Finite Group Databasebeta

← #18081145

Subgroups — #18081145

Order 4864.

368 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563752C211yesmaximal, characteristic
2#14563488C211yesmaximal, characteristic
3C2×#11926297C211yesmaximal, characteristic
4C2×#11926295C211yesmaximal, characteristic
5#14561470C211yesmaximal, characteristic
6#14561470C211yesmaximal, characteristic
7C4×C19×C4⋊C8C211yesmaximal, characteristic
8C2×C4⋊(C19⋊C8)C2211yescharacteristic
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×#10597260—21no—
13#11926299—21no—
14#11926299—21no—
15#11926299—21no—
16#11926297—22no—
17#11926295—22no—
18C2×C19×C4⋊C8C411yescharacteristic
19C2×C19×C4⋊C8C411yescharacteristic
20C2×C4×C8×C19C2211yescharacteristic
21C2×C4×C8×C19C2211yescharacteristic
22C43×C19C2211yescharacteristic
23C19×#336C411yescharacteristic
24C19×#336C411yescharacteristic
25C22×C8×C19C2×C411yescharacteristic
26C22×C8×C19C2×C411yescharacteristic
27C22×C8×C19C2×C411yescharacteristic
28C22×C8×C19C2×C411yescharacteristic
29C2×C42×C19C2×C411yescharacteristic
30C2×C42×C19C2×C411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19Q811yescharacteristic
34C2×C42×C19Q811yescharacteristic
35C2×C42×C19C2311yescharacteristic
36C22×C19⋊C8—21no—
37C22×C19⋊C8—21no—
38C22×C19⋊C8—21no—
39C22×C19⋊C8—21no—
40C19×C4⋊C8—22no—
41C19×C4⋊C8—22no—
42C4×C8×C19—21no—
43C4×C8×C19—21no—
44C4×C8×C19—21no—
45C4×C8×C19—21no—
46C4⋊(C19⋊C8)—21no—
47C4⋊(C19⋊C8)—21no—
48C4⋊(C19⋊C8)—21no—
49C4⋊(C19⋊C8)—21no—
50C4⋊(C19⋊C8)—21no—
51C4⋊(C19⋊C8)—21no—
52C4⋊(C19⋊C8)D412yes—
53C4⋊(C19⋊C8)Q812yes—
54#10597260—42no—
55C22×C4×C19C4⋊C411yescharacteristic
56C22×C4×C19C4⋊C411yescharacteristic
57C22×C4×C19C4⋊C411yescharacteristic
58C22×C4×C19C4⋊C411yescharacteristic
59C22×C4×C19C22×C411yescharacteristic
60C22×C4×C19C2×D411yescharacteristic
61C22×C4×C19C2×Q811yescharacteristic
62C2×C8×C19—21no—
63C2×C8×C19—21no—
64C2×C8×C19—21no—
65C2×C8×C19—21no—
66C2×C8×C19—21no—
67C2×C8×C19—21no—
68C2×C8×C19—21no—
69C2×C8×C19—21no—
70C2×C8×C19—21no—
71C2×C8×C19—21no—
72C2×C8×C19M1612yes—
73C2×C8×C19M1612yes—
74C42×C19—22no—
75C42×C19—21no—
76C42×C19—21no—
77C42×C19—21no—
78C42×C19—21no—
79C42×C19—21no—
80C42×C19—21no—
81C42×C19—21no—
82C42×C19—21no—
83C42×C19—41no—
84C42×C19C2×D411yescharacteristic
85C42×C19C2×Q811yescharacteristic
86C42×C19#4111yescharacteristic
87C42×C19#4111yescharacteristic
88C2×C19⋊C8—22no—
89C2×C19⋊C8—22no—
90C2×C19⋊C8—41no—
91C2×C19⋊C8—41no—
92C2×C19⋊C8—41no—
93C2×C19⋊C8—41no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—41no—
96C2×C19⋊C8—41no—
97C2×C19⋊C8—41no—
98C2×C19⋊C8—41no—
99C2×C19⋊C8—41no—
100#9606—191nomaximal, Sylow
101C23×C19C2×C4⋊C411yescharacteristic
102C2×C4×C19—21no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19#10812yes—
116C2×C4×C19C4×D411yescharacteristic
117C2×C4×C19C4×Q811yescharacteristic
118C2×C4×C19#12111yescharacteristic
119C2×C4×C19C22⋊Q811yescharacteristic
120C2×C4×C19#12511yescharacteristic
121C2×C4×C19C4⋊Q811yescharacteristic
122C2×C4×C19C2×M1611yescharacteristic
123C2×C4×C19C2×M1611yescharacteristic
124C2×C4×C19#13111yescharacteristic
125C2×C4×C19#13111yescharacteristic
126C2×C4×C19#13511yescharacteristic
127C2×C4×C19#13511yescharacteristic
128C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C19#13711yescharacteristic
130C8×C19—22no—
131C8×C19—22no—
132C8×C19—41no—
133C8×C19—41no—
134C19⋊C8—42no—
135C19⋊C8—42no—
136C19⋊C8—81no—
137C19⋊C8—81no—
138#1831—191no—
139#1767—191no—
140C4×C4⋊C8D1911yescharacteristic
141C2×#335—191no—
142C2×#334—191no—
143#1277—191no—
144#1277—191no—
145C22×C19#38911yescharacteristic
146C22×C19#42311yescharacteristic
147C22×C19#42411yescharacteristic
148C22×C19#42711yescharacteristic
149C22×C19#42811yescharacteristic
150C22×C19C2×#10811yescharacteristic
151C22×C19#43011yescharacteristic
152C4×C19—22no—
153C4×C19—21no—
154C4×C19—21no—
155C4×C19—41no—
156C4×C19—41no—
157C4×C19—41no—
158C4×C19#43511yescharacteristic
159C4×C19#43511yescharacteristic
160C4×C19#44611yescharacteristic
161C4×C19#44611yescharacteristic
162C4×C19#46311yescharacteristic
163C4×C19#46411yescharacteristic
164C4×C19#47811yescharacteristic
165C4×C19#47911yescharacteristic
166C2×C4⋊C8—191no—
167C2×C4⋊C8—191no—
168C2×C4⋊C8—191no—
169C2×C4⋊C8—191no—
170C2×C4⋊C8Dic1911yescharacteristic
171C2×C4⋊C8Dic1911yescharacteristic
172C2×#97—381no—
173C2×C4×C8C2×D1911yescharacteristic
174C2×C4×C8C2×D1911yescharacteristic
175C43C2×D1911yescharacteristic
176#336—381no—
177#336—381no—
178#336—381no—
179#336Dic1911yescharacteristic
180#336Dic1911yescharacteristic
181#335—382no—
182#334—382no—
183C2×C19#156811yescharacteristic
184C2×C19#156911yescharacteristic
185C2×C19#157211yescharacteristic
186C2×C19#157411yescharacteristic
187C2×C19#194011yescharacteristic
188C2×C19#194911yescharacteristic
189C2×C19#195011yescharacteristic
190C22×C8—381no—
191C22×C8—381no—
192C22×C8—381no—
193C22×C8—381no—
194C22×C8C2×Dic1911yescharacteristic
195C22×C8C2×Dic1911yescharacteristic
196C22×C8C2×Dic1911yescharacteristic
197C22×C8C2×Dic1911yescharacteristic
198C2×C42Dic3811yescharacteristic
199C2×C42Dic3811yescharacteristic
200C2×C42D7611yescharacteristic
201C2×C42D7611yescharacteristic
202C2×C42C2×Dic1911yescharacteristic
203C2×C42C2×Dic1911yescharacteristic
204C2×C42C22×D1911yescharacteristic
205C4⋊C8—22no—
206C4⋊C8—22no—
207C4⋊C8—192no—
208C4⋊C8—192no—
209C4⋊C8—381no—
210C4⋊C8—381no—
211C4⋊C8—381no—
212C4⋊C8—381no—
213C4⋊C8—381no—
214C4⋊C8—381no—
215#97—762no—
216C4×C8—21no—
217C4×C8—21no—
218C4×C8—21no—
219C4×C8—21no—
220C19#960611yescharacteristic, complemented, Sylow
221C22×C4C4⋊Dic1911yescharacteristic
222C22×C4C4⋊Dic1911yescharacteristic
223C22×C4C4⋊Dic1911yescharacteristic
224C22×C4C4⋊Dic1911yescharacteristic
225C22×C4C2×Dic3811yescharacteristic
226C22×C4C2×D7611yescharacteristic
227C22×C4C22×Dic1911yescharacteristic
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—382no—
239C2×C8—382no—
240C2×C8—761no—
241C2×C8—761no—
242C2×C8—761no—
243C2×C8—761no—
244C2×C8—761no—
245C2×C8—761no—
246C2×C8—761no—
247C2×C8—761no—
248C2×C8—761no—
249C2×C8—761no—
250C2×C8#6452012yes—
251C2×C8#6452012yes—
252C42—21no—
253C42—21no—
254C42—22no—
255C42—21no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—41no—
262C42D4×D1911yescharacteristic
263C42#6454311yescharacteristic
264C42Q8×D1911yescharacteristic
265C42#6454511yescharacteristic
266C23C2×C4⋊Dic1911yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4#1059727612yes—
281C2×C4#1059733411yescharacteristic
282C2×C4#1059733611yescharacteristic
283C2×C4#1059734111yescharacteristic
284C2×C4#1059734311yescharacteristic
285C2×C4#1059735011yescharacteristic
286C2×C4#1059735011yescharacteristic
287C2×C4#1059735411yescharacteristic
288C2×C4#1059735511yescharacteristic
289C2×C4C2×#6452011yescharacteristic
290C2×C4C2×#6452011yescharacteristic
291C2×C4D4×Dic1911yescharacteristic
292C2×C4Q8×Dic1911yescharacteristic
293C2×C4#1059739411yescharacteristic
294C2×C4#1059739411yescharacteristic
295C8—22no—
296C8—22no—
297C8—41no—
298C8—41no—
299C8—762no—
300C8—762no—
301C8—1521no—
302C8—1521no—
303C22#1192644311yescharacteristic
304C22#1192656811yescharacteristic
305C22#1192657111yescharacteristic
306C22#1192658211yescharacteristic
307C22#1192658611yescharacteristic
308C22C2×#1059727611yescharacteristic
309C22#1192659311yescharacteristic
310C4—21no—
311C4—21no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4#1192661611yescharacteristic
317C4#1192661611yescharacteristic
318C4#1192667511yescharacteristic
319C4#1192667511yescharacteristic
320C4#1192676011yescharacteristic
321C4#1192676711yescharacteristic
322C4#1192684511yescharacteristic
323C4#1192685211yescharacteristic
324C2#1456239811yescharacteristic
325C2#1456240211yescharacteristic
326C2#1456241511yescharacteristic
327C2#1456242411yescharacteristic
328C2#1456435911yescharacteristic
329C2#1456440511yescharacteristic
330C2#1456441111yescharacteristic
subgroupG/H
centerC22×C4C2×D76
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC4×C19×C4⋊C8C2
socle, prime radicalC23×C19C2×C4⋊C4
cosocleC2×C42×C19C23
hypercenterC4×C4⋊C8D19
hypocenterC19#9606
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
220. C19#9606semidirect

Maximal subgroups

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

subgroupindex
#145637522
#145634882
C2×#119262972
C2×#119262952
#145614702
C4×C19×C4⋊C82
#960619