Finite Group Databasebeta

← #18078309

Subgroups — #18078309

Order 4864.

902 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 139 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#14571922C211yesmaximal, characteristic
2#14563545C211yesmaximal, characteristic
3C2×#11926280C212yesmaximal, complemented
4#14561514C212yesmaximal, complemented
5C2×C19×#381C211yesmaximal, characteristic
6C2×#10597370C412yescomplemented
7C2×#10597370C2211yescharacteristic
8C2×C22⋊(C19⋊C8)—22no—
9C2×C22⋊(C19⋊C8)C2212yes—
10#11926417—22no—
11#11926417—21no—
12#11926404C412yescomplemented
13#11926404C2211yescharacteristic
14#11926400—21no—
15#11926280—24no—
16C24×C4×C19C2211yescharacteristic
17C22×C22⋊C4×C19—21no—
18C19×#381—24no—
19C2×C19×#95—21no—
20C2×C19×#95C2212yes—
21C25×C19D411yescharacteristic
22C23×C4×C19—22no—
23C23×C4×C19—22no—
24C23×C4×C19—22no—
25C23×C4×C19—44no—
26C23×C4×C19C2×C412yes—
27C23×C4×C19D412yes—
28C23×C4×C19D411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C22×Dic38C2×C411yescharacteristic
31C2×C22⋊C4×C19—24no—
32C2×C22⋊C4×C19—44no—
33C2×C22⋊Dic19—22no—
34C2×C22⋊Dic19—22no—
35C2×C22⋊Dic19—21no—
36C2×C22⋊Dic19—21no—
37C2×C4⋊Dic19C2×C411yescharacteristic
38C2×C4⋊Dic19C2×C412yes—
39#10597370—22no—
40#10597370—22no—
41#10597370—44no—
42C2×Dic19⋊C4—22no—
43C2×Dic19⋊C4—21no—
44C22×C19⋊C8—22no—
45C19×#95—24no—
46C19×#95—22no—
47C19×#95D414yes—
48C19⋊#95—22no—
49C19⋊#95—21no—
50C22⋊(C19⋊C8)—22no—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—44no—
53C24×C19—24no—
54C24×C19—21no—
55C24×C19—21no—
56C24×C19—22no—
57C24×C19—22no—
58C24×C19—42no—
59C24×C19C22⋊C412yes—
60C24×C19C2×D411yescharacteristic
61C22×C4×C19—24no—
62C22×C4×C19—24no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—24no—
66C22×C4×C19—24no—
67C22×C4×C19—24no—
68C22×C4×C19—42no—
69C22×C4×C19—42no—
70C22×C4×C19—42no—
71C22×C4×C19—42no—
72C22×C4×C19—48no—
73C22×C4×C19—48no—
74C22×C4×C19—44no—
75C22×C4×C19—44no—
76C22×C4×C19—42no—
77C22×C4×C19—42no—
78C22×C4×C19C22⋊C412yes—
79C22×C4×C19C22×C411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D412yes—
82C22×C4×C19#4112yes—
83C22×Dic19—21no—
84C22×Dic19—21no—
85C22×Dic19—22no—
86C2×Dic38—22no—
87C2×Dic38—42no—
88C22⋊C4×C19—48no—
89C22⋊Dic19—44no—
90C22⋊Dic19—44no—
91C22⋊Dic19—41no—
92C22⋊Dic19—41no—
93C22⋊Dic19—42no—
94C4⋊Dic19—22no—
95C4⋊Dic19—42no—
96Dic19⋊C4—44no—
97Dic19⋊C4—42no—
98C2×C19⋊C8—44no—
99C2×C19⋊C8—42no—
100#9154—191nomaximal, Sylow
101C23×C19—22no—
102C23×C19—22no—
103C23×C19—24no—
104C23×C19—24no—
105C23×C19—22no—
106C23×C19—22no—
107C23×C19—22no—
108C23×C19—22no—
109C23×C19—22no—
110C23×C19—22no—
111C23×C19—48no—
112C23×C19—48no—
113C23×C19—42no—
114C23×C19—42no—
115C23×C19—42no—
116C23×C19—42no—
117C23×C19#9914yes—
118C23×C19C2×C22⋊C411yescharacteristic
119C23×C19#12011yescharacteristic
120C23×C19#12311yescharacteristic
121C23×C19#13512yes—
122C23×C19#13712yes—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19—22no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19—48no—
131C2×C4×C19—48no—
132C2×C4×C19—42no—
133C2×C4×C19—42no—
134C2×C4×C19—44no—
135C2×C4×C19—44no—
136C2×C4×C19—44no—
137C2×C4×C19—84no—
138C2×C4×C19—84no—
139C2×C4×C19C4×D412yes—
140C2×C4×C19#12112yes—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—42no—
144C2×Dic19—42no—
145C2×Dic19—42no—
146C2×Dic19—42no—
147C2×Dic19—42no—
148Dic38—82no—
149C19⋊C8—82no—
150#2848—191no—
151C2×#381D1911yescharacteristic
152#1779—191no—
153C2×#328—192no—
154#1294—192no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—24no—
160C22×C19—24no—
161C22×C19—24no—
162C22×C19—24no—
163C22×C19—24no—
164C22×C19—48no—
165C22×C19—48no—
166C22×C19—42no—
167C22×C19—42no—
168C22×C19—42no—
169C22×C19—42no—
170C22×C19#38611yescharacteristic
171C22×C19C2×#9912yes—
172C22×C19#41611yescharacteristic
173C22×C19#41911yescharacteristic
174C22×C19#42112yes—
175C22×C19#45212yes—
176C22×C19#48512yes—
177C4×C19—22no—
178C4×C19—22no—
179C4×C19—42no—
180C4×C19—84no—
181Dic19—81no—
182Dic19—81no—
183Dic19—82no—
184C24×C4C2×D1911yescharacteristic
185C2×C22⋊Q8—191no—
186C2×C22⋊Q8—192no—
187C22×C22⋊C4—21no—
188C2×C22⋊C8—192no—
189C2×C22⋊C8—382no—
190#385—382no—
191#385—381no—
192#381—24no—
193#380—192no—
194#380—191no—
195#379—381no—
196C2×#95—21no—
197C2×#95C2×D1912yes—
198#328—384no—
199C2×C19—22no—
200C2×C19—22no—
201C2×C19—44no—
202C2×C19#151112yes—
203C2×C19#151612yes—
204C2×C19#187311yescharacteristic
205C2×C19#189711yescharacteristic
206C2×C19#189811yescharacteristic
207C25C22⋊D1911yescharacteristic
208C22×Q8—191no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—44no—
213C23×C4C4×D1912yes—
214C23×C4D7612yes—
215C23×C4C22⋊D1911yescharacteristic
216C23×C4C22×D1911yescharacteristic
217C22×C8—382no—
218C22⋊Q8—382no—
219C22⋊Q8—382no—
220C22⋊Q8—764no—
221C2×C4⋊C4—191no—
222C2×C4⋊C4—192no—
223C2×C4⋊C4—382no—
224C2×C4⋊C4—381no—
225C2×C22⋊C4—24no—
226C2×C22⋊C4—44no—
227C2×C22⋊C4—382no—
228C2×C22⋊C4—382no—
229C2×C22⋊C4—381no—
230C2×C22⋊C4—381no—
231C22⋊C8—382no—
232C22⋊C8—382no—
233C22⋊C8—764no—
234#95—24no—
235#95—22no—
236#95—382no—
237#95—381no—
238#95C22⋊D1914yes—
239C19#915411yescharacteristic, complemented, Sylow
240C24—21no—
241C24—24no—
242C24—21no—
243C24—22no—
244C24—22no—
245C24—42no—
246C24(C2×D19)⋊C412yes—
247C24C2×C22⋊D1911yescharacteristic
248C2×Q8—382no—
249C2×Q8—762no—
250C22×C4—21no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—21no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—48no—
262C22×C4—48no—
263C22×C4—44no—
264C22×C4—44no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—382no—
268C22×C4—381no—
269C22×C4—381no—
270C22×C4(C2×D19)⋊C412yes—
271C22×C4C2×C4×D1911yescharacteristic
272C22×C4C2×D7611yescharacteristic
273C22×C4#6454112yes—
274C22×C4C2×C22⋊D1912yes—
275C2×C8—764no—
276C2×C8—762no—
277C4⋊C4—382no—
278C4⋊C4—762no—
279C4⋊C4—764no—
280C4⋊C4—762no—
281C22⋊C4—48no—
282C22⋊C4—764no—
283C22⋊C4—762no—
284C22⋊C4—761no—
285C22⋊C4—764no—
286C22⋊C4—761no—
287C23—22no—
288C23—22no—
289C23—24no—
290C23—24no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—48no—
298C23—48no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—42no—
303C23#1059726314yes—
304C23C2×(C2×D19)⋊C411yescharacteristic
305C23#1059737511yescharacteristic
306C23#1059739612yes—
307C23#1059739712yes—
308C23#1059739911yescharacteristic
309Q8—1522no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—48no—
318C2×C4—48no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—84no—
325C2×C4—84no—
326C2×C4—762no—
327C2×C4—762no—
328C2×C4—762no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—762no—
332C2×C4—762no—
333C2×C4C4×C22⋊D1912yes—
334C2×C4#1059737612yes—
335C8—1522no—
336C22—24no—
337C22—24no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—24no—
343C22—24no—
344C22—24no—
345C22—48no—
346C22—48no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22#1192642311yescharacteristic
352C22C2×#1059726312yes—
353C22#1192653811yescharacteristic
354C22#1192655211yescharacteristic
355C22#1192656212yes—
356C22#1192670612yes—
357C22#1192688512yes—
358C4—22no—
359C4—22no—
360C4—42no—
361C4—84no—
362C4—1522no—
363C4—1521no—
364C4—1521no—
365C2—22no—
366C2—22no—
367C2—44no—
368C2#1456216712yes—
369C2#1456218912yes—
370C2#1456394711yescharacteristic
371C2#1456408311yescharacteristic
372C2#1456408811yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#381C2
socleC23×C19C2×C22⋊C4
prime radicalC25×C19D4
cosocleC23×C4×C19C23
hypercenterC2×#381D19
hypocenterC19#9154
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. C2×#11926280C2semidirect
4. #14561514C2semidirect
6. C2×#10597370C4semidirect
12. #11926404C4semidirect
239. C19#9154semidirect

Maximal subgroups

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

subgroupindex
#145719222
#145635452
C2×#119262802
#145615142
C2×C19×#3812
#915419