Finite Group Databasebeta

← #34057249

Subgroups — #34057249

Order 19072.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750319C211yesmaximal, characteristic
2#23750317C211yesmaximal, characteristic, complemented
3#23750025C211yesmaximal, characteristic, complemented
4#23749954C211yesmaximal, characteristic, complemented
5#23749951C211yesmaximal, characteristic, complemented
6#23749944C211yesmaximal, characteristic, complemented
7#23749930C211yesmaximal, characteristic, complemented
8#23749928C211yesmaximal, characteristic, complemented
9#23749874C211yesmaximal, characteristic, complemented
10#23749873C211yesmaximal, characteristic, complemented
11#23749710C211yesmaximal, characteristic, complemented
12#23749700C211yesmaximal, characteristic, complemented
13#23749668C211yesmaximal, characteristic, complemented
14#23749666C211yesmaximal, characteristic, complemented
15#485×C149C211yesmaximal, characteristic, complemented
16C2×#14558723C2211yescharacteristic
17C2×#14558720C2211yescharacteristic
18C2×#14558719C2211yescharacteristic
19#18011906—21no—
20#18011905—21no—
21#18011902—21no—
22#18011902C2211yescharacteristic
23#18011902C2211yescharacteristic
24#18011895—21no—
25#18011893—21no—
26#18011887C2211yescharacteristic
27#18011886C2211yescharacteristic
28#18011885C2211yescharacteristic
29#18011884—21no—
30Q8×Dic149C2211yescharacteristic
31C4×D596—21no—
32#18011873C2211yescharacteristic
33C4×C22⋊D149C2211yescharacteristic
34#18011869C2211yescharacteristic
35#18011867—21no—
36C2×C4⋊Dic149C2211yescharacteristic
37C4⋊C4×D149C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011843C2211yescharacteristic
43#18011842C2211yescharacteristic
44#18011842C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C22⋊Q8×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59C2×D596—21no—
60C2×D596C2311yescharacteristic
61C2×C22⋊D149—21no—
62C2×C22⋊D149D411yescharacteristic
63C22×Dic149—21no—
64C2×C4×D149—21no—
65C2×C4×D149—21no—
66C2×C4×D149C2311yescharacteristic
67#14558723—22no—
68#14558720—22no—
69#14558719—22no—
70C2×#11924746C2311yescharacteristic
71C2×#11924746C2311yescharacteristic
72C4⋊Dic149—21no—
73C4⋊Dic149—21no—
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84C22⋊Dic149D411yescharacteristic
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713D411yescharacteristic
91C4×Dic149—21no—
92C4×Dic149—21no—
93C4×Dic149C2311yescharacteristic
94C2×Q8×C149C2311yescharacteristic
95C22×C4×C149C2311yescharacteristic
96C2×C8×C149C2311yescharacteristic
97C2×C8×C149C2311yescharacteristic
98C4⋊C4×C149—21no—
99C4⋊C4×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C22⋊C4×C149—21no—
103C22⋊C4×C149—21no—
104C42×C149—21no—
105C22×D149—21no—
106C22×D149C2×D411yescharacteristic
107D596—21no—
108D596—21no—
109D596—42no—
110C22⋊D149—41no—
111C22⋊D149—81no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—42no—
116C2×Dic149C2×D411yescharacteristic
117C2×Dic149C2×D411yescharacteristic
118C2×Dic149C2×D411yescharacteristic
119C4×D149—21no—
120C4×D149—21no—
121C4×D149—81no—
122C4×D149—81no—
123#11924746—21no—
124#11924746#4112yes—
125C23×C149C2×D411yescharacteristic
126Q8×C149—21no—
127Q8×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149C2×D411yescharacteristic
135C2×C4×C149C2411yescharacteristic
136C8×C149—21no—
137C8×C149—21no—
138C22×C149—21no—
139C22×C149—21no—
140C22×C149—21no—
141C22×C149C22×D411yescharacteristic
142C2×D149—21no—
143C2×D149—21no—
144C2×D149—21no—
145C2×D149—41no—
146C2×D149—41no—
147C2×D149—41no—
148C4×C149—21no—
149C4×C149—41no—
150C4×C149—41no—
151C4×C149—41no—
152C4×C149—41no—
153C4×C149C2×#4111yescharacteristic
154C4×C1492−1+411yescharacteristic
155Dic149—21no—
156Dic149—21no—
157Dic149—21no—
158Dic149—41no—
159Dic149—41no—
160Dic149—41no—
161C2×C149—41no—
162C2×C149#54711yescharacteristic
163C2×C149#57511yescharacteristic
164C2×C149#57711yescharacteristic
165D149—41no—
166D149—81no—
167C149#335111yescharacteristic, complemented, Sylow
168#3351—1491nomaximal, Sylow
169#553—1491no—
170#552—1491no—
171#499—1491no—
172#485D14911yescharacteristic, complemented
173#483—1491no—
174#482—1491no—
175#481—1491no—
176#479—1491no—
177#478—1491no—
178#468—1491no—
179#468—1491no—
180C4×SD16—1491no—
181#436—1491no—
182#428—1491no—
183#428—1491no—
184C2×SD16—1491no—
185C2×M16—1491no—
186C2×M16—1491no—
187#126—2981no—
188#126—2981no—
189#125—2981no—
190#125—1491no—
191#125—1491no—
192#123—2981no—
193#123—2981no—
194C22⋊Q8—1491no—
195C22⋊Q8C2×D14911yescharacteristic
196#121—2981no—
197#121—1491no—
198#121—1491no—
199C4×Q8—1491no—
200C4×D4—2981no—
201C4×D4—1491no—
202C4×D4—1491no—
203#117—2981no—
204#117—1491no—
205#117C2×D14911yescharacteristic
206C2×C4⋊C4—1491no—
207C2×C4⋊C4—1491no—
208#107—1491no—
209#107—1491no—
210#107—1491no—
211#107C2×D14911yescharacteristic
212#106—1491no—
213#106—1491no—
214#106—1491no—
215#106—1491no—
216#106C2×D14911yescharacteristic
217C4⋊C8—1491no—
218#103—1491no—
219#103C2×D14911yescharacteristic
220#103C2×D14911yescharacteristic
221#102—1491no—
222#102—1491no—
223#102—1491no—
224C22⋊C8—1491no—
225C22⋊C8C2×D14911yescharacteristic
226C4×C8—1491no—
227C2×Q8C22×D14911yescharacteristic
228C2×D4—2981no—
229C2×D4—2981no—
230C2×D4—1491no—
231C2×D4—1491no—
232C22×C4—2981no—
233C22×C4—2981no—
234C22×C4—2981no—
235C22×C4—1491no—
236C22×C4C22×D14911yescharacteristic
237SD16—2982no—
238M16—2982no—
239M16—2982no—
240C2×C8—1491no—
241C2×C8—1491no—
242C2×C8C22×D14911yescharacteristic
243C2×C8C22×D14911yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—2981no—
246C4⋊C4—2981no—
247C4⋊C4—2981no—
248C4⋊C4—2981no—
249C4⋊C4—2981no—
250C4⋊C4—2981no—
251C4⋊C4—2981no—
252C4⋊C4—2981no—
253C4⋊C4—1491no—
254C4⋊C4—1491no—
255C4⋊C4—1491no—
256C4⋊C4—1491no—
257C4⋊C4C22×D14911yescharacteristic
258C4⋊C4C22×D14911yescharacteristic
259C4⋊C4C22×D14911yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—2981no—
263C22⋊C4—2981no—
264C22⋊C4—2981no—
265C22⋊C4—2981no—
266C22⋊C4—2981no—
267C22⋊C4—1491no—
268C22⋊C4—1491no—
269C42—21no—
270C42—2981no—
271C42—2981no—
272C42—1491no—
273C23—2981no—
274C23—1491no—
275C23D4×D14911yescharacteristic
276Q8—21no—
277Q8—21no—
278D4—2981no—
279D4—2981no—
280D4—5962no—
281D4—5961no—
282D4—11921no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—2981no—
290C2×C4—2981no—
291C2×C4—2981no—
292C2×C4—2981no—
293C2×C4—2981no—
294C2×C4—5962no—
295C2×C4—1491no—
296C2×C4—1491no—
297C2×C4—1491no—
298C2×C4—11921no—
299C2×C4—11921no—
300C2×C4D4×D14911yescharacteristic
301C2×C4C23×D14911yescharacteristic
302C8—21no—
303C8—21no—
304C8—2981no—
305C8—1492no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—2981no—
310C22—2981no—
311C22—2981no—
312C22—5961no—
313C22—5961no—
314C22—5961no—
315C22C2×D4×D14911yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—2981no—
322C4—2981no—
323C4—2981no—
324C4—5961no—
325C4—5961no—
326C4—5961no—
327C4#41×D14911yescharacteristic
328C4#1801195811yescharacteristic
329C2—41no—
330C2—5961no—
331C2—11921no—
332C2#2375027311yescharacteristic
333C2#2375042411yescharacteristic
334C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#485×C149C2
socleC22×C149C22×D4
prime radical#23750319C2
hypercenter#485D149
hypocenterC149#3351
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #23750317C2semidirect
3. #23750025C2semidirect
4. #23749954C2semidirect
5. #23749951C2semidirect
6. #23749944C2semidirect
7. #23749930C2semidirect
8. #23749928C2semidirect
9. #23749874C2semidirect
10. #23749873C2semidirect
11. #23749710C2semidirect
12. #23749700C2semidirect
13. #23749668C2semidirect
14. #23749666C2semidirect
15. #485×C149C2semidirect
167. C149#3351semidirect
172. #485D149semidirect

Maximal subgroups

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

subgroupindex
#237503192
#237503172
#237500252
#237499542
#237499512
#237499442
#237499302
#237499282
#237498742
#237498732
#237497102
#237497002
#237496682
#237496662
#485×C1492
#3351149