Finite Group Databasebeta

← #18085112

Subgroups — #18085112

Order 4864.

594 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926831C211yesmaximal, characteristic
2C2×#11926746C211yesmaximal, characteristic
3#14564429C211yesmaximal, characteristic
4C2×#11926293C211yesmaximal, characteristic, complemented
5C2×#11926290C211yesmaximal, characteristic, complemented
6#14561470C211yesmaximal, characteristic, complemented
7C2×C19×#498C211yesmaximal, characteristic, complemented
8C22×#64527—21no—
9C2×C4×D76C2211yescharacteristic
10#11926831—22no—
11#11926831—22no—
12#11926746—22no—
13#11926746—22no—
14C2×#10597265—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#11926293—22no—
22#11926290—22no—
23C2×C19×C4⋊Q8C2211yescharacteristic
24C2×C19×C4⋊Q8C2211yescharacteristic
25C19×#498—22no—
26C19×#498—22no—
27C2×C19×#106—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×#106—28no—
60C4×C8×C19—21no—
61C4×C8×C19—21no—
62#10597292—24no—
63(C2×D19)⋊C8—44no—
64#10597266—24no—
65#10597265—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—41no—
79C2×Q8×C19—41no—
80C2×Q8×C19—41no—
81C2×Q8×C19—82no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19#4111yescharacteristic
87C22×Dic19—21no—
88C2×D76—21no—
89C2×D76—21no—
90C2×D76—21no—
91C2×D76—21no—
92C2×D76—21no—
93C2×D76SD1612yes—
94C2×C4×D19—41no—
95C2×C4×D19—41no—
96C2×C4×D19—42no—
97C2×C4×D19—42no—
98C2×C8×C19—22no—
99C2×C8×C19—22no—
100C2×C8×C19SD1614yescomplemented
101C4⋊C4×C19—22no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19—22no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C42×C19C2×D411yescharacteristic
110C42×C19C2×D411yescharacteristic
111C42×C19C2×D411yescharacteristic
112C42×C19C2×D411yescharacteristic
113#64527—48no—
114(C2×D19)⋊C4—41no—
115(C2×D19)⋊C4—41no—
116C4⋊Dic19—21no—
117C4⋊Dic19—21no—
118C2×C19⋊C8—22no—
119C2×C19⋊C8—22no—
120C2×C19⋊C8—41no—
121C2×C19⋊C8—41no—
122C2×C19⋊C8—41no—
123C2×C19⋊C8—41no—
124C2×C19⋊C8—41no—
125C2×C19⋊C8—42no—
126#10271—191nomaximal, Sylow
127C23×C19#12111yescharacteristic
128C22×D19—22no—
129C22×D19—41no—
130C22×D19—42no—
131C22×D19—41no—
132C22×D19—42no—
133Q8×C19—42no—
134Q8×C19—42no—
135Q8×C19—82no—
136Q8×C19—82no—
137Q8×C19—81no—
138Q8×C19—81no—
139C2×C4×C19—22no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19—81no—
143C2×C4×C19—81no—
144C2×C4×C19—82no—
145C2×C4×C19#12011yescharacteristic
146C2×C4×C19#12011yescharacteristic
147C2×C4×C19#12011yescharacteristic
148C2×C4×C19#12111yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19#12711yescharacteristic
151C2×C4×C19C2×SD1612yes—
152C2×C4×C19C2×SD1611yescharacteristic
153C2×C4×C19#13511yescharacteristic
154C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C19#13712yes—
156C2×C4×C19#13711yescharacteristic
157C2×Dic19—41no—
158C2×Dic19—42no—
159D76—22no—
160D76—22no—
161D76—41no—
162D76—41no—
163C4×D19—82no—
164C4×D19—81no—
165C4×D19—81no—
166C8×C19—24no—
167C19⋊C8—42no—
168C19⋊C8—42no—
169C19⋊C8—81no—
170C2×#498D1911yescharacteristic, complemented
171C2×#476—191no—
172C2×#461—191no—
173#1954—191no—
174C2×#333—191no—
175C2×#332—191no—
176#1277—191no—
177C22×C19#39211yescharacteristic
178C22×C19#46112yes—
179C22×C19#46511yescharacteristic
180C22×C19#46811yescharacteristic
181C22×C19#47112yes—
182C2×D19—44no—
183C2×D19—42no—
184C2×D19—82no—
185C2×D19—81no—
186C2×D19—81no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—82no—
190C4×C19—82no—
191C4×C19#44811yescharacteristic
192C4×C19#44812yes—
193C4×C19#44911yescharacteristic
194C4×C19#45011yescharacteristic
195C4×C19#45211yescharacteristic
196C4×C19#49211yescharacteristic
197C4×C19#49711yescharacteristic
198Dic19—81no—
199C22×SD16—381no—
200C2×C4⋊Q8C2×D1911yescharacteristic
201C2×C4⋊Q8C2×D1911yescharacteristic
202C2×C4×D4—191no—
203#498—22no—
204#498—22no—
205#476—382no—
206#476—382no—
207#461—382no—
208#461—382no—
209C2×#106—22no—
210C2×#106—381no—
211C2×C4⋊C8—191no—
212C2×C4⋊C8—191no—
213C2×C4⋊C8—191no—
214C2×#103—381no—
215C2×#102—381no—
216C2×C22⋊C8—382no—
217C2×C4×C8C2×D1911yescharacteristic
218#333—382no—
219#332—382no—
220C2×C19#167112yes—
221C2×C19#169112yes—
222C2×C19#200011yescharacteristic
223C2×C19#201311yescharacteristic
224C2×C19#201911yescharacteristic
225D19—82no—
226C22×Q8—21no—
227C22×Q8—21no—
228C22×D4—191no—
229C23×C4—381no—
230C2×SD16—384no—
231C2×SD16—762no—
232C2×SD16—762no—
233C22×C8—381no—
234C22×C8—381no—
235C22×C8—381no—
236C22×C8C22⋊D1912yes—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8C22⋊D1912yes—
244C4⋊Q8C22⋊D1912yes—
245C4×D4—381no—
246C4×D4—381no—
247C4×D4—381no—
248C4×D4—381no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—191no—
254C2×C22⋊C4—381no—
255C2×C42C22×D1911yescharacteristic
256#106—28no—
257#106—384no—
258C4⋊C8—192no—
259C4⋊C8—192no—
260C4⋊C8—381no—
261C4⋊C8—381no—
262C4⋊C8—381no—
263C4⋊C8—381no—
264#103—384no—
265#102—384no—
266C22⋊C8—764no—
267C4×C8—21no—
268C4×C8—21no—
269C19#1027111yescharacteristic, complemented, Sylow
270C24—381no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—82no—
280C2×D4—192no—
281C2×D4—381no—
282C2×D4—381no—
283C2×D4—381no—
284C2×D4—381no—
285C2×D4—381no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—381no—
289C22×C4—761no—
290C22×C4—762no—
291C22×C4—762no—
292C22×C4—761no—
293C22×C4D4×D1911yescharacteristic
294C22×C4#6454311yescharacteristic
295C22×C4C2×C22⋊D1911yescharacteristic
296SD16—768no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—382no—
300C2×C8—382no—
301C2×C8—761no—
302C2×C8—761no—
303C2×C8—761no—
304C2×C8—761no—
305C2×C8—761no—
306C2×C8—762no—
307C2×C8#6452714yescomplemented
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—381no—
317C4⋊C4—381no—
318C22⋊C4—761no—
319C22⋊C4—761no—
320C42D4×D1911yescharacteristic
321C42D4×D1911yescharacteristic
322C42C2×C22⋊D1911yescharacteristic
323C42C2×C22⋊D1911yescharacteristic
324C23—382no—
325C23—761no—
326C23—762no—
327C23—761no—
328C23—762no—
329C23#1059738411yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—82no—
333Q8—82no—
334Q8—81no—
335Q8—81no—
336D4—382no—
337D4—382no—
338D4—761no—
339D4—761no—
340C2×C4—22no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—81no—
344C2×C4—82no—
345C2×C4—81no—
346C2×C4—761no—
347C2×C4—762no—
348C2×C4—1521no—
349C2×C4—1521no—
350C2×C4—1522no—
351C2×C4SD16×D1911yescharacteristic
352C2×C4#1059736011yescharacteristic
353C2×C4#1059736111yescharacteristic
354C2×C4#1059736211yescharacteristic
355C2×C4#1059738311yescharacteristic
356C2×C4#1059738311yescharacteristic
357C2×C4#1059738511yescharacteristic
358C2×C4#1059738511yescharacteristic
359C2×C4#1059738611yescharacteristic
360C2×C4C2×#6452712yes—
361C2×C4#1059738812yes—
362C2×C4#1059739911yescharacteristic
363C8—24no—
364C8—762no—
365C8—762no—
366C8—1521no—
367C22—762no—
368C22—764no—
369C22—1522no—
370C22—1521no—
371C22—1521no—
372C22#1192645211yescharacteristic
373C22#1192674612yes—
374C22#1192677011yescharacteristic
375C22#1192678711yescharacteristic
376C22#1192680412yes—
377C4—21no—
378C4—21no—
379C4—82no—
380C4—82no—
381C4—1521no—
382C4#1192668111yescharacteristic
383C4#1192668312yes—
384C4#1192668811yescharacteristic
385C4#1192669311yescharacteristic
386C4#1192670311yescharacteristic
387C4#1192691811yescharacteristic
388C4#1192693611yescharacteristic
389C2—1522no—
390C2#1456300712yes—
391C2#1456313112yes—
392C2#1456463511yescharacteristic
393C2#1456471811yescharacteristic
394C2#1456474711yescharacteristic
subgroupG/H
centerC23#10597384
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC2×C19×#498C2
socleC23×C19#121
prime radicalC22×D76D4
hypercenterC2×#498D19
hypocenterC19#10271
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
4. C2×#11926293C2semidirect
5. C2×#11926290C2semidirect
6. #14561470C2semidirect
7. C2×C19×#498C2semidirect
100. C2×C8×C19SD16semidirect
170. C2×#498D19semidirect
269. C19#10271semidirect
307. C2×C8#64527semidirect

Maximal subgroups

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

subgroupindex
C2×#119268312
C2×#119267462
#145644292
C2×#119262932
C2×#119262902
#145614702
C2×C19×#4982
#1027119