Finite Group Databasebeta

← #18083058

Subgroups — #18083058

Order 4864.

650 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 103 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#14574393C211yesmaximal, characteristic
2C2×#11926874C211yesmaximal, characteristic, complemented
3#14568102C211yesmaximal, characteristic
4#14564619C211yesmaximal, characteristic, complemented
5#14562202C211yesmaximal, characteristic
6#14561482C211yesmaximal, characteristic, complemented
7C19×#1823C211yesmaximal, characteristic, complemented
8C2×#10597375—22no—
9C2×#10597370C2211yescharacteristic
10C2×#10597376C2211yescharacteristic
11#11926875—21no—
12#11926874—22no—
13#11926874—22no—
14#11926863—21no—
15#11926773—22no—
16#11926697—21no—
17#11926685—21no—
18C2×#10597265—21no—
19C2×#10597267—21no—
20C2×C22⋊(C19⋊C8)C2211yescharacteristic
21#11926479—22no—
22#11926445—21no—
23#11926413—21no—
24C4×C22⋊Dic19C2211yescharacteristic
25#11926310—22no—
26#11926277—22no—
27C22×C4⋊C4×C19C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C19×#380C2211yescharacteristic
30C19×#340—22no—
31C23×C4×C19—21no—
32C23×C4×C19C2311yescharacteristic
33C22×C22⋊D19—21no—
34C22×D76D411yescharacteristic
35C22×Dic38D411yescharacteristic
36C22×C8×C19D412yes—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19D412yes—
44C2×C22⋊C4×C19—21no—
45C2×C22⋊Dic19—21no—
46C2×C22⋊Dic19D412yes—
47#10597376—21no—
48#10597376—21no—
49#10597376—21no—
50#10597376—21no—
51#10597375—44no—
52#10597375—44no—
53C2×(C2×D19)⋊C4—24no—
54C2×(C2×D19)⋊C4—21no—
55C2×C4⋊Dic19D411yescharacteristic
56C2×C4⋊Dic19D411yescharacteristic
57#10597370—21no—
58#10597370—21no—
59#10597370—21no—
60#10597370—21no—
61C2×Dic19⋊C4—24no—
62C2×Dic19⋊C4—21no—
63C2×C4×Dic19—21no—
64C22×C19⋊C8—21no—
65C2×#64516—22no—
66C19×C22⋊C8—21no—
67C19×C22⋊C8—21no—
68C19×#95—21no—
69C19⋊#95—21no—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)D412yes—
72#10597278—22no—
73#10597274—22no—
74#10597273—22no—
75#10597267—24no—
76#10597265—24no—
77C24×C19C2×D411yescharacteristic
78C23×D19—21no—
79C22×C4×C19—22no—
80C22×C4×C19—42no—
81C22×C4×C19—41no—
82C22×C4×C19—41no—
83C22×C4×C19—42no—
84C22×C4×C19—42no—
85C22×C4×C19—41no—
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19#4111yescharacteristic
92C2×C22⋊D19—41no—
93C2×C22⋊D19—41no—
94C2×C22⋊D19—42no—
95C2×C22⋊D19—42no—
96C22×Dic19—22no—
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—21no—
100C2×D76—21no—
101C2×D76—21no—
102C2×D76—42no—
103C2×Dic38—21no—
104C2×Dic38—21no—
105C2×Dic38—42no—
106C2×C8×C19—22no—
107C2×C8×C19—42no—
108C4⋊C4×C19—22no—
109C4⋊C4×C19—22no—
110C4⋊C4×C19—42no—
111C4⋊C4×C19—41no—
112C4⋊C4×C19—41no—
113C22⋊C4×C19—42no—
114C22⋊Dic19—22no—
115C22⋊Dic19—41no—
116C22⋊Dic19—41no—
117C22⋊Dic19SD1614yescomplemented
118(C2×D19)⋊C4—48no—
119(C2×D19)⋊C4—41no—
120(C2×D19)⋊C4—41no—
121C4⋊Dic19—21no—
122C4⋊Dic19—21no—
123C4⋊Dic19—21no—
124C4⋊Dic19—21no—
125Dic19⋊C4—48no—
126Dic19⋊C4—41no—
127Dic19⋊C4—41no—
128C4×Dic19—42no—
129C2×C19⋊C8—22no—
130C2×C19⋊C8—42no—
131#64516—82no—
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—
144C2×C4×C19—22no—
145C2×C4×C19—22no—
146C2×C4×C19—22no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—42no—
151C2×C4×C19—44no—
152C2×C4×C19—82no—
153C2×C4×C19—81no—
154C2×C4×C19—81no—
155C2×C4×C19—81no—
156C2×C4×C19—81no—
157C2×C4×C19—81no—
158C2×C4×C19#12011yescharacteristic
159C2×C4×C19#12011yescharacteristic
160C2×C4×C19#12111yescharacteristic
161C2×C4×C19#12111yescharacteristic
162C22⋊D19—82no—
163C22⋊D19—81no—
164C22⋊D19—81no—
165C2×Dic19—24no—
166C2×Dic19—42no—
167C2×Dic19—42no—
168C2×Dic19—41no—
169C2×Dic19—41no—
170C2×Dic19—41no—
171C2×Dic19—42no—
172C2×Dic19—81no—
173C2×Dic19—81no—
174D76—42no—
175D76—81no—
176Dic38—42no—
177Dic38—42no—
178C8×C19—42no—
179C19⋊C8—42no—
180#3187—191no—
181C2×#483—191no—
182#2501—191no—
183#1996—191no—
184#1823D1911yescharacteristic, complemented
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—82no—
208C4×C19—161no—
209C4×C19#45812yes—
210Dic19—44no—
211Dic19—81no—
212Dic19—81no—
213Dic19—81no—
214C2×#123—382no—
215C2×C22⋊Q8—191no—
216C2×#121—191no—
217C22×C4⋊C4C2×D1911yescharacteristic
218#483—381no—
219#483—382no—
220#483—382no—
221#481—381no—
222#465—382no—
223#450—381no—
224#448—381no—
225C2×#106—381no—
226C2×#103—381no—
227C2×C22⋊C8—191no—
228C2×C22⋊C8C2×D1911yescharacteristic
229#399—382no—
230#390—381no—
231#384—381no—
232#380C2×D1911yescharacteristic
233C4×C22⋊C4—191no—
234#342—382no—
235#340—22no—
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×Q8—191no—
246C22×D4—191no—
247C22×D4—381no—
248C23×C4—21no—
249C23×C4C22×D1911yescharacteristic
250C2×SD16—382no—
251C22×C8—381no—
252C22×C8C22⋊D1912yes—
253#123—764no—
254#123—764no—
255C22⋊Q8—381no—
256C22⋊Q8—381no—
257C22⋊Q8—381no—
258C22⋊Q8—381no—
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—191no—
271C2×C4⋊C4—384no—
272C2×C4⋊C4—381no—
273C2×C4⋊C4D7612yes—
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—384no—
281#106—382no—
282#103—384no—
283#103—382no—
284#102—382no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8—192no—
288C22⋊C8—381no—
289#95—21no—
290#95—381no—
291C19#996011yescharacteristic, complemented, Sylow
292C24—381no—
293C24D4×D1911yescharacteristic
294C2×Q8—381no—
295C2×Q8—381no—
296C2×Q8—762no—
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—42no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4—382no—
312C22×C4—381no—
313C22×C4—381no—
314C22×C4—381no—
315C22×C4C2×D7611yescharacteristic
316C22×C4#6454111yescharacteristic
317C22×C4D4×D1911yescharacteristic
318C22×C4D4×D1911yescharacteristic
319C22×C4D4×D1911yescharacteristic
320C22×C4C2×C22⋊D1911yescharacteristic
321SD16—1522no—
322C2×C8—22no—
323C2×C8—42no—
324C2×C8—382no—
325C2×C8—762no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—381no—
332C4⋊C4—381no—
333C4⋊C4—381no—
334C4⋊C4—381no—
335C4⋊C4—768no—
336C4⋊C4—761no—
337C4⋊C4—761no—
338C22⋊C4—42no—
339C22⋊C4—194no—
340C22⋊C4—382no—
341C22⋊C4—768no—
342C22⋊C4—761no—
343C22⋊C4—761no—
344C22⋊C4—761no—
345C22⋊C4—761no—
346C42—762no—
347C23—41no—
348C23—41no—
349C23—762no—
350C23—762no—
351C23—762no—
352C23—761no—
353C23#1059732811yescharacteristic
354C23#1059733011yescharacteristic
355C23#1059735712yes—
356C23SD16×D1912yes—
357C23#1059738611yescharacteristic
358Q8—762no—
359Q8—762no—
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—42no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—82no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—384no—
380C2×C4—762no—
381C2×C4—762no—
382C2×C4—762no—
383C2×C4—761no—
384C2×C4—761no—
385C2×C4—761no—
386C2×C4—1521no—
387C2×C4—1521no—
388C2×C4#1059732811yescharacteristic
389C2×C4#1059733011yescharacteristic
390C2×C4#1059737611yescharacteristic
391C2×C4#1059738311yescharacteristic
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#1192645311yescharacteristic
407C22#1192669612yes—
408C22#1192674312yes—
409C22#1192691511yescharacteristic
410C22#1192693211yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—82no—
415C4—161no—
416C4—764no—
417C4—1521no—
418C4—1521no—
419C4—1521no—
420C4#1192673312yes—
421C2—21no—
422C2—22no—
423C2—21no—
424C2—22no—
425C2—3041no—
426C2#1456469711yescharacteristic
427C2#1456472411yescharacteristic
428C2#1456476611yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1823C2
socleC22×C19#392
prime radicalC2×#10597376C22
hypercenter#1823D19
hypocenterC19#9960
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
2. C2×#11926874C2semidirect
4. #14564619C2semidirect
6. #14561482C2semidirect
7. C19×#1823C2semidirect
117. C22⋊Dic19SD16semidirect
184. #1823D19semidirect
291. C19#9960semidirect

Maximal subgroups

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

subgroupindex
#145743932
C2×#119268742
#145681022
#145646192
#145622022
#145614822
C19×#18232
#996019