Finite Group Databasebeta

← #18075577

Subgroups — #18075577

Order 4864.

336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 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#14572565C211yesmaximal, characteristic
2#14562393C211yesmaximal, characteristic
3#14562390C211yesmaximal, characteristic
4#14562372C211yesmaximal, characteristic
5#14562372C211yesmaximal, characteristic
6C19⋊#1309C211yesmaximal, characteristic
7C19×#1309C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926671—21no—
10#11926671—21no—
11#11926668—21no—
12#11926668—21no—
13#11926572C412yes—
14#11926568C2211yescharacteristic
15#11926568C2211yescharacteristic
16#11926502C412yes—
17C2×C4×C19⋊C8C2211yescharacteristic
18#11926296—21no—
19#11926296—21no—
20#11926294—21no—
21#11926294—21no—
22#11926291—21no—
23#11926291—21no—
24#11926289—21no—
25#11926289—21no—
26C19×#423C2211yescharacteristic
27C19×#423C2211yescharacteristic
28C19×#423C2211yescharacteristic
29C2×M16×C19—21no—
30C2×M16×C19—21no—
31C2×M16×C19C2×C412yes—
32C2×C42×C19C2311yescharacteristic
33#10597372C2×C412yes—
34#10597370—21no—
35#10597370—21no—
36C2×#64520—21no—
37C2×#64520—21no—
38C22×C19⋊C8C2×C411yescharacteristic
39C22×C19⋊C8C2×C411yescharacteristic
40#10597316Q812yes—
41#10597315D411yescharacteristic
42#10597315D411yescharacteristic
43C4×Dic38—21no—
44C4×Dic38—21no—
45C19×C4⋊C8—21no—
46C19×C4⋊C8—21no—
47C19×C4⋊C8—21no—
48C19×C4⋊C8—21no—
49C19×C4⋊C8—21no—
50C19×C4⋊C8—21no—
51#10597272—22no—
52Dic19⋊C8—22no—
53Dic19⋊C8—22no—
54C8×Dic19—22no—
55C4⋊(C19⋊C8)—21no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)—21no—
58C4⋊(C19⋊C8)—21no—
59C4×C19⋊C8D411yescharacteristic
60C4×C19⋊C8D411yescharacteristic
61C4×C19⋊C8D411yescharacteristic
62C4×C19⋊C8D411yescharacteristic
63C22×C4×C19C22×C411yescharacteristic
64C22×C4×C19#4111yescharacteristic
65C22×C4×C19#4111yescharacteristic
66C2×Dic38—21no—
67C2×Dic38—21no—
68M16×C19—42no—
69M16×C19—81no—
70M16×C19—81no—
71C2×C8×C19—22no—
72C2×C8×C19—41no—
73C2×C8×C19—41no—
74C42×C19C2×D411yescharacteristic
75C42×C19C2×D411yescharacteristic
76C42×C19C2×D411yescharacteristic
77C42×C19C2×Q811yescharacteristic
78C22⋊Dic19—22no—
79C4⋊Dic19—21no—
80C4⋊Dic19—21no—
81C4⋊Dic19C4⋊C412yes—
82C4⋊Dic19C4⋊C412yes—
83Dic19⋊C4—22no—
84Dic19⋊C4—22no—
85C4×Dic19—22no—
86#64520—81no—
87#64520—81no—
88C2×C19⋊C8—22no—
89C2×C19⋊C8—41no—
90C2×C19⋊C8—41no—
91C2×C19⋊C8—41no—
92C2×C19⋊C8C22⋊C411yescharacteristic
93C2×C19⋊C8C22⋊C411yescharacteristic
94C2×C19⋊C8C22⋊C411yescharacteristic
95C2×C19⋊C8C22⋊C411yescharacteristic
96#8641—191nomaximal, Sylow
97C23×C19#11711yescharacteristic
98C2×C4×C19—21no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—21no—
104C2×C4×C19C2×C22⋊C411yescharacteristic
105C2×C4×C19C2×C4⋊C411yescharacteristic
106C2×C4×C19#12111yescharacteristic
107C2×C4×C19#12111yescharacteristic
108C2×C4×C19C22⋊Q811yescharacteristic
109C2×C4×C19C22⋊Q811yescharacteristic
110C2×Dic19—22no—
111C2×Dic19—22no—
112Dic38—41no—
113Dic38—41no—
114Dic38—41no—
115Dic38—41no—
116C8×C19—42no—
117C8×C19—81no—
118C8×C19—81no—
119C19⋊C8—21no—
120C19⋊C8—21no—
121C19⋊C8—21no—
122C19⋊C8—81no—
123C19⋊C8—81no—
124C19⋊C8#10112yes—
125#2960—191no—
126#1567—191no—
127#1566—191no—
128#1561—191no—
129#1561—191no—
130#1309—191no—
131#1309D1911yescharacteristic
132C22×C19—21no—
133C22×C19—21no—
134C22×C19—21no—
135C22×C19#38011yescharacteristic
136C4×C19—21no—
137C4×C19—21no—
138C4×C19—21no—
139C4×C19C2×#10111yescharacteristic
140C4×C19#41311yescharacteristic
141C4×C19#47111yescharacteristic
142C4×C19#47111yescharacteristic
143C4×C19#47211yescharacteristic
144C4×C19#47311yescharacteristic
145Dic19—42no—
146Dic19—42no—
147#533—191no—
148#446—381no—
149#446—381no—
150C8×Q8—381no—
151C8×Q8—381no—
152#424—192no—
153#423—191no—
154#423—191no—
155#423C2×D1911yescharacteristic
156#423C2×D1911yescharacteristic
157#423C2×D1911yescharacteristic
158#405—192no—
159C2×C4×C8—191no—
160#335—381no—
161#335—381no—
162#334—381no—
163#334—381no—
164#332—381no—
165#332—381no—
166#332—381no—
167#332—381no—
168C2×C19—41no—
169C2×C19#180111yescharacteristic
170C2×C19#181511yescharacteristic
171C2×C19#181611yescharacteristic
172C2×M16—21no—
173C2×M16—21no—
174C2×M16—381no—
175C2×M16—381no—
176C2×M16C4×D1912yes—
177C22×C8—191no—
178C22×C8—191no—
179C4⋊Q8—191no—
180C4⋊Q8—191no—
181#125—192no—
182C22⋊Q8—381no—
183C22⋊Q8—381no—
184C4×Q8—381no—
185C4×Q8—381no—
186#117—192no—
187C2×C42C22×D1911yescharacteristic
188C4⋊C8—21no—
189C4⋊C8—21no—
190C4⋊C8—21no—
191C4⋊C8—21no—
192C4⋊C8—21no—
193C4⋊C8—21no—
194C4⋊C8—382no—
195C4⋊C8—382no—
196C4⋊C8—381no—
197C4⋊C8—381no—
198C4⋊C8—381no—
199C4⋊C8—381no—
200#97—382no—
201C4×C8—191no—
202C4×C8—191no—
203C4×C8—191no—
204C4×C8—191no—
205C4×C8—382no—
206C19#864111yescharacteristic, complemented, Sylow
207C2×Q8—381no—
208C2×Q8—381no—
209C22×C4C2×C4×D1911yescharacteristic
210C22×C4#6454111yescharacteristic
211C22×C4#6454111yescharacteristic
212M16—42no—
213M16—81no—
214M16—81no—
215M16—1521no—
216M16—1521no—
217C2×C8—22no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—191no—
221C2×C8—191no—
222C2×C8—191no—
223C2×C8—191no—
224C2×C8—382no—
225C2×C8—761no—
226C2×C8—761no—
227C2×C8—761no—
228C4⋊C4—192no—
229C4⋊C4—192no—
230C4⋊C4—381no—
231C4⋊C4—381no—
232C4⋊C4—382no—
233C4⋊C4—382no—
234C22⋊C4—382no—
235C42—382no—
236C42D4×D1911yescharacteristic
237C42D4×D1911yescharacteristic
238C42D4×D1911yescharacteristic
239C42Q8×D1911yescharacteristic
240C23#1059731811yescharacteristic
241Q8—761no—
242Q8—761no—
243Q8—761no—
244Q8—761no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—382no—
252C2×C4—382no—
253C2×C4C22⋊C4×D1911yescharacteristic
254C2×C4#1059733011yescharacteristic
255C2×C4#1059733011yescharacteristic
256C2×C4C4⋊C4×D1911yescharacteristic
257C2×C4#1059734211yescharacteristic
258C2×C4#1059734211yescharacteristic
259C8—42no—
260C8—81no—
261C8—81no—
262C8—192no—
263C8—381no—
264C8—381no—
265C8—381no—
266C8—1521no—
267C8—1521no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22#1192640311yescharacteristic
272C4—21no—
273C4—21no—
274C4—21no—
275C4—762no—
276C4—762no—
277C4#101×D1911yescharacteristic
278C4#1192652511yescharacteristic
279C4#1192680611yescharacteristic
280C4#1192681011yescharacteristic
281C4#1192681311yescharacteristic
282C4#1192681811yescharacteristic
283C2—41no—
284C2#1456363011yescharacteristic
285C2#1456369311yescharacteristic
286C2#1456369811yescharacteristic
subgroupG/H
centerC22#11926403
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1309C2
socleC22×C19#380
prime radicalC23×C19#117
cosocleC2×C42×C19C23
hypercenter#1309D19
hypocenterC19#8641
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1309

Complements

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

NH ≅ G/Ntype
206. C19#8641semidirect

Maximal subgroups

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

subgroupindex
#145725652
#145623932
#145623902
#145623722
C19⋊#13092
C19×#13092
#864119