Finite Group Databasebeta

← #18074290

Subgroups — #18074290

Order 4864.

998 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#11927199C211yesmaximal, characteristic
2#14563627C211yesmaximal, characteristic, complemented
3#14562315C212yesmaximal, complemented
4#14562061C212yesmaximal, complemented
5C19×#1460C211yesmaximal, characteristic, complemented
6C22×#64541C412yes—
7#11927199—24no—
8#11927199—24no—
9C2×#10597315C2211yescharacteristic
10C2×#10597329—22no—
11C2×#10597370C412yes—
12C2×#10597384—21no—
13C2×C4×D76C2211yescharacteristic
14C2×C4⋊C4×D19—21no—
15#11926568C2212yes—
16C2×#10597290—21no—
17#11926313—21no—
18#11926292—24no—
19#11926273—24no—
20C2×C4×D4×C19C2211yescharacteristic
21C19×#431C2212yes—
22C19×#323—22no—
23C22×D4×C19D411yescharacteristic
24C23×C4×C19C2×C412yes—
25C22×C22⋊D19—22no—
26C2×#64541—24no—
27C2×#64541—24no—
28C2×#64541—48no—
29C22×D76C2×C411yescharacteristic
30C22×C4×D19—22no—
31C22×C4×D19—21no—
32C22×Dic38C2×C412yes—
33C4×D4×C19—22no—
34C4×D4×C19—22no—
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C22⋊C4×C19D412yes—
37C2×C42×C19C2311yescharacteristic
38C2×C22⋊Dic19—22no—
39#10597384—28no—
40C2×(C2×D19)⋊C4—21no—
41C2×C4⋊Dic19—21no—
42C2×C4⋊Dic19—21no—
43C2×C4⋊Dic19C2×C411yescharacteristic
44#10597370—24no—
45#10597370—24no—
46C2×Dic19⋊C4—22no—
47C2×#64520—22no—
48C4⋊C4×D19—28no—
49#10597329—216no—
50C4×D76—22no—
51C4×D76D414yes—
52#10597315—22no—
53#10597315D414yes—
54C19×C4⋊C8—22no—
55C19×C22⋊C8—22no—
56C4×C8×C19—22no—
57#10597290—42no—
58C4⋊(C19⋊C8)—22no—
59C4⋊(C19⋊C8)—22no—
60C24×C19C22⋊C412yes—
61C23×D19—21no—
62C2×D4×C19—22no—
63C2×D4×C19—22no—
64C2×D4×C19—21no—
65C2×D4×C19—21no—
66C22×C4×C19—22no—
67C22×C4×C19—22no—
68C22×C4×C19—44no—
69C22×C4×C19C22⋊C412yes—
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C2×C22⋊D19—28no—
74C2×C22⋊D19—48no—
75C22×Dic19—21no—
76C22×Dic19—22no—
77#64541—48no—
78#64541—416no—
79#64541—48no—
80C2×D76—21no—
81C2×D76—24no—
82C2×D76C22⋊C412yes—
83C2×C4×D19—28no—
84C2×C4×D19—24no—
85C2×C4×D19—48no—
86C2×C4×D19—42no—
87C2×C4×D19—41no—
88C2×C4×D19—41no—
89C2×Dic38—22no—
90C2×Dic38—44no—
91C2×Dic38C22⋊C414yes—
92C2×C8×C19—42no—
93C4⋊C4×C19—22no—
94C22⋊C4×C19—24no—
95C42×C19C2×D412yes—
96C42×C19C2×D412yes—
97C22⋊Dic19—28no—
98(C2×D19)⋊C4—24no—
99C4⋊Dic19—21no—
100C4⋊Dic19—24no—
101C4⋊Dic19—24no—
102C4⋊Dic19C22⋊C412yes—
103Dic19⋊C4—28no—
104#64520—42no—
105#64520—42no—
106C2×C19⋊C8—42no—
107#8393—191nomaximal, Sylow
108C23×C19—22no—
109C23×C19—22no—
110C23×C19—22no—
111C23×C19—42no—
112C23×C19—42no—
113C23×C19C2×C22⋊C411yescharacteristic
114C22×D19—24no—
115C22×D19—22no—
116C22×D19—42no—
117C22×D19—41no—
118C22×D19—41no—
119D4×C19—42no—
120D4×C19—42no—
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—41no—
124C2×C4×C19—44no—
125C2×C4×C19—44no—
126C2×C4×C19—42no—
127C2×C4×C19C2×C22⋊C411yescharacteristic
128C2×C4×C19C2×C22⋊C411yescharacteristic
129C2×C4×C19#12012yes—
130C2×C4×C19#12012yes—
131C2×C4×C19#13512yes—
132C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C19#13711yescharacteristic
134C22⋊D19—416no—
135C2×Dic19—22no—
136C2×Dic19—24no—
137C2×Dic19—44no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140D76—24no—
141D76—22no—
142D76#10014yescomplemented
143C4×D19—416no—
144C4×D19—44no—
145C4×D19—44no—
146Dic38—44no—
147Dic38—44no—
148C8×C19—82no—
149C19⋊C8—82no—
150C2×#547—191no—
151#1800—191no—
152#1548—192no—
153#1486—192no—
154#1460D1911yescharacteristic, complemented
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—42no—
158C22×C19—42no—
159C22×C19—42no—
160C22×C19—82no—
161C22×C19—82no—
162C22×C19#37911yescharacteristic
163C22×C19#41611yescharacteristic
164C22×C19#41711yescharacteristic
165C2×D19—24no—
166C2×D19—44no—
167C2×D19—44no—
168C2×D19—42no—
169C2×D19—42no—
170C4×C19—22no—
171C4×C19—21no—
172C4×C19—42no—
173C4×C19C2×#10012yes—
174C4×C19#44912yes—
175C4×C19#45212yes—
176Dic19—44no—
177Dic19—42no—
178C22×#41—192no—
179#547—384no—
180#547—384no—
181C2×C4⋊Q8—191no—
182C2×#123—382no—
183C2×C22⋊Q8—192no—
184C2×#121—381no—
185C2×C4×D4—191no—
186C2×C4×D4C2×D1911yescharacteristic
187C22×C4⋊C4—381no—
188#431C2×D1912yes—
189#423—192no—
190C2×#100—381no—
191#343—381no—
192#333—384no—
193D4⋊C8—384no—
194#323—22no—
195C2×C19—21no—
196C2×C19—21no—
197C2×C19—82no—
198C2×C19#178311yescharacteristic
199C2×C19#178811yescharacteristic
200C2×C19#179611yescharacteristic
201D19—44no—
202C2×#41—384no—
203C2×#41—384no—
204C2×#41—768no—
205C22×Q8—192no—
206C22×D4—191no—
207C22×D4—382no—
208C22×D4D7611yescharacteristic
209C23×C4—382no—
210C23×C4—381no—
211C23×C4C4×D1912yes—
212C2×M16—382no—
213C4⋊Q8—194no—
214C4⋊Q8—382no—
215#123—3816no—
216C22⋊Q8—384no—
217C22⋊Q8—384no—
218#121—388no—
219C4×D4—22no—
220C4×D4—22no—
221C4×D4—194no—
222C4×D4—382no—
223C2×C4⋊C4—191no—
224C2×C4⋊C4—388no—
225C2×C4⋊C4—382no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4D7611yescharacteristic
229C2×C22⋊C4—382no—
230C2×C22⋊C4—381no—
231C2×C22⋊C4C22⋊D1912yes—
232C2×C42C22×D1911yescharacteristic
233C4⋊C8—22no—
234C4⋊C8—382no—
235C4⋊C8—382no—
236#100—762no—
237C22⋊C8—22no—
238C4×C8—22no—
239C19#839311yescharacteristic, complemented, Sylow
240C24—381no—
241C24(C2×D19)⋊C412yes—
242#41—768no—
243#41—7616no—
244#41—768no—
245C2×Q8—194no—
246C2×Q8—382no—
247C2×Q8—764no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—192no—
253C2×D4—384no—
254C2×D4—388no—
255C2×D4—381no—
256C2×D4—768no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—44no—
260C22×C4—388no—
261C22×C4—381no—
262C22×C4—382no—
263C22×C4—384no—
264C22×C4—768no—
265C22×C4—762no—
266C22×C4—761no—
267C22×C4—761no—
268C22×C4(C2×D19)⋊C412yes—
269C22×C4C2×C4×D1911yescharacteristic
270C22×C4C2×D7611yescharacteristic
271C22×C4C2×C22⋊D1911yescharacteristic
272M16—762no—
273M16—762no—
274C2×C8—42no—
275C2×C8—762no—
276C4⋊C4—22no—
277C4⋊C4—192no—
278C4⋊C4—388no—
279C4⋊C4—384no—
280C4⋊C4—381no—
281C4⋊C4—384no—
282C22⋊C4—24no—
283C22⋊C4—388no—
284C22⋊C4—384no—
285C42D4×D1912yes—
286C42D4×D1912yes—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—42no—
291C23—42no—
292C23—384no—
293C23—382no—
294C23—762no—
295C23—761no—
296C23—761no—
297C23C2×(C2×D19)⋊C411yescharacteristic
298Q8—764no—
299Q8—764no—
300D4—42no—
301D4—42no—
302D4—194no—
303D4—384no—
304D4—382no—
305D4—7616no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—42no—
312C2×C4—382no—
313C2×C4—384no—
314C2×C4—7616no—
315C2×C4—764no—
316C2×C4—761no—
317C2×C4—761no—
318C2×C4—764no—
319C2×C4—764no—
320C2×C4C22⋊C4×D1911yescharacteristic
321C2×C4C22⋊C4×D1911yescharacteristic
322C2×C4#1059732812yes—
323C2×C4#1059735012yes—
324C2×C4#1059735411yescharacteristic
325C2×C4#1059735511yescharacteristic
326C2×C4#1059738312yes—
327C8—82no—
328C8—1522no—
329C22—21no—
330C22—21no—
331C22—42no—
332C22—42no—
333C22—42no—
334C22—82no—
335C22—82no—
336C22—384no—
337C22—764no—
338C22—764no—
339C22—762no—
340C22—762no—
341C22#1192639911yescharacteristic
342C22#1192654111yescharacteristic
343C22#1192654611yescharacteristic
344C4—22no—
345C4—21no—
346C4—42no—
347C4—764no—
348C4—762no—
349C4#100×D1912yes—
350C4#1192669112yes—
351C4#1192670812yes—
352C2—21no—
353C2—21no—
354C2—82no—
355C2—764no—
356C2#1456355411yescharacteristic
357C2#1456357611yescharacteristic
358C2#1456360811yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1460C2
socleC22×C19#379
prime radicalC2×#11927199C2
cosocleC2×C42×C19C23
hypercenter#1460D19
hypocenterC19#8393
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #14563627C2semidirect
3. #14562315C2semidirect
4. #14562061C2semidirect
5. C19×#1460C2semidirect
142. D76#100semidirect
154. #1460D19semidirect
239. C19#8393semidirect

Maximal subgroups

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

subgroupindex
C2×#119271992
#145636272
#145623152
#145620612
C19×#14602
#839319