Finite Group Databasebeta

← #18078394

Subgroups — #18078394

Order 4864.

432 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573444C211yesmaximal, characteristic
2#14572303C211yesmaximal, characteristic
3C2×#11926290C211yesmaximal, characteristic, complemented
4#14562023C211yesmaximal, characteristic
5#14561531C211yesmaximal, characteristic, complemented
6#14561509C211yesmaximal, characteristic, complemented
7C19×#1548C211yesmaximal, characteristic, complemented
8C4×#64541C2211yescharacteristic
9#11926836C412yes—
10#11926831C412yes—
11#11926826—21no—
12#11926821—21no—
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#11926290—21no—
24#11926290—21no—
25#11926276—21no—
26#11926273—21no—
27C2×C19×C4⋊Q8C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C19×#423C2211yescharacteristic
30C19×#333—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—81no—
76C2×Q8×C19—81no—
77C22×C4×C19—41no—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19#4111yescharacteristic
80C22×C4×C19#4111yescharacteristic
81C2×C22⋊D19—21no—
82#64541—21no—
83#64541—21no—
84#64541—21no—
85#64541—21no—
86C2×D76C22⋊C411yescharacteristic
87C2×C4×D19—21no—
88C2×C4×D19—21no—
89C2×C4×D19—21no—
90C2×Dic38C22⋊C411yescharacteristic
91M16×C19—41no—
92M16×C19—41no—
93C2×C8×C19—22no—
94C2×C8×C19—41no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—22no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C42×C19C22×C411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C42×C19C2×D411yescharacteristic
103C22⋊Dic19—21no—
104(C2×D19)⋊C4—21no—
105(C2×D19)⋊C4—21no—
106C4⋊Dic19C22⋊C411yescharacteristic
107C4⋊Dic19C22⋊C411yescharacteristic
108Dic19⋊C4—21no—
109Dic19⋊C4—21no—
110C4×Dic19—21no—
111C4×Dic19—21no—
112C4×Dic19—21no—
113#64520—41no—
114#64520—41no—
115C2×C19⋊C8—22no—
116C2×C19⋊C8—21no—
117C2×C19⋊C8—21no—
118C2×C19⋊C8—41no—
119C2×C19⋊C8—41no—
120C2×C19⋊C8—41no—
121C2×C19⋊C8—81no—
122#9168—191nomaximal, Sylow
123C23×C19#12311yescharacteristic
124C22×D19—21no—
125Q8×C19—82no—
126Q8×C19—81no—
127Q8×C19—81no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—41no—
131C2×C4×C19—42no—
132C2×C4×C19—82no—
133C2×C4×C19C2×C22⋊C411yescharacteristic
134C2×C4×C19C4×D411yescharacteristic
135C2×C4×C19C4×D411yescharacteristic
136C2×C4×C19#12011yescharacteristic
137C2×C4×C19#12111yescharacteristic
138C2×C4×C19#12111yescharacteristic
139C2×C4×C19#13511yescharacteristic
140C2×C4×C19#13511yescharacteristic
141C2×C4×C19#13711yescharacteristic
142C2×C4×C19#13711yescharacteristic
143C22⋊D19—41no—
144C22⋊D19—41no—
145C2×Dic19—21no—
146C2×Dic19—21no—
147C2×Dic19—21no—
148D76—21no—
149D76—21no—
150C4×D19—41no—
151C4×D19—41no—
152C4×D19—41no—
153C4×D19—41no—
154C4×D19—81no—
155Dic38—21no—
156Dic38—21no—
157C8×C19—42no—
158C8×C19—81no—
159C19⋊C8—42no—
160C19⋊C8—41no—
161C19⋊C8—41no—
162C19⋊C8—81no—
163#3079—191no—
164#2925—191no—
165#1548D1911yescharacteristic, complemented
166C2×#332—191no—
167#1477—191no—
168#1301—191no—
169#1292—191no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19#38611yescharacteristic
173C22×C19#48511yescharacteristic
174C22×C19#48511yescharacteristic
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—82no—
182C4×C19#41611yescharacteristic
183C4×C19#41911yescharacteristic
184C4×C19#45211yescharacteristic
185C4×C19#45211yescharacteristic
186C4×C19#47111yescharacteristic
187C4×C19#47211yescharacteristic
188Dic19—41no—
189Dic19—41no—
190Dic19—41no—
191C2×C4⋊Q8C2×D1911yescharacteristic
192C4×#41—191no—
193#477—192no—
194#476—192no—
195#475—381no—
196#474—381no—
197#433—382no—
198#432—381no—
199#431—381no—
200#431C2×D1911yescharacteristic
201#428—381no—
202#423—191no—
203#423C2×D1911yescharacteristic
204C2×C4⋊C8—191no—
205C2×C4⋊C8—191no—
206#417—381no—
207#408—381no—
208#405—381no—
209#333—22no—
210#332—381no—
211#332—381no—
212Q8⋊C8—381no—
213D4⋊C8—381no—
214C2×C19—21no—
215C2×C19—21no—
216C2×C19#187311yescharacteristic
217C2×C19#190211yescharacteristic
218C2×C19#190711yescharacteristic
219D19—81no—
220C2×#41—191no—
221C22×Q8—21no—
222C2×M16—21no—
223C2×M16—381no—
224C22×C8—381no—
225C22×C8—381no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8C4×D1912yes—
230C4×Q8—191no—
231C4×Q8—191no—
232C4×D4—191no—
233C4×D4—191no—
234C4×D4—381no—
235C4×D4—381no—
236#117—191no—
237#117—381no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C42—381no—
241C2×C42C22×D1911yescharacteristic
242#107—382no—
243#106—382no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—192no—
247C4⋊C8—191no—
248C4⋊C8—191no—
249C4⋊C8—381no—
250C4⋊C8—381no—
251C4⋊C8—381no—
252C4⋊C8—381no—
253C4⋊C8C22⋊D1912yes—
254#103—382no—
255#102—382no—
256C22⋊C8—21no—
257C22⋊C8—382no—
258C22⋊C8—382no—
259#97—382no—
260C4×C8—21no—
261C4×C8—382no—
262C19#916811yescharacteristic, complemented, Sylow
263#41—381no—
264#41—381no—
265#41—381no—
266#41—381no—
267C2×Q8—22no—
268C2×Q8—41no—
269C2×Q8—81no—
270C2×Q8—81no—
271C2×Q8—191no—
272C2×D4—191no—
273C2×D4—381no—
274C22×C4—41no—
275C22×C4—381no—
276C22×C4—381no—
277C22×C4—381no—
278C22×C4#6454111yescharacteristic
279C22×C4D4×D1911yescharacteristic
280C22×C4#6454311yescharacteristic
281M16—41no—
282M16—41no—
283M16—761no—
284M16—761no—
285C2×C8—22no—
286C2×C8—41no—
287C2×C8—381no—
288C2×C8—381no—
289C2×C8—382no—
290C2×C8—761no—
291C2×C8—761no—
292C2×C8—761no—
293C2×C8—1521no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—191no—
299C4⋊C4—191no—
300C4⋊C4—381no—
301C4⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C42—381no—
306C42—381no—
307C42—381no—
308C42C2×C4×D1911yescharacteristic
309C42D4×D1911yescharacteristic
310C42D4×D1911yescharacteristic
311C42C2×C22⋊D1911yescharacteristic
312C23—381no—
313C23#1059732911yescharacteristic
314Q8—82no—
315Q8—81no—
316Q8—81no—
317Q8—381no—
318Q8—381no—
319D4—381no—
320D4—381no—
321D4—761no—
322D4—761no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—381no—
329C2×C4—381no—
330C2×C4—381no—
331C2×C4—761no—
332C2×C4—761no—
333C2×C4—761no—
334C2×C4—761no—
335C2×C4—1521no—
336C2×C4C22⋊C4×D1911yescharacteristic
337C2×C4(C22⋊D19)⋊C411yescharacteristic
338C2×C4#1059733011yescharacteristic
339C2×C4#1059736111yescharacteristic
340C2×C4#1059736211yescharacteristic
341C2×C4#1059736411yescharacteristic
342C2×C4#1059736511yescharacteristic
343C2×C4C4×C22⋊D1911yescharacteristic
344C2×C4#1059738311yescharacteristic
345C2×C4#1059738411yescharacteristic
346C8—42no—
347C8—81no—
348C8—762no—
349C8—761no—
350C8—761no—
351C8—1521no—
352C22—21no—
353C22—21no—
354C22—761no—
355C22—761no—
356C22—761no—
357C22#1192642011yescharacteristic
358C22#1192688311yescharacteristic
359C22#1192688411yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—82no—
364C4—761no—
365C4—761no—
366C4—761no—
367C4#1192653911yescharacteristic
368C4#1192655111yescharacteristic
369C4#1192670311yescharacteristic
370C4#1192670511yescharacteristic
371C4#1192680611yescharacteristic
372C4#1192681311yescharacteristic
373C2—21no—
374C2—21no—
375C2—1521no—
376C2#1456394411yescharacteristic
377C2#1456410511yescharacteristic
378C2#1456414011yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1548C2
socleC22×C19#386
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1548D19
hypocenterC19#9168
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
3. C2×#11926290C2semidirect
5. #14561531C2semidirect
6. #14561509C2semidirect
7. C19×#1548C2semidirect
165. #1548D19semidirect
262. C19#9168semidirect

Maximal subgroups

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

subgroupindex
#145734442
#145723032
C2×#119262902
#145620232
#145615312
#145615092
C19×#15482
#916819