Finite Group Databasebeta

← #18081677

Subgroups — #18081677

Order 4864.

764 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14571980C211yesmaximal, characteristic
2C2×#11926279C214yesmaximal, complemented
3#14561862C211yesmaximal, characteristic, complemented
4C19×#1797C211yesmaximal, characteristic, complemented
5C2×#10597320C411yescharacteristic, complemented
6C2×#10597376—21no—
7C2×#10597376—21no—
8C2×#10597376C2212yes—
9#11926446—21no—
10#11926446—21no—
11#11926446C412yescomplemented
12#11926414C411yescharacteristic, complemented
13C2×C19⋊#95—21no—
14C2×C19⋊#95—21no—
15C2×C19⋊#95C2212yes—
16#11926279—28no—
17C22×C42×C19C2211yescharacteristic
18C2×C19×C4⋊C8—21no—
19C2×C19×C22⋊C8C2212yes—
20C19×#336—21no—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—22no—
25C23×Dic19—22no—
26C22×D76—21no—
27C22×D76—21no—
28C22×D76C2×C412yes—
29C22×C8×C19—22no—
30C2×C42×C19—42no—
31C2×C42×C19C2×C411yescharacteristic
32C2×C42×C19C2×C411yescharacteristic
33C2×C42×C19D411yescharacteristic
34C2×C42×C19D411yescharacteristic
35#10597376—24no—
36#10597376—24no—
37#10597376—44no—
38#10597376—42no—
39#10597376—42no—
40C2×(C2×D19)⋊C4—22no—
41C2×(C2×D19)⋊C4—22no—
42C2×(C2×D19)⋊C4—22no—
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19C2×C412yes—
46#10597320—42no—
47C19×C4⋊C8—42no—
48C19×C22⋊C8—24no—
49C19⋊#95—22no—
50C19⋊#95—42no—
51C19⋊#95—42no—
52C19⋊#95D414yescomplemented
53C24×C19C2×D411yescharacteristic
54C23×D19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—41no—
58C22×C4×C19—41no—
59C22×C4×C19—41no—
60C22×C4×C19—41no—
61C22×C4×C19—41no—
62C22×C4×C19C22⋊C411yescharacteristic
63C22×C4×C19C22⋊C411yescharacteristic
64C22×C4×C19C22⋊C411yescharacteristic
65C22×C4×C19C22⋊C411yescharacteristic
66C22×C4×C19D812yes—
67C22×C4×C19SD1612yes—
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D412yes—
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19#4112yes—
72C2×C22⋊D19—44no—
73C2×C22⋊D19—42no—
74C2×C22⋊D19—42no—
75C2×C22⋊D19—44no—
76C22×Dic19—22no—
77C22×Dic19—24no—
78C22×Dic19—42no—
79C22×Dic19—42no—
80C22×Dic19—42no—
81C22×Dic19—42no—
82C22×Dic19—42no—
83C22×Dic19—42no—
84C2×D76—24no—
85C2×D76—42no—
86C2×D76—42no—
87C2×D76—42no—
88C2×D76—42no—
89C2×D76—42no—
90C2×D76—42no—
91C2×D76—42no—
92C2×D76—42no—
93C2×C8×C19—42no—
94C2×C8×C19—42no—
95C2×C8×C19—42no—
96C42×C19—22no—
97C42×C19—22no—
98C42×C19—41no—
99C42×C19—41no—
100(C2×D19)⋊C4—44no—
101(C2×D19)⋊C4—44no—
102(C2×D19)⋊C4—42no—
103(C2×D19)⋊C4—42no—
104C4⋊Dic19—24no—
105C4⋊Dic19—42no—
106C4⋊Dic19—42no—
107#9715—191nomaximal, Sylow
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—21no—
112C23×C19C2×C22⋊C411yescharacteristic
113C23×C19#12112yes—
114C23×C19C2×D811yescharacteristic
115C23×C19C2×SD1611yescharacteristic
116C23×C19AGL(1,ℤ/8)12yes—
117C22×D19—42no—
118C22×D19—42no—
119C22×D19—42no—
120C22×D19—42no—
121C22×D19—42no—
122C22×D19—42no—
123C22×D19—42no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—42no—
140C2×C4×C19—42no—
141C2×C4×C19—44no—
142C2×C4×C19#9912yes—
143C2×C4×C19#10212yes—
144C2×C4×C19#10212yes—
145C2×C4×C19C4×D412yes—
146C2×C4×C19#12411yescharacteristic
147C2×C4×C19#12711yescharacteristic
148C22⋊D19—84no—
149C22⋊D19—84no—
150C2×Dic19—44no—
151C2×Dic19—44no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155C2×Dic19—44no—
156C2×Dic19—82no—
157C2×Dic19—82no—
158C2×Dic19—82no—
159C2×Dic19—82no—
160D76—84no—
161D76—84no—
162D76—84no—
163C8×C19—82no—
164#2856—191no—
165#1797D1911yescharacteristic, complemented
166C2×#327—194no—
167#1434—191no—
168C22×C19—22no—
169C22×C19—22no—
170C22×C19—22no—
171C22×C19—22no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19#39011yescharacteristic
177C22×C19C2×#9911yescharacteristic
178C22×C19#41011yescharacteristic
179C22×C19C2×#10211yescharacteristic
180C22×C19#41811yescharacteristic
181C22×C19#42111yescharacteristic
182C22×C19#42111yescharacteristic
183C22×C19#45912yes—
184C22×C19#46012yes—
185C2×D19—82no—
186C2×D19—82no—
187C2×D19—82no—
188C2×D19—82no—
189C2×D19—82no—
190C2×D19—82no—
191C2×D19—82no—
192C4×C19—21no—
193C4×C19—22no—
194C4×C19—21no—
195C4×C19—22no—
196C4×C19—22no—
197C4×C19—22no—
198C4×C19—41no—
199Dic19—84no—
200Dic19—82no—
201C2×#127—191no—
202C2×#121—192no—
203C2×#121—381no—
204C2×#121—381no—
205C22×C42C2×D1911yescharacteristic
206C2×C4⋊C8—21no—
207C2×C22⋊C8C2×D1912yes—
208#390—192no—
209#390—381no—
210#390—381no—
211#384—191no—
212C2×#95—192no—
213C2×#95—381no—
214C2×#95—381no—
215#336—21no—
216#327—388no—
217C2×C19—22no—
218C2×C19—22no—
219C2×C19#151011yescharacteristic
220C2×C19#151411yescharacteristic
221C2×C19#151711yescharacteristic
222C2×C19#151911yescharacteristic
223C2×C19#196311yescharacteristic
224C2×C19#196411yescharacteristic
225C2×C19#198211yescharacteristic
226D19—162no—
227C22×D4—192no—
228C22×D4—382no—
229C22×D4—381no—
230C22×D4—381no—
231C23×C4—382no—
232C23×C4D7611yescharacteristic
233C23×C4D7611yescharacteristic
234C23×C4C22×D1911yescharacteristic
235C22×C8—22no—
236#127—762no—
237#121—384no—
238#121—384no—
239#121—764no—
240#121—762no—
241#121—762no—
242C2×C4⋊C4—192no—
243C2×C4⋊C4—381no—
244C2×C4⋊C4—381no—
245C2×C22⋊C4—382no—
246C2×C22⋊C4—382no—
247C2×C22⋊C4—382no—
248C2×C42—42no—
249C2×C42C4×D1911yescharacteristic
250C2×C42C4×D1911yescharacteristic
251C2×C42C22⋊D1911yescharacteristic
252C2×C42C22⋊D1911yescharacteristic
253C4⋊C8—42no—
254C22⋊C8—24no—
255#95—194no—
256#95—382no—
257#95—762no—
258#95—762no—
259C19#971511yescharacteristic, complemented, Sylow
260C24—382no—
261C24C2×D7611yescharacteristic
262C2×D4—384no—
263C2×D4—762no—
264C2×D4—762no—
265C2×D4—762no—
266C2×D4—762no—
267C2×D4—762no—
268C2×D4—762no—
269C2×D4—764no—
270C2×D4—762no—
271C2×D4—762no—
272C2×D4—764no—
273C2×D4—762no—
274C2×D4—762no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—384no—
283C22×C4—382no—
284C22×C4—762no—
285C22×C4—762no—
286C22×C4—762no—
287C22×C4—762no—
288C22×C4—762no—
289C22×C4—762no—
290C22×C4#6451612yes—
291C22×C4D15212yes—
292C22×C4(C2×D19)⋊C411yescharacteristic
293C22×C4(C2×D19)⋊C411yescharacteristic
294C22×C4(C2×D19)⋊C411yescharacteristic
295C22×C4(C2×D19)⋊C411yescharacteristic
296C22×C4C2×C4×D1911yescharacteristic
297C22×C4D4×D1912yes—
298C22×C4#6454512yes—
299C22×C4C2×C22⋊D1911yescharacteristic
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—42no—
303C4⋊C4—384no—
304C4⋊C4—762no—
305C4⋊C4—762no—
306C22⋊C4—764no—
307C22⋊C4—762no—
308C22⋊C4—762no—
309C22⋊C4—764no—
310C42—22no—
311C42—22no—
312C42—41no—
313C42—41no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—762no—
319C23—762no—
320C23—762no—
321C23—762no—
322C23—762no—
323C23—762no—
324C23—762no—
325C23#1059734112yes—
326C23C2×#6451611yescharacteristic
327C23C2×D15211yescharacteristic
328C23#1059735412yes—
329C23C2×(C2×D19)⋊C411yescharacteristic
330D4—1524no—
331D4—1524no—
332D4—1524no—
333D4—1524no—
334D4—1524no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—44no—
353C2×C4—764no—
354C2×C4—764no—
355C2×C4—762no—
356C2×C4—762no—
357C2×C4—762no—
358C2×C4—764no—
359C2×C4—1522no—
360C2×C4—1522no—
361C2×C4—1522no—
362C2×C4—1522no—
363C2×C4#1059726312yes—
364C2×C4#1059727812yes—
365C2×C4#1059727812yes—
366C2×C4#1059733912yes—
367C2×C4#1059738611yescharacteristic
368C2×C4#1059739311yescharacteristic
369C8—82no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—1522no—
379C22—1522no—
380C22—1522no—
381C22—1522no—
382C22—1522no—
383C22—1522no—
384C22—1522no—
385C22#1192644511yescharacteristic
386C22C2×#1059726311yescharacteristic
387C22#1192651711yescharacteristic
388C22C2×#1059727811yescharacteristic
389C22#1192655011yescharacteristic
390C22#1192656011yescharacteristic
391C22#1192656011yescharacteristic
392C22#1192674012yes—
393C22#1192674512yes—
394C4—22no—
395C4—21no—
396C4—21no—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—41no—
401C4—1524no—
402C4—1522no—
403C2—22no—
404C2—22no—
405C2—3042no—
406C2#1456216511yescharacteristic
407C2#1456218311yescharacteristic
408C2#1456219611yescharacteristic
409C2#1456220411yescharacteristic
410C2#1456446611yescharacteristic
411C2#1456447011yescharacteristic
412C2#1456456111yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1797C2
socleC23×C19C2×C22⋊C4
prime radical#14571980C2
cosocleC23×C4×C19C23
hypercenter#1797D19
hypocenterC19#9715
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#11926279C2semidirect
3. #14561862C2semidirect
4. C19×#1797C2semidirect
5. C2×#10597320C4semidirect
11. #11926446C4semidirect
12. #11926414C4semidirect
52. C19⋊#95D4semidirect
165. #1797D19semidirect
259. C19#9715semidirect

Maximal subgroups

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

subgroupindex
#145719802
C2×#119262792
#145618622
C19×#17972
#971519