Finite Group Databasebeta

← #18079443

Subgroups — #18079443

Order 4864.

536 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 115 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#14566000C211yesmaximal, characteristic
2#14564580C211yesmaximal, characteristic
3#14562147C211yesmaximal, characteristic
4#14562082C211yesmaximal, characteristic
5#14561527C211yesmaximal, characteristic
6#14561492C211yesmaximal, characteristic
7C19×#3113C211yesmaximal, characteristic
8C2×Q8×Dic19—21no—
9#11926601C2211yescharacteristic
10C4×#64520C2211yescharacteristic
11C4⋊C4×Dic19—22no—
12C4⋊C4×Dic19—21no—
13C4×C4⋊Dic19—21no—
14C4×C4⋊Dic19C2211yescharacteristic
15#11926390—21no—
16#11926390C2211yescharacteristic
17#11926303—22no—
18#11926281—21no—
19#11926281—21no—
20Q8⋊(C19⋊C8)—22no—
21C19×#533C2211yescharacteristic
22C2×C4×Q8×C19C2211yescharacteristic
23C19×#483—21no—
24C19×#475C412yescomplemented
25C19×#462C412yescomplemented
26C19×#451—21no—
27C19×#441—22no—
28C19×#432C2211yescharacteristic
29C22×Q8×C19D411yescharacteristic
30C2×Q16×C19—22no—
31C19×C4⋊Q8C2×C411yescharacteristic
32C19×C4⋊Q8C2×C411yescharacteristic
33C19×#125—21no—
34C19×C22⋊Q8—21no—
35C19×C22⋊Q8—21no—
36C4×Q8×C19—21no—
37C4×Q8×C19—21no—
38C4×Q8×C19—21no—
39C4×Q8×C19—21no—
40C4×Q8×C19C2×C412yes—
41C4×Q8×C19D412yes—
42C19×#117—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19D411yescharacteristic
45C2×C42×C19—21no—
46C2×C42×C19C2311yescharacteristic
47Q8×Dic19—28no—
48C2×C4⋊Dic19—22no—
49C2×C4⋊Dic19—21no—
50C2×C4×Dic19—22no—
51C2×C4×Dic19—21no—
52C2×C4×Dic19—22no—
53C2×C4×Dic19D412yes—
54C2×#64520—21no—
55C19×#106—22no—
56C19×C4⋊C8C2×C412yes—
57C19×#103—22no—
58C19×#103—22no—
59C19×C22⋊C8—21no—
60C19×#97—21no—
61C19⋊#95—22no—
62C19⋊#95—21no—
63C19⋊#95—21no—
64C19⋊#95D411yescharacteristic
65C19⋊#95D411yescharacteristic
66C22⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—21no—
68#10597260—21no—
69#10597260—21no—
70C4×C19⋊C8—21no—
71C2×Q8×C19—24no—
72C2×Q8×C19—21no—
73C2×Q8×C19—21no—
74C2×Q8×C19—21no—
75C2×Q8×C19C22⋊C412yes—
76C22×C4×C19—21no—
77C22×C4×C19—21no—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×Dic19—21no—
82C22×Dic19—22no—
83C22×Dic19—21no—
84Q16×C19—44no—
85C2×C8×C19—22no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—41no—
94C4⋊C4×C19—41no—
95C4⋊C4×C19C22⋊C412yes—
96C22⋊C4×C19—41no—
97C42×C19—22no—
98C42×C19—22no—
99C42×C19—41no—
100C42×C19C22×C411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C42×C19#4111yescharacteristic
103C42×C19#4111yescharacteristic
104C4⋊Dic19—28no—
105C4⋊Dic19—24no—
106C4×Dic19—28no—
107C4×Dic19—24no—
108C4×Dic19—42no—
109C4×Dic19—82no—
110#64520—22no—
111#64520—41no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8—41no—
114#9324—191nomaximal, Sylow
115C23×C19#12011yescharacteristic
116Q8×C19—24no—
117Q8×C19—22no—
118Q8×C19—42no—
119Q8×C19—81no—
120Q8×C19#10414yes—
121C2×C4×C19—24no—
122C2×C4×C19—22no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19C2×C22⋊C411yescharacteristic
133C2×C4×C19C4×D411yescharacteristic
134C2×C4×C19C4×D411yescharacteristic
135C2×C4×C19#12111yescharacteristic
136C2×C4×C19#12111yescharacteristic
137C2×C4×C19#12311yescharacteristic
138C2×Dic19—22no—
139C2×Dic19—24no—
140C2×Dic19—22no—
141C2×Dic19—41no—
142C2×Dic19—42no—
143C2×Dic19—41no—
144C2×Dic19—42no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C8×C19—42no—
148C19⋊C8—42no—
149C19⋊C8—81no—
150#3113D1911yescharacteristic
151#2276—191no—
152#1986—191no—
153#1506—191no—
154#1491—191no—
155#1300—191no—
156#1285—191no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19#38611yescharacteristic
160C22×C19#45511yescharacteristic
161C22×C19#45611yescharacteristic
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—24no—
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—42no—
169C4×C19—81no—
170C4×C19—81no—
171C4×C19C2×#10412yes—
172Dic19—44no—
173Dic19—42no—
174Dic19—42no—
175#533C2×D1911yescharacteristic
176C2×C4×Q8—381no—
177C2×C4×Q8C2×D1911yescharacteristic
178#483—21no—
179#475Dic1912yescomplemented
180#462Dic1912yescomplemented
181#451—21no—
182#441—22no—
183#432—191no—
184#432C2×D1911yescharacteristic
185C4×M16—191no—
186C4×C4⋊C4—191no—
187C4×C4⋊C4—381no—
188C4×C4⋊C4—382no—
189C4×C4⋊C4—381no—
190#376—191no—
191#376—381no—
192#339—382no—
193#328—381no—
194#328—381no—
195Q8⋊C8—382no—
196C2×C19—21no—
197C2×C19—21no—
198C2×C19#188211yescharacteristic
199C2×C19#189611yescharacteristic
200C2×C19#190511yescharacteristic
201C22×Q8C22⋊D1911yescharacteristic
202C2×Q16—22no—
203C2×M16—381no—
204C4⋊Q8C2×Dic1911yescharacteristic
205C4⋊Q8C2×Dic1911yescharacteristic
206#125—21no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×Q8—21no—
212C4×Q8—21no—
213C4×Q8—388no—
214C4×Q8C2×Dic1912yes—
215C4×Q8C22⋊D1912yes—
216#117—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—382no—
219C2×C4⋊C4—381no—
220C2×C4⋊C4C22⋊D1911yescharacteristic
221C2×C42—21no—
222C2×C42—192no—
223C2×C42—382no—
224C2×C42—381no—
225C2×C42—382no—
226C2×C42C22×D1911yescharacteristic
227#106—22no—
228C4⋊C8—381no—
229C4⋊C8C2×Dic1912yes—
230#103—22no—
231#103—22no—
232C22⋊C8—21no—
233C22⋊C8—381no—
234#97—21no—
235#97—381no—
236#97—381no—
237C4×C8—381no—
238#95—191no—
239#95—191no—
240#95—382no—
241#95—381no—
242#95—381no—
243C19#932411yescharacteristic, complemented, Sylow
244C2×Q8—24no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8C22⋊Dic1912yes—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—381no—
252C22×C4—381no—
253C22×C4—382no—
254C22×C4D4×D1911yescharacteristic
255C22×C4D4×D1911yescharacteristic
256C22×C4C2×C22⋊D1911yescharacteristic
257Q16—44no—
258M16—382no—
259M16—761no—
260C2×C8—22no—
261C2×C8—761no—
262C2×C8—761no—
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—388no—
273C4⋊C4—384no—
274C4⋊C4C22⋊Dic1912yes—
275C22⋊C4—41no—
276C42—22no—
277C42—22no—
278C42—41no—
279C42—388no—
280C42—384no—
281C42—762no—
282C42—1522no—
283C42#6454311yescharacteristic
284C42#6454311yescharacteristic
285C42C22×Dic1911yescharacteristic
286C42C2×C22⋊D1911yescharacteristic
287C23#1059738311yescharacteristic
288Q8—24no—
289Q8—22no—
290Q8—42no—
291Q8—81no—
292Q8#1059729414yes—
293C2×C4—24no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—382no—
305C2×C4—382no—
306C2×C4—384no—
307C2×C4—761no—
308C2×C4—761no—
309C2×C4—762no—
310C2×C4—762no—
311C2×C4—761no—
312C2×C4—761no—
313C2×C4D4×Dic1911yescharacteristic
314C2×C4D4×Dic1911yescharacteristic
315C2×C4#1059738111yescharacteristic
316C2×C4#1059738511yescharacteristic
317C2×C4#1059738511yescharacteristic
318C2×C4C2×C22⋊Dic1911yescharacteristic
319C8—42no—
320C8—762no—
321C8—1521no—
322C22—21no—
323C22—21no—
324C22#1192642411yescharacteristic
325C22#1192672011yescharacteristic
326C22#1192672511yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—24no—
332C4—21no—
333C4—42no—
334C4—81no—
335C4—81no—
336C4—764no—
337C4—762no—
338C4—762no—
339C4C2×#1059729412yes—
340C2—21no—
341C2—21no—
342C2#1456400611yescharacteristic
343C2#1456407911yescharacteristic
344C2#1456413111yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3113C2
socleC22×C19#386
prime radicalC23×C19#120
cosocleC2×C42×C19C23
hypercenter#3113D19
hypocenterC19#9324
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
24. C19×#475C4semidirect
25. C19×#462C4semidirect
179. #475Dic19semidirect
180. #462Dic19semidirect
243. C19#9324semidirect

Maximal subgroups

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

subgroupindex
#145660002
#145645802
#145621472
#145620822
#145615272
#145614922
C19×#31132
#932419