Finite Group Databasebeta

← #18070634

Subgroups — #18070634

Order 4864.

654 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 117 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#14566122C211yesmaximal, characteristic
2#14563614C212yesmaximal, complemented
3#14561460C212yesmaximal, complemented
4#14561456C211yesmaximal, characteristic, complemented
5C19×#1270C211yesmaximal, characteristic, complemented
6C22×#64543C411yescharacteristic
7C2×#10597338C411yescharacteristic
8C2×C42×D19C2211yescharacteristic
9C2×Dic19⋊C8—22no—
10C2×(C2×D19)⋊C8—22no—
11#11926450C2211yescharacteristic
12#11926449C411yescharacteristic
13#11926447C411yescharacteristic
14#11926420—22no—
15C22⋊C4×Dic19—22no—
16#11926299C2212yes—
17C19×#390C2211yescharacteristic
18C19×#336C2212yes—
19C22×D4×C19C2×C411yescharacteristic
20C22×C22⋊D19—21no—
21C23×Dic19—21no—
22C2×#64543—22no—
23C2×#64543—42no—
24C2×#64543—42no—
25C2×#64543C814yescomplemented
26C22×C4×D19C2×C411yescharacteristic
27C22×C4×D19D412yes—
28C22×Dic38C2×C411yescharacteristic
29C22×C8×C19—22no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C22⋊C4×C19—22no—
32C2×C42×C19C2311yescharacteristic
33C2×C22⋊Dic19—22no—
34C2×(C2×D19)⋊C4—21no—
35C2×C4⋊Dic19C2×C411yescharacteristic
36C2×C4×Dic19—21no—
37C2×C4×Dic19C2×C411yescharacteristic
38C2×C4×Dic19D412yes—
39C22×C19⋊C8—22no—
40#10597338—42no—
41C42×D19—42no—
42C19⋊#95—22no—
43C19⋊#95—22no—
44(C2×D19)⋊C8—44no—
45Dic19⋊C8—44no—
46C24×C19—21no—
47C23×D19C22⋊C411yescharacteristic
48C2×D4×C19—21no—
49C2×D4×C19—41no—
50C2×D4×C19—41no—
51C2×D4×C19C2×C812yes—
52C22×C4×C19—21no—
53C22×C4×C19C22×C411yescharacteristic
54C22×C4×C19C2×D412yes—
55C2×C22⋊D19—24no—
56C2×C22⋊D19—42no—
57C2×C22⋊D19—42no—
58C22×Dic19—21no—
59C22×Dic19—24no—
60C22×Dic19—21no—
61C22×Dic19—42no—
62C22×Dic19—42no—
63C22×Dic19C22⋊C412yes—
64C22×Dic19C22⋊C411yescharacteristic
65#64543—48no—
66#64543—48no—
67C2×C4×D19—22no—
68C2×C4×D19—22no—
69C2×C4×D19—22no—
70C2×C4×D19—22no—
71C2×C4×D19—42no—
72C2×C4×D19—42no—
73C2×C4×D19C2×C812yes—
74C2×C4×D19M1612yes—
75C2×Dic38—21no—
76C2×Dic38—41no—
77C2×Dic38—41no—
78C2×Dic38C2×C812yes—
79C2×C8×C19—42no—
80C2×C8×C19—42no—
81C2×C8×C19—42no—
82C4⋊C4×C19—41no—
83C22⋊C4×C19—42no—
84C22⋊C4×C19—42no—
85C42×C19—41no—
86C22⋊Dic19—44no—
87(C2×D19)⋊C4—42no—
88C4⋊Dic19—41no—
89C4×Dic19—24no—
90C4×Dic19—41no—
91C4×Dic19—42no—
92C2×C19⋊C8—42no—
93C2×C19⋊C8—42no—
94C2×C19⋊C8—42no—
95#7597—191nomaximal, Sylow
96C23×C19—22no—
97C23×C19—41no—
98C23×C19—41no—
99C23×C19—42no—
100C23×C19—42no—
101C23×C19C2×C22⋊C411yescharacteristic
102C22×D19—21no—
103C22×D19—21no—
104C22×D19—22no—
105C22×D19—22no—
106C22×D19C22⋊C812yes—
107D4×C19—42no—
108D4×C19—42no—
109C2×C4×C19—22no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—22no—
113C2×C4×C19—41no—
114C2×C4×C19—42no—
115C2×C4×C19C22×C811yescharacteristic
116C2×C4×C19C2×M1611yescharacteristic
117C2×C4×C19AGL(1,ℤ/8)12yes—
118C2×C4×C19#13712yes—
119C22⋊D19—48no—
120C2×Dic19—22no—
121C2×Dic19—22no—
122C2×Dic19—22no—
123C2×Dic19—22no—
124C2×Dic19—41no—
125C2×Dic19—41no—
126C2×Dic19—48no—
127C2×Dic19—41no—
128C2×Dic19—42no—
129C2×Dic19C22⋊C812yes—
130C2×Dic19#9912yes—
131C2×Dic19#10012yes—
132C4×D19—24no—
133C4×D19—24no—
134C4×D19—44no—
135C4×D19—44no—
136Dic38—42no—
137Dic38—42no—
138C8×C19—82no—
139C19⋊C8—82no—
140#2297—191no—
141#1797—192no—
142#1272—192no—
143#1270—191no—
144#1270D1911yescharacteristic, complemented
145C22×C19—42no—
146C22×C19—44no—
147C22×C19—81no—
148C22×C19—81no—
149C22×C19—82no—
150C22×C19C2×C22⋊C811yescharacteristic
151C22×C19C2×#9911yescharacteristic
152C22×C19C2×#10011yescharacteristic
153C22×C19#41712yes—
154C22×C19#42112yes—
155C2×D19—22no—
156C2×D19—24no—
157C2×D19—41no—
158C2×D19—41no—
159C2×D19—42no—
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—22no—
163C4×C19—22no—
164C4×C19—81no—
165Dic19—42no—
166Dic19—42no—
167Dic19—81no—
168Dic19#32314yes—
169C22×#41—191no—
170C2×#117—191no—
171C22×C42—191no—
172C2×C4⋊C8—382no—
173C2×C22⋊C8—382no—
174#391—191no—
175#391—191no—
176#390—191no—
177#390C2×D1911yescharacteristic
178#386—382no—
179C4×C22⋊C4—382no—
180#336—192no—
181#336C2×D1912yes—
182C2×C19—82no—
183C2×C19C2×#32311yescharacteristic
184C2×C19#147712yes—
185C2×C19#151312yes—
186C2×C19#153611yescharacteristic
187C2×C19#156011yescharacteristic
188D19—42no—
189C2×#41—194no—
190C2×#41—382no—
191C2×#41—762no—
192C2×#41—762no—
193C22×Q8—191no—
194C22×D4—381no—
195C22×D4C4×D1911yescharacteristic
196C23×C4—191no—
197C23×C4—192no—
198C23×C4—381no—
199C22×C8—22no—
200C22×C8—382no—
201#117—762no—
202C2×C4⋊C4—191no—
203C2×C4⋊C4C4×D1911yescharacteristic
204C2×C22⋊C4—22no—
205C2×C22⋊C4—381no—
206C2×C22⋊C4—382no—
207C2×C42—192no—
208C2×C42—191no—
209C2×C42—381no—
210C2×C42—762no—
211C2×C42C22×D1911yescharacteristic
212C4⋊C8—764no—
213C22⋊C8—764no—
214#95—382no—
215#95—382no—
216C19#759711yescharacteristic, complemented, Sylow
217C24—21no—
218C24—191no—
219#41—768no—
220#41—768no—
221C2×Q8—192no—
222C2×Q8—381no—
223C2×Q8—761no—
224C2×Q8—761no—
225C2×D4—21no—
226C2×D4—41no—
227C2×D4—41no—
228C2×D4—384no—
229C2×D4—762no—
230C2×D4—762no—
231C2×D4C8×D1912yes—
232C22×C4—21no—
233C22×C4—191no—
234C22×C4—192no—
235C22×C4—192no—
236C22×C4—192no—
237C22×C4—382no—
238C22×C4—382no—
239C22×C4—384no—
240C22×C4—381no—
241C22×C4—382no—
242C22×C4—382no—
243C22×C4—381no—
244C22×C4—762no—
245C22×C4—762no—
246C22×C4—762no—
247C22×C4—762no—
248C22×C4C2×C4×D1911yescharacteristic
249C22×C4D4×D1912yes—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—762no—
254C2×C8—762no—
255C2×C8—762no—
256C4⋊C4—41no—
257C4⋊C4—761no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—762no—
261C22⋊C4—764no—
262C42—41no—
263C42—384no—
264C42—761no—
265C42—762no—
266C23—22no—
267C23—42no—
268C23—42no—
269C23—41no—
270C23—41no—
271C23—192no—
272C23—382no—
273C23—382no—
274C23—381no—
275C23—381no—
276C23C22⋊C4×D1911yescharacteristic
277Q8—762no—
278Q8—762no—
279D4—42no—
280D4—42no—
281D4—768no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—192no—
289C2×C4—192no—
290C2×C4—192no—
291C2×C4—384no—
292C2×C4—384no—
293C2×C4—382no—
294C2×C4—382no—
295C2×C4—382no—
296C2×C4—382no—
297C2×C4—764no—
298C2×C4—764no—
299C2×C4—768no—
300C2×C4—761no—
301C2×C4—761no—
302C2×C4—762no—
303C2×C4—761no—
304C2×C4C2×C8×D1911yescharacteristic
305C2×C4M16×D1911yescharacteristic
306C2×C4#1059735712yes—
307C2×C4#1059736112yes—
308C8—82no—
309C8—1522no—
310C22—42no—
311C22—44no—
312C22—81no—
313C22—82no—
314C22—81no—
315C22—382no—
316C22—384no—
317C22—761no—
318C22—762no—
319C22—761no—
320C22C22⋊C8×D1911yescharacteristic
321C22#99×D1911yescharacteristic
322C22#100×D1911yescharacteristic
323C22#1192654212yes—
324C22#1192655912yes—
325C4—22no—
326C4—22no—
327C4—21no—
328C4—21no—
329C4—81no—
330C4—194no—
331C4—762no—
332C4—762no—
333C4—1521no—
334C2—82no—
335C2—762no—
336C2D19×#32311yescharacteristic
337C2#1456201912yes—
338C2#1456217512yes—
339C2#1456226811yescharacteristic
340C2#1456236711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC2×C4×C19C22×C8
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19C2×C22⋊C4
prime radicalC22×#64543C4
cosocleC2×C42×C19C23
hypercenter#1270D19
hypocenterC19#7597
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #14563614C2semidirect
3. #14561460C2semidirect
4. #14561456C2semidirect
5. C19×#1270C2semidirect
25. C2×#64543C8semidirect
144. #1270D19semidirect
216. C19#7597semidirect

Maximal subgroups

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

subgroupindex
#145661222
#145636142
#145614602
#145614562
C19×#12702
#759719