Finite Group Databasebeta

← #18078317

Subgroups — #18078317

Order 4864.

692 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 143 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
2C2×#11926410C211yesmaximal, characteristic, complemented
3C2×#11926279C212yesmaximal
4#14561515C212yesmaximal, complemented
5C19×#1817C211yesmaximal, characteristic, complemented
6C2×#10597375—21no—
7C2×#10597376C2211yescharacteristic
8C22×C4⋊Dic19—21no—
9#11926446C412yescomplemented
10#11926442C412yescomplemented
11#11926435—22no—
12#11926423—21no—
13#11926410—24no—
14#11926404C2211yescharacteristic
15C2×C19⋊#95—21no—
16C2×C19⋊#95C2212yes—
17#11926279—24no—
18C22×C42×C19C2211yescharacteristic
19C2×C19×C22⋊C8C2212yes—
20C19×#336—22no—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—21no—
25C23×Dic19—22no—
26C22×D76C2×C411yescharacteristic
27C22×C8×C19—22no—
28C2×C42×C19—22no—
29C2×C42×C19—22no—
30C2×C42×C19C2×C412yes—
31C2×C42×C19D412yes—
32C2×C22⋊Dic19—21no—
33#10597376—22no—
34#10597376—22no—
35#10597375—42no—
36#10597375—42no—
37C2×(C2×D19)⋊C4—22no—
38C2×(C2×D19)⋊C4—22no—
39C2×(C2×D19)⋊C4—21no—
40C2×C4⋊Dic19—24no—
41C2×C4⋊Dic19—42no—
42C2×C4⋊Dic19—42no—
43C2×C4⋊Dic19C2×C411yescharacteristic
44C2×C4⋊Dic19C2×C412yes—
45C2×Dic19⋊C4—22no—
46C19×C22⋊C8—22no—
47C19×C22⋊C8—22no—
48C19⋊#95—24no—
49C19⋊#95—22no—
50C19⋊#95—22no—
51C19⋊#95—21no—
52C19⋊#95D414yes—
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—42no—
62C22×C4×C19—42no—
63C22×C4×C19C22⋊C412yes—
64C22×C4×C19C22⋊C412yes—
65C22×C4×C19D812yes—
66C22×C4×C19SD1612yes—
67C22×C4×C19C22×C411yescharacteristic
68C22×C4×C19C2×D412yes—
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19#4112yes—
71C2×C22⋊D19—41no—
72C2×C22⋊D19—41no—
73C2×C22⋊D19—41no—
74C2×C22⋊D19—41no—
75C2×C22⋊D19—41no—
76C2×C22⋊D19—41no—
77C22×Dic19—22no—
78C22×Dic19—21no—
79C22×Dic19—24no—
80C22×Dic19—44no—
81C22×Dic19—44no—
82C22×Dic19—42no—
83C22×Dic19—42no—
84C2×D76—22no—
85C2×D76—42no—
86C2×C8×C19—44no—
87C2×C8×C19—42no—
88C42×C19—24no—
89C42×C19—24no—
90C22⋊Dic19—41no—
91C22⋊Dic19—41no—
92(C2×D19)⋊C4—44no—
93(C2×D19)⋊C4—44no—
94(C2×D19)⋊C4—42no—
95C4⋊Dic19—22no—
96C4⋊Dic19—48no—
97C4⋊Dic19—42no—
98Dic19⋊C4—44no—
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#10214yes—
130C2×C4×C19C4×D412yes—
131C2×C4×C19#12112yes—
132C22⋊D19—81no—
133C22⋊D19—81no—
134C22⋊D19—81no—
135C22⋊D19—81no—
136C2×Dic19—44no—
137C2×Dic19—44no—
138C2×Dic19—41no—
139C2×Dic19—42no—
140C2×Dic19—41no—
141C2×Dic19—42no—
142C2×Dic19—41no—
143C2×Dic19—42no—
144C2×Dic19—44no—
145C2×Dic19—84no—
146C2×Dic19—84no—
147D76—82no—
148C8×C19—82no—
149#2854—191no—
150C2×#382—191no—
151#1817D1911yescharacteristic, complemented
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—
180Dic19—84no—
181Dic19—81no—
182Dic19—82no—
183C2×#123—381no—
184C2×#121—191no—
185C22×C4⋊C4—381no—
186C22×C42C2×D1911yescharacteristic
187C2×C22⋊C8C2×D1912yes—
188#390—192no—
189#389—192no—
190#388—382no—
191#386—381no—
192#382—384no—
193#380—191no—
194C2×#95—192no—
195C2×#95—381no—
196#336—22no—
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—382no—
211C23×C4D7611yescharacteristic
212C23×C4D7611yescharacteristic
213C23×C4C22×D1911yescharacteristic
214C22×C8—22no—
215#123—762no—
216#123—762no—
217#121—382no—
218#121—382no—
219C2×C4⋊C4—191no—
220C2×C4⋊C4—192no—
221C2×C4⋊C4—384no—
222C2×C4⋊C4—382no—
223C2×C4⋊C4—762no—
224C2×C4⋊C4—762no—
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×C42C22⋊D1912yes—
233C22⋊C8—22no—
234C22⋊C8—22no—
235#95—194no—
236#95—384no—
237#95—382no—
238#95—382no—
239#95—381no—
240C19#915611yescharacteristic, complemented, Sylow
241C24—381no—
242C24C2×D7611yescharacteristic
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—42no—
258C22×C4—42no—
259C22×C4—384no—
260C22×C4—382no—
261C22×C4—381no—
262C22×C4—764no—
263C22×C4—764no—
264C22×C4—762no—
265C22×C4—762no—
266C22×C4#6451612yes—
267C22×C4D15212yes—
268C22×C4(C2×D19)⋊C412yes—
269C22×C4(C2×D19)⋊C412yes—
270C22×C4C2×C4×D1911yescharacteristic
271C22×C4D4×D1912yes—
272C22×C4#6454312yes—
273C22×C4C2×C22⋊D1911yescharacteristic
274C2×C8—44no—
275C2×C8—42no—
276C4⋊C4—382no—
277C4⋊C4—762no—
278C4⋊C4—768no—
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—
294C23#1059732811yescharacteristic
295C23#1059733211yescharacteristic
296C23C2×#6451611yescharacteristic
297C23C2×D15211yescharacteristic
298C23#1059735411yescharacteristic
299C23#1059735511yescharacteristic
300C23C2×(C2×D19)⋊C411yescharacteristic
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—764no—
322C2×C4—764no—
323C2×C4—762no—
324C2×C4—761no—
325C2×C4—761no—
326C2×C4—762no—
327C2×C4—761no—
328C2×C4—764no—
329C2×C4—762no—
330C2×C4—1524no—
331C2×C4—1524no—
332C2×C4#1059727814yes—
333C2×C4(C22⋊D19)⋊C412yes—
334C2×C4#1059738512yes—
335C8—82no—
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#1192642111yescharacteristic
350C22#1192651712yes—
351C22C2×#1059727811yescharacteristic
352C22#1192654611yescharacteristic
353C22#1192656012yes—
354C22#1192668011yescharacteristic
355C22#1192668511yescharacteristic
356C22#1192685811yescharacteristic
357C22#1192686311yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—1524no—
363C4—1521no—
364C4—1522no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—3041no—
370C2#1456217412yes—
371C2#1456219612yes—
372C2#1456395011yescharacteristic
373C2#1456408111yescharacteristic
374C2#1456409111yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1817C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1817D19
hypocenterC19#9156
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. C2×#11926410C2semidirect
4. #14561515C2semidirect
5. C19×#1817C2semidirect
9. #11926446C4semidirect
10. #11926442C4semidirect
151. #1817D19semidirect
240. C19#9156semidirect

Maximal subgroups

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

subgroupindex
#145719662
C2×#119264102
C2×#119262792
#145615152
C19×#18172
#915619