Finite Group Databasebeta

← #18078421

Subgroups — #18078421

Order 4864.

510 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573118C211yesmaximal, characteristic
2#14572200C211yesmaximal, characteristic
3#14562307C211yesmaximal, characteristic, complemented
4#14562020C211yesmaximal, characteristic
5#14561532C211yesmaximal, characteristic, complemented
6#14561510C211yesmaximal, characteristic, complemented
7C2×C19×#332C211yesmaximal, characteristic, complemented
8C2×#10597388—21no—
9C2×#10597347—21no—
10C4×#64541C2211yescharacteristic
11#11926751—21no—
12#11926751C412yes—
13#11926746—21no—
14#11926746C412yes—
15#11926597C2211yescharacteristic
16#11926570—21no—
17#11926569—22no—
18#11926568C2211yescharacteristic
19#11926568C2211yescharacteristic
20#11926566—21no—
21C4⋊C8×D19—21no—
22#11926553—21no—
23#11926290—22no—
24#11926274—21no—
25#11926271—21no—
26C2×C19×C4⋊Q8C2211yescharacteristic
27C2×C19×C4⋊C8C2211yescharacteristic
28C2×C19×C4⋊C8C2211yescharacteristic
29C19×#332—21no—
30C19×#332—21no—
31C22×Q8×C19—21no—
32C2×#64541D411yescharacteristic
33C22×C8×C19—21no—
34C22×C8×C19—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8—21no—
38C19×C4⋊Q8C2×C412yes—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C42×C19C2311yescharacteristic
42C2×#64528—22no—
43#10597388—42no—
44#10597388—42no—
45C2×#64527—22no—
46C4×C22⋊D19—21no—
47C4×C22⋊D19—21no—
48#10597372D411yescharacteristic
49C2×#64520—21no—
50C2×#64520—21no—
51#10597347—42no—
52#10597347—42no—
53C2×#64515—22no—
54C2×C8×D19—22no—
55C4×D76C2×C411yescharacteristic
56C4×D76D411yescharacteristic
57#10597318—21no—
58C42×D19—21no—
59C4×Dic38C2×C411yescharacteristic
60C4×Dic38D411yescharacteristic
61C19×C4⋊C8—21no—
62C19×C4⋊C8—21no—
63C19×C4⋊C8—21no—
64C19×C4⋊C8D411yescharacteristic
65C19×C4⋊C8D411yescharacteristic
66#10597292—22no—
67#10597292—22no—
68C22⋊(C19⋊C8)—21no—
69Dic19⋊C8—22no—
70Dic19⋊C8—22no—
71C4⋊(C19⋊C8)—21no—
72C4⋊(C19⋊C8)—21no—
73C4⋊(C19⋊C8)—21no—
74C4⋊(C19⋊C8)C2×C412yes—
75C4⋊(C19⋊C8)D412yes—
76C4×C19⋊C8—21no—
77C2×Q8×C19—22no—
78C2×Q8×C19—41no—
79C2×Q8×C19—41no—
80C2×Q8×C19—41no—
81C2×Q8×C19—41no—
82C2×Q8×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19#4111yescharacteristic
86C22×C4×C19#4111yescharacteristic
87C2×C22⋊D19—21no—
88#64541—21no—
89#64541—21no—
90#64541D812yes—
91#64541SD1612yes—
92C2×D76C22⋊C411yescharacteristic
93C2×C4×D19—21no—
94C2×C4×D19—21no—
95C2×C4×D19—21no—
96C2×Dic38C22⋊C411yescharacteristic
97C2×C8×C19—21no—
98C2×C8×C19—21no—
99C2×C8×C19—41no—
100C2×C8×C19—41no—
101C2×C8×C19—41no—
102C2×C8×C19—81no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19—22no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C42×C19C22×C411yescharacteristic
108C42×C19C2×D411yescharacteristic
109C42×C19C2×D411yescharacteristic
110C42×C19C2×D411yescharacteristic
111C22⋊Dic19—21no—
112#64528—44no—
113#64527—44no—
114(C2×D19)⋊C4—21no—
115(C2×D19)⋊C4—21no—
116C4⋊Dic19C22⋊C411yescharacteristic
117C4⋊Dic19C22⋊C411yescharacteristic
118Dic19⋊C4—21no—
119Dic19⋊C4—21no—
120C4×Dic19—21no—
121C4×Dic19—21no—
122C4×Dic19—21no—
123#64520—41no—
124#64520—41no—
125#64520—41no—
126#64520—41no—
127C2×C19⋊C8—22no—
128C2×C19⋊C8—22no—
129C2×C19⋊C8—41no—
130#64515—44no—
131C8×D19—44no—
132#9171—191nomaximal, Sylow
133C23×C19#12311yescharacteristic
134C22×D19—21no—
135Q8×C19—42no—
136Q8×C19—42no—
137Q8×C19—81no—
138Q8×C19—81no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—41no—
142C2×C4×C19—42no—
143C2×C4×C19—81no—
144C2×C4×C19—81no—
145C2×C4×C19C2×C22⋊C411yescharacteristic
146C2×C4×C19C4×D411yescharacteristic
147C2×C4×C19C4×D411yescharacteristic
148C2×C4×C19#12011yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19#12111yescharacteristic
151C2×C4×C19C2×D811yescharacteristic
152C2×C4×C19C2×SD1611yescharacteristic
153C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C19#13711yescharacteristic
155C22⋊D19—22no—
156C22⋊D19—22no—
157C2×Dic19—21no—
158C2×Dic19—21no—
159C2×Dic19—21no—
160D76—21no—
161D76#10212yes—
162C4×D19—22no—
163C4×D19—22no—
164C4×D19—41no—
165C4×D19—41no—
166C4×D19—81no—
167Dic38—21no—
168Dic38#10212yes—
169C8×C19—41no—
170C8×C19—41no—
171C8×C19—81no—
172C19⋊C8—42no—
173C19⋊C8—42no—
174C19⋊C8—81no—
175#3039—191no—
176#2906—191no—
177#1546—191no—
178C2×#332D1911yescharacteristic, complemented
179#1477—191no—
180#1301—191no—
181#1292—191no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19#38611yescharacteristic
185C22×C19#48011yescharacteristic
186C22×C19#48111yescharacteristic
187C2×D19—22no—
188C2×D19—41no—
189C2×D19—41no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—82no—
194C4×C19C2×#10211yescharacteristic
195C4×C19#41711yescharacteristic
196C4×C19#44711yescharacteristic
197C4×C19#44811yescharacteristic
198C4×C19#47111yescharacteristic
199C4×C19#47311yescharacteristic
200Dic19—22no—
201Dic19—41no—
202Dic19—41no—
203C2×#137—381no—
204C2×#131—381no—
205C2×C4⋊Q8C2×D1911yescharacteristic
206C4×#41—191no—
207#462—192no—
208#462—381no—
209#461—192no—
210#461—381no—
211#431—191no—
212#424—382no—
213#424—381no—
214#423—191no—
215#423—191no—
216#423—381no—
217C2×C4⋊C8—381no—
218C2×C4⋊C8C2×D1911yescharacteristic
219C2×C4⋊C8C2×D1911yescharacteristic
220#419—381no—
221#332—21no—
222#332—21no—
223#332—382no—
224Q8⋊C8—381no—
225D4⋊C8—381no—
226C2×C19—21no—
227C2×C19—21no—
228C2×C19#187411yescharacteristic
229C2×C19#190211yescharacteristic
230C2×C19#190811yescharacteristic
231D19—42no—
232C2×#41—191no—
233C22×Q8—21no—
234#137—762no—
235#137—762no—
236C2×Q16—382no—
237C2×SD16—382no—
238#131—762no—
239#131—762no—
240C2×M16—382no—
241C2×M16—381no—
242C2×M16—381no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—382no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8C4×D1912yes—
250C4×Q8—191no—
251C4×Q8—191no—
252C4×D4—191no—
253C4×D4—191no—
254C4×D4—381no—
255C4×D4—381no—
256#117—191no—
257#117—381no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C42—381no—
261C2×C42C22×D1911yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—192no—
266C4⋊C8—192no—
267C4⋊C8—382no—
268C4⋊C8—382no—
269C4⋊C8—381no—
270C4⋊C8—381no—
271C4⋊C8—381no—
272C4⋊C8C22⋊D1911yescharacteristic
273C4⋊C8C22⋊D1911yescharacteristic
274#103—382no—
275#103—382no—
276C22⋊C8—381no—
277C4×C8—381no—
278C19#917111yescharacteristic, complemented, Sylow
279#41—192no—
280#41—192no—
281#41—381no—
282#41—381no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—191no—
290C2×D4—191no—
291C2×D4—381no—
292C22×C4—41no—
293C22×C4—381no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4#6454111yescharacteristic
297C22×C4D4×D1911yescharacteristic
298C22×C4#6454311yescharacteristic
299Q16—764no—
300SD16—764no—
301M16—764no—
302M16—761no—
303M16—761no—
304M16—761no—
305M16—761no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—81no—
312C2×C8—382no—
313C2×C8—382no—
314C2×C8—764no—
315C2×C8—761no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—191no—
321C4⋊C4—191no—
322C4⋊C4—381no—
323C4⋊C4—381no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C22⋊C4—381no—
327C42—381no—
328C42—381no—
329C42—381no—
330C42C2×C4×D1911yescharacteristic
331C42D4×D1911yescharacteristic
332C42D4×D1911yescharacteristic
333C42C2×C22⋊D1911yescharacteristic
334C23—381no—
335C23#1059732911yescharacteristic
336Q8—42no—
337Q8—42no—
338Q8—81no—
339Q8—81no—
340Q8—192no—
341Q8—381no—
342D4—192no—
343D4—382no—
344D4—382no—
345D4—381no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—381no—
353C2×C4—382no—
354C2×C4—382no—
355C2×C4—381no—
356C2×C4—381no—
357C2×C4—761no—
358C2×C4—761no—
359C2×C4—1521no—
360C2×C4C22⋊C4×D1911yescharacteristic
361C2×C4(C22⋊D19)⋊C411yescharacteristic
362C2×C4#1059733011yescharacteristic
363C2×C4D8×D1911yescharacteristic
364C2×C4#1059735711yescharacteristic
365C2×C4SD16×D1911yescharacteristic
366C2×C4#1059736111yescharacteristic
367C2×C4C4×C22⋊D1911yescharacteristic
368C2×C4#1059738311yescharacteristic
369C2×C4#1059738411yescharacteristic
370C8—41no—
371C8—41no—
372C8—81no—
373C8—762no—
374C8—762no—
375C8—1521no—
376C22—21no—
377C22—21no—
378C22—382no—
379C22—761no—
380C22—761no—
381C22#1192642011yescharacteristic
382C22#1192685611yescharacteristic
383C22#1192686111yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—82no—
388C4—382no—
389C4—761no—
390C4—761no—
391C4#102×D1911yescharacteristic
392C4#1192654211yescharacteristic
393C4#1192667611yescharacteristic
394C4#1192668111yescharacteristic
395C4#1192680411yescharacteristic
396C4#1192681611yescharacteristic
397C2—21no—
398C2—21no—
399C2—762no—
400C2#1456394911yescharacteristic
401C2#1456411111yescharacteristic
402C2#1456415311yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#332C2
socleC22×C19#386
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenterC2×#332D19
hypocenterC19#9171
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #14562307C2semidirect
5. #14561532C2semidirect
6. #14561510C2semidirect
7. C2×C19×#332C2semidirect
178. C2×#332D19semidirect
278. C19#9171semidirect

Maximal subgroups

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

subgroupindex
#145731182
#145722002
#145623072
#145620202
#145615322
#145615102
C2×C19×#3322
#917119