Finite Group Databasebeta

← #18085459

Subgroups — #18085459

Order 4864.

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

normal subgroups only

This group has 672 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#14568114C211yesmaximal, characteristic, complemented
2#14568107C211yesmaximal, characteristic
3#14563713C211yesmaximal, characteristic, complemented
4#14562155C211yesmaximal, characteristic, complemented
5#14562151C211yesmaximal, characteristic
6#14561520C211yesmaximal, characteristic, complemented
7C19×#3193C211yesmaximal, characteristic
8C2×#10597381—22no—
9C22×C4⋊Dic19C2211yescharacteristic
10#11926508C2211yescharacteristic
11#11926480—22no—
12#11926474—22no—
13#11926451—21no—
14#11926447—21no—
15#11926416—22no—
16#11926413—21no—
17#11926413—21no—
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—
54#10597381—48no—
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×Dic19⋊C4—24no—
62C2×Dic19⋊C4—24no—
63C2×C4×Dic19—21no—
64C2×C4×Dic19—21no—
65C2×#64520—21no—
66C19×#107—22no—
67C19×#103—22no—
68C19×#102—22no—
69C19×C22⋊C8—21no—
70C19×C22⋊C8—21no—
71C19⋊#95—24no—
72C19⋊#95D412yes—
73C19⋊#95D412yes—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C24×C19—21no—
77C24×C19C2×D411yescharacteristic
78C2×Q8×C19—21no—
79C2×Q8×C19—21no—
80C2×Q8×C19—42no—
81C2×D4×C19—21no—
82C2×D4×C19—21no—
83C2×D4×C19—42no—
84C2×D4×C19—44no—
85C2×D4×C19—41no—
86C2×D4×C19—41no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—42no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19#4111yescharacteristic
97C22×Dic19—22no—
98C22×Dic19—22no—
99C22×Dic19—22no—
100C22×Dic19—22no—
101C22×Dic19—22no—
102C22×Dic19—44no—
103SD16×C19—82no—
104M16×C19—42no—
105C2×C8×C19—22no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—41no—
111C4⋊C4×C19—41no—
112C22⋊C4×C19—41no—
113C22⋊C4×C19—41no—
114C22⋊C4×C19—41no—
115C22⋊C4×C19—41no—
116C22⋊Dic19—24no—
117C22⋊Dic19—24no—
118C22⋊Dic19—48no—
119C4⋊Dic19—41no—
120C4⋊Dic19—41no—
121C4⋊Dic19—41no—
122C4⋊Dic19—41no—
123Dic19⋊C4—48no—
124Dic19⋊C4—84no—
125C4×Dic19—42no—
126C4×Dic19—42no—
127#64520—42no—
128C2×C19⋊C8—41no—
129#10331—191nomaximal, Sylow
130C23×C19—22no—
131C23×C19—22no—
132C23×C19—41no—
133C23×C19—42no—
134C23×C19—42no—
135C23×C19—41no—
136C23×C19—42no—
137C23×C19#12011yescharacteristic
138C23×C19#12011yescharacteristic
139C23×C19#12111yescharacteristic
140Q8×C19—42no—
141Q8×C19—81no—
142D4×C19—42no—
143D4×C19—81no—
144D4×C19—82no—
145D4×C19—82no—
146C2×C4×C19—22no—
147C2×C4×C19—22no—
148C2×C4×C19—22no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—42no—
153C2×C4×C19—42no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—42no—
158C2×C4×C19#12011yescharacteristic
159C2×C4×C19#12111yescharacteristic
160C2×C4×C19#12111yescharacteristic
161C2×C4×C19#12711yescharacteristic
162C2×Dic19—24no—
163C2×Dic19—24no—
164C2×Dic19—42no—
165C2×Dic19—42no—
166C2×Dic19—42no—
167C2×Dic19—42no—
168C2×Dic19—44no—
169C2×Dic19—42no—
170C2×Dic19—44no—
171C2×Dic19—82no—
172C8×C19—42no—
173C19⋊C8—81no—
174#3193D1911yescharacteristic
175#2502—191no—
176#2501—191no—
177#1821—191no—
178#1508—191no—
179#1507—191no—
180#1297—191no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—44no—
189C22×C19—84no—
190C22×C19—81no—
191C22×C19—81no—
192C22×C19—81no—
193C22×C19#39211yescharacteristic
194C22×C19#45312yes—
195C22×C19#45612yes—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—21no—
199C4×C19—81no—
200C4×C19—81no—
201C4×C19—81no—
202C4×C19#45812yes—
203Dic19—44no—
204Dic19—44no—
205Dic19—82no—
206C2×#123—382no—
207C2×C22⋊Q8C2×D1911yescharacteristic
208C2×#121C2×D1911yescharacteristic
209C22×C4⋊C4—191no—
210#484—21no—
211#480—21no—
212#468—22no—
213#450—21no—
214#448—21no—
215#407—191no—
216#407C2×D1911yescharacteristic
217#399—382no—
218#398—382no—
219#391—381no—
220#390—381no—
221#385—382no—
222#384—381no—
223#384—381no—
224C4×C22⋊C4—191no—
225C4×C22⋊C4—191no—
226#343—382no—
227#328—382no—
228#327—382no—
229C2×C19—22no—
230C2×C19—22no—
231C2×C19—41no—
232C2×C19—161no—
233C2×C19#200211yescharacteristic
234C2×C19#200511yescharacteristic
235C2×C19#202211yescharacteristic
236C22×Q8C22⋊D1911yescharacteristic
237C22×D4—21no—
238C22×D4C22⋊D1911yescharacteristic
239C23×C4—192no—
240C23×C4C22×D1911yescharacteristic
241C2×SD16—22no—
242C2×M16—381no—
243C2×M16C22⋊D1912yes—
244#123—768no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249#121—21no—
250#121—21no—
251#121—21no—
252#121—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—384no—
255C2×C4⋊C4—381no—
256C2×C4⋊C4—381no—
257C2×C4⋊C4—381no—
258C2×C4⋊C4—381no—
259C2×C4⋊C4—381no—
260C2×C4⋊C4—381no—
261C2×C4⋊C4—384no—
262C2×C4⋊C4C22⋊D1911yescharacteristic
263C2×C4⋊C4C22⋊D1911yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—381no—
267C2×C22⋊C4—381no—
268C2×C22⋊C4—384no—
269C2×C42—381no—
270C2×C42—381no—
271#107—22no—
272#103—22no—
273#102—22no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8—381no—
277C22⋊C8—381no—
278#95—192no—
279#95—192no—
280#95—384no—
281C19#1033111yescharacteristic, complemented, Sylow
282C24—21no—
283C24D4×D1911yescharacteristic
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—42no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—42no—
290C2×D4—44no—
291C2×D4—41no—
292C2×D4—41no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—42no—
297C22×C4—382no—
298C22×C4—382no—
299C22×C4—382no—
300C22×C4—382no—
301C22×C4—382no—
302C22×C4—764no—
303C22×C4D4×D1911yescharacteristic
304C22×C4D4×D1911yescharacteristic
305C22×C4#6454311yescharacteristic
306C22×C4C2×C22⋊D1911yescharacteristic
307C22×C4C2×C22⋊D1911yescharacteristic
308C22×C4C2×C22⋊D1911yescharacteristic
309SD16—82no—
310M16—42no—
311M16—762no—
312C2×C8—22no—
313C2×C8—761no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—768no—
321C4⋊C4—761no—
322C4⋊C4—761no—
323C4⋊C4—761no—
324C4⋊C4—761no—
325C4⋊C4—1524no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—384no—
331C22⋊C4—384no—
332C22⋊C4—768no—
333C42—762no—
334C42—762no—
335C23—22no—
336C23—22no—
337C23—41no—
338C23—42no—
339C23—42no—
340C23—41no—
341C23—42no—
342C23#1059738311yescharacteristic
343C23#1059738311yescharacteristic
344C23#1059738411yescharacteristic
345Q8—42no—
346Q8—81no—
347D4—42no—
348D4—81no—
349D4—82no—
350D4—82no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—384no—
364C2×C4—384no—
365C2×C4—762no—
366C2×C4—762no—
367C2×C4—762no—
368C2×C4—762no—
369C2×C4—764no—
370C2×C4—762no—
371C2×C4—764no—
372C2×C4—1522no—
373C2×C4#1059738511yescharacteristic
374C2×C4#1059738511yescharacteristic
375C2×C4#1059738611yescharacteristic
376C2×C4#1059739911yescharacteristic
377C8—42no—
378C8—1521no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—44no—
387C22—84no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22#1192645211yescharacteristic
392C22#1192671012yes—
393C22#1192672512yes—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—81no—
398C4—81no—
399C4—81no—
400C4—764no—
401C4—764no—
402C4—1522no—
403C4#1192673412yes—
404C2—22no—
405C2—22no—
406C2—41no—
407C2—161no—
408C2#1456464711yescharacteristic
409C2#1456466811yescharacteristic
410C2#1456476411yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#3193C2
socleC22×C19#392
prime radicalC2×C19×#121C22
hypercenter#3193D19
hypocenterC19#10331
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
1. #14568114C2semidirect
3. #14563713C2semidirect
4. #14562155C2semidirect
6. #14561520C2semidirect
281. C19#10331semidirect

Maximal subgroups

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

subgroupindex
#145681142
#145681072
#145637132
#145621552
#145621512
#145615202
C19×#31932
#1033119