Finite Group Databasebeta

← #18078385

Subgroups — #18078385

Order 4864.

436 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572724C211yesmaximal, characteristic
2#14563465C211yesmaximal, characteristic
3#14562250C211yesmaximal, characteristic
4#14562134C211yesmaximal, characteristic
5#14561533C211yesmaximal, characteristic
6#14561492C211yesmaximal, characteristic
7C19×#3113C211yesmaximal, characteristic
8#11926675—22no—
9#11926675—21no—
10Q8×C19⋊C8—21no—
11#11926601—21no—
12#11926601C2211yescharacteristic
13#11926597—21no—
14#11926597C2211yescharacteristic
15C2×#10597292—21no—
16C2×#10597260C2211yescharacteristic
17C4×C4⋊Dic19C2211yescharacteristic
18#11926306—21no—
19#11926286—22no—
20#11926281—21no—
21#11926281—21no—
22C19×#533C2211yescharacteristic
23C2×C4×Q8×C19C2211yescharacteristic
24C19×#483—21no—
25C19×#475C411yescharacteristic, complemented
26C19×#475C411yescharacteristic, complemented
27C19×#462C411yescharacteristic, complemented
28C19×#462C411yescharacteristic, complemented
29C19×#451—21no—
30C19×#441—21no—
31C19×#441—21no—
32C19×#432C2211yescharacteristic
33C22×Q8×C19D411yescharacteristic
34C2×Q16×C19—21no—
35C2×Q16×C19—21no—
36C19×C4⋊Q8C2×C411yescharacteristic
37C19×C4⋊Q8C2×C411yescharacteristic
38C19×#125—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C4×Q8×C19—21no—
42C4×Q8×C19—21no—
43C4×Q8×C19—21no—
44C4×Q8×C19—21no—
45C4×Q8×C19C2×C411yescharacteristic
46C4×Q8×C19C2×C411yescharacteristic
47C4×Q8×C19D411yescharacteristic
48C4×Q8×C19D411yescharacteristic
49C19×#117—21no—
50C2×C4⋊C4×C19—21no—
51C2×C4⋊C4×C19D411yescharacteristic
52C2×C42×C19—21no—
53C2×C42×C19C2311yescharacteristic
54C2×C4⋊Dic19—21no—
55C2×C4×Dic19—21no—
56C22×C19⋊C8—21no—
57C19×#106—21no—
58C19×#106—21no—
59C19×C4⋊C8C2×C411yescharacteristic
60C19×C4⋊C8C2×C411yescharacteristic
61C19×#103—21no—
62C19×#103—21no—
63C19×#103—21no—
64C19×#103—21no—
65C19×C22⋊C8—21no—
66C19×#97—21no—
67#10597292—24no—
68C19⋊#95—21no—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)D411yescharacteristic
71C22⋊(C19⋊C8)D411yescharacteristic
72C4⋊(C19⋊C8)—22no—
73C4⋊(C19⋊C8)—22no—
74C4⋊(C19⋊C8)—21no—
75C4⋊(C19⋊C8)—21no—
76#10597260—22no—
77#10597260—21no—
78#10597260—21no—
79#10597260D412yes—
80C4×C19⋊C8—22no—
81C4×C19⋊C8—21no—
82C2×Q8×C19—21no—
83C2×Q8×C19—22no—
84C2×Q8×C19—21no—
85C2×Q8×C19—21no—
86C2×Q8×C19—41no—
87C2×Q8×C19C22⋊C411yescharacteristic
88C2×Q8×C19C22⋊C411yescharacteristic
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19#4111yescharacteristic
94C22×Dic19—41no—
95Q16×C19—42no—
96Q16×C19—42no—
97C2×C8×C19—21no—
98C2×C8×C19—21no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C4⋊C4×C19C22⋊C411yescharacteristic
111C4⋊C4×C19C22⋊C411yescharacteristic
112C22⋊C4×C19—41no—
113C42×C19—21no—
114C42×C19—21no—
115C42×C19—21no—
116C42×C19—21no—
117C42×C19—41no—
118C42×C19C22×C411yescharacteristic
119C42×C19C2×D411yescharacteristic
120C42×C19C2×D411yescharacteristic
121C42×C19#4111yescharacteristic
122C4⋊Dic19—22no—
123C4⋊Dic19—41no—
124C4×Dic19—81no—
125C2×C19⋊C8—22no—
126C2×C19⋊C8—21no—
127C2×C19⋊C8—21no—
128C2×C19⋊C8—22no—
129C2×C19⋊C8—41no—
130C2×C19⋊C8—41no—
131#9166—191nomaximal, Sylow
132C23×C19#12111yescharacteristic
133Q8×C19—21no—
134Q8×C19—21no—
135Q8×C19—21no—
136Q8×C19—42no—
137Q8×C19—41no—
138Q8×C19—41no—
139Q8×C19—81no—
140Q8×C19#10412yes—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—41no—
150C2×C4×C19—42no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19C2×C22⋊C411yescharacteristic
156C2×C4×C19C4×D411yescharacteristic
157C2×C4×C19C4×D411yescharacteristic
158C2×C4×C19#12011yescharacteristic
159C2×C4×C19#12111yescharacteristic
160C2×C4×C19#12311yescharacteristic
161C2×Dic19—42no—
162C2×Dic19—81no—
163C2×Dic19—81no—
164C8×C19—41no—
165C8×C19—41no—
166C19⋊C8—41no—
167C19⋊C8—41no—
168C19⋊C8—42no—
169C19⋊C8—42no—
170#3113D1911yescharacteristic
171#2984—191no—
172#1763—191no—
173#1531—191no—
174#1503—191no—
175#1302—191no—
176#1285—191no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19#38611yescharacteristic
180C22×C19#47111yescharacteristic
181C22×C19#47311yescharacteristic
182C4×C19—21no—
183C4×C19—22no—
184C4×C19—21no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—41no—
189C4×C19—41no—
190C4×C19—41no—
191C4×C19—81no—
192C4×C19—81no—
193C4×C19C2×#10411yescharacteristic
194C4×C19#42111yescharacteristic
195Dic19—82no—
196#533C2×D1911yescharacteristic
197C2×C4×Q8C2×D1911yescharacteristic
198#483—21no—
199#475Dic1911yescharacteristic, complemented
200#475Dic1911yescharacteristic, complemented
201#462Dic1911yescharacteristic, complemented
202#462Dic1911yescharacteristic, complemented
203#451—21no—
204#446—382no—
205#446—381no—
206C8×Q8—381no—
207#441—21no—
208#441—21no—
209#432—191no—
210#432—381no—
211#432C2×D1911yescharacteristic
212#431—191no—
213#431—381no—
214C2×#103—381no—
215C2×#97—191no—
216C4×C4⋊C4—191no—
217#340—381no—
218#330—382no—
219#328—381no—
220#328—381no—
221C2×C19—21no—
222C2×C19—21no—
223C2×C19#187111yescharacteristic
224C2×C19#190511yescharacteristic
225C2×C19#190811yescharacteristic
226C22×Q8C22⋊D1911yescharacteristic
227C2×Q16—21no—
228C2×Q16—21no—
229C22×C8—381no—
230C4⋊Q8C2×Dic1911yescharacteristic
231C4⋊Q8C2×Dic1911yescharacteristic
232#125—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8C2×Dic1911yescharacteristic
240C4×Q8C2×Dic1911yescharacteristic
241C4×Q8C22⋊D1911yescharacteristic
242C4×Q8C22⋊D1911yescharacteristic
243#117—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—381no—
246C2×C4⋊C4C22⋊D1911yescharacteristic
247C2×C42—21no—
248C2×C42—381no—
249C2×C42C22×D1911yescharacteristic
250#106—21no—
251#106—21no—
252C4⋊C8—382no—
253C4⋊C8—382no—
254C4⋊C8—381no—
255C4⋊C8—381no—
256C4⋊C8C2×Dic1911yescharacteristic
257C4⋊C8C2×Dic1911yescharacteristic
258#103—21no—
259#103—21no—
260#103—21no—
261#103—21no—
262#103—384no—
263C22⋊C8—21no—
264C22⋊C8—191no—
265C22⋊C8—191no—
266C22⋊C8—381no—
267#97—21no—
268#97—192no—
269#97—382no—
270#97—381no—
271#97—381no—
272C4×C8—382no—
273C4×C8—381no—
274#95—381no—
275C19#916611yescharacteristic, complemented, Sylow
276C2×Q8—21no—
277C2×Q8—22no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—41no—
281C2×Q8C22⋊Dic1911yescharacteristic
282C2×Q8C22⋊Dic1911yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—761no—
286C22×C4D4×D1911yescharacteristic
287C22×C4#6454311yescharacteristic
288C22×C4C2×C22⋊D1911yescharacteristic
289Q16—42no—
290Q16—42no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—382no—
294C2×C8—381no—
295C2×C8—382no—
296C2×C8—381no—
297C2×C8—761no—
298C2×C8—761no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—382no—
311C4⋊C4—761no—
312C4⋊C4C22⋊Dic1911yescharacteristic
313C4⋊C4C22⋊Dic1911yescharacteristic
314C22⋊C4—41no—
315C42—21no—
316C42—21no—
317C42—21no—
318C42—21no—
319C42—41no—
320C42—1521no—
321C42D4×D1911yescharacteristic
322C42#6454311yescharacteristic
323C42C22×Dic1911yescharacteristic
324C42C2×C22⋊D1911yescharacteristic
325C23#1059738511yescharacteristic
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—42no—
330Q8—41no—
331Q8—41no—
332Q8—81no—
333Q8#1059729412yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—762no—
349C2×C4—1521no—
350C2×C4—1521no—
351C2×C4D4×Dic1911yescharacteristic
352C2×C4D4×Dic1911yescharacteristic
353C2×C4#1059738111yescharacteristic
354C2×C4#1059738311yescharacteristic
355C2×C4#1059738511yescharacteristic
356C2×C4C2×C22⋊Dic1911yescharacteristic
357C8—41no—
358C8—41no—
359C8—762no—
360C8—761no—
361C8—762no—
362C8—761no—
363C22—21no—
364C22—21no—
365C22#1192642411yescharacteristic
366C22#1192680911yescharacteristic
367C22#1192681711yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—22no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—81no—
378C4—81no—
379C4—1522no—
380C4C2×#1059729411yescharacteristic
381C4#1192656111yescharacteristic
382C2—21no—
383C2—21no—
384C2#1456393811yescharacteristic
385C2#1456413111yescharacteristic
386C2#1456415211yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3113C2
socleC22×C19#386
prime radicalC23×C19#121
cosocleC2×C42×C19C23
hypercenter#3113D19
hypocenterC19#9166
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
25. C19×#475C4semidirect
26. C19×#475C4semidirect
27. C19×#462C4semidirect
28. C19×#462C4semidirect
199. #475Dic19semidirect
200. #475Dic19semidirect
201. #462Dic19semidirect
202. #462Dic19semidirect
275. C19#9166semidirect

Maximal subgroups

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

subgroupindex
#145727242
#145634652
#145622502
#145621342
#145615332
#145614922
C19×#31132
#916619