Finite Group Databasebeta

← #18085288

Subgroups — #18085288

Order 4864.

576 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 107 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#14574781C211yesmaximal, characteristic
2#14574779C211yesmaximal, characteristic
3#14572031C211yesmaximal, characteristic
4#14564611C211yesmaximal, characteristic
5#14562308C211yesmaximal, characteristic
6#14561467C211yesmaximal, characteristic
7C19×#1546C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9C2×#10597315C2211yescharacteristic
10C2×#10597390—22no—
11#11926942—21no—
12#11926940—21no—
13#11926896—21no—
14#11926895—21no—
15#11926875—22no—
16#11926874—22no—
17#11926830—22no—
18#11926826—22no—
19#11926597C2211yescharacteristic
20#11926413—22no—
21#11926413—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#10597390—44no—
40#10597390—44no—
41#10597372—21no—
42C2×C4⋊Dic19—21no—
43C2×C4⋊Dic19D412yes—
44#10597370—21no—
45#10597370—21no—
46C2×Dic19⋊C4—28no—
47C2×C4×Dic19—21no—
48C2×C4×Dic19—21no—
49C2×C4×Dic19D412yes—
50#10597316—21no—
51#10597315—21no—
52#10597315—21no—
53#10597315—21no—
54#10597315—21no—
55#10597315D411yescharacteristic
56#10597315D411yescharacteristic
57C4×Dic38—21no—
58C4×Dic38—21no—
59C19×C4⋊C8—21no—
60C19×C4⋊C8—21no—
61C19×C4⋊C8D412yes—
62C19×C22⋊C8—21no—
63C4×C8×C19—21no—
64C22⋊(C19⋊C8)—21no—
65#10597274—24no—
66#10597273—24no—
67#10597267—24no—
68#10597265—24no—
69C4⋊(C19⋊C8)D412yes—
70C4×C19⋊C8—21no—
71C2×Q8×C19—41no—
72C2×Q8×C19—41no—
73C2×Q8×C19—42no—
74C2×Q8×C19—42no—
75C22×C4×C19—22no—
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×Dic19—22no—
80C22×Dic19—22no—
81C2×Dic38—21no—
82C2×Dic38—21no—
83C2×Dic38—41no—
84C2×Dic38—41no—
85C2×Dic38—42no—
86C2×Dic38—42no—
87M16×C19—42no—
88C2×C8×C19—22no—
89C2×C8×C19—41no—
90C4⋊C4×C19—22no—
91C4⋊C4×C19—22no—
92C4⋊C4×C19—41no—
93C4⋊C4×C19—41no—
94C42×C19C2×D411yescharacteristic
95C42×C19C2×D411yescharacteristic
96C42×C19C2×D411yescharacteristic
97C42×C19#4111yescharacteristic
98C22⋊Dic19—41no—
99C4⋊Dic19—21no—
100C4⋊Dic19—22no—
101C4⋊Dic19—21no—
102C4⋊Dic19—22no—
103C4⋊Dic19—21no—
104C4⋊Dic19—21no—
105C4⋊Dic19—41no—
106C4⋊Dic19—41no—
107Dic19⋊C4—416no—
108Dic19⋊C4—41no—
109Dic19⋊C4—41no—
110C4×Dic19—24no—
111C4×Dic19—24no—
112C4×Dic19—22no—
113C4×Dic19—41no—
114C4×Dic19SD1614yes—
115C2×C19⋊C8—22no—
116#10299—191nomaximal, Sylow
117C23×C19#12011yescharacteristic
118Q8×C19—82no—
119Q8×C19—81no—
120Q8×C19—81no—
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—42no—
124C2×C4×C19—44no—
125C2×C4×C19#12011yescharacteristic
126C2×C4×C19#12011yescharacteristic
127C2×C4×C19#12111yescharacteristic
128C2×C4×C19#12111yescharacteristic
129C2×C4×C19#12111yescharacteristic
130C2×C4×C19#12711yescharacteristic
131C2×C4×C19C2×SD1612yes—
132C2×C4×C19AGL(1,ℤ/8)12yes—
133C2×Dic19—24no—
134C2×Dic19—24no—
135C2×Dic19—24no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—42no—
139C2×Dic19—44no—
140Dic38—42no—
141Dic38—42no—
142Dic38—82no—
143Dic38—81no—
144Dic38—81no—
145C8×C19—42no—
146C8×C19—81no—
147C19⋊C8—42no—
148#3229—191no—
149#3229—191no—
150#2868—191no—
151#1994—191no—
152#1546—191no—
153#1546D1911yescharacteristic
154#1276—191no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19#39211yescharacteristic
158C22×C19#45012yes—
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—82no—
162C4×C19#45612yes—
163C4×C19#45612yes—
164C4×C19#46012yes—
165C4×C19#49211yescharacteristic
166C4×C19#49611yescharacteristic
167Dic19—28no—
168Dic19—81no—
169Dic19—81no—
170Dic19—82no—
171#533—191no—
172C2×C4⋊Q8—191no—
173C2×C4⋊Q8—382no—
174C2×C4⋊Q8C2×D1911yescharacteristic
175#498—381no—
176#498—381no—
177#487—381no—
178#487—381no—
179#483—382no—
180#483—382no—
181#475—382no—
182#475—382no—
183#431—191no—
184#431C2×D1911yescharacteristic
185#423C2×D1911yescharacteristic
186#384—382no—
187#384—382no—
188C43—191no—
189#339—382no—
190#332—22no—
191#332—382no—
192C2×C19—22no—
193C2×C19#200511yescharacteristic
194C2×C19#200511yescharacteristic
195C2×C19#201411yescharacteristic
196C22×Q8—21no—
197C22×Q8—381no—
198C2×M16—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—191no—
204C4⋊Q8—191no—
205C4⋊Q8—381no—
206C4⋊Q8—381no—
207C4⋊Q8—381no—
208C4⋊Q8—381no—
209C4⋊Q8—764no—
210C4⋊Q8—764no—
211#125—381no—
212C22⋊Q8—381no—
213C22⋊Q8—381no—
214C4×Q8—381no—
215C4×Q8—381no—
216#117—381no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—192no—
219C2×C4⋊C4—388no—
220C2×C4⋊C4—381no—
221C2×C4⋊C4D7612yes—
222C2×C42—192no—
223C2×C42—381no—
224C2×C42—381no—
225C2×C42C22×D1911yescharacteristic
226#106—384no—
227#106—384no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—192no—
231C4⋊C8C22⋊D1912yes—
232#103—384no—
233#103—384no—
234C22⋊C8—21no—
235C22⋊C8—381no—
236C4×C8—21no—
237C4×C8—381no—
238C19#1029911yescharacteristic, complemented, Sylow
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—381no—
244C2×Q8—381no—
245C2×Q8—761no—
246C2×Q8—761no—
247C2×Q8—762no—
248C2×Q8—762no—
249C22×C4—22no—
250C22×C4—382no—
251C22×C4—382no—
252C22×C4C2×D7611yescharacteristic
253C22×C4D4×D1911yescharacteristic
254C22×C4D4×D1911yescharacteristic
255M16—42no—
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—382no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—382no—
264C4⋊C4—381no—
265C4⋊C4—381no—
266C4⋊C4—382no—
267C4⋊C4—381no—
268C4⋊C4—381no—
269C4⋊C4—7616no—
270C4⋊C4—761no—
271C4⋊C4—761no—
272C4⋊C4—761no—
273C4⋊C4—761no—
274C22⋊C4—761no—
275C42—194no—
276C42—384no—
277C42—384no—
278C42—382no—
279C42—761no—
280C42#6454111yescharacteristic
281C42D4×D1911yescharacteristic
282C42D4×D1911yescharacteristic
283C42C2×C22⋊D1911yescharacteristic
284C23#1059732811yescharacteristic
285Q8—81no—
286Q8—81no—
287Q8—82no—
288Q8—762no—
289Q8—762no—
290Q8—1521no—
291Q8—1521no—
292Q8—1522no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—384no—
298C2×C4—384no—
299C2×C4—384no—
300C2×C4—764no—
301C2×C4—761no—
302C2×C4—761no—
303C2×C4—762no—
304C2×C4#1059732811yescharacteristic
305C2×C4#1059733011yescharacteristic
306C2×C4#1059733011yescharacteristic
307C2×C4#1059735712yes—
308C2×C4SD16×D1912yes—
309C2×C4#1059737611yescharacteristic
310C2×C4#1059738311yescharacteristic
311C2×C4#1059738611yescharacteristic
312C8—42no—
313C8—81no—
314C8—762no—
315C22—21no—
316C22—21no—
317C22#1192645311yescharacteristic
318C22#1192669612yes—
319C4—21no—
320C4—21no—
321C4—82no—
322C4—388no—
323C4—1521no—
324C4—1521no—
325C4—1522no—
326C4#1192672512yes—
327C4#1192672912yes—
328C4#1192674312yes—
329C4#1192691511yescharacteristic
330C4#1192693211yescharacteristic
331C2—22no—
332C2#1456467211yescharacteristic
333C2#1456467311yescharacteristic
334C2#1456472411yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1546C2
socleC22×C19#392
prime radicalC23×C19#120
hypercenter#1546D19
hypocenterC19#10299
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
238. C19#10299semidirect

Maximal subgroups

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

subgroupindex
#145747812
#145747792
#145720312
#145646112
#145623082
#145614672
C19×#15462
#1029919