Finite Group Databasebeta

← #18071335

Subgroups — #18071335

Order 4864.

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

normal subgroups only

This group has 574 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#14564768C211yesmaximal, characteristic, complemented
3#14564718C211yesmaximal, characteristic, complemented
4#14561458C211yesmaximal, characteristic, complemented
5#14561455C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic, complemented
7C19×#2057C211yesmaximal, characteristic, complemented
8C22×#64527—21no—
9C2×#10597340—21no—
10C2×#10597341—21no—
11C2×#10597292—21no—
12C2×#10597266—21no—
13#11926466—21no—
14#11926461—21no—
15#11926454—21no—
16#11926446C2211yescharacteristic
17#11926446C2211yescharacteristic
18#11926418—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C19×#107—21no—
24C19×#389C2211yescharacteristic
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×D76—21no—
29C22×D76—21no—
30C22×D76D411yescharacteristic
31C22×D76D411yescharacteristic
32C22×C4×D19—21no—
33C22×C8×C19—21no—
34C19×C4⋊Q8—42no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19D411yescharacteristic
39C2×C4⋊C4×C19D411yescharacteristic
40C2×C42×C19C2311yescharacteristic
41C2×#64527—42no—
42C2×#64527—42no—
43C2×#64527—42no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×(C2×D19)⋊C4—21no—
50C2×(C2×D19)⋊C4—21no—
51C2×C4⋊Dic19D411yescharacteristic
52C2×C4⋊Dic19D411yescharacteristic
53C2×Dic19⋊C4—21no—
54C22×C19⋊C8—21no—
55C22×C19⋊C8—21no—
56#10597341—42no—
57#10597341—42no—
58#10597340—42no—
59#10597340—42no—
60C19×#107—42no—
61C19×#95—21no—
62#10597292—42no—
63C19⋊#95—21no—
64#10597266—42no—
65C23×D19—21no—
66C23×D19—21no—
67C2×Q8×C19—22no—
68C2×Q8×C19—41no—
69C2×Q8×C19—41no—
70C2×Q8×C19—41no—
71C2×Q8×C19—41no—
72C2×Q8×C19—41no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—41no—
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×Dic19—21no—
80C22×Dic19—21no—
81C2×D76—21no—
82C2×D76—21no—
83C2×D76—21no—
84C2×D76—41no—
85C2×D76—41no—
86C2×D76—41no—
87C2×D76—41no—
88C2×D76—42no—
89C2×D76—42no—
90C2×D76—42no—
91C2×D76—81no—
92C2×D76—81no—
93C2×D76—81no—
94C2×D76D812yes—
95C2×C4×D19—42no—
96C2×C4×D19—42no—
97C2×C4×D19—81no—
98C2×C8×C19—22no—
99C2×C8×C19—41no—
100C2×C8×C19—41no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19—41no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19SD1612yescomplemented
110C42×C19—41no—
111#64527—48no—
112(C2×D19)⋊C4—42no—
113(C2×D19)⋊C4—42no—
114(C2×D19)⋊C4—41no—
115(C2×D19)⋊C4—41no—
116(C2×D19)⋊C4—41no—
117(C2×D19)⋊C4—41no—
118(C2×D19)⋊C4—41no—
119(C2×D19)⋊C4—41no—
120(C2×D19)⋊C4—41no—
121(C2×D19)⋊C4—41no—
122(C2×D19)⋊C4—81no—
123C4⋊Dic19—41no—
124C4⋊Dic19—41no—
125Dic19⋊C4—42no—
126C2×C19⋊C8—22no—
127C2×C19⋊C8—41no—
128C2×C19⋊C8—41no—
129C2×C19⋊C8—41no—
130C2×C19⋊C8—41no—
131C2×C19⋊C8—41no—
132#7752—191nomaximal, Sylow
133C23×C19#12011yescharacteristic
134C22×D19—22no—
135C22×D19—41no—
136C22×D19—41no—
137C22×D19—41no—
138C22×D19—41no—
139C22×D19—41no—
140C22×D19—41no—
141C22×D19—41no—
142C22×D19—41no—
143C22×D19—41no—
144C22×D19—41no—
145C22×D19—41no—
146C22×D19—41no—
147C22×D19—41no—
148Q8×C19—42no—
149Q8×C19—42no—
150Q8×C19—81no—
151Q8×C19—81no—
152C2×C4×C19—21no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—22no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—42no—
164C2×C4×C19—41no—
165C2×C4×C19—81no—
166C2×C4×C19—81no—
167C2×C4×C19C2×D811yescharacteristic
168C2×C4×C19C2×SD1611yescharacteristic
169C2×C4×C19#13511yescharacteristic
170C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C19#13711yescharacteristic
173C2×Dic19—41no—
174C2×Dic19—41no—
175C2×Dic19—41no—
176C2×Dic19—41no—
177C2×Dic19—41no—
178C2×Dic19—41no—
179D76—42no—
180D76—42no—
181D76—81no—
182D76—81no—
183D76—84no—
184D76—84no—
185C4×D19—84no—
186C8×C19—42no—
187C19⋊C8—42no—
188C19⋊C8—81no—
189#2682—191no—
190#2057D1911yescharacteristic, complemented
191#2023—191no—
192#2013—191no—
193#1271—191no—
194#1270—191no—
195#1270—191no—
196C22×C19#44711yescharacteristic
197C22×C19#45011yescharacteristic
198C22×C19#45211yescharacteristic
199C22×C19#45311yescharacteristic
200C22×C19#45511yescharacteristic
201C22×C19#45611yescharacteristic
202C22×C19B(4,𝔽2)11yescharacteristic
203C2×D19—42no—
204C2×D19—42no—
205C2×D19—42no—
206C2×D19—81no—
207C2×D19—81no—
208C2×D19—81no—
209C2×D19—81no—
210C2×D19—81no—
211C2×D19—81no—
212C2×D19—81no—
213C2×D19—81no—
214C2×D19—81no—
215C2×D19—81no—
216C2×D19—81no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—21no—
220C4×C19—21no—
221C4×C19—21no—
222C4×C19—21no—
223C4×C19—42no—
224C4×C19—81no—
225C4×C19—82no—
226Dic19—81no—
227Dic19—81no—
228C22×SD16—381no—
229C2×C4⋊Q8C2×D1911yescharacteristic
230C2×#123—381no—
231C2×#121—381no—
232C2×#107—21no—
233C2×#103—381no—
234C2×#102—381no—
235#396—381no—
236#394—381no—
237#392—381no—
238#390—191no—
239#390—191no—
240#389C2×D1911yescharacteristic
241#385—381no—
242#340—21no—
243#340—381no—
244#336—191no—
245#336—191no—
246#336C2×D1911yescharacteristic
247C2×C19#159511yescharacteristic
248C2×C19#160411yescharacteristic
249C2×C19#160611yescharacteristic
250C2×C19#163111yescharacteristic
251C2×C19#163911yescharacteristic
252C2×C19#164711yescharacteristic
253C2×C19#166111yescharacteristic
254D19—82no—
255D19—161no—
256C22×Q8—21no—
257C22×D4—191no—
258C22×D4—191no—
259C22×D4—381no—
260C22×D4—381no—
261C23×C4—381no—
262C2×SD16—762no—
263C2×SD16—762no—
264C2×SD16—762no—
265C22×C8—21no—
266C22×C8—381no—
267C22×C8—381no—
268C4⋊Q8—42no—
269#123—762no—
270#123—762no—
271#121—762no—
272#121—762no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—191no—
277C2×C4⋊C4—191no—
278C2×C4⋊C4—381no—
279C2×C4⋊C4C22⋊D1911yescharacteristic
280C2×C4⋊C4C22⋊D1911yescharacteristic
281C2×C22⋊C4—381no—
282C2×C22⋊C4—381no—
283C2×C22⋊C4—381no—
284C2×C22⋊C4—381no—
285C2×C22⋊C4—381no—
286C2×C22⋊C4—381no—
287C2×C22⋊C4—381no—
288C2×C42C22×D1911yescharacteristic
289#107—42no—
290#103—762no—
291#102—762no—
292#95—21no—
293#95—381no—
294C19#775211yescharacteristic, complemented, Sylow
295C24—381no—
296C24—381no—
297C2×Q8—22no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×D4—192no—
304C2×D4—381no—
305C2×D4—381no—
306C2×D4—381no—
307C2×D4—761no—
308C2×D4—761no—
309C2×D4—761no—
310C2×D4—761no—
311C2×D4—762no—
312C2×D4—762no—
313C2×D4—762no—
314C2×D4—1521no—
315C2×D4—1521no—
316C2×D4—1521no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—381no—
321C22×C4—381no—
322C22×C4—762no—
323C22×C4—762no—
324C22×C4—1521no—
325C22×C4D4×D1911yescharacteristic
326C22×C4D4×D1911yescharacteristic
327C22×C4C2×C22⋊D1911yescharacteristic
328SD16—768no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—382no—
333C2×C8—761no—
334C2×C8—761no—
335C2×C8—761no—
336C2×C8—761no—
337C2×C8—761no—
338C4⋊C4—21no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—761no—
347C4⋊C4—761no—
348C4⋊C4—762no—
349C4⋊C4#6452712yescomplemented
350C22⋊C4—762no—
351C22⋊C4—762no—
352C22⋊C4—761no—
353C22⋊C4—761no—
354C22⋊C4—761no—
355C22⋊C4—761no—
356C22⋊C4—761no—
357C22⋊C4—761no—
358C22⋊C4—761no—
359C22⋊C4—761no—
360C22⋊C4—1521no—
361C42—41no—
362C23—382no—
363C23—761no—
364C23—761no—
365C23—761no—
366C23—761no—
367C23—761no—
368C23—761no—
369C23—761no—
370C23—761no—
371C23—761no—
372C23—761no—
373C23—761no—
374C23—761no—
375C23—761no—
376C23#1059738311yescharacteristic
377Q8—42no—
378Q8—42no—
379Q8—81no—
380Q8—81no—
381D4—762no—
382D4—762no—
383D4—1521no—
384D4—1521no—
385D4—1524no—
386D4—1524no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—761no—
403C2×C4—761no—
404C2×C4—761no—
405C2×C4—761no—
406C2×C4—761no—
407C2×C4—761no—
408C2×C4—1524no—
409C2×C4D8×D1911yescharacteristic
410C2×C4#1059735711yescharacteristic
411C2×C4#1059736411yescharacteristic
412C2×C4#1059736511yescharacteristic
413C2×C4C2×#6452711yescharacteristic
414C2×C4#1059739511yescharacteristic
415C8—42no—
416C8—762no—
417C8—1521no—
418C22—762no—
419C22—762no—
420C22—762no—
421C22—1521no—
422C22—1521no—
423C22—1521no—
424C22—1521no—
425C22—1521no—
426C22—1521no—
427C22—1521no—
428C22—1521no—
429C22—1521no—
430C22—1521no—
431C22—1521no—
432C22#1192667611yescharacteristic
433C22#1192669411yescharacteristic
434C22#1192670511yescharacteristic
435C22#1192671011yescharacteristic
436C22#1192672011yescharacteristic
437C22#1192672611yescharacteristic
438C22#1192673011yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—42no—
446C4—81no—
447C4—82no—
448C4—1521no—
449C4—1521no—
450C2—3041no—
451C2—1522no—
452C2#1456255111yescharacteristic
453C2#1456260311yescharacteristic
454C2#1456261411yescharacteristic
455C2#1456276011yescharacteristic
456C2#1456281311yescharacteristic
457C2#1456286711yescharacteristic
458C2#1456295011yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2057C2
socleC23×C19#120
prime radical#14569997C2
hypercenter#2057D19
hypocenterC19#7752
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
2. #14564768C2semidirect
3. #14564718C2semidirect
4. #14561458C2semidirect
5. #14561455C2semidirect
6. #14561455C2semidirect
7. C19×#2057C2semidirect
109. C4⋊C4×C19SD16semidirect
190. #2057D19semidirect
294. C19#7752semidirect
349. C4⋊C4#64527semidirect

Maximal subgroups

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

subgroupindex
#145699972
#145647682
#145647182
#145614582
#145614552
C19×#20572
#775219