Finite Group Databasebeta

← #34056144

Subgroups — #34056144

Order 19072.

322 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750238C211yesmaximal, characteristic
2#23750233C211yesmaximal, characteristic
3#23749935C211yesmaximal, characteristic, complemented
4#23749931C211yesmaximal, characteristic, complemented
5#23749929C211yesmaximal, characteristic, complemented
6#23749884C211yesmaximal, characteristic
7#23749882C211yesmaximal, characteristic
8#23749867C211yesmaximal, characteristic
9#23749865C211yesmaximal, characteristic
10#23749836C211yesmaximal, characteristic, complemented
11#23749835C211yesmaximal, characteristic, complemented
12#23749834C211yesmaximal, characteristic, complemented
13#23749834C211yesmaximal, characteristic, complemented
14#23749650C211yesmaximal, characteristic
15#479×C149C211yesmaximal, characteristic, complemented
16C2×Dic596C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558726C2211yescharacteristic
20C2×#14558719C2211yescharacteristic
21C2×C8×D149C2211yescharacteristic
22#18011911C2211yescharacteristic
23#18011909C2211yescharacteristic
24#18011906—21no—
25#18011906—21no—
26#18011906—21no—
27#18011905—21no—
28#18011903—21no—
29#18011902—21no—
30#18011902—21no—
31#18011902C2211yescharacteristic
32#18011901—21no—
33#18011891C2211yescharacteristic
34#18011891C2211yescharacteristic
35#18011891C2211yescharacteristic
36#18011887C2211yescharacteristic
37C4×Dic298C2211yescharacteristic
38#18011876C2211yescharacteristic
39#18011876C2211yescharacteristic
40#18011868C2211yescharacteristic
41#18011844C2211yescharacteristic
42#18011842C2211yescharacteristic
43C4⋊#11924746C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011834C2211yescharacteristic
49#18011834C2211yescharacteristic
50#18011834C2211yescharacteristic
51#18011834C2211yescharacteristic
52#125×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59C2×Dic298C2311yescharacteristic
60C2×Dic298C2311yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×C4×D149C2311yescharacteristic
63Dic596—41no—
64Dic596—41no—
65#14558726—41no—
66#14558726—41no—
67#14558719—41no—
68C2×#11924746C2311yescharacteristic
69C2×#11924746C2311yescharacteristic
70C8×D149—41no—
71C4⋊Dic149—21no—
72C4⋊Dic149—21no—
73C4⋊Dic149—21no—
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149—21no—
77C4⋊Dic149C2311yescharacteristic
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715D411yescharacteristic
86#14558715D411yescharacteristic
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713D411yescharacteristic
92#14558713D411yescharacteristic
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C4⋊C4×C149—21no—
101C4⋊C4×C149—21no—
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C42×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149C2×D411yescharacteristic
109Dic298—21no—
110Dic298—21no—
111Dic298—21no—
112Dic298—21no—
113Dic298—21no—
114Dic298—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149C2×D411yescharacteristic
120C2×Dic149C2×D411yescharacteristic
121C2×Dic149C2×D411yescharacteristic
122C4×D149—21no—
123C4×D149—21no—
124#11924746—21no—
125#11924746—21no—
126Q8×C149—21no—
127Q8×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149C2×D411yescharacteristic
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2411yescharacteristic
135C8×C149—21no—
136C8×C149—21no—
137C22×C149C22×D411yescharacteristic
138C2×D149—21no—
139C2×D149—21no—
140C2×D149—21no—
141C4×C149—21no—
142C4×C149—21no—
143C4×C149—41no—
144C4×C149—41no—
145C4×C149—41no—
146C4×C149—41no—
147C4×C149H(5,𝔽2)11yescharacteristic
148C4×C1492−1+411yescharacteristic
149Dic149—21no—
150Dic149—21no—
151Dic149—21no—
152Dic149—41no—
153Dic149—41no—
154Dic149—41no—
155Dic149—41no—
156C2×C149#53711yescharacteristic
157C2×C149#57811yescharacteristic
158C2×C149#57811yescharacteristic
159D149—41no—
160C149#326111yescharacteristic, complemented, Sylow
161#3261—1491nomaximal, Sylow
162#541—1491no—
163#541—1491no—
164#479—1491no—
165#479—1491no—
166#479—1491no—
167#479D14911yescharacteristic, complemented
168#470—1491no—
169#470—1491no—
170#467—1491no—
171#467—1491no—
172#462—1491no—
173#462—1491no—
174#462—1491no—
175#462—1491no—
176#424—1491no—
177C2×Q16—1491no—
178C2×Q16—1491no—
179C2×Q16—1491no—
180C2×Q16—1491no—
181C2×M16—1491no—
182C22×C8—1491no—
183C4⋊Q8—1491no—
184C4⋊Q8—1491no—
185#126—2981no—
186#126—2981no—
187#126—2981no—
188#126—2981no—
189#125—2981no—
190#125—2981no—
191#125—2981no—
192#125—2981no—
193#125—1491no—
194#125C2×D14911yescharacteristic
195C22⋊Q8—1491no—
196C22⋊Q8—1491no—
197C22⋊Q8—1491no—
198C22⋊Q8—1491no—
199C4×Q8—1491no—
200C4×Q8—1491no—
201C4×Q8—1491no—
202C4×Q8C2×D14911yescharacteristic
203#117—1491no—
204#107—1491no—
205#107C2×D14911yescharacteristic
206#106—1491no—
207#106C2×D14911yescharacteristic
208C4⋊C8—1491no—
209C4⋊C8—1491no—
210C4⋊C8—1491no—
211C4⋊C8C2×D14911yescharacteristic
212#103—1491no—
213#103—1491no—
214#103—1491no—
215#103—1491no—
216#103—1491no—
217#103—1491no—
218#103C2×D14911yescharacteristic
219#103C2×D14911yescharacteristic
220C2×Q8—1491no—
221C2×Q8—1491no—
222C2×Q8—1491no—
223C2×Q8C22×D14911yescharacteristic
224C22×C4—1491no—
225Q16—5961no—
226Q16—5961no—
227Q16—5961no—
228Q16—5961no—
229M16—5961no—
230C2×C8—5961no—
231C2×C8—1491no—
232C2×C8—1491no—
233C2×C8C22×D14911yescharacteristic
234C2×C8C22×D14911yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—2981no—
239C4⋊C4—2981no—
240C4⋊C4—2981no—
241C4⋊C4—2981no—
242C4⋊C4—2981no—
243C4⋊C4—2981no—
244C4⋊C4—2981no—
245C4⋊C4—2981no—
246C4⋊C4—2981no—
247C4⋊C4—2981no—
248C4⋊C4—2981no—
249C4⋊C4—2981no—
250C4⋊C4—2981no—
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—1491no—
262C22⋊C4—1491no—
263C42—21no—
264C42—2981no—
265C42—2981no—
266C42—2981no—
267C42—1491no—
268C42C22×D14911yescharacteristic
269C23—1491no—
270Q8—21no—
271Q8—21no—
272Q8—2981no—
273Q8—2981no—
274Q8—2981no—
275Q8—2981no—
276Q8—2981no—
277Q8—2981no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—2981no—
283C2×C4—2981no—
284C2×C4—2981no—
285C2×C4—2981no—
286C2×C4—2981no—
287C2×C4—2981no—
288C2×C4—1491no—
289C2×C4—1491no—
290C2×C4—1491no—
291C2×C4D4×D14911yescharacteristic
292C2×C4D4×D14911yescharacteristic
293C2×C4C23×D14911yescharacteristic
294C8—21no—
295C8—21no—
296C8—2981no—
297C8—2981no—
298C22—2981no—
299C22—2981no—
300C22—2981no—
301C22C2×D4×D14911yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—2981no—
309C4—2981no—
310C4—2981no—
311C4—5961no—
312C4—5961no—
313C4—5961no—
314C4—5961no—
315C4#1801195711yescharacteristic
316C4#1801195911yescharacteristic
317C2—5961no—
318C2#2375020511yescharacteristic
319C2#2375043911yescharacteristic
320C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#479×C149C2
socleC22×C149C22×D4
prime radicalC22×D149C2×D4
hypercenter#479D149
hypocenterC149#3261
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
3. #23749935C2semidirect
4. #23749931C2semidirect
5. #23749929C2semidirect
10. #23749836C2semidirect
11. #23749835C2semidirect
12. #23749834C2semidirect
13. #23749834C2semidirect
15. #479×C149C2semidirect
160. C149#3261semidirect
167. #479D149semidirect

Maximal subgroups

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

subgroupindex
#237502382
#237502332
#237499352
#237499312
#237499292
#237498842
#237498822
#237498672
#237498652
#237498362
#237498352
#237498342
#237496502
#479×C1492
#3261149