Finite Group Databasebeta

← #24990502

Subgroups — #24990502

Order 11008.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143708C211yesmaximal, characteristic
2#19134712C211yesmaximal, characteristic, complemented
3C4×#13063253C211yesmaximal, characteristic
4#19133348C211yesmaximal, characteristic, complemented
5#19132983C211yesmaximal, characteristic
6#19132444C211yesmaximal, characteristic, complemented
7C43×#1276C211yesmaximal, characteristic, complemented
8C4×#10621898C2211yescharacteristic
9#14583029—21no—
10#14582978—21no—
11#14582967—22no—
12#14582955—21no—
13#14582921—21no—
14C2×C4⋊(C43⋊C8)C2211yescharacteristic
15C2×C4⋊(C43⋊C8)C2211yescharacteristic
16C2×#13063253C411yescharacteristic
17C2×#13063253C411yescharacteristic
18C4×#10621877C2211yescharacteristic
19#14582659C411yescharacteristic
20#14582659C411yescharacteristic
21#14582654—22no—
22#14582651—21no—
23#14582649—21no—
24#14582631—21no—
25#14582628—21no—
26C43×#431C2211yescharacteristic
27C43×#431C2211yescharacteristic
28C43×C43C2211yescharacteristic
29C2×#10621898C2×C411yescharacteristic
30C2×#10621877C2×C411yescharacteristic
31C2×#10621877C2×C411yescharacteristic
32C2×#10621872—22no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8D412yes—
35C4×Dic86D411yescharacteristic
36C4×Dic86Q811yescharacteristic
37C4×D172D411yescharacteristic
38C4×D172Q811yescharacteristic
39C4×C22⋊D43—21no—
40C4×C22⋊D43—21no—
41#13063284C2×C411yescharacteristic
42#13063282—21no—
43C42×D43—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48Dic43⋊C8—22no—
49#13063253—22no—
50#13063253—22no—
51(C2×D43)⋊C8—22no—
52#13063236—21no—
53#13063235—22no—
54C4×C43⋊C8—21no—
55C2×C42×C43—21no—
56C2×C42×C43—21no—
57C2×C42×C43C2×C411yescharacteristic
58C2×C42×C43C2×C411yescharacteristic
59C2×C42×C43C2311yescharacteristic
60C4⋊C8×C43—21no—
61C4⋊C8×C43D411yescharacteristic
62C4⋊C8×C43D411yescharacteristic
63C22⋊C8×C43—21no—
64C22⋊C8×C43—21no—
65C4×C8×C43—21no—
66C4×C8×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43#4111yescharacteristic
72C2×C22⋊D43—21no—
73#10621898—21no—
74#10621898—21no—
75#10621898—21no—
76#10621898—21no—
77C2×D172C4⋊C411yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×Dic86C4⋊C411yescharacteristic
82C2×C8×C43—21no—
83C2×C8×C43—21no—
84C2×C8×C43—41no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43—21no—
88C42×C43—41no—
89C42×C43—41no—
90C42×C43—42no—
91C42×C43M1612yescomplemented
92C42×C43C2×D411yescharacteristic
93C42×C43C2×D411yescharacteristic
94C42×C43C2×Q811yescharacteristic
95C42×C43#4111yescharacteristic
96C22⋊Dic43—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99C4⋊Dic43C4⋊C411yescharacteristic
100C4⋊Dic43C4⋊C411yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106#10621877—21no—
107#10621877—21no—
108#10621877—21no—
109#10621877M1612yescomplemented
110C2×C43⋊C8—21no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—42no—
114C2×C43⋊C8—42no—
115C2×C43⋊C8—41no—
116#10621872—82no—
117C23×C43C4×D411yescharacteristic
118C22×D43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43C2×C4⋊C411yescharacteristic
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43#12011yescharacteristic
131C2×C4×C43C22⋊Q811yescharacteristic
132C2×C4×C43C22⋊Q811yescharacteristic
133C2×C4×C43#12311yescharacteristic
134C2×C4×C43C2×M1611yescharacteristic
135C2×C4×C43C2×M1611yescharacteristic
136C2×C4×C43#13111yescharacteristic
137C2×C4×C43#13111yescharacteristic
138C22⋊D43—41no—
139C22⋊D43—41no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143D172—21no—
144D172—21no—
145C4×D43—41no—
146C4×D43—41no—
147C4×D43—41no—
148C4×D43—41no—
149C4×D43—81no—
150Dic86—21no—
151Dic86—21no—
152C8×C43—41no—
153C8×C43—41no—
154C8×C43—81no—
155C43⋊C8—22no—
156C43⋊C8—41no—
157C43⋊C8—42no—
158C43⋊C8—81no—
159#8842—431nomaximal, Sylow
160C22×C43—21no—
161C22×C43—21no—
162C22×C43#38511yescharacteristic
163C22×C43#43511yescharacteristic
164C22×C43#43611yescharacteristic
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—42no—
172C4×C43—42no—
173C4×C43#42311yescharacteristic
174C4×C43#42411yescharacteristic
175C4×C43#43511yescharacteristic
176C4×C43#43611yescharacteristic
177C4×C43#45411yescharacteristic
178C4×C43#45511yescharacteristic
179Dic43—41no—
180Dic43—41no—
181Dic43—41no—
182#2989—431no—
183#1831—431no—
184C4×#104—431no—
185#1565—431no—
186#1477—431no—
187#1283—431no—
188#1276D4311yescharacteristic, complemented
189C2×C43—21no—
190C2×C43—21no—
191C2×C43#185111yescharacteristic
192C2×C43#186011yescharacteristic
193C2×C43#186111yescharacteristic
194D43—81no—
195C4×#41—431no—
196#446—861no—
197#436—861no—
198#435—862no—
199#432—861no—
200#431C2×D4311yescharacteristic
201#431C2×D4311yescharacteristic
202#423—861no—
203C2×C4⋊C8—431no—
204C2×C4⋊C8—431no—
205C2×#104—431no—
206C2×#104—431no—
207C4×M16—431no—
208C43C2×D4311yescharacteristic
209#339—431no—
210#339—431no—
211#336—862no—
212#335—861no—
213#334—861no—
214Q8⋊C8—861no—
215D4⋊C8—861no—
216C43#884211yescharacteristic, complemented, Sylow
217C2×#41—431no—
218C2×M16—431no—
219C2×M16—431no—
220C2×M16—862no—
221C22×C8—432no—
222C22×C8—861no—
223C4×Q8—431no—
224C4×Q8—431no—
225C4×D4—431no—
226C4×D4—431no—
227C4×D4—861no—
228C4×D4—861no—
229#117—431no—
230#117—861no—
231C2×C42—21no—
232C2×C42—21no—
233C2×C42—861no—
234C2×C42C4×D4311yescharacteristic
235C2×C42C4×D4311yescharacteristic
236C2×C42C22×D4311yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—862no—
239C4⋊C8—861no—
240C4⋊C8—861no—
241C4⋊C8—861no—
242C4⋊C8—861no—
243C4⋊C8D17211yescharacteristic
244C4⋊C8D17211yescharacteristic
245#104—862no—
246#104—862no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—862no—
250#97—862no—
251#97—861no—
252C4×C8—21no—
253C4×C8—21no—
254C4×C8—861no—
255#41—861no—
256#41—861no—
257#41—861no—
258#41—861no—
259C2×Q8—431no—
260C2×D4—431no—
261C2×D4—861no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4C2×C4×D4311yescharacteristic
268C22×C4D4×D4311yescharacteristic
269C22×C4#1062190011yescharacteristic
270M16—432no—
271M16—861no—
272M16—861no—
273M16—861no—
274M16—3442no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—41no—
278C2×C8—861no—
279C2×C8—861no—
280C2×C8—862no—
281C2×C8—1722no—
282C2×C8—1721no—
283C2×C8—1722no—
284C4⋊C4—431no—
285C4⋊C4—431no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—41no—
295C42—41no—
296C42—42no—
297C42—861no—
298C42—861no—
299C42—861no—
300C42#1062187212yescomplemented
301C42C2×D17211yescharacteristic
302C42#1062189811yescharacteristic
303C42D4×D4311yescharacteristic
304C42Q8×D4311yescharacteristic
305C23—861no—
306C23(C22⋊D43)⋊C411yescharacteristic
307Q8—861no—
308Q8—861no—
309D4—861no—
310D4—861no—
311D4—1721no—
312D4—1721no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—3441no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4C4⋊C4×D4311yescharacteristic
331C2×C4C4×D17211yescharacteristic
332C2×C4#1306329511yescharacteristic
333C2×C4#1306330311yescharacteristic
334C2×C4#1306330511yescharacteristic
335C2×C4#1306330711yescharacteristic
336C2×C4M16×D4311yescharacteristic
337C2×C4C2×#1062187211yescharacteristic
338C2×C4#1306333111yescharacteristic
339C2×C4#1306333311yescharacteristic
340C8—41no—
341C8—41no—
342C8—81no—
343C8—862no—
344C8—3441no—
345C8—1722no—
346C8—1721no—
347C22—21no—
348C22—21no—
349C22—1721no—
350C22—1721no—
351C22—1721no—
352C22#1458277311yescharacteristic
353C22#1458296711yescharacteristic
354C22#1458297411yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—42no—
359C4—42no—
360C4—1721no—
361C4—1721no—
362C4—1721no—
363C4#1458292111yescharacteristic
364C4#1458292411yescharacteristic
365C4#1458297211yescharacteristic
366C4#1458297811yescharacteristic
367C4#1458307311yescharacteristic
368C4#1458307811yescharacteristic
369C2—21no—
370C2—21no—
371C2—3441no—
372C2#1913477911yescharacteristic
373C2#1913482911yescharacteristic
374C2#1913483611yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1276C2
socleC22×C43#385
prime radicalC2×#10621898C2×C4
cosocleC2×C42×C43C23
hypercenter#1276D43
hypocenterC43#8842
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
2. #19134712C2semidirect
4. #19133348C2semidirect
6. #19132444C2semidirect
7. C43×#1276C2semidirect
91. C42×C43M16semidirect
109. #10621877M16semidirect
188. #1276D43semidirect
216. C43#8842semidirect
300. C42#10621872semidirect

Maximal subgroups

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

subgroupindex
#191437082
#191347122
C4×#130632532
#191333482
#191329832
#191324442
C43×#12762
#884243