Finite Group Databasebeta

← #18078310

Subgroups — #18078310

Order 4864.

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

normal subgroups only

This group has 902 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
1C2×#11926407C211yesmaximal, characteristic
2#14563545C211yesmaximal, characteristic
3C2×#11926281C212yesmaximal, complemented
4#14561513C212yesmaximal, complemented
5C19×#2848C211yesmaximal, characteristic
6C22×C22⋊Dic19—21no—
7C2×C22⋊(C19⋊C8)—22no—
8C2×C22⋊(C19⋊C8)C2212yes—
9#11926407—24no—
10C2×C19⋊#95—21no—
11C2×C19⋊#95C2212yes—
12#11926281—24no—
13C24×C4×C19C2211yescharacteristic
14C2×C19×C22⋊Q8C412yescomplemented
15C2×C19×C22⋊Q8C2211yescharacteristic
16C19×#385—22no—
17C19×#385—21no—
18C19×#380C412yescomplemented
19C19×#380C2211yescharacteristic
20C19×#379—21no—
21C25×C19D411yescharacteristic
22C22×Q8×C19C2×C411yescharacteristic
23C23×C4×C19—22no—
24C23×C4×C19—22no—
25C23×C4×C19—44no—
26C23×C4×C19C2×C412yes—
27C23×C4×C19D412yes—
28C23×C4×C19D411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C23×Dic19—22no—
31C19×C22⋊Q8—22no—
32C19×C22⋊Q8—22no—
33C19×C22⋊Q8—44no—
34C2×C4⋊C4×C19—22no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C4⋊C4×C19C2×C412yes—
38C2×C22⋊C4×C19—22no—
39C2×C22⋊C4×C19—22no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊Dic19—24no—
43C2×C22⋊Dic19—44no—
44C22×C19⋊C8—22no—
45C19×#95—22no—
46C19×#95—21no—
47C19⋊#95—24no—
48C19⋊#95—22no—
49C19⋊#95D414yes—
50C22⋊(C19⋊C8)—22no—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—44no—
53C24×C19—24no—
54C24×C19—21no—
55C24×C19—21no—
56C24×C19—22no—
57C24×C19—22no—
58C24×C19—42no—
59C24×C19C22⋊C412yes—
60C24×C19C2×D411yescharacteristic
61C2×Q8×C19—22no—
62C2×Q8×C19—42no—
63C22×C4×C19—24no—
64C22×C4×C19—24no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—24no—
68C22×C4×C19—24no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—22no—
72C22×C4×C19—42no—
73C22×C4×C19—42no—
74C22×C4×C19—42no—
75C22×C4×C19—42no—
76C22×C4×C19—48no—
77C22×C4×C19—48no—
78C22×C4×C19C22⋊C412yes—
79C22×C4×C19C22×C411yescharacteristic
80C22×C4×C19C2×D412yes—
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19#4112yes—
83C22×Dic19—24no—
84C22×Dic19—44no—
85C22×Dic19—44no—
86C22×Dic19—42no—
87C22×Dic19—42no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—42no—
90C4⋊C4×C19—44no—
91C4⋊C4×C19—42no—
92C22⋊C4×C19—44no—
93C22⋊C4×C19—44no—
94C22⋊C4×C19—41no—
95C22⋊C4×C19—41no—
96C22⋊C4×C19—42no—
97C22⋊Dic19—48no—
98C2×C19⋊C8—44no—
99C2×C19⋊C8—42no—
100#9154—191nomaximal, Sylow
101C23×C19—22no—
102C23×C19—22no—
103C23×C19—24no—
104C23×C19—24no—
105C23×C19—22no—
106C23×C19—22no—
107C23×C19—22no—
108C23×C19—22no—
109C23×C19—22no—
110C23×C19—22no—
111C23×C19—48no—
112C23×C19—48no—
113C23×C19—42no—
114C23×C19—42no—
115C23×C19—42no—
116C23×C19—42no—
117C23×C19#9914yes—
118C23×C19C2×C22⋊C411yescharacteristic
119C23×C19#12011yescharacteristic
120C23×C19#12311yescharacteristic
121C23×C19#13512yes—
122C23×C19#13712yes—
123Q8×C19—82no—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19—22no—
128C2×C4×C19—22no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—48no—
132C2×C4×C19—48no—
133C2×C4×C19—42no—
134C2×C4×C19—42no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—42no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19C4×D412yes—
143C2×C4×C19#12112yes—
144C2×Dic19—44no—
145C2×Dic19—44no—
146C2×Dic19—44no—
147C2×Dic19—84no—
148C2×Dic19—84no—
149C19⋊C8—82no—
150#2848D1911yescharacteristic
151C2×#381—191no—
152#1779—191no—
153C2×#328—192no—
154#1294—192no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—24no—
160C22×C19—24no—
161C22×C19—24no—
162C22×C19—24no—
163C22×C19—24no—
164C22×C19—48no—
165C22×C19—48no—
166C22×C19—42no—
167C22×C19—42no—
168C22×C19—42no—
169C22×C19—42no—
170C22×C19#38611yescharacteristic
171C22×C19C2×#9912yes—
172C22×C19#41611yescharacteristic
173C22×C19#41911yescharacteristic
174C22×C19#42112yes—
175C22×C19#45212yes—
176C22×C19#48512yes—
177C4×C19—22no—
178C4×C19—22no—
179C4×C19—42no—
180C4×C19—81no—
181C4×C19—81no—
182C4×C19—82no—
183Dic19—84no—
184C24×C4C2×D1911yescharacteristic
185C2×C22⋊Q8Dic1912yescomplemented
186C2×C22⋊Q8C2×D1911yescharacteristic
187C22×C22⋊C4—381no—
188C2×C22⋊C8—192no—
189C2×C22⋊C8—382no—
190#385—21no—
191#385—22no—
192#381—384no—
193#380Dic1912yescomplemented
194#380C2×D1911yescharacteristic
195#379—21no—
196C2×#95—192no—
197C2×#95—381no—
198#328—384no—
199C2×C19—22no—
200C2×C19—22no—
201C2×C19—44no—
202C2×C19#151112yes—
203C2×C19#151612yes—
204C2×C19#187311yescharacteristic
205C2×C19#189711yescharacteristic
206C2×C19#189811yescharacteristic
207C25C22⋊D1911yescharacteristic
208C22×Q8C2×Dic1911yescharacteristic
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—44no—
212C23×C4—382no—
213C23×C4C2×Dic1912yes—
214C23×C4C22⋊D1912yes—
215C23×C4C22⋊D1911yescharacteristic
216C23×C4C22×D1911yescharacteristic
217C22×C8—382no—
218C22⋊Q8—22no—
219C22⋊Q8—22no—
220C22⋊Q8—44no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4C2×Dic1911yescharacteristic
224C2×C4⋊C4C2×Dic1912yes—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—384no—
230C2×C22⋊C4—764no—
231C22⋊C8—382no—
232C22⋊C8—382no—
233C22⋊C8—764no—
234#95—22no—
235#95—21no—
236#95—194no—
237#95—384no—
238#95—382no—
239C19#915411yescharacteristic, complemented, Sylow
240C24—21no—
241C24—21no—
242C24—24no—
243C24—22no—
244C24—22no—
245C24—42no—
246C24C22⋊Dic1912yes—
247C24C2×C22⋊D1911yescharacteristic
248C2×Q8—22no—
249C2×Q8—42no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—48no—
264C22×C4—48no—
265C22×C4—384no—
266C22×C4—764no—
267C22×C4—764no—
268C22×C4—762no—
269C22×C4—762no—
270C22×C4C22⋊Dic1912yes—
271C22×C4D4×D1912yes—
272C22×C4#6454312yes—
273C22×C4C22×Dic1911yescharacteristic
274C22×C4C2×C22⋊D1911yescharacteristic
275C2×C8—764no—
276C2×C8—762no—
277C4⋊C4—22no—
278C4⋊C4—42no—
279C4⋊C4—44no—
280C4⋊C4—42no—
281C22⋊C4—44no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—42no—
285C22⋊C4—44no—
286C22⋊C4—768no—
287C23—22no—
288C23—22no—
289C23—24no—
290C23—24no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—48no—
298C23—48no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—42no—
303C23#1059729114yes—
304C23#1059738111yescharacteristic
305C23#1059738311yescharacteristic
306C23#1059738812yes—
307C23#1059739612yes—
308C23C2×C22⋊Dic1911yescharacteristic
309Q8—82no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—48no—
318C2×C4—48no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—764no—
329C2×C4—764no—
330C2×C4—764no—
331C2×C4—1524no—
332C2×C4—1524no—
333C2×C4D4×Dic1912yes—
334C2×C4#1059738512yes—
335C8—1522no—
336C22—24no—
337C22—24no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—24no—
343C22—24no—
344C22—24no—
345C22—48no—
346C22—48no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22#1192642411yescharacteristic
352C22C2×#1059729112yes—
353C22#1192654011yescharacteristic
354C22#1192655311yescharacteristic
355C22#1192656112yes—
356C22#1192670412yes—
357C22#1192688212yes—
358C4—22no—
359C4—22no—
360C4—42no—
361C4—82no—
362C4—81no—
363C4—81no—
364C4—1524no—
365C2—22no—
366C2—22no—
367C2—44no—
368C2#1456216812yes—
369C2#1456219112yes—
370C2#1456394811yescharacteristic
371C2#1456408411yescharacteristic
372C2#1456408911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2848C2
socleC23×C19C2×C22⋊C4
prime radicalC25×C19D4
cosocleC23×C4×C19C23
hypercenter#2848D19
hypocenterC19#9154
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2848

Complements

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

NH ≅ G/Ntype
3. C2×#11926281C2semidirect
4. #14561513C2semidirect
14. C2×C19×C22⋊Q8C4semidirect
18. C19×#380C4semidirect
185. C2×C22⋊Q8Dic19semidirect
193. #380Dic19semidirect
239. C19#9154semidirect

Maximal subgroups

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

subgroupindex
C2×#119264072
#145635452
C2×#119262812
#145615132
C19×#28482
#915419