Finite Group Databasebeta

← #18081907

Subgroups — #18081907

Order 4864.

416 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573958C211yesmaximal, characteristic
2#14562383C211yesmaximal, characteristic, complemented
3#14562133C211yesmaximal, characteristic, complemented
4#14562129C211yesmaximal, characteristic
5#14562037C211yesmaximal, characteristic, complemented
6#14562033C211yesmaximal, characteristic
7C19×#1770C211yesmaximal, characteristic, complemented
8#11927101C2211yescharacteristic
9#11927094C2211yescharacteristic
10#11926899—21no—
11#11926899—21no—
12#11926895C411yescharacteristic, complemented
13#11926895C411yescharacteristic, complemented
14#11926891C411yescharacteristic, complemented
15#11926891C411yescharacteristic, complemented
16#11926597C2211yescharacteristic
17#11926597C2211yescharacteristic
18#11926541—21no—
19#11926541—21no—
20#11926297—21no—
21#11926295—21no—
22#11926280—22no—
23#11926277—22no—
24#11926274—22no—
25#11926271—22no—
26C2×C19×C4⋊C8C2211yescharacteristic
27C2×C19×#97—21no—
28C2×C4×C8×C19C2211yescharacteristic
29C4×C4⋊C4×C19C2211yescharacteristic
30C19×#336—21no—
31C2×#64541—21no—
32C22×C8×C19—21no—
33C22×C8×C19D411yescharacteristic
34C22×C8×C19D411yescharacteristic
35C2×C4⋊C4×C19—21no—
36C2×C42×C19—21no—
37C2×C42×C19C2311yescharacteristic
38#10597376—21no—
39#10597376—21no—
40#10597372—21no—
41#10597370—21no—
42#10597370—21no—
43#10597321—21no—
44#10597320C2×C411yescharacteristic
45C4×D76—21no—
46C4×D76—21no—
47#10597316—21no—
48#10597315C2×C411yescharacteristic
49#10597315C2×C411yescharacteristic
50#10597315C2×C411yescharacteristic
51C4×Dic38—21no—
52C4×Dic38—21no—
53C19×C4⋊C8—21no—
54C19×C4⋊C8D412yes—
55C19×#97—42no—
56C4×C8×C19C2×C411yescharacteristic
57C4×C8×C19C2×C411yescharacteristic
58C4×C8×C19D411yescharacteristic
59C4×C8×C19D411yescharacteristic
60C19×#95D412yes—
61C22⋊(C19⋊C8)—21no—
62C22⋊(C19⋊C8)—21no—
63#10597278—21no—
64#10597278—21no—
65#10597278—21no—
66#10597278—21no—
67#10597273—21no—
68#10597273—21no—
69#10597273—21no—
70#10597273—21no—
71C4⋊(C19⋊C8)—21no—
72C4⋊(C19⋊C8)—21no—
73C4×C19⋊C8—21no—
74C4×C19⋊C8—21no—
75C22×C4×C19—22no—
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C2×C22⋊D19—41no—
80#64541—41no—
81#64541—41no—
82#64541—41no—
83#64541—41no—
84C2×D76—21no—
85C2×D76—21no—
86C2×D76—21no—
87C2×C4×D19—41no—
88C2×Dic38—21no—
89C2×Dic38—21no—
90C2×Dic38—21no—
91C2×C8×C19—21no—
92C2×C8×C19—21no—
93C2×C8×C19—21no—
94C2×C8×C19—21no—
95C2×C8×C19—22no—
96C2×C8×C19—41no—
97C2×C8×C19—41no—
98C2×C8×C19C22⋊C411yescharacteristic
99C2×C8×C19C22⋊C411yescharacteristic
100C2×C8×C19C22⋊C411yescharacteristic
101C2×C8×C19C22⋊C411yescharacteristic
102C4⋊C4×C19—42no—
103C42×C19—41no—
104C42×C19—41no—
105C42×C19C22×C411yescharacteristic
106C42×C19C2×D411yescharacteristic
107C42×C19C2×D411yescharacteristic
108C42×C19#4111yescharacteristic
109C22⋊Dic19—41no—
110(C2×D19)⋊C4—41no—
111(C2×D19)⋊C4—41no—
112C4⋊Dic19—21no—
113C4⋊Dic19—21no—
114C4⋊Dic19—21no—
115C4⋊Dic19—21no—
116C4⋊Dic19—21no—
117C4⋊Dic19—21no—
118Dic19⋊C4—41no—
119Dic19⋊C4—41no—
120C4×Dic19—41no—
121C2×C19⋊C8—41no—
122C2×C19⋊C8—41no—
123#9754—191nomaximal, Sylow
124C23×C19#12111yescharacteristic
125C22×D19—41no—
126C2×C4×C19—22no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19C2×C22⋊C411yescharacteristic
132C2×C4×C19C4×D411yescharacteristic
133C2×C4×C19C4×D411yescharacteristic
134C2×C4×C19#12111yescharacteristic
135C2×C4×C19#12411yescharacteristic
136C2×C4×C19#12711yescharacteristic
137C2×C4×C19#13511yescharacteristic
138C2×C4×C19#13511yescharacteristic
139C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C19#13711yescharacteristic
141C22⋊D19—81no—
142C22⋊D19—81no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146D76—41no—
147D76—41no—
148D76—42no—
149D76—81no—
150C4×D19—81no—
151C4×D19—81no—
152Dic38—41no—
153Dic38—41no—
154Dic38—42no—
155Dic38—81no—
156C8×C19—21no—
157C8×C19—21no—
158C8×C19—21no—
159C8×C19—21no—
160C8×C19—42no—
161C19⋊C8—81no—
162C19⋊C8—81no—
163#3131—191no—
164#1770D1911yescharacteristic, complemented
165#1564—191no—
166#1503—191no—
167#1502—191no—
168#1481—191no—
169#1480—191no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19#39011yescharacteristic
173C22×C19#46311yescharacteristic
174C22×C19#46411yescharacteristic
175C2×D19—81no—
176C2×D19—81no—
177C2×D19—81no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—82no—
182C4×C19#41611yescharacteristic
183C4×C19#41711yescharacteristic
184C4×C19#44412yes—
185C4×C19#46311yescharacteristic
186C4×C19#46411yescharacteristic
187Dic19—81no—
188Dic19—81no—
189Dic19—81no—
190#533—191no—
191#532—191no—
192#488—381no—
193#488—381no—
194#487—191no—
195#487—191no—
196#486—191no—
197#486—191no—
198#431—191no—
199#431—191no—
200C2×C4⋊C8C2×D1911yescharacteristic
201#416—381no—
202#416—381no—
203C2×#97—21no—
204C2×C4×C8C2×D1911yescharacteristic
205C4×C4⋊C4C2×D1911yescharacteristic
206#336—21no—
207#335—381no—
208#334—381no—
209#328—382no—
210#327—382no—
211Q8⋊C8—382no—
212D4⋊C8—382no—
213C2×C19—21no—
214C2×C19—21no—
215C2×C19#197511yescharacteristic
216C2×C19#197611yescharacteristic
217C2×C19#198311yescharacteristic
218D19—161no—
219C2×#41—381no—
220C22×C8—21no—
221C22×C8C22⋊D1911yescharacteristic
222C22×C8C22⋊D1911yescharacteristic
223C4⋊Q8—191no—
224C4⋊Q8—191no—
225C4⋊Q8—191no—
226#127—191no—
227#125—381no—
228#124—381no—
229C22⋊Q8—381no—
230C22⋊Q8—381no—
231#121—381no—
232#121—381no—
233C4×Q8—381no—
234C4×Q8—381no—
235C4×D4—381no—
236C4×D4—381no—
237#117—381no—
238C2×C4⋊C4—21no—
239C2×C42—21no—
240C2×C42C22×D1911yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—381no—
243C4⋊C8—381no—
244C4⋊C8D7612yes—
245#103—381no—
246#103—381no—
247#103—381no—
248#103—381no—
249#102—381no—
250#102—381no—
251#102—381no—
252#102—381no—
253C22⋊C8—381no—
254C22⋊C8—381no—
255#97—42no—
256C4×C8—381no—
257C4×C8—381no—
258C4×C8C4×D1911yescharacteristic
259C4×C8C4×D1911yescharacteristic
260C4×C8D7611yescharacteristic
261C4×C8D7611yescharacteristic
262#95D7612yes—
263C19#975411yescharacteristic, complemented, Sylow
264#41—761no—
265#41—761no—
266#41—761no—
267#41—761no—
268C2×Q8—381no—
269C2×Q8—381no—
270C2×Q8—381no—
271C2×D4—381no—
272C2×D4—381no—
273C2×D4—381no—
274C2×D4—761no—
275C22×C4—22no—
276C22×C4—761no—
277C22×C4C2×D7611yescharacteristic
278C22×C4#6454111yescharacteristic
279C22×C4C2×C22⋊D1911yescharacteristic
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—22no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—761no—
288C2×C8—761no—
289C2×C8(C2×D19)⋊C411yescharacteristic
290C2×C8(C2×D19)⋊C411yescharacteristic
291C2×C8(C2×D19)⋊C411yescharacteristic
292C2×C8(C2×D19)⋊C411yescharacteristic
293C4⋊C4—42no—
294C4⋊C4—381no—
295C4⋊C4—381no—
296C4⋊C4—381no—
297C4⋊C4—381no—
298C4⋊C4—381no—
299C4⋊C4—381no—
300C4⋊C4—761no—
301C4⋊C4—761no—
302C22⋊C4—761no—
303C22⋊C4—761no—
304C22⋊C4—761no—
305C42—41no—
306C42—41no—
307C42—761no—
308C42C2×C4×D1911yescharacteristic
309C42C2×D7611yescharacteristic
310C42C2×D7611yescharacteristic
311C42#6454111yescharacteristic
312C23—761no—
313C23#1059737611yescharacteristic
314Q8—761no—
315Q8—761no—
316Q8—762no—
317Q8—1521no—
318D4—761no—
319D4—761no—
320D4—762no—
321D4—1521no—
322D4—1521no—
323D4—1521no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—761no—
332C2×C4—1521no—
333C2×C4—1521no—
334C2×C4C4×D7611yescharacteristic
335C2×C4C4×D7611yescharacteristic
336C2×C4#1059732011yescharacteristic
337C2×C4#1059732111yescharacteristic
338C2×C4C2×(C2×D19)⋊C411yescharacteristic
339C2×C4#1059737611yescharacteristic
340C2×C4#1059737811yescharacteristic
341C2×C4#1059738811yescharacteristic
342C2×C4#1059739611yescharacteristic
343C2×C4#1059739611yescharacteristic
344C8—21no—
345C8—21no—
346C8—21no—
347C8—21no—
348C8—42no—
349C8—1521no—
350C8—1521no—
351C22—21no—
352C22—21no—
353C22—1521no—
354C22—1521no—
355C22—1521no—
356C22#1192644611yescharacteristic
357C22#1192675911yescharacteristic
358C22#1192676611yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—1521no—
364C4—1521no—
365C4—1521no—
366C4#1192653811yescharacteristic
367C4#1192654311yescharacteristic
368C4#1192666712yes—
369C4#1192675911yescharacteristic
370C4#1192676611yescharacteristic
371C2—21no—
372C2—21no—
373C2—3041no—
374C2#1456452811yescharacteristic
375C2#1456453311yescharacteristic
376C2#1456456711yescharacteristic
subgroupG/H
centerC2×C4#10597376
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1770C2
socleC22×C19#390
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#1770D19
hypocenterC19#9754
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1770

Complements

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

NH ≅ G/Ntype
2. #14562383C2semidirect
3. #14562133C2semidirect
5. #14562037C2semidirect
7. C19×#1770C2semidirect
12. #11926895C4semidirect
13. #11926895C4semidirect
14. #11926891C4semidirect
15. #11926891C4semidirect
164. #1770D19semidirect
263. C19#9754semidirect

Maximal subgroups

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

subgroupindex
#145739582
#145623832
#145621332
#145621292
#145620372
#145620332
C19×#17702
#975419