Finite Group Databasebeta

← #25081897

Subgroups — #25081897

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#19145543C211yesmaximal, characteristic
2#19144400C211yesmaximal, characteristic
3#19143676C211yesmaximal, characteristic
4#19134051C214yesmaximal, complemented
5#19133963C214yesmaximal, complemented
6#19133369C211yesmaximal, characteristic
7#19133280C211yesmaximal, characteristic
8#19133253C211yesmaximal, characteristic
9C2×C43×#475C211yesmaximal, characteristic
10#14583456C2211yescharacteristic
11#14583278C2212yes—
12#14583249C2212yes—
13#14583206—22no—
14#14583194C2212yes—
15#14583184C2212yes—
16#14583106—22no—
17#14583055—22no—
18Q8×C43⋊C8—22no—
19Q8×C43⋊C8C2214yes—
20#14582952—22no—
21#14582952C2211yescharacteristic
22#14582952C2211yescharacteristic
23#14582939—21no—
24#14582923C2211yescharacteristic
25#14582908—21no—
26#14582651C2214yes—
27#14582647C2212yes—
28#14582645C2214yes—
29#14582644C2212yes—
30C2×C4⋊Q8×C43C2211yescharacteristic
31C2×C4×Q8×C43C2211yescharacteristic
32C43×#475—22no—
33C43×#475C2214yes—
34C2×#106×C43—21no—
35C2×C4⋊C8×C43C2211yescharacteristic
36C2×#103×C43—21no—
37C2×#10621885—24no—
38C2×#10621877—21no—
39#13063325C2311yescharacteristic
40#13063325C2311yescharacteristic
41#13063317—21no—
42#13063304—21no—
43#13063304—21no—
44C4×Dic86—21no—
45C4×Dic86—21no—
46#13063284—21no—
47#13063258—22no—
48#13063256—22no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—24no—
51C4⋊(C43⋊C8)D412yes—
52C4⋊(C43⋊C8)C2312yes—
53C4⋊(C43⋊C8)C2312yes—
54#13063249—22no—
55#13063249—22no—
56#13063249—24no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)D412yes—
59C4×C43⋊C8—21no—
60C4×C43⋊C8—24no—
61C4×C43⋊C8C2312yes—
62C22×Q8×C43—21no—
63C22×Q8×C43D411yescharacteristic
64C22×C8×C43—21no—
65C4⋊Q8×C43—21no—
66C4⋊Q8×C43—21no—
67C4⋊Q8×C43—21no—
68C4⋊Q8×C43C2312yes—
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71C4×Q8×C43D412yes—
72C4×Q8×C43C2312yes—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43D411yescharacteristic
77C2×C42×C43—21no—
78C2×C42×C43C2311yescharacteristic
79#106×C43—24no—
80C4⋊C8×C43—21no—
81C4⋊C8×C43C2312yes—
82#103×C43—24no—
83C2×Q8×C43—21no—
84C2×Q8×C43—22no—
85C2×Q8×C43—22no—
86C2×Q8×C43—41no—
87C2×Q8×C43—82no—
88C2×Q8×C43Q1614yescomplemented
89C2×Q8×C43C2×D412yes—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—41no—
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43#4111yescharacteristic
96C2×Dic86—21no—
97C2×Dic86—21no—
98C2×C8×C43—22no—
99C2×C8×C43—42no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43C2×D412yes—
108C42×C43—22no—
109C42×C43—22no—
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C42×C43C2411yescharacteristic
114C22⋊Dic43—41no—
115#10621885—84no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120Dic43⋊C4—41no—
121Dic43⋊C4—41no—
122C4×Dic43—41no—
123#10621877—42no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8C2×D414yes—
127C23×C43#12111yescharacteristic
128Q8×C43—22no—
129Q8×C43—24no—
130Q8×C43—44no—
131Q8×C43—82no—
132Q8×C43C2×Q1614yes—
133C2×C4×C43—22no—
134C2×C4×C43—24no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—41no—
138C2×C4×C43—42no—
139C2×C4×C43—81no—
140C2×C4×C43—82no—
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43C2×Q1612yes—
145C2×C4×C43#13512yes—
146C2×C4×C43C22×D411yescharacteristic
147C2×C4×C43C22×D411yescharacteristic
148C2×C4×C43C2×#4111yescharacteristic
149C2×Dic43—41no—
150C2×Dic43—41no—
151Dic86—42no—
152Dic86—81no—
153C8×C43—42no—
154C43⋊C8—24no—
155C43⋊C8—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—24no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—42no—
167C4×C43—82no—
168C4×C43#46712yes—
169C4×C43C22×Q1611yescharacteristic
170C4×C43C2×#13511yescharacteristic
171C4×C43#57712yes—
172Dic43—81no—
173Dic43—81no—
174#3209—431no—
175#3078—431no—
176C2×#475D4311yescharacteristic
177#2982—431no—
178#1684—434no—
179#1670—434no—
180#1571—431no—
181#1549—431no—
182#1542—431no—
183C2×C43—22no—
184C2×C43#304311yescharacteristic
185C2×C43C2×#46711yescharacteristic
186C2×C43#306911yescharacteristic
187#533—431no—
188C2×C4⋊Q8C2×D4311yescharacteristic
189C2×C4×Q8C2×D4311yescharacteristic
190#494—432no—
191#487—432no—
192#479—862no—
193#477—432no—
194#475—22no—
195#475—432no—
196#475C2×D4314yes—
197#462—862no—
198#451—862no—
199C8×Q8—434no—
200C8×Q8—862no—
201#431—431no—
202#431—431no—
203#431—862no—
204#428—861no—
205C2×#106—21no—
206#423—431no—
207C2×C4⋊C8C2×D4311yescharacteristic
208#419—861no—
209C2×#103—21no—
210#335—434no—
211#333—432no—
212#332—434no—
213#332—432no—
214C43#1939911yescharacteristic, complemented, Sylow
215C22×Q8—21no—
216C22×Q8C22⋊D4311yescharacteristic
217C2×Q16—864no—
218C2×M16—861no—
219C22×C8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—431no—
224C4⋊Q8—431no—
225C4⋊Q8C22×D4312yes—
226#125—861no—
227C22⋊Q8—861no—
228C22⋊Q8—861no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—861no—
232C4×Q8—861no—
233C4×Q8C22⋊D4312yes—
234C4×Q8C22×D4312yes—
235#117—861no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4C22⋊D4311yescharacteristic
240C2×C42—21no—
241C2×C42C22×D4311yescharacteristic
242#107—862no—
243#106—24no—
244#106—862no—
245C4⋊C8—21no—
246C4⋊C8—432no—
247C4⋊C8—432no—
248C4⋊C8—432no—
249C4⋊C8—864no—
250C4⋊C8—861no—
251C4⋊C8C22×D4312yes—
252#103—24no—
253#103—864no—
254#103—862no—
255#103—862no—
256C22⋊C8—432no—
257C22⋊C8—861no—
258C4×C8—432no—
259C4×C8—864no—
260C4×C8—861no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—82no—
266C2×Q8—861no—
267C2×Q8—861no—
268C2×Q8#1062188514yescomplemented
269C2×Q8C2×C22⋊D4312yes—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4D4×D4311yescharacteristic
274C22×C4#1062190011yescharacteristic
275C22×C4C2×C22⋊D4311yescharacteristic
276Q16—3444no—
277M16—1722no—
278C2×C8—22no—
279C2×C8—42no—
280C2×C8—434no—
281C2×C8—862no—
282C2×C8—862no—
283C4⋊C4—22no—
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—861no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4—1721no—
295C4⋊C4—1721no—
296C4⋊C4C2×C22⋊D4312yes—
297C22⋊C4—1721no—
298C42—22no—
299C42—22no—
300C42—1721no—
301C42D4×D4311yescharacteristic
302C42#1062190011yescharacteristic
303C42C2×C22⋊D4311yescharacteristic
304C42C23×D4311yescharacteristic
305C23#1306329711yescharacteristic
306Q8—24no—
307Q8—22no—
308Q8—44no—
309Q8—82no—
310Q8—3441no—
311Q8—1722no—
312Q8C2×#1062188514yes—
313C2×C4—22no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—81no—
320C2×C4—82no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4#1306329711yescharacteristic
324C2×C4#1306329711yescharacteristic
325C2×C4#1306329711yescharacteristic
326C2×C4C2×#1062188512yes—
327C2×C4#1306334512yes—
328C2×C4C2×D4×D4311yescharacteristic
329C2×C4C22×C22⋊D4311yescharacteristic
330C2×C4C2×#1062190011yescharacteristic
331C8—42no—
332C8—864no—
333C8—1722no—
334C8—1722no—
335C22—21no—
336C22—21no—
337C22#1458313812yes—
338C22C2×#1306329711yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—24no—
343C4—42no—
344C4—82no—
345C4—3441no—
346C4—3441no—
347C4#1458313812yes—
348C4C22×#1062188511yescharacteristic
349C4C2×#1306334511yescharacteristic
350C4#1458370512yes—
351C2—22no—
352C2#1914411311yescharacteristic
353C2C2×#1458313811yescharacteristic
354C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#475C2
socleC22×C43C2×#121
prime radicalC23×C43#121
hypercenterC2×#475D43
hypocenterC43#19399
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
4. #19134051C2semidirect
5. #19133963C2semidirect
88. C2×Q8×C43Q16semidirect
214. C43#19399semidirect
268. C2×Q8#10621885semidirect

Maximal subgroups

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

subgroupindex
#191455432
#191444002
#191436762
#191340512
#191339632
#191333692
#191332802
#191332532
C2×C43×#4752
#1939943