Finite Group Databasebeta

← #18085370

Subgroups — #18085370

Order 4864.

570 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926949C211yesmaximal, characteristic
2C2×#11926942C211yesmaximal, characteristic
3C2×#11926895C211yesmaximal, characteristic
4#14564596C211yesmaximal, characteristic
5#14564437C211yesmaximal, characteristic
6#14564437C211yesmaximal, characteristic
7C19×#1273C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597315C2211yescharacteristic
10C2×#10597315C2211yescharacteristic
11#11926949—22no—
12#11926949—22no—
13#11926942—22no—
14#11926942—22no—
15#11926895—22no—
16#11926895—22no—
17C2×#10597275—22no—
18C2×#10597274—22no—
19C2×#10597273—22no—
20C2×#10597273—22no—
21C2×#10597273—22no—
22#11926414C2211yescharacteristic
23#11926307—22no—
24C2×C4×C8×C19C2211yescharacteristic
25C2×C4×C8×C19C2211yescharacteristic
26C2×C4×C8×C19C2211yescharacteristic
27C22×Dic38—21no—
28C22×Dic38—21no—
29C22×Dic38—21no—
30C22×C8×C19D412yes—
31C22×C8×C19D412yes—
32C22×C8×C19D412yes—
33C2×C42×C19C2311yescharacteristic
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19—21no—
42C2×C4⋊Dic19—21no—
43#10597315—21no—
44#10597315—21no—
45#10597315—21no—
46#10597315—21no—
47#10597315—21no—
48#10597315—21no—
49#10597315—21no—
50#10597315—21no—
51#10597315—21no—
52#10597315D412yes—
53#10597315D412yes—
54#10597315D412yes—
55C4×C8×C19—21no—
56C4×C8×C19—21no—
57C4×C8×C19—21no—
58C4×C8×C19—21no—
59C4×C8×C19—21no—
60C4×C8×C19—21no—
61#10597275—28no—
62#10597274—28no—
63#10597273—28no—
64#10597273—44no—
65#10597273—44no—
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×Dic19—41no—
70C22×Dic19—41no—
71C22×Dic19—41no—
72C22×Dic19—41no—
73C2×Dic38—22no—
74C2×Dic38—22no—
75C2×Dic38—22no—
76C2×Dic38—42no—
77C2×Dic38—42no—
78C2×Dic38—42no—
79C2×Dic38—42no—
80C2×Dic38—42no—
81C2×Dic38—42no—
82C2×Dic38—41no—
83C2×Dic38—41no—
84C2×Dic38—41no—
85C2×C8×C19—22no—
86C2×C8×C19—22no—
87C2×C8×C19—22no—
88C2×C8×C19—22no—
89C2×C8×C19—22no—
90C2×C8×C19—22no—
91C2×C8×C19—22no—
92C2×C8×C19SD1614yes—
93C2×C8×C19Q1614yes—
94C42×C19C2×D411yescharacteristic
95C42×C19C2×D411yescharacteristic
96C42×C19C2×D411yescharacteristic
97C42×C19#4111yescharacteristic
98C4⋊Dic19—22no—
99C4⋊Dic19—22no—
100C4⋊Dic19—22no—
101C4⋊Dic19—22no—
102C4⋊Dic19—22no—
103C4⋊Dic19—22no—
104C4⋊Dic19—41no—
105C4⋊Dic19—41no—
106C4⋊Dic19—41no—
107C4⋊Dic19—41no—
108C4⋊Dic19—41no—
109C4⋊Dic19—41no—
110C4⋊Dic19—42no—
111C4⋊Dic19—42no—
112C4⋊Dic19—42no—
113#10314—191nomaximal, Sylow
114C23×C19#12711yescharacteristic
115C2×C4×C19#12011yescharacteristic
116C2×C4×C19#12011yescharacteristic
117C2×C4×C19#12011yescharacteristic
118C2×C4×C19#12111yescharacteristic
119C2×C4×C19#12111yescharacteristic
120C2×C4×C19#12111yescharacteristic
121C2×C4×C19C2×SD1612yes—
122C2×C4×C19C2×Q1612yes—
123C2×C4×C19#13512yes—
124C2×C4×C19AGL(1,ℤ/8)12yes—
125C2×C4×C19#13712yes—
126C2×C4×C19#13712yes—
127C2×Dic19—42no—
128C2×Dic19—42no—
129C2×Dic19—42no—
130C2×Dic19—81no—
131C2×Dic19—81no—
132C2×Dic19—81no—
133C2×Dic19—81no—
134C2×Dic19—81no—
135C2×Dic19—81no—
136C2×Dic19—81no—
137C2×Dic19—81no—
138C2×Dic19—81no—
139Dic38—44no—
140Dic38—44no—
141Dic38—44no—
142Dic38—82no—
143Dic38—82no—
144Dic38—82no—
145C8×C19—24no—
146C8×C19—24no—
147C8×C19—42no—
148C2×#500—191no—
149C2×#498—191no—
150C2×#487—191no—
151#1990—191no—
152#1956—191no—
153#1956—191no—
154#1273D1911yescharacteristic
155C22×C19#39211yescharacteristic
156C22×C19#49211yescharacteristic
157C22×C19#49411yescharacteristic
158C22×C19#49511yescharacteristic
159C22×C19#49611yescharacteristic
160C22×C19#49711yescharacteristic
161C22×C19#49711yescharacteristic
162C4×C19#44812yes—
163C4×C19#44912yes—
164C4×C19#45112yes—
165C4×C19#46112yes—
166C4×C19#46212yes—
167C4×C19#46312yes—
168Dic19—82no—
169Dic19—82no—
170Dic19—82no—
171Dic19—161no—
172C2×C4⋊Q8—191no—
173C2×C4⋊Q8—191no—
174C2×C4⋊Q8—191no—
175#500—382no—
176#500—382no—
177#498—382no—
178#498—382no—
179#487—382no—
180#487—382no—
181C2×#107—382no—
182C2×#106—382no—
183C2×#103—382no—
184C2×#103—382no—
185C2×#103—382no—
186C2×C4×C8C2×D1911yescharacteristic
187C2×C4×C8C2×D1911yescharacteristic
188C2×C4×C8C2×D1911yescharacteristic
189#384—191no—
190#340—382no—
191C2×C19#170711yescharacteristic
192C2×C19#171411yescharacteristic
193C2×C19#171811yescharacteristic
194C2×C19#172311yescharacteristic
195C2×C19#201211yescharacteristic
196C2×C19#201311yescharacteristic
197C2×C19#201611yescharacteristic
198C22×Q8—381no—
199C22×Q8—381no—
200C22×Q8—381no—
201C22×C8D7612yes—
202C22×C8D7612yes—
203C22×C8D7612yes—
204C4⋊Q8—192no—
205C4⋊Q8—192no—
206C4⋊Q8—192no—
207C4⋊Q8—381no—
208C4⋊Q8—381no—
209C4⋊Q8—381no—
210C4⋊Q8—381no—
211C4⋊Q8—381no—
212C4⋊Q8—381no—
213C4⋊Q8—381no—
214C4⋊Q8—381no—
215C4⋊Q8—381no—
216C2×C4⋊C4—381no—
217C2×C4⋊C4—381no—
218C2×C4⋊C4—381no—
219C2×C4⋊C4—381no—
220C2×C4⋊C4—381no—
221C2×C4⋊C4—381no—
222C2×C4⋊C4—381no—
223C2×C4⋊C4—381no—
224C2×C4⋊C4—381no—
225C2×C42C22×D1911yescharacteristic
226#107—388no—
227#106—388no—
228#103—388no—
229#103—764no—
230#103—764no—
231C4×C8—21no—
232C4×C8—21no—
233C4×C8—21no—
234C4×C8—21no—
235C4×C8—21no—
236C4×C8—21no—
237C19#1031411yescharacteristic, complemented, Sylow
238C2×Q8—382no—
239C2×Q8—382no—
240C2×Q8—382no—
241C2×Q8—761no—
242C2×Q8—761no—
243C2×Q8—761no—
244C2×Q8—762no—
245C2×Q8—762no—
246C2×Q8—762no—
247C2×Q8—762no—
248C2×Q8—762no—
249C2×Q8—762no—
250C22×C4—761no—
251C22×C4—761no—
252C22×C4—761no—
253C22×C4—761no—
254C22×C4C2×D7611yescharacteristic
255C22×C4C2×D7611yescharacteristic
256C22×C4C2×D7611yescharacteristic
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8#6451614yes—
265C2×C8Dic7614yes—
266C4⋊C4—382no—
267C4⋊C4—382no—
268C4⋊C4—382no—
269C4⋊C4—382no—
270C4⋊C4—382no—
271C4⋊C4—382no—
272C4⋊C4—761no—
273C4⋊C4—761no—
274C4⋊C4—761no—
275C4⋊C4—761no—
276C4⋊C4—761no—
277C4⋊C4—761no—
278C4⋊C4—762no—
279C4⋊C4—762no—
280C4⋊C4—762no—
281C42D4×D1911yescharacteristic
282C42D4×D1911yescharacteristic
283C42D4×D1911yescharacteristic
284C42#6454511yescharacteristic
285C23#1059732011yescharacteristic
286Q8—764no—
287Q8—764no—
288Q8—764no—
289Q8—1522no—
290Q8—1522no—
291Q8—1522no—
292C2×C4—762no—
293C2×C4—762no—
294C2×C4—762no—
295C2×C4—1521no—
296C2×C4—1521no—
297C2×C4—1521no—
298C2×C4—1521no—
299C2×C4—1521no—
300C2×C4—1521no—
301C2×C4—1521no—
302C2×C4—1521no—
303C2×C4—1521no—
304C2×C4#1059732811yescharacteristic
305C2×C4#1059732811yescharacteristic
306C2×C4#1059732811yescharacteristic
307C2×C4#1059734111yescharacteristic
308C2×C4#1059734111yescharacteristic
309C2×C4#1059734111yescharacteristic
310C2×C4C2×#6451612yes—
311C2×C4#1059735012yes—
312C2×C4C2×Dic7612yes—
313C2×C4#1059735412yes—
314C2×C4#1059735512yes—
315C2×C4#1059735512yes—
316C8—24no—
317C8—24no—
318C8—42no—
319C22#1192645411yescharacteristic
320C22#1192691711yescharacteristic
321C22#1192692411yescharacteristic
322C22#1192692811yescharacteristic
323C22#1192693311yescharacteristic
324C22#1192693811yescharacteristic
325C22#1192693811yescharacteristic
326C4—3041no—
327C4—1522no—
328C4—1522no—
329C4—1522no—
330C4#1192668512yes—
331C4#1192669112yes—
332C4#1192670212yes—
333C4#1192675012yes—
334C4#1192675512yes—
335C4#1192676012yes—
336C2#1456323211yescharacteristic
337C2#1456325711yescharacteristic
338C2#1456328111yescharacteristic
339C2#1456331211yescharacteristic
340C2#1456471511yescharacteristic
341C2#1456472011yescharacteristic
342C2#1456473711yescharacteristic
subgroupG/H
centerC23#10597320
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1273C2
socle, prime radicalC23×C19#127
hypercenter#1273D19
hypocenterC19#10314
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1273

Complements

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

NH ≅ G/Ntype
237. C19#10314semidirect

Maximal subgroups

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

subgroupindex
C2×#119269492
C2×#119269422
C2×#119268952
#145645962
#145644372
C19×#12732
#1031419