Finite Group Databasebeta

← #18085767

Subgroups — #18085767

Order 4864.

396 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 73 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#14569829C211yesmaximal, characteristic
2#14564620C211yesmaximal, characteristic
3#14562169C211yesmaximal, characteristic
4#14562154C211yesmaximal, characteristic
5#14561542C211yesmaximal, characteristic
6#14561488C211yesmaximal, characteristic
7C19×#1297C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9#11926508C2211yescharacteristic
10#11926480—21no—
11#11926478—21no—
12#11926476—21no—
13#11926467—21no—
14#11926442—21no—
15#11926428—21no—
16#11926407C2211yescharacteristic
17#11926404C2211yescharacteristic
18#11926310—21no—
19#11926310—21no—
20#11926282—21no—
21#11926282—21no—
22#11926280—21no—
23#11926280—21no—
24C19×#407C2211yescharacteristic
25C4×C22⋊C4×C19C2211yescharacteristic
26C4×C22⋊C4×C19C2211yescharacteristic
27C23×C4×C19C2311yescharacteristic
28C22×Dic38Q811yescharacteristic
29C2×M16×C19—21no—
30C2×C22⋊C4×C19—21no—
31C2×C22⋊C4×C19—21no—
32C2×C42×C19—21no—
33C2×C42×C19—21no—
34C2×C22⋊Dic19—21no—
35C2×C22⋊Dic19—21no—
36C2×C22⋊Dic19D411yescharacteristic
37C2×C22⋊Dic19D411yescharacteristic
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19Q811yescharacteristic
42#10597370—21no—
43#10597370—21no—
44#10597370—21no—
45#10597370—21no—
46C2×Dic19⋊C4—21no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—21no—
51C2×#64520—21no—
52C19×C22⋊C8—21no—
53C19×C22⋊C8—21no—
54C19×#95—21no—
55C19×#95D411yescharacteristic
56C19×#95D411yescharacteristic
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95—21no—
60C19⋊#95—21no—
61C19⋊#95D411yescharacteristic
62C19⋊#95D411yescharacteristic
63C22⋊(C19⋊C8)—21no—
64C22⋊(C19⋊C8)—21no—
65C24×C19C2×D411yescharacteristic
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—41no—
69C22×C4×C19—81no—
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×Q811yescharacteristic
73C22×C4×C19#4111yescharacteristic
74C22×C4×C19#4111yescharacteristic
75C22×C4×C19#4111yescharacteristic
76C22×Dic19—21no—
77C22×Dic19—21no—
78C22×Dic19—21no—
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C2×Dic38—21no—
83C2×Dic38—21no—
84C2×Dic38—81no—
85M16×C19—81no—
86C2×C8×C19—41no—
87C22⋊C4×C19—22no—
88C22⋊C4×C19—42no—
89C22⋊C4×C19—41no—
90C42×C19—81no—
91C42×C19—81no—
92C22⋊Dic19—41no—
93C22⋊Dic19—41no—
94C22⋊Dic19—41no—
95C22⋊Dic19—41no—
96C22⋊Dic19—81no—
97C4⋊Dic19—21no—
98C4⋊Dic19—21no—
99C4⋊Dic19—42no—
100C4⋊Dic19—81no—
101C4⋊Dic19—81no—
102Dic19⋊C4—42no—
103Dic19⋊C4—41no—
104Dic19⋊C4—41no—
105Dic19⋊C4—81no—
106Dic19⋊C4—81no—
107Dic19⋊C4—81no—
108#64520—81no—
109C2×C19⋊C8—41no—
110#10385—191nomaximal, Sylow
111C23×C19—21no—
112C23×C19—21no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19#12011yescharacteristic
116C23×C19C22⋊Q811yescharacteristic
117C23×C19#12411yescharacteristic
118C2×C4×C19—22no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—81no—
132C2×C4×C19—81no—
133C2×C4×C19C22⋊Q811yescharacteristic
134C2×C4×C19C22⋊Q811yescharacteristic
135C2×C4×C19#12411yescharacteristic
136C2×C4×C19#12411yescharacteristic
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151C2×Dic19—81no—
152C2×Dic19—81no—
153Dic38—81no—
154Dic38—81no—
155C8×C19—81no—
156C19⋊C8—81no—
157#2667—191no—
158#1996—191no—
159#1511—191no—
160#1508—191no—
161#1305—191no—
162#1297D1911yescharacteristic
163#1284—191no—
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—81no—
173C22×C19—81no—
174C22×C19#39311yescharacteristic
175C22×C19#45511yescharacteristic
176C22×C19#45611yescharacteristic
177C4×C19—21no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—42no—
182C4×C19—81no—
183C4×C19—82no—
184Dic19—81no—
185Dic19—81no—
186Dic19—81no—
187Dic19—81no—
188Dic19—81no—
189Dic19—81no—
190C2×C22⋊Q8—191no—
191#407—191no—
192#407C2×D1911yescharacteristic
193#399—381no—
194#398—381no—
195#398—381no—
196#396—381no—
197#389—381no—
198#387—381no—
199#381—191no—
200#380—191no—
201C4×C22⋊C4C2×D1911yescharacteristic
202C4×C22⋊C4C2×D1911yescharacteristic
203#342—381no—
204#342—381no—
205#328—381no—
206#328—381no—
207#328—381no—
208#328—381no—
209C2×C19—21no—
210C2×C19—21no—
211C2×C19—41no—
212C2×C19—41no—
213C2×C19#202811yescharacteristic
214C2×C19#203111yescharacteristic
215C2×C19#203211yescharacteristic
216C22×Q8—191no—
217C23×C4C22×D1911yescharacteristic
218C2×M16—21no—
219C2×M16—381no—
220C22⋊Q8—381no—
221C22⋊Q8—381no—
222C22⋊Q8—381no—
223C22⋊Q8—381no—
224C2×C4⋊C4—191no—
225C2×C4⋊C4—381no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4—381no—
230C2×C4⋊C4—381no—
231C2×C4⋊C4—381no—
232C2×C4⋊C4—381no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—191no—
236C2×C22⋊C4—191no—
237C2×C22⋊C4—381no—
238C2×C22⋊C4—381no—
239C2×C42—21no—
240C2×C42—21no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8—381no—
244C22⋊C8—381no—
245#95—21no—
246#95—191no—
247#95—191no—
248#95—381no—
249#95—381no—
250#95—381no—
251#95—381no—
252#95D7611yescharacteristic
253#95D7611yescharacteristic
254C19#1038511yescharacteristic, complemented, Sylow
255C24D4×D1911yescharacteristic
256C2×Q8—381no—
257C2×Q8—381no—
258C2×Q8—1521no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—81no—
263C22×C4—381no—
264C22×C4—381no—
265C22×C4—381no—
266C22×C4—381no—
267C22×C4—381no—
268C22×C4—381no—
269C22×C4C2×D7611yescharacteristic
270C22×C4#6454111yescharacteristic
271C22×C4#6454111yescharacteristic
272C22×C4D4×D1911yescharacteristic
273C22×C4#6454311yescharacteristic
274C22×C4Q8×D1911yescharacteristic
275M16—81no—
276M16—1521no—
277C2×C8—41no—
278C2×C8—761no—
279C4⋊C4—381no—
280C4⋊C4—381no—
281C4⋊C4—762no—
282C4⋊C4—762no—
283C4⋊C4—761no—
284C4⋊C4—761no—
285C4⋊C4—1521no—
286C4⋊C4—1521no—
287C4⋊C4—1521no—
288C4⋊C4—1521no—
289C4⋊C4—1521no—
290C22⋊C4—22no—
291C22⋊C4—42no—
292C22⋊C4—41no—
293C22⋊C4—761no—
294C22⋊C4—761no—
295C22⋊C4—761no—
296C22⋊C4—761no—
297C22⋊C4—1521no—
298C42—81no—
299C42—81no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23#1059732811yescharacteristic
305C23#1059733111yescharacteristic
306C23#1059734211yescharacteristic
307Q8—1521no—
308Q8—1521no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—761no—
325C2×C4—761no—
326C2×C4—761no—
327C2×C4—761no—
328C2×C4—761no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—761no—
332C2×C4—761no—
333C2×C4—761no—
334C2×C4—761no—
335C2×C4—761no—
336C2×C4—761no—
337C2×C4—761no—
338C2×C4—1521no—
339C2×C4—1521no—
340C2×C4#1059732111yescharacteristic
341C2×C4#1059733111yescharacteristic
342C2×C4#1059734211yescharacteristic
343C2×C4#1059734311yescharacteristic
344C8—81no—
345C8—1521no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22#1192645711yescharacteristic
357C22#1192672311yescharacteristic
358C22#1192672811yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—42no—
364C4—81no—
365C4—82no—
366C4—1521no—
367C4—1521no—
368C4—1521no—
369C4—1521no—
370C4—1521no—
371C4—1521no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2#1456479511yescharacteristic
377C2#1456480811yescharacteristic
378C2#1456481311yescharacteristic
subgroupG/H
centerC22#11926457
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1297C2
socleC22×C19#393
prime radicalC24×C19C2×D4
hypercenter#1297D19
hypocenterC19#10385
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
254. C19#10385semidirect

Maximal subgroups

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

subgroupindex
#145698292
#145646202
#145621692
#145621542
#145615422
#145614882
C19×#12972
#1038519