Finite Group Databasebeta

← #18078327

Subgroups — #18078327

Order 4864.

980 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 980 conjugacy classes of subgroups — too many to draw. Only its 135 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#14571917C211yesmaximal, characteristic
2C2×#11926407C211yesmaximal, characteristic, complemented
3C2×#11926279C212yesmaximal, complemented
4#14561515C212yesmaximal, complemented
5C19×#1779C211yesmaximal, characteristic, complemented
6C2×#10597376C412yescomplemented
7C2×#10597376C2211yescharacteristic
8C2×#10597399—21no—
9C22×C22⋊Dic19—21no—
10#11926423—22no—
11#11926423—21no—
12#11926407—24no—
13#11926404C412yescomplemented
14#11926404C2211yescharacteristic
15C2×C19⋊#95—21no—
16C2×C19⋊#95C2212yes—
17#11926279—24no—
18C24×C4×C19C2211yescharacteristic
19C2×C19×C22⋊C8—22no—
20C2×C19×C22⋊C8C2212yes—
21C25×C19D411yescharacteristic
22C23×C4×C19—22no—
23C23×C4×C19—22no—
24C23×C4×C19—44no—
25C23×C4×C19C2×C412yes—
26C23×C4×C19D412yes—
27C23×C4×C19D411yescharacteristic
28C23×C4×C19C2311yescharacteristic
29C22×C22⋊D19—22no—
30C22×C22⋊D19—21no—
31C23×Dic19—22no—
32C22×D76C2×C411yescharacteristic
33C22×C8×C19—22no—
34#10597399—44no—
35C2×C22⋊Dic19—24no—
36C2×C22⋊Dic19—22no—
37C2×C22⋊Dic19—21no—
38C2×C22⋊Dic19—44no—
39#10597376—22no—
40#10597376—22no—
41#10597376—44no—
42C2×(C2×D19)⋊C4—22no—
43C2×(C2×D19)⋊C4—21no—
44C2×C4⋊Dic19C2×C411yescharacteristic
45C2×C4⋊Dic19C2×C412yes—
46C19×C22⋊C8—22no—
47C19×C22⋊C8—22no—
48C19×C22⋊C8—44no—
49C19⋊#95—24no—
50C19⋊#95—22no—
51C19⋊#95—22no—
52C19⋊#95—21no—
53C19⋊#95D414yescomplemented
54C24×C19—24no—
55C24×C19—21no—
56C24×C19—21no—
57C24×C19—22no—
58C24×C19—22no—
59C24×C19—42no—
60C24×C19C22⋊C412yes—
61C24×C19C2×D411yescharacteristic
62C23×D19—21no—
63C22×C4×C19—24no—
64C22×C4×C19—24no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—24no—
68C22×C4×C19—24no—
69C22×C4×C19—42no—
70C22×C4×C19—42no—
71C22×C4×C19—42no—
72C22×C4×C19—42no—
73C22×C4×C19—48no—
74C22×C4×C19—48no—
75C22×C4×C19C22⋊C412yes—
76C22×C4×C19C22×C411yescharacteristic
77C22×C4×C19C2×D412yes—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19#4112yes—
80C2×C22⋊D19—44no—
81C2×C22⋊D19—44no—
82C2×C22⋊D19—44no—
83C2×C22⋊D19—41no—
84C2×C22⋊D19—41no—
85C2×C22⋊D19—42no—
86C2×C22⋊D19—42no—
87C22×Dic19—21no—
88C22×Dic19—22no—
89C22×Dic19—24no—
90C22×Dic19—44no—
91C22×Dic19—44no—
92C22×Dic19—42no—
93C22×Dic19—42no—
94C2×D76—22no—
95C2×D76—42no—
96C2×C8×C19—44no—
97C2×C8×C19—42no—
98C22⋊Dic19—48no—
99C22⋊Dic19—44no—
100C22⋊Dic19—42no—
101(C2×D19)⋊C4—44no—
102(C2×D19)⋊C4—42no—
103C4⋊Dic19—22no—
104C4⋊Dic19—42no—
105#9158—191nomaximal, Sylow
106C23×C19—22no—
107C23×C19—22no—
108C23×C19—24no—
109C23×C19—24no—
110C23×C19—22no—
111C23×C19—22no—
112C23×C19—22no—
113C23×C19—22no—
114C23×C19—22no—
115C23×C19—22no—
116C23×C19—48no—
117C23×C19—48no—
118C23×C19—42no—
119C23×C19—42no—
120C23×C19—42no—
121C23×C19—42no—
122C23×C19#9914yes—
123C23×C19C2×C22⋊C411yescharacteristic
124C23×C19#12011yescharacteristic
125C23×C19#12311yescharacteristic
126C23×C19#13512yes—
127C23×C19AGL(1,ℤ/8)12yes—
128C22×D19—41no—
129C22×D19—42no—
130C22×D19—41no—
131C22×D19—41no—
132C22×D19—42no—
133C2×C4×C19—22no—
134C2×C4×C19—22no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—22no—
138C2×C4×C19—42no—
139C2×C4×C19—42no—
140C2×C4×C19—48no—
141C2×C4×C19—48no—
142C2×C4×C19—42no—
143C2×C4×C19—42no—
144C2×C4×C19C4×D412yes—
145C2×C4×C19#12112yes—
146C22⋊D19—88no—
147C22⋊D19—82no—
148C22⋊D19—82no—
149C2×Dic19—44no—
150C2×Dic19—44no—
151C2×Dic19—41no—
152C2×Dic19—42no—
153C2×Dic19—41no—
154C2×Dic19—41no—
155C2×Dic19—42no—
156C2×Dic19—42no—
157C2×Dic19—44no—
158C2×Dic19—84no—
159C2×Dic19—84no—
160D76—82no—
161C8×C19—82no—
162#2847—191no—
163C2×#381—191no—
164#1779D1911yescharacteristic, complemented
165C2×#327—192no—
166#1294—192no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—24no—
172C22×C19—24no—
173C22×C19—24no—
174C22×C19—24no—
175C22×C19—24no—
176C22×C19—48no—
177C22×C19—48no—
178C22×C19—42no—
179C22×C19—42no—
180C22×C19—42no—
181C22×C19—42no—
182C22×C19#38611yescharacteristic
183C22×C19C2×#9912yes—
184C22×C19#41611yescharacteristic
185C22×C19#41811yescharacteristic
186C22×C19#42112yes—
187C22×C19#44912yes—
188C22×C19#48212yes—
189C2×D19—81no—
190C2×D19—81no—
191C2×D19—81no—
192C2×D19—82no—
193C2×D19—82no—
194C4×C19—22no—
195C4×C19—22no—
196C4×C19—42no—
197Dic19—84no—
198Dic19—81no—
199Dic19—82no—
200C24×C4C2×D1911yescharacteristic
201C2×#121—191no—
202C2×#121—192no—
203C2×#120—381no—
204C22×C22⋊C4—381no—
205C2×C22⋊C8—22no—
206C2×C22⋊C8C2×D1912yes—
207#386—381no—
208#386—382no—
209#381—384no—
210#380—192no—
211#380—191no—
212C2×#95—192no—
213C2×#95—381no—
214#327—384no—
215C2×C19—22no—
216C2×C19—22no—
217C2×C19—44no—
218C2×C19#151012yes—
219C2×C19#151612yes—
220C2×C19#187511yescharacteristic
221C2×C19#189711yescharacteristic
222C2×C19#189811yescharacteristic
223D19—161no—
224C25D7611yescharacteristic
225C22×D4—191no—
226C22×D4—382no—
227C22×D4—381no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—44no—
231C23×C4—382no—
232C23×C4C4×D1912yes—
233C23×C4D7611yescharacteristic
234C23×C4C22⋊D1912yes—
235C23×C4C22×D1911yescharacteristic
236C22×C8—22no—
237#121—382no—
238#121—382no—
239#121—764no—
240#120—764no—
241C2×C4⋊C4—191no—
242C2×C4⋊C4—192no—
243C2×C22⋊C4—384no—
244C2×C22⋊C4—382no—
245C2×C22⋊C4—381no—
246C2×C22⋊C4—382no—
247C2×C22⋊C4—381no—
248C2×C22⋊C4—764no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251C22⋊C8—44no—
252#95—194no—
253#95—384no—
254#95—382no—
255#95—382no—
256#95—381no—
257C19#915811yescharacteristic, complemented, Sylow
258C24—24no—
259C24—21no—
260C24—21no—
261C24—22no—
262C24—22no—
263C24—42no—
264C24—381no—
265C24(C2×D19)⋊C412yes—
266C24C2×D7611yescharacteristic
267C2×D4—382no—
268C2×D4—762no—
269C2×D4—764no—
270C2×D4—764no—
271C2×D4—764no—
272C2×D4—761no—
273C2×D4—761no—
274C2×D4—762no—
275C2×D4—762no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—48no—
287C22×C4—48no—
288C22×C4—384no—
289C22×C4—381no—
290C22×C4—382no—
291C22×C4—764no—
292C22×C4—764no—
293C22×C4—762no—
294C22×C4—762no—
295C22×C4(C2×D19)⋊C412yes—
296C22×C4C2×C4×D1911yescharacteristic
297C22×C4D4×D1912yes—
298C22×C4#6454312yes—
299C22×C4C2×C22⋊D1911yescharacteristic
300C2×C8—44no—
301C2×C8—42no—
302C4⋊C4—382no—
303C4⋊C4—762no—
304C22⋊C4—764no—
305C22⋊C4—768no—
306C22⋊C4—764no—
307C22⋊C4—762no—
308C22⋊C4—762no—
309C23—22no—
310C23—22no—
311C23—24no—
312C23—24no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—48no—
320C23—48no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—761no—
326C23—761no—
327C23—762no—
328C23—761no—
329C23—762no—
330C23#1059726314yes—
331C23#1059732811yescharacteristic
332C23#1059733211yescharacteristic
333C23#1059735012yes—
334C23#1059735412yes—
335C23C2×(C2×D19)⋊C411yescharacteristic
336D4—1522no—
337D4—1528no—
338D4—1522no—
339D4—1522no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—48no—
348C2×C4—48no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—764no—
352C2×C4—764no—
353C2×C4—761no—
354C2×C4—761no—
355C2×C4—762no—
356C2×C4—762no—
357C2×C4—761no—
358C2×C4—764no—
359C2×C4—762no—
360C2×C4—1524no—
361C2×C4—1524no—
362C2×C4(C22⋊D19)⋊C412yes—
363C2×C4#1059738512yes—
364C8—82no—
365C22—24no—
366C22—24no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—24no—
372C22—24no—
373C22—24no—
374C22—48no—
375C22—48no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22—1521no—
381C22—1522no—
382C22—1522no—
383C22—1521no—
384C22—1521no—
385C22#1192642111yescharacteristic
386C22C2×#1059726312yes—
387C22#1192654111yescharacteristic
388C22#1192655011yescharacteristic
389C22#1192656012yes—
390C22#1192669112yes—
391C22#1192686912yes—
392C4—22no—
393C4—22no—
394C4—42no—
395C4—1524no—
396C4—1521no—
397C4—1522no—
398C2—22no—
399C2—22no—
400C2—44no—
401C2—3041no—
402C2#1456216512yes—
403C2#1456219212yes—
404C2#1456395511yescharacteristic
405C2#1456408111yescharacteristic
406C2#1456408611yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1779C2
socleC23×C19C2×C22⋊C4
prime radical#14571917C2
cosocleC23×C4×C19C23
hypercenter#1779D19
hypocenterC19#9158
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. C2×#11926407C2semidirect
3. C2×#11926279C2semidirect
4. #14561515C2semidirect
5. C19×#1779C2semidirect
6. C2×#10597376C4semidirect
13. #11926404C4semidirect
53. C19⋊#95D4semidirect
164. #1779D19semidirect
257. C19#9158semidirect

Maximal subgroups

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

subgroupindex
#145719172
C2×#119264072
C2×#119262792
#145615152
C19×#17792
#915819