Finite Group Databasebeta

← #18081600

Subgroups — #18081600

Order 4864.

622 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14571991C211yesmaximal, characteristic
2#14563786C211yesmaximal, characteristic, complemented
3C4⋊C8×Dic19C211yesmaximal, characteristic, complemented
4C2×#11926291C211yesmaximal, characteristic, complemented
5C2×#11926289C211yesmaximal, characteristic, complemented
6C2×#11926288C211yesmaximal, characteristic
7C2×C19×#331C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597382—22no—
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×Dic19⋊C8—22no—
13C2×C8×Dic19—21no—
14#11926447—21no—
15#11926447—21no—
16#11926447C414yes—
17C42×Dic19C2211yescharacteristic
18#11926298—21no—
19#11926291—22no—
20#11926289—22no—
21#11926288—22no—
22C2×C19×#127C2211yescharacteristic
23C2×C19×C4⋊C8C2211yescharacteristic
24C2×C19×C4⋊C8C2211yescharacteristic
25C19×#331—22no—
26C22×D4×C19—21no—
27C22×D4×C19—21no—
28C22×D4×C19C2×C412yes—
29C22×Dic38—21no—
30C22×C8×C19—21no—
31C22×C8×C19—21no—
32C19×#127—21no—
33C19×#127—21no—
34C19×#127—21no—
35C19×#127—21no—
36C2×C42×C19C2311yescharacteristic
37C2×C22⋊Dic19—24no—
38C2×C22⋊Dic19—24no—
39#10597382—44no—
40#10597382—44no—
41C2×C4⋊Dic19—21no—
42C2×C4⋊Dic19C2×C412yes—
43C2×C4×Dic19C2×C412yes—
44C2×C4×Dic19D411yescharacteristic
45C2×C4×Dic19D411yescharacteristic
46C2×C4×Dic19D412yes—
47C22×C19⋊C8—21no—
48C22×C19⋊C8—21no—
49#10597315—21no—
50#10597315—21no—
51#10597315—21no—
52#10597315—21no—
53C19×C4⋊C8—21no—
54C19×C4⋊C8—21no—
55C19×C4⋊C8—21no—
56C19×C4⋊C8D412yes—
57Dic19⋊C8—44no—
58C8×Dic19—42no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)—21no—
62C4⋊(C19⋊C8)D412yes—
63C24×C19—22no—
64C2×D4×C19—22no—
65C2×D4×C19—22no—
66C2×D4×C19—44no—
67C2×D4×C19—41no—
68C2×D4×C19—41no—
69C2×D4×C19—41no—
70C2×D4×C19—41no—
71C2×D4×C19—42no—
72C2×D4×C19—42no—
73C2×D4×C19—41no—
74C2×D4×C19—41no—
75C2×D4×C19—41no—
76C2×D4×C19—41no—
77C22×C4×C19C22×C411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×Dic19—22no—
81C22×Dic19C22⋊C412yes—
82C22×Dic19C22⋊C412yes—
83C2×Dic38—41no—
84C2×Dic38—41no—
85C2×Dic38—42no—
86C2×Dic38—42no—
87C2×C8×C19—22no—
88C2×C8×C19—41no—
89C2×C8×C19—41no—
90C2×C8×C19—41no—
91C2×C8×C19—42no—
92C42×C19C2×D411yescharacteristic
93C42×C19C2×D411yescharacteristic
94C42×C19#4111yescharacteristic
95C42×C19#4111yescharacteristic
96C22⋊Dic19—48no—
97C22⋊Dic19—48no—
98C4⋊Dic19—22no—
99C4⋊Dic19—22no—
100C4⋊Dic19—41no—
101C4⋊Dic19—41no—
102C4×Dic19—21no—
103C4×Dic19—21no—
104C4×Dic19—21no—
105C4×Dic19—21no—
106C4×Dic19—42no—
107C4×Dic19D814yes—
108C4×Dic19SD1614yes—
109C2×C19⋊C8—22no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8—42no—
114#9698—191nomaximal, Sylow
115C23×C19—42no—
116C23×C19—44no—
117C23×C19—44no—
118C23×C19—42no—
119C23×C19—42no—
120C23×C19C2×C22⋊C411yescharacteristic
121D4×C19—82no—
122D4×C19—82no—
123D4×C19—81no—
124D4×C19—81no—
125D4×C19—81no—
126D4×C19—81no—
127D4×C19—82no—
128D4×C19—81no—
129D4×C19—81no—
130C2×C4×C19—22no—
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19C4×D411yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19#12111yescharacteristic
135C2×C4×C19#12411yescharacteristic
136C2×C4×C19#12711yescharacteristic
137C2×C4×C19C2×D812yes—
138C2×C4×C19C2×SD1612yes—
139C2×C4×C19#13511yescharacteristic
140C2×C4×C19#13511yescharacteristic
141C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C19#13711yescharacteristic
143C2×Dic19—22no—
144C2×Dic19—22no—
145C2×Dic19—22no—
146C2×Dic19—22no—
147C2×Dic19—42no—
148C2×Dic19—44no—
149C2×Dic19#10214yes—
150C2×Dic19#10214yes—
151Dic38—82no—
152Dic38—81no—
153Dic38—81no—
154C8×C19—42no—
155C8×C19—81no—
156C19⋊C8—42no—
157C19⋊C8—81no—
158#2858—191no—
159#1842—191no—
160C4×C4⋊C8—191no—
161C2×#332—191no—
162C2×#332—191no—
163C2×#331—191no—
164C2×#331D1911yescharacteristic
165C22×C19—84no—
166C22×C19—84no—
167C22×C19—82no—
168C22×C19—82no—
169C22×C19—82no—
170C22×C19#39011yescharacteristic
171C22×C19#41312yes—
172C22×C19C2×#10212yes—
173C22×C19#41611yescharacteristic
174C22×C19#41711yescharacteristic
175C4×C19—21no—
176C4×C19—21no—
177C4×C19#46311yescharacteristic
178C4×C19#46311yescharacteristic
179C4×C19#46411yescharacteristic
180C4×C19#46411yescharacteristic
181C4×C19#48612yes—
182C4×C19#49211yescharacteristic
183C4×C19#49311yescharacteristic
184Dic19—24no—
185Dic19—24no—
186Dic19—82no—
187C2×C4⋊Q8—191no—
188C2×#127C2×D1911yescharacteristic
189C2×#124—382no—
190C2×C4⋊C8—191no—
191C2×C4⋊C8—191no—
192C2×C4⋊C8—382no—
193C2×C4⋊C8C2×D1911yescharacteristic
194C2×C4⋊C8C2×D1911yescharacteristic
195C2×C4×C8—381no—
196#390—194no—
197#390—381no—
198#390—381no—
199C43—191no—
200#336—381no—
201#332—382no—
202#332—382no—
203#331—22no—
204#331—382no—
205C2×C19—162no—
206C2×C19#154012yes—
207C2×C19#154712yes—
208C2×C19#195711yescharacteristic
209C2×C19#196711yescharacteristic
210C2×C19#198311yescharacteristic
211C22×Q8—381no—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4C4×D1912yes—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—381no—
218C22×C8—381no—
219C4⋊Q8—381no—
220C4⋊Q8—381no—
221C4⋊Q8—381no—
222C4⋊Q8—381no—
223#127—21no—
224#127—21no—
225#127—21no—
226#127—21no—
227#124—764no—
228#124—764no—
229C2×C4⋊C4—192no—
230C2×C4⋊C4—381no—
231C2×C22⋊C4—384no—
232C2×C22⋊C4—384no—
233C2×C42—192no—
234C2×C42—191no—
235C2×C42—191no—
236C2×C42—192no—
237C2×C42C22×D1911yescharacteristic
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—192no—
242C4⋊C8—381no—
243C4⋊C8—381no—
244C4⋊C8—381no—
245C4⋊C8—764no—
246C4⋊C8C22⋊D1912yes—
247C4×C8—762no—
248C19#969811yescharacteristic, complemented, Sylow
249C24—22no—
250C2×Q8—761no—
251C2×Q8—761no—
252C2×Q8—762no—
253C2×Q8—762no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—44no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—42no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—41no—
266C2×D4—41no—
267C22×C4—192no—
268C22×C4—192no—
269C22×C4—382no—
270C22×C4C2×C4×D1911yescharacteristic
271C22×C4D4×D1911yescharacteristic
272C22×C4D4×D1911yescharacteristic
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—42no—
278C2×C8—382no—
279C2×C8—761no—
280C2×C8—761no—
281C2×C8—761no—
282C2×C8—762no—
283C4⋊C4—382no—
284C4⋊C4—382no—
285C4⋊C4—761no—
286C4⋊C4—761no—
287C22⋊C4—768no—
288C22⋊C4—768no—
289C42—194no—
290C42—194no—
291C42—381no—
292C42—381no—
293C42—381no—
294C42—381no—
295C42—762no—
296C42#6454111yescharacteristic
297C42D4×D1911yescharacteristic
298C42#6454311yescharacteristic
299C42C2×C22⋊D1911yescharacteristic
300C23—44no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—44no—
305C23C22⋊C4×D1911yescharacteristic
306Q8—1522no—
307Q8—1521no—
308Q8—1521no—
309D4—82no—
310D4—82no—
311D4—82no—
312D4—81no—
313D4—81no—
314D4—81no—
315D4—81no—
316D4—81no—
317D4—81no—
318C2×C4—22no—
319C2×C4—194no—
320C2×C4—194no—
321C2×C4—382no—
322C2×C4—382no—
323C2×C4—382no—
324C2×C4—382no—
325C2×C4—764no—
326C2×C4—762no—
327C2×C4(C22⋊D19)⋊C411yescharacteristic
328C2×C4#1059733011yescharacteristic
329C2×C4#1059733111yescharacteristic
330C2×C4D8×D1912yes—
331C2×C4#1059735711yescharacteristic
332C2×C4#1059735811yescharacteristic
333C2×C4SD16×D1912yes—
334C2×C4#1059736111yescharacteristic
335C2×C4#1059736211yescharacteristic
336C2×C4C4×C22⋊D1911yescharacteristic
337C2×C4#1059738511yescharacteristic
338C2×C4#1059738611yescharacteristic
339C8—42no—
340C8—81no—
341C8—762no—
342C8—1521no—
343C22—84no—
344C22—82no—
345C22—82no—
346C22—82no—
347C22—84no—
348C22#1192644411yescharacteristic
349C22#1192652512yes—
350C22#102×D1912yes—
351C22#1192653711yescharacteristic
352C22#1192654211yescharacteristic
353C4—21no—
354C4—21no—
355C4—384no—
356C4—384no—
357C4—1522no—
358C4#1192675711yescharacteristic
359C4#1192675811yescharacteristic
360C4#1192676411yescharacteristic
361C4#1192676511yescharacteristic
362C4#1192688912yes—
363C4#1192691511yescharacteristic
364C4#1192691911yescharacteristic
365C2—162no—
366C2#1456228112yes—
367C2#1456230912yes—
368C2#1456443911yescharacteristic
369C2#1456448111yescharacteristic
370C2#1456456611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#331C2
socleC23×C19C2×C22⋊C4
prime radicalC2×C19×#127C22
cosocleC2×C42×C19C23
hypercenterC2×#331D19
hypocenterC19#9698
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #14563786C2semidirect
3. C4⋊C8×Dic19C2semidirect
4. C2×#11926291C2semidirect
5. C2×#11926289C2semidirect
248. C19#9698semidirect

Maximal subgroups

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

subgroupindex
#145719912
#145637862
C4⋊C8×Dic192
C2×#119262912
C2×#119262892
C2×#119262882
C2×C19×#3312
#969819