Finite Group Databasebeta

← #18080344

Subgroups — #18080344

Order 4864.

818 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 115 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#14565992C211yesmaximal, characteristic, complemented
2#14563579C212yesmaximal
3#14561965C211yesmaximal, characteristic, complemented
4#14561487C212yesmaximal, complemented
5C19×#2406C211yesmaximal, characteristic
6C2×#10597372—21no—
7C2×#10597294—24no—
8#11926508C2212yes—
9C4⋊C4×Dic19—24no—
10C4×C22⋊Dic19—21no—
11C4×C22⋊Dic19C2212yes—
12#11926270—22no—
13C22×#41×C19C2211yescharacteristic
14C2×C19×#123—21no—
15C22×C4⋊C4×C19C2211yescharacteristic
16C19×#395C412yescomplemented
17C19×#394C412yescomplemented
18C19×#386—21no—
19C19×#385—22no—
20C19×#381C2211yescharacteristic
21C2×#41×C19—22no—
22C2×#41×C19—22no—
23C2×#41×C19—44no—
24C22×Q8×C19C2×C411yescharacteristic
25C22×D4×C19—21no—
26C22×D4×C19C2×C411yescharacteristic
27C23×C4×C19—21no—
28C23×C4×C19D411yescharacteristic
29C23×C4×C19D411yescharacteristic
30C23×C4×C19C2311yescharacteristic
31C19×#123—44no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19—22no—
34C2×C4⋊C4×C19—22no—
35C2×C4⋊C4×C19C2×C412yes—
36C2×C4⋊C4×C19D412yes—
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—22no—
39C2×C22⋊C4×C19—22no—
40C2×C22⋊Dic19—22no—
41#10597372—28no—
42C2×C4⋊Dic19—22no—
43C2×C4×Dic19—22no—
44C2×C4×Dic19—22no—
45C2×C4×Dic19D414yes—
46C2×#64520—22no—
47C19×#95—22no—
48C19×#95—21no—
49C19×#95C2×C412yes—
50#10597294—48no—
51C19⋊#95—22no—
52C19⋊#95—22no—
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—22no—
55C24×C19—21no—
56C24×C19C2×D411yescharacteristic
57#41×C19—28no—
58#41×C19—44no—
59#41×C19—44no—
60#41×C19—44no—
61C2×Q8×C19—22no—
62C2×Q8×C19—42no—
63C2×D4×C19—24no—
64C2×D4×C19—22no—
65C2×D4×C19—42no—
66C2×D4×C19—42no—
67C2×D4×C19—41no—
68C2×D4×C19—41no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—24no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—22no—
76C22×C4×C19—42no—
77C22×C4×C19—42no—
78C22×C4×C19—42no—
79C22×C4×C19—42no—
80C22×C4×C19—42no—
81C22×C4×C19C22⋊C412yes—
82C22×C4×C19C22⋊C412yes—
83C22×C4×C19C22×C411yescharacteristic
84C22×C4×C19C2×D412yes—
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19#4112yes—
87C22×Dic19—24no—
88C4⋊C4×C19—24no—
89C4⋊C4×C19—24no—
90C4⋊C4×C19—44no—
91C22⋊C4×C19—44no—
92C22⋊C4×C19—42no—
93C22⋊C4×C19—44no—
94C22⋊Dic19—28no—
95C4⋊Dic19—28no—
96C4×Dic19—28no—
97C4×Dic19—44no—
98C4×Dic19—82no—
99#64520—44no—
100C2×C19⋊C8—42no—
101#9476—191nomaximal, Sylow
102C23×C19—22no—
103C23×C19—22no—
104C23×C19—22no—
105C23×C19—41no—
106C23×C19—41no—
107C23×C19—42no—
108C23×C19—41no—
109C23×C19—42no—
110C23×C19C2×C22⋊C411yescharacteristic
111C23×C19#12011yescharacteristic
112C23×C19#12311yescharacteristic
113Q8×C19—24no—
114Q8×C19—42no—
115D4×C19—24no—
116D4×C19—42no—
117D4×C19—44no—
118D4×C19—44no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—24no—
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19—24no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—42no—
130C2×C4×C19—48no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—42no—
134C2×C4×C19—42no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—81no—
139C2×C4×C19#10414yescomplemented
140C2×C4×C19C4×D412yes—
141C2×C4×C19#12112yes—
142C2×Dic19—28no—
143C2×Dic19—44no—
144C2×Dic19—44no—
145C19⋊C8—82no—
146#2406D1911yescharacteristic
147#2274—191no—
148#1789—192no—
149#1463—191no—
150#1284—192no—
151C22×C19—21no—
152C22×C19—21no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—44no—
159C22×C19—44no—
160C22×C19—42no—
161C22×C19—82no—
162C22×C19—81no—
163C22×C19—81no—
164C22×C19#38611yescharacteristic
165C22×C19C2×#10412yes—
166C22×C19B(4,𝔽2)12yes—
167C4×C19—22no—
168C4×C19—22no—
169C4×C19—24no—
170C4×C19—42no—
171C4×C19—42no—
172C4×C19—82no—
173Dic19—48no—
174C22×#41C2×D1911yescharacteristic
175C2×#123—21no—
176C2×#117—381no—
177C22×C4⋊C4C2×D1911yescharacteristic
178C2×#104—384no—
179#407—192no—
180#395Dic1912yescomplemented
181#394Dic1912yescomplemented
182#386—21no—
183#385—22no—
184#381C2×D1911yescharacteristic
185C4×C4⋊C4—384no—
186C4×C22⋊C4—192no—
187C4×C22⋊C4—381no—
188#324—382no—
189C2×C19—22no—
190C2×C19—22no—
191C2×C19—41no—
192C2×C19—82no—
193C2×C19#188911yescharacteristic
194C2×C19#189611yescharacteristic
195C2×C19#191211yescharacteristic
196C2×#41—22no—
197C2×#41—22no—
198C2×#41—44no—
199C22×Q8C2×Dic1911yescharacteristic
200C22×D4—21no—
201C22×D4C2×Dic1911yescharacteristic
202C23×C4—21no—
203C23×C4C22⋊D1911yescharacteristic
204C23×C4C22⋊D1911yescharacteristic
205C23×C4C22×D1911yescharacteristic
206C2×M16—382no—
207#123—44no—
208#117—388no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—382no—
213C2×C4⋊C4C2×Dic1912yes—
214C2×C4⋊C4C22⋊D1912yes—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—382no—
219C2×C42—194no—
220C2×C42—382no—
221C2×C42—382no—
222#104—768no—
223C22⋊C8—382no—
224C22⋊C8—382no—
225#95—22no—
226#95—21no—
227#95—382no—
228#95—382no—
229#95C2×Dic1912yes—
230C19#947611yescharacteristic, complemented, Sylow
231C24—21no—
232C24C2×C22⋊D1911yescharacteristic
233#41—28no—
234#41—44no—
235#41—44no—
236#41—44no—
237C2×Q8—22no—
238C2×Q8—42no—
239C2×D4—24no—
240C2×D4—22no—
241C2×D4—42no—
242C2×D4—42no—
243C2×D4—41no—
244C2×D4—41no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—24no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—384no—
258C22×C4C22⋊Dic1912yes—
259C22×C4C22⋊Dic1912yes—
260C22×C4D4×D1912yes—
261C22×C4#6454312yes—
262C22×C4C22×Dic1911yescharacteristic
263C22×C4C2×C22⋊D1911yescharacteristic
264M16—764no—
265C2×C8—762no—
266C4⋊C4—24no—
267C4⋊C4—24no—
268C4⋊C4—44no—
269C4⋊C4—388no—
270C22⋊C4—44no—
271C22⋊C4—42no—
272C22⋊C4—44no—
273C22⋊C4—388no—
274C42—388no—
275C42—764no—
276C42—1522no—
277C23—22no—
278C23—22no—
279C23—22no—
280C23—41no—
281C23—41no—
282C23—42no—
283C23—42no—
284C23—41no—
285C23#1059738111yescharacteristic
286C23#1059738311yescharacteristic
287C23C2×C22⋊Dic1911yescharacteristic
288Q8—24no—
289Q8—42no—
290D4—24no—
291D4—42no—
292D4—44no—
293D4—44no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—48no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—388no—
315C2×C4—764no—
316C2×C4—764no—
317C2×C4#1059729414yescomplemented
318C2×C4D4×Dic1912yes—
319C2×C4#1059738512yes—
320C8—1522no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—44no—
329C22—44no—
330C22—42no—
331C22—82no—
332C22—81no—
333C22—81no—
334C22#1192642411yescharacteristic
335C22C2×#1059729412yes—
336C22#1192673012yes—
337C4—22no—
338C4—22no—
339C4—24no—
340C4—42no—
341C4—42no—
342C4—82no—
343C4—768no—
344C2—22no—
345C2—22no—
346C2—41no—
347C2—82no—
348C2#1456404411yescharacteristic
349C2#1456407911yescharacteristic
350C2#1456417311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2406C2
socleC22×C19#386
prime radicalC22×#41×C19C22
cosocleC23×C4×C19C23
hypercenter#2406D19
hypocenterC19#9476
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2406

Complements

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

NH ≅ G/Ntype
1. #14565992C2semidirect
3. #14561965C2semidirect
4. #14561487C2semidirect
16. C19×#395C4semidirect
17. C19×#394C4semidirect
139. C2×C4×C19#104semidirect
180. #395Dic19semidirect
181. #394Dic19semidirect
230. C19#9476semidirect
317. C2×C4#10597294semidirect

Maximal subgroups

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

subgroupindex
#145659922
#145635792
#145619652
#145614872
C19×#24062
#947619