Finite Group Databasebeta

← #24993148

Subgroups — #24993148

Order 11008.

492 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145538C211yesmaximal, characteristic
2#19143542C211yesmaximal, characteristic, complemented
3#19135435C211yesmaximal, characteristic
4#19133283C211yesmaximal, characteristic, complemented
5C2×#14582642C211yesmaximal, characteristic
6#19132491C211yesmaximal, characteristic, complemented
7C43×#1283C211yesmaximal, characteristic, complemented
8#14583456C2211yescharacteristic
9C2×#13063322C2211yescharacteristic
10#14583272—21no—
11#14583246—21no—
12#14583100—22no—
13#14583052C414yes—
14#14583029—21no—
15#14583027—22no—
16C8×Dic86—21no—
17#14582927—21no—
18#14582923C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×#13063241—21no—
21C2×#13063241—21no—
22#14582857—21no—
23#14582647—21no—
24#14582646—21no—
25#14582642—21no—
26#14582642—21no—
27C43×#431C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C4×M16×C43C2211yescharacteristic
30C22×D172—21no—
31C22×D172—21no—
32C22×D172C2×C412yes—
33C2×#10621873—24no—
34C2×#10621877—21no—
35C22×C43⋊C8—21no—
36#13063325D411yescharacteristic
37#13063325D411yescharacteristic
38#13063322—21no—
39#13063322—21no—
40#13063322—21no—
41#13063322—21no—
42#13063317—21no—
43#13063304—21no—
44#13063304C2×C412yes—
45C4×Dic86—21no—
46C4×Dic86D412yes—
47#13063284—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)D411yescharacteristic
52C4⋊(C43⋊C8)D411yescharacteristic
53Dic43⋊C8—22no—
54Dic43⋊C8—22no—
55#13063247—24no—
56#13063241—42no—
57#13063241—42no—
58#13063235—22no—
59C8×Dic43—22no—
60C2×M16×C43D411yescharacteristic
61C2×M16×C43D411yescharacteristic
62C22×C8×C43—21no—
63C2×C42×C43C2311yescharacteristic
64C4⋊C8×C43—21no—
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67C22⋊C8×C43C2×C412yes—
68#97×C43—21no—
69C4×C8×C43—21no—
70C4×C8×C43—21no—
71C23×D43—22no—
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43#4111yescharacteristic
75C2×D172—22no—
76C2×D172—22no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172—41no—
85C2×D172—81no—
86C2×D172—81no—
87C2×D172—82no—
88C2×Dic86—21no—
89C2×Dic86C22⋊C412yes—
90M16×C43—21no—
91M16×C43—21no—
92M16×C43—21no—
93M16×C43SD1612yescomplemented
94C2×C8×C43—21no—
95C2×C8×C43—22no—
96C2×C8×C43—21no—
97C2×C8×C43—41no—
98C2×C8×C43—81no—
99C42×C43C2×D411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43#4111yescharacteristic
103C22⋊Dic43—22no—
104C4⋊Dic43—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43C22⋊C412yes—
108Dic43⋊C4—22no—
109Dic43⋊C4—22no—
110C4×Dic43—22no—
111#10621877—41no—
112#10621877—41no—
113C2×C43⋊C8—21no—
114C2×C43⋊C8—21no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118#10621873—84no—
119C23×C43C4×D411yescharacteristic
120C22×D43—42no—
121C22×D43—42no—
122C22×D43—42no—
123C22×D43—82no—
124C22×D43—82no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—41no—
128C2×C4×C43C2×C22⋊C411yescharacteristic
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43#12011yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#12311yescharacteristic
134C2×C4×C43C2×SD1611yescharacteristic
135C2×C4×C43#13511yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43#13711yescharacteristic
138C2×Dic43—22no—
139C2×Dic43—22no—
140D172—44no—
141D172—82no—
142D172—82no—
143D172—81no—
144D172—81no—
145D172—81no—
146D172—81no—
147D172—81no—
148D172—81no—
149Dic86—41no—
150Dic86—41no—
151Dic86—42no—
152C8×C43—22no—
153C8×C43—42no—
154C8×C43—41no—
155C8×C43—81no—
156C43⋊C8—41no—
157C43⋊C8—41no—
158C43⋊C8—81no—
159#9274—431nomaximal, Sylow
160C22×C43—21no—
161C22×C43—21no—
162C22×C43#38611yescharacteristic
163C22×C43C4×SD1611yescharacteristic
164C22×C43#44011yescharacteristic
165C2×D43—82no—
166C2×D43—82no—
167C2×D43—82no—
168C2×D43—162no—
169C2×D43—162no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43#44811yescharacteristic
174C4×C43#44911yescharacteristic
175C4×C43#46011yescharacteristic
176C4×C43#46411yescharacteristic
177C4×C43#47111yescharacteristic
178C4×C43#47211yescharacteristic
179Dic43—42no—
180Dic43—42no—
181#3208—431no—
182#2962—431no—
183#1965—431no—
184#1550—431no—
185C2×#331—431no—
186#1301—431no—
187#1283D4311yescharacteristic, complemented
188C2×C43—21no—
189C2×C43—21no—
190C2×C43#188011yescharacteristic
191C2×C43#190711yescharacteristic
192C2×C43#191411yescharacteristic
193D43—162no—
194#533—431no—
195C2×#127—431no—
196#492—861no—
197#486—861no—
198#460—862no—
199#450—434no—
200#446—861no—
201#446—862no—
202C8×Q8—861no—
203#431C2×D4311yescharacteristic
204#424—861no—
205#423—431no—
206C2×C4⋊C8—431no—
207C2×C4⋊C8C2×D4311yescharacteristic
208C2×#100—861no—
209C2×#100—861no—
210#405—861no—
211C4×M16C2×D4311yescharacteristic
212#333—861no—
213#332—861no—
214#331—861no—
215#331—861no—
216C43#927411yescharacteristic, complemented, Sylow
217C22×D4—432no—
218C22×D4—861no—
219C22×D4—861no—
220C2×SD16—864no—
221C2×M16—861no—
222C2×M16D17211yescharacteristic
223C2×M16D17211yescharacteristic
224C22×C8—21no—
225C22×C8—861no—
226C4⋊Q8—431no—
227C4⋊Q8—431no—
228#127—861no—
229#127—861no—
230#127—861no—
231#127—861no—
232#125—861no—
233C22⋊Q8—432no—
234C22⋊Q8—861no—
235C4×Q8—432no—
236C4×Q8—861no—
237#117—861no—
238C2×C42C22×D4311yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—431no—
243C4⋊C8—431no—
244C4⋊C8—862no—
245C4⋊C8—862no—
246C4⋊C8—861no—
247C4⋊C8—861no—
248C4⋊C8—861no—
249#102—864no—
250#100—1722no—
251#100—1722no—
252C22⋊C8C4×D4312yes—
253#97—21no—
254#97—862no—
255C4×C8—21no—
256C4×C8—21no—
257C4×C8—862no—
258C24—862no—
259C2×Q8—432no—
260C2×Q8—861no—
261C2×D4—862no—
262C2×D4—862no—
263C2×D4—3441no—
264C2×D4—3441no—
265C2×D4—3442no—
266C2×D4—1721no—
267C2×D4—1721no—
268C2×D4—1721no—
269C2×D4—1721no—
270C2×D4—1721no—
271C2×D4—1721no—
272C2×D4—1721no—
273C2×D4—1721no—
274C22×C4C2×C4×D4311yescharacteristic
275C22×C4C2×D17211yescharacteristic
276C22×C4#1062189811yescharacteristic
277SD16—3444no—
278M16—21no—
279M16—21no—
280M16—21no—
281M16—1721no—
282M16—1721no—
283M16#1062187312yescomplemented
284C2×C8—21no—
285C2×C8—22no—
286C2×C8—21no—
287C2×C8—41no—
288C2×C8—81no—
289C2×C8—861no—
290C2×C8—861no—
291C2×C8—1721no—
292C2×C8—1721no—
293C2×C8—1721no—
294C4⋊C4—432no—
295C4⋊C4—862no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4—862no—
300C22⋊C4—862no—
301C42—862no—
302C42D4×D4311yescharacteristic
303C42D4×D4311yescharacteristic
304C42D4×D4311yescharacteristic
305C42#1062190211yescharacteristic
306C23—3442no—
307C23—3442no—
308C23—1722no—
309C23—1722no—
310C23—1722no—
311C23C4×D17211yescharacteristic
312Q8—1722no—
313Q8—1721no—
314Q8—1721no—
315D4—3442no—
316D4—3442no—
317D4—3441no—
318D4—3441no—
319D4—3441no—
320D4—3441no—
321D4—3441no—
322D4—3441no—
323D4—1724no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—862no—
328C2×C4—862no—
329C2×C4C22⋊C4×D4311yescharacteristic
330C2×C4#1306328711yescharacteristic
331C2×C4#1306329511yescharacteristic
332C2×C4#1306329811yescharacteristic
333C2×C4#1306330011yescharacteristic
334C2×C4#1306331011yescharacteristic
335C2×C4C2×#1062187311yescharacteristic
336C2×C4#1306334711yescharacteristic
337C2×C4#1306335311yescharacteristic
338C2×C4#1306335811yescharacteristic
339C8—22no—
340C8—42no—
341C8—41no—
342C8—81no—
343C8—3441no—
344C8—1721no—
345C8—1721no—
346C22—21no—
347C22—21no—
348C22—3442no—
349C22—3442no—
350C22—3442no—
351C22—6882no—
352C22—6882no—
353C22#1458277711yescharacteristic
354C22C4×#1062187311yescharacteristic
355C22#1458300111yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—1722no—
360C4—1722no—
361C4#1458304011yescharacteristic
362C4#1458304611yescharacteristic
363C4#1458310011yescharacteristic
364C4#1458312211yescharacteristic
365C4#1458316511yescharacteristic
366C4#1458316811yescharacteristic
367C2—21no—
368C2—21no—
369C2—6882no—
370C2#1913494911yescharacteristic
371C2#1913510411yescharacteristic
372C2#1913514111yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1283C2
socleC22×C43#386
prime radicalC2×#13063322C22
cosocleC2×C42×C43C23
hypercenter#1283D43
hypocenterC43#9274
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
2. #19143542C2semidirect
4. #19133283C2semidirect
6. #19132491C2semidirect
7. C43×#1283C2semidirect
93. M16×C43SD16semidirect
187. #1283D43semidirect
216. C43#9274semidirect
283. M16#10621873semidirect

Maximal subgroups

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

subgroupindex
#191455382
#191435422
#191354352
#191332832
C2×#145826422
#191324912
C43×#12832
#927443