Finite Group Databasebeta

← #18083301

Subgroups — #18083301

Order 4864.

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

normal subgroups only

This group has 568 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#14573436C211yesmaximal, characteristic, complemented
2#14568544C211yesmaximal, characteristic
3#14562199C211yesmaximal, characteristic, complemented
4#14562060C211yesmaximal, characteristic
5#14562031C211yesmaximal, characteristic, complemented
6#14561494C211yesmaximal, characteristic, complemented
7C19×#3101C211yesmaximal, characteristic
8C2×#10597370—21no—
9C2×C4×Dic38C2211yescharacteristic
10#11926848—22no—
11#11926836—21no—
12#11926826—21no—
13#11926597C2211yescharacteristic
14#11926587—21no—
15#11926568C2211yescharacteristic
16#11926552—21no—
17#11926475—21no—
18#11926458—21no—
19#11926432—22no—
20#11926410C2211yescharacteristic
21#11926404—21no—
22#11926281—22no—
23#11926276—22no—
24D4⋊(C19⋊C8)—22no—
25C19×#533C2211yescharacteristic
26C2×C4×D4×C19C2211yescharacteristic
27C19×#483—21no—
28C19×#476—21no—
29C19×#461—21no—
30C19×#450—21no—
31C4×SD16×C19—22no—
32C19×#431C2211yescharacteristic
33C22×D4×C19D411yescharacteristic
34C23×C4×C19—21no—
35C22×Dic38D411yescharacteristic
36C2×SD16×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×D4×C19—21no—
45C4×D4×C19—21no—
46C4×D4×C19—21no—
47C4×D4×C19—21no—
48C19×#117—21no—
49C2×C4⋊C4×C19D411yescharacteristic
50C2×C22⋊C4×C19—21no—
51C2×C42×C19C2311yescharacteristic
52C2×C22⋊Dic19—22no—
53C2×C22⋊Dic19—22no—
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19D411yescharacteristic
56#10597370—42no—
57#10597370—42no—
58C2×Dic19⋊C4—22no—
59C2×Dic19⋊C4—21no—
60C2×C4×Dic19—21no—
61C2×#64520—21no—
62C4×Dic38—21no—
63C4×Dic38—21no—
64C4×Dic38—21no—
65C4×Dic38—21no—
66C19×#106—22no—
67C19×C4⋊C8—21no—
68C19×#103—22no—
69C19×#102—22no—
70C19×C22⋊C8—21no—
71C4×C8×C19D412yes—
72C19⋊#95—22no—
73C19⋊#95—21no—
74C19⋊#95D412yes—
75C22⋊(C19⋊C8)—21no—
76#10597267—22no—
77#10597267—22no—
78#10597265—22no—
79#10597264—22no—
80C4⋊(C19⋊C8)—21no—
81C4⋊(C19⋊C8)—21no—
82C4⋊(C19⋊C8)D412yes—
83C4×C19⋊C8—21no—
84C24×C19—21no—
85C2×Q8×C19—21no—
86C2×Q8×C19—21no—
87C2×D4×C19—21no—
88C2×D4×C19—21no—
89C2×D4×C19—42no—
90C22×C4×C19—21no—
91C22×C4×C19—41no—
92C22×C4×C19—41no—
93C22×C4×C19—41no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×Dic19—21no—
101C22×Dic19—22no—
102C22×Dic19—21no—
103C2×Dic38—21no—
104C2×Dic38—21no—
105C2×Dic38—21no—
106C2×Dic38—21no—
107C2×Dic38—21no—
108C2×Dic38SD1612yescomplemented
109SD16×C19—44no—
110C2×C8×C19—22no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—21no—
113C4⋊C4×C19—21no—
114C4⋊C4×C19—21no—
115C4⋊C4×C19—21no—
116C4⋊C4×C19—21no—
117C4⋊C4×C19—41no—
118C4⋊C4×C19—41no—
119C22⋊C4×C19—41no—
120C22⋊C4×C19—41no—
121C22⋊C4×C19—41no—
122C42×C19—41no—
123C42×C19C2×D411yescharacteristic
124C42×C19C2×D411yescharacteristic
125C42×C19C2×D411yescharacteristic
126C42×C19#4111yescharacteristic
127C22⋊Dic19—44no—
128C22⋊Dic19—44no—
129C4⋊Dic19—21no—
130C4⋊Dic19—21no—
131C4⋊Dic19—41no—
132C4⋊Dic19—41no—
133Dic19⋊C4—44no—
134Dic19⋊C4—41no—
135Dic19⋊C4—41no—
136C4×Dic19—41no—
137C4×Dic19—41no—
138#64520—41no—
139#64520—41no—
140C2×C19⋊C8—22no—
141C2×C19⋊C8—41no—
142#10001—191nomaximal, Sylow
143C23×C19—22no—
144C23×C19—41no—
145C23×C19—41no—
146C23×C19—41no—
147C23×C19—41no—
148C23×C19—41no—
149C23×C19—41no—
150C23×C19#12011yescharacteristic
151Q8×C19—42no—
152Q8×C19—81no—
153D4×C19—22no—
154D4×C19—22no—
155D4×C19—41no—
156D4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—81no—
165C2×C4×C19—81no—
166C2×C4×C19—81no—
167C2×C4×C19—81no—
168C2×C4×C19#12011yescharacteristic
169C2×C4×C19#12011yescharacteristic
170C2×C4×C19#12111yescharacteristic
171C2×C4×C19#12111yescharacteristic
172C2×C4×C19#12111yescharacteristic
173C2×C4×C19#12711yescharacteristic
174C2×C4×C19C2×SD1611yescharacteristic
175C2×C4×C19#13511yescharacteristic
176C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C19#13711yescharacteristic
178C2×Dic19—22no—
179C2×Dic19—41no—
180C2×Dic19—41no—
181C2×Dic19—42no—
182C2×Dic19—42no—
183C2×Dic19—42no—
184C2×Dic19—41no—
185C2×Dic19—42no—
186Dic38—22no—
187Dic38—22no—
188Dic38—41no—
189Dic38—41no—
190C8×C19—42no—
191C19⋊C8—42no—
192C19⋊C8—81no—
193#3101D1911yescharacteristic
194#3078—191no—
195#2536—191no—
196#1518—191no—
197#1486—191no—
198#1479—191no—
199#1286—191no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—42no—
203C22×C19—42no—
204C22×C19—42no—
205C22×C19—81no—
206C22×C19—81no—
207C22×C19—81no—
208C22×C19—81no—
209C22×C19#39211yescharacteristic
210C22×C19#45011yescharacteristic
211C22×C19#45211yescharacteristic
212C4×C19—21no—
213C4×C19—21no—
214C4×C19—21no—
215C4×C19—21no—
216C4×C19—81no—
217C4×C19—81no—
218C4×C19—81no—
219C4×C19#44811yescharacteristic
220C4×C19#44911yescharacteristic
221C4×C19#46511yescharacteristic
222C4×C19#46811yescharacteristic
223Dic19—42no—
224Dic19—82no—
225Dic19—81no—
226#533C2×D1911yescharacteristic
227C2×C22⋊Q8—381no—
228C2×C4×Q8—191no—
229C2×C4×D4C2×D1911yescharacteristic
230#483—21no—
231#479—382no—
232#477—381no—
233#476—21no—
234#475—381no—
235#461—21no—
236#450—21no—
237C4×SD16—22no—
238#431—191no—
239#431C2×D1911yescharacteristic
240#428—381no—
241#423—191no—
242#419—381no—
243#398—381no—
244#394—381no—
245#388—382no—
246#382—191no—
247#380—381no—
248#328—382no—
249Q8⋊C8—382no—
250D4⋊C8—382no—
251C2×C19—21no—
252C2×C19—21no—
253C2×C19—82no—
254C2×C19#200011yescharacteristic
255C2×C19#200911yescharacteristic
256C2×C19#201011yescharacteristic
257C22×Q8—191no—
258C22×D4C22⋊D1911yescharacteristic
259C23×C4—21no—
260C2×SD16—22no—
261C2×M16—381no—
262C4⋊Q8C22⋊D1911yescharacteristic
263C4⋊Q8C22⋊D1911yescharacteristic
264#125—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—762no—
268C22⋊Q8—762no—
269C4×Q8—21no—
270C4×Q8—21no—
271C4×Q8—381no—
272C4×Q8—381no—
273C4×Q8—381no—
274C4×Q8—381no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279#117—21no—
280C2×C4⋊C4—191no—
281C2×C4⋊C4—382no—
282C2×C4⋊C4—381no—
283C2×C4⋊C4—381no—
284C2×C4⋊C4C22⋊D1911yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—382no—
287C2×C22⋊C4—382no—
288C2×C42—381no—
289C2×C42C22×D1911yescharacteristic
290#107—382no—
291#106—22no—
292#106—382no—
293C4⋊C8—21no—
294C4⋊C8—192no—
295C4⋊C8—381no—
296C4⋊C8—381no—
297#103—22no—
298#103—382no—
299#103—382no—
300#102—22no—
301C22⋊C8—21no—
302C22⋊C8—381no—
303C4×C8—381no—
304C4×C8C22⋊D1912yes—
305#95—192no—
306#95—382no—
307#95—381no—
308C19#1000111yescharacteristic, complemented, Sylow
309C24—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—192no—
313C2×Q8—381no—
314C2×Q8—381no—
315C2×Q8—381no—
316C2×Q8—381no—
317C2×Q8—381no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—42no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—381no—
329C22×C4—382no—
330C22×C4—381no—
331C22×C4D4×D1911yescharacteristic
332C22×C4D4×D1911yescharacteristic
333C22×C4C2×C22⋊D1911yescharacteristic
334SD16—44no—
335M16—761no—
336M16—761no—
337C2×C8—22no—
338C2×C8—382no—
339C2×C8—761no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—381no—
349C4⋊C4—381no—
350C4⋊C4—764no—
351C4⋊C4—761no—
352C4⋊C4—761no—
353C4⋊C4—761no—
354C4⋊C4—761no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—764no—
359C22⋊C4—764no—
360C42—41no—
361C42—761no—
362C42—761no—
363C42D4×D1911yescharacteristic
364C42#6454311yescharacteristic
365C42C2×C22⋊D1911yescharacteristic
366C42C2×C22⋊D1911yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23#1059738311yescharacteristic
375Q8—42no—
376Q8—81no—
377Q8—382no—
378Q8—382no—
379Q8—761no—
380Q8—761no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—382no—
397C2×C4—761no—
398C2×C4—761no—
399C2×C4—762no—
400C2×C4—762no—
401C2×C4—762no—
402C2×C4—762no—
403C2×C4—761no—
404C2×C4SD16×D1911yescharacteristic
405C2×C4#1059736011yescharacteristic
406C2×C4#1059736111yescharacteristic
407C2×C4#1059736211yescharacteristic
408C2×C4#1059738311yescharacteristic
409C2×C4#1059738411yescharacteristic
410C2×C4#1059738511yescharacteristic
411C2×C4#1059738511yescharacteristic
412C2×C4#1059738611yescharacteristic
413C2×C4#1059739911yescharacteristic
414C8—42no—
415C8—762no—
416C8—1521no—
417C22—21no—
418C22—21no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#1192645211yescharacteristic
427C22#1192669311yescharacteristic
428C22#1192670311yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—762no—
437C4—1522no—
438C4—1521no—
439C4#1192668111yescharacteristic
440C4#1192668811yescharacteristic
441C4#1192677011yescharacteristic
442C4#1192678711yescharacteristic
443C2—21no—
444C2—21no—
445C2—82no—
446C2#1456463511yescharacteristic
447C2#1456469211yescharacteristic
448C2#1456470011yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3101C2
socleC22×C19#392
prime radicalC22×D4×C19D4
hypercenter#3101D19
hypocenterC19#10001
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3101

Complements

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

NH ≅ G/Ntype
1. #14573436C2semidirect
3. #14562199C2semidirect
5. #14562031C2semidirect
6. #14561494C2semidirect
108. C2×Dic38SD16semidirect
308. C19#10001semidirect

Maximal subgroups

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

subgroupindex
#145734362
#145685442
#145621992
#145620602
#145620312
#145614942
C19×#31012
#1000119