Finite Group Databasebeta

← #18075089

Subgroups — #18075089

Order 4864.

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

normal subgroups only

This group has 648 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#14564601C211yesmaximal, characteristic, complemented
2#14562262C211yesmaximal, characteristic, complemented
3#14562173C212yesmaximal, complemented
4#14562095C212yesmaximal, complemented
5C19×#3553C211yesmaximal, characteristic
6#11926601C2212yes—
7C2×C4×C19⋊C8C2211yescharacteristic
8#11926410C2211yescharacteristic
9#11926306—22no—
10#11926286—22no—
11#11926281—22no—
12#11926278—22no—
13Q8⋊(C19⋊C8)—22no—
14D4⋊(C19⋊C8)—22no—
15C19×#564C411yescharacteristic, complemented
16C19×#563C412yescomplemented
17C19×#562C411yescharacteristic, complemented
18C19×#554—22no—
19C19×#553—22no—
20C19×#552—22no—
21C19×#541—22no—
22C19×#539—22no—
23C19×#539—22no—
24C19×#529C2212yes—
25C2×C19×#125C2211yescharacteristic
26C19×C4⋊Q8—22no—
27C19×#126—22no—
28C19×#126—22no—
29C19×#126—22no—
30C19×#126—22no—
31C19×#126—22no—
32C19×#125—22no—
33C19×#125—22no—
34C19×#125—22no—
35C19×#125—22no—
36C19×#125—22no—
37C19×#125—22no—
38C19×#125C2×C411yescharacteristic
39C19×#125C2×C411yescharacteristic
40C19×#125C2×C412yes—
41C19×#125D412yes—
42C19×#124C2×C412yes—
43C19×#123—22no—
44C19×#123—22no—
45C19×#123—22no—
46C19×#123—22no—
47C19×#123—22no—
48C19×C22⋊Q8—22no—
49C19×C22⋊Q8—22no—
50C19×C22⋊Q8—22no—
51C19×C22⋊Q8—22no—
52C19×C22⋊Q8—22no—
53C19×C22⋊Q8—22no—
54C19×C22⋊Q8D412yes—
55C19×#121—22no—
56C19×#121—22no—
57C19×#121D412yes—
58C4×Q8×C19—22no—
59C4×Q8×C19D412yes—
60C4×D4×C19—22no—
61C4×D4×C19—22no—
62C4×D4×C19—22no—
63C4×D4×C19—22no—
64C4×D4×C19D412yes—
65C19×#117—22no—
66C19×#117—22no—
67C2×C4⋊C4×C19—22no—
68C2×C4⋊C4×C19—22no—
69C2×C4⋊C4×C19D412yes—
70C2×C42×C19C2311yescharacteristic
71C2×C4⋊Dic19—21no—
72C22×C19⋊C8—21no—
73C19⋊#95—22no—
74C22⋊(C19⋊C8)—22no—
75C4⋊(C19⋊C8)—22no—
76#10597260—22no—
77C4×C19⋊C8—22no—
78C2×Q8×C19—22no—
79C2×Q8×C19C22⋊C412yes—
80C2×D4×C19—22no—
81C2×D4×C19—22no—
82C2×D4×C19C22⋊C412yes—
83C22×C4×C19—22no—
84C22×C4×C19—22no—
85C22×C4×C19—22no—
86C22×C4×C19—22no—
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D412yes—
89C22×Dic19—41no—
90C4⋊C4×C19—22no—
91C4⋊C4×C19—22no—
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×C19—22no—
99C4⋊C4×C19—22no—
100C4⋊C4×C19—22no—
101C4⋊C4×C19—22no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19—22no—
105C4⋊C4×C19C22⋊C412yes—
106C4⋊C4×C19C22⋊C412yes—
107C4⋊C4×C19C22⋊C412yes—
108C4⋊C4×C19C22⋊C412yes—
109C22⋊C4×C19—22no—
110C22⋊C4×C19—22no—
111C22⋊C4×C19—22no—
112C22⋊C4×C19—22no—
113C22⋊C4×C19—22no—
114C22⋊C4×C19—22no—
115C22⋊C4×C19—22no—
116C22⋊C4×C19—22no—
117C22⋊C4×C19—22no—
118C42×C19—22no—
119C42×C19—22no—
120C42×C19—22no—
121C42×C19C22×C411yescharacteristic
122C42×C19C2×D411yescharacteristic
123C42×C19C2×D412yes—
124C4⋊Dic19—42no—
125C2×C19⋊C8—22no—
126C2×C19⋊C8—41no—
127C2×C19⋊C8—41no—
128C2×C19⋊C8—42no—
129#8529—191nomaximal, Sylow
130C23×C19—22no—
131C23×C19#12011yescharacteristic
132Q8×C19—42no—
133Q8×C19—82no—
134D4×C19—42no—
135D4×C19—42no—
136D4×C19—42no—
137D4×C19—82no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—22no—
141C2×C4×C19—22no—
142C2×C4×C19—22no—
143C2×C4×C19—22no—
144C2×C4×C19—22no—
145C2×C4×C19—42no—
146C2×C4×C19—82no—
147C2×C4×C19—82no—
148C2×C4×C19—82no—
149C2×C4×C19—82no—
150C2×C4×C19C2×C22⋊C411yescharacteristic
151C2×C4×C19C2×C22⋊C412yes—
152C2×C4×C19#12012yes—
153C2×C4×C19#12011yescharacteristic
154C2×Dic19—82no—
155C2×Dic19—81no—
156C19⋊C8—42no—
157C19⋊C8—82no—
158#3553D1911yescharacteristic
159#1991—191no—
160#1534—191no—
161#1512—192no—
162#1494—192no—
163C22×C19—22no—
164C22×C19—42no—
165C22×C19—42no—
166C22×C19—42no—
167C22×C19#37911yescharacteristic
168C22×C19#45411yescharacteristic
169C22×C19#45611yescharacteristic
170C4×C19—21no—
171C4×C19—21no—
172C4×C19—22no—
173C4×C19—22no—
174C4×C19—42no—
175C4×C19—42no—
176C4×C19—42no—
177C4×C19—42no—
178C4×C19—42no—
179Dic19—161no—
180#564Dic1911yescharacteristic, complemented
181#563Dic1912yescomplemented
182#562Dic1911yescharacteristic, complemented
183#554—22no—
184#553—22no—
185#552—22no—
186#541—22no—
187#539—22no—
188#539—22no—
189#529C2×D1912yes—
190C2×#125C2×D1911yescharacteristic
191#432—192no—
192C2×C4×C8—191no—
193#382—191no—
194#340—382no—
195#330—382no—
196#328—382no—
197#327—382no—
198Q8⋊C8—382no—
199D4⋊C8—382no—
200C2×C19—21no—
201C2×C19—21no—
202C2×C19—82no—
203C2×C19#179311yescharacteristic
204C2×C19#179412yes—
205C22×C8—381no—
206C4⋊Q8—22no—
207#126—22no—
208#126—22no—
209#126—22no—
210#126—22no—
211#126—22no—
212#125—22no—
213#125—22no—
214#125—22no—
215#125—22no—
216#125—22no—
217#125—22no—
218#125C2×Dic1911yescharacteristic
219#125C2×Dic1911yescharacteristic
220#125C2×Dic1912yes—
221#125C22⋊D1912yes—
222#124C2×Dic1912yes—
223#123—22no—
224#123—22no—
225#123—22no—
226#123—22no—
227#123—22no—
228C22⋊Q8—22no—
229C22⋊Q8—22no—
230C22⋊Q8—22no—
231C22⋊Q8—22no—
232C22⋊Q8—22no—
233C22⋊Q8—22no—
234C22⋊Q8C22⋊D1912yes—
235#121—22no—
236#121—22no—
237#121C22⋊D1912yes—
238C4×Q8—22no—
239C4×Q8C22⋊D1912yes—
240C4×D4—22no—
241C4×D4—22no—
242C4×D4—22no—
243C4×D4—22no—
244C4×D4C22⋊D1912yes—
245#117—22no—
246#117—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—381no—
250C2×C4⋊C4C22⋊D1912yes—
251C2×C42C22×D1911yescharacteristic
252C4⋊C8—382no—
253C22⋊C8—382no—
254#97—382no—
255C4×C8—382no—
256#95—382no—
257C19#852911yescharacteristic, complemented, Sylow
258C2×Q8—22no—
259C2×Q8C22⋊Dic1912yes—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4C22⋊Dic1912yes—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—761no—
268C22×C4C2×C22⋊D1911yescharacteristic
269C22×C4C2×C22⋊D1912yes—
270C2×C8—382no—
271C2×C8—761no—
272C2×C8—761no—
273C2×C8—762no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—762no—
290C4⋊C4C22⋊Dic1912yes—
291C4⋊C4C22⋊Dic1912yes—
292C4⋊C4C22⋊Dic1912yes—
293C4⋊C4C22⋊Dic1912yes—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C42—22no—
304C42—22no—
305C42—22no—
306C42C22×Dic1911yescharacteristic
307C42C2×C22⋊D1912yes—
308C42C2×C22⋊D1911yescharacteristic
309C23—22no—
310C23#1059739911yescharacteristic
311Q8—42no—
312Q8—82no—
313D4—42no—
314D4—42no—
315D4—42no—
316D4—82no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—1522no—
330C2×C4—1521no—
331C2×C4C2×C22⋊Dic1911yescharacteristic
332C2×C4C2×C22⋊Dic1912yes—
333C2×C4#1059739912yes—
334C2×C4#1059739911yescharacteristic
335C8—762no—
336C8—1522no—
337C22—22no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22#1192640011yescharacteristic
342C22#1192671711yescharacteristic
343C22#1192672711yescharacteristic
344C4—21no—
345C4—21no—
346C4—22no—
347C4—22no—
348C4—42no—
349C4—42no—
350C4—42no—
351C4—42no—
352C4—42no—
353C4—3041no—
354C2—21no—
355C2—21no—
356C2—82no—
357C2#1456359411yescharacteristic
358C2#1456359912yes—
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3553C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3553D19
hypocenterC19#8529
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3553

Complements

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

NH ≅ G/Ntype
1. #14564601C2semidirect
2. #14562262C2semidirect
3. #14562173C2semidirect
4. #14562095C2semidirect
15. C19×#564C4semidirect
16. C19×#563C4semidirect
17. C19×#562C4semidirect
180. #564Dic19semidirect
181. #563Dic19semidirect
182. #562Dic19semidirect
257. C19#8529semidirect

Maximal subgroups

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

subgroupindex
#145646012
#145622622
#145621732
#145620952
C19×#35532
#852919