Finite Group Databasebeta

← #18073868

Subgroups — #18073868

Order 4864.

1502 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 207 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
1C23×Dic19⋊C4C211yesmaximal, characteristic
2#14563545C211yesmaximal, characteristic
3C2×#11926269C214yesmaximal, complemented
4C19×#1779C211yesmaximal, characteristic
5C24×Dic19C411yescharacteristic
6C24×Dic19C411yescharacteristic
7C22×Dic19⋊C4—28no—
8C22×Dic19⋊C4—22no—
9C22×Dic19⋊C4—22no—
10C22×Dic19⋊C4C412yes—
11C22×Dic19⋊C4C2212yes—
12C2×C22⋊(C19⋊C8)—22no—
13C2×C22⋊(C19⋊C8)C2212yes—
14#11926269—28no—
15C24×C4×C19C2211yescharacteristic
16C2×C19×C22⋊C8—22no—
17C2×C19×C22⋊C8C2212yes—
18C25×C19C2×C411yescharacteristic
19C23×C4×C19—24no—
20C23×C4×C19—44no—
21C23×C4×C19C2×C411yescharacteristic
22C23×C4×C19D412yes—
23C23×C4×C19D412yes—
24C23×C4×C19C2311yescharacteristic
25C23×Dic19—22no—
26C23×Dic19—22no—
27C23×Dic19—24no—
28C23×Dic19—24no—
29C23×Dic19—22no—
30C23×Dic19—24no—
31C23×Dic19—44no—
32C23×Dic19C814yescomplemented
33C23×Dic19C2×C412yes—
34C23×Dic19C2×C412yes—
35C22×C8×C19—22no—
36C2×Dic19⋊C4—216no—
37C2×Dic19⋊C4—216no—
38C2×Dic19⋊C4—24no—
39C2×Dic19⋊C4—22no—
40C2×Dic19⋊C4—24no—
41C2×Dic19⋊C4—22no—
42C2×Dic19⋊C4—24no—
43C2×Dic19⋊C4—24no—
44C2×Dic19⋊C4D418yes—
45C22×C19⋊C8—22no—
46C19×C22⋊C8—24no—
47C19×C22⋊C8—44no—
48C22⋊(C19⋊C8)—24no—
49C22⋊(C19⋊C8)—44no—
50C24×C19—24no—
51C24×C19—24no—
52C24×C19—22no—
53C24×C19—22no—
54C24×C19C22⋊C412yes—
55C24×C19C2×C812yes—
56C24×C19M1612yes—
57C24×C19C22×C411yescharacteristic
58C22×C4×C19—24no—
59C22×C4×C19—24no—
60C22×C4×C19—22no—
61C22×C4×C19—24no—
62C22×C4×C19—24no—
63C22×C4×C19—42no—
64C22×C4×C19—42no—
65C22×C4×C19—42no—
66C22×C4×C19—42no—
67C22×C4×C19—416no—
68C22×C4×C19C22⋊C412yes—
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D414yes—
71C22×C4×C19C2×D411yescharacteristic
72C22×Dic19—216no—
73C22×Dic19—28no—
74C22×Dic19—28no—
75C22×Dic19—28no—
76C22×Dic19—22no—
77C22×Dic19—22no—
78C22×Dic19—22no—
79C22×Dic19—22no—
80C22×Dic19—216no—
81C22×Dic19—28no—
82C22×Dic19—22no—
83C22×Dic19—22no—
84C22×Dic19—416no—
85C22×Dic19—44no—
86C22×Dic19—44no—
87C22×Dic19—44no—
88C22×Dic19C22⋊C414yes—
89C22×Dic19C22⋊C414yes—
90C22×Dic19C2×C814yes—
91C22×Dic19M1614yes—
92C2×C8×C19—44no—
93C2×C8×C19—42no—
94Dic19⋊C4—216no—
95Dic19⋊C4—28no—
96Dic19⋊C4—28no—
97C2×C19⋊C8—44no—
98C2×C19⋊C8—42no—
99#8299—191nomaximal, Sylow
100C23×C19—28no—
101C23×C19—216no—
102C23×C19—28no—
103C23×C19—28no—
104C23×C19—28no—
105C23×C19—22no—
106C23×C19—24no—
107C23×C19—22no—
108C23×C19—24no—
109C23×C19—22no—
110C23×C19—22no—
111C23×C19—22no—
112C23×C19—22no—
113C23×C19C22⋊C814yes—
114C23×C19#9914yes—
115C23×C19#10114yes—
116C23×C19C2×C22⋊C412yes—
117C23×C19C2×C22⋊C411yescharacteristic
118C23×C19C22×C811yescharacteristic
119C23×C19C2×M1611yescharacteristic
120C23×C19C2×M1612yes—
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—44no—
127C2×C4×C19—48no—
128C2×C4×C19—48no—
129C2×C4×C19—44no—
130C2×C4×C19#12012yes—
131C2×C4×C19#12012yes—
132C2×Dic19—232no—
133C2×Dic19—24no—
134C2×Dic19—24no—
135C2×Dic19—24no—
136C2×Dic19—24no—
137C2×Dic19—24no—
138C2×Dic19—24no—
139C2×Dic19—24no—
140C2×Dic19—416no—
141C2×Dic19—44no—
142C2×Dic19—44no—
143C2×Dic19—44no—
144C2×Dic19C22⋊C818yescomplemented
145C8×C19—82no—
146C19⋊C8—82no—
147C23×C4⋊C4—191no—
148#1779—191no—
149#1779D1911yescharacteristic
150C2×#324—194no—
151C22×C19—216no—
152C22×C19—216no—
153C22×C19—24no—
154C22×C19—22no—
155C22×C19—22no—
156C22×C19—24no—
157C22×C19—24no—
158C22×C19—24no—
159C22×C19—24no—
160C22×C19—24no—
161C22×C19—22no—
162C22×C19—24no—
163C22×C19—22no—
164C22×C19#32418yescomplemented
165C22×C19#37911yescharacteristic
166C22×C19C2×C22⋊C812yes—
167C22×C19C2×C22⋊C811yescharacteristic
168C22×C19#40712yes—
169C22×C19#40711yescharacteristic
170C22×C19C2×#9912yes—
171C22×C19C2×#10112yes—
172C4×C19—22no—
173C4×C19—22no—
174C4×C19—42no—
175Dic19—28no—
176Dic19—44no—
177C24×C4—191no—
178C24×C4—191no—
179C24×C4C2×D1911yescharacteristic
180C22×C4⋊C4—192no—
181C22×C4⋊C4—192no—
182C22×C4⋊C4—388no—
183C22×C4⋊C4—382no—
184C22×C4⋊C4—382no—
185C2×C22⋊C8—22no—
186C2×C22⋊C8—192no—
187C2×C22⋊C8—382no—
188C2×C22⋊C8C2×D1912yes—
189#324—388no—
190C2×C19—28no—
191C2×C19—22no—
192C2×C19—22no—
193C2×C19C2×#32412yes—
194C2×C19#146312yes—
195C2×C19#177911yescharacteristic
196C2×C19#178111yescharacteristic
197C2×C19#178411yescharacteristic
198C25C4×D1911yescharacteristic
199C23×C4—24no—
200C23×C4—44no—
201C23×C4—192no—
202C23×C4—194no—
203C23×C4—192no—
204C23×C4—384no—
205C23×C4—384no—
206C23×C4—384no—
207C23×C4—382no—
208C23×C4—382no—
209C23×C4—382no—
210C23×C4—764no—
211C23×C4C4×D1911yescharacteristic
212C23×C4D7612yes—
213C23×C4C22⋊D1912yes—
214C23×C4C22×D1911yescharacteristic
215C22×C8—22no—
216C22×C8—382no—
217C2×C4⋊C4—198no—
218C2×C4⋊C4—384no—
219C2×C4⋊C4—384no—
220C2×C4⋊C4—3816no—
221C2×C4⋊C4—3816no—
222C2×C4⋊C4—384no—
223C2×C4⋊C4—382no—
224C2×C4⋊C4—384no—
225C2×C4⋊C4—382no—
226C22⋊C8—24no—
227C22⋊C8—44no—
228C22⋊C8—384no—
229C22⋊C8—764no—
230C19#829911yescharacteristic, complemented, Sylow
231C24—24no—
232C24—24no—
233C24—22no—
234C24—22no—
235C24C8×D1912yes—
236C24#6451512yes—
237C24(C2×D19)⋊C412yes—
238C24C2×C4×D1911yescharacteristic
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—416no—
249C22×C4—194no—
250C22×C4—194no—
251C22×C4—194no—
252C22×C4—194no—
253C22×C4—3816no—
254C22×C4—388no—
255C22×C4—3816no—
256C22×C4—388no—
257C22×C4—388no—
258C22×C4—382no—
259C22×C4—382no—
260C22×C4—382no—
261C22×C4—382no—
262C22×C4—388no—
263C22×C4—382no—
264C22×C4—382no—
265C22×C4—7616no—
266C22×C4—764no—
267C22×C4—764no—
268C22×C4—764no—
269C22×C4(C2×D19)⋊C412yes—
270C22×C4C2×D7611yescharacteristic
271C22×C4D4×D1914yes—
272C22×C4C2×C22⋊D1911yescharacteristic
273C2×C8—44no—
274C2×C8—42no—
275C2×C8—764no—
276C2×C8—762no—
277C4⋊C4—3816no—
278C4⋊C4—388no—
279C4⋊C4—388no—
280C23—28no—
281C23—216no—
282C23—28no—
283C23—22no—
284C23—24no—
285C23—24no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—28no—
292C23—28no—
293C23#1059726314yes—
294C23(C2×D19)⋊C814yes—
295C23#1059728114yes—
296C23C22⋊C4×D1912yes—
297C23C2×C8×D1911yescharacteristic
298C23C2×#6451511yescharacteristic
299C23M16×D1912yes—
300C23C2×(C2×D19)⋊C411yescharacteristic
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—44no—
307C2×C4—48no—
308C2×C4—48no—
309C2×C4—44no—
310C2×C4—198no—
311C2×C4—3832no—
312C2×C4—384no—
313C2×C4—384no—
314C2×C4—384no—
315C2×C4—384no—
316C2×C4—384no—
317C2×C4—384no—
318C2×C4—384no—
319C2×C4—7616no—
320C2×C4—764no—
321C2×C4—764no—
322C2×C4—764no—
323C2×C4#1059732812yes—
324C2×C4#1059738312yes—
325C8—82no—
326C8—1522no—
327C22—216no—
328C22—216no—
329C22—24no—
330C22—22no—
331C22—22no—
332C22—24no—
333C22—24no—
334C22—24no—
335C22—24no—
336C22—24no—
337C22—22no—
338C22—24no—
339C22—22no—
340C22#1192626918yescomplemented
341C22#1192639911yescharacteristic
342C22C22⋊C8×D1912yes—
343C22C2×(C2×D19)⋊C811yescharacteristic
344C22#1192650612yes—
345C22#1192650711yescharacteristic
346C22C2×#1059726312yes—
347C22C2×#1059728112yes—
348C4—22no—
349C4—22no—
350C4—42no—
351C4—388no—
352C4—764no—
353C2—22no—
354C2—22no—
355C2—28no—
356C2C2×#1192626912yes—
357C2#1456196412yes—
358C2#1456354411yescharacteristic
359C2#1456354911yescharacteristic
360C2#1456355811yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC23×C19C22×C8
FrattiniC23×C4C22×D19
FittingC19×#1779C2
socleC23×C19C2×C22⋊C4
prime radicalC25×C19C2×C4
cosocleC23×C4×C19C23
hypercenter#1779D19
hypocenterC19#8299
LCSG ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. C2×#11926269C2semidirect
32. C23×Dic19C8semidirect
144. C2×Dic19C22⋊C8semidirect
164. C22×C19#324semidirect
230. C19#8299semidirect
340. C22#11926269semidirect

Maximal subgroups

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

subgroupindex
C23×Dic19⋊C42
#145635452
C2×#119262692
C19×#17792
#829919