Finite Group Databasebeta

← #18083615

Subgroups — #18083615

Order 4864.

714 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926916C211yesmaximal, characteristic
2C2×#11926741C211yesmaximal, characteristic
3#14568843C211yesmaximal, characteristic, complemented
4C2×#11926292C211yesmaximal, characteristic, complemented
5C2×#11926274C211yesmaximal, characteristic, complemented
6#14561476C211yesmaximal, characteristic, complemented
7C19×#1982C211yesmaximal, characteristic
8C22×#64526—21no—
9C22×#64526—22no—
10C2×#10597315C2211yescharacteristic
11C2×C4×Dic38C2211yescharacteristic
12#11926916—22no—
13#11926916—22no—
14#11926741—22no—
15#11926741—22no—
16C2×C4⋊(C19⋊C8)C2211yescharacteristic
17C2×#10597289—21no—
18C2×C4×C19⋊C8C2211yescharacteristic
19#11926465—22no—
20#11926450—21no—
21#11926443—22no—
22#11926414—21no—
23#11926292—22no—
24#11926274—22no—
25C2×C19×#127C2211yescharacteristic
26C2×C19×C4⋊C8C2211yescharacteristic
27C2×C19×#102—22no—
28C4×C4⋊C4×C19C2211yescharacteristic
29C22×D4×C19—21no—
30C22×D4×C19—21no—
31C22×D4×C19—21no—
32C22×Dic38D411yescharacteristic
33C22×Dic38D412yes—
34C22×C8×C19—21no—
35C19×#127—21no—
36C19×#127—21no—
37C19×#127—21no—
38C19×#127D412yes—
39C2×C4⋊C4×C19D412yes—
40C2×C42×C19—21no—
41C2×C42×C19C2311yescharacteristic
42C2×#64526—28no—
43C2×#64526—24no—
44C2×#64526—48no—
45C2×#64526—42no—
46C2×#64526—42no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19—24no—
50C2×C4⋊Dic19D411yescharacteristic
51C2×Dic19⋊C4—21no—
52C2×C4×Dic19—21no—
53C22×C19⋊C8—21no—
54C22×C19⋊C8—21no—
55#10597315—21no—
56#10597315—21no—
57#10597315—21no—
58#10597315—21no—
59C4×Dic38—21no—
60C4×Dic38—21no—
61C4×Dic38—21no—
62C4×Dic38—21no—
63C19×C4⋊C8—21no—
64C19×C4⋊C8—21no—
65C19×#102—44no—
66C19×#95—21no—
67#10597289—24no—
68C19⋊#95—24no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)D412yes—
71C4×C19⋊C8—21no—
72C4×C19⋊C8D412yes—
73C24×C19—41no—
74C2×D4×C19—22no—
75C2×D4×C19—22no—
76C2×D4×C19—22no—
77C2×D4×C19—44no—
78C2×D4×C19—41no—
79C2×D4×C19—41no—
80C2×D4×C19—41no—
81C2×D4×C19—41no—
82C2×D4×C19—42no—
83C2×D4×C19—41no—
84C2×D4×C19—41no—
85C2×D4×C19—42no—
86C2×D4×C19—41no—
87C22×C4×C19—22no—
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×Dic19—21no—
92C22×Dic19—22no—
93C22×Dic19—21no—
94C2×Dic38—21no—
95C2×Dic38—21no—
96C2×Dic38—21no—
97C2×Dic38—21no—
98C2×Dic38—21no—
99C2×Dic38—22no—
100C2×Dic38—22no—
101C2×Dic38—44no—
102C2×Dic38SD1612yescomplemented
103C2×C8×C19—41no—
104C2×C8×C19—42no—
105C4⋊C4×C19—22no—
106C4⋊C4×C19SD1614yescomplemented
107C42×C19—41no—
108C42×C19—41no—
109C42×C19C2×D411yescharacteristic
110C42×C19C2×D411yescharacteristic
111C42×C19C2×D411yescharacteristic
112C42×C19#4111yescharacteristic
113#64526—416no—
114#64526—48no—
115C4⋊Dic19—21no—
116C4⋊Dic19—21no—
117C4⋊Dic19—41no—
118C4⋊Dic19—41no—
119C4⋊Dic19—41no—
120C4⋊Dic19—41no—
121C4⋊Dic19—84no—
122Dic19⋊C4—41no—
123Dic19⋊C4—41no—
124C4×Dic19—41no—
125C4×Dic19—41no—
126C2×C19⋊C8—24no—
127C2×C19⋊C8—22no—
128C2×C19⋊C8—22no—
129C2×C19⋊C8—41no—
130C2×C19⋊C8—41no—
131#10049—191nomaximal, Sylow
132C23×C19—42no—
133C23×C19—81no—
134C23×C19—82no—
135C23×C19—81no—
136C23×C19—82no—
137C23×C19#12011yescharacteristic
138D4×C19—44no—
139D4×C19—42no—
140D4×C19—42no—
141D4×C19—44no—
142D4×C19—82no—
143D4×C19—81no—
144D4×C19—81no—
145D4×C19—81no—
146D4×C19—81no—
147C2×C4×C19—22no—
148C2×C4×C19—24no—
149C2×C4×C19—42no—
150C2×C4×C19—42no—
151C2×C4×C19#12011yescharacteristic
152C2×C4×C19#12011yescharacteristic
153C2×C4×C19#12111yescharacteristic
154C2×C4×C19#12111yescharacteristic
155C2×C4×C19#12111yescharacteristic
156C2×C4×C19#12711yescharacteristic
157C2×C4×C19C2×SD1612yes—
158C2×C4×C19C2×SD1611yescharacteristic
159C2×C4×C19#13511yescharacteristic
160C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C19#13712yes—
162C2×C4×C19#13711yescharacteristic
163C2×Dic19—22no—
164C2×Dic19—41no—
165C2×Dic19—41no—
166C2×Dic19—41no—
167C2×Dic19—42no—
168C2×Dic19—42no—
169C2×Dic19—44no—
170Dic38—22no—
171Dic38—22no—
172Dic38—41no—
173Dic38—41no—
174Dic38—44no—
175Dic38—82no—
176C8×C19—81no—
177C19⋊C8—24no—
178C19⋊C8—42no—
179C2×#492—191no—
180C2×#460—191no—
181#2567—191no—
182#1982D1911yescharacteristic
183C2×#333—191no—
184C2×Q8⋊C8—191no—
185#1279—191no—
186C22×C19—82no—
187C22×C19—82no—
188C22×C19—82no—
189C22×C19—162no—
190C22×C19—162no—
191C22×C19#39211yescharacteristic
192C22×C19#44811yescharacteristic
193C22×C19#44812yes—
194C22×C19#44911yescharacteristic
195C22×C19#45312yes—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—44no—
199C4×C19#45011yescharacteristic
200C4×C19#45211yescharacteristic
201C4×C19#46112yes—
202C4×C19#46511yescharacteristic
203C4×C19#46811yescharacteristic
204C4×C19#49211yescharacteristic
205C4×C19#49711yescharacteristic
206Dic19—42no—
207Dic19—82no—
208Dic19—81no—
209C22×SD16—382no—
210C22×SD16—381no—
211C2×C4⋊Q8—191no—
212C2×#127C2×D1911yescharacteristic
213C2×C4×Q8—191no—
214#492—382no—
215#492—382no—
216#460—382no—
217#460—382no—
218C2×C4⋊C8—191no—
219C2×C4⋊C8C2×D1911yescharacteristic
220C2×#102—22no—
221C2×#102—381no—
222C2×C4×C8—191no—
223#395—382no—
224#391—381no—
225#389—382no—
226#384—381no—
227C4×C4⋊C4C2×D1911yescharacteristic
228#333—382no—
229Q8⋊C8—382no—
230C2×C19—162no—
231C2×C19#162212yes—
232C2×C19#162312yes—
233C2×C19#200011yescharacteristic
234C2×C19#200211yescharacteristic
235C2×C19#201311yescharacteristic
236C22×Q8—191no—
237C22×Q8—192no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4—21no—
241C2×SD16—384no—
242C2×SD16—388no—
243C2×SD16—768no—
244C2×SD16—762no—
245C2×SD16—762no—
246C22×C8—21no—
247C22×C8—381no—
248C22×C8—381no—
249C4⋊Q8—381no—
250C4⋊Q8—381no—
251C4⋊Q8—381no—
252C4⋊Q8—381no—
253#127—21no—
254#127—21no—
255#127—21no—
256#127D7612yes—
257C4×Q8—381no—
258C4×Q8—381no—
259C4×Q8—381no—
260C4×Q8—381no—
261C2×C4⋊C4—191no—
262C2×C4⋊C4—381no—
263C2×C4⋊C4—381no—
264C2×C4⋊C4—381no—
265C2×C4⋊C4—384no—
266C2×C4⋊C4C22⋊D1912yes—
267C2×C42—21no—
268C2×C42—381no—
269C2×C42C22×D1911yescharacteristic
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—192no—
273C4⋊C8—381no—
274#102—44no—
275#102—384no—
276C4×C8—192no—
277C4×C8—381no—
278#95—21no—
279#95—384no—
280C19#1004911yescharacteristic, complemented, Sylow
281C24—41no—
282C2×Q8—192no—
283C2×Q8—381no—
284C2×Q8—381no—
285C2×Q8—382no—
286C2×Q8—381no—
287C2×Q8—382no—
288C2×Q8—381no—
289C2×Q8—381no—
290C2×Q8—764no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—44no—
295C2×D4—42no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C22×C4—22no—
305C22×C4—381no—
306C22×C4—382no—
307C22×C4—381no—
308C22×C4D4×D1911yescharacteristic
309C22×C4D4×D1911yescharacteristic
310C22×C4C2×C22⋊D1911yescharacteristic
311SD16—7616no—
312SD16—768no—
313C2×C8—42no—
314C2×C8—41no—
315C2×C8—384no—
316C2×C8—382no—
317C2×C8—382no—
318C2×C8—761no—
319C2×C8—761no—
320C4⋊C4—22no—
321C4⋊C4—381no—
322C4⋊C4—381no—
323C4⋊C4—761no—
324C4⋊C4—761no—
325C4⋊C4—761no—
326C4⋊C4—761no—
327C4⋊C4—761no—
328C4⋊C4—761no—
329C4⋊C4—1524no—
330C4⋊C4#6452614yescomplemented
331C42—41no—
332C42—41no—
333C42—761no—
334C42—761no—
335C42C2×D7611yescharacteristic
336C42#6454111yescharacteristic
337C42D4×D1911yescharacteristic
338C42D4×D1911yescharacteristic
339C23—42no—
340C23—81no—
341C23—82no—
342C23—81no—
343C23—82no—
344C23#1059738311yescharacteristic
345Q8—382no—
346Q8—382no—
347Q8—764no—
348Q8—761no—
349Q8—761no—
350Q8—1522no—
351D4—44no—
352D4—42no—
353D4—42no—
354D4—44no—
355D4—82no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—382no—
365C2×C4—761no—
366C2×C4—761no—
367C2×C4—761no—
368C2×C4—762no—
369C2×C4—762no—
370C2×C4—764no—
371C2×C4#1059732811yescharacteristic
372C2×C4#1059732811yescharacteristic
373C2×C4#1059733011yescharacteristic
374C2×C4#1059733011yescharacteristic
375C2×C4#1059735711yescharacteristic
376C2×C4#1059735811yescharacteristic
377C2×C4SD16×D1911yescharacteristic
378C2×C4#1059736111yescharacteristic
379C2×C4#1059737611yescharacteristic
380C2×C4C2×#6452612yes—
381C2×C4#1059738611yescharacteristic
382C2×C4#1059739712yes—
383C8—81no—
384C8—384no—
385C8—762no—
386C22—82no—
387C22—82no—
388C22—82no—
389C22—162no—
390C22—162no—
391C22#1192645311yescharacteristic
392C22#1192668111yescharacteristic
393C22#1192668212yes—
394C22#1192668611yescharacteristic
395C22#1192671012yes—
396C4—21no—
397C4—21no—
398C4—44no—
399C4—762no—
400C4—1522no—
401C4—1521no—
402C4#1192669611yescharacteristic
403C4#1192670711yescharacteristic
404C4#1192674912yes—
405C4#1192677211yescharacteristic
406C4#1192678911yescharacteristic
407C4#1192691611yescharacteristic
408C4#1192693911yescharacteristic
409C2—162no—
410C2#1456270512yes—
411C2#1456271212yes—
412C2#1456463911yescharacteristic
413C2#1456465111yescharacteristic
414C2#1456471711yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1982C2
socleC23×C19#120
prime radicalC2×C19×#127C22
hypercenter#1982D19
hypocenterC19#10049
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
3. #14568843C2semidirect
4. C2×#11926292C2semidirect
5. C2×#11926274C2semidirect
6. #14561476C2semidirect
102. C2×Dic38SD16semidirect
106. C4⋊C4×C19SD16semidirect
280. C19#10049semidirect
330. C4⋊C4#64526semidirect

Maximal subgroups

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

subgroupindex
C2×#119269162
C2×#119267412
#145688432
C2×#119262922
C2×#119262742
#145614762
C19×#19822
#1004919