Finite Group Databasebeta

← #18086943

Subgroups — #18086943

Order 4864.

604 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 121 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#14569749C211yesmaximal, characteristic
2#14563825C212yesmaximal
3#14561899C211yesmaximal, characteristic
4#14561515C212yesmaximal
5C19×#1280C211yesmaximal, characteristic
6C2×#10597370—21no—
7C22×C4⋊Dic19C2211yescharacteristic
8C22×Dic19⋊C4—21no—
9C2×#10597275—22no—
10#11926476—22no—
11#11926465—22no—
12#11926404—21no—
13#11926404C2212yes—
14C2×C19⋊#95—21no—
15C2×C19⋊#95C2211yescharacteristic
16#11926307—22no—
17C2×C19×C22⋊C8C2212yes—
18C2×C19×#95C2211yescharacteristic
19C23×C4×C19D411yescharacteristic
20C23×C4×C19D411yescharacteristic
21C23×C4×C19C2311yescharacteristic
22C23×Dic19—21no—
23C23×Dic19—21no—
24C22×Dic38—21no—
25C22×C8×C19—22no—
26C2×C22⋊Dic19—22no—
27C2×C4⋊Dic19—22no—
28C2×C4⋊Dic19—21no—
29C2×C4⋊Dic19—21no—
30C2×C4⋊Dic19—21no—
31C2×C4⋊Dic19—42no—
32C2×C4⋊Dic19D412yes—
33C2×C4⋊Dic19D412yes—
34#10597370—42no—
35#10597370—42no—
36C2×Dic19⋊C4—22no—
37C2×Dic19⋊C4—42no—
38C2×Dic19⋊C4—42no—
39C2×Dic19⋊C4—42no—
40C19×C22⋊C8—22no—
41C19×C22⋊C8Q814yescomplemented
42C19×#95—22no—
43C19⋊#95—22no—
44C19⋊#95—22no—
45C19⋊#95—21no—
46C19⋊#95—42no—
47C19⋊#95Q812yescomplemented
48#10597275—44no—
49C24×C19C2×D411yescharacteristic
50C22×C4×C19—21no—
51C22×C4×C19—21no—
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—41no—
55C22×C4×C19—41no—
56C22×C4×C19—41no—
57C22×C4×C19—41no—
58C22×C4×C19—41no—
59C22×C4×C19—41no—
60C22×C4×C19D812yes—
61C22×C4×C19Q1612yes—
62C22×C4×C19C2×D412yes—
63C22×C4×C19C2×Q812yes—
64C22×C4×C19C2×Q811yescharacteristic
65C22×C4×C19#4111yescharacteristic
66C22×Dic19—22no—
67C22×Dic19—22no—
68C22×Dic19—22no—
69C22×Dic19—22no—
70C22×Dic19—22no—
71C22×Dic19—22no—
72C22×Dic19—41no—
73C22×Dic19—41no—
74C22×Dic19—41no—
75C22×Dic19—41no—
76C22×Dic19—41no—
77C22×Dic19—41no—
78C22×Dic19—41no—
79C22×Dic19—41no—
80C22×Dic19—41no—
81C22×Dic19—41no—
82C2×Dic38—42no—
83C2×Dic38—81no—
84C2×Dic38—81no—
85C2×C8×C19—24no—
86C2×C8×C19—42no—
87C2×C8×C19—42no—
88C22⋊Dic19—42no—
89C22⋊Dic19—42no—
90C4⋊Dic19—24no—
91C4⋊Dic19—42no—
92C4⋊Dic19—42no—
93C4⋊Dic19—42no—
94C4⋊Dic19—42no—
95C4⋊Dic19—81no—
96C4⋊Dic19—81no—
97Dic19⋊C4—44no—
98Dic19⋊C4—48no—
99#10567—191nomaximal, Sylow
100C23×C19—21no—
101C23×C19—21no—
102C23×C19—21no—
103C23×C19—21no—
104C23×C19#12011yescharacteristic
105C23×C19C22⋊Q811yescharacteristic
106C23×C19C4⋊Q811yescharacteristic
107C23×C19C2×D811yescharacteristic
108C23×C19C2×Q1611yescharacteristic
109C23×C19AGL(1,ℤ/8)11yescharacteristic
110C23×C19#13711yescharacteristic
111C2×C4×C19—22no—
112C2×C4×C19—22no—
113C2×C4×C19—22no—
114C2×C4×C19—22no—
115C2×C4×C19—42no—
116C2×C4×C19—41no—
117C2×C4×C19—41no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—42no—
123C2×C4×C19—42no—
124C2×C4×C19—81no—
125C2×C4×C19—81no—
126C2×C4×C19C22⋊Q812yes—
127C2×C4×C19C4⋊Q812yes—
128C2×Dic19—24no—
129C2×Dic19—42no—
130C2×Dic19—42no—
131C2×Dic19—42no—
132C2×Dic19—42no—
133C2×Dic19—42no—
134C2×Dic19—42no—
135C2×Dic19—42no—
136C2×Dic19—42no—
137C2×Dic19—42no—
138C2×Dic19—42no—
139C2×Dic19—42no—
140C2×Dic19—42no—
141C2×Dic19—42no—
142C2×Dic19—42no—
143C2×Dic19—42no—
144C2×Dic19—81no—
145C2×Dic19—81no—
146C2×Dic19—81no—
147C2×Dic19—81no—
148Dic38—84no—
149C8×C19—44no—
150#2659—191no—
151#1852—192no—
152#1444—191no—
153#1294—192no—
154#1280D1911yescharacteristic
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19#39511yescharacteristic
168C22×C19#44711yescharacteristic
169C22×C19#45111yescharacteristic
170C22×C19#45311yescharacteristic
171C22×C19#45611yescharacteristic
172C22×C19B(4,𝔽2)11yescharacteristic
173C22×C19#45811yescharacteristic
174C22×C19#47411yescharacteristic
175C22×C19#47711yescharacteristic
176C22×C19#50011yescharacteristic
177C22×C19#50111yescharacteristic
178C4×C19—22no—
179C4×C19—22no—
180C4×C19—42no—
181C4×C19—42no—
182Dic19—44no—
183Dic19—82no—
184Dic19—82no—
185Dic19—82no—
186C2×C22⋊Q8—381no—
187C22×C4⋊C4—191no—
188C22×C4⋊C4—381no—
189C2×#107—382no—
190C2×C22⋊C8C2×D1912yes—
191#398—382no—
192#395—382no—
193#380—192no—
194#380—381no—
195C2×#95—191no—
196C2×#95—381no—
197C2×#95C2×D1911yescharacteristic
198#340—382no—
199C2×C19—21no—
200C2×C19—21no—
201C2×C19—21no—
202C2×C19—21no—
203C2×C19#159511yescharacteristic
204C2×C19#160511yescharacteristic
205C2×C19#161011yescharacteristic
206C2×C19#161411yescharacteristic
207C2×C19#205711yescharacteristic
208C2×C19#206011yescharacteristic
209C2×C19#206211yescharacteristic
210C22×Q8—381no—
211C23×C4—381no—
212C23×C4—381no—
213C23×C4D7611yescharacteristic
214C23×C4D7611yescharacteristic
215C23×C4C22×D1911yescharacteristic
216C22×C8—22no—
217C22⋊Q8—762no—
218C22⋊Q8—762no—
219C2×C4⋊C4—192no—
220C2×C4⋊C4—192no—
221C2×C4⋊C4—382no—
222C2×C4⋊C4—382no—
223C2×C4⋊C4—381no—
224C2×C4⋊C4—381no—
225C2×C4⋊C4—381no—
226C2×C4⋊C4—762no—
227C2×C4⋊C4—762no—
228C2×C4⋊C4—762no—
229C2×C4⋊C4—762no—
230C2×C22⋊C4—382no—
231#107—764no—
232C22⋊C8—22no—
233C22⋊C8Dic3814yescomplemented
234#95—22no—
235#95—192no—
236#95—382no—
237#95—382no—
238#95—381no—
239#95—762no—
240C19#1056711yescharacteristic, complemented, Sylow
241C24C2×D7611yescharacteristic
242C2×Q8—762no—
243C2×Q8—1521no—
244C2×Q8—1521no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—382no—
256C22×C4—382no—
257C22×C4—382no—
258C22×C4—382no—
259C22×C4—382no—
260C22×C4—382no—
261C22×C4—761no—
262C22×C4—761no—
263C22×C4—761no—
264C22×C4—761no—
265C22×C4—761no—
266C22×C4—761no—
267C22×C4—761no—
268C22×C4—761no—
269C22×C4—761no—
270C22×C4—761no—
271C22×C4D15212yes—
272C22×C4Dic7612yes—
273C22×C4C2×Dic3812yes—
274C22×C4D4×D1912yes—
275C22×C4#6454311yescharacteristic
276C22×C4Q8×D1911yescharacteristic
277C2×C8—24no—
278C2×C8—42no—
279C2×C8—42no—
280C4⋊C4—384no—
281C4⋊C4—762no—
282C4⋊C4—762no—
283C4⋊C4—764no—
284C4⋊C4—762no—
285C4⋊C4—762no—
286C4⋊C4—768no—
287C4⋊C4—1521no—
288C4⋊C4—1521no—
289C22⋊C4—762no—
290C22⋊C4—762no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23#1059731511yescharacteristic
296C23#1059732811yescharacteristic
297C23#1059734311yescharacteristic
298C23C2×D15211yescharacteristic
299C23C2×Dic7611yescharacteristic
300C23#1059735411yescharacteristic
301C23#1059735511yescharacteristic
302Q8—1524no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—384no—
319C2×C4—762no—
320C2×C4—762no—
321C2×C4—762no—
322C2×C4—762no—
323C2×C4—762no—
324C2×C4—762no—
325C2×C4—762no—
326C2×C4—762no—
327C2×C4—762no—
328C2×C4—762no—
329C2×C4—762no—
330C2×C4—762no—
331C2×C4—762no—
332C2×C4—762no—
333C2×C4—762no—
334C2×C4—1521no—
335C2×C4—1521no—
336C2×C4—1521no—
337C2×C4—1521no—
338C2×C4#1059732412yes—
339C2×C4#1059733412yes—
340C8—44no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22#1192646511yescharacteristic
354C22#1192668011yescharacteristic
355C22#1192670211yescharacteristic
356C22#1192671411yescharacteristic
357C22#1192672911yescharacteristic
358C22#1192673211yescharacteristic
359C22#1192673511yescharacteristic
360C22#1192682511yescharacteristic
361C22#1192684011yescharacteristic
362C22#1192694911yescharacteristic
363C22#1192695311yescharacteristic
364C4—22no—
365C4—22no—
366C4—42no—
367C4—42no—
368C4—764no—
369C4—1522no—
370C4—1522no—
371C4—1522no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2#1456255511yescharacteristic
377C2#1456261111yescharacteristic
378C2#1456264011yescharacteristic
379C2#1456266211yescharacteristic
380C2#1456496411yescharacteristic
381C2#1456498111yescharacteristic
382C2#1456498911yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1280C2
socleC23×C19#120
prime radicalC24×C19C2×D4
hypercenter#1280D19
hypocenterC19#10567
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
41. C19×C22⋊C8Q8semidirect
47. C19⋊#95Q8semidirect
233. C22⋊C8Dic38semidirect
240. C19#10567semidirect

Maximal subgroups

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

subgroupindex
#145697492
#145638252
#145618992
#145615152
C19×#12802
#1056719