Finite Group Databasebeta

← #18078336

Subgroups — #18078336

Order 4864.

452 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572649C211yesmaximal, characteristic
2#14563445C211yesmaximal, characteristic
3#14562230C211yesmaximal, characteristic, complemented
4#14562147C211yesmaximal, characteristic, complemented
5#14561527C211yesmaximal, characteristic, complemented
6#14561506C211yesmaximal, characteristic, complemented
7C19×#3116C211yesmaximal, characteristic
8#11926675—21no—
9#11926616—22no—
10D4×C19⋊C8—21no—
11#11926601—21no—
12#11926601C2211yescharacteristic
13C2×#10597294—21no—
14C4×#64520C2211yescharacteristic
15C4×#64520C2211yescharacteristic
16C2×#10597260—21no—
17#11926390C2211yescharacteristic
18#11926303—21no—
19#11926286—21no—
20#11926286—21no—
21#11926281—22no—
22C19×#533C2211yescharacteristic
23C4×#41×C19C2211yescharacteristic
24C19×#485—21no—
25C19×#477C411yescharacteristic, complemented
26C19×#476C411yescharacteristic, complemented
27C19×#462C411yescharacteristic, complemented
28C19×#461C411yescharacteristic, complemented
29C19×#452—21no—
30C19×#441—21no—
31C19×#440—21no—
32C19×#432C2211yescharacteristic
33C2×#41×C19D411yescharacteristic
34C2×Q16×C19—21no—
35C2×SD16×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×C19C2×C411yescharacteristic
44C4×Q8×C19D411yescharacteristic
45C4×D4×C19—21no—
46C4×D4×C19—21no—
47C4×D4×C19C2×C411yescharacteristic
48C4×D4×C19D411yescharacteristic
49C19×#117—21no—
50C19×#117—21no—
51C19×#117D411yescharacteristic
52C2×C42×C19—21no—
53C2×C42×C19C2311yescharacteristic
54C2×C4×Dic19—21no—
55C2×#64520—21no—
56C2×#64520—21no—
57C22×C19⋊C8—22no—
58C19×#107—21no—
59C19×#106—21no—
60C19×C4⋊C8C2×C411yescharacteristic
61C19×C4⋊C8C2×C411yescharacteristic
62C19×#103—21no—
63C19×#103—21no—
64C19×#103—21no—
65C19×#102—21no—
66C19×C22⋊C8—21no—
67C19×#97—21no—
68#10597294—24no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C22⋊(C19⋊C8)—22no—
72C22⋊(C19⋊C8)D412yes—
73C4⋊(C19⋊C8)—22no—
74C4⋊(C19⋊C8)—21no—
75#10597260—22no—
76#10597260—21no—
77#10597260—21no—
78#10597260D411yescharacteristic
79#10597260D411yescharacteristic
80C4×C19⋊C8—21no—
81C4×C19⋊C8—21no—
82#41×C19—22no—
83#41×C19—41no—
84C2×Q8×C19—21no—
85C2×Q8×C19—21no—
86C2×Q8×C19C22⋊C411yescharacteristic
87C2×D4×C19—21no—
88C2×D4×C19C22⋊C411yescharacteristic
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19#4111yescharacteristic
95C22×Dic19—41no—
96Q16×C19—42no—
97SD16×C19—42no—
98C2×C8×C19—21no—
99C2×C8×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—41no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19C22⋊C411yescharacteristic
109C4⋊C4×C19C22⋊C411yescharacteristic
110C22⋊C4×C19—21no—
111C22⋊C4×C19—21no—
112C22⋊C4×C19—21no—
113C22⋊C4×C19—41no—
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—
124#64520—22no—
125#64520—42no—
126#64520—41no—
127C2×C19⋊C8—21no—
128C2×C19⋊C8—21no—
129C2×C19⋊C8—22no—
130C2×C19⋊C8—44no—
131C2×C19⋊C8—41no—
132#9159—191nomaximal, Sylow
133C23×C19—21no—
134C23×C19#12111yescharacteristic
135Q8×C19—21no—
136Q8×C19—21no—
137Q8×C19—41no—
138Q8×C19—41no—
139Q8×C19—81no—
140D4×C19—21no—
141D4×C19—42no—
142D4×C19#10412yes—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—42no—
151C2×C4×C19—42no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—81no—
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—22no—
167C19⋊C8—42no—
168C19⋊C8—41no—
169C19⋊C8—42no—
170#3116D1911yescharacteristic
171#2970—191no—
172#1759—191no—
173#1526—191no—
174#1506—191no—
175#1300—191no—
176#1291—191no—
177C22×C19—21no—
178C22×C19—22no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—41no—
182C22×C19—41no—
183C22×C19#38611yescharacteristic
184C4×C19—21no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—41no—
190C4×C19—41no—
191C4×C19—41no—
192C4×C19—81no—
193C4×C19—81no—
194C4×C19C2×#10411yescharacteristic
195C4×C19#42111yescharacteristic
196Dic19—82no—
197#533C2×D1911yescharacteristic
198C4×#41C2×D1911yescharacteristic
199#485—21no—
200#477Dic1911yescharacteristic, complemented
201#476Dic1911yescharacteristic, complemented
202#462Dic1911yescharacteristic, complemented
203#461Dic1911yescharacteristic, complemented
204#452—21no—
205#446—381no—
206#441—21no—
207#440—21no—
208#435—382no—
209C8×D4—381no—
210#432—191no—
211#432—381no—
212#432C2×D1911yescharacteristic
213C2×#104—381no—
214C4×M16—191no—
215C4×M16—191no—
216C2×#97—381no—
217#376—191no—
218#339—381no—
219#330—381no—
220#330—381no—
221#328—382no—
222C2×C19—41no—
223C2×C19—42no—
224C2×C19#187111yescharacteristic
225C2×C19#190211yescharacteristic
226C2×C19#190611yescharacteristic
227C2×#41C22⋊D1911yescharacteristic
228C2×Q16—21no—
229C2×SD16—21no—
230C2×M16—381no—
231C2×M16—381no—
232C22×C8—382no—
233C4⋊Q8C2×Dic1911yescharacteristic
234C4⋊Q8C2×Dic1911yescharacteristic
235#125—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8C2×Dic1911yescharacteristic
241C4×Q8C22⋊D1911yescharacteristic
242C4×D4—21no—
243C4×D4—21no—
244C4×D4C2×Dic1911yescharacteristic
245C4×D4C22⋊D1911yescharacteristic
246#117—21no—
247#117—21no—
248#117C22⋊D1911yescharacteristic
249C2×C42—21no—
250C2×C42—381no—
251C2×C42C22×D1911yescharacteristic
252#107—21no—
253#106—21no—
254C4⋊C8—382no—
255C4⋊C8—381no—
256C4⋊C8C2×Dic1911yescharacteristic
257C4⋊C8C2×Dic1911yescharacteristic
258#104—384no—
259#103—21no—
260#103—21no—
261#103—21no—
262#102—21no—
263C22⋊C8—21no—
264C22⋊C8—192no—
265C22⋊C8—382no—
266#97—21no—
267#97—191no—
268#97—191no—
269#97—382no—
270#97—381no—
271#97—381no—
272C4×C8—381no—
273C4×C8—381no—
274#95—381no—
275#95—381no—
276C19#915911yescharacteristic, complemented, Sylow
277#41—22no—
278#41—41no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8C22⋊Dic1911yescharacteristic
282C2×D4—21no—
283C2×D4C22⋊Dic1911yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—761no—
288C22×C4D4×D1911yescharacteristic
289C22×C4#6454311yescharacteristic
290C22×C4C2×C22⋊D1911yescharacteristic
291Q16—42no—
292SD16—42no—
293M16—382no—
294M16—762no—
295M16—761no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—381no—
299C2×C8—381no—
300C2×C8—382no—
301C2×C8—764no—
302C2×C8—761no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4C22⋊Dic1911yescharacteristic
312C4⋊C4C22⋊Dic1911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—41no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—41no—
321C42—382no—
322C42—761no—
323C42D4×D1911yescharacteristic
324C42#6454311yescharacteristic
325C42C22×Dic1911yescharacteristic
326C42C2×C22⋊D1911yescharacteristic
327C23—21no—
328C23#1059738511yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—41no—
332Q8—41no—
333Q8—81no—
334D4—21no—
335D4—42no—
336D4#1059729412yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—762no—
350C2×C4—1521no—
351C2×C4—1521no—
352C2×C4D4×Dic1911yescharacteristic
353C2×C4D4×Dic1911yescharacteristic
354C2×C4#1059738111yescharacteristic
355C2×C4#1059738311yescharacteristic
356C2×C4#1059738511yescharacteristic
357C2×C4C2×C22⋊Dic1911yescharacteristic
358C8—41no—
359C8—41no—
360C8—382no—
361C8—762no—
362C8—761no—
363C8—762no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22#1192642411yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—1522no—
382C4C2×#1059729411yescharacteristic
383C4#1192656111yescharacteristic
384C2—41no—
385C2—42no—
386C2#1456393811yescharacteristic
387C2#1456411011yescharacteristic
388C2#1456413811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3116C2
socleC22×C19#386
prime radicalC2×#41×C19D4
cosocleC2×C42×C19C23
hypercenter#3116D19
hypocenterC19#9159
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3116

Complements

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

NH ≅ G/Ntype
3. #14562230C2semidirect
4. #14562147C2semidirect
5. #14561527C2semidirect
6. #14561506C2semidirect
25. C19×#477C4semidirect
26. C19×#476C4semidirect
27. C19×#462C4semidirect
28. C19×#461C4semidirect
200. #477Dic19semidirect
201. #476Dic19semidirect
202. #462Dic19semidirect
203. #461Dic19semidirect
276. C19#9159semidirect

Maximal subgroups

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

subgroupindex
#145726492
#145634452
#145622302
#145621472
#145615272
#145615062
C19×#31162
#915919