Finite Group Databasebeta

← #18076809

Subgroups — #18076809

Order 4864.

390 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572760C211yesmaximal, characteristic
2#14563806C211yesmaximal, characteristic, complemented
3#14562426C211yesmaximal, characteristic, complemented
4#14562017C211yesmaximal, characteristic
5#14561525C211yesmaximal, characteristic, complemented
6#14561473C211yesmaximal, characteristic, complemented
7C19×#1489C211yesmaximal, characteristic
8#11926675—21no—
9#11926616—22no—
10D4×C19⋊C8—21no—
11#11926601—21no—
12#11926597C2211yescharacteristic
13#11926597C2211yescharacteristic
14C2×#10597279—22no—
15#11926568C2211yescharacteristic
16C2×C4⋊(C19⋊C8)—21no—
17C2×C4×C19⋊C8C2211yescharacteristic
18#11926296—21no—
19#11926294—21no—
20Q8⋊(C19⋊C8)C411yescharacteristic
21Q8⋊(C19⋊C8)C411yescharacteristic
22D4⋊(C19⋊C8)C411yescharacteristic
23D4⋊(C19⋊C8)C411yescharacteristic
24C4×#41×C19C2211yescharacteristic
25C19×#423C2211yescharacteristic
26C4×M16×C19C2211yescharacteristic
27C19×Q8⋊C8—21no—
28C19×D4⋊C8—21no—
29C2×#41×C19Q811yescharacteristic
30C2×M16×C19—21no—
31C2×M16×C19—21no—
32C4×Q8×C19C2×C411yescharacteristic
33C4×Q8×C19D411yescharacteristic
34C4×D4×C19—21no—
35C4×D4×C19—21no—
36C4×D4×C19C2×C411yescharacteristic
37C4×D4×C19D411yescharacteristic
38C19×#117—21no—
39C19×#117Q811yescharacteristic
40C2×C42×C19—21no—
41C2×C42×C19C2311yescharacteristic
42C2×#64520D412yes—
43C22×C19⋊C8—21no—
44C22×C19⋊C8—22no—
45C19×C4⋊C8—21no—
46C19×C4⋊C8—21no—
47C19×#97—21no—
48C4×C8×C19—21no—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)—21no—
51C22⋊(C19⋊C8)—21no—
52#10597279—44no—
53C4⋊(C19⋊C8)—22no—
54C4⋊(C19⋊C8)—21no—
55C4⋊(C19⋊C8)—21no—
56C4⋊(C19⋊C8)C2×C411yescharacteristic
57C4⋊(C19⋊C8)C2×C411yescharacteristic
58C4⋊(C19⋊C8)D411yescharacteristic
59C4⋊(C19⋊C8)D411yescharacteristic
60#10597260—22no—
61C4×C19⋊C8—21no—
62C4×C19⋊C8—21no—
63C4×C19⋊C8—21no—
64C4×C19⋊C8C2×C411yescharacteristic
65C4×C19⋊C8C2×C411yescharacteristic
66#41×C19—22no—
67#41×C19—41no—
68C2×Q8×C19C4⋊C411yescharacteristic
69C2×D4×C19—21no—
70C2×D4×C19C4⋊C411yescharacteristic
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×Q811yescharacteristic
76C22×C4×C19#4111yescharacteristic
77M16×C19—22no—
78M16×C19—41no—
79M16×C19—42no—
80C2×C8×C19—41no—
81C2×C8×C19—41no—
82C4⋊C4×C19—21no—
83C4⋊C4×C19—21no—
84C4⋊C4×C19C4⋊C411yescharacteristic
85C4⋊C4×C19C4⋊C411yescharacteristic
86C22⋊C4×C19—21no—
87C22⋊C4×C19—21no—
88C22⋊C4×C19—21no—
89C42×C19—21no—
90C42×C19—21no—
91C42×C19—21no—
92C42×C19C22×C411yescharacteristic
93C42×C19C2×D411yescharacteristic
94C42×C19C2×D411yescharacteristic
95C42×C19#4111yescharacteristic
96#64520—42no—
97C2×C19⋊C8—22no—
98C2×C19⋊C8—22no—
99C2×C19⋊C8—21no—
100C2×C19⋊C8—21no—
101C2×C19⋊C8—21no—
102C2×C19⋊C8—21no—
103C2×C19⋊C8—21no—
104C2×C19⋊C8—21no—
105C2×C19⋊C8—22no—
106C2×C19⋊C8—82no—
107#8898—191nomaximal, Sylow
108C23×C19—21no—
109C23×C19C22⋊Q811yescharacteristic
110Q8×C19—21no—
111Q8×C19—21no—
112D4×C19—21no—
113D4×C19—42no—
114D4×C19#10812yescomplemented
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—42no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19C2×C4⋊C411yescharacteristic
130C2×C4×C19C4×D411yescharacteristic
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19#12011yescharacteristic
133C2×C4×C19C22⋊Q811yescharacteristic
134C2×C4×C19#12311yescharacteristic
135C8×C19—42no—
136C8×C19—81no—
137C19⋊C8—22no—
138C19⋊C8—22no—
139C19⋊C8—41no—
140C19⋊C8—41no—
141C19⋊C8—41no—
142C19⋊C8—42no—
143C19⋊C8—41no—
144#2990—191no—
145#1848—191no—
146#1574—191no—
147#1489D1911yescharacteristic
148#1476—191no—
149#1299—191no—
150#1278—191no—
151C22×C19—21no—
152C22×C19—22no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—41no—
156C22×C19—41no—
157C22×C19#38511yescharacteristic
158C4×C19—21no—
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—41no—
162C4×C19—41no—
163C4×C19—41no—
164C4×C19C2×#10811yescharacteristic
165C4×C19#43011yescharacteristic
166C4×C19#44311yescharacteristic
167C4×C19#44411yescharacteristic
168C4×C19#45311yescharacteristic
169C4×C19#45611yescharacteristic
170C4×#41C2×D1911yescharacteristic
171#446—381no—
172#435—382no—
173C8×D4—381no—
174#432—381no—
175#431—191no—
176#431—191no—
177C2×#108—382no—
178#423—191no—
179#423C2×D1911yescharacteristic
180C2×C4⋊C8—381no—
181C4×M16C2×D1911yescharacteristic
182C2×C4×C8—191no—
183#335—381no—
184#334—381no—
185Q8⋊C8—21no—
186Q8⋊C8—191no—
187Q8⋊C8—191no—
188D4⋊C8—21no—
189D4⋊C8—191no—
190D4⋊C8—191no—
191C2×C19—41no—
192C2×C19—42no—
193C2×C19#185511yescharacteristic
194C2×C19#185911yescharacteristic
195C2×C19#186611yescharacteristic
196C2×#41Dic3811yescharacteristic
197C2×M16—21no—
198C2×M16—21no—
199C2×M16—192no—
200C22×C8—381no—
201C22×C8—382no—
202C4×Q8C4×D1911yescharacteristic
203C4×Q8C22⋊D1911yescharacteristic
204C4×D4—21no—
205C4×D4—21no—
206C4×D4C4×D1911yescharacteristic
207C4×D4C22⋊D1911yescharacteristic
208#117—21no—
209#117Dic3811yescharacteristic
210C2×C42—21no—
211C2×C42C22×D1911yescharacteristic
212#108—764no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—191no—
216C4⋊C8—191no—
217C4⋊C8—191no—
218C4⋊C8—191no—
219C4⋊C8—382no—
220C4⋊C8—381no—
221C4⋊C8—381no—
222C22⋊C8—382no—
223C22⋊C8—381no—
224C22⋊C8—381no—
225#97—21no—
226#97—382no—
227C4×C8—21no—
228C4×C8—191no—
229C4×C8—191no—
230C4×C8—381no—
231C4×C8—381no—
232C4×C8—381no—
233C19#889811yescharacteristic, complemented, Sylow
234#41—22no—
235#41—41no—
236C2×Q8Dic19⋊C411yescharacteristic
237C2×D4—21no—
238C2×D4Dic19⋊C411yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×Dic3811yescharacteristic
243C22×C4D4×D1911yescharacteristic
244C22×C4#6454311yescharacteristic
245M16—22no—
246M16—41no—
247M16—42no—
248M16—762no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—382no—
252C2×C8—382no—
253C2×C8—381no—
254C2×C8—381no—
255C2×C8—381no—
256C2×C8—381no—
257C2×C8—382no—
258C2×C8—381no—
259C2×C8—381no—
260C2×C8—1522no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4Dic19⋊C411yescharacteristic
264C4⋊C4Dic19⋊C411yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42C2×C4×D1911yescharacteristic
272C42D4×D1911yescharacteristic
273C42#6454311yescharacteristic
274C42C2×C22⋊D1911yescharacteristic
275C23—21no—
276C23#1059732411yescharacteristic
277Q8—21no—
278Q8—21no—
279D4—21no—
280D4—42no—
281D4#1059727912yescomplemented
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4#1059732411yescharacteristic
297C2×C4(C22⋊D19)⋊C411yescharacteristic
298C2×C4(C22⋊D19)⋊C411yescharacteristic
299C2×C4C2×Dic19⋊C411yescharacteristic
300C2×C4#1059738111yescharacteristic
301C2×C4#1059738311yescharacteristic
302C8—42no—
303C8—81no—
304C8—382no—
305C8—382no—
306C8—761no—
307C8—761no—
308C8—761no—
309C8—762no—
310C8—761no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—41no—
316C22—41no—
317C22#1192641611yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4C2×#1059727911yescharacteristic
325C4#1192659211yescharacteristic
326C4#1192665811yescharacteristic
327C4#1192666311yescharacteristic
328C4#1192671011yescharacteristic
329C4#1192672511yescharacteristic
330C2—41no—
331C2—42no—
332C2#1456383911yescharacteristic
333C2#1456385911yescharacteristic
334C2#1456390811yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1489C2
socleC22×C19#385
prime radicalC2×#41×C19Q8
cosocleC2×C42×C19C23
hypercenter#1489D19
hypocenterC19#8898
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. #14563806C2semidirect
3. #14562426C2semidirect
5. #14561525C2semidirect
6. #14561473C2semidirect
114. D4×C19#108semidirect
233. C19#8898semidirect
281. D4#10597279semidirect

Maximal subgroups

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

subgroupindex
#145727602
#145638062
#145624262
#145620172
#145615252
#145614732
C19×#14892
#889819