Finite Group Databasebeta

← #25015948

Subgroups — #25015948

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×#14582702C211yesmaximal, characteristic, complemented
3C2×#14582702C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic
5C2×#14582699C211yesmaximal, characteristic
6#19132673C211yesmaximal, characteristic, complemented
7C43×#1942C211yesmaximal, characteristic, complemented
8C22×Dic172C2211yescharacteristic
9C22×#10621873—21no—
10C22×D344C2211yescharacteristic
11C2×#13063313—21no—
12C22×C43⋊C16C2211yescharacteristic
13C22×C43⋊C16C2211yescharacteristic
14#14583283—22no—
15#14583283—22no—
16#14582702—22no—
17#14582702—22no—
18#14582699—22no—
19#14582699—22no—
20C2×#107×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×C4×C8×C43C2211yescharacteristic
23C43×#389—21no—
24C43×#340—21no—
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×(C2×D43)⋊C4—41no—
45C2×(C2×D43)⋊C4—41no—
46C2×C43⋊C16—21no—
47C2×C43⋊C16—21no—
48C2×C43⋊C16—21no—
49C2×C43⋊C16—21no—
50C2×C43⋊C16—21no—
51C2×C43⋊C16—21no—
52C22×C8×C43D411yescharacteristic
53C22×C8×C43C2311yescharacteristic
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—41no—
57C2×C42×C43D411yescharacteristic
58#107×C43—21no—
59#107×C43—21no—
60#107×C43—21no—
61#107×C43D412yes—
62C4×C8×C43—21no—
63C4×C8×C43—21no—
64#95×C43—41no—
65C23×D43—41no—
66C22×C4×C43—41no—
67C22×C4×C43—41no—
68C22×C4×C43D811yescharacteristic
69C22×C4×C43D811yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
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
93C4⋊C4×C43—22no—
94C4⋊C4×C43—41no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—82no—
98C42×C43—21no—
99C42×C43—21no—
100(C2×D43)⋊C4—44no—
101(C2×D43)⋊C4—44no—
102Dic172—22no—
103Dic172—22no—
104Dic172—41no—
105Dic172—41no—
106D344—22no—
107D344—22no—
108D344—41no—
109D344—41no—
110#10621873—48no—
111C43⋊C16—41no—
112C43⋊C16—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—42no—
128C2×C4×C43—81no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43#12011yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12411yescharacteristic
136C2×C4×C43C2×SD1611yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×Dic43—42no—
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—82no—
173C4×C43—161no—
174C4×C43#39411yescharacteristic
175C4×C43#45011yescharacteristic
176C4×C43#46011yescharacteristic
177C4×C43#49011yescharacteristic
178Dic43—82no—
179C2×#495—431no—
180C2×#358—431no—
181C2×#358—431no—
182C2×#357—431no—
183C2×#357—431no—
184#1942D4311yescharacteristic, complemented
185#1374—431no—
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×C16—431no—
199C22×C16—431no—
200#495—862no—
201#495—862no—
202C2×#107C2×D4311yescharacteristic
203C2×#107C2×D4311yescharacteristic
204C2×C4×C8C2×D4311yescharacteristic
205#389—21no—
206#358—862no—
207#358—862no—
208#357—862no—
209#357—862no—
210#340—21no—
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×C8C22⋊D4311yescharacteristic
230C22×C8C22×D4311yescharacteristic
231#124—864no—
232#124—1722no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—41no—
236C2×C22⋊C4—1721no—
237C2×C22⋊C4—1721no—
238C2×C42C22⋊D4311yescharacteristic
239C2×C16—861no—
240C2×C16—861no—
241C2×C16—861no—
242C2×C16—861no—
243C2×C16—861no—
244C2×C16—861no—
245#107—21no—
246#107—21no—
247#107—21no—
248#107D17212yes—
249C4×C8—21no—
250C4×C8—21no—
251#95—41no—
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—41no—
266C22×C4—41no—
267C22×C4—1721no—
268C22×C4#1062188211yescharacteristic
269C22×C4#1062188211yescharacteristic
270C22×C4C2×C22⋊D4311yescharacteristic
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#1062188412yes—
283C2×C8C2×D17211yescharacteristic
284C2×C8#1062189811yescharacteristic
285C2×C8D4×D4311yescharacteristic
286C2×C8D4×D4311yescharacteristic
287C2×C8#1062190211yescharacteristic
288C2×C8#1062190211yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—82no—
294C22⋊C4—1724no—
295C22⋊C4—1724no—
296C42—21no—
297C42—21no—
298C16—1721no—
299C16—1721no—
300C23—3441no—
301C23—3441no—
302C23—3441no—
303C23—3441no—
304C23—3441no—
305C23—3441no—
306C23—1722no—
307C23C2×#1062188211yescharacteristic
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—42no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—3441no—
329C2×C4—3441no—
330C2×C4—1722no—
331C2×C4#1306329311yescharacteristic
332C2×C4#1306329911yescharacteristic
333C2×C4#1306331411yescharacteristic
334C2×C4C2×#1062188411yescharacteristic
335C2×C4#1306335011yescharacteristic
336C2×C4#1306335011yescharacteristic
337C8—22no—
338C8#1306330011yescharacteristic
339C8#1306330011yescharacteristic
340C8#1306331011yescharacteristic
341C8#1306331011yescharacteristic
342C22—3442no—
343C22—3442no—
344C22—3442no—
345C22—6881no—
346C22—6881no—
347C22—6881no—
348C22—6881no—
349C22#1458303211yescharacteristic
350C22#1458309411yescharacteristic
351C22#1458324711yescharacteristic
352C22#1458332911yescharacteristic
353C22#1458332911yescharacteristic
354C22#1458333511yescharacteristic
355C22#1458334011yescharacteristic
356C4—41no—
357C4—41no—
358C4—82no—
359C4—161no—
360C4—3442no—
361C4#1458281611yescharacteristic
362C4#1458304911yescharacteristic
363C4#1458309911yescharacteristic
364C4#1458326511yescharacteristic
365C2—6882no—
366C2#1913582911yescharacteristic
367C2#1913651611yescharacteristic
368C2#1913653311yescharacteristic
369C2#1913665011yescharacteristic
370C2#1913665711yescharacteristic
371C2#1913682911yescharacteristic
372C2#1913683411yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1942C2
socleC23×C43C2×D8
prime radicalC22×D344C22
hypercenter#1942D43
hypocenterC43#13408
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1942

Complements

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

NH ≅ G/Ntype
2. C2×#14582702C2semidirect
3. C2×#14582702C2semidirect
6. #19132673C2semidirect
7. C43×#1942C2semidirect
184. #1942D43semidirect
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×#145827022
C2×#145826992
#191326732
C43×#19422
#1340843