Finite Group Databasebeta

← #18071593

Subgroups — #18071593

Order 4864.

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

normal subgroups only

This group has 462 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#14565192C211yesmaximal, characteristic, complemented
3#14565039C211yesmaximal, characteristic
4#14561459C211yesmaximal, characteristic, complemented
5#14561458C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic
7C19×#2084C211yesmaximal, characteristic, complemented
8C2×#10597343—21no—
9C2×#10597342—21no—
10C2×#10597266—21no—
11#11926466—21no—
12#11926466—21no—
13#11926465—21no—
14#11926446C2211yescharacteristic
15#11926442C2211yescharacteristic
16#11926422—21no—
17#11926306—21no—
18#11926306—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C2×C19×#106—21no—
23C19×#389C2211yescharacteristic
24C19×#384C2211yescharacteristic
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×D76D411yescharacteristic
28C22×C4×D19—21no—
29C22×Dic38—21no—
30C22×C8×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C42×C19C2311yescharacteristic
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19D411yescharacteristic
45C2×C4⋊Dic19D411yescharacteristic
46C2×C4⋊Dic19D411yescharacteristic
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C22×C19⋊C8—21no—
50C22×C19⋊C8—21no—
51#10597343—42no—
52#10597343—42no—
53#10597342—42no—
54#10597342—42no—
55C19×#106—42no—
56C19×#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59#10597266—42no—
60C23×D19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—41no—
64C22×C4×C19C2×D411yescharacteristic
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×Dic19—21no—
68C22×Dic19—21no—
69C22×Dic19—21no—
70C2×D76—21no—
71C2×D76—41no—
72C2×D76—41no—
73C2×D76SD1612yes—
74C2×C4×D19—42no—
75C2×C4×D19—42no—
76C2×C4×D19—81no—
77C2×Dic38—42no—
78C2×Dic38—42no—
79C2×Dic38—81no—
80C2×C8×C19—22no—
81C2×C8×C19—41no—
82C2×C8×C19—41no—
83C4⋊C4×C19—21no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—42no—
86C4⋊C4×C19—41no—
87C4⋊C4×C19—41no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19D812yes—
93C42×C19—41no—
94(C2×D19)⋊C4—42no—
95(C2×D19)⋊C4—42no—
96(C2×D19)⋊C4—41no—
97(C2×D19)⋊C4—41no—
98(C2×D19)⋊C4—41no—
99(C2×D19)⋊C4—41no—
100(C2×D19)⋊C4—81no—
101C4⋊Dic19—21no—
102C4⋊Dic19—42no—
103C4⋊Dic19—41no—
104C4⋊Dic19—41no—
105C4⋊Dic19SD1612yes—
106Dic19⋊C4—42no—
107Dic19⋊C4—41no—
108Dic19⋊C4—41no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8—41no—
114C2×C19⋊C8—41no—
115#7791—191nomaximal, Sylow
116C23×C19#12011yescharacteristic
117C22×D19—22no—
118C22×D19—41no—
119C22×D19—41no—
120C22×D19—41no—
121C22×D19—41no—
122C22×D19—41no—
123C22×D19—41no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—22no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—81no—
137C2×C4×C19—81no—
138C2×C4×C19—81no—
139C2×C4×C19C2×D811yescharacteristic
140C2×C4×C19C2×SD1611yescharacteristic
141C2×C4×C19C2×SD1611yescharacteristic
142C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C19#13711yescharacteristic
145C2×Dic19—22no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154D76—42no—
155D76—81no—
156C4×D19—84no—
157Dic38—84no—
158C8×C19—42no—
159C19⋊C8—81no—
160C19⋊C8—81no—
161#2683—191no—
162#2099—191no—
163#2084D1911yescharacteristic, complemented
164#2071—191no—
165#1271—191no—
166#1271—191no—
167#1270—191no—
168C22×C19#44711yescharacteristic
169C22×C19#44811yescharacteristic
170C22×C19#45011yescharacteristic
171C22×C19#45411yescharacteristic
172C22×C19#45511yescharacteristic
173C22×C19#45611yescharacteristic
174C22×C19#45811yescharacteristic
175C2×D19—42no—
176C2×D19—42no—
177C2×D19—42no—
178C2×D19—81no—
179C2×D19—81no—
180C2×D19—81no—
181C2×D19—81no—
182C4×C19—21no—
183C4×C19—21no—
184C4×C19—21no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—42no—
189C4×C19—81no—
190C4×C19—161no—
191Dic19—42no—
192Dic19—81no—
193Dic19—81no—
194C2×C22⋊Q8—381no—
195C2×C22⋊Q8—381no—
196C2×#106—21no—
197C2×#102—381no—
198#396—381no—
199#396—381no—
200#395—381no—
201#390—191no—
202#389—191no—
203#389C2×D1911yescharacteristic
204#386—381no—
205#384C2×D1911yescharacteristic
206#340—21no—
207#340—381no—
208#340—381no—
209#340—381no—
210#336—191no—
211#336—191no—
212#336C2×D1911yescharacteristic
213C2×C19#160811yescharacteristic
214C2×C19#161011yescharacteristic
215C2×C19#161611yescharacteristic
216C2×C19#162711yescharacteristic
217C2×C19#163911yescharacteristic
218C2×C19#165111yescharacteristic
219C2×C19#166411yescharacteristic
220D19—82no—
221C22×Q8—381no—
222C22×D4—191no—
223C23×C4—381no—
224C22×C8—21no—
225C22×C8—381no—
226C22×C8—381no—
227C22⋊Q8—762no—
228C22⋊Q8—762no—
229C22⋊Q8—762no—
230C22⋊Q8—762no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—191no—
236C2×C4⋊C4—191no—
237C2×C4⋊C4—191no—
238C2×C4⋊C4—381no—
239C2×C4⋊C4—381no—
240C2×C4⋊C4—381no—
241C2×C4⋊C4C22⋊D1911yescharacteristic
242C2×C4⋊C4C22⋊D1911yescharacteristic
243C2×C22⋊C4—381no—
244C2×C22⋊C4—381no—
245C2×C22⋊C4—381no—
246C2×C22⋊C4—381no—
247C2×C22⋊C4—381no—
248C2×C42C22×D1911yescharacteristic
249#106—42no—
250#102—762no—
251#95—21no—
252#95—381no—
253#95—381no—
254C19#779111yescharacteristic, complemented, Sylow
255C24—381no—
256C2×Q8—762no—
257C2×Q8—762no—
258C2×Q8—1521no—
259C2×D4—192no—
260C2×D4—381no—
261C2×D4—761no—
262C2×D4—761no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—381no—
267C22×C4—381no—
268C22×C4—381no—
269C22×C4—762no—
270C22×C4—762no—
271C22×C4—1521no—
272C22×C4D4×D1911yescharacteristic
273C22×C4D4×D1911yescharacteristic
274C22×C4C2×C22⋊D1911yescharacteristic
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—761no—
279C2×C8—761no—
280C2×C8—761no—
281C2×C8—761no—
282C2×C8—761no—
283C2×C8—761no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—192no—
294C4⋊C4—381no—
295C4⋊C4—761no—
296C4⋊C4—761no—
297C4⋊C4—762no—
298C4⋊C4—762no—
299C4⋊C4—761no—
300C4⋊C4—761no—
301C4⋊C4#6452512yes—
302C22⋊C4—762no—
303C22⋊C4—762no—
304C22⋊C4—761no—
305C22⋊C4—761no—
306C22⋊C4—761no—
307C22⋊C4—761no—
308C22⋊C4—1521no—
309C42—41no—
310C23—382no—
311C23—761no—
312C23—761no—
313C23—761no—
314C23—761no—
315C23—761no—
316C23—761no—
317C23#1059738311yescharacteristic
318Q8—1524no—
319D4—762no—
320D4—1521no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—382no—
337C2×C4—761no—
338C2×C4—761no—
339C2×C4—761no—
340C2×C4—761no—
341C2×C4—761no—
342C2×C4—761no—
343C2×C4—761no—
344C2×C4—761no—
345C2×C4—1524no—
346C2×C4SD16×D1911yescharacteristic
347C2×C4SD16×D1911yescharacteristic
348C2×C4#1059736011yescharacteristic
349C2×C4#1059736111yescharacteristic
350C2×C4C2×#6452511yescharacteristic
351C2×C4#1059739511yescharacteristic
352C8—42no—
353C8—1521no—
354C8—1521no—
355C22—762no—
356C22—762no—
357C22—762no—
358C22—1521no—
359C22—1521no—
360C22—1521no—
361C22—1521no—
362C22#1192667711yescharacteristic
363C22#1192668111yescharacteristic
364C22#1192669311yescharacteristic
365C22#1192671511yescharacteristic
366C22#1192672011yescharacteristic
367C22#1192672611yescharacteristic
368C22#1192673311yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—81no—
377C4—161no—
378C4—762no—
379C4—1521no—
380C4—1521no—
381C2—1522no—
382C2#1456262411yescharacteristic
383C2#1456263711yescharacteristic
384C2#1456267011yescharacteristic
385C2#1456273611yescharacteristic
386C2#1456281211yescharacteristic
387C2#1456289511yescharacteristic
388C2#1456296711yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2084C2
socleC23×C19#120
prime radicalC22×D76D4
hypercenter#2084D19
hypocenterC19#7791
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
2. #14565192C2semidirect
4. #14561459C2semidirect
5. #14561458C2semidirect
7. C19×#2084C2semidirect
163. #2084D19semidirect
254. C19#7791semidirect

Maximal subgroups

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

subgroupindex
#145700062
#145651922
#145650392
#145614592
#145614582
#145614552
C19×#20842
#779119