Finite Group Databasebeta

← #18073891

Subgroups — #18073891

Order 4864.

810 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×#10597335C211yesmaximal, characteristic
2#14563701C212yesmaximal
3C2×#11926270C211yesmaximal, characteristic
4C2×#11926269C212yesmaximal
5C2×C19×#324C211yesmaximal, characteristic
6C2×#10597335—24no—
7C2×#10597335—24no—
8C2×#10597335—22no—
9C2×#10597335—22no—
10C22×C4⋊Dic19C411yescharacteristic
11C22×Dic19⋊C4C411yescharacteristic
12C22×Dic19⋊C4C411yescharacteristic
13C22×Dic19⋊C4C411yescharacteristic
14C22×Dic19⋊C4C2211yescharacteristic
15C22×C4×Dic19C2211yescharacteristic
16C2×C22⋊(C19⋊C8)C2212yes—
17#11926298—24no—
18#11926270—22no—
19#11926269—24no—
20C22×C4⋊C4×C19C2211yescharacteristic
21C2×C19×C22⋊C8C2212yes—
22C19×#324—22no—
23C23×C4×C19C2×C411yescharacteristic
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19C2×C411yescharacteristic
27C23×Dic19C2×C411yescharacteristic
28C23×Dic19C2×C411yescharacteristic
29C23×Dic19C2×C411yescharacteristic
30C22×C8×C19—22no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19D412yes—
34C2×C4⋊C4×C19D412yes—
35C2×C4⋊Dic19—22no—
36C2×C4⋊Dic19—22no—
37C2×C4⋊Dic19—22no—
38C2×Dic19⋊C4—22no—
39C2×Dic19⋊C4—22no—
40C2×Dic19⋊C4—22no—
41C2×Dic19⋊C4—21no—
42C2×Dic19⋊C4—22no—
43C2×Dic19⋊C4—21no—
44C2×Dic19⋊C4—22no—
45C2×Dic19⋊C4—22no—
46C2×Dic19⋊C4—22no—
47C2×Dic19⋊C4—22no—
48C2×Dic19⋊C4—22no—
49C2×Dic19⋊C4—22no—
50C2×Dic19⋊C4D414yes—
51C2×C4×Dic19—21no—
52C2×C4×Dic19—22no—
53C2×C4×Dic19—21no—
54C2×C4×Dic19D414yes—
55C22×C19⋊C8—22no—
56#10597335—216no—
57#10597335—216no—
58C19×C22⋊C8—22no—
59C19×C22⋊C8—22no—
60C22⋊(C19⋊C8)—22no—
61C22⋊(C19⋊C8)—22no—
62C24×C19C22×C411yescharacteristic
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—22no—
68C22×C4×C19—22no—
69C22×C4×C19—42no—
70C22×C4×C19—42no—
71C22×C4×C19C22⋊C412yes—
72C22×C4×C19C22⋊C412yes—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D412yes—
75C22×C4×C19C2×D412yes—
76C22×C4×C19C2×D411yescharacteristic
77C22×Dic19—21no—
78C22×Dic19—21no—
79C22×Dic19—24no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C22×Dic19—21no—
83C22×Dic19—21no—
84C22×Dic19—21no—
85C22×Dic19—21no—
86C22×Dic19—22no—
87C22×Dic19—22no—
88C22×Dic19—22no—
89C22×Dic19—22no—
90C22×Dic19—42no—
91C22×Dic19C22⋊C412yes—
92C22×Dic19C22⋊C412yes—
93C22×Dic19C22⋊C412yes—
94C22×Dic19C22⋊C412yes—
95C2×C8×C19—44no—
96C2×C8×C19—42no—
97C4⋊C4×C19—24no—
98C4⋊C4×C19—24no—
99C4⋊Dic19—28no—
100Dic19⋊C4—28no—
101Dic19⋊C4—28no—
102Dic19⋊C4—28no—
103Dic19⋊C4—24no—
104Dic19⋊C4—24no—
105C4×Dic19—24no—
106C4×Dic19—24no—
107C2×C19⋊C8—44no—
108C2×C19⋊C8—42no—
109#8306—191nomaximal, Sylow
110C23×C19—22no—
111C23×C19—22no—
112C23×C19C2×C22⋊C411yescharacteristic
113C23×C19C2×C22⋊C411yescharacteristic
114C23×C19C2×C22⋊C411yescharacteristic
115C23×C19#13112yes—
116C23×C19#13112yes—
117C2×C4×C19—24no—
118C2×C4×C19—22no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—22no—
122C2×C4×C19—41no—
123C2×C4×C19—42no—
124C2×C4×C19—41no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19—42no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19#12012yes—
131C2×C4×C19#12012yes—
132C2×Dic19—24no—
133C2×Dic19—24no—
134C2×Dic19—22no—
135C2×Dic19—22no—
136C2×Dic19—22no—
137C2×Dic19—22no—
138C2×Dic19—22no—
139C2×Dic19—24no—
140C2×Dic19—24no—
141C2×Dic19—42no—
142C2×Dic19—42no—
143C2×Dic19—42no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—42no—
149C2×Dic19—42no—
150C2×Dic19#10114yes—
151C8×C19—82no—
152C19⋊C8—82no—
153C22×#125—191no—
154#1817—192no—
155C2×#324—192no—
156C2×#324—191no—
157C2×#324D1911yescharacteristic
158C22×C19—24no—
159C22×C19—24no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19#37911yescharacteristic
165C22×C19#40812yes—
166C22×C19#40812yes—
167C22×C19#40811yescharacteristic
168C22×C19#40811yescharacteristic
169C22×C19#41012yes—
170C22×C19C2×#10112yes—
171C4×C19—22no—
172C4×C19—22no—
173C4×C19—42no—
174C4×C19—42no—
175Dic19—24no—
176Dic19—42no—
177Dic19—42no—
178Dic19—42no—
179C2×#125—384no—
180C2×#125—384no—
181C2×#125—382no—
182C2×#125—382no—
183C22×C4⋊C4—191no—
184C22×C4⋊C4—191no—
185C22×C4⋊C4—191no—
186C22×C4⋊C4—191no—
187C22×C4⋊C4—191no—
188C22×C4⋊C4C2×D1911yescharacteristic
189C22×C42—191no—
190C2×C22⋊C8—192no—
191C2×C22⋊C8C2×D1912yes—
192#336—384no—
193#324—22no—
194#324—384no—
195#324—382no—
196C2×C19—22no—
197C2×C19—21no—
198C2×C19—21no—
199C2×C19#147014yes—
200C2×C19#178011yescharacteristic
201C2×C19#178211yescharacteristic
202C2×C19#178411yescharacteristic
203C23×C4—191no—
204C23×C4—191no—
205C23×C4—191no—
206C23×C4—191no—
207C23×C4C4×D1911yescharacteristic
208C23×C4C4×D1911yescharacteristic
209C23×C4C22×D1911yescharacteristic
210C22×C8—22no—
211C22×C8—382no—
212#125—3816no—
213#125—3816no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—194no—
217C2×C4⋊C4—382no—
218C2×C4⋊C4—382no—
219C2×C4⋊C4—382no—
220C2×C4⋊C4—382no—
221C2×C4⋊C4—382no—
222C2×C4⋊C4—382no—
223C2×C4⋊C4—382no—
224C2×C4⋊C4—382no—
225C2×C4⋊C4—382no—
226C2×C4⋊C4—382no—
227C2×C4⋊C4—382no—
228C2×C4⋊C4—382no—
229C2×C4⋊C4—381no—
230C2×C4⋊C4—382no—
231C2×C4⋊C4—381no—
232C2×C4⋊C4D7612yes—
233C2×C4⋊C4C22⋊D1912yes—
234C2×C42—194no—
235C2×C42—381no—
236C2×C42—382no—
237C2×C42—381no—
238C22⋊C8—22no—
239C22⋊C8—22no—
240C22⋊C8—382no—
241C22⋊C8—382no—
242C19#830611yescharacteristic, complemented, Sylow
243C24C2×C4×D1911yescharacteristic
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—192no—
253C22×C4—192no—
254C22×C4—192no—
255C22×C4—192no—
256C22×C4—384no—
257C22×C4—381no—
258C22×C4—381no—
259C22×C4—381no—
260C22×C4—381no—
261C22×C4—381no—
262C22×C4—382no—
263C22×C4—382no—
264C22×C4—382no—
265C22×C4—382no—
266C22×C4—381no—
267C22×C4—381no—
268C22×C4—381no—
269C22×C4—762no—
270C22×C4(C2×D19)⋊C412yes—
271C22×C4(C2×D19)⋊C412yes—
272C22×C4C2×D7611yescharacteristic
273C22×C4D4×D1912yes—
274C22×C4D4×D1912yes—
275C22×C4C2×C22⋊D1911yescharacteristic
276C2×C8—44no—
277C2×C8—42no—
278C2×C8—764no—
279C2×C8—762no—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—388no—
283C4⋊C4—388no—
284C4⋊C4—388no—
285C4⋊C4—388no—
286C4⋊C4—384no—
287C4⋊C4—384no—
288C42—384no—
289C42—384no—
290C23—22no—
291C23—22no—
292C23C22⋊C4×D1911yescharacteristic
293C23C22⋊C4×D1911yescharacteristic
294C23#1059734712yes—
295C23#1059735312yes—
296C23C2×(C2×D19)⋊C411yescharacteristic
297C2×C4—24no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—194no—
311C2×C4—384no—
312C2×C4—384no—
313C2×C4—382no—
314C2×C4—382no—
315C2×C4—382no—
316C2×C4—382no—
317C2×C4—382no—
318C2×C4—384no—
319C2×C4—384no—
320C2×C4—762no—
321C2×C4—762no—
322C2×C4—762no—
323C2×C4—761no—
324C2×C4—761no—
325C2×C4—761no—
326C2×C4—761no—
327C2×C4—762no—
328C2×C4—762no—
329C2×C4#1059732812yes—
330C2×C4#1059738312yes—
331C8—82no—
332C8—1522no—
333C22—24no—
334C22—24no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22#1192639911yescharacteristic
340C22#1192650912yes—
341C22#1192650912yes—
342C22#1192651011yescharacteristic
343C22#1192651211yescharacteristic
344C22#1192651612yes—
345C22#101×D1912yes—
346C4—22no—
347C4—22no—
348C4—42no—
349C4—42no—
350C4—384no—
351C4—762no—
352C4—762no—
353C4—762no—
354C2—22no—
355C2—21no—
356C2—21no—
357C2#1456198914yes—
358C2#1456354611yescharacteristic
359C2#1456355111yescharacteristic
360C2#1456355711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutator, prime radicalC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#324C2
socleC23×C19C2×C22⋊C4
cosocleC23×C4×C19C23
hypercenterC2×#324D19
hypocenterC19#8306
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
242. C19#8306semidirect

Maximal subgroups

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

subgroupindex
C22×#105973352
#145637012
C2×#119262702
C2×#119262692
C2×C19×#3242
#830619