Finite Group Databasebeta

← #18085273

Subgroups — #18085273

Order 4864.

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

normal subgroups only

This group has 528 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#14574580C211yesmaximal, characteristic
2#14572012C211yesmaximal, characteristic
3#14564613C211yesmaximal, characteristic
4#14562316C211yesmaximal, characteristic
5#14562315C211yesmaximal, characteristic
6#14561467C211yesmaximal, characteristic
7C19×#3209C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9#11926923—21no—
10#11926896—21no—
11#11926754—22no—
12#11926699—22no—
13#11926597C2211yescharacteristic
14#11926568C2211yescharacteristic
15#11926451—22no—
16#11926449—22no—
17#11926409—22no—
18C42×Dic19C2211yescharacteristic
19#11926303—22no—
20#11926293—22no—
21#11926292—22no—
22C19×#533C2211yescharacteristic
23C2×C19×C4⋊Q8C2211yescharacteristic
24C19×#494—21no—
25C19×#487—21no—
26C19×#462—22no—
27C19×#451—22no—
28C19×#431C2211yescharacteristic
29C22×Q8×C19D412yes—
30C22×Dic38D412yes—
31C2×Q16×C19—24no—
32C19×C4⋊Q8—21no—
33C19×C4⋊Q8—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8D411yescharacteristic
37C19×C4⋊Q8D411yescharacteristic
38C19×#125—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C4×Q8×C19—21no—
42C4×Q8×C19—21no—
43C19×#117—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C42×C19C2311yescharacteristic
47C2×#64528—24no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19—21no—
50C2×C4×Dic19—21no—
51C2×C4×Dic19—21no—
52C2×C4×Dic19D412yes—
53C2×#64520—21no—
54#10597315—21no—
55#10597315—21no—
56#10597315—21no—
57#10597315—21no—
58C19×C4⋊C8D412yes—
59C19×#103—24no—
60C19×C22⋊C8—21no—
61C4×C8×C19—21no—
62C19⋊#95—28no—
63C22⋊(C19⋊C8)—21no—
64#10597267—24no—
65C4⋊(C19⋊C8)—21no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)D412yes—
68C4×C19⋊C8—21no—
69C2×Q8×C19—21no—
70C2×Q8×C19—21no—
71C2×Q8×C19—22no—
72C2×Q8×C19—22no—
73C2×Q8×C19—44no—
74C22×C4×C19—22no—
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×Dic19—22no—
79C22×Dic19—22no—
80C2×Dic38—22no—
81C2×Dic38—22no—
82C2×Dic38—44no—
83Q16×C19—84no—
84C2×C8×C19—22no—
85C4⋊C4×C19—21no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—41no—
93C4⋊C4×C19—41no—
94C4⋊C4×C19—41no—
95C22⋊C4×C19—41no—
96C42×C19—41no—
97C42×C19C2×D411yescharacteristic
98C42×C19C2×D411yescharacteristic
99C42×C19C2×D411yescharacteristic
100C42×C19#4111yescharacteristic
101#64528—84no—
102C4⋊Dic19—41no—
103C4⋊Dic19—41no—
104C4⋊Dic19—41no—
105C4⋊Dic19—41no—
106C4×Dic19—22no—
107C4×Dic19—42no—
108C4×Dic19—42no—
109C4×Dic19Q1614yescomplemented
110#64520—42no—
111C2×C19⋊C8—22no—
112C2×C19⋊C8—41no—
113#10297—191nomaximal, Sylow
114C23×C19#12011yescharacteristic
115Q8×C19—42no—
116Q8×C19—42no—
117Q8×C19—44no—
118Q8×C19—82no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—44no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—42no—
125C2×C4×C19#12011yescharacteristic
126C2×C4×C19#12011yescharacteristic
127C2×C4×C19#12111yescharacteristic
128C2×C4×C19#12111yescharacteristic
129C2×C4×C19#12111yescharacteristic
130C2×C4×C19#12711yescharacteristic
131C2×C4×C19C2×Q1612yes—
132C2×C4×C19#13712yes—
133C2×Dic19—24no—
134C2×Dic19—42no—
135C2×Dic19—42no—
136C2×Dic19—44no—
137C2×Dic19—42no—
138Dic38—44no—
139Dic38—82no—
140C8×C19—42no—
141C19⋊C8—42no—
142C19⋊C8—81no—
143#3209—191no—
144#3209D1911yescharacteristic
145#2862—191no—
146#1994—191no—
147#1548—191no—
148#1548—191no—
149#1276—191no—
150C22×C19—21no—
151C22×C19—21no—
152C22×C19#39211yescharacteristic
153C22×C19#45112yes—
154C4×C19—21no—
155C4×C19—21no—
156C4×C19—82no—
157C4×C19—81no—
158C4×C19—81no—
159C4×C19#45512yes—
160C4×C19#45512yes—
161C4×C19#46212yes—
162C4×C19#49411yescharacteristic
163C4×C19#49711yescharacteristic
164Dic19—44no—
165Dic19—82no—
166#533C2×D1911yescharacteristic
167C2×C4⋊Q8—191no—
168C2×C4⋊Q8C2×D1911yescharacteristic
169#494—21no—
170#494—381no—
171#487—21no—
172#487—381no—
173#462—22no—
174#462—382no—
175#451—22no—
176#451—382no—
177#431—191no—
178#431C2×D1911yescharacteristic
179#423—191no—
180#391—382no—
181#391—382no—
182#382—382no—
183C43—191no—
184#339—382no—
185#333—382no—
186#333—382no—
187C2×C19—22no—
188C2×C19#200411yescharacteristic
189C2×C19#200411yescharacteristic
190C2×C19#201611yescharacteristic
191C22×Q8—192no—
192C22×Q8C22⋊D1912yes—
193C2×Q16—24no—
194C2×Q16—384no—
195C2×M16—381no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—381no—
201C4⋊Q8—381no—
202C4⋊Q8—381no—
203C4⋊Q8—381no—
204C4⋊Q8C22⋊D1911yescharacteristic
205C4⋊Q8C22⋊D1911yescharacteristic
206#125—21no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211#117—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—381no—
215C2×C4⋊C4—381no—
216C2×C42—192no—
217C2×C42—381no—
218C2×C42—381no—
219C2×C42C22×D1911yescharacteristic
220C4⋊C8—192no—
221C4⋊C8—381no—
222C4⋊C8—381no—
223C4⋊C8C22⋊D1912yes—
224#103—24no—
225#103—384no—
226C22⋊C8—21no—
227C22⋊C8—381no—
228C4×C8—21no—
229C4×C8—381no—
230#95—388no—
231C19#1029711yescharacteristic, complemented, Sylow
232C2×Q8—21no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—21no—
236C2×Q8—44no—
237C2×Q8—382no—
238C2×Q8—382no—
239C2×Q8—764no—
240C22×C4—22no—
241C22×C4—382no—
242C22×C4—382no—
243C22×C4D4×D1911yescharacteristic
244C22×C4D4×D1911yescharacteristic
245C22×C4C2×C22⋊D1911yescharacteristic
246Q16—84no—
247Q16—1524no—
248M16—762no—
249C2×C8—22no—
250C2×C8—382no—
251C2×C8—761no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—761no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C4⋊C4—761no—
266C22⋊C4—41no—
267C42—41no—
268C42—194no—
269C42—382no—
270C42—762no—
271C42—762no—
272C42D4×D1911yescharacteristic
273C42#6454311yescharacteristic
274C42C2×C22⋊D1911yescharacteristic
275C42C2×C22⋊D1911yescharacteristic
276C23#1059738311yescharacteristic
277Q8—42no—
278Q8—42no—
279Q8—44no—
280Q8—82no—
281Q8—764no—
282Q8—1522no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—44no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—384no—
290C2×C4—762no—
291C2×C4—762no—
292C2×C4—764no—
293C2×C4—762no—
294C2×C4Q16×D1912yes—
295C2×C4#1059736412yes—
296C2×C4#1059738311yescharacteristic
297C2×C4#1059738411yescharacteristic
298C2×C4#1059738511yescharacteristic
299C2×C4#1059738511yescharacteristic
300C2×C4#1059738611yescharacteristic
301C2×C4#1059739911yescharacteristic
302C8—42no—
303C8—762no—
304C8—1521no—
305C22—21no—
306C22—21no—
307C22#1192645211yescharacteristic
308C22#1192669812yes—
309C4—21no—
310C4—21no—
311C4—81no—
312C4—82no—
313C4—81no—
314C4—764no—
315C4—1522no—
316C4#1192672012yes—
317C4#1192672212yes—
318C4#1192675212yes—
319C4#1192692211yescharacteristic
320C4#1192693711yescharacteristic
321C2—22no—
322C2#1456466111yescharacteristic
323C2#1456466211yescharacteristic
324C2#1456473311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3209C2
socleC22×C19#392
prime radicalC23×C19#120
hypercenter#3209D19
hypocenterC19#10297
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
109. C4×Dic19Q16semidirect
231. C19#10297semidirect

Maximal subgroups

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

subgroupindex
#145745802
#145720122
#145646132
#145623162
#145623152
#145614672
C19×#32092
#1029719