Finite Group Databasebeta

← #18075691

Subgroups — #18075691

Order 4864.

434 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
1C2×#11926622C211yesmaximal, characteristic
2#14563772C211yesmaximal, characteristic, complemented
3#14562381C211yesmaximal, characteristic, complemented
4#14562060C211yesmaximal, characteristic
5#14561531C211yesmaximal, characteristic, complemented
6#14561530C211yesmaximal, characteristic, complemented
7C19×#1486C211yesmaximal, characteristic
8C22×#64520—21no—
9#11926622—21no—
10#11926622—21no—
11#11926622C412yes—
12#11926622C412yes—
13#11926597C2211yescharacteristic
14#11926568C2211yescharacteristic
15C2×C4⋊(C19⋊C8)C2211yescharacteristic
16C2×C22⋊(C19⋊C8)—21no—
17C2×C4×C19⋊C8C2211yescharacteristic
18#11926308—21no—
19#11926308—21no—
20#11926296—21no—
21#11926294—21no—
22D4⋊(C19⋊C8)—22no—
23C2×C4×D4×C19C2211yescharacteristic
24C19×#431C2211yescharacteristic
25C19×#423C2211yescharacteristic
26C19×D4⋊C8—22no—
27C22×D4×C19Q811yescharacteristic
28C23×C4×C19—21no—
29C2×M16×C19—21no—
30C4×D4×C19—21no—
31C4×D4×C19—21no—
32C4×D4×C19C2×C412yes—
33C4×D4×C19D412yes—
34C2×C4⋊C4×C19Q811yescharacteristic
35C2×C22⋊C4×C19—21no—
36C2×C42×C19C2311yescharacteristic
37C2×#64520—22no—
38C2×#64520—22no—
39C2×#64520—21no—
40C2×#64520—42no—
41C2×#64520—42no—
42C22×C19⋊C8—21no—
43C22×C19⋊C8D411yescharacteristic
44C22×C19⋊C8D411yescharacteristic
45C19×C4⋊C8—21no—
46C19×C4⋊C8—21no—
47C19×C4⋊C8—21no—
48C19×C22⋊C8—21no—
49C4×C8×C19—21no—
50C22⋊(C19⋊C8)—22no—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—21no—
53C4⋊(C19⋊C8)—21no—
54C4⋊(C19⋊C8)—21no—
55C4⋊(C19⋊C8)—21no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)C2×C412yes—
58C4×C19⋊C8—21no—
59C4×C19⋊C8C2×C411yescharacteristic
60C4×C19⋊C8C2×C411yescharacteristic
61C4×C19⋊C8D411yescharacteristic
62C4×C19⋊C8D411yescharacteristic
63C24×C19—21no—
64C2×D4×C19—21no—
65C2×D4×C19—42no—
66C2×D4×C19C4⋊C412yes—
67C22×C4×C19—21no—
68C22×C4×C19—22no—
69C22×C4×C19—22no—
70C22×C4×C19—41no—
71C22×C4×C19—41no—
72C22×C4×C19—41no—
73C22×C4×C19—41no—
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×Q811yescharacteristic
76C22×C4×C19#4111yescharacteristic
77M16×C19—41no—
78M16×C19—41no—
79C2×C8×C19—41no—
80C2×C8×C19—41no—
81C4⋊C4×C19—21no—
82C4⋊C4×C19C4⋊C412yes—
83C22⋊C4×C19—22no—
84C22⋊C4×C19—22no—
85C42×C19C22×C411yescharacteristic
86C42×C19C2×D411yescharacteristic
87C42×C19C2×D411yescharacteristic
88C42×C19#4111yescharacteristic
89#64520—44no—
90#64520—44no—
91#64520—41no—
92#64520—41no—
93C2×C19⋊C8—21no—
94C2×C19⋊C8—21no—
95C2×C19⋊C8—21no—
96C2×C19⋊C8—21no—
97C2×C19⋊C8—22no—
98C2×C19⋊C8—41no—
99C2×C19⋊C8—41no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102C2×C19⋊C8C22⋊C411yescharacteristic
103C2×C19⋊C8C22⋊C411yescharacteristic
104C2×C19⋊C8C22⋊C411yescharacteristic
105C2×C19⋊C8C22⋊C411yescharacteristic
106#8664—191nomaximal, Sylow
107C23×C19—22no—
108C23×C19—42no—
109C23×C19—42no—
110C23×C19—41no—
111C23×C19—41no—
112C23×C19C22⋊Q811yescharacteristic
113D4×C19—24no—
114D4×C19—42no—
115C2×C4×C19—22no—
116C2×C4×C19—22no—
117C2×C4×C19—41no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19—42no—
124C2×C4×C19C2×C22⋊C411yescharacteristic
125C2×C4×C19C2×C4⋊C411yescharacteristic
126C2×C4×C19#11711yescharacteristic
127C2×C4×C19#12111yescharacteristic
128C2×C4×C19#12111yescharacteristic
129C2×C4×C19C22⋊Q811yescharacteristic
130C2×C4×C19#13511yescharacteristic
131C2×C4×C19#13511yescharacteristic
132C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
134C8×C19—81no—
135C8×C19—81no—
136C19⋊C8—21no—
137C19⋊C8—21no—
138C19⋊C8—21no—
139C19⋊C8—21no—
140C19⋊C8—42no—
141C19⋊C8—81no—
142C19⋊C8—81no—
143C2×#436—191no—
144#1837—191no—
145#1564—191no—
146#1486—191no—
147#1486D1911yescharacteristic
148#1301—191no—
149#1301—191no—
150C22×C19—21no—
151C22×C19—21no—
152C22×C19—42no—
153C22×C19—42no—
154C22×C19—42no—
155C22×C19—82no—
156C22×C19—82no—
157C22×C19#38011yescharacteristic
158C22×C19#47811yescharacteristic
159C22×C19#47811yescharacteristic
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—42no—
164C4×C19#41611yescharacteristic
165C4×C19#41811yescharacteristic
166C4×C19#43012yes—
167C4×C19#46311yescharacteristic
168C4×C19#46311yescharacteristic
169C22×M16—381no—
170C2×C4×D4C2×D1911yescharacteristic
171#436—192no—
172#436—192no—
173#436—381no—
174#436—381no—
175#431—191no—
176#431C2×D1911yescharacteristic
177#423—191no—
178#423C2×D1911yescharacteristic
179C2×C4⋊C8—191no—
180C2×C22⋊C8—381no—
181C2×C4×C8—191no—
182#341—381no—
183#341—381no—
184#335—381no—
185#334—381no—
186D4⋊C8—22no—
187D4⋊C8—382no—
188C2×C19—21no—
189C2×C19—21no—
190C2×C19—82no—
191C2×C19#180411yescharacteristic
192C2×C19#181111yescharacteristic
193C2×C19#181411yescharacteristic
194C22×D4Dic3811yescharacteristic
195C23×C4—21no—
196C2×M16—21no—
197C2×M16—382no—
198C2×M16—382no—
199C2×M16—381no—
200C2×M16—762no—
201C2×M16—762no—
202C22×C8—191no—
203C22×C8—191no—
204C22×C8—381no—
205C4×D4—21no—
206C4×D4—21no—
207C4×D4C4×D1912yes—
208C4×D4C22⋊D1912yes—
209C2×C4⋊C4Dic3811yescharacteristic
210C2×C22⋊C4—21no—
211C2×C42C22×D1911yescharacteristic
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—192no—
216C4⋊C8—381no—
217C4⋊C8—381no—
218C4⋊C8—381no—
219C4⋊C8—381no—
220C22⋊C8—21no—
221C22⋊C8—382no—
222C22⋊C8—382no—
223C22⋊C8—381no—
224C4×C8—21no—
225C4×C8—191no—
226C4×C8—191no—
227C4×C8—191no—
228C4×C8—191no—
229C4×C8—381no—
230C19#866411yescharacteristic, complemented, Sylow
231C24—21no—
232C2×D4—21no—
233C2×D4—42no—
234C2×D4Dic19⋊C412yes—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C2×Dic3811yescharacteristic
243C22×C4D4×D1911yescharacteristic
244C22×C4#6454311yescharacteristic
245M16—41no—
246M16—41no—
247M16—764no—
248M16—764no—
249M16—761no—
250M16—761no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—191no—
254C2×C8—191no—
255C2×C8—191no—
256C2×C8—191no—
257C2×C8—381no—
258C2×C8—381no—
259C2×C8—381no—
260C2×C8—381no—
261C2×C8—382no—
262C2×C8—761no—
263C2×C8—761no—
264C2×C8—761no—
265C2×C8—761no—
266C4⋊C4—21no—
267C4⋊C4Dic19⋊C412yes—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C42C2×C4×D1911yescharacteristic
271C42D4×D1911yescharacteristic
272C42#6454311yescharacteristic
273C42C2×C22⋊D1911yescharacteristic
274C23—22no—
275C23—42no—
276C23—42no—
277C23—41no—
278C23—41no—
279C23#1059732411yescharacteristic
280D4—24no—
281D4—42no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4#1059732311yescharacteristic
292C2×C4#1059732411yescharacteristic
293C2×C4C22⋊C4×D1911yescharacteristic
294C2×C4#1059735711yescharacteristic
295C2×C4#1059735811yescharacteristic
296C2×C4#1059736011yescharacteristic
297C2×C4#1059736211yescharacteristic
298C2×C4C2×Dic19⋊C411yescharacteristic
299C2×C4#1059738511yescharacteristic
300C2×C4#1059738511yescharacteristic
301C8—81no—
302C8—81no—
303C8—381no—
304C8—381no—
305C8—381no—
306C8—381no—
307C8—762no—
308C8—1521no—
309C8—1521no—
310C22—21no—
311C22—21no—
312C22—42no—
313C22—42no—
314C22—42no—
315C22—82no—
316C22—82no—
317C22#1192640211yescharacteristic
318C22#1192684211yescharacteristic
319C22#1192684611yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—42no—
324C4#1192653711yescharacteristic
325C4#1192654711yescharacteristic
326C4#1192659212yes—
327C4#1192675711yescharacteristic
328C4#1192676111yescharacteristic
329C2—21no—
330C2—21no—
331C2—82no—
332C2#1456364311yescharacteristic
333C2#1456367511yescharacteristic
334C2#1456368711yescharacteristic
subgroupG/H
centerC2×C4#10597385
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1486C2
socleC22×C19#380
prime radicalC22×D4×C19Q8
cosocleC2×C42×C19C23
hypercenter#1486D19
hypocenterC19#8664
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #14563772C2semidirect
3. #14562381C2semidirect
5. #14561531C2semidirect
6. #14561530C2semidirect
230. C19#8664semidirect

Maximal subgroups

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

subgroupindex
C2×#119266222
#145637722
#145623812
#145620602
#145615312
#145615302
C19×#14862
#866419