Finite Group Databasebeta

← #18085271

Subgroups — #18085271

Order 4864.

504 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574786C211yesmaximal, characteristic
2#14574781C211yesmaximal, characteristic
3#14572012C211yesmaximal, characteristic
4#14564611C211yesmaximal, characteristic
5#14562308C211yesmaximal, characteristic
6#14561467C211yesmaximal, characteristic
7C19×#1549C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9C2×#10597315C2211yescharacteristic
10#11926947—21no—
11#11926942—21no—
12#11926896—21no—
13#11926895—21no—
14#11926879—22no—
15#11926875—22no—
16#11926836—22no—
17#11926830—22no—
18#11926597C2211yescharacteristic
19#11926451—22no—
20#11926449—22no—
21#11926409—22no—
22C42×Dic19C2211yescharacteristic
23#11926305—22no—
24#11926291—22no—
25C2×C19×C4⋊Q8C2211yescharacteristic
26C19×#431C2211yescharacteristic
27C19×#423C2211yescharacteristic
28C19×#332—22no—
29C22×Q8×C19—21no—
30C22×Dic38—21no—
31C2×M16×C19—21no—
32C19×C4⋊Q8—21no—
33C19×C4⋊Q8—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19D412yes—
38C2×C42×C19C2311yescharacteristic
39#10597372—21no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19D412yes—
42#10597370—21no—
43#10597370—21no—
44C2×C4×Dic19—21no—
45C2×C4×Dic19—21no—
46C2×C4×Dic19D412yes—
47#10597316—21no—
48#10597315—21no—
49#10597315—21no—
50#10597315—21no—
51#10597315—21no—
52#10597315D411yescharacteristic
53#10597315D411yescharacteristic
54C4×Dic38—21no—
55C4×Dic38—21no—
56C19×C4⋊C8—21no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8D412yes—
59C19×C22⋊C8—21no—
60C4×C8×C19—21no—
61C19⋊#95—28no—
62C22⋊(C19⋊C8)—21no—
63#10597274—24no—
64#10597273—24no—
65#10597267—24no—
66#10597264—24no—
67C4⋊(C19⋊C8)D412yes—
68C4×C19⋊C8—21no—
69C2×Q8×C19—44no—
70C2×Q8×C19—41no—
71C2×Q8×C19—41no—
72C22×C4×C19—22no—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×Dic19—22no—
77C22×Dic19—22no—
78C2×Dic38—21no—
79C2×Dic38—21no—
80C2×Dic38—41no—
81C2×Dic38—41no—
82C2×Dic38—42no—
83C2×Dic38—42no—
84M16×C19—42no—
85C2×C8×C19—22no—
86C2×C8×C19—41no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C42×C19C2×D411yescharacteristic
92C42×C19C2×D411yescharacteristic
93C42×C19C2×D411yescharacteristic
94C42×C19#4111yescharacteristic
95C22⋊Dic19—41no—
96C4⋊Dic19—21no—
97C4⋊Dic19—22no—
98C4⋊Dic19—21no—
99C4⋊Dic19—22no—
100C4⋊Dic19—21no—
101C4⋊Dic19—21no—
102C4⋊Dic19—41no—
103C4⋊Dic19—41no—
104Dic19⋊C4—41no—
105Dic19⋊C4—41no—
106C4×Dic19—24no—
107C4×Dic19—22no—
108C4×Dic19—22no—
109C4×Dic19—42no—
110C4×Dic19—41no—
111C2×C19⋊C8—22no—
112#10296—191nomaximal, Sylow
113C23×C19#12011yescharacteristic
114Q8×C19—82no—
115Q8×C19—82no—
116C2×C4×C19—22no—
117C2×C4×C19—22no—
118C2×C4×C19—44no—
119C2×C4×C19—42no—
120C2×C4×C19#12011yescharacteristic
121C2×C4×C19#12011yescharacteristic
122C2×C4×C19#12111yescharacteristic
123C2×C4×C19#12111yescharacteristic
124C2×C4×C19#12111yescharacteristic
125C2×C4×C19#12711yescharacteristic
126C2×C4×C19#13512yes—
127C2×C4×C19#13712yes—
128C2×Dic19—24no—
129C2×Dic19—42no—
130C2×Dic19—42no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—42no—
134C2×Dic19—44no—
135Dic38—42no—
136Dic38—42no—
137Dic38—82no—
138Dic38—81no—
139Dic38—81no—
140C8×C19—42no—
141C8×C19—81no—
142C19⋊C8—42no—
143#3230—191no—
144#3229—191no—
145#2862—191no—
146#1994—191no—
147#1549D1911yescharacteristic
148#1546—191no—
149#1276—191no—
150C22×C19—21no—
151C22×C19—21no—
152C22×C19#39211yescharacteristic
153C22×C19#45212yes—
154C4×C19—21no—
155C4×C19—21no—
156C4×C19—82no—
157C4×C19#45412yes—
158C4×C19#45612yes—
159C4×C19#46412yes—
160C4×C19#49511yescharacteristic
161C4×C19#49711yescharacteristic
162Dic19—44no—
163Dic19—81no—
164Dic19—81no—
165Dic19—82no—
166#533—191no—
167C2×C4⋊Q8—191no—
168C2×C4⋊Q8C2×D1911yescharacteristic
169#500—381no—
170#498—381no—
171#487—381no—
172#487—381no—
173#484—382no—
174#483—382no—
175#477—382no—
176#475—382no—
177#431—191no—
178#431C2×D1911yescharacteristic
179#423C2×D1911yescharacteristic
180#391—382no—
181#391—382no—
182#382—382no—
183C43—191no—
184#339—382no—
185#332—22no—
186#332—382no—
187C2×C19—22no—
188C2×C19#200311yescharacteristic
189C2×C19#200511yescharacteristic
190C2×C19#201511yescharacteristic
191C22×Q8—21no—
192C22×Q8—381no—
193C2×M16—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—191no—
199C4⋊Q8—191no—
200C4⋊Q8—381no—
201C4⋊Q8—381no—
202C4⋊Q8—381no—
203C4⋊Q8—381no—
204#125—381no—
205C22⋊Q8—381no—
206C22⋊Q8—381no—
207C4×Q8—381no—
208C4×Q8—381no—
209#117—381no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—192no—
212C2×C4⋊C4—381no—
213C2×C4⋊C4D7612yes—
214C2×C42—192no—
215C2×C42—381no—
216C2×C42—381no—
217C2×C42C22×D1911yescharacteristic
218#107—384no—
219#106—384no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—192no—
223C4⋊C8C22⋊D1912yes—
224#103—384no—
225#103—384no—
226C22⋊C8—21no—
227C22⋊C8—381no—
228C4×C8—21no—
229C4×C8—381no—
230#95—388no—
231C19#1029611yescharacteristic, complemented, Sylow
232C2×Q8—44no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—381no—
236C2×Q8—381no—
237C2×Q8—761no—
238C2×Q8—761no—
239C2×Q8—762no—
240C2×Q8—762no—
241C22×C4—22no—
242C22×C4—382no—
243C22×C4—382no—
244C22×C4C2×D7611yescharacteristic
245C22×C4D4×D1911yescharacteristic
246C22×C4D4×D1911yescharacteristic
247M16—42no—
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—382no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—382no—
256C4⋊C4—381no—
257C4⋊C4—381no—
258C4⋊C4—382no—
259C4⋊C4—381no—
260C4⋊C4—381no—
261C4⋊C4—761no—
262C4⋊C4—761no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C22⋊C4—761no—
266C42—384no—
267C42—382no—
268C42—382no—
269C42—762no—
270C42—761no—
271C42#6454111yescharacteristic
272C42D4×D1911yescharacteristic
273C42D4×D1911yescharacteristic
274C42C2×C22⋊D1911yescharacteristic
275C23#1059732811yescharacteristic
276Q8—82no—
277Q8—82no—
278Q8—762no—
279Q8—762no—
280Q8—1521no—
281Q8—1521no—
282Q8—1522no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—384no—
288C2×C4—762no—
289C2×C4—762no—
290C2×C4—761no—
291C2×C4—761no—
292C2×C4—762no—
293C2×C4—764no—
294C2×C4#1059732811yescharacteristic
295C2×C4#1059733011yescharacteristic
296C2×C4#1059733011yescharacteristic
297C2×C4#1059736212yes—
298C2×C4#1059736412yes—
299C2×C4#1059737611yescharacteristic
300C2×C4#1059738311yescharacteristic
301C2×C4#1059738611yescharacteristic
302C8—42no—
303C8—81no—
304C8—762no—
305C22—21no—
306C22—21no—
307C22#1192645311yescharacteristic
308C22#1192670912yes—
309C4—21no—
310C4—21no—
311C4—82no—
312C4—764no—
313C4—1521no—
314C4—1521no—
315C4—1522no—
316C4#1192671512yes—
317C4#1192672912yes—
318C4#1192676912yes—
319C4#1192692511yescharacteristic
320C4#1192693711yescharacteristic
321C2—22no—
322C2#1456465811yescharacteristic
323C2#1456467311yescharacteristic
324C2#1456473011yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1549C2
socleC22×C19#392
prime radicalC23×C19#120
hypercenter#1549D19
hypocenterC19#10296
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
231. C19#10296semidirect

Maximal subgroups

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

subgroupindex
#145747862
#145747812
#145720122
#145646112
#145623082
#145614672
C19×#15492
#1029619