Finite Group Databasebeta

← #18079713

Subgroups — #18079713

Order 4864.

500 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 93 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#14573584C211yesmaximal, characteristic
2#14566522C211yesmaximal, characteristic
3#14564619C211yesmaximal, characteristic
4#14563732C211yesmaximal, characteristic
5#14562156C211yesmaximal, characteristic
6#14561520C211yesmaximal, characteristic
7C19×#1305C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9C2×#10597372C2211yescharacteristic
10#11926886—22no—
11#11926880—21no—
12#11926875—21no—
13#11926586C412yescomplemented
14#11926554C412yescomplemented
15#11926440—21no—
16#11926438—22no—
17#11926408—21no—
18C4⋊C4×Dic19—21no—
19C4×C22⋊Dic19C2211yescharacteristic
20C4×C22⋊Dic19C2211yescharacteristic
21#11926389—21no—
22#11926310—22no—
23#11926305—22no—
24#11926282—21no—
25#11926282—21no—
26C19×#407C2211yescharacteristic
27C19×#407C2211yescharacteristic
28C19×#380C2211yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C22×Dic38C2×C411yescharacteristic
31C2×M16×C19—21no—
32C2×M16×C19C2×C412yes—
33C2×C4⋊C4×C19—21no—
34C2×C22⋊C4×C19D412yes—
35C2×C22⋊Dic19—21no—
36C2×C22⋊Dic19—21no—
37C2×C22⋊Dic19—21no—
38C2×C22⋊Dic19—21no—
39#10597372—21no—
40#10597372—21no—
41#10597372C2×C412yes—
42#10597372D412yes—
43C2×C4⋊Dic19C2×C411yescharacteristic
44C2×C4⋊Dic19D411yescharacteristic
45C2×C4⋊Dic19D411yescharacteristic
46#10597370—21no—
47#10597370—21no—
48#10597370—21no—
49#10597370—21no—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4—22no—
52C2×C4×Dic19—21no—
53C2×C4×Dic19—22no—
54C2×C4×Dic19—21no—
55C2×C4×Dic19—21no—
56C19×C22⋊C8—21no—
57C19×C22⋊C8—21no—
58C19×C22⋊C8—21no—
59C19×C22⋊C8—21no—
60C19×#95—21no—
61C19⋊#95—22no—
62C19⋊#95—22no—
63C19⋊#95—21no—
64C19⋊#95D411yescharacteristic
65C19⋊#95D411yescharacteristic
66#10597275—22no—
67#10597274—22no—
68#10597273—22no—
69#10597273—22no—
70C24×C19C2×D411yescharacteristic
71C22×C4×C19—22no—
72C22×C4×C19—42no—
73C22×C4×C19C22×C411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19#4111yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C22×Dic19—21no—
83C22×Dic19—21no—
84C22×Dic19—21no—
85C22×Dic19—41no—
86C2×Dic38—21no—
87C2×Dic38—21no—
88C2×Dic38—42no—
89M16×C19—42no—
90M16×C19—42no—
91C2×C8×C19—22no—
92C2×C8×C19—41no—
93C4⋊C4×C19—42no—
94C22⋊C4×C19—42no—
95C22⋊Dic19—22no—
96C22⋊Dic19—22no—
97C22⋊Dic19—22no—
98C22⋊Dic19—42no—
99C22⋊Dic19—41no—
100C22⋊Dic19—41no—
101C22⋊Dic19—41no—
102C4⋊Dic19—21no—
103C4⋊Dic19—21no—
104C4⋊Dic19—21no—
105C4⋊Dic19—21no—
106C4⋊Dic19C22⋊C412yes—
107C4⋊Dic19C22⋊C412yes—
108Dic19⋊C4—41no—
109Dic19⋊C4—41no—
110Dic19⋊C4—82no—
111C4×Dic19—22no—
112C4×Dic19—22no—
113C4×Dic19—44no—
114C4×Dic19—42no—
115C4×Dic19—42no—
116#9363—191nomaximal, Sylow
117C23×C19—21no—
118C23×C19—21no—
119C23×C19—41no—
120C23×C19—41no—
121C23×C19C4×D411yescharacteristic
122C23×C19#12011yescharacteristic
123C23×C19#12111yescharacteristic
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—42no—
131C2×C4×C19—42no—
132C2×C4×C19—42no—
133C2×C4×C19C2×C22⋊C411yescharacteristic
134C2×C4×C19C4×D411yescharacteristic
135C2×C4×C19#12111yescharacteristic
136C2×C4×C19#12311yescharacteristic
137C2×Dic19—22no—
138C2×Dic19—22no—
139C2×Dic19—22no—
140C2×Dic19—41no—
141C2×Dic19—42no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—42no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151C2×Dic19—81no—
152C2×Dic19—81no—
153C2×Dic19—81no—
154C2×Dic19—81no—
155Dic38—42no—
156Dic38—81no—
157C8×C19—42no—
158C8×C19—81no—
159#3095—191no—
160#2346—191no—
161#1996—191no—
162#1826—191no—
163#1508—191no—
164#1305D1911yescharacteristic
165#1297—191no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—81no—
175C22×C19—81no—
176C22×C19#38611yescharacteristic
177C22×C19#45511yescharacteristic
178C22×C19#45611yescharacteristic
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—82no—
183C4×C19#41012yes—
184Dic19—42no—
185Dic19—42no—
186Dic19—42no—
187Dic19—81no—
188Dic19—82no—
189Dic19—81no—
190Dic19—81no—
191C2×C22⋊Q8—191no—
192C2×#117—191no—
193#485—382no—
194#484—381no—
195#483—381no—
196#428—192no—
197#419—192no—
198#407C2×D1911yescharacteristic
199#407C2×D1911yescharacteristic
200#389—381no—
201#388—382no—
202#382—381no—
203#380C2×D1911yescharacteristic
204C4×C4⋊C4—381no—
205C4×C22⋊C4—191no—
206C4×C22⋊C4—191no—
207#376—381no—
208#342—382no—
209#339—382no—
210#328—381no—
211#328—381no—
212C2×C19—21no—
213C2×C19—21no—
214C2×C19—41no—
215C2×C19—41no—
216C2×C19#188211yescharacteristic
217C2×C19#189911yescharacteristic
218C2×C19#190611yescharacteristic
219C22×Q8—191no—
220C23×C4C22×D1911yescharacteristic
221C2×M16—21no—
222C2×M16C4×D1912yes—
223C22⋊Q8—381no—
224C22⋊Q8—381no—
225C22⋊Q8—381no—
226C22⋊Q8—381no—
227#117—192no—
228#117—192no—
229#117—381no—
230#117—381no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—191no—
233C2×C4⋊C4—191no—
234C2×C4⋊C4—191no—
235C2×C4⋊C4—381no—
236C2×C4⋊C4—382no—
237C2×C22⋊C4—381no—
238C2×C22⋊C4—381no—
239C2×C22⋊C4—381no—
240C2×C22⋊C4—381no—
241C2×C22⋊C4D7612yes—
242C2×C42—381no—
243C2×C42—382no—
244C2×C42—381no—
245C2×C42—381no—
246#107—382no—
247#106—382no—
248#103—382no—
249#103—382no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254#95—21no—
255#95—191no—
256#95—191no—
257#95—382no—
258#95—382no—
259#95—381no—
260C19#936311yescharacteristic, complemented, Sylow
261C24C2×D7611yescharacteristic
262C2×Q8—381no—
263C2×Q8—381no—
264C2×Q8—762no—
265C22×C4—22no—
266C22×C4—42no—
267C22×C4—381no—
268C22×C4—381no—
269C22×C4—381no—
270C22×C4—381no—
271C22×C4—381no—
272C22×C4—381no—
273C22×C4—761no—
274C22×C4C2×C4×D1911yescharacteristic
275C22×C4#6454111yescharacteristic
276C22×C4D4×D1911yescharacteristic
277C22×C4D4×D1911yescharacteristic
278C22×C4D4×D1911yescharacteristic
279C22×C4#6454511yescharacteristic
280M16—42no—
281M16—42no—
282C2×C8—22no—
283C2×C8—41no—
284C4⋊C4—42no—
285C4⋊C4—192no—
286C4⋊C4—192no—
287C4⋊C4—381no—
288C4⋊C4—381no—
289C4⋊C4—381no—
290C4⋊C4—381no—
291C4⋊C4—761no—
292C4⋊C4—761no—
293C4⋊C4—1522no—
294C22⋊C4—42no—
295C22⋊C4—382no—
296C22⋊C4—382no—
297C22⋊C4—382no—
298C22⋊C4—762no—
299C22⋊C4—761no—
300C22⋊C4—761no—
301C22⋊C4—761no—
302C42—382no—
303C42—382no—
304C42—762no—
305C42—762no—
306C42—764no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23C4×D7611yescharacteristic
312C23#1059732811yescharacteristic
313C23#1059734111yescharacteristic
314Q8—762no—
315Q8—1521no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—382no—
326C2×C4—382no—
327C2×C4—382no—
328C2×C4—761no—
329C2×C4—762no—
330C2×C4—761no—
331C2×C4—761no—
332C2×C4—761no—
333C2×C4—761no—
334C2×C4—762no—
335C2×C4—761no—
336C2×C4—761no—
337C2×C4—761no—
338C2×C4—761no—
339C2×C4—1521no—
340C2×C4—1521no—
341C2×C4—1521no—
342C2×C4—1521no—
343C2×C4C22⋊C4×D1911yescharacteristic
344C2×C4#1059733011yescharacteristic
345C2×C4#1059733911yescharacteristic
346C2×C4#1059734011yescharacteristic
347C8—42no—
348C8—81no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22#1192642211yescharacteristic
360C22#1192672411yescharacteristic
361C22#1192672911yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—762no—
367C4—762no—
368C4—762no—
369C4—1521no—
370C4—1522no—
371C4—1521no—
372C4—1521no—
373C4#1192651612yes—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2#1456400311yescharacteristic
379C2#1456409211yescharacteristic
380C2#1456413711yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1305C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#1305D19
hypocenterC19#9363
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
13. #11926586C4semidirect
14. #11926554C4semidirect
260. C19#9363semidirect

Maximal subgroups

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

subgroupindex
#145735842
#145665222
#145646192
#145637322
#145621562
#145615202
C19×#13052
#936319