Finite Group Databasebeta

← #25015949

Subgroups — #25015949

Order 11008.

482 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
1C2×#14583283C211yesmaximal, characteristic
2C2×#14582704C211yesmaximal, characteristic, complemented
3C2×#14582704C211yesmaximal, characteristic, complemented
4C2×#14582701C211yesmaximal, characteristic
5C2×#14582701C211yesmaximal, characteristic
6#19135328C211yesmaximal, characteristic, complemented
7C43×#1374C211yesmaximal, characteristic, complemented
8C22×Dic172C2211yescharacteristic
9C22×#10621873—21no—
10C22×D344C2211yescharacteristic
11C2×#13063313—21no—
12#14583283—22no—
13#14583283—22no—
14C2×#13063259C2211yescharacteristic
15C2×#13063259C2211yescharacteristic
16#14582797—21no—
17#14582704—22no—
18#14582704—22no—
19#14582701—22no—
20#14582701—22no—
21#14582662—21no—
22C22×C16×C43C2211yescharacteristic
23C22×C16×C43C2211yescharacteristic
24C2×C4×C8×C43C2211yescharacteristic
25C22×Dic86—21no—
26C22×D172—21no—
27C2×Dic172—21no—
28C2×Dic172—21no—
29C2×Dic172—21no—
30C2×Dic172—21no—
31C2×Dic172—21no—
32C2×Dic172D412yes—
33C2×#10621873—24no—
34C2×#10621873—42no—
35C2×#10621873—42no—
36C2×D344—21no—
37C2×D344—21no—
38C2×D344—21no—
39C2×D344—21no—
40C2×D344—21no—
41C2×D344D412yes—
42#13063313—24no—
43#13063313—42no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×Dic43⋊C4—41no—
47C2×(C2×D43)⋊C4—41no—
48C2×(C2×D43)⋊C4—41no—
49#13063259—21no—
50#13063259—21no—
51#13063259—21no—
52#13063259D412yes—
53C43⋊#95—41no—
54C22×C8×C43D411yescharacteristic
55C22×C8×C43C2311yescharacteristic
56C2×C42×C43D411yescharacteristic
57C2×C16×C43—21no—
58C2×C16×C43—21no—
59C2×C16×C43—21no—
60C2×C16×C43—21no—
61C2×C16×C43—21no—
62C2×C16×C43—21no—
63C4×C8×C43—21no—
64C4×C8×C43—21no—
65C23×D43—41no—
66C22×C4×C43D811yescharacteristic
67C22×C4×C43D811yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—41no—
70C22×Dic43—41no—
71C22×Dic43—41no—
72C2×D172—22no—
73C2×D172—41no—
74C2×D172—41no—
75C2×D172—41no—
76C2×D172—41no—
77C2×D172—41no—
78C2×Dic86—22no—
79C2×Dic86—41no—
80C2×Dic86—41no—
81C2×Dic86—41no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84C2×C8×C43—21no—
85C2×C8×C43—21no—
86C2×C8×C43SD1612yes—
87C2×C8×C43C2×D411yescharacteristic
88C2×C8×C43C2×D411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43#4111yescharacteristic
91C2×C8×C43#4111yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C42×C43—21no—
94C42×C43—21no—
95(C2×D43)⋊C4—44no—
96(C2×D43)⋊C4—44no—
97C4⋊Dic43—22no—
98C4⋊Dic43—41no—
99C4⋊Dic43—41no—
100C4⋊Dic43—41no—
101Dic43⋊C4—82no—
102Dic172—22no—
103Dic172—22no—
104Dic172—41no—
105Dic172—41no—
106D344—22no—
107D344—22no—
108D344—41no—
109D344—41no—
110#10621873—48no—
111C16×C43—41no—
112C16×C43—41no—
113C23×C43C2×D811yescharacteristic
114C22×D43—42no—
115C22×D43—81no—
116C22×D43—81no—
117C22×D43—81no—
118C22×D43—81no—
119C22×D43—81no—
120C22×D43—81no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43#12011yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12411yescharacteristic
130C2×C4×C43C2×SD1611yescharacteristic
131C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
133C2×Dic43—42no—
134C2×Dic43—42no—
135C2×Dic43—81no—
136C2×Dic43—81no—
137C2×Dic43—81no—
138C2×Dic43—81no—
139C2×Dic43—81no—
140C2×Dic43—81no—
141C2×Dic43—81no—
142D172—42no—
143D172—42no—
144D172—81no—
145D172—81no—
146Dic86—42no—
147Dic86—42no—
148Dic86—81no—
149Dic86—81no—
150C8×C43—22no—
151C8×C43#12111yescharacteristic
152C8×C43#12111yescharacteristic
153C8×C43#12311yescharacteristic
154C8×C43#12311yescharacteristic
155#13408—431nomaximal, Sylow
156C22×C43#44711yescharacteristic
157C22×C43#45911yescharacteristic
158C22×C43#48611yescharacteristic
159C22×C43#50811yescharacteristic
160C22×C43#50811yescharacteristic
161C22×C43#50911yescharacteristic
162C22×C43#51011yescharacteristic
163C2×D43—82no—
164C2×D43—82no—
165C2×D43—82no—
166C2×D43—161no—
167C2×D43—161no—
168C2×D43—161no—
169C2×D43—161no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43#39411yescharacteristic
173C4×C43#45011yescharacteristic
174C4×C43#46011yescharacteristic
175C4×C43#49011yescharacteristic
176Dic43—82no—
177Dic43—82no—
178Dic43—161no—
179C2×#495—431no—
180C2×#358—431no—
181C2×#358—431no—
182C2×#357—431no—
183C2×#357—431no—
184#1942—431no—
185#1374D4311yescharacteristic, complemented
186C2×C43#204111yescharacteristic
187C2×C43#218611yescharacteristic
188C2×C43#218911yescharacteristic
189C2×C43#221011yescharacteristic
190C2×C43#221111yescharacteristic
191C2×C43#224211yescharacteristic
192C2×C43#224311yescharacteristic
193D43—162no—
194C22×Q16—431no—
195C22×SD16—861no—
196C22×D8—431no—
197C2×#124—861no—
198C22×C16C2×D4311yescharacteristic
199C22×C16C2×D4311yescharacteristic
200#495—862no—
201#495—862no—
202C2×#107—431no—
203C2×#107—431no—
204C2×C4×C8C2×D4311yescharacteristic
205#389—861no—
206#358—862no—
207#358—862no—
208#357—862no—
209#357—862no—
210#340—861no—
211C43#1340811yescharacteristic, complemented, Sylow
212C22×Q8—861no—
213C22×D4—861no—
214C2×Q16—432no—
215C2×Q16—861no—
216C2×Q16—861no—
217C2×Q16—861no—
218C2×Q16—861no—
219C2×Q16—861no—
220C2×SD16—864no—
221C2×SD16—1722no—
222C2×SD16—1722no—
223C2×D8—432no—
224C2×D8—861no—
225C2×D8—861no—
226C2×D8—861no—
227C2×D8—861no—
228C2×D8—861no—
229C22×C8D17211yescharacteristic
230C22×C8C22×D4311yescharacteristic
231#124—864no—
232#124—1722no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—1721no—
236C2×C22⋊C4—1721no—
237C2×C22⋊C4—1721no—
238C2×C42D17211yescharacteristic
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245#107—432no—
246#107—861no—
247#107—861no—
248#107—861no—
249C4×C8—21no—
250C4×C8—21no—
251#95—1721no—
252C24—1721no—
253C2×Q8—862no—
254C2×Q8—1721no—
255C2×Q8—1721no—
256C2×Q8—1721no—
257C2×Q8—1721no—
258C2×Q8—1721no—
259C2×D4—862no—
260C2×D4—1721no—
261C2×D4—1721no—
262C2×D4—1721no—
263C2×D4—1721no—
264C2×D4—1721no—
265C22×C4—1721no—
266C22×C4—1721no—
267C22×C4—1721no—
268C22×C4D34411yescharacteristic
269C22×C4D34411yescharacteristic
270C22×C4C2×D17211yescharacteristic
271Q16—862no—
272Q16—862no—
273Q16—1721no—
274Q16—1721no—
275SD16—1728no—
276D8—862no—
277D8—862no—
278D8—1721no—
279D8—1721no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8#1062187312yes—
283C2×C8#1062189811yescharacteristic
284C2×C8#1062189811yescharacteristic
285C2×C8D4×D4311yescharacteristic
286C2×C8D4×D4311yescharacteristic
287C2×C8D4×D4311yescharacteristic
288C2×C8#1062190211yescharacteristic
289C4⋊C4—862no—
290C4⋊C4—3442no—
291C4⋊C4—1721no—
292C4⋊C4—1721no—
293C4⋊C4—1721no—
294C22⋊C4—1724no—
295C22⋊C4—1724no—
296C42—21no—
297C42—21no—
298C16—41no—
299C16—41no—
300C23—3441no—
301C23—3441no—
302C23—3441no—
303C23—3441no—
304C23—3441no—
305C23—3441no—
306C23—1722no—
307C23C2×D34411yescharacteristic
308Q8—3441no—
309Q8—3441no—
310Q8—1722no—
311Q8—1722no—
312D4—3441no—
313D4—3441no—
314D4—1722no—
315D4—1722no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—3441no—
323C2×C4—3441no—
324C2×C4—3441no—
325C2×C4—3441no—
326C2×C4—3441no—
327C2×C4—3441no—
328C2×C4—3441no—
329C2×C4—1722no—
330C2×C4—1722no—
331C2×C4#1306329511yescharacteristic
332C2×C4#1306330011yescharacteristic
333C2×C4#1306331311yescharacteristic
334C2×C4C2×#1062187311yescharacteristic
335C2×C4#1306335311yescharacteristic
336C2×C4#1306335311yescharacteristic
337C8—22no—
338C8#1306329811yescharacteristic
339C8#1306329811yescharacteristic
340C8#1306331011yescharacteristic
341C8#1306331011yescharacteristic
342C22—3442no—
343C22—3442no—
344C22—3442no—
345C22—6881no—
346C22—6881no—
347C22—6881no—
348C22—6881no—
349C22#1458303511yescharacteristic
350C22#1458309511yescharacteristic
351C22#1458324611yescharacteristic
352C22#1458333111yescharacteristic
353C22#1458333111yescharacteristic
354C22#1458333711yescharacteristic
355C22#1458334211yescharacteristic
356C4—41no—
357C4—41no—
358C4—3442no—
359C4—3442no—
360C4—6881no—
361C4#1458281711yescharacteristic
362C4#1458305211yescharacteristic
363C4#1458310011yescharacteristic
364C4#1458326411yescharacteristic
365C2—6882no—
366C2#1913583011yescharacteristic
367C2#1913652011yescharacteristic
368C2#1913653711yescharacteristic
369C2#1913665111yescharacteristic
370C2#1913665811yescharacteristic
371C2#1913682711yescharacteristic
372C2#1913683211yescharacteristic
subgroupG/H
centerC23C2×D344
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1374C2
socleC23×C43C2×D8
prime radicalC22×D344C22
hypercenter#1374D43
hypocenterC43#13408
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
2. C2×#14582704C2semidirect
3. C2×#14582704C2semidirect
6. #19135328C2semidirect
7. C43×#1374C2semidirect
185. #1374D43semidirect
211. C43#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#145832832
C2×#145827042
C2×#145827012
#191353282
C43×#13742
#1340843