Finite Group Databasebeta

← #25079731

Subgroups — #25079731

Order 11008.

638 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145912C212yesmaximal
2#19145109C211yesmaximal, characteristic, complemented
3#19143308C211yesmaximal, characteristic
4#19134095C214yesmaximal, complemented
5#19133995C212yesmaximal, complemented
6#19133985C212yesmaximal, complemented
7#19133283C212yesmaximal, complemented
8C2×C43×#335C211yesmaximal, characteristic, complemented
9C2×#13063331—21no—
10#14583456C2212yes—
11#14583449C2211yescharacteristic
12#14583304C2211yescharacteristic
13#14583304C2211yescharacteristic
14#14583301—21no—
15#14583301—21no—
16#14583297C2212yes—
17#14583190C2214yes—
18#14583185—22no—
19#14583128—24no—
20#14583105C2214yes—
21#14583100—22no—
22#14582978—21no—
23#14582978C2212yes—
24C8×D172—21no—
25C8×D172C2212yes—
26#14582937—21no—
27#14582937—21no—
28#14582923C2211yescharacteristic
29#14582865—21no—
30#14582647C2214yes—
31#14582646C2214yes—
32C2×C4⋊C8×C43C2212yes—
33C2×C4×C8×C43C2211yescharacteristic
34C43×#335C2212yes—
35C43×#335C2212yes—
36C2×#10621898—21no—
37C2×#10621873—24no—
38#13063331—44no—
39C2×#10621877—21no—
40C2×#10621872—22no—
41C2×C8×D43—22no—
42#13063325D411yescharacteristic
43#13063325C2312yes—
44#13063325C2312yes—
45#13063322D411yescharacteristic
46#13063317—22no—
47#13063313—21no—
48#13063304—22no—
49#13063304—22no—
50#13063299—21no—
51#13063299D412yes—
52C4×Dic86—22no—
53C4×Dic86—22no—
54C4×D172—21no—
55C4×D172C2312yes—
56#13063284—22no—
57#13063259—21no—
58#13063259—21no—
59#13063259—21no—
60#13063259—21no—
61#13063257—22no—
62#13063257—22no—
63#13063257—24no—
64C4⋊(C43⋊C8)—21no—
65C4⋊(C43⋊C8)C2312yes—
66#13063250—24no—
67#13063247—24no—
68(C2×D43)⋊C8—22no—
69(C2×D43)⋊C8—22no—
70C22×C8×C43—22no—
71C22×C8×C43D411yescharacteristic
72C22×C8×C43D411yescharacteristic
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43—22no—
75C4⋊C8×C43C2314yes—
76C4×C8×C43D411yescharacteristic
77C4×C8×C43D411yescharacteristic
78C4×C8×C43C2311yescharacteristic
79C4×C8×C43C2311yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C2×C22⋊D43—22no—
84#10621898—42no—
85#10621898—42no—
86C2×D172—21no—
87C2×D172—21no—
88C2×D172C2×D412yes—
89C2×C4×D43—22no—
90C2×Dic86—21no—
91C2×Dic86—22no—
92C2×Dic86—22no—
93C2×C8×C43—22no—
94C2×C8×C43—24no—
95C2×C8×C43—82no—
96C2×C8×C43SD1614yescomplemented
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43#4111yescharacteristic
104C42×C43C2411yescharacteristic
105C22⋊Dic43—42no—
106(C2×D43)⋊C4—22no—
107(C2×D43)⋊C4—22no—
108C4⋊Dic43—21no—
109C4⋊Dic43—22no—
110C4⋊Dic43—22no—
111C4⋊Dic43—22no—
112C4⋊Dic43—22no—
113C4⋊Dic43C2×D412yes—
114Dic43⋊C4—42no—
115Dic43⋊C4—42no—
116C4×Dic43—42no—
117#10621877—42no—
118C2×C43⋊C8—22no—
119#10621873—84no—
120#10621872—44no—
121C8×D43—44no—
122C23×C43#12111yescharacteristic
123C22×D43—22no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—41no—
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12111yescharacteristic
130C2×C4×C43C2×SD1612yes—
131C2×C4×C43#13712yes—
132C2×C4×C43C22×D411yescharacteristic
133C2×C4×C43C22×D411yescharacteristic
134C2×C4×C43C2×#4111yescharacteristic
135C22⋊D43—44no—
136C2×Dic43—22no—
137C2×Dic43—42no—
138C2×Dic43—42no—
139D172—22no—
140D172—22no—
141D172—42no—
142D172—42no—
143C4×D43—42no—
144C4×D43—42no—
145Dic86—42no—
146Dic86—42no—
147Dic86—42no—
148Dic86—82no—
149C8×C43—21no—
150C8×C43—21no—
151C8×C43—44no—
152C8×C43C2×SD1612yes—
153C8×C43C2×SD1612yes—
154C43⋊C8—42no—
155#19195—431nomaximal, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43#46112yes—
159C22×C43C2×#12111yescharacteristic
160C2×D43—42no—
161C2×D43—42no—
162C2×D43—42no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43#46112yes—
167C4×C43C22×SD1611yescharacteristic
168C4×C43C2×#13711yescharacteristic
169C4×C43#57611yescharacteristic
170C4×C43#57811yescharacteristic
171Dic43—42no—
172Dic43—82no—
173Dic43—82no—
174#3246—432no—
175#3160—431no—
176#2931—431no—
177#1691—434no—
178#1675—432no—
179#1673—432no—
180C2×#335D4311yescharacteristic, complemented
181#1550—432no—
182C2×C43—22no—
183C2×C43C2×#46111yescharacteristic
184C2×C43#306111yescharacteristic
185C2×C43#306711yescharacteristic
186D43—82no—
187C2×#131—861no—
188#533—432no—
189#532—431no—
190#500—431no—
191#500—431no—
192#499—861no—
193#499—861no—
194#498—432no—
195#476—434no—
196#475—862no—
197#465—864no—
198#461—434no—
199#460—862no—
200#436—432no—
201#436—861no—
202C8×D4—432no—
203C8×D4—861no—
204#427—861no—
205#427—861no—
206#423—431no—
207C2×C4⋊C8C2×D4312yes—
208#408—861no—
209C2×C4×C8C2×D4311yescharacteristic
210#335C2×D4312yes—
211#335C2×D4312yes—
212#333—434no—
213#332—434no—
214C43#1919511yescharacteristic, complemented, Sylow
215C2×#41—861no—
216C2×SD16—864no—
217#131—1724no—
218C2×M16—861no—
219C2×M16—862no—
220C22×C8—22no—
221C22×C8—862no—
222C22×C8D17211yescharacteristic
223C22×C8D17211yescharacteristic
224C4⋊Q8—431no—
225C4⋊Q8—432no—
226C4⋊Q8—432no—
227#127—431no—
228#125—862no—
229#124—861no—
230C22⋊Q8—862no—
231C22⋊Q8—862no—
232#121—432no—
233#121—861no—
234C4×Q8—862no—
235C4×Q8—862no—
236C4×D4—432no—
237C4×D4—861no—
238#117—862no—
239C2×C42C22×D4311yescharacteristic
240#107—861no—
241#107—861no—
242#107—861no—
243#107—861no—
244#106—864no—
245#106—862no—
246#106—862no—
247C4⋊C8—22no—
248C4⋊C8—432no—
249C4⋊C8—861no—
250C4⋊C8C22×D4314yes—
251#103—864no—
252#102—864no—
253C22⋊C8—862no—
254C22⋊C8—862no—
255C4×C8D17211yescharacteristic
256C4×C8D17211yescharacteristic
257C4×C8C22×D4311yescharacteristic
258C4×C8C22×D4311yescharacteristic
259#41—1722no—
260#41—1722no—
261C2×Q8—861no—
262C2×Q8—862no—
263C2×Q8—862no—
264C2×D4—432no—
265C2×D4—862no—
266C2×D4—861no—
267C2×D4—861no—
268C22×C4—862no—
269C22×C4C2×D17211yescharacteristic
270C22×C4D4×D4311yescharacteristic
271C22×C4#1062190211yescharacteristic
272SD16—3444no—
273M16—1722no—
274M16—1724no—
275C2×C8—22no—
276C2×C8—24no—
277C2×C8—82no—
278C2×C8—862no—
279C2×C8—1724no—
280C2×C8#1062187314yescomplemented
281C2×C8C2×D17211yescharacteristic
282C2×C8C2×D17211yescharacteristic
283C2×C8C2×D17211yescharacteristic
284C2×C8C2×D17211yescharacteristic
285C4⋊C4—432no—
286C4⋊C4—861no—
287C4⋊C4—862no—
288C4⋊C4—862no—
289C4⋊C4—862no—
290C4⋊C4—862no—
291C4⋊C4—1722no—
292C4⋊C4—1722no—
293C22⋊C4—862no—
294C22⋊C4—862no—
295C22⋊C4—1722no—
296C42—1722no—
297C42C2×D17211yescharacteristic
298C42D4×D4311yescharacteristic
299C42#1062190211yescharacteristic
300C42C23×D4311yescharacteristic
301C23—862no—
302C23#1306330011yescharacteristic
303Q8—3442no—
304Q8—1722no—
305Q8—1722no—
306Q8—1722no—
307D4—862no—
308D4—862no—
309D4—1722no—
310D4—1724no—
311D4—1722no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—862no—
316C2×C4—1722no—
317C2×C4—1722no—
318C2×C4—1722no—
319C2×C4—1722no—
320C2×C4#1306330011yescharacteristic
321C2×C4#1306330011yescharacteristic
322C2×C4#1306330011yescharacteristic
323C2×C4C2×#1062187312yes—
324C2×C4#1306335812yes—
325C2×C4C2×D4×D4311yescharacteristic
326C2×C4C22×D17211yescharacteristic
327C2×C4C2×#1062190211yescharacteristic
328C8—21no—
329C8—21no—
330C8—44no—
331C8—1722no—
332C8C2×#1062187312yes—
333C8C2×#1062187312yes—
334C22—21no—
335C22—21no—
336C22—1722no—
337C22—1722no—
338C22—1722no—
339C22#1458310512yes—
340C22C2×#1306330011yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—3442no—
345C4—3442no—
346C4—1722no—
347C4#1458310512yes—
348C4C22×#1062187311yescharacteristic
349C4C2×#1306335811yescharacteristic
350C4#1458370011yescharacteristic
351C4#1458371211yescharacteristic
352C2—22no—
353C2—3442no—
354C2C2×#1458310511yescharacteristic
355C2#1914426711yescharacteristic
356C2#1914431611yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#335C2
socleC22×C43C2×#121
prime radical#14583449C22
hypercenterC2×#335D43
hypocenterC43#19195
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. #19145109C2semidirect
4. #19134095C2semidirect
5. #19133995C2semidirect
6. #19133985C2semidirect
7. #19133283C2semidirect
8. C2×C43×#335C2semidirect
96. C2×C8×C43SD16semidirect
180. C2×#335D43semidirect
214. C43#19195semidirect
280. C2×C8#10621873semidirect

Maximal subgroups

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

subgroupindex
#191459122
#191451092
#191433082
#191340952
#191339952
#191339852
#191332832
C2×C43×#3352
#1919543