Finite Group Databasebeta

← #18069335

Subgroups — #18069335

Order 4864.

412 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 83 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#14561899C211yesmaximal, characteristic
2#14561478C211yesmaximal, characteristic
3C19×#1280C211yesmaximal, characteristic
4C22×C4⋊Dic19C411yescharacteristic
5C22×Dic19⋊C4—21no—
6C2×C22⋊(C19⋊C8)—21no—
7C2×C19⋊#95—21no—
8C2×C19⋊#95C411yescharacteristic
9C2×C19×C22⋊C8—21no—
10C2×C19×#95C2211yescharacteristic
11C23×C4×C19C2×C411yescharacteristic
12C23×C4×C19D411yescharacteristic
13C23×C4×C19D411yescharacteristic
14C23×Dic19—21no—
15C23×Dic19—21no—
16C22×C8×C19—41no—
17C2×C4⋊Dic19—41no—
18C2×C4⋊Dic19—42no—
19C2×Dic19⋊C4—42no—
20C2×Dic19⋊C4—42no—
21C2×Dic19⋊C4—41no—
22C2×Dic19⋊C4—41no—
23C22×C19⋊C8—41no—
24C19×C22⋊C8—22no—
25C19×C22⋊C8—41no—
26C19×#95—41no—
27C19⋊#95—21no—
28C19⋊#95—42no—
29C19⋊#95C812yescomplemented
30C22⋊(C19⋊C8)—22no—
31C22⋊(C19⋊C8)—41no—
32C24×C19C22⋊C411yescharacteristic
33C22×C4×C19—21no—
34C22×C4×C19—21no—
35C22×C4×C19—21no—
36C22×C4×C19—21no—
37C22×C4×C19—21no—
38C22×C4×C19—21no—
39C22×C4×C19—41no—
40C22×C4×C19—41no—
41C22×C4×C19—41no—
42C22×C4×C19—41no—
43C22×C4×C19—41no—
44C22×C4×C19—41no—
45C22×C4×C19C2×C811yescharacteristic
46C22×C4×C19M1611yescharacteristic
47C22×C4×C19D811yescharacteristic
48C22×C4×C19SD1611yescharacteristic
49C22×C4×C19SD1611yescharacteristic
50C22×C4×C19Q1611yescharacteristic
51C22×Dic19—22no—
52C22×Dic19—22no—
53C22×Dic19—22no—
54C22×Dic19—22no—
55C22×Dic19—41no—
56C22×Dic19—41no—
57C22×Dic19—41no—
58C22×Dic19—41no—
59C22×Dic19—41no—
60C22×Dic19—41no—
61C22×Dic19—41no—
62C22×Dic19—41no—
63C22×Dic19—41no—
64C22×Dic19—41no—
65C2×C8×C19—42no—
66C2×C8×C19—81no—
67C2×C8×C19—81no—
68C4⋊Dic19—42no—
69C4⋊Dic19—42no—
70Dic19⋊C4—44no—
71Dic19⋊C4—44no—
72C2×C19⋊C8—42no—
73C2×C19⋊C8—81no—
74C2×C19⋊C8—81no—
75#7123—191nomaximal, Sylow
76C23×C19—21no—
77C23×C19—21no—
78C23×C19—21no—
79C23×C19—21no—
80C23×C19C22⋊C811yescharacteristic
81C23×C19#9911yescharacteristic
82C23×C19#10111yescharacteristic
83C23×C19#10211yescharacteristic
84C23×C19#10311yescharacteristic
85C23×C19#10411yescharacteristic
86C23×C19#10411yescharacteristic
87C2×C4×C19—21no—
88C2×C4×C19—21no—
89C2×C4×C19—21no—
90C2×C4×C19—21no—
91C2×C4×C19—21no—
92C2×C4×C19—21no—
93C2×C4×C19—42no—
94C2×C4×C19—41no—
95C2×C4×C19—41no—
96C2×C4×C19—41no—
97C2×C4×C19—41no—
98C2×C4×C19—41no—
99C2×C4×C19—41no—
100C2×C4×C19—41no—
101C2×C4×C19—41no—
102C2×C4×C19—41no—
103C2×C4×C19—41no—
104C2×C4×C19—41no—
105C2×C4×C19—41no—
106C2×C4×C19—81no—
107C2×C4×C19—81no—
108C2×Dic19—24no—
109C2×Dic19—42no—
110C2×Dic19—42no—
111C2×Dic19—42no—
112C2×Dic19—42no—
113C2×Dic19—42no—
114C2×Dic19—42no—
115C2×Dic19—42no—
116C2×Dic19—42no—
117C2×Dic19—42no—
118C2×Dic19—81no—
119C2×Dic19—81no—
120C2×Dic19—81no—
121C2×Dic19—81no—
122C8×C19—82no—
123C19⋊C8—82no—
124#1444—191no—
125#1280—191no—
126#1280D1911yescharacteristic
127C22×C19—21no—
128C22×C19—21no—
129C22×C19—21no—
130C22×C19—21no—
131C22×C19—21no—
132C22×C19—21no—
133C22×C19—21no—
134C22×C19—21no—
135C22×C19—21no—
136C22×C19—21no—
137C22×C19—21no—
138C22×C19—21no—
139C22×C19#32411yescharacteristic
140C22×C19D4⋊C811yescharacteristic
141C22×C19Q8⋊C811yescharacteristic
142C22×C19#32711yescharacteristic
143C22×C19#32811yescharacteristic
144C22×C19#33011yescharacteristic
145C22×C19#33211yescharacteristic
146C22×C19AΣL(1,𝔽16)11yescharacteristic
147C22×C19#35211yescharacteristic
148C22×C19#35311yescharacteristic
149C22×C19#35611yescharacteristic
150C4×C19—41no—
151C4×C19—41no—
152C4×C19—41no—
153C4×C19—41no—
154C4×C19—41no—
155C4×C19—41no—
156Dic19—44no—
157Dic19—82no—
158C22×C4⋊C4—191no—
159C22×C4⋊C4—381no—
160C2×C22⋊C8—21no—
161C2×C22⋊C8—381no—
162C2×#95—191no—
163C2×#95—381no—
164C2×#95C2×D1911yescharacteristic
165C2×C19—21no—
166C2×C19—21no—
167C2×C19—21no—
168C2×C19—21no—
169C2×C19#127111yescharacteristic
170C2×C19#132511yescharacteristic
171C2×C19#132611yescharacteristic
172C2×C19#134311yescharacteristic
173C2×C19#134611yescharacteristic
174C2×C19#135211yescharacteristic
175C2×C19#135411yescharacteristic
176C23×C4—381no—
177C23×C4—381no—
178C23×C4C4×D1911yescharacteristic
179C23×C4D7611yescharacteristic
180C23×C4C22⋊D1911yescharacteristic
181C22×C8—41no—
182C22×C8—761no—
183C2×C4⋊C4—761no—
184C2×C4⋊C4—762no—
185C2×C4⋊C4—762no—
186C2×C4⋊C4—761no—
187C2×C4⋊C4—761no—
188C2×C4⋊C4—762no—
189C22⋊C8—22no—
190C22⋊C8—41no—
191C22⋊C8—382no—
192C22⋊C8—761no—
193#95—41no—
194#95—192no—
195#95—381no—
196#95—762no—
197C19#712311yescharacteristic, complemented, Sylow
198C24(C2×D19)⋊C411yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—382no—
212C22×C4—382no—
213C22×C4—382no—
214C22×C4—382no—
215C22×C4—761no—
216C22×C4—761no—
217C22×C4—761no—
218C22×C4—761no—
219C22×C4—761no—
220C22×C4—761no—
221C22×C4—761no—
222C22×C4—761no—
223C22×C4—761no—
224C22×C4—761no—
225C22×C4C8×D1911yescharacteristic
226C22×C4#6451511yescharacteristic
227C22×C4#6451611yescharacteristic
228C22×C4D15211yescharacteristic
229C22×C4#6452611yescharacteristic
230C22×C4#6452811yescharacteristic
231C2×C8—42no—
232C2×C8—81no—
233C2×C8—81no—
234C2×C8—762no—
235C2×C8—1521no—
236C2×C8—1521no—
237C4⋊C4—762no—
238C4⋊C4—764no—
239C4⋊C4—764no—
240C4⋊C4—762no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23#1059726211yescharacteristic
246C23#1059726311yescharacteristic
247C23#1059726711yescharacteristic
248C23(C2×D19)⋊C811yescharacteristic
249C23#1059727811yescharacteristic
250C23#1059728111yescharacteristic
251C23#1059728211yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—384no—
274C2×C4—762no—
275C2×C4—762no—
276C2×C4—762no—
277C2×C4—762no—
278C2×C4—762no—
279C2×C4—762no—
280C2×C4—762no—
281C2×C4—762no—
282C2×C4—762no—
283C2×C4—1521no—
284C2×C4—1521no—
285C2×C4—1521no—
286C2×C4—1521no—
287C8—82no—
288C8—1522no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22#1192626911yescharacteristic
302C22#1192627311yescharacteristic
303C22#1192627411yescharacteristic
304C22#1192627911yescharacteristic
305C22#1192628011yescharacteristic
306C22#1192628511yescharacteristic
307C22#1192628911yescharacteristic
308C22#1192633211yescharacteristic
309C22#1192633311yescharacteristic
310C22#1192633611yescharacteristic
311C22#1192634211yescharacteristic
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—764no—
319C4—1522no—
320C2—21no—
321C2—21no—
322C2—21no—
323C2—21no—
324C2#1456145711yescharacteristic
325C2#1456158011yescharacteristic
326C2#1456158411yescharacteristic
327C2#1456163311yescharacteristic
328C2#1456164211yescharacteristic
329C2#1456165811yescharacteristic
330C2#1456166411yescharacteristic
subgroupG/H
centerC23#10597263
commutatorC22×C4×C19C2×C8
FrattiniC2×#95C2×D19
FittingC19×#1280C2
socleC23×C19#99
prime radicalC24×C19C22⋊C4
cosocleC2×C19×#95C22
hypercenter#1280D19
hypocenterC19#7123
LCSG ▷ C22×C4×C19 ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24 ◁ C2×#95 ◁ #1280

Complements

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

NH ≅ G/Ntype
29. C19⋊#95C8semidirect
197. C19#7123semidirect

Maximal subgroups

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

subgroupindex
#145618992
#145614782
C19×#12802
#712319