Finite Group Databasebeta

← #18083117

Subgroups — #18083117

Order 4864.

772 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×#11926857C212yesmaximal, complemented
2#14569737C211yesmaximal, characteristic
3C2×#11926277C212yesmaximal, complemented
4#14561478C211yesmaximal, characteristic, complemented
5C19×#1445C211yesmaximal, characteristic, complemented
6C2×#10597376—22no—
7C2×#10597376C2212yes—
8#11926857—24no—
9#11926857—24no—
10C2×#10597264—22no—
11C2×#10597266—22no—
12C2×C22⋊(C19⋊C8)C2212yes—
13#11926481—22no—
14#11926454—22no—
15#11926277—24no—
16C22×C4⋊C4×C19C2211yescharacteristic
17C2×C19×#95—22no—
18C2×C19×#95C2211yescharacteristic
19C2×C19×#95C2211yescharacteristic
20C23×C4×C19—21no—
21C23×C4×C19—21no—
22C23×C4×C19D412yes—
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—22no—
25C22×D76—22no—
26C22×D76D412yes—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19D412yescomplemented
31#10597376—22no—
32#10597376—22no—
33#10597376—22no—
34#10597376—22no—
35#10597376—44no—
36#10597376—44no—
37C2×(C2×D19)⋊C4—24no—
38C2×(C2×D19)⋊C4—22no—
39C2×C4⋊Dic19—22no—
40C2×C4⋊Dic19D412yes—
41C22×C19⋊C8—22no—
42C19×#95—22no—
43C19×#95—22no—
44C19×#95—44no—
45C22⋊(C19⋊C8)—22no—
46C22⋊(C19⋊C8)D414yescomplemented
47#10597266—28no—
48#10597264—28no—
49C24×C19C2×D411yescharacteristic
50C23×D19—22no—
51C22×C4×C19—22no—
52C22×C4×C19—22no—
53C22×C4×C19—22no—
54C22×C4×C19—22no—
55C22×C4×C19—42no—
56C22×C4×C19—42no—
57C22×C4×C19—42no—
58C22×C4×C19—41no—
59C22×C4×C19—42no—
60C22×C4×C19—41no—
61C22×C4×C19—41no—
62C22×C4×C19—41no—
63C22×C4×C19—42no—
64C22×C4×C19—42no—
65C22×C4×C19—42no—
66C22×C4×C19D814yes—
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19C2×D412yes—
69C22×C4×C19C2×D412yes—
70C22×C4×C19#4111yescharacteristic
71C2×C22⋊D19—42no—
72C2×C22⋊D19—42no—
73C2×C22⋊D19—44no—
74C2×C22⋊D19—44no—
75C22×Dic19—22no—
76C2×D76—22no—
77C2×D76—22no—
78C2×D76—44no—
79C2×D76—44no—
80C2×D76—82no—
81C2×D76—82no—
82C4⋊C4×C19—24no—
83C4⋊C4×C19—42no—
84(C2×D19)⋊C4—48no—
85(C2×D19)⋊C4—42no—
86(C2×D19)⋊C4—42no—
87C4⋊Dic19—22no—
88C4⋊Dic19—22no—
89C4⋊Dic19—44no—
90C2×C19⋊C8—24no—
91C2×C19⋊C8—44no—
92#9970—191nomaximal, Sylow
93C23×C19—21no—
94C23×C19—21no—
95C23×C19—22no—
96C23×C19#12011yescharacteristic
97C23×C19#12111yescharacteristic
98C23×C19#12711yescharacteristic
99C23×C19C2×D812yes—
100C23×C19AGL(1,ℤ/8)12yes—
101C22×D19—42no—
102C22×D19—44no—
103C22×D19—42no—
104C22×D19—42no—
105C22×D19—44no—
106C2×C4×C19—24no—
107C2×C4×C19—24no—
108C2×C4×C19—41no—
109C2×C4×C19—42no—
110C2×C4×C19—41no—
111C2×C4×C19—42no—
112C2×C4×C19—42no—
113C2×C4×C19—44no—
114C2×C4×C19—44no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19—44no—
118C2×C4×C19—82no—
119C2×C4×C19—82no—
120C2×C4×C19—81no—
121C2×C4×C19—82no—
122C2×C4×C19—81no—
123C2×C4×C19—81no—
124C2×C4×C19—81no—
125C2×C4×C19#12012yes—
126C2×C4×C19#12112yes—
127C22⋊D19—84no—
128C22⋊D19—82no—
129C22⋊D19—82no—
130C2×Dic19—42no—
131C2×Dic19—44no—
132D76—44no—
133D76—82no—
134D76—88no—
135C19⋊C8—44no—
136C2×#480—192no—
137#2656—191no—
138C2×#327—192no—
139#1445D1911yescharacteristic, complemented
140#1280—191no—
141C22×C19—22no—
142C22×C19—22no—
143C22×C19—22no—
144C22×C19—22no—
145C22×C19—21no—
146C22×C19—21no—
147C22×C19—21no—
148C22×C19—21no—
149C22×C19#39211yescharacteristic
150C22×C19#44712yes—
151C22×C19#45511yescharacteristic
152C22×C19#45611yescharacteristic
153C22×C19#45812yes—
154C22×C19#45912yes—
155C22×C19#49311yescharacteristic
156C22×C19#49611yescharacteristic
157C2×D19—84no—
158C2×D19—84no—
159C2×D19—82no—
160C2×D19—82no—
161C2×D19—82no—
162C4×C19—22no—
163C4×C19—22no—
164C4×C19—44no—
165C4×C19—82no—
166C4×C19—82no—
167Dic19—82no—
168C2×#121—192no—
169C2×#121—382no—
170C22×C4⋊C4C2×D1911yescharacteristic
171#480—384no—
172#480—384no—
173C2×#107—382no—
174C2×#102—382no—
175C2×C22⋊C8—192no—
176#399—382no—
177#392—382no—
178C2×#95—22no—
179C2×#95C2×D1911yescharacteristic
180C2×#95C2×D1911yescharacteristic
181#327—384no—
182C2×C19—21no—
183C2×C19—22no—
184C2×C19—21no—
185C2×C19#160712yes—
186C2×C19#161012yes—
187C2×C19#200711yescharacteristic
188C2×C19#201111yescharacteristic
189C2×C19#202211yescharacteristic
190D19—162no—
191C22×D4—192no—
192C22×D4—382no—
193C22×D4—382no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4C22⋊D1912yes—
197C23×C4C22×D1911yescharacteristic
198C22×C8—382no—
199#121—382no—
200#121—382no—
201#121—382no—
202#121—382no—
203#121—764no—
204#121—764no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—192no—
209C2×C4⋊C4—382no—
210C2×C4⋊C4D7612yescomplemented
211C2×C22⋊C4—384no—
212C2×C22⋊C4—382no—
213#107—388no—
214#102—388no—
215C22⋊C8—194no—
216C22⋊C8—382no—
217#95—22no—
218#95—22no—
219#95—44no—
220C19#997011yescharacteristic, complemented, Sylow
221C24—382no—
222C24C2×C22⋊D1911yescharacteristic
223C2×D4—382no—
224C2×D4—382no—
225C2×D4—764no—
226C2×D4—764no—
227C2×D4—762no—
228C2×D4—764no—
229C2×D4—762no—
230C2×D4—764no—
231C2×D4—1522no—
232C2×D4—1522no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—42no—
248C22×C4—382no—
249C22×C4#6452514yes—
250C22×C4C2×D7611yescharacteristic
251C22×C4#6454111yescharacteristic
252C22×C4D4×D1912yes—
253C22×C4D4×D1912yes—
254C2×C8—384no—
255C2×C8—764no—
256C4⋊C4—24no—
257C4⋊C4—42no—
258C4⋊C4—382no—
259C4⋊C4—382no—
260C4⋊C4—764no—
261C22⋊C4—768no—
262C22⋊C4—762no—
263C22⋊C4—762no—
264C23—21no—
265C23—21no—
266C23—22no—
267C23—764no—
268C23—762no—
269C23—762no—
270C23—762no—
271C23—764no—
272C23#1059737611yescharacteristic
273C23C2×#6452512yes—
274C23#1059738311yescharacteristic
275C23#1059738611yescharacteristic
276C23#1059739512yes—
277D4—764no—
278D4—1522no—
279D4—1528no—
280D4—1522no—
281D4—1522no—
282D4—1524no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—42no—
294C2×C4—44no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—82no—
301C2×C4—81no—
302C2×C4—764no—
303C2×C4—762no—
304C2×C4#1059732812yes—
305C2×C4#1059733012yes—
306C8—764no—
307C22—22no—
308C22—22no—
309C22—21no—
310C22—21no—
311C22—22no—
312C22—22no—
313C22—21no—
314C22—21no—
315C22—1524no—
316C22—1522no—
317C22—1524no—
318C22—1522no—
319C22—1522no—
320C22#1192645311yescharacteristic
321C22#1192667712yes—
322C22#1192672111yescharacteristic
323C22#1192672611yescharacteristic
324C22#1192673312yes—
325C22#1192673912yes—
326C22#1192692011yescharacteristic
327C22#1192693411yescharacteristic
328C4—22no—
329C4—22no—
330C4—44no—
331C4—82no—
332C4—82no—
333C4—1522no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—3042no—
338C2#1456262012yes—
339C2#1456263712yes—
340C2#1456468111yescharacteristic
341C2#1456470511yescharacteristic
342C2#1456476611yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1445C2
socleC23×C19#120
prime radical#14569737C2
hypercenter#1445D19
hypocenterC19#9970
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
1. C2×#11926857C2semidirect
3. C2×#11926277C2semidirect
4. #14561478C2semidirect
5. C19×#1445C2semidirect
30. C2×C4⋊C4×C19D4semidirect
46. C22⋊(C19⋊C8)D4semidirect
139. #1445D19semidirect
210. C2×C4⋊C4D76semidirect
220. C19#9970semidirect

Maximal subgroups

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

subgroupindex
C2×#119268572
#145697372
C2×#119262772
#145614782
C19×#14452
#997019