Finite Group Databasebeta

← #18079296

Subgroups — #18079296

Order 4864.

488 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572659C211yesmaximal, characteristic
2#14563645C211yesmaximal, characteristic
3#14562199C211yesmaximal, characteristic, complemented
4#14562038C211yesmaximal, characteristic, complemented
5#14561530C211yesmaximal, characteristic, complemented
6#14561495C211yesmaximal, characteristic, complemented
7C19×#3077C211yesmaximal, characteristic
8D4×C19⋊C8—22no—
9D4×C19⋊C8—22no—
10#11926597C2211yescharacteristic
11#11926597C2211yescharacteristic
12C2×C4⋊(C19⋊C8)C2211yescharacteristic
13C2×#10597289—21no—
14C2×C22⋊(C19⋊C8)—22no—
15#11926410C2211yescharacteristic
16#11926306—21no—
17#11926281—22no—
18Q8⋊(C19⋊C8)—22no—
19C19×#533C2211yescharacteristic
20C2×C4×D4×C19C2211yescharacteristic
21C19×#478—22no—
22C19×#476C412yescomplemented
23C19×#474C412yescomplemented
24C19×#428—21no—
25C19×#423C2211yescharacteristic
26C19×#418—21no—
27C22×D4×C19D411yescharacteristic
28C23×C4×C19—21no—
29C2×M16×C19—21no—
30C19×C4⋊Q8C2×C411yescharacteristic
31C19×C4⋊Q8C2×C411yescharacteristic
32C19×#125—21no—
33C19×C22⋊Q8—21no—
34C19×C22⋊Q8—21no—
35C4×Q8×C19—21no—
36C4×Q8×C19—21no—
37C4×D4×C19—21no—
38C4×D4×C19—21no—
39C4×D4×C19C2×C412yes—
40C4×D4×C19D412yes—
41C19×#117—21no—
42C2×C4⋊C4×C19D411yescharacteristic
43C2×C22⋊C4×C19—21no—
44C2×C42×C19C2311yescharacteristic
45C2×C4⋊Dic19—21no—
46C22×C19⋊C8—24no—
47C22×C19⋊C8—21no—
48C19×#107—22no—
49C19×#106—22no—
50C19×C4⋊C8—21no—
51C19×C4⋊C8C2×C412yes—
52C19×#102—22no—
53C19×#102—22no—
54#10597289—42no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C22⋊(C19⋊C8)—24no—
58C22⋊(C19⋊C8)—21no—
59C22⋊(C19⋊C8)D412yes—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)—21no—
62C4⋊(C19⋊C8)—21no—
63C4⋊(C19⋊C8)—21no—
64C4×C19⋊C8—21no—
65C4×C19⋊C8D412yes—
66C24×C19—21no—
67C2×Q8×C19—21no—
68C2×Q8×C19—21no—
69C2×D4×C19—21no—
70C2×D4×C19—21no—
71C2×D4×C19—21no—
72C2×D4×C19C22⋊C412yes—
73C2×D4×C19SD1612yes—
74C2×D4×C19Q1612yes—
75C22×C4×C19—21no—
76C22×C4×C19—22no—
77C22×C4×C19—22no—
78C22×C4×C19—82no—
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19#4111yescharacteristic
82C22×Dic19—41no—
83M16×C19—41no—
84M16×C19—41no—
85C2×C8×C19—22no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—41no—
93C4⋊C4×C19C22⋊C412yes—
94C22⋊C4×C19—22no—
95C22⋊C4×C19—22no—
96C22⋊C4×C19—41no—
97C42×C19—41no—
98C42×C19C22×C411yescharacteristic
99C42×C19C2×D411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19#4111yescharacteristic
102C4⋊Dic19—41no—
103C4⋊Dic19—41no—
104C2×C19⋊C8—22no—
105C2×C19⋊C8—22no—
106C2×C19⋊C8—41no—
107C2×C19⋊C8—41no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—84no—
110#9303—191nomaximal, Sylow
111C23×C19—22no—
112C23×C19—22no—
113C23×C19—22no—
114C23×C19—81no—
115C23×C19—81no—
116C23×C19#12111yescharacteristic
117Q8×C19—42no—
118Q8×C19—81no—
119D4×C19—22no—
120D4×C19—22no—
121D4×C19—22no—
122D4×C19#10314yes—
123C2×C4×C19—22no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—44no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—82no—
130C2×C4×C19—81no—
131C2×C4×C19C2×C22⋊C411yescharacteristic
132C2×C4×C19C4×D411yescharacteristic
133C2×C4×C19C4×D411yescharacteristic
134C2×C4×C19#12011yescharacteristic
135C2×C4×C19#12111yescharacteristic
136C2×C4×C19#12311yescharacteristic
137C2×C4×C19C2×SD1611yescharacteristic
138C2×C4×C19C2×Q1611yescharacteristic
139C2×C4×C19#13511yescharacteristic
140C2×C4×C19#13511yescharacteristic
141C2×Dic19—81no—
142C2×Dic19—81no—
143C2×Dic19—81no—
144C8×C19—42no—
145C19⋊C8—42no—
146C19⋊C8—42no—
147C19⋊C8—81no—
148#3077D1911yescharacteristic
149#2972—191no—
150#1804—191no—
151#1518—191no—
152#1481—191no—
153#1301—191no—
154#1286—191no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—24no—
158C22×C19—42no—
159C22×C19—42no—
160C22×C19—82no—
161C22×C19—82no—
162C22×C19#38611yescharacteristic
163C22×C19#46511yescharacteristic
164C22×C19#46711yescharacteristic
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—42no—
170C4×C19—81no—
171C4×C19—81no—
172C4×C19C2×#10311yescharacteristic
173C4×C19#41611yescharacteristic
174C4×C19#46511yescharacteristic
175C4×C19#46711yescharacteristic
176Dic19—161no—
177#533C2×D1911yescharacteristic
178C2×C4×D4C2×D1911yescharacteristic
179#478—22no—
180#476Dic1912yescomplemented
181#474Dic1912yescomplemented
182C8×D4—382no—
183C8×D4—382no—
184#431—191no—
185#431—191no—
186#428—21no—
187#423C2×D1911yescharacteristic
188C2×C4⋊C8—191no—
189#418—21no—
190C2×#102—381no—
191C2×C22⋊C8—382no—
192#382—191no—
193#340—381no—
194#328—382no—
195Q8⋊C8—382no—
196C2×C19—21no—
197C2×C19—21no—
198C2×C19—44no—
199C2×C19#188111yescharacteristic
200C2×C19#189211yescharacteristic
201C2×C19#190411yescharacteristic
202C22×D4C22⋊D1911yescharacteristic
203C23×C4—21no—
204C2×M16—21no—
205C22×C8—384no—
206C22×C8—381no—
207C4⋊Q8C2×Dic1911yescharacteristic
208C4⋊Q8C2×Dic1911yescharacteristic
209#125—21no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×D4—21no—
215C4×D4—21no—
216C4×D4C2×Dic1912yes—
217C4×D4C22⋊D1912yes—
218#117—21no—
219C2×C4⋊C4—381no—
220C2×C4⋊C4C22⋊D1911yescharacteristic
221C2×C22⋊C4—21no—
222C2×C42C22×D1911yescharacteristic
223#107—22no—
224#106—22no—
225C4⋊C8—21no—
226C4⋊C8—381no—
227C4⋊C8—381no—
228C4⋊C8—381no—
229C4⋊C8—381no—
230C4⋊C8C2×Dic1912yes—
231#102—22no—
232#102—22no—
233#102—762no—
234C22⋊C8—192no—
235C22⋊C8—384no—
236C22⋊C8—381no—
237C4×C8—192no—
238C4×C8—381no—
239#95—381no—
240#95—381no—
241C19#930311yescharacteristic, complemented, Sylow
242C24—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4#6452712yes—
249C2×D4#6452812yes—
250C2×D4C22⋊Dic1912yes—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—82no—
255C22×C4—761no—
256C22×C4D4×D1911yescharacteristic
257C22×C4#6454311yescharacteristic
258C22×C4C2×C22⋊D1911yescharacteristic
259M16—41no—
260M16—41no—
261C2×C8—22no—
262C2×C8—382no—
263C2×C8—382no—
264C2×C8—761no—
265C2×C8—761no—
266C2×C8—761no—
267C2×C8—1524no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—761no—
276C4⋊C4—761no—
277C4⋊C4C22⋊Dic1912yes—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C22⋊C4—41no—
281C42—41no—
282C42D4×D1911yescharacteristic
283C42#6454311yescharacteristic
284C42C22×Dic1911yescharacteristic
285C42C2×C22⋊D1911yescharacteristic
286C23—22no—
287C23—22no—
288C23—22no—
289C23—81no—
290C23—81no—
291C23#1059738511yescharacteristic
292Q8—42no—
293Q8—81no—
294D4—22no—
295D4—22no—
296D4—22no—
297D4#1059729214yes—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—44no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—82no—
305C2×C4—81no—
306C2×C4—1521no—
307C2×C4—1521no—
308C2×C4—1521no—
309C2×C4D4×Dic1911yescharacteristic
310C2×C4D4×Dic1911yescharacteristic
311C2×C4#1059738111yescharacteristic
312C2×C4#1059738311yescharacteristic
313C2×C4#1059738511yescharacteristic
314C2×C4C2×#6452711yescharacteristic
315C2×C4C2×#6452811yescharacteristic
316C2×C4#1059739611yescharacteristic
317C2×C4#1059739611yescharacteristic
318C2×C4C2×C22⋊Dic1911yescharacteristic
319C8—42no—
320C8—762no—
321C8—762no—
322C8—1521no—
323C22—21no—
324C22—21no—
325C22—24no—
326C22—42no—
327C22—42no—
328C22—82no—
329C22—82no—
330C22#1192642411yescharacteristic
331C22#1192677511yescharacteristic
332C22#1192678311yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—81no—
339C4—81no—
340C4—3041no—
341C4C2×#1059729211yescharacteristic
342C4#1192654011yescharacteristic
343C4#1192677511yescharacteristic
344C4#1192678311yescharacteristic
345C2—21no—
346C2—21no—
347C2—44no—
348C2#1456399911yescharacteristic
349C2#1456405911yescharacteristic
350C2#1456412411yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3077C2
socleC22×C19#386
prime radicalC22×D4×C19D4
cosocleC2×C42×C19C23
hypercenter#3077D19
hypocenterC19#9303
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
3. #14562199C2semidirect
4. #14562038C2semidirect
5. #14561530C2semidirect
6. #14561495C2semidirect
22. C19×#476C4semidirect
23. C19×#474C4semidirect
180. #476Dic19semidirect
181. #474Dic19semidirect
241. C19#9303semidirect

Maximal subgroups

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

subgroupindex
#145726592
#145636452
#145621992
#145620382
#145615302
#145614952
C19×#30772
#930319