Finite Group Databasebeta

← #18085887

Subgroups — #18085887

Order 4864.

620 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14569749C211yesmaximal, characteristic
2#14563942C212yesmaximal
3C2×#11926280C212yesmaximal
4#14561478C211yesmaximal, characteristic
5C19×#1444C211yesmaximal, characteristic
6C2×#10597370C2212yes—
7C2×#10597267—22no—
8C2×C22⋊(C19⋊C8)C2212yes—
9#11926476—22no—
10#11926465—22no—
11#11926404—21no—
12#11926404—21no—
13#11926306—22no—
14#11926280—24no—
15C22×C4⋊C4×C19—21no—
16C22×C4⋊C4×C19C2211yescharacteristic
17C2×C19×#95—21no—
18C2×C19×#95C2211yescharacteristic
19C2×C19×#95C2211yescharacteristic
20C23×C4×C19—21no—
21C23×C4×C19—21no—
22C23×C4×C19D411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C22×Dic38D412yes—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19—42no—
28C2×C4⋊C4×C19—42no—
29C2×C4⋊C4×C19—42no—
30C2×C4⋊C4×C19—42no—
31C2×C22⋊Dic19—22no—
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19D412yes—
37#10597370—22no—
38#10597370—22no—
39#10597370—22no—
40#10597370—22no—
41C2×Dic19⋊C4—22no—
42C22×C19⋊C8—22no—
43C19×#95—22no—
44C19×#95—21no—
45C19×#95—42no—
46C19×#95D412yes—
47C19⋊#95—22no—
48C19⋊#95—22no—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)—22no—
51#10597267—44no—
52C24×C19C2×D411yescharacteristic
53C22×C4×C19—22no—
54C22×C4×C19—22no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—22no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—22no—
61C22×C4×C19—41no—
62C22×C4×C19—41no—
63C22×C4×C19—41no—
64C22×C4×C19—41no—
65C22×C4×C19—41no—
66C22×C4×C19—41no—
67C22×C4×C19—41no—
68C22×C4×C19—41no—
69C22×C4×C19—41no—
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×C19SD1612yes—
78C22×C4×C19Q1612yes—
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D412yes—
81C22×C4×C19#4111yescharacteristic
82C22×C4×C19#4112yes—
83C22×Dic19—22no—
84C22×Dic19—22no—
85C2×Dic38—22no—
86C2×Dic38—22no—
87C2×Dic38—42no—
88C2×Dic38—42no—
89C4⋊C4×C19—24no—
90C4⋊C4×C19—42no—
91C4⋊C4×C19—48no—
92C22⋊Dic19—42no—
93C22⋊Dic19—42no—
94C4⋊Dic19—22no—
95C4⋊Dic19—22no—
96C4⋊Dic19—81no—
97C4⋊Dic19—81no—
98C4⋊Dic19—81no—
99C4⋊Dic19—81no—
100Dic19⋊C4—42no—
101Dic19⋊C4—42no—
102C2×C19⋊C8—42no—
103C2×C19⋊C8—42no—
104C2×C19⋊C8—42no—
105#10406—191nomaximal, Sylow
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19#12011yescharacteristic
111C23×C19#12111yescharacteristic
112C23×C19#12411yescharacteristic
113C23×C19C2×SD1611yescharacteristic
114C23×C19C2×Q1611yescharacteristic
115C23×C19#13711yescharacteristic
116C23×C19#13711yescharacteristic
117C2×C4×C19—22no—
118C2×C4×C19—22no—
119C2×C4×C19—24no—
120C2×C4×C19—22no—
121C2×C4×C19—22no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—42no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19—42no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—42no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—42no—
140C2×C4×C19—81no—
141C2×C4×C19—81no—
142C2×C4×C19—81no—
143C2×C4×C19—81no—
144C2×C4×C19—81no—
145C2×C4×C19—81no—
146C2×C4×C19#12112yes—
147C2×C4×C19#12312yes—
148C2×Dic19—42no—
149C2×Dic19—42no—
150C2×Dic19—42no—
151C2×Dic19—42no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154Dic38—44no—
155Dic38—82no—
156C19⋊C8—82no—
157#2659—191no—
158#1872—192no—
159C2×#328—192no—
160#1444D1911yescharacteristic
161#1280—191no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19#39411yescharacteristic
175C22×C19#44811yescharacteristic
176C22×C19#45111yescharacteristic
177C22×C19#45311yescharacteristic
178C22×C19#45611yescharacteristic
179C22×C19B(4,𝔽2)11yescharacteristic
180C22×C19#45811yescharacteristic
181C22×C19#46111yescharacteristic
182C22×C19#46211yescharacteristic
183C22×C19#48711yescharacteristic
184C22×C19#49111yescharacteristic
185C4×C19—22no—
186C4×C19—22no—
187C4×C19—44no—
188C4×C19—42no—
189C4×C19—42no—
190C4×C19—82no—
191Dic19—82no—
192Dic19—82no—
193C2×C22⋊Q8—192no—
194C22×C4⋊C4—21no—
195C22×C4⋊C4C2×D1911yescharacteristic
196C2×#103—382no—
197C2×C22⋊C8—192no—
198#398—382no—
199#395—382no—
200#380—381no—
201#380—381no—
202C2×#95—21no—
203C2×#95C2×D1911yescharacteristic
204C2×#95C2×D1911yescharacteristic
205#340—382no—
206#328—384no—
207C2×C19—21no—
208C2×C19—21no—
209C2×C19—21no—
210C2×C19—21no—
211C2×C19#159611yescharacteristic
212C2×C19#160511yescharacteristic
213C2×C19#161111yescharacteristic
214C2×C19#161411yescharacteristic
215C2×C19#203911yescharacteristic
216C2×C19#204311yescharacteristic
217C2×C19#204411yescharacteristic
218C22×Q8—192no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4C22⋊D1911yescharacteristic
222C23×C4C22⋊D1911yescharacteristic
223C23×C4C22×D1911yescharacteristic
224C22×C8—382no—
225C22⋊Q8—382no—
226C22⋊Q8—382no—
227C22⋊Q8—382no—
228C22⋊Q8—382no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—42no—
231C2×C4⋊C4—42no—
232C2×C4⋊C4—42no—
233C2×C4⋊C4—42no—
234C2×C4⋊C4—192no—
235C2×C4⋊C4—382no—
236C2×C4⋊C4—381no—
237C2×C4⋊C4—381no—
238C2×C4⋊C4—381no—
239C2×C4⋊C4—381no—
240C2×C22⋊C4—382no—
241#103—764no—
242C22⋊C8—382no—
243C22⋊C8—382no—
244#95—21no—
245#95—22no—
246#95—42no—
247#95—382no—
248#95—382no—
249#95D7612yes—
250C19#1040611yescharacteristic, complemented, Sylow
251C24C2×C22⋊D1911yescharacteristic
252C2×Q8—382no—
253C2×Q8—382no—
254C2×Q8—762no—
255C2×Q8—762no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
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—382no—
281C22×C4—382no—
282C22×C4#6452612yes—
283C22×C4#6452812yes—
284C22×C4C2×D7611yescharacteristic
285C22×C4#6454111yescharacteristic
286C22×C4D4×D1912yes—
287C22×C4#6454512yes—
288C2×C8—762no—
289C2×C8—762no—
290C2×C8—762no—
291C4⋊C4—24no—
292C4⋊C4—42no—
293C4⋊C4—48no—
294C4⋊C4—382no—
295C4⋊C4—382no—
296C4⋊C4—762no—
297C4⋊C4—762no—
298C4⋊C4—1521no—
299C4⋊C4—1521no—
300C4⋊C4—1521no—
301C4⋊C4—1521no—
302C22⋊C4—762no—
303C22⋊C4—762no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23#1059737611yescharacteristic
309C23C2×#6452611yescharacteristic
310C23#1059738311yescharacteristic
311C23C2×#6452811yescharacteristic
312C23#1059739311yescharacteristic
313C23#1059739711yescharacteristic
314C23#1059739711yescharacteristic
315Q8—764no—
316Q8—1522no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—762no—
347C2×C4—762no—
348C2×C4—762no—
349C2×C4—762no—
350C2×C4—762no—
351C2×C4—762no—
352C2×C4#1059734012yes—
353C2×C4#1059734112yes—
354C8—1522no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22#1192646111yescharacteristic
368C22#1192668211yescharacteristic
369C22#1192669911yescharacteristic
370C22#1192671111yescharacteristic
371C22#1192672611yescharacteristic
372C22#1192673011yescharacteristic
373C22#1192673311yescharacteristic
374C22#1192674911yescharacteristic
375C22#1192675411yescharacteristic
376C22#1192689611yescharacteristic
377C22#1192691411yescharacteristic
378C4—22no—
379C4—22no—
380C4—44no—
381C4—42no—
382C4—42no—
383C4—82no—
384C4—1522no—
385C4—1522no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2#1456255711yescharacteristic
391C2#1456260811yescharacteristic
392C2#1456264211yescharacteristic
393C2#1456265911yescharacteristic
394C2#1456485911yescharacteristic
395C2#1456488111yescharacteristic
396C2#1456488611yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1444C2
socleC23×C19#120
prime radicalC24×C19C2×D4
hypercenter#1444D19
hypocenterC19#10406
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1444

Complements

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

NH ≅ G/Ntype
250. C19#10406semidirect

Maximal subgroups

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

subgroupindex
#145697492
#145639422
C2×#119262802
#145614782
C19×#14442
#1040619