Finite Group Databasebeta

← #18083786

Subgroups — #18083786

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×#11926895C211yesmaximal, characteristic
2C2×#11926829C211yesmaximal, characteristic
3#14568840C211yesmaximal, characteristic
4#14564557C211yesmaximal, characteristic
5C2×#11926292C211yesmaximal, characteristic
6#14561475C211yesmaximal, characteristic
7C2×C19×Q8⋊C8C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597315C2211yescharacteristic
10#11926895—22no—
11#11926895—22no—
12#11926829—22no—
13#11926829—22no—
14C2×#10597265—21no—
15C2×C4⋊(C19⋊C8)C2211yescharacteristic
16C2×#10597273—22no—
17C2×#10597273—22no—
18C2×#10597292—21no—
19#11926464—22no—
20#11926451—21no—
21#11926442—22no—
22#11926413—21no—
23C4×C4⋊Dic19C2211yescharacteristic
24#11926292—22no—
25C2×C4×Q8×C19C2211yescharacteristic
26C2×C19×C4⋊C8C2211yescharacteristic
27C2×C4×C8×C19C2211yescharacteristic
28C19×Q8⋊C8—22no—
29C22×Q8×C19D411yescharacteristic
30C22×Dic38—21no—
31C22×Dic38D412yes—
32C22×C8×C19—21no—
33C22×C8×C19—21no—
34C4×Q8×C19—21no—
35C4×Q8×C19—21no—
36C4×Q8×C19—21no—
37C4×Q8×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19D411yescharacteristic
40C2×C42×C19—21no—
41C2×C42×C19C2311yescharacteristic
42C2×C4⋊Dic19—21no—
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19—21no—
46C2×C4⋊Dic19D412yes—
47C2×Dic19⋊C4—24no—
48C2×C4×Dic19—21no—
49C22×C19⋊C8—21no—
50#10597315—21no—
51#10597315—21no—
52#10597315—21no—
53#10597315—21no—
54#10597315—21no—
55#10597315—21no—
56#10597315—21no—
57#10597315D412yes—
58C19×C4⋊C8—21no—
59C19×C4⋊C8—21no—
60C4×C8×C19—21no—
61C4×C8×C19D412yes—
62#10597292—24no—
63C19⋊#95—24no—
64C19⋊#95—21no—
65#10597273—28no—
66#10597273—44no—
67#10597265—24no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)D412yes—
70C2×Q8×C19—21no—
71C2×Q8×C19—21no—
72C2×Q8×C19—21no—
73C2×Q8×C19—21no—
74C2×Q8×C19—21no—
75C2×Q8×C19Q1612yes—
76C22×C4×C19—21no—
77C22×C4×C19—21no—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×Dic19—22no—
82C22×Dic19—22no—
83C22×Dic19—41no—
84C2×Dic38—22no—
85C2×Dic38—22no—
86C2×Dic38—22no—
87C2×Dic38—44no—
88C2×Dic38—42no—
89C2×Dic38—42no—
90C2×Dic38—41no—
91C2×C8×C19—22no—
92C2×C8×C19—42no—
93C2×C8×C19—41no—
94C2×C8×C19—42no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—21no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C42×C19—41no—
100C42×C19—41no—
101C42×C19C2×D411yescharacteristic
102C42×C19C2×D411yescharacteristic
103C42×C19C2×D411yescharacteristic
104C42×C19#4111yescharacteristic
105C4⋊Dic19—22no—
106C4⋊Dic19—22no—
107C4⋊Dic19—22no—
108C4⋊Dic19—41no—
109C4⋊Dic19—41no—
110C4⋊Dic19—41no—
111C4⋊Dic19—41no—
112C4⋊Dic19—41no—
113C4⋊Dic19—41no—
114C4⋊Dic19SD1614yes—
115Dic19⋊C4—84no—
116C4×Dic19—41no—
117C4×Dic19—41no—
118C2×C19⋊C8—22no—
119C2×C19⋊C8—41no—
120C2×C19⋊C8—41no—
121#10073—191nomaximal, Sylow
122C23×C19#12011yescharacteristic
123Q8×C19—22no—
124Q8×C19—22no—
125Q8×C19—41no—
126Q8×C19—41no—
127C2×C4×C19—22no—
128C2×C4×C19—22no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—42no—
133C2×C4×C19#12011yescharacteristic
134C2×C4×C19#12011yescharacteristic
135C2×C4×C19#12111yescharacteristic
136C2×C4×C19#12111yescharacteristic
137C2×C4×C19#12111yescharacteristic
138C2×C4×C19#12711yescharacteristic
139C2×C4×C19C2×SD1612yes—
140C2×C4×C19C2×Q1611yescharacteristic
141C2×C4×C19#13511yescharacteristic
142C2×C4×C19#13711yescharacteristic
143C2×C4×C19#13711yescharacteristic
144C2×C4×C19#13712yes—
145C2×Dic19—24no—
146C2×Dic19—42no—
147C2×Dic19—42no—
148C2×Dic19—42no—
149C2×Dic19—42no—
150C2×Dic19—44no—
151C2×Dic19—82no—
152Dic38—44no—
153Dic38—44no—
154Dic38—81no—
155Dic38—81no—
156Dic38—82no—
157C8×C19—42no—
158C8×C19—81no—
159C19⋊C8—42no—
160C2×#487—191no—
161C2×#475—191no—
162#2567—191no—
163#1981—191no—
164C2×#333—191no—
165C2×Q8⋊C8D1911yescharacteristic
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#45111yescharacteristic
177C4×C19#45211yescharacteristic
178C4×C19#46112yes—
179C4×C19#46711yescharacteristic
180C4×C19#47011yescharacteristic
181C4×C19#49211yescharacteristic
182C4×C19#49711yescharacteristic
183Dic19—44no—
184Dic19—82no—
185Dic19—82no—
186C2×C4⋊Q8—191no—
187C2×C4⋊Q8—191no—
188C2×C4×Q8C2×D1911yescharacteristic
189#487—382no—
190#487—382no—
191#475—382no—
192#475—382no—
193C2×#106—381no—
194C2×C4⋊C8—191no—
195C2×C4⋊C8C2×D1911yescharacteristic
196C2×#103—382no—
197C2×#103—381no—
198C2×#103—382no—
199C2×C4×C8C2×D1911yescharacteristic
200#395—382no—
201#391—381no—
202#389—382no—
203#384—381no—
204C4×C4⋊C4—191no—
205#333—382no—
206Q8⋊C8—22no—
207C2×C19#164312yes—
208C2×C19#164512yes—
209C2×C19#200111yescharacteristic
210C2×C19#200411yescharacteristic
211C2×C19#201311yescharacteristic
212C22×Q8—192no—
213C22×Q8—381no—
214C22×Q8D7611yescharacteristic
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—381no—
218C4⋊Q8—192no—
219C4⋊Q8—381no—
220C4⋊Q8—381no—
221C4⋊Q8—381no—
222C4⋊Q8—381no—
223C4⋊Q8—381no—
224C4⋊Q8—381no—
225C4⋊Q8—381no—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—192no—
232C2×C4⋊C4—381no—
233C2×C4⋊C4—381no—
234C2×C4⋊C4—381no—
235C2×C4⋊C4—381no—
236C2×C4⋊C4—384no—
237C2×C4⋊C4D7611yescharacteristic
238C2×C42—21no—
239C2×C42—381no—
240C2×C42C22×D1911yescharacteristic
241#106—384no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—192no—
245C4⋊C8—381no—
246#103—388no—
247#103—384no—
248#103—764no—
249C4×C8—21no—
250C4×C8C22⋊D1912yes—
251#95—384no—
252#95—381no—
253C19#1007311yescharacteristic, complemented, Sylow
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—382no—
260C2×Q8—382no—
261C2×Q8—382no—
262C2×Q8—764no—
263C2×Q8—761no—
264C2×Q8—762no—
265C2×Q8—762no—
266C2×Q8Dic7612yes—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—382no—
270C22×C4—382no—
271C22×C4—761no—
272C22×C4C2×D7611yescharacteristic
273C22×C4D4×D1911yescharacteristic
274C22×C4D4×D1911yescharacteristic
275C2×C8—22no—
276C2×C8—42no—
277C2×C8—41no—
278C2×C8—42no—
279C2×C8—382no—
280C2×C8—761no—
281C2×C8—761no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—194no—
287C4⋊C4—382no—
288C4⋊C4—382no—
289C4⋊C4—382no—
290C4⋊C4—761no—
291C4⋊C4—761no—
292C4⋊C4—761no—
293C4⋊C4—761no—
294C4⋊C4—761no—
295C4⋊C4—761no—
296C4⋊C4—1524no—
297C42—41no—
298C42—41no—
299C42—761no—
300C42—761no—
301C42#6454111yescharacteristic
302C42D4×D1911yescharacteristic
303C42D4×D1911yescharacteristic
304C42C2×C22⋊D1911yescharacteristic
305C23#1059732811yescharacteristic
306Q8—22no—
307Q8—22no—
308Q8—41no—
309Q8—41no—
310Q8—764no—
311Q8—764no—
312Q8—1522no—
313Q8—1521no—
314Q8—1521no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—384no—
322C2×C4—762no—
323C2×C4—762no—
324C2×C4—762no—
325C2×C4—762no—
326C2×C4—764no—
327C2×C4—1522no—
328C2×C4#1059732811yescharacteristic
329C2×C4#1059733011yescharacteristic
330C2×C4#1059733011yescharacteristic
331C2×C4#1059735011yescharacteristic
332C2×C4C2×Dic7611yescharacteristic
333C2×C4#1059735511yescharacteristic
334C2×C4#1059735511yescharacteristic
335C2×C4SD16×D1912yes—
336C2×C4#1059736412yes—
337C2×C4#1059737611yescharacteristic
338C2×C4#1059738311yescharacteristic
339C2×C4#1059738611yescharacteristic
340C8—42no—
341C8—81no—
342C8—762no—
343C22#1192645311yescharacteristic
344C22#1192668412yes—
345C22#1192670211yescharacteristic
346C22#1192670811yescharacteristic
347C22#1192672312yes—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—81no—
352C4—764no—
353C4—1522no—
354C4—1522no—
355C4#1192670211yescharacteristic
356C4#1192670811yescharacteristic
357C4#1192674812yes—
358C4#1192678511yescharacteristic
359C4#1192680211yescharacteristic
360C4#1192691511yescharacteristic
361C4#1192693711yescharacteristic
362C2#1456284512yes—
363C2#1456285912yes—
364C2#1456464511yescharacteristic
365C2#1456466311yescharacteristic
366C2#1456471911yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC2×C19×Q8⋊C8C2
socle, prime radicalC23×C19#120
hypercenterC2×Q8⋊C8D19
hypocenterC19#10073
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

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×#119268952
C2×#119268292
#145688402
#145645572
C2×#119262922
#145614752
C2×C19×Q8⋊C82
#1007319