Finite Group Databasebeta

← #18080739

Subgroups — #18080739

Order 4864.

444 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#14564428C211yesmaximal, characteristic
2#14563505C211yesmaximal, characteristic, complemented
3C4×#10597278C211yesmaximal, characteristic
4C2×#11926271C211yesmaximal, characteristic
5#14561474C211yesmaximal, characteristic, complemented
6C19⋊#1273C211yesmaximal, characteristic, complemented
7C2×C19×#335C211yesmaximal, characteristic, complemented
8C2×C4×D76C2211yescharacteristic
9C2×#10597278C411yescharacteristic
10C2×#10597278C411yescharacteristic
11C2×(C2×D19)⋊C8—21no—
12C2×(C2×D19)⋊C8—21no—
13C2×#10597272—21no—
14C2×C4×C19⋊C8C2211yescharacteristic
15C2×C4×C19⋊C8C2211yescharacteristic
16C4×C4⋊Dic19C2211yescharacteristic
17#11926307C411yescharacteristic
18#11926307C411yescharacteristic
19#11926298—21no—
20#11926271—22no—
21C2×C19×C4⋊C8C2211yescharacteristic
22C2×C19×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C19C2211yescharacteristic
24C19×#335—22no—
25C22×D76C2×C411yescharacteristic
26C22×C4×D19—21no—
27C22×C8×C19—21no—
28C22×C8×C19—21no—
29C22×C8×C19C2×C411yescharacteristic
30C22×C8×C19C2×C411yescharacteristic
31C2×C42×C19C2311yescharacteristic
32C2×(C2×D19)⋊C4—21no—
33C2×C4⋊Dic19C2×C411yescharacteristic
34C2×C4⋊Dic19C2×C411yescharacteristic
35C2×C4⋊Dic19C2×C411yescharacteristic
36C2×C4×Dic19—21no—
37C22×C19⋊C8—21no—
38C22×C19⋊C8D411yescharacteristic
39C22×C19⋊C8D411yescharacteristic
40C4×D76—21no—
41C4×D76—21no—
42C4×D76—21no—
43C4×D76—21no—
44C19×C4⋊C8—21no—
45C19×C4⋊C8—21no—
46C19×C4⋊C8—21no—
47C19×C4⋊C8D412yes—
48C4×C8×C19—21no—
49C4×C8×C19—21no—
50C19⋊#95—21no—
51#10597278—22no—
52#10597278—22no—
53(C2×D19)⋊C8—42no—
54(C2×D19)⋊C8—42no—
55#10597272—42no—
56C4×C19⋊C8—21no—
57C4×C19⋊C8—21no—
58C4×C19⋊C8—21no—
59C4×C19⋊C8—21no—
60C23×D19—21no—
61C22×C4×C19C22×C411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19#4111yescharacteristic
64C22×Dic19—21no—
65C22×Dic19—21no—
66C22×Dic19—21no—
67C2×D76—21no—
68C2×D76—21no—
69C2×D76—21no—
70C2×D76—21no—
71C2×D76—21no—
72C2×D76M1612yes—
73C2×C4×D19—41no—
74C2×C4×D19—41no—
75C2×C4×D19—41no—
76C2×C4×D19—41no—
77C2×C4×D19—41no—
78C2×C4×D19—41no—
79C2×C8×C19—21no—
80C2×C8×C19—21no—
81C2×C8×C19—21no—
82C2×C8×C19—22no—
83C2×C8×C19—21no—
84C2×C8×C19—21no—
85C2×C8×C19—41no—
86C2×C8×C19—41no—
87C2×C8×C19—41no—
88C2×C8×C19—41no—
89C2×C8×C19—41no—
90C2×C8×C19M1612yes—
91C42×C19C2×D411yescharacteristic
92C42×C19#4111yescharacteristic
93C42×C19#4111yescharacteristic
94C42×C19#4111yescharacteristic
95(C2×D19)⋊C4—41no—
96(C2×D19)⋊C4—41no—
97C4⋊Dic19—21no—
98C4⋊Dic19—21no—
99C4⋊Dic19—21no—
100C4⋊Dic19—21no—
101C4⋊Dic19—21no—
102C4⋊Dic19—21no—
103C4×Dic19—41no—
104C4×Dic19—41no—
105C2×C19⋊C8—21no—
106C2×C19⋊C8—21no—
107C2×C19⋊C8—22no—
108C2×C19⋊C8—21no—
109C2×C19⋊C8—21no—
110C2×C19⋊C8—21no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8D812yes—
114#9545—191nomaximal, Sylow
115C23×C19C4×D411yescharacteristic
116C22×D19—22no—
117C22×D19—41no—
118C22×D19—41no—
119C22×D19—41no—
120C22×D19—41no—
121C22×D19—41no—
122C22×D19—41no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19#11711yescharacteristic
126C2×C4×C19C4×D411yescharacteristic
127C2×C4×C19#12111yescharacteristic
128C2×C4×C19#12311yescharacteristic
129C2×C4×C19#12411yescharacteristic
130C2×C4×C19#12611yescharacteristic
131C2×C4×C19C2×M1611yescharacteristic
132C2×C4×C19C2×M1611yescharacteristic
133C2×C4×C19#13111yescharacteristic
134C2×C4×C19#13111yescharacteristic
135C2×C4×C19C2×D811yescharacteristic
136C2×C4×C19#13511yescharacteristic
137C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C19#13711yescharacteristic
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148D76—22no—
149D76—22no—
150D76—41no—
151D76—41no—
152C4×D19—81no—
153C4×D19—81no—
154C4×D19—81no—
155C4×D19—81no—
156C8×C19—22no—
157C8×C19—41no—
158C8×C19—42no—
159C8×C19—81no—
160C19⋊C8—22no—
161C19⋊C8—42no—
162C19⋊C8—41no—
163#1954—191no—
164#1770—191no—
165C4×#102—191no—
166C2×#335D1911yescharacteristic, complemented
167C2×D4⋊C8—191no—
168#1279—191no—
169#1273—191no—
170C22×C19#38811yescharacteristic
171C22×C19#43511yescharacteristic
172C22×C19#43611yescharacteristic
173C22×C19C4×D811yescharacteristic
174C22×C19#44011yescharacteristic
175C22×C19#44311yescharacteristic
176C22×C19#44411yescharacteristic
177C2×D19—42no—
178C2×D19—42no—
179C2×D19—42no—
180C2×D19—81no—
181C2×D19—81no—
182C2×D19—81no—
183C2×D19—81no—
184C4×C19—21no—
185C4×C19—21no—
186C4×C19#43211yescharacteristic
187C4×C19#43311yescharacteristic
188C4×C19#43511yescharacteristic
189C4×C19#43511yescharacteristic
190C4×C19#45911yescharacteristic
191C4×C19#46411yescharacteristic
192C4×C19#48011yescharacteristic
193C4×C19#48211yescharacteristic
194Dic19—81no—
195Dic19—81no—
196Dic19—81no—
197C2×C4×D4—191no—
198C2×C4⋊C8C2×D1911yescharacteristic
199C2×C4⋊C8C2×D1911yescharacteristic
200C2×#102—191no—
201C2×#102—191no—
202C2×C22⋊C8—381no—
203C2×C22⋊C8—381no—
204C2×#97—381no—
205C2×C4×C8—191no—
206C2×C4×C8—191no—
207C2×C4×C8C2×D1911yescharacteristic
208C4×C4⋊C4—191no—
209#340—191no—
210#340—191no—
211#336—381no—
212#335—22no—
213D4⋊C8—382no—
214C2×C19#158111yescharacteristic
215C2×C19#158511yescharacteristic
216C2×C19#158911yescharacteristic
217C2×C19#159211yescharacteristic
218C2×C19#192411yescharacteristic
219C2×C19#192511yescharacteristic
220C2×C19#192911yescharacteristic
221D19—82no—
222C22×D4—191no—
223C23×C4—381no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—191no—
227C22×C8—191no—
228C22×C8—381no—
229C22×C8C4×D1911yescharacteristic
230C22×C8C4×D1911yescharacteristic
231C4×D4—381no—
232C4×D4—381no—
233C4×D4—381no—
234C4×D4—381no—
235C2×C4⋊C4—191no—
236C2×C4⋊C4—191no—
237C2×C4⋊C4—191no—
238C2×C22⋊C4—381no—
239C2×C42—381no—
240C2×C42C22×D1911yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8C22⋊D1912yes—
245#102—382no—
246#102—382no—
247C22⋊C8—762no—
248C22⋊C8—762no—
249#97—762no—
250C4×C8—21no—
251C4×C8—21no—
252C4×C8—381no—
253C4×C8—381no—
254C4×C8—381no—
255C4×C8—381no—
256#95—381no—
257C19#954511yescharacteristic, complemented, Sylow
258C24—381no—
259C2×D4—192no—
260C2×D4—381no—
261C2×D4—381no—
262C2×D4—381no—
263C2×D4—381no—
264C2×D4—381no—
265C22×C4—381no—
266C22×C4—381no—
267C22×C4—381no—
268C22×C4—761no—
269C22×C4—761no—
270C22×C4—761no—
271C22×C4—761no—
272C22×C4—761no—
273C22×C4—761no—
274C22×C4C2×C4×D1911yescharacteristic
275C22×C4D4×D1911yescharacteristic
276C22×C4#6454511yescharacteristic
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—192no—
289C2×C8—381no—
290C2×C8—381no—
291C2×C8—382no—
292C2×C8—381no—
293C2×C8—381no—
294C2×C8—381no—
295C2×C8—761no—
296C2×C8—761no—
297C2×C8#6451512yes—
298C4⋊C4—381no—
299C4⋊C4—381no—
300C4⋊C4—381no—
301C4⋊C4—381no—
302C4⋊C4—381no—
303C4⋊C4—381no—
304C22⋊C4—761no—
305C22⋊C4—761no—
306C42—761no—
307C42—761no—
308C42#6454111yescharacteristic
309C42#6454311yescharacteristic
310C42#6454511yescharacteristic
311C42C2×C22⋊D1911yescharacteristic
312C23—382no—
313C23—761no—
314C23—761no—
315C23—761no—
316C23—761no—
317C23—761no—
318C23—761no—
319C23#1059733911yescharacteristic
320D4—382no—
321D4—382no—
322D4—761no—
323D4—761no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—761no—
327C2×C4—761no—
328C2×C4—761no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—761no—
332C2×C4—761no—
333C2×C4—761no—
334C2×C4—761no—
335C2×C4—1521no—
336C2×C4—1521no—
337C2×C4—1521no—
338C2×C4—1521no—
339C2×C4#1059733811yescharacteristic
340C2×C4#1059734011yescharacteristic
341C2×C4#1059734411yescharacteristic
342C2×C4C2×#6451511yescharacteristic
343C2×C4#1059734711yescharacteristic
344C2×C4M16×D1911yescharacteristic
345C2×C4#1059735311yescharacteristic
346C2×C4D8×D1911yescharacteristic
347C2×C4#1059735711yescharacteristic
348C2×C4#1059736411yescharacteristic
349C2×C4#1059736511yescharacteristic
350C2×C4C4×C22⋊D1911yescharacteristic
351C2×C4#1059738511yescharacteristic
352C2×C4#1059739311yescharacteristic
353C8—22no—
354C8—41no—
355C8—42no—
356C8—81no—
357C8—382no—
358C8—762no—
359C8—761no—
360C22—762no—
361C22—762no—
362C22—762no—
363C22—1521no—
364C22—1521no—
365C22—1521no—
366C22—1521no—
367C22#1192643411yescharacteristic
368C22#1192661411yescharacteristic
369C22#1192662111yescharacteristic
370C22#1192662611yescharacteristic
371C22#1192664311yescharacteristic
372C22#1192666011yescharacteristic
373C22#1192666511yescharacteristic
374C4—21no—
375C4—21no—
376C4—1521no—
377C4—1521no—
378C4—1521no—
379C4#1192660011yescharacteristic
380C4#1192660411yescharacteristic
381C4#1192661311yescharacteristic
382C4#1192661511yescharacteristic
383C4#1192673711yescharacteristic
384C4#1192676811yescharacteristic
385C4#1192685911yescharacteristic
386C4#1192687111yescharacteristic
387C2—1522no—
388C2#1456246311yescharacteristic
389C2#1456249111yescharacteristic
390C2#1456251911yescharacteristic
391C2#1456253611yescharacteristic
392C2#1456424711yescharacteristic
393C2#1456425411yescharacteristic
394C2#1456428211yescharacteristic
subgroupG/H
centerC22×C4D4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#335C2
socleC23×C19C4×D4
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenterC2×#335D19
hypocenterC19#9545
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. #14563505C2semidirect
5. #14561474C2semidirect
6. C19⋊#1273C2semidirect
7. C2×C19×#335C2semidirect
166. C2×#335D19semidirect
257. C19#9545semidirect

Maximal subgroups

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

subgroupindex
#145644282
#145635052
C4×#105972782
C2×#119262712
#145614742
C19⋊#12732
C2×C19×#3352
#954519