Finite Group Databasebeta

← #18078600

Subgroups — #18078600

Order 4864.

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

normal subgroups only

This group has 762 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
1#14569369C211yesmaximal, characteristic
2#14566249C211yesmaximal, characteristic, complemented
3#14562204C212yesmaximal, complemented
4#14561503C212yesmaximal, complemented
5C2×C19×#323C211yesmaximal, characteristic, complemented
6C2×#10597376C2211yescharacteristic
7C2×#10597399—21no—
8C22×C22⋊Dic19—21no—
9#11926469C412yescomplemented
10#11926460—22no—
11#11926453C412yescomplemented
12#11926423—21no—
13#11926419—24no—
14#11926404—21no—
15#11926404C2211yescharacteristic
16#11926404C2212yes—
17#11926279—24no—
18C22×C22⋊C4×C19C2211yescharacteristic
19C2×C19×C22⋊C8C2212yes—
20C19×#323—22no—
21C25×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—21no—
25C22×C22⋊D19—22no—
26C23×Dic19—22no—
27C22×D76C2×C411yescharacteristic, complemented
28C22×C8×C19—22no—
29C2×C22⋊C4×C19—22no—
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19C2×C412yes—
32C2×C22⋊C4×C19D412yes—
33#10597399—42no—
34#10597399—42no—
35C2×C22⋊Dic19—22no—
36C2×C22⋊Dic19—22no—
37C2×C22⋊Dic19—22no—
38C2×C22⋊Dic19—21no—
39C2×C22⋊Dic19—42no—
40C2×C22⋊Dic19—42no—
41#10597376—22no—
42#10597376—22no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—22no—
45C2×C4⋊Dic19—22no—
46C2×C4⋊Dic19—22no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19C2×C411yescharacteristic, complemented
49C19×C22⋊C8—22no—
50C19×C22⋊C8—22no—
51C19⋊#95—22no—
52C19⋊#95—22no—
53C19⋊#95C2×C412yescomplemented
54C19⋊#95D414yescomplemented
55C24×C19—21no—
56C24×C19—21no—
57C24×C19—21no—
58C24×C19—21no—
59C24×C19—81no—
60C24×C19—81no—
61C24×C19C22⋊C412yes—
62C24×C19D812yes—
63C24×C19SD1612yes—
64C24×C19C2×D411yescharacteristic
65C23×D19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—81no—
69C22×C4×C19—81no—
70C22×C4×C19C22⋊C412yes—
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D412yes—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19#4112yes—
75C2×C22⋊D19—44no—
76C2×C22⋊D19—41no—
77C2×C22⋊D19—41no—
78C2×C22⋊D19—41no—
79C2×C22⋊D19—41no—
80C2×C22⋊D19—41no—
81C2×C22⋊D19—41no—
82C2×C22⋊D19—82no—
83C2×C22⋊D19—82no—
84C22×Dic19—21no—
85C22×Dic19—22no—
86C22×Dic19—24no—
87C22×Dic19—44no—
88C22×Dic19—82no—
89C22×Dic19—82no—
90C2×D76—22no—
91C2×D76—81no—
92C2×C8×C19—42no—
93C2×C8×C19—82no—
94C22⋊C4×C19—24no—
95C22⋊C4×C19—24no—
96C22⋊Dic19—44no—
97C22⋊Dic19—44no—
98C22⋊Dic19—42no—
99C22⋊Dic19—41no—
100C22⋊Dic19—41no—
101C22⋊Dic19—42no—
102(C2×D19)⋊C4—42no—
103(C2×D19)⋊C4—82no—
104C4⋊Dic19—22no—
105C4⋊Dic19—82no—
106C4⋊Dic19—82no—
107C4⋊Dic19—81no—
108#9203—191nomaximal, Sylow
109C23×C19—22no—
110C23×C19—22no—
111C23×C19—22no—
112C23×C19—22no—
113C23×C19—22no—
114C23×C19—22no—
115C23×C19—41no—
116C23×C19—41no—
117C23×C19—42no—
118C23×C19—42no—
119C23×C19—42no—
120C23×C19—42no—
121C23×C19—81no—
122C23×C19—81no—
123C23×C19—82no—
124C23×C19—82no—
125C23×C19—82no—
126C23×C19—82no—
127C23×C19#10214yes—
128C23×C19C2×C22⋊C411yescharacteristic
129C23×C19#12011yescharacteristic
130C23×C19#12311yescharacteristic
131C23×C19C2×D811yescharacteristic
132C23×C19C2×SD1611yescharacteristic
133C23×C19AGL(1,ℤ/8)11yescharacteristic
134C23×C19#13711yescharacteristic
135C22×D19—42no—
136C22×D19—42no—
137C22×D19—41no—
138C22×D19—41no—
139C22×D19—41no—
140C2×C4×C19—22no—
141C2×C4×C19—42no—
142C2×C4×C19—41no—
143C2×C4×C19—42no—
144C2×C4×C19—41no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19—81no—
148C2×C4×C19C4×D412yes—
149C2×C4×C19#12112yes—
150C22⋊D19—88no—
151C22⋊D19—81no—
152C22⋊D19—81no—
153C22⋊D19—81no—
154C22⋊D19—81no—
155C2×Dic19—44no—
156C2×Dic19—44no—
157C2×Dic19—42no—
158C2×Dic19—42no—
159C2×Dic19—41no—
160C2×Dic19—42no—
161C2×Dic19—41no—
162C2×Dic19—41no—
163C2×Dic19—44no—
164C2×Dic19—88no—
165D76—82no—
166C8×C19—82no—
167#2617—191no—
168#2315—191no—
169#1519—192no—
170C2×#323D1911yescharacteristic, complemented
171#1289—192no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—24no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19—41no—
183C22×C19—44no—
184C22×C19—44no—
185C22×C19—44no—
186C22×C19—42no—
187C22×C19—42no—
188C22×C19—82no—
189C22×C19—82no—
190C22×C19—82no—
191C22×C19#38611yescharacteristic
192C22×C19C2×#10211yescharacteristic
193C22×C19#41711yescharacteristic
194C22×C19#44711yescharacteristic
195C22×C19#44811yescharacteristic
196C22×C19#48011yescharacteristic
197C22×C19#48111yescharacteristic
198C2×D19—82no—
199C2×D19—82no—
200C2×D19—81no—
201C2×D19—81no—
202C2×D19—81no—
203C4×C19—22no—
204C4×C19—22no—
205C4×C19—42no—
206Dic19—84no—
207Dic19—82no—
208Dic19—81no—
209C2×#121—191no—
210C2×#120—381no—
211C22×C22⋊C4—381no—
212C22×C22⋊C4C2×D1911yescharacteristic
213C2×C22⋊C8C2×D1912yes—
214#397—192no—
215#394—382no—
216#392—192no—
217#386—381no—
218#385—384no—
219#380—191no—
220#380—192no—
221#380—381no—
222#327—384no—
223#323—22no—
224C2×C19—21no—
225C2×C19—21no—
226C2×C19—21no—
227C2×C19—21no—
228C2×C19—21no—
229C2×C19—21no—
230C2×C19—44no—
231C2×C19#187411yescharacteristic
232C2×C19#191111yescharacteristic
233C2×C19#191311yescharacteristic
234D19—161no—
235C25D7611yescharacteristic
236C22×D4—191no—
237C22×D4—381no—
238C22×D4—382no—
239C23×C4—382no—
240C23×C4D7611yescharacteristic
241C23×C4C22×D1911yescharacteristic
242C22×C8—22no—
243#121—382no—
244#121—382no—
245#120—762no—
246#120—762no—
247C2×C4⋊C4—191no—
248C2×C4⋊C4—382no—
249C2×C4⋊C4—382no—
250C2×C4⋊C4—381no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—382no—
254C2×C22⋊C4—382no—
255C2×C22⋊C4—382no—
256C2×C22⋊C4—381no—
257C2×C22⋊C4—381no—
258C2×C22⋊C4—382no—
259C2×C22⋊C4—762no—
260C2×C22⋊C4—762no—
261C2×C22⋊C4C4×D1912yes—
262C2×C22⋊C4C22⋊D1912yes—
263C22⋊C8—22no—
264C22⋊C8—22no—
265#95—192no—
266#95—194no—
267#95—382no—
268#95—382no—
269C19#920311yescharacteristic, complemented, Sylow
270C24—21no—
271C24—21no—
272C24—21no—
273C24—21no—
274C24—81no—
275C24—81no—
276C24—381no—
277C24#6451612yes—
278C24D15212yes—
279C24(C2×D19)⋊C412yes—
280C24C2×D7611yescharacteristic
281C2×D4—382no—
282C2×D4—764no—
283C2×D4—761no—
284C2×D4—761no—
285C2×D4—761no—
286C2×D4—761no—
287C2×D4—761no—
288C2×D4—761no—
289C2×D4—1521no—
290C2×D4—1522no—
291C2×D4—1522no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—81no—
295C22×C4—81no—
296C22×C4—384no—
297C22×C4—382no—
298C22×C4—381no—
299C22×C4—764no—
300C22×C4—1522no—
301C22×C4—1522no—
302C22×C4(C2×D19)⋊C412yes—
303C22×C4C2×C4×D1911yescharacteristic
304C22×C4D4×D1912yes—
305C22×C4#6454312yes—
306C22×C4C2×C22⋊D1911yescharacteristic
307C2×C8—42no—
308C2×C8—82no—
309C4⋊C4—382no—
310C4⋊C4—1522no—
311C4⋊C4—1521no—
312C4⋊C4—1522no—
313C22⋊C4—24no—
314C22⋊C4—24no—
315C22⋊C4—764no—
316C22⋊C4—764no—
317C22⋊C4—761no—
318C22⋊C4—762no—
319C22⋊C4—761no—
320C22⋊C4—762no—
321C22⋊C4—762no—
322C22⋊C4—1522no—
323C23—22no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—22no—
328C23—22no—
329C23—41no—
330C23—41no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—42no—
335C23—81no—
336C23—81no—
337C23—82no—
338C23—82no—
339C23—82no—
340C23—82no—
341C23—762no—
342C23—762no—
343C23—761no—
344C23—761no—
345C23—761no—
346C23#1059727814yes—
347C23#1059732811yescharacteristic
348C23#1059733211yescharacteristic
349C23C2×#6451611yescharacteristic
350C23C2×D15211yescharacteristic
351C23#1059735411yescharacteristic
352C23#1059735511yescharacteristic
353C23C2×(C2×D19)⋊C411yescharacteristic
354D4—1522no—
355D4—1528no—
356D4—1521no—
357D4—1521no—
358D4—1521no—
359D4—1521no—
360C2×C4—22no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—81no—
368C2×C4—762no—
369C2×C4—764no—
370C2×C4—764no—
371C2×C4—762no—
372C2×C4—762no—
373C2×C4—761no—
374C2×C4—761no—
375C2×C4—761no—
376C2×C4—764no—
377C2×C4—1528no—
378C2×C4(C22⋊D19)⋊C412yes—
379C2×C4#1059738512yes—
380C8—82no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—24no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—44no—
393C22—44no—
394C22—44no—
395C22—42no—
396C22—42no—
397C22—82no—
398C22—82no—
399C22—82no—
400C22—1522no—
401C22—1522no—
402C22—1521no—
403C22—1521no—
404C22—1521no—
405C22#1192642111yescharacteristic
406C22C2×#1059727811yescharacteristic
407C22#1192654611yescharacteristic
408C22#1192668011yescharacteristic
409C22#1192668511yescharacteristic
410C22#1192685811yescharacteristic
411C22#1192686311yescharacteristic
412C4—22no—
413C4—22no—
414C4—42no—
415C4—1524no—
416C4—1522no—
417C4—1521no—
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2—21no—
423C2—21no—
424C2—44no—
425C2—3041no—
426C2#1456395011yescharacteristic
427C2#1456416511yescharacteristic
428C2#1456417511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#323C2
socleC22×C19#386
prime radical#14569369C2
cosocleC23×C4×C19C23
hypercenterC2×#323D19
hypocenterC19#9203
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. #14566249C2semidirect
3. #14562204C2semidirect
4. #14561503C2semidirect
5. C2×C19×#323C2semidirect
9. #11926469C4semidirect
11. #11926453C4semidirect
27. C22×D76C2×C4semidirect
48. C2×C4⋊Dic19C2×C4semidirect
53. C19⋊#95C2×C4semidirect
54. C19⋊#95D4semidirect
170. C2×#323D19semidirect
269. C19#9203semidirect

Maximal subgroups

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

subgroupindex
#145693692
#145662492
#145622042
#145615032
C2×C19×#3232
#920319