Finite Group Databasebeta

← #18078422

Subgroups — #18078422

Order 4864.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573118C211yesmaximal, characteristic
2#14572303C211yesmaximal, characteristic
3C2×#11926290C211yesmaximal, characteristic, complemented
4#14562023C211yesmaximal, characteristic
5#14561531C211yesmaximal, characteristic, complemented
6#14561509C211yesmaximal, characteristic, complemented
7C19×#1546C211yesmaximal, characteristic, complemented
8C2×#10597388—21no—
9C4×#64541C2211yescharacteristic
10#11926751—21no—
11#11926751C412yes—
12#11926746—21no—
13#11926746C412yes—
14#11926604—22no—
15#11926600—21no—
16#11926596—21no—
17#11926568C2211yescharacteristic
18C2×C4⋊(C19⋊C8)C2211yescharacteristic
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20#11926553—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×#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
41C2×#64528—22no—
42#10597388—42no—
43#10597388—42no—
44C2×#64527—22no—
45C4×C22⋊D19—21no—
46C4×C22⋊D19—21no—
47#10597372D411yescharacteristic
48C2×#64520—21no—
49C22×C19⋊C8—21no—
50C22×C19⋊C8—21no—
51C4×D76C2×C411yescharacteristic
52C4×D76D411yescharacteristic
53#10597318—21no—
54C42×D19—21no—
55C4×Dic38C2×C411yescharacteristic
56C4×Dic38D411yescharacteristic
57C19×C4⋊C8—21no—
58C19×C4⋊C8—21no—
59C19×C4⋊C8D412yes—
60C19×C22⋊C8—21no—
61C4×C8×C19—21no—
62#10597292—22no—
63#10597292—22no—
64(C2×D19)⋊C8—22no—
65(C2×D19)⋊C8—22no—
66#10597272—22no—
67C8×Dic19—22no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)—21no—
71C4⋊(C19⋊C8)—21no—
72C4⋊(C19⋊C8)C2×C412yes—
73C4⋊(C19⋊C8)D411yescharacteristic
74C4⋊(C19⋊C8)D411yescharacteristic
75C2×Q8×C19—22no—
76C2×Q8×C19—41no—
77C2×Q8×C19—41no—
78C2×Q8×C19—41no—
79C2×Q8×C19—41no—
80C2×Q8×C19—41no—
81C22×C4×C19—41no—
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C22×C4×C19#4111yescharacteristic
85C2×C22⋊D19—21no—
86#64541—21no—
87#64541—21no—
88#64541—21no—
89#64541—21no—
90C2×D76C22⋊C411yescharacteristic
91C2×C4×D19—21no—
92C2×C4×D19—21no—
93C2×C4×D19—21no—
94C2×Dic38C22⋊C411yescharacteristic
95M16×C19—41no—
96M16×C19—41no—
97C2×C8×C19—22no—
98C2×C8×C19—41no—
99C4⋊C4×C19—22no—
100C4⋊C4×C19—22no—
101C4⋊C4×C19—41no—
102C4⋊C4×C19—41no—
103C42×C19C22×C411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19C2×D411yescharacteristic
106C42×C19C2×D411yescharacteristic
107C22⋊Dic19—21no—
108#64528—44no—
109#64527—44no—
110(C2×D19)⋊C4—21no—
111(C2×D19)⋊C4—21no—
112C4⋊Dic19C22⋊C411yescharacteristic
113C4⋊Dic19C22⋊C411yescharacteristic
114Dic19⋊C4—21no—
115Dic19⋊C4—21no—
116C4×Dic19—21no—
117C4×Dic19—21no—
118C4×Dic19—21no—
119#64520—41no—
120#64520—41no—
121C2×C19⋊C8—22no—
122C2×C19⋊C8—21no—
123C2×C19⋊C8—21no—
124C2×C19⋊C8—41no—
125C2×C19⋊C8—41no—
126C2×C19⋊C8—41no—
127C2×C19⋊C8—81no—
128#9172—191nomaximal, Sylow
129C23×C19#12311yescharacteristic
130C22×D19—21no—
131Q8×C19—42no—
132Q8×C19—42no—
133Q8×C19—81no—
134Q8×C19—81no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—41no—
138C2×C4×C19—42no—
139C2×C4×C19—81no—
140C2×C4×C19—81no—
141C2×C4×C19C2×C22⋊C411yescharacteristic
142C2×C4×C19C4×D411yescharacteristic
143C2×C4×C19C4×D411yescharacteristic
144C2×C4×C19#12011yescharacteristic
145C2×C4×C19#12111yescharacteristic
146C2×C4×C19#12111yescharacteristic
147C2×C4×C19#13511yescharacteristic
148C2×C4×C19#13511yescharacteristic
149C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
151C22⋊D19—41no—
152C22⋊D19—41no—
153C2×Dic19—21no—
154C2×Dic19—21no—
155C2×Dic19—21no—
156D76—21no—
157D76—21no—
158C4×D19—41no—
159C4×D19—41no—
160C4×D19—41no—
161C4×D19—41no—
162C4×D19—81no—
163Dic38—21no—
164Dic38—21no—
165C8×C19—42no—
166C8×C19—81no—
167C19⋊C8—42no—
168C19⋊C8—41no—
169C19⋊C8—41no—
170C19⋊C8—81no—
171#3039—191no—
172#2925—191no—
173#1546D1911yescharacteristic, complemented
174C2×#332—191no—
175#1477—191no—
176#1301—191no—
177#1292—191no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19#38611yescharacteristic
181C22×C19#48211yescharacteristic
182C22×C19#48211yescharacteristic
183C2×D19—41no—
184C2×D19—41no—
185C2×D19—41no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—82no—
190C4×C19#41611yescharacteristic
191C4×C19#41811yescharacteristic
192C4×C19#44911yescharacteristic
193C4×C19#44911yescharacteristic
194C4×C19#47111yescharacteristic
195C4×C19#47311yescharacteristic
196Dic19—41no—
197Dic19—41no—
198Dic19—41no—
199C2×#137—381no—
200C2×C4⋊Q8C2×D1911yescharacteristic
201C4×#41—191no—
202#462—192no—
203#462—381no—
204#461—192no—
205#461—381no—
206#433—382no—
207#432—381no—
208#431—381no—
209#431C2×D1911yescharacteristic
210#423—191no—
211#423C2×D1911yescharacteristic
212C2×C4⋊C8—191no—
213C2×C4⋊C8—191no—
214#419—381no—
215#408—381no—
216#405—381no—
217#332—22no—
218#332—381no—
219#332—381no—
220Q8⋊C8—381no—
221D4⋊C8—381no—
222C2×C19—21no—
223C2×C19—21no—
224C2×C19#187511yescharacteristic
225C2×C19#190211yescharacteristic
226C2×C19#190811yescharacteristic
227D19—81no—
228C2×#41—191no—
229C22×Q8—21no—
230#137—762no—
231#137—762no—
232C2×Q16—382no—
233C2×SD16—382no—
234C2×M16—21no—
235C2×M16—381no—
236C22×C8—381no—
237C22×C8—381no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8C4×D1912yes—
242C4×Q8—191no—
243C4×Q8—191no—
244C4×D4—191no—
245C4×D4—191no—
246C4×D4—381no—
247C4×D4—381no—
248#117—191no—
249#117—381no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C42—381no—
253C2×C42C22×D1911yescharacteristic
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—192no—
257C4⋊C8—191no—
258C4⋊C8—191no—
259C4⋊C8—381no—
260C4⋊C8—381no—
261C4⋊C8—381no—
262C4⋊C8—381no—
263C4⋊C8C22⋊D1912yes—
264#103—382no—
265#103—382no—
266C22⋊C8—21no—
267C22⋊C8—382no—
268C22⋊C8—382no—
269#97—382no—
270C4×C8—21no—
271C4×C8—382no—
272C19#917211yescharacteristic, complemented, Sylow
273#41—381no—
274#41—381no—
275#41—381no—
276#41—381no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—191no—
284C2×D4—191no—
285C2×D4—381no—
286C22×C4—41no—
287C22×C4—381no—
288C22×C4—381no—
289C22×C4—381no—
290C22×C4#6454111yescharacteristic
291C22×C4D4×D1911yescharacteristic
292C22×C4#6454311yescharacteristic
293Q16—764no—
294SD16—764no—
295M16—41no—
296M16—41no—
297M16—761no—
298M16—761no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—381no—
302C2×C8—381no—
303C2×C8—382no—
304C2×C8—761no—
305C2×C8—761no—
306C2×C8—761no—
307C2×C8—1521no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—191no—
313C4⋊C4—191no—
314C4⋊C4—381no—
315C4⋊C4—381no—
316C22⋊C4—381no—
317C22⋊C4—381no—
318C22⋊C4—381no—
319C42—381no—
320C42—381no—
321C42—381no—
322C42C2×C4×D1911yescharacteristic
323C42D4×D1911yescharacteristic
324C42D4×D1911yescharacteristic
325C42C2×C22⋊D1911yescharacteristic
326C23—381no—
327C23#1059732911yescharacteristic
328Q8—42no—
329Q8—42no—
330Q8—81no—
331Q8—81no—
332Q8—381no—
333Q8—381no—
334D4—381no—
335D4—381no—
336D4—761no—
337D4—761no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—381no—
345C2×C4—381no—
346C2×C4—381no—
347C2×C4—761no—
348C2×C4—761no—
349C2×C4—761no—
350C2×C4—761no—
351C2×C4—1521no—
352C2×C4C22⋊C4×D1911yescharacteristic
353C2×C4(C22⋊D19)⋊C411yescharacteristic
354C2×C4#1059733011yescharacteristic
355C2×C4#1059735711yescharacteristic
356C2×C4#1059735811yescharacteristic
357C2×C4#1059736011yescharacteristic
358C2×C4#1059736211yescharacteristic
359C2×C4C4×C22⋊D1911yescharacteristic
360C2×C4#1059738311yescharacteristic
361C2×C4#1059738411yescharacteristic
362C8—42no—
363C8—81no—
364C8—762no—
365C8—761no—
366C8—761no—
367C8—1521no—
368C22—21no—
369C22—21no—
370C22—761no—
371C22—761no—
372C22—761no—
373C22#1192642011yescharacteristic
374C22#1192686611yescharacteristic
375C22#1192686711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—82no—
380C4—761no—
381C4—761no—
382C4—761no—
383C4#1192653711yescharacteristic
384C4#1192654711yescharacteristic
385C4#1192668611yescharacteristic
386C4#1192668811yescharacteristic
387C4#1192681011yescharacteristic
388C4#1192681811yescharacteristic
389C2—21no—
390C2—21no—
391C2—1521no—
392C2#1456395411yescharacteristic
393C2#1456410511yescharacteristic
394C2#1456414711yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1546C2
socleC22×C19#386
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1546D19
hypocenterC19#9172
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. C2×#11926290C2semidirect
5. #14561531C2semidirect
6. #14561509C2semidirect
7. C19×#1546C2semidirect
173. #1546D19semidirect
272. C19#9172semidirect

Maximal subgroups

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

subgroupindex
#145731182
#145723032
C2×#119262902
#145620232
#145615312
#145615092
C19×#15462
#917219