Finite Group Databasebeta

← #25069389

Subgroups — #25069389

Order 11008.

970 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 970 conjugacy classes of subgroups — too many to draw. Only its 167 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#19144725C212yesmaximal, complemented
3#19133585C214yesmaximal, complemented
4#19133551C214yesmaximal, complemented
5#19133106C212yesmaximal, complemented
6#19132936C211yesmaximal, characteristic
7C43×#2398C211yesmaximal, characteristic
8#14583608—24no—
9#14583606—22no—
10D4×Dic86—22no—
11#14583530—21no—
12#14583525C2214yes—
13#14583456C2212yes—
14C2×#13063304—22no—
15#14583374—21no—
16#14583229C2214yes—
17#14583184—22no—
18#14583109—22no—
19#14583055C2214yes—
20#14583004—24no—
21#14582956C2212yes—
22#14582635C2218yes—
23#14582623C2214yes—
24C2×C4×Q8×C43C2211yescharacteristic
25C2×C4×D4×C43C2211yescharacteristic
26C43×#400—21no—
27C43×#397C2212yes—
28C43×#394—21no—
29C43×#393C2212yes—
30C4×C22⋊C4×C43—22no—
31C43×#376C2211yescharacteristic
32C22×Dic86—22no—
33C2×#10621885—24no—
34#13063325D412yes—
35#13063325D412yes—
36#13063324—24no—
37#13063317—22no—
38#13063316—24no—
39#13063304—24no—
40#13063304—24no—
41#13063304—22no—
42#13063304—24no—
43#13063304C2314yes—
44#13063302—28no—
45#13063302—28no—
46C4×Dic86—22no—
47C4×Dic86D414yes—
48D4×Dic43—24no—
49D4×Dic43—24no—
50#13063284—22no—
51C2×C4⋊Dic43—22no—
52C2×Dic43⋊C4—24no—
53C2×C22⋊Dic43—24no—
54#13063256—24no—
55C4⋊(C43⋊C8)—22no—
56#13063249—24no—
57#13063248—24no—
58C22⋊(C43⋊C8)C2314yes—
59#13063236—22no—
60C22×Q8×C43C2311yescharacteristic
61C22×D4×C43D411yescharacteristic
62C23×C4×C43D412yes—
63C4×Q8×C43—22no—
64C4×Q8×C43—22no—
65C4×D4×C43—22no—
66C4×D4×C43—22no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C4⋊C4×C43C2311yescharacteristic
70C2×C22⋊C4×C43—22no—
71C2×C22⋊C4×C43—22no—
72C2×C22⋊C4×C43C2312yes—
73C2×C42×C43—21no—
74C2×C42×C43—21no—
75C2×C42×C43C2311yescharacteristic
76#95×C43—21no—
77#95×C43—22no—
78#95×C43—22no—
79#95×C43C2312yes—
80C24×C43C2×D412yes—
81C2×Q8×C43—22no—
82C2×Q8×C43—42no—
83C2×D4×C43—22no—
84C2×D4×C43—24no—
85C22×C4×C43—22no—
86C22×C4×C43—22no—
87C22×C4×C43—21no—
88C22×C4×C43—22no—
89C22×C4×C43—21no—
90C22×C4×C43—44no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D412yes—
94C22×C4×C43C2411yescharacteristic
95C22×Dic43—24no—
96C22×Dic43—24no—
97C2×Dic86—22no—
98C2×Dic86—24no—
99C2×Dic86—84no—
100C2×Dic86C2×D414yes—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—42no—
104C22⋊C4×C43—24no—
105C22⋊C4×C43—44no—
106C22⋊C4×C43—44no—
107C42×C43—42no—
108C42×C43—41no—
109C42×C43—41no—
110C42×C43C2×D412yes—
111C42×C43C2×D412yes—
112C22⋊Dic43—28no—
113C22⋊Dic43—24no—
114#10621885—48no—
115C4⋊Dic43—24no—
116C4⋊Dic43—22no—
117C4⋊Dic43—22no—
118C4⋊Dic43—22no—
119C4⋊Dic43C2×D414yes—
120Dic43⋊C4—28no—
121Dic43⋊C4—24no—
122Dic43⋊C4—24no—
123C4×Dic43—24no—
124C2×C43⋊C8—24no—
125C23×C43—22no—
126C23×C43—22no—
127C23×C43—42no—
128C23×C43—42no—
129C23×C43#13714yes—
130C23×C43C22×D411yescharacteristic
131Q8×C43—24no—
132Q8×C43—42no—
133D4×C43—28no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—44no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—41no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—82no—
149C2×C4×C43#12012yes—
150C2×C4×C43#12011yescharacteristic
151C2×C4×C43#12011yescharacteristic
152C2×C4×C43C22×D412yes—
153C2×Dic43—24no—
154C2×Dic43—24no—
155C2×Dic43—84no—
156C2×Dic43—84no—
157Dic86—44no—
158Dic86—44no—
159Dic86—84no—
160C43⋊C8—44no—
161#18181—431nomaximal, Sylow
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—24no—
165C22×C43—44no—
166C22×C43—42no—
167C22×C43—42no—
168C22×C43—82no—
169C22×C43C2×#12011yescharacteristic
170C22×C43C2×#13712yes—
171C4×C43—22no—
172C4×C43—21no—
173C4×C43—22no—
174C4×C43—42no—
175C4×C43—42no—
176C4×C43—82no—
177C4×C43—81no—
178C4×C43#45512yes—
179Dic43—44no—
180Dic43—44no—
181#3501—431no—
182#3113—432no—
183#2398D4311yescharacteristic
184#1608—434no—
185#1602—434no—
186#1506—432no—
187#1466—431no—
188C2×C43—22no—
189C2×C43—44no—
190C2×C43#300411yescharacteristic
191C2×C43C2×#45511yescharacteristic
192C2×C43#302511yescharacteristic
193#554—864no—
194#554—862no—
195D4×Q8—862no—
196#544—861no—
197#543—434no—
198#533—432no—
199C2×C22⋊Q8—862no—
200#518—861no—
201C2×C4×Q8C2×D4311yescharacteristic
202C2×C4×D4C2×D4311yescharacteristic
203#483—434no—
204#475—862no—
205#462—862no—
206#451—434no—
207#441—864no—
208#432—432no—
209#400—21no—
210#397C2×D4312yes—
211#394—21no—
212#393C2×D4312yes—
213C4×C22⋊C4—22no—
214#376C2×D4311yescharacteristic
215#328—438no—
216#323—434no—
217C43#1818111yescharacteristic, complemented, Sylow
218C22×Q8—862no—
219C22×Q8C22×D4311yescharacteristic
220C22×D4C22⋊D4311yescharacteristic
221C23×C4C22⋊D4312yes—
222C2×Q16—864no—
223C4⋊Q8—432no—
224C4⋊Q8—432no—
225C4⋊Q8—864no—
226#125—864no—
227#125—862no—
228C22⋊Q8—434no—
229C22⋊Q8—868no—
230C22⋊Q8—868no—
231C22⋊Q8—864no—
232C22⋊Q8—864no—
233C22⋊Q8—862no—
234C22⋊Q8—864no—
235C4×Q8—22no—
236C4×Q8—22no—
237C4×Q8—434no—
238C4×Q8—862no—
239C4×D4—22no—
240C4×D4—22no—
241C4×D4—864no—
242C4×D4—864no—
243#117—862no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—864no—
246C2×C4⋊C4—862no—
247C2×C4⋊C4C22⋊D4311yescharacteristic
248C2×C4⋊C4C22×D4311yescharacteristic
249C2×C22⋊C4—22no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—864no—
252C2×C22⋊C4C22×D4312yes—
253C2×C42—21no—
254C2×C42—21no—
255C2×C42C22×D4311yescharacteristic
256#106—864no—
257C4⋊C8—862no—
258#103—864no—
259#103—864no—
260C22⋊C8—434no—
261#97—862no—
262#95—21no—
263#95—22no—
264#95—22no—
265#95C22×D4312yes—
266C24C2×C22⋊D4312yes—
267C2×Q8—22no—
268C2×Q8—42no—
269C2×Q8—434no—
270C2×Q8—864no—
271C2×Q8—862no—
272C2×Q8—3444no—
273C2×D4—24no—
274C2×D4—22no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—44no—
281C22×C4—864no—
282C22×C4—864no—
283C22×C4C2×C22⋊D4311yescharacteristic
284C22×C4C2×C22⋊D4311yescharacteristic
285C22×C4C2×C22⋊D4312yes—
286C22×C4C23×D4311yescharacteristic
287Q16—1728no—
288C2×C8—864no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—42no—
292C4⋊C4—434no—
293C4⋊C4—864no—
294C4⋊C4—868no—
295C4⋊C4—864no—
296C4⋊C4—862no—
297C4⋊C4—862no—
298C4⋊C4—862no—
299C4⋊C4—864no—
300C22⋊C4—24no—
301C22⋊C4—44no—
302C22⋊C4—44no—
303C22⋊C4—868no—
304C22⋊C4—864no—
305C42—42no—
306C42—41no—
307C42—41no—
308C42—864no—
309C42D4×D4312yes—
310C42D4×D4312yes—
311C23—22no—
312C23—22no—
313C23—42no—
314C23—42no—
315C23#1306335514yes—
316C23C22×C22⋊D4311yescharacteristic
317Q8—24no—
318Q8—42no—
319Q8—3444no—
320Q8—1724no—
321Q8—1724no—
322D4—28no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—44no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—864no—
339C2×C4—864no—
340C2×C4—3444no—
341C2×C4—3444no—
342C2×C4#1306329311yescharacteristic
343C2×C4#1306329312yes—
344C2×C4#1306329311yescharacteristic
345C2×C4C2×D4×D4312yes—
346C8—1724no—
347C22—21no—
348C22—21no—
349C22—24no—
350C22—44no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22C2×#1306329311yescharacteristic
355C22C2×#1306335512yes—
356C4—22no—
357C4—22no—
358C4—21no—
359C4—42no—
360C4—42no—
361C4—82no—
362C4—81no—
363C4—1724no—
364C4—1724no—
365C4#1458307612yes—
366C2—22no—
367C2—44no—
368C2#1914382811yescharacteristic
369C2C2×#1458307611yescharacteristic
370C2#1914398611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2398C2
socleC22×C43C2×#120
prime radicalC22×D4×C43D4
hypercenter#2398D43
hypocenterC43#18181
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2398

Complements

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

NH ≅ G/Ntype
2. #19144725C2semidirect
3. #19133585C2semidirect
4. #19133551C2semidirect
5. #19133106C2semidirect
217. C43#18181semidirect

Maximal subgroups

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

subgroupindex
#191483982
#191447252
#191335852
#191335512
#191331062
#191329362
C43×#23982
#1818143