Finite Group Databasebeta

← #18078525

Subgroups — #18078525

Order 4864.

478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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#14569495C211yesmaximal, characteristic
3#14562232C212yesmaximal
4#14561500C212yesmaximal, complemented
5C4×C19×#101C211yesmaximal, characteristic, complemented
6C2×#10597321C2211yescharacteristic
7#11926675—24no—
8#11926601—21no—
9#11926601C2212yes—
10#11926597—21no—
11#11926479—21no—
12#11926464C411yescharacteristic
13#11926464C411yescharacteristic
14#11926461C411yescharacteristic
15#11926461C411yescharacteristic
16#11926455—21no—
17#11926435—21no—
18#11926435—21no—
19#11926412C2211yescharacteristic
20#11926283—24no—
21C2×C4×Q8×C19C2211yescharacteristic
22C2×C19×#101—21no—
23C4×M16×C19C2212yes—
24C19×#343—21no—
25C22×Q8×C19D411yescharacteristic
26C22×D76C2×C411yescharacteristic
27C22×Dic38C2×C411yescharacteristic
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×(C2×D19)⋊C4—21no—
43C2×Dic19⋊C4—21no—
44C2×Dic19⋊C4—21no—
45#10597321—22no—
46#10597321—22no—
47C19×#101—24no—
48C19×#97—22no—
49C4×C8×C19—22no—
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)—22no—
60#10597260—22no—
61#10597260D414yes—
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—81no—
79C2×Dic38—22no—
80C2×Dic38—81no—
81M16×C19—24no—
82M16×C19—42no—
83C2×C8×C19—42no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—22no—
87C42×C19—21no—
88C42×C19—21no—
89C42×C19—21no—
90C42×C19—21no—
91C42×C19C2×D412yes—
92C42×C19#4112yes—
93(C2×D19)⋊C4—42no—
94(C2×D19)⋊C4—42no—
95(C2×D19)⋊C4—41no—
96(C2×D19)⋊C4—42no—
97(C2×D19)⋊C4—41no—
98(C2×D19)⋊C4—81no—
99(C2×D19)⋊C4—81no—
100Dic19⋊C4—81no—
101Dic19⋊C4—81no—
102C2×C19⋊C8—24no—
103#9188—191nomaximal, Sylow
104C23×C19C2×C22⋊C411yescharacteristic
105C22×D19—41no—
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—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—41no—
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—82no—
141Dic38—82no—
142C8×C19—44no—
143C19⋊C8—44no—
144#2983—191no—
145#2632—191no—
146C4×#101D1911yescharacteristic, complemented
147#1527—192no—
148#1288—192no—
149C22×C19—21no—
150C22×C19—21no—
151C22×C19#38611yescharacteristic
152C22×C19C2×#10411yescharacteristic
153C22×C19#42111yescharacteristic
154C2×D19—81no—
155C2×D19—81no—
156C2×D19—81no—
157C2×D19—81no—
158C2×D19—81no—
159C2×D19—81no—
160C2×D19—81no—
161C4×C19—22no—
162C4×C19—22no—
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—22no—
166C4×C19—41no—
167C4×C19—41no—
168C4×C19—41no—
169Dic19—81no—
170Dic19—81no—
171Dic19—81no—
172C2×#124—191no—
173C2×C4×Q8C2×D1911yescharacteristic
174#446—384no—
175#432—192no—
176#432—381no—
177#431—381no—
178C2×#101—21no—
179C4×M16C2×D1912yes—
180#399—381no—
181#395—191no—
182#395—191no—
183#394—191no—
184#394—191no—
185#393—381no—
186#388—381no—
187#388—381no—
188#383—191no—
189#343—21no—
190#329—384no—
191C2×C19—21no—
192C2×C19—21no—
193C2×C19#187111yescharacteristic
194C2×C19#191211yescharacteristic
195C2×C19#191411yescharacteristic
196D19—161no—
197C22×Q8—191no—
198C22×Q8C22⋊D1911yescharacteristic
199C22×D4—191no—
200C2×M16—22no—
201#124—382no—
202#124—382no—
203C4×Q8—22no—
204C4×Q8—22no—
205C2×C4⋊C4—381no—
206C2×C4⋊C4—381no—
207C2×C4⋊C4C4×D1911yescharacteristic
208C2×C4⋊C4C4×D1911yescharacteristic
209C2×C4⋊C4C22⋊D1911yescharacteristic
210C2×C22⋊C4—381no—
211C2×C22⋊C4—381no—
212C2×C22⋊C4—381no—
213C2×C22⋊C4—381no—
214C2×C22⋊C4—381no—
215C2×C22⋊C4—381no—
216C2×C42D7611yescharacteristic
217C2×C42D7611yescharacteristic
218C2×C42C22×D1911yescharacteristic
219C4⋊C8—382no—
220C4⋊C8—382no—
221C4⋊C8—382no—
222#101—24no—
223C22⋊C8—382no—
224#97—22no—
225#97—194no—
226#97—382no—
227C4×C8—22no—
228C4×C8—382no—
229#95—191no—
230#95—191no—
231#95—381no—
232#95—381no—
233#95—381no—
234#95—381no—
235C19#918811yescharacteristic, complemented, Sylow
236C24—381no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—382no—
241C2×Q8—1521no—
242C2×D4—382no—
243C2×D4—1521no—
244C22×C4—381no—
245C22×C4—381no—
246C22×C4—381no—
247C22×C4(C2×D19)⋊C411yescharacteristic
248C22×C4(C2×D19)⋊C411yescharacteristic
249C22×C4(C2×D19)⋊C411yescharacteristic
250C22×C4(C2×D19)⋊C411yescharacteristic
251C22×C4C2×C4×D1911yescharacteristic
252C22×C4C2×D7611yescharacteristic
253C22×C4C2×C22⋊D1911yescharacteristic
254M16—24no—
255M16—42no—
256C2×C8—42no—
257C2×C8—384no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—1521no—
262C4⋊C4—1521no—
263C22⋊C4—762no—
264C22⋊C4—762no—
265C22⋊C4—762no—
266C22⋊C4—761no—
267C22⋊C4—761no—
268C22⋊C4—1521no—
269C22⋊C4—1521no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42D4×D1912yes—
275C42#6454312yes—
276C23—761no—
277C23—761no—
278C23—761no—
279C23—761no—
280C23—761no—
281C23—761no—
282C23—761no—
283C23C2×(C2×D19)⋊C411yescharacteristic
284Q8—44no—
285Q8—1522no—
286D4—1522no—
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—761no—
301C2×C4—761no—
302C2×C4—761no—
303C2×C4—761no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4—761no—
307C2×C4—761no—
308C2×C4—761no—
309C2×C4#1059726212yes—
310C2×C4(C22⋊D19)⋊C412yes—
311C2×C4#1059732811yescharacteristic
312C2×C4#1059733211yescharacteristic
313C2×C4#1059738512yes—
314C8—44no—
315C8—764no—
316C22—21no—
317C22—21no—
318C22—1521no—
319C22—1521no—
320C22—1521no—
321C22—1521no—
322C22—1521no—
323C22—1521no—
324C22—1521no—
325C22#1192642111yescharacteristic
326C22C2×#1059726211yescharacteristic
327C22#1192656211yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—1521no—
337C4—1521no—
338C4—1521no—
339C2—21no—
340C2—21no—
341C2—3041no—
342C2#1456393511yescharacteristic
343C2#1456417011yescharacteristic
344C2#1456418011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC4×C19×#101C2
socleC22×C19#386
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenterC4×#101D19
hypocenterC19#9188
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
1. #14572720C2semidirect
4. #14561500C2semidirect
5. C4×C19×#101C2semidirect
146. C4×#101D19semidirect
235. C19#9188semidirect

Maximal subgroups

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

subgroupindex
#145727202
#145694952
#145622322
#145615002
C4×C19×#1012
#918819