Finite Group Databasebeta

← #25081901

Subgroups — #25081901

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145545C211yesmaximal, characteristic
2#19144402C211yesmaximal, characteristic
3C2×#14583185C211yesmaximal, characteristic
4#19143675C211yesmaximal, characteristic
5#19134054C214yesmaximal, complemented
6#19133966C214yesmaximal, complemented
7#19133281C211yesmaximal, characteristic
8#19133253C211yesmaximal, characteristic
9C43×#1571C211yesmaximal, characteristic
10#14583456C2211yescharacteristic
11C2×#13063325C2211yescharacteristic
12C2×C4×Dic86C2211yescharacteristic
13#14583279C2212yes—
14#14583250C2212yes—
15#14583207—22no—
16#14583195C2212yes—
17#14583185—22no—
18#14583185C2212yes—
19#14583185C2214yes—
20#14583110—22no—
21#14583057—22no—
22C8×Dic86C2214yes—
23#14583023—22no—
24#14582952C2211yescharacteristic
25#14582949—22no—
26#14582941—21no—
27C2×#13063257—21no—
28#14582909—21no—
29C2×#13063250—21no—
30#14582647C2212yes—
31#14582644C2212yes—
32#14582644C2214yes—
33C43×#431C2211yescharacteristic
34C43×#423C2211yescharacteristic
35C2×C4⋊C8×C43C2211yescharacteristic
36C43×#335C2214yes—
37C22×Dic86—21no—
38C22×Dic86D411yescharacteristic
39C2×Dic172—24no—
40#13063325—21no—
41#13063325—21no—
42#13063325—21no—
43#13063325C2312yes—
44#13063325C2311yescharacteristic
45#13063325C2311yescharacteristic
46#13063317—21no—
47#13063304—21no—
48#13063304—21no—
49C4×Dic86—21no—
50C4×Dic86—21no—
51C4×Dic86—21no—
52C4×Dic86—21no—
53C4×Dic86D412yes—
54C4×Dic86C2312yes—
55#13063284—21no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43—21no—
58C2×C4⋊Dic43D411yescharacteristic
59C2×Dic43⋊C4—21no—
60C2×C4×Dic43—21no—
61#13063259—22no—
62#13063257—24no—
63#13063257—22no—
64C4⋊(C43⋊C8)C2312yes—
65Dic43⋊C8—24no—
66#13063250—24no—
67#13063250—22no—
68#13063250—22no—
69#13063250—24no—
70C22⋊(C43⋊C8)—21no—
71C4×C43⋊C8—21no—
72C8×Dic43—24no—
73C2×M16×C43—21no—
74C22×C8×C43—21no—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43—21no—
77C4⋊C8×C43—21no—
78C4⋊C8×C43D412yes—
79C4⋊C8×C43C2312yes—
80C4⋊C8×C43C2312yes—
81C22⋊C8×C43D412yes—
82C4×C8×C43C2312yes—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—41no—
89C2×Dic86—21no—
90C2×Dic86—22no—
91C2×Dic86—22no—
92C2×Dic86—21no—
93C2×Dic86—21no—
94C2×Dic86—41no—
95C2×Dic86—82no—
96C2×Dic86Q1614yescomplemented
97C2×Dic86C2×D412yes—
98M16×C43—42no—
99C2×C8×C43—22no—
100C2×C8×C43—22no—
101C2×C8×C43—42no—
102C2×C8×C43C2×D414yes—
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43#4111yescharacteristic
106C42×C43C2411yescharacteristic
107C22⋊Dic43—41no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43—22no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—22no—
114C4⋊Dic43—21no—
115C4⋊Dic43—41no—
116C4⋊Dic43—41no—
117C4⋊Dic43C2×D412yes—
118Dic43⋊C4—22no—
119Dic43⋊C4—22no—
120Dic43⋊C4—41no—
121Dic43⋊C4—41no—
122C4×Dic43—22no—
123C4×Dic43—22no—
124C4×Dic43—41no—
125C2×C43⋊C8—22no—
126Dic172—84no—
127C23×C43#12111yescharacteristic
128C2×C4×C43—22no—
129C2×C4×C43—41no—
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43C2×Q1612yes—
134C2×C4×C43#13512yes—
135C2×C4×C43C22×D411yescharacteristic
136C2×C4×C43C22×D411yescharacteristic
137C2×C4×C43C2×#4111yescharacteristic
138C2×Dic43—22no—
139C2×Dic43—24no—
140C2×Dic43—22no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—42no—
144C2×Dic43—81no—
145C2×Dic43—82no—
146Dic86—22no—
147Dic86—24no—
148Dic86—42no—
149Dic86—44no—
150Dic86—82no—
151Dic86—81no—
152Dic86C2×Q1614yes—
153C8×C43—24no—
154C8×C43—42no—
155C8×C43—42no—
156C43⋊C8—42no—
157#19399—431nomaximal, Sylow
158C22×C43—21no—
159C22×C43—21no—
160C22×C43#46712yes—
161C22×C43C2×#12111yescharacteristic
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43#46712yes—
166C4×C43C22×Q1611yescharacteristic
167C4×C43C2×#13511yescharacteristic
168C4×C43#57712yes—
169Dic43—24no—
170Dic43—42no—
171Dic43—82no—
172Dic43—81no—
173Dic43—81no—
174#3209—431no—
175#3078—431no—
176C2×#475—431no—
177#2982—431no—
178#1684—434no—
179#1670—434no—
180#1571D4311yescharacteristic
181#1549—431no—
182#1542—431no—
183C2×C43—22no—
184C2×C43#304311yescharacteristic
185C2×C43C2×#46711yescharacteristic
186C2×C43#306911yescharacteristic
187#533—431no—
188C2×C4⋊Q8—431no—
189C2×C4×Q8—431no—
190#494—432no—
191#487—432no—
192#479—862no—
193#477—432no—
194#475—434no—
195#475—432no—
196#475—862no—
197#462—862no—
198#451—862no—
199C8×Q8—434no—
200C8×Q8—862no—
201#431—431no—
202#431—862no—
203#431C2×D4311yescharacteristic
204#428—861no—
205C2×#106—861no—
206#423C2×D4311yescharacteristic
207C2×C4⋊C8C2×D4311yescharacteristic
208#419—861no—
209C2×#103—861no—
210#335C2×D4314yes—
211#333—432no—
212#332—432no—
213#332—434no—
214C43#1939911yescharacteristic, complemented, Sylow
215C22×Q8—431no—
216C22×Q8—861no—
217C2×Q16—864no—
218C2×M16—21no—
219C22×C8—21no—
220C4⋊Q8—432no—
221C4⋊Q8—431no—
222C4⋊Q8—431no—
223C4⋊Q8—861no—
224C4⋊Q8—861no—
225C4⋊Q8—861no—
226#125—861no—
227C22⋊Q8—861no—
228C22⋊Q8—861no—
229C4×Q8—432no—
230C4×Q8—432no—
231C4×Q8—861no—
232C4×Q8—861no—
233C4×Q8—861no—
234C4×Q8—861no—
235#117—861no—
236C2×C4⋊C4—431no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C42—861no—
241C2×C42C22×D4311yescharacteristic
242#107—862no—
243#106—864no—
244#106—862no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—432no—
248C4⋊C8—864no—
249C4⋊C8D17212yes—
250C4⋊C8C22×D4312yes—
251C4⋊C8C22×D4312yes—
252#103—864no—
253#103—862no—
254#103—862no—
255#103—864no—
256C22⋊C8—861no—
257C22⋊C8D17212yes—
258C4×C8—864no—
259C4×C8—861no—
260C4×C8C22×D4312yes—
261C2×Q8—434no—
262C2×Q8—432no—
263C2×Q8—861no—
264C2×Q8—862no—
265C2×Q8—862no—
266C2×Q8—861no—
267C2×Q8—861no—
268C2×Q8—3442no—
269C2×Q8—1721no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—1721no—
273C22×C4C2×D17211yescharacteristic
274C22×C4D4×D4311yescharacteristic
275C22×C4#1062190211yescharacteristic
276Q16—3444no—
277M16—42no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—42no—
281C2×C8—862no—
282C2×C8C2×D17214yes—
283C4⋊C4—432no—
284C4⋊C4—861no—
285C4⋊C4—862no—
286C4⋊C4—862no—
287C4⋊C4—862no—
288C4⋊C4—861no—
289C4⋊C4—861no—
290C4⋊C4—861no—
291C4⋊C4—862no—
292C4⋊C4—861no—
293C4⋊C4—1721no—
294C4⋊C4—1721no—
295C4⋊C4—1721no—
296C4⋊C4—1721no—
297C22⋊C4—1721no—
298C42—862no—
299C42—862no—
300C42—1721no—
301C42C2×D17211yescharacteristic
302C42D4×D4311yescharacteristic
303C42#1062190211yescharacteristic
304C42C23×D4311yescharacteristic
305C23#1306330011yescharacteristic
306Q8—434no—
307Q8—864no—
308Q8—862no—
309Q8—3441no—
310Q8—3442no—
311Q8—1722no—
312Q8—1724no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—862no—
316C2×C4—864no—
317C2×C4—862no—
318C2×C4—3442no—
319C2×C4—3441no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1722no—
323C2×C4#1306330011yescharacteristic
324C2×C4#1306330011yescharacteristic
325C2×C4#1306330011yescharacteristic
326C2×C4Q16×D4312yes—
327C2×C4#1306334412yes—
328C2×C4C2×D4×D4311yescharacteristic
329C2×C4C22×D17211yescharacteristic
330C2×C4C2×#1062190211yescharacteristic
331C8—24no—
332C8—42no—
333C8—42no—
334C8—1722no—
335C22—21no—
336C22—21no—
337C22#1458314112yes—
338C22C2×#1306330011yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—864no—
343C4—3441no—
344C4—3442no—
345C4—3441no—
346C4—1722no—
347C4#1458314112yes—
348C4C2×Q16×D4311yescharacteristic
349C4C2×#1306334411yescharacteristic
350C4#1458371112yes—
351C2—22no—
352C2#1914411711yescharacteristic
353C2C2×#1458314111yescharacteristic
354C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1571C2
socleC22×C43C2×#121
prime radicalC23×C43#121
hypercenter#1571D43
hypocenterC43#19399
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
5. #19134054C2semidirect
6. #19133966C2semidirect
96. C2×Dic86Q16semidirect
214. C43#19399semidirect

Maximal subgroups

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

subgroupindex
#191455452
#191444022
C2×#145831852
#191436752
#191340542
#191339662
#191332812
#191332532
C43×#15712
#1939943