Finite Group Databasebeta

← #18079198

Subgroups — #18079198

Order 4864.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572353C211yesmaximal, characteristic
2#14564609C211yesmaximal, characteristic, complemented
3#14562320C211yesmaximal, characteristic, complemented
4#14562195C211yesmaximal, characteristic
5#14561494C211yesmaximal, characteristic, complemented
6#14561465C211yesmaximal, characteristic, complemented
7C19×#3206C211yesmaximal, characteristic
8C2×#10597394—21no—
9#11926616—22no—
10#11926616—22no—
11#11926597C2211yescharacteristic
12#11926568C2211yescharacteristic
13#11926511—21no—
14C2×#10597260C2211yescharacteristic
15#11926410C2211yescharacteristic
16#11926306—21no—
17#11926306—21no—
18#11926290—22no—
19#11926278—22no—
20C19×#532C2211yescharacteristic
21C2×C19×C4⋊Q8C2211yescharacteristic
22C19×#492C412yescomplemented
23C19×#487C412yescomplemented
24C19×#461—22no—
25C19×#448—22no—
26C19×#431C2211yescharacteristic
27C2×#41×C19—21no—
28C22×Q8×C19—21no—
29C2×SD16×C19—24no—
30C19×C4⋊Q8—21no—
31C19×C4⋊Q8—21no—
32C19×C4⋊Q8—21no—
33C19×C4⋊Q8C2×C412yes—
34C19×C4⋊Q8C2×C411yescharacteristic
35C19×#127C2×C411yescharacteristic
36C19×#124—21no—
37C19×#121—21no—
38C19×#121D412yes—
39C4×D4×C19—21no—
40C4×D4×C19D412yes—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C42×C19C2311yescharacteristic
44#10597394—42no—
45#10597394—42no—
46C2×C4⋊Dic19—21no—
47C2×#64520—22no—
48C2×#64520—21no—
49C22×C19⋊C8—22no—
50C22×C19⋊C8D411yescharacteristic
51C22×C19⋊C8D411yescharacteristic
52C19×C4⋊C8—21no—
53C19×#103—24no—
54C19×C22⋊C8—21no—
55C4×C8×C19C2×C412yes—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C22⋊(C19⋊C8)—24no—
59C22⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)—21no—
62C4⋊(C19⋊C8)D412yes—
63#10597260—21no—
64#10597260—21no—
65C4×C19⋊C8—21no—
66#41×C19—41no—
67#41×C19—41no—
68#41×C19—41no—
69#41×C19—41no—
70C2×Q8×C19—21no—
71C2×Q8×C19—22no—
72C2×Q8×C19—41no—
73C2×Q8×C19—82no—
74C2×D4×C19—22no—
75C2×D4×C19—21no—
76C2×D4×C19—21no—
77C2×D4×C19C22⋊C412yes—
78C22×C4×C19—22no—
79C22×C4×C19—41no—
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19#4111yescharacteristic
83C22×Dic19—41no—
84SD16×C19—84no—
85C2×C8×C19—22no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19C22⋊C412yes—
92C22⋊C4×C19—22no—
93C22⋊C4×C19—22no—
94C42×C19C22×C411yescharacteristic
95C42×C19C2×D411yescharacteristic
96C42×C19C2×D411yescharacteristic
97C42×C19#4111yescharacteristic
98C4⋊Dic19—41no—
99C4⋊Dic19—41no—
100#64520—44no—
101#64520—41no—
102#64520—41no—
103C2×C19⋊C8—21no—
104C2×C19⋊C8—21no—
105C2×C19⋊C8—21no—
106C2×C19⋊C8—22no—
107C2×C19⋊C8—21no—
108C2×C19⋊C8—21no—
109C2×C19⋊C8—44no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8SD1612yescomplemented
112#9289—191nomaximal, Sylow
113C23×C19—22no—
114C23×C19#12111yescharacteristic
115Q8×C19—44no—
116Q8×C19—41no—
117Q8×C19—41no—
118Q8×C19—82no—
119D4×C19—42no—
120D4×C19—42no—
121D4×C19—42no—
122D4×C19—41no—
123D4×C19—41no—
124D4×C19—81no—
125C2×C4×C19—22no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—82no—
132C2×C4×C19C2×C22⋊C411yescharacteristic
133C2×C4×C19C4×D411yescharacteristic
134C2×C4×C19C4×D411yescharacteristic
135C2×C4×C19#12011yescharacteristic
136C2×C4×C19#12111yescharacteristic
137C2×C4×C19#12311yescharacteristic
138C2×C4×C19C2×SD1611yescharacteristic
139C2×C4×C19#13511yescharacteristic
140C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C19#13711yescharacteristic
142C2×Dic19—81no—
143C2×Dic19—81no—
144C2×Dic19—81no—
145C8×C19—42no—
146C19⋊C8—22no—
147C19⋊C8—42no—
148C19⋊C8—41no—
149C19⋊C8—81no—
150#3206D1911yescharacteristic
151#2932—191no—
152#1993—191no—
153#1549—191no—
154#1517—191no—
155#1286—191no—
156#1275—191no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—42no—
160C22×C19—42no—
161C22×C19—42no—
162C22×C19#38611yescharacteristic
163C22×C19#46111yescharacteristic
164C22×C19#46311yescharacteristic
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—42no—
170C4×C19—82no—
171C4×C19C4×SD1611yescharacteristic
172C4×C19#44011yescharacteristic
173C4×C19#45011yescharacteristic
174C4×C19#45211yescharacteristic
175Dic19—161no—
176C2×#131—381no—
177#532C2×D1911yescharacteristic
178C2×C4⋊Q8C2×D1911yescharacteristic
179#492Dic1912yescomplemented
180#487Dic1912yescomplemented
181#461—22no—
182#448—22no—
183#435—382no—
184#435—382no—
185#431—191no—
186#431C2×D1911yescharacteristic
187#423—191no—
188#408—381no—
189C2×#97—191no—
190#382—191no—
191#340—381no—
192#340—381no—
193#332—382no—
194#327—382no—
195C2×C19—21no—
196C2×C19—21no—
197C2×C19—82no—
198C2×C19#187711yescharacteristic
199C2×C19#190211yescharacteristic
200C2×C19#191011yescharacteristic
201C2×#41—21no—
202C22×Q8—21no—
203C2×SD16—24no—
204#131—762no—
205#131—762no—
206C2×M16—382no—
207C2×M16—381no—
208C22×C8—191no—
209C22×C8—191no—
210C22×C8—382no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8C2×Dic1912yes—
215C4⋊Q8C2×Dic1911yescharacteristic
216#127C2×Dic1911yescharacteristic
217#124—21no—
218#121—21no—
219#121C22⋊D1912yes—
220C4×D4—21no—
221C4×D4C22⋊D1912yes—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—381no—
225C2×C42C22×D1911yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—192no—
228C4⋊C8—381no—
229C4⋊C8—381no—
230#103—24no—
231C22⋊C8—21no—
232C22⋊C8—384no—
233C22⋊C8—381no—
234#97—381no—
235#97—381no—
236C4×C8—381no—
237C4×C8C2×Dic1912yes—
238#95—381no—
239#95—381no—
240C19#928911yescharacteristic, complemented, Sylow
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8—82no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4C22⋊Dic1912yes—
253C22×C4—22no—
254C22×C4—41no—
255C22×C4—761no—
256C22×C4D4×D1911yescharacteristic
257C22×C4#6454311yescharacteristic
258C22×C4C2×C22⋊D1911yescharacteristic
259SD16—84no—
260M16—764no—
261M16—761no—
262M16—761no—
263C2×C8—22no—
264C2×C8—192no—
265C2×C8—381no—
266C2×C8—381no—
267C2×C8—381no—
268C2×C8—382no—
269C2×C8—381no—
270C2×C8—381no—
271C2×C8—764no—
272C2×C8—761no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—761no—
279C4⋊C4—761no—
280C4⋊C4C22⋊Dic1912yes—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C42D4×D1911yescharacteristic
284C42#6454311yescharacteristic
285C42C22×Dic1911yescharacteristic
286C42C2×C22⋊D1911yescharacteristic
287C23—22no—
288C23#1059738511yescharacteristic
289Q8—44no—
290Q8—41no—
291Q8—41no—
292Q8—82no—
293D4—42no—
294D4—42no—
295D4—42no—
296D4—41no—
297D4—41no—
298D4—81no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—1521no—
307C2×C4—1521no—
308C2×C4—1521no—
309C2×C4SD16×D1911yescharacteristic
310C2×C4#1059736011yescharacteristic
311C2×C4#1059736111yescharacteristic
312C2×C4#1059736211yescharacteristic
313C2×C4D4×Dic1911yescharacteristic
314C2×C4D4×Dic1911yescharacteristic
315C2×C4#1059738111yescharacteristic
316C2×C4#1059738311yescharacteristic
317C2×C4#1059738511yescharacteristic
318C2×C4C2×C22⋊Dic1911yescharacteristic
319C8—42no—
320C8—382no—
321C8—762no—
322C8—761no—
323C8—1521no—
324C22—21no—
325C22—21no—
326C22—42no—
327C22—42no—
328C22—42no—
329C22#1192642411yescharacteristic
330C22#1192674711yescharacteristic
331C22#1192676111yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—42no—
337C4—82no—
338C4—3041no—
339C4SD16×Dic1911yescharacteristic
340C4#1192664511yescharacteristic
341C4#1192669311yescharacteristic
342C4#1192670311yescharacteristic
343C2—21no—
344C2—21no—
345C2—82no—
346C2#1456397111yescharacteristic
347C2#1456411011yescharacteristic
348C2#1456416311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3206C2
socleC22×C19#386
prime radicalC19×#532C22
cosocleC2×C42×C19C23
hypercenter#3206D19
hypocenterC19#9289
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
2. #14564609C2semidirect
3. #14562320C2semidirect
5. #14561494C2semidirect
6. #14561465C2semidirect
22. C19×#492C4semidirect
23. C19×#487C4semidirect
111. C2×C19⋊C8SD16semidirect
179. #492Dic19semidirect
180. #487Dic19semidirect
240. C19#9289semidirect

Maximal subgroups

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

subgroupindex
#145723532
#145646092
#145623202
#145621952
#145614942
#145614652
C19×#32062
#928919