Finite Group Databasebeta

← #18078319

Subgroups — #18078319

Order 4864.

692 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 147 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
3C2×#11926277C212yesmaximal
4#14561514C212yesmaximal, complemented
5C2×C19×#382C211yesmaximal, characteristic, complemented
6C2×#10597375—21no—
7C2×#10597376C2211yescharacteristic
8C2×C22⋊(C19⋊C8)C2212yes—
9#11926446C412yescomplemented
10#11926442C412yescomplemented
11#11926435—22no—
12#11926423—21no—
13#11926404C2211yescharacteristic
14#11926299—22no—
15#11926277—24no—
16C22×C4⋊C4×C19—21no—
17C22×C42×C19C2211yescharacteristic
18C19×#382—24no—
19C2×C19×#95—21no—
20C2×C19×#95C2212yes—
21C23×C4×C19—22no—
22C23×C4×C19D411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C22×C22⋊D19—21no—
26C22×D76C2×C411yescharacteristic
27C2×C4⋊C4×C19—24no—
28C2×C4⋊C4×C19—42no—
29C2×C4⋊C4×C19—42no—
30C2×C42×C19—22no—
31C2×C42×C19—22no—
32C2×C42×C19C2×C412yes—
33C2×C42×C19D412yes—
34C2×C22⋊Dic19—21no—
35#10597376—22no—
36#10597376—22no—
37#10597375—42no—
38#10597375—42no—
39C2×(C2×D19)⋊C4—22no—
40C2×(C2×D19)⋊C4—22no—
41C2×(C2×D19)⋊C4—21no—
42C2×C4⋊Dic19C2×C411yescharacteristic
43C2×C4⋊Dic19C2×C412yes—
44C2×Dic19⋊C4—22no—
45C22×C19⋊C8—22no—
46C19×#95—24no—
47C19×#95—22no—
48C19×#95D414yes—
49C19⋊#95—22no—
50C19⋊#95—21no—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—22no—
53C24×C19C2×D411yescharacteristic
54C23×D19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—24no—
62C22×C4×C19—42no—
63C22×C4×C19—42no—
64C22×C4×C19—44no—
65C22×C4×C19—44no—
66C22×C4×C19—42no—
67C22×C4×C19—42no—
68C22×C4×C19C22⋊C412yes—
69C22×C4×C19C22⋊C412yes—
70C22×C4×C19D812yes—
71C22×C4×C19SD1612yes—
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D412yes—
75C22×C4×C19#4112yes—
76C2×C22⋊D19—41no—
77C2×C22⋊D19—41no—
78C2×C22⋊D19—41no—
79C2×C22⋊D19—41no—
80C2×C22⋊D19—41no—
81C2×C22⋊D19—41no—
82C22×Dic19—22no—
83C22×Dic19—21no—
84C2×D76—22no—
85C2×D76—42no—
86C4⋊C4×C19—48no—
87C42×C19—24no—
88C42×C19—24no—
89C22⋊Dic19—41no—
90C22⋊Dic19—41no—
91(C2×D19)⋊C4—44no—
92(C2×D19)⋊C4—44no—
93(C2×D19)⋊C4—42no—
94C4⋊Dic19—22no—
95C4⋊Dic19—42no—
96Dic19⋊C4—44no—
97C2×C19⋊C8—44no—
98C2×C19⋊C8—42no—
99#9156—191nomaximal, Sylow
100C23×C19—22no—
101C23×C19—22no—
102C23×C19C2×C22⋊C411yescharacteristic
103C23×C19#12011yescharacteristic
104C23×C19#12311yescharacteristic
105C23×C19C2×D811yescharacteristic
106C23×C19C2×SD1611yescharacteristic
107C23×C19AGL(1,ℤ/8)11yescharacteristic
108C23×C19#13711yescharacteristic
109C22×D19—41no—
110C22×D19—42no—
111C22×D19—41no—
112C22×D19—41no—
113C22×D19—42no—
114C2×C4×C19—22no—
115C2×C4×C19—22no—
116C2×C4×C19—22no—
117C2×C4×C19—22no—
118C2×C4×C19—22no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19—42no—
128C2×C4×C19—42no—
129C2×C4×C19—44no—
130C2×C4×C19—44no—
131C2×C4×C19—44no—
132C2×C4×C19—84no—
133C2×C4×C19—84no—
134C2×C4×C19#10214yes—
135C2×C4×C19C4×D412yes—
136C2×C4×C19#12112yes—
137C22⋊D19—81no—
138C22⋊D19—81no—
139C22⋊D19—81no—
140C22⋊D19—81no—
141C2×Dic19—41no—
142C2×Dic19—42no—
143C2×Dic19—41no—
144C2×Dic19—42no—
145C2×Dic19—41no—
146C2×Dic19—42no—
147D76—82no—
148C19⋊C8—82no—
149#2854—191no—
150C2×#382D1911yescharacteristic, complemented
151#1817—191no—
152C2×#327—192no—
153#1294—192no—
154C22×C19—21no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—22no—
159C22×C19—22no—
160C22×C19—22no—
161C22×C19—22no—
162C22×C19#38611yescharacteristic
163C22×C19#41012yes—
164C22×C19C2×#10211yescharacteristic
165C22×C19#41711yescharacteristic
166C22×C19#42112yes—
167C22×C19#44711yescharacteristic
168C22×C19#44811yescharacteristic
169C22×C19#48011yescharacteristic
170C22×C19#48111yescharacteristic
171C2×D19—81no—
172C2×D19—81no—
173C2×D19—81no—
174C2×D19—82no—
175C2×D19—82no—
176C4×C19—24no—
177C4×C19—22no—
178C4×C19—22no—
179C4×C19—42no—
180C4×C19—84no—
181Dic19—81no—
182Dic19—82no—
183C2×#123—381no—
184C2×#121—191no—
185C22×C4⋊C4—21no—
186C22×C42C2×D1911yescharacteristic
187C2×C22⋊C8—192no—
188#390—192no—
189#389—192no—
190#388—382no—
191#386—381no—
192#382—24no—
193#380—191no—
194C2×#95—21no—
195C2×#95C2×D1912yes—
196#336—382no—
197#327—384no—
198C2×C19—21no—
199C2×C19—21no—
200C2×C19—21no—
201C2×C19—21no—
202C2×C19#151212yes—
203C2×C19#151712yes—
204C2×C19#187411yescharacteristic
205C2×C19#189711yescharacteristic
206C2×C19#189911yescharacteristic
207D19—161no—
208C22×D4—191no—
209C22×D4—381no—
210C23×C4—22no—
211C23×C4C22⋊D1911yescharacteristic
212C23×C4C22⋊D1911yescharacteristic
213C23×C4C22×D1911yescharacteristic
214C22×C8—382no—
215#123—762no—
216#123—762no—
217#121—382no—
218#121—382no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—42no—
221C2×C4⋊C4—42no—
222C2×C4⋊C4—191no—
223C2×C4⋊C4—192no—
224C2×C4⋊C4—382no—
225C2×C22⋊C4—381no—
226C2×C22⋊C4—382no—
227C2×C22⋊C4—382no—
228C2×C22⋊C4—381no—
229C2×C42—22no—
230C2×C42—22no—
231C2×C42C4×D1912yes—
232C2×C42D7612yes—
233C22⋊C8—382no—
234C22⋊C8—382no—
235#95—24no—
236#95—22no—
237#95—382no—
238#95—381no—
239#95C22⋊D1914yes—
240C19#915611yescharacteristic, complemented, Sylow
241C24—381no—
242C24C2×C22⋊D1911yescharacteristic
243C2×D4—382no—
244C2×D4—762no—
245C2×D4—761no—
246C2×D4—761no—
247C2×D4—761no—
248C2×D4—761no—
249C2×D4—761no—
250C2×D4—761no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—24no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—44no—
261C22×C4—44no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—382no—
265C22×C4—381no—
266C22×C4(C2×D19)⋊C412yes—
267C22×C4(C2×D19)⋊C412yes—
268C22×C4#6452512yes—
269C22×C4#6452712yes—
270C22×C4C2×C4×D1911yescharacteristic
271C22×C4C2×D7611yescharacteristic
272C22×C4#6454112yes—
273C22×C4C2×C22⋊D1912yes—
274C2×C8—764no—
275C2×C8—762no—
276C4⋊C4—48no—
277C4⋊C4—382no—
278C4⋊C4—762no—
279C4⋊C4—764no—
280C22⋊C4—764no—
281C22⋊C4—761no—
282C22⋊C4—761no—
283C22⋊C4—762no—
284C22⋊C4—764no—
285C42—24no—
286C42—24no—
287C23—22no—
288C23—22no—
289C23—761no—
290C23—761no—
291C23—762no—
292C23—761no—
293C23—762no—
294C23C2×(C2×D19)⋊C411yescharacteristic
295C23#1059737511yescharacteristic
296C23C2×#6452511yescharacteristic
297C23#1059737811yescharacteristic
298C23C2×#6452711yescharacteristic
299C23#1059738811yescharacteristic
300C23#1059739911yescharacteristic
301D4—1522no—
302D4—1521no—
303D4—1521no—
304D4—1521no—
305D4—1521no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—84no—
325C2×C4—84no—
326C2×C4—762no—
327C2×C4—761no—
328C2×C4—761no—
329C2×C4—762no—
330C2×C4—761no—
331C2×C4—762no—
332C2×C4#1059726614yes—
333C2×C4C4×C22⋊D1912yes—
334C2×C4#1059737612yes—
335C8—1522no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—1521no—
345C22—1522no—
346C22—1522no—
347C22—1521no—
348C22—1521no—
349C22#1192642311yescharacteristic
350C22#1192651712yes—
351C22C2×#1059726611yescharacteristic
352C22#1192654311yescharacteristic
353C22#1192656212yes—
354C22#1192667811yescharacteristic
355C22#1192668311yescharacteristic
356C22#1192685711yescharacteristic
357C22#1192686211yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—84no—
363C4—1521no—
364C4—1522no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—3041no—
370C2#1456217112yes—
371C2#1456219412yes—
372C2#1456395211yescharacteristic
373C2#1456408311yescharacteristic
374C2#1456409311yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#382C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenterC2×#382D19
hypocenterC19#9156
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #14563703C2semidirect
4. #14561514C2semidirect
5. C2×C19×#382C2semidirect
9. #11926446C4semidirect
10. #11926442C4semidirect
150. C2×#382D19semidirect
240. C19#9156semidirect

Maximal subgroups

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

subgroupindex
#145719662
#145637032
C2×#119262772
#145615142
C2×C19×#3822
#915619