Finite Group Databasebeta

← #18085466

Subgroups — #18085466

Order 4864.

600 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 89 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#14568121C211yesmaximal, characteristic, complemented
3#14563713C211yesmaximal, characteristic, complemented
4#14562155C211yesmaximal, characteristic, complemented
5#14562151C211yesmaximal, characteristic
6#14561520C211yesmaximal, characteristic, complemented
7C19×#3193C211yesmaximal, characteristic
8C22×C4⋊Dic19C2211yescharacteristic
9#11926508C2211yescharacteristic
10#11926483—22no—
11#11926469—22no—
12#11926451—21no—
13#11926447—21no—
14#11926424—22no—
15#11926409—21no—
16#11926409—21no—
17#11926405—22no—
18C4×C22⋊Dic19C2211yescharacteristic
19C4×C22⋊Dic19C2211yescharacteristic
20#11926312—22no—
21#11926281—22no—
22#11926278—22no—
23C2×C19×C22⋊Q8C2211yescharacteristic
24C2×C19×#121C2211yescharacteristic
25C19×#484—21no—
26C19×#480—21no—
27C19×#468—22no—
28C19×#450—21no—
29C19×#448—21no—
30C19×#407C2211yescharacteristic
31C22×Q8×C19D411yescharacteristic
32C22×D4×C19—21no—
33C22×D4×C19D411yescharacteristic
34C23×C4×C19C2311yescharacteristic
35C23×Dic19D412yes—
36C2×SD16×C19—22no—
37C2×M16×C19D412yes—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C19×#121—21no—
43C19×#121—21no—
44C19×#121—21no—
45C19×#121—21no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19D411yescharacteristic
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C22⋊C4×C19—21no—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊Dic19—21no—
52C2×C22⋊Dic19—21no—
53C2×C22⋊Dic19—24no—
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19—21no—
56C2×C4⋊Dic19—21no—
57C2×C4⋊Dic19—21no—
58C2×C4⋊Dic19—21no—
59C2×C4⋊Dic19—21no—
60C2×C4×Dic19—21no—
61C2×C4×Dic19—21no—
62C2×#64520—21no—
63C19×#107—22no—
64C19×#103—22no—
65C19×#102—22no—
66C19×C22⋊C8—21no—
67C19×C22⋊C8—21no—
68C19⋊#95—24no—
69C19⋊#95—24no—
70C19⋊#95—24no—
71C19⋊#95D412yes—
72C19⋊#95D412yes—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C24×C19—21no—
76C24×C19C2×D411yescharacteristic
77C2×Q8×C19—21no—
78C2×Q8×C19—21no—
79C2×Q8×C19—42no—
80C2×D4×C19—21no—
81C2×D4×C19—21no—
82C2×D4×C19—42no—
83C2×D4×C19—44no—
84C2×D4×C19—41no—
85C2×D4×C19—41no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
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
96C22×Dic19—22no—
97C22×Dic19—22no—
98C22×Dic19—22no—
99C22×Dic19—22no—
100C22×Dic19—22no—
101C22×Dic19—44no—
102SD16×C19—82no—
103M16×C19—42no—
104C2×C8×C19—22no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19—41no—
110C4⋊C4×C19—41no—
111C22⋊C4×C19—41no—
112C22⋊C4×C19—41no—
113C22⋊C4×C19—41no—
114C22⋊C4×C19—41no—
115C22⋊Dic19—42no—
116C22⋊Dic19—42no—
117C22⋊Dic19—84no—
118C4⋊Dic19—41no—
119C4⋊Dic19—41no—
120C4⋊Dic19—41no—
121C4⋊Dic19—41no—
122C4×Dic19—42no—
123C4×Dic19—42no—
124#64520—42no—
125C2×C19⋊C8—41no—
126#10332—191nomaximal, Sylow
127C23×C19—22no—
128C23×C19—22no—
129C23×C19—41no—
130C23×C19—42no—
131C23×C19—42no—
132C23×C19—41no—
133C23×C19—42no—
134C23×C19#12011yescharacteristic
135C23×C19#12011yescharacteristic
136C23×C19#12111yescharacteristic
137Q8×C19—42no—
138Q8×C19—81no—
139D4×C19—42no—
140D4×C19—81no—
141D4×C19—82no—
142D4×C19—82no—
143C2×C4×C19—22no—
144C2×C4×C19—22no—
145C2×C4×C19—22no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—42no—
150C2×C4×C19—42no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—42no—
155C2×C4×C19#12011yescharacteristic
156C2×C4×C19#12111yescharacteristic
157C2×C4×C19#12111yescharacteristic
158C2×C4×C19#12711yescharacteristic
159C2×Dic19—42no—
160C2×Dic19—42no—
161C2×Dic19—42no—
162C2×Dic19—42no—
163C2×Dic19—44no—
164C2×Dic19—42no—
165C2×Dic19—42no—
166C2×Dic19—42no—
167C2×Dic19—44no—
168C2×Dic19—82no—
169C8×C19—42no—
170C19⋊C8—81no—
171#3193D1911yescharacteristic
172#2504—191no—
173#2503—191no—
174#1821—191no—
175#1508—191no—
176#1507—191no—
177#1297—191no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—44no—
186C22×C19—84no—
187C22×C19—81no—
188C22×C19—81no—
189C22×C19—81no—
190C22×C19#39211yescharacteristic
191C22×C19#45412yes—
192C22×C19#45512yes—
193C4×C19—21no—
194C4×C19—21no—
195C4×C19—21no—
196C4×C19—81no—
197C4×C19—81no—
198C4×C19—81no—
199C4×C19#45812yes—
200Dic19—82no—
201Dic19—82no—
202Dic19—82no—
203C2×C22⋊Q8C2×D1911yescharacteristic
204C2×#121C2×D1911yescharacteristic
205C22×C4⋊C4—191no—
206#484—21no—
207#480—21no—
208#468—22no—
209#450—21no—
210#448—21no—
211#407—191no—
212#407C2×D1911yescharacteristic
213#400—382no—
214#397—382no—
215#391—381no—
216#390—381no—
217#386—382no—
218#382—381no—
219#382—381no—
220#381—382no—
221C4×C22⋊C4—191no—
222C4×C22⋊C4—191no—
223#343—382no—
224#328—382no—
225#327—382no—
226C2×C19—22no—
227C2×C19—22no—
228C2×C19—41no—
229C2×C19—161no—
230C2×C19#200311yescharacteristic
231C2×C19#200411yescharacteristic
232C2×C19#202211yescharacteristic
233C22×Q8C22⋊D1911yescharacteristic
234C22×D4—21no—
235C22×D4C22⋊D1911yescharacteristic
236C23×C4—192no—
237C23×C4C22×D1911yescharacteristic
238C2×SD16—22no—
239C2×M16—381no—
240C2×M16C22⋊D1912yes—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245#121—21no—
246#121—21no—
247#121—21no—
248#121—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—381no—
251C2×C4⋊C4—381no—
252C2×C4⋊C4—381no—
253C2×C4⋊C4—381no—
254C2×C4⋊C4—381no—
255C2×C4⋊C4—381no—
256C2×C4⋊C4C22⋊D1911yescharacteristic
257C2×C4⋊C4C22⋊D1911yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—381no—
261C2×C22⋊C4—381no—
262C2×C22⋊C4—384no—
263C2×C42—381no—
264C2×C42—381no—
265#107—22no—
266#103—22no—
267#102—22no—
268C22⋊C8—21no—
269C22⋊C8—21no—
270C22⋊C8—381no—
271C22⋊C8—381no—
272#95—192no—
273#95—192no—
274#95—384no—
275#95—384no—
276#95—384no—
277C19#1033211yescharacteristic, complemented, Sylow
278C24—21no—
279C24D4×D1911yescharacteristic
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—42no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—42no—
286C2×D4—44no—
287C2×D4—41no—
288C2×D4—41no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—382no—
294C22×C4—382no—
295C22×C4—382no—
296C22×C4—382no—
297C22×C4—382no—
298C22×C4—764no—
299C22×C4D4×D1911yescharacteristic
300C22×C4D4×D1911yescharacteristic
301C22×C4#6454311yescharacteristic
302C22×C4C2×C22⋊D1911yescharacteristic
303C22×C4C2×C22⋊D1911yescharacteristic
304C22×C4C2×C22⋊D1911yescharacteristic
305SD16—82no—
306M16—42no—
307M16—762no—
308C2×C8—22no—
309C2×C8—761no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—761no—
317C4⋊C4—761no—
318C4⋊C4—761no—
319C4⋊C4—761no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—762no—
325C22⋊C4—762no—
326C22⋊C4—1524no—
327C42—762no—
328C42—762no—
329C23—22no—
330C23—22no—
331C23—41no—
332C23—42no—
333C23—42no—
334C23—41no—
335C23—42no—
336C23#1059738311yescharacteristic
337C23#1059738311yescharacteristic
338C23#1059738411yescharacteristic
339Q8—42no—
340Q8—81no—
341D4—42no—
342D4—81no—
343D4—82no—
344D4—82no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—762no—
358C2×C4—762no—
359C2×C4—762no—
360C2×C4—762no—
361C2×C4—764no—
362C2×C4—762no—
363C2×C4—762no—
364C2×C4—762no—
365C2×C4—764no—
366C2×C4—1522no—
367C2×C4#1059738511yescharacteristic
368C2×C4#1059738511yescharacteristic
369C2×C4#1059738611yescharacteristic
370C2×C4#1059739911yescharacteristic
371C8—42no—
372C8—1521no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—44no—
381C22—84no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22#1192645211yescharacteristic
386C22#1192671512yes—
387C22#1192672012yes—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—1522no—
395C4—1522no—
396C4—1522no—
397C4#1192673412yes—
398C2—22no—
399C2—22no—
400C2—41no—
401C2—161no—
402C2#1456465411yescharacteristic
403C2#1456466111yescharacteristic
404C2#1456476411yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#3193C2
socleC22×C19#392
prime radicalC2×C19×#121C22
hypercenter#3193D19
hypocenterC19#10332
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3193

Complements

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

NH ≅ G/Ntype
2. #14568121C2semidirect
3. #14563713C2semidirect
4. #14562155C2semidirect
6. #14561520C2semidirect
277. C19#10332semidirect

Maximal subgroups

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

subgroupindex
#145681282
#145681212
#145637132
#145621552
#145621512
#145615202
C19×#31932
#1033219