Finite Group Databasebeta

← #18080364

Subgroups — #18080364

Order 4864.

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

normal subgroups only

This group has 726 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#14566238C211yesmaximal, characteristic, complemented
2#14563579C212yesmaximal
3#14561965C211yesmaximal, characteristic, complemented
4#14561487C212yesmaximal, complemented
5C19×#2406C211yesmaximal, characteristic
6C2×#10597294—24no—
7#11926508C2212yes—
8#11926430—24no—
9#11926407—21no—
10#11926404—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—
41C2×C4⋊Dic19—22no—
42C2×C4×Dic19D414yes—
43C2×#64520—22no—
44C19×#95—22no—
45C19×#95—21no—
46C19×#95C2×C412yes—
47#10597294—48no—
48C19⋊#95—22no—
49C19⋊#95—24no—
50C19⋊#95—22no—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—22no—
53C24×C19—21no—
54C24×C19C2×D411yescharacteristic
55#41×C19—28no—
56#41×C19—44no—
57#41×C19—44no—
58#41×C19—44no—
59C2×Q8×C19—22no—
60C2×Q8×C19—42no—
61C2×D4×C19—24no—
62C2×D4×C19—22no—
63C2×D4×C19—42no—
64C2×D4×C19—42no—
65C2×D4×C19—41no—
66C2×D4×C19—41no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—22no—
73C22×C4×C19—42no—
74C22×C4×C19—42no—
75C22×C4×C19—42no—
76C22×C4×C19—42no—
77C22×C4×C19—42no—
78C22×C4×C19—42no—
79C22×C4×C19C22⋊C412yes—
80C22×C4×C19C22⋊C412yes—
81C22×C4×C19C22×C411yescharacteristic
82C22×C4×C19C2×D412yes—
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19#4112yes—
85C22×Dic19—24no—
86C4⋊C4×C19—24no—
87C4⋊C4×C19—24no—
88C4⋊C4×C19—44no—
89C22⋊C4×C19—44no—
90C22⋊C4×C19—44no—
91C22⋊C4×C19—42no—
92C22⋊Dic19—44no—
93C4⋊Dic19—82no—
94C4×Dic19—44no—
95#64520—44no—
96C2×C19⋊C8—42no—
97#9480—191nomaximal, Sylow
98C23×C19—22no—
99C23×C19—22no—
100C23×C19—22no—
101C23×C19—41no—
102C23×C19—41no—
103C23×C19—42no—
104C23×C19—41no—
105C23×C19—42no—
106C23×C19C2×C22⋊C411yescharacteristic
107C23×C19#12011yescharacteristic
108C23×C19#12311yescharacteristic
109Q8×C19—24no—
110Q8×C19—42no—
111D4×C19—24no—
112D4×C19—42no—
113D4×C19—44no—
114D4×C19—44no—
115C2×C4×C19—24no—
116C2×C4×C19—22no—
117C2×C4×C19—22no—
118C2×C4×C19—22no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—42no—
124C2×C4×C19—48no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—42no—
132C2×C4×C19—42no—
133C2×C4×C19—42no—
134C2×C4×C19—81no—
135C2×C4×C19C4×D412yes—
136C2×C4×C19#12112yes—
137C2×Dic19—44no—
138C2×Dic19—44no—
139C2×Dic19—44no—
140C19⋊C8—82no—
141#2406D1911yescharacteristic
142#2313—191no—
143#1789—192no—
144#1463—191no—
145#1284—192no—
146C22×C19—21no—
147C22×C19—21no—
148C22×C19—21no—
149C22×C19—21no—
150C22×C19—21no—
151C22×C19—21no—
152C22×C19—21no—
153C22×C19—44no—
154C22×C19—44no—
155C22×C19—42no—
156C22×C19—82no—
157C22×C19—81no—
158C22×C19—81no—
159C22×C19#38611yescharacteristic
160C22×C19#42112yes—
161C22×C19B(4,𝔽2)12yes—
162C4×C19—22no—
163C4×C19—22no—
164C4×C19—42no—
165C4×C19—42no—
166C4×C19—42no—
167C4×C19—82no—
168Dic19—84no—
169C22×#41C2×D1911yescharacteristic
170C2×#123—21no—
171C22×C4⋊C4C2×D1911yescharacteristic
172C2×#104—384no—
173#407—192no—
174#395Dic1912yescomplemented
175#394Dic1912yescomplemented
176#387—384no—
177#386—21no—
178#385—22no—
179#381—381no—
180#381C2×D1911yescharacteristic
181#380—381no—
182C4×C22⋊C4—192no—
183#324—382no—
184C2×C19—22no—
185C2×C19—22no—
186C2×C19—41no—
187C2×C19—82no—
188C2×C19#188911yescharacteristic
189C2×C19#189711yescharacteristic
190C2×C19#191211yescharacteristic
191C2×#41—22no—
192C2×#41—22no—
193C2×#41—44no—
194C22×Q8C2×Dic1911yescharacteristic
195C22×D4—21no—
196C22×D4C2×Dic1911yescharacteristic
197C23×C4—21no—
198C23×C4C22⋊D1911yescharacteristic
199C23×C4C22⋊D1911yescharacteristic
200C23×C4C22×D1911yescharacteristic
201C2×M16—382no—
202#123—44no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—382no—
207C2×C4⋊C4C2×Dic1912yes—
208C2×C4⋊C4C22⋊D1912yes—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—382no—
213C2×C42—194no—
214#104—768no—
215C22⋊C8—382no—
216C22⋊C8—382no—
217#95—22no—
218#95—21no—
219#95—382no—
220#95—384no—
221#95—382no—
222#95C2×Dic1912yes—
223C19#948011yescharacteristic, complemented, Sylow
224C24—21no—
225C24C2×C22⋊D1911yescharacteristic
226#41—28no—
227#41—44no—
228#41—44no—
229#41—44no—
230C2×Q8—22no—
231C2×Q8—42no—
232C2×D4—24no—
233C2×D4—22no—
234C2×D4—42no—
235C2×D4—42no—
236C2×D4—41no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—384no—
251C22×C4C22⋊Dic1912yes—
252C22×C4C22⋊Dic1912yes—
253C22×C4D4×D1912yes—
254C22×C4#6454312yes—
255C22×C4C22×Dic1911yescharacteristic
256C22×C4C2×C22⋊D1911yescharacteristic
257M16—764no—
258C2×C8—762no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—44no—
262C4⋊C4—1522no—
263C22⋊C4—44no—
264C22⋊C4—44no—
265C22⋊C4—42no—
266C22⋊C4—764no—
267C42—764no—
268C23—22no—
269C23—22no—
270C23—22no—
271C23—41no—
272C23—41no—
273C23—42no—
274C23—42no—
275C23—41no—
276C23#1059738111yescharacteristic
277C23#1059738311yescharacteristic
278C23C2×C22⋊Dic1911yescharacteristic
279Q8—24no—
280Q8—42no—
281D4—24no—
282D4—42no—
283D4—44no—
284D4—44no—
285C2×C4—24no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—48no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—81no—
305C2×C4—764no—
306C2×C4—764no—
307C2×C4—764no—
308C2×C4D4×Dic1912yes—
309C2×C4#1059738512yes—
310C8—1522no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—44no—
319C22—44no—
320C22—42no—
321C22—82no—
322C22—81no—
323C22—81no—
324C22#1192642411yescharacteristic
325C22#1192656112yes—
326C22#1192673012yes—
327C4—22no—
328C4—22no—
329C4—42no—
330C4—42no—
331C4—42no—
332C4—82no—
333C4—1524no—
334C2—22no—
335C2—22no—
336C2—41no—
337C2—82no—
338C2#1456404411yescharacteristic
339C2#1456408411yescharacteristic
340C2#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#9480
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. #14566238C2semidirect
3. #14561965C2semidirect
4. #14561487C2semidirect
16. C19×#395C4semidirect
17. C19×#394C4semidirect
174. #395Dic19semidirect
175. #394Dic19semidirect
223. C19#9480semidirect

Maximal subgroups

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

subgroupindex
#145662382
#145635792
#145619652
#145614872
C19×#24062
#948019