Finite Group Databasebeta

← #18079936

Subgroups — #18079936

Order 4864.

466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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#14572718C211yesmaximal, characteristic
2#14568844C211yesmaximal, characteristic
3#14563628C211yesmaximal, characteristic
4#14562316C211yesmaximal, characteristic
5#14561537C211yesmaximal, characteristic
6#14561536C211yesmaximal, characteristic
7C19×#1548C211yesmaximal, characteristic
8C2×C4×Dic38C2211yescharacteristic
9#11926674—22no—
10#11926671—22no—
11#11926598—22no—
12#11926597C2211yescharacteristic
13#11926568C2211yescharacteristic
14C2×#10597281—21no—
15#11926463C414yes—
16#11926449—21no—
17#11926440—22no—
18#11926413—21no—
19C4×C4⋊Dic19C2211yescharacteristic
20#11926312—21no—
21#11926293—22no—
22C2×C19×C4⋊Q8C2211yescharacteristic
23C19×#431C2211yescharacteristic
24C19×#423C2211yescharacteristic
25C19×#333—22no—
26C22×Q8×C19C2×C412yes—
27C22×Dic38D411yescharacteristic
28C2×M16×C19—21no—
29C19×C4⋊Q8—21no—
30C19×C4⋊Q8—21no—
31C19×C4⋊Q8—21no—
32C19×C4⋊Q8—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C42×C19C2311yescharacteristic
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19D411yescharacteristic
38C2×Dic19⋊C4—24no—
39C2×Dic19⋊C4C2×C412yes—
40C2×C4×Dic19—21no—
41C2×C4×Dic19D412yes—
42C2×#64520—21no—
43C4×Dic38—21no—
44C4×Dic38—21no—
45C4×Dic38—21no—
46C4×Dic38—21no—
47C19×C4⋊C8—21no—
48C19×C4⋊C8—21no—
49C19×C4⋊C8D412yes—
50C19×C22⋊C8—21no—
51C4×C8×C19—21no—
52C19⋊#95—24no—
53C19⋊#95C2×C412yes—
54C22⋊(C19⋊C8)—21no—
55#10597281—42no—
56#10597272—24no—
57Dic19⋊C8—24no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)D412yes—
61C4×C19⋊C8—21no—
62C2×Q8×C19—22no—
63C2×Q8×C19—22no—
64C2×Q8×C19—82no—
65C22×C4×C19—22no—
66C22×C4×C19C22×C411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×Dic19—22no—
70C22×Dic19C22⋊C412yes—
71C22×Dic19C22⋊C412yes—
72C2×Dic38—21no—
73C2×Dic38—21no—
74C2×Dic38—21no—
75C2×Dic38—21no—
76C2×Dic38—21no—
77C2×Dic38—21no—
78M16×C19—41no—
79M16×C19—41no—
80C2×C8×C19—22no—
81C2×C8×C19—41no—
82C4⋊C4×C19—41no—
83C4⋊C4×C19—41no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—41no—
86C42×C19C2×D411yescharacteristic
87C42×C19C2×D411yescharacteristic
88C42×C19#4111yescharacteristic
89C42×C19#4111yescharacteristic
90C4⋊Dic19—24no—
91C4⋊Dic19—21no—
92C4⋊Dic19—21no—
93Dic19⋊C4—22no—
94Dic19⋊C4—22no—
95Dic19⋊C4—84no—
96C4×Dic19—22no—
97C4×Dic19—22no—
98C4×Dic19—41no—
99C4×Dic19—41no—
100#64520—41no—
101#64520—41no—
102C2×C19⋊C8—22no—
103C2×C19⋊C8—41no—
104#9400—191nomaximal, Sylow
105C23×C19C2×C22⋊C411yescharacteristic
106Q8×C19—82no—
107Q8×C19—82no—
108C2×C4×C19—22no—
109C2×C4×C19—41no—
110C2×C4×C19—44no—
111C2×C4×C19—42no—
112C2×C4×C19C4×D411yescharacteristic
113C2×C4×C19C4×D411yescharacteristic
114C2×C4×C19#12011yescharacteristic
115C2×C4×C19#12111yescharacteristic
116C2×C4×C19#12111yescharacteristic
117C2×C4×C19#12311yescharacteristic
118C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C19#13711yescharacteristic
120C2×C4×C19#13711yescharacteristic
121C2×C4×C19#13711yescharacteristic
122C2×Dic19—24no—
123C2×Dic19—22no—
124C2×Dic19—22no—
125C2×Dic19—22no—
126C2×Dic19—22no—
127C2×Dic19—42no—
128C2×Dic19—42no—
129C2×Dic19—42no—
130Dic38—41no—
131Dic38—41no—
132Dic38—41no—
133Dic38—41no—
134C8×C19—42no—
135C8×C19—81no—
136C19⋊C8—42no—
137C19⋊C8—81no—
138#2983—191no—
139#2567—191no—
140#1801—191no—
141#1548—191no—
142#1548D1911yescharacteristic
143#1303—191no—
144#1303—191no—
145C22×C19—21no—
146C22×C19—21no—
147C22×C19#38611yescharacteristic
148C22×C19#41711yescharacteristic
149C22×C19#41911yescharacteristic
150C4×C19—21no—
151C4×C19—21no—
152C4×C19—21no—
153C4×C19—82no—
154C4×C19#45612yes—
155C4×C19#46811yescharacteristic
156C4×C19#46811yescharacteristic
157C4×C19#47011yescharacteristic
158C4×C19#47011yescharacteristic
159Dic19—44no—
160Dic19—42no—
161Dic19—42no—
162C2×C4⋊Q8C2×D1911yescharacteristic
163C2×C4×Q8—191no—
164#446—382no—
165#446—382no—
166#432—382no—
167#431—191no—
168#431C2×D1911yescharacteristic
169#423—191no—
170#423C2×D1911yescharacteristic
171C2×#101—381no—
172#395—194no—
173#391—381no—
174#389—382no—
175#384—381no—
176C4×C4⋊C4—191no—
177#343—381no—
178#333—22no—
179#333—382no—
180C2×C19—21no—
181C2×C19—21no—
182C2×C19#188611yescharacteristic
183C2×C19#189411yescharacteristic
184C2×C19#191411yescharacteristic
185C22×Q8—191no—
186C22×Q8C4×D1912yes—
187C2×M16—21no—
188C2×M16—381no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4×Q8—381no—
194C4×Q8—381no—
195C4×Q8—381no—
196C4×Q8—381no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—192no—
200C2×C4⋊C4—191no—
201C2×C4⋊C4—381no—
202C2×C4⋊C4—384no—
203C2×C42—192no—
204C2×C42—381no—
205C2×C42C22×D1911yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—192no—
209C4⋊C8—384no—
210C4⋊C8—381no—
211C4⋊C8—381no—
212C4⋊C8C22⋊D1912yes—
213#101—762no—
214C22⋊C8—21no—
215C22⋊C8—381no—
216#97—384no—
217C4×C8—21no—
218C4×C8—381no—
219#95—192no—
220#95—384no—
221C19#940011yescharacteristic, complemented, Sylow
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—82no—
225C2×Q8—381no—
226C2×Q8—381no—
227C2×Q8—381no—
228C2×Q8—381no—
229C2×Q8—381no—
230C2×Q8—381no—
231C22×C4—22no—
232C22×C4—192no—
233C22×C4—192no—
234C22×C4—382no—
235C22×C4C2×C4×D1911yescharacteristic
236C22×C4D4×D1911yescharacteristic
237C22×C4D4×D1911yescharacteristic
238M16—41no—
239M16—41no—
240M16—761no—
241M16—761no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—382no—
245C2×C8—761no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—384no—
251C4⋊C4—381no—
252C4⋊C4—382no—
253C4⋊C4—381no—
254C4⋊C4—382no—
255C4⋊C4—1524no—
256C42—382no—
257C42—382no—
258C42—761no—
259C42—761no—
260C42#6454111yescharacteristic
261C42D4×D1911yescharacteristic
262C42#6454311yescharacteristic
263C42C2×C22⋊D1911yescharacteristic
264C23C22⋊C4×D1911yescharacteristic
265Q8—82no—
266Q8—82no—
267Q8—761no—
268Q8—761no—
269Q8—761no—
270Q8—761no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—44no—
274C2×C4—42no—
275C2×C4—384no—
276C2×C4—382no—
277C2×C4—382no—
278C2×C4—382no—
279C2×C4—382no—
280C2×C4—762no—
281C2×C4—762no—
282C2×C4—762no—
283C2×C4(C22⋊D19)⋊C411yescharacteristic
284C2×C4#1059732911yescharacteristic
285C2×C4#1059733011yescharacteristic
286C2×C4#1059736011yescharacteristic
287C2×C4#1059736111yescharacteristic
288C2×C4#1059736411yescharacteristic
289C2×C4#1059736411yescharacteristic
290C2×C4C4×C22⋊D1911yescharacteristic
291C2×C4#1059738311yescharacteristic
292C2×C4#1059738411yescharacteristic
293C8—42no—
294C8—81no—
295C8—762no—
296C8—1521no—
297C22—21no—
298C22—21no—
299C22#1192642011yescharacteristic
300C22#1192654411yescharacteristic
301C22#1192655111yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—82no—
306C4—764no—
307C4—762no—
308C4—762no—
309C4#1192672512yes—
310C4#1192678711yescharacteristic
311C4#1192679311yescharacteristic
312C4#1192679911yescharacteristic
313C4#1192680111yescharacteristic
314C2—21no—
315C2—21no—
316C2#1456402511yescharacteristic
317C2#1456406511yescharacteristic
318C2#1456417911yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1548C2
socleC22×C19#386
prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1548D19
hypocenterC19#9400
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
221. C19#9400semidirect

Maximal subgroups

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

subgroupindex
#145727182
#145688442
#145636282
#145623162
#145615372
#145615362
C19×#15482
#940019