Finite Group Databasebeta

← #18079709

Subgroups — #18079709

Order 4864.

500 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 107 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#14566528C211yesmaximal, characteristic
2#14564621C211yesmaximal, characteristic
3#14563734C211yesmaximal, characteristic
4#14562155C211yesmaximal, characteristic
5#14561540C211yesmaximal, characteristic
6#14561520C211yesmaximal, characteristic
7C19×#3095C211yesmaximal, characteristic
8#11926508C2211yescharacteristic
9#11926443—21no—
10#11926437—22no—
11#11926412—21no—
12#11926404C2211yescharacteristic
13C4⋊C4×Dic19—21no—
14C4×C4⋊Dic19—21no—
15C4×C22⋊Dic19C2211yescharacteristic
16C4×C22⋊Dic19C2211yescharacteristic
17#11926311—22no—
18#11926303—22no—
19#11926281—21no—
20#11926281—21no—
21C2×C19×C22⋊Q8C2211yescharacteristic
22C2×C19×#117C2211yescharacteristic
23C19×#485—22no—
24C19×#484—21no—
25C19×#483—21no—
26C19×#428C412yescomplemented
27C19×#419C412yescomplemented
28C19×#407C2211yescharacteristic
29C22×Q8×C19C2×C411yescharacteristic
30C23×C4×C19C2311yescharacteristic
31C2×M16×C19C2×C412yes—
32C19×C22⋊Q8—21no—
33C19×C22⋊Q8—21no—
34C19×C22⋊Q8—21no—
35C19×C22⋊Q8—21no—
36C19×#117—21no—
37C19×#117—21no—
38C19×#117C2×C412yes—
39C19×#117D412yes—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19C2×C411yescharacteristic
42C2×C4⋊C4×C19D411yescharacteristic
43C2×C4⋊C4×C19D411yescharacteristic
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19—21no—
46C2×C42×C19—21no—
47C2×C22⋊Dic19—21no—
48C2×C22⋊Dic19—21no—
49C2×C22⋊Dic19D412yes—
50C2×C4⋊Dic19—22no—
51C2×C4⋊Dic19—21no—
52C2×C4×Dic19—21no—
53C2×C4×Dic19—21no—
54C2×C4×Dic19—22no—
55C2×#64520—21no—
56C19×#107—22no—
57C19×#106—22no—
58C19×#103—22no—
59C19×#103—22no—
60C19×C22⋊C8—21no—
61C19×C22⋊C8—21no—
62C19⋊#95—22no—
63C19⋊#95—22no—
64C19⋊#95—21no—
65C19⋊#95—21no—
66C19⋊#95D411yescharacteristic
67C19⋊#95D411yescharacteristic
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)—21no—
70C24×C19C2×D411yescharacteristic
71C2×Q8×C19—21no—
72C2×Q8×C19—21no—
73C2×Q8×C19—42no—
74C22×C4×C19—21no—
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19—21no—
78C22×C4×C19—42no—
79C22×C4×C19C22×C411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C22×C4×C19#4111yescharacteristic
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—22no—
88C22×Dic19—41no—
89M16×C19—42no—
90C2×C8×C19—22no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—41no—
96C4⋊C4×C19—41no—
97C4⋊C4×C19C22⋊C412yes—
98C4⋊C4×C19C22⋊C412yes—
99C22⋊C4×C19—22no—
100C22⋊C4×C19—22no—
101C22⋊C4×C19—41no—
102C22⋊C4×C19—41no—
103C42×C19—22no—
104C42×C19—22no—
105C22⋊Dic19—22no—
106C22⋊Dic19—42no—
107C22⋊Dic19—41no—
108C22⋊Dic19—42no—
109C4⋊Dic19—44no—
110C4⋊Dic19—42no—
111C4×Dic19—42no—
112C4×Dic19—42no—
113C4×Dic19—82no—
114#64520—42no—
115C2×C19⋊C8—41no—
116#9362—191nomaximal, Sylow
117C23×C19—21no—
118C23×C19—21no—
119C23×C19—41no—
120C23×C19—41no—
121C23×C19C4×D411yescharacteristic
122C23×C19#12011yescharacteristic
123C23×C19#12111yescharacteristic
124Q8×C19—42no—
125Q8×C19—81no—
126C2×C4×C19—22no—
127C2×C4×C19—22no—
128C2×C4×C19—22no—
129C2×C4×C19—22no—
130C2×C4×C19—22no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—42no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—81no—
140C2×C4×C19—81no—
141C2×C4×C19C2×C22⋊C411yescharacteristic
142C2×C4×C19C4×D411yescharacteristic
143C2×C4×C19#12111yescharacteristic
144C2×C4×C19#12311yescharacteristic
145C2×Dic19—22no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—42no—
150C2×Dic19—42no—
151C2×Dic19—42no—
152C2×Dic19—41no—
153C2×Dic19—42no—
154C2×Dic19—41no—
155C2×Dic19—81no—
156C2×Dic19—81no—
157C8×C19—42no—
158C19⋊C8—81no—
159#3095D1911yescharacteristic
160#2347—191no—
161#1996—191no—
162#1826—191no—
163#1508—191no—
164#1305—191no—
165#1297—191no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—81no—
175C22×C19—81no—
176C22×C19#38611yescharacteristic
177C22×C19#45511yescharacteristic
178C22×C19#45611yescharacteristic
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—42no—
183C4×C19—42no—
184C4×C19—81no—
185C4×C19—81no—
186C4×C19#41012yes—
187Dic19—42no—
188Dic19—82no—
189Dic19—81no—
190Dic19—82no—
191C2×C22⋊Q8C2×D1911yescharacteristic
192C2×#117C2×D1911yescharacteristic
193#485—22no—
194#484—21no—
195#483—21no—
196#428Dic1912yescomplemented
197#419Dic1912yescomplemented
198#407—191no—
199#407C2×D1911yescharacteristic
200#389—381no—
201#388—382no—
202#383—381no—
203#380—191no—
204C4×C4⋊C4—381no—
205C4×C4⋊C4—381no—
206C4×C22⋊C4—191no—
207C4×C22⋊C4—191no—
208#342—382no—
209#339—382no—
210#328—381no—
211#328—381no—
212C2×C19—21no—
213C2×C19—21no—
214C2×C19—41no—
215C2×C19—41no—
216C2×C19#188211yescharacteristic
217C2×C19#189911yescharacteristic
218C2×C19#190611yescharacteristic
219C22×Q8C2×Dic1911yescharacteristic
220C23×C4C22×D1911yescharacteristic
221C2×M16—381no—
222C2×M16C2×Dic1912yes—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227#117—21no—
228#117—21no—
229#117C2×Dic1912yes—
230#117C22⋊D1912yes—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—382no—
233C2×C4⋊C4—381no—
234C2×C4⋊C4C2×Dic1911yescharacteristic
235C2×C4⋊C4C22⋊D1911yescharacteristic
236C2×C4⋊C4C22⋊D1911yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—192no—
240C2×C22⋊C4—381no—
241C2×C22⋊C4—381no—
242C2×C42—21no—
243C2×C42—381no—
244C2×C42—381no—
245C2×C42—382no—
246#107—22no—
247#106—22no—
248#103—22no—
249#103—22no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—381no—
253C22⋊C8—381no—
254#95—191no—
255#95—191no—
256#95—382no—
257#95—382no—
258#95—381no—
259#95—381no—
260C19#936211yescharacteristic, complemented, Sylow
261C24D4×D1911yescharacteristic
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—42no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—42no—
270C22×C4—381no—
271C22×C4—381no—
272C22×C4—382no—
273C22×C4—761no—
274C22×C4D4×D1911yescharacteristic
275C22×C4#6454311yescharacteristic
276C22×C4#6454311yescharacteristic
277C22×C4C22×Dic1911yescharacteristic
278C22×C4C2×C22⋊D1911yescharacteristic
279C22×C4C2×C22⋊D1911yescharacteristic
280M16—42no—
281M16—762no—
282C2×C8—22no—
283C2×C8—761no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—762no—
291C4⋊C4—764no—
292C4⋊C4C22⋊Dic1912yes—
293C4⋊C4C22⋊Dic1912yes—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—382no—
299C22⋊C4—762no—
300C22⋊C4—761no—
301C22⋊C4—762no—
302C42—22no—
303C42—22no—
304C42—762no—
305C42—762no—
306C42—1522no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23D4×Dic1911yescharacteristic
312C23#1059738311yescharacteristic
313C23#1059738511yescharacteristic
314Q8—42no—
315Q8—81no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—382no—
332C2×C4—761no—
333C2×C4—761no—
334C2×C4—761no—
335C2×C4—762no—
336C2×C4—761no—
337C2×C4—762no—
338C2×C4—762no—
339C2×C4—762no—
340C2×C4—761no—
341C2×C4—1521no—
342C2×C4—1521no—
343C2×C4D4×Dic1911yescharacteristic
344C2×C4#1059738111yescharacteristic
345C2×C4#1059738511yescharacteristic
346C2×C4C2×C22⋊Dic1911yescharacteristic
347C8—42no—
348C8—1521no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22#1192642411yescharacteristic
360C22#1192672011yescharacteristic
361C22#1192672511yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—42no—
367C4—81no—
368C4—81no—
369C4—762no—
370C4—1522no—
371C4—1521no—
372C4—1522no—
373C4#1192651812yes—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2#1456400611yescharacteristic
379C2#1456409411yescharacteristic
380C2#1456413811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3095C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#3095D19
hypocenterC19#9362
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
26. C19×#428C4semidirect
27. C19×#419C4semidirect
196. #428Dic19semidirect
197. #419Dic19semidirect
260. C19#9362semidirect

Maximal subgroups

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

subgroupindex
#145665282
#145646212
#145637342
#145621552
#145615402
#145615202
C19×#30952
#936219