Finite Group Databasebeta

← #18081494

Subgroups — #18081494

Order 4864.

736 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10597320C211yesmaximal, characteristic
2C4×C4⋊(C19⋊C8)C211yesmaximal, characteristic, complemented
3C2×#11926273C214yesmaximal, complemented
4C4×C19×C4⋊C8C211yesmaximal, characteristic, complemented
5C2×#10597320C411yescharacteristic
6C2×C4×D76—21no—
7C2×C4×D76—21no—
8C2×C4×D76C2212yes—
9C2×C4⋊(C19⋊C8)C2212yes—
10C2×C4×C19⋊C8—21no—
11#11926446—21no—
12#11926446—21no—
13#11926446C412yes—
14#11926414C411yescharacteristic
15#11926299—21no—
16#11926273—28no—
17C2×C19×C4⋊C8—21no—
18C2×C4×C8×C19C2212yes—
19C43×C19C2211yescharacteristic
20C19×#336—21no—
21C22×D76—21no—
22C22×D76—21no—
23C22×D76C2×C412yes—
24C22×C4×D19—22no—
25C22×C8×C19—22no—
26C2×C42×C19C2×C411yescharacteristic
27C2×C42×C19C2×C411yescharacteristic
28C2×C42×C19D411yescharacteristic
29C2×C42×C19D411yescharacteristic
30C2×C42×C19D411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19C2311yescharacteristic
33C2×(C2×D19)⋊C4—22no—
34C2×(C2×D19)⋊C4—22no—
35C2×(C2×D19)⋊C4—22no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19C2×C412yes—
39C22×C19⋊C8—22no—
40#10597320—22no—
41#10597320C814yescomplemented
42C4×D76—24no—
43C4×D76—24no—
44C4×D76—44no—
45C4×D76—42no—
46C4×D76—42no—
47C19×C4⋊C8—24no—
48C4×C8×C19—24no—
49C4⋊(C19⋊C8)—22no—
50C4⋊(C19⋊C8)D414yescomplemented
51C4×C19⋊C8—42no—
52C23×D19—22no—
53C22×C4×C19C22⋊C411yescharacteristic
54C22×C4×C19C22⋊C411yescharacteristic
55C22×C4×C19C22⋊C411yescharacteristic
56C22×C4×C19C22⋊C411yescharacteristic
57C22×C4×C19C22×C411yescharacteristic
58C22×C4×C19C2×D411yescharacteristic
59C22×C4×C19C2×D411yescharacteristic
60C22×Dic19—22no—
61C2×D76—24no—
62C2×D76—24no—
63C2×D76—24no—
64C2×D76—24no—
65C2×D76—22no—
66C2×D76—42no—
67C2×D76—42no—
68C2×D76—42no—
69C2×D76—42no—
70C2×D76C2×C814yes—
71C2×C4×D19—44no—
72C2×C4×D19—42no—
73C2×C4×D19—42no—
74C2×C4×D19—44no—
75C2×C8×C19—24no—
76C2×C8×C19—42no—
77C2×C8×C19—42no—
78C42×C19—22no—
79C42×C19—22no—
80C42×C19—22no—
81C42×C19—41no—
82C42×C19C2×C812yes—
83C42×C19M1612yes—
84C42×C19D812yes—
85C42×C19SD1612yes—
86C42×C19C2×D412yes—
87C42×C19#4112yes—
88(C2×D19)⋊C4—44no—
89(C2×D19)⋊C4—44no—
90(C2×D19)⋊C4—42no—
91(C2×D19)⋊C4—42no—
92C4⋊Dic19—24no—
93C4⋊Dic19—42no—
94C4⋊Dic19—42no—
95C2×C19⋊C8—24no—
96C2×C19⋊C8—42no—
97C2×C19⋊C8—42no—
98#9674—191nomaximal, Sylow
99C23×C19C2×C22⋊C411yescharacteristic
100C22×D19—24no—
101C22×D19—42no—
102C22×D19—42no—
103C22×D19—42no—
104C22×D19—42no—
105C22×D19—42no—
106C22×D19—42no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19C22⋊C812yes—
117C2×C4×C19C22⋊C812yes—
118C2×C4×C19#10212yes—
119C2×C4×C19#10212yes—
120C2×C4×C19#10412yes—
121C2×C4×C19C4×D412yes—
122C2×C4×C19#12112yes—
123C2×C4×C19#12411yescharacteristic
124C2×C4×C19#12711yescharacteristic
125C2×C4×C19C22×C811yescharacteristic
126C2×C4×C19C2×M1611yescharacteristic
127C2×C4×C19#13112yes—
128C2×C4×C19C2×D811yescharacteristic
129C2×C4×C19C2×SD1611yescharacteristic
130C2×C4×C19AGL(1,ℤ/8)12yes—
131C2×Dic19—42no—
132C2×Dic19—42no—
133C2×Dic19—42no—
134D76—28no—
135D76—48no—
136D76—48no—
137D76—44no—
138C4×D19—84no—
139C4×D19—84no—
140C8×C19—44no—
141C19⋊C8—44no—
142C4×#127—191no—
143C4×C4⋊C8—191no—
144C4×C4⋊C8D1911yescharacteristic, complemented
145C2×D4⋊C8—194no—
146C22×C19#39011yescharacteristic
147C22×C19C2×C22⋊C811yescharacteristic
148C22×C19#40811yescharacteristic
149C22×C19C2×#10211yescharacteristic
150C22×C19#41811yescharacteristic
151C22×C19C2×#10411yescharacteristic
152C22×C19#42111yescharacteristic
153C2×D19—44no—
154C2×D19—44no—
155C2×D19—44no—
156C2×D19—82no—
157C2×D19—82no—
158C2×D19—82no—
159C2×D19—82no—
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—22no—
163C4×C19—22no—
164C4×C19—41no—
165C4×C19D4⋊C814yescomplemented
166C4×C19C8×D412yes—
167C4×C19#43612yes—
168C4×C19#45912yes—
169C4×C19#46012yes—
170Dic19—82no—
171C2×#127—191no—
172C2×C4×D4—192no—
173C2×C4×D4—381no—
174C2×C4×D4—381no—
175C2×C4⋊C8—21no—
176C2×C4⋊C8—192no—
177C2×C4×C8—381no—
178C2×C4×C8C2×D1912yes—
179#390—192no—
180#390—381no—
181#390—381no—
182#384—191no—
183C43C2×D1911yescharacteristic
184#336—21no—
185#336—381no—
186D4⋊C8—388no—
187C2×C19C2×D4⋊C811yescharacteristic
188C2×C19#147811yescharacteristic
189C2×C19#148011yescharacteristic
190C2×C19#148411yescharacteristic
191C2×C19#195411yescharacteristic
192C2×C19#198011yescharacteristic
193C2×C19#198211yescharacteristic
194D19—84no—
195C22×D4—192no—
196C22×D4—381no—
197C22×D4—381no—
198C23×C4—382no—
199C22×C8—22no—
200C22×C8—382no—
201#127—194no—
202#127—382no—
203C4×D4—384no—
204C4×D4—384no—
205C4×D4—764no—
206C4×D4—762no—
207C4×D4—762no—
208C2×C4⋊C4—192no—
209C2×C4⋊C4—381no—
210C2×C4⋊C4—381no—
211C2×C22⋊C4—382no—
212C2×C22⋊C4—382no—
213C2×C22⋊C4—382no—
214C2×C42C4×D1911yescharacteristic
215C2×C42C4×D1911yescharacteristic
216C2×C42D7611yescharacteristic
217C2×C42D7611yescharacteristic
218C2×C42C22⋊D1911yescharacteristic
219C2×C42C22⋊D1911yescharacteristic
220C2×C42C22×D1911yescharacteristic
221C4⋊C8—24no—
222C4⋊C8—194no—
223C4⋊C8—382no—
224C4×C8—24no—
225C4×C8—762no—
226C19#967411yescharacteristic, complemented, Sylow
227C24—382no—
228C2×D4—194no—
229C2×D4—384no—
230C2×D4—384no—
231C2×D4—384no—
232C2×D4—382no—
233C2×D4—384no—
234C2×D4—762no—
235C2×D4—762no—
236C2×D4—762no—
237C2×D4—762no—
238C22×C4—382no—
239C22×C4—764no—
240C22×C4—762no—
241C22×C4—762no—
242C22×C4—764no—
243C22×C4(C2×D19)⋊C411yescharacteristic
244C22×C4(C2×D19)⋊C411yescharacteristic
245C22×C4(C2×D19)⋊C411yescharacteristic
246C22×C4(C2×D19)⋊C411yescharacteristic
247C22×C4C2×C4×D1911yescharacteristic
248C22×C4C2×D7611yescharacteristic
249C22×C4C2×C22⋊D1911yescharacteristic
250C2×C8—24no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—384no—
254C2×C8—762no—
255C2×C8—762no—
256C4⋊C4—384no—
257C4⋊C4—762no—
258C4⋊C4—762no—
259C22⋊C4—764no—
260C22⋊C4—762no—
261C22⋊C4—762no—
262C22⋊C4—764no—
263C42—22no—
264C42—22no—
265C42—22no—
266C42—41no—
267C42C8×D1912yes—
268C42#6451512yes—
269C42#6451612yes—
270C42D15212yes—
271C42D4×D1912yes—
272C42#6454512yes—
273C23—384no—
274C23—762no—
275C23—762no—
276C23—762no—
277C23—762no—
278C23—762no—
279C23—762no—
280C23C2×(C2×D19)⋊C411yescharacteristic
281D4—388no—
282D4—768no—
283D4—768no—
284D4—764no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—762no—
295C2×C4—762no—
296C2×C4—762no—
297C2×C4—1524no—
298C2×C4—1524no—
299C2×C4#1059726212yes—
300C2×C4(C2×D19)⋊C812yes—
301C2×C4(C2×D19)⋊C812yes—
302C2×C4#1059727812yes—
303C2×C4#1059727812yes—
304C2×C4#1059733912yes—
305C2×C4#1059734112yes—
306C2×C4C2×C8×D1911yescharacteristic
307C2×C4C2×#6451511yescharacteristic
308C2×C4C2×#6451611yescharacteristic
309C2×C4C2×D15211yescharacteristic
310C2×C4#1059735312yes—
311C2×C4#1059735412yes—
312C2×C4#1059738611yescharacteristic
313C2×C4#1059739311yescharacteristic
314C8—44no—
315C8—764no—
316C22—764no—
317C22—764no—
318C22—764no—
319C22—1522no—
320C22—1522no—
321C22—1522no—
322C22—1522no—
323C22#1192644511yescharacteristic
324C22C2×(C2×D19)⋊C811yescharacteristic
325C22#1192651211yescharacteristic
326C22C2×#1059727811yescharacteristic
327C22#1192655011yescharacteristic
328C22C2×#1059726211yescharacteristic
329C22#1192656211yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—22no—
334C4—41no—
335C4—1522no—
336C4#1192627314yescomplemented
337C4#1192660912yes—
338C4#1192662112yes—
339C4#1192674012yes—
340C4#1192674512yes—
341C2—1524no—
342C2C2×#1192627311yescharacteristic
343C2#1456202711yescharacteristic
344C2#1456203511yescharacteristic
345C2#1456205311yescharacteristic
346C2#1456442811yescharacteristic
347C2#1456455311yescharacteristic
348C2#1456456111yescharacteristic
subgroupG/H
centerC22×C4C2×D76
commutatorC2×C4×C19C22×C8
FrattiniC2×C42C22×D19
FittingC4×C19×C4⋊C8C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597320C4
cosocleC2×C42×C19C23
hypercenterC4×C4⋊C8D19
hypocenterC19#9674
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊(C19⋊C8)C2semidirect
3. C2×#11926273C2semidirect
4. C4×C19×C4⋊C8C2semidirect
41. #10597320C8semidirect
50. C4⋊(C19⋊C8)D4semidirect
144. C4×C4⋊C8D19semidirect
165. C4×C19D4⋊C8semidirect
226. C19#9674semidirect
336. C4#11926273semidirect

Maximal subgroups

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

subgroupindex
C4×#105973202
C4×C4⋊(C19⋊C8)2
C2×#119262732
C4×C19×C4⋊C82
#967419