Finite Group Databasebeta

← #18071086

Subgroups — #18071086

Order 4864.

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

normal subgroups only

This group has 470 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#14571974C211yesmaximal, characteristic
2#14563397C211yesmaximal, characteristic
3#14561460C212yesmaximal, complemented
4#14561459C212yesmaximal, complemented
5C19×#1797C211yesmaximal, characteristic
6C2×#10597370C411yescharacteristic
7C2×C22⋊(C19⋊C8)—21no—
8C2×#10597260—21no—
9#11926450C411yescharacteristic
10#11926450C2211yescharacteristic
11#11926442C411yescharacteristic
12#11926442C2211yescharacteristic
13#11926428—21no—
14#11926428—21no—
15#11926417—21no—
16#11926407—21no—
17#11926404C411yescharacteristic
18#11926299C2212yes—
19C22×C42×C19C2211yescharacteristic
20C2×C19×C4⋊C8—21no—
21C2×C19×C22⋊C8—21no—
22C19×#336C2212yes—
23C23×C4×C19C2×C411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C22×Dic38C2×C411yescharacteristic
27C22×C8×C19—22no—
28C2×C42×C19—42no—
29C2×C42×C19C2×C411yescharacteristic
30C2×C42×C19D411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19C2311yescharacteristic
33C2×C22⋊Dic19—21no—
34C2×C22⋊Dic19—21no—
35C2×C4⋊Dic19C2×C411yescharacteristic
36C2×C4⋊Dic19C2×C411yescharacteristic
37C2×C4⋊Dic19C2×C411yescharacteristic
38#10597370—42no—
39C2×Dic19⋊C4—21no—
40C2×Dic19⋊C4—21no—
41C2×Dic19⋊C4—21no—
42C22×C19⋊C8—22no—
43C19×C4⋊C8—42no—
44C19×C22⋊C8—42no—
45C19⋊#95—21no—
46C19⋊#95—21no—
47C19⋊#95—21no—
48C19⋊#95—21no—
49C19⋊#95—21no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C22⋊(C19⋊C8)—24no—
53#10597260—42no—
54C24×C19C22⋊C411yescharacteristic
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—22no—
61C22×C4×C19—41no—
62C22×C4×C19—41no—
63C22×C4×C19—41no—
64C22×C4×C19—41no—
65C22×C4×C19C22⋊C411yescharacteristic
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×Dic19—21no—
72C22×Dic19—21no—
73C22×Dic19—21no—
74C22×Dic19—21no—
75C2×Dic38—22no—
76C2×Dic38—41no—
77C2×Dic38—41no—
78C2×C8×C19—42no—
79C2×C8×C19—42no—
80C2×C8×C19—42no—
81C42×C19—22no—
82C42×C19—22no—
83C42×C19—41no—
84C42×C19—41no—
85C22⋊Dic19—42no—
86C22⋊Dic19—42no—
87C4⋊Dic19—22no—
88C4⋊Dic19—41no—
89C4⋊Dic19—41no—
90Dic19⋊C4—42no—
91Dic19⋊C4—42no—
92Dic19⋊C4—41no—
93Dic19⋊C4—41no—
94C2×C19⋊C8—24no—
95C2×C19⋊C8—42no—
96C2×C19⋊C8—42no—
97#7701—191nomaximal, Sylow
98C23×C19—21no—
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—21no—
102C23×C19—21no—
103C23×C19—21no—
104C23×C19#10412yes—
105C23×C19C2×C22⋊C411yescharacteristic
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—44no—
121C2×C4×C19—44no—
122C2×C4×C19—42no—
123C2×C4×C19—42no—
124C2×C4×C19#9912yes—
125C2×C4×C19#13112yes—
126C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C19#13711yescharacteristic
128C2×C4×C19#13712yes—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141Dic38—82no—
142C8×C19—82no—
143C19⋊C8—44no—
144#2855—191no—
145#1797D1911yescharacteristic
146#1749—191no—
147#1272—192no—
148#1271—192no—
149C22×C19—22no—
150C22×C19—22no—
151C22×C19—22no—
152C22×C19—41no—
153C22×C19—41no—
154C22×C19—41no—
155C22×C19—41no—
156C22×C19#40811yescharacteristic
157C22×C19C2×#9911yescharacteristic
158C22×C19#41311yescharacteristic
159C22×C19#41711yescharacteristic
160C22×C19#41911yescharacteristic
161C22×C19C2×#10411yescharacteristic
162C22×C19#42111yescharacteristic
163C4×C19—22no—
164C4×C19—22no—
165C4×C19—22no—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—41no—
169C4×C19—41no—
170Dic19—81no—
171Dic19—81no—
172Dic19—81no—
173Dic19—81no—
174C2×C22⋊Q8—191no—
175C22×C42C2×D1911yescharacteristic
176C2×C4⋊C8—21no—
177C2×C22⋊C8—21no—
178C2×C22⋊C8—381no—
179C2×#97—381no—
180#391—191no—
181#391—191no—
182#389—191no—
183#389—191no—
184#387—381no—
185#387—381no—
186#385—381no—
187#381—381no—
188#380—191no—
189#336—192no—
190#336C2×D1912yes—
191C2×C19—42no—
192C2×C19#146811yescharacteristic
193C2×C19#148311yescharacteristic
194C2×C19#149711yescharacteristic
195C2×C19#150811yescharacteristic
196C2×C19#151311yescharacteristic
197C2×C19#153211yescharacteristic
198C2×C19#155911yescharacteristic
199C22×Q8—191no—
200C23×C4C4×D1911yescharacteristic
201C23×C4D7611yescharacteristic
202C23×C4C22⋊D1911yescharacteristic
203C22×C8—22no—
204C22×C8—382no—
205C22⋊Q8—762no—
206C2×C4⋊C4—191no—
207C2×C4⋊C4—191no—
208C2×C4⋊C4—191no—
209C2×C4⋊C4—381no—
210C2×C4⋊C4—381no—
211C2×C4⋊C4—381no—
212C2×C22⋊C4—381no—
213C2×C22⋊C4—381no—
214C2×C42—42no—
215C2×C42C4×D1911yescharacteristic
216C2×C42D7611yescharacteristic
217C2×C42C22⋊D1911yescharacteristic
218C2×C42C22×D1911yescharacteristic
219C4⋊C8—42no—
220C22⋊C8—42no—
221C22⋊C8—384no—
222#97—762no—
223#95—381no—
224#95—381no—
225#95—381no—
226#95—381no—
227#95—381no—
228#95—381no—
229#95—381no—
230C19#770111yescharacteristic, complemented, Sylow
231C24(C2×D19)⋊C411yescharacteristic
232C2×Q8—382no—
233C2×Q8—761no—
234C2×Q8—761no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—381no—
246C22×C4—381no—
247C22×C4—381no—
248C22×C4—381no—
249C22×C4(C2×D19)⋊C411yescharacteristic
250C22×C4(C2×D19)⋊C411yescharacteristic
251C22×C4(C2×D19)⋊C411yescharacteristic
252C22×C4C2×C4×D1911yescharacteristic
253C22×C4C2×D7611yescharacteristic
254C22×C4C2×C22⋊D1911yescharacteristic
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—384no—
259C2×C8—762no—
260C2×C8—762no—
261C4⋊C4—382no—
262C4⋊C4—761no—
263C4⋊C4—761no—
264C4⋊C4—762no—
265C4⋊C4—761no—
266C4⋊C4—761no—
267C4⋊C4—762no—
268C22⋊C4—762no—
269C22⋊C4—762no—
270C42—22no—
271C42—22no—
272C42—41no—
273C42—41no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23#1059728212yes—
281C23C2×(C2×D19)⋊C411yescharacteristic
282Q8—1522no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—761no—
302C2×C4—761no—
303C2×C4—761no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4—761no—
307C2×C4—761no—
308C2×C4—761no—
309C2×C4—761no—
310C2×C4—761no—
311C2×C4—761no—
312C2×C4—761no—
313C2×C4#1059726312yes—
314C2×C4#1059734712yes—
315C2×C4#1059735512yes—
316C2×C4#1059737811yescharacteristic
317C2×C4#1059738811yescharacteristic
318C8—82no—
319C8—764no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22#1192651011yescharacteristic
328C22C2×#1059726311yescharacteristic
329C22#1192652611yescharacteristic
330C22#1192654311yescharacteristic
331C22#1192655411yescharacteristic
332C22C2×#1059728211yescharacteristic
333C22#1192656211yescharacteristic
334C4—22no—
335C4—21no—
336C4—21no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—1521no—
342C4—1521no—
343C4—1521no—
344C4—1521no—
345C2—42no—
346C2#1456198111yescharacteristic
347C2#1456204611yescharacteristic
348C2#1456210911yescharacteristic
349C2#1456215611yescharacteristic
350C2#1456217611yescharacteristic
351C2#1456225611yescharacteristic
352C2#1456236311yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1797C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1797D19
hypocenterC19#7701
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #14561460C2semidirect
4. #14561459C2semidirect
230. C19#7701semidirect

Maximal subgroups

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

subgroupindex
#145719742
#145633972
#145614602
#145614592
C19×#17972
#770119