Finite Group Databasebeta

← #18080370

Subgroups — #18080370

Order 4864.

518 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 93 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#14567918C211yesmaximal, characteristic
2#14566235C211yesmaximal, characteristic
3#14563734C211yesmaximal, characteristic
4#14561964C211yesmaximal, characteristic
5#14561489C211yesmaximal, characteristic
6#14561488C211yesmaximal, characteristic
7C19×#1826C211yesmaximal, characteristic
8C22×Dic19⋊C4C2211yescharacteristic
9#11926508C2211yescharacteristic
10#11926482C412yescomplemented
11#11926475C412yescomplemented
12#11926428—22no—
13#11926428—22no—
14#11926426—22no—
15#11926416—21no—
16#11926407C2211yescharacteristic
17#11926405—21no—
18#11926405—21no—
19#11926402—21no—
20C4×C22⋊Dic19C2211yescharacteristic
21#11926303—22no—
22#11926269—22no—
23C2×C19×#117C2211yescharacteristic
24C19×#407C2211yescharacteristic
25C4×C22⋊C4×C19C2211yescharacteristic
26C19×#339—22no—
27C23×C4×C19C2311yescharacteristic
28C23×Dic19D411yescharacteristic
29C23×Dic19D411yescharacteristic
30C2×M16×C19—21no—
31C19×#117—21no—
32C19×#117—21no—
33C19×#117—21no—
34C19×#117—21no—
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C42×C19—21no—
40C2×C42×C19D412yes—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19—21no—
43C2×Dic19⋊C4—21no—
44C2×Dic19⋊C4—21no—
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—21no—
47C2×Dic19⋊C4—22no—
48C2×Dic19⋊C4—22no—
49C2×Dic19⋊C4C2×C412yes—
50C2×Dic19⋊C4D412yes—
51C2×C4×Dic19D412yes—
52C2×#64520—21no—
53C19×C22⋊C8—21no—
54C19×C22⋊C8—21no—
55C19×#95—21no—
56C19⋊#95—22no—
57C19⋊#95—24no—
58C19⋊#95—21no—
59C19⋊#95—21no—
60C19⋊#95—22no—
61C19⋊#95—22no—
62C19⋊#95—22no—
63C19⋊#95C2×C412yes—
64C22⋊(C19⋊C8)—21no—
65C22⋊(C19⋊C8)—21no—
66C24×C19C2×D411yescharacteristic
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—22no—
70C22×C4×C19—42no—
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19#4111yescharacteristic
76C22×C4×C19#4111yescharacteristic
77C22×Dic19—21no—
78C22×Dic19—21no—
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—22no—
82C22×Dic19—22no—
83C22×Dic19—42no—
84C22×Dic19—42no—
85C22×Dic19C22⋊C412yes—
86C22×Dic19C22⋊C412yes—
87M16×C19—42no—
88C2×C8×C19—41no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—21no—
93C22⋊C4×C19—42no—
94C22⋊C4×C19—41no—
95C22⋊C4×C19—41no—
96C42×C19—42no—
97C42×C19—41no—
98C42×C19—41no—
99C22⋊Dic19—42no—
100C22⋊Dic19—42no—
101Dic19⋊C4—22no—
102Dic19⋊C4—22no—
103Dic19⋊C4—22no—
104Dic19⋊C4—22no—
105Dic19⋊C4—44no—
106Dic19⋊C4—82no—
107C4×Dic19—42no—
108#64520—42no—
109C2×C19⋊C8—41no—
110#9482—191nomaximal, Sylow
111C23×C19—22no—
112C23×C19—22no—
113C23×C19—41no—
114C23×C19C2×C22⋊C411yescharacteristic
115C23×C19#12011yescharacteristic
116C23×C19#12311yescharacteristic
117C2×C4×C19—22no—
118C2×C4×C19—22no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—42no—
124C2×C4×C19—42no—
125C2×C4×C19—42no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19C4×D411yescharacteristic
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19#12111yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×Dic19—22no—
135C2×Dic19—22no—
136C2×Dic19—22no—
137C2×Dic19—22no—
138C2×Dic19—42no—
139C2×Dic19—42no—
140C2×Dic19—42no—
141C2×Dic19—42no—
142C2×Dic19—42no—
143C2×Dic19—42no—
144C2×Dic19—42no—
145C2×Dic19—42no—
146C2×Dic19—42no—
147C2×Dic19—42no—
148C2×Dic19—81no—
149C8×C19—81no—
150C19⋊C8—81no—
151#2484—191no—
152#2313—191no—
153#1826—191no—
154#1826D1911yescharacteristic
155#1463—191no—
156#1284—191no—
157#1284—191no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—44no—
166C22×C19#38611yescharacteristic
167C22×C19#42112yes—
168C22×C19#45812yes—
169C4×C19—21no—
170C4×C19—21no—
171C4×C19—21no—
172C4×C19—21no—
173C4×C19—82no—
174C4×C19—81no—
175C4×C19—81no—
176Dic19—42no—
177Dic19—42no—
178Dic19—82no—
179Dic19—82no—
180C2×#117C2×D1911yescharacteristic
181C22×C4⋊C4—191no—
182#407—191no—
183#407C2×D1911yescharacteristic
184#400—192no—
185#398—192no—
186#387—382no—
187#387—382no—
188#387—382no—
189#385—381no—
190#381—191no—
191#381—381no—
192#381—381no—
193#380—381no—
194C4×C22⋊C4—191no—
195C4×C22⋊C4C2×D1911yescharacteristic
196#339—22no—
197#339—382no—
198#324—382no—
199C2×C19—22no—
200C2×C19—22no—
201C2×C19—41no—
202C2×C19#189011yescharacteristic
203C2×C19#189711yescharacteristic
204C2×C19#191211yescharacteristic
205C23×C4—191no—
206C23×C4—191no—
207C23×C4C22×D1911yescharacteristic
208C2×M16—21no—
209C2×M16—381no—
210#117—21no—
211#117—21no—
212#117—21no—
213#117—21no—
214C2×C4⋊C4—192no—
215C2×C4⋊C4—192no—
216C2×C4⋊C4—381no—
217C2×C4⋊C4—381no—
218C2×C4⋊C4—381no—
219C2×C4⋊C4—381no—
220C2×C4⋊C4—382no—
221C2×C4⋊C4—382no—
222C2×C4⋊C4C4×D1911yescharacteristic
223C2×C4⋊C4C4×D1911yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—381no—
227C2×C22⋊C4—381no—
228C2×C42—21no—
229C2×C42—192no—
230C2×C42C22⋊D1912yes—
231C22⋊C8—21no—
232C22⋊C8—21no—
233C22⋊C8—381no—
234C22⋊C8—381no—
235#95—21no—
236#95—192no—
237#95—382no—
238#95—382no—
239#95—382no—
240#95—382no—
241#95—384no—
242#95—381no—
243#95—381no—
244C19#948211yescharacteristic, complemented, Sylow
245C24D4×D1911yescharacteristic
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—42no—
250C22×C4—192no—
251C22×C4—192no—
252C22×C4—381no—
253C22×C4—381no—
254C22×C4—381no—
255C22×C4—381no—
256C22×C4—382no—
257C22×C4—382no—
258C22×C4—762no—
259C22×C4—762no—
260C22×C4C2×C4×D1911yescharacteristic
261C22×C4#6454111yescharacteristic
262C22×C4D4×D1911yescharacteristic
263C22×C4D4×D1911yescharacteristic
264C22×C4#6454311yescharacteristic
265C22×C4C2×C22⋊D1911yescharacteristic
266M16—42no—
267M16—762no—
268C2×C8—41no—
269C2×C8—761no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—382no—
275C4⋊C4—382no—
276C4⋊C4—382no—
277C4⋊C4—382no—
278C4⋊C4—764no—
279C4⋊C4—1522no—
280C22⋊C4—42no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—762no—
284C22⋊C4—762no—
285C42—42no—
286C42—41no—
287C42—41no—
288C42—762no—
289C23—22no—
290C23—22no—
291C23—41no—
292C23C22⋊C4×D1911yescharacteristic
293C23#1059732911yescharacteristic
294C23#1059738311yescharacteristic
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—382no—
309C2×C4—382no—
310C2×C4—382no—
311C2×C4—382no—
312C2×C4—762no—
313C2×C4—762no—
314C2×C4—762no—
315C2×C4—762no—
316C2×C4—762no—
317C2×C4—762no—
318C2×C4—762no—
319C2×C4—762no—
320C2×C4—762no—
321C2×C4—762no—
322C2×C4—1521no—
323C2×C4(C22⋊D19)⋊C411yescharacteristic
324C2×C4#1059733011yescharacteristic
325C2×C4C4×C22⋊D1911yescharacteristic
326C2×C4#1059738411yescharacteristic
327C8—81no—
328C8—1521no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—44no—
337C22#1192642011yescharacteristic
338C22#1192655912yes—
339C22#1192673312yes—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—82no—
345C4—81no—
346C4—81no—
347C4—762no—
348C4—762no—
349C4—1522no—
350C4—1522no—
351C2—22no—
352C2—22no—
353C2—41no—
354C2#1456404511yescharacteristic
355C2#1456408011yescharacteristic
356C2#1456416911yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1826C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#1826D19
hypocenterC19#9482
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
10. #11926482C4semidirect
11. #11926475C4semidirect
244. C19#9482semidirect

Maximal subgroups

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

subgroupindex
#145679182
#145662352
#145637342
#145619642
#145614892
#145614882
C19×#18262
#948219