Finite Group Databasebeta

← #18080285

Subgroups — #18080285

Order 4864.

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

normal subgroups only

This group has 554 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#14568128C211yesmaximal, characteristic
2#14566236C211yesmaximal, characteristic, complemented
3#14563713C211yesmaximal, characteristic, complemented
4#14562164C211yesmaximal, characteristic
5#14561489C211yesmaximal, characteristic, complemented
6#14561487C211yesmaximal, characteristic, complemented
7C19×#1510C211yesmaximal, characteristic
8C22×C4⋊Dic19C2211yescharacteristic
9#11926508C2211yescharacteristic
10#11926469—22no—
11#11926447C412yescomplemented
12#11926429—22no—
13#11926427—22no—
14#11926424—21no—
15#11926424—21no—
16#11926409C412yescomplemented
17#11926407C2211yescharacteristic
18#11926402—21no—
19C22⋊C4×Dic19—21no—
20C4×C22⋊Dic19C2211yescharacteristic
21#11926312—22no—
22#11926278—22no—
23C2×C19×#121C2211yescharacteristic
24C19×#407C2211yescharacteristic
25C19×#381C2211yescharacteristic
26C19×#327—22no—
27C22×D4×C19—21no—
28C22×D4×C19C2×C411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C23×Dic19D411yescharacteristic
31C23×Dic19D411yescharacteristic
32C2×M16×C19—21no—
33C19×#121—21no—
34C19×#121—21no—
35C19×#121—21no—
36C19×#121—21no—
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19—22no—
43C2×C22⋊Dic19—22no—
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19—21no—
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19C2×C412yes—
49C2×C4⋊Dic19D412yes—
50C2×Dic19⋊C4—22no—
51C2×C4×Dic19—22no—
52C2×C4×Dic19C2×C412yes—
53C2×#64520—21no—
54C19×C22⋊C8—21no—
55C19×C22⋊C8—21no—
56C19×#95—21no—
57C19×#95D412yes—
58C19⋊#95—22no—
59C19⋊#95—22no—
60C19⋊#95—21no—
61C19⋊#95—21no—
62C19⋊#95—22no—
63C19⋊#95—22no—
64C19⋊#95D412yes—
65C22⋊(C19⋊C8)—21no—
66C22⋊(C19⋊C8)—21no—
67C24×C19—21no—
68C24×C19C2×D411yescharacteristic
69C2×D4×C19—21no—
70C2×D4×C19—21no—
71C2×D4×C19—42no—
72C2×D4×C19—44no—
73C2×D4×C19—41no—
74C2×D4×C19—41no—
75C22×C4×C19—21no—
76C22×C4×C19—22no—
77C22×C4×C19—42no—
78C22×C4×C19C22×C411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19#4111yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C22×Dic19—21no—
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—22no—
89C22×Dic19—22no—
90C22×Dic19—81no—
91C22×Dic19—81no—
92C22×Dic19C22⋊C412yes—
93C22×Dic19C22⋊C412yes—
94M16×C19—42no—
95C2×C8×C19—41no—
96C4⋊C4×C19—21no—
97C4⋊C4×C19—21no—
98C22⋊C4×C19—42no—
99C22⋊C4×C19—41no—
100C22⋊C4×C19—41no—
101C22⋊Dic19—42no—
102C22⋊Dic19—42no—
103C22⋊Dic19—82no—
104C22⋊Dic19—82no—
105C4⋊Dic19—22no—
106C4⋊Dic19—22no—
107C4⋊Dic19—22no—
108C4⋊Dic19—22no—
109Dic19⋊C4—82no—
110C4×Dic19—42no—
111C4×Dic19—82no—
112#64520—42no—
113C2×C19⋊C8—41no—
114#9465—191nomaximal, Sylow
115C23×C19—22no—
116C23×C19—22no—
117C23×C19—41no—
118C23×C19—42no—
119C23×C19—42no—
120C23×C19—41no—
121C23×C19—42no—
122C23×C19C2×C22⋊C411yescharacteristic
123C23×C19#12011yescharacteristic
124C23×C19#12311yescharacteristic
125D4×C19—81no—
126D4×C19—81no—
127D4×C19—82no—
128D4×C19—82no—
129C2×C4×C19—22no—
130C2×C4×C19—22no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—41no—
139C2×C4×C19—42no—
140C2×C4×C19C4×D411yescharacteristic
141C2×C4×C19C4×D411yescharacteristic
142C2×C4×C19#12111yescharacteristic
143C2×C4×C19#12111yescharacteristic
144C2×Dic19—22no—
145C2×Dic19—22no—
146C2×Dic19—42no—
147C2×Dic19—42no—
148C2×Dic19—42no—
149C2×Dic19—42no—
150C2×Dic19—42no—
151C2×Dic19—42no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155C2×Dic19—42no—
156C2×Dic19—81no—
157C2×Dic19—81no—
158C8×C19—81no—
159C19⋊C8—81no—
160#2504—191no—
161#2313—191no—
162#1821—191no—
163#1510—191no—
164#1510D1911yescharacteristic
165#1284—191no—
166#1284—191no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—44no—
175C22×C19—84no—
176C22×C19—81no—
177C22×C19—81no—
178C22×C19—81no—
179C22×C19#38611yescharacteristic
180C22×C19#41012yes—
181C22×C19#45412yes—
182C4×C19—21no—
183C4×C19—21no—
184C4×C19—21no—
185C4×C19—21no—
186C4×C19—82no—
187C4×C19—81no—
188Dic19—42no—
189Dic19—42no—
190Dic19—82no—
191Dic19—82no—
192C2×#121C2×D1911yescharacteristic
193C22×C4⋊C4—191no—
194#407—191no—
195#407C2×D1911yescharacteristic
196#397—382no—
197#390—192no—
198#387—382no—
199#387—382no—
200#386—381no—
201#386—381no—
202#382—192no—
203#381—191no—
204#381C2×D1911yescharacteristic
205#380—381no—
206C4×C22⋊C4—191no—
207C4×C22⋊C4—381no—
208#343—382no—
209#327—22no—
210#327—382no—
211C2×C19—22no—
212C2×C19—22no—
213C2×C19—41no—
214C2×C19—161no—
215C2×C19#188811yescharacteristic
216C2×C19#189911yescharacteristic
217C2×C19#191111yescharacteristic
218C22×D4—21no—
219C22×D4C4×D1911yescharacteristic
220C23×C4—191no—
221C23×C4—191no—
222C23×C4C22×D1911yescharacteristic
223C2×M16—21no—
224C2×M16—381no—
225#121—21no—
226#121—21no—
227#121—21no—
228#121—21no—
229C2×C4⋊C4—192no—
230C2×C4⋊C4—192no—
231C2×C4⋊C4—381no—
232C2×C4⋊C4—381no—
233C2×C4⋊C4—381no—
234C2×C4⋊C4—381no—
235C2×C4⋊C4—382no—
236C2×C4⋊C4C4×D1911yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—381no—
240C2×C22⋊C4—381no—
241C2×C22⋊C4—382no—
242C2×C22⋊C4—382no—
243C2×C42—192no—
244C2×C42—382no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—381no—
248C22⋊C8—381no—
249#95—21no—
250#95—192no—
251#95—382no—
252#95—382no—
253#95—382no—
254#95—382no—
255#95—381no—
256#95—381no—
257#95C22⋊D1912yes—
258C19#946511yescharacteristic, complemented, Sylow
259C24—21no—
260C24D4×D1911yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—42no—
264C2×D4—44no—
265C2×D4—41no—
266C2×D4—41no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—42no—
270C22×C4—192no—
271C22×C4—192no—
272C22×C4—381no—
273C22×C4—381no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4—382no—
277C22×C4—382no—
278C22×C4—1521no—
279C22×C4—1521no—
280C22×C4C2×C4×D1911yescharacteristic
281C22×C4#6454111yescharacteristic
282C22×C4D4×D1911yescharacteristic
283C22×C4D4×D1911yescharacteristic
284C22×C4#6454311yescharacteristic
285C22×C4C2×C22⋊D1911yescharacteristic
286M16—42no—
287M16—762no—
288C2×C8—41no—
289C2×C8—761no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—382no—
293C4⋊C4—382no—
294C4⋊C4—382no—
295C4⋊C4—382no—
296C4⋊C4—1522no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—762no—
301C22⋊C4—762no—
302C22⋊C4—1522no—
303C22⋊C4—1522no—
304C42—762no—
305C42—1522no—
306C23—22no—
307C23—22no—
308C23—41no—
309C23—42no—
310C23—42no—
311C23—41no—
312C23—42no—
313C23C22⋊C4×D1911yescharacteristic
314C23#1059732911yescharacteristic
315C23#1059738311yescharacteristic
316D4—81no—
317D4—81no—
318D4—82no—
319D4—82no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—382no—
332C2×C4—382no—
333C2×C4—762no—
334C2×C4—762no—
335C2×C4—762no—
336C2×C4—762no—
337C2×C4—762no—
338C2×C4—762no—
339C2×C4—762no—
340C2×C4—762no—
341C2×C4—762no—
342C2×C4—762no—
343C2×C4—1521no—
344C2×C4—1521no—
345C2×C4(C22⋊D19)⋊C411yescharacteristic
346C2×C4#1059733011yescharacteristic
347C2×C4C4×C22⋊D1911yescharacteristic
348C2×C4#1059738411yescharacteristic
349C8—81no—
350C8—1521no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—44no—
359C22—84no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22#1192642011yescharacteristic
364C22#1192651612yes—
365C22#1192671512yes—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—82no—
371C4—81no—
372C4—762no—
373C4—762no—
374C4—1522no—
375C4—1522no—
376C2—22no—
377C2—22no—
378C2—41no—
379C2—161no—
380C2#1456403511yescharacteristic
381C2#1456409011yescharacteristic
382C2#1456416411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1510C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#1510D19
hypocenterC19#9465
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #14566236C2semidirect
3. #14563713C2semidirect
5. #14561489C2semidirect
6. #14561487C2semidirect
11. #11926447C4semidirect
16. #11926409C4semidirect
258. C19#9465semidirect

Maximal subgroups

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

subgroupindex
#145681282
#145662362
#145637132
#145621642
#145614892
#145614872
C19×#15102
#946519