Finite Group Databasebeta

← #18074313

Subgroups — #18074313

Order 4864.

802 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 127 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×#11927259C211yesmaximal, characteristic
2#14562321C212yesmaximal, complemented
3#14562059C212yesmaximal, complemented
4#14561956C211yesmaximal, characteristic, complemented
5C19×#1800C211yesmaximal, characteristic, complemented
6#11927259—24no—
7#11927259—24no—
8C2×#10597315C2211yescharacteristic
9C2×#10597331—22no—
10C2×#10597376C412yes—
11C2×#10597384—21no—
12C2×C4×D76C2211yescharacteristic
13C2×#10597372C412yes—
14C2×#10597338—21no—
15#11926597C2212yes—
16#11926289—24no—
17#11926271—24no—
18#11926268—22no—
19C2×C4×D4×C19C2211yescharacteristic
20C19×#423C2212yes—
21C2×C19×#100—21no—
22C19×#343—21no—
23C22×D4×C19D411yescharacteristic
24C23×C4×C19C2×C412yes—
25C22×C22⋊D19—22no—
26C22×D76C2×C411yescharacteristic
27C22×C4×D19—21no—
28C22×Dic38—21no—
29C2×M16×C19—22no—
30C4×D4×C19—22no—
31C4×D4×C19—22no—
32C2×C4⋊C4×C19D411yescharacteristic
33C2×C22⋊C4×C19D412yes—
34C2×C42×C19C2311yescharacteristic
35C2×C22⋊Dic19—22no—
36#10597384—28no—
37#10597376—24no—
38#10597376—24no—
39C2×(C2×D19)⋊C4—22no—
40C2×(C2×D19)⋊C4—21no—
41#10597372—24no—
42#10597372—24no—
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19C2×C412yes—
45C2×C4⋊Dic19C2×C411yescharacteristic
46C2×C4×Dic19—22no—
47#10597338—28no—
48#10597331—216no—
49C4×D76—22no—
50C4×D76D414yes—
51#10597315—22no—
52#10597315D414yes—
53C19×C4⋊C8—22no—
54C19×C4⋊C8—22no—
55C19×#100—42no—
56C22⋊(C19⋊C8)—22no—
57C4⋊(C19⋊C8)—22no—
58C4×C19⋊C8—22no—
59C24×C19C22⋊C412yes—
60C23×D19—21no—
61C2×D4×C19—22no—
62C2×D4×C19—22no—
63C2×D4×C19—21no—
64C2×D4×C19—21no—
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—44no—
68C22×C4×C19C22⋊C412yes—
69C22×C4×C19C22×C411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C2×C22⋊D19—28no—
73C2×C22⋊D19—84no—
74C22×Dic19—21no—
75C22×Dic19—22no—
76C2×D76—21no—
77C2×D76—42no—
78C2×D76C22⋊C412yes—
79C2×C4×D19—24no—
80C2×C4×D19—42no—
81C2×C4×D19—41no—
82C2×C4×D19—41no—
83C2×Dic38—24no—
84C2×Dic38—82no—
85M16×C19—42no—
86M16×C19—42no—
87C2×C8×C19—42no—
88C4⋊C4×C19—22no—
89C22⋊C4×C19—24no—
90C42×C19C2×D412yes—
91C42×C19C2×D412yes—
92C22⋊Dic19—28no—
93(C2×D19)⋊C4—28no—
94(C2×D19)⋊C4—24no—
95C4⋊Dic19—22no—
96C4⋊Dic19—21no—
97C4⋊Dic19—24no—
98C4⋊Dic19C22⋊C414yes—
99C4⋊Dic19C22⋊C412yes—
100C4×Dic19—28no—
101C2×C19⋊C8—42no—
102#8397—191nomaximal, Sylow
103C23×C19—22no—
104C23×C19—22no—
105C23×C19—22no—
106C23×C19—42no—
107C23×C19—42no—
108C23×C19C2×C22⋊C411yescharacteristic
109C22×D19—22no—
110C22×D19—42no—
111C22×D19—42no—
112C22×D19—41no—
113C22×D19—41no—
114D4×C19—42no—
115D4×C19—42no—
116C2×C4×C19—22no—
117C2×C4×C19—22no—
118C2×C4×C19—41no—
119C2×C4×C19—44no—
120C2×C4×C19—44no—
121C2×C4×C19—42no—
122C2×C4×C19C2×C22⋊C411yescharacteristic
123C2×C4×C19C2×C22⋊C411yescharacteristic
124C2×C4×C19#12012yes—
125C2×C4×C19#12012yes—
126C2×C4×C19#13512yes—
127C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C19#13711yescharacteristic
129C22⋊D19—88no—
130C2×Dic19—22no—
131C2×Dic19—24no—
132C2×Dic19—44no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135D76—24no—
136D76—42no—
137C4×D19—44no—
138C4×D19—44no—
139Dic38—84no—
140C8×C19—82no—
141C19⋊C8—82no—
142C2×#555—191no—
143#1800D1911yescharacteristic, complemented
144#1549—192no—
145#1486—192no—
146#1460—191no—
147C22×C19—21no—
148C22×C19—21no—
149C22×C19—42no—
150C22×C19—42no—
151C22×C19—42no—
152C22×C19—82no—
153C22×C19—82no—
154C22×C19#37911yescharacteristic
155C22×C19#41611yescharacteristic
156C22×C19#41711yescharacteristic
157C2×D19—42no—
158C2×D19—42no—
159C2×D19—42no—
160C2×D19—82no—
161C2×D19—82no—
162C4×C19—22no—
163C4×C19—21no—
164C4×C19—42no—
165C4×C19#41312yes—
166C4×C19#44912yes—
167C4×C19#45212yes—
168Dic19—44no—
169Dic19—42no—
170#555—384no—
171#555—384no—
172C2×C4⋊Q8—191no—
173C2×#124—382no—
174C2×#121—192no—
175C2×#121—381no—
176C2×C4×D4—191no—
177C2×C4×D4C2×D1911yescharacteristic
178C2×#117—192no—
179C2×#117—381no—
180#431—192no—
181#423C2×D1912yes—
182C2×#100—21no—
183#343—21no—
184#332—384no—
185D4⋊C8—384no—
186#323—382no—
187C2×C19—21no—
188C2×C19—21no—
189C2×C19—82no—
190C2×C19#178511yescharacteristic
191C2×C19#178811yescharacteristic
192C2×C19#179511yescharacteristic
193D19—82no—
194C22×Q8—381no—
195C22×D4—191no—
196C22×D4—382no—
197C22×D4C22⋊D1911yescharacteristic
198C23×C4—381no—
199C23×C4C4×D1912yes—
200C2×M16—22no—
201C4⋊Q8—194no—
202C4⋊Q8—382no—
203#124—3816no—
204#121—384no—
205#121—384no—
206#121—388no—
207C4×D4—22no—
208C4×D4—22no—
209C4×D4—194no—
210C4×D4—382no—
211#117—388no—
212#117—384no—
213#117—384no—
214C2×C4⋊C4—191no—
215C2×C4⋊C4—192no—
216C2×C4⋊C4—381no—
217C2×C4⋊C4C22⋊D1911yescharacteristic
218C2×C22⋊C4—382no—
219C2×C22⋊C4—382no—
220C2×C22⋊C4—381no—
221C2×C22⋊C4D7612yes—
222C2×C42—382no—
223C2×C42C22×D1911yescharacteristic
224C4⋊C8—22no—
225C4⋊C8—22no—
226C4⋊C8—382no—
227#100—42no—
228C22⋊C8—382no—
229C4×C8—382no—
230C19#839711yescharacteristic, complemented, Sylow
231C24—381no—
232C24(C2×D19)⋊C412yes—
233C2×Q8—384no—
234C2×Q8—1522no—
235C2×D4—21no—
236C2×D4—22no—
237C2×D4—21no—
238C2×D4—22no—
239C2×D4—192no—
240C2×D4—388no—
241C2×D4—381no—
242C2×D4—762no—
243C2×D4—1524no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—44no—
247C22×C4—381no—
248C22×C4—382no—
249C22×C4—384no—
250C22×C4—761no—
251C22×C4—761no—
252C22×C4—762no—
253C22×C4(C2×D19)⋊C412yes—
254C22×C4C2×C4×D1911yescharacteristic
255C22×C4C2×D7611yescharacteristic
256C22×C4C2×C22⋊D1911yescharacteristic
257M16—42no—
258M16—42no—
259C2×C8—42no—
260C2×C8—762no—
261C4⋊C4—22no—
262C4⋊C4—192no—
263C4⋊C4—194no—
264C4⋊C4—384no—
265C4⋊C4—381no—
266C4⋊C4—382no—
267C22⋊C4—24no—
268C22⋊C4—388no—
269C22⋊C4—388no—
270C22⋊C4—384no—
271C42—388no—
272C42D4×D1912yes—
273C42D4×D1912yes—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—42no—
278C23—42no—
279C23—382no—
280C23—762no—
281C23—762no—
282C23—761no—
283C23—761no—
284C23C2×(C2×D19)⋊C411yescharacteristic
285Q8—1524no—
286D4—42no—
287D4—42no—
288D4—384no—
289D4—762no—
290D4—1528no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—382no—
298C2×C4—384no—
299C2×C4—764no—
300C2×C4—761no—
301C2×C4—761no—
302C2×C4—764no—
303C2×C4—764no—
304C2×C4C22⋊C4×D1911yescharacteristic
305C2×C4C22⋊C4×D1911yescharacteristic
306C2×C4#1059732812yes—
307C2×C4#1059737811yescharacteristic
308C2×C4#1059738312yes—
309C2×C4#1059738811yescharacteristic
310C2×C4#1059739612yes—
311C8—82no—
312C8—1522no—
313C22—21no—
314C22—21no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—82no—
319C22—82no—
320C22—762no—
321C22—762no—
322C22—762no—
323C22—1522no—
324C22—1522no—
325C22#1192639911yescharacteristic
326C22#1192653811yescharacteristic
327C22#1192654311yescharacteristic
328C4—22no—
329C4—21no—
330C4—42no—
331C4—764no—
332C4—762no—
333C4#1192652512yes—
334C4#1192668712yes—
335C4#1192670412yes—
336C2—21no—
337C2—21no—
338C2—82no—
339C2—1522no—
340C2#1456356011yescharacteristic
341C2#1456357311yescharacteristic
342C2#1456360611yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1800C2
socleC22×C19#379
prime radicalC2×#11927259C2
cosocleC2×C42×C19C23
hypercenter#1800D19
hypocenterC19#8397
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
2. #14562321C2semidirect
3. #14562059C2semidirect
4. #14561956C2semidirect
5. C19×#1800C2semidirect
143. #1800D19semidirect
230. C19#8397semidirect

Maximal subgroups

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

subgroupindex
C2×#119272592
#145623212
#145620592
#145619562
C19×#18002
#839719