Finite Group Databasebeta

← #34053942

Subgroups — #34053942

Order 19072.

806 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#14558737C211yesmaximal, characteristic, complemented
2C2×#18011938C212yesmaximal, complemented
3#121×D149C211yesmaximal, characteristic, complemented
4#23749773C212yesmaximal, complemented
5#23749769C212yesmaximal, complemented
6#23749764C211yesmaximal, characteristic, complemented
7#23749761C211yesmaximal, characteristic, complemented
8#23749758C211yesmaximal, characteristic, complemented
9#23749625C212yesmaximal, complemented
10#23749587C211yesmaximal, characteristic, complemented
11#448×C149C211yesmaximal, characteristic, complemented
12C2×#14558737—28no—
13C2×#14558737—21no—
14C2×#14558737—21no—
15C2×#14558737C2212yes—
16C2×#14558737C2212yescomplemented
17C22×D596—21no—
18C22×D596C2211yescharacteristic, complemented
19C2×D4×D149—21no—
20C2×D4×D149C2211yescharacteristic, complemented
21C22×C4×D149—21no—
22C22×C4×D149C2211yescharacteristic
23#18011938—28no—
24C2×#14558723C2212yescomplemented
25C2×D1192C2212yescomplemented
26C2×#14558721C2212yescomplemented
27C2×#14558719C2212yescomplemented
28#18011886C2211yescharacteristic, complemented
29#18011885C2211yescharacteristic
30#18011884—21no—
31#18011883—21no—
32#18011882C2211yescharacteristic, complemented
33C4⋊C4×D149C2211yescharacteristic, complemented
34C22⋊C4×D149—21no—
35#18011835C2212yescomplemented
36#18011833C2212yescomplemented
37#18011831C2212yescomplemented
38C22⋊#11924746C2211yescharacteristic, complemented
39#18011823C2212yescomplemented
40C22×Q8×C149C2211yescharacteristic, complemented
41C2×SD16×C149C2212yescomplemented
42#121×C149C2211yescharacteristic
43#103×C149C2212yescomplemented
44C22⋊C8×C149C2211yescharacteristic, complemented
45C23×D149—21no—
46C23×D149—21no—
47C23×D149D411yescharacteristic
48#14558737—28no—
49#14558737—28no—
50#14558737—24no—
51#14558737—24no—
52#14558737—24no—
53#14558737D418yescomplemented
54C2×D596—28no—
55C2×D596—22no—
56C2×D596—22no—
57C2×D596—24no—
58C2×D596—21no—
59C2×D596—21no—
60C2×D596C2311yescharacteristic
61C2×D596C2312yes—
62C2×C22⋊D149—21no—
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65D4×D149—24no—
66D4×D149—44no—
67C22×Dic149D411yescharacteristic
68C2×C4×D149—28no—
69C2×C4×D149—22no—
70C2×C4×D149—22no—
71C2×C4×D149—24no—
72C2×C4×D149—21no—
73C2×C4×D149D411yescharacteristic
74C2×C4×D149D411yescharacteristic
75C2×C4×D149C2311yescharacteristic
76C2×C4×D149C2311yescharacteristic
77#14558723—24no—
78D1192—24no—
79#14558721—24no—
80#14558719—24no—
81C2×#11924746C2312yes—
82C4⋊Dic149C2311yescharacteristic
83#14558715—21no—
84C22⋊Dic149—21no—
85#14558713—21no—
86#14558713—21no—
87C2×Q8×C149—24no—
88C2×Q8×C149—21no—
89C2×Q8×C149C2312yes—
90C2×D4×C149—21no—
91C2×D4×C149C2311yescharacteristic
92C22×C4×C149—21no—
93C22×C4×C149C2311yescharacteristic
94SD16×C149—24no—
95C2×C8×C149C2312yes—
96C4⋊C4×C149C2311yescharacteristic
97C22⋊C4×C149—21no—
98C22×D149—24no—
99C22×D149—22no—
100C22×D149—22no—
101C22×D149—22no—
102C22×D149—21no—
103C22×D149—41no—
104C22×D149—42no—
105C22×D149—42no—
106C22×D149—42no—
107C22×D149—42no—
108C22×D149—42no—
109C22×D149C2×D411yescharacteristic
110C22×D149C2×D411yescharacteristic
111D596—28no—
112D596—24no—
113D596—28no—
114D596—22no—
115D596—22no—
116D596—42no—
117D596C2×D414yescomplemented
118C22⋊D149—42no—
119C22⋊D149—42no—
120C22⋊D149—42no—
121C2×Dic149—22no—
122C2×Dic149—21no—
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C4×D149—28no—
126C4×D149—22no—
127C4×D149—22no—
128C4×D149—28no—
129C4×D149—22no—
130C4×D149—42no—
131C4×D149C2×D414yes—
132#11924746—22no—
133C23×C149—21no—
134C23×C149C2×D411yescharacteristic
135Q8×C149—24no—
136Q8×C149—22no—
137Q8×C149C2×D414yescomplemented
138D4×C149—22no—
139D4×C149—42no—
140C2×C4×C149—24no—
141C2×C4×C149—22no—
142C2×C4×C149—22no—
143C2×C4×C149—21no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2411yescharacteristic
146C8×C149—22no—
147C22×C149—21no—
148C22×C149—21no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149AGL(1,ℤ/8)12yescomplemented
153C22×C149C22×D411yescharacteristic
154C2×D149—21no—
155C2×D149—21no—
156C2×D149—21no—
157C2×D149—24no—
158C2×D149—21no—
159C2×D149—21no—
160C2×D149—44no—
161C2×D149—48no—
162C2×D149—42no—
163C2×D149—42no—
164C2×D149—41no—
165C2×D149—41no—
166C2×D149—41no—
167C2×D149—84no—
168C2×D149#12012yes—
169C4×C149—24no—
170C4×C149—21no—
171C4×C149—41no—
172C4×C149C22×D412yes—
173Dic149—21no—
174Dic149—41no—
175Dic149#12012yes—
176C2×C149—22no—
177C2×C149—81no—
178C2×C149C2×#12011yescharacteristic
179C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C149#57511yescharacteristic
181D149—22no—
182D149—41no—
183D149—44no—
184D149—81no—
185C149#300611yescharacteristic, complemented, Sylow
186#3006—1491nomaximal, Sylow
187C22×#41—1491no—
188C2×AGL(1,ℤ/8)—1492no—
189C2×#121—1491no—
190#449—1492no—
191#449—1492no—
192#448—1491no—
193#448D14911yescharacteristic, complemented
194#447—1491no—
195#447—1491no—
196#417—1492no—
197#407—1491no—
198C2×#41—2988no—
199C2×#41—2981no—
200C2×#41—2981no—
201C2×#41—1492no—
202C2×#41—1492no—
203C22×Q8C2×D14911yescharacteristic, complemented
204C22×D4—2981no—
205C22×D4—2981no—
206C22×D4—1491no—
207C22×D4—1491no—
208C23×C4—2981no—
209C23×C4—1491no—
210AGL(1,ℤ/8)—2988no—
211C2×SD16—1492no—
212C2×SD16C2×D14912yescomplemented
213C2×D8—1492no—
214C2×D8—1492no—
215C2×M16—1492no—
216#121—2981no—
217#121—2981no—
218#121—1491no—
219#121—1491no—
220#121—1491no—
221#121C2×D14911yescharacteristic
222C2×C4⋊C4—1491no—
223C2×C22⋊C4—2981no—
224#103—1492no—
225#103C2×D14912yescomplemented
226#102—1492no—
227#102—1492no—
228C22⋊C8—1491no—
229C22⋊C8—1492no—
230C22⋊C8C2×D14911yescharacteristic, complemented
231C24—2981no—
232C24—2981no—
233C24—1491no—
234#41—2988no—
235#41—2988no—
236#41—2984no—
237#41—2984no—
238#41—2984no—
239#41—1498no—
240C2×Q8—24no—
241C2×Q8—21no—
242C2×Q8C22×D14912yes—
243C2×D4—21no—
244C2×D4—2988no—
245C2×D4—2982no—
246C2×D4—2982no—
247C2×D4—2984no—
248C2×D4—2981no—
249C2×D4—2981no—
250C2×D4—2981no—
251C2×D4—2984no—
252C2×D4—2981no—
253C2×D4—2981no—
254C2×D4—5964no—
255C2×D4—1491no—
256C2×D4—1492no—
257C2×D4C22×D14911yescharacteristic
258C22×C4—21no—
259C22×C4—2988no—
260C22×C4—2982no—
261C22×C4—2982no—
262C22×C4—2984no—
263C22×C4—2981no—
264C22×C4—1491no—
265C22×C4—1491no—
266C22×C4—1491no—
267C22×C4—1491no—
268C22×C4—1491no—
269C22×C4C22×D14911yescharacteristic
270SD16—24no—
271SD16—2984no—
272D8—2984no—
273D8—2984no—
274M16—2984no—
275C2×C8—1492no—
276C2×C8C22×D14912yes—
277C4⋊C4—2981no—
278C4⋊C4—1491no—
279C4⋊C4C22×D14911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C23—21no—
285C23—2984no—
286C23—2982no—
287C23—2982no—
288C23—2982no—
289C23—2981no—
290C23—5961no—
291C23—5962no—
292C23—5962no—
293C23—5962no—
294C23—5962no—
295C23—5962no—
296C23—1491no—
297C23—1491no—
298C23D4×D14911yescharacteristic
299Q8—24no—
300Q8—22no—
301Q8D4×D14914yescomplemented
302D4—22no—
303D4—42no—
304D4—2988no—
305D4—2984no—
306D4—2988no—
307D4—2982no—
308D4—2982no—
309D4—5962no—
310D4—5962no—
311D4—5962no—
312D4—5962no—
313D4—1494no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—2988no—
319C2×C4—2982no—
320C2×C4—2988no—
321C2×C4—2982no—
322C2×C4—2982no—
323C2×C4—2982no—
324C2×C4—2981no—
325C2×C4—5962no—
326C2×C4—1491no—
327C2×C4—1491no—
328C2×C4—1494no—
329C2×C4D4×D14911yescharacteristic
330C2×C4C23×D14911yescharacteristic
331C8—22no—
332C8—2982no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—2981no—
339C22—2981no—
340C22—2981no—
341C22—2981no—
342C22—2981no—
343C22—2984no—
344C22—5964no—
345C22—5968no—
346C22—5962no—
347C22—5962no—
348C22—5961no—
349C22—5961no—
350C22—5961no—
351C22—1492no—
352C22—11924no—
353C22#1801193812yescomplemented
354C22C2×D4×D14911yescharacteristic
355C4—24no—
356C4—21no—
357C4—41no—
358C4—2981no—
359C4—5961no—
360C4—1492no—
361C4C2×D4×D14912yes—
362C2—22no—
363C2—81no—
364C2—2982no—
365C2—5961no—
366C2—5964no—
367C2—11921no—
368C2#120×D14911yescharacteristic
369C2C2×#1801193811yescharacteristic
370C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#448×C149C2
socleC22×C149C22×D4
hypercenter#448D149
hypocenterC149#3006
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C22×#14558737C2semidirect
2. C2×#18011938C2semidirect
3. #121×D149C2semidirect
4. #23749773C2semidirect
5. #23749769C2semidirect
6. #23749764C2semidirect
7. #23749761C2semidirect
8. #23749758C2semidirect
9. #23749625C2semidirect
10. #23749587C2semidirect
11. #448×C149C2semidirect
16. C2×#14558737C22semidirect
18. C22×D596C22semidirect
20. C2×D4×D149C22semidirect
24. C2×#14558723C22semidirect
25. C2×D1192C22semidirect
26. C2×#14558721C22semidirect
27. C2×#14558719C22semidirect
28. #18011886C22semidirect
32. #18011882C22semidirect
33. C4⋊C4×D149C22semidirect
35. #18011835C22semidirect
36. #18011833C22semidirect
37. #18011831C22semidirect
38. C22⋊#11924746C22semidirect
39. #18011823C22semidirect
40. C22×Q8×C149C22semidirect
41. C2×SD16×C149C22semidirect
43. #103×C149C22semidirect
44. C22⋊C8×C149C22semidirect
53. #14558737D4semidirect
117. D596C2×D4semidirect
137. Q8×C149C2×D4semidirect
152. C22×C149AGL(1,ℤ/8)semidirect
185. C149#3006semidirect
193. #448D149semidirect
203. C22×Q8C2×D149semidirect
212. C2×SD16C2×D149semidirect
225. #103C2×D149semidirect
230. C22⋊C8C2×D149semidirect
301. Q8D4×D149semidirect
353. C22#18011938semidirect

Maximal subgroups

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

subgroupindex
C22×#145587372
C2×#180119382
#121×D1492
#237497732
#237497692
#237497642
#237497612
#237497582
#237496252
#237495872
#448×C1492
#3006149