Finite Group Databasebeta

← #18081929

Subgroups — #18081929

Order 4864.

370 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574145C211yesmaximal, characteristic
2#14563765C211yesmaximal, characteristic
3#14562200C211yesmaximal, characteristic
4#14562199C211yesmaximal, characteristic
5#14562198C211yesmaximal, characteristic
6#14561928C211yesmaximal, characteristic
7C19×#1518C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926947C411yescharacteristic, complemented
10#11926947C411yescharacteristic, complemented
11#11926943—21no—
12#11926943—21no—
13#11926940C411yescharacteristic, complemented
14#11926940C411yescharacteristic, complemented
15#11926597C2211yescharacteristic
16#11926580—21no—
17#11926580—21no—
18C2×C4×C19⋊C8C2211yescharacteristic
19#11926410C2211yescharacteristic
20#11926306—21no—
21#11926306—21no—
22#11926282—22no—
23#11926281—22no—
24#11926280—22no—
25#11926266—21no—
26#11926265—21no—
27C19×#533C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C19×#382C2211yescharacteristic
30C19×#328—22no—
31C19×C4⋊Q8C2×C411yescharacteristic
32C19×C4⋊Q8C2×C411yescharacteristic
33C19×#125—21no—
34C19×C22⋊Q8—21no—
35C19×C22⋊Q8—21no—
36C4×Q8×C19—21no—
37C4×Q8×C19—21no—
38C19×#117—21no—
39C2×C4⋊C4×C19—21no—
40C2×C42×C19C2311yescharacteristic
41#10597372—21no—
42C2×C4⋊Dic19—21no—
43#10597370—21no—
44#10597370—21no—
45C22×C19⋊C8D411yescharacteristic
46C22×C19⋊C8D411yescharacteristic
47#10597316—21no—
48#10597315C2×C411yescharacteristic
49#10597315C2×C411yescharacteristic
50C4×Dic38—21no—
51C4×Dic38—21no—
52C19×C4⋊C8—21no—
53C19×C22⋊C8D412yes—
54C4×C8×C19—21no—
55C19×#95—21no—
56C19×#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C22⋊(C19⋊C8)D412yes—
60#10597265—21no—
61#10597265—21no—
62#10597265—21no—
63#10597265—21no—
64#10597264—21no—
65#10597264—21no—
66#10597264—21no—
67#10597264—21no—
68C4⋊(C19⋊C8)—21no—
69C4×C19⋊C8—21no—
70C4×C19⋊C8C2×C411yescharacteristic
71C4×C19⋊C8C2×C411yescharacteristic
72C4×C19⋊C8D411yescharacteristic
73C4×C19⋊C8D411yescharacteristic
74C2×Q8×C19—21no—
75C2×Q8×C19—21no—
76C22×C4×C19—41no—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×Dic19—41no—
81C2×Dic38—21no—
82C2×Dic38—21no—
83C2×C8×C19—22no—
84C4⋊C4×C19—21no—
85C4⋊C4×C19—21no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C22⋊C4×C19—41no—
93C42×C19—41no—
94C42×C19C22×C411yescharacteristic
95C42×C19C2×D411yescharacteristic
96C42×C19#4111yescharacteristic
97C42×C19#4111yescharacteristic
98C22⋊Dic19—41no—
99C4⋊Dic19—21no—
100C4⋊Dic19—21no—
101C4⋊Dic19—21no—
102C4⋊Dic19—21no—
103C4⋊Dic19—41no—
104C4⋊Dic19—41no—
105Dic19⋊C4—41no—
106Dic19⋊C4—41no—
107C4×Dic19—41no—
108C2×C19⋊C8—21no—
109C2×C19⋊C8—21no—
110C2×C19⋊C8—21no—
111C2×C19⋊C8—21no—
112C2×C19⋊C8—22no—
113C2×C19⋊C8C22⋊C411yescharacteristic
114C2×C19⋊C8C22⋊C411yescharacteristic
115C2×C19⋊C8C22⋊C411yescharacteristic
116C2×C19⋊C8C22⋊C411yescharacteristic
117#9759—191nomaximal, Sylow
118C23×C19#12711yescharacteristic
119Q8×C19—81no—
120Q8×C19—81no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—81no—
126C2×C4×C19—81no—
127C2×C4×C19—81no—
128C2×C4×C19C2×C22⋊C411yescharacteristic
129C2×C4×C19C4×D411yescharacteristic
130C2×C4×C19C4×D411yescharacteristic
131C2×C4×C19#12111yescharacteristic
132C2×C4×C19#12111yescharacteristic
133C2×C4×C19#12411yescharacteristic
134C2×C4×C19#13711yescharacteristic
135C2×C4×C19#13711yescharacteristic
136C2×C4×C19#13711yescharacteristic
137C2×C4×C19#13711yescharacteristic
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—81no—
141C2×Dic19—81no—
142C2×Dic19—81no—
143Dic38—81no—
144Dic38—81no—
145C8×C19—42no—
146C19⋊C8—21no—
147C19⋊C8—21no—
148C19⋊C8—21no—
149C19⋊C8—21no—
150C19⋊C8—42no—
151#3160—191no—
152#1835—191no—
153#1518—191no—
154#1518—191no—
155#1518—191no—
156#1518D1911yescharacteristic
157#1452—191no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19#39011yescharacteristic
161C22×C19#49711yescharacteristic
162C22×C19#49711yescharacteristic
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—81no—
168C4×C19—81no—
169C4×C19—161no—
170C4×C19#41911yescharacteristic
171C4×C19#41911yescharacteristic
172C4×C19#49111yescharacteristic
173C4×C19#49111yescharacteristic
174Dic19—81no—
175Dic19—81no—
176Dic19—161no—
177#533—191no—
178#533C2×D1911yescharacteristic
179#500—191no—
180#500—191no—
181#499—381no—
182#499—381no—
183#498—191no—
184#498—191no—
185#431—191no—
186#431C2×D1911yescharacteristic
187#427—381no—
188#427—381no—
189C2×C4×C8—191no—
190#382—191no—
191#382C2×D1911yescharacteristic
192#340—381no—
193#340—381no—
194#328—22no—
195#328—382no—
196#328—382no—
197#328—382no—
198#322—381no—
199#322—381no—
200C2×C19—21no—
201C2×C19—21no—
202C2×C19#196011yescharacteristic
203C2×C19#197611yescharacteristic
204C2×C19#197611yescharacteristic
205C22×C8—191no—
206C22×C8—191no—
207C4⋊Q8—191no—
208C4⋊Q8—191no—
209C4⋊Q8C4×D1911yescharacteristic
210C4⋊Q8C4×D1911yescharacteristic
211#125—21no—
212#125—381no—
213C22⋊Q8—21no—
214C22⋊Q8—21no—
215C22⋊Q8—381no—
216C22⋊Q8—381no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×Q8—381no—
220C4×Q8—381no—
221#117—21no—
222#117—381no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—381no—
225C2×C42C22×D1911yescharacteristic
226#107—381no—
227#107—381no—
228#107—381no—
229#107—381no—
230#106—381no—
231#106—381no—
232#106—381no—
233#106—381no—
234C4⋊C8—21no—
235C4⋊C8—381no—
236C22⋊C8—192no—
237C22⋊C8C22⋊D1912yes—
238C4×C8—21no—
239C4×C8—191no—
240C4×C8—191no—
241C4×C8—191no—
242C4×C8—191no—
243C4×C8—381no—
244#95—21no—
245#95—21no—
246#95—381no—
247#95—381no—
248C19#975911yescharacteristic, complemented, Sylow
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—381no—
252C2×Q8—381no—
253C22×C4—41no—
254C22×C4—761no—
255C22×C4D4×D1911yescharacteristic
256C22×C4D4×D1911yescharacteristic
257C22×C4C2×C22⋊D1911yescharacteristic
258C2×C8—22no—
259C2×C8—191no—
260C2×C8—191no—
261C2×C8—191no—
262C2×C8—191no—
263C2×C8—381no—
264C2×C8—381no—
265C2×C8—381no—
266C2×C8—381no—
267C2×C8—382no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—381no—
277C4⋊C4—381no—
278C4⋊C4—381no—
279C4⋊C4—381no—
280C4⋊C4—761no—
281C4⋊C4—761no—
282C4⋊C4—761no—
283C4⋊C4—761no—
284C22⋊C4—41no—
285C22⋊C4—761no—
286C42—41no—
287C42—761no—
288C42C2×C4×D1911yescharacteristic
289C42#6454111yescharacteristic
290C42D4×D1911yescharacteristic
291C42#6454311yescharacteristic
292C23#1059738611yescharacteristic
293Q8—81no—
294Q8—81no—
295Q8—1521no—
296Q8—1521no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4—1521no—
307C2×C4—1521no—
308C2×C4—1521no—
309C2×C4C22⋊C4×D1911yescharacteristic
310C2×C4(C22⋊D19)⋊C411yescharacteristic
311C2×C4#1059733011yescharacteristic
312C2×C4#1059733111yescharacteristic
313C2×C4#1059736111yescharacteristic
314C2×C4#1059736111yescharacteristic
315C2×C4#1059736411yescharacteristic
316C2×C4#1059736411yescharacteristic
317C2×C4C4×C22⋊D1911yescharacteristic
318C2×C4#1059738511yescharacteristic
319C8—42no—
320C8—381no—
321C8—381no—
322C8—381no—
323C8—381no—
324C8—762no—
325C22—21no—
326C22—21no—
327C22#1192644411yescharacteristic
328C22#1192693511yescharacteristic
329C22#1192693711yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—81no—
335C4—81no—
336C4—161no—
337C4—3041no—
338C4—1521no—
339C4—1521no—
340C4#1192655111yescharacteristic
341C4#1192655111yescharacteristic
342C4#1192691111yescharacteristic
343C4#1192691111yescharacteristic
344C2—21no—
345C2—21no—
346C2#1456445311yescharacteristic
347C2#1456453011yescharacteristic
348C2#1456453211yescharacteristic
subgroupG/H
centerC22#11926444
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1518C2
socleC22×C19#390
prime radicalC23×C19#127
cosocleC2×C42×C19C23
hypercenter#1518D19
hypocenterC19#9759
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
9. #11926947C4semidirect
10. #11926947C4semidirect
13. #11926940C4semidirect
14. #11926940C4semidirect
248. C19#9759semidirect

Maximal subgroups

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

subgroupindex
#145741452
#145637652
#145622002
#145621992
#145621982
#145619282
C19×#15182
#975919