Finite Group Databasebeta

← #18075153

Subgroups — #18075153

Order 4864.

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

normal subgroups only

This group has 910 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
1C22×#10597325C211yesmaximal, characteristic
2#14563709C211yesmaximal, characteristic
3#14563707C212yesmaximal
4#14563707C212yesmaximal
5C19×#1819C211yesmaximal, characteristic
6C2×#10597325—22no—
7C2×#10597325—22no—
8C2×#10597325—24no—
9C2×#10597325—24no—
10C22×C4⋊Dic19C411yescharacteristic, complemented
11C22×Dic19⋊C4C411yescharacteristic, complemented
12C22×Dic19⋊C4C411yescharacteristic, complemented
13C22×C22⋊Dic19C2211yescharacteristic
14C22×C22⋊Dic19C2211yescharacteristic
15C22×C4×Dic19C411yescharacteristic, complemented
16#11926400C2212yes—
17#11926311—22no—
18#11926310—24no—
19#11926310—24no—
20C22×C22⋊C4×C19C2211yescharacteristic
21C19×#379C2212yes—
22C19×#342—22no—
23C25×C19C2311yescharacteristic
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19C2×C411yescharacteristic
26C23×Dic19C2×C411yescharacteristic
27C23×Dic19C2×C411yescharacteristic
28C23×Dic19C2×C411yescharacteristic
29C23×Dic19C2×C411yescharacteristic
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19—22no—
32C2×C22⋊C4×C19—22no—
33C2×C22⋊C4×C19—22no—
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19D412yes—
36C2×C22⋊C4×C19D412yes—
37C2×C22⋊Dic19—21no—
38C2×C22⋊Dic19—22no—
39C2×C22⋊Dic19—21no—
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—22no—
42C2×C22⋊Dic19—21no—
43C2×C22⋊Dic19—22no—
44C2×C22⋊Dic19—22no—
45C2×C22⋊Dic19—22no—
46C2×C22⋊Dic19D414yes—
47C2×C22⋊Dic19D414yes—
48C2×C4⋊Dic19—22no—
49C2×C4⋊Dic19—22no—
50C2×C4⋊Dic19—22no—
51C2×Dic19⋊C4—22no—
52C2×Dic19⋊C4—22no—
53C2×Dic19⋊C4—22no—
54C2×Dic19⋊C4—22no—
55C2×Dic19⋊C4—22no—
56C2×Dic19⋊C4—22no—
57C2×C4×Dic19—22no—
58C2×C4×Dic19—22no—
59C2×C4×Dic19—22no—
60#10597325—216no—
61#10597325—216no—
62C24×C19—42no—
63C24×C19—42no—
64C24×C19—42no—
65C24×C19C22×C411yescharacteristic
66C24×C19C2×D411yescharacteristic
67C24×C19C2×D412yes—
68C24×C19C2×D412yes—
69C24×C19C2×D411yescharacteristic
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—42no—
75C22×C4×C19—42no—
76C22×C4×C19—42no—
77C22×C4×C19C22⋊C412yes—
78C22×C4×C19C22⋊C412yes—
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C22×Dic19—21no—
83C22×Dic19—21no—
84C22×Dic19—21no—
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—42no—
88C22×Dic19—42no—
89C22×Dic19—42no—
90C22×Dic19—42no—
91C22×Dic19—42no—
92C22×Dic19C22⋊C412yes—
93C22×Dic19C22⋊C412yes—
94C22×Dic19C22⋊C412yes—
95C22×Dic19C22⋊C412yes—
96C22⋊C4×C19—24no—
97C22⋊C4×C19—24no—
98C22⋊C4×C19—44no—
99C22⋊C4×C19—44no—
100C22⋊C4×C19—44no—
101C22⋊Dic19—24no—
102C22⋊Dic19—24no—
103C22⋊Dic19—24no—
104C22⋊Dic19—24no—
105C22⋊Dic19—44no—
106C22⋊Dic19—44no—
107C22⋊Dic19—44no—
108C4⋊Dic19—28no—
109Dic19⋊C4—28no—
110Dic19⋊C4—28no—
111C4×Dic19—28no—
112#8545—191nomaximal, Sylow
113C23×C19—22no—
114C23×C19—22no—
115C23×C19—22no—
116C23×C19—22no—
117C23×C19—24no—
118C23×C19—24no—
119C23×C19—22no—
120C23×C19—41no—
121C23×C19—41no—
122C23×C19—42no—
123C23×C19—42no—
124C23×C19—42no—
125C23×C19—42no—
126C23×C19—41no—
127C23×C19—41no—
128C23×C19—88no—
129C23×C19C2×C22⋊C411yescharacteristic
130C23×C19C2×C22⋊C411yescharacteristic
131C23×C19C2×C22⋊C411yescharacteristic
132C23×C19#12012yes—
133C23×C19#12012yes—
134C2×C4×C19—22no—
135C2×C4×C19—22no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—42no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19—82no—
143C2×C4×C19—82no—
144C2×C4×C19—82no—
145C2×Dic19—22no—
146C2×Dic19—22no—
147C2×Dic19—22no—
148C2×Dic19—22no—
149C2×Dic19—42no—
150C2×Dic19—42no—
151C2×Dic19—42no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155C2×Dic19—42no—
156C2×Dic19—42no—
157C2×Dic19—42no—
158C2×Dic19—42no—
159C2×Dic19—42no—
160C2×Dic19—42no—
161C2×Dic19—82no—
162C2×Dic19—82no—
163C2×Dic19—82no—
164C22×#126—191no—
165#1819—192no—
166#1819—192no—
167#1819—191no—
168#1819D1911yescharacteristic
169C22×C19—28no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—22no—
177C22×C19—22no—
178C22×C19—22no—
179C22×C19—22no—
180C22×C19—22no—
181C22×C19—22no—
182C22×C19—82no—
183C22×C19—84no—
184C22×C19—84no—
185C22×C19—82no—
186C22×C19#37911yescharacteristic
187C22×C19#41012yes—
188C22×C19#41012yes—
189C22×C19#41012yes—
190C4×C19—42no—
191C4×C19—42no—
192C4×C19—162no—
193Dic19—42no—
194Dic19—42no—
195Dic19—42no—
196Dic19—42no—
197Dic19—162no—
198C2×#126—384no—
199C2×#126—384no—
200C2×#126—382no—
201C2×#126—382no—
202C22×C4⋊C4—191no—
203C22×C4⋊C4—191no—
204C22×C4⋊C4—191no—
205C22×C22⋊C4—191no—
206C22×C22⋊C4—191no—
207C22×C22⋊C4C2×D1911yescharacteristic
208C22×C42—191no—
209#379—192no—
210#379C2×D1912yes—
211#342—22no—
212#342—384no—
213#342—384no—
214#342—382no—
215C2×C19—22no—
216C2×C19—22no—
217C2×C19—22no—
218C2×C19—42no—
219C2×C19—42no—
220C2×C19#178211yescharacteristic
221C2×C19#178211yescharacteristic
222C2×C19#178211yescharacteristic
223C25C22×D1911yescharacteristic
224C23×C4—191no—
225C23×C4—191no—
226C23×C4—191no—
227C23×C4—191no—
228C23×C4C4×D1911yescharacteristic
229C23×C4C4×D1911yescharacteristic
230#126—3816no—
231#126—3816no—
232C2×C4⋊C4—382no—
233C2×C4⋊C4—382no—
234C2×C4⋊C4—382no—
235C2×C4⋊C4—382no—
236C2×C4⋊C4—382no—
237C2×C4⋊C4—382no—
238C2×C4⋊C4—382no—
239C2×C4⋊C4—382no—
240C2×C4⋊C4—382no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—194no—
247C2×C22⋊C4—194no—
248C2×C22⋊C4—381no—
249C2×C22⋊C4—381no—
250C2×C22⋊C4—382no—
251C2×C22⋊C4—382no—
252C2×C22⋊C4—381no—
253C2×C22⋊C4—381no—
254C2×C22⋊C4—382no—
255C2×C22⋊C4—382no—
256C2×C22⋊C4—382no—
257C2×C22⋊C4D7612yes—
258C2×C22⋊C4C22⋊D1912yes—
259C2×C42—382no—
260C2×C42—382no—
261C2×C42—382no—
262C19#854511yescharacteristic, complemented, Sylow
263C24—42no—
264C24—42no—
265C24—42no—
266C24C2×C4×D1911yescharacteristic
267C24C2×D7611yescharacteristic
268C24D4×D1912yes—
269C24D4×D1912yes—
270C24C2×C22⋊D1911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—192no—
279C22×C4—192no—
280C22×C4—192no—
281C22×C4—192no—
282C22×C4—381no—
283C22×C4—381no—
284C22×C4—381no—
285C22×C4—381no—
286C22×C4—381no—
287C22×C4—381no—
288C22×C4—381no—
289C22×C4—381no—
290C22×C4—762no—
291C22×C4—762no—
292C22×C4—762no—
293C22×C4—762no—
294C22×C4—762no—
295C22×C4(C2×D19)⋊C412yes—
296C22×C4(C2×D19)⋊C412yes—
297C4⋊C4—388no—
298C4⋊C4—388no—
299C4⋊C4—388no—
300C22⋊C4—24no—
301C22⋊C4—24no—
302C22⋊C4—44no—
303C22⋊C4—44no—
304C22⋊C4—44no—
305C22⋊C4—384no—
306C22⋊C4—384no—
307C22⋊C4—384no—
308C22⋊C4—384no—
309C22⋊C4—764no—
310C22⋊C4—764no—
311C22⋊C4—764no—
312C42—388no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—24no—
317C23—24no—
318C23—22no—
319C23—22no—
320C23—41no—
321C23—41no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—41no—
327C23—41no—
328C23—88no—
329C23C22⋊C4×D1911yescharacteristic
330C23C22⋊C4×D1911yescharacteristic
331C23#1059732812yes—
332C23C2×(C2×D19)⋊C411yescharacteristic
333C23#1059738312yes—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—382no—
346C2×C4—382no—
347C2×C4—382no—
348C2×C4—382no—
349C2×C4—762no—
350C2×C4—762no—
351C2×C4—762no—
352C2×C4—762no—
353C2×C4—762no—
354C2×C4—762no—
355C2×C4—762no—
356C2×C4—762no—
357C2×C4—762no—
358C2×C4—762no—
359C2×C4—762no—
360C2×C4—762no—
361C2×C4—1522no—
362C2×C4—1522no—
363C2×C4—1522no—
364C22—28no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—84no—
378C22—84no—
379C22—82no—
380C22—82no—
381C22#1192639911yescharacteristic
382C22#1192651612yes—
383C22#1192651612yes—
384C22#1192651712yes—
385C4—42no—
386C4—42no—
387C4—162no—
388C4—3042no—
389C4—762no—
390C4—762no—
391C4—762no—
392C4—762no—
393C2—22no—
394C2—22no—
395C2—22no—
396C2—42no—
397C2—42no—
398C2#1456355111yescharacteristic
399C2#1456355111yescharacteristic
400C2#1456355211yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC24×C19C22×C4
FrattiniC25C22×D19
FittingC19×#1819C2
socleC22×C19#379
prime radical, cosocleC25×C19C23
hypercenter#1819D19
hypocenterC19#8545
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
10. C22×C4⋊Dic19C4semidirect
11. C22×Dic19⋊C4C4semidirect
12. C22×Dic19⋊C4C4semidirect
15. C22×C4×Dic19C4semidirect
262. C19#8545semidirect

Maximal subgroups

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

subgroupindex
C22×#105973252
#145637092
#145637072
C19×#18192
#854519