Finite Group Databasebeta

← #18080267

Subgroups — #18080267

Order 4864.

528 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 93 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#14568113C211yesmaximal, characteristic
2#14566236C211yesmaximal, characteristic
3#14563713C211yesmaximal, characteristic
4#14562169C211yesmaximal, characteristic
5#14562167C211yesmaximal, characteristic
6#14561488C211yesmaximal, characteristic
7C19×#1284C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9C22×C4⋊Dic19C2211yescharacteristic
10#11926508C2211yescharacteristic
11#11926476—22no—
12#11926450C412yescomplemented
13#11926429—22no—
14#11926427—22no—
15#11926419—21no—
16#11926419—21no—
17#11926414C412yescomplemented
18#11926407C2211yescharacteristic
19#11926402—21no—
20C22⋊C4×Dic19—21no—
21#11926312—22no—
22#11926282—22no—
23#11926280—22no—
24C19×#407C2211yescharacteristic
25C19×#381C2211yescharacteristic
26C4×C22⋊C4×C19C2211yescharacteristic
27C23×C4×C19C2311yescharacteristic
28C23×Dic19D411yescharacteristic
29C23×Dic19D411yescharacteristic
30C22×Dic38C2×C411yescharacteristic
31C2×M16×C19—21no—
32C2×C22⋊C4×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C42×C19C2×C412yes—
35C2×C22⋊Dic19—21no—
36C2×C22⋊Dic19—21no—
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19—22no—
42C2×C4⋊Dic19—22no—
43C2×C4⋊Dic19C2×C411yescharacteristic
44C2×C4⋊Dic19C2×C412yes—
45C2×C4⋊Dic19D412yes—
46#10597370—21no—
47#10597370—21no—
48#10597370—21no—
49#10597370—21no—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4—22no—
52C2×C4×Dic19—22no—
53C2×#64520—21no—
54C19×C22⋊C8—21no—
55C19×C22⋊C8—21no—
56C19×#95—21no—
57C19×#95—21no—
58C19×#95D412yes—
59C19⋊#95—22no—
60C19⋊#95—22no—
61C19⋊#95—21no—
62C19⋊#95—22no—
63C19⋊#95—22no—
64C19⋊#95D412yes—
65C22⋊(C19⋊C8)—21no—
66C22⋊(C19⋊C8)—21no—
67C24×C19C2×D411yescharacteristic
68C22×C4×C19—22no—
69C22×C4×C19—22no—
70C22×C4×C19—42no—
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19#4111yescharacteristic
76C22×C4×C19#4111yescharacteristic
77C22×Dic19—21no—
78C22×Dic19—21no—
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C22×Dic19—21no—
83C22×Dic19—22no—
84C22×Dic19—81no—
85C22×Dic19—81no—
86C22×Dic19C22⋊C412yes—
87C22×Dic19C22⋊C412yes—
88C2×Dic38—21no—
89C2×Dic38—21no—
90C2×Dic38—42no—
91M16×C19—42no—
92C2×C8×C19—41no—
93C22⋊C4×C19—24no—
94C22⋊C4×C19—42no—
95C42×C19—42no—
96C22⋊Dic19—42no—
97C22⋊Dic19—41no—
98C22⋊Dic19—41no—
99C4⋊Dic19—22no—
100C4⋊Dic19—22no—
101C4⋊Dic19—22no—
102C4⋊Dic19—22no—
103C4⋊Dic19—21no—
104C4⋊Dic19—21no—
105C4⋊Dic19—82no—
106C4⋊Dic19—82no—
107Dic19⋊C4—41no—
108Dic19⋊C4—41no—
109Dic19⋊C4—82no—
110C4×Dic19—82no—
111#64520—42no—
112C2×C19⋊C8—41no—
113#9461—191nomaximal, Sylow
114C23×C19—22no—
115C23×C19—22no—
116C23×C19—41no—
117C23×C19C2×C22⋊C411yescharacteristic
118C23×C19#12011yescharacteristic
119C23×C19#12311yescharacteristic
120C2×C4×C19—22no—
121C2×C4×C19—22no—
122C2×C4×C19—24no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—42no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—42no—
132C2×C4×C19C4×D411yescharacteristic
133C2×C4×C19C4×D411yescharacteristic
134C2×C4×C19#12111yescharacteristic
135C2×C4×C19#12111yescharacteristic
136C2×Dic19—22no—
137C2×Dic19—22no—
138C2×Dic19—42no—
139C2×Dic19—42no—
140C2×Dic19—42no—
141C2×Dic19—42no—
142C2×Dic19—42no—
143C2×Dic19—42no—
144C2×Dic19—42no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—42no—
148C2×Dic19—42no—
149C2×Dic19—81no—
150C2×Dic19—81no—
151Dic38—81no—
152Dic38—81no—
153C8×C19—81no—
154C19⋊C8—81no—
155#2502—191no—
156#2313—191no—
157#1821—191no—
158#1511—191no—
159#1511—191no—
160#1284—191no—
161#1284D1911yescharacteristic
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—44no—
170C22×C19#38611yescharacteristic
171C22×C19#41012yes—
172C22×C19#45612yes—
173C4×C19—21no—
174C4×C19—21no—
175C4×C19—21no—
176C4×C19—21no—
177C4×C19—44no—
178C4×C19—82no—
179Dic19—42no—
180Dic19—42no—
181Dic19—82no—
182Dic19—81no—
183Dic19—81no—
184C2×C22⋊Q8—191no—
185C22×C4⋊C4—191no—
186#407—191no—
187#407C2×D1911yescharacteristic
188#398—382no—
189#391—192no—
190#387—382no—
191#387—382no—
192#385—381no—
193#385—381no—
194#384—192no—
195#381—191no—
196#381C2×D1911yescharacteristic
197#380—381no—
198C4×C22⋊C4—381no—
199C4×C22⋊C4C2×D1911yescharacteristic
200#343—382no—
201#328—382no—
202#328—382no—
203C2×C19—22no—
204C2×C19—22no—
205C2×C19—41no—
206C2×C19#188611yescharacteristic
207C2×C19#189911yescharacteristic
208C2×C19#191111yescharacteristic
209C22×Q8—191no—
210C23×C4—191no—
211C23×C4—191no—
212C23×C4C22×D1911yescharacteristic
213C2×M16—21no—
214C2×M16—381no—
215C22⋊Q8—381no—
216C22⋊Q8—381no—
217C22⋊Q8—381no—
218C22⋊Q8—381no—
219C2×C4⋊C4—192no—
220C2×C4⋊C4—192no—
221C2×C4⋊C4—191no—
222C2×C4⋊C4—381no—
223C2×C4⋊C4—381no—
224C2×C4⋊C4—381no—
225C2×C4⋊C4—381no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4—382no—
228C2×C4⋊C4—382no—
229C2×C4⋊C4—382no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—381no—
233C2×C22⋊C4—381no—
234C2×C42—382no—
235C2×C42C4×D1912yes—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8—381no—
239C22⋊C8—381no—
240#95—21no—
241#95—21no—
242#95—192no—
243#95—382no—
244#95—382no—
245#95—382no—
246#95—382no—
247#95—381no—
248#95D7612yes—
249C19#946111yescharacteristic, complemented, Sylow
250C24D4×D1911yescharacteristic
251C2×Q8—381no—
252C2×Q8—381no—
253C2×Q8—762no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—42no—
257C22×C4—192no—
258C22×C4—192no—
259C22×C4—381no—
260C22×C4—381no—
261C22×C4—381no—
262C22×C4—381no—
263C22×C4—381no—
264C22×C4—381no—
265C22×C4—382no—
266C22×C4—1521no—
267C22×C4—1521no—
268C22×C4C2×C4×D1911yescharacteristic
269C22×C4C2×D7611yescharacteristic
270C22×C4#6454111yescharacteristic
271C22×C4D4×D1911yescharacteristic
272C22×C4D4×D1911yescharacteristic
273C22×C4#6454511yescharacteristic
274M16—42no—
275M16—762no—
276C2×C8—41no—
277C2×C8—761no—
278C4⋊C4—382no—
279C4⋊C4—382no—
280C4⋊C4—382no—
281C4⋊C4—382no—
282C4⋊C4—381no—
283C4⋊C4—381no—
284C4⋊C4—761no—
285C4⋊C4—761no—
286C4⋊C4—1522no—
287C4⋊C4—1522no—
288C4⋊C4—1522no—
289C22⋊C4—24no—
290C22⋊C4—42no—
291C22⋊C4—762no—
292C22⋊C4—761no—
293C22⋊C4—761no—
294C42—42no—
295C42—1522no—
296C23—22no—
297C23—22no—
298C23—41no—
299C23C22⋊C4×D1911yescharacteristic
300C23#1059732811yescharacteristic
301C23#1059734011yescharacteristic
302Q8—1521no—
303Q8—1521no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—382no—
317C2×C4—382no—
318C2×C4—762no—
319C2×C4—762no—
320C2×C4—762no—
321C2×C4—762no—
322C2×C4—762no—
323C2×C4—762no—
324C2×C4—762no—
325C2×C4—761no—
326C2×C4—761no—
327C2×C4—762no—
328C2×C4—762no—
329C2×C4—1521no—
330C2×C4—1521no—
331C2×C4C4×D7611yescharacteristic
332C2×C4#1059733011yescharacteristic
333C2×C4#1059733911yescharacteristic
334C2×C4#1059734111yescharacteristic
335C8—81no—
336C8—1521no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—44no—
345C22#1192642211yescharacteristic
346C22#1192651612yes—
347C22#1192672812yes—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—44no—
353C4—82no—
354C4—762no—
355C4—762no—
356C4—1522no—
357C4—1521no—
358C4—1521no—
359C2—22no—
360C2—22no—
361C2—41no—
362C2#1456402711yescharacteristic
363C2#1456409211yescharacteristic
364C2#1456416611yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1284C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#1284D19
hypocenterC19#9461
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
12. #11926450C4semidirect
17. #11926414C4semidirect
249. C19#9461semidirect

Maximal subgroups

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

subgroupindex
#145681132
#145662362
#145637132
#145621692
#145621672
#145614882
C19×#12842
#946119