Finite Group Databasebeta

← #18074671

Subgroups — #18074671

Order 4864.

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

normal subgroups only

This group has 838 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
1#14563715C211yesmaximal, characteristic, complemented
2#14562139C212yesmaximal, complemented
3#14562139C212yesmaximal, complemented
4#14561903C211yesmaximal, characteristic, complemented
5C19×#3492C211yesmaximal, characteristic
6#11926508C2212yes—
7C2×C19⋊#95—22no—
8C2×C19⋊#95C2211yescharacteristic
9C2×C19⋊#95C2211yescharacteristic
10#11926313—22no—
11#11926281—22no—
12#11926281—22no—
13#11926278—22no—
14#11926278—22no—
15C19×#554—22no—
16C19×#553—22no—
17C19×#552—22no—
18C19×#547—22no—
19C19×#544C411yescharacteristic, complemented
20C19×#539—22no—
21C19×#537C411yescharacteristic, complemented
22C19×#525—22no—
23C19×#525C2212yes—
24C19×#520C412yescomplemented
25C22×C4⋊C4×C19C2211yescharacteristic
26C2×#41×C19—22no—
27C2×#41×C19C2×C412yes—
28C23×C4×C19D412yes—
29C23×C4×C19C2311yescharacteristic
30C23×Dic19—21no—
31C23×Dic19—21no—
32C19×C4⋊Q8—22no—
33C19×#126—24no—
34C19×#125—24no—
35C19×#125—22no—
36C19×#123—24no—
37C19×#123—24no—
38C19×#123—22no—
39C19×C22⋊Q8—22no—
40C19×C22⋊Q8—24no—
41C19×C22⋊Q8—22no—
42C19×C22⋊Q8—22no—
43C19×C22⋊Q8D412yes—
44C19×C22⋊Q8D412yes—
45C19×#121—22no—
46C19×#121—22no—
47C19×#121—22no—
48C19×#121D412yes—
49C19×#121D412yes—
50C19×#120—22no—
51C4×Q8×C19—22no—
52C4×D4×C19—24no—
53C4×D4×C19—22no—
54C4×D4×C19—24no—
55C4×D4×C19—22no—
56C4×D4×C19—22no—
57C19×#117—22no—
58C19×#117—22no—
59C19×#117C2×C412yes—
60C2×C4⋊C4×C19—22no—
61C2×C4⋊C4×C19—22no—
62C2×C4⋊C4×C19—22no—
63C2×C4⋊C4×C19C2×C411yescharacteristic
64C2×C4⋊C4×C19C2×C411yescharacteristic
65C2×C4⋊C4×C19D412yes—
66C2×#64520—22no—
67C19⋊#95—22no—
68C19⋊#95—22no—
69C19⋊#95—44no—
70C22⋊(C19⋊C8)—22no—
71C22⋊(C19⋊C8)—22no—
72C24×C19C2×D411yescharacteristic
73#41×C19—44no—
74#41×C19—82no—
75#41×C19—82no—
76C2×Q8×C19—22no—
77C2×Q8×C19C22⋊C412yes—
78C2×D4×C19—22no—
79C2×D4×C19—22no—
80C2×D4×C19—22no—
81C2×D4×C19—22no—
82C2×D4×C19C22⋊C412yes—
83C22×C4×C19—22no—
84C22×C4×C19—24no—
85C22×C4×C19—22no—
86C22×C4×C19—22no—
87C22×C4×C19—42no—
88C22×C4×C19—42no—
89C22×C4×C19—42no—
90C22×C4×C19C22⋊C412yes—
91C22×C4×C19C22⋊C412yes—
92C22×C4×C19C22×C411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D412yes—
95C22×C4×C19C2×D412yes—
96C22×Dic19—22no—
97C22×Dic19—22no—
98C22×Dic19—42no—
99C22×Dic19—42no—
100C22×Dic19—41no—
101C22×Dic19—41no—
102C22×Dic19—42no—
103C22×Dic19—42no—
104C22×Dic19—41no—
105C22×Dic19—41no—
106C4⋊C4×C19—24no—
107C4⋊C4×C19—22no—
108C4⋊C4×C19—22no—
109C4⋊C4×C19—24no—
110C4⋊C4×C19—22no—
111C4⋊C4×C19—22no—
112C4⋊C4×C19—24no—
113C4⋊C4×C19—22no—
114C4⋊C4×C19—22no—
115C4⋊C4×C19C22⋊C412yes—
116C4⋊C4×C19C22⋊C412yes—
117C22⋊C4×C19—24no—
118C22⋊C4×C19—24no—
119C22⋊C4×C19—22no—
120C22⋊C4×C19—22no—
121C22⋊C4×C19—22no—
122C22⋊C4×C19—22no—
123C22⋊C4×C19—22no—
124C42×C19—24no—
125C42×C19—22no—
126#64520—44no—
127C2×C19⋊C8—42no—
128#8454—191nomaximal, Sylow
129C23×C19—22no—
130C23×C19—21no—
131C23×C19—21no—
132C23×C19—21no—
133C23×C19—21no—
134C23×C19—22no—
135C23×C19C2×C22⋊C411yescharacteristic
136C23×C19#12011yescharacteristic
137C23×C19#12011yescharacteristic
138Q8×C19—42no—
139Q8×C19—82no—
140D4×C19—42no—
141D4×C19—44no—
142D4×C19—42no—
143D4×C19—42no—
144D4×C19—42no—
145D4×C19—42no—
146D4×C19—82no—
147C2×C4×C19—22no—
148C2×C4×C19—22no—
149C2×C4×C19—22no—
150C2×C4×C19—22no—
151C2×C4×C19—22no—
152C2×C4×C19—22no—
153C2×C4×C19—22no—
154C2×C4×C19—42no—
155C2×C4×C19—42no—
156C2×C4×C19—44no—
157C2×C4×C19—42no—
158C2×C4×C19—42no—
159C2×C4×C19—42no—
160C2×C4×C19—42no—
161C2×C4×C19—82no—
162C2×C4×C19—84no—
163C2×C4×C19C2×C22⋊C412yes—
164C2×C4×C19#12012yes—
165C2×Dic19—44no—
166C2×Dic19—44no—
167C2×Dic19—42no—
168C2×Dic19—42no—
169C2×Dic19—82no—
170C2×Dic19—82no—
171C2×Dic19—81no—
172C2×Dic19—81no—
173C2×Dic19—81no—
174C2×Dic19—81no—
175C19⋊C8—82no—
176#3492D1911yescharacteristic
177#1821—191no—
178#1504—192no—
179#1504—192no—
180#1445—191no—
181C22×C19—22no—
182C22×C19—22no—
183C22×C19—22no—
184C22×C19—22no—
185C22×C19—21no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—21no—
190C22×C19—21no—
191C22×C19—42no—
192C22×C19—42no—
193C22×C19—42no—
194C22×C19#37911yescharacteristic
195C22×C19#41012yes—
196C22×C19#45311yescharacteristic
197C22×C19#45411yescharacteristic
198C22×C19#45511yescharacteristic
199C22×C19#45611yescharacteristic
200C4×C19—22no—
201C4×C19—22no—
202C4×C19—42no—
203C4×C19—42no—
204C4×C19—42no—
205C4×C19—42no—
206C4×C19—42no—
207Dic19—82no—
208Dic19—82no—
209#554—22no—
210#553—22no—
211#552—22no—
212#547—22no—
213#544Dic1911yescharacteristic, complemented
214#539—22no—
215#537Dic1911yescharacteristic, complemented
216#525—22no—
217#525C2×D1912yes—
218#520Dic1912yescomplemented
219C22×C4⋊C4C2×D1911yescharacteristic
220#407—192no—
221C2×#95—191no—
222C2×#95—191no—
223C2×#95—382no—
224#343—382no—
225#328—382no—
226#328—382no—
227#327—382no—
228#327—382no—
229C2×C19—21no—
230C2×C19—21no—
231C2×C19—22no—
232C2×C19—21no—
233C2×C19—21no—
234C2×C19—82no—
235C2×C19#178211yescharacteristic
236C2×C19#179211yescharacteristic
237C2×C19#179311yescharacteristic
238C2×#41—22no—
239C2×#41C2×Dic1912yes—
240C23×C4—381no—
241C23×C4—381no—
242C23×C4C22⋊D1912yes—
243C23×C4C22×D1911yescharacteristic
244C2×M16—382no—
245C4⋊Q8—22no—
246#126—24no—
247#125—24no—
248#125—22no—
249#123—24no—
250#123—24no—
251#123—22no—
252C22⋊Q8—22no—
253C22⋊Q8—24no—
254C22⋊Q8—22no—
255C22⋊Q8—22no—
256C22⋊Q8C22⋊D1912yes—
257C22⋊Q8C22⋊D1912yes—
258#121—22no—
259#121—22no—
260#121—22no—
261#121C22⋊D1912yes—
262#121C22⋊D1912yes—
263#120—22no—
264C4×Q8—22no—
265C4×D4—24no—
266C4×D4—22no—
267C4×D4—24no—
268C4×D4—22no—
269C4×D4—22no—
270#117—22no—
271#117—22no—
272#117C2×Dic1912yes—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4C2×Dic1911yescharacteristic
277C2×C4⋊C4C2×Dic1911yescharacteristic
278C2×C4⋊C4C22⋊D1912yes—
279C22⋊C8—382no—
280C22⋊C8—382no—
281#95—382no—
282#95—382no—
283#95—764no—
284C19#845411yescharacteristic, complemented, Sylow
285C24C2×C22⋊D1911yescharacteristic
286#41—44no—
287#41—82no—
288#41—82no—
289C2×Q8—22no—
290C2×Q8C22⋊Dic1912yes—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4C22⋊Dic1912yes—
296C22×C4—22no—
297C22×C4—24no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—382no—
304C22×C4—382no—
305C22×C4—762no—
306C22×C4—761no—
307C22×C4—761no—
308C22×C4—762no—
309C22×C4—762no—
310C22×C4—762no—
311C22×C4—761no—
312C22×C4—761no—
313C22×C4C22⋊Dic1912yes—
314C22×C4C22⋊Dic1912yes—
315C22×C4C22×Dic1911yescharacteristic
316C22×C4C2×C22⋊D1911yescharacteristic
317C22×C4C2×C22⋊D1912yes—
318C22×C4C2×C22⋊D1912yes—
319M16—764no—
320C2×C8—762no—
321C4⋊C4—24no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—24no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—24no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4C22⋊Dic1912yes—
331C4⋊C4C22⋊Dic1912yes—
332C22⋊C4—24no—
333C22⋊C4—24no—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C42—24no—
340C42—22no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—22no—
346C23—22no—
347C23C2×C22⋊Dic1911yescharacteristic
348C23#1059739911yescharacteristic
349C23#1059739911yescharacteristic
350Q8—42no—
351Q8—82no—
352D4—42no—
353D4—42no—
354D4—42no—
355D4—42no—
356D4—42no—
357D4—44no—
358D4—82no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—44no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—82no—
374C2×C4—84no—
375C2×C4—764no—
376C2×C4—764no—
377C2×C4—762no—
378C2×C4—762no—
379C2×C4—1522no—
380C2×C4—1522no—
381C2×C4—1521no—
382C2×C4—1521no—
383C2×C4—1521no—
384C2×C4—1521no—
385C2×C4C2×C22⋊Dic1912yes—
386C2×C4#1059739912yes—
387C8—1522no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—42no—
399C22—42no—
400C22—42no—
401C22#1192640011yescharacteristic
402C22#1192651812yes—
403C22#1192671211yescharacteristic
404C22#1192671711yescharacteristic
405C22#1192672211yescharacteristic
406C22#1192672711yescharacteristic
407C4—22no—
408C4—22no—
409C4—42no—
410C4—42no—
411C4—42no—
412C4—42no—
413C4—42no—
414C4—1522no—
415C4—1522no—
416C2—21no—
417C2—21no—
418C2—21no—
419C2—21no—
420C2—22no—
421C2—82no—
422C2#1456355311yescharacteristic
423C2#1456358911yescharacteristic
424C2#1456359411yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3492C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenter#3492D19
hypocenterC19#8454
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3492

Complements

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

NH ≅ G/Ntype
1. #14563715C2semidirect
2. #14562139C2semidirect
3. #14562139C2semidirect
4. #14561903C2semidirect
19. C19×#544C4semidirect
21. C19×#537C4semidirect
24. C19×#520C4semidirect
213. #544Dic19semidirect
215. #537Dic19semidirect
218. #520Dic19semidirect
284. C19#8454semidirect

Maximal subgroups

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

subgroupindex
#145637152
#145621392
#145619032
C19×#34922
#845419