Finite Group Databasebeta

← #18081580

Subgroups — #18081580

Order 4864.

570 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572031C211yesmaximal, characteristic
2#14563786C211yesmaximal, characteristic
3C4⋊C8×Dic19C211yesmaximal, characteristic
4C2×#11926291C211yesmaximal, characteristic
5C2×#11926290C211yesmaximal, characteristic
6C2×#11926289C211yesmaximal, characteristic
7C2×C19×#332C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597390—21no—
10C2×#10597390—21no—
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×C4⋊(C19⋊C8)C2211yescharacteristic
13C2×Dic19⋊C8—22no—
14C2×C8×Dic19—21no—
15#11926413—22no—
16#11926413C414yes—
17C42×Dic19C2211yescharacteristic
18#11926298—21no—
19#11926291—22no—
20#11926290—22no—
21#11926289—22no—
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C19×C4⋊C8C2211yescharacteristic
24C2×C19×C4⋊C8C2211yescharacteristic
25C19×#332—22no—
26C22×Q8×C19—21no—
27C22×Dic38—21no—
28C22×C8×C19—21no—
29C22×C8×C19—21no—
30C19×C4⋊Q8—21no—
31C19×C4⋊Q8—21no—
32C19×C4⋊Q8—21no—
33C19×C4⋊Q8—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19C2×C412yes—
36C2×C42×C19C2311yescharacteristic
37#10597390—42no—
38#10597390—42no—
39#10597390—42no—
40#10597390—42no—
41C2×C4⋊Dic19—21no—
42C2×C4⋊Dic19C2×C412yes—
43C2×Dic19⋊C4—24no—
44C2×Dic19⋊C4—24no—
45C2×C4×Dic19C2×C412yes—
46C2×C4×Dic19D411yescharacteristic
47C2×C4×Dic19D411yescharacteristic
48C2×C4×Dic19D412yes—
49C22×C19⋊C8—21no—
50C22×C19⋊C8—21no—
51#10597315—21no—
52#10597315—21no—
53#10597315—21no—
54#10597315—21no—
55C19×C4⋊C8—21no—
56C19×C4⋊C8—21no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8D412yes—
59Dic19⋊C8—44no—
60C8×Dic19—42no—
61C4⋊(C19⋊C8)—21no—
62C4⋊(C19⋊C8)—21no—
63C4⋊(C19⋊C8)—21no—
64C4⋊(C19⋊C8)D412yes—
65C2×Q8×C19—41no—
66C2×Q8×C19—41no—
67C2×Q8×C19—41no—
68C2×Q8×C19—41no—
69C2×Q8×C19—41no—
70C2×Q8×C19—41no—
71C22×C4×C19—22no—
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×Dic19—22no—
76C22×Dic19C22⋊C412yes—
77C22×Dic19C22⋊C412yes—
78C2×Dic38—41no—
79C2×Dic38—41no—
80C2×Dic38—41no—
81C2×Dic38—41no—
82C2×Dic38—41no—
83C2×Dic38—41no—
84C2×C8×C19—22no—
85C2×C8×C19—41no—
86C2×C8×C19—41no—
87C2×C8×C19—41no—
88C2×C8×C19—42no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19—22no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—41no—
93C42×C19C2×D411yescharacteristic
94C42×C19C2×D411yescharacteristic
95C42×C19#4111yescharacteristic
96C42×C19#4111yescharacteristic
97C4⋊Dic19—22no—
98C4⋊Dic19—22no—
99C4⋊Dic19—41no—
100C4⋊Dic19—41no—
101Dic19⋊C4—48no—
102Dic19⋊C4—48no—
103C4×Dic19—21no—
104C4×Dic19—21no—
105C4×Dic19—24no—
106C4×Dic19D812yes—
107C4×Dic19SD1612yes—
108C4×Dic19SD1614yes—
109C4×Dic19Q1614yes—
110C2×C19⋊C8—22no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8—41no—
114C2×C19⋊C8—42no—
115#9694—191nomaximal, Sylow
116C23×C19C2×C22⋊C411yescharacteristic
117Q8×C19—81no—
118Q8×C19—81no—
119Q8×C19—81no—
120Q8×C19—81no—
121C2×C4×C19—22no—
122C2×C4×C19—42no—
123C2×C4×C19—42no—
124C2×C4×C19—42no—
125C2×C4×C19C4×D411yescharacteristic
126C2×C4×C19C4×D411yescharacteristic
127C2×C4×C19#12111yescharacteristic
128C2×C4×C19#12111yescharacteristic
129C2×C4×C19#12411yescharacteristic
130C2×C4×C19#12711yescharacteristic
131C2×C4×C19C2×D811yescharacteristic
132C2×C4×C19C2×SD1611yescharacteristic
133C2×C4×C19C2×SD1612yes—
134C2×C4×C19C2×Q1612yes—
135C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
137C2×Dic19—22no—
138C2×Dic19—22no—
139C2×Dic19—42no—
140C2×Dic19—42no—
141C2×Dic19—42no—
142C2×Dic19#10114yes—
143C2×Dic19#10214yes—
144C2×Dic19#10314yes—
145C2×Dic19#10314yes—
146Dic38—81no—
147Dic38—81no—
148Dic38—81no—
149Dic38—81no—
150C8×C19—42no—
151C8×C19—81no—
152C19⋊C8—42no—
153C19⋊C8—81no—
154#2868—191no—
155#1842—191no—
156C4×C4⋊C8—191no—
157C2×#332—191no—
158C2×#332—191no—
159C2×#332—191no—
160C2×#332D1911yescharacteristic
161C22×C19#39011yescharacteristic
162C22×C19C2×#10112yes—
163C22×C19C2×#10211yescharacteristic
164C22×C19C2×#10312yes—
165C22×C19#41811yescharacteristic
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—82no—
169C4×C19#45911yescharacteristic
170C4×C19#45911yescharacteristic
171C4×C19#46011yescharacteristic
172C4×C19#46011yescharacteristic
173C4×C19#48712yes—
174C4×C19#49211yescharacteristic
175C4×C19#49411yescharacteristic
176Dic19—24no—
177Dic19—82no—
178Dic19#33218yescomplemented
179C2×C4⋊Q8—191no—
180C2×C4⋊Q8—381no—
181C2×C4⋊Q8—381no—
182C2×C4⋊Q8C2×D1911yescharacteristic
183C2×C4⋊C8—191no—
184C2×C4⋊C8—191no—
185C2×C4⋊C8—382no—
186C2×C4⋊C8C2×D1911yescharacteristic
187C2×C4⋊C8C2×D1911yescharacteristic
188C2×C4×C8—381no—
189#384—194no—
190#384—382no—
191C43—191no—
192#336—381no—
193#332—22no—
194#332—382no—
195#332—382no—
196#332—382no—
197C2×C19C2×#33212yes—
198C2×C19#154912yes—
199C2×C19#195611yescharacteristic
200C2×C19#196611yescharacteristic
201C2×C19#198211yescharacteristic
202C22×Q8—21no—
203C22×Q8—381no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—381no—
207C22×C8—381no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—381no—
213C4⋊Q8—381no—
214C4⋊Q8—381no—
215C4⋊Q8—381no—
216C4⋊Q8—762no—
217C4⋊Q8—762no—
218C4⋊Q8—762no—
219C4⋊Q8—762no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—192no—
222C2×C4⋊C4—384no—
223C2×C4⋊C4—384no—
224C2×C4⋊C4—381no—
225C2×C4⋊C4C4×D1912yes—
226C2×C42—191no—
227C2×C42—192no—
228C2×C42—192no—
229C2×C42—191no—
230C2×C42C22×D1911yescharacteristic
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—192no—
235C4⋊C8—381no—
236C4⋊C8—381no—
237C4⋊C8—381no—
238C4⋊C8—764no—
239C4⋊C8C22⋊D1912yes—
240C4×C8—762no—
241C19#969411yescharacteristic, complemented, Sylow
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—761no—
249C2×Q8—761no—
250C2×Q8—761no—
251C2×Q8—761no—
252C2×Q8—761no—
253C2×Q8—761no—
254C22×C4—22no—
255C22×C4—192no—
256C22×C4—192no—
257C22×C4—382no—
258C22×C4C2×C4×D1911yescharacteristic
259C22×C4D4×D1911yescharacteristic
260C22×C4D4×D1911yescharacteristic
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—42no—
266C2×C8—382no—
267C2×C8—761no—
268C2×C8—761no—
269C2×C8—761no—
270C2×C8—762no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—382no—
276C4⋊C4—382no—
277C4⋊C4—768no—
278C4⋊C4—768no—
279C4⋊C4—761no—
280C4⋊C4—761no—
281C42—192no—
282C42—194no—
283C42—192no—
284C42—194no—
285C42—384no—
286C42—381no—
287C42—381no—
288C42#6454111yescharacteristic
289C42D4×D1911yescharacteristic
290C42#6454311yescharacteristic
291C42C2×C22⋊D1911yescharacteristic
292C23C22⋊C4×D1911yescharacteristic
293Q8—81no—
294Q8—81no—
295Q8—81no—
296Q8—81no—
297Q8—1521no—
298Q8—1521no—
299Q8—1521no—
300Q8—1521no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—194no—
306C2×C4—194no—
307C2×C4—194no—
308C2×C4—194no—
309C2×C4—382no—
310C2×C4—382no—
311C2×C4—762no—
312C2×C4—762no—
313C2×C4—762no—
314C2×C4(C22⋊D19)⋊C411yescharacteristic
315C2×C4#1059733011yescharacteristic
316C2×C4#1059733111yescharacteristic
317C2×C4D8×D1911yescharacteristic
318C2×C4#1059735711yescharacteristic
319C2×C4SD16×D1912yes—
320C2×C4SD16×D1911yescharacteristic
321C2×C4#1059736011yescharacteristic
322C2×C4Q16×D1912yes—
323C2×C4C4×C22⋊D1911yescharacteristic
324C2×C4#1059738511yescharacteristic
325C2×C4#1059738611yescharacteristic
326C8—42no—
327C8—81no—
328C8—762no—
329C8—1521no—
330C22#1192644411yescharacteristic
331C22#101×D1912yes—
332C22#102×D1911yescharacteristic
333C22#103×D1912yes—
334C22#1192654711yescharacteristic
335C4—21no—
336C4—21no—
337C4—82no—
338C4—198no—
339C4—384no—
340C4—1522no—
341C4#1192673711yescharacteristic
342C4#1192673811yescharacteristic
343C4#1192674211yescharacteristic
344C4#1192674311yescharacteristic
345C4#1192689312yes—
346C4#1192691511yescharacteristic
347C4#1192692211yescharacteristic
348C2D19×#33212yes—
349C2#1456231812yes—
350C2#1456443511yescharacteristic
351C2#1456447711yescharacteristic
352C2#1456456011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#332C2
socle, prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenterC2×#332D19
hypocenterC19#9694
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
178. Dic19#332semidirect
241. C19#9694semidirect

Maximal subgroups

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

subgroupindex
#145720312
#145637862
C4⋊C8×Dic192
C2×#119262912
C2×#119262902
C2×#119262892
C2×C19×#3322
#969419