Finite Group Databasebeta

← #18077621

Subgroups — #18077621

Order 4864.

516 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 103 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
2#14566918C211yesmaximal, characteristic
3#14562079C212yesmaximal
4#14561529C212yesmaximal, complemented
5C4×C19×#101C211yesmaximal, characteristic, complemented
6C2×C4×D76C2211yescharacteristic
7#11926675—24no—
8#11926601—21no—
9#11926601C2212yes—
10#11926597—21no—
11#11926483C411yescharacteristic
12#11926483C411yescharacteristic
13#11926470—21no—
14#11926461C411yescharacteristic
15#11926461C411yescharacteristic
16#11926455—21no—
17C4×(C2×D19)⋊C4—21no—
18C4×(C2×D19)⋊C4—21no—
19#11926390C2211yescharacteristic
20#11926273—24no—
21C2×C4×Q8×C19C2211yescharacteristic
22C2×C19×#101—21no—
23C4×M16×C19C2212yes—
24C19×#343—21no—
25C22×Q8×C19D411yescharacteristic
26C22×D76C2×C411yescharacteristic
27C22×C4×D19—21no—
28C2×M16×C19—22no—
29C4×Q8×C19—22no—
30C4×Q8×C19—22no—
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C4⋊C4×C19C2×C411yescharacteristic
33C2×C4⋊C4×C19D411yescharacteristic
34C2×C42×C19D411yescharacteristic
35C2×C42×C19D411yescharacteristic
36C2×C42×C19C2311yescharacteristic
37C2×(C2×D19)⋊C4—21no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×C4⋊Dic19C2×C411yescharacteristic
43C2×C4×Dic19—21no—
44C4×D76—22no—
45C4×D76—22no—
46C19×#101—24no—
47C19×#97—22no—
48C4×C8×C19—22no—
49C19⋊#95—21no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95C2×C411yescharacteristic
55C19⋊#95C2×C411yescharacteristic
56C22⋊(C19⋊C8)—22no—
57C4⋊(C19⋊C8)—22no—
58C4⋊(C19⋊C8)—22no—
59C4⋊(C19⋊C8)D414yes—
60#10597260—22no—
61#10597260—22no—
62C4×C19⋊C8—22no—
63C23×D19—21no—
64C2×Q8×C19—22no—
65C2×Q8×C19—22no—
66C2×Q8×C19—41no—
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×Dic19—21no—
75C22×Dic19—21no—
76C22×Dic19—21no—
77C2×D76—22no—
78C2×D76—42no—
79C2×C4×D19—42no—
80C2×C4×D19—42no—
81C2×C4×D19—41no—
82C2×C4×D19—41no—
83M16×C19—24no—
84M16×C19—42no—
85C2×C8×C19—42no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—22no—
89C42×C19—21no—
90C42×C19—21no—
91C42×C19—21no—
92C42×C19—21no—
93C42×C19C2×D412yes—
94C42×C19#4112yes—
95(C2×D19)⋊C4—42no—
96(C2×D19)⋊C4—42no—
97(C2×D19)⋊C4—42no—
98(C2×D19)⋊C4—42no—
99(C2×D19)⋊C4—42no—
100C4⋊Dic19—22no—
101C4×Dic19—42no—
102C2×C19⋊C8—24no—
103#9032—191nomaximal, Sylow
104C23×C19C2×C22⋊C411yescharacteristic
105C22×D19—22no—
106C22×D19—41no—
107C22×D19—41no—
108C22×D19—41no—
109C22×D19—41no—
110C22×D19—41no—
111C22×D19—41no—
112Q8×C19—44no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—22no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19#10412yes—
127C2×C4×C19C4×D412yes—
128C2×C4×C19#12011yescharacteristic
129C2×C4×C19#12112yes—
130C2×C4×C19#12311yescharacteristic
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140D76—24no—
141D76—42no—
142C4×D19—82no—
143C4×D19—82no—
144C8×C19—44no—
145C19⋊C8—44no—
146#2983—191no—
147#2398—191no—
148C4×#101D1911yescharacteristic, complemented
149#1490—192no—
150#1300—192no—
151C22×C19—21no—
152C22×C19—21no—
153C22×C19#38611yescharacteristic
154C22×C19C2×#10411yescharacteristic
155C22×C19#42111yescharacteristic
156C2×D19—42no—
157C2×D19—42no—
158C2×D19—42no—
159C2×D19—81no—
160C2×D19—81no—
161C2×D19—81no—
162C2×D19—81no—
163C4×C19—22no—
164C4×C19—22no—
165C4×C19—21no—
166C4×C19—22no—
167C4×C19—41no—
168C4×C19—41no—
169C4×C19—41no—
170C4×C19#45412yes—
171Dic19—81no—
172Dic19—81no—
173Dic19—81no—
174C2×C4×Q8C2×D1911yescharacteristic
175C2×C4×D4—191no—
176#446—384no—
177#432—192no—
178#432—381no—
179#431—381no—
180C2×#101—21no—
181C4×M16C2×D1912yes—
182#400—191no—
183#400—191no—
184#397—381no—
185#394—191no—
186#394—191no—
187#393—381no—
188C4×C22⋊C4—381no—
189C4×C22⋊C4—381no—
190#376—191no—
191#343—21no—
192D4⋊C8—384no—
193C2×C19—21no—
194C2×C19—21no—
195C2×C19#187111yescharacteristic
196C2×C19#188811yescharacteristic
197C2×C19#189111yescharacteristic
198D19—82no—
199C22×Q8C22⋊D1911yescharacteristic
200C22×D4—191no—
201C23×C4—381no—
202C2×M16—22no—
203C4×Q8—22no—
204C4×Q8—22no—
205C4×D4—382no—
206C4×D4—382no—
207C2×C4⋊C4—191no—
208C2×C4⋊C4C4×D1911yescharacteristic
209C2×C4⋊C4C4×D1911yescharacteristic
210C2×C4⋊C4C22⋊D1911yescharacteristic
211C2×C22⋊C4—381no—
212C2×C22⋊C4—381no—
213C2×C22⋊C4—381no—
214C2×C22⋊C4—381no—
215C2×C22⋊C4—381no—
216C2×C42—381no—
217C2×C42D7611yescharacteristic
218C2×C42D7611yescharacteristic
219C2×C42C22×D1911yescharacteristic
220C4⋊C8—194no—
221C4⋊C8—382no—
222C4⋊C8—382no—
223#101—24no—
224C22⋊C8—382no—
225#97—22no—
226#97—382no—
227#97—382no—
228C4×C8—22no—
229C4×C8—382no—
230#95—191no—
231#95—191no—
232#95—381no—
233#95—381no—
234#95—381no—
235#95—381no—
236#95—381no—
237C19#903211yescharacteristic, complemented, Sylow
238C24—381no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×D4—382no—
243C2×D4—762no—
244C22×C4—381no—
245C22×C4—381no—
246C22×C4—381no—
247C22×C4—762no—
248C22×C4—762no—
249C22×C4—761no—
250C22×C4—761no—
251C22×C4(C2×D19)⋊C411yescharacteristic
252C22×C4(C2×D19)⋊C411yescharacteristic
253C22×C4(C2×D19)⋊C411yescharacteristic
254C22×C4(C2×D19)⋊C411yescharacteristic
255C22×C4C2×C4×D1911yescharacteristic
256C22×C4C2×D7611yescharacteristic
257C22×C4C2×C22⋊D1911yescharacteristic
258M16—24no—
259M16—42no—
260C2×C8—42no—
261C2×C8—384no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—382no—
266C22⋊C4—762no—
267C22⋊C4—762no—
268C22⋊C4—762no—
269C22⋊C4—762no—
270C22⋊C4—762no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—762no—
276C42D4×D1912yes—
277C42#6454312yes—
278C23—382no—
279C23—761no—
280C23—761no—
281C23—761no—
282C23—761no—
283C23—761no—
284C23—761no—
285C23C2×(C2×D19)⋊C411yescharacteristic
286Q8—44no—
287D4—384no—
288D4—762no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—761no—
303C2×C4—761no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4—761no—
307C2×C4—761no—
308C2×C4—761no—
309C2×C4—761no—
310C2×C4—761no—
311C2×C4—1522no—
312C2×C4—1522no—
313C2×C4#1059726212yes—
314C2×C4(C22⋊D19)⋊C412yes—
315C2×C4#1059732811yescharacteristic
316C2×C4#1059733211yescharacteristic
317C2×C4#1059738512yes—
318C8—44no—
319C8—764no—
320C22—21no—
321C22—21no—
322C22—762no—
323C22—762no—
324C22—762no—
325C22—1521no—
326C22—1521no—
327C22—1521no—
328C22—1521no—
329C22#1192642111yescharacteristic
330C22C2×#1059726211yescharacteristic
331C22#1192656211yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—1521no—
340C4—1521no—
341C4—1521no—
342C4#1192671912yes—
343C2—21no—
344C2—21no—
345C2—1522no—
346C2#1456393511yescharacteristic
347C2#1456403611yescharacteristic
348C2#1456405111yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC4×C19×#101C2
socleC22×C19#386
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenterC4×#101D19
hypocenterC19#9032
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
1. #14572720C2semidirect
4. #14561529C2semidirect
5. C4×C19×#101C2semidirect
148. C4×#101D19semidirect
237. C19#9032semidirect

Maximal subgroups

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

subgroupindex
#145727202
#145669182
#145620792
#145615292
C4×C19×#1012
#903219