Finite Group Databasebeta

← #18081722

Subgroups — #18081722

Order 4864.

422 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574194C211yesmaximal, characteristic
2C4×#10597276C211yesmaximal, characteristic, complemented
3#14562229C211yesmaximal, characteristic, complemented
4#14562226C211yesmaximal, characteristic
5#14562055C211yesmaximal, characteristic, complemented
6#14562051C211yesmaximal, characteristic
7C8×M16×C19C211yesmaximal, characteristic, complemented
8#11927101C2211yescharacteristic
9#11927094C2211yescharacteristic
10#11926942C411yescharacteristic
11#11926917C411yescharacteristic
12#11926895C411yescharacteristic
13#11926891C411yescharacteristic
14#11926773—21no—
15#11926773—21no—
16C4×#64516—21no—
17C4×#64516—21no—
18C2×#10597276—21no—
19C4×#64520C2211yescharacteristic
20C4×#64520C2211yescharacteristic
21#11926309—21no—
22#11926285—22no—
23#11926283—22no—
24#11926274—22no—
25#11926271—22no—
26C19×#431C2211yescharacteristic
27C4×M16×C19C2211yescharacteristic
28C2×C4×C8×C19C2211yescharacteristic
29C19×#322—21no—
30C82×C19—21no—
31C2×#64541—21no—
32C2×M16×C19—21no—
33C22×C8×C19D411yescharacteristic
34C22×C8×C19D411yescharacteristic
35C2×C42×C19C2311yescharacteristic
36#10597376—21no—
37#10597376—21no—
38#10597372—21no—
39#10597370—21no—
40#10597370—21no—
41C2×#64520—21no—
42C2×#64520—21no—
43C2×#64516—21no—
44C2×#64516—21no—
45#10597321—21no—
46#10597320C2×C411yescharacteristic
47C4×D76—21no—
48C4×D76—21no—
49#10597316—21no—
50#10597315C2×C411yescharacteristic
51#10597315C2×C411yescharacteristic
52#10597315C2×C411yescharacteristic
53C4×Dic38—21no—
54C4×Dic38—21no—
55C19×C4⋊C8D412yes—
56C19×C22⋊C8—21no—
57C19×#97D412yes—
58C4×C8×C19—21no—
59C4×C8×C19—21no—
60C4×C8×C19C2×C411yescharacteristic
61C4×C8×C19C2×C411yescharacteristic
62C4×C8×C19D411yescharacteristic
63C4×C8×C19D411yescharacteristic
64#10597278—21no—
65#10597278—21no—
66#10597276—24no—
67#10597274—21no—
68#10597274—21no—
69#10597273—21no—
70#10597273—21no—
71#10597260—21no—
72#10597260—21no—
73C4×C19⋊C8—21no—
74C4×C19⋊C8—21no—
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19#4111yescharacteristic
77C22×C4×C19#4111yescharacteristic
78C2×C22⋊D19—41no—
79#64541—82no—
80C2×D76—21no—
81C2×D76—21no—
82C2×D76—21no—
83C2×C4×D19—41no—
84C2×Dic38—21no—
85C2×Dic38—21no—
86C2×Dic38—21no—
87M16×C19—24no—
88C2×C8×C19—22no—
89C2×C8×C19—22no—
90C2×C8×C19—22no—
91C2×C8×C19—41no—
92C2×C8×C19C22⋊C411yescharacteristic
93C2×C8×C19C22⋊C411yescharacteristic
94C2×C8×C19C22⋊C411yescharacteristic
95C2×C8×C19C22⋊C411yescharacteristic
96C42×C19C22×C411yescharacteristic
97C42×C19C2×D411yescharacteristic
98C42×C19C2×D411yescharacteristic
99C42×C19C2×D411yescharacteristic
100C22⋊Dic19—41no—
101(C2×D19)⋊C4—41no—
102(C2×D19)⋊C4—41no—
103C4⋊Dic19—21no—
104C4⋊Dic19—21no—
105C4⋊Dic19—21no—
106C4⋊Dic19—21no—
107C4⋊Dic19—21no—
108C4⋊Dic19—21no—
109Dic19⋊C4—41no—
110Dic19⋊C4—41no—
111C4×Dic19—41no—
112#64520—22no—
113#64520—22no—
114#64520—41no—
115#64520—41no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—41no—
118#64516—42no—
119#64516—42no—
120#9723—191nomaximal, Sylow
121C23×C19#12411yescharacteristic
122C22×D19—41no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19C2×C22⋊C411yescharacteristic
128C2×C4×C19C4×D411yescharacteristic
129C2×C4×C19C4×D411yescharacteristic
130C2×C4×C19#12111yescharacteristic
131C2×C4×C19#12111yescharacteristic
132C2×C4×C19#12711yescharacteristic
133C22⋊D19—82no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137D76—41no—
138D76—41no—
139D76—42no—
140D76—81no—
141C4×D19—82no—
142Dic38—41no—
143Dic38—41no—
144Dic38—42no—
145Dic38—81no—
146C8×C19—24no—
147C8×C19—21no—
148C8×C19—21no—
149C8×C19—21no—
150C8×C19—42no—
151C8×C19#10412yes—
152C19⋊C8—42no—
153C19⋊C8—42no—
154#3167—191no—
155C4×#108—191no—
156#1526—191no—
157#1525—191no—
158#1485—191no—
159#1484—191no—
160C8×M16D1911yescharacteristic, complemented
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19#39011yescharacteristic
165C2×D19—81no—
166C2×D19—81no—
167C2×D19—81no—
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—21no—
171C4×C19C2×#10411yescharacteristic
172C4×C19#42111yescharacteristic
173C4×C19#44312yes—
174C4×C19#47112yes—
175Dic19—81no—
176Dic19—81no—
177Dic19—81no—
178#533—191no—
179#532—191no—
180#498—191no—
181#492—191no—
182#487—191no—
183#486—191no—
184#465—381no—
185#465—381no—
186C4×SD16—381no—
187C4×SD16—381no—
188#431C2×D1911yescharacteristic
189C2×#108—381no—
190C4×M16—191no—
191C4×M16—191no—
192C4×M16C2×D1911yescharacteristic
193C2×C4×C8C2×D1911yescharacteristic
194#341—381no—
195#330—382no—
196#329—382no—
197Q8⋊C8—382no—
198D4⋊C8—382no—
199#322—21no—
200C82—21no—
201C2×C19—41no—
202C2×C19#197411yescharacteristic
203C2×C19#197711yescharacteristic
204C2×C19#198011yescharacteristic
205D19—161no—
206C2×#41—381no—
207C2×SD16—381no—
208C2×SD16—381no—
209C2×M16—21no—
210C2×M16—381no—
211C2×M16—381no—
212C22×C8D7611yescharacteristic
213C22×C8D7611yescharacteristic
214C4⋊Q8—191no—
215C4⋊Q8—191no—
216C4⋊Q8—191no—
217#127—191no—
218#125—381no—
219#124—381no—
220C22⋊Q8—381no—
221C22⋊Q8—381no—
222#121—381no—
223#121—381no—
224C4×Q8—381no—
225C4×Q8—381no—
226C4×D4—381no—
227C4×D4—381no—
228#117—381no—
229C2×C42C22×D1911yescharacteristic
230#108—384no—
231#106—381no—
232#106—381no—
233C4⋊C8D7612yes—
234#103—381no—
235#103—381no—
236#102—381no—
237#102—381no—
238C22⋊C8—21no—
239#97—381no—
240#97—381no—
241#97D7612yes—
242C4×C8—21no—
243C4×C8—21no—
244C4×C8—381no—
245C4×C8—381no—
246C4×C8C4×D1911yescharacteristic
247C4×C8C4×D1911yescharacteristic
248C4×C8C22⋊D1911yescharacteristic
249C4×C8C22⋊D1911yescharacteristic
250C19#972311yescharacteristic, complemented, Sylow
251#41—1522no—
252C2×Q8—381no—
253C2×Q8—381no—
254C2×Q8—381no—
255C2×D4—381no—
256C2×D4—381no—
257C2×D4—381no—
258C2×D4—761no—
259C22×C4—761no—
260C22×C4C2×D7611yescharacteristic
261C22×C4#6454111yescharacteristic
262C22×C4#6454111yescharacteristic
263SD16—762no—
264SD16—762no—
265M16—24no—
266M16—382no—
267M16—382no—
268M16—761no—
269M16—761no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—761no—
275C2×C8—761no—
276C2×C8(C2×D19)⋊C411yescharacteristic
277C2×C8(C2×D19)⋊C411yescharacteristic
278C2×C8(C2×D19)⋊C411yescharacteristic
279C2×C8(C2×D19)⋊C411yescharacteristic
280C4⋊C4—381no—
281C4⋊C4—381no—
282C4⋊C4—381no—
283C4⋊C4—381no—
284C4⋊C4—381no—
285C4⋊C4—381no—
286C4⋊C4—761no—
287C4⋊C4—761no—
288C22⋊C4—761no—
289C22⋊C4—761no—
290C22⋊C4—761no—
291C42—761no—
292C42C2×C4×D1911yescharacteristic
293C42C2×D7611yescharacteristic
294C42C2×D7611yescharacteristic
295C42C2×C22⋊D1911yescharacteristic
296C23—761no—
297C23#1059732111yescharacteristic
298Q8—761no—
299Q8—761no—
300Q8—762no—
301Q8—1521no—
302D4—761no—
303D4—761no—
304D4—762no—
305D4—1521no—
306D4—1522no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—761no—
312C2×C4—761no—
313C2×C4—761no—
314C2×C4—1522no—
315C2×C4C4×D7611yescharacteristic
316C2×C4C4×D7611yescharacteristic
317C2×C4#1059732011yescharacteristic
318C2×C4C2×(C2×D19)⋊C411yescharacteristic
319C2×C4#1059737611yescharacteristic
320C2×C4#1059737611yescharacteristic
321C8—24no—
322C8—21no—
323C8—21no—
324C8—21no—
325C8—42no—
326C8—762no—
327C8—762no—
328C8#1059728212yes—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—1521no—
333C22—1521no—
334C22—1521no—
335C22#1192644611yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—1521no—
340C4—1521no—
341C4—1521no—
342C4C2×#1059728211yescharacteristic
343C4#1192656011yescharacteristic
344C4#1192666212yes—
345C4#1192680712yes—
346C2—41no—
347C2—3041no—
348C2#1456452311yescharacteristic
349C2#1456453811yescharacteristic
350C2#1456455411yescharacteristic
subgroupG/H
centerC2×C4#10597376
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC8×M16×C19C2
socleC22×C19#390
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenterC8×M16D19
hypocenterC19#9723
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
2. C4×#10597276C2semidirect
3. #14562229C2semidirect
5. #14562055C2semidirect
7. C8×M16×C19C2semidirect
160. C8×M16D19semidirect
250. C19#9723semidirect

Maximal subgroups

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

subgroupindex
#145741942
C4×#105972762
#145622292
#145622262
#145620552
#145620512
C8×M16×C192
#972319