Finite Group Databasebeta

← #18085105

Subgroups — #18085105

Order 4864.

594 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926821C211yesmaximal, characteristic
2C2×#11926746C211yesmaximal, characteristic
3#14564429C211yesmaximal, characteristic
4C2×#11926290C211yesmaximal, characteristic, complemented
5C2×#11926290C211yesmaximal, characteristic, complemented
6#14561470C211yesmaximal, characteristic, complemented
7C2×C19×#487C211yesmaximal, characteristic, complemented
8C22×#64527—21no—
9C2×C4×D76C2211yescharacteristic
10#11926821—22no—
11#11926821—22no—
12#11926746—22no—
13#11926746—22no—
14C2×#10597264—21no—
15C2×C4⋊(C19⋊C8)C2211yescharacteristic
16C2×C4⋊(C19⋊C8)C2211yescharacteristic
17C2×C4⋊(C19⋊C8)C2211yescharacteristic
18C2×#10597292—21no—
19C2×#10597266—21no—
20C2×(C2×D19)⋊C8—22no—
21#11926290—22no—
22#11926290—22no—
23C2×C19×C4⋊Q8C2211yescharacteristic
24C2×C19×C4⋊Q8C2211yescharacteristic
25C19×#487—22no—
26C19×#487—22no—
27C2×C19×#103—22no—
28C2×C4×C8×C19C2211yescharacteristic
29C22×Q8×C19—21no—
30C22×Q8×C19—21no—
31C22×D76D411yescharacteristic
32C22×C4×D19—21no—
33C22×C8×C19D412yes—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8—21no—
38C19×C4⋊Q8—21no—
39C19×C4⋊Q8—21no—
40C19×C4⋊Q8D412yes—
41C19×C4⋊Q8D412yes—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C42×C19C2311yescharacteristic
47C2×#64527—24no—
48C2×#64527—42no—
49C2×#64527—42no—
50C2×(C2×D19)⋊C4—21no—
51C2×C4⋊Dic19D411yescharacteristic
52C22×C19⋊C8—21no—
53C22×C19⋊C8—21no—
54C22×C19⋊C8—21no—
55C4×D76—21no—
56C4×D76—21no—
57C4×D76—21no—
58C4×D76—21no—
59C19×#103—28no—
60C4×C8×C19—21no—
61C4×C8×C19—21no—
62#10597292—24no—
63(C2×D19)⋊C8—44no—
64#10597266—24no—
65#10597264—24no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—21no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)D412yes—
71C4⋊(C19⋊C8)D412yes—
72C23×D19—21no—
73C2×Q8×C19—22no—
74C2×Q8×C19—22no—
75C2×Q8×C19—41no—
76C2×Q8×C19—41no—
77C2×Q8×C19—41no—
78C2×Q8×C19—42no—
79C2×Q8×C19—41no—
80C2×Q8×C19—41no—
81C2×Q8×C19—42no—
82C2×Q8×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19#4111yescharacteristic
88C22×Dic19—21no—
89C2×D76—21no—
90C2×D76—21no—
91C2×D76—21no—
92C2×D76—21no—
93C2×D76—21no—
94C2×D76SD1612yes—
95C2×C4×D19—41no—
96C2×C4×D19—41no—
97C2×C4×D19—42no—
98C2×C4×D19—42no—
99C2×C8×C19—22no—
100C2×C8×C19—22no—
101C2×C8×C19—22no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19—22no—
105C4⋊C4×C19—22no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C42×C19C2×D411yescharacteristic
111C42×C19C2×D411yescharacteristic
112C42×C19C2×D411yescharacteristic
113C42×C19C2×D411yescharacteristic
114#64527—48no—
115(C2×D19)⋊C4—41no—
116(C2×D19)⋊C4—41no—
117C4⋊Dic19—21no—
118C4⋊Dic19—21no—
119C2×C19⋊C8—22no—
120C2×C19⋊C8—22no—
121C2×C19⋊C8—41no—
122C2×C19⋊C8—41no—
123C2×C19⋊C8—41no—
124C2×C19⋊C8—41no—
125C2×C19⋊C8—41no—
126C2×C19⋊C8—42no—
127#10270—191nomaximal, Sylow
128C23×C19#12111yescharacteristic
129C22×D19—22no—
130C22×D19—41no—
131C22×D19—42no—
132C22×D19—41no—
133C22×D19—42no—
134Q8×C19—44no—
135Q8×C19—42no—
136Q8×C19—42no—
137Q8×C19—81no—
138Q8×C19—81no—
139Q8×C19—81no—
140Q8×C19—81no—
141C2×C4×C19—22no—
142C2×C4×C19—42no—
143C2×C4×C19—42no—
144C2×C4×C19—82no—
145C2×C4×C19—81no—
146C2×C4×C19—81no—
147C2×C4×C19#12011yescharacteristic
148C2×C4×C19#12011yescharacteristic
149C2×C4×C19#12011yescharacteristic
150C2×C4×C19#12111yescharacteristic
151C2×C4×C19#12111yescharacteristic
152C2×C4×C19#12711yescharacteristic
153C2×C4×C19C2×SD1611yescharacteristic
154C2×C4×C19#13512yes—
155C2×C4×C19#13511yescharacteristic
156C2×C4×C19AGL(1,ℤ/8)12yes—
157C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C19#13711yescharacteristic
159C2×Dic19—41no—
160C2×Dic19—42no—
161D76—22no—
162D76—22no—
163D76—41no—
164D76—41no—
165C4×D19—82no—
166C4×D19—81no—
167C4×D19—81no—
168C8×C19—42no—
169C19⋊C8—42no—
170C19⋊C8—42no—
171C19⋊C8—81no—
172C2×#487D1911yescharacteristic, complemented
173C2×#474—191no—
174C2×#461—191no—
175#1954—191no—
176C2×#332—191no—
177C2×#332—191no—
178#1277—191no—
179C22×C19#39211yescharacteristic
180C22×C19#46312yes—
181C22×C19#46511yescharacteristic
182C22×C19#46811yescharacteristic
183C22×C19#47312yes—
184C2×D19—44no—
185C2×D19—42no—
186C2×D19—82no—
187C2×D19—81no—
188C2×D19—81no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—82no—
192C4×C19—82no—
193C4×C19#44811yescharacteristic
194C4×C19#44911yescharacteristic
195C4×C19#44912yes—
196C4×C19#45011yescharacteristic
197C4×C19#45211yescharacteristic
198C4×C19#49511yescharacteristic
199C4×C19#49611yescharacteristic
200Dic19—81no—
201C22×SD16—381no—
202C2×C4⋊Q8C2×D1911yescharacteristic
203C2×C4⋊Q8C2×D1911yescharacteristic
204C2×C4×D4—191no—
205#487—22no—
206#487—22no—
207#474—382no—
208#474—382no—
209#461—382no—
210#461—382no—
211C2×#107—381no—
212C2×C4⋊C8—191no—
213C2×C4⋊C8—191no—
214C2×C4⋊C8—191no—
215C2×#103—22no—
216C2×#103—381no—
217C2×#102—381no—
218C2×C22⋊C8—382no—
219C2×C4×C8C2×D1911yescharacteristic
220#332—382no—
221#332—382no—
222C2×C19#167912yes—
223C2×C19#169912yes—
224C2×C19#200011yescharacteristic
225C2×C19#201211yescharacteristic
226C2×C19#202011yescharacteristic
227D19—82no—
228C22×Q8—21no—
229C22×Q8—21no—
230C22×D4—191no—
231C23×C4—381no—
232C2×SD16—384no—
233C2×SD16—762no—
234C2×SD16—762no—
235C22×C8—381no—
236C22×C8—381no—
237C22×C8—381no—
238C22×C8C22⋊D1912yes—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8C22⋊D1912yes—
246C4⋊Q8C22⋊D1912yes—
247C4×D4—381no—
248C4×D4—381no—
249C4×D4—381no—
250C4×D4—381no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—191no—
256C2×C22⋊C4—381no—
257C2×C42C22×D1911yescharacteristic
258#107—384no—
259C4⋊C8—192no—
260C4⋊C8—192no—
261C4⋊C8—381no—
262C4⋊C8—381no—
263C4⋊C8—381no—
264C4⋊C8—381no—
265#103—28no—
266#103—384no—
267#102—384no—
268C22⋊C8—764no—
269C4×C8—21no—
270C4×C8—21no—
271C19#1027011yescharacteristic, complemented, Sylow
272C24—381no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—42no—
278C2×Q8—42no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×D4—192no—
284C2×D4—381no—
285C2×D4—381no—
286C2×D4—381no—
287C2×D4—381no—
288C2×D4—381no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—381no—
292C22×C4—761no—
293C22×C4—762no—
294C22×C4—762no—
295C22×C4—761no—
296C22×C4D4×D1911yescharacteristic
297C22×C4#6454311yescharacteristic
298C22×C4C2×C22⋊D1911yescharacteristic
299SD16—768no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—382no—
304C2×C8—382no—
305C2×C8—761no—
306C2×C8—761no—
307C2×C8—761no—
308C2×C8—761no—
309C2×C8—761no—
310C2×C8—762no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—381no—
320C4⋊C4—381no—
321C22⋊C4—761no—
322C22⋊C4—761no—
323C42D4×D1911yescharacteristic
324C42D4×D1911yescharacteristic
325C42C2×C22⋊D1911yescharacteristic
326C42C2×C22⋊D1911yescharacteristic
327C23—382no—
328C23—761no—
329C23—762no—
330C23—761no—
331C23—762no—
332C23#1059738411yescharacteristic
333Q8—44no—
334Q8—42no—
335Q8—42no—
336Q8—81no—
337Q8—81no—
338Q8—81no—
339Q8—81no—
340D4—382no—
341D4—382no—
342D4—761no—
343D4—761no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—761no—
351C2×C4—762no—
352C2×C4—1521no—
353C2×C4—1521no—
354C2×C4—1522no—
355C2×C4SD16×D1911yescharacteristic
356C2×C4#1059736011yescharacteristic
357C2×C4#1059736111yescharacteristic
358C2×C4#1059736211yescharacteristic
359C2×C4#1059738311yescharacteristic
360C2×C4#1059738311yescharacteristic
361C2×C4#1059738511yescharacteristic
362C2×C4#1059738511yescharacteristic
363C2×C4#1059738611yescharacteristic
364C2×C4#1059739512yes—
365C2×C4#1059739612yes—
366C2×C4#1059739911yescharacteristic
367C8—42no—
368C8—762no—
369C8—762no—
370C8—1521no—
371C22—762no—
372C22—764no—
373C22—1521no—
374C22—1522no—
375C22—1521no—
376C22#1192645211yescharacteristic
377C22#1192675612yes—
378C22#1192677011yescharacteristic
379C22#1192678711yescharacteristic
380C22#1192681612yes—
381C4—21no—
382C4—21no—
383C4—82no—
384C4—82no—
385C4—1521no—
386C4#1192668111yescharacteristic
387C4#1192668811yescharacteristic
388C4#1192668912yes—
389C4#1192669311yescharacteristic
390C4#1192670311yescharacteristic
391C4#1192692611yescharacteristic
392C4#1192693411yescharacteristic
393C2—1522no—
394C2#1456305512yes—
395C2#1456317912yes—
396C2#1456463511yescharacteristic
397C2#1456471211yescharacteristic
398C2#1456475411yescharacteristic
subgroupG/H
centerC23#10597384
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC2×C19×#487C2
socleC23×C19#121
prime radicalC22×D76D4
hypercenterC2×#487D19
hypocenterC19#10270
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
4. C2×#11926290C2semidirect
5. C2×#11926290C2semidirect
6. #14561470C2semidirect
7. C2×C19×#487C2semidirect
172. C2×#487D19semidirect
271. C19#10270semidirect

Maximal subgroups

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

subgroupindex
C2×#119268212
C2×#119267462
#145644292
C2×#119262902
#145614702
C2×C19×#4872
#1027019