Finite Group Databasebeta

← #18079382

Subgroups — #18079382

Order 4864.

512 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573118C211yesmaximal, characteristic
2#14572743C211yesmaximal, characteristic
3#14564588C211yesmaximal, characteristic, complemented
4#14563652C211yesmaximal, characteristic
5#14561537C211yesmaximal, characteristic, complemented
6#14561509C211yesmaximal, characteristic, complemented
7C19×#1546C211yesmaximal, characteristic, complemented
8C2×#10597388—21no—
9C4×#64541C2211yescharacteristic
10#11926751—21no—
11#11926751C412yescomplemented
12#11926746—21no—
13#11926746C412yescomplemented
14C8×Dic38—21no—
15C8×D76—21no—
16(C22⋊D19)⋊C8—22no—
17#11926596—21no—
18#11926568C2211yescharacteristic
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20C4⋊C8×D19—21no—
21C2×#10597282—21no—
22#11926553—21no—
23C4×C4⋊Dic19C2211yescharacteristic
24#11926306—22no—
25#11926305—21no—
26C2×C19×C4⋊Q8C2211yescharacteristic
27C19×#431C2211yescharacteristic
28C19×#423C2211yescharacteristic
29C19×#332—21no—
30C19×#332—21no—
31C22×Q8×C19—21no—
32C2×#64541D411yescharacteristic
33C2×M16×C19—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8C2×C412yes—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C42×C19C2311yescharacteristic
41C2×#64528—22no—
42#10597388—42no—
43#10597388—42no—
44C2×#64527—22no—
45C4×C22⋊D19—21no—
46C4×C22⋊D19—21no—
47#10597372D411yescharacteristic
48C2×C4⋊Dic19—21no—
49C2×C4×Dic19—21no—
50C2×#64520—21no—
51C22×C19⋊C8D412yes—
52C2×C8×D19—22no—
53C4×D76C2×C411yescharacteristic
54C4×D76D411yescharacteristic
55#10597318—21no—
56C42×D19—21no—
57C4×Dic38C2×C411yescharacteristic
58C4×Dic38D411yescharacteristic
59C19×C4⋊C8—21no—
60C19×C4⋊C8—21no—
61C19×C4⋊C8D411yescharacteristic
62C19×C4⋊C8D411yescharacteristic
63C19×C22⋊C8—21no—
64C4×C8×C19—21no—
65#10597292—22no—
66#10597292—22no—
67C19⋊#95—21no—
68#10597282—42no—
69(C2×D19)⋊C8—22no—
70Dic19⋊C8—22no—
71C8×Dic19—22no—
72C4⋊(C19⋊C8)—21no—
73C4⋊(C19⋊C8)—21no—
74C4⋊(C19⋊C8)—21no—
75C4⋊(C19⋊C8)C2×C412yes—
76C2×Q8×C19—22no—
77C2×Q8×C19—41no—
78C2×Q8×C19—41no—
79C2×Q8×C19—41no—
80C2×Q8×C19—41no—
81C2×Q8×C19—41no—
82C22×C4×C19—41no—
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19#4111yescharacteristic
86C2×C22⋊D19—21no—
87C22×Dic19—41no—
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
97M16×C19—41no—
98M16×C19—41no—
99C2×C8×C19—21no—
100C2×C8×C19—21no—
101C2×C8×C19—41no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19—41no—
105C4⋊C4×C19—41no—
106C42×C19C22×C411yescharacteristic
107C42×C19C2×D411yescharacteristic
108C42×C19C2×D411yescharacteristic
109C42×C19#4111yescharacteristic
110C22⋊Dic19—21no—
111#64528—44no—
112#64527—44no—
113(C2×D19)⋊C4—21no—
114(C2×D19)⋊C4—21no—
115C4⋊Dic19—22no—
116C4⋊Dic19—41no—
117C4⋊Dic19C22⋊C411yescharacteristic
118C4⋊Dic19C22⋊C411yescharacteristic
119Dic19⋊C4—21no—
120Dic19⋊C4—21no—
121C4×Dic19—21no—
122C4×Dic19—21no—
123C4×Dic19—21no—
124C4×Dic19—41no—
125C4×Dic19—41no—
126#64520—41no—
127#64520—41no—
128C2×C19⋊C8—22no—
129C2×C19⋊C8—22no—
130C2×C19⋊C8—42no—
131C8×D19—82no—
132#9316—191nomaximal, Sylow
133C23×C19#12111yescharacteristic
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#12311yescharacteristic
151C2×C4×C19C2×D811yescharacteristic
152C2×C4×C19C2×SD1611yescharacteristic
153C2×C4×C19#13511yescharacteristic
154C2×C4×C19#13511yescharacteristic
155C22⋊D19—22no—
156C22⋊D19—22no—
157C2×Dic19—21no—
158C2×Dic19—21no—
159C2×Dic19—21no—
160C2×Dic19—42no—
161C2×Dic19—81no—
162C2×Dic19—81no—
163D76—21no—
164D76#10212yes—
165C4×D19—22no—
166C4×D19—22no—
167C4×D19—41no—
168C4×D19—41no—
169C4×D19—81no—
170Dic38—21no—
171Dic38#10212yes—
172C8×C19—41no—
173C8×C19—41no—
174C8×C19—81no—
175C19⋊C8—42no—
176C19⋊C8—42no—
177#3039—191no—
178#2988—191no—
179#1988—191no—
180#1806—191no—
181#1546D1911yescharacteristic, complemented
182#1303—191no—
183#1292—191no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19#38611yescharacteristic
187C22×C19#46511yescharacteristic
188C22×C19#46611yescharacteristic
189C2×D19—22no—
190C2×D19—41no—
191C2×D19—41no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—21no—
195C4×C19—82no—
196C4×C19C2×#10211yescharacteristic
197C4×C19#41611yescharacteristic
198C4×C19#45511yescharacteristic
199C4×C19#45611yescharacteristic
200C4×C19#46511yescharacteristic
201C4×C19#46611yescharacteristic
202Dic19—22no—
203Dic19—41no—
204Dic19—41no—
205Dic19—82no—
206C2×#137—381no—
207C2×C4⋊Q8C2×D1911yescharacteristic
208C4×#41—191no—
209#462—192no—
210#462—381no—
211#461—192no—
212#461—381no—
213C8×Q8—381no—
214C8×D4—381no—
215C8×D4—382no—
216#431—381no—
217#431C2×D1911yescharacteristic
218#423—191no—
219#423C2×D1911yescharacteristic
220C2×C4⋊C8—191no—
221C2×C4⋊C8—381no—
222C2×#104—381no—
223#419—381no—
224C4×C4⋊C4—191no—
225#340—382no—
226#339—381no—
227#332—21no—
228#332—21no—
229C2×C19—21no—
230C2×C19—21no—
231C2×C19#188211yescharacteristic
232C2×C19#189311yescharacteristic
233C2×C19#190211yescharacteristic
234D19—42no—
235C2×#41—191no—
236C22×Q8—21no—
237#137—762no—
238#137—762no—
239C2×Q16—382no—
240C2×SD16—382no—
241C2×M16—21no—
242C2×M16—381no—
243C22×C8—192no—
244C22×C8—382no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8C4×D1912yes—
249C4×Q8—191no—
250C4×Q8—191no—
251C4×D4—191no—
252C4×D4—191no—
253C4×D4—381no—
254C4×D4—381no—
255#117—191no—
256#117—381no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—381no—
260C2×C42—381no—
261C2×C42—381no—
262C2×C42C22×D1911yescharacteristic
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—192no—
266C4⋊C8—382no—
267C4⋊C8—381no—
268C4⋊C8—381no—
269C4⋊C8—381no—
270C4⋊C8C22⋊D1911yescharacteristic
271C4⋊C8C22⋊D1911yescharacteristic
272#104—762no—
273#103—382no—
274#103—382no—
275C22⋊C8—21no—
276C22⋊C8—382no—
277C4×C8—21no—
278C4×C8—382no—
279#95—381no—
280C19#931611yescharacteristic, complemented, Sylow
281#41—192no—
282#41—192no—
283#41—381no—
284#41—381no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—191no—
292C2×D4—191no—
293C2×D4—381no—
294C22×C4—41no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4—381no—
298C22×C4—761no—
299C22×C4#6454111yescharacteristic
300C22×C4D4×D1911yescharacteristic
301C22×C4D4×D1911yescharacteristic
302Q16—764no—
303SD16—764no—
304M16—41no—
305M16—41no—
306M16—761no—
307M16—761no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—41no—
311C2×C8—382no—
312C2×C8—382no—
313C2×C8—762no—
314C2×C8—1522no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—191no—
320C4⋊C4—191no—
321C4⋊C4—382no—
322C4⋊C4—381no—
323C4⋊C4—381no—
324C4⋊C4—761no—
325C22⋊C4—381no—
326C22⋊C4—381no—
327C22⋊C4—381no—
328C42—381no—
329C42—381no—
330C42—381no—
331C42—761no—
332C42—761no—
333C42C2×C4×D1911yescharacteristic
334C42D4×D1911yescharacteristic
335C42#6454311yescharacteristic
336C42C2×C22⋊D1911yescharacteristic
337C23—381no—
338C23#1059733011yescharacteristic
339Q8—42no—
340Q8—42no—
341Q8—81no—
342Q8—81no—
343Q8—192no—
344Q8—381no—
345D4—192no—
346D4—382no—
347D4—382no—
348D4—381no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—381no—
356C2×C4—382no—
357C2×C4—382no—
358C2×C4—381no—
359C2×C4—381no—
360C2×C4—761no—
361C2×C4—761no—
362C2×C4—762no—
363C2×C4—1521no—
364C2×C4—1521no—
365C2×C4—1521no—
366C2×C4C22⋊C4×D1911yescharacteristic
367C2×C4(C22⋊D19)⋊C411yescharacteristic
368C2×C4#1059732911yescharacteristic
369C2×C4D8×D1911yescharacteristic
370C2×C4#1059735811yescharacteristic
371C2×C4SD16×D1911yescharacteristic
372C2×C4#1059736211yescharacteristic
373C2×C4C4×C22⋊D1911yescharacteristic
374C2×C4#1059738311yescharacteristic
375C2×C4#1059738411yescharacteristic
376C8—41no—
377C8—41no—
378C8—81no—
379C8—762no—
380C8—762no—
381C22—21no—
382C22—21no—
383C22—382no—
384C22—761no—
385C22—761no—
386C22#1192642011yescharacteristic
387C22#1192677211yescharacteristic
388C22#1192677911yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—82no—
393C4—382no—
394C4—761no—
395C4—761no—
396C4—1522no—
397C4#102×D1911yescharacteristic
398C4#1192653711yescharacteristic
399C4#1192672011yescharacteristic
400C4#1192672511yescharacteristic
401C4#1192677011yescharacteristic
402C4#1192677711yescharacteristic
403C2—21no—
404C2—21no—
405C2—762no—
406C2#1456400111yescharacteristic
407C2#1456406011yescharacteristic
408C2#1456411111yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1546C2
socleC22×C19#386
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1546D19
hypocenterC19#9316
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. #14564588C2semidirect
5. #14561537C2semidirect
6. #14561509C2semidirect
7. C19×#1546C2semidirect
11. #11926751C4semidirect
13. #11926746C4semidirect
181. #1546D19semidirect
280. C19#9316semidirect

Maximal subgroups

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

subgroupindex
#145731182
#145727432
#145645882
#145636522
#145615372
#145615092
C19×#15462
#931619