Finite Group Databasebeta

← #18083378

Subgroups — #18083378

Order 4864.

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

normal subgroups only

This group has 734 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#14573631C211yesmaximal, characteristic, complemented
2#14566914C211yesmaximal, characteristic, complemented
3#14564468C211yesmaximal, characteristic, complemented
4#14562061C211yesmaximal, characteristic, complemented
5#14562060C211yesmaximal, characteristic, complemented
6#14561463C211yesmaximal, characteristic, complemented
7C19×#3100C211yesmaximal, characteristic, complemented
8C2×C4×D76C2211yescharacteristic
9C2×C4×C22⋊D19—22no—
10#11926855—21no—
11#11926821—21no—
12#11926736—21no—
13#11926677—21no—
14C4×#64525—22no—
15#11926597C2211yescharacteristic
16#11926568C2211yescharacteristic
17C2×#10597294—22no—
18#11926480—21no—
19#11926479—21no—
20#11926453—21no—
21#11926452—21no—
22#11926390C2211yescharacteristic
23#11926273—22no—
24D4⋊(C19⋊C8)—22no—
25C19×#532C2211yescharacteristic
26C2×C4×D4×C19C2211yescharacteristic
27C19×#480—21no—
28C19×#474—21no—
29C19×#459—21no—
30C19×#447—21no—
31C4×D8×C19—22no—
32C19×#431C2211yescharacteristic
33C2×#41×C19—21no—
34C22×D4×C19D411yescharacteristic
35C23×C4×C19—21no—
36C22×C22⋊D19—22no—
37C22×D76D411yescharacteristic
38C22×C4×D19—21no—
39C2×D8×C19—22no—
40C19×C4⋊Q8D411yescharacteristic, complemented
41C19×#127D411yescharacteristic, complemented
42C19×#124—21no—
43C19×#121—21no—
44C19×#121—21no—
45C4×D4×C19—21no—
46C4×D4×C19—21no—
47C4×D4×C19—21no—
48C4×D4×C19—21no—
49C4×D4×C19—21no—
50C4×D4×C19—21no—
51C2×C4⋊C4×C19D411yescharacteristic
52C2×C22⋊C4×C19—21no—
53C2×C42×C19C2311yescharacteristic
54C2×C22⋊Dic19—22no—
55C2×#64525—22no—
56C4×C22⋊D19—44no—
57C4×C22⋊D19—44no—
58C2×(C2×D19)⋊C4—22no—
59C2×(C2×D19)⋊C4—21no—
60C2×C4⋊Dic19D411yescharacteristic
61C2×Dic19⋊C4—22no—
62C2×C4×Dic19D412yes—
63C2×#64520—21no—
64C4×D76—21no—
65C4×D76—21no—
66C4×D76—21no—
67C4×D76—21no—
68C19×#107—22no—
69C19×C4⋊C8—21no—
70C19×#102—22no—
71C19×#102—22no—
72C19×C22⋊C8—21no—
73C4×C8×C19D412yescomplemented
74#10597294—44no—
75#10597289—22no—
76C19⋊#95—21no—
77C19⋊#95—21no—
78C22⋊(C19⋊C8)—21no—
79#10597266—22no—
80#10597264—22no—
81C4⋊(C19⋊C8)—21no—
82C4⋊(C19⋊C8)—21no—
83C4⋊(C19⋊C8)—21no—
84C4×C19⋊C8D412yescomplemented
85C24×C19—21no—
86C23×D19—21no—
87#41×C19—42no—
88#41×C19—42no—
89C2×Q8×C19—21no—
90C2×D4×C19—21no—
91C2×D4×C19—21no—
92C2×D4×C19—21no—
93C2×D4×C19—21no—
94C2×D4×C19—21no—
95C2×D4×C19—42no—
96C2×D4×C19—41no—
97C22×C4×C19—21no—
98C22×C4×C19—41no—
99C22×C4×C19—41no—
100C22×C4×C19—41no—
101C22×C4×C19—42no—
102C22×C4×C19—42no—
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C2×C22⋊D19—44no—
107C2×C22⋊D19—44no—
108C2×C22⋊D19—44no—
109C22×Dic19—22no—
110C22×Dic19—21no—
111C2×D76—21no—
112C2×D76—21no—
113C2×D76—42no—
114C2×C4×D19—41no—
115C2×C4×D19—41no—
116C2×C4×D19—42no—
117C2×C4×D19—42no—
118D8×C19—44no—
119C2×C8×C19—22no—
120C4⋊C4×C19—21no—
121C4⋊C4×C19—21no—
122C4⋊C4×C19—21no—
123C4⋊C4×C19—21no—
124C22⋊C4×C19—41no—
125C22⋊C4×C19—41no—
126C22⋊C4×C19—41no—
127C22⋊C4×C19—41no—
128C42×C19C2×D411yescharacteristic
129C42×C19C2×D411yescharacteristic
130C42×C19C2×D411yescharacteristic
131C42×C19#4111yescharacteristic
132C22⋊Dic19—44no—
133#64525—44no—
134(C2×D19)⋊C4—44no—
135(C2×D19)⋊C4—41no—
136(C2×D19)⋊C4—41no—
137C4⋊Dic19—21no—
138C4⋊Dic19—21no—
139Dic19⋊C4—44no—
140C4×Dic19—22no—
141C4×Dic19D814yescomplemented
142#64520—42no—
143C2×C19⋊C8—22no—
144C2×C19⋊C8—41no—
145#10012—191nomaximal, Sylow
146C23×C19—22no—
147C23×C19—42no—
148C23×C19—41no—
149C23×C19—41no—
150C23×C19—42no—
151C23×C19—41no—
152C23×C19#12011yescharacteristic
153C22×D19—22no—
154C22×D19—41no—
155C22×D19—42no—
156C22×D19—41no—
157C22×D19—42no—
158Q8×C19—42no—
159D4×C19—22no—
160D4×C19—22no—
161D4×C19—41no—
162D4×C19—41no—
163D4×C19—42no—
164D4×C19—42no—
165D4×C19—42no—
166D4×C19—82no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—42no—
172C2×C4×C19—82no—
173C2×C4×C19—81no—
174C2×C4×C19—81no—
175C2×C4×C19—81no—
176C2×C4×C19—81no—
177C2×C4×C19#12011yescharacteristic
178C2×C4×C19#12011yescharacteristic
179C2×C4×C19#12111yescharacteristic
180C2×C4×C19#12111yescharacteristic
181C2×C4×C19#12111yescharacteristic
182C2×C4×C19#12711yescharacteristic
183C2×C4×C19C2×D812yes—
184C2×C4×C19AGL(1,ℤ/8)12yes—
185C22⋊D19—416no—
186C2×Dic19—24no—
187C2×Dic19—42no—
188C2×Dic19—42no—
189C2×Dic19—41no—
190C2×Dic19—42no—
191D76—22no—
192D76—22no—
193D76—41no—
194D76—41no—
195C4×D19—82no—
196C4×D19—81no—
197C4×D19—81no—
198C8×C19—42no—
199C19⋊C8—42no—
200C19⋊C8—81no—
201#3100—191no—
202#3100D1911yescharacteristic, complemented
203#2397—191no—
204#1963—191no—
205#1486—191no—
206#1486—191no—
207#1274—191no—
208C22×C19—21no—
209C22×C19—21no—
210C22×C19—44no—
211C22×C19—42no—
212C22×C19—82no—
213C22×C19—81no—
214C22×C19—81no—
215C22×C19—81no—
216C22×C19—81no—
217C22×C19—81no—
218C22×C19#39211yescharacteristic
219C22×C19#44712yes—
220C2×D19—44no—
221C2×D19—42no—
222C2×D19—82no—
223C2×D19—81no—
224C2×D19—81no—
225C4×C19—21no—
226C4×C19—21no—
227C4×C19—21no—
228C4×C19—21no—
229C4×C19—81no—
230C4×C19—81no—
231C4×C19#45912yes—
232C4×C19#49311yescharacteristic
233C4×C19#49611yescharacteristic
234Dic19—44no—
235Dic19—81no—
236#532C2×D1911yescharacteristic
237C2×C4×D4—191no—
238C2×C4×D4—382no—
239C2×C4×D4C2×D1911yescharacteristic
240#480—21no—
241#480—381no—
242#474—21no—
243#474—381no—
244#459—21no—
245#459—381no—
246#447—21no—
247#447—381no—
248C4×D8—22no—
249C4×D8—382no—
250#431—191no—
251#431C2×D1911yescharacteristic
252#423—191no—
253C2×#104—382no—
254#399—381no—
255#399—381no—
256#392—381no—
257#392—381no—
258#376—191no—
259D4⋊C8—382no—
260D4⋊C8—382no—
261C2×C19—22no—
262C2×C19—82no—
263C2×C19—161no—
264C2×C19#201011yescharacteristic
265C2×C19#201011yescharacteristic
266C2×C19#201111yescharacteristic
267D19—82no—
268C2×#41—21no—
269C22×D4—191no—
270C22×D4—382no—
271C22×D4C22⋊D1911yescharacteristic
272C23×C4—21no—
273C23×C4—381no—
274C2×D8—22no—
275C2×D8—382no—
276C2×M16—381no—
277C4⋊Q8C22⋊D1911yescharacteristic, complemented
278#127C22⋊D1911yescharacteristic, complemented
279#124—21no—
280#121—21no—
281#121—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—381no—
289C4×D4—381no—
290C4×D4—381no—
291C4×D4—381no—
292C4×D4—764no—
293C4×D4—764no—
294C2×C4⋊C4—191no—
295C2×C4⋊C4—382no—
296C2×C4⋊C4C22⋊D1911yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—382no—
299C2×C22⋊C4—382no—
300C2×C22⋊C4—381no—
301C2×C42—192no—
302C2×C42C22×D1911yescharacteristic
303#107—22no—
304#107—382no—
305C4⋊C8—21no—
306C4⋊C8—381no—
307C4⋊C8—381no—
308C4⋊C8—381no—
309#104—764no—
310#102—22no—
311#102—22no—
312#102—382no—
313#102—382no—
314C22⋊C8—21no—
315C22⋊C8—381no—
316C4×C8—192no—
317C4×C8C22⋊D1912yescomplemented
318#95—381no—
319#95—381no—
320C19#1001211yescharacteristic, complemented, Sylow
321C24—21no—
322C24—381no—
323#41—42no—
324#41—42no—
325C2×Q8—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—42no—
332C2×D4—41no—
333C2×D4—381no—
334C2×D4—381no—
335C2×D4—762no—
336C2×D4—764no—
337C2×D4—764no—
338C2×D4—764no—
339C22×C4—21no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—382no—
346C22×C4—381no—
347C22×C4—761no—
348C22×C4—761no—
349C22×C4—762no—
350C22×C4—762no—
351C22×C4D4×D1911yescharacteristic
352C22×C4D4×D1911yescharacteristic
353C22×C4C2×C22⋊D1911yescharacteristic
354D8—44no—
355D8—764no—
356M16—762no—
357C2×C8—22no—
358C2×C8—382no—
359C2×C8—761no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—381no—
365C4⋊C4—381no—
366C4⋊C4—764no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—764no—
372C22⋊C4—764no—
373C22⋊C4—761no—
374C22⋊C4—761no—
375C42—194no—
376C42—382no—
377C42D4×D1911yescharacteristic
378C42#6454311yescharacteristic
379C42C2×C22⋊D1911yescharacteristic
380C42C2×C22⋊D1911yescharacteristic
381C23—22no—
382C23—41no—
383C23—42no—
384C23—42no—
385C23—41no—
386C23—41no—
387C23—382no—
388C23—761no—
389C23—762no—
390C23—762no—
391C23—761no—
392C23#1059738311yescharacteristic
393Q8—42no—
394D4—22no—
395D4—22no—
396D4—41no—
397D4—41no—
398D4—42no—
399D4—42no—
400D4—42no—
401D4—82no—
402D4—382no—
403D4—382no—
404D4—761no—
405D4—761no—
406D4—7616no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—82no—
417C2×C4—384no—
418C2×C4—762no—
419C2×C4—762no—
420C2×C4—762no—
421C2×C4—761no—
422C2×C4—1521no—
423C2×C4—1521no—
424C2×C4—1522no—
425C2×C4D8×D1912yes—
426C2×C4#1059735712yes—
427C2×C4#1059738311yescharacteristic
428C2×C4#1059738411yescharacteristic
429C2×C4#1059738511yescharacteristic
430C2×C4#1059738511yescharacteristic
431C2×C4#1059738611yescharacteristic
432C2×C4#1059739911yescharacteristic
433C8—42no—
434C8—762no—
435C8—1521no—
436C22—21no—
437C22—21no—
438C22—44no—
439C22—42no—
440C22—82no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—764no—
447C22—762no—
448C22—1522no—
449C22—1521no—
450C22—1521no—
451C22#1192645211yescharacteristic
452C22#1192667612yes—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—81no—
458C4—81no—
459C4—764no—
460C4—1521no—
461C4#1192673712yes—
462C4#1192691911yescharacteristic
463C4#1192693211yescharacteristic
464C2—22no—
465C2—82no—
466C2—161no—
467C2—1522no—
468C2#1456469911yescharacteristic
469C2#1456470011yescharacteristic
470C2#1456470411yescharacteristic
subgroupG/H
centerC2×C4#10597386
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3100C2
socleC22×C19#392
hypercenter#3100D19
hypocenterC19#10012
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #14573631C2semidirect
2. #14566914C2semidirect
3. #14564468C2semidirect
4. #14562061C2semidirect
5. #14562060C2semidirect
6. #14561463C2semidirect
7. C19×#3100C2semidirect
40. C19×C4⋊Q8D4semidirect
41. C19×#127D4semidirect
73. C4×C8×C19D4semidirect
84. C4×C19⋊C8D4semidirect
141. C4×Dic19D8semidirect
202. #3100D19semidirect
277. C4⋊Q8C22⋊D19semidirect
278. #127C22⋊D19semidirect
317. C4×C8C22⋊D19semidirect
320. C19#10012semidirect

Maximal subgroups

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

subgroupindex
#145736312
#145669142
#145644682
#145620612
#145620602
#145614632
C19×#31002
#1001219