Finite Group Databasebeta

← #18082684

Subgroups — #18082684

Order 4864.

506 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572032C211yesmaximal, characteristic
2#14563751C211yesmaximal, characteristic
3#14563490C211yesmaximal, characteristic
4#14561519C211yesmaximal, characteristic
5#14561519C211yesmaximal, characteristic
6#14561518C211yesmaximal, characteristic
7C19×#1296C211yesmaximal, characteristic
8C2×#10597334—21no—
9C2×#10597334—21no—
10C2×#10597334C412yes—
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×C4⋊(C19⋊C8)C2211yescharacteristic
13C2×#10597272—21no—
14#11926414C2211yescharacteristic
15#11926413—21no—
16#11926413—21no—
17#11926413C412yes—
18C42×Dic19C2211yescharacteristic
19#11926298—21no—
20#11926298—21no—
21#11926298—21no—
22C2×C19×C4⋊C8C2211yescharacteristic
23C2×C19×C4⋊C8C2211yescharacteristic
24C19×#384C2211yescharacteristic
25C22×Dic38—22no—
26C22×C8×C19—21no—
27C22×C8×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19C2×C412yes—
31C2×C42×C19C2311yescharacteristic
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19C2×C412yes—
35C2×Dic19⋊C4—22no—
36C2×Dic19⋊C4—22no—
37C2×Dic19⋊C4—22no—
38C2×C4×Dic19C2×C411yescharacteristic
39C2×C4×Dic19C2×C411yescharacteristic
40C2×C4×Dic19D411yescharacteristic
41C2×C4×Dic19D411yescharacteristic
42C2×C4×Dic19D411yescharacteristic
43C2×C4×Dic19D411yescharacteristic
44C22×C19⋊C8—21no—
45C22×C19⋊C8—21no—
46#10597334—42no—
47#10597334—42no—
48#10597334—42no—
49#10597334—42no—
50#10597334—44no—
51C19×C4⋊C8—21no—
52C19×C4⋊C8—21no—
53C19×C4⋊C8—21no—
54C19×C4⋊C8Q812yescomplemented
55#10597272—42no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)—21no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)Q812yescomplemented
60C22×C4×C19—22no—
61C22×C4×C19C22×C411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×Dic19—22no—
65C22×Dic19C22⋊C411yescharacteristic
66C22×Dic19C22⋊C411yescharacteristic
67C22×Dic19C22⋊C411yescharacteristic
68C22×Dic19C22⋊C411yescharacteristic
69C2×Dic38—44no—
70C2×Dic38—44no—
71C2×Dic38—44no—
72C2×C8×C19—22no—
73C2×C8×C19—41no—
74C2×C8×C19—41no—
75C2×C8×C19—41no—
76C2×C8×C19—41no—
77C2×C8×C19—41no—
78C4⋊C4×C19—42no—
79C4⋊C4×C19—41no—
80C4⋊C4×C19—41no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19—41no—
83C42×C19C2×Q811yescharacteristic
84C42×C19C2×Q811yescharacteristic
85C42×C19#4111yescharacteristic
86C42×C19#4111yescharacteristic
87C4⋊Dic19—41no—
88C4⋊Dic19—41no—
89C4⋊Dic19—41no—
90C4⋊Dic19—41no—
91C4⋊Dic19—42no—
92Dic19⋊C4—44no—
93Dic19⋊C4—44no—
94Dic19⋊C4—44no—
95C4×Dic19—21no—
96C4×Dic19—21no—
97C4×Dic19—21no—
98C4×Dic19—21no—
99C4×Dic19—21no—
100C4×Dic19—21no—
101C4×Dic19—22no—
102C4×Dic19—22no—
103C4×Dic19SD1612yes—
104C4×Dic19Q1612yes—
105C2×C19⋊C8—22no—
106C2×C19⋊C8—41no—
107C2×C19⋊C8—41no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8—41no—
111#9903—191nomaximal, Sylow
112C23×C19C2×C22⋊C411yescharacteristic
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19—42no—
118C2×C4×C19C4×Q811yescharacteristic
119C2×C4×C19C4×Q811yescharacteristic
120C2×C4×C19C22⋊Q811yescharacteristic
121C2×C4×C19C22⋊Q811yescharacteristic
122C2×C4×C19#12411yescharacteristic
123C2×C4×C19C4⋊Q811yescharacteristic
124C2×C4×C19C2×SD1611yescharacteristic
125C2×C4×C19C2×Q1611yescharacteristic
126C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C19#13711yescharacteristic
131C2×C4×C19#13711yescharacteristic
132C2×Dic19—21no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137C2×Dic19—21no—
138C2×Dic19—21no—
139C2×Dic19—21no—
140C2×Dic19—42no—
141C2×Dic19—42no—
142C2×Dic19—42no—
143C2×Dic19#10012yes—
144C2×Dic19#10112yes—
145C2×Dic19#10312yes—
146C2×Dic19#10312yes—
147Dic38—88no—
148C8×C19—42no—
149C8×C19—81no—
150C19⋊C8—42no—
151C19⋊C8—81no—
152#2868—191no—
153#1831—191no—
154#1767—191no—
155#1296—191no—
156#1296—191no—
157#1296—191no—
158#1296D1911yescharacteristic
159C22×C19#39111yescharacteristic
160C22×C19C2×#10011yescharacteristic
161C22×C19C2×#10111yescharacteristic
162C22×C19C2×#10311yescharacteristic
163C22×C19#41811yescharacteristic
164C22×C19#41811yescharacteristic
165C22×C19#41911yescharacteristic
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—82no—
169C4×C19#47611yescharacteristic
170C4×C19#47611yescharacteristic
171C4×C19#47711yescharacteristic
172C4×C19#47711yescharacteristic
173C4×C19#48911yescharacteristic
174C4×C19#48911yescharacteristic
175C4×C19#50111yescharacteristic
176C4×C19#50111yescharacteristic
177Dic19—22no—
178Dic19—22no—
179Dic19—22no—
180Dic19—22no—
181Dic19—82no—
182C2×C4⋊Q8—192no—
183C2×C4⋊Q8—381no—
184C2×C4⋊Q8—381no—
185C2×C4⋊C8—191no—
186C2×C4⋊C8—191no—
187C2×C4⋊C8C2×D1911yescharacteristic
188C2×C4⋊C8C2×D1911yescharacteristic
189C2×#97—381no—
190#384—192no—
191#384—191no—
192#384—381no—
193#384—381no—
194#384C2×D1911yescharacteristic
195C43—191no—
196#336—381no—
197#336—381no—
198#336—381no—
199C2×C19#154811yescharacteristic
200C2×C19#154911yescharacteristic
201C2×C19#155511yescharacteristic
202C2×C19#155611yescharacteristic
203C2×C19#198711yescharacteristic
204C2×C19#199311yescharacteristic
205C2×C19#199711yescharacteristic
206C22×Q8—382no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—381no—
210C22×C8—381no—
211C4⋊Q8—764no—
212C4⋊Q8—762no—
213C4⋊Q8—762no—
214C4⋊Q8—762no—
215C4⋊Q8—762no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—192no—
219C2×C4⋊C4—382no—
220C2×C4⋊C4—382no—
221C2×C4⋊C4—382no—
222C2×C4⋊C4—381no—
223C2×C4⋊C4—381no—
224C2×C4⋊C4C4×D1912yes—
225C2×C42—191no—
226C2×C42—191no—
227C2×C42—191no—
228C2×C42—191no—
229C2×C42—191no—
230C2×C42—191no—
231C2×C42C22×D1911yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—192no—
236C4⋊C8—381no—
237C4⋊C8—381no—
238C4⋊C8—381no—
239C4⋊C8Dic3812yescomplemented
240#97—762no—
241C19#990311yescharacteristic, complemented, Sylow
242C2×Q8—764no—
243C2×Q8—764no—
244C2×Q8—764no—
245C22×C4—22no—
246C22×C4—191no—
247C22×C4—191no—
248C22×C4—191no—
249C22×C4—191no—
250C22×C4—382no—
251C22×C4C2×C4×D1911yescharacteristic
252C22×C4D4×D1911yescharacteristic
253C22×C4D4×D1911yescharacteristic
254C2×C8—22no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—382no—
261C2×C8—761no—
262C2×C8—761no—
263C2×C8—761no—
264C2×C8—761no—
265C2×C8—761no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—762no—
272C4⋊C4—764no—
273C4⋊C4—764no—
274C4⋊C4—764no—
275C4⋊C4—761no—
276C4⋊C4—761no—
277C4⋊C4—761no—
278C4⋊C4—761no—
279C42—192no—
280C42—192no—
281C42—382no—
282C42—382no—
283C42—381no—
284C42—381no—
285C42—381no—
286C42—381no—
287C42—381no—
288C42—381no—
289C42C2×Dic3811yescharacteristic
290C42#6454111yescharacteristic
291C42#6454311yescharacteristic
292C42Q8×D1911yescharacteristic
293C23C22⋊C4×D1911yescharacteristic
294Q8—1528no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—192no—
301C2×C4—192no—
302C2×C4—192no—
303C2×C4—192no—
304C2×C4—381no—
305C2×C4—381no—
306C2×C4—381no—
307C2×C4—381no—
308C2×C4—381no—
309C2×C4—381no—
310C2×C4—381no—
311C2×C4—381no—
312C2×C4—762no—
313C2×C4—762no—
314C2×C4—762no—
315C2×C4C4×Dic3811yescharacteristic
316C2×C4#1059732411yescharacteristic
317C2×C4#1059733111yescharacteristic
318C2×C4#1059733311yescharacteristic
319C2×C4#1059733411yescharacteristic
320C2×C4#1059734211yescharacteristic
321C2×C4#1059735711yescharacteristic
322C2×C4#1059735711yescharacteristic
323C2×C4SD16×D1911yescharacteristic
324C2×C4#1059736011yescharacteristic
325C2×C4#1059736011yescharacteristic
326C2×C4#1059736111yescharacteristic
327C2×C4Q16×D1911yescharacteristic
328C2×C4#1059736411yescharacteristic
329C8—42no—
330C8—81no—
331C8—762no—
332C8—1521no—
333C22#1192644811yescharacteristic
334C22#100×D1911yescharacteristic
335C22#101×D1911yescharacteristic
336C22#103×D1911yescharacteristic
337C22#1192654711yescharacteristic
338C22#1192654711yescharacteristic
339C22#1192655111yescharacteristic
340C4—21no—
341C4—21no—
342C4—82no—
343C4—382no—
344C4—382no—
345C4—382no—
346C4—382no—
347C4—1522no—
348C4#1192683211yescharacteristic
349C4#1192683311yescharacteristic
350C4#1192683711yescharacteristic
351C4#1192683811yescharacteristic
352C4#1192690211yescharacteristic
353C4#1192690511yescharacteristic
354C4#1192695111yescharacteristic
355C4#1192695211yescharacteristic
356C2#1456231411yescharacteristic
357C2#1456231811yescharacteristic
358C2#1456234711yescharacteristic
359C2#1456235011yescharacteristic
360C2#1456458111yescharacteristic
361C2#1456460611yescharacteristic
362C2#1456462211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1296C2
socle, prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1296D19
hypocenterC19#9903
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
54. C19×C4⋊C8Q8semidirect
59. C4⋊(C19⋊C8)Q8semidirect
239. C4⋊C8Dic38semidirect
241. C19#9903semidirect

Maximal subgroups

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

subgroupindex
#145720322
#145637512
#145634902
#145615192
#145615182
C19×#12962
#990319