Finite Group Databasebeta

← #18082949

Subgroups — #18082949

Order 4864.

574 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 85 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#14569016C211yesmaximal, characteristic
2#14567918C211yesmaximal, characteristic
3#14563734C211yesmaximal, characteristic
4#14562168C211yesmaximal, characteristic
5#14561964C211yesmaximal, characteristic
6#14561489C211yesmaximal, characteristic
7C19×#3095C211yesmaximal, characteristic
8C22×Dic19⋊C4C2211yescharacteristic
9#11926508C2211yescharacteristic
10#11926482—21no—
11#11926475—21no—
12#11926475—21no—
13#11926463—21no—
14#11926439—22no—
15#11926428—22no—
16#11926416—21no—
17#11926416—21no—
18#11926416—21no—
19#11926407C2211yescharacteristic
20#11926405—21no—
21C4×C22⋊Dic19C2211yescharacteristic
22#11926303—22no—
23#11926281—22no—
24#11926269—22no—
25C2×C19×C22⋊Q8C2211yescharacteristic
26C2×C19×#117C2211yescharacteristic
27C19×#485—22no—
28C19×#484—21no—
29C19×#483—21no—
30C19×#428—21no—
31C19×#419—21no—
32C19×#407C2211yescharacteristic
33C22×Q8×C19D411yescharacteristic
34C23×C4×C19C2311yescharacteristic
35C23×Dic19D411yescharacteristic
36C23×Dic19D411yescharacteristic
37C2×M16×C19—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C19×#117—21no—
43C19×#117—21no—
44C19×#117—21no—
45C19×#117—21no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19D411yescharacteristic
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C4⋊C4×C19D411yescharacteristic
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—21no—
52C2×C42×C19—21no—
53C2×C22⋊Dic19—21no—
54C2×C22⋊Dic19—21no—
55C2×Dic19⋊C4—22no—
56C2×Dic19⋊C4—22no—
57C2×Dic19⋊C4—21no—
58C2×Dic19⋊C4—21no—
59C2×Dic19⋊C4—21no—
60C2×Dic19⋊C4—21no—
61C2×Dic19⋊C4—21no—
62C2×Dic19⋊C4—21no—
63C2×Dic19⋊C4—22no—
64C2×C4×Dic19D412yes—
65C2×#64520—21no—
66C19×#107—22no—
67C19×#106—22no—
68C19×#103—22no—
69C19×#103—22no—
70C19×C22⋊C8—21no—
71C19×C22⋊C8D412yes—
72C19⋊#95—22no—
73C19⋊#95—22no—
74C19⋊#95—22no—
75C19⋊#95—22no—
76C19⋊#95—22no—
77C19⋊#95—21no—
78C19⋊#95—21no—
79C19⋊#95D412yes—
80C22⋊(C19⋊C8)—21no—
81C22⋊(C19⋊C8)—21no—
82C24×C19C2×D411yescharacteristic
83C2×Q8×C19—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—42no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—42no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19#4111yescharacteristic
97C22×Dic19—22no—
98C22×Dic19—21no—
99C22×Dic19—21no—
100C22×Dic19—21no—
101C22×Dic19—22no—
102C22×Dic19—21no—
103C22×Dic19—21no—
104C22×Dic19—21no—
105C22×Dic19—42no—
106C22×Dic19—42no—
107M16×C19—42no—
108C2×C8×C19—22no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—21no—
113C4⋊C4×C19—21no—
114C4⋊C4×C19—21no—
115C4⋊C4×C19—41no—
116C4⋊C4×C19—41no—
117C22⋊C4×C19—41no—
118C22⋊C4×C19—41no—
119C22⋊C4×C19—41no—
120C22⋊C4×C19—41no—
121C42×C19—41no—
122C42×C19—41no—
123C22⋊Dic19—24no—
124C22⋊Dic19—42no—
125Dic19⋊C4—44no—
126Dic19⋊C4—44no—
127Dic19⋊C4—41no—
128Dic19⋊C4—41no—
129Dic19⋊C4—41no—
130Dic19⋊C4—41no—
131Dic19⋊C4—82no—
132C4×Dic19—42no—
133#64520—42no—
134C2×C19⋊C8—41no—
135#9945—191nomaximal, Sylow
136C23×C19—22no—
137C23×C19—22no—
138C23×C19—41no—
139C23×C19#12011yescharacteristic
140C23×C19#12011yescharacteristic
141C23×C19#12111yescharacteristic
142Q8×C19—42no—
143Q8×C19—81no—
144C2×C4×C19—22no—
145C2×C4×C19—22no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—42no—
151C2×C4×C19—42no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—42no—
157C2×C4×C19—42no—
158C2×C4×C19#12011yescharacteristic
159C2×C4×C19#12111yescharacteristic
160C2×C4×C19#12111yescharacteristic
161C2×C4×C19#12711yescharacteristic
162C2×Dic19—22no—
163C2×Dic19—22no—
164C2×Dic19—24no—
165C2×Dic19—22no—
166C2×Dic19—42no—
167C2×Dic19—41no—
168C2×Dic19—41no—
169C2×Dic19—41no—
170C2×Dic19—41no—
171C2×Dic19—42no—
172C2×Dic19—42no—
173C2×Dic19—42no—
174C2×Dic19—42no—
175C2×Dic19—41no—
176C2×Dic19—42no—
177C2×Dic19—42no—
178C2×Dic19—81no—
179C8×C19—42no—
180C19⋊C8—81no—
181#3095D1911yescharacteristic
182#2583—191no—
183#2484—191no—
184#1826—191no—
185#1511—191no—
186#1463—191no—
187#1284—191no—
188C22×C19—21no—
189C22×C19—21no—
190C22×C19—21no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—44no—
196C22×C19#39211yescharacteristic
197C22×C19#45612yes—
198C22×C19#45812yes—
199C4×C19—21no—
200C4×C19—21no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—81no—
204C4×C19—81no—
205C4×C19—81no—
206C4×C19—81no—
207Dic19—44no—
208Dic19—42no—
209Dic19—82no—
210Dic19—81no—
211C2×C22⋊Q8C2×D1911yescharacteristic
212C2×#117C2×D1911yescharacteristic
213C22×C4⋊C4—191no—
214#485—22no—
215#484—21no—
216#483—21no—
217#428—21no—
218#419—21no—
219#407—191no—
220#407C2×D1911yescharacteristic
221#400—381no—
222#398—381no—
223#398—381no—
224#395—381no—
225#389—382no—
226#387—382no—
227#385—381no—
228#385—381no—
229#385—381no—
230#381—191no—
231#381—381no—
232C4×C22⋊C4—191no—
233#339—382no—
234#328—382no—
235#324—382no—
236C2×C19—22no—
237C2×C19—22no—
238C2×C19—41no—
239C2×C19#200511yescharacteristic
240C2×C19#201011yescharacteristic
241C2×C19#202211yescharacteristic
242C22×Q8C22⋊D1911yescharacteristic
243C23×C4—191no—
244C23×C4—191no—
245C23×C4C22×D1911yescharacteristic
246C2×M16—21no—
247C2×M16—381no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252#117—21no—
253#117—21no—
254#117—21no—
255#117—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—382no—
258C2×C4⋊C4—382no—
259C2×C4⋊C4—381no—
260C2×C4⋊C4—381no—
261C2×C4⋊C4—381no—
262C2×C4⋊C4—381no—
263C2×C4⋊C4—381no—
264C2×C4⋊C4—381no—
265C2×C4⋊C4—382no—
266C2×C4⋊C4C22⋊D1911yescharacteristic
267C2×C4⋊C4C22⋊D1911yescharacteristic
268C2×C4⋊C4C22⋊D1911yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—381no—
272C2×C22⋊C4—381no—
273C2×C42—21no—
274C2×C42—192no—
275#107—22no—
276#106—22no—
277#103—22no—
278#103—22no—
279C22⋊C8—21no—
280C22⋊C8—381no—
281C22⋊C8—381no—
282C22⋊C8C22⋊D1912yes—
283#95—192no—
284#95—382no—
285#95—382no—
286#95—382no—
287#95—382no—
288#95—382no—
289#95—381no—
290#95—381no—
291C19#994511yescharacteristic, complemented, Sylow
292C24D4×D1911yescharacteristic
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—42no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—382no—
302C22×C4—381no—
303C22×C4—381no—
304C22×C4—381no—
305C22×C4—382no—
306C22×C4—381no—
307C22×C4—381no—
308C22×C4—381no—
309C22×C4—762no—
310C22×C4—762no—
311C22×C4D4×D1911yescharacteristic
312C22×C4D4×D1911yescharacteristic
313C22×C4#6454311yescharacteristic
314C22×C4C2×C22⋊D1911yescharacteristic
315C22×C4C2×C22⋊D1911yescharacteristic
316C22×C4C2×C22⋊D1911yescharacteristic
317M16—42no—
318M16—762no—
319C2×C8—22no—
320C2×C8—761no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—764no—
330C4⋊C4—764no—
331C4⋊C4—761no—
332C4⋊C4—761no—
333C4⋊C4—761no—
334C4⋊C4—761no—
335C4⋊C4—1522no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—384no—
341C22⋊C4—762no—
342C42—41no—
343C42—41no—
344C42—762no—
345C23—22no—
346C23—22no—
347C23—41no—
348C23#1059738311yescharacteristic
349C23#1059738311yescharacteristic
350C23#1059738411yescharacteristic
351Q8—42no—
352Q8—81no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—384no—
368C2×C4—382no—
369C2×C4—382no—
370C2×C4—382no—
371C2×C4—762no—
372C2×C4—761no—
373C2×C4—761no—
374C2×C4—761no—
375C2×C4—761no—
376C2×C4—762no—
377C2×C4—762no—
378C2×C4—762no—
379C2×C4—762no—
380C2×C4—761no—
381C2×C4—762no—
382C2×C4—762no—
383C2×C4—1521no—
384C2×C4#1059738511yescharacteristic
385C2×C4#1059738511yescharacteristic
386C2×C4#1059738611yescharacteristic
387C2×C4#1059739911yescharacteristic
388C8—42no—
389C8—1521no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—44no—
398C22#1192645211yescharacteristic
399C22#1192672512yes—
400C22#1192673312yes—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—764no—
410C4—762no—
411C4—1522no—
412C4—1521no—
413C2—22no—
414C2—22no—
415C2—41no—
416C2#1456466811yescharacteristic
417C2#1456469911yescharacteristic
418C2#1456476311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#3095C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#3095D19
hypocenterC19#9945
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
291. C19#9945semidirect

Maximal subgroups

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

subgroupindex
#145690162
#145679182
#145637342
#145621682
#145619642
#145614892
C19×#30952
#994519