Finite Group Databasebeta

← #18083308

Subgroups — #18083308

Order 4864.

548 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 99 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#14573428C211yesmaximal, characteristic
2#14568993C211yesmaximal, characteristic
3#14562199C211yesmaximal, characteristic, complemented
4#14562064C211yesmaximal, characteristic, complemented
5#14562027C211yesmaximal, characteristic
6#14561494C211yesmaximal, characteristic, complemented
7C19×#3104C211yesmaximal, characteristic, complemented
8C2×C4×D76C2211yescharacteristic
9#11926841—22no—
10#11926831—21no—
11#11926821—21no—
12#11926597C2211yescharacteristic
13#11926587—21no—
14#11926568C2211yescharacteristic
15#11926548—21no—
16#11926479—21no—
17#11926455—21no—
18#11926446—21no—
19#11926442—21no—
20#11926415—22no—
21#11926410C2211yescharacteristic
22#11926281—22no—
23Q8⋊(C19⋊C8)—22no—
24#11926273—22no—
25C19×#533C2211yescharacteristic
26C2×C4×Q8×C19C2211yescharacteristic
27C19×#484—21no—
28C19×#477—21no—
29C19×#462—21no—
30C19×#451—21no—
31C4×Q16×C19—22no—
32C19×#431C2211yescharacteristic
33C22×Q8×C19D411yescharacteristic
34C22×D76D411yescharacteristic
35C22×C4×D19—21no—
36C2×Q16×C19—22no—
37C19×C4⋊Q8D411yescharacteristic
38C19×C4⋊Q8D411yescharacteristic
39C19×#125—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C4×Q8×C19—21no—
43C4×Q8×C19—21no—
44C4×Q8×C19—21no—
45C4×Q8×C19—21no—
46C4×Q8×C19—21no—
47C4×Q8×C19—21no—
48C19×#117—21no—
49C2×C4⋊C4×C19—21no—
50C2×C4⋊C4×C19D411yescharacteristic
51C2×C42×C19—21no—
52C2×C42×C19C2311yescharacteristic
53C2×(C2×D19)⋊C4—22no—
54C2×(C2×D19)⋊C4—21no—
55C2×(C2×D19)⋊C4—22no—
56C2×C4⋊Dic19—21no—
57C2×C4⋊Dic19D411yescharacteristic
58C2×Dic19⋊C4—22no—
59C2×#64520—21no—
60C4×D76—21no—
61C4×D76—21no—
62C4×D76—21no—
63C4×D76—21no—
64C19×#107—22no—
65C19×C4⋊C8—21no—
66C19×#103—22no—
67C19×#103—22no—
68C19×C22⋊C8—21no—
69C4×C8×C19D412yes—
70C19⋊#95—22no—
71C19⋊#95—21no—
72C19⋊#95D412yes—
73C22⋊(C19⋊C8)—21no—
74#10597266—22no—
75#10597266—22no—
76#10597265—22no—
77#10597264—22no—
78C4⋊(C19⋊C8)—21no—
79C4⋊(C19⋊C8)—21no—
80C4⋊(C19⋊C8)D412yes—
81C4×C19⋊C8—21no—
82C23×D19—21no—
83C2×Q8×C19—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—21no—
86C2×Q8×C19—21no—
87C2×Q8×C19—42no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×Dic19—21no—
94C22×Dic19—22no—
95C2×D76—21no—
96C2×D76—21no—
97C2×D76—21no—
98C2×D76—21no—
99C2×D76—21no—
100C2×D76Q1612yescomplemented
101C2×C4×D19—41no—
102C2×C4×D19—41no—
103C2×C4×D19—82no—
104Q16×C19—44no—
105C2×C8×C19—22no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—41no—
113C4⋊C4×C19—41no—
114C4⋊C4×C19—41no—
115C4⋊C4×C19—41no—
116C22⋊C4×C19—41no—
117C42×C19—41no—
118C42×C19—41no—
119C42×C19—41no—
120C42×C19C2×D411yescharacteristic
121C42×C19C2×D411yescharacteristic
122C42×C19C2×D411yescharacteristic
123C42×C19#4111yescharacteristic
124(C2×D19)⋊C4—44no—
125(C2×D19)⋊C4—41no—
126(C2×D19)⋊C4—41no—
127(C2×D19)⋊C4—82no—
128C4⋊Dic19—21no—
129C4⋊Dic19—21no—
130C4⋊Dic19—41no—
131C4⋊Dic19—41no—
132Dic19⋊C4—82no—
133#64520—41no—
134#64520—41no—
135C2×C19⋊C8—22no—
136C2×C19⋊C8—41no—
137#10002—191nomaximal, Sylow
138C23×C19#12011yescharacteristic
139C22×D19—22no—
140C22×D19—42no—
141C22×D19—42no—
142C22×D19—41no—
143C22×D19—41no—
144Q8×C19—22no—
145Q8×C19—22no—
146Q8×C19—41no—
147Q8×C19—41no—
148Q8×C19—42no—
149Q8×C19—81no—
150C2×C4×C19—22no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19#12011yescharacteristic
161C2×C4×C19#12011yescharacteristic
162C2×C4×C19#12111yescharacteristic
163C2×C4×C19#12111yescharacteristic
164C2×C4×C19#12111yescharacteristic
165C2×C4×C19#12711yescharacteristic
166C2×C4×C19C2×Q1611yescharacteristic
167C2×C4×C19#13511yescharacteristic
168C2×C4×C19#13711yescharacteristic
169C2×C4×C19#13711yescharacteristic
170C2×Dic19—42no—
171C2×Dic19—42no—
172C2×Dic19—42no—
173C2×Dic19—41no—
174C2×Dic19—42no—
175D76—22no—
176D76—22no—
177D76—41no—
178D76—41no—
179C4×D19—82no—
180C4×D19—82no—
181C8×C19—42no—
182C19⋊C8—42no—
183C19⋊C8—81no—
184#3104D1911yescharacteristic, complemented
185#3077—191no—
186#2580—191no—
187#1518—191no—
188#1487—191no—
189#1478—191no—
190#1286—191no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19#39211yescharacteristic
194C22×C19#45111yescharacteristic
195C22×C19#45211yescharacteristic
196C2×D19—44no—
197C2×D19—42no—
198C2×D19—82no—
199C2×D19—81no—
200C2×D19—81no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—21no—
204C4×C19—21no—
205C4×C19—42no—
206C4×C19—81no—
207C4×C19—81no—
208C4×C19—81no—
209C4×C19#45111yescharacteristic
210C4×C19#45211yescharacteristic
211C4×C19#46711yescharacteristic
212C4×C19#47011yescharacteristic
213Dic19—82no—
214Dic19—81no—
215#533C2×D1911yescharacteristic
216C2×C4×Q8C2×D1911yescharacteristic
217C2×C4×D4—191no—
218#484—21no—
219#478—382no—
220#477—21no—
221#476—381no—
222#474—381no—
223#462—21no—
224#451—21no—
225C4×Q16—22no—
226#431—191no—
227#431C2×D1911yescharacteristic
228#428—381no—
229#423—191no—
230#418—381no—
231#399—381no—
232#393—381no—
233#390—381no—
234#389—381no—
235#385—382no—
236#382—191no—
237#328—382no—
238Q8⋊C8—382no—
239D4⋊C8—382no—
240C2×C19—21no—
241C2×C19—21no—
242C2×C19#200111yescharacteristic
243C2×C19#200811yescharacteristic
244C2×C19#201011yescharacteristic
245D19—82no—
246C22×Q8C22⋊D1911yescharacteristic
247C22×D4—191no—
248C23×C4—381no—
249C2×Q16—22no—
250C2×M16—381no—
251C4⋊Q8C22⋊D1911yescharacteristic
252C4⋊Q8C22⋊D1911yescharacteristic
253#125—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×D4—381no—
263C4×D4—381no—
264C4×D4—381no—
265C4×D4—381no—
266#117—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—191no—
269C2×C4⋊C4—381no—
270C2×C4⋊C4—382no—
271C2×C4⋊C4C22⋊D1911yescharacteristic
272C2×C22⋊C4—382no—
273C2×C22⋊C4—381no—
274C2×C22⋊C4—382no—
275C2×C42—21no—
276C2×C42C22×D1911yescharacteristic
277#107—22no—
278#107—382no—
279#106—382no—
280C4⋊C8—21no—
281C4⋊C8—192no—
282C4⋊C8—381no—
283C4⋊C8—381no—
284#103—22no—
285#103—22no—
286#102—382no—
287#102—382no—
288C22⋊C8—21no—
289C22⋊C8—381no—
290C4×C8—381no—
291C4×C8C22⋊D1912yes—
292#95—192no—
293#95—382no—
294#95—381no—
295C19#1000211yescharacteristic, complemented, Sylow
296C24—381no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8—42no—
302C2×D4—192no—
303C2×D4—381no—
304C2×D4—381no—
305C2×D4—381no—
306C2×D4—381no—
307C2×D4—381no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—382no—
311C22×C4—381no—
312C22×C4—761no—
313C22×C4—761no—
314C22×C4—1522no—
315C22×C4D4×D1911yescharacteristic
316C22×C4D4×D1911yescharacteristic
317C22×C4C2×C22⋊D1911yescharacteristic
318Q16—44no—
319M16—761no—
320M16—761no—
321C2×C8—22no—
322C2×C8—382no—
323C2×C8—761no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—381no—
335C4⋊C4—381no—
336C4⋊C4—761no—
337C4⋊C4—761no—
338C4⋊C4—1522no—
339C22⋊C4—41no—
340C22⋊C4—764no—
341C22⋊C4—761no—
342C22⋊C4—761no—
343C22⋊C4—1522no—
344C42—41no—
345C42—41no—
346C42—41no—
347C42D4×D1911yescharacteristic
348C42#6454311yescharacteristic
349C42C2×C22⋊D1911yescharacteristic
350C42C2×C22⋊D1911yescharacteristic
351C23—382no—
352C23—762no—
353C23—762no—
354C23—761no—
355C23—761no—
356C23#1059738311yescharacteristic
357Q8—22no—
358Q8—22no—
359Q8—41no—
360Q8—41no—
361Q8—42no—
362Q8—81no—
363D4—382no—
364D4—382no—
365D4—761no—
366D4—761no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—762no—
378C2×C4—762no—
379C2×C4—762no—
380C2×C4—762no—
381C2×C4—761no—
382C2×C4—1522no—
383C2×C4—1522no—
384C2×C4Q16×D1911yescharacteristic
385C2×C4#1059736411yescharacteristic
386C2×C4#1059736411yescharacteristic
387C2×C4#1059736511yescharacteristic
388C2×C4#1059738311yescharacteristic
389C2×C4#1059738411yescharacteristic
390C2×C4#1059738511yescharacteristic
391C2×C4#1059738511yescharacteristic
392C2×C4#1059738611yescharacteristic
393C2×C4#1059739911yescharacteristic
394C8—42no—
395C8—762no—
396C8—1521no—
397C22—21no—
398C22—21no—
399C22—764no—
400C22—762no—
401C22—1522no—
402C22—1521no—
403C22—1521no—
404C22#1192645211yescharacteristic
405C22#1192669811yescharacteristic
406C22#1192670511yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—42no—
412C4—81no—
413C4—81no—
414C4—81no—
415C4—1522no—
416C4—1521no—
417C4#1192669811yescharacteristic
418C4#1192670511yescharacteristic
419C4#1192678211yescharacteristic
420C4#1192679911yescharacteristic
421C2—21no—
422C2—21no—
423C2—1522no—
424C2#1456464211yescharacteristic
425C2#1456468511yescharacteristic
426C2#1456470011yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3104C2
socleC22×C19#392
prime radicalC22×D76D4
hypercenter#3104D19
hypocenterC19#10002
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
3. #14562199C2semidirect
4. #14562064C2semidirect
6. #14561494C2semidirect
7. C19×#3104C2semidirect
100. C2×D76Q16semidirect
184. #3104D19semidirect
295. C19#10002semidirect

Maximal subgroups

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

subgroupindex
#145734282
#145689932
#145621992
#145620642
#145620272
#145614942
C19×#31042
#1000219