Finite Group Databasebeta

← #18077609

Subgroups — #18077609

Order 4864.

534 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 111 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#14572664C211yesmaximal, characteristic
2C4×#10597290C211yesmaximal, characteristic
3#14562082C212yesmaximal, complemented
4#14561528C212yesmaximal, complemented
5C19×#2398C211yesmaximal, characteristic
6#11926616—24no—
7#11926601C2212yes—
8C2×#10597290—21no—
9#11926508—21no—
10C2×C22⋊(C19⋊C8)—21no—
11C4×#64520C2212yes—
12#11926313—21no—
13Q8⋊(C19⋊C8)—24no—
14C2×C4×Q8×C19C2211yescharacteristic
15C2×C4×D4×C19C2211yescharacteristic
16C19×#400—21no—
17C19×#397C411yescharacteristic
18C19×#397C411yescharacteristic
19C19×#394—21no—
20C19×#393C411yescharacteristic
21C19×#393C411yescharacteristic
22C4×C22⋊C4×C19—21no—
23C4×C22⋊C4×C19—21no—
24C19×#376C2211yescharacteristic
25C22×Q8×C19C2×C411yescharacteristic
26C22×D4×C19D411yescharacteristic
27C23×C4×C19D411yescharacteristic
28C23×C4×C19D411yescharacteristic
29C4×Q8×C19—22no—
30C4×Q8×C19—22no—
31C4×D4×C19—22no—
32C4×D4×C19—22no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C22⋊C4×C19—21no—
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19C2×C411yescharacteristic
41C2×C22⋊C4×C19C2×C411yescharacteristic
42C2×C42×C19—21no—
43C2×C42×C19—21no—
44C2×C42×C19C2311yescharacteristic
45C2×#64520—22no—
46C2×#64520—22no—
47C22×C19⋊C8—22no—
48C19×#95—21no—
49C19×#95—21no—
50C19×#95—21no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95C2×C411yescharacteristic
54C19×#95C2×C411yescharacteristic
55#10597290—24no—
56C22⋊(C19⋊C8)—22no—
57C22⋊(C19⋊C8)—22no—
58C22⋊(C19⋊C8)—22no—
59C4⋊(C19⋊C8)D414yes—
60#10597260—22no—
61#10597260—22no—
62C4×C19⋊C8—22no—
63C24×C19C22⋊C411yescharacteristic
64C24×C19C22⋊C411yescharacteristic
65C2×Q8×C19—22no—
66C2×Q8×C19—42no—
67C2×D4×C19—22no—
68C2×D4×C19—22no—
69C2×D4×C19—41no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19—21no—
78C22×C4×C19—42no—
79C22×C4×C19—42no—
80C22×C4×C19C22⋊C411yescharacteristic
81C22×C4×C19C22⋊C411yescharacteristic
82C22×C4×C19C22×C411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C4⋊C4×C19—22no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—42no—
88C22⋊C4×C19—22no—
89C22⋊C4×C19—22no—
90C22⋊C4×C19—42no—
91C22⋊C4×C19—42no—
92C22⋊C4×C19—42no—
93C22⋊C4×C19—42no—
94C42×C19—42no—
95C42×C19—41no—
96C42×C19—41no—
97C42×C19C2×D412yes—
98C42×C19#4112yes—
99#64520—24no—
100#64520—42no—
101#64520—82no—
102C2×C19⋊C8—24no—
103C2×C19⋊C8—42no—
104C2×C19⋊C8—82no—
105#9029—191nomaximal, Sylow
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—41no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19#10412yes—
116C23×C19C2×C22⋊C411yescharacteristic
117Q8×C19—24no—
118Q8×C19—42no—
119D4×C19—44no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—81no—
143C2×C4×C19—81no—
144C2×C4×C19C4×D412yes—
145C2×C4×C19#12011yescharacteristic
146C2×C4×C19#12112yes—
147C2×C4×C19#12311yescharacteristic
148C19⋊C8—44no—
149C19⋊C8—44no—
150#2973—191no—
151#2398D1911yescharacteristic
152C4×#100—191no—
153#1491—192no—
154#1300—192no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—22no—
158C22×C19—42no—
159C22×C19—42no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19—41no—
165C22×C19—81no—
166C22×C19—81no—
167C22×C19#38611yescharacteristic
168C22×C19C2×#10411yescharacteristic
169C22×C19#42111yescharacteristic
170C4×C19—22no—
171C4×C19—21no—
172C4×C19—22no—
173C4×C19—41no—
174C4×C19—41no—
175C4×C19—42no—
176C4×C19—81no—
177C4×C19—81no—
178C4×C19—81no—
179C4×C19#45512yes—
180C2×C4×Q8C2×D1911yescharacteristic
181C2×C4×D4C2×D1911yescharacteristic
182#435—384no—
183#432—192no—
184C2×#100—381no—
185#407—381no—
186C2×C22⋊C8—381no—
187C4×M16—192no—
188#400—21no—
189#397Dic1911yescharacteristic
190#397Dic1911yescharacteristic
191#394—21no—
192#393Dic1911yescharacteristic
193#393Dic1911yescharacteristic
194C4×C22⋊C4—21no—
195C4×C22⋊C4—21no—
196#376C2×D1911yescharacteristic
197#343—381no—
198Q8⋊C8—384no—
199C2×C19—21no—
200C2×C19—21no—
201C2×C19—42no—
202C2×C19—81no—
203C2×C19#187111yescharacteristic
204C2×C19#188511yescharacteristic
205C2×C19#189111yescharacteristic
206C22×Q8C2×Dic1911yescharacteristic
207C22×D4C22⋊D1911yescharacteristic
208C23×C4C22⋊D1911yescharacteristic
209C23×C4C22⋊D1911yescharacteristic
210C2×M16—382no—
211C2×M16—382no—
212C22×C8—382no—
213C4×Q8—22no—
214C4×Q8—22no—
215C4×D4—22no—
216C4×D4—22no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×Dic1911yescharacteristic
219C2×C4⋊C4C22⋊D1911yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4C2×Dic1911yescharacteristic
225C2×C22⋊C4C2×Dic1911yescharacteristic
226C2×C42—21no—
227C2×C42—21no—
228C2×C42C22×D1911yescharacteristic
229C4⋊C8—194no—
230#100—384no—
231C22⋊C8—382no—
232C22⋊C8—382no—
233C22⋊C8—382no—
234#97—382no—
235#97—382no—
236C4×C8—382no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95C2×Dic1911yescharacteristic
243#95C2×Dic1911yescharacteristic
244C19#902911yescharacteristic, complemented, Sylow
245C24C22⋊Dic1911yescharacteristic
246C24C22⋊Dic1911yescharacteristic
247C2×Q8—22no—
248C2×Q8—42no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4C22⋊Dic1911yescharacteristic
263C22×C4C22⋊Dic1911yescharacteristic
264C22×C4C22×Dic1911yescharacteristic
265C22×C4C2×C22⋊D1911yescharacteristic
266C22×C4C2×C22⋊D1911yescharacteristic
267M16—384no—
268M16—762no—
269M16—1522no—
270C2×C8—384no—
271C2×C8—762no—
272C2×C8—1522no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C42—42no—
283C42—41no—
284C42—41no—
285C42D4×D1912yes—
286C42#6454312yes—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23#1059729412yes—
297C23C2×C22⋊Dic1911yescharacteristic
298Q8—24no—
299Q8—42no—
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4D4×Dic1912yes—
326C2×C4#1059738111yescharacteristic
327C2×C4#1059738311yescharacteristic
328C2×C4#1059738512yes—
329C8—764no—
330C8—764no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22#1192642411yescharacteristic
344C22C2×#1059729411yescharacteristic
345C22#1192656111yescharacteristic
346C4—22no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—42no—
352C4—81no—
353C4—81no—
354C4—81no—
355C4#1192672112yes—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—81no—
360C2#1456393811yescharacteristic
361C2#1456402411yescharacteristic
362C2#1456405411yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2398C2
socleC22×C19#386
prime radicalC22×D4×C19D4
cosocleC2×C42×C19C23
hypercenter#2398D19
hypocenterC19#9029
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2398

Complements

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

NH ≅ G/Ntype
3. #14562082C2semidirect
4. #14561528C2semidirect
244. C19#9029semidirect

Maximal subgroups

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

subgroupindex
#145726642
C4×#105972902
#145620822
#145615282
C19×#23982
#902919