Finite Group Databasebeta

← #18078508

Subgroups — #18078508

Order 4864.

530 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 107 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#14572676C211yesmaximal, characteristic
2C4×#10597291C211yesmaximal, characteristic
3#14562155C212yesmaximal, complemented
4#14561487C212yesmaximal, complemented
5C19×#2638C211yesmaximal, characteristic
6#11926622—24no—
7#11926597—21no—
8C2×#10597291—21no—
9#11926508—21no—
10#11926508C2212yes—
11C4×C22⋊Dic19C2212yes—
12#11926311—21no—
13#11926281—24no—
14C2×C19×C22⋊Q8C2211yescharacteristic
15C2×C4×D4×C19C2211yescharacteristic
16C19×#398C411yescharacteristic, complemented
17C19×#397—21no—
18C19×#397C411yescharacteristic, complemented
19C19×#395C411yescharacteristic, complemented
20C19×#394—21no—
21C19×#393C411yescharacteristic, complemented
22C19×#387—21no—
23C19×#385—21no—
24C19×#381C2211yescharacteristic
25C22×Q8×C19C2×C411yescharacteristic
26C22×D4×C19D411yescharacteristic
27C23×C4×C19D411yescharacteristic
28C23×C4×C19C2311yescharacteristic
29C19×C22⋊Q8—22no—
30C19×C22⋊Q8—22no—
31C4×D4×C19—22no—
32C4×D4×C19—22no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19C2×C411yescharacteristic
43C2×C22⋊C4×C19D411yescharacteristic
44C2×C42×C19D411yescharacteristic
45C2×C22⋊Dic19—22no—
46C2×C4×Dic19—22no—
47C2×#64520—22no—
48C2×#64520—22no—
49C19×#95—21no—
50C19×#95—21no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C19×#95C2×C411yescharacteristic
55C19×#95C2×C411yescharacteristic
56#10597291—24no—
57C19⋊#95—22no—
58C22⋊(C19⋊C8)—22no—
59C22⋊(C19⋊C8)—22no—
60C22⋊(C19⋊C8)D414yes—
61C4⋊(C19⋊C8)—22no—
62C4×C19⋊C8—22no—
63C24×C19C22⋊C411yescharacteristic
64C24×C19C2×D411yescharacteristic
65C2×Q8×C19—22no—
66C2×Q8×C19—81no—
67C2×D4×C19—22no—
68C2×D4×C19—22no—
69C2×D4×C19—41no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—21no—
76C22×C4×C19—81no—
77C22×C4×C19—81no—
78C22×C4×C19C22⋊C411yescharacteristic
79C22×C4×C19C22⋊C411yescharacteristic
80C22×C4×C19C22⋊C411yescharacteristic
81C22×C4×C19C22×C411yescharacteristic
82C22×C4×C19C2×D412yes—
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19#4112yes—
85C22×Dic19—42no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—42no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—81no—
92C22⋊C4×C19—22no—
93C22⋊C4×C19—22no—
94C22⋊C4×C19—42no—
95C22⋊C4×C19—42no—
96C22⋊C4×C19—81no—
97C22⋊C4×C19—81no—
98C42×C19—21no—
99C42×C19—21no—
100C22⋊Dic19—24no—
101C22⋊Dic19—42no—
102C4×Dic19—82no—
103#64520—82no—
104#64520—82no—
105C2×C19⋊C8—24no—
106#9184—191nomaximal, Sylow
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—21no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19—41no—
116C23×C19C2×C22⋊C411yescharacteristic
117C23×C19#12112yes—
118Q8×C19—82no—
119D4×C19—44no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—42no—
125C2×C4×C19—42no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—81no—
144C2×C4×C19#10412yes—
145C2×C4×C19C4×D412yes—
146C2×C4×C19#12011yescharacteristic
147C2×C4×C19#12311yescharacteristic
148C2×Dic19—44no—
149C2×Dic19—82no—
150C2×Dic19—82no—
151C19⋊C8—44no—
152#2975—191no—
153#2638D1911yescharacteristic
154C4×#99—191no—
155#1508—192no—
156#1284—192no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—22no—
160C22×C19—22no—
161C22×C19—22no—
162C22×C19—42no—
163C22×C19—41no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—81no—
167C22×C19—81no—
168C22×C19—81no—
169C22×C19#38611yescharacteristic
170C22×C19C2×#10411yescharacteristic
171C22×C19#42111yescharacteristic
172C4×C19—22no—
173C4×C19—21no—
174C4×C19—21no—
175C4×C19—22no—
176C4×C19—41no—
177C4×C19—41no—
178C4×C19—81no—
179C4×C19—81no—
180C4×C19—81no—
181C4×C19—81no—
182Dic19—84no—
183C2×C22⋊Q8C2×D1911yescharacteristic
184C2×C4×D4C2×D1911yescharacteristic
185#436—384no—
186#431—381no—
187C2×#99—381no—
188#407—192no—
189#407—381no—
190#398Dic1911yescharacteristic, complemented
191#397—21no—
192#397Dic1911yescharacteristic, complemented
193#395Dic1911yescharacteristic, complemented
194#394—21no—
195#393Dic1911yescharacteristic, complemented
196#387—21no—
197#385—21no—
198#381C2×D1911yescharacteristic
199C4×C22⋊C4—192no—
200#342—381no—
201#328—384no—
202C2×C19—21no—
203C2×C19—21no—
204C2×C19—42no—
205C2×C19—81no—
206C2×C19#187111yescharacteristic
207C2×C19#190911yescharacteristic
208C2×C19#191311yescharacteristic
209C22×Q8C2×Dic1911yescharacteristic
210C22×D4C22⋊D1911yescharacteristic
211C23×C4C22⋊D1911yescharacteristic
212C23×C4C22×D1911yescharacteristic
213C2×M16—382no—
214C2×M16—382no—
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217C4×D4—22no—
218C4×D4—22no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4C2×Dic1911yescharacteristic
223C2×C4⋊C4C2×Dic1911yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—382no—
229C2×C22⋊C4C2×Dic1911yescharacteristic
230C2×C22⋊C4C22⋊D1911yescharacteristic
231C2×C42—382no—
232C2×C42C22⋊D1911yescharacteristic
233C4⋊C8—382no—
234#99—384no—
235C22⋊C8—194no—
236C22⋊C8—382no—
237C22⋊C8—382no—
238C4×C8—382no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—382no—
245#95C2×Dic1911yescharacteristic
246#95C2×Dic1911yescharacteristic
247C19#918411yescharacteristic, complemented, Sylow
248C24C22⋊Dic1911yescharacteristic
249C24C2×C22⋊D1911yescharacteristic
250C2×Q8—22no—
251C2×Q8—81no—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4—762no—
264C22×C4C22⋊Dic1911yescharacteristic
265C22×C4C22⋊Dic1911yescharacteristic
266C22×C4C22⋊Dic1911yescharacteristic
267C22×C4D4×D1912yes—
268C22×C4#6454312yes—
269C22×C4C22×Dic1911yescharacteristic
270C22×C4C2×C22⋊D1911yescharacteristic
271M16—1522no—
272M16—1522no—
273C2×C8—384no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—42no—
279C4⋊C4—81no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—81no—
285C22⋊C4—81no—
286C22⋊C4—384no—
287C22⋊C4—762no—
288C42—21no—
289C42—21no—
290C42—1522no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23#1059738512yes—
301C23C2×C22⋊Dic1911yescharacteristic
302Q8—82no—
303D4—44no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—764no—
329C2×C4—1522no—
330C2×C4—1522no—
331C2×C4#1059729412yes—
332C2×C4D4×Dic1912yes—
333C2×C4#1059738111yescharacteristic
334C2×C4#1059738311yescharacteristic
335C8—764no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22#1192642411yescharacteristic
349C22C2×#1059729411yescharacteristic
350C22#1192656111yescharacteristic
351C4—21no—
352C4—21no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—1524no—
362C2—21no—
363C2—21no—
364C2—42no—
365C2—81no—
366C2#1456393811yescharacteristic
367C2#1456415811yescharacteristic
368C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2638C2
socleC22×C19#386
prime radicalC22×D4×C19D4
cosocleC23×C4×C19C23
hypercenter#2638D19
hypocenterC19#9184
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2638

Complements

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

NH ≅ G/Ntype
3. #14562155C2semidirect
4. #14561487C2semidirect
16. C19×#398C4semidirect
18. C19×#397C4semidirect
19. C19×#395C4semidirect
21. C19×#393C4semidirect
190. #398Dic19semidirect
192. #397Dic19semidirect
193. #395Dic19semidirect
195. #393Dic19semidirect
247. C19#9184semidirect

Maximal subgroups

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

subgroupindex
#145726762
C4×#105972912
#145621552
#145614872
C19×#26382
#918419