Finite Group Databasebeta

← #25125439

Subgroups — #25125439

Order 11008.

1126 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582937C211yesmaximal, characteristic, complemented
2C22×(C2×D43)⋊C8C211yesmaximal, characteristic
3#19136974C212yesmaximal
4#19136030C214yesmaximal, complemented
5#19136025C212yesmaximal, complemented
6#19136020C212yesmaximal, complemented
7#19134311C212yesmaximal, complemented
8C43×#1735C211yesmaximal, characteristic, complemented
9C23×C4×D43C2211yescharacteristic
10C23×C43⋊C8C2211yescharacteristic
11C2×#13063284C2212yes—
12#14582937—24no—
13C2×#13063259C2211yescharacteristic, complemented
14C2×#13063259C2211yescharacteristic, complemented
15C2×#13063257C2212yescomplemented
16C2×(C2×D43)⋊C8—24no—
17C2×(C2×D43)⋊C8C2212yes—
18C2×(C2×D43)⋊C8C2212yes—
19#14582760—22no—
20#14582756C2214yes—
21#14582756C2214yes—
22#14582754—22no—
23C4×(C2×D43)⋊C4—24no—
24#14582661C2214yescomplemented
25#14582661C2214yescomplemented
26C23×C8×C43C2211yescharacteristic
27C2×#117×C43C2212yes—
28C43×#340C2212yescomplemented
29C43×#340C2212yescomplemented
30C24×D43D411yescharacteristic
31C23×Dic43D411yescharacteristic
32C22×C4×D43—22no—
33C22×C4×D43—24no—
34C22×C4×D43—24no—
35C22×C4×D43—22no—
36C22×C4×D43D412yes—
37C22×C4×D43C2312yes—
38C22×C43⋊C8—22no—
39C22×C43⋊C8—24no—
40C22×C43⋊C8C2312yes—
41#13063284—24no—
42#13063284—24no—
43C2×C4⋊Dic43C2312yes—
44C2×C4⋊Dic43C2312yes—
45C2×C22⋊Dic43—22no—
46C2×(C2×D43)⋊C4—24no—
47C2×(C2×D43)⋊C4—24no—
48C2×C4×Dic43—22no—
49#13063259—22no—
50#13063259—22no—
51#13063257—24no—
52(C2×D43)⋊C8—24no—
53(C2×D43)⋊C8—24no—
54C43⋊#95—24no—
55C43⋊#95—24no—
56C23×C4×C43C2311yescharacteristic
57C22×C8×C43—24no—
58C22×C8×C43D414yes—
59C22×C8×C43C2311yescharacteristic
60C22×C8×C43C2311yescharacteristic
61#117×C43—24no—
62#117×C43—24no—
63C2×C4⋊C4×C43C2314yes—
64C2×C22⋊C4×C43—22no—
65C2×C42×C43—22no—
66C24×C43C2×D411yescharacteristic
67C23×D43—22no—
68C23×D43—24no—
69C23×D43—24no—
70C23×D43—42no—
71C23×D43C2×D412yes—
72C22×C4×C43—24no—
73C22×C4×C43C2×D412yes—
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43#4112yes—
76C22×C4×C43#4114yes—
77C22×C4×C43#4114yes—
78C22×C4×C43C2411yescharacteristic
79C22×Dic43—22no—
80C22×Dic43—24no—
81C22×Dic43—22no—
82C22×Dic43—22no—
83C22×Dic43C2×D412yes—
84C2×C4×D43—24no—
85C2×C4×D43—28no—
86C2×C4×D43—22no—
87C2×C4×D43—22no—
88C2×C4×D43—24no—
89C2×C4×D43—24no—
90C2×C4×D43—44no—
91C2×C4×D43—44no—
92C2×C4×D43—48no—
93C2×C8×C43—28no—
94C2×C8×C43—22no—
95C2×C8×C43—22no—
96C2×C8×C43C2×D412yes—
97C2×C8×C43C2×D412yes—
98C4⋊C4×C43—24no—
99C4⋊C4×C43—24no—
100C22⋊C4×C43—44no—
101C42×C43—44no—
102C22⋊Dic43—44no—
103(C2×D43)⋊C4—48no—
104(C2×D43)⋊C4—48no—
105C4⋊Dic43—22no—
106C4⋊Dic43—22no—
107C4⋊Dic43—22no—
108C4⋊Dic43—22no—
109C4×Dic43—44no—
110C2×C43⋊C8—22no—
111C2×C43⋊C8—24no—
112C2×C43⋊C8—44no—
113C23×C43—22no—
114C23×C43—22no—
115C23×C43#12112yes—
116C23×C43#12314yes—
117C23×C43C22×D411yescharacteristic
118C22×D43—28no—
119C22×D43—22no—
120C22×D43—24no—
121C22×D43—22no—
122C22×D43—24no—
123C22×D43—416no—
124C22×D43—44no—
125C22×D43—44no—
126C22×D43#13514yes—
127C2×C4×C43—44no—
128C2×C4×C43—44no—
129C2×C4×C43—44no—
130C2×C4×C43#12112yes—
131C2×C4×C43#12314yes—
132C2×C4×C43#12314yes—
133C2×C4×C43#12414yes—
134C2×C4×C43#12618yes—
135C2×C4×C43C22×D411yescharacteristic
136C2×C4×C43C2×#4112yes—
137C2×C4×C43C2×#4112yes—
138C2×C4×C43C2×#4111yescharacteristic
139C2×Dic43—22no—
140C2×Dic43—24no—
141C2×Dic43—44no—
142C2×Dic43—42no—
143C2×Dic43—42no—
144C2×Dic43—44no—
145C2×Dic43—44no—
146C4×D43—42no—
147C4×D43—42no—
148C4×D43—44no—
149C4×D43—48no—
150C8×C43—22no—
151C8×C43—22no—
152C43⋊C8—42no—
153#23638—431nomaximal, Sylow
154C22×C43—28no—
155C22×C43—22no—
156C22×C43—22no—
157C22×C43#39714yes—
158C22×C43C2×#12111yescharacteristic
159C22×C43C2×#12312yes—
160C22×C43C2×#13512yes—
161C22×C43#57512yes—
162C2×D43—28no—
163C2×D43—24no—
164C2×D43—416no—
165C2×D43—44no—
166C2×D43—42no—
167C2×D43—42no—
168C4×C43—84no—
169C4×C43#39714yes—
170C4×C43C2×#12311yescharacteristic
171C4×C43C2×#12411yescharacteristic
172C4×C43C2×#12612yes—
173Dic43—42no—
174Dic43—82no—
175Dic43—82no—
176C2×#427—431no—
177C22×C22⋊C8—431no—
178#2280—432no—
179#2077—434no—
180#2076—432no—
181#2075—432no—
182#1735—432no—
183#1735D4311yescharacteristic, complemented
184C2×C43—24no—
185C2×C43C2×#39711yescharacteristic
186C2×C43#305011yescharacteristic
187C2×C43#305411yescharacteristic
188C2×C43#309114yes—
189D43—44no—
190C24×C4—431no—
191C23×C8—431no—
192C23×C8C2×D4311yescharacteristic
193C2×#117—432no—
194C2×#117C2×D4312yes—
195#427—864no—
196C2×#107—431no—
197C2×#107—431no—
198C2×#106—432no—
199C2×C22⋊C8—432no—
200C2×C22⋊C8—432no—
201C2×C22⋊C8—864no—
202#381—862no—
203#380—434no—
204#380—434no—
205#379—862no—
206C4×C22⋊C4—864no—
207#340—434no—
208#340—434no—
209#340C2×D4312yescomplemented
210#340C2×D4312yescomplemented
211C43#2363811yescharacteristic, complemented, Sylow
212C25—431no—
213C23×C4—431no—
214C23×C4—432no—
215C23×C4—432no—
216C23×C4—862no—
217C23×C4—864no—
218C23×C4—864no—
219C23×C4—862no—
220C23×C4C22×D4311yescharacteristic
221C22×C8—24no—
222C22×C8—432no—
223C22×C8—862no—
224C22×C8—864no—
225C22×C8D17214yes—
226C22×C8C22×D4311yescharacteristic
227C22×C8C22×D4311yescharacteristic
228#117—24no—
229#117—24no—
230#117—864no—
231#117—864no—
232C2×C4⋊C4—432no—
233C2×C4⋊C4—432no—
234C2×C4⋊C4C22×D4314yes—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—864no—
237C2×C22⋊C4—864no—
238C2×C22⋊C4—862no—
239C2×C42—22no—
240C2×C42—862no—
241#107—862no—
242#107—862no—
243#106—864no—
244C22⋊C8—864no—
245C22⋊C8—864no—
246#95—864no—
247#95—864no—
248C24—432no—
249C24—864no—
250C24—862no—
251C24—864no—
252C24—1722no—
253C24D4×D4311yescharacteristic
254C22×C4—24no—
255C22×C4—432no—
256C22×C4—862no—
257C22×C4—864no—
258C22×C4—864no—
259C22×C4—868no—
260C22×C4—862no—
261C22×C4—864no—
262C22×C4—864no—
263C22×C4—862no—
264C22×C4—862no—
265C22×C4—862no—
266C22×C4—1724no—
267C22×C4—1724no—
268C22×C4—1728no—
269C22×C4C2×D17212yes—
270C22×C4#1062189814yes—
271C22×C4D4×D4311yescharacteristic
272C22×C4#1062190014yes—
273C22×C4#1062190212yes—
274C22×C4C23×D4311yescharacteristic
275C2×C8—28no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—862no—
279C2×C8—864no—
280C2×C8—1724no—
281C2×C8C2×D17212yes—
282C2×C8C2×D17212yes—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—862no—
286C4⋊C4—862no—
287C4⋊C4—862no—
288C4⋊C4—862no—
289C22⋊C4—44no—
290C22⋊C4—1728no—
291C22⋊C4—1728no—
292C22⋊C4—1724no—
293C42—44no—
294C42—1724no—
295C23—22no—
296C23—22no—
297C23—434no—
298C23—868no—
299C23—862no—
300C23—864no—
301C23—862no—
302C23—864no—
303C23—17216no—
304C23—1724no—
305C23—1724no—
306C23#1306330012yes—
307C23#1306330714yes—
308C23C2×D4×D4311yescharacteristic
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—862no—
313C2×C4—864no—
314C2×C4—1722no—
315C2×C4—1722no—
316C2×C4—1724no—
317C2×C4—1724no—
318C2×C4—1724no—
319C2×C4—1728no—
320C2×C4—1722no—
321C2×C4—1722no—
322C2×C4—1724no—
323C2×C4#1306330012yes—
324C2×C4#1306330714yes—
325C2×C4#1306330914yes—
326C2×C4#1306331314yes—
327C2×C4#1306332018yes—
328C2×C4C22×D17211yescharacteristic
329C2×C4C2×#1062190012yes—
330C2×C4C2×#1062189812yes—
331C2×C4C2×#1062190211yescharacteristic
332C8—22no—
333C8—22no—
334C8—1722no—
335C22—22no—
336C22—28no—
337C22—22no—
338C22—868no—
339C22—864no—
340C22—17216no—
341C22—1722no—
342C22—1722no—
343C22—1724no—
344C22#1458282614yes—
345C22C2×#1306330011yescharacteristic
346C22C2×#1306330712yes—
347C22#135×D4312yes—
348C22#1458369612yes—
349C4—84no—
350C4—3442no—
351C4—3442no—
352C4—1722no—
353C4#1458282614yes—
354C4C2×#1306330911yescharacteristic
355C4C2×#1306331311yescharacteristic
356C4C2×#1306332012yes—
357C2—24no—
358C2—1724no—
359C2C2×#1458282611yescharacteristic
360C2#1914417711yescharacteristic
361C2#1914420511yescharacteristic
362C2#1914450614yes—
subgroupG/H
centerC22×C4D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1735C2
socleC23×C43C22×D4
prime radicalC24×D43D4
hypercenter#1735D43
hypocenterC43#23638
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
1. C2×#14582937C2semidirect
4. #19136030C2semidirect
5. #19136025C2semidirect
6. #19136020C2semidirect
7. #19134311C2semidirect
8. C43×#1735C2semidirect
13. C2×#13063259C22semidirect
14. C2×#13063259C22semidirect
15. C2×#13063257C22semidirect
24. #14582661C22semidirect
25. #14582661C22semidirect
28. C43×#340C22semidirect
29. C43×#340C22semidirect
183. #1735D43semidirect
209. #340C2×D43semidirect
210. #340C2×D43semidirect
211. C43#23638semidirect

Maximal subgroups

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

subgroupindex
C2×#145829372
C22×(C2×D43)⋊C82
#191369742
#191360302
#191360252
#191360202
#191343112
C43×#17352
#2363843