋊C4—24no—
125C4×Dic43—28no—
126C4×Dic43—24no—
127C2×C43⋊C8—24no—
128C23×C43—22no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43C22×D411yescharacteristic
136Q8×C43—28no—
137D4×C43—24no—
138D4×C43—42no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—84no—
152C2×C4×C43#12011yescharacteristic
153C2×C4×C43#12011yescharacteristic
154C2×C4×C43#12012yes—
155C2×C4×C43C2×SD1614yes—
156C2×C4×C43C2×SD1612yes—
157C2×C4×C43#13712yes—
158C2×C4×C43C22×D412yes—
159C2×Dic43—24no—
160C2×Dic43—24no—
161Dic86—44no—
162Dic86—44no—
163Dic86—84no—
164C43⋊C8—44no—
165#18220—431nomaximal, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—42no—
169C22×C43—42no—
170C22×C43—42no—
171C22×C43—81no—
172C22×C43—81no—
173C22×C43—81no—
174C22×C43—81no—
175C22×C43C2×#12011yescharacteristic
176C22×C43C22×SD1611yescharacteristic
177C22×C43C2×#13711yescharacteristic
178C4×C43—24no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—22no—
182C4×C43—42no—
183C4×C43—82no—
184C4×C43—81no—
185C4×C43#44814yes—
186Dic43—44no—
187Dic43—44no—
188#3502—431no—
189#3101—432no—
190#2536D4311yescharacteristic
191#1611—434no—
192#1599—434no—
193#1518—432no—
194#1461—431no—
195C2×C43—21no—
196C2×C43—21no—
197C2×C43—82no—
198C2×C43C2×#44811yescharacteristic
199C2×C43#302011yescharacteristic
200C2×C43#302511yescharacteristic
201Q82—862no—
202#557—864no—
203#557—862no—
204#544—434no—
205#544—861no—
206#533—432no—
207#533—862no—
208C2×C22⋊Q8—21no—
209#519—861no—
210C2×C4×Q8C2×D4311yescharacteristic
211C2×C4×D4C2×D4311yescharacteristic
212#483—434no—
213#476—862no—
214#461—862no—
215#450—434no—
216C4×SD16—864no—
217#431—432no—
218#398C2×D4312yes—
219#394C2×D4312yes—
220#388—22no—
221#382C2×D4311yescharacteristic
222#380—21no—
223#328—438no—
224#324—434no—
225C43#1822011yescharacteristic, complemented, Sylow
226C22×Q8C22⋊D4311yescharacteristic
227C22×D4C22×D4311yescharacteristic
228C23×C4—21no—
229C2×SD16—864no—
230C4⋊Q8—432no—
231C4⋊Q8—432no—
232C4⋊Q8—862no—
233C4⋊Q8—862no—
234C4⋊Q8—868no—
235C4⋊Q8—864no—
236#125—864no—
237#125—868no—
238#125—864no—
239#125—862no—
240C22⋊Q8—44no—
241C22⋊Q8—434no—
242C22⋊Q8—862no—
243C22⋊Q8—864no—
244C4×Q8—22no—
245C4×Q8—22no—
246C4×Q8—434no—
247C4×Q8—864no—
248C4×Q8—864no—
249C4×Q8—864no—
250C4×Q8—864no—
251C4×Q8—862no—
252C4×D4—22no—
253C4×D4—22no—
254#117—862no—
255#117—864no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4C22⋊D4311yescharacteristic
259C2×C4⋊C4C22×D4311yescharacteristic
260C2×C4⋊C4C22×D4312yes—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C42C22⋊D4312yes—
265C2×C42C22×D4311yescharacteristic
266#106—864no—
267C4⋊C8—862no—
268#103—864no—
269#102—864no—
270C22⋊C8—434no—
271C4×C8—862no—
272#95—22no—
273#95—21no—
274#95C22×D4312yes—
275C24—21no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×Q8—434no—
279C2×Q8—864no—
280C2×Q8—862no—
281C2×Q8#1062188314yescomplemented
282C2×D4—22no—
283C2×D4—42no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4C2×C22⋊D4312yes—
290C22×C4C2×C22⋊D4312yes—
291C22×C4C2×C22⋊D4311yescharacteristic
292C22×C4C2×C22⋊D4311yescharacteristic
293C22×C4C23×D4311yescharacteristic
294SD16—1728no—
295C2×C8—864no—
296C4⋊C4—22no—
297C4⋊C4—24no—
298C4⋊C4—22no—
299C4⋊C4—42no—
300C4⋊C4—44no—
301C4⋊C4—434no—
302C4⋊C4—864no—
303C4⋊C4—864no—
304C4⋊C4—864no—
305C4⋊C4—868no—
306C4⋊C4—862no—
307C4⋊C4—862no—
308C4⋊C4—864no—
309C4⋊C4—862no—
310C4⋊C4—864no—
311C22⋊C4—44no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—44no—
315C22⋊C4—864no—
316C42—22no—
317C42—22no—
318C42—868no—
319C42—864no—
320C42D4×D4312yes—
321C42D4×D4312yes—
322C23—22no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23C22×C22⋊D4311yescharacteristic
330Q8—28no—
331Q8—3444no—
332Q8—1724no—
333Q8—1724no—
334D4—24no—
335D4—42no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—84no—
349C2×C4—864no—
350C2×C4—864no—
351C2×C4#1306329311yescharacteristic
352C2×C4#1306329311yescharacteristic
353C2×C4#1306329312yes—
354C2×C4C2×#1062188314yes—
355C2×C4C2×#1062188312yes—
356C2×C4#1306335512yes—
357C2×C4C2×D4×D4312yes—
358C8—1724no—
359C22—21no—
360C22—21no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22C2×#1306329311yescharacteristic
369C22C22×#1062188311yescharacteristic
370C22C2×#1306335511yescharacteristic
371C4—21no—
372C4—21no—
373C4—22no—
374C4—24no—
375C4—42no—
376C4—82no—
377C4—81no—
378C4—1724no—
379C4—1724no—
380C4#1458303714yes—
381C2—21no—
382C2—21no—
383C2—82no—
384C2C2×#1458303711yescharacteristic
385C2#1914395811yescharacteristic
386C2#1914398611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2536C2
socleC22×C43C2×#120
prime radicalC22×D4×C43C23
hypercenter#2536D43
hypocenterC43#18220
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2536

Complements

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

NH ≅ G/Ntype
1. #19148405C2semidirect
3. #19133602C2semidirect
5. #19133158C2semidirect
6. #19132919C2semidirect
84. C2×Q8×C43SD16semidirect
225. C43#18220semidirect
281. C2×Q8#10621883semidirect

Maximal subgroups

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

subgroupindex
#191484052
#191446032
#191336022
#191335342
#191331582
#191329192
C43×#25362
#1822043