Finite Group Databasebeta

← #18071811

Subgroups — #18071811

Order 4864.

516 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 85 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#14569997C211yesmaximal, characteristic
2#14565169C211yesmaximal, characteristic, complemented
3#14565169C211yesmaximal, characteristic, complemented
4#14561458C211yesmaximal, characteristic, complemented
5#14561455C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic, complemented
7C19×#2100C211yesmaximal, characteristic, complemented
8C2×#10597340—21no—
9C2×#10597341—21no—
10C2×#10597265—21no—
11C2×#10597265—21no—
12C2×#10597266—21no—
13C2×#10597266—21no—
14#11926466—21no—
15#11926461—21no—
16#11926454—21no—
17#11926446C2211yescharacteristic
18#11926446C2211yescharacteristic
19#11926418—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C19×#389C2211yescharacteristic
23C19×#384C2211yescharacteristic
24C19×#340—21no—
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×D76—21no—
28C22×D76—21no—
29C22×D76D411yescharacteristic
30C22×D76D411yescharacteristic
31C22×C4×D19—21no—
32C22×C8×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C4⋊C4×C19D411yescharacteristic
39C2×C42×C19C2311yescharacteristic
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×C4⋊Dic19D411yescharacteristic
48C2×C4⋊Dic19D411yescharacteristic
49C2×Dic19⋊C4—21no—
50C22×C19⋊C8—21no—
51C22×C19⋊C8—21no—
52#10597341—42no—
53#10597341—42no—
54#10597340—42no—
55#10597340—42no—
56C19×#95—21no—
57C19⋊#95—21no—
58#10597266—42no—
59#10597266—42no—
60#10597265—42no—
61#10597265—42no—
62C23×D19—21no—
63C23×D19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—41no—
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×Dic19—21no—
71C22×Dic19—21no—
72C2×D76—21no—
73C2×D76—21no—
74C2×D76—21no—
75C2×D76—41no—
76C2×D76—41no—
77C2×D76—41no—
78C2×D76—41no—
79C2×D76—42no—
80C2×D76—42no—
81C2×D76—42no—
82C2×D76—81no—
83C2×D76—81no—
84C2×D76—81no—
85C2×D76SD1612yes—
86C2×C4×D19—42no—
87C2×C4×D19—42no—
88C2×C4×D19—81no—
89C2×C8×C19—41no—
90C2×C8×C19—41no—
91C2×C8×C19—41no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—41no—
94C4⋊C4×C19—42no—
95C4⋊C4×C19—41no—
96C4⋊C4×C19—41no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—41no—
100C4⋊C4×C19—41no—
101C4⋊C4×C19SD1612yes—
102C42×C19—41no—
103(C2×D19)⋊C4—42no—
104(C2×D19)⋊C4—42no—
105(C2×D19)⋊C4—41no—
106(C2×D19)⋊C4—41no—
107(C2×D19)⋊C4—41no—
108(C2×D19)⋊C4—41no—
109(C2×D19)⋊C4—41no—
110(C2×D19)⋊C4—41no—
111(C2×D19)⋊C4—41no—
112(C2×D19)⋊C4—41no—
113(C2×D19)⋊C4—81no—
114C4⋊Dic19—41no—
115C4⋊Dic19—41no—
116Dic19⋊C4—42no—
117C2×C19⋊C8—22no—
118C2×C19⋊C8—22no—
119C2×C19⋊C8—41no—
120C2×C19⋊C8—41no—
121C2×C19⋊C8—41no—
122C2×C19⋊C8—41no—
123#7825—191nomaximal, Sylow
124C23×C19#12011yescharacteristic
125C22×D19—22no—
126C22×D19—41no—
127C22×D19—41no—
128C22×D19—41no—
129C22×D19—41no—
130C22×D19—41no—
131C22×D19—41no—
132C22×D19—41no—
133C22×D19—41no—
134C22×D19—41no—
135C22×D19—41no—
136C22×D19—41no—
137C22×D19—41no—
138C22×D19—41no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—22no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—81no—
152C2×C4×C19—81no—
153C2×C4×C19—81no—
154C2×C4×C19C2×SD1611yescharacteristic
155C2×C4×C19C2×SD1611yescharacteristic
156C2×C4×C19#13511yescharacteristic
157C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C19#13711yescharacteristic
160C2×Dic19—41no—
161C2×Dic19—41no—
162C2×Dic19—41no—
163C2×Dic19—41no—
164C2×Dic19—41no—
165C2×Dic19—41no—
166D76—42no—
167D76—42no—
168D76—81no—
169D76—81no—
170D76—84no—
171D76—84no—
172C4×D19—84no—
173C8×C19—81no—
174C19⋊C8—42no—
175C19⋊C8—42no—
176#2682—191no—
177#2100D1911yescharacteristic, complemented
178#2094—191no—
179#2094—191no—
180#1271—191no—
181#1270—191no—
182#1270—191no—
183C22×C19#45011yescharacteristic
184C22×C19#45011yescharacteristic
185C22×C19#45211yescharacteristic
186C22×C19#45311yescharacteristic
187C22×C19#45311yescharacteristic
188C22×C19#45411yescharacteristic
189C22×C19#45811yescharacteristic
190C2×D19—42no—
191C2×D19—42no—
192C2×D19—42no—
193C2×D19—81no—
194C2×D19—81no—
195C2×D19—81no—
196C2×D19—81no—
197C2×D19—81no—
198C2×D19—81no—
199C2×D19—81no—
200C2×D19—81no—
201C2×D19—81no—
202C2×D19—81no—
203C2×D19—81no—
204C4×C19—21no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—21no—
209C4×C19—21no—
210C4×C19—42no—
211C4×C19—81no—
212C4×C19—161no—
213Dic19—81no—
214Dic19—81no—
215C2×#123—381no—
216C2×#121—381no—
217C2×#106—381no—
218C2×#106—381no—
219C2×#102—381no—
220C2×#102—381no—
221#396—381no—
222#394—381no—
223#392—381no—
224#390—191no—
225#390—191no—
226#389C2×D1911yescharacteristic
227#385—381no—
228#384C2×D1911yescharacteristic
229#340—21no—
230#340—21no—
231#336—191no—
232#336—191no—
233#336C2×D1911yescharacteristic
234C2×C19#161311yescharacteristic
235C2×C19#161611yescharacteristic
236C2×C19#161811yescharacteristic
237C2×C19#162911yescharacteristic
238C2×C19#163111yescharacteristic
239C2×C19#163511yescharacteristic
240C2×C19#165611yescharacteristic
241D19—82no—
242D19—161no—
243C22×D4—191no—
244C22×D4—191no—
245C22×D4—381no—
246C22×D4—381no—
247C23×C4—381no—
248C22×C8—21no—
249C22×C8—381no—
250C22×C8—381no—
251#123—762no—
252#123—762no—
253#121—762no—
254#121—762no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—191no—
260C2×C4⋊C4—191no—
261C2×C4⋊C4—381no—
262C2×C4⋊C4C22⋊D1911yescharacteristic
263C2×C4⋊C4C22⋊D1911yescharacteristic
264C2×C22⋊C4—381no—
265C2×C22⋊C4—381no—
266C2×C22⋊C4—381no—
267C2×C22⋊C4—381no—
268C2×C22⋊C4—381no—
269C2×C22⋊C4—381no—
270C2×C22⋊C4—381no—
271C2×C42C22×D1911yescharacteristic
272#106—762no—
273#106—762no—
274#102—762no—
275#102—762no—
276#95—21no—
277#95—381no—
278C19#782511yescharacteristic, complemented, Sylow
279C24—381no—
280C24—381no—
281C2×D4—192no—
282C2×D4—381no—
283C2×D4—381no—
284C2×D4—381no—
285C2×D4—761no—
286C2×D4—761no—
287C2×D4—761no—
288C2×D4—761no—
289C2×D4—762no—
290C2×D4—762no—
291C2×D4—762no—
292C2×D4—1521no—
293C2×D4—1521no—
294C2×D4—1521no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—41no—
298C22×C4—381no—
299C22×C4—381no—
300C22×C4—762no—
301C22×C4—762no—
302C22×C4—1521no—
303C22×C4D4×D1911yescharacteristic
304C22×C4D4×D1911yescharacteristic
305C22×C4C2×C22⋊D1911yescharacteristic
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—382no—
310C2×C8—382no—
311C2×C8—761no—
312C2×C8—761no—
313C2×C8—761no—
314C2×C8—761no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—42no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—761no—
325C4⋊C4—761no—
326C4⋊C4—762no—
327C4⋊C4#6452712yes—
328C22⋊C4—762no—
329C22⋊C4—762no—
330C22⋊C4—761no—
331C22⋊C4—761no—
332C22⋊C4—761no—
333C22⋊C4—761no—
334C22⋊C4—761no—
335C22⋊C4—761no—
336C22⋊C4—761no—
337C22⋊C4—761no—
338C22⋊C4—1521no—
339C42—41no—
340C23—382no—
341C23—761no—
342C23—761no—
343C23—761no—
344C23—761no—
345C23—761no—
346C23—761no—
347C23—761no—
348C23—761no—
349C23—761no—
350C23—761no—
351C23—761no—
352C23—761no—
353C23—761no—
354C23#1059738311yescharacteristic
355D4—762no—
356D4—762no—
357D4—1521no—
358D4—1521no—
359D4—1524no—
360D4—1524no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—761no—
377C2×C4—761no—
378C2×C4—761no—
379C2×C4—761no—
380C2×C4—761no—
381C2×C4—761no—
382C2×C4—1524no—
383C2×C4SD16×D1911yescharacteristic
384C2×C4#1059736011yescharacteristic
385C2×C4#1059736411yescharacteristic
386C2×C4#1059736511yescharacteristic
387C2×C4C2×#6452711yescharacteristic
388C2×C4#1059739511yescharacteristic
389C8—81no—
390C8—762no—
391C8—762no—
392C22—762no—
393C22—762no—
394C22—762no—
395C22—1521no—
396C22—1521no—
397C22—1521no—
398C22—1521no—
399C22—1521no—
400C22—1521no—
401C22—1521no—
402C22—1521no—
403C22—1521no—
404C22—1521no—
405C22—1521no—
406C22#1192669311yescharacteristic
407C22#1192669411yescharacteristic
408C22#1192670511yescharacteristic
409C22#1192671011yescharacteristic
410C22#1192671011yescharacteristic
411C22#1192671611yescharacteristic
412C22#1192673311yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—42no—
420C4—81no—
421C4—161no—
422C4—1521no—
423C4—1521no—
424C2—3041no—
425C2—1522no—
426C2#1456265311yescharacteristic
427C2#1456267111yescharacteristic
428C2#1456268211yescharacteristic
429C2#1456275011yescharacteristic
430C2#1456276011yescharacteristic
431C2#1456278311yescharacteristic
432C2#1456292711yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2100C2
socleC23×C19#120
prime radical#14569997C2
hypercenter#2100D19
hypocenterC19#7825
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
2. #14565169C2semidirect
3. #14565169C2semidirect
4. #14561458C2semidirect
5. #14561455C2semidirect
6. #14561455C2semidirect
7. C19×#2100C2semidirect
177. #2100D19semidirect
278. C19#7825semidirect

Maximal subgroups

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

subgroupindex
#145699972
#145651692
#145614582
#145614552
C19×#21002
#782519