Finite Group Databasebeta

← #34057524

Subgroups — #34057524

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#23750344C211yesmaximal, characteristic, complemented
2#23750331C211yesmaximal, characteristic, complemented
3#23749992C211yesmaximal, characteristic, complemented
4#23749983C211yesmaximal, characteristic, complemented
5#23749929C211yesmaximal, characteristic, complemented
6#23749927C211yesmaximal, characteristic, complemented
7#23749908C211yesmaximal, characteristic, complemented
8#23749839C211yesmaximal, characteristic
9#23749837C211yesmaximal, characteristic
10#23749829C211yesmaximal, characteristic, complemented
11#23749755C211yesmaximal, characteristic, complemented
12#23749734C211yesmaximal, characteristic
13#23749728C211yesmaximal, characteristic, complemented
14C4×#14558725C211yesmaximal, characteristic, complemented
15#488×C149C211yesmaximal, characteristic, complemented
16C2×#14558725C2211yescharacteristic
17C2×#14558723C2211yescharacteristic
18C2×#14558721C2211yescharacteristic
19#18011910C2211yescharacteristic
20#18011909C2211yescharacteristic
21#18011904—21no—
22#18011904—21no—
23#18011902C2211yescharacteristic
24#18011898C2211yescharacteristic
25#18011891—21no—
26#18011889—21no—
27#18011889—21no—
28#18011888—21no—
29Q8×Dic149C2211yescharacteristic
30C4×Dic298C2211yescharacteristic
31C4×Dic298C2211yescharacteristic
32C4×D596C2211yescharacteristic
33D4×Dic149C2211yescharacteristic
34#18011873C2211yescharacteristic
35#18011873C2211yescharacteristic
36#18011867—21no—
37C4⋊C4×D149—21no—
38#18011844C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011821C2211yescharacteristic
51#18011821C2211yescharacteristic
52#125×C149C2211yescharacteristic
53#124×C149C2211yescharacteristic
54#103×C149C2211yescharacteristic
55#103×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298D411yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C22×Dic149—21no—
64C2×C4×D149—21no—
65C2×C4×D149—21no—
66C2×C4×D149—21no—
67#14558725—22no—
68#14558723—22no—
69#14558721—22no—
70C2×#11924746C2311yescharacteristic
71C2×#11924746C2311yescharacteristic
72C4⋊Dic149—21no—
73C4⋊Dic149—21no—
74C4⋊Dic149D411yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715D411yescharacteristic
83#14558715D411yescharacteristic
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90C4×Dic149—21no—
91C4×Dic149—21no—
92C4×Dic149C2311yescharacteristic
93C4×Dic149C2311yescharacteristic
94C2×Q8×C149C2311yescharacteristic
95C2×D4×C149C2311yescharacteristic
96C2×C8×C149C2311yescharacteristic
97C2×C8×C149C2311yescharacteristic
98C4⋊C4×C149—21no—
99C4⋊C4×C149—21no—
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C22⋊C4×C149—21no—
103C22⋊C4×C149—21no—
104C42×C149C2311yescharacteristic
105C22×D149—21no—
106Dic298—21no—
107Dic298—21no—
108Dic298—41no—
109Dic298—81no—
110D596—21no—
111D596#4112yes—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—42no—
116C2×Dic149C2×D411yescharacteristic
117C2×Dic149C2×D411yescharacteristic
118C2×Dic149C2×D411yescharacteristic
119C2×Dic149C2×D411yescharacteristic
120C4×D149—42no—
121C4×D149—81no—
122C4×D149—81no—
123#11924746—21no—
124#11924746—21no—
125C23×C149—21no—
126Q8×C149—21no—
127Q8×C149—21no—
128D4×C149—21no—
129D4×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×C149—41no—
139C22×C149—41no—
140C22×C149—41no—
141C22×C149C22×D411yescharacteristic
142C2×D149—22no—
143C2×D149—41no—
144C2×D149—41no—
145C4×C149—21no—
146C4×C149—21no—
147C4×C149—41no—
148C4×C149—41no—
149C4×C149—41no—
150C4×C149C2×#4111yescharacteristic
151C4×C1492−1+411yescharacteristic
152Dic149—21no—
153Dic149—21no—
154Dic149—21no—
155Dic149—21no—
156Dic149—41no—
157Dic149—41no—
158Dic149—41no—
159C2×C149—81no—
160C2×C149#54811yescharacteristic
161C2×C149#57511yescharacteristic
162C2×C149#57711yescharacteristic
163D149—42no—
164C149#337611yescharacteristic, complemented, Sylow
165#3376—1491nomaximal, Sylow
166#556—1491no—
167#554—1491no—
168#491—1491no—
169#489—1491no—
170#488D14911yescharacteristic, complemented
171#479—1491no—
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#124C2×D14911yescharacteristic
192C22⋊Q8—2981no—
193C22⋊Q8—2981no—
194C22⋊Q8—2981no—
195C22⋊Q8—2981no—
196C4×Q8—1491no—
197C4×Q8—1491no—
198C4×Q8—1491no—
199C4×D4—1491no—
200C4×D4—1491no—
201C4×D4—1491no—
202C4×D4—1491no—
203#117—2981no—
204C2×C4⋊C4—2981no—
205#107—1491no—
206#106—1491no—
207#106—1491no—
208C4⋊C8—1491no—
209C4⋊C8—1491no—
210C4⋊C8—1491no—
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#102C2×D14911yescharacteristic
220#102C2×D14911yescharacteristic
221#97—1491no—
222#97—1491no—
223C4×C8C2×D14911yescharacteristic
224C2×Q8—2981no—
225C2×Q8—1491no—
226C2×Q8—1491no—
227C2×Q8C22×D14911yescharacteristic
228C2×D4—1491no—
229C2×D4C22×D14911yescharacteristic
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—2981no—
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⋊C4—1491no—
255C4⋊C4C22×D14911yescharacteristic
256C4⋊C4C22×D14911yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—2981no—
260C22⋊C4—2981no—
261C22⋊C4—2981no—
262C22⋊C4—2981no—
263C22⋊C4—2981no—
264C22⋊C4—2981no—
265C42—2981no—
266C42—2981no—
267C42—1491no—
268C42—1491no—
269C42C22×D14911yescharacteristic
270C23—21no—
271C23—2981no—
272Q8—21no—
273Q8—21no—
274Q8—2981no—
275Q8—2981no—
276Q8—5961no—
277Q8—11921no—
278D4—21no—
279D4—21no—
280D4—2981no—
281D4—1492no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—2981no—
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—41no—
304C22—41no—
305C22—41no—
306C22—2982no—
307C22—5961no—
308C22—5961no—
309C22C2×D4×D14911yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—2981no—
316C4—2981no—
317C4—2981no—
318C4—2981no—
319C4—5961no—
320C4—5961no—
321C4—5961no—
322C4#41×D14911yescharacteristic
323C4#1801195811yescharacteristic
324C2—81no—
325C2—5962no—
326C2#2375028311yescharacteristic
327C2#2375042211yescharacteristic
328C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#488×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558721C22
hypercenter#488D149
hypocenterC149#3376
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. #23750344C2semidirect
2. #23750331C2semidirect
3. #23749992C2semidirect
4. #23749983C2semidirect
5. #23749929C2semidirect
6. #23749927C2semidirect
7. #23749908C2semidirect
10. #23749829C2semidirect
11. #23749755C2semidirect
13. #23749728C2semidirect
14. C4×#14558725C2semidirect
15. #488×C149C2semidirect
164. C149#3376semidirect
170. #488D149semidirect

Maximal subgroups

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

subgroupindex
#237503442
#237503312
#237499922
#237499832
#237499292
#237499272
#237499082
#237498392
#237498372
#237498292
#237497552
#237497342
#237497282
C4×#145587252
#488×C1492
#3376149