Finite Group Databasebeta

← #18071349

Subgroups — #18071349

Order 4864.

536 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 87 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#14570006C211yesmaximal, characteristic
2#14564965C211yesmaximal, characteristic, complemented
3#14564718C211yesmaximal, characteristic
4#14561459C211yesmaximal, characteristic, complemented
5#14561458C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic
7C19×#2058C211yesmaximal, characteristic, complemented
8C22×#64527—21no—
9C2×#10597343—21no—
10C2×#10597342—21no—
11C2×#10597265—21no—
12C2×#10597292—21no—
13#11926466—21no—
14#11926466—21no—
15#11926465—21no—
16#11926446C2211yescharacteristic
17#11926442C2211yescharacteristic
18#11926422—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C19×#106—21no—
24C19×#389C2211yescharacteristic
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×D76D411yescharacteristic
29C22×C4×D19—21no—
30C22×Dic38—21no—
31C22×C8×C19—21no—
32C19×C4⋊Q8—42no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C42×C19C2311yescharacteristic
39C2×#64527—42no—
40C2×#64527—42no—
41C2×#64527—42no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19D411yescharacteristic
49C2×C4⋊Dic19D411yescharacteristic
50C2×C4⋊Dic19D411yescharacteristic
51C2×Dic19⋊C4—21no—
52C2×Dic19⋊C4—21no—
53C22×C19⋊C8—21no—
54C22×C19⋊C8—21no—
55#10597343—42no—
56#10597343—42no—
57#10597342—42no—
58#10597342—42no—
59C19×#106—42no—
60C19×#95—21no—
61#10597292—42no—
62C19⋊#95—21no—
63C19⋊#95—21no—
64#10597265—42no—
65C23×D19—21no—
66C2×Q8×C19—22no—
67C2×Q8×C19—41no—
68C2×Q8×C19—41no—
69C2×Q8×C19—41no—
70C2×Q8×C19—41no—
71C2×Q8×C19—41no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—41no—
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×Dic19—21no—
79C22×Dic19—21no—
80C22×Dic19—21no—
81C2×D76—21no—
82C2×D76—41no—
83C2×D76—41no—
84C2×D76SD1612yes—
85C2×C4×D19—42no—
86C2×C4×D19—42no—
87C2×C4×D19—81no—
88C2×Dic38—42no—
89C2×Dic38—42no—
90C2×Dic38—81no—
91C2×C8×C19—22no—
92C2×C8×C19—41no—
93C2×C8×C19—41no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—22no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—41no—
100C4⋊C4×C19—41no—
101C4⋊C4×C19—41no—
102C4⋊C4×C19SD1612yescomplemented
103C42×C19—41no—
104#64527—48no—
105(C2×D19)⋊C4—42no—
106(C2×D19)⋊C4—42no—
107(C2×D19)⋊C4—41no—
108(C2×D19)⋊C4—41no—
109(C2×D19)⋊C4—41no—
110(C2×D19)⋊C4—41no—
111(C2×D19)⋊C4—81no—
112C4⋊Dic19—21no—
113C4⋊Dic19—42no—
114C4⋊Dic19—41no—
115C4⋊Dic19—41no—
116C4⋊Dic19SD1612yescomplemented
117Dic19⋊C4—42no—
118Dic19⋊C4—41no—
119Dic19⋊C4—41no—
120C2×C19⋊C8—22no—
121C2×C19⋊C8—22no—
122C2×C19⋊C8—41no—
123C2×C19⋊C8—41no—
124C2×C19⋊C8—41no—
125C2×C19⋊C8—41no—
126#7754—191nomaximal, Sylow
127C23×C19#12011yescharacteristic
128C22×D19—22no—
129C22×D19—41no—
130C22×D19—41no—
131C22×D19—41no—
132C22×D19—41no—
133C22×D19—41no—
134C22×D19—41no—
135Q8×C19—42no—
136Q8×C19—42no—
137Q8×C19—81no—
138Q8×C19—81no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—22no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—42no—
152C2×C4×C19—81no—
153C2×C4×C19—81no—
154C2×C4×C19C2×SD1611yescharacteristic
155C2×C4×C19C2×SD1611yescharacteristic
156C2×C4×C19C2×SD1611yescharacteristic
157C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C19#13711yescharacteristic
160C2×Dic19—22no—
161C2×Dic19—41no—
162C2×Dic19—41no—
163C2×Dic19—41no—
164C2×Dic19—41no—
165C2×Dic19—41no—
166C2×Dic19—41no—
167C2×Dic19—41no—
168C2×Dic19—41no—
169D76—42no—
170D76—81no—
171C4×D19—84no—
172Dic38—84no—
173C8×C19—42no—
174C19⋊C8—42no—
175C19⋊C8—42no—
176#2683—191no—
177#2058—191no—
178#2058D1911yescharacteristic, complemented
179#2013—191no—
180#1271—191no—
181#1271—191no—
182#1270—191no—
183C22×C19#44811yescharacteristic
184C22×C19#45011yescharacteristic
185C22×C19#45011yescharacteristic
186C22×C19#45311yescharacteristic
187C22×C19#45611yescharacteristic
188C22×C19#45611yescharacteristic
189C22×C19B(4,𝔽2)11yescharacteristic
190C2×D19—42no—
191C2×D19—42no—
192C2×D19—42no—
193C2×D19—81no—
194C2×D19—81no—
195C2×D19—81no—
196C2×D19—81no—
197C4×C19—21no—
198C4×C19—21no—
199C4×C19—21no—
200C4×C19—21no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—42no—
204C4×C19—82no—
205C4×C19—81no—
206Dic19—42no—
207Dic19—81no—
208Dic19—81no—
209C22×SD16—381no—
210C2×C4⋊Q8C2×D1911yescharacteristic
211C2×C22⋊Q8—381no—
212C2×C22⋊Q8—381no—
213C2×#106—21no—
214C2×#106—381no—
215C2×#103—381no—
216#396—381no—
217#396—381no—
218#395—381no—
219#390—191no—
220#389—191no—
221#389C2×D1911yescharacteristic
222#386—381no—
223#340—21no—
224#340—381no—
225#336—191no—
226#336—191no—
227#336C2×D1911yescharacteristic
228C2×C19#159611yescharacteristic
229C2×C19#160411yescharacteristic
230C2×C19#160411yescharacteristic
231C2×C19#162911yescharacteristic
232C2×C19#165111yescharacteristic
233C2×C19#165111yescharacteristic
234C2×C19#166011yescharacteristic
235D19—82no—
236C22×Q8—21no—
237C22×Q8—381no—
238C22×D4—191no—
239C23×C4—381no—
240C2×SD16—762no—
241C2×SD16—762no—
242C2×SD16—762no—
243C22×C8—21no—
244C22×C8—381no—
245C22×C8—381no—
246C4⋊Q8—42no—
247C22⋊Q8—762no—
248C22⋊Q8—762no—
249C22⋊Q8—762no—
250C22⋊Q8—762no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—191no—
255C2×C4⋊C4—191no—
256C2×C4⋊C4—191no—
257C2×C4⋊C4—381no—
258C2×C4⋊C4—381no—
259C2×C4⋊C4—381no—
260C2×C4⋊C4C22⋊D1911yescharacteristic
261C2×C4⋊C4C22⋊D1911yescharacteristic
262C2×C22⋊C4—381no—
263C2×C22⋊C4—381no—
264C2×C22⋊C4—381no—
265C2×C22⋊C4—381no—
266C2×C22⋊C4—381no—
267C2×C42C22×D1911yescharacteristic
268#106—42no—
269#106—762no—
270#103—762no—
271#95—21no—
272#95—381no—
273#95—381no—
274C19#775411yescharacteristic, complemented, Sylow
275C24—381no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—762no—
283C2×Q8—762no—
284C2×Q8—1521no—
285C2×D4—192no—
286C2×D4—381no—
287C2×D4—761no—
288C2×D4—761no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—381no—
293C22×C4—381no—
294C22×C4—381no—
295C22×C4—762no—
296C22×C4—762no—
297C22×C4—1521no—
298C22×C4D4×D1911yescharacteristic
299C22×C4D4×D1911yescharacteristic
300C22×C4C2×C22⋊D1911yescharacteristic
301SD16—768no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—382no—
306C2×C8—382no—
307C2×C8—761no—
308C2×C8—761no—
309C2×C8—761no—
310C2×C8—761no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—192no—
320C4⋊C4—381no—
321C4⋊C4—761no—
322C4⋊C4—761no—
323C4⋊C4—762no—
324C4⋊C4—762no—
325C4⋊C4—761no—
326C4⋊C4—761no—
327C4⋊C4#6452712yescomplemented
328C22⋊C4—762no—
329C22⋊C4—762no—
330C22⋊C4—761no—
331C22⋊C4—761no—
332C22⋊C4—761no—
333C22⋊C4—761no—
334C22⋊C4—1521no—
335C42—41no—
336C23—382no—
337C23—761no—
338C23—761no—
339C23—761no—
340C23—761no—
341C23—761no—
342C23—761no—
343C23#1059738311yescharacteristic
344Q8—42no—
345Q8—42no—
346Q8—81no—
347Q8—81no—
348Q8—1524no—
349D4—762no—
350D4—1521no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—382no—
367C2×C4—761no—
368C2×C4—761no—
369C2×C4—761no—
370C2×C4—761no—
371C2×C4—761no—
372C2×C4—761no—
373C2×C4—761no—
374C2×C4—761no—
375C2×C4—1524no—
376C2×C4SD16×D1911yescharacteristic
377C2×C4SD16×D1911yescharacteristic
378C2×C4#1059736011yescharacteristic
379C2×C4#1059736111yescharacteristic
380C2×C4C2×#6452711yescharacteristic
381C2×C4#1059739511yescharacteristic
382C8—42no—
383C8—762no—
384C8—762no—
385C22—762no—
386C22—762no—
387C22—762no—
388C22—1521no—
389C22—1521no—
390C22—1521no—
391C22—1521no—
392C22#1192668111yescharacteristic
393C22#1192669311yescharacteristic
394C22#1192669411yescharacteristic
395C22#1192671011yescharacteristic
396C22#1192672511yescharacteristic
397C22#1192672611yescharacteristic
398C22#1192673011yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—42no—
406C4—81no—
407C4—82no—
408C4—762no—
409C4—1521no—
410C4—1521no—
411C2—1522no—
412C2#1456255611yescharacteristic
413C2#1456260211yescharacteristic
414C2#1456260311yescharacteristic
415C2#1456275011yescharacteristic
416C2#1456289511yescharacteristic
417C2#1456289711yescharacteristic
418C2#1456294511yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2058C2
socleC23×C19#120
prime radicalC22×D76D4
hypercenter#2058D19
hypocenterC19#7754
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2058

Complements

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

NH ≅ G/Ntype
2. #14564965C2semidirect
4. #14561459C2semidirect
5. #14561458C2semidirect
7. C19×#2058C2semidirect
102. C4⋊C4×C19SD16semidirect
116. C4⋊Dic19SD16semidirect
178. #2058D19semidirect
274. C19#7754semidirect
327. C4⋊C4#64527semidirect

Maximal subgroups

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

subgroupindex
#145700062
#145649652
#145647182
#145614592
#145614582
#145614552
C19×#20582
#775419