Finite Group Databasebeta

← #18078528

Subgroups — #18078528

Order 4864.

478 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 107 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#14572720C211yesmaximal, characteristic, complemented
2C4×#10597293C211yesmaximal, characteristic, complemented
3#14562233C212yesmaximal
4#14561499C212yesmaximal, complemented
5C19×#2632C211yesmaximal, characteristic
6#11926675—24no—
7#11926601—21no—
8#11926601C2212yes—
9#11926597—21no—
10C2×#10597293—21no—
11C4×#64520C2212yes—
12#11926313—21no—
13#11926284—24no—
14C2×C19×#124C2211yescharacteristic
15C2×C4×Q8×C19C2211yescharacteristic
16C19×#399—21no—
17C19×#395C411yescharacteristic
18C19×#395C411yescharacteristic
19C19×#394C411yescharacteristic
20C19×#394C411yescharacteristic
21C19×#393—21no—
22C19×#388—21no—
23C19×#388—21no—
24C19×#383C2211yescharacteristic
25C22×Q8×C19C2×C411yescharacteristic
26C22×Q8×C19D411yescharacteristic
27C22×D4×C19C2×C411yescharacteristic
28C19×#124—22no—
29C19×#124—22no—
30C4×Q8×C19—22no—
31C4×Q8×C19—22no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C42×C19D411yescharacteristic
44C2×C42×C19D411yescharacteristic
45C2×C42×C19C2311yescharacteristic
46C2×#64520—22no—
47C19×#95—21no—
48C19×#95—21no—
49C19×#95—21no—
50C19×#95—21no—
51C19×#95C2×C411yescharacteristic
52C19×#95C2×C411yescharacteristic
53#10597293—24no—
54C22⋊(C19⋊C8)—22no—
55C4⋊(C19⋊C8)—22no—
56C4⋊(C19⋊C8)—22no—
57C4⋊(C19⋊C8)—22no—
58#10597260—22no—
59#10597260—22no—
60#10597260D414yes—
61C4×C19⋊C8—22no—
62C4×C19⋊C8—22no—
63C24×C19—21no—
64C2×Q8×C19—22no—
65C2×Q8×C19—22no—
66C2×Q8×C19—22no—
67C2×Q8×C19—41no—
68C2×Q8×C19—81no—
69C2×D4×C19—22no—
70C2×D4×C19—81no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22×C411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C4⋊C4×C19—22no—
82C4⋊C4×C19—22no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—81no—
85C4⋊C4×C19—81no—
86C22⋊C4×C19—42no—
87C22⋊C4×C19—42no—
88C22⋊C4×C19—41no—
89C22⋊C4×C19—42no—
90C22⋊C4×C19—41no—
91C22⋊C4×C19—81no—
92C22⋊C4×C19—81no—
93C42×C19—21no—
94C42×C19—21no—
95C42×C19—21no—
96C42×C19—21no—
97C42×C19C2×D412yes—
98C42×C19#4112yes—
99#64520—24no—
100#64520—42no—
101C2×C19⋊C8—24no—
102C2×C19⋊C8—42no—
103#9188—191nomaximal, Sylow
104C23×C19—41no—
105C23×C19—41no—
106C23×C19—41no—
107C23×C19—41no—
108C23×C19—41no—
109C23×C19—41no—
110C23×C19—41no—
111C23×C19C2×C22⋊C411yescharacteristic
112Q8×C19—44no—
113Q8×C19—82no—
114D4×C19—82no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
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#10412yes—
138C2×C4×C19C4×D412yes—
139C2×C4×C19#12011yescharacteristic
140C2×C4×C19#12112yes—
141C2×C4×C19#12311yescharacteristic
142C19⋊C8—44no—
143C19⋊C8—44no—
144#2983—191no—
145#2632D1911yescharacteristic
146C4×#101—191no—
147#1527—192no—
148#1288—192no—
149C22×C19—21no—
150C22×C19—21no—
151C22×C19—81no—
152C22×C19—81no—
153C22×C19—81no—
154C22×C19—81no—
155C22×C19—81no—
156C22×C19—81no—
157C22×C19—81no—
158C22×C19#38611yescharacteristic
159C22×C19C2×#10411yescharacteristic
160C22×C19#42111yescharacteristic
161C4×C19—22no—
162C4×C19—22no—
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—22no—
166C4×C19—41no—
167C4×C19—41no—
168C4×C19—41no—
169C4×C19—81no—
170C4×C19—81no—
171C4×C19—81no—
172C2×#124C2×D1911yescharacteristic
173C2×C4×Q8C2×D1911yescharacteristic
174#446—384no—
175#432—192no—
176#432—381no—
177#431—381no—
178C2×#101—381no—
179C4×M16—192no—
180#399—21no—
181#395Dic1911yescharacteristic
182#395Dic1911yescharacteristic
183#394Dic1911yescharacteristic
184#394Dic1911yescharacteristic
185#393—21no—
186#388—21no—
187#388—21no—
188#383C2×D1911yescharacteristic
189#343—381no—
190#329—384no—
191C2×C19—21no—
192C2×C19—21no—
193C2×C19—161no—
194C2×C19#187111yescharacteristic
195C2×C19#191211yescharacteristic
196C2×C19#191411yescharacteristic
197C22×Q8C2×Dic1911yescharacteristic
198C22×Q8C22⋊D1911yescharacteristic
199C22×D4C2×Dic1911yescharacteristic
200C2×M16—382no—
201#124—22no—
202#124—22no—
203C4×Q8—22no—
204C4×Q8—22no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×Dic1911yescharacteristic
208C2×C4⋊C4C2×Dic1911yescharacteristic
209C2×C4⋊C4C22⋊D1911yescharacteristic
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C42C22⋊D1911yescharacteristic
217C2×C42C22⋊D1911yescharacteristic
218C2×C42C22×D1911yescharacteristic
219C4⋊C8—382no—
220C4⋊C8—382no—
221C4⋊C8—382no—
222#101—384no—
223C22⋊C8—382no—
224#97—194no—
225#97—382no—
226#97—382no—
227C4×C8—382no—
228C4×C8—382no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95C2×Dic1911yescharacteristic
234#95C2×Dic1911yescharacteristic
235C19#918811yescharacteristic, complemented, Sylow
236C24—21no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×Q8—81no—
242C2×D4—22no—
243C2×D4—81no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4C22⋊Dic1911yescharacteristic
248C22×C4C22⋊Dic1911yescharacteristic
249C22×C4C22⋊Dic1911yescharacteristic
250C22×C4C22⋊Dic1911yescharacteristic
251C22×C4C22×Dic1911yescharacteristic
252C22×C4C2×C22⋊D1911yescharacteristic
253C22×C4C2×C22⋊D1911yescharacteristic
254M16—384no—
255M16—762no—
256C2×C8—384no—
257C2×C8—762no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C22⋊C4—42no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—81no—
269C22⋊C4—81no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42D4×D1912yes—
275C42#6454312yes—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23C2×C22⋊Dic1911yescharacteristic
284Q8—44no—
285Q8—82no—
286D4—82no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4#1059729412yes—
310C2×C4D4×Dic1912yes—
311C2×C4#1059738111yescharacteristic
312C2×C4#1059738311yescharacteristic
313C2×C4#1059738512yes—
314C8—764no—
315C8—764no—
316C22—21no—
317C22—21no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22#1192642411yescharacteristic
326C22C2×#1059729411yescharacteristic
327C22#1192656111yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C2—21no—
340C2—21no—
341C2—161no—
342C2#1456393811yescharacteristic
343C2#1456417311yescharacteristic
344C2#1456418311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2632C2
socleC22×C19#386
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenter#2632D19
hypocenterC19#9188
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2632

Complements

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

NH ≅ G/Ntype
1. #14572720C2semidirect
2. C4×#10597293C2semidirect
4. #14561499C2semidirect
235. C19#9188semidirect

Maximal subgroups

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

subgroupindex
#145727202
C4×#105972932
#145622332
#145614992
C19×#26322
#918819