Finite Group Databasebeta

← #34056345

Subgroups — #34056345

Order 19072.

476 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011944C211yesmaximal, characteristic, complemented
2C2×#18011940C211yesmaximal, characteristic, complemented
3#23750285C211yesmaximal, characteristic, complemented
4#23750281C211yesmaximal, characteristic, complemented
5#23750006C211yesmaximal, characteristic, complemented
6#23749872C211yesmaximal, characteristic, complemented
7#23749850C211yesmaximal, characteristic, complemented
8#23749846C211yesmaximal, characteristic, complemented
9#23749782C211yesmaximal, characteristic, complemented
10#23749780C211yesmaximal, characteristic, complemented
11#23749771C211yesmaximal, characteristic, complemented
12#23749768C211yesmaximal, characteristic, complemented
13#23749719C211yesmaximal, characteristic, complemented
14#23749701C211yesmaximal, characteristic, complemented
15#468×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C22×Dic298C2211yescharacteristic
19C2×Q8×D149C2211yescharacteristic
20#18011944—24no—
21#18011940—24no—
22C2×Dic596C2211yescharacteristic
23C2×Dic596C2211yescharacteristic
24C2×#14558726C2211yescharacteristic
25C2×#14558726C2211yescharacteristic
26C2×#14558725C2211yescharacteristic
27C2×#14558725C2211yescharacteristic
28C2×#14558724C2211yescharacteristic
29C2×#14558721C2211yescharacteristic
30C2×#14558719C2211yescharacteristic
31#18011900C2211yescharacteristic
32#18011898C2211yescharacteristic
33#18011897—21no—
34#18011897—21no—
35#18011891C2211yescharacteristic
36#18011889—21no—
37#18011888—21no—
38#18011886C2211yescharacteristic
39#18011884—21no—
40#18011883—21no—
41#18011876C2211yescharacteristic
42#18011876C2211yescharacteristic
43D4×Dic149—21no—
44#18011873—21no—
45C4×C22⋊D149C2211yescharacteristic
46#18011840C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011834C2211yescharacteristic
49#18011834C2211yescharacteristic
50#18011831C2211yescharacteristic
51C22⋊#11924746C2211yescharacteristic
52#18011823C2211yescharacteristic
53C8×Dic149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C2×M16×C149C2211yescharacteristic
56C22⋊Q8×C149C2211yescharacteristic
57#121×C149C2211yescharacteristic
58#107×C149C2211yescharacteristic
59#103×C149C2211yescharacteristic
60#102×C149C2211yescharacteristic
61#14558736—22no—
62#14558736—41no—
63#14558735—22no—
64#14558735—41no—
65C2×Dic298—21no—
66C2×Dic298—22no—
67C2×Dic298—21no—
68C2×Dic298—41no—
69C2×Dic298C2311yescharacteristic
70C2×Dic298C2311yescharacteristic
71C2×Dic298C2311yescharacteristic
72Q8×D149—22no—
73Q8×D149—41no—
74C2×D596—21no—
75C2×D596C2311yescharacteristic
76C2×C22⋊D149—21no—
77C2×C22⋊D149—21no—
78C2×C22⋊D149D411yescharacteristic
79C22×Dic149—21no—
80C22×Dic149—21no—
81C2×C4×D149—21no—
82C2×C4×D149—21no—
83C2×C4×D149C2311yescharacteristic
84Dic596—22no—
85Dic596D414yescomplemented
86#14558726—22no—
87#14558726—41no—
88#14558725—22no—
89#14558725—22no—
90#14558724—22no—
91#14558721—41no—
92#14558719—22no—
93C2×#11924746C2311yescharacteristic
94C2×#11924746C2311yescharacteristic
95C4⋊Dic149—21no—
96#14558715—21no—
97#14558715—21no—
98#14558715D411yescharacteristic
99C22⋊Dic149—21no—
100C22⋊Dic149—21no—
101C22⋊Dic149D411yescharacteristic
102#14558713—21no—
103#14558713—21no—
104#14558713—21no—
105#14558713—21no—
106#14558713D411yescharacteristic
107C4×Dic149—21no—
108C4×Dic149—21no—
109C4×Dic149C2311yescharacteristic
110C2×Q8×C149C2311yescharacteristic
111C2×D4×C149—21no—
112C2×D4×C149C2311yescharacteristic
113C22×C4×C149C2311yescharacteristic
114SD16×C149—22no—
115M16×C149—22no—
116C2×C8×C149C2311yescharacteristic
117C2×C8×C149C2311yescharacteristic
118C4⋊C4×C149—21no—
119C4⋊C4×C149C2311yescharacteristic
120C4⋊C4×C149C2311yescharacteristic
121C22⋊C4×C149—21no—
122C22⋊C4×C149—21no—
123C22×D149—21no—
124C22×D149C2×D411yescharacteristic
125Dic298—21no—
126Dic298—21no—
127Dic298—21no—
128Dic298—21no—
129Dic298—42no—
130Dic298—42no—
131Dic298C2×D412yes—
132Dic298C2×D412yes—
133D596—21no—
134D596—21no—
135D596—42no—
136C22⋊D149—41no—
137C22⋊D149—42no—
138C22⋊D149—42no—
139C2×Dic149—21no—
140C2×Dic149—21no—
141C2×Dic149—21no—
142C2×Dic149—42no—
143C2×Dic149—42no—
144C2×Dic149C2×D411yescharacteristic
145C2×Dic149C2×D411yescharacteristic
146C2×Dic149C2×D411yescharacteristic
147C4×D149—21no—
148C4×D149—21no—
149C4×D149—42no—
150C4×D149—42no—
151#11924746—21no—
152#11924746—21no—
153C23×C149—21no—
154C23×C149C2×D411yescharacteristic
155Q8×C149—21no—
156Q8×C149—21no—
157D4×C149—21no—
158D4×C149—21no—
159D4×C149—42no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149C2×D411yescharacteristic
166C2×C4×C149C2411yescharacteristic
167C8×C149—21no—
168C8×C149C2×D412yes—
169C22×C149—21no—
170C22×C149—21no—
171C22×C149—21no—
172C22×C149—41no—
173C22×C149—41no—
174C22×C149—41no—
175C22×C149C22×D411yescharacteristic
176C2×D149—21no—
177C2×D149—21no—
178C2×D149—21no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C4×C149—21no—
183C4×C149—41no—
184C4×C149—41no—
185C4×C149—41no—
186C4×C149C22×D411yescharacteristic
187C4×C149H(5,𝔽2)11yescharacteristic
188Dic149—21no—
189Dic149—22no—
190Dic149—22no—
191Dic149—21no—
192Dic149—21no—
193Dic149—41no—
194C2×C149—41no—
195C2×C149—81no—
196C2×C149D4211yescharacteristic
197C2×C149#57511yescharacteristic
198C2×C149#57811yescharacteristic
199D149—41no—
200D149—81no—
201C149#327711yescharacteristic, complemented, Sylow
202#3277—1491nomaximal, Sylow
203C2×#137—1491no—
204C2×#137—1491no—
205#548—1491no—
206#548—1491no—
207#495—1491no—
208#468—1491no—
209#468D14911yescharacteristic, complemented
210#464—1491no—
211#464—1491no—
212#451—1491no—
213#451—1491no—
214#449—1491no—
215#449—1491no—
216C4×Q16—1491no—
217#436—1491no—
218C2×#41—1491no—
219C2×#41—1491no—
220C22×Q8—1491no—
221C22×Q8—1491no—
222#137—2984no—
223#137—2984no—
224C2×Q16—1491no—
225C2×Q16—1491no—
226C2×Q16—1491no—
227C2×Q16—1491no—
228C2×SD16—1491no—
229C2×SD16—1491no—
230C2×SD16—1491no—
231C2×SD16C2×D14911yescharacteristic
232C2×D8—1491no—
233C2×M16—1491no—
234C2×M16C2×D14911yescharacteristic
235#124—2981no—
236#124—2981no—
237#124—1491no—
238#124—1491no—
239C22⋊Q8—2981no—
240C22⋊Q8—2981no—
241C22⋊Q8—1491no—
242C22⋊Q8C2×D14911yescharacteristic
243#121—2981no—
244#121—2981no—
245#121—1491no—
246#121C2×D14911yescharacteristic
247C4×Q8—1491no—
248C4×Q8—1491no—
249C4×D4—2981no—
250C4×D4—2981no—
251C4×D4—1491no—
252#107C2×D14911yescharacteristic
253C4⋊C8—1491no—
254#103—1491no—
255#103—1491no—
256#103—1491no—
257#103C2×D14911yescharacteristic
258#102—1491no—
259#102C2×D14911yescharacteristic
260C22⋊C8—1491no—
261C22⋊C8—1491no—
262C4×C8—1491no—
263#41—2982no—
264#41—2982no—
265#41—5961no—
266#41—5961no—
267C2×Q8—2981no—
268C2×Q8—2982no—
269C2×Q8—2981no—
270C2×Q8—2982no—
271C2×Q8—5961no—
272C2×Q8—5961no—
273C2×Q8—1491no—
274C2×Q8—1491no—
275C2×Q8—1491no—
276C2×Q8C22×D14911yescharacteristic
277C2×D4—21no—
278C2×D4—2981no—
279C2×D4—2981no—
280C2×D4—2981no—
281C2×D4—1491no—
282C2×D4—1491no—
283C2×D4C22×D14911yescharacteristic
284C22×C4—2981no—
285C22×C4—2981no—
286C22×C4—2981no—
287C22×C4—2981no—
288C22×C4—1491no—
289C22×C4C22×D14911yescharacteristic
290Q16—2982no—
291Q16—2982no—
292Q16—5961no—
293Q16—1494no—
294SD16—22no—
295SD16—2982no—
296SD16—2982no—
297SD16—2982no—
298D8—5961no—
299M16—22no—
300M16—2982no—
301C2×C8—1491no—
302C2×C8—1491no—
303C2×C8C22×D14911yescharacteristic
304C2×C8C22×D14911yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—2981no—
307C4⋊C4—2981no—
308C4⋊C4—2981no—
309C4⋊C4—1491no—
310C4⋊C4C22×D14911yescharacteristic
311C4⋊C4C22×D14911yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—2981no—
315C22⋊C4—2981no—
316C22⋊C4—2981no—
317C22⋊C4—2981no—
318C22⋊C4—2981no—
319C22⋊C4—2981no—
320C22⋊C4—1491no—
321C22⋊C4—1491no—
322C42—2981no—
323C42—2981no—
324C42—1491no—
325C23—21no—
326C23—2981no—
327C23—1491no—
328C23D4×D14911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—2981no—
332Q8—2981no—
333Q8—2981no—
334Q8—2981no—
335Q8—5962no—
336Q8—5962no—
337Q8—1492no—
338Q8—1492no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—2981no—
343D4—2981no—
344D4—5962no—
345D4—5961no—
346D4—5962no—
347D4—5962no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—2981no—
354C2×C4—2981no—
355C2×C4—2981no—
356C2×C4—2981no—
357C2×C4—2981no—
358C2×C4—5962no—
359C2×C4—5962no—
360C2×C4—5962no—
361C2×C4—5962no—
362C2×C4—1491no—
363C2×C4—1491no—
364C2×C4—1491no—
365C2×C4D4×D14911yescharacteristic
366C2×C4C23×D14911yescharacteristic
367C8—21no—
368C8—2981no—
369C8—2981no—
370C8D4×D14912yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—2981no—
378C22—2981no—
379C22—2981no—
380C22—5961no—
381C22—5961no—
382C22—5961no—
383C22C2×D4×D14911yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—2981no—
389C4—2981no—
390C4—2981no—
391C4—2982no—
392C4—2982no—
393C4—5961no—
394C4C2×D4×D14911yescharacteristic
395C4#1801195711yescharacteristic
396C2—41no—
397C2—81no—
398C2—5961no—
399C2—11921no—
400C2#2375025911yescharacteristic
401C2#2375042111yescharacteristic
402C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#468×C149C2
socleC22×C149C22×D4
hypercenter#468D149
hypocenterC149#3277
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#18011944C2semidirect
2. C2×#18011940C2semidirect
3. #23750285C2semidirect
4. #23750281C2semidirect
5. #23750006C2semidirect
6. #23749872C2semidirect
7. #23749850C2semidirect
8. #23749846C2semidirect
9. #23749782C2semidirect
10. #23749780C2semidirect
11. #23749771C2semidirect
12. #23749768C2semidirect
13. #23749719C2semidirect
14. #23749701C2semidirect
15. #468×C149C2semidirect
85. Dic596D4semidirect
201. C149#3277semidirect
209. #468D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119442
C2×#180119402
#237502852
#237502812
#237500062
#237498722
#237498502
#237498462
#237497822
#237497802
#237497712
#237497682
#237497192
#237497012
#468×C1492
#3277149