Finite Group Databasebeta

← #25069665

Subgroups — #25069665

Order 11008.

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

normal subgroups only

This group has 974 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#19148398C211yesmaximal, characteristic
2#19144635C212yesmaximal, complemented
3#19139949C211yesmaximal, characteristic
4#19133622C214yesmaximal, complemented
5#19133554C214yesmaximal, complemented
6#19133160C212yesmaximal, complemented
7C43×#1460C211yesmaximal, characteristic
8#14583608—24no—
9#14583606—22no—
10D4×Dic86—22no—
11#14583530—21no—
12#14583525C2214yes—
13#14583456C2212yes—
14C2×#13063304—22no—
15#14583374—21no—
16C2×C4×Dic86C2211yescharacteristic
17#14583235C2214yes—
18#14583195—22no—
19#14583110—22no—
20#14583057C2214yes—
21C4×Dic172—24no—
22#14582835C2212yes—
23#14582811C2212yes—
24#14582802—21no—
25#14582795—21no—
26#14582772—22no—
27#14582765C2211yescharacteristic
28#14582637C2218yes—
29C2×C4×D4×C43C2211yescharacteristic
30C43×#431C2212yes—
31C43×#323C2214yes—
32C22×Dic86—22no—
33C22×Dic86C2311yescharacteristic
34C2×Dic172—24no—
35#13063325D412yes—
36#13063325D412yes—
37#13063324—24no—
38#13063317—22no—
39#13063316—24no—
40#13063304—24no—
41#13063304—24no—
42#13063304—22no—
43#13063304—24no—
44#13063304C2314yes—
45#13063302—28no—
46#13063302—28no—
47C4×Dic86—22no—
48C4×Dic86—22no—
49C4×Dic86—22no—
50C4×Dic86D414yes—
51D4×Dic43—24no—
52D4×Dic43—24no—
53#13063284—22no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43C2311yescharacteristic
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—21no—
59C2×Dic43⋊C4—22no—
60C2×C22⋊Dic43—24no—
61C2×C22⋊Dic43—22no—
62C2×C22⋊Dic43—22no—
63C2×C4×Dic43—21no—
64#13063259—24no—
65#13063250—24no—
66#13063250—24no—
67C43⋊#95—22no—
68C43⋊#95—21no—
69C43⋊#95C2312yes—
70C22×D4×C43D411yescharacteristic
71C23×C4×C43D412yes—
72C4×D4×C43—22no—
73C4×D4×C43—22no—
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C22⋊C4×C43C2312yes—
76C2×C42×C43C2311yescharacteristic
77C4⋊C8×C43—22no—
78C22⋊C8×C43C2314yes—
79C4×C8×C43—22no—
80C24×C43C2×D412yes—
81C2×D4×C43—22no—
82C2×D4×C43—22no—
83C2×D4×C43Q1614yescomplemented
84C22×C4×C43—22no—
85C22×C4×C43—22no—
86C22×C4×C43—82no—
87C22×C4×C43C2×D412yes—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2411yescharacteristic
91C22×Dic43—24no—
92C22×Dic43—24no—
93C22×Dic43—21no—
94C22×Dic43—22no—
95C22×Dic43—21no—
96C2×Dic86—22no—
97C2×Dic86—22no—
98C2×Dic86—24no—
99C2×Dic86—42no—
100C2×Dic86—84no—
101C2×Dic86C2×D414yes—
102C2×C8×C43—24no—
103C4⋊C4×C43—22no—
104C22⋊C4×C43—24no—
105C42×C43C2×D412yes—
106C42×C43C2×D412yes—
107C22⋊Dic43—28no—
108C22⋊Dic43—24no—
109C22⋊Dic43—44no—
110C22⋊Dic43—82no—
111C4⋊Dic43—24no—
112C4⋊Dic43—22no—
113C4⋊Dic43—22no—
114C4⋊Dic43—22no—
115C4⋊Dic43—22no—
116C4⋊Dic43—42no—
117C4⋊Dic43C2×D414yes—
118Dic43⋊C4—28no—
119Dic43⋊C4—24no—
120Dic43⋊C4—24no—
121Dic43⋊C4—41no—
122Dic43⋊C4—41no—
123Dic43⋊C4—82no—
124C4×Dic43—24no—
125C4×Dic43—42no—
126Dic172—48no—
127C23×C43—22no—
128C23×C43—22no—
129C23×C43—42no—
130C23×C43—42no—
131C23×C43C2×Q1614yes—
132C23×C43C22×D411yescharacteristic
133D4×C43—28no—
134C2×C4×C43—22no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—44no—
138C2×C4×C43—42no—
139C2×C4×C43—82no—
140C2×C4×C43#12011yescharacteristic
141C2×C4×C43#12011yescharacteristic
142C2×C4×C43#12012yes—
143C2×C4×C43C2×Q1612yes—
144C2×C4×C43#13712yes—
145C2×C4×C43C22×D412yes—
146C2×Dic43—22no—
147C2×Dic43—24no—
148C2×Dic43—24no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—42no—
153C2×Dic43—42no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—42no—
157C2×Dic43—84no—
158C2×Dic43—84no—
159Dic86—24no—
160Dic86—42no—
161Dic86—44no—
162Dic86—44no—
163Dic86—84no—
164C8×C43—44no—
165#18213—431nomaximal, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—24no—
169C22×C43—44no—
170C22×C43—42no—
171C22×C43—42no—
172C22×C43—82no—
173C22×C43C2×#12011yescharacteristic
174C22×C43C22×Q1611yescharacteristic
175C22×C43C2×#13711yescharacteristic
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—22no—
179C4×C43—42no—
180C4×C43#45114yes—
181Dic43—44no—
182Dic43—42no—
183Dic43—44no—
184Dic43—82no—
185Dic43—81no—
186#3501—431no—
187#3104—432no—
188#2580—431no—
189#1614—434no—
190#1602—434no—
191#1518—432no—
192#1460D4311yescharacteristic
193C2×C43—21no—
194C2×C43—21no—
195C2×C43—44no—
196C2×C43C2×#45111yescharacteristic
197C2×C43#301911yescharacteristic
198C2×C43#302511yescharacteristic
199#554—864no—
200#554—862no—
201D4×Q8—862no—
202#544—861no—
203#543—434no—
204#533—432no—
205C2×C22⋊Q8—862no—
206#518—861no—
207C2×C4×Q8—431no—
208C2×C4×D4C2×D4311yescharacteristic
209#484—434no—
210#477—862no—
211#462—862no—
212#451—434no—
213C4×Q16—864no—
214#431C2×D4312yes—
215#399—432no—
216#393—432no—
217#390—861no—
218#389—861no—
219#385—862no—
220#382—431no—
221#328—438no—
222#323C2×D4314yes—
223C43#1821311yescharacteristic, complemented, Sylow
224C22×Q8—431no—
225C22×Q8—862no—
226C22×D4D17211yescharacteristic
227C23×C4D17212yes—
228C2×Q16—864no—
229C4⋊Q8—432no—
230C4⋊Q8—432no—
231C4⋊Q8—864no—
232#125—864no—
233#125—862no—
234C22⋊Q8—434no—
235C22⋊Q8—868no—
236C22⋊Q8—868no—
237C22⋊Q8—864no—
238C22⋊Q8—864no—
239C22⋊Q8—862no—
240C22⋊Q8—864no—
241C4×Q8—434no—
242C4×Q8—862no—
243C4×Q8—862no—
244C4×Q8—862no—
245C4×D4—22no—
246C4×D4—22no—
247C4×D4—864no—
248C4×D4—864no—
249#117—862no—
250C2×C4⋊C4—431no—
251C2×C4⋊C4—864no—
252C2×C4⋊C4—862no—
253C2×C4⋊C4—862no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4D17211yescharacteristic
257C2×C22⋊C4—864no—
258C2×C22⋊C4—862no—
259C2×C22⋊C4—862no—
260C2×C22⋊C4C22×D4312yes—
261C2×C42—861no—
262C2×C42C22×D4311yescharacteristic
263#107—864no—
264C4⋊C8—22no—
265#103—864no—
266#103—864no—
267C22⋊C8C22×D4314yes—
268C4×C8—22no—
269#95—432no—
270#95—861no—
271#95—862no—
272C24C2×D17212yes—
273C2×Q8—434no—
274C2×Q8—864no—
275C2×Q8—862no—
276C2×Q8—862no—
277C2×Q8—3444no—
278C2×Q8—1722no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4Dic17214yescomplemented
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—82no—
285C22×C4—864no—
286C22×C4—864no—
287C22×C4—861no—
288C22×C4—862no—
289C22×C4—861no—
290C22×C4C2×D17212yes—
291C22×C4C2×D17211yescharacteristic
292C22×C4C2×D17211yescharacteristic
293C22×C4C23×D4311yescharacteristic
294Q16—1728no—
295C2×C8—24no—
296C4⋊C4—22no—
297C4⋊C4—434no—
298C4⋊C4—864no—
299C4⋊C4—868no—
300C4⋊C4—864no—
301C4⋊C4—862no—
302C4⋊C4—862no—
303C4⋊C4—862no—
304C4⋊C4—864no—
305C4⋊C4—862no—
306C4⋊C4—3442no—
307C4⋊C4—1721no—
308C4⋊C4—1721no—
309C4⋊C4—1722no—
310C22⋊C4—24no—
311C22⋊C4—868no—
312C22⋊C4—864no—
313C22⋊C4—3442no—
314C22⋊C4—1724no—
315C42—864no—
316C42—1722no—
317C42D4×D4312yes—
318C42D4×D4312yes—
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23C2×Dic17214yes—
324C23C22×D17211yescharacteristic
325Q8—864no—
326Q8—3444no—
327Q8—1724no—
328Q8—1724no—
329Q8—1722no—
330D4—28no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—44no—
335C2×C4—42no—
336C2×C4—82no—
337C2×C4—862no—
338C2×C4—864no—
339C2×C4—864no—
340C2×C4—3444no—
341C2×C4—3444no—
342C2×C4—1721no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1722no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4#1306329511yescharacteristic
351C2×C4#1306329511yescharacteristic
352C2×C4#1306329512yes—
353C2×C4C2×Dic17212yes—
354C2×C4#1306335812yes—
355C2×C4C2×D4×D4312yes—
356C8—44no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—44no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22C2×#1306329511yescharacteristic
365C22C22×Dic17211yescharacteristic
366C22C2×#1306335811yescharacteristic
367C4—21no—
368C4—21no—
369C4—22no—
370C4—42no—
371C4—3442no—
372C4—3441no—
373C4—1724no—
374C4—1724no—
375C4—1722no—
376C4#1458305714yes—
377C2—21no—
378C2—21no—
379C2—44no—
380C2C2×#1458305711yescharacteristic
381C2#1914395511yescharacteristic
382C2#1914398911yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1460C2
socleC22×C43C2×#120
prime radicalC22×D4×C43D4
hypercenter#1460D43
hypocenterC43#18213
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #19144635C2semidirect
4. #19133622C2semidirect
5. #19133554C2semidirect
6. #19133160C2semidirect
83. C2×D4×C43Q16semidirect
223. C43#18213semidirect
281. C2×D4Dic172semidirect

Maximal subgroups

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

subgroupindex
#191483982
#191446352
#191399492
#191336222
#191335542
#191331602
C43×#14602
#1821343