Finite Group Databasebeta

← #34056577

Subgroups — #34056577

Order 19072.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750313C211yesmaximal, characteristic, complemented
2#23750283C211yesmaximal, characteristic
3#23749965C211yesmaximal, characteristic, complemented
4#23749937C211yesmaximal, characteristic, complemented
5#23749929C211yesmaximal, characteristic, complemented
6#23749865C211yesmaximal, characteristic, complemented
7#23749853C211yesmaximal, characteristic, complemented
8#23749844C211yesmaximal, characteristic, complemented
9#23749788C211yesmaximal, characteristic, complemented
10#23749782C211yesmaximal, characteristic, complemented
11C4×Dic596C211yesmaximal, characteristic, complemented
12C8×D596C211yesmaximal, characteristic, complemented
13#23749618C211yesmaximal, characteristic, complemented
14#103×D149C211yesmaximal, characteristic, complemented
15#488×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic
18C2×Dic596C2211yescharacteristic
19C2×#14558726C2211yescharacteristic
20C2×#14558724C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22C2×C8×D149C2211yescharacteristic
23#18011906—21no—
24#18011902—21no—
25#18011897—21no—
26#18011896—21no—
27#18011891C2211yescharacteristic
28#18011891C2211yescharacteristic
29#18011888—21no—
30#18011887C2211yescharacteristic
31#18011884—21no—
32#18011882C2211yescharacteristic
33C4×Dic298C2211yescharacteristic
34C4×Dic298C2211yescharacteristic
35C4×D596C2211yescharacteristic
36#18011871—21no—
37#18011869—21no—
38#18011869C2211yescharacteristic
39C4⋊C4×D149C2211yescharacteristic
40#18011845C2211yescharacteristic
41#18011844C2211yescharacteristic
42#18011842C2211yescharacteristic
43C4⋊#11924746C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011834C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52#125×C149C2211yescharacteristic
53#124×C149C2211yescharacteristic
54#103×C149C2211yescharacteristic
55#103×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59#14558735—22no—
60#14558735—41no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C2×Dic298C2311yescharacteristic
64Q8×D149—22no—
65Q8×D149—41no—
66C2×D596D411yescharacteristic
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C22×Dic149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149C2311yescharacteristic
73C2×C4×D149C2311yescharacteristic
74Dic596—22no—
75#14558726—41no—
76#14558724—41no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C8×D149—41no—
80C8×D149—41no—
81C4⋊Dic149—21no—
82C4⋊Dic149—21no—
83C4⋊Dic149D411yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85C4⋊Dic149C2311yescharacteristic
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89#14558715—21no—
90C22⋊Dic149—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713D411yescharacteristic
96#14558713D411yescharacteristic
97C4×Dic149—21no—
98C4×Dic149—21no—
99C4×Dic149—21no—
100C2×Q8×C149C2311yescharacteristic
101C2×D4×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C2×C8×C149C2311yescharacteristic
104C4⋊C4×C149—21no—
105C4⋊C4×C149—21no—
106C4⋊C4×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C22⋊C4×C149—21no—
109C22⋊C4×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149C2×D411yescharacteristic
112C22×D149C2×D411yescharacteristic
113Dic298—21no—
114Dic298—21no—
115Dic298—21no—
116Dic298—42no—
117Dic298#4112yes—
118D596—22no—
119C22⋊D149—42no—
120C22⋊D149—42no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—42no—
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C4×D149—21no—
129C4×D149—21no—
130C4×D149—21no—
131C4×D149—21no—
132C4×D149—42no—
133C4×D149—42no—
134#11924746—21no—
135#11924746—21no—
136C23×C149—21no—
137Q8×C149—21no—
138Q8×C149—21no—
139D4×C149—21no—
140D4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149C2×D411yescharacteristic
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2411yescharacteristic
147C8×C149—21no—
148C8×C149—21no—
149C22×C149—41no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149C22×D411yescharacteristic
153C2×D149—21no—
154C2×D149—21no—
155C2×D149—21no—
156C2×D149—21no—
157C2×D149—21no—
158C2×D149#13512yes—
159C4×C149—21no—
160C4×C149—21no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149—41no—
164C4×C149C2×#4111yescharacteristic
165C4×C149H(5,𝔽2)11yescharacteristic
166Dic149—21no—
167Dic149—21no—
168Dic149—22no—
169Dic149—41no—
170Dic149—41no—
171Dic149—41no—
172C2×C149—81no—
173C2×C149#54611yescharacteristic
174C2×C149C2×#13511yescharacteristic
175C2×C149#57811yescharacteristic
176D149—22no—
177D149—41no—
178C149#330011yescharacteristic, complemented, Sylow
179#3300—1491nomaximal, Sylow
180#552—1491no—
181#548—1491no—
182#488D14911yescharacteristic, complemented
183#485—1491no—
184#480—1491no—
185#479—1491no—
186#467—1491no—
187#465—1491no—
188#464—1491no—
189#452—1491no—
190#451—1491no—
191C4×Q16—1491no—
192C8×D4—1491no—
193#416—1491no—
194C2×#103—1491no—
195C2×#41—1491no—
196C22×Q8—1491no—
197C2×Q16—1491no—
198C2×Q16—1491no—
199C2×SD16—1491no—
200C22×C8—1491no—
201C22×C8—1491no—
202#126—2981no—
203#125—2981no—
204#125C2×D14911yescharacteristic
205#124—2981no—
206#124C2×D14911yescharacteristic
207#123—2981no—
208C22⋊Q8—2981no—
209C22⋊Q8—1491no—
210C22⋊Q8—1491no—
211C22⋊Q8—1491no—
212#121—2981no—
213#121—1491no—
214C4×Q8—1491no—
215C4×Q8—1491no—
216C4×D4—2981no—
217C4×D4—1491no—
218#117—2981no—
219#117—1491no—
220C2×C4⋊C4—1491no—
221#107—1491no—
222#107—1491no—
223#106—1491no—
224C4⋊C8—1491no—
225#103—1491no—
226#103—1491no—
227#103—1491no—
228#103—1491no—
229#103—1491no—
230#103C2×D14911yescharacteristic
231#103C2×D14911yescharacteristic
232#102—1491no—
233#102C2×D14911yescharacteristic
234#102C2×D14911yescharacteristic
235C22⋊C8—1491no—
236C22⋊C8—1491no—
237C4×C8C2×D14911yescharacteristic
238#41—2982no—
239#41—5961no—
240C2×Q8—2981no—
241C2×Q8—2982no—
242C2×Q8—5961no—
243C2×Q8—1491no—
244C2×Q8—1491no—
245C2×Q8C22×D14911yescharacteristic
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4C22×D14911yescharacteristic
250C22×C4—2981no—
251C22×C4—2981no—
252C22×C4—2981no—
253C22×C4—1491no—
254C22×C4—1491no—
255Q16—2982no—
256Q16—5961no—
257SD16—5961no—
258C2×C8—5961no—
259C2×C8—5961no—
260C2×C8—1491no—
261C2×C8—1491no—
262C2×C8C22×D14911yescharacteristic
263C2×C8C22×D14911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—2981no—
272C4⋊C4—1491no—
273C4⋊C4—1491no—
274C4⋊C4—1491no—
275C4⋊C4C22×D14911yescharacteristic
276C4⋊C4C22×D14911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—1491no—
285C22⋊C4—1491no—
286C42—2981no—
287C42—2981no—
288C42—2981no—
289C42C22×D14911yescharacteristic
290C23—21no—
291C23—1491no—
292C23—1491no—
293Q8—21no—
294Q8—21no—
295Q8—2981no—
296Q8—2981no—
297Q8—2981no—
298Q8—5962no—
299Q8—1492no—
300D4—21no—
301D4—21no—
302D4—2982no—
303D4—5962no—
304D4—5962no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—2981no—
309C2×C4—2981no—
310C2×C4—2981no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—5962no—
317C2×C4—5962no—
318C2×C4—5962no—
319C2×C4—1491no—
320C2×C4—1491no—
321C2×C4D4×D14911yescharacteristic
322C2×C4D4×D14911yescharacteristic
323C2×C4C23×D14911yescharacteristic
324C8—21no—
325C8—21no—
326C8—2981no—
327C8—2981no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—2981no—
332C22—2981no—
333C22—2981no—
334C22—2981no—
335C22—2981no—
336C22—1492no—
337C22C2×D4×D14911yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—2981no—
344C4—2981no—
345C4—2982no—
346C4—5961no—
347C4—5961no—
348C4—5961no—
349C4#41×D14911yescharacteristic
350C4#1801195711yescharacteristic
351C2—81no—
352C2—2982no—
353C2—5961no—
354C2#2375026811yescharacteristic
355C2#135×D14911yescharacteristic
356C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#488×C149C2
socleC22×C149C22×D4
prime radical#23750283C2
hypercenter#488D149
hypocenterC149#3300
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #23750313C2semidirect
3. #23749965C2semidirect
4. #23749937C2semidirect
5. #23749929C2semidirect
6. #23749865C2semidirect
7. #23749853C2semidirect
8. #23749844C2semidirect
9. #23749788C2semidirect
10. #23749782C2semidirect
11. C4×Dic596C2semidirect
12. C8×D596C2semidirect
13. #23749618C2semidirect
14. #103×D149C2semidirect
15. #488×C149C2semidirect
178. C149#3300semidirect
182. #488D149semidirect

Maximal subgroups

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

subgroupindex
#237503132
#237502832
#237499652
#237499372
#237499292
#237498652
#237498532
#237498442
#237497882
#237497822
C4×Dic5962
C8×D5962
#237496182
#103×D1492
#488×C1492
#3300149