Finite Group Databasebeta

← #18074002

Subgroups — #18074002

Order 4864.

876 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563703C211yesmaximal, characteristic
2C2×#11926281C214yesmaximal
3#14561862C211yesmaximal, characteristic
4C2×C19×#533C211yesmaximal, characteristic
5C2×C22⋊(C19⋊C8)C2212yes—
6C2×C19⋊#95—21no—
7C2×C19⋊#95—21no—
8C2×C19⋊#95C2212yes—
9#11926299—21no—
10#11926299—21no—
11#11926281—28no—
12C19×#533—28no—
13C2×C19×C4⋊Q8C411yescharacteristic, complemented
14C2×C19×C4⋊Q8C411yescharacteristic, complemented
15C2×C19×#125—21no—
16C2×C19×C22⋊Q8—21no—
17C2×C19×C22⋊Q8C2212yes—
18C2×C4×Q8×C19—21no—
19C2×C4×Q8×C19C412yescomplemented
20C2×C19×#117—21no—
21C22×C42×C19C2211yescharacteristic
22C22×Q8×C19—21no—
23C22×Q8×C19C2×C412yes—
24C23×C4×C19D411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C23×Dic19—22no—
28C19×C4⋊Q8—24no—
29C19×C4⋊Q8—24no—
30C19×#125—28no—
31C19×C22⋊Q8—28no—
32C19×C22⋊Q8—24no—
33C19×C22⋊Q8D418yes—
34C4×Q8×C19—28no—
35C4×Q8×C19—24no—
36C4×Q8×C19—24no—
37C19×#117—28no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—22no—
42C2×C4⋊C4×C19—22no—
43C2×C4⋊C4×C19C2×C412yes—
44C2×C22⋊C4×C19—22no—
45C2×C42×C19—22no—
46C2×C42×C19—24no—
47C2×C42×C19C2×C411yescharacteristic
48C2×C42×C19C2×C411yescharacteristic
49C2×C42×C19D411yescharacteristic
50C2×C42×C19D411yescharacteristic
51C22×C19⋊C8—22no—
52C19⋊#95—24no—
53C19⋊#95—24no—
54C19⋊#95—42no—
55C22⋊(C19⋊C8)—24no—
56C24×C19C2×D411yescharacteristic
57C2×Q8×C19—24no—
58C2×Q8×C19—22no—
59C2×Q8×C19—42no—
60C2×Q8×C19—42no—
61C2×Q8×C19—42no—
62C2×Q8×C19—42no—
63C2×Q8×C19C22⋊C414yes—
64C22×C4×C19—22no—
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—22no—
68C22×C4×C19—22no—
69C22×C4×C19—22no—
70C22×C4×C19—41no—
71C22×C4×C19—41no—
72C22×C4×C19—41no—
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19SD1612yes—
78C22×C4×C19Q1612yes—
79C22×C4×C19C22×C411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D414yes—
82C22×Dic19—24no—
83C22×Dic19—42no—
84C22×Dic19—42no—
85C22×Dic19—42no—
86C22×Dic19—42no—
87C22×Dic19—42no—
88C22×Dic19—42no—
89C4⋊C4×C19—24no—
90C4⋊C4×C19—24no—
91C4⋊C4×C19—28no—
92C4⋊C4×C19—24no—
93C4⋊C4×C19—22no—
94C4⋊C4×C19—28no—
95C4⋊C4×C19C22⋊C414yes—
96C22⋊C4×C19—28no—
97C42×C19—28no—
98C42×C19—22no—
99C42×C19—22no—
100C42×C19—22no—
101C42×C19—22no—
102C2×C19⋊C8—42no—
103C2×C19⋊C8—42no—
104C2×C19⋊C8—42no—
105#8333—191nomaximal, Sylow
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19C2×C22⋊C411yescharacteristic
111C23×C19#12012yes—
112C23×C19C2×SD1611yescharacteristic
113C23×C19C2×Q1611yescharacteristic
114C23×C19#13712yes—
115Q8×C19—44no—
116Q8×C19—44no—
117Q8×C19—48no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—24no—
129C2×C4×C19—24no—
130C2×C4×C19—21no—
131C2×C4×C19—24no—
132C2×C4×C19—24no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—44no—
136C2×C4×C19—44no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—42no—
140C2×C4×C19—42no—
141C2×C4×C19#10312yes—
142C2×C4×C19#10312yes—
143C2×C4×C19#10412yes—
144C2×C4×C19C2×C22⋊C412yes—
145C2×C4×C19#12012yes—
146C2×Dic19—44no—
147C2×Dic19—44no—
148C2×Dic19—44no—
149C2×Dic19—82no—
150C2×Dic19—82no—
151C2×Dic19—82no—
152C2×Dic19—82no—
153C19⋊C8—82no—
154C2×#533D1911yescharacteristic
155#1817—191no—
156C2×#328—194no—
157#1434—191no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—22no—
161C22×C19—22no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—22no—
165C22×C19—22no—
166C22×C19#37911yescharacteristic
167C22×C19#41011yescharacteristic
168C22×C19#41011yescharacteristic
169C22×C19C2×#10311yescharacteristic
170C22×C19#41911yescharacteristic
171C22×C19C2×#10411yescharacteristic
172C22×C19#42111yescharacteristic
173C22×C19#44812yes—
174C22×C19#45112yes—
175C4×C19—22no—
176C4×C19—22no—
177C4×C19—22no—
178C4×C19—22no—
179C4×C19—22no—
180C4×C19—44no—
181C4×C19—41no—
182C4×C19—44no—
183Dic19—84no—
184#533—28no—
185C2×C4⋊Q8Dic1911yescharacteristic, complemented
186C2×C4⋊Q8Dic1911yescharacteristic, complemented
187C2×#125—21no—
188C2×C22⋊Q8—21no—
189C2×C22⋊Q8C2×D1912yes—
190C2×C4×Q8—21no—
191C2×C4×Q8Dic1912yescomplemented
192C2×#117—21no—
193C22×C42C2×D1911yescharacteristic
194C2×C22⋊C8—192no—
195C2×#95—192no—
196C2×#95—381no—
197C2×#95—381no—
198#336—381no—
199#336—381no—
200#328—388no—
201C2×C19—22no—
202C2×C19—22no—
203C2×C19#150311yescharacteristic
204C2×C19#150611yescharacteristic
205C2×C19#151511yescharacteristic
206C2×C19#151811yescharacteristic
207C2×C19#178211yescharacteristic
208C2×C19#178711yescharacteristic
209C2×C19#178911yescharacteristic
210C22×Q8—21no—
211C22×Q8C2×Dic1912yes—
212C23×C4—382no—
213C23×C4C22⋊D1911yescharacteristic
214C23×C4C22⋊D1911yescharacteristic
215C23×C4C22×D1911yescharacteristic
216C22×C8—382no—
217C4⋊Q8—24no—
218C4⋊Q8—24no—
219#125—28no—
220C22⋊Q8—28no—
221C22⋊Q8—24no—
222C22⋊Q8C22⋊D1918yes—
223C4×Q8—28no—
224C4×Q8—24no—
225C4×Q8—24no—
226#117—28no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4C2×Dic1912yes—
233C2×C22⋊C4—22no—
234C2×C42—22no—
235C2×C42—24no—
236C2×C42C2×Dic1911yescharacteristic
237C2×C42C2×Dic1911yescharacteristic
238C2×C42C22⋊D1911yescharacteristic
239C2×C42C22⋊D1911yescharacteristic
240C22⋊C8—384no—
241#95—384no—
242#95—384no—
243#95—762no—
244C19#833311yescharacteristic, complemented, Sylow
245C24C2×C22⋊D1911yescharacteristic
246C2×Q8—24no—
247C2×Q8—22no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8C22⋊Dic1914yes—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—384no—
263C22×C4—762no—
264C22×C4—762no—
265C22×C4—762no—
266C22×C4—762no—
267C22×C4—762no—
268C22×C4—762no—
269C22×C4#6452712yes—
270C22×C4#6452812yes—
271C22×C4C22⋊Dic1911yescharacteristic
272C22×C4C22⋊Dic1911yescharacteristic
273C22×C4C22⋊Dic1911yescharacteristic
274C22×C4C22⋊Dic1911yescharacteristic
275C22×C4C22×Dic1911yescharacteristic
276C22×C4C2×C22⋊D1911yescharacteristic
277C22×C4C2×C22⋊D1914yes—
278C2×C8—762no—
279C2×C8—762no—
280C2×C8—762no—
281C4⋊C4—24no—
282C4⋊C4—24no—
283C4⋊C4—28no—
284C4⋊C4—24no—
285C4⋊C4—22no—
286C4⋊C4—28no—
287C4⋊C4C22⋊Dic1914yes—
288C22⋊C4—28no—
289C42—28no—
290C42—22no—
291C42—22no—
292C42—22no—
293C42—22no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23C2×#6452711yescharacteristic
299C23#1059738812yes—
300C23C2×#6452811yescharacteristic
301C23C2×C22⋊Dic1911yescharacteristic
302C23#1059739912yes—
303Q8—44no—
304Q8—44no—
305Q8—48no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—764no—
330C2×C4—764no—
331C2×C4—764no—
332C2×C4—1522no—
333C2×C4—1522no—
334C2×C4—1522no—
335C2×C4—1522no—
336C2×C4#1059729212yes—
337C2×C4#1059729212yes—
338C2×C4#1059729412yes—
339C2×C4C2×C22⋊Dic1912yes—
340C2×C4#1059739912yes—
341C8—1522no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—22no—
346C22—21no—
347C22—21no—
348C22—22no—
349C22—22no—
350C22#1192640011yescharacteristic
351C22#1192651811yescharacteristic
352C22#1192651811yescharacteristic
353C22C2×#1059729211yescharacteristic
354C22#1192655311yescharacteristic
355C22C2×#1059729411yescharacteristic
356C22#1192656111yescharacteristic
357C22#1192668312yes—
358C22#1192670012yes—
359C4—22no—
360C4—22no—
361C4—22no—
362C4—22no—
363C4—22no—
364C4—44no—
365C4—41no—
366C4—44no—
367C4—1524no—
368C2—22no—
369C2—22no—
370C2#1456213411yescharacteristic
371C2#1456214711yescharacteristic
372C2#1456218611yescharacteristic
373C2#1456219911yescharacteristic
374C2#1456355311yescharacteristic
375C2#1456357011yescharacteristic
376C2#1456357911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#533C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC2×#533D19
hypocenterC19#8333
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
13. C2×C19×C4⋊Q8C4semidirect
14. C2×C19×C4⋊Q8C4semidirect
19. C2×C4×Q8×C19C4semidirect
185. C2×C4⋊Q8Dic19semidirect
186. C2×C4⋊Q8Dic19semidirect
191. C2×C4×Q8Dic19semidirect
244. C19#8333semidirect

Maximal subgroups

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

subgroupindex
#145637032
C2×#119262812
#145618622
C2×C19×#5332
#833319