Finite Group Databasebeta

← #34057516

Subgroups — #34057516

Order 19072.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750347C211yesmaximal, characteristic, complemented
2#23750331C211yesmaximal, characteristic, complemented
3#23749992C211yesmaximal, characteristic, complemented
4#23749986C211yesmaximal, characteristic, complemented
5#23749982C211yesmaximal, characteristic, complemented
6#23749928C211yesmaximal, characteristic, complemented
7#23749909C211yesmaximal, characteristic, complemented
8#23749843C211yesmaximal, characteristic
9#23749841C211yesmaximal, characteristic
10#23749829C211yesmaximal, characteristic, complemented
11#23749752C211yesmaximal, characteristic, complemented
12#23749736C211yesmaximal, characteristic
13#23749724C211yesmaximal, characteristic, complemented
14C4×#14558723C211yesmaximal, characteristic, complemented
15#479×C149C211yesmaximal, characteristic, complemented
16C2×#14558725C2211yescharacteristic
17C2×#14558723C2211yescharacteristic
18C2×D1192C2211yescharacteristic
19#18011910C2211yescharacteristic
20#18011909C2211yescharacteristic
21#18011906—21no—
22#18011905—21no—
23#18011902C2211yescharacteristic
24#18011900C2211yescharacteristic
25#18011899C2211yescharacteristic
26#18011891—21no—
27#18011889—21no—
28#18011889—21no—
29#18011889—21no—
30C4×Dic298C2211yescharacteristic
31#18011876C2211yescharacteristic
32C4×D596C2211yescharacteristic
33#18011873C2211yescharacteristic
34#18011873C2211yescharacteristic
35#18011873C2211yescharacteristic
36#18011868—21no—
37C4⋊C4×D149—21no—
38#18011842C2211yescharacteristic
39#18011840C2211yescharacteristic
40#18011840C2211yescharacteristic
41#18011836C2211yescharacteristic
42#18011835C2211yescharacteristic
43#18011834C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011821C2211yescharacteristic
50#18011821C2211yescharacteristic
51C4×#11924746C2211yescharacteristic
52#125×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298D411yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×D596C2311yescharacteristic
64C2×C4×D149—21no—
65C2×C4×D149—21no—
66C2×C4×D149—21no—
67C2×C4×D149—21no—
68#14558725—22no—
69#14558723—22no—
70D1192—22no—
71C2×#11924746C2311yescharacteristic
72C2×#11924746C2311yescharacteristic
73C4⋊Dic149—21no—
74C4⋊Dic149D411yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715D411yescharacteristic
82#14558715D411yescharacteristic
83#14558713—21no—
84#14558713—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91C4×Dic149—21no—
92C4×Dic149C2311yescharacteristic
93C4×Dic149C2311yescharacteristic
94C2×Q8×C149C2311yescharacteristic
95C2×C8×C149C2311yescharacteristic
96C2×C8×C149C2311yescharacteristic
97C4⋊C4×C149—21no—
98C4⋊C4×C149—21no—
99C4⋊C4×C149—21no—
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C42×C149—21no—
104C42×C149C2311yescharacteristic
105C22×D149—21no—
106C22×D149—21no—
107Dic298—21no—
108Dic298—21no—
109Dic298—41no—
110Dic298—81no—
111D596—21no—
112D596—21no—
113D596—21no—
114D596#4112yes—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149C2×D411yescharacteristic
118C2×Dic149C2×D411yescharacteristic
119C2×Dic149C2×D411yescharacteristic
120C2×Dic149C2×D411yescharacteristic
121C4×D149—42no—
122C4×D149—42no—
123C4×D149—81no—
124C4×D149—81no—
125#11924746—21no—
126#11924746—21no—
127Q8×C149—21no—
128Q8×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2×D411yescharacteristic
135C2×C4×C149C2411yescharacteristic
136C8×C149—21no—
137C8×C149—21no—
138C22×C149C22×D411yescharacteristic
139C2×D149—22no—
140C2×D149—41no—
141C2×D149—41no—
142C2×D149—41no—
143C2×D149—41no—
144C2×D149—41no—
145C4×C149—21no—
146C4×C149—21no—
147C4×C149—41no—
148C4×C149—41no—
149C4×C149—41no—
150C4×C149—41no—
151C4×C149C2×#4111yescharacteristic
152C4×C1492−1+411yescharacteristic
153Dic149—21no—
154Dic149—21no—
155Dic149—21no—
156Dic149—21no—
157Dic149—41no—
158Dic149—41no—
159C2×C149#54811yescharacteristic
160C2×C149#57511yescharacteristic
161C2×C149#57711yescharacteristic
162D149—42no—
163D149—81no—
164C149#337611yescharacteristic, complemented, Sylow
165#3376—1491nomaximal, Sylow
166#556—1491no—
167#554—1491no—
168#491—1491no—
169#489—1491no—
170#488—1491no—
171#479D14911yescharacteristic, complemented
172#478—1491no—
173#475—1491no—
174#463—1491no—
175#463—1491no—
176#461—1491no—
177#446—1491no—
178#442—1491no—
179#440—1491no—
180C4×SD16—1491no—
181C2×SD16—1491no—
182C2×SD16—1491no—
183C2×D8—1491no—
184C4⋊Q8—1491no—
185C4⋊Q8—1491no—
186#126—2981no—
187#126—2981no—
188#125—1491no—
189#125C2×D14911yescharacteristic
190#124—1491no—
191#124—1491no—
192C22⋊Q8—2981no—
193C22⋊Q8—2981no—
194C22⋊Q8—2981no—
195C22⋊Q8—2981no—
196C4×Q8—1491no—
197C4×Q8—1491no—
198C4×Q8C2×D14911yescharacteristic
199C4×D4—1491no—
200C4×D4—1491no—
201C4×D4—1491no—
202C4×D4—1491no—
203#117—2981no—
204C2×C4⋊C4—2981no—
205#107C2×D14911yescharacteristic
206#106—1491no—
207#106C2×D14911yescharacteristic
208C4⋊C8—1491no—
209C4⋊C8—1491no—
210C4⋊C8C2×D14911yescharacteristic
211#103—1491no—
212#103—1491no—
213#103—1491no—
214#103—1491no—
215#103C2×D14911yescharacteristic
216#103C2×D14911yescharacteristic
217#102—1491no—
218#102—1491no—
219#102—1491no—
220#102—1491no—
221#97—1491no—
222#97—1491no—
223C4×C8—1491no—
224C2×Q8—2981no—
225C2×Q8—1491no—
226C2×Q8—1491no—
227C2×Q8C22×D14911yescharacteristic
228C2×D4—1491no—
229C2×D4—1491no—
230C22×C4—2981no—
231C22×C4—2981no—
232C22×C4—2981no—
233C22×C4—2981no—
234SD16—2982no—
235SD16—2982no—
236D8—2982no—
237C2×C8—1491no—
238C2×C8—1491no—
239C2×C8C22×D14911yescharacteristic
240C2×C8C22×D14911yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—2981no—
245C4⋊C4—2981no—
246C4⋊C4—2981no—
247C4⋊C4—2981no—
248C4⋊C4—2981no—
249C4⋊C4—2981no—
250C4⋊C4—1491no—
251C4⋊C4—1491no—
252C4⋊C4—1491no—
253C4⋊C4—1491no—
254C4⋊C4C22×D14911yescharacteristic
255C4⋊C4C22×D14911yescharacteristic
256C4⋊C4C22×D14911yescharacteristic
257C22⋊C4—2981no—
258C22⋊C4—2981no—
259C22⋊C4—2981no—
260C22⋊C4—2981no—
261C22⋊C4—2981no—
262C22⋊C4—2981no—
263C22⋊C4—2981no—
264C22⋊C4—2981no—
265C42—21no—
266C42—2981no—
267C42—1491no—
268C42—1491no—
269C42C22×D14911yescharacteristic
270C23—2981no—
271C23—2981no—
272Q8—21no—
273Q8—21no—
274Q8—2981no—
275Q8—2981no—
276Q8—5961no—
277Q8—11921no—
278D4—2981no—
279D4—2981no—
280D4—2981no—
281D4—1492no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—2981no—
287C2×C4—2981no—
288C2×C4—5962no—
289C2×C4—5962no—
290C2×C4—1491no—
291C2×C4—1491no—
292C2×C4—1491no—
293C2×C4—1491no—
294C2×C4—11921no—
295C2×C4—11921no—
296C2×C4D4×D14911yescharacteristic
297C2×C4D4×D14911yescharacteristic
298C2×C4C23×D14911yescharacteristic
299C8—21no—
300C8—21no—
301C8—2981no—
302C8—2981no—
303C22—2982no—
304C22—5961no—
305C22—5961no—
306C22—5961no—
307C22—5961no—
308C22—5961no—
309C22C2×D4×D14911yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—2981no—
317C4—2981no—
318C4—2981no—
319C4—2981no—
320C4—5961no—
321C4—5961no—
322C4#41×D14911yescharacteristic
323C4#1801195911yescharacteristic
324C2—5962no—
325C2—11921no—
326C2#2375028511yescharacteristic
327C2#2375042211yescharacteristic
328C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#479×C149C2
socleC22×C149C22×D4
prime radicalC2×D1192C22
hypercenter#479D149
hypocenterC149#3376
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #23750347C2semidirect
2. #23750331C2semidirect
3. #23749992C2semidirect
4. #23749986C2semidirect
5. #23749982C2semidirect
6. #23749928C2semidirect
7. #23749909C2semidirect
10. #23749829C2semidirect
11. #23749752C2semidirect
13. #23749724C2semidirect
14. C4×#14558723C2semidirect
15. #479×C149C2semidirect
164. C149#3376semidirect
171. #479D149semidirect

Maximal subgroups

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

subgroupindex
#237503472
#237503312
#237499922
#237499862
#237499822
#237499282
#237499092
#237498432
#237498412
#237498292
#237497522
#237497362
#237497242
C4×#145587232
#479×C1492
#3376149