Finite Group Databasebeta

← #18080206

Subgroups — #18080206

Order 4864.

490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 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#14572664C211yesmaximal, characteristic
2#14568831C211yesmaximal, characteristic
3#14562261C212yesmaximal, complemented
4#14561492C212yesmaximal, complemented
5C19×#1466C211yesmaximal, characteristic
6C2×#10597316C2211yescharacteristic
7#11926616—24no—
8#11926601C2212yes—
9#11926508—21no—
10C2×C22⋊(C19⋊C8)—21no—
11#11926467—21no—
12#11926467—21no—
13#11926447C411yescharacteristic
14#11926447C411yescharacteristic
15#11926417—21no—
16#11926417—21no—
17#11926413C411yescharacteristic
18#11926409C411yescharacteristic
19C4×C4⋊Dic19C2211yescharacteristic
20#11926285—24no—
21C2×C4×D4×C19C2211yescharacteristic
22C19×#432C2212yes—
23C19×#323—21no—
24C19×#323—21no—
25C22×D4×C19C2×C411yescharacteristic
26C23×C4×C19D411yescharacteristic
27C23×C4×C19D411yescharacteristic
28C4×D4×C19—22no—
29C4×D4×C19—22no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C22⋊C4×C19D411yescharacteristic
32C2×C22⋊C4×C19D411yescharacteristic
33C2×C42×C19C2311yescharacteristic
34C2×C22⋊Dic19—21no—
35C2×C22⋊Dic19—21no—
36C2×C22⋊Dic19—21no—
37C2×C22⋊Dic19—21no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19C2×C411yescharacteristic
40C2×C4⋊Dic19C2×C411yescharacteristic
41C2×Dic19⋊C4—21no—
42C2×Dic19⋊C4—21no—
43C2×Dic19⋊C4—21no—
44C2×Dic19⋊C4—21no—
45C2×C4×Dic19C2×C411yescharacteristic
46C2×C4×Dic19C2×C411yescharacteristic
47C2×#64520—22no—
48C22×C19⋊C8—22no—
49#10597316—22no—
50#10597316—22no—
51C19×C4⋊C8—22no—
52C19×C22⋊C8—22no—
53C19×#97—22no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C22⋊(C19⋊C8)—22no—
58C22⋊(C19⋊C8)—22no—
59C22⋊(C19⋊C8)—22no—
60C4⋊(C19⋊C8)—22no—
61#10597260D414yes—
62C24×C19C22⋊C411yescharacteristic
63C24×C19C22⋊C411yescharacteristic
64C2×D4×C19—22no—
65C2×D4×C19—22no—
66C2×D4×C19—41no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—81no—
72C22×C4×C19—81no—
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22×C411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×Dic19—21no—
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C2×C8×C19—42no—
83C4⋊C4×C19—22no—
84C22⋊C4×C19—22no—
85C22⋊C4×C19—22no—
86C42×C19C2×D412yes—
87C42×C19#4112yes—
88C22⋊Dic19—42no—
89C22⋊Dic19—42no—
90C22⋊Dic19—81no—
91C22⋊Dic19—81no—
92C4⋊Dic19—22no—
93C4⋊Dic19—22no—
94C4⋊Dic19—42no—
95Dic19⋊C4—41no—
96Dic19⋊C4—42no—
97Dic19⋊C4—41no—
98Dic19⋊C4—81no—
99Dic19⋊C4—81no—
100C4×Dic19—41no—
101C4×Dic19—41no—
102#64520—82no—
103C2×C19⋊C8—24no—
104C2×C19⋊C8—82no—
105#9449—191nomaximal, Sylow
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—41no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19#10112yes—
116C23×C19C2×C22⋊C411yescharacteristic
117D4×C19—44no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—42no—
125C2×C4×C19—42no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—81no—
129C2×C4×C19—81no—
130C2×C4×C19C4×D412yes—
131C2×C4×C19#12011yescharacteristic
132C2×C4×C19#12112yes—
133C2×C4×C19#12311yescharacteristic
134C2×Dic19—22no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C8×C19—82no—
147C19⋊C8—44no—
148#2973—191no—
149#2566—191no—
150#1534—192no—
151#1466D1911yescharacteristic
152#1285—192no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—22no—
156C22×C19—42no—
157C22×C19—42no—
158C22×C19—41no—
159C22×C19—41no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—81no—
164C22×C19—81no—
165C22×C19#38611yescharacteristic
166C22×C19C2×#10111yescharacteristic
167C22×C19#41311yescharacteristic
168C4×C19—22no—
169C4×C19—22no—
170C4×C19—21no—
171C4×C19—21no—
172C4×C19—41no—
173C4×C19—41no—
174Dic19—42no—
175Dic19—81no—
176Dic19—81no—
177Dic19—81no—
178C2×#125—191no—
179C2×C4×D4C2×D1911yescharacteristic
180#435—384no—
181#432—192no—
182#432C2×D1912yes—
183#407—381no—
184C2×C22⋊C8—381no—
185#396—381no—
186#396—381no—
187#390—191no—
188#390—191no—
189#385—381no—
190#385—381no—
191#384—191no—
192#382—191no—
193C4×C4⋊C4—191no—
194#330—384no—
195#323—21no—
196#323—21no—
197C2×C19—21no—
198C2×C19—21no—
199C2×C19—42no—
200C2×C19—81no—
201C2×C19#188411yescharacteristic
202C2×C19#190111yescharacteristic
203C2×C19#191111yescharacteristic
204C22×D4C4×D1911yescharacteristic
205C23×C4D7611yescharacteristic
206C23×C4D7611yescharacteristic
207C2×M16—382no—
208C22×C8—382no—
209#125—382no—
210#125—382no—
211C4×D4—22no—
212C4×D4—22no—
213C2×C4⋊C4—191no—
214C2×C4⋊C4—191no—
215C2×C4⋊C4—381no—
216C2×C4⋊C4—381no—
217C2×C4⋊C4—381no—
218C2×C4⋊C4—381no—
219C2×C4⋊C4—381no—
220C2×C4⋊C4C4×D1911yescharacteristic
221C2×C22⋊C4—381no—
222C2×C22⋊C4—381no—
223C2×C22⋊C4—381no—
224C2×C22⋊C4—381no—
225C2×C22⋊C4C22⋊D1911yescharacteristic
226C2×C22⋊C4C22⋊D1911yescharacteristic
227C2×C42—191no—
228C2×C42—191no—
229C2×C42C22×D1911yescharacteristic
230C4⋊C8—22no—
231C4⋊C8—382no—
232C22⋊C8—22no—
233C22⋊C8—382no—
234C22⋊C8—382no—
235C22⋊C8—382no—
236#97—22no—
237#97—194no—
238#95—381no—
239#95—381no—
240#95—381no—
241C19#944911yescharacteristic, complemented, Sylow
242C24(C2×D19)⋊C411yescharacteristic
243C24(C2×D19)⋊C411yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4—381no—
254C22×C4—381no—
255C22×C4—381no—
256C22×C4—381no—
257C22×C4(C2×D19)⋊C411yescharacteristic
258C22×C4(C2×D19)⋊C411yescharacteristic
259C22×C4C2×C4×D1911yescharacteristic
260C22×C4C2×D7611yescharacteristic
261C22×C4C2×C22⋊D1911yescharacteristic
262M16—1522no—
263C2×C8—42no—
264C2×C8—384no—
265C2×C8—1522no—
266C4⋊C4—22no—
267C4⋊C4—382no—
268C4⋊C4—382no—
269C4⋊C4—762no—
270C4⋊C4—762no—
271C4⋊C4—761no—
272C4⋊C4—761no—
273C4⋊C4—1521no—
274C4⋊C4—1521no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—762no—
278C22⋊C4—762no—
279C22⋊C4—1521no—
280C22⋊C4—1521no—
281C42—761no—
282C42—761no—
283C42D4×D1912yes—
284C42#6454312yes—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#1059728112yes—
295C23C2×(C2×D19)⋊C411yescharacteristic
296D4—44no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—382no—
310C2×C4—761no—
311C2×C4—761no—
312C2×C4—761no—
313C2×C4—761no—
314C2×C4—761no—
315C2×C4—761no—
316C2×C4—761no—
317C2×C4—761no—
318C2×C4—761no—
319C2×C4—761no—
320C2×C4—761no—
321C2×C4(C22⋊D19)⋊C412yes—
322C2×C4#1059732811yescharacteristic
323C2×C4#1059733211yescharacteristic
324C2×C4#1059738512yes—
325C8—82no—
326C8—764no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22#1192642111yescharacteristic
340C22C2×#1059728111yescharacteristic
341C22#1192652611yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—22no—
346C4—41no—
347C4—41no—
348C4—762no—
349C4—1521no—
350C4—1521no—
351C4—1521no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—81no—
356C2#1456401611yescharacteristic
357C2#1456410111yescharacteristic
358C2#1456416511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1466C2
socleC22×C19#386
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenter#1466D19
hypocenterC19#9449
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #14562261C2semidirect
4. #14561492C2semidirect
241. C19#9449semidirect

Maximal subgroups

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

subgroupindex
#145726642
#145688312
#145622612
#145614922
C19×#14662
#944919