Finite Group Databasebeta

← #18083304

Subgroups — #18083304

Order 4864.

568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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#14573643C211yesmaximal, characteristic
2#14573440C211yesmaximal, characteristic, complemented
3#14562198C211yesmaximal, characteristic, complemented
4#14562060C211yesmaximal, characteristic
5#14562030C211yesmaximal, characteristic, complemented
6#14561493C211yesmaximal, characteristic, complemented
7C19×#2536C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926874—21no—
10#11926851—22no—
11#11926839—21no—
12#11926834—21no—
13#11926829—21no—
14#11926749—21no—
15#11926695—21no—
16C4×#64526—22no—
17#11926597C2211yescharacteristic
18#11926597C2211yescharacteristic
19#11926584—21no—
20#11926568C2211yescharacteristic
21#11926553—21no—
22#11926280—22no—
23Q8⋊(C19⋊C8)—22no—
24D4⋊(C19⋊C8)—22no—
25C2×C19×C22⋊Q8—21no—
26C2×C4×Q8×C19C2211yescharacteristic
27C2×C4×D4×C19C2211yescharacteristic
28C19×#398—21no—
29C19×#394—21no—
30C19×#388—22no—
31C19×#382C2211yescharacteristic
32C19×#380—21no—
33C22×Q8×C19D411yescharacteristic
34C22×D4×C19D411yescharacteristic
35C23×C4×C19—21no—
36C19×C22⋊Q8—42no—
37C19×C22⋊Q8—42no—
38C4×Q8×C19—21no—
39C4×Q8×C19—21no—
40C4×Q8×C19—21no—
41C4×Q8×C19—21no—
42C4×D4×C19—21no—
43C4×D4×C19—21no—
44C4×D4×C19—21no—
45C4×D4×C19—21no—
46C2×C4⋊C4×C19—22no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19—21no—
49C2×C4⋊C4×C19D411yescharacteristic
50C2×C4⋊C4×C19D411yescharacteristic
51C2×C22⋊C4×C19—22no—
52C2×C22⋊C4×C19—22no—
53C2×C22⋊C4×C19—21no—
54C2×C42×C19—21no—
55C2×C42×C19C2311yescharacteristic
56C2×#64526—22no—
57#10597372—21no—
58#10597370—21no—
59#10597370—21no—
60C2×#64520—21no—
61#10597316—21no—
62#10597315D411yescharacteristic
63#10597315D411yescharacteristic
64C4×Dic38—21no—
65C4×Dic38—21no—
66C19×#95—22no—
67C19×#95—21no—
68C19×#95D412yes—
69#10597292—22no—
70#10597292—22no—
71#10597289—22no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)—21no—
74#10597267—22no—
75#10597265—22no—
76#10597265—22no—
77#10597264—22no—
78C4⋊(C19⋊C8)—21no—
79C4⋊(C19⋊C8)—21no—
80C4⋊(C19⋊C8)—21no—
81C4⋊(C19⋊C8)D412yes—
82C4×C19⋊C8—21no—
83C4×C19⋊C8D412yes—
84C24×C19—21no—
85C2×Q8×C19—21no—
86C2×Q8×C19—21no—
87C2×Q8×C19—21no—
88C2×Q8×C19—21no—
89C2×Q8×C19—21no—
90C2×Q8×C19SD1612yescomplemented
91C2×D4×C19—21no—
92C2×D4×C19—21no—
93C2×D4×C19—42no—
94C22×C4×C19—21no—
95C22×C4×C19—21no—
96C22×C4×C19—22no—
97C22×C4×C19—21no—
98C22×C4×C19—41no—
99C22×C4×C19—41no—
100C22×C4×C19—41no—
101C22×C4×C19—41no—
102C22×C4×C19—41no—
103C22×C4×C19—41no—
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C2×Dic38—21no—
108C2×Dic38—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—21no—
113C4⋊C4×C19—44no—
114C4⋊C4×C19—41no—
115C4⋊C4×C19—41no—
116C4⋊C4×C19—41no—
117C4⋊C4×C19—41no—
118C22⋊C4×C19—44no—
119C22⋊C4×C19—44no—
120C22⋊C4×C19—41no—
121C22⋊C4×C19—41no—
122C42×C19—41no—
123C42×C19—41no—
124C42×C19C2×D411yescharacteristic
125C42×C19C2×D411yescharacteristic
126C42×C19C2×D411yescharacteristic
127C42×C19#4111yescharacteristic
128C22⋊Dic19—41no—
129#64526—44no—
130C4⋊Dic19—21no—
131C4⋊Dic19—21no—
132C4⋊Dic19—21no—
133C4⋊Dic19—21no—
134Dic19⋊C4—41no—
135Dic19⋊C4—41no—
136C4×Dic19—41no—
137#64520—41no—
138#64520—41no—
139C2×C19⋊C8—22no—
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—22no—
152Q8×C19—22no—
153Q8×C19—41no—
154Q8×C19—41no—
155D4×C19—22no—
156D4×C19—22no—
157D4×C19—41no—
158D4×C19—41no—
159C2×C4×C19—22no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—42no—
165C2×C4×C19—42no—
166C2×C4×C19—42no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—42no—
170C2×C4×C19—41no—
171C2×C4×C19—41no—
172C2×C4×C19—81no—
173C2×C4×C19—81no—
174C2×C4×C19—81no—
175C2×C4×C19—81no—
176C2×C4×C19#12011yescharacteristic
177C2×C4×C19#12011yescharacteristic
178C2×C4×C19#12111yescharacteristic
179C2×C4×C19#12111yescharacteristic
180C2×C4×C19#12111yescharacteristic
181C2×C4×C19#12711yescharacteristic
182C2×C4×C19C2×SD1611yescharacteristic
183C2×C4×C19#13511yescharacteristic
184C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C19#13711yescharacteristic
186C2×Dic19—41no—
187C2×Dic19—41no—
188Dic38—42no—
189Dic38—81no—
190C19⋊C8—42no—
191C19⋊C8—42no—
192C19⋊C8—81no—
193#3101—191no—
194#3078—191no—
195#2536D1911yescharacteristic
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—42no—
217C4×C19—82no—
218C4×C19—81no—
219C4×C19—81no—
220C4×C19#44811yescharacteristic
221C4×C19#44911yescharacteristic
222C4×C19#46511yescharacteristic
223C4×C19#46811yescharacteristic
224Dic19—81no—
225Dic19—81no—
226#533—191no—
227C2×C22⋊Q8—21no—
228C2×C4×Q8C2×D1911yescharacteristic
229C2×C4×D4C2×D1911yescharacteristic
230#483—381no—
231#479—382no—
232#477—381no—
233#476—381no—
234#475—381no—
235#461—381no—
236#450—381no—
237C4×SD16—382no—
238#431—191no—
239#431—191no—
240#428—381no—
241#423—191no—
242#419—381no—
243#398—21no—
244#394—21no—
245#388—22no—
246#382C2×D1911yescharacteristic
247#380—21no—
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×Q8C22⋊D1911yescharacteristic
258C22×D4C22⋊D1911yescharacteristic
259C23×C4—21no—
260C2×SD16—382no—
261C2×M16—381no—
262C4⋊Q8—191no—
263C4⋊Q8—191no—
264#125—381no—
265C22⋊Q8—42no—
266C22⋊Q8—42no—
267C22⋊Q8—381no—
268C22⋊Q8—381no—
269C4×Q8—21no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×Q8—21no—
273C4×Q8—381no—
274C4×Q8—381no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279#117—381no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4C22⋊D1911yescharacteristic
284C2×C4⋊C4C22⋊D1911yescharacteristic
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—21no—
288C2×C42—21no—
289C2×C42C22×D1911yescharacteristic
290#107—382no—
291#106—382no—
292#106—382no—
293C4⋊C8—192no—
294C4⋊C8—381no—
295C4⋊C8—381no—
296C4⋊C8—381no—
297#103—382no—
298#103—382no—
299#103—382no—
300#102—382no—
301C22⋊C8—381no—
302C22⋊C8—381no—
303C4×C8—192no—
304C4×C8—381no—
305#95—22no—
306#95—21no—
307#95C22⋊D1912yes—
308C19#1000111yescharacteristic, complemented, Sylow
309C24—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—381no—
316C2×Q8—381no—
317C2×Q8#6452612yescomplemented
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—42no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4C2×C22⋊D1911yescharacteristic
332C22×C4C2×C22⋊D1911yescharacteristic
333C22×C4C2×C22⋊D1911yescharacteristic
334SD16—764no—
335M16—761no—
336M16—761no—
337C2×C8—382no—
338C2×C8—382no—
339C2×C8—761no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—44no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—381no—
350C4⋊C4—381no—
351C4⋊C4—381no—
352C4⋊C4—381no—
353C4⋊C4—761no—
354C4⋊C4—761no—
355C22⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—761no—
360C42—41no—
361C42—41no—
362C42—761no—
363C42D4×D1911yescharacteristic
364C42D4×D1911yescharacteristic
365C42D4×D1911yescharacteristic
366C42#6454311yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23#1059739911yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—41no—
378Q8—41no—
379Q8—762no—
380Q8—1521no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—761no—
403C2×C4—761no—
404C2×C4#1059737811yescharacteristic
405C2×C4C2×#6452611yescharacteristic
406C2×C4#1059738311yescharacteristic
407C2×C4#1059738311yescharacteristic
408C2×C4#1059738411yescharacteristic
409C2×C4#1059738511yescharacteristic
410C2×C4#1059738511yescharacteristic
411C2×C4#1059738611yescharacteristic
412C2×C4#1059739611yescharacteristic
413C2×C4#1059739711yescharacteristic
414C8—762no—
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#1192669511yescharacteristic
428C22#1192670611yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—82no—
435C4—81no—
436C4—81no—
437C4—1521no—
438C4—1521no—
439C4#1192668211yescharacteristic
440C4#1192668711yescharacteristic
441C4#1192677111yescharacteristic
442C4#1192678811yescharacteristic
443C2—21no—
444C2—21no—
445C2—82no—
446C2#1456463811yescharacteristic
447C2#1456469511yescharacteristic
448C2#1456470011yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2536C2
socleC22×C19#392
prime radicalC22×D4×C19D4
hypercenter#2536D19
hypocenterC19#10001
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2536

Complements

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

NH ≅ G/Ntype
2. #14573440C2semidirect
3. #14562198C2semidirect
5. #14562030C2semidirect
6. #14561493C2semidirect
90. C2×Q8×C19SD16semidirect
308. C19#10001semidirect
317. C2×Q8#64526semidirect

Maximal subgroups

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

subgroupindex
#145736432
#145734402
#145621982
#145620602
#145620302
#145614932
C19×#25362
#1000119