Finite Group Databasebeta

← #18075736

Subgroups — #18075736

Order 4864.

386 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572602C211yesmaximal, characteristic
2C4×#10597279C211yesmaximal, characteristic, complemented
3#14562393C211yesmaximal, characteristic, complemented
4#14562074C211yesmaximal, characteristic
5#14561525C211yesmaximal, characteristic, complemented
6#14561524C211yesmaximal, characteristic, complemented
7C19×#1489C211yesmaximal, characteristic
8#11926675C411yescharacteristic
9#11926675C411yescharacteristic
10#11926622C411yescharacteristic
11#11926622C411yescharacteristic
12#11926616—21no—
13#11926616—21no—
14#11926597—21no—
15#11926597C2211yescharacteristic
16C2×#10597279—21no—
17#11926568C2211yescharacteristic
18C4×#64520—21no—
19C4×#64520C2211yescharacteristic
20C2×C4×C19⋊C8C2211yescharacteristic
21#11926308—21no—
22#11926296—21no—
23#11926296—21no—
24Q8⋊(C19⋊C8)—21no—
25D4⋊(C19⋊C8)—21no—
26C4×#41×C19C2211yescharacteristic
27C19×#423C2211yescharacteristic
28C4×M16×C19C2211yescharacteristic
29C19×Q8⋊C8—21no—
30C19×D4⋊C8—21no—
31C2×#41×C19Q811yescharacteristic
32C2×M16×C19—21no—
33C2×M16×C19—21no—
34C4×Q8×C19C2×C411yescharacteristic
35C4×Q8×C19D411yescharacteristic
36C4×D4×C19—21no—
37C4×D4×C19—21no—
38C4×D4×C19C2×C411yescharacteristic
39C4×D4×C19D411yescharacteristic
40C19×#117—21no—
41C19×#117Q811yescharacteristic
42C2×C42×C19—21no—
43C2×C42×C19C2311yescharacteristic
44C2×#64520—21no—
45C2×#64520—21no—
46C2×#64520—21no—
47C2×#64520—21no—
48C22×C19⋊C8D411yescharacteristic
49C22×C19⋊C8D411yescharacteristic
50C19×C4⋊C8—21no—
51C19×C4⋊C8—21no—
52C19×#97—21no—
53C4×C8×C19—21no—
54C22⋊(C19⋊C8)—21no—
55C22⋊(C19⋊C8)—21no—
56C22⋊(C19⋊C8)—21no—
57#10597279—24no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)—21no—
62C4⋊(C19⋊C8)C2×C411yescharacteristic
63C4⋊(C19⋊C8)C2×C411yescharacteristic
64#10597260—21no—
65#10597260—21no—
66#10597260—21no—
67C4×C19⋊C8—21no—
68C4×C19⋊C8—21no—
69C4×C19⋊C8C2×C411yescharacteristic
70C4×C19⋊C8C2×C411yescharacteristic
71C4×C19⋊C8D411yescharacteristic
72C4×C19⋊C8D411yescharacteristic
73#41×C19—42no—
74C2×Q8×C19C4⋊C411yescharacteristic
75C2×D4×C19—21no—
76C2×D4×C19C4⋊C411yescharacteristic
77C22×C4×C19—21no—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×Q811yescharacteristic
82C22×C4×C19#4111yescharacteristic
83M16×C19—22no—
84M16×C19—41no—
85M16×C19—81no—
86C2×C8×C19—41no—
87C2×C8×C19—41no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19C4⋊C411yescharacteristic
91C4⋊C4×C19C4⋊C411yescharacteristic
92C22⋊C4×C19—21no—
93C22⋊C4×C19—21no—
94C22⋊C4×C19—21no—
95C42×C19—21no—
96C42×C19—21no—
97C42×C19—21no—
98C42×C19C22×C411yescharacteristic
99C42×C19C2×D411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19#4111yescharacteristic
102#64520—22no—
103#64520—42no—
104#64520—41no—
105#64520—42no—
106#64520—81no—
107C2×C19⋊C8—22no—
108C2×C19⋊C8—21no—
109C2×C19⋊C8—21no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8C22⋊C411yescharacteristic
114C2×C19⋊C8C22⋊C411yescharacteristic
115C2×C19⋊C8C22⋊C411yescharacteristic
116C2×C19⋊C8C22⋊C411yescharacteristic
117#8673—191nomaximal, Sylow
118C23×C19—21no—
119C23×C19C22⋊Q811yescharacteristic
120Q8×C19—22no—
121D4×C19—22no—
122D4×C19—42no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—22no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—42no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19C2×C22⋊C411yescharacteristic
137C2×C4×C19C2×C4⋊C411yescharacteristic
138C2×C4×C19#11711yescharacteristic
139C2×C4×C19#12111yescharacteristic
140C2×C4×C19#12111yescharacteristic
141C2×C4×C19C22⋊Q811yescharacteristic
142C8×C19—42no—
143C8×C19—81no—
144C19⋊C8—21no—
145C19⋊C8—21no—
146C19⋊C8—21no—
147C19⋊C8—42no—
148C19⋊C8—41no—
149C19⋊C8—41no—
150C19⋊C8—81no—
151C19⋊C8#10412yes—
152#2965—191no—
153C4×#108—191no—
154#1567—191no—
155#1489—191no—
156#1489D1911yescharacteristic
157#1299—191no—
158#1299—191no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19—41no—
165C22×C19#38011yescharacteristic
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—41no—
170C4×C19—41no—
171C4×C19—41no—
172C4×C19C2×#10411yescharacteristic
173C4×C19#42111yescharacteristic
174C4×C19#43012yes—
175C4×C19#47211yescharacteristic
176C4×C19#47311yescharacteristic
177C4×#41C2×D1911yescharacteristic
178#446—191no—
179#446—191no—
180#436—191no—
181#436—191no—
182#435—381no—
183#435—381no—
184#431—191no—
185#431—381no—
186C2×#108—381no—
187#423—191no—
188#423C2×D1911yescharacteristic
189C4×M16—191no—
190C4×M16—381no—
191C4×M16C2×D1911yescharacteristic
192C2×C4×C8—191no—
193#341—381no—
194#335—381no—
195#335—381no—
196Q8⋊C8—21no—
197Q8⋊C8—381no—
198D4⋊C8—21no—
199D4⋊C8—381no—
200C2×C19—41no—
201C2×C19—81no—
202C2×C19#180611yescharacteristic
203C2×C19#181111yescharacteristic
204C2×C19#181611yescharacteristic
205C2×#41Dic3811yescharacteristic
206C2×M16—21no—
207C2×M16—21no—
208C2×M16—381no—
209C2×M16—381no—
210C2×M16—381no—
211C2×M16—381no—
212C22×C8—191no—
213C22×C8—191no—
214C4×Q8C4×D1911yescharacteristic
215C4×Q8C22⋊D1911yescharacteristic
216C4×D4—21no—
217C4×D4—21no—
218C4×D4C4×D1911yescharacteristic
219C4×D4C22⋊D1911yescharacteristic
220#117—21no—
221#117Dic3811yescharacteristic
222C2×C42—21no—
223C2×C42C22×D1911yescharacteristic
224#108—384no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—191no—
228C4⋊C8—191no—
229C4⋊C8—381no—
230C4⋊C8—381no—
231C4⋊C8—381no—
232C4⋊C8—381no—
233C22⋊C8—381no—
234C22⋊C8—381no—
235C22⋊C8—381no—
236#97—21no—
237#97—381no—
238#97—381no—
239#97—381no—
240C4×C8—21no—
241C4×C8—191no—
242C4×C8—191no—
243C4×C8—191no—
244C4×C8—191no—
245C4×C8—381no—
246C4×C8—381no—
247C19#867311yescharacteristic, complemented, Sylow
248#41—42no—
249C2×Q8Dic19⋊C411yescharacteristic
250C2×D4—21no—
251C2×D4Dic19⋊C411yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4C2×Dic3811yescharacteristic
256C22×C4D4×D1911yescharacteristic
257C22×C4#6454311yescharacteristic
258M16—22no—
259M16—41no—
260M16—81no—
261M16—382no—
262M16—762no—
263M16—762no—
264M16—761no—
265M16—1521no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—191no—
269C2×C8—191no—
270C2×C8—191no—
271C2×C8—191no—
272C2×C8—382no—
273C2×C8—381no—
274C2×C8—381no—
275C2×C8—761no—
276C2×C8—761no—
277C2×C8—761no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4Dic19⋊C411yescharacteristic
281C4⋊C4Dic19⋊C411yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C42—21no—
286C42—21no—
287C42—21no—
288C42C2×C4×D1911yescharacteristic
289C42D4×D1911yescharacteristic
290C42#6454311yescharacteristic
291C42C2×C22⋊D1911yescharacteristic
292C23—21no—
293C23#1059732411yescharacteristic
294Q8—22no—
295D4—22no—
296D4—42no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4#1059732311yescharacteristic
311C2×C4#1059732411yescharacteristic
312C2×C4C22⋊C4×D1911yescharacteristic
313C2×C4C2×Dic19⋊C411yescharacteristic
314C2×C4#1059738511yescharacteristic
315C2×C4#1059738511yescharacteristic
316C8—42no—
317C8—81no—
318C8—192no—
319C8—381no—
320C8—381no—
321C8—381no—
322C8—762no—
323C8—761no—
324C8—761no—
325C8—1521no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22#1192640211yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4#104×D1911yescharacteristic
340C4#1192655911yescharacteristic
341C4#1192659212yes—
342C4#1192681211yescharacteristic
343C4#1192681711yescharacteristic
344C2—41no—
345C2—81no—
346C2#1456365311yescharacteristic
347C2#1456367511yescharacteristic
348C2#1456369711yescharacteristic
subgroupG/H
centerC2×C4#10597385
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1489C2
socleC22×C19#380
prime radicalC2×#41×C19Q8
cosocleC2×C42×C19C23
hypercenter#1489D19
hypocenterC19#8673
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. C4×#10597279C2semidirect
3. #14562393C2semidirect
5. #14561525C2semidirect
6. #14561524C2semidirect
247. C19#8673semidirect

Maximal subgroups

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

subgroupindex
#145726022
C4×#105972792
#145623932
#145620742
#145615252
#145615242
C19×#14892
#867319