Finite Group Databasebeta

← #18083302

Subgroups — #18083302

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#14573639C211yesmaximal, characteristic
2#14568540C211yesmaximal, characteristic
3#14562199C211yesmaximal, characteristic, complemented
4#14562059C211yesmaximal, characteristic
5#14562030C211yesmaximal, characteristic, complemented
6#14561495C211yesmaximal, characteristic, complemented
7C19×#3078C211yesmaximal, characteristic, complemented
8C2×#10597392—21no—
9C2×C4×D76C2211yescharacteristic
10#11926872—21no—
11#11926831—21no—
12#11926746—21no—
13#11926694—21no—
14C4×#64527—22no—
15#11926597C2211yescharacteristic
16#11926597C2211yescharacteristic
17#11926474—21no—
18#11926461—21no—
19#11926435—22no—
20#11926410C2211yescharacteristic
21#11926401—21no—
22#11926281—22no—
23Q8⋊(C19⋊C8)—22no—
24#11926271—22no—
25C19×#533C2211yescharacteristic
26C2×C4×Q8×C19C2211yescharacteristic
27C19×#479—22no—
28C19×#477—21no—
29C19×#475—21no—
30C19×#428—21no—
31C19×#423C2211yescharacteristic
32C19×#419—21no—
33C22×Q8×C19D411yescharacteristic
34C22×D76D411yescharacteristic
35C22×C4×D19—21no—
36C2×M16×C19—21no—
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
53#10597392—42no—
54#10597392—42no—
55C2×#64527—22no—
56C2×(C2×D19)⋊C4—22no—
57C2×(C2×D19)⋊C4—22no—
58C2×(C2×D19)⋊C4—21no—
59C2×C4⋊Dic19—21no—
60C2×C4⋊Dic19D411yescharacteristic
61C2×Dic19⋊C4—22no—
62C4×D76—21no—
63C4×D76—21no—
64C4×D76—21no—
65C4×D76—21no—
66C19×#107—22no—
67C19×#106—22no—
68C19×C4⋊C8—21no—
69C19×C4⋊C8D412yes—
70C19×#103—22no—
71C19×#103—22no—
72#10597292—22no—
73C19⋊#95—22no—
74C19⋊#95—21no—
75C19⋊#95D412yes—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)—21no—
78#10597266—22no—
79#10597265—22no—
80C4⋊(C19⋊C8)—21no—
81C4⋊(C19⋊C8)—21no—
82C4×C19⋊C8—21no—
83C4×C19⋊C8D412yes—
84C23×D19—21no—
85C2×Q8×C19—21no—
86C2×Q8×C19—21no—
87C2×Q8×C19—21no—
88C2×Q8×C19—21no—
89C2×Q8×C19—21no—
90C2×Q8×C19—21no—
91C2×Q8×C19—21no—
92C2×Q8×C19SD1612yescomplemented
93C22×C4×C19—21no—
94C22×C4×C19—21no—
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×Dic19—21no—
99C22×Dic19—22no—
100C2×D76—21no—
101C2×D76—21no—
102C2×D76—42no—
103C2×C4×D19—41no—
104C2×C4×D19—41no—
105C2×C4×D19—41no—
106C2×C4×D19—41no—
107C2×C4×D19—41no—
108C2×C4×D19—41no—
109M16×C19—41no—
110M16×C19—41no—
111C2×C8×C19—22no—
112C4⋊C4×C19—21no—
113C4⋊C4×C19—21no—
114C4⋊C4×C19—21no—
115C4⋊C4×C19—21no—
116C4⋊C4×C19—21no—
117C4⋊C4×C19—21no—
118C4⋊C4×C19—41no—
119C4⋊C4×C19—41no—
120C4⋊C4×C19—41no—
121C4⋊C4×C19—41no—
122C22⋊C4×C19—41no—
123C42×C19—41no—
124C42×C19—41no—
125C42×C19—41no—
126C42×C19C2×D411yescharacteristic
127C42×C19C2×D411yescharacteristic
128C42×C19C2×D411yescharacteristic
129C42×C19#4111yescharacteristic
130#64527—44no—
131(C2×D19)⋊C4—44no—
132(C2×D19)⋊C4—44no—
133(C2×D19)⋊C4—41no—
134(C2×D19)⋊C4—41no—
135C4⋊Dic19—21no—
136C4⋊Dic19—21no—
137C4⋊Dic19—41no—
138C4⋊Dic19—41no—
139Dic19⋊C4—44no—
140C2×C19⋊C8—22no—
141C2×C19⋊C8—41no—
142#10001—191nomaximal, Sylow
143C23×C19#12011yescharacteristic
144C22×D19—22no—
145C22×D19—41no—
146C22×D19—41no—
147C22×D19—41no—
148C22×D19—41no—
149C22×D19—41no—
150C22×D19—41no—
151Q8×C19—22no—
152Q8×C19—22no—
153Q8×C19—42no—
154Q8×C19—41no—
155Q8×C19—41no—
156Q8×C19—81no—
157C2×C4×C19—22no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—42no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19#12011yescharacteristic
167C2×C4×C19#12011yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×C4×C19#12111yescharacteristic
170C2×C4×C19#12111yescharacteristic
171C2×C4×C19#12711yescharacteristic
172C2×C4×C19C2×SD1611yescharacteristic
173C2×C4×C19#13511yescharacteristic
174C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C19#13711yescharacteristic
176C2×Dic19—42no—
177C2×Dic19—42no—
178C2×Dic19—41no—
179C2×Dic19—41no—
180C2×Dic19—42no—
181C2×Dic19—41no—
182D76—22no—
183D76—22no—
184D76—41no—
185D76—41no—
186C4×D19—81no—
187C4×D19—81no—
188C4×D19—81no—
189C4×D19—81no—
190C8×C19—42no—
191C19⋊C8—42no—
192C19⋊C8—81no—
193#3101—191no—
194#3078D1911yescharacteristic, complemented
195#2536—191no—
196#1518—191no—
197#1486—191no—
198#1479—191no—
199#1286—191no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19#39211yescharacteristic
203C22×C19#45011yescharacteristic
204C22×C19#45211yescharacteristic
205C2×D19—42no—
206C2×D19—42no—
207C2×D19—42no—
208C2×D19—81no—
209C2×D19—81no—
210C2×D19—81no—
211C2×D19—81no—
212C4×C19—21no—
213C4×C19—21no—
214C4×C19—21no—
215C4×C19—21no—
216C4×C19—42no—
217C4×C19—81no—
218C4×C19—81no—
219C4×C19—81no—
220C4×C19#44811yescharacteristic
221C4×C19#44911yescharacteristic
222C4×C19#46511yescharacteristic
223C4×C19#46811yescharacteristic
224Dic19—82no—
225Dic19—81no—
226#533C2×D1911yescharacteristic
227C2×C22⋊Q8—381no—
228C2×C4×Q8C2×D1911yescharacteristic
229C2×C4×D4—191no—
230#483—381no—
231#479—22no—
232#477—21no—
233#476—381no—
234#475—21no—
235#461—381no—
236#450—381no—
237C4×SD16—382no—
238#431—191no—
239#431—191no—
240#428—21no—
241#423C2×D1911yescharacteristic
242#419—21no—
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#200011yescharacteristic
254C2×C19#200911yescharacteristic
255C2×C19#201011yescharacteristic
256D19—82no—
257C22×Q8C22⋊D1911yescharacteristic
258C22×D4—191no—
259C23×C4—381no—
260C2×SD16—382no—
261C2×M16—21no—
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—21no—
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×D4—381no—
276C4×D4—381no—
277C4×D4—381no—
278C4×D4—381no—
279#117—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—191no—
282C2×C4⋊C4—382no—
283C2×C4⋊C4—381no—
284C2×C4⋊C4C22⋊D1911yescharacteristic
285C2×C22⋊C4—382no—
286C2×C22⋊C4—382no—
287C2×C22⋊C4—381no—
288C2×C42—21no—
289C2×C42C22×D1911yescharacteristic
290#107—22no—
291#106—22no—
292#106—382no—
293C4⋊C8—21no—
294C4⋊C8—381no—
295C4⋊C8—381no—
296C4⋊C8C22⋊D1912yes—
297#103—22no—
298#103—22no—
299#103—382no—
300#102—382no—
301C22⋊C8—381no—
302C22⋊C8—381no—
303C4×C8—192no—
304C4×C8—381no—
305#95—192no—
306#95—382no—
307#95—381no—
308C19#1000111yescharacteristic, complemented, Sylow
309C24—381no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8#6452712yescomplemented
318C2×D4—381no—
319C2×D4—381no—
320C2×D4—762no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—382no—
324C22×C4—381no—
325C22×C4—761no—
326C22×C4—761no—
327C22×C4—761no—
328C22×C4—761no—
329C22×C4—761no—
330C22×C4—761no—
331C22×C4D4×D1911yescharacteristic
332C22×C4D4×D1911yescharacteristic
333C22×C4C2×C22⋊D1911yescharacteristic
334SD16—764no—
335M16—41no—
336M16—41no—
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—41no—
349C4⋊C4—41no—
350C4⋊C4—381no—
351C4⋊C4—381no—
352C4⋊C4—764no—
353C4⋊C4—761no—
354C4⋊C4—761no—
355C22⋊C4—41no—
356C22⋊C4—764no—
357C22⋊C4—764no—
358C22⋊C4—761no—
359C22⋊C4—761no—
360C42—41no—
361C42—41no—
362C42—41no—
363C42D4×D1911yescharacteristic
364C42#6454311yescharacteristic
365C42C2×C22⋊D1911yescharacteristic
366C42C2×C22⋊D1911yescharacteristic
367C23—382no—
368C23—761no—
369C23—761no—
370C23—761no—
371C23—761no—
372C23—761no—
373C23—761no—
374C23#1059738311yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—42no—
378Q8—41no—
379Q8—41no—
380Q8—81no—
381D4—382no—
382D4—382no—
383D4—761no—
384D4—761no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—762no—
395C2×C4—762no—
396C2×C4—762no—
397C2×C4—761no—
398C2×C4—761no—
399C2×C4—761no—
400C2×C4—1521no—
401C2×C4—1521no—
402C2×C4—1521no—
403C2×C4—1521no—
404C2×C4#1059738311yescharacteristic
405C2×C4#1059738411yescharacteristic
406C2×C4#1059738511yescharacteristic
407C2×C4#1059738511yescharacteristic
408C2×C4#1059738611yescharacteristic
409C2×C4C2×#6452711yescharacteristic
410C2×C4#1059738811yescharacteristic
411C2×C4#1059739511yescharacteristic
412C2×C4#1059739611yescharacteristic
413C2×C4#1059739911yescharacteristic
414C8—42no—
415C8—762no—
416C8—1521no—
417C22—21no—
418C22—21no—
419C22—762no—
420C22—762no—
421C22—762no—
422C22—1521no—
423C22—1521no—
424C22—1521no—
425C22—1521no—
426C22#1192645211yescharacteristic
427C22#1192669411yescharacteristic
428C22#1192670411yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—1522no—
438C4—1521no—
439C4#1192668311yescharacteristic
440C4#1192668911yescharacteristic
441C4#1192677511yescharacteristic
442C4#1192679211yescharacteristic
443C2—21no—
444C2—21no—
445C2—1522no—
446C2#1456463611yescharacteristic
447C2#1456469311yescharacteristic
448C2#1456469911yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3078C2
socleC22×C19#392
prime radicalC22×D76D4
hypercenter#3078D19
hypocenterC19#10001
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. #14562199C2semidirect
5. #14562030C2semidirect
6. #14561495C2semidirect
7. C19×#3078C2semidirect
92. C2×Q8×C19SD16semidirect
194. #3078D19semidirect
308. C19#10001semidirect
317. C2×Q8#64527semidirect

Maximal subgroups

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

subgroupindex
#145736392
#145685402
#145621992
#145620592
#145620302
#145614952
C19×#30782
#1000119