Finite Group Databasebeta

← #18083782

Subgroups — #18083782

Order 4864.

566 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926896C211yesmaximal, characteristic
2#14568840C211yesmaximal, characteristic
3#14564559C211yesmaximal, characteristic
4C2×#11926292C211yesmaximal, characteristic
5C2×Q8⋊(C19⋊C8)C211yesmaximal, characteristic
6#14561474C211yesmaximal, characteristic
7C2×C19×#475C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9#11926896—22no—
10#11926896—22no—
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×#10597292—22no—
13C2×#10597267—22no—
14C2×C4×C19⋊C8C2211yescharacteristic
15#11926464—22no—
16#11926451—21no—
17#11926442—22no—
18#11926413—21no—
19C4×C4⋊Dic19C2211yescharacteristic
20#11926292—22no—
21Q8⋊(C19⋊C8)—22no—
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C4×Q8×C19C2211yescharacteristic
24C19×#475—22no—
25C19×#475—22no—
26C2×C19×#106—21no—
27C2×C19×C4⋊C8C2211yescharacteristic
28C2×C19×#103—21no—
29C22×Q8×C19—21no—
30C22×Q8×C19D411yescharacteristic
31C22×Dic38D412yes—
32C22×C8×C19—21no—
33C19×C4⋊Q8—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8D412yes—
37C4×Q8×C19—21no—
38C4×Q8×C19—21no—
39C4×Q8×C19—21no—
40C4×Q8×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19D411yescharacteristic
45C2×C42×C19—21no—
46C2×C42×C19C2311yescharacteristic
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19D412yes—
50C2×Dic19⋊C4—24no—
51C2×C4×Dic19—21no—
52C22×C19⋊C8—21no—
53C22×C19⋊C8—21no—
54#10597315—21no—
55#10597315—21no—
56#10597315—21no—
57#10597315—21no—
58C19×#106—24no—
59C19×C4⋊C8—21no—
60C19×C4⋊C8D412yes—
61C19×#103—24no—
62#10597292—44no—
63C19⋊#95—24no—
64C19⋊#95—21no—
65#10597267—28no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—21no—
68C4×C19⋊C8—21no—
69C4×C19⋊C8D412yes—
70C2×Q8×C19—21no—
71C2×Q8×C19—21no—
72C2×Q8×C19—21no—
73C2×Q8×C19—22no—
74C2×Q8×C19—21no—
75C2×Q8×C19—21no—
76C2×Q8×C19—41no—
77C2×Q8×C19—42no—
78C2×Q8×C19—42no—
79C2×Q8×C19Q1612yes—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—41no—
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×Dic19—22no—
87C22×Dic19—22no—
88C2×Dic38—22no—
89C2×Dic38—22no—
90C2×Dic38—44no—
91C2×C8×C19—22no—
92C2×C8×C19—41no—
93C2×C8×C19—41no—
94C4⋊C4×C19—22no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—21no—
97C4⋊C4×C19—21no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—41no—
100C4⋊C4×C19—41no—
101C4⋊C4×C19—41no—
102C42×C19—41no—
103C42×C19—41no—
104C42×C19C2×D411yescharacteristic
105C42×C19C2×D411yescharacteristic
106C42×C19C2×D411yescharacteristic
107C42×C19#4111yescharacteristic
108C4⋊Dic19—22no—
109C4⋊Dic19—41no—
110C4⋊Dic19—41no—
111C4⋊Dic19—41no—
112C4⋊Dic19—41no—
113C4⋊Dic19SD1614yes—
114Dic19⋊C4—84no—
115C4×Dic19—41no—
116C4×Dic19—41no—
117C2×C19⋊C8—22no—
118C2×C19⋊C8—42no—
119C2×C19⋊C8—41no—
120C2×C19⋊C8—42no—
121#10073—191nomaximal, Sylow
122C23×C19#12011yescharacteristic
123Q8×C19—22no—
124Q8×C19—22no—
125Q8×C19—41no—
126Q8×C19—41no—
127Q8×C19—44no—
128Q8×C19—81no—
129Q8×C19—81no—
130C2×C4×C19—22no—
131C2×C4×C19—22no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19—82no—
138C2×C4×C19#12011yescharacteristic
139C2×C4×C19#12011yescharacteristic
140C2×C4×C19#12111yescharacteristic
141C2×C4×C19#12111yescharacteristic
142C2×C4×C19#12111yescharacteristic
143C2×C4×C19#12711yescharacteristic
144C2×C4×C19C2×SD1612yes—
145C2×C4×C19C2×Q1611yescharacteristic
146C2×C4×C19#13511yescharacteristic
147C2×C4×C19#13711yescharacteristic
148C2×C4×C19#13711yescharacteristic
149C2×C4×C19#13712yes—
150C2×Dic19—24no—
151C2×Dic19—42no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—44no—
155Dic38—44no—
156Dic38—82no—
157C8×C19—42no—
158C19⋊C8—42no—
159C19⋊C8—81no—
160C2×#487—191no—
161C2×#475D1911yescharacteristic
162#2567—191no—
163#1981—191no—
164C2×#333—191no—
165C2×Q8⋊C8—191no—
166#1279—191no—
167C22×C19#39211yescharacteristic
168C22×C19#44812yes—
169C22×C19#45111yescharacteristic
170C22×C19#45211yescharacteristic
171C22×C19#45512yes—
172C4×C19—21no—
173C4×C19—21no—
174C4×C19—42no—
175C4×C19—81no—
176C4×C19—82no—
177C4×C19#45111yescharacteristic
178C4×C19#45211yescharacteristic
179C4×C19#46112yes—
180C4×C19#46711yescharacteristic
181C4×C19#47011yescharacteristic
182C4×C19#49211yescharacteristic
183C4×C19#49711yescharacteristic
184Dic19—44no—
185Dic19—82no—
186C2×C4⋊Q8—191no—
187C2×C4⋊Q8C2×D1911yescharacteristic
188C2×C4×Q8C2×D1911yescharacteristic
189#487—382no—
190#487—382no—
191#475—22no—
192#475—22no—
193C2×#106—21no—
194C2×C4⋊C8—191no—
195C2×C4⋊C8C2×D1911yescharacteristic
196C2×#103—21no—
197C2×#103—382no—
198C2×#103—382no—
199C2×C4×C8—191no—
200#395—382no—
201#391—381no—
202#389—382no—
203#384—381no—
204C4×C4⋊C4—191no—
205#333—382no—
206Q8⋊C8—382no—
207C2×C19#164312yes—
208C2×C19#164512yes—
209C2×C19#200111yescharacteristic
210C2×C19#200411yescharacteristic
211C2×C19#201311yescharacteristic
212C22×Q8—21no—
213C22×Q8—192no—
214C22×Q8C22⋊D1911yescharacteristic
215C22×C8—21no—
216C22×C8—381no—
217C22×C8—381no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—381no—
222C4⋊Q8—381no—
223C4⋊Q8—381no—
224C4⋊Q8—381no—
225C4⋊Q8C22⋊D1912yes—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—192no—
234C2×C4⋊C4—381no—
235C2×C4⋊C4—381no—
236C2×C4⋊C4—384no—
237C2×C4⋊C4C22⋊D1911yescharacteristic
238C2×C42—21no—
239C2×C42—381no—
240C2×C42C22×D1911yescharacteristic
241#106—24no—
242C4⋊C8—21no—
243C4⋊C8—381no—
244C4⋊C8—381no—
245C4⋊C8C22⋊D1912yes—
246#103—24no—
247#103—388no—
248#103—764no—
249C4×C8—192no—
250C4×C8—381no—
251#95—384no—
252#95—381no—
253C19#1007311yescharacteristic, complemented, Sylow
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—41no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—382no—
264C2×Q8—382no—
265C2×Q8—764no—
266C2×Q8#6452812yes—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4—382no—
271C22×C4—382no—
272C22×C4D4×D1911yescharacteristic
273C22×C4D4×D1911yescharacteristic
274C22×C4C2×C22⋊D1911yescharacteristic
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—382no—
279C2×C8—762no—
280C2×C8—761no—
281C2×C8—762no—
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—194no—
291C4⋊C4—382no—
292C4⋊C4—761no—
293C4⋊C4—761no—
294C4⋊C4—761no—
295C4⋊C4—761no—
296C4⋊C4—1524no—
297C42—41no—
298C42—41no—
299C42—761no—
300C42—761no—
301C42D4×D1911yescharacteristic
302C42#6454311yescharacteristic
303C42C2×C22⋊D1911yescharacteristic
304C42C2×C22⋊D1911yescharacteristic
305C23#1059738311yescharacteristic
306Q8—22no—
307Q8—22no—
308Q8—41no—
309Q8—41no—
310Q8—44no—
311Q8—81no—
312Q8—81no—
313Q8—764no—
314Q8—1522no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4—384no—
324C2×C4—762no—
325C2×C4—762no—
326C2×C4—762no—
327C2×C4—764no—
328C2×C4SD16×D1912yes—
329C2×C4#1059736112yes—
330C2×C4#1059738311yescharacteristic
331C2×C4#1059738411yescharacteristic
332C2×C4#1059738511yescharacteristic
333C2×C4#1059738511yescharacteristic
334C2×C4#1059738611yescharacteristic
335C2×C4#1059738811yescharacteristic
336C2×C4C2×#6452811yescharacteristic
337C2×C4#1059739611yescharacteristic
338C2×C4#1059739711yescharacteristic
339C2×C4#1059739911yescharacteristic
340C8—42no—
341C8—762no—
342C8—1521no—
343C22#1192645211yescharacteristic
344C22#1192668112yes—
345C22#1192669911yescharacteristic
346C22#1192670411yescharacteristic
347C22#1192672012yes—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—81no—
352C4—82no—
353C4—764no—
354C4—1522no—
355C4#1192670011yescharacteristic
356C4#1192670611yescharacteristic
357C4#1192674712yes—
358C4#1192678311yescharacteristic
359C4#1192680011yescharacteristic
360C4#1192691511yescharacteristic
361C4#1192693511yescharacteristic
362C2#1456284112yes—
363C2#1456285512yes—
364C2#1456464311yescharacteristic
365C2#1456466111yescharacteristic
366C2#1456471611yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC2×C19×#475C2
socle, prime radicalC23×C19#120
hypercenterC2×#475D19
hypocenterC19#10073
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
253. C19#10073semidirect

Maximal subgroups

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

subgroupindex
C2×#119268962
#145688402
#145645592
C2×#119262922
C2×Q8⋊(C19⋊C8)2
#145614742
C2×C19×#4752
#1007319