Finite Group Databasebeta

← #18081789

Subgroups — #18081789

Order 4864.

522 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926890C211yesmaximal, characteristic
2#14564583C211yesmaximal, characteristic, complemented
3C4⋊C4×C19⋊C8C211yesmaximal, characteristic, complemented
4C2×#11926294C211yesmaximal, characteristic, complemented
5C2×#11926292C211yesmaximal, characteristic, complemented
6C2×#11926288C211yesmaximal, characteristic
7C19×#1982C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9#11926890—22no—
10#11926890C414yescomplemented
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×C4⋊(C19⋊C8)C2211yescharacteristic
13C2×#10597289—21no—
14C2×#10597289—21no—
15C2×C4×C19⋊C8—21no—
16C2×C4×C19⋊C8C2211yescharacteristic
17#11926306—22no—
18#11926299—21no—
19#11926294—22no—
20#11926292—22no—
21#11926288—22no—
22C2×C19×#127C2211yescharacteristic
23C2×C19×C4⋊C8C2211yescharacteristic
24C2×C19×#102—22no—
25C4×C4⋊C4×C19C2211yescharacteristic
26C22×D4×C19—21no—
27C22×D4×C19—21no—
28C22×D4×C19—21no—
29C22×Dic38—21no—
30C22×C8×C19—21no—
31C19×#127—21no—
32C19×#127—21no—
33C19×#127—21no—
34C19×#127C2×C412yes—
35C2×C4⋊C4×C19D412yes—
36C2×C42×C19—21no—
37C2×C42×C19C2311yescharacteristic
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19—21no—
40C22×C19⋊C8—21no—
41C22×C19⋊C8—21no—
42C22×C19⋊C8D411yescharacteristic
43C22×C19⋊C8D411yescharacteristic
44#10597315—21no—
45#10597315—21no—
46#10597315—21no—
47#10597315C2×C412yes—
48C19×C4⋊C8—21no—
49C19×C4⋊C8—21no—
50C19×#102—44no—
51C19×#95—21no—
52#10597289—24no—
53#10597289—24no—
54C4⋊(C19⋊C8)—21no—
55C4⋊(C19⋊C8)—21no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)D412yes—
58C4×C19⋊C8—42no—
59C4×C19⋊C8C2×C412yes—
60C4×C19⋊C8D412yes—
61C24×C19—41no—
62C2×D4×C19—22no—
63C2×D4×C19—22no—
64C2×D4×C19—22no—
65C2×D4×C19—41no—
66C2×D4×C19—41no—
67C2×D4×C19—41no—
68C2×D4×C19—42no—
69C2×D4×C19—42no—
70C2×D4×C19—41no—
71C2×D4×C19—41no—
72C2×D4×C19—41no—
73C2×D4×C19—41no—
74C2×D4×C19—82no—
75C22×C4×C19—22no—
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C22×Dic19—41no—
80C2×Dic38—22no—
81C2×Dic38—41no—
82C2×Dic38—82no—
83C2×C8×C19—41no—
84C2×C8×C19—42no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19SD1614yes—
87C42×C19—41no—
88C42×C19—41no—
89C42×C19C22×C411yescharacteristic
90C42×C19C2×D411yescharacteristic
91C42×C19C2×D411yescharacteristic
92C42×C19#4111yescharacteristic
93C4⋊Dic19—22no—
94C4⋊Dic19—22no—
95C4⋊Dic19—41no—
96C4⋊Dic19—41no—
97C2×C19⋊C8—21no—
98C2×C19⋊C8—21no—
99C2×C19⋊C8—21no—
100C2×C19⋊C8—21no—
101C2×C19⋊C8—22no—
102C2×C19⋊C8—41no—
103C2×C19⋊C8—41no—
104C2×C19⋊C8—41no—
105C2×C19⋊C8—42no—
106C2×C19⋊C8C22⋊C412yes—
107C2×C19⋊C8C22⋊C412yes—
108#9735—191nomaximal, Sylow
109C23×C19—42no—
110C23×C19—81no—
111C23×C19—81no—
112C23×C19—82no—
113C23×C19—82no—
114C23×C19#12111yescharacteristic
115D4×C19—42no—
116D4×C19—42no—
117D4×C19—44no—
118D4×C19—82no—
119D4×C19—82no—
120D4×C19—81no—
121D4×C19—81no—
122D4×C19—81no—
123D4×C19—81no—
124C2×C4×C19—22no—
125C2×C4×C19—24no—
126C2×C4×C19—42no—
127C2×C4×C19—42no—
128C2×C4×C19C2×C22⋊C411yescharacteristic
129C2×C4×C19C4×D411yescharacteristic
130C2×C4×C19C4×D411yescharacteristic
131C2×C4×C19#12111yescharacteristic
132C2×C4×C19#12411yescharacteristic
133C2×C4×C19#12711yescharacteristic
134C2×C4×C19C2×SD1612yes—
135C2×C4×C19#13512yes—
136C2×C4×C19#13511yescharacteristic
137C2×C4×C19#13511yescharacteristic
138C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C19#13711yescharacteristic
140C2×Dic19—42no—
141C2×Dic19—82no—
142Dic38—82no—
143Dic38—82no—
144C8×C19—81no—
145C19⋊C8—22no—
146C19⋊C8—22no—
147C19⋊C8—42no—
148C19⋊C8—81no—
149C2×#486—191no—
150#1987—191no—
151#1982D1911yescharacteristic
152C8×C4⋊C4—191no—
153C2×#334—191no—
154C2×#333—191no—
155C2×#331—191no—
156C22×C19—82no—
157C22×C19—82no—
158C22×C19—82no—
159C22×C19—162no—
160C22×C19—162no—
161C22×C19#39011yescharacteristic
162C22×C19#46311yescharacteristic
163C22×C19#46411yescharacteristic
164C22×C19#46512yes—
165C22×C19#47212yes—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—44no—
169C4×C19#41611yescharacteristic
170C4×C19#41711yescharacteristic
171C4×C19C4×SD1612yes—
172C4×C19#46311yescharacteristic
173C4×C19#46411yescharacteristic
174C4×C19#49211yescharacteristic
175C4×C19#49511yescharacteristic
176Dic19—82no—
177C2×C4⋊Q8—191no—
178C2×#127C2×D1911yescharacteristic
179#486—194no—
180#486—382no—
181C2×C4⋊C8—191no—
182C2×C4⋊C8—191no—
183C2×C4⋊C8C2×D1911yescharacteristic
184C2×#102—22no—
185C2×#102—381no—
186C2×#102—381no—
187C2×C4×C8—191no—
188C2×C4×C8—381no—
189C4×C4⋊C4C2×D1911yescharacteristic
190#340—382no—
191#336—381no—
192#334—382no—
193#333—382no—
194#331—382no—
195C2×C19—162no—
196C2×C19#167712yes—
197C2×C19#167812yes—
198C2×C19#196811yescharacteristic
199C2×C19#197811yescharacteristic
200C2×C19#198311yescharacteristic
201C22×Q8—381no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×C8—21no—
206C22×C8—191no—
207C22×C8—191no—
208C22×C8—381no—
209C22×C8—381no—
210C4⋊Q8—192no—
211C4⋊Q8—381no—
212C4⋊Q8—381no—
213C4⋊Q8—381no—
214#127—21no—
215#127—21no—
216#127—21no—
217#127C4×D1912yes—
218C2×C4⋊C4—381no—
219C2×C4⋊C4—381no—
220C2×C4⋊C4C22⋊D1912yes—
221C2×C42—21no—
222C2×C42C22×D1911yescharacteristic
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—192no—
226C4⋊C8—381no—
227C4⋊C8—381no—
228C4⋊C8—381no—
229#102—44no—
230#102—384no—
231#102—384no—
232C4×C8—192no—
233C4×C8—192no—
234C4×C8—762no—
235#95—21no—
236C19#973511yescharacteristic, complemented, Sylow
237C24—41no—
238C2×Q8—382no—
239C2×Q8—761no—
240C2×Q8—1522no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—42no—
245C2×D4—41no—
246C2×D4—42no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—82no—
254C22×C4—22no—
255C22×C4—761no—
256C22×C4D4×D1911yescharacteristic
257C22×C4#6454311yescharacteristic
258C22×C4C2×C22⋊D1911yescharacteristic
259C2×C8—42no—
260C2×C8—41no—
261C2×C8—192no—
262C2×C8—192no—
263C2×C8—381no—
264C2×C8—381no—
265C2×C8—381no—
266C2×C8—381no—
267C2×C8—382no—
268C2×C8—761no—
269C2×C8—761no—
270C2×C8—761no—
271C2×C8—762no—
272C4⋊C4—22no—
273C4⋊C4—382no—
274C4⋊C4—382no—
275C4⋊C4—761no—
276C4⋊C4—761no—
277C4⋊C4#6452614yes—
278C42—41no—
279C42—41no—
280C42C2×C4×D1911yescharacteristic
281C42#6454111yescharacteristic
282C42D4×D1911yescharacteristic
283C42D4×D1911yescharacteristic
284C23—42no—
285C23—82no—
286C23—81no—
287C23—81no—
288C23—82no—
289C23#1059738511yescharacteristic
290Q8—1522no—
291Q8—1522no—
292D4—42no—
293D4—42no—
294D4—44no—
295D4—82no—
296D4—82no—
297D4—81no—
298D4—81no—
299D4—81no—
300D4—81no—
301C2×C4—22no—
302C2×C4—24no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—762no—
306C2×C4—1522no—
307C2×C4C22⋊C4×D1911yescharacteristic
308C2×C4(C22⋊D19)⋊C411yescharacteristic
309C2×C4#1059733011yescharacteristic
310C2×C4#1059733111yescharacteristic
311C2×C4#1059735711yescharacteristic
312C2×C4#1059735811yescharacteristic
313C2×C4#1059736111yescharacteristic
314C2×C4#1059736211yescharacteristic
315C2×C4C4×C22⋊D1911yescharacteristic
316C2×C4C2×#6452612yes—
317C2×C4#1059738611yescharacteristic
318C2×C4#1059739612yes—
319C8—81no—
320C8—382no—
321C8—382no—
322C8—762no—
323C8—1521no—
324C22—82no—
325C22—82no—
326C22—82no—
327C22—162no—
328C22—162no—
329C22#1192644411yescharacteristic
330C22#1192675711yescharacteristic
331C22#1192676411yescharacteristic
332C22#1192677112yes—
333C22#1192681212yes—
334C4—21no—
335C4—21no—
336C4—44no—
337C4—1522no—
338C4#1192653711yescharacteristic
339C4#1192654211yescharacteristic
340C4C4×#6452612yes—
341C4#1192675811yescharacteristic
342C4#1192676511yescharacteristic
343C4#1192691611yescharacteristic
344C4#1192692611yescharacteristic
345C2—162no—
346C2#1456304212yes—
347C2#1456304912yes—
348C2#1456448811yescharacteristic
349C2#1456454411yescharacteristic
350C2#1456456611yescharacteristic
subgroupG/H
centerC23#10597385
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1982C2
socleC23×C19#121
prime radicalC2×C19×#127C22
cosocleC2×C42×C19C23
hypercenter#1982D19
hypocenterC19#9735
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. #14564583C2semidirect
3. C4⋊C4×C19⋊C8C2semidirect
4. C2×#11926294C2semidirect
5. C2×#11926292C2semidirect
10. #11926890C4semidirect
236. C19#9735semidirect

Maximal subgroups

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

subgroupindex
C2×#119268902
#145645832
C4⋊C4×C19⋊C82
C2×#119262942
C2×#119262922
C2×#119262882
C19×#19822
#973519