Finite Group Databasebeta

← #18083054

Subgroups — #18083054

Order 4864.

650 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 105 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#14574388C211yesmaximal, characteristic
2#14568102C211yesmaximal, characteristic
3#14564621C211yesmaximal, characteristic, complemented
4#14563721C211yesmaximal, characteristic, complemented
5#14562204C211yesmaximal, characteristic
6#14561481C211yesmaximal, characteristic, complemented
7C2×C19×#483C211yesmaximal, characteristic, complemented
8C2×#10597375—22no—
9C2×#10597376C2211yescharacteristic
10#11926872—21no—
11#11926862—21no—
12#11926775—22no—
13#11926694—21no—
14#11926683—21no—
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926479—22no—
17#11926445—21no—
18#11926413—21no—
19#11926404C2211yescharacteristic
20C4×C22⋊Dic19C2211yescharacteristic
21#11926311—22no—
22#11926306—22no—
23#11926279—22no—
24C2×C19×C22⋊Q8C2211yescharacteristic
25C22×C4⋊C4×C19C2211yescharacteristic
26C19×#483—22no—
27C19×#483—22no—
28C2×C19×#106—21no—
29C2×C19×#103—21no—
30C2×C19×C22⋊C8C2211yescharacteristic
31C22×Q8×C19D411yescharacteristic
32C23×C4×C19—21no—
33C23×C4×C19C2311yescharacteristic
34C22×C22⋊D19—21no—
35C22×D76D411yescharacteristic
36C22×C8×C19—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19D411yescharacteristic
48C2×C4⋊C4×C19D412yes—
49C2×C22⋊C4×C19—21no—
50C2×C22⋊Dic19—21no—
51C2×C22⋊Dic19D412yes—
52C2×#64527—22no—
53#10597376—21no—
54#10597376—21no—
55#10597376—21no—
56#10597376—21no—
57#10597375—44no—
58#10597375—44no—
59C2×(C2×D19)⋊C4—24no—
60C2×(C2×D19)⋊C4—21no—
61C2×C4⋊Dic19—21no—
62C2×C4⋊Dic19D411yescharacteristic
63C2×Dic19⋊C4—24no—
64C2×C4×Dic19—21no—
65C22×C19⋊C8D412yes—
66C19×#106—24no—
67C19×#103—24no—
68C19×C22⋊C8—21no—
69C19×C22⋊C8D412yes—
70#10597292—22no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75#10597266—22no—
76#10597265—22no—
77C24×C19C2×D411yescharacteristic
78C23×D19—21no—
79C2×Q8×C19—21no—
80C2×Q8×C19—21no—
81C2×Q8×C19—42no—
82C22×C4×C19—22no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—42no—
86C22×C4×C19—41no—
87C22×C4×C19—41no—
88C22×C4×C19—42no—
89C22×C4×C19—42no—
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19#4111yescharacteristic
96C2×C22⋊D19—41no—
97C2×C22⋊D19—41no—
98C2×C22⋊D19—42no—
99C2×C22⋊D19—42no—
100C22×Dic19—22no—
101C22×Dic19—21no—
102C22×Dic19—41no—
103C2×D76—21no—
104C2×D76—21no—
105C2×D76—42no—
106C2×C8×C19—22no—
107C2×C8×C19—42no—
108C4⋊C4×C19—22no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—22no—
112C4⋊C4×C19—41no—
113C4⋊C4×C19—41no—
114C4⋊C4×C19—41no—
115C4⋊C4×C19—41no—
116C22⋊C4×C19—41no—
117C22⋊C4×C19—41no—
118C22⋊Dic19—22no—
119C22⋊Dic19—42no—
120C22⋊Dic19SD1614yescomplemented
121#64527—82no—
122(C2×D19)⋊C4—48no—
123(C2×D19)⋊C4—41no—
124(C2×D19)⋊C4—41no—
125C4⋊Dic19—21no—
126C4⋊Dic19—21no—
127C4⋊Dic19—42no—
128Dic19⋊C4—48no—
129C4×Dic19—42no—
130C2×C19⋊C8—22no—
131C2×C19⋊C8—42no—
132#9960—191nomaximal, Sylow
133C23×C19—41no—
134C23×C19—41no—
135C23×C19#12011yescharacteristic
136C23×C19#12111yescharacteristic
137C23×C19#12711yescharacteristic
138C23×C19C2×SD1612yes—
139C23×C19AGL(1,ℤ/8)12yes—
140C22×D19—42no—
141C22×D19—42no—
142C22×D19—41no—
143C22×D19—42no—
144Q8×C19—42no—
145Q8×C19—42no—
146C2×C4×C19—22no—
147C2×C4×C19—22no—
148C2×C4×C19—22no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—42no—
155C2×C4×C19—44no—
156C2×C4×C19—82no—
157C2×C4×C19—81no—
158C2×C4×C19—81no—
159C2×C4×C19—81no—
160C2×C4×C19—81no—
161C2×C4×C19#12011yescharacteristic
162C2×C4×C19#12011yescharacteristic
163C2×C4×C19#12111yescharacteristic
164C2×C4×C19#12111yescharacteristic
165C22⋊D19—82no—
166C22⋊D19—81no—
167C22⋊D19—81no—
168C2×Dic19—24no—
169C2×Dic19—42no—
170C2×Dic19—42no—
171C2×Dic19—41no—
172C2×Dic19—42no—
173C2×Dic19—81no—
174C2×Dic19—81no—
175C2×Dic19—81no—
176D76—42no—
177D76—81no—
178C8×C19—42no—
179C19⋊C8—42no—
180#3187—191no—
181C2×#483D1911yescharacteristic, complemented
182#2501—191no—
183#1996—191no—
184#1823—191no—
185#1519—191no—
186#1282—191no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—21no—
190C22×C19—21no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19—42no—
194C22×C19—42no—
195C22×C19#39211yescharacteristic
196C22×C19#45012yes—
197C22×C19#46012yes—
198C22×C19#49211yescharacteristic
199C22×C19#49611yescharacteristic
200C2×D19—84no—
201C2×D19—81no—
202C2×D19—81no—
203C2×D19—81no—
204C4×C19—21no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—81no—
208C4×C19—82no—
209C4×C19—81no—
210C4×C19#45812yes—
211Dic19—44no—
212Dic19—81no—
213Dic19—161no—
214C2×#123—382no—
215C2×C22⋊Q8C2×D1911yescharacteristic
216C2×#121—191no—
217C22×C4⋊C4C2×D1911yescharacteristic
218#483—22no—
219#483—22no—
220#483—381no—
221#481—381no—
222#465—382no—
223#450—381no—
224#448—381no—
225C2×#106—21no—
226C2×#103—21no—
227C2×C22⋊C8—191no—
228C2×C22⋊C8C2×D1911yescharacteristic
229#399—382no—
230#390—381no—
231#384—381no—
232#380—191no—
233C4×C22⋊C4—191no—
234#342—382no—
235#340—382no—
236#327—382no—
237C2×C19—22no—
238C2×C19—21no—
239C2×C19—22no—
240C2×C19—21no—
241C2×C19#200911yescharacteristic
242C2×C19#201411yescharacteristic
243C2×C19#202211yescharacteristic
244D19—161no—
245C22×Q8C22⋊D1911yescharacteristic
246C22×D4—191no—
247C22×D4—381no—
248C23×C4—21no—
249C23×C4C22×D1911yescharacteristic
250C2×SD16—382no—
251C22×C8—21no—
252C22×C8—192no—
253#123—764no—
254#123—764no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259#121—381no—
260#121—381no—
261#121—381no—
262#121—381no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—191no—
270C2×C4⋊C4—384no—
271C2×C4⋊C4—381no—
272C2×C4⋊C4C22⋊D1912yes—
273C2×C4⋊C4C22⋊D1911yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—192no—
276C2×C22⋊C4—384no—
277C2×C22⋊C4—381no—
278C2×C22⋊C4—381no—
279C2×C42—381no—
280#106—24no—
281#106—382no—
282#103—24no—
283#103—382no—
284#102—382no—
285C22⋊C8—21no—
286C22⋊C8—381no—
287C22⋊C8—381no—
288C22⋊C8C22⋊D1912yes—
289#95—381no—
290#95—381no—
291C19#996011yescharacteristic, complemented, Sylow
292C24—381no—
293C24D4×D1911yescharacteristic
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—42no—
297C2×D4—381no—
298C2×D4—381no—
299C2×D4—762no—
300C2×D4—761no—
301C2×D4—761no—
302C2×D4—762no—
303C2×D4—762no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—382no—
313C22×C4—381no—
314C22×C4—761no—
315C22×C4D4×D1911yescharacteristic
316C22×C4D4×D1911yescharacteristic
317C22×C4#6454311yescharacteristic
318C22×C4C2×C22⋊D1911yescharacteristic
319C22×C4C2×C22⋊D1911yescharacteristic
320C22×C4C2×C22⋊D1911yescharacteristic
321SD16—1522no—
322C2×C8—22no—
323C2×C8—42no—
324C2×C8—382no—
325C2×C8—762no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—381no—
335C4⋊C4—381no—
336C4⋊C4—762no—
337C4⋊C4—768no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—194no—
341C22⋊C4—382no—
342C22⋊C4—768no—
343C22⋊C4—761no—
344C22⋊C4—761no—
345C22⋊C4—762no—
346C42—762no—
347C23—41no—
348C23—41no—
349C23—762no—
350C23—762no—
351C23—762no—
352C23—761no—
353C23SD16×D1912yes—
354C23#1059736012yes—
355C23#1059738311yescharacteristic
356C23#1059738511yescharacteristic
357C23#1059738611yescharacteristic
358Q8—42no—
359Q8—42no—
360D4—762no—
361D4—1521no—
362D4—1521no—
363D4—1521no—
364D4—1522no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—44no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—82no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—384no—
381C2×C4—762no—
382C2×C4—762no—
383C2×C4—762no—
384C2×C4—761no—
385C2×C4—1521no—
386C2×C4—1521no—
387C2×C4—1521no—
388C2×C4#1059738311yescharacteristic
389C2×C4#1059738411yescharacteristic
390C2×C4#1059738511yescharacteristic
391C2×C4#1059739911yescharacteristic
392C8—42no—
393C8—762no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—42no—
401C22—42no—
402C22—1524no—
403C22—1521no—
404C22—1521no—
405C22—1521no—
406C22#1192645211yescharacteristic
407C22#1192669312yes—
408C22#1192674212yes—
409C22#1192691511yescharacteristic
410C22#1192693011yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—81no—
415C4—82no—
416C4—81no—
417C4—3041no—
418C4—764no—
419C4—1521no—
420C4#1192673312yes—
421C2—21no—
422C2—22no—
423C2—21no—
424C2—22no—
425C2—3041no—
426C2#1456469311yescharacteristic
427C2#1456472111yescharacteristic
428C2#1456476311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#483C2
socleC22×C19#392
prime radicalC2×#10597376C22
hypercenterC2×#483D19
hypocenterC19#9960
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. #14564621C2semidirect
4. #14563721C2semidirect
6. #14561481C2semidirect
7. C2×C19×#483C2semidirect
120. C22⋊Dic19SD16semidirect
181. C2×#483D19semidirect
291. C19#9960semidirect

Maximal subgroups

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

subgroupindex
#145743882
#145681022
#145646212
#145637212
#145622042
#145614812
C2×C19×#4832
#996019