Finite Group Databasebeta

← #18074718

Subgroups — #18074718

Order 4864.

718 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 131 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#14563712C211yesmaximal, characteristic, complemented
2#14563706C211yesmaximal, characteristic, complemented
3#14562191C212yesmaximal, complemented
4#14562191C212yesmaximal, complemented
5C19×#3493C211yesmaximal, characteristic
6C2×C22⋊(C19⋊C8)C2211yescharacteristic
7C2×C22⋊(C19⋊C8)C2211yescharacteristic
8#11926407C2212yes—
9#11926311—22no—
10#11926299—22no—
11#11926281—22no—
12#11926281—22no—
13#11926278—22no—
14#11926278—22no—
15C19×#556—22no—
16C19×#555—22no—
17C19×#553—22no—
18C19×#552—22no—
19C19×#544C411yescharacteristic, complemented
20C19×#538—22no—
21C19×#537C411yescharacteristic, complemented
22C19×#529—22no—
23C19×#525C2212yes—
24C19×#520C412yescomplemented
25C2×C19×#117C2211yescharacteristic
26C2×#41×C19C2×C412yes—
27C23×C4×C19C2311yescharacteristic
28C19×C4⋊Q8—22no—
29C19×#126—24no—
30C19×#126—24no—
31C19×#125—22no—
32C19×#125—22no—
33C19×#124—22no—
34C19×#124—24no—
35C19×#123—24no—
36C19×#123—22no—
37C19×C22⋊Q8—22no—
38C19×C22⋊Q8—22no—
39C19×C22⋊Q8D412yes—
40C19×C22⋊Q8D412yes—
41C19×#121—24no—
42C19×#121—22no—
43C19×#121—22no—
44C19×#121D412yes—
45C19×#121D412yes—
46C19×#120—22no—
47C4×Q8×C19—22no—
48C4×Q8×C19—22no—
49C4×D4×C19—22no—
50C4×D4×C19—22no—
51C4×D4×C19—24no—
52C4×D4×C19—22no—
53C4×D4×C19—22no—
54C19×#117—24no—
55C19×#117—22no—
56C19×#117—22no—
57C19×#117—22no—
58C19×#117C2×C412yes—
59C2×C4⋊C4×C19—22no—
60C2×C4⋊C4×C19C2×C411yescharacteristic
61C2×C4⋊C4×C19C2×C411yescharacteristic
62C2×C22⋊C4×C19D412yes—
63C2×C42×C19D412yes—
64C2×C22⋊Dic19—22no—
65C22×C19⋊C8—21no—
66C22×C19⋊C8—21no—
67C19⋊#95—22no—
68C19⋊#95—22no—
69C22⋊(C19⋊C8)—22no—
70C22⋊(C19⋊C8)—22no—
71C24×C19C2×D411yescharacteristic
72#41×C19—44no—
73C2×Q8×C19—22no—
74C2×Q8×C19C22⋊C412yes—
75C2×D4×C19—22no—
76C2×D4×C19—22no—
77C2×D4×C19—22no—
78C2×D4×C19—22no—
79C2×D4×C19C22⋊C412yes—
80C22×C4×C19—24no—
81C22×C4×C19—22no—
82C22×C4×C19—42no—
83C22×C4×C19C22⋊C412yes—
84C22×C4×C19C22⋊C412yes—
85C22×C4×C19C22×C411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D412yes—
88C22×C4×C19C2×D412yes—
89C22×Dic19—42no—
90C4⋊C4×C19—24no—
91C4⋊C4×C19—24no—
92C4⋊C4×C19—22no—
93C4⋊C4×C19—22no—
94C4⋊C4×C19—22no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—22no—
97C4⋊C4×C19—22no—
98C4⋊C4×C19C22⋊C412yes—
99C4⋊C4×C19C22⋊C412yes—
100C22⋊C4×C19—24no—
101C22⋊C4×C19—24no—
102C22⋊C4×C19—22no—
103C22⋊C4×C19—24no—
104C22⋊C4×C19—22no—
105C22⋊C4×C19—22no—
106C22⋊C4×C19—22no—
107C22⋊C4×C19—22no—
108C42×C19—24no—
109C42×C19—22no—
110C42×C19—22no—
111C42×C19—22no—
112C22⋊Dic19—44no—
113C2×C19⋊C8—42no—
114C2×C19⋊C8—42no—
115C2×C19⋊C8—41no—
116C2×C19⋊C8—41no—
117#8463—191nomaximal, Sylow
118C23×C19—22no—
119C23×C19—22no—
120C23×C19—41no—
121C23×C19—41no—
122C23×C19C2×C22⋊C411yescharacteristic
123C23×C19#12012yes—
124Q8×C19—42no—
125Q8×C19—82no—
126D4×C19—42no—
127D4×C19—44no—
128D4×C19—82no—
129D4×C19—82no—
130D4×C19—82no—
131C2×C4×C19—22no—
132C2×C4×C19—22no—
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—44no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19—84no—
144C2×C4×C19C2×C22⋊C412yes—
145C2×C4×C19#12011yescharacteristic
146C2×C4×C19#12011yescharacteristic
147C2×Dic19—82no—
148C2×Dic19—82no—
149C2×Dic19—82no—
150C19⋊C8—81no—
151C19⋊C8—81no—
152#3493D1911yescharacteristic
153#1820—191no—
154#1818—191no—
155#1516—192no—
156#1516—192no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—22no—
160C22×C19—22no—
161C22×C19—22no—
162C22×C19—42no—
163C22×C19—42no—
164C22×C19—42no—
165C22×C19—82no—
166C22×C19#37911yescharacteristic
167C22×C19#41012yes—
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—22no—
171C4×C19—42no—
172C4×C19—42no—
173C4×C19—42no—
174C4×C19—42no—
175C4×C19—42no—
176Dic19—162no—
177#556—22no—
178#555—22no—
179#553—22no—
180#552—22no—
181#544Dic1911yescharacteristic, complemented
182#538—22no—
183#537Dic1911yescharacteristic, complemented
184#529—22no—
185#525C2×D1912yes—
186#520Dic1912yescomplemented
187C2×#117C2×D1911yescharacteristic
188C2×C22⋊C8—191no—
189C2×C22⋊C8—191no—
190#381—192no—
191#342—382no—
192#336—382no—
193#328—382no—
194#328—382no—
195#327—382no—
196#327—382no—
197C2×C19—22no—
198C2×C19—42no—
199C2×C19—82no—
200C2×C19#178211yescharacteristic
201C2×C19#179411yescharacteristic
202C2×C19#179411yescharacteristic
203C2×#41C2×Dic1912yes—
204C23×C4C22×D1911yescharacteristic
205C22×C8—381no—
206C22×C8—381no—
207C4⋊Q8—22no—
208#126—24no—
209#126—24no—
210#125—22no—
211#125—22no—
212#124—22no—
213#124—24no—
214#123—24no—
215#123—22no—
216C22⋊Q8—22no—
217C22⋊Q8—22no—
218C22⋊Q8C22⋊D1912yes—
219C22⋊Q8C22⋊D1912yes—
220#121—24no—
221#121—22no—
222#121—22no—
223#121C22⋊D1912yes—
224#121C22⋊D1912yes—
225#120—22no—
226C4×Q8—22no—
227C4×Q8—22no—
228C4×D4—22no—
229C4×D4—22no—
230C4×D4—24no—
231C4×D4—22no—
232C4×D4—22no—
233#117—24no—
234#117—22no—
235#117—22no—
236#117—22no—
237#117C2×Dic1912yes—
238C2×C4⋊C4—22no—
239C2×C4⋊C4C2×Dic1911yescharacteristic
240C2×C4⋊C4C2×Dic1911yescharacteristic
241C2×C22⋊C4—382no—
242C2×C22⋊C4C22⋊D1912yes—
243C2×C42C22⋊D1912yes—
244C22⋊C8—382no—
245C22⋊C8—382no—
246#95—382no—
247#95—382no—
248C19#846311yescharacteristic, complemented, Sylow
249C24C2×C22⋊D1911yescharacteristic
250#41—44no—
251C2×Q8—22no—
252C2×Q8C22⋊Dic1912yes—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—22no—
257C2×D4C22⋊Dic1912yes—
258C22×C4—24no—
259C22×C4—22no—
260C22×C4—42no—
261C22×C4—762no—
262C22×C4C22⋊Dic1912yes—
263C22×C4C22⋊Dic1912yes—
264C22×C4C22×Dic1911yescharacteristic
265C22×C4C2×C22⋊D1911yescharacteristic
266C22×C4C2×C22⋊D1912yes—
267C22×C4C2×C22⋊D1912yes—
268C2×C8—762no—
269C2×C8—762no—
270C2×C8—761no—
271C2×C8—761no—
272C4⋊C4—24no—
273C4⋊C4—24no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4C22⋊Dic1912yes—
281C4⋊C4C22⋊Dic1912yes—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—22no—
285C22⋊C4—24no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—764no—
291C42—24no—
292C42—22no—
293C42—22no—
294C42—22no—
295C23—22no—
296C23—22no—
297C23—41no—
298C23—41no—
299C23C2×C22⋊Dic1911yescharacteristic
300C23#1059739912yes—
301Q8—42no—
302Q8—82no—
303D4—42no—
304D4—44no—
305D4—82no—
306D4—82no—
307D4—82no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—84no—
321C2×C4—1522no—
322C2×C4—1522no—
323C2×C4—1522no—
324C2×C4C2×C22⋊Dic1912yes—
325C2×C4#1059739911yescharacteristic
326C2×C4#1059739911yescharacteristic
327C8—1521no—
328C8—1521no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—82no—
338C22#1192640011yescharacteristic
339C22#1192651812yes—
340C4—21no—
341C4—21no—
342C4—22no—
343C4—42no—
344C4—42no—
345C4—42no—
346C4—42no—
347C4—42no—
348C4—3042no—
349C2—22no—
350C2—42no—
351C2—82no—
352C2#1456355311yescharacteristic
353C2#1456359911yescharacteristic
354C2#1456359911yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3493C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenter#3493D19
hypocenterC19#8463
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3493

Complements

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

NH ≅ G/Ntype
1. #14563712C2semidirect
2. #14563706C2semidirect
3. #14562191C2semidirect
4. #14562191C2semidirect
19. C19×#544C4semidirect
21. C19×#537C4semidirect
24. C19×#520C4semidirect
181. #544Dic19semidirect
183. #537Dic19semidirect
186. #520Dic19semidirect
248. C19#8463semidirect

Maximal subgroups

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

subgroupindex
#145637122
#145637062
#145621912
C19×#34932
#846319