Finite Group Databasebeta

← #18078827

Subgroups — #18078827

Order 4864.

474 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566113C211yesmaximal, characteristic
2#14564613C211yesmaximal, characteristic
3#14562134C211yesmaximal, characteristic
4#14562064C211yesmaximal, characteristic
5#14561537C211yesmaximal, characteristic
6#14561467C211yesmaximal, characteristic
7C19×#3104C211yesmaximal, characteristic
8#11926597C2211yescharacteristic
9#11926568C2211yescharacteristic
10#11926451—21no—
11#11926443—21no—
12#11926430—22no—
13C4×C4⋊Dic19—21no—
14C4×C4⋊Dic19C2211yescharacteristic
15#11926390—21no—
16C42×Dic19C2211yescharacteristic
17#11926303—21no—
18#11926303—21no—
19#11926281—22no—
20Q8⋊(C19⋊C8)—22no—
21C19×#533C2211yescharacteristic
22C2×C4×Q8×C19C2211yescharacteristic
23C19×#484—21no—
24C19×#477C412yescomplemented
25C19×#462C412yescomplemented
26C19×#451—21no—
27C4×Q16×C19—22no—
28C19×#431C2211yescharacteristic
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
47C2×C4⋊Dic19—22no—
48C2×C4⋊Dic19—21no—
49C2×C4×Dic19—21no—
50C2×C4×Dic19—21no—
51C2×C4×Dic19—21no—
52C2×C4×Dic19D411yescharacteristic
53C2×C4×Dic19D411yescharacteristic
54C2×#64520—21no—
55C19×#107—22no—
56C19×C4⋊C8C2×C412yes—
57C19×#103—22no—
58C19×#103—22no—
59C19×C22⋊C8—21no—
60C4×C8×C19—21no—
61C19⋊#95—22no—
62C19⋊#95—22no—
63C19⋊#95—22no—
64C19⋊#95D412yes—
65C22⋊(C19⋊C8)—21no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—21no—
68C4⋊(C19⋊C8)—21no—
69C4×C19⋊C8—21no—
70C2×Q8×C19—21no—
71C2×Q8×C19—21no—
72C2×Q8×C19—21no—
73C2×Q8×C19—42no—
74C2×Q8×C19C22⋊C412yes—
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×Dic19—21no—
81C22×Dic19—21no—
82C22×Dic19—22no—
83Q16×C19—44no—
84C2×C8×C19—22no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—41no—
93C4⋊C4×C19—41no—
94C4⋊C4×C19C22⋊C412yes—
95C22⋊C4×C19—41no—
96C42×C19—22no—
97C42×C19—22no—
98C42×C19—41no—
99C42×C19C22×C411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19#4111yescharacteristic
102C42×C19#4111yescharacteristic
103C4⋊Dic19—44no—
104C4⋊Dic19—42no—
105C4×Dic19—21no—
106C4×Dic19—21no—
107C4×Dic19—21no—
108C4×Dic19—42no—
109C4×Dic19—42no—
110C4×Dic19—41no—
111C4×Dic19—41no—
112C4×Dic19Q1612yescomplemented
113#64520—41no—
114#64520—41no—
115C2×C19⋊C8—41no—
116C2×C19⋊C8—41no—
117#9236—191nomaximal, Sylow
118C23×C19#12011yescharacteristic
119Q8×C19—22no—
120Q8×C19—22no—
121Q8×C19—42no—
122Q8×C19—42no—
123Q8×C19—81no—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
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×C4×C19C2×Q1611yescharacteristic
139C2×C4×C19#13511yescharacteristic
140C2×C4×C19#13711yescharacteristic
141C2×C4×C19#13711yescharacteristic
142C2×Dic19—22no—
143C2×Dic19—22no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—42no—
149C2×Dic19—42no—
150C2×Dic19—42no—
151C8×C19—42no—
152C19⋊C8—81no—
153C19⋊C8—81no—
154#3104D1911yescharacteristic
155#2295—191no—
156#1994—191no—
157#1503—191no—
158#1487—191no—
159#1303—191no—
160#1276—191no—
161C22×C19—21no—
162C22×C19—21no—
163C22×C19#38611yescharacteristic
164C22×C19#45111yescharacteristic
165C22×C19#45211yescharacteristic
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—42no—
170C4×C19—42no—
171C4×C19—81no—
172C4×C19—81no—
173C4×C19#42112yes—
174C4×C19C4×Q1611yescharacteristic
175C4×C19#44111yescharacteristic
176C4×C19#46211yescharacteristic
177C4×C19#46411yescharacteristic
178Dic19—42no—
179Dic19—42no—
180Dic19—82no—
181#533C2×D1911yescharacteristic
182C2×C4×Q8C2×D1911yescharacteristic
183#484—21no—
184#477Dic1912yescomplemented
185#462Dic1912yescomplemented
186#451—21no—
187C4×Q16—22no—
188#431—191no—
189#431C2×D1911yescharacteristic
190#423—191no—
191#391—381no—
192#389—381no—
193#387—382no—
194C4×C4⋊C4—191no—
195C4×C4⋊C4—381no—
196#376—381no—
197C43—191no—
198#339—381no—
199#339—381no—
200#328—382no—
201Q8⋊C8—382no—
202C2×C19—21no—
203C2×C19—21no—
204C2×C19#187811yescharacteristic
205C2×C19#189711yescharacteristic
206C2×C19#190611yescharacteristic
207C22×Q8C22⋊D1911yescharacteristic
208C2×Q16—22no—
209C2×M16—381no—
210C4⋊Q8C2×Dic1911yescharacteristic
211C4⋊Q8C2×Dic1911yescharacteristic
212#125—21no—
213C22⋊Q8—21no—
214C22⋊Q8—21no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×Q8C2×Dic1912yes—
220C4×Q8C22⋊D1912yes—
221#117—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—382no—
224C2×C4⋊C4—381no—
225C2×C4⋊C4C22⋊D1911yescharacteristic
226C2×C42—21no—
227C2×C42—191no—
228C2×C42—191no—
229C2×C42—381no—
230C2×C42—381no—
231C2×C42—381no—
232C2×C42C22×D1911yescharacteristic
233#107—22no—
234C4⋊C8—381no—
235C4⋊C8—381no—
236C4⋊C8—381no—
237C4⋊C8C2×Dic1912yes—
238#103—22no—
239#103—22no—
240C22⋊C8—21no—
241C22⋊C8—381no—
242C4×C8—21no—
243C4×C8—381no—
244#95—192no—
245#95—382no—
246#95—382no—
247#95—382no—
248C19#923611yescharacteristic, complemented, Sylow
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—42no—
253C2×Q8C22⋊Dic1912yes—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—381no—
257C22×C4—381no—
258C22×C4—382no—
259C22×C4D4×D1911yescharacteristic
260C22×C4D4×D1911yescharacteristic
261C22×C4C2×C22⋊D1911yescharacteristic
262Q16—44no—
263M16—761no—
264M16—761no—
265C2×C8—22no—
266C2×C8—761no—
267C2×C8—761no—
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—762no—
278C4⋊C4—764no—
279C4⋊C4C22⋊Dic1912yes—
280C22⋊C4—41no—
281C42—22no—
282C42—22no—
283C42—41no—
284C42—192no—
285C42—381no—
286C42—381no—
287C42—381no—
288C42—762no—
289C42—762no—
290C42—761no—
291C42—761no—
292C42#6454311yescharacteristic
293C42#6454311yescharacteristic
294C42C22×Dic1911yescharacteristic
295C42C2×C22⋊D1911yescharacteristic
296C23#1059738311yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—42no—
300Q8—42no—
301Q8—81no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—382no—
311C2×C4—382no—
312C2×C4—761no—
313C2×C4—761no—
314C2×C4—761no—
315C2×C4—761no—
316C2×C4—762no—
317C2×C4—762no—
318C2×C4—762no—
319C2×C4Q16×D1911yescharacteristic
320C2×C4#1059736411yescharacteristic
321C2×C4#1059736411yescharacteristic
322C2×C4#1059736511yescharacteristic
323C2×C4D4×Dic1911yescharacteristic
324C2×C4D4×Dic1911yescharacteristic
325C2×C4#1059738111yescharacteristic
326C2×C4#1059738511yescharacteristic
327C2×C4#1059738511yescharacteristic
328C2×C4C2×C22⋊Dic1911yescharacteristic
329C8—42no—
330C8—1521no—
331C8—1521no—
332C22—21no—
333C22—21no—
334C22#1192642411yescharacteristic
335C22#1192669811yescharacteristic
336C22#1192670511yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—81no—
343C4—81no—
344C4—762no—
345C4—762no—
346C4—1522no—
347C4#1192656112yes—
348C4Q16×Dic1911yescharacteristic
349C4#1192665111yescharacteristic
350C4#1192675211yescharacteristic
351C4#1192676811yescharacteristic
352C2—21no—
353C2—21no—
354C2#1456397811yescharacteristic
355C2#1456408411yescharacteristic
356C2#1456413811yescharacteristic
subgroupG/H
centerC2×C4#10597385
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3104C2
socleC22×C19#386
prime radicalC23×C19#120
cosocleC2×C42×C19C23
hypercenter#3104D19
hypocenterC19#9236
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
24. C19×#477C4semidirect
25. C19×#462C4semidirect
112. C4×Dic19Q16semidirect
184. #477Dic19semidirect
185. #462Dic19semidirect
248. C19#9236semidirect

Maximal subgroups

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

subgroupindex
#145661132
#145646132
#145621342
#145620642
#145615372
#145614672
C19×#31042
#923619