Finite Group Databasebeta

← #34053507

Subgroups — #34053507

Order 19072.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011943C211yesmaximal, characteristic
2C4×#14558737C211yesmaximal, characteristic
3C4×Q8×D149C211yesmaximal, characteristic, complemented
4#23749730C211yesmaximal, characteristic, complemented
5#23749727C211yesmaximal, characteristic, complemented
6#23749723C211yesmaximal, characteristic, complemented
7Q16×Dic149C211yesmaximal, characteristic, complemented
8#23749717C211yesmaximal, characteristic, complemented
9#23749712C211yesmaximal, characteristic, complemented
10#23749710C211yesmaximal, characteristic, complemented
11#23749664C211yesmaximal, characteristic, complemented
12#23749632C211yesmaximal, characteristic, complemented
13#23749625C211yesmaximal, characteristic
14#23749577C211yesmaximal, characteristic, complemented
15#441×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic
18#18011943C418yescomplemented
19C2×#14558726C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21C2×#14558723C2211yescharacteristic
22C2×#14558719C2211yescharacteristic
23C2×#14558719C2211yescharacteristic
24Q8×Dic149C2211yescharacteristic
25Q8×Dic149C2211yescharacteristic
26C4×Dic298—21no—
27C4×Dic298C2211yescharacteristic
28#18011876—21no—
29#18011876C2211yescharacteristic
30C4×D596—21no—
31C4×D596C2211yescharacteristic
32#18011873—21no—
33#18011873C2211yescharacteristic
34#18011869—21no—
35#18011869C2211yescharacteristic
36C4⋊C4×D149—21no—
37C4⋊C4×D149C2211yescharacteristic
38C42×D149—21no—
39C42×D149—21no—
40C42×D149C2211yescharacteristic
41#18011845C2211yescharacteristic
42#18011844C2211yescharacteristic
43#18011842C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011822C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C8×Dic149C2211yescharacteristic
53C2×Q16×C149C2211yescharacteristic
54C4×Q8×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59#97×C149C2211yescharacteristic
60#14558737—22no—
61#14558737C2×C414yes—
62C2×Dic298—21no—
63C2×Dic298C2311yescharacteristic
64Q8×D149—22no—
65Q8×D149C2×C414yescomplemented
66C2×D596—21no—
67C2×D596C2311yescharacteristic
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149—21no—
73C2×C4×D149D411yescharacteristic
74C2×C4×D149D411yescharacteristic
75C2×C4×D149C2311yescharacteristic
76#14558726C2×C414yescomplemented
77#14558725C2×C414yescomplemented
78#14558723C2×C414yescomplemented
79#14558719—22no—
80#14558719C2×C414yescomplemented
81C2×#11924746C2311yescharacteristic
82C2×#11924746C2311yescharacteristic
83C4⋊Dic149—21no—
84C4⋊Dic149—21no—
85C4⋊Dic149C2311yescharacteristic
86C4⋊Dic149C2311yescharacteristic
87#14558715—21no—
88#14558715—21no—
89#14558715—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
97C4×Dic149—21no—
98C4×Dic149D411yescharacteristic
99C4×Dic149D411yescharacteristic
100C4×Dic149C2311yescharacteristic
101C2×Q8×C149C2311yescharacteristic
102C2×Q8×C149C2311yescharacteristic
103Q16×C149C2×C414yescomplemented
104C2×C8×C149C2311yescharacteristic
105C2×C8×C149C2311yescharacteristic
106C4⋊C4×C149—21no—
107C4⋊C4×C149—21no—
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C42×C149—21no—
111C42×C149—21no—
112C42×C149C2311yescharacteristic
113C22×D149—21no—
114C22×D149C2×D411yescharacteristic
115Dic298—21no—
116Dic298—24no—
117Dic298C22×C412yes—
118D596—24no—
119D596—21no—
120D596C22×C412yes—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C4×D149—24no—
128C4×D149—24no—
129C4×D149—22no—
130C4×D149—41no—
131C4×D149—42no—
132C4×D149—42no—
133C4×D149—42no—
134C4×D149C22×C412yes—
135C4×D149#4112yes—
136#11924746—21no—
137#11924746C22×C412yes—
138Q8×C149—21no—
139Q8×C149—21no—
140Q8×C149C22×C412yes—
141Q8×C149C22×C412yes—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2×D411yescharacteristic
148C2×C4×C149C2411yescharacteristic
149C8×C149—21no—
150C8×C149C22×C412yes—
151C22×C149C22×D411yescharacteristic
152C2×D149—21no—
153C2×D149—21no—
154C2×D149—22no—
155C2×D149—41no—
156C2×D149—41no—
157C2×D149C4×D412yes—
158C4×C149—22no—
159C4×C149—22no—
160C4×C149—21no—
161C4×C149—21no—
162C4×C149—41no—
163C4×C149—41no—
164C4×C149C23×C411yescharacteristic
165C4×C149C2×#4111yescharacteristic
166Dic149—22no—
167Dic149—21no—
168Dic149—41no—
169Dic149—41no—
170Dic149C4×D412yes—
171Dic149#13712yescomplemented
172C2×C149C2×C4×D411yescharacteristic
173C2×C149C2×#13711yescharacteristic
174C2×C149#57511yescharacteristic
175D149—22no—
176D149—42no—
177C149C4×#13711yescharacteristic, complemented, Sylow
178C4×#137—1491nomaximal, Sylow
179C2×#137—1491no—
180C4×#41—1491no—
181C2×C4×Q8—1491no—
182#441—1491no—
183#441D14911yescharacteristic, complemented
184#440—1491no—
185#440—1491no—
186C4×Q16—1491no—
187C4×Q16—1491no—
188C4×SD16—1491no—
189C4×SD16—1491no—
190#428—1491no—
191#419—1491no—
192#417—1491no—
193C4×M16—1491no—
194C2×#41—1491no—
195C22×Q8—1491no—
196#137—1498no—
197C2×Q16—1491no—
198C2×Q16C2×D14911yescharacteristic
199C2×SD16—1491no—
200C2×SD16—1491no—
201C2×M16—1491no—
202C2×M16—1491no—
203C4×Q8—2981no—
204C4×Q8—2981no—
205C4×Q8—1491no—
206C4×Q8—1491no—
207C4×Q8—1491no—
208C4×Q8—1491no—
209C4×Q8C2×D14911yescharacteristic
210C4×Q8C2×D14911yescharacteristic
211C4×D4—2981no—
212C4×D4—2981no—
213C4×D4—1491no—
214C4×D4—1491no—
215#117—2981no—
216#117—1491no—
217C2×C4⋊C4—2981no—
218C2×C4⋊C4—1491no—
219C2×C42—2981no—
220C2×C42—2981no—
221C2×C42—1491no—
222#107—1491no—
223#107—1491no—
224#106—1491no—
225#106C2×D14911yescharacteristic
226#103—1491no—
227#103—1491no—
228#103—1491no—
229#103—1491no—
230#103C2×D14911yescharacteristic
231#103C2×D14911yescharacteristic
232#102—1491no—
233#102—1491no—
234#97—1491no—
235#97C2×D14911yescharacteristic
236C4×C8—1491no—
237C4×C8—1491no—
238#41—2982no—
239#41—1494no—
240C2×Q8—2981no—
241C2×Q8—2982no—
242C2×Q8—1494no—
243C2×Q8—1491no—
244C2×Q8C22×D14911yescharacteristic
245C2×Q8C22×D14911yescharacteristic
246C2×D4—2981no—
247C2×D4—1491no—
248C22×C4—2981no—
249C22×C4—2981no—
250C22×C4—2981no—
251C22×C4—2981no—
252C22×C4—2981no—
253C22×C4—1491no—
254C22×C4—1491no—
255C22×C4—1491no—
256Q16—1494no—
257Q16C4×D14914yescomplemented
258SD16—1494no—
259SD16—1494no—
260M16—2982no—
261M16—1494no—
262C2×C8—1491no—
263C2×C8—1491no—
264C2×C8C22×D14911yescharacteristic
265C2×C8C22×D14911yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—2981no—
272C4⋊C4—2981no—
273C4⋊C4—1491no—
274C4⋊C4—1491no—
275C4⋊C4C22×D14911yescharacteristic
276C4⋊C4C22×D14911yescharacteristic
277C22⋊C4—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C42—21no—
281C42—21no—
282C42—2981no—
283C42—2981no—
284C42—2981no—
285C42—2981no—
286C42—2981no—
287C42—1491no—
288C42—1491no—
289C42—1491no—
290C42C22×D14911yescharacteristic
291C23—2981no—
292C23—1491no—
293Q8—21no—
294Q8—21no—
295Q8—2984no—
296Q8—2981no—
297Q8—1492no—
298Q8C2×C4×D14912yes—
299Q8C2×C4×D14912yes—
300D4—2984no—
301D4—2981no—
302D4—1492no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—2984no—
308C2×C4—2984no—
309C2×C4—2982no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—5961no—
314C2×C4—5962no—
315C2×C4—5962no—
316C2×C4—5962no—
317C2×C4—1491no—
318C2×C4—1491no—
319C2×C4—1491no—
320C2×C4—1492no—
321C2×C4—1492no—
322C2×C4D4×D14911yescharacteristic
323C2×C4D4×D14911yescharacteristic
324C2×C4C23×D14911yescharacteristic
325C8—21no—
326C8—2981no—
327C8—1492no—
328C8C2×C4×D14912yes—
329C22—2981no—
330C22—2981no—
331C22—2982no—
332C22—5961no—
333C22—5961no—
334C22—1492no—
335C22C2×D4×D14911yescharacteristic
336C4—21no—
337C4—21no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—2981no—
343C4—2982no—
344C4—5961no—
345C4—5961no—
346C4—1492no—
347C4—1492no—
348C4C22×C4×D14911yescharacteristic
349C4#41×D14911yescharacteristic
350C2—2982no—
351C2—5962no—
352C2C4×D4×D14911yescharacteristic
353C2#137×D14911yescharacteristic
354C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutatorC4×C149C23×C4
FrattiniC2×C4C23×D149
Fitting#441×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558737C22
cosocleC2×C4×C149C24
hypercenter#441D149
hypocenterC149C4×#137
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D149C2semidirect
4. #23749730C2semidirect
5. #23749727C2semidirect
6. #23749723C2semidirect
7. Q16×Dic149C2semidirect
8. #23749717C2semidirect
9. #23749712C2semidirect
10. #23749710C2semidirect
11. #23749664C2semidirect
12. #23749632C2semidirect
14. #23749577C2semidirect
15. #441×C149C2semidirect
18. #18011943C4semidirect
65. Q8×D149C2×C4semidirect
76. #14558726C2×C4semidirect
77. #14558725C2×C4semidirect
78. #14558723C2×C4semidirect
80. #14558719C2×C4semidirect
103. Q16×C149C2×C4semidirect
171. Dic149#137semidirect
177. C149C4×#137semidirect
183. #441D149semidirect
257. Q16C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119432
C4×#145587372
C4×Q8×D1492
#237497302
#237497272
#237497232
Q16×Dic1492
#237497172
#237497122
#237497102
#237496642
#237496322
#237496252
#237495772
#441×C1492
C4×#137149