Finite Group Databasebeta

← #18082593

Subgroups — #18082593

Order 4864.

556 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563615C211yesmaximal, characteristic
2#14563397C211yesmaximal, characteristic
3#14561478C212yesmaximal
4#14561478C212yesmaximal
5C2×C19×#387C211yesmaximal, characteristic
6C2×C4⋊(C19⋊C8)—21no—
7C2×C22⋊(C19⋊C8)C2212yes—
8C2×C22⋊(C19⋊C8)C2212yes—
9C2×#10597260—21no—
10#11926299—21no—
11#11926299—21no—
12C22×C4⋊C4×C19C411yescharacteristic
13C22×C4⋊C4×C19C411yescharacteristic
14C22×C42×C19C2211yescharacteristic
15C19×#387—21no—
16C19×#387—21no—
17C19×#387—21no—
18C19×#387—21no—
19C2×C19×#95C411yescharacteristic
20C2×C19×#95C411yescharacteristic
21C2×C19×#95C2211yescharacteristic
22C2×C19×#95C2211yescharacteristic
23C23×C4×C19C2×C411yescharacteristic
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19C2×C411yescharacteristic
26C23×C4×C19C2×C411yescharacteristic
27C23×C4×C19C2×C411yescharacteristic
28C23×C4×C19C2×C411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19—22no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—42no—
37C2×C42×C19—42no—
38C2×C42×C19D411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×C42×C19D411yescharacteristic
42C22×C19⋊C8—22no—
43C22×C19⋊C8—22no—
44C19×#95—21no—
45C19×#95—21no—
46C19×#95—21no—
47C19×#95—21no—
48C19×#95—21no—
49C19×#95—21no—
50C19×#95—21no—
51C19×#95—21no—
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—24no—
54C22⋊(C19⋊C8)Q814yes—
55C4⋊(C19⋊C8)—42no—
56#10597260—42no—
57C24×C19C22×C411yescharacteristic
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—22no—
65C22×C4×C19—22no—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—22no—
69C22×C4×C19—22no—
70C22×C4×C19—41no—
71C22×C4×C19—41no—
72C22×C4×C19—41no—
73C22×C4×C19—41no—
74C22×C4×C19—41no—
75C22×C4×C19—41no—
76C22×C4×C19—41no—
77C22×C4×C19—41no—
78C22×C4×C19—41no—
79C22×C4×C19—41no—
80C22×C4×C19—41no—
81C22×C4×C19—41no—
82C22×C4×C19—41no—
83C22×C4×C19C22⋊C411yescharacteristic
84C22×C4×C19C22⋊C411yescharacteristic
85C22×C4×C19C22⋊C411yescharacteristic
86C22×C4×C19C22⋊C411yescharacteristic
87C22×C4×C19M1612yes—
88C22×C4×C19M1612yes—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×Q812yes—
92C22×C4×C19#4112yes—
93C4⋊C4×C19—24no—
94C4⋊C4×C19—24no—
95C4⋊C4×C19—42no—
96C4⋊C4×C19—42no—
97C42×C19—22no—
98C42×C19—22no—
99C42×C19—41no—
100C42×C19—41no—
101C2×C19⋊C8—24no—
102C2×C19⋊C8—42no—
103C2×C19⋊C8—42no—
104C2×C19⋊C8—42no—
105C2×C19⋊C8—42no—
106C2×C19⋊C8—42no—
107#9881—191nomaximal, Sylow
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—21no—
112C23×C19C2×C22⋊C411yescharacteristic
113C23×C19C4×Q812yes—
114C23×C19C2×M1611yescharacteristic
115C23×C19C2×M1611yescharacteristic
116C23×C19#13112yes—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—42no—
135C2×C4×C19—42no—
136C2×C4×C19—44no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—42no—
140C2×C4×C19—42no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—82no—
154C2×C4×C19—82no—
155C2×C4×C19#9912yes—
156C2×C4×C19C22⋊Q812yes—
157C2×C4×C19#12411yescharacteristic
158C2×C4×C19C4⋊Q811yescharacteristic
159C19⋊C8—44no—
160C19⋊C8—82no—
161C2×#387D1911yescharacteristic
162#1797—191no—
163#1749—191no—
164#1280—192no—
165#1280—192no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—22no—
171C22×C19—22no—
172C22×C19—22no—
173C22×C19—22no—
174C22×C19#39111yescharacteristic
175C22×C19#40711yescharacteristic
176C22×C19#40811yescharacteristic
177C22×C19C2×#9911yescharacteristic
178C22×C19#41011yescharacteristic
179C22×C19#41311yescharacteristic
180C22×C19#41311yescharacteristic
181C22×C19#44612yes—
182C22×C19#44612yes—
183C4×C19—22no—
184C4×C19—22no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—42no—
188C4×C19—41no—
189C4×C19—41no—
190C4×C19—42no—
191C4×C19—41no—
192C4×C19—81no—
193C4×C19—81no—
194C22×C4⋊C4Dic1911yescharacteristic
195C22×C4⋊C4Dic1911yescharacteristic
196C22×C42C2×D1911yescharacteristic
197C2×C4⋊C8—381no—
198C2×C22⋊C8—192no—
199C2×C22⋊C8—192no—
200C2×#97—381no—
201#387—21no—
202#387—21no—
203#387—21no—
204#387—21no—
205C2×#95Dic1911yescharacteristic
206C2×#95Dic1911yescharacteristic
207C2×#95C2×D1911yescharacteristic
208C2×#95C2×D1911yescharacteristic
209#336—381no—
210#336—381no—
211C2×C19—22no—
212C2×C19—22no—
213C2×C19#146411yescharacteristic
214C2×C19#146511yescharacteristic
215C2×C19#146811yescharacteristic
216C2×C19#147311yescharacteristic
217C2×C19#198511yescharacteristic
218C2×C19#199611yescharacteristic
219C2×C19#199811yescharacteristic
220C23×C4C2×Dic1911yescharacteristic
221C23×C4C2×Dic1911yescharacteristic
222C23×C4C2×Dic1911yescharacteristic
223C23×C4C2×Dic1911yescharacteristic
224C23×C4C2×Dic1911yescharacteristic
225C23×C4C2×Dic1911yescharacteristic
226C23×C4C22×D1911yescharacteristic
227C22×C8—382no—
228C22×C8—382no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—42no—
236C2×C42—42no—
237C2×C42C22⋊D1911yescharacteristic
238C2×C42C22⋊D1911yescharacteristic
239C2×C42C22⋊D1911yescharacteristic
240C2×C42C22⋊D1911yescharacteristic
241C4⋊C8—762no—
242C22⋊C8—194no—
243C22⋊C8—382no—
244C22⋊C8—384no—
245#97—762no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254C19#988111yescharacteristic, complemented, Sylow
255C24C22×Dic1911yescharacteristic
256C22×C4—22no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4#6452012yes—
282C22×C4#6452012yes—
283C22×C4C22⋊Dic1911yescharacteristic
284C22×C4C22⋊Dic1911yescharacteristic
285C22×C4C22⋊Dic1911yescharacteristic
286C22×C4C22⋊Dic1911yescharacteristic
287C22×C4Q8×D1912yes—
288C22×C4#6454512yes—
289C22×C4C2×C22⋊D1911yescharacteristic
290C22×C4C2×C22⋊D1911yescharacteristic
291C2×C8—384no—
292C2×C8—762no—
293C2×C8—762no—
294C2×C8—762no—
295C2×C8—762no—
296C2×C8—762no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C42—22no—
302C42—22no—
303C42—41no—
304C42—41no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×#6452011yescharacteristic
310C23C2×#6452011yescharacteristic
311C23Q8×Dic1912yes—
312C23#1059739412yes—
313C23C2×C22⋊Dic1911yescharacteristic
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4#1059729112yes—
353C2×C4#1059739011yescharacteristic
354C2×C4#1059739212yes—
355C2×C4#1059739311yescharacteristic
356C8—764no—
357C8—1522no—
358C22—22no—
359C22—22no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22#1192645111yescharacteristic
367C22#1192650811yescharacteristic
368C22#1192651111yescharacteristic
369C22C2×#1059729111yescharacteristic
370C22#1192651811yescharacteristic
371C22#1192652811yescharacteristic
372C22#1192652811yescharacteristic
373C22#1192667512yes—
374C22#1192667512yes—
375C4—22no—
376C4—21no—
377C4—21no—
378C4—22no—
379C4—42no—
380C4—41no—
381C4—41no—
382C4—42no—
383C4—41no—
384C4—81no—
385C4—81no—
386C2—22no—
387C2—22no—
388C2#1456196911yescharacteristic
389C2#1456197311yescharacteristic
390C2#1456198311yescharacteristic
391C2#1456200411yescharacteristic
392C2#1456457611yescharacteristic
393C2#1456462111yescharacteristic
394C2#1456462911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutator, prime radicalC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#387C2
socleC23×C19C2×C22⋊C4
cosocleC23×C4×C19C23
hypercenterC2×#387D19
hypocenterC19#9881
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
254. C19#9881semidirect

Maximal subgroups

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

subgroupindex
#145636152
#145633972
#145614782
C2×C19×#3872
#988119