Finite Group Databasebeta

← #18075122

Subgroups — #18075122

Order 4864.

794 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 794 conjugacy classes of subgroups — too many to draw. Only its 119 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#14577438C211yesmaximal, characteristic
2#14564103C212yesmaximal, complemented
3#14561998C212yesmaximal, complemented
4#14561973C211yesmaximal, characteristic
5C19×#1870C211yesmaximal, characteristic
6#11927253—24no—
7#11927251—22no—
8D4×Dic38—22no—
9#11927175—21no—
10#11927170—21no—
11#11927170C412yes—
12#11927101—21no—
13C2×#10597370—21no—
14C2×#10597370C2212yes—
15#11927019C412yes—
16C2×#10597281—22no—
17#11926508C2212yes—
18#11926312—22no—
19#11926270—21no—
20#11926269—24no—
21#11926268—21no—
22C22×M16×C19C2211yescharacteristic
23C2×C4×D4×C19C2211yescharacteristic
24C2×C19×C22⋊C8—21no—
25C2×C19×C22⋊C8C2211yescharacteristic
26C19×#336—21no—
27C22×D4×C19C2×C411yescharacteristic
28C23×C4×C19D411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C22×Dic38—21no—
31C22×Dic38D412yes—
32C2×M16×C19—22no—
33C2×M16×C19—42no—
34C22×C8×C19—21no—
35C22×C8×C19—21no—
36C4×D4×C19—22no—
37C4×D4×C19—22no—
38C2×C4⋊C4×C19D411yescharacteristic
39C2×C22⋊C4×C19C2×C411yescharacteristic
40C2×C22⋊C4×C19D411yescharacteristic
41C2×C42×C19D411yescharacteristic
42C2×C22⋊Dic19—22no—
43C2×C22⋊Dic19C2×C414yes—
44D4×Dic19—24no—
45D4×Dic19—24no—
46#10597372—22no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19D412yes—
49#10597370—22no—
50#10597370—22no—
51#10597370—22no—
52#10597370—22no—
53#10597370—22no—
54#10597370—22no—
55#10597370—22no—
56#10597370—22no—
57C2×Dic19⋊C4—22no—
58C2×Dic19⋊C4D414yes—
59C2×#64520—22no—
60#10597336—24no—
61#10597334—24no—
62#10597324—24no—
63#10597324—24no—
64#10597324—24no—
65#10597324—24no—
66#10597316—22no—
67#10597315—21no—
68#10597315—21no—
69C4×Dic38—22no—
70C4×Dic38—22no—
71C19×C22⋊C8—22no—
72C19×C22⋊C8—42no—
73C22⋊(C19⋊C8)—22no—
74C22⋊(C19⋊C8)—22no—
75#10597281—44no—
76C24×C19C22⋊C411yescharacteristic
77C24×C19C22×C411yescharacteristic
78C2×D4×C19—22no—
79C2×D4×C19—22no—
80C2×D4×C19—22no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19—41no—
87C22×C4×C19C22⋊C411yescharacteristic
88C22×C4×C19C22⋊C411yescharacteristic
89C22×C4×C19C22⋊C411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D412yes—
92C22×C4×C19C2×D412yes—
93C22×C4×C19C2×D411yescharacteristic
94C22×Dic19—22no—
95C22×Dic19—22no—
96C22×Dic19C22⋊C414yes—
97C22×Dic19C22⋊C414yes—
98C2×Dic38—22no—
99C2×Dic38—22no—
100C2×Dic38—22no—
101C2×Dic38—22no—
102C2×Dic38—42no—
103C2×Dic38—42no—
104C2×Dic38—81no—
105C2×Dic38—81no—
106M16×C19—24no—
107M16×C19—42no—
108C2×C8×C19—22no—
109C2×C8×C19—41no—
110C2×C8×C19—41no—
111C2×C8×C19—41no—
112C2×C8×C19—41no—
113C2×C8×C19—41no—
114C4⋊C4×C19—22no—
115C22⋊C4×C19—22no—
116C22⋊C4×C19—22no—
117C42×C19—21no—
118C42×C19—21no—
119C22⋊Dic19—24no—
120C22⋊Dic19—24no—
121C22⋊Dic19—24no—
122C4⋊Dic19—22no—
123C4⋊Dic19—22no—
124C4⋊Dic19—22no—
125C4⋊Dic19—22no—
126C4⋊Dic19—22no—
127C4⋊Dic19—22no—
128Dic19⋊C4—24no—
129Dic19⋊C4—24no—
130Dic19⋊C4—24no—
131Dic19⋊C4—24no—
132C4×Dic19—24no—
133#64520—42no—
134#64520—42no—
135C2×C19⋊C8—42no—
136#8537—191nomaximal, Sylow
137C23×C19—21no—
138C23×C19—21no—
139C23×C19—21no—
140C23×C19—21no—
141C23×C19—41no—
142C23×C19—41no—
143C23×C19—41no—
144C23×C19—41no—
145C23×C19#10112yescomplemented
146C23×C19C2×C22⋊C412yes—
147C23×C19C2×C22⋊C411yescharacteristic
148D4×C19—28no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—22no—
152C2×C4×C19—21no—
153C2×C4×C19—22no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—41no—
158C2×C4×C19—42no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—81no—
164C2×C4×C19#10112yescomplemented
165C2×C4×C19#12011yescharacteristic
166C2×C4×C19#12011yescharacteristic
167C2×C4×C19#12012yes—
168C2×Dic19—24no—
169C2×Dic19—24no—
170C2×Dic19—44no—
171C2×Dic19—44no—
172C2×Dic19—82no—
173C2×Dic19—82no—
174Dic38—42no—
175Dic38—42no—
176Dic38—82no—
177Dic38—82no—
178Dic38—82no—
179C8×C19—42no—
180C8×C19—81no—
181C19⋊C8—82no—
182#3501—191no—
183#1901—192no—
184#1870D1911yescharacteristic
185#1472—192no—
186#1465—191no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—22no—
190C22×C19—22no—
191C22×C19—22no—
192C22×C19—22no—
193C22×C19—42no—
194C22×C19—41no—
195C22×C19—41no—
196C22×C19—81no—
197C22×C19—81no—
198C22×C19—81no—
199C22×C19#37911yescharacteristic
200C22×C19C2×#10111yescharacteristic
201C22×C19C2×#10111yescharacteristic
202C4×C19—22no—
203C4×C19—22no—
204C4×C19—21no—
205C4×C19—41no—
206C4×C19—41no—
207C4×C19B(4,𝔽2)11yescharacteristic
208C4×C19#45811yescharacteristic
209Dic19—44no—
210Dic19—44no—
211C22×M16C2×D1911yescharacteristic
212#554—382no—
213#554—384no—
214D4×Q8—382no—
215#544—381no—
216#543—192no—
217#543—381no—
218#533—381no—
219C2×C22⋊Q8—192no—
220C2×C22⋊Q8—381no—
221#518—192no—
222C2×C4×D4C2×D1911yescharacteristic
223C2×#101—382no—
224#407—192no—
225C2×C22⋊C8—21no—
226C2×C22⋊C8C2×D1911yescharacteristic
227#343—382no—
228#336—21no—
229#324—384no—
230#324—381no—
231#323—381no—
232C2×C19—21no—
233C2×C19—21no—
234C2×C19—42no—
235C2×C19—42no—
236C2×C19#178411yescharacteristic
237C2×C19#179011yescharacteristic
238C2×C19#179111yescharacteristic
239C22×Q8—192no—
240C22×Q8—381no—
241C22×D4C4×D1911yescharacteristic
242C23×C4C22⋊D1911yescharacteristic
243C23×C4C22×D1911yescharacteristic
244C2×M16—22no—
245C2×M16—42no—
246C2×M16—382no—
247C22×C8—21no—
248C22×C8—21no—
249C4⋊Q8—381no—
250C4⋊Q8—381no—
251C4⋊Q8—384no—
252#125—382no—
253#125—384no—
254C22⋊Q8—384no—
255C22⋊Q8—384no—
256C22⋊Q8—384no—
257C22⋊Q8—384no—
258C22⋊Q8—382no—
259C22⋊Q8—382no—
260C22⋊Q8—382no—
261C22⋊Q8—382no—
262C22⋊Q8—382no—
263C22⋊Q8—382no—
264C22⋊Q8—382no—
265C22⋊Q8—382no—
266C4×Q8—382no—
267C4×Q8—382no—
268C4×D4—22no—
269C4×D4—22no—
270C4×D4—384no—
271C4×D4—384no—
272#117—382no—
273C2×C4⋊C4—194no—
274C2×C4⋊C4—192no—
275C2×C4⋊C4—382no—
276C2×C4⋊C4—381no—
277C2×C4⋊C4D7611yescharacteristic
278C2×C22⋊C4—194no—
279C2×C22⋊C4—382no—
280C2×C22⋊C4C4×D1911yescharacteristic
281C2×C22⋊C4D7611yescharacteristic
282C2×C42C22⋊D1911yescharacteristic
283#101—764no—
284C22⋊C8—22no—
285C22⋊C8—42no—
286C22⋊C8—382no—
287C22⋊C8—382no—
288C19#853711yescharacteristic, complemented, Sylow
289C24(C2×D19)⋊C411yescharacteristic
290C24C2×C4×D1911yescharacteristic
291C2×Q8—382no—
292C2×Q8—382no—
293C2×Q8—382no—
294C2×Q8—382no—
295C2×Q8—762no—
296C2×Q8—762no—
297C2×Q8—1521no—
298C2×Q8—1521no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—22no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—194no—
309C22×C4—194no—
310C22×C4—382no—
311C22×C4—382no—
312C22×C4(C2×D19)⋊C411yescharacteristic
313C22×C4(C2×D19)⋊C411yescharacteristic
314C22×C4(C2×D19)⋊C411yescharacteristic
315C22×C4C2×D7611yescharacteristic
316C22×C4D4×D1912yes—
317C22×C4D4×D1912yes—
318C22×C4C2×C22⋊D1911yescharacteristic
319M16—24no—
320M16—42no—
321M16—762no—
322M16—762no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—762no—
330C4⋊C4—22no—
331C4⋊C4—384no—
332C4⋊C4—384no—
333C4⋊C4—382no—
334C4⋊C4—382no—
335C4⋊C4—382no—
336C4⋊C4—382no—
337C4⋊C4—384no—
338C4⋊C4—382no—
339C4⋊C4—384no—
340C4⋊C4—382no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—384no—
344C22⋊C4—384no—
345C22⋊C4—384no—
346C42—21no—
347C42—21no—
348C42—384no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23#1059728112yescomplemented
358C23C22⋊C4×D1912yes—
359C23C2×(C2×D19)⋊C411yescharacteristic
360Q8—762no—
361Q8—762no—
362Q8—1522no—
363Q8—1522no—
364Q8—1522no—
365D4—28no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—384no—
382C2×C4—384no—
383C2×C4—764no—
384C2×C4—764no—
385C2×C4—1522no—
386C2×C4—1522no—
387C2×C4#1059728112yescomplemented
388C2×C4#1059732812yes—
389C2×C4#1059738311yescharacteristic
390C2×C4#1059738311yescharacteristic
391C8—42no—
392C8—81no—
393C8—1522no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—42no—
401C22—41no—
402C22—41no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22#1192639911yescharacteristic
407C22C2×#1059728111yescharacteristic
408C22C2×#1059728111yescharacteristic
409C4—22no—
410C4—21no—
411C4—22no—
412C4—41no—
413C4—41no—
414C4—764no—
415C4—764no—
416C4#1192673011yescharacteristic
417C4#1192673311yescharacteristic
418C2—21no—
419C2—21no—
420C2—42no—
421C2—42no—
422C2#1456355811yescharacteristic
423C2#1456358211yescharacteristic
424C2#1456358511yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1870C2
socleC22×C19#379
prime radicalC22×D4×C19C2×C4
cosocleC23×C4×C19C23
hypercenter#1870D19
hypocenterC19#8537
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #14564103C2semidirect
3. #14561998C2semidirect
145. C23×C19#101semidirect
164. C2×C4×C19#101semidirect
288. C19#8537semidirect
357. C23#10597281semidirect
387. C2×C4#10597281semidirect

Maximal subgroups

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

subgroupindex
#145774382
#145641032
#145619982
#145619732
C19×#18702
#853719