Finite Group Databasebeta

← #18075068

Subgroups — #18075068

Order 4864.

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

normal subgroups only

This group has 910 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#14562361C212yesmaximal, complemented
2#14562259C212yesmaximal, complemented
3#14561969C212yesmaximal, complemented
4C2×C19×#536C211yesmaximal, characteristic
5#11926601C2214yes—
6#11926293—24no—
7#11926284—24no—
8#11926270—22no—
9#11926268—22no—
10C22×#41×C19C411yescharacteristic
11C23×Q8×C19C411yescharacteristic
12C19×#536—24no—
13C19×#536—24no—
14C2×C19×C4⋊Q8C411yescharacteristic
15C2×C19×C4⋊Q8C2211yescharacteristic
16C2×C19×#124C411yescharacteristic
17C2×C19×#124C2211yescharacteristic
18C2×C19×#123—22no—
19C2×C19×C22⋊Q8—22no—
20C2×C19×#117C2211yescharacteristic
21C2×#41×C19—22no—
22C2×#41×C19—22no—
23C2×#41×C19—42no—
24C2×#41×C19—42no—
25C22×Q8×C19—22no—
26C22×Q8×C19—22no—
27C22×Q8×C19—21no—
28C22×Q8×C19—42no—
29C22×Q8×C19—42no—
30C22×Q8×C19C2×C411yescharacteristic
31C22×Q8×C19C2×C411yescharacteristic
32C22×Q8×C19C2×C411yescharacteristic
33C22×D4×C19—21no—
34C22×D4×C19C2×C411yescharacteristic
35C23×C4×C19—21no—
36C23×C4×C19—21no—
37C23×C4×C19C2×C411yescharacteristic
38C19×C4⋊Q8—22no—
39C19×C4⋊Q8—22no—
40C19×C4⋊Q8—22no—
41C19×C4⋊Q8D414yes—
42C19×#124—22no—
43C19×#124—22no—
44C19×#124—22no—
45C19×#124D414yes—
46C19×#123—216no—
47C19×C22⋊Q8—216no—
48C19×#117—22no—
49C19×#117—22no—
50C2×C4⋊C4×C19—22no—
51C2×C4⋊C4×C19—22no—
52C2×C4⋊C4×C19D412yes—
53C2×C22⋊C4×C19—22no—
54C2×C22⋊C4×C19—22no—
55C2×C22⋊C4×C19D412yes—
56C2×C42×C19C2×C411yescharacteristic
57C2×C42×C19C2311yescharacteristic
58C22⋊(C19⋊C8)—24no—
59C4⋊(C19⋊C8)—24no—
60#10597260—24no—
61C24×C19—21no—
62C24×C19C22⋊C411yescharacteristic
63#41×C19—48no—
64#41×C19—48no—
65C2×Q8×C19—24no—
66C2×Q8×C19—21no—
67C2×Q8×C19—21no—
68C2×Q8×C19—21no—
69C2×Q8×C19—48no—
70C2×Q8×C19—48no—
71C2×Q8×C19—42no—
72C2×Q8×C19—41no—
73C2×Q8×C19—41no—
74C2×Q8×C19—41no—
75C2×Q8×C19—41no—
76C2×Q8×C19—41no—
77C2×Q8×C19—41no—
78C2×Q8×C19—42no—
79C2×Q8×C19C22⋊C412yes—
80C2×Q8×C19C22⋊C412yes—
81C2×Q8×C19C22⋊C412yes—
82C2×D4×C19—24no—
83C2×D4×C19—21no—
84C2×D4×C19—41no—
85C2×D4×C19—41no—
86C2×D4×C19—42no—
87C2×D4×C19—42no—
88C2×D4×C19C22⋊C412yes—
89C22×C4×C19—22no—
90C22×C4×C19—22no—
91C22×C4×C19—21no—
92C22×C4×C19—21no—
93C22×C4×C19—24no—
94C22×C4×C19—24no—
95C22×C4×C19—21no—
96C22×C4×C19—21no—
97C22×C4×C19—21no—
98C22×C4×C19—42no—
99C22×C4×C19—42no—
100C22×C4×C19—42no—
101C22×C4×C19—42no—
102C22×C4×C19C22⋊C411yescharacteristic
103C22×C4×C19C22⋊C412yes—
104C22×C4×C19C22×C411yescharacteristic
105C22×C4×C19C2×D412yes—
106C4⋊C4×C19—28no—
107C4⋊C4×C19—28no—
108C4⋊C4×C19—24no—
109C22⋊C4×C19—28no—
110C22⋊C4×C19—28no—
111C22⋊C4×C19—24no—
112C42×C19—21no—
113C42×C19—21no—
114C42×C19C2×D412yes—
115C42×C19C2×D412yes—
116C2×C19⋊C8—44no—
117#8524—191nomaximal, Sylow
118C23×C19—21no—
119C23×C19—21no—
120C23×C19—22no—
121C23×C19—42no—
122C23×C19—44no—
123C23×C19—41no—
124C23×C19—41no—
125C23×C19#10012yes—
126C23×C19C2×C22⋊C411yescharacteristic
127Q8×C19—42no—
128Q8×C19—42no—
129Q8×C19—42no—
130Q8×C19—48no—
131Q8×C19—42no—
132Q8×C19—42no—
133Q8×C19—42no—
134D4×C19—42no—
135D4×C19—42no—
136D4×C19—48no—
137C2×C4×C19—24no—
138C2×C4×C19—24no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—22no—
144C2×C4×C19—22no—
145C2×C4×C19—22no—
146C2×C4×C19—22no—
147C2×C4×C19—42no—
148C2×C4×C19—48no—
149C2×C4×C19—48no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—42no—
157C2×C4×C19#10012yes—
158C2×C4×C19C2×C22⋊C411yescharacteristic
159C2×C4×C19C2×C22⋊C411yescharacteristic
160C2×C4×C19#12014yes—
161C19⋊C8—84no—
162C2×#536D1911yescharacteristic
163#1558—192no—
164#1533—192no—
165#1464—192no—
166C22×C19—22no—
167C22×C19—22no—
168C22×C19—42no—
169C22×C19—42no—
170C22×C19—42no—
171C22×C19—44no—
172C22×C19—42no—
173C22×C19—82no—
174C22×C19—82no—
175C22×C19#37911yescharacteristic
176C22×C19C2×#10011yescharacteristic
177C22×C19C2×#10011yescharacteristic
178C4×C19—24no—
179C4×C19—22no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—42no—
183C4×C19—42no—
184C4×C19—42no—
185C4×C19—42no—
186C22×#41Dic1911yescharacteristic
187C23×Q8Dic1911yescharacteristic
188#536—24no—
189#536—24no—
190C2×C4⋊Q8Dic1911yescharacteristic
191C2×C4⋊Q8C2×D1911yescharacteristic
192C2×#124Dic1911yescharacteristic
193C2×#124C2×D1911yescharacteristic
194C2×#123—22no—
195C2×C22⋊Q8—22no—
196C2×#117C2×D1911yescharacteristic
197#432—194no—
198#333—384no—
199#329—384no—
200#324—382no—
201#323—382no—
202C2×C19—21no—
203C2×C19—21no—
204C2×C19—42no—
205C2×C19—82no—
206C2×C19#178311yescharacteristic
207C2×C19#179612yes—
208C2×#41—22no—
209C2×#41—22no—
210C2×#41—42no—
211C2×#41—42no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—21no—
215C22×Q8—42no—
216C22×Q8—42no—
217C22×Q8C2×Dic1911yescharacteristic
218C22×Q8C2×Dic1911yescharacteristic
219C22×Q8C2×Dic1911yescharacteristic
220C22×D4—21no—
221C22×D4C2×Dic1911yescharacteristic
222C23×C4—21no—
223C23×C4—21no—
224C23×C4C2×Dic1911yescharacteristic
225C4⋊Q8—22no—
226C4⋊Q8—22no—
227C4⋊Q8—22no—
228C4⋊Q8C22⋊D1914yes—
229#124—22no—
230#124—22no—
231#124—22no—
232#124C22⋊D1914yes—
233#123—216no—
234C22⋊Q8—216no—
235#117—22no—
236#117—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4C22⋊D1912yes—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4C22⋊D1912yes—
243C2×C42C2×Dic1911yescharacteristic
244C2×C42C22×D1911yescharacteristic
245C4⋊C8—384no—
246C22⋊C8—384no—
247#97—384no—
248C19#852411yescharacteristic, complemented, Sylow
249C24—21no—
250C24C22⋊Dic1911yescharacteristic
251#41—48no—
252#41—48no—
253C2×Q8—24no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—48no—
258C2×Q8—48no—
259C2×Q8—42no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—42no—
267C2×Q8C22⋊Dic1912yes—
268C2×Q8C22⋊Dic1912yes—
269C2×Q8C22⋊Dic1912yes—
270C2×D4—24no—
271C2×D4—21no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4C22⋊Dic1912yes—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4C22⋊Dic1911yescharacteristic
291C22×C4C22⋊Dic1912yes—
292C22×C4C22×Dic1911yescharacteristic
293C22×C4C2×C22⋊D1912yes—
294C2×C8—764no—
295C4⋊C4—28no—
296C4⋊C4—28no—
297C4⋊C4—24no—
298C22⋊C4—28no—
299C22⋊C4—28no—
300C22⋊C4—24no—
301C42—21no—
302C42—21no—
303C42C2×C22⋊D1912yes—
304C42C2×C22⋊D1912yes—
305C23—21no—
306C23—21no—
307C23—22no—
308C23—42no—
309C23—44no—
310C23—41no—
311C23—41no—
312C23#1059729012yes—
313C23C2×C22⋊Dic1911yescharacteristic
314Q8—42no—
315Q8—42no—
316Q8—42no—
317Q8—48no—
318Q8—42no—
319Q8—42no—
320Q8—42no—
321D4—42no—
322D4—42no—
323D4—48no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—42no—
335C2×C4—48no—
336C2×C4—48no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4#1059729012yes—
345C2×C4C2×C22⋊Dic1911yescharacteristic
346C2×C4C2×C22⋊Dic1911yescharacteristic
347C2×C4#1059739914yes—
348C8—1524no—
349C22—22no—
350C22—22no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—44no—
355C22—42no—
356C22—82no—
357C22—82no—
358C22#1192640011yescharacteristic
359C22C2×#1059729011yescharacteristic
360C22C2×#1059729011yescharacteristic
361C4—24no—
362C4—22no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—42no—
367C4—42no—
368C4—42no—
369C2—21no—
370C2—21no—
371C2—42no—
372C2—82no—
373C2#1456355611yescharacteristic
374C2#1456361012yes—
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#536C2
socleC22×C19#379
prime radicalC22×#41×C19C4
cosocleC2×C42×C19C23
hypercenterC2×#536D19
hypocenterC19#8524
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #14562361C2semidirect
2. #14562259C2semidirect
3. #14561969C2semidirect
248. C19#8524semidirect

Maximal subgroups

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

subgroupindex
#145623612
#145622592
#145619692
C2×C19×#5362
#852419