Finite Group Databasebeta

← #25099795

Subgroups — #25099795

Order 11008.

814 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621885C211yesmaximal, characteristic
2#19137241C211yesmaximal, characteristic
3#19136960C211yesmaximal, characteristic
4#19135234C212yesmaximal
5#19135164C212yesmaximal
6#19134934C212yesmaximal
7#19134847C212yesmaximal
8C4×#13063258C211yesmaximal, characteristic
9#19134426C211yesmaximal, characteristic
10#19134348C211yesmaximal, characteristic
11C43×#1763C211yesmaximal, characteristic
12C22×#10621885C2211yescharacteristic
13C2×Q8×Dic43C2212yes—
14C2×C4×Dic86C2211yescharacteristic
15C4×#10621885C418yescomplemented
16C2×#13063258C2212yes—
17C2×#13063258C2211yescharacteristic
18C2×#13063250C2212yes—
19C2×#13063249C2211yescharacteristic
20C2×#13063248C2211yescharacteristic
21C2×C4×C43⋊C8C2211yescharacteristic
22#14582804C2212yes—
23#14582795C2212yes—
24#14582783—22no—
25#14582766—21no—
26#14582763—21no—
27C4⋊C4×Dic43—22no—
28C4⋊C4×Dic43C2212yes—
29C4×C4⋊Dic43—21no—
30C4×C4⋊Dic43C2211yescharacteristic
31#14582745—21no—
32#14582745C2211yescharacteristic
33#14582662C2212yes—
34#14582661C2212yes—
35#14582653C2212yes—
36#14582653C2212yes—
37C2×C4×Q8×C43C2211yescharacteristic
38C2×#103×C43C2212yes—
39C2×#97×C43C2211yescharacteristic
40C4×C4⋊C4×C43C2211yescharacteristic
41C43×#340C2212yes—
42C22×Dic86C2311yescharacteristic
43C2×#10621885—24no—
44C2×#10621885C2×C414yes—
45C22×C43⋊C8C2311yescharacteristic
46C22×C43⋊C8C2311yescharacteristic
47Q8×Dic43—24no—
48Q8×Dic43—24no—
49C4×Dic86—22no—
50C4×Dic86C2×C414yes—
51C2×C4⋊Dic43—22no—
52C2×C4⋊Dic43C2311yescharacteristic
53C2×C4⋊Dic43C2312yes—
54C2×Dic43⋊C4—21no—
55C2×Dic43⋊C4—22no—
56C2×C4×Dic43—21no—
57C2×C4×Dic43—22no—
58C2×C4×Dic43—21no—
59C2×C4×Dic43—22no—
60C2×C4×Dic43C2312yes—
61#13063258—24no—
62#13063258C2×C414yes—
63#13063250—24no—
64#13063249C2×C414yes—
65#13063248C2×C414yes—
66C4×C43⋊C8C2×C414yes—
67C43⋊#95—21no—
68C43⋊#95—22no—
69C43⋊#95—22no—
70C43⋊#95—22no—
71C43⋊#95—22no—
72C43⋊#95D411yescharacteristic
73C43⋊#95D411yescharacteristic
74C43⋊#95D412yes—
75C22×Q8×C43C2311yescharacteristic
76C22×C8×C43C2312yes—
77C4×Q8×C43—22no—
78C4×Q8×C43C2×C414yes—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43C2312yes—
81C2×C4⋊C4×C43C2311yescharacteristic
82C2×C42×C43—21no—
83C2×C42×C43—21no—
84C2×C42×C43C2311yescharacteristic
85#103×C43—24no—
86#97×C43—22no—
87#95×C43—21no—
88C2×Q8×C43—21no—
89C2×Q8×C43—22no—
90C2×Q8×C43C22×C412yes—
91C2×Q8×C43#4114yes—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—22no—
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2411yescharacteristic
98C22×Dic43—21no—
99C22×Dic43—22no—
100C22×Dic43—21no—
101C22×Dic43C2×D412yes—
102C22×Dic43C2×D412yes—
103C2×Dic86—22no—
104C2×Dic86—22no—
105C2×Dic86—21no—
106C2×Dic86C22×C412yes—
107C2×C8×C43—22no—
108C2×C8×C43—22no—
109C2×C8×C43—22no—
110C4⋊C4×C43—24no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—22no—
113C4⋊C4×C43—22no—
114C4⋊C4×C43C22×C412yes—
115C42×C43—24no—
116C42×C43—81no—
117C42×C43C22×C412yes—
118C42×C43#4112yes—
119#10621885—28no—
120C4⋊Dic43—28no—
121C4⋊Dic43—21no—
122C4⋊Dic43—22no—
123C4⋊Dic43C22×C412yes—
124C4⋊Dic43#4114yes—
125Dic43⋊C4—24no—
126Dic43⋊C4—82no—
127C4×Dic43—28no—
128C4×Dic43—24no—
129C4×Dic43—22no—
130C4×Dic43—22no—
131C4×Dic43—82no—
132C4×Dic43—81no—
133C2×C43⋊C8—22no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8C22×C412yes—
136C2×C43⋊C8C22×C412yes—
137C23×C43C22×D411yescharacteristic
138Q8×C43—22no—
139Q8×C43—24no—
140Q8×C43#11714yes—
141C2×C4×C43—22no—
142C2×C4×C43—24no—
143C2×C4×C43—21no—
144C2×C4×C43—22no—
145C2×C4×C43—21no—
146C2×C4×C43—22no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43C4×D412yes—
153C2×C4×C43C4×D412yes—
154C2×C4×C43C23×C411yescharacteristic
155C2×C4×C43C2×#4112yes—
156C2×C4×C43C2×#4111yescharacteristic
157C2×C4×C43C2×#4112yes—
158C2×Dic43—22no—
159C2×Dic43—22no—
160C2×Dic43—22no—
161C2×Dic43—22no—
162C2×Dic43—24no—
163C2×Dic43—22no—
164C2×Dic43—22no—
165C2×Dic43—22no—
166C2×Dic43—22no—
167C2×Dic43—42no—
168C2×Dic43—42no—
169C2×Dic43—41no—
170C2×Dic43—42no—
171C2×Dic43—41no—
172Dic86—22no—
173Dic86—22no—
174Dic86—42no—
175C8×C43—42no—
176C43⋊C8—22no—
177C43⋊C8—22no—
178#21135—431nomaximal, Sylow
179C22×C43C2×C4×D411yescharacteristic
180C22×C43#52512yes—
181C22×C43#57611yescharacteristic
182C22×C43#57812yes—
183C22×C43#57811yescharacteristic
184C4×C43—22no—
185C4×C43—22no—
186C4×C43—24no—
187C4×C43—42no—
188C4×C43—82no—
189C4×C43C2×#11711yescharacteristic
190C4×C43C4×#4111yescharacteristic
191C4×C43#52912yes—
192Dic43—42no—
193Dic43—44no—
194Dic43—42no—
195Dic43—42no—
196Dic43—42no—
197C2×C4×Q16—431no—
198#2320—431no—
199#2276—431no—
200#1928—432no—
201#1918—432no—
202#1878—432no—
203#1863—432no—
204C4×#107—431no—
205#1763—431no—
206#1763D4311yescharacteristic
207#1746—431no—
208C2×C43#229011yescharacteristic
209C2×C43#295011yescharacteristic
210C2×C43#295111yescharacteristic
211C2×C43#312412yes—
212C2×C43#312712yes—
213C22×Q16—431no—
214C2×C4×Q8—432no—
215C2×C4×Q8—431no—
216C2×C4×Q8C2×D4311yescharacteristic
217C4×Q16—438no—
218C2×#107—431no—
219C2×#107—432no—
220C2×#103—431no—
221C2×#103—431no—
222C2×#103—432no—
223C2×#103C2×D4312yes—
224C2×#97C2×D4311yescharacteristic
225C2×C4×C8—431no—
226#391—432no—
227#389—432no—
228#387—862no—
229#383—861no—
230#382—861no—
231C4×C4⋊C4—432no—
232C4×C4⋊C4—431no—
233C4×C4⋊C4—861no—
234C4×C4⋊C4—862no—
235C4×C4⋊C4C2×D4311yescharacteristic
236#376—431no—
237#376—861no—
238#340—432no—
239#340—432no—
240#340C2×D4312yes—
241#336—432no—
242#336—432no—
243C43#2113511yescharacteristic, complemented, Sylow
244C22×Q8—431no—
245C22×Q8C22×D4311yescharacteristic
246C2×Q16—434no—
247C2×Q16—864no—
248C22×C8—431no—
249C22×C8—431no—
250C22×C8C22×D4312yes—
251C4×Q8—22no—
252C4×Q8—434no—
253C4×Q8—864no—
254C4×Q8—864no—
255C4×Q8—862no—
256C4×Q8C4×D4314yes—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—432no—
259C2×C4⋊C4—431no—
260C2×C4⋊C4—862no—
261C2×C4⋊C4—861no—
262C2×C4⋊C4—862no—
263C2×C4⋊C4C22×D4312yes—
264C2×C4⋊C4C22×D4311yescharacteristic
265C2×C42—21no—
266C2×C42—21no—
267C2×C42—432no—
268C2×C42—862no—
269C2×C42—861no—
270C2×C42—862no—
271C2×C42—861no—
272C2×C42C22×D4311yescharacteristic
273#107—434no—
274#107—864no—
275#103—24no—
276#103—434no—
277#103—434no—
278#103—864no—
279#97—22no—
280C4×C8—434no—
281#95—21no—
282#95—431no—
283#95—431no—
284#95—432no—
285#95—862no—
286#95—862no—
287#95—862no—
288#95—862no—
289#95—861no—
290C2×Q8—22no—
291C2×Q8—21no—
292C2×Q8—432no—
293C2×Q8—861no—
294C2×Q8—862no—
295C2×Q8—862no—
296C2×Q8C2×C4×D4312yes—
297C2×Q8#1062189814yes—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—432no—
302C22×C4—432no—
303C22×C4—861no—
304C22×C4—862no—
305C22×C4—861no—
306C22×C4D4×D4311yescharacteristic
307C22×C4D4×D4311yescharacteristic
308C22×C4C23×D4311yescharacteristic
309Q16—868no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—432no—
314C2×C8—432no—
315C2×C8—862no—
316C2×C8—862no—
317C4⋊C4—24no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—432no—
322C4⋊C4—434no—
323C4⋊C4—868no—
324C4⋊C4—864no—
325C4⋊C4—861no—
326C4⋊C4—862no—
327C4⋊C4—3442no—
328C4⋊C4C2×C4×D4312yes—
329C42—24no—
330C42—81no—
331C42—868no—
332C42—864no—
333C42—862no—
334C42—862no—
335C42—3441no—
336C42—3442no—
337C42C2×C4×D4312yes—
338C42#1062190012yes—
339C23C2×D4×D4311yescharacteristic
340Q8—22no—
341Q8—24no—
342Q8—862no—
343Q8—862no—
344Q8—1722no—
345Q8#1306328214yes—
346C2×C4—22no—
347C2×C4—24no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—862no—
358C2×C4—862no—
359C2×C4—862no—
360C2×C4—864no—
361C2×C4—862no—
362C2×C4—862no—
363C2×C4—862no—
364C2×C4—862no—
365C2×C4—862no—
366C2×C4—1722no—
367C2×C4—1722no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4—1722no—
371C2×C4(C22⋊D43)⋊C412yes—
372C2×C4(C22⋊D43)⋊C412yes—
373C2×C4C22×C4×D4311yescharacteristic
374C2×C4#41×D4312yes—
375C2×C4C2×#1062190011yescharacteristic
376C2×C4C2×#1062189812yes—
377C8—42no—
378C8—862no—
379C8—862no—
380C22C2×(C22⋊D43)⋊C411yescharacteristic
381C22#1458340812yes—
382C22#1458370311yescharacteristic
383C22#1458371512yes—
384C22#1458371511yescharacteristic
385C4—24no—
386C4—22no—
387C4—22no—
388C4—42no—
389C4—82no—
390C4—1722no—
391C4—1722no—
392C4—1722no—
393C4—1724no—
394C4—1722no—
395C4C2×#1306328211yescharacteristic
396C4#1458336711yescharacteristic
397C4#1458342912yes—
398C2#1913703411yescharacteristic
399C2#1914345911yescharacteristic
400C2#1914346611yescharacteristic
401C2#1914485512yes—
402C2#1914489412yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1763C2
socle, prime radicalC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenter#1763D43
hypocenterC43#21135
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
15. C4×#10621885C4semidirect
243. C43#21135semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106218852
#191372412
#191369602
#191352342
#191351642
#191349342
#191348472
C4×#130632582
#191344262
#191343482
C43×#17632
#2113543