Finite Group Databasebeta

← #18085153

Subgroups — #18085153

Order 4864.

510 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926895C211yesmaximal, characteristic
2C2×#11926839C211yesmaximal, characteristic
3C2×#11926829C211yesmaximal, characteristic
4C2×#11926292C211yesmaximal, characteristic
5C2×#11926291C211yesmaximal, characteristic
6#14561470C211yesmaximal, characteristic
7C19×#1984C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597315C2211yescharacteristic
10#11926895—22no—
11#11926895—22no—
12#11926839—22no—
13#11926839—22no—
14#11926829—22no—
15#11926829—22no—
16C2×#10597264—21no—
17C2×#10597265—21no—
18C2×C4⋊(C19⋊C8)C2211yescharacteristic
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20C2×#10597273—22no—
21C2×#10597292—21no—
22C2×#10597292—21no—
23#11926292—22no—
24#11926291—22no—
25C2×C4×Q8×C19C2211yescharacteristic
26C2×C19×C4⋊C8C2211yescharacteristic
27C2×C4×C8×C19C2211yescharacteristic
28C19×#336—22no—
29C22×Q8×C19D411yescharacteristic
30C22×Dic38—21no—
31C22×Dic38—21no—
32C22×C8×C19—21no—
33C22×C8×C19D412yes—
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—
46C22×C19⋊C8—21no—
47C22×C19⋊C8—21no—
48#10597315—21no—
49#10597315—21no—
50#10597315—21no—
51#10597315—21no—
52#10597315—21no—
53#10597315—21no—
54#10597315D412yes—
55#10597315D412yes—
56C19×C4⋊C8—21no—
57C19×C4⋊C8—21no—
58C4×C8×C19—21no—
59C4×C8×C19—21no—
60#10597292—24no—
61#10597292—24no—
62#10597273—28no—
63#10597265—24no—
64#10597264—24no—
65C4⋊(C19⋊C8)—21no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)D412yes—
68C4⋊(C19⋊C8)D412yes—
69C2×Q8×C19—21no—
70C2×Q8×C19—21no—
71C2×Q8×C19—21no—
72C2×Q8×C19—21no—
73C2×Q8×C19—21no—
74C2×Q8×C19Q1612yes—
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19#4111yescharacteristic
80C22×Dic19—41no—
81C22×Dic19—41no—
82C2×Dic38—22no—
83C2×Dic38—22no—
84C2×Dic38—42no—
85C2×Dic38—42no—
86C2×Dic38—41no—
87C2×Dic38—41no—
88C2×Dic38—82no—
89C2×C8×C19—22no—
90C2×C8×C19—22no—
91C2×C8×C19—22no—
92C2×C8×C19—41no—
93C2×C8×C19—42no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—41no—
97C4⋊C4×C19—41no—
98C42×C19—41no—
99C42×C19—41no—
100C42×C19C2×D411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C42×C19C2×D411yescharacteristic
103C42×C19C2×D411yescharacteristic
104C4⋊Dic19—22no—
105C4⋊Dic19—22no—
106C4⋊Dic19—22no—
107C4⋊Dic19—22no—
108C4⋊Dic19—41no—
109C4⋊Dic19—41no—
110C4⋊Dic19—41no—
111C4⋊Dic19—41no—
112C2×C19⋊C8—22no—
113C2×C19⋊C8—22no—
114C2×C19⋊C8—41no—
115C2×C19⋊C8—41no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—41no—
118#10277—191nomaximal, Sylow
119C23×C19#12111yescharacteristic
120Q8×C19—22no—
121Q8×C19—22no—
122Q8×C19—41no—
123Q8×C19—41no—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—42no—
130C2×C4×C19#12011yescharacteristic
131C2×C4×C19#12011yescharacteristic
132C2×C4×C19#12011yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19#12111yescharacteristic
135C2×C4×C19#12711yescharacteristic
136C2×C4×C19C2×Q1611yescharacteristic
137C2×C4×C19#13512yes—
138C2×C4×C19#13511yescharacteristic
139C2×C4×C19#13712yes—
140C2×C4×C19#13711yescharacteristic
141C2×C4×C19#13711yescharacteristic
142C2×Dic19—42no—
143C2×Dic19—42no—
144C2×Dic19—82no—
145C2×Dic19—82no—
146Dic38—44no—
147Dic38—82no—
148Dic38—81no—
149Dic38—81no—
150Dic38—82no—
151C8×C19—42no—
152C8×C19—81no—
153C19⋊C8—42no—
154C19⋊C8—42no—
155C2×#487—191no—
156C2×#477—191no—
157C2×#475—191no—
158#1984D1911yescharacteristic
159C2×#333—191no—
160C2×#332—191no—
161#1277—191no—
162C22×C19#39211yescharacteristic
163C22×C19#46412yes—
164C22×C19#46711yescharacteristic
165C22×C19#47011yescharacteristic
166C22×C19#47112yes—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—42no—
170C4×C19—81no—
171C4×C19#45111yescharacteristic
172C4×C19#45111yescharacteristic
173C4×C19#45212yes—
174C4×C19#45211yescharacteristic
175C4×C19#45211yescharacteristic
176C4×C19#49511yescharacteristic
177C4×C19#49711yescharacteristic
178Dic19—82no—
179Dic19—82no—
180C2×C4⋊Q8—191no—
181C2×C4⋊Q8—191no—
182C2×C4×Q8C2×D1911yescharacteristic
183#487—382no—
184#487—382no—
185#477—382no—
186#477—382no—
187#475—382no—
188#475—382no—
189C2×#107—381no—
190C2×#106—381no—
191C2×C4⋊C8—191no—
192C2×C4⋊C8—191no—
193C2×C4⋊C8C2×D1911yescharacteristic
194C2×#103—381no—
195C2×#103—381no—
196C2×#103—382no—
197C2×C4×C8C2×D1911yescharacteristic
198#336—22no—
199#333—382no—
200#332—382no—
201C2×C19#168412yes—
202C2×C19#170412yes—
203C2×C19#200111yescharacteristic
204C2×C19#201511yescharacteristic
205C2×C19#201911yescharacteristic
206C22×Q8—381no—
207C22×Q8—381no—
208C22×Q8D7611yescharacteristic
209C22×C8—21no—
210C22×C8—381no—
211C22×C8—381no—
212C22×C8C22⋊D1912yes—
213C4⋊Q8—192no—
214C4⋊Q8—192no—
215C4⋊Q8—381no—
216C4⋊Q8—381no—
217C4⋊Q8—381no—
218C4⋊Q8—381no—
219C4⋊Q8—381no—
220C4⋊Q8—381no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4—381no—
230C2×C4⋊C4D7611yescharacteristic
231C2×C42—21no—
232C2×C42C22×D1911yescharacteristic
233#107—384no—
234#106—384no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—192no—
238C4⋊C8—192no—
239C4⋊C8—381no—
240C4⋊C8—381no—
241#103—388no—
242#103—384no—
243#103—384no—
244C4×C8—21no—
245C4×C8—21no—
246C19#1027711yescharacteristic, complemented, Sylow
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—382no—
253C2×Q8—382no—
254C2×Q8—761no—
255C2×Q8—761no—
256C2×Q8—762no—
257C2×Q8—762no—
258C2×Q8—1522no—
259C2×Q8Dic7612yes—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—761no—
263C22×C4—761no—
264C22×C4C2×D7611yescharacteristic
265C22×C4#6454111yescharacteristic
266C22×C4C2×C22⋊D1911yescharacteristic
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—42no—
272C2×C8—382no—
273C2×C8—382no—
274C2×C8—761no—
275C2×C8—761no—
276C2×C8—761no—
277C2×C8—761no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—382no—
283C4⋊C4—382no—
284C4⋊C4—382no—
285C4⋊C4—382no—
286C4⋊C4—761no—
287C4⋊C4—761no—
288C4⋊C4—761no—
289C4⋊C4—761no—
290C42—41no—
291C42—41no—
292C42D4×D1911yescharacteristic
293C42D4×D1911yescharacteristic
294C42D4×D1911yescharacteristic
295C42D4×D1911yescharacteristic
296C23#1059737611yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—41no—
300Q8—41no—
301Q8—764no—
302Q8—1522no—
303Q8—1522no—
304Q8—1521no—
305Q8—1521no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—762no—
313C2×C4—762no—
314C2×C4—1522no—
315C2×C4—1522no—
316C2×C4#1059732811yescharacteristic
317C2×C4#1059732811yescharacteristic
318C2×C4#1059733011yescharacteristic
319C2×C4#1059733011yescharacteristic
320C2×C4#1059735011yescharacteristic
321C2×C4C2×Dic7611yescharacteristic
322C2×C4#1059735511yescharacteristic
323C2×C4#1059735511yescharacteristic
324C2×C4#1059738311yescharacteristic
325C2×C4#1059738611yescharacteristic
326C2×C4#1059738812yes—
327C2×C4#1059739612yes—
328C8—42no—
329C8—81no—
330C8—762no—
331C8—762no—
332C22#1192645311yescharacteristic
333C22#1192676612yes—
334C22#1192678511yescharacteristic
335C22#1192680211yescharacteristic
336C22#1192680712yes—
337C4—21no—
338C4—21no—
339C4—42no—
340C4—81no—
341C4—1522no—
342C4—1522no—
343C4#1192670211yescharacteristic
344C4#1192670211yescharacteristic
345C4#1192670412yes—
346C4#1192670811yescharacteristic
347C4#1192670811yescharacteristic
348C4#1192692611yescharacteristic
349C4#1192693611yescharacteristic
350C2#1456309312yes—
351C2#1456321712yes—
352C2#1456464511yescharacteristic
353C2#1456472811yescharacteristic
354C2#1456475011yescharacteristic
subgroupG/H
centerC23#10597376
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1984C2
socle, prime radicalC23×C19#121
hypercenter#1984D19
hypocenterC19#10277
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
246. C19#10277semidirect

Maximal subgroups

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

subgroupindex
C2×#119268952
C2×#119268392
C2×#119268292
C2×#119262922
C2×#119262912
#145614702
C19×#19842
#1027719