Finite Group Databasebeta

← #18071168

Subgroups — #18071168

Order 4864.

506 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 103 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#14571966C211yesmaximal, characteristic
2#14563703C211yesmaximal, characteristic, complemented
3#14561459C212yesmaximal, complemented
4#14561455C212yesmaximal, complemented
5C19×#1817C211yesmaximal, characteristic, complemented
6C2×#10597375—21no—
7C2×#10597376C411yescharacteristic
8C2×C22⋊(C19⋊C8)—21no—
9#11926446C411yescharacteristic
10#11926446C2211yescharacteristic
11#11926442C411yescharacteristic
12#11926442C2211yescharacteristic
13#11926435—21no—
14#11926435—21no—
15#11926423—21no—
16#11926404C411yescharacteristic
17#11926299—21no—
18#11926299C2212yes—
19C22×C42×C19C2211yescharacteristic
20C2×C19×C22⋊C8—21no—
21C19×#336—21no—
22C19×#336C2212yes—
23C23×C4×C19C2×C411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C22×C22⋊D19—21no—
27C22×D76C2×C411yescharacteristic
28C22×C8×C19—22no—
29C2×C42×C19—42no—
30C2×C42×C19C2×C411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19C2311yescharacteristic
34C2×C22⋊Dic19—21no—
35#10597376—42no—
36#10597375—44no—
37C2×(C2×D19)⋊C4—21no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×C4⋊Dic19C2×C411yescharacteristic
43C2×C4⋊Dic19C2×C411yescharacteristic
44C2×C4⋊Dic19C2×C411yescharacteristic
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—21no—
47C22×C19⋊C8—22no—
48C19×C22⋊C8—42no—
49C19⋊#95—21no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C22⋊(C19⋊C8)—42no—
53C24×C19C22⋊C411yescharacteristic
54C23×D19—21no—
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19—22no—
59C22×C4×C19—22no—
60C22×C4×C19—22no—
61C22×C4×C19—41no—
62C22×C4×C19—41no—
63C22×C4×C19—41no—
64C22×C4×C19C22⋊C411yescharacteristic
65C22×C4×C19C22⋊C411yescharacteristic
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22×C411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C2×C22⋊D19—42no—
71C2×C22⋊D19—42no—
72C2×C22⋊D19—42no—
73C22×Dic19—21no—
74C22×Dic19—21no—
75C22×Dic19—21no—
76C2×D76—22no—
77C2×D76—41no—
78C2×D76—41no—
79C2×C8×C19—42no—
80C2×C8×C19—42no—
81C2×C8×C19—42no—
82C42×C19—41no—
83C42×C19—41no—
84C42×C19—41no—
85C42×C19—41no—
86C22⋊Dic19—42no—
87(C2×D19)⋊C4—42no—
88(C2×D19)⋊C4—42no—
89(C2×D19)⋊C4—42no—
90(C2×D19)⋊C4—42no—
91(C2×D19)⋊C4—42no—
92C4⋊Dic19—22no—
93C4⋊Dic19—41no—
94C4⋊Dic19—41no—
95Dic19⋊C4—42no—
96Dic19⋊C4—42no—
97C2×C19⋊C8—42no—
98C2×C19⋊C8—42no—
99C2×C19⋊C8—42no—
100#7718—191nomaximal, Sylow
101C23×C19—21no—
102C23×C19—21no—
103C23×C19—21no—
104C23×C19—21no—
105C23×C19—21no—
106C23×C19—21no—
107C23×C19#9912yes—
108C23×C19C2×C22⋊C411yescharacteristic
109C22×D19—41no—
110C22×D19—41no—
111C22×D19—41no—
112C22×D19—41no—
113C22×D19—41no—
114C22×D19—41no—
115C22×D19—41no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—44no—
132C2×C4×C19—44no—
133C2×C4×C19—44no—
134C2×C4×C19#13112yes—
135C2×C4×C19#13512yes—
136C2×C4×C19AGL(1,ℤ/8)12yes—
137C22⋊D19—84no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147D76—82no—
148C8×C19—82no—
149C19⋊C8—82no—
150#2854—191no—
151#1817—191no—
152#1817D1911yescharacteristic, complemented
153#1271—192no—
154#1270—192no—
155C22×C19—22no—
156C22×C19—22no—
157C22×C19—22no—
158C22×C19—41no—
159C22×C19—41no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19#40811yescharacteristic
163C22×C19C2×#9911yescharacteristic
164C22×C19#41311yescharacteristic
165C22×C19#41611yescharacteristic
166C22×C19#41811yescharacteristic
167C22×C19#42111yescharacteristic
168C22×C19#42111yescharacteristic
169C2×D19—81no—
170C2×D19—81no—
171C2×D19—81no—
172C2×D19—81no—
173C2×D19—81no—
174C2×D19—81no—
175C2×D19—81no—
176C4×C19—22no—
177C4×C19—22no—
178C4×C19—22no—
179C4×C19—41no—
180C4×C19—41no—
181C4×C19—41no—
182Dic19—81no—
183Dic19—81no—
184Dic19—81no—
185C2×#123—381no—
186C2×#121—191no—
187C22×C42C2×D1911yescharacteristic
188C2×C22⋊C8—21no—
189C2×C22⋊C8—381no—
190#390—191no—
191#390—191no—
192#389—191no—
193#389—191no—
194#388—381no—
195#388—381no—
196#386—381no—
197#380—191no—
198#336—21no—
199#336—192no—
200#336—381no—
201#336C2×D1912yes—
202C2×C19—42no—
203C2×C19#146811yescharacteristic
204C2×C19#148211yescharacteristic
205C2×C19#149611yescharacteristic
206C2×C19#151011yescharacteristic
207C2×C19#151611yescharacteristic
208C2×C19#153511yescharacteristic
209C2×C19#155311yescharacteristic
210D19—161no—
211C22×D4—191no—
212C22×D4—381no—
213C23×C4C4×D1911yescharacteristic
214C23×C4D7611yescharacteristic
215C23×C4C22⋊D1911yescharacteristic
216C22×C8—22no—
217C22×C8—382no—
218#123—764no—
219#121—762no—
220C2×C4⋊C4—191no—
221C2×C4⋊C4—191no—
222C2×C4⋊C4—191no—
223C2×C4⋊C4—381no—
224C2×C4⋊C4—381no—
225C2×C22⋊C4—381no—
226C2×C22⋊C4—381no—
227C2×C22⋊C4—381no—
228C2×C22⋊C4—381no—
229C2×C22⋊C4—381no—
230C2×C22⋊C4—381no—
231C2×C42—42no—
232C2×C42C4×D1911yescharacteristic
233C2×C42D7611yescharacteristic
234C2×C42C22⋊D1911yescharacteristic
235C2×C42C22×D1911yescharacteristic
236C22⋊C8—42no—
237C22⋊C8—762no—
238#95—381no—
239#95—381no—
240#95—381no—
241C19#771811yescharacteristic, complemented, Sylow
242C24—381no—
243C24(C2×D19)⋊C411yescharacteristic
244C2×D4—382no—
245C2×D4—761no—
246C2×D4—761no—
247C2×D4—762no—
248C2×D4—762no—
249C2×D4—762no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—381no—
260C22×C4—381no—
261C22×C4—381no—
262C22×C4(C2×D19)⋊C411yescharacteristic
263C22×C4(C2×D19)⋊C411yescharacteristic
264C22×C4(C2×D19)⋊C411yescharacteristic
265C22×C4C2×C4×D1911yescharacteristic
266C22×C4C2×D7611yescharacteristic
267C22×C4C2×C22⋊D1911yescharacteristic
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—762no—
272C2×C8—762no—
273C2×C8—762no—
274C4⋊C4—382no—
275C4⋊C4—761no—
276C4⋊C4—761no—
277C4⋊C4—762no—
278C4⋊C4—762no—
279C22⋊C4—762no—
280C22⋊C4—762no—
281C22⋊C4—762no—
282C22⋊C4—762no—
283C22⋊C4—762no—
284C22⋊C4—762no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—41no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—761no—
296C23—761no—
297C23—761no—
298C23—761no—
299C23—761no—
300C23—761no—
301C23—761no—
302C23#1059726312yes—
303C23C2×(C2×D19)⋊C411yescharacteristic
304D4—1522no—
305D4—1524no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—761no—
325C2×C4—761no—
326C2×C4—761no—
327C2×C4—761no—
328C2×C4—761no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—761no—
332C2×C4—761no—
333C2×C4#1059735012yes—
334C2×C4#1059735312yes—
335C2×C4#1059739512yes—
336C8—82no—
337C8—1522no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—1521no—
346C22—1521no—
347C22—1521no—
348C22—1521no—
349C22—1521no—
350C22—1521no—
351C22—1521no—
352C22#1192651211yescharacteristic
353C22C2×#1059726311yescharacteristic
354C22#1192652611yescharacteristic
355C22#1192654111yescharacteristic
356C22#1192654811yescharacteristic
357C22#1192656011yescharacteristic
358C22#1192656211yescharacteristic
359C4—22no—
360C4—22no—
361C4—22no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—1521no—
366C4—1521no—
367C4—1521no—
368C2—42no—
369C2—3041no—
370C2#1456198411yescharacteristic
371C2#1456204411yescharacteristic
372C2#1456210311yescharacteristic
373C2#1456216311yescharacteristic
374C2#1456219211yescharacteristic
375C2#1456226711yescharacteristic
376C2#1456233811yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1817C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597376C4
cosocleC2×C42×C19C23
hypercenter#1817D19
hypocenterC19#7718
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. #14563703C2semidirect
3. #14561459C2semidirect
4. #14561455C2semidirect
5. C19×#1817C2semidirect
152. #1817D19semidirect
241. C19#7718semidirect

Maximal subgroups

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

subgroupindex
#145719662
#145637032
#145614592
#145614552
C19×#18172
#771819