Finite Group Databasebeta

← #3350×C151 #34066682

Subgroups — #3350×C151 #34066682

Order 19328.

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#556×C151C211yesmaximal, characteristic, complemented
2#553×C151C211yesmaximal, characteristic
3#501×C151C211yesmaximal, characteristic, complemented
4#485×C151C211yesmaximal, characteristic, complemented
5#483×C151C211yesmaximal, characteristic, complemented
6#482×C151C211yesmaximal, characteristic, complemented
7#482×C151C211yesmaximal, characteristic, complemented
8#479×C151C211yesmaximal, characteristic, complemented
9#476×C151C211yesmaximal, characteristic, complemented
10#468×C151C211yesmaximal, characteristic, complemented
11#465×C151C211yesmaximal, characteristic, complemented
12#440×C151C211yesmaximal, characteristic, complemented
13#435×C151C211yesmaximal, characteristic, complemented
14#428×C151C211yesmaximal, characteristic, complemented
15#427×C151C211yesmaximal, characteristic, complemented
16C2×SD16×C151C2211yescharacteristic
17C2×M16×C151C2211yescharacteristic
18C22×C8×C151C2211yescharacteristic
19C4⋊Q8×C151C2211yescharacteristic
20#126×C151—21no—
21#126×C151—21no—
22#126×C151—21no—
23#125×C151C2211yescharacteristic
24#124×C151—21no—
25#123×C151—21no—
26C22⋊Q8×C151C2211yescharacteristic
27C22⋊Q8×C151C2211yescharacteristic
28#121×C151—21no—
29#121×C151C2211yescharacteristic
30#121×C151C2211yescharacteristic
31C4×Q8×C151—21no—
32C4×Q8×C151C2211yescharacteristic
33C4×D4×C151—21no—
34C4×D4×C151C2211yescharacteristic
35C4×D4×C151C2211yescharacteristic
36#117×C151C2211yescharacteristic
37#117×C151C2211yescharacteristic
38#117×C151C2211yescharacteristic
39C2×C4⋊C4×C151C2211yescharacteristic
40#107×C151C2211yescharacteristic
41#107×C151C2211yescharacteristic
42#107×C151C2211yescharacteristic
43#107×C151C2211yescharacteristic
44#106×C151C2211yescharacteristic
45#106×C151C2211yescharacteristic
46#106×C151C2211yescharacteristic
47#106×C151C2211yescharacteristic
48#106×C151C2211yescharacteristic
49C4⋊C8×C151C2211yescharacteristic
50#103×C151C2211yescharacteristic
51#103×C151C2211yescharacteristic
52#103×C151C2211yescharacteristic
53#102×C151C2211yescharacteristic
54#102×C151C2211yescharacteristic
55#102×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57C22⋊C8×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59C2×Q8×C151—21no—
60C2×Q8×C151C2311yescharacteristic
61C2×D4×C151—21no—
62C2×D4×C151—21no—
63C2×D4×C151D411yescharacteristic
64C2×D4×C151C2311yescharacteristic
65C22×C4×C151—21no—
66C22×C4×C151—21no—
67C22×C4×C151C2311yescharacteristic
68C22×C4×C151C2311yescharacteristic
69SD16×C151—22no—
70M16×C151—22no—
71C2×C8×C151—22no—
72C2×C8×C151C2311yescharacteristic
73C2×C8×C151C2311yescharacteristic
74C2×C8×C151C2311yescharacteristic
75C2×C8×C151C2311yescharacteristic
76C4⋊C4×C151—21no—
77C4⋊C4×C151—21no—
78C4⋊C4×C151—21no—
79C4⋊C4×C151—21no—
80C4⋊C4×C151—21no—
81C4⋊C4×C151—21no—
82C4⋊C4×C151—21no—
83C4⋊C4×C151D411yescharacteristic
84C4⋊C4×C151C2311yescharacteristic
85C4⋊C4×C151C2311yescharacteristic
86C4⋊C4×C151C2311yescharacteristic
87C4⋊C4×C151C2311yescharacteristic
88C4⋊C4×C151C2311yescharacteristic
89C4⋊C4×C151C2311yescharacteristic
90C22⋊C4×C151—21no—
91C22⋊C4×C151—21no—
92C22⋊C4×C151—21no—
93C22⋊C4×C151—21no—
94C22⋊C4×C151—21no—
95C22⋊C4×C151—21no—
96C22⋊C4×C151—21no—
97C22⋊C4×C151—21no—
98C22⋊C4×C151D411yescharacteristic
99C22⋊C4×C151D411yescharacteristic
100C42×C151—21no—
101C42×C151—21no—
102C42×C151—21no—
103C42×C151—21no—
104C42×C151C2311yescharacteristic
105C23×C151—21no—
106C23×C151C2×D411yescharacteristic
107C23×C151C2×D411yescharacteristic
108Q8×C151—21no—
109Q8×C151—21no—
110Q8×C151—42no—
111D4×C151—21no—
112D4×C151—21no—
113D4×C151—41no—
114D4×C151—42no—
115D4×C151—81no—
116C2×C4×C151—21no—
117C2×C4×C151—21no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—81no—
128C2×C4×C151—81no—
129C2×C4×C151C2×D411yescharacteristic
130C2×C4×C151C2×D411yescharacteristic
131C2×C4×C151C2×D411yescharacteristic
132C2×C4×C151C2×D411yescharacteristic
133C2×C4×C151C2411yescharacteristic
134C8×C151—21no—
135C8×C151—21no—
136C8×C151—21no—
137C8×C151#4112yes—
138C22×C151—21no—
139C22×C151—21no—
140C22×C151—21no—
141C22×C151—21no—
142C22×C151—21no—
143C22×C151—21no—
144C22×C151—41no—
145C22×C151—41no—
146C22×C151—41no—
147C22×C151C22×D411yescharacteristic
148C4×C151—21no—
149C4×C151—21no—
150C4×C151—21no—
151C4×C151—21no—
152C4×C151—41no—
153C4×C151—41no—
154C4×C151—41no—
155C4×C151—41no—
156C4×C151—41no—
157C4×C151—41no—
158C4×C151—41no—
159C4×C151C2×#4111yescharacteristic
160C4×C1512−1+411yescharacteristic
161C2×C151—41no—
162C2×C151—41no—
163C2×C151—81no—
164C2×C151#54711yescharacteristic
165C2×C151#57511yescharacteristic
166C2×C151#57711yescharacteristic
167C151#335011yescharacteristic, direct product factor, Sylow
168#3350C15111yesmaximal, characteristic, direct product factor, Sylow
169#556C2×C15111yescharacteristic, complemented
170#553C2×C15111yescharacteristic
171#501C2×C15111yescharacteristic, complemented
172#485C2×C15111yescharacteristic, complemented
173#483C2×C15111yescharacteristic, complemented
174#482C2×C15111yescharacteristic, complemented
175#482C2×C15111yescharacteristic, complemented
176#479C2×C15111yescharacteristic, complemented
177#476C2×C15111yescharacteristic, complemented
178#468C2×C15111yescharacteristic, complemented
179#465C2×C15111yescharacteristic, complemented
180#440C2×C15111yescharacteristic, complemented
181#435C2×C15111yescharacteristic, complemented
182#428C2×C15111yescharacteristic, complemented
183#427C2×C15111yescharacteristic, complemented
184C2×SD16C22×C15111yescharacteristic
185C2×M16C22×C15111yescharacteristic
186C22×C8C22×C15111yescharacteristic
187C4⋊Q8C22×C15111yescharacteristic
188#126—21no—
189#126—21no—
190#126—21no—
191#125C22×C15111yescharacteristic
192#124—21no—
193#123—21no—
194C22⋊Q8C22×C15111yescharacteristic
195C22⋊Q8C22×C15111yescharacteristic
196#121—21no—
197#121C22×C15111yescharacteristic
198#121C22×C15111yescharacteristic
199C4×Q8—21no—
200C4×Q8C22×C15111yescharacteristic
201C4×D4—21no—
202C4×D4C22×C15111yescharacteristic
203C4×D4C22×C15111yescharacteristic
204#117C22×C15111yescharacteristic
205#117C22×C15111yescharacteristic
206#117C22×C15111yescharacteristic
207C2×C4⋊C4C22×C15111yescharacteristic
208#107C22×C15111yescharacteristic
209#107C22×C15111yescharacteristic
210#107C22×C15111yescharacteristic
211#107C22×C15111yescharacteristic
212#106C22×C15111yescharacteristic
213#106C22×C15111yescharacteristic
214#106C22×C15111yescharacteristic
215#106C22×C15111yescharacteristic
216#106C22×C15111yescharacteristic
217C4⋊C8C22×C15111yescharacteristic
218#103C22×C15111yescharacteristic
219#103C22×C15111yescharacteristic
220#103C22×C15111yescharacteristic
221#102C22×C15111yescharacteristic
222#102C22×C15111yescharacteristic
223#102C22×C15111yescharacteristic
224C22⋊C8C22×C15111yescharacteristic
225C22⋊C8C22×C15111yescharacteristic
226#97C22×C15111yescharacteristic
227C2×Q8—21no—
228C2×Q8C23×C15111yescharacteristic
229C2×D4—21no—
230C2×D4—21no—
231C2×D4D4×C15111yescharacteristic
232C2×D4C23×C15111yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4C23×C15111yescharacteristic
236C22×C4C23×C15111yescharacteristic
237SD16—22no—
238M16—22no—
239C2×C8—22no—
240C2×C8C23×C15111yescharacteristic
241C2×C8C23×C15111yescharacteristic
242C2×C8C23×C15111yescharacteristic
243C2×C8C23×C15111yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4D4×C15111yescharacteristic
252C4⋊C4C23×C15111yescharacteristic
253C4⋊C4C23×C15111yescharacteristic
254C4⋊C4C23×C15111yescharacteristic
255C4⋊C4C23×C15111yescharacteristic
256C4⋊C4C23×C15111yescharacteristic
257C4⋊C4C23×C15111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4D4×C15111yescharacteristic
267C22⋊C4D4×C15111yescharacteristic
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42C23×C15111yescharacteristic
273C23—21no—
274C23C2×D4×C15111yescharacteristic
275C23C2×D4×C15111yescharacteristic
276Q8—21no—
277Q8—21no—
278Q8—42no—
279D4—21no—
280D4—21no—
281D4—41no—
282D4—42no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4C2×D4×C15111yescharacteristic
298C2×C4C2×D4×C15111yescharacteristic
299C2×C4C2×D4×C15111yescharacteristic
300C2×C4C2×D4×C15111yescharacteristic
301C2×C4C24×C15111yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8#41×C15112yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22C22×D4×C15111yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4C2×#41×C15111yescharacteristic
328C42−1+4×C15111yescharacteristic
329C2—41no—
330C2—41no—
331C2—81no—
332C2#547×C15111yescharacteristic
333C2#575×C15111yescharacteristic
334C2#577×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×D4
commutator, Frattini, cosocleC2×C4C24×C151
prime radical#553×C151C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #556×C151C2semidirect
3. #501×C151C2semidirect
4. #485×C151C2semidirect
5. #483×C151C2semidirect
6. #482×C151C2semidirect
7. #482×C151C2semidirect
8. #479×C151C2semidirect
9. #476×C151C2semidirect
10. #468×C151C2semidirect
11. #465×C151C2semidirect
12. #440×C151C2semidirect
13. #435×C151C2semidirect
14. #428×C151C2semidirect
15. #427×C151C2semidirect
167. C151#3350direct (N × H)
168. #3350C151direct (N × H)
169. #556C2×C151semidirect
171. #501C2×C151semidirect
172. #485C2×C151semidirect
173. #483C2×C151semidirect
174. #482C2×C151semidirect
175. #482C2×C151semidirect
176. #479C2×C151semidirect
177. #476C2×C151semidirect
178. #468C2×C151semidirect
179. #465C2×C151semidirect
180. #440C2×C151semidirect
181. #435C2×C151semidirect
182. #428C2×C151semidirect
183. #427C2×C151semidirect

Maximal subgroups

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

subgroupindex
#556×C1512
#553×C1512
#501×C1512
#485×C1512
#483×C1512
#482×C1512
#479×C1512
#476×C1512
#468×C1512
#465×C1512
#440×C1512
#435×C1512
#428×C1512
#427×C1512
#3350151