Finite Group Databasebeta

← #18078063

Subgroups — #18078063

Order 4864.

602 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572675C211yesmaximal, characteristic, complemented
2#14566360C211yesmaximal, characteristic
3#14562027C211yesmaximal, characteristic, complemented
4#14562025C211yesmaximal, characteristic, complemented
5#14561955C211yesmaximal, characteristic, complemented
6#14561464C211yesmaximal, characteristic, complemented
7C19×#1274C211yesmaximal, characteristic, complemented
8C2×#10597320C411yescharacteristic
9C2×C4×D76C2211yescharacteristic
10C2×C4×D76C2211yescharacteristic
11#11926623—22no—
12#11926621—22no—
13#11926597C2211yescharacteristic
14#11926597C2211yescharacteristic
15#11926506—22no—
16#11926446C411yescharacteristic
17#11926446C411yescharacteristic
18#11926422—22no—
19#11926422—22no—
20#11926410C411yescharacteristic
21#11926273—22no—
22#11926271—22no—
23#11926267—22no—
24C19×#431C2211yescharacteristic
25C19×#431C2211yescharacteristic
26C19×#376C2211yescharacteristic
27C22×D76—22no—
28C22×D76C2×C411yescharacteristic
29C22×D76C2×C411yescharacteristic
30C22×C4×D19—21no—
31C22×C4×D19D412yes—
32C2×C42×C19C2×C411yescharacteristic
33C2×C42×C19C2×C411yescharacteristic
34C2×C42×C19C2311yescharacteristic
35C2×(C2×D19)⋊C4—21no—
36C2×(C2×D19)⋊C4—22no—
37C2×(C2×D19)⋊C4—22no—
38C2×(C2×D19)⋊C4D412yes—
39C2×C4⋊Dic19C2×C411yescharacteristic
40C2×C4⋊Dic19C2×C411yescharacteristic
41C2×#64515—24no—
42#10597320—22no—
43#10597320—22no—
44C4×D76—21no—
45C4×D76—21no—
46C4×D76—21no—
47C4×D76—21no—
48C4×D76—21no—
49C4×D76—21no—
50C4×D76—21no—
51C4×D76—21no—
52C19×C4⋊C8—21no—
53C19×C4⋊C8—21no—
54C19×C22⋊C8—21no—
55C19×C22⋊C8—21no—
56C4×C8×C19—21no—
57C4×C8×C19D412yescomplemented
58C19×#95—21no—
59C19×#95—21no—
60C19⋊#95—22no—
61C22⋊(C19⋊C8)—21no—
62C22⋊(C19⋊C8)—21no—
63(C2×D19)⋊C8—24no—
64C4⋊(C19⋊C8)—21no—
65C4⋊(C19⋊C8)—21no—
66C4×C19⋊C8—21no—
67C4×C19⋊C8D412yescomplemented
68C23×D19—21no—
69C23×D19C22⋊C412yes—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×Dic19—21no—
76C22×Dic19C22⋊C412yes—
77C2×D76—21no—
78C2×D76—21no—
79C2×D76—21no—
80C2×D76—21no—
81C2×D76—21no—
82C2×D76—21no—
83C2×D76—21no—
84C2×D76—21no—
85C2×D76—21no—
86C2×D76—21no—
87C2×D76—21no—
88C2×D76—28no—
89C2×D76—82no—
90C2×D76—82no—
91C2×D76M1612yescomplemented
92C2×C4×D19—22no—
93C2×C4×D19—22no—
94C2×C4×D19—41no—
95C2×C4×D19—41no—
96C2×C4×D19—82no—
97C2×C4×D19—82no—
98C2×C8×C19—22no—
99C2×C8×C19—41no—
100C42×C19—21no—
101C42×C19—21no—
102C42×C19—21no—
103C42×C19M1612yescomplemented
104C42×C19C2×D411yescharacteristic
105C42×C19C2×D411yescharacteristic
106C42×C19#4111yescharacteristic
107C42×C19#4111yescharacteristic
108(C2×D19)⋊C4—22no—
109(C2×D19)⋊C4—22no—
110(C2×D19)⋊C4—41no—
111(C2×D19)⋊C4—41no—
112(C2×D19)⋊C4—82no—
113(C2×D19)⋊C4—82no—
114C4⋊Dic19—21no—
115C4⋊Dic19—21no—
116C4⋊Dic19—21no—
117C4⋊Dic19—21no—
118C2×C19⋊C8—22no—
119C2×C19⋊C8—41no—
120#64515—84no—
121#9105—191nomaximal, Sylow
122C23×C19C2×C22⋊C411yescharacteristic
123C22×D19—22no—
124C22×D19—22no—
125C22×D19—22no—
126C22×D19—22no—
127C22×D19—42no—
128C22×D19—42no—
129C22×D19—42no—
130C22×D19—42no—
131C22×D19—41no—
132C22×D19—41no—
133C2×C4×C19—22no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19C4×D411yescharacteristic
142C2×C4×C19C4×D411yescharacteristic
143C2×C4×C19#12011yescharacteristic
144C2×C4×C19#12111yescharacteristic
145C2×C4×C19#12111yescharacteristic
146C2×C4×C19#12311yescharacteristic
147C2×C4×C19C2×M1611yescharacteristic
148C2×C4×C19C2×M1611yescharacteristic
149C2×C4×C19#13111yescharacteristic
150C2×C4×C19#13111yescharacteristic
151C2×Dic19—22no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—41no—
155D76—22no—
156D76—22no—
157D76—41no—
158D76—41no—
159D76—41no—
160D76—41no—
161D76—41no—
162D76—41no—
163D76—88no—
164C4×D19—44no—
165C4×D19—82no—
166C4×D19—82no—
167C4×D19—82no—
168C8×C19—42no—
169C8×C19—81no—
170C19⋊C8—42no—
171C19⋊C8—81no—
172#2975—191no—
173#2328—191no—
174#1478—191no—
175#1478—191no—
176#1460—191no—
177#1274—191no—
178#1274D1911yescharacteristic, complemented
179C22×C19—21no—
180C22×C19—21no—
181C22×C19#38611yescharacteristic
182C22×C19#40711yescharacteristic
183C22×C19#40811yescharacteristic
184C2×D19—44no—
185C2×D19—44no—
186C2×D19—42no—
187C2×D19—42no—
188C2×D19—42no—
189C2×D19—42no—
190C2×D19—82no—
191C2×D19—81no—
192C2×D19—81no—
193C2×D19—82no—
194C4×C19—21no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—42no—
199C4×C19—81no—
200C4×C19#43511yescharacteristic
201C4×C19#43511yescharacteristic
202C4×C19#43611yescharacteristic
203C4×C19#43611yescharacteristic
204Dic19—42no—
205Dic19—81no—
206C2×#127—191no—
207C2×C4×D4—191no—
208C2×C4×D4—191no—
209#436—382no—
210#436—382no—
211#431—191no—
212#431—191no—
213#431C2×D1911yescharacteristic
214#431C2×D1911yescharacteristic
215#407—382no—
216#390—191no—
217#390—191no—
218#386—382no—
219#386—382no—
220#382—191no—
221#376C2×D1911yescharacteristic
222D4⋊C8—382no—
223D4⋊C8—382no—
224#323—382no—
225C2×C19—21no—
226C2×C19—21no—
227C2×C19#187011yescharacteristic
228C2×C19#191011yescharacteristic
229C2×C19#191111yescharacteristic
230D19—82no—
231D19—82no—
232C22×D4—191no—
233C22×D4—191no—
234C22×D4—382no—
235C23×C4—192no—
236C23×C4—381no—
237C2×M16—384no—
238#127—382no—
239#127—382no—
240C4×D4—381no—
241C4×D4—381no—
242C4×D4—381no—
243C4×D4—381no—
244C4×D4—381no—
245C4×D4—381no—
246C4×D4—381no—
247C4×D4—381no—
248C2×C4⋊C4—191no—
249C2×C4⋊C4—191no—
250C2×C22⋊C4—192no—
251C2×C22⋊C4—381no—
252C2×C22⋊C4—382no—
253C2×C22⋊C4—382no—
254C2×C42C4×D1911yescharacteristic
255C2×C42C4×D1911yescharacteristic
256C2×C42C22×D1911yescharacteristic
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—381no—
260C4⋊C8—381no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—384no—
264C22⋊C8—381no—
265C22⋊C8—381no—
266C4×C8—21no—
267C4×C8—192no—
268C4×C8—381no—
269C4×C8D7612yescomplemented
270#95—21no—
271#95—21no—
272#95—382no—
273C19#910511yescharacteristic, complemented, Sylow
274C24—192no—
275C24—381no—
276C2×D4—192no—
277C2×D4—388no—
278C2×D4—381no—
279C2×D4—381no—
280C2×D4—381no—
281C2×D4—381no—
282C2×D4—381no—
283C2×D4—381no—
284C2×D4—381no—
285C2×D4—381no—
286C2×D4—381no—
287C2×D4—381no—
288C2×D4—381no—
289C2×D4—1522no—
290C2×D4—1522no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—192no—
294C22×C4—382no—
295C22×C4—382no—
296C22×C4—381no—
297C22×C4—761no—
298C22×C4—761no—
299C22×C4—1522no—
300C22×C4—1522no—
301C22×C4C2×C4×D1911yescharacteristic
302C22×C4D4×D1911yescharacteristic
303C22×C4D4×D1911yescharacteristic
304M16—1524no—
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—382no—
308C2×C8—761no—
309C4⋊C4—381no—
310C4⋊C4—381no—
311C4⋊C4—381no—
312C4⋊C4—381no—
313C22⋊C4—382no—
314C22⋊C4—382no—
315C22⋊C4—761no—
316C22⋊C4—761no—
317C22⋊C4—1522no—
318C22⋊C4—1522no—
319C42—21no—
320C42—21no—
321C42—21no—
322C42#6451512yescomplemented
323C42C2×D7611yescharacteristic
324C42#6454111yescharacteristic
325C42D4×D1911yescharacteristic
326C42#6454511yescharacteristic
327C23—382no—
328C23—382no—
329C23—382no—
330C23—382no—
331C23—762no—
332C23—762no—
333C23—762no—
334C23—762no—
335C23—761no—
336C23—761no—
337C23C22⋊C4×D1911yescharacteristic
338D4—382no—
339D4—382no—
340D4—761no—
341D4—761no—
342D4—761no—
343D4—761no—
344D4—761no—
345D4—761no—
346D4—1528no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—382no—
356C2×C4—764no—
357C2×C4—762no—
358C2×C4—762no—
359C2×C4—761no—
360C2×C4—1522no—
361C2×C4—1522no—
362C2×C4—1522no—
363C2×C4C4×D7611yescharacteristic
364C2×C4#1059732811yescharacteristic
365C2×C4#1059733011yescharacteristic
366C2×C4#1059733911yescharacteristic
367C2×C4#1059734011yescharacteristic
368C2×C4#1059734111yescharacteristic
369C2×C4C2×#6451511yescharacteristic
370C2×C4#1059734711yescharacteristic
371C2×C4M16×D1911yescharacteristic
372C2×C4#1059735311yescharacteristic
373C8—42no—
374C8—81no—
375C8—762no—
376C8—1521no—
377C22—21no—
378C22—21no—
379C22—764no—
380C22—764no—
381C22—762no—
382C22—762no—
383C22—762no—
384C22—762no—
385C22—1522no—
386C22—1522no—
387C22—1521no—
388C22—1521no—
389C22#1192642211yescharacteristic
390C22#1192650611yescharacteristic
391C22#1192650911yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—81no—
398C4—762no—
399C4—1521no—
400C4#1192661411yescharacteristic
401C4#1192661711yescharacteristic
402C4#1192662111yescharacteristic
403C4#1192662311yescharacteristic
404C2—21no—
405C2—21no—
406C2—1522no—
407C2—1522no—
408C2#1456393111yescharacteristic
409C2#1456416111yescharacteristic
410C2#1456416611yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1274C2
socleC22×C19#386
prime radicalC2×#10597320C4
cosocleC2×C42×C19C23
hypercenter#1274D19
hypocenterC19#9105
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
1. #14572675C2semidirect
3. #14562027C2semidirect
4. #14562025C2semidirect
5. #14561955C2semidirect
6. #14561464C2semidirect
7. C19×#1274C2semidirect
57. C4×C8×C19D4semidirect
67. C4×C19⋊C8D4semidirect
91. C2×D76M16semidirect
103. C42×C19M16semidirect
178. #1274D19semidirect
269. C4×C8D76semidirect
273. C19#9105semidirect
322. C42#64515semidirect

Maximal subgroups

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

subgroupindex
#145726752
#145663602
#145620272
#145620252
#145619552
#145614642
C19×#12742
#910519