Finite Group Databasebeta

← #18086670

Subgroups — #18086670

Order 4864.

382 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 95 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#14574977C211yesmaximal, characteristic
2#14564613C211yesmaximal, characteristic
3#14564611C211yesmaximal, characteristic
4#14563751C211yesmaximal, characteristic
5#14562323C211yesmaximal, characteristic
6#14561509C211yesmaximal, characteristic
7C19×#1550C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926839—21no—
10#11926836—21no—
11#11926783—22no—
12#11926754—21no—
13#11926751—21no—
14#11926568C2211yescharacteristic
15C2×C4⋊(C19⋊C8)C2211yescharacteristic
16C42×Dic19C2211yescharacteristic
17#11926305—21no—
18#11926305—21no—
19#11926303—21no—
20#11926303—21no—
21#11926298—22no—
22#11926292—21no—
23#11926291—21no—
24C19×#533C2211yescharacteristic
25C19×#423C2211yescharacteristic
26C2×C19×C4⋊C8C2211yescharacteristic
27C19×#333—21no—
28C19×#332—21no—
29C2×M16×C19—21no—
30C22×C8×C19—21no—
31C19×C4⋊Q8D411yescharacteristic
32C19×C4⋊Q8D411yescharacteristic
33C19×#125—21no—
34C19×C22⋊Q8—21no—
35C19×C22⋊Q8—21no—
36C4×Q8×C19—21no—
37C4×Q8×C19—21no—
38C19×#117—21no—
39C2×C42×C19C2311yescharacteristic
40C2×#64528—22no—
41#10597372—21no—
42#10597370—21no—
43#10597370—21no—
44C2×C4×Dic19—21no—
45C2×C4×Dic19—21no—
46C2×C4×Dic19D411yescharacteristic
47C2×C4×Dic19D411yescharacteristic
48C2×#64520—21no—
49C22×C19⋊C8D412yes—
50#10597316—21no—
51#10597315D411yescharacteristic
52#10597315D411yescharacteristic
53C4×Dic38—21no—
54C4×Dic38—21no—
55C19×C4⋊C8—21no—
56C19×C4⋊C8—21no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8—21no—
59#10597292—22no—
60#10597267—22no—
61#10597264—22no—
62C4⋊(C19⋊C8)—21no—
63C4⋊(C19⋊C8)—21no—
64C4⋊(C19⋊C8)—21no—
65C4⋊(C19⋊C8)—21no—
66C2×Q8×C19—21no—
67C2×Q8×C19—21no—
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19#4111yescharacteristic
71C22×Dic19—21no—
72C22×Dic19—21no—
73C2×Dic38—21no—
74C2×Dic38—21no—
75M16×C19—41no—
76M16×C19—41no—
77C2×C8×C19—42no—
78C2×C8×C19—41no—
79C2×C8×C19—41no—
80C4⋊C4×C19—21no—
81C4⋊C4×C19—21no—
82C4⋊C4×C19—21no—
83C4⋊C4×C19—21no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—41no—
86C22⋊C4×C19—41no—
87C42×C19—41no—
88C42×C19C2×D411yescharacteristic
89C42×C19C2×D411yescharacteristic
90C42×C19#4111yescharacteristic
91C42×C19#4111yescharacteristic
92C22⋊Dic19—41no—
93#64528—82no—
94C4⋊Dic19—21no—
95C4⋊Dic19—21no—
96C4⋊Dic19—21no—
97C4⋊Dic19—21no—
98Dic19⋊C4—41no—
99Dic19⋊C4—41no—
100C4×Dic19—21no—
101C4×Dic19—21no—
102C4×Dic19—21no—
103C4×Dic19—42no—
104C4×Dic19—41no—
105C4×Dic19—41no—
106C4×Dic19—41no—
107C4×Dic19Q1612yescomplemented
108#64520—41no—
109#64520—41no—
110C2×C19⋊C8—22no—
111C2×C19⋊C8—42no—
112C2×C19⋊C8—41no—
113#10523—191nomaximal, Sylow
114C23×C19#12111yescharacteristic
115Q8×C19—41no—
116Q8×C19—41no—
117Q8×C19—81no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19#12011yescharacteristic
124C2×C4×C19#12111yescharacteristic
125C2×C4×C19#12111yescharacteristic
126C2×C4×C19#12311yescharacteristic
127C2×C4×C19#12311yescharacteristic
128C2×C4×C19#12411yescharacteristic
129C2×C4×C19C2×Q1611yescharacteristic
130C2×C4×C19#13511yescharacteristic
131C2×C4×C19#13711yescharacteristic
132C2×C4×C19#13711yescharacteristic
133C2×Dic19—22no—
134C2×Dic19—22no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141Dic38—41no—
142Dic38—41no—
143Dic38—81no—
144C8×C19—81no—
145C8×C19—81no—
146C19⋊C8—42no—
147C19⋊C8—81no—
148#3249—191no—
149#1994—191no—
150#1994—191no—
151#1831—191no—
152#1550—191no—
153#1550D1911yescharacteristic
154#1292—191no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19#39411yescharacteristic
158C22×C19#46711yescharacteristic
159C22×C19#47011yescharacteristic
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—81no—
164C4×C19—81no—
165C4×C19#45411yescharacteristic
166C4×C19#45511yescharacteristic
167C4×C19#46211yescharacteristic
168C4×C19#46211yescharacteristic
169C4×C19#46411yescharacteristic
170C4×C19#46411yescharacteristic
171Dic19—42no—
172Dic19—42no—
173Dic19—81no—
174Dic19—81no—
175#533—191no—
176#533C2×D1911yescharacteristic
177#477—381no—
178#477—381no—
179#467—382no—
180#462—381no—
181#462—381no—
182#423—191no—
183#423C2×D1911yescharacteristic
184C2×C4⋊C8—191no—
185C2×C4⋊C8C2×D1911yescharacteristic
186C43—191no—
187#339—381no—
188#339—381no—
189#339—381no—
190#339—381no—
191#336—382no—
192#333—21no—
193#333—381no—
194#332—21no—
195#332—381no—
196C2×C19—21no—
197C2×C19—21no—
198C2×C19#204011yescharacteristic
199C2×C19#205011yescharacteristic
200C2×C19#205611yescharacteristic
201C2×Q16—382no—
202C2×M16—21no—
203C2×M16—381no—
204C22×C8—21no—
205C22×C8—192no—
206C4⋊Q8—191no—
207C4⋊Q8—191no—
208C4⋊Q8C22⋊D1911yescharacteristic
209C4⋊Q8C22⋊D1911yescharacteristic
210#125—21no—
211#125—381no—
212C22⋊Q8—21no—
213C22⋊Q8—21no—
214C22⋊Q8—381no—
215C22⋊Q8—381no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—381no—
219C4×Q8—381no—
220#117—21no—
221#117—381no—
222C2×C42—191no—
223C2×C42—191no—
224C2×C42—381no—
225C2×C42—381no—
226C2×C42C22×D1911yescharacteristic
227#107—382no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—381no—
233C4⋊C8—381no—
234C4⋊C8—381no—
235C4⋊C8—381no—
236#103—382no—
237#103—382no—
238C19#1052311yescharacteristic, complemented, Sylow
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—381no—
242C2×Q8—381no—
243C22×C4—381no—
244C22×C4—381no—
245C22×C4#6454111yescharacteristic
246C22×C4D4×D1911yescharacteristic
247C22×C4D4×D1911yescharacteristic
248Q16—1522no—
249M16—41no—
250M16—41no—
251M16—761no—
252M16—761no—
253C2×C8—42no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—382no—
257C2×C8—762no—
258C2×C8—761no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—381no—
266C4⋊C4—381no—
267C4⋊C4—381no—
268C4⋊C4—381no—
269C4⋊C4—761no—
270C4⋊C4—761no—
271C22⋊C4—41no—
272C22⋊C4—761no—
273C42—41no—
274C42—192no—
275C42—381no—
276C42—381no—
277C42—381no—
278C42—761no—
279C42—761no—
280C42—762no—
281C42—761no—
282C42#6454111yescharacteristic
283C42D4×D1911yescharacteristic
284C42#6454311yescharacteristic
285C42C2×C22⋊D1911yescharacteristic
286C23#1059733011yescharacteristic
287Q8—41no—
288Q8—41no—
289Q8—81no—
290Q8—761no—
291Q8—761no—
292Q8—1521no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—382no—
299C2×C4—382no—
300C2×C4—761no—
301C2×C4—761no—
302C2×C4—761no—
303C2×C4—761no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4#1059732911yescharacteristic
307C2×C4#1059733011yescharacteristic
308C2×C4#1059733111yescharacteristic
309C2×C4#1059736111yescharacteristic
310C2×C4#1059736211yescharacteristic
311C2×C4Q16×D1911yescharacteristic
312C2×C4#1059736411yescharacteristic
313C2×C4#1059737511yescharacteristic
314C2×C4#1059738311yescharacteristic
315C2×C4#1059738511yescharacteristic
316C8—81no—
317C8—81no—
318C8—762no—
319C8—1521no—
320C22—21no—
321C22—21no—
322C22#1192645911yescharacteristic
323C22#1192678411yescharacteristic
324C22#1192680111yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—81no—
329C4—81no—
330C4—762no—
331C4—762no—
332C4—1521no—
333C4—1521no—
334C4#1192671511yescharacteristic
335C4#1192672011yescharacteristic
336C4#1192675211yescharacteristic
337C4#1192675311yescharacteristic
338C4#1192676411yescharacteristic
339C4#1192676911yescharacteristic
340C2—21no—
341C2—21no—
342C2#1456486211yescharacteristic
343C2#1456492011yescharacteristic
344C2#1456495611yescharacteristic
subgroupG/H
centerC22#11926459
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1550C2
socleC22×C19#394
prime radicalC23×C19#121
hypercenter#1550D19
hypocenterC19#10523
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
107. C4×Dic19Q16semidirect
238. C19#10523semidirect

Maximal subgroups

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

subgroupindex
#145749772
#145646132
#145646112
#145637512
#145623232
#145615092
C19×#15502
#1052319