Finite Group Databasebeta

← #34056583

Subgroups — #34056583

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#23750316C211yesmaximal, characteristic, complemented
2#23750287C211yesmaximal, characteristic
3#23749980C211yesmaximal, characteristic, complemented
4#23749968C211yesmaximal, characteristic, complemented
5#23749940C211yesmaximal, characteristic, complemented
6#23749932C211yesmaximal, characteristic, complemented
7#23749865C211yesmaximal, characteristic, complemented
8#23749857C211yesmaximal, characteristic, complemented
9#23749847C211yesmaximal, characteristic, complemented
10#23749786C211yesmaximal, characteristic, complemented
11#23749779C211yesmaximal, characteristic, complemented
12C8×D596C211yesmaximal, characteristic, complemented
13#23749620C211yesmaximal, characteristic, complemented
14#103×D149C211yesmaximal, characteristic, complemented
15C4×Q16×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×C8×D149C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22#18011905—21no—
23#18011903C2211yescharacteristic
24#18011901—21no—
25#18011899—21no—
26#18011899C2211yescharacteristic
27#18011896—21no—
28#18011891—21no—
29#18011891C2211yescharacteristic
30#18011887C2211yescharacteristic
31#18011887C2211yescharacteristic
32#18011886—21no—
33#18011886C2211yescharacteristic
34C4×D596—21no—
35C4×D596C2211yescharacteristic
36#18011869C2211yescharacteristic
37#18011868—21no—
38C4⋊C4×D149C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011823C2211yescharacteristic
52C2×Q16×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54C4×Q8×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59#14558737—22no—
60#14558737—41no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63Q8×D149—22no—
64Q8×D149—41no—
65C2×D596—21no—
66C2×D596—21no—
67C2×D596D411yescharacteristic
68C2×D596C2311yescharacteristic
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72C2×C4×D149C2311yescharacteristic
73C2×C4×D149C2311yescharacteristic
74#14558726—41no—
75#14558723—41no—
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C8×D149—41no—
79C8×D149—41no—
80C4⋊Dic149—21no—
81C4⋊Dic149D411yescharacteristic
82C4⋊Dic149C2311yescharacteristic
83C4⋊Dic149C2311yescharacteristic
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713—21no—
95#14558713—21no—
96#14558713D411yescharacteristic
97#14558713D411yescharacteristic
98C4×Dic149—21no—
99C2×Q8×C149C2311yescharacteristic
100C2×Q8×C149C2311yescharacteristic
101Q16×C149—22no—
102C2×C8×C149C2311yescharacteristic
103C2×C8×C149C2311yescharacteristic
104C4⋊C4×C149—21no—
105C4⋊C4×C149—21no—
106C4⋊C4×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C42×C149—21no—
109C42×C149—21no—
110C42×C149C2311yescharacteristic
111C22×D149—21no—
112C22×D149C2×D411yescharacteristic
113C22×D149C2×D411yescharacteristic
114Dic298—21no—
115Dic298—21no—
116Dic298—42no—
117D596—22no—
118D596—21no—
119D596—21no—
120D596—42no—
121D596—42no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C4×D149—21no—
128C4×D149—21no—
129C4×D149—21no—
130C4×D149—21no—
131C4×D149—42no—
132C4×D149—42no—
133C4×D149—42no—
134#11924746—21no—
135#11924746—21no—
136Q8×C149—21no—
137Q8×C149—21no—
138Q8×C149—21no—
139Q8×C149#4112yes—
140C2×C4×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×C149C22×D411yescharacteristic
150C2×D149—21no—
151C2×D149—21no—
152C2×D149—21no—
153C2×D149—21no—
154C2×D149—21no—
155C2×D149—41no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149#13512yes—
159C4×C149—22no—
160C4×C149—21no—
161C4×C149—21no—
162C4×C149—41no—
163C4×C149—41no—
164C4×C149—41no—
165C4×C149C2×#4111yescharacteristic
166C4×C149H(5,𝔽2)11yescharacteristic
167Dic149—21no—
168Dic149—21no—
169Dic149—41no—
170Dic149—41no—
171Dic149—41no—
172C2×C149#54611yescharacteristic
173C2×C149C2×#13511yescharacteristic
174C2×C149#57811yescharacteristic
175D149—22no—
176D149—41no—
177D149—81no—
178C149#330011yescharacteristic, complemented, Sylow
179#3300—1491nomaximal, Sylow
180#552—1491no—
181#548—1491no—
182#488—1491no—
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×Q16D14911yescharacteristic, complemented
192C8×D4—1491no—
193#416—1491no—
194C2×#103—1491no—
195C2×#41—1491no—
196C22×Q8—1491no—
197C2×Q16—1491no—
198C2×Q16C2×D14911yescharacteristic
199C2×SD16—1491no—
200C22×C8—1491no—
201C22×C8—1491no—
202#126—2981no—
203#125—2981no—
204#125—1491no—
205#124—2981no—
206#124—1491no—
207#123—2981no—
208C22⋊Q8—2981no—
209C22⋊Q8—1491no—
210C22⋊Q8—1491no—
211C22⋊Q8—1491no—
212#121—2981no—
213#121—1491no—
214C4×Q8C2×D14911yescharacteristic
215C4×Q8C2×D14911yescharacteristic
216C4×D4—2981no—
217C4×D4—1491no—
218#117—2981no—
219#117—1491no—
220C2×C4⋊C4—1491no—
221#107—1491no—
222#107C2×D14911yescharacteristic
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#102—1491no—
234#102—1491no—
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×Q8C22×D14911yescharacteristic
245C2×Q8C22×D14911yescharacteristic
246C2×D4—2981no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4—1491no—
250C22×C4—2981no—
251C22×C4—2981no—
252C22×C4—2981no—
253C22×C4—1491no—
254C22×C4—1491no—
255Q16—22no—
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—2981no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—1491no—
285C22⋊C4—1491no—
286C42—21no—
287C42—21no—
288C42—2981no—
289C42C22×D14911yescharacteristic
290C23—2981no—
291C23—1491no—
292C23—1491no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—2981no—
297Q8—2981no—
298Q8—5962no—
299Q8#1455873612yes—
300D4—2982no—
301D4—2981no—
302D4—2981no—
303D4—5962no—
304D4—5962no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
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—2981no—
329C22—2981no—
330C22—2981no—
331C22—2981no—
332C22—2981no—
333C22—5961no—
334C22—5961no—
335C22—5961no—
336C22—1492no—
337C22C2×D4×D14911yescharacteristic
338C4—21no—
339C4—21no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—2981no—
345C4—2981no—
346C4—5961no—
347C4—5961no—
348C4—5961no—
349C4C2×#1455873611yescharacteristic
350C4#1801195711yescharacteristic
351C2—2982no—
352C2—5961no—
353C2—11921no—
354C2#2375027111yescharacteristic
355C2#135×D14911yescharacteristic
356C2#2375043811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×Q16×C149C2
socleC22×C149C22×D4
prime radical#23750287C2
hypercenterC4×Q16D149
hypocenterC149#3300
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #23750316C2semidirect
3. #23749980C2semidirect
4. #23749968C2semidirect
5. #23749940C2semidirect
6. #23749932C2semidirect
7. #23749865C2semidirect
8. #23749857C2semidirect
9. #23749847C2semidirect
10. #23749786C2semidirect
11. #23749779C2semidirect
12. C8×D596C2semidirect
13. #23749620C2semidirect
14. #103×D149C2semidirect
15. C4×Q16×C149C2semidirect
178. C149#3300semidirect
191. C4×Q16D149semidirect

Maximal subgroups

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

subgroupindex
#237503162
#237502872
#237499802
#237499682
#237499402
#237499322
#237498652
#237498572
#237498472
#237497862
#237497792
C8×D5962
#237496202
#103×D1492
C4×Q16×C1492
#3300149