Finite Group Databasebeta

← #18083958

Subgroups — #18083958

Order 4864.

474 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 85 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#14574841C211yesmaximal, characteristic
2#14574015C211yesmaximal, characteristic
3#14562361C211yesmaximal, characteristic
4#14562237C211yesmaximal, characteristic
5#14562146C211yesmaximal, characteristic
6#14561528C211yesmaximal, characteristic
7C19×#2660C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926954—21no—
10#11926914—21no—
11#11926912—22no—
12#11926894—21no—
13#11926894—21no—
14#11926879—21no—
15#11926874—21no—
16#11926848—22no—
17#11926601C2211yescharacteristic
18#11926601C2211yescharacteristic
19#11926553—22no—
20C4×#64520C2211yescharacteristic
21#11926293—22no—
22#11926286—22no—
23#11926280—22no—
24C2×C19×C4⋊Q8C2211yescharacteristic
25C2×C19×#125C2211yescharacteristic
26C19×#398—22no—
27C19×#395—22no—
28C19×#384—21no—
29C19×#382—21no—
30C19×#376C2211yescharacteristic
31C22×Q8×C19D412yes—
32C19×C4⋊Q8—21no—
33C19×C4⋊Q8—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×#125—21no—
37C19×#125—21no—
38C19×#125—21no—
39C19×#125—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—24no—
45C2×C4⋊C4×C19D411yescharacteristic
46C2×C4⋊C4×C19D411yescharacteristic
47C2×C42×C19—21no—
48C2×C42×C19C2311yescharacteristic
49#10597372—21no—
50#10597370—21no—
51#10597370—21no—
52C2×#64520—21no—
53#10597316—21no—
54#10597315D411yescharacteristic
55#10597315D411yescharacteristic
56C4×Dic38—21no—
57C4×Dic38—21no—
58C19×#95—24no—
59C19×#95—21no—
60C19×#95D412yes—
61#10597292—24no—
62#10597292—24no—
63C22⋊(C19⋊C8)—21no—
64C22⋊(C19⋊C8)—21no—
65#10597267—22no—
66#10597267—22no—
67#10597265—22no—
68#10597264—22no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)D412yes—
71#10597260—21no—
72#10597260—21no—
73#10597260D412yes—
74C4×C19⋊C8—21no—
75C2×Q8×C19—22no—
76C2×Q8×C19—22no—
77C2×Q8×C19—44no—
78C22×C4×C19—22no—
79C22×C4×C19—21no—
80C22×C4×C19—22no—
81C22×C4×C19—21no—
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C2×Dic38—21no—
86C2×Dic38—21no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—41no—
93C4⋊C4×C19—41no—
94C4⋊C4×C19—41no—
95C4⋊C4×C19—41no—
96C4⋊C4×C19—41no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—84no—
100C42×C19—24no—
101C42×C19C2×D411yescharacteristic
102C42×C19C2×D411yescharacteristic
103C42×C19C2×D411yescharacteristic
104C42×C19#4111yescharacteristic
105C22⋊Dic19—41no—
106C4⋊Dic19—21no—
107C4⋊Dic19—21no—
108C4⋊Dic19—21no—
109C4⋊Dic19—21no—
110Dic19⋊C4—41no—
111Dic19⋊C4—41no—
112C4×Dic19—41no—
113#64520—42no—
114C2×C19⋊C8—22no—
115C2×C19⋊C8—22no—
116C2×C19⋊C8—41no—
117#10099—191nomaximal, Sylow
118C23×C19#12011yescharacteristic
119Q8×C19—44no—
120Q8×C19—82no—
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—24no—
124C2×C4×C19—41no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19—42no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—42no—
131C2×C4×C19—42no—
132C2×C4×C19—44no—
133C2×C4×C19#12011yescharacteristic
134C2×C4×C19#12011yescharacteristic
135C2×C4×C19#12111yescharacteristic
136C2×C4×C19#12111yescharacteristic
137C2×C4×C19#12111yescharacteristic
138C2×C4×C19#12711yescharacteristic
139C2×Dic19—41no—
140C2×Dic19—41no—
141Dic38—42no—
142Dic38—81no—
143C19⋊C8—42no—
144C19⋊C8—42no—
145C19⋊C8—81no—
146#3236—191no—
147#3139—191no—
148#2660D1911yescharacteristic
149#1558—191no—
150#1528—191no—
151#1506—191no—
152#1300—191no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19#39211yescharacteristic
156C22×C19#45512yes—
157C4×C19—21no—
158C4×C19—21no—
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—44no—
163C4×C19—81no—
164C4×C19—82no—
165C4×C19—81no—
166C4×C19#45612yes—
167Dic19—81no—
168Dic19—81no—
169#533—191no—
170C2×C4⋊Q8C2×D1911yescharacteristic
171C2×#125C2×D1911yescharacteristic
172#501—381no—
173#491—382no—
174#491—381no—
175#487—381no—
176#487—381no—
177#484—381no—
178#483—381no—
179#479—382no—
180#432—191no—
181#432—191no—
182#419—382no—
183C4×M16—191no—
184#398—22no—
185#395—22no—
186#384—21no—
187#382—21no—
188#376C2×D1911yescharacteristic
189#333—382no—
190#330—382no—
191#328—382no—
192C2×C19—22no—
193C2×C19#200411yescharacteristic
194C2×C19#200511yescharacteristic
195C2×C19#200911yescharacteristic
196C22×Q8C22⋊D1912yes—
197C2×M16—381no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—191no—
203C4⋊Q8—191no—
204#125—21no—
205#125—21no—
206#125—21no—
207#125—21no—
208#125—381no—
209C22⋊Q8—381no—
210C22⋊Q8—381no—
211C4×Q8—381no—
212C4×Q8—381no—
213#117—381no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4C22⋊D1911yescharacteristic
220C2×C4⋊C4C22⋊D1911yescharacteristic
221C2×C42—21no—
222C2×C42C22×D1911yescharacteristic
223#107—382no—
224#106—382no—
225C4⋊C8—192no—
226C4⋊C8—381no—
227#103—382no—
228#103—382no—
229#103—384no—
230#103—384no—
231C22⋊C8—381no—
232C22⋊C8—381no—
233#97—192no—
234#97—381no—
235#97—381no—
236C4×C8—381no—
237#95—24no—
238#95—21no—
239#95C22⋊D1912yes—
240C19#1009911yescharacteristic, complemented, Sylow
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—44no—
244C2×Q8—381no—
245C2×Q8—381no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4C2×C22⋊D1911yescharacteristic
251C22×C4C2×C22⋊D1911yescharacteristic
252C22×C4C2×C22⋊D1911yescharacteristic
253M16—762no—
254C2×C8—382no—
255C2×C8—382no—
256C2×C8—761no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—84no—
270C4⋊C4—381no—
271C4⋊C4—381no—
272C4⋊C4—381no—
273C4⋊C4—381no—
274C4⋊C4—761no—
275C4⋊C4—761no—
276C22⋊C4—761no—
277C42—24no—
278C42—761no—
279C42D4×D1911yescharacteristic
280C42D4×D1911yescharacteristic
281C42D4×D1911yescharacteristic
282C42#6454311yescharacteristic
283C23#1059739911yescharacteristic
284Q8—44no—
285Q8—82no—
286Q8—762no—
287Q8—1521no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—44no—
300C2×C4—761no—
301C2×C4—761no—
302C2×C4#1059738311yescharacteristic
303C2×C4#1059738311yescharacteristic
304C2×C4#1059738411yescharacteristic
305C2×C4#1059738511yescharacteristic
306C2×C4#1059738511yescharacteristic
307C2×C4#1059738611yescharacteristic
308C8—762no—
309C8—762no—
310C8—1521no—
311C22—21no—
312C22—21no—
313C22#1192645211yescharacteristic
314C22#1192672212yes—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—44no—
321C4—82no—
322C4—81no—
323C4—81no—
324C4—1521no—
325C4—1521no—
326C4#1192672612yes—
327C2—22no—
328C2#1456466211yescharacteristic
329C2#1456467111yescharacteristic
330C2#1456469511yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2660C2
socleC22×C19#392
prime radicalC23×C19#120
hypercenter#2660D19
hypocenterC19#10099
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2660

Complements

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

NH ≅ G/Ntype
240. C19#10099semidirect

Maximal subgroups

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

subgroupindex
#145748412
#145740152
#145623612
#145622372
#145621462
#145615282
C19×#26602
#1009919