Finite Group Databasebeta

← #18075050

Subgroups — #18075050

Order 4864.

976 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 976 conjugacy classes of subgroups — too many to draw. Only its 139 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#14563563C211yesmaximal, characteristic
2#14563553C211yesmaximal, characteristic
3#14562168C214yesmaximal, complemented
4C2×C19×#536C211yesmaximal, characteristic
5C2×#10597293—21no—
6C2×#10597290—21no—
7C2×#10597291—21no—
8C2×#10597291—21no—
9#11926508C2212yes—
10#11926407C2212yes—
11#11926281—28no—
12C22×#41×C19C2211yescharacteristic
13C23×Q8×C19C411yescharacteristic, complemented
14C19×#536—28no—
15C2×C19×C4⋊Q8—21no—
16C2×C19×#124—21no—
17C2×C19×#123—21no—
18C2×C19×#123—21no—
19C2×C19×C22⋊Q8C412yescomplemented
20C2×C19×C22⋊Q8C2212yes—
21C2×C19×#117C411yescharacteristic, complemented
22C2×#41×C19—24no—
23C2×#41×C19—42no—
24C2×#41×C19—42no—
25C22×Q8×C19—24no—
26C22×Q8×C19—21no—
27C22×Q8×C19—42no—
28C22×Q8×C19—42no—
29C22×Q8×C19C2×C412yes—
30C22×Q8×C19D411yescharacteristic
31C22×D4×C19D411yescharacteristic
32C22×D4×C19D411yescharacteristic
33C22×D4×C19D411yescharacteristic
34C23×C4×C19—21no—
35C23×C4×C19C2×C411yescharacteristic
36C23×C4×C19C2×C411yescharacteristic
37C23×C4×C19C2311yescharacteristic
38C19×C4⋊Q8—28no—
39C19×#124—28no—
40C19×#123—28no—
41C19×#123—28no—
42C19×C22⋊Q8—24no—
43C19×C22⋊Q8—24no—
44C19×C22⋊Q8—24no—
45C19×C22⋊Q8D418yes—
46C19×#117—24no—
47C2×C4⋊C4×C19—22no—
48C2×C4⋊C4×C19—22no—
49C2×C4⋊C4×C19C2×C412yes—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—22no—
52C2×C22⋊C4×C19—22no—
53C2×C42×C19—21no—
54C2×C22⋊Dic19—22no—
55C2×#64520—22no—
56#10597293—42no—
57#10597291—42no—
58#10597291—42no—
59#10597290—42no—
60C19⋊#95—24no—
61C22⋊(C19⋊C8)—24no—
62C24×C19C22⋊C411yescharacteristic
63C24×C19C22⋊C411yescharacteristic
64C24×C19C2×D411yescharacteristic
65#41×C19—416no—
66C2×Q8×C19—24no—
67C2×Q8×C19—22no—
68C2×Q8×C19—22no—
69C2×Q8×C19—22no—
70C2×Q8×C19—41no—
71C2×Q8×C19—416no—
72C2×Q8×C19—42no—
73C2×Q8×C19—42no—
74C2×Q8×C19—42no—
75C2×Q8×C19—42no—
76C2×Q8×C19C22⋊C414yes—
77C2×D4×C19—22no—
78C2×D4×C19—22no—
79C2×D4×C19—22no—
80C2×D4×C19—22no—
81C2×D4×C19—22no—
82C2×D4×C19—22no—
83C2×D4×C19—41no—
84C2×D4×C19—41no—
85C2×D4×C19—41no—
86C22×C4×C19—22no—
87C22×C4×C19—22no—
88C22×C4×C19—22no—
89C22×C4×C19—24no—
90C22×C4×C19—22no—
91C22×C4×C19—22no—
92C22×C4×C19—22no—
93C22×C4×C19—41no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19—42no—
98C22×C4×C19—42no—
99C22×C4×C19C22⋊C411yescharacteristic
100C22×C4×C19C22⋊C411yescharacteristic
101C22×C4×C19C22×C411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D414yes—
104C22×Dic19—42no—
105C4⋊C4×C19—28no—
106C4⋊C4×C19—22no—
107C4⋊C4×C19—28no—
108C4⋊C4×C19C22⋊C414yes—
109C22⋊C4×C19—24no—
110C22⋊C4×C19—28no—
111C22⋊C4×C19—28no—
112C42×C19—24no—
113C22⋊Dic19—42no—
114C22⋊Dic19—42no—
115#64520—42no—
116#64520—42no—
117C2×C19⋊C8—42no—
118#8520—191nomaximal, Sylow
119C23×C19—21no—
120C23×C19—21no—
121C23×C19—21no—
122C23×C19—21no—
123C23×C19—21no—
124C23×C19—21no—
125C23×C19—21no—
126C23×C19—42no—
127C23×C19—42no—
128C23×C19—42no—
129C23×C19#9912yes—
130C23×C19C2×C22⋊C411yescharacteristic
131C23×C19#12012yes—
132Q8×C19—44no—
133Q8×C19—44no—
134Q8×C19—44no—
135Q8×C19—48no—
136D4×C19—44no—
137D4×C19—44no—
138D4×C19—44no—
139C2×C4×C19—28no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—24no—
147C2×C4×C19—24no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—44no—
152C2×C4×C19—44no—
153C2×C4×C19—44no—
154C2×C4×C19—48no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19#9912yes—
158C2×C4×C19C2×C22⋊C412yes—
159C2×C4×C19#12012yes—
160C2×Dic19—82no—
161C2×Dic19—84no—
162C19⋊C8—82no—
163C2×#536D1911yescharacteristic
164#1785—191no—
165#1782—191no—
166#1511—194no—
167C22×C19—22no—
168C22×C19—24no—
169C22×C19—22no—
170C22×C19—22no—
171C22×C19—42no—
172C22×C19—42no—
173C22×C19—42no—
174C22×C19—42no—
175C22×C19—41no—
176C22×C19—81no—
177C22×C19—81no—
178C22×C19—81no—
179C22×C19—81no—
180C22×C19#37911yescharacteristic
181C22×C19C2×#9911yescharacteristic
182C22×C19C2×#9911yescharacteristic
183C4×C19—22no—
184C4×C19—22no—
185C4×C19—22no—
186C4×C19—44no—
187C4×C19—41no—
188C4×C19—44no—
189Dic19—162no—
190C22×#41C2×D1911yescharacteristic
191C23×Q8Dic1911yescharacteristic, complemented
192#536—28no—
193C2×C4⋊Q8—21no—
194C2×#124—21no—
195C2×#123—21no—
196C2×#123—21no—
197C2×C22⋊Q8Dic1912yescomplemented
198C2×C22⋊Q8C2×D1912yes—
199C2×#117Dic1911yescharacteristic, complemented
200C2×#101—381no—
201C2×#100—381no—
202C2×#99—381no—
203C2×#99—381no—
204#407—192no—
205#381—192no—
206#328—388no—
207C2×C19—21no—
208C2×C19—21no—
209C2×C19—42no—
210C2×C19—42no—
211C2×C19—81no—
212C2×C19#178111yescharacteristic
213C2×C19#179612yes—
214C2×#41—24no—
215C2×#41—42no—
216C2×#41—42no—
217C22×Q8—24no—
218C22×Q8—21no—
219C22×Q8—42no—
220C22×Q8—42no—
221C22×Q8C2×Dic1912yes—
222C22×Q8C22⋊D1911yescharacteristic
223C22×D4C22⋊D1911yescharacteristic
224C22×D4C22⋊D1911yescharacteristic
225C22×D4C22⋊D1911yescharacteristic
226C23×C4—21no—
227C23×C4C2×Dic1911yescharacteristic
228C23×C4C2×Dic1911yescharacteristic
229C23×C4C22×D1911yescharacteristic
230C2×M16—382no—
231C4⋊Q8—28no—
232#124—28no—
233#123—28no—
234#123—28no—
235C22⋊Q8—24no—
236C22⋊Q8—24no—
237C22⋊Q8—24no—
238C22⋊Q8C22⋊D1918yes—
239#117—24no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4C2×Dic1912yes—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—382no—
247C2×C42—21no—
248#101—762no—
249#100—762no—
250#99—762no—
251#99—762no—
252C22⋊C8—384no—
253#95—384no—
254C19#852011yescharacteristic, complemented, Sylow
255C24C22⋊Dic1911yescharacteristic
256C24C22⋊Dic1911yescharacteristic
257C24C2×C22⋊D1911yescharacteristic
258#41—416no—
259C2×Q8—24no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—416no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—42no—
269C2×Q8C22⋊Dic1914yes—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—762no—
293C22×C4C22⋊Dic1911yescharacteristic
294C22×C4C22⋊Dic1911yescharacteristic
295C22×C4C22×Dic1911yescharacteristic
296C22×C4C2×C22⋊D1911yescharacteristic
297C22×C4C2×C22⋊D1914yes—
298M16—762no—
299M16—762no—
300C2×C8—762no—
301C4⋊C4—28no—
302C4⋊C4—22no—
303C4⋊C4—28no—
304C4⋊C4C22⋊Dic1914yes—
305C22⋊C4—24no—
306C22⋊C4—28no—
307C22⋊C4—28no—
308C22⋊C4—762no—
309C22⋊C4—762no—
310C42—24no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23#1059729112yes—
322C23C2×C22⋊Dic1911yescharacteristic
323C23#1059739912yes—
324Q8—44no—
325Q8—44no—
326Q8—44no—
327Q8—48no—
328D4—44no—
329D4—44no—
330D4—44no—
331C2×C4—28no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—48no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—1522no—
350C2×C4—1524no—
351C2×C4#1059729112yes—
352C2×C4C2×C22⋊Dic1912yes—
353C2×C4#1059739912yes—
354C8—1522no—
355C22—22no—
356C22—24no—
357C22—22no—
358C22—22no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22#1192640011yescharacteristic
369C22C2×#1059729111yescharacteristic
370C22C2×#1059729111yescharacteristic
371C4—22no—
372C4—22no—
373C4—22no—
374C4—44no—
375C4—41no—
376C4—44no—
377C4—3042no—
378C2—21no—
379C2—21no—
380C2—42no—
381C2—42no—
382C2—81no—
383C2#1456355011yescharacteristic
384C2#1456361012yes—
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#536C2
socleC22×C19#379
prime radicalC22×#41×C19C22
cosocleC23×C4×C19C23
hypercenterC2×#536D19
hypocenterC19#8520
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
3. #14562168C2semidirect
13. C23×Q8×C19C4semidirect
19. C2×C19×C22⋊Q8C4semidirect
21. C2×C19×#117C4semidirect
191. C23×Q8Dic19semidirect
197. C2×C22⋊Q8Dic19semidirect
199. C2×#117Dic19semidirect
254. C19#8520semidirect

Maximal subgroups

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

subgroupindex
#145635632
#145635532
#145621682
C2×C19×#5362
#852019