Finite Group Databasebeta

← #18075878

Subgroups — #18075878

Order 4864.

830 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 139 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×#11926404C211yesmaximal, characteristic
2#14563545C211yesmaximal, characteristic
3#14561477C214yesmaximal, complemented
4C19×#1779C211yesmaximal, characteristic
5C22×C4⋊Dic19C411yescharacteristic
6C22×C4⋊Dic19C411yescharacteristic
7C22×C22⋊Dic19C412yes—
8C2×C22⋊(C19⋊C8)—21no—
9C2×C22⋊(C19⋊C8)—21no—
10C2×C22⋊(C19⋊C8)C2212yes—
11#11926404—21no—
12#11926404—21no—
13#11926404—21no—
14#11926404—21no—
15C2×C19⋊#95C2212yes—
16C24×C4×C19C2211yescharacteristic
17C2×C19×C22⋊C8—21no—
18C2×C19×C22⋊C8—21no—
19C2×C19×C22⋊C8C2212yes—
20C25×C19C2×C411yescharacteristic
21C23×C4×C19—24no—
22C23×C4×C19—42no—
23C23×C4×C19—42no—
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C23×C4×C19D411yescharacteristic
27C23×C4×C19D411yescharacteristic
28C23×C4×C19D411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C23×Dic19C2×C412yes—
31C23×Dic19C2×C412yes—
32C22×C8×C19—22no—
33C2×C22⋊Dic19—22no—
34C2×C22⋊Dic19—22no—
35C2×C22⋊Dic19—44no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19—42no—
41C2×C4⋊Dic19—42no—
42C22×C19⋊C8—22no—
43C19×C22⋊C8—24no—
44C19×C22⋊C8—42no—
45C19×C22⋊C8—42no—
46C19⋊#95—22no—
47C19⋊#95—22no—
48C22⋊(C19⋊C8)—24no—
49C22⋊(C19⋊C8)—42no—
50C22⋊(C19⋊C8)—42no—
51C24×C19—22no—
52C24×C19—22no—
53C24×C19—22no—
54C24×C19—22no—
55C24×C19—22no—
56C24×C19—41no—
57C24×C19—41no—
58C24×C19C22⋊C411yescharacteristic
59C24×C19C22⋊C411yescharacteristic
60C24×C19C22×C411yescharacteristic
61C22×C4×C19—22no—
62C22×C4×C19—22no—
63C22×C4×C19—22no—
64C22×C4×C19—22no—
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—22no—
68C22×C4×C19—22no—
69C22×C4×C19—22no—
70C22×C4×C19—22no—
71C22×C4×C19—22no—
72C22×C4×C19—41no—
73C22×C4×C19—41no—
74C22×C4×C19—41no—
75C22×C4×C19—41no—
76C22×C4×C19—41no—
77C22×C4×C19—41no—
78C22×C4×C19—416no—
79C22×C4×C19C22⋊C411yescharacteristic
80C22×C4×C19C22⋊C411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19#4114yes—
84C22×Dic19—22no—
85C22×Dic19—22no—
86C22×Dic19—24no—
87C22×Dic19—24no—
88C22×Dic19—42no—
89C22×Dic19—42no—
90C22×Dic19—42no—
91C22×Dic19—42no—
92C2×C8×C19—42no—
93C2×C8×C19—42no—
94C2×C8×C19—42no—
95C22⋊Dic19—44no—
96C22⋊Dic19—44no—
97C4⋊Dic19—42no—
98C4⋊Dic19—42no—
99C4⋊Dic19—42no—
100C4⋊Dic19—42no—
101C2×C19⋊C8—42no—
102C2×C19⋊C8—42no—
103C2×C19⋊C8—42no—
104#8704—191nomaximal, Sylow
105C23×C19—21no—
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—28no—
110C23×C19—21no—
111C23×C19—21no—
112C23×C19—21no—
113C23×C19—21no—
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—21no—
117C23×C19—21no—
118C23×C19—21no—
119C23×C19—21no—
120C23×C19—21no—
121C23×C19—21no—
122C23×C19—44no—
123C23×C19—44no—
124C23×C19—44no—
125C23×C19—44no—
126C23×C19—44no—
127C23×C19—44no—
128C23×C19#10012yes—
129C23×C19#10112yes—
130C23×C19C2×C22⋊C411yescharacteristic
131C23×C19#11712yes—
132C23×C19#13112yes—
133C23×C19#13112yes—
134C2×C4×C19—28no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—44no—
144C2×C4×C19—44no—
145C2×C4×C19—44no—
146C2×C4×C19—44no—
147C2×C4×C19—44no—
148C2×C4×C19#9912yes—
149C2×C4×C19#9912yes—
150C2×C4×C19#12312yes—
151C2×C4×C19#12312yes—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155C2×Dic19—42no—
156C2×Dic19—42no—
157C2×Dic19—42no—
158C2×Dic19—84no—
159C2×Dic19—84no—
160C8×C19—82no—
161C19⋊C8—82no—
162C2×#380—191no—
163#1779—191no—
164#1779D1911yescharacteristic
165#1280—194no—
166C22×C19—22no—
167C22×C19—22no—
168C22×C19—22no—
169C22×C19—22no—
170C22×C19—22no—
171C22×C19—22no—
172C22×C19—22no—
173C22×C19—22no—
174C22×C19—22no—
175C22×C19—22no—
176C22×C19—22no—
177C22×C19—22no—
178C22×C19—416no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19—41no—
183C22×C19—41no—
184C22×C19—41no—
185C22×C19—41no—
186C22×C19—41no—
187C22×C19#38111yescharacteristic
188C22×C19#40811yescharacteristic
189C22×C19#40811yescharacteristic
190C22×C19C2×#9911yescharacteristic
191C22×C19C2×#9911yescharacteristic
192C22×C19C2×#10011yescharacteristic
193C22×C19C2×#10111yescharacteristic
194C22×C19#43314yes—
195C4×C19—22no—
196C4×C19—22no—
197C4×C19—22no—
198C4×C19—22no—
199Dic19—82no—
200Dic19—82no—
201C24×C4C2×D1911yescharacteristic
202C22×C4⋊C4—191no—
203C22×C4⋊C4—191no—
204C22×C22⋊C4—192no—
205C2×C22⋊C8—21no—
206C2×C22⋊C8—21no—
207C2×C22⋊C8—192no—
208C2×C22⋊C8—381no—
209C2×C22⋊C8—381no—
210C2×C22⋊C8C2×D1912yes—
211#380—381no—
212#380—381no—
213#380—381no—
214#380—381no—
215C2×#95—192no—
216C2×C19—24no—
217C2×C19—42no—
218C2×C19—42no—
219C2×C19#147111yescharacteristic
220C2×C19#147111yescharacteristic
221C2×C19#147211yescharacteristic
222C2×C19#147211yescharacteristic
223C2×C19#181811yescharacteristic
224C2×C19#181911yescharacteristic
225C2×C19#182111yescharacteristic
226C25C4×D1911yescharacteristic
227C23×C4—24no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—192no—
231C23×C4—192no—
232C23×C4C4×D1911yescharacteristic
233C23×C4D7611yescharacteristic
234C23×C4D7611yescharacteristic
235C23×C4C22⋊D1911yescharacteristic
236C23×C4C22⋊D1911yescharacteristic
237C23×C4C22×D1911yescharacteristic
238C22×C8—22no—
239C22×C8—382no—
240C2×C4⋊C4—381no—
241C2×C4⋊C4—381no—
242C2×C4⋊C4—381no—
243C2×C4⋊C4—381no—
244C2×C4⋊C4—762no—
245C2×C4⋊C4—762no—
246C2×C22⋊C4—382no—
247C2×C22⋊C4—382no—
248C2×C22⋊C4—764no—
249C22⋊C8—24no—
250C22⋊C8—42no—
251C22⋊C8—42no—
252C22⋊C8—384no—
253C22⋊C8—762no—
254C22⋊C8—762no—
255#95—382no—
256#95—382no—
257C19#870411yescharacteristic, complemented, Sylow
258C24—22no—
259C24—22no—
260C24—22no—
261C24—22no—
262C24—22no—
263C24—41no—
264C24—41no—
265C24(C2×D19)⋊C411yescharacteristic
266C24(C2×D19)⋊C411yescharacteristic
267C24C2×C4×D1911yescharacteristic
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—416no—
286C22×C4—382no—
287C22×C4—382no—
288C22×C4—384no—
289C22×C4—384no—
290C22×C4—762no—
291C22×C4—762no—
292C22×C4—762no—
293C22×C4—762no—
294C22×C4(C2×D19)⋊C411yescharacteristic
295C22×C4(C2×D19)⋊C411yescharacteristic
296C22×C4C2×D7611yescharacteristic
297C22×C4#6454314yes—
298C22×C4C2×C22⋊D1911yescharacteristic
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—762no—
303C2×C8—762no—
304C2×C8—762no—
305C4⋊C4—762no—
306C4⋊C4—762no—
307C4⋊C4—762no—
308C4⋊C4—762no—
309C22⋊C4—764no—
310C22⋊C4—764no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—28no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—44no—
329C23—44no—
330C23—44no—
331C23—44no—
332C23—44no—
333C23—44no—
334C23#1059728012yes—
335C23#1059728112yes—
336C23#1059732312yes—
337C23#1059734712yes—
338C23#1059735312yes—
339C23C2×(C2×D19)⋊C411yescharacteristic
340C2×C4—28no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—762no—
355C2×C4—762no—
356C2×C4—762no—
357C2×C4—762no—
358C2×C4—762no—
359C2×C4—762no—
360C2×C4—1524no—
361C2×C4—1524no—
362C2×C4#1059726312yes—
363C2×C4#1059726312yes—
364C2×C4#1059733212yes—
365C2×C4#1059738112yes—
366C8—82no—
367C8—1522no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—416no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22#1192640511yescharacteristic
390C22#1192651011yescharacteristic
391C22#1192651211yescharacteristic
392C22C2×#1059726311yescharacteristic
393C22C2×#1059726311yescharacteristic
394C22C2×#1059728011yescharacteristic
395C22C2×#1059728111yescharacteristic
396C22#1192660214yes—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—1522no—
402C4—1522no—
403C2—24no—
404C2—42no—
405C2—42no—
406C2#1456199411yescharacteristic
407C2#1456199611yescharacteristic
408C2#1456199811yescharacteristic
409C2#1456200011yescharacteristic
410C2#1456370411yescharacteristic
411C2#1456370711yescharacteristic
412C2#1456371311yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1779C2
socleC23×C19C2×C22⋊C4
prime radicalC25×C19C2×C4
cosocleC23×C4×C19C23
hypercenter#1779D19
hypocenterC19#8704
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. #14561477C2semidirect
257. C19#8704semidirect

Maximal subgroups

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

subgroupindex
C2×#119264042
#145635452
#145614772
C19×#17792
#870419