Finite Group Databasebeta

← #18085152

Subgroups — #18085152

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×#11926894C211yesmaximal, characteristic
2C2×#11926839C211yesmaximal, characteristic
3#14564572C211yesmaximal, characteristic
4C2×#11926292C211yesmaximal, characteristic
5C2×#11926290C211yesmaximal, characteristic
6#14561469C211yesmaximal, characteristic
7C2×C19×#475C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9#11926894—22no—
10#11926894—22no—
11#11926839—22no—
12#11926839—22no—
13C2×#10597264—21no—
14C2×C4⋊(C19⋊C8)C2211yescharacteristic
15C2×C4⋊(C19⋊C8)C2211yescharacteristic
16C2×#10597292—22no—
17C2×#10597292—21no—
18C2×C4×C19⋊C8C2211yescharacteristic
19#11926299—22no—
20#11926292—22no—
21#11926290—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×Dic38—21no—
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—
49C22×C19⋊C8—21no—
50C22×C19⋊C8—21no—
51C22×C19⋊C8D412yes—
52#10597315—21no—
53#10597315—21no—
54#10597315—21no—
55#10597315D412yes—
56C19×#106—24no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8D412yes—
59C19×#103—24no—
60#10597292—24no—
61#10597292—28no—
62#10597264—24no—
63C4⋊(C19⋊C8)—21no—
64C4⋊(C19⋊C8)—21no—
65C4⋊(C19⋊C8)—21no—
66C4⋊(C19⋊C8)D412yes—
67C4×C19⋊C8—21no—
68C4×C19⋊C8—21no—
69C2×Q8×C19—21no—
70C2×Q8×C19—21no—
71C2×Q8×C19—21no—
72C2×Q8×C19—22no—
73C2×Q8×C19—21no—
74C2×Q8×C19—21no—
75C2×Q8×C19—41no—
76C2×Q8×C19—42no—
77C2×Q8×C19—42no—
78C2×Q8×C19Q1612yes—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—41no—
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19#4111yescharacteristic
85C22×Dic19—41no—
86C2×Dic38—22no—
87C2×Dic38—41no—
88C2×Dic38—82no—
89C2×C8×C19—22no—
90C2×C8×C19—41no—
91C2×C8×C19—41no—
92C4⋊C4×C19—22no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—41no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—41no—
100C42×C19—41no—
101C42×C19—41no—
102C42×C19C2×D411yescharacteristic
103C42×C19C2×D411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19C2×D411yescharacteristic
106C4⋊Dic19—22no—
107C4⋊Dic19—22no—
108C4⋊Dic19—41no—
109C4⋊Dic19—41no—
110C2×C19⋊C8—22no—
111C2×C19⋊C8—22no—
112C2×C19⋊C8—22no—
113C2×C19⋊C8—22no—
114C2×C19⋊C8—41no—
115C2×C19⋊C8—41no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—42no—
118#10277—191nomaximal, Sylow
119C23×C19#12111yescharacteristic
120Q8×C19—22no—
121Q8×C19—22no—
122Q8×C19—41no—
123Q8×C19—41no—
124Q8×C19—44no—
125Q8×C19—81no—
126Q8×C19—81no—
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—42no—
134C2×C4×C19—82no—
135C2×C4×C19#12011yescharacteristic
136C2×C4×C19#12011yescharacteristic
137C2×C4×C19#12011yescharacteristic
138C2×C4×C19#12111yescharacteristic
139C2×C4×C19#12111yescharacteristic
140C2×C4×C19#12711yescharacteristic
141C2×C4×C19C2×Q1611yescharacteristic
142C2×C4×C19#13511yescharacteristic
143C2×C4×C19#13512yes—
144C2×C4×C19#13711yescharacteristic
145C2×C4×C19#13711yescharacteristic
146C2×C4×C19#13712yes—
147C2×Dic19—42no—
148C2×Dic19—82no—
149Dic38—82no—
150Dic38—82no—
151C8×C19—42no—
152C19⋊C8—42no—
153C19⋊C8—42no—
154C19⋊C8—81no—
155C2×#487—191no—
156C2×#477—191no—
157C2×#475D1911yescharacteristic
158#1984—191no—
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—82no—
171C4×C19—81no—
172C4×C19#45111yescharacteristic
173C4×C19#45111yescharacteristic
174C4×C19#45212yes—
175C4×C19#45211yescharacteristic
176C4×C19#45211yescharacteristic
177C4×C19#49511yescharacteristic
178C4×C19#49711yescharacteristic
179Dic19—82no—
180C2×C4⋊Q8—191no—
181C2×C4⋊Q8C2×D1911yescharacteristic
182C2×C4×Q8C2×D1911yescharacteristic
183#487—382no—
184#487—382no—
185#477—382no—
186#477—382no—
187#475—22no—
188#475—22no—
189C2×#107—381no—
190C2×#106—21no—
191C2×C4⋊C8—191no—
192C2×C4⋊C8—191no—
193C2×C4⋊C8C2×D1911yescharacteristic
194C2×#103—21no—
195C2×#103—382no—
196C2×#103—381no—
197C2×C4×C8—191no—
198#336—382no—
199#333—382no—
200#332—382no—
201C2×C19#168412yes—
202C2×C19#170412yes—
203C2×C19#200111yescharacteristic
204C2×C19#201511yescharacteristic
205C2×C19#201911yescharacteristic
206C22×Q8—21no—
207C22×Q8—381no—
208C22×Q8C22⋊D1911yescharacteristic
209C22×C8—21no—
210C22×C8—192no—
211C22×C8—381no—
212C22×C8—381no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—192no—
217C4⋊Q8—381no—
218C4⋊Q8—381no—
219C4⋊Q8—381no—
220C4⋊Q8C22⋊D1912yes—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4—381no—
230C2×C4⋊C4C22⋊D1911yescharacteristic
231C2×C42—21no—
232C2×C42C22×D1911yescharacteristic
233#107—384no—
234#106—24no—
235C4⋊C8—21no—
236C4⋊C8—192no—
237C4⋊C8—381no—
238C4⋊C8—381no—
239C4⋊C8—381no—
240C4⋊C8C22⋊D1912yes—
241#103—24no—
242#103—384no—
243#103—388no—
244C4×C8—381no—
245C4×C8—381no—
246C19#1027711yescharacteristic, complemented, Sylow
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—22no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—41no—
254C2×Q8—42no—
255C2×Q8—42no—
256C2×Q8—382no—
257C2×Q8—761no—
258C2×Q8—1522no—
259C2×Q8#6452812yes—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—761no—
264C22×C4D4×D1911yescharacteristic
265C22×C4#6454311yescharacteristic
266C22×C4C2×C22⋊D1911yescharacteristic
267C2×C8—22no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—382no—
271C2×C8—382no—
272C2×C8—382no—
273C2×C8—382no—
274C2×C8—761no—
275C2×C8—761no—
276C2×C8—761no—
277C2×C8—762no—
278C4⋊C4—21no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—382no—
287C4⋊C4—382no—
288C4⋊C4—761no—
289C4⋊C4—761no—
290C42—41no—
291C42—41no—
292C42D4×D1911yescharacteristic
293C42D4×D1911yescharacteristic
294C42C2×C22⋊D1911yescharacteristic
295C42C2×C22⋊D1911yescharacteristic
296C23#1059738511yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—41no—
300Q8—41no—
301Q8—44no—
302Q8—81no—
303Q8—81no—
304Q8—1522no—
305Q8—1522no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—82no—
314C2×C4—762no—
315C2×C4—1522no—
316C2×C4#1059736112yes—
317C2×C4#1059736212yes—
318C2×C4#1059738311yescharacteristic
319C2×C4#1059738311yescharacteristic
320C2×C4#1059738411yescharacteristic
321C2×C4#1059738511yescharacteristic
322C2×C4#1059738611yescharacteristic
323C2×C4#1059738811yescharacteristic
324C2×C4C2×#6452811yescharacteristic
325C2×C4#1059739611yescharacteristic
326C2×C4#1059739711yescharacteristic
327C2×C4#1059739911yescharacteristic
328C8—42no—
329C8—762no—
330C8—762no—
331C8—1521no—
332C22#1192645211yescharacteristic
333C22#1192676412yes—
334C22#1192678311yescharacteristic
335C22#1192680011yescharacteristic
336C22#1192680912yes—
337C4—21no—
338C4—21no—
339C4—42no—
340C4—82no—
341C4—81no—
342C4—1522no—
343C4#1192669911yescharacteristic
344C4#1192670011yescharacteristic
345C4#1192670312yes—
346C4#1192670411yescharacteristic
347C4#1192670611yescharacteristic
348C4#1192692511yescharacteristic
349C4#1192693511yescharacteristic
350C2#1456309112yes—
351C2#1456321512yes—
352C2#1456464311yescharacteristic
353C2#1456472711yescharacteristic
354C2#1456474611yescharacteristic
subgroupG/H
centerC23#10597385
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC2×C19×#475C2
socle, prime radicalC23×C19#121
hypercenterC2×#475D19
hypocenterC19#10277
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
246. C19#10277semidirect

Maximal subgroups

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

subgroupindex
C2×#119268942
C2×#119268392
#145645722
C2×#119262922
C2×#119262902
#145614692
C2×C19×#4752
#1027719