Finite Group Databasebeta

← #18080204

Subgroups — #18080204

Order 4864.

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

normal subgroups only

This group has 486 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#14572720C211yesmaximal, characteristic, complemented
2#14562259C212yesmaximal
3#14561979C211yesmaximal, characteristic, complemented
4#14561491C212yesmaximal, complemented
5C19×#2545C211yesmaximal, characteristic
6#11926675—24no—
7#11926601—21no—
8#11926601C2212yes—
9#11926601C2212yes—
10#11926597—21no—
11#11926284—24no—
12#11926270—21no—
13#11926270—21no—
14C2×C19×C4⋊Q8C411yescharacteristic
15C2×C19×#124C411yescharacteristic
16C2×C19×#124C2211yescharacteristic
17C2×C4×Q8×C19C2211yescharacteristic
18C19×#396—21no—
19C19×#396—21no—
20C19×#391C411yescharacteristic
21C19×#390C411yescharacteristic
22C19×#388—21no—
23C19×#388—21no—
24C4×C4⋊C4×C19C2211yescharacteristic
25C22×Q8×C19C2×C411yescharacteristic
26C22×Q8×C19C2×C411yescharacteristic
27C22×D4×C19C2×C411yescharacteristic
28C19×C4⋊Q8—42no—
29C19×#124—22no—
30C19×#124—22no—
31C19×#124—42no—
32C4×Q8×C19—22no—
33C4×Q8×C19—22no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C4⋊C4×C19D411yescharacteristic
39C2×C4⋊C4×C19D411yescharacteristic
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19—21no—
46C2×C42×C19C2×C411yescharacteristic
47C2×C42×C19C2×C411yescharacteristic
48C2×C42×C19D411yescharacteristic
49C2×C42×C19D411yescharacteristic
50C2×C42×C19C2311yescharacteristic
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C22⋊(C19⋊C8)—22no—
55C22⋊(C19⋊C8)—22no—
56C4⋊(C19⋊C8)—22no—
57C4⋊(C19⋊C8)—22no—
58C4⋊(C19⋊C8)—22no—
59C4⋊(C19⋊C8)—22no—
60#10597260—22no—
61#10597260—22no—
62#10597260D414yes—
63C4×C19⋊C8—22no—
64C24×C19—21no—
65C2×Q8×C19—22no—
66C2×Q8×C19—22no—
67C2×Q8×C19—22no—
68C2×Q8×C19—41no—
69C2×Q8×C19—41no—
70C2×Q8×C19—41no—
71C2×D4×C19—22no—
72C2×D4×C19—41no—
73C2×D4×C19—41no—
74C22×C4×C19—21no—
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22⋊C411yescharacteristic
79C22×C4×C19C22⋊C411yescharacteristic
80C22×C4×C19C22⋊C411yescharacteristic
81C22×C4×C19C22×C411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C4⋊C4×C19—22no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—42no—
88C4⋊C4×C19—42no—
89C4⋊C4×C19—42no—
90C22⋊C4×C19—42no—
91C22⋊C4×C19—42no—
92C22⋊C4×C19—42no—
93C22⋊C4×C19—42no—
94C22⋊C4×C19—41no—
95C22⋊C4×C19—42no—
96C22⋊C4×C19—41no—
97C42×C19—21no—
98C42×C19—21no—
99C42×C19—21no—
100C42×C19—21no—
101C42×C19—41no—
102C42×C19—41no—
103C42×C19C2×D412yes—
104C42×C19#4112yes—
105C2×C19⋊C8—24no—
106C2×C19⋊C8—42no—
107#9448—191nomaximal, Sylow
108C23×C19—41no—
109C23×C19—41no—
110C23×C19—41no—
111C23×C19—41no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19C2×C22⋊C411yescharacteristic
116Q8×C19—44no—
117Q8×C19—82no—
118D4×C19—82no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—22no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
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#10012yes—
142C2×C4×C19C4×D412yes—
143C2×C4×C19#12011yescharacteristic
144C2×C4×C19#12112yes—
145C2×C4×C19#12311yescharacteristic
146C19⋊C8—44no—
147C19⋊C8—82no—
148#2983—191no—
149#2545D1911yescharacteristic
150#1533—192no—
151#1467—191no—
152#1285—192no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—81no—
156C22×C19—81no—
157C22×C19—81no—
158C22×C19—81no—
159C22×C19—81no—
160C22×C19—81no—
161C22×C19—81no—
162C22×C19#38611yescharacteristic
163C22×C19C2×#10011yescharacteristic
164C22×C19#41311yescharacteristic
165C4×C19—22no—
166C4×C19—22no—
167C4×C19—22no—
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—42no—
171C4×C19—41no—
172C4×C19—41no—
173C4×C19—41no—
174C4×C19—81no—
175C4×C19—81no—
176C2×C4⋊Q8Dic1911yescharacteristic
177C2×#124Dic1911yescharacteristic
178C2×#124C2×D1911yescharacteristic
179C2×C4×Q8C2×D1911yescharacteristic
180#446—384no—
181#432—192no—
182#432—192no—
183#432—381no—
184#431—381no—
185#396—21no—
186#396—21no—
187#391Dic1911yescharacteristic
188#390Dic1911yescharacteristic
189#388—21no—
190#388—21no—
191C4×C4⋊C4C2×D1911yescharacteristic
192#329—384no—
193#324—381no—
194#324—381no—
195C2×C19—21no—
196C2×C19—21no—
197C2×C19—161no—
198C2×C19#188411yescharacteristic
199C2×C19#190011yescharacteristic
200C2×C19#191211yescharacteristic
201C22×Q8C2×Dic1911yescharacteristic
202C22×Q8C2×Dic1911yescharacteristic
203C22×D4C2×Dic1911yescharacteristic
204C4⋊Q8—42no—
205#124—22no—
206#124—22no—
207#124—42no—
208C4×Q8—22no—
209C4×Q8—22no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×Dic1911yescharacteristic
214C2×C4⋊C4C22⋊D1911yescharacteristic
215C2×C4⋊C4C22⋊D1911yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C42C2×Dic1911yescharacteristic
223C2×C42C2×Dic1911yescharacteristic
224C2×C42C22⋊D1911yescharacteristic
225C2×C42C22⋊D1911yescharacteristic
226C2×C42C22×D1911yescharacteristic
227C4⋊C8—382no—
228C4⋊C8—382no—
229C4⋊C8—382no—
230C4⋊C8—382no—
231C22⋊C8—382no—
232C22⋊C8—382no—
233#97—194no—
234#97—382no—
235#97—382no—
236C4×C8—382no—
237#95—21no—
238#95—21no—
239#95—21no—
240C19#944811yescharacteristic, complemented, Sylow
241C24—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—22no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×D4—22no—
249C2×D4—41no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4C22⋊Dic1911yescharacteristic
255C22×C4C22⋊Dic1911yescharacteristic
256C22×C4C22⋊Dic1911yescharacteristic
257C22×C4C22⋊Dic1911yescharacteristic
258C22×C4C22×Dic1911yescharacteristic
259C22×C4C2×C22⋊D1911yescharacteristic
260C22×C4C2×C22⋊D1911yescharacteristic
261C2×C8—384no—
262C2×C8—762no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—41no—
281C42—41no—
282C42D4×D1912yes—
283C42#6454312yes—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23C2×C22⋊Dic1911yescharacteristic
292Q8—44no—
293Q8—82no—
294D4—82no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4#1059729012yes—
318C2×C4D4×Dic1912yes—
319C2×C4#1059738111yescharacteristic
320C2×C4#1059738311yescharacteristic
321C2×C4#1059738512yes—
322C8—764no—
323C8—1522no—
324C22—21no—
325C22—21no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22#1192642411yescharacteristic
334C22C2×#1059729011yescharacteristic
335C22#1192652811yescharacteristic
336C4—22no—
337C4—22no—
338C4—21no—
339C4—21no—
340C4—22no—
341C4—42no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C2—21no—
348C2—21no—
349C2—161no—
350C2#1456401911yescharacteristic
351C2#1456409911yescharacteristic
352C2#1456417311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2545C2
socleC22×C19#386
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenter#2545D19
hypocenterC19#9448
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2545

Complements

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

NH ≅ G/Ntype
1. #14572720C2semidirect
3. #14561979C2semidirect
4. #14561491C2semidirect
240. C19#9448semidirect

Maximal subgroups

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

subgroupindex
#145727202
#145622592
#145619792
#145614912
C19×#25452
#944819