Finite Group Databasebeta

← #18078607

Subgroups — #18078607

Order 4864.

622 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 131 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#14569377C211yesmaximal, characteristic
2#14562202C212yesmaximal
3C2×#11926270C211yesmaximal, characteristic, complemented
4#14561502C212yesmaximal, complemented
5C19×#2316C211yesmaximal, characteristic, complemented
6C2×#10597375—21no—
7C2×#10597376C2211yescharacteristic
8C2×C22⋊(C19⋊C8)C2212yes—
9#11926474C412yescomplemented
10#11926466—22no—
11#11926461C412yescomplemented
12#11926423—21no—
13#11926404C2211yescharacteristic
14#11926277—24no—
15#11926270—22no—
16C2×C19×#117—21no—
17C22×C4⋊C4×C19C2211yescharacteristic
18C19×#389—24no—
19C19×#380—21no—
20C19×#380C2212yes—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—21no—
25C22×D76C2×C411yescharacteristic
26C19×#117—42no—
27C19×#117—42no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—22no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19C2×C412yes—
34C2×C4⋊C4×C19D412yes—
35C2×C22⋊C4×C19—22no—
36C2×C42×C19—22no—
37C2×C22⋊Dic19—21no—
38#10597376—22no—
39#10597376—22no—
40#10597375—42no—
41#10597375—42no—
42C2×(C2×D19)⋊C4—22no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—22no—
45C2×C4⋊Dic19—21no—
46C2×C4⋊Dic19C2×C411yescharacteristic
47C2×Dic19⋊C4—22no—
48C22×C19⋊C8—22no—
49C19×#95—22no—
50C19×#95D414yes—
51C19⋊#95—22no—
52C19⋊#95C2×C412yes—
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—22no—
55C24×C19C2×D411yescharacteristic
56C23×D19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—24no—
64C22×C4×C19—81no—
65C22×C4×C19—81no—
66C22×C4×C19C22⋊C412yes—
67C22×C4×C19C22⋊C412yes—
68C22×C4×C19D812yes—
69C22×C4×C19SD1612yes—
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D412yes—
73C22×C4×C19#4112yes—
74C2×C22⋊D19—41no—
75C2×C22⋊D19—41no—
76C2×C22⋊D19—41no—
77C2×C22⋊D19—41no—
78C2×C22⋊D19—41no—
79C2×C22⋊D19—41no—
80C22×Dic19—22no—
81C22×Dic19—21no—
82C2×D76—22no—
83C2×D76—81no—
84C4⋊C4×C19—24no—
85C4⋊C4×C19—24no—
86C4⋊C4×C19—44no—
87C4⋊C4×C19—82no—
88C4⋊C4×C19—82no—
89C22⋊C4×C19—42no—
90C22⋊C4×C19—42no—
91C42×C19—44no—
92C22⋊Dic19—41no—
93C22⋊Dic19—41no—
94(C2×D19)⋊C4—44no—
95(C2×D19)⋊C4—42no—
96(C2×D19)⋊C4—82no—
97C4⋊Dic19—22no—
98C4⋊Dic19—81no—
99Dic19⋊C4—44no—
100C2×C19⋊C8—42no—
101C2×C19⋊C8—82no—
102#9204—191nomaximal, Sylow
103C23×C19—41no—
104C23×C19—41no—
105C23×C19C2×C22⋊C411yescharacteristic
106C23×C19#12011yescharacteristic
107C23×C19#12311yescharacteristic
108C23×C19C2×D811yescharacteristic
109C23×C19C2×SD1611yescharacteristic
110C23×C19AGL(1,ℤ/8)11yescharacteristic
111C23×C19#13711yescharacteristic
112C22×D19—42no—
113C22×D19—42no—
114C22×D19—41no—
115C22×D19—41no—
116C22×D19—41no—
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—42no—
125C2×C4×C19—41no—
126C2×C4×C19—42no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19—44no—
131C2×C4×C19—44no—
132C2×C4×C19—44no—
133C2×C4×C19—81no—
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—42no—
142C2×Dic19—42no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—42no—
146C2×Dic19—41no—
147D76—82no—
148C19⋊C8—82no—
149#2618—191no—
150#2316D1911yescharacteristic, complemented
151#1519—192no—
152C2×#324—191no—
153#1289—192no—
154C22×C19—21no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19#38611yescharacteristic
165C22×C19C2×#10211yescharacteristic
166C22×C19#41711yescharacteristic
167C22×C19#44711yescharacteristic
168C22×C19#44811yescharacteristic
169C22×C19#48011yescharacteristic
170C22×C19#48111yescharacteristic
171C2×D19—82no—
172C2×D19—82no—
173C2×D19—81no—
174C2×D19—81no—
175C2×D19—81no—
176C4×C19—24no—
177C4×C19—22no—
178C4×C19—22no—
179C4×C19—42no—
180C4×C19—84no—
181Dic19—82no—
182Dic19—81no—
183C2×#123—381no—
184C2×#121—191no—
185C2×#117—21no—
186C22×C4⋊C4C2×D1911yescharacteristic
187C2×C22⋊C8—192no—
188#398—192no—
189#396—382no—
190#394—192no—
191#389—24no—
192#386—381no—
193#380—21no—
194#380—191no—
195#380C2×D1912yes—
196#327—384no—
197#324—382no—
198C2×C19—21no—
199C2×C19—21no—
200C2×C19—21no—
201C2×C19—21no—
202C2×C19—21no—
203C2×C19—21no—
204C2×C19#187411yescharacteristic
205C2×C19#191211yescharacteristic
206C2×C19#191311yescharacteristic
207D19—161no—
208C22×D4—191no—
209C22×D4—381no—
210C23×C4C22⋊D1911yescharacteristic
211C23×C4C22⋊D1911yescharacteristic
212C23×C4C22×D1911yescharacteristic
213C22×C8—382no—
214#123—762no—
215#123—762no—
216#121—382no—
217#121—382no—
218#117—42no—
219#117—42no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—191no—
226C2×C4⋊C4—382no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4C4×D1912yes—
229C2×C4⋊C4D7612yes—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—381no—
232C2×C22⋊C4—382no—
233C2×C22⋊C4—381no—
234C2×C22⋊C4—382no—
235C2×C42—22no—
236C22⋊C8—382no—
237C22⋊C8—382no—
238#95—22no—
239#95—192no—
240#95—382no—
241#95C22⋊D1914yes—
242C19#920411yescharacteristic, complemented, Sylow
243C24—381no—
244C24C2×C22⋊D1911yescharacteristic
245C2×D4—382no—
246C2×D4—761no—
247C2×D4—761no—
248C2×D4—761no—
249C2×D4—761no—
250C2×D4—761no—
251C2×D4—761no—
252C2×D4—1521no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—24no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4—382no—
263C22×C4—381no—
264C22×C4(C2×D19)⋊C412yes—
265C22×C4(C2×D19)⋊C412yes—
266C22×C4#6452512yes—
267C22×C4#6452712yes—
268C22×C4C2×C4×D1911yescharacteristic
269C22×C4C2×D7611yescharacteristic
270C22×C4#6454112yes—
271C22×C4C2×C22⋊D1912yes—
272C2×C8—762no—
273C2×C8—1522no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—44no—
277C4⋊C4—82no—
278C4⋊C4—82no—
279C4⋊C4—382no—
280C4⋊C4—764no—
281C4⋊C4—1521no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—761no—
285C22⋊C4—761no—
286C22⋊C4—762no—
287C22⋊C4—764no—
288C22⋊C4—1522no—
289C42—44no—
290C23—41no—
291C23—41no—
292C23—762no—
293C23—762no—
294C23—761no—
295C23—761no—
296C23—761no—
297C23C2×(C2×D19)⋊C411yescharacteristic
298C23#1059737511yescharacteristic
299C23C2×#6452511yescharacteristic
300C23#1059737811yescharacteristic
301C23C2×#6452711yescharacteristic
302C23#1059738811yescharacteristic
303C23#1059739911yescharacteristic
304D4—1522no—
305D4—1521no—
306D4—1521no—
307D4—1521no—
308D4—1521no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—81no—
326C2×C4—762no—
327C2×C4—762no—
328C2×C4—762no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—761no—
332C2×C4#1059726614yes—
333C2×C4C4×C22⋊D1912yes—
334C2×C4#1059737612yes—
335C8—1522no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—1522no—
347C22—1522no—
348C22—1521no—
349C22—1521no—
350C22—1521no—
351C22#1192642311yescharacteristic
352C22C2×#1059726611yescharacteristic
353C22#1192654311yescharacteristic
354C22#1192667811yescharacteristic
355C22#1192668311yescharacteristic
356C22#1192685711yescharacteristic
357C22#1192686211yescharacteristic
358C4—22no—
359C4—22no—
360C4—24no—
361C4—42no—
362C4—84no—
363C4—1522no—
364C4—1521no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—3041no—
372C2#1456395211yescharacteristic
373C2#1456417211yescharacteristic
374C2#1456417711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2316C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#2316D19
hypocenterC19#9204
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
3. C2×#11926270C2semidirect
4. #14561502C2semidirect
5. C19×#2316C2semidirect
9. #11926474C4semidirect
11. #11926461C4semidirect
150. #2316D19semidirect
242. C19#9204semidirect

Maximal subgroups

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

subgroupindex
#145693772
#145622022
C2×#119262702
#145615022
C19×#23162
#920419