Finite Group Databasebeta

← #18082995

Subgroups — #18082995

Order 4864.

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

normal subgroups only

This group has 610 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×#11926862C211yesmaximal, characteristic
3#14568109C211yesmaximal, characteristic, complemented
4#14564470C211yesmaximal, characteristic
5#14562206C211yesmaximal, characteristic, complemented
6#14561482C211yesmaximal, characteristic, complemented
7C19×#1824C211yesmaximal, characteristic, complemented
8C2×#10597370C2211yescharacteristic
9C2×#10597376C2211yescharacteristic
10#11926875—21no—
11#11926863—21no—
12#11926862—22no—
13#11926862—22no—
14#11926773—22no—
15#11926697—21no—
16#11926685—21no—
17C2×#10597265—21no—
18C2×#10597266—21no—
19C2×#10597263—22no—
20C2×C22⋊(C19⋊C8)C2211yescharacteristic
21#11926475—22no—
22#11926449—21no—
23#11926417—22no—
24#11926413—21no—
25C4×C22⋊Dic19C2211yescharacteristic
26#11926280—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—
51C2×(C2×D19)⋊C4—21no—
52C2×C4⋊Dic19D411yescharacteristic
53C2×C4⋊Dic19D411yescharacteristic
54#10597370—21no—
55#10597370—21no—
56#10597370—21no—
57#10597370—21no—
58C2×Dic19⋊C4—21no—
59C2×Dic19⋊C4—24no—
60C2×C4×Dic19—21no—
61C22×C19⋊C8—21no—
62C2×#64516—22no—
63C19×C22⋊C8—21no—
64C19×C22⋊C8—21no—
65C19×#95—21no—
66C19⋊#95—24no—
67C19⋊#95—21no—
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)D412yes—
70#10597278—22no—
71#10597274—22no—
72#10597273—22no—
73#10597266—24no—
74#10597265—24no—
75#10597263—44no—
76C24×C19C2×D411yescharacteristic
77C23×D19—21no—
78C22×C4×C19—22no—
79C22×C4×C19—42no—
80C22×C4×C19—41no—
81C22×C4×C19—41no—
82C22×C4×C19—41no—
83C22×C4×C19—82no—
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19#4111yescharacteristic
90C2×C22⋊D19—41no—
91C2×C22⋊D19—41no—
92C2×C22⋊D19—42no—
93C2×C22⋊D19—42no—
94C22×Dic19—22no—
95C22×Dic19—21no—
96C22×Dic19—21no—
97C22×Dic19—21no—
98C2×D76—21no—
99C2×D76—21no—
100C2×D76—42no—
101C2×Dic38—21no—
102C2×Dic38—21no—
103C2×Dic38—42no—
104C2×C8×C19—22no—
105C2×C8×C19—42no—
106C4⋊C4×C19—22no—
107C4⋊C4×C19—22no—
108C4⋊C4×C19—42no—
109C4⋊C4×C19—41no—
110C4⋊C4×C19—41no—
111C22⋊C4×C19—42no—
112C22⋊Dic19—22no—
113C22⋊Dic19—41no—
114C22⋊Dic19—41no—
115C22⋊Dic19SD1614yescomplemented
116(C2×D19)⋊C4—41no—
117(C2×D19)⋊C4—41no—
118C4⋊Dic19—21no—
119C4⋊Dic19—21no—
120C4⋊Dic19—21no—
121C4⋊Dic19—21no—
122Dic19⋊C4—41no—
123Dic19⋊C4—41no—
124Dic19⋊C4—84no—
125C4×Dic19—42no—
126C2×C19⋊C8—22no—
127C2×C19⋊C8—42no—
128#64516—82no—
129#9951—191nomaximal, Sylow
130C23×C19—41no—
131C23×C19—41no—
132C23×C19#12011yescharacteristic
133C23×C19#12111yescharacteristic
134C23×C19#12711yescharacteristic
135C23×C19C2×SD1612yes—
136C23×C19#13712yes—
137C22×D19—41no—
138C22×D19—42no—
139C22×D19—81no—
140C22×D19—81no—
141C2×C4×C19—22no—
142C2×C4×C19—22no—
143C2×C4×C19—22no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—44no—
148C2×C4×C19—42no—
149C2×C4×C19—82no—
150C2×C4×C19—82no—
151C2×C4×C19—81no—
152C2×C4×C19—81no—
153C2×C4×C19—81no—
154C2×C4×C19#12011yescharacteristic
155C2×C4×C19#12011yescharacteristic
156C2×C4×C19#12111yescharacteristic
157C2×C4×C19#12111yescharacteristic
158C22⋊D19—82no—
159C22⋊D19—81no—
160C22⋊D19—81no—
161C2×Dic19—24no—
162C2×Dic19—42no—
163C2×Dic19—42no—
164C2×Dic19—42no—
165C2×Dic19—42no—
166C2×Dic19—41no—
167C2×Dic19—41no—
168C2×Dic19—41no—
169C2×Dic19—42no—
170D76—42no—
171D76—42no—
172Dic38—42no—
173Dic38—81no—
174C8×C19—42no—
175C19⋊C8—42no—
176#3187—191no—
177C2×#481—191no—
178#2502—191no—
179#1964—191no—
180#1824D1911yescharacteristic, complemented
181#1520—191no—
182#1282—191no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—42no—
190C22×C19—42no—
191C22×C19#39211yescharacteristic
192C22×C19#44812yes—
193C22×C19#46112yes—
194C22×C19#49211yescharacteristic
195C22×C19#49711yescharacteristic
196C2×D19—81no—
197C2×D19—81no—
198C2×D19—81no—
199C2×D19—162no—
200C4×C19—21no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—82no—
204C4×C19—161no—
205C4×C19#45812yes—
206Dic19—44no—
207Dic19—81no—
208Dic19—81no—
209Dic19—81no—
210C2×C22⋊Q8—191no—
211C2×#121—191no—
212C22×C4⋊C4C2×D1911yescharacteristic
213#483—381no—
214#481—381no—
215#481—382no—
216#481—382no—
217#465—382no—
218#450—381no—
219#448—381no—
220C2×#106—381no—
221C2×#102—381no—
222C2×#99—382no—
223C2×C22⋊C8—191no—
224C2×C22⋊C8C2×D1911yescharacteristic
225#398—382no—
226#391—381no—
227#385—382no—
228#384—381no—
229#380C2×D1911yescharacteristic
230C4×C22⋊C4—191no—
231#340—22no—
232#328—382no—
233C2×C19—22no—
234C2×C19—21no—
235C2×C19—22no—
236C2×C19—21no—
237C2×C19#200811yescharacteristic
238C2×C19#201311yescharacteristic
239C2×C19#202211yescharacteristic
240D19—161no—
241C22×Q8—191no—
242C22×D4—191no—
243C22×D4—381no—
244C23×C4—21no—
245C23×C4C22×D1911yescharacteristic
246C2×SD16—382no—
247C22×C8—381no—
248C22×C8C22⋊D1912yes—
249C22⋊Q8—381no—
250C22⋊Q8—381no—
251C22⋊Q8—381no—
252C22⋊Q8—381no—
253#121—381no—
254#121—381no—
255#121—381no—
256#121—381no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—191no—
264C2×C4⋊C4—191no—
265C2×C4⋊C4—381no—
266C2×C4⋊C4—384no—
267C2×C4⋊C4D7612yes—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—192no—
270C2×C22⋊C4—381no—
271C2×C22⋊C4—381no—
272C2×C42—381no—
273#106—384no—
274#106—382no—
275#103—382no—
276#102—384no—
277#102—382no—
278#99—764no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—192no—
282C22⋊C8—381no—
283#95—21no—
284#95—384no—
285#95—381no—
286C19#995111yescharacteristic, complemented, Sylow
287C24—381no—
288C24D4×D1911yescharacteristic
289C2×Q8—381no—
290C2×Q8—381no—
291C2×Q8—762no—
292C2×D4—381no—
293C2×D4—381no—
294C2×D4—762no—
295C2×D4—761no—
296C2×D4—761no—
297C2×D4—762no—
298C2×D4—762no—
299C22×C4—22no—
300C22×C4—42no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—82no—
305C22×C4—382no—
306C22×C4—381no—
307C22×C4—381no—
308C22×C4—381no—
309C22×C4C2×D7611yescharacteristic
310C22×C4#6454111yescharacteristic
311C22×C4D4×D1911yescharacteristic
312C22×C4D4×D1911yescharacteristic
313C22×C4D4×D1911yescharacteristic
314C22×C4C2×C22⋊D1911yescharacteristic
315SD16—1522no—
316C2×C8—22no—
317C2×C8—42no—
318C2×C8—382no—
319C2×C8—762no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—42no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—381no—
326C4⋊C4—381no—
327C4⋊C4—381no—
328C4⋊C4—381no—
329C4⋊C4—761no—
330C4⋊C4—761no—
331C4⋊C4—1524no—
332C22⋊C4—42no—
333C22⋊C4—194no—
334C22⋊C4—382no—
335C22⋊C4—761no—
336C22⋊C4—761no—
337C22⋊C4—761no—
338C22⋊C4—761no—
339C42—762no—
340C23—41no—
341C23—41no—
342C23—762no—
343C23—761no—
344C23—1521no—
345C23—1521no—
346C23#1059732811yescharacteristic
347C23#1059733011yescharacteristic
348C23SD16×D1912yes—
349C23#1059736412yes—
350C23#1059738611yescharacteristic
351Q8—762no—
352Q8—1521no—
353D4—762no—
354D4—762no—
355D4—1521no—
356D4—1521no—
357D4—1522no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—44no—
365C2×C4—42no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—384no—
372C2×C4—762no—
373C2×C4—762no—
374C2×C4—762no—
375C2×C4—762no—
376C2×C4—761no—
377C2×C4—761no—
378C2×C4—761no—
379C2×C4—762no—
380C2×C4#1059732811yescharacteristic
381C2×C4#1059733011yescharacteristic
382C2×C4#1059737611yescharacteristic
383C2×C4#1059738311yescharacteristic
384C8—42no—
385C8—762no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—42no—
393C22—42no—
394C22—3042no—
395C22—1521no—
396C22—1521no—
397C22—1521no—
398C22#1192645311yescharacteristic
399C22#1192668412yes—
400C22#1192674812yes—
401C22#1192691511yescharacteristic
402C22#1192693711yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—82no—
407C4—161no—
408C4—764no—
409C4—1521no—
410C4—1521no—
411C4—1521no—
412C4#1192673312yes—
413C2—21no—
414C2—22no—
415C2—22no—
416C2—21no—
417C2—3041no—
418C2#1456469011yescharacteristic
419C2#1456471911yescharacteristic
420C2#1456476611yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1824C2
socleC22×C19#392
prime radicalC2×#10597376C22
hypercenter#1824D19
hypocenterC19#9951
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
3. #14568109C2semidirect
5. #14562206C2semidirect
6. #14561482C2semidirect
7. C19×#1824C2semidirect
115. C22⋊Dic19SD16semidirect
180. #1824D19semidirect
286. C19#9951semidirect

Maximal subgroups

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

subgroupindex
#145743932
C2×#119268622
#145681092
#145644702
#145622062
#145614822
C19×#18242
#995119