Finite Group Databasebeta

← #18085748

Subgroups — #18085748

Order 4864.

404 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 75 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#14569807C211yesmaximal, characteristic
2#14564621C211yesmaximal, characteristic
3#14562155C211yesmaximal, characteristic
4#14561542C211yesmaximal, characteristic
5#14561520C211yesmaximal, characteristic
6#14561487C211yesmaximal, characteristic
7C19×#1511C211yesmaximal, characteristic
8#11926508C2211yescharacteristic
9#11926486—21no—
10#11926467—21no—
11#11926465—21no—
12#11926456—21no—
13#11926448—21no—
14#11926427—21no—
15#11926404C2211yescharacteristic
16C4×C22⋊Dic19C2211yescharacteristic
17C4×C22⋊Dic19C2211yescharacteristic
18#11926311—21no—
19#11926311—21no—
20#11926281—21no—
21#11926281—21no—
22C2×C19×C22⋊Q8C2211yescharacteristic
23C19×#407C2211yescharacteristic
24C19×#381C2211yescharacteristic
25C19×#328—21no—
26C19×#328—21no—
27C22×Q8×C19Q811yescharacteristic, complemented
28C23×C4×C19C2311yescharacteristic
29C22×Dic38—21no—
30C2×M16×C19—21no—
31C19×C22⋊Q8—21no—
32C19×C22⋊Q8—21no—
33C19×C22⋊Q8—21no—
34C19×C22⋊Q8—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19Q811yescharacteristic, complemented
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊Dic19—21no—
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19D411yescharacteristic
42C2×C22⋊Dic19D411yescharacteristic
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19—21no—
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—21no—
47C2×C4×Dic19—21no—
48C2×C4×Dic19—21no—
49C2×#64520—21no—
50C19×C22⋊C8—21no—
51C19×C22⋊C8—21no—
52C19×#95—21no—
53C19×#95D411yescharacteristic
54C19×#95D411yescharacteristic
55C19⋊#95—21no—
56C19⋊#95—21no—
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
66C2×Q8×C19—21no—
67C2×Q8×C19—21no—
68C2×Q8×C19—81no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—81no—
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×Q811yescharacteristic
77C22×C4×C19#4111yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C22×C4×C19#4111yescharacteristic
80C22×Dic19—21no—
81C22×Dic19—21no—
82C22×Dic19—21no—
83C22×Dic19—21no—
84C22×Dic19—41no—
85C2×Dic38—42no—
86C2×Dic38—81no—
87C2×Dic38—81no—
88M16×C19—81no—
89C2×C8×C19—41no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—41no—
93C4⋊C4×C19—41no—
94C22⋊C4×C19—41no—
95C22⋊C4×C19—41no—
96C22⋊C4×C19—81no—
97C22⋊Dic19—22no—
98C22⋊Dic19—42no—
99C22⋊Dic19—41no—
100C22⋊Dic19—41no—
101C22⋊Dic19—41no—
102C4⋊Dic19—42no—
103C4⋊Dic19—81no—
104Dic19⋊C4—81no—
105Dic19⋊C4—81no—
106C4×Dic19—81no—
107C4×Dic19—81no—
108#64520—81no—
109C2×C19⋊C8—41no—
110#10383—191nomaximal, Sylow
111C23×C19—21no—
112C23×C19—21no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19#12011yescharacteristic
116C23×C19C22⋊Q811yescharacteristic
117C23×C19#12411yescharacteristic
118Q8×C19—81no—
119Q8×C19—81no—
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—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—81no—
135C2×C4×C19—81no—
136C2×C4×C19C22⋊Q811yescharacteristic
137C2×C4×C19C22⋊Q811yescharacteristic
138C2×C4×C19#12411yescharacteristic
139C2×C4×C19#12411yescharacteristic
140C2×Dic19—22no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—42no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153C2×Dic19—81no—
154C2×Dic19—81no—
155Dic38—84no—
156C8×C19—81no—
157C19⋊C8—81no—
158#2665—191no—
159#1996—191no—
160#1511D1911yescharacteristic
161#1508—191no—
162#1305—191no—
163#1297—191no—
164#1284—191no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—81no—
174C22×C19—81no—
175C22×C19#39311yescharacteristic
176C22×C19#45511yescharacteristic
177C22×C19#45611yescharacteristic
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—81no—
183C4×C19—81no—
184C4×C19—81no—
185C4×C19—81no—
186Dic19—42no—
187Dic19—81no—
188Dic19—81no—
189Dic19—81no—
190Dic19—82no—
191C2×C22⋊Q8C2×D1911yescharacteristic
192#407—191no—
193#407C2×D1911yescharacteristic
194#400—381no—
195#396—381no—
196#395—381no—
197#393—381no—
198#391—381no—
199#387—381no—
200#381C2×D1911yescharacteristic
201#380—191no—
202C4×C22⋊C4—191no—
203C4×C22⋊C4—191no—
204#342—381no—
205#342—381no—
206#328—21no—
207#328—21no—
208#328—381no—
209#328—381no—
210C2×C19—21no—
211C2×C19—21no—
212C2×C19—41no—
213C2×C19—41no—
214C2×C19#202811yescharacteristic
215C2×C19#203111yescharacteristic
216C2×C19#203211yescharacteristic
217C22×Q8—381no—
218C22×Q8Dic3811yescharacteristic, complemented
219C23×C4C22×D1911yescharacteristic
220C2×M16—21no—
221C2×M16—381no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4—381no—
230C2×C4⋊C4—381no—
231C2×C4⋊C4Dic3811yescharacteristic, complemented
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—191no—
235C2×C22⋊C4—191no—
236C2×C22⋊C4—381no—
237C2×C22⋊C4—381no—
238C2×C42—381no—
239C2×C42—381no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—381no—
243C22⋊C8—381no—
244#95—21no—
245#95—191no—
246#95—191no—
247#95—381no—
248#95—381no—
249#95—381no—
250#95—381no—
251#95—381no—
252#95—381no—
253#95C22⋊D1911yescharacteristic
254#95C22⋊D1911yescharacteristic
255C19#1038311yescharacteristic, complemented, Sylow
256C24D4×D1911yescharacteristic
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—81no—
260C2×Q8—762no—
261C2×Q8—1521no—
262C2×Q8—1521no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—81no—
268C22×C4—381no—
269C22×C4—381no—
270C22×C4—381no—
271C22×C4—381no—
272C22×C4—761no—
273C22×C4C2×Dic3811yescharacteristic
274C22×C4#6454111yescharacteristic
275C22×C4D4×D1911yescharacteristic
276C22×C4#6454311yescharacteristic
277C22×C4#6454311yescharacteristic
278C22×C4C2×C22⋊D1911yescharacteristic
279M16—81no—
280M16—1521no—
281C2×C8—41no—
282C2×C8—761no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—762no—
288C4⋊C4—1521no—
289C4⋊C4—1521no—
290C4⋊C4—1521no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—81no—
294C22⋊C4—382no—
295C22⋊C4—762no—
296C22⋊C4—761no—
297C22⋊C4—761no—
298C22⋊C4—761no—
299C42—1521no—
300C42—1521no—
301C23—21no—
302C23—21no—
303C23—41no—
304C23—41no—
305C23#1059732411yescharacteristic
306C23#1059733111yescharacteristic
307C23#1059738311yescharacteristic
308Q8—81no—
309Q8—81no—
310Q8—1524no—
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—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—382no—
328C2×C4—761no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—762no—
332C2×C4—761no—
333C2×C4—761no—
334C2×C4—761no—
335C2×C4—761no—
336C2×C4—761no—
337C2×C4—761no—
338C2×C4—761no—
339C2×C4—761no—
340C2×C4—1521no—
341C2×C4—1521no—
342C2×C4#1059732411yescharacteristic
343C2×C4#1059733111yescharacteristic
344C2×C4#1059737011yescharacteristic
345C2×C4#1059738211yescharacteristic
346C8—81no—
347C8—1521no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—81no—
357C22—81no—
358C22#1192645611yescharacteristic
359C22#1192672011yescharacteristic
360C22#1192672511yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—81no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—762no—
370C4—1521no—
371C4—1521no—
372C4—1521no—
373C4—1522no—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2#1456479411yescharacteristic
379C2#1456480511yescharacteristic
380C2#1456481211yescharacteristic
subgroupG/H
centerC22#11926456
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1511C2
socleC22×C19#393
prime radicalC24×C19C2×D4
hypercenter#1511D19
hypocenterC19#10383
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
27. C22×Q8×C19Q8semidirect
36. C2×C4⋊C4×C19Q8semidirect
218. C22×Q8Dic38semidirect
231. C2×C4⋊C4Dic38semidirect
255. C19#10383semidirect

Maximal subgroups

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

subgroupindex
#145698072
#145646212
#145621552
#145615422
#145615202
#145614872
C19×#15112
#1038319