Finite Group Databasebeta

← #18078408

Subgroups — #18078408

Order 4864.

432 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573444C211yesmaximal, characteristic
2#14572303C211yesmaximal, characteristic
3C2×#11926293C211yesmaximal, characteristic, complemented
4#14562023C211yesmaximal, characteristic
5#14561531C211yesmaximal, characteristic, complemented
6#14561509C211yesmaximal, characteristic, complemented
7C19×#1549C211yesmaximal, characteristic, complemented
8C4×#64541C2211yescharacteristic
9#11926836—21no—
10#11926831—21no—
11#11926826C412yes—
12#11926821C412yes—
13#11926604—22no—
14#11926600—21no—
15#11926596—21no—
16#11926584—21no—
17#11926568C2211yescharacteristic
18C2×C4⋊(C19⋊C8)C2211yescharacteristic
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20#11926543—21no—
21#11926512—21no—
22#11926502—21no—
23#11926293—21no—
24#11926293—21no—
25#11926276—21no—
26#11926273—21no—
27C2×C19×C4⋊Q8C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C19×#423C2211yescharacteristic
30C19×#332—22no—
31C22×Q8×C19—21no—
32C2×#64541D411yescharacteristic
33C2×M16×C19—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8C2×C412yes—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C42×C19C2311yescharacteristic
41C4×C22⋊D19—21no—
42C4×C22⋊D19—21no—
43#10597372D411yescharacteristic
44C2×#64520—21no—
45C22×C19⋊C8—21no—
46C22×C19⋊C8—21no—
47C4×D76C2×C411yescharacteristic
48C4×D76D411yescharacteristic
49#10597318—21no—
50C42×D19—21no—
51C4×Dic38C2×C411yescharacteristic
52C4×Dic38D411yescharacteristic
53C19×C4⋊C8—21no—
54C19×C4⋊C8—21no—
55C19×C4⋊C8D412yes—
56C19×C22⋊C8—21no—
57C4×C8×C19—21no—
58(C2×D19)⋊C8—22no—
59(C2×D19)⋊C8—22no—
60#10597272—22no—
61C8×Dic19—22no—
62#10597267—22no—
63#10597266—22no—
64#10597265—22no—
65#10597264—22no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—21no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)C2×C412yes—
71C4⋊(C19⋊C8)D411yescharacteristic
72C4⋊(C19⋊C8)D411yescharacteristic
73C2×Q8×C19—22no—
74C2×Q8×C19—41no—
75C2×Q8×C19—82no—
76C22×C4×C19—41no—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C22×C4×C19#4111yescharacteristic
80C2×C22⋊D19—21no—
81#64541—21no—
82#64541—21no—
83#64541—21no—
84#64541—21no—
85C2×D76C22⋊C411yescharacteristic
86C2×C4×D19—21no—
87C2×C4×D19—21no—
88C2×C4×D19—21no—
89C2×Dic38C22⋊C411yescharacteristic
90M16×C19—41no—
91M16×C19—41no—
92C2×C8×C19—22no—
93C2×C8×C19—41no—
94C4⋊C4×C19—22no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—41no—
97C4⋊C4×C19—41no—
98C42×C19C22×C411yescharacteristic
99C42×C19C2×D411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C22⋊Dic19—21no—
103(C2×D19)⋊C4—21no—
104(C2×D19)⋊C4—21no—
105C4⋊Dic19C22⋊C411yescharacteristic
106C4⋊Dic19C22⋊C411yescharacteristic
107Dic19⋊C4—21no—
108Dic19⋊C4—21no—
109C4×Dic19—21no—
110C4×Dic19—21no—
111C4×Dic19—21no—
112#64520—41no—
113#64520—41no—
114C2×C19⋊C8—22no—
115C2×C19⋊C8—21no—
116C2×C19⋊C8—21no—
117C2×C19⋊C8—41no—
118C2×C19⋊C8—41no—
119C2×C19⋊C8—41no—
120C2×C19⋊C8—81no—
121#9170—191nomaximal, Sylow
122C23×C19#12311yescharacteristic
123C22×D19—21no—
124Q8×C19—82no—
125Q8×C19—82no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—41no—
129C2×C4×C19—42no—
130C2×C4×C19—82no—
131C2×C4×C19C2×C22⋊C411yescharacteristic
132C2×C4×C19C4×D411yescharacteristic
133C2×C4×C19C4×D411yescharacteristic
134C2×C4×C19#12011yescharacteristic
135C2×C4×C19#12111yescharacteristic
136C2×C4×C19#12111yescharacteristic
137C2×C4×C19#13511yescharacteristic
138C2×C4×C19#13511yescharacteristic
139C2×C4×C19#13711yescharacteristic
140C2×C4×C19#13711yescharacteristic
141C22⋊D19—41no—
142C22⋊D19—41no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—21no—
146D76—21no—
147D76—21no—
148C4×D19—41no—
149C4×D19—41no—
150C4×D19—41no—
151C4×D19—41no—
152C4×D19—81no—
153Dic38—21no—
154Dic38—21no—
155C8×C19—42no—
156C8×C19—81no—
157C19⋊C8—42no—
158C19⋊C8—41no—
159C19⋊C8—41no—
160C19⋊C8—81no—
161#3079—191no—
162#2925—191no—
163#1549D1911yescharacteristic, complemented
164C2×#333—191no—
165#1477—191no—
166#1301—191no—
167#1292—191no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19#38611yescharacteristic
171C22×C19#48511yescharacteristic
172C22×C19#48511yescharacteristic
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—41no—
176C4×C19—21no—
177C4×C19—21no—
178C4×C19—21no—
179C4×C19—82no—
180C4×C19#41611yescharacteristic
181C4×C19#41911yescharacteristic
182C4×C19#45211yescharacteristic
183C4×C19#45211yescharacteristic
184C4×C19#47111yescharacteristic
185C4×C19#47311yescharacteristic
186Dic19—41no—
187Dic19—41no—
188Dic19—41no—
189C2×C4⋊Q8C2×D1911yescharacteristic
190C4×#41—191no—
191#477—381no—
192#476—381no—
193#475—192no—
194#474—192no—
195#433—382no—
196#432—381no—
197#431—381no—
198#431C2×D1911yescharacteristic
199#428—381no—
200#423—191no—
201#423C2×D1911yescharacteristic
202C2×C4⋊C8—191no—
203C2×C4⋊C8—191no—
204#417—381no—
205#408—381no—
206#405—381no—
207#333—381no—
208#333—381no—
209#332—22no—
210Q8⋊C8—381no—
211D4⋊C8—381no—
212C2×C19—21no—
213C2×C19—21no—
214C2×C19#187311yescharacteristic
215C2×C19#190311yescharacteristic
216C2×C19#190811yescharacteristic
217D19—81no—
218C2×#41—191no—
219C22×Q8—21no—
220C2×M16—21no—
221C2×M16—381no—
222C22×C8—381no—
223C22×C8—381no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8C4×D1912yes—
228C4×Q8—191no—
229C4×Q8—191no—
230C4×D4—191no—
231C4×D4—191no—
232C4×D4—381no—
233C4×D4—381no—
234#117—191no—
235#117—381no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C42—381no—
239C2×C42C22×D1911yescharacteristic
240#107—382no—
241#106—382no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—192no—
245C4⋊C8—191no—
246C4⋊C8—191no—
247C4⋊C8—381no—
248C4⋊C8—381no—
249C4⋊C8—381no—
250C4⋊C8—381no—
251C4⋊C8C22⋊D1912yes—
252#103—382no—
253#102—382no—
254C22⋊C8—21no—
255C22⋊C8—382no—
256C22⋊C8—382no—
257#97—382no—
258C4×C8—21no—
259C4×C8—382no—
260C19#917011yescharacteristic, complemented, Sylow
261#41—381no—
262#41—381no—
263#41—381no—
264#41—381no—
265C2×Q8—22no—
266C2×Q8—41no—
267C2×Q8—82no—
268C2×Q8—191no—
269C2×D4—191no—
270C2×D4—381no—
271C22×C4—41no—
272C22×C4—381no—
273C22×C4—381no—
274C22×C4—381no—
275C22×C4#6454111yescharacteristic
276C22×C4D4×D1911yescharacteristic
277C22×C4#6454311yescharacteristic
278M16—41no—
279M16—41no—
280M16—761no—
281M16—761no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—381no—
285C2×C8—381no—
286C2×C8—382no—
287C2×C8—761no—
288C2×C8—761no—
289C2×C8—761no—
290C2×C8—1521no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—191no—
296C4⋊C4—191no—
297C4⋊C4—381no—
298C4⋊C4—381no—
299C22⋊C4—381no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C42—381no—
303C42—381no—
304C42—381no—
305C42C2×C4×D1911yescharacteristic
306C42D4×D1911yescharacteristic
307C42D4×D1911yescharacteristic
308C42C2×C22⋊D1911yescharacteristic
309C23—381no—
310C23#1059732911yescharacteristic
311Q8—82no—
312Q8—82no—
313Q8—381no—
314Q8—381no—
315D4—381no—
316D4—381no—
317D4—761no—
318D4—761no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—82no—
324C2×C4—381no—
325C2×C4—381no—
326C2×C4—381no—
327C2×C4—761no—
328C2×C4—761no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—1521no—
332C2×C4C22⋊C4×D1911yescharacteristic
333C2×C4(C22⋊D19)⋊C411yescharacteristic
334C2×C4#1059733011yescharacteristic
335C2×C4#1059736111yescharacteristic
336C2×C4#1059736211yescharacteristic
337C2×C4#1059736411yescharacteristic
338C2×C4#1059736511yescharacteristic
339C2×C4C4×C22⋊D1911yescharacteristic
340C2×C4#1059738311yescharacteristic
341C2×C4#1059738411yescharacteristic
342C8—42no—
343C8—81no—
344C8—762no—
345C8—761no—
346C8—761no—
347C8—1521no—
348C22—21no—
349C22—21no—
350C22—761no—
351C22—761no—
352C22—761no—
353C22#1192642011yescharacteristic
354C22#1192688311yescharacteristic
355C22#1192688411yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—82no—
360C4—761no—
361C4—761no—
362C4—761no—
363C4#1192653911yescharacteristic
364C4#1192655111yescharacteristic
365C4#1192670311yescharacteristic
366C4#1192670511yescharacteristic
367C4#1192681011yescharacteristic
368C4#1192681811yescharacteristic
369C2—21no—
370C2—21no—
371C2—1521no—
372C2#1456394411yescharacteristic
373C2#1456411211yescharacteristic
374C2#1456414711yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1549C2
socleC22×C19#386
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1549D19
hypocenterC19#9170
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
3. C2×#11926293C2semidirect
5. #14561531C2semidirect
6. #14561509C2semidirect
7. C19×#1549C2semidirect
163. #1549D19semidirect
260. C19#9170semidirect

Maximal subgroups

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

subgroupindex
#145734442
#145723032
C2×#119262932
#145620232
#145615312
#145615092
C19×#15492
#917019