Finite Group Databasebeta

← C2×#1342×C151 #50316612

Subgroups — C2×#1342×C151 #50316612

Order 38656.

428 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
1C2×#470×C151C211yesmaximal, characteristic
2C2×#349×C151C211yesmaximal, characteristic
3C2×#338×C151C211yesmaximal, characteristic
4#1342×C151C214yesmaximal, direct product factor
5C22×Q16×C151C411yescharacteristic
6C22×M16×C151—21no—
7C22×M16×C151C2211yescharacteristic
8C2×C22⋊Q8×C151—21no—
9C2×M32×C151—21no—
10#470×C151—21no—
11#470×C151—21no—
12#470×C151C412yes—
13#470×C151C2212yes—
14C2×#106×C151C411yescharacteristic
15C2×#103×C151—21no—
16#349×C151—21no—
17#349×C151C2212yes—
18#338×C151—21no—
19#338×C151C2212yes—
20C22×Q8×C151—21no—
21C23×C4×C151D411yescharacteristic
22C2×Q16×C151—21no—
23C2×Q16×C151—41no—
24C2×Q16×C151—41no—
25C2×Q16×C151C2×C412yes—
26C2×M16×C151—22no—
27C2×M16×C151—22no—
28C2×M16×C151—41no—
29C2×M16×C151—41no—
30C2×M16×C151—41no—
31C2×M16×C151—41no—
32C2×M16×C151—41no—
33C2×M16×C151—41no—
34C2×M16×C151C2×C411yescharacteristic
35C2×M16×C151D411yescharacteristic
36C2×M16×C151D411yescharacteristic
37C2×M16×C151C2311yescharacteristic
38C22×C8×C151—22no—
39C22×C8×C151C2×C411yescharacteristic
40C22×C8×C151D411yescharacteristic
41C22⋊Q8×C151—22no—
42C22⋊Q8×C151—22no—
43C22⋊Q8×C151—41no—
44C22⋊Q8×C151—41no—
45C2×C4⋊C4×C151—21no—
46C2×C4⋊C4×C151—41no—
47C2×C22⋊C4×C151—41no—
48M32×C151—22no—
49M32×C151—41no—
50C2×C16×C151—41no—
51#106×C151—21no—
52#106×C151C2×C412yes—
53#103×C151—22no—
54#103×C151—22no—
55C24×C151SD1611yescharacteristic
56C2×Q8×C151—22no—
57C2×Q8×C151—41no—
58C2×Q8×C151—41no—
59C2×Q8×C151—41no—
60C2×Q8×C151—41no—
61C2×Q8×C151—41no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151—21no—
65C22×C4×C151—21no—
66C22×C4×C151—41no—
67C22×C4×C151—41no—
68C22×C4×C151C22⋊C411yescharacteristic
69C22×C4×C151C22⋊C411yescharacteristic
70C22×C4×C151D811yescharacteristic
71C22×C4×C151D811yescharacteristic
72C22×C4×C151SD1611yescharacteristic
73C22×C4×C151C2×D411yescharacteristic
74Q16×C151—42no—
75Q16×C151—42no—
76M16×C151—41no—
77M16×C151—41no—
78M16×C151—41no—
79M16×C151—41no—
80M16×C151—42no—
81M16×C151—42no—
82M16×C151—42no—
83M16×C151—42no—
84C2×C8×C151—21no—
85C2×C8×C151—21no—
86C2×C8×C151—21no—
87C2×C8×C151—21no—
88C2×C8×C151—24no—
89C2×C8×C151—42no—
90C2×C8×C151—42no—
91C2×C8×C151C22⋊C411yescharacteristic
92C2×C8×C151C22⋊C411yescharacteristic
93C2×C8×C151C22×C411yescharacteristic
94C2×C8×C151C2×D411yescharacteristic
95C4⋊C4×C151—22no—
96C4⋊C4×C151—41no—
97C4⋊C4×C151—42no—
98C4⋊C4×C151—42no—
99C22⋊C4×C151—42no—
100C22⋊C4×C151—42no—
101C16×C151—42no—
102C23×C151—21no—
103C23×C151—21no—
104C23×C151—42no—
105C23×C151#10211yescharacteristic
106C23×C151#10211yescharacteristic
107C23×C151C2×SD1611yescharacteristic
108Q8×C151—42no—
109Q8×C151—42no—
110Q8×C151—81no—
111Q8×C151—81no—
112C2×C4×C151—21no—
113C2×C4×C151—21no—
114C2×C4×C151—21no—
115C2×C4×C151—21no—
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—42no—
123C2×C4×C151—42no—
124C2×C4×C151—82no—
125C2×C4×C151—81no—
126C2×C4×C151—81no—
127C2×C4×C151#9911yescharacteristic
128C2×C4×C151#9911yescharacteristic
129C2×C4×C151#10211yescharacteristic
130C2×C4×C151#10211yescharacteristic
131C2×C4×C151#10411yescharacteristic
132C2×C4×C151#10411yescharacteristic
133C2×C4×C151C2×C22⋊C411yescharacteristic
134C2×C4×C151C2×D811yescharacteristic
135C8×C151—21no—
136C8×C151—21no—
137C8×C151—21no—
138C8×C151—21no—
139C8×C151—44no—
140C22×C151—22no—
141C22×C151—21no—
142C22×C151—21no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151—42no—
146C22×C151—81no—
147C22×C151#32711yescharacteristic
148C22×C151#32711yescharacteristic
149C22×C151C2×#10211yescharacteristic
150C4×C151—21no—
151C4×C151—21no—
152C4×C151—82no—
153C4×C151—82no—
154C4×C151#32711yescharacteristic
155C4×C151#32711yescharacteristic
156C4×C151C2×#9911yescharacteristic
157C4×C151C2×#10411yescharacteristic
158C2×C151—21no—
159C2×C151—21no—
160C2×C151—41no—
161C2×C151—41no—
162C2×C151#134212yesdirect product factor
163C2×C151C2×#32711yescharacteristic
164C2×#1342C15111yesmaximal, characteristic, direct product factor, Sylow
165C151C2×#134211yescharacteristic, direct product factor, Sylow
166C2×#470C2×C15111yescharacteristic
167C2×#349C2×C15111yescharacteristic
168C2×#338C2×C15111yescharacteristic
169#1342C2×C15114yesdirect product factor
170C22×Q16C4×C15111yescharacteristic
171C22×M16—21no—
172C22×M16C22×C15111yescharacteristic
173C2×C22⋊Q8—21no—
174C2×M32—21no—
175#470—21no—
176#470—21no—
177#470C4×C15112yes—
178#470C22×C15112yes—
179C2×#106C4×C15111yescharacteristic
180C2×#103—21no—
181#349—21no—
182#349C22×C15112yes—
183#338—21no—
184#338C22×C15112yes—
185C22×Q8—21no—
186C23×C4D4×C15111yescharacteristic
187C2×Q16—21no—
188C2×Q16—41no—
189C2×Q16—41no—
190C2×Q16C2×C4×C15112yes—
191C2×M16—22no—
192C2×M16—22no—
193C2×M16—41no—
194C2×M16—41no—
195C2×M16—41no—
196C2×M16—41no—
197C2×M16—41no—
198C2×M16—41no—
199C2×M16C2×C4×C15111yescharacteristic
200C2×M16D4×C15111yescharacteristic
201C2×M16D4×C15111yescharacteristic
202C2×M16C23×C15111yescharacteristic
203C22×C8—22no—
204C22×C8C2×C4×C15111yescharacteristic
205C22×C8D4×C15111yescharacteristic
206C22⋊Q8—22no—
207C22⋊Q8—22no—
208C22⋊Q8—41no—
209C22⋊Q8—41no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—41no—
212C2×C22⋊C4—41no—
213M32—22no—
214M32—41no—
215C2×C16—41no—
216#106—21no—
217#106C2×C4×C15112yes—
218#103—22no—
219#103—22no—
220C24SD16×C15111yescharacteristic
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4C22⋊C4×C15111yescharacteristic
234C22×C4C22⋊C4×C15111yescharacteristic
235C22×C4D8×C15111yescharacteristic
236C22×C4D8×C15111yescharacteristic
237C22×C4SD16×C15111yescharacteristic
238C22×C4C2×D4×C15111yescharacteristic
239Q16—42no—
240Q16—42no—
241M16—41no—
242M16—41no—
243M16—41no—
244M16—41no—
245M16—42no—
246M16—42no—
247M16—42no—
248M16—42no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—24no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8C22⋊C4×C15111yescharacteristic
257C2×C8C22⋊C4×C15111yescharacteristic
258C2×C8C22×C4×C15111yescharacteristic
259C2×C8C2×D4×C15111yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C16—42no—
267C23—21no—
268C23—21no—
269C23—42no—
270C23#102×C15111yescharacteristic
271C23#102×C15111yescharacteristic
272C23C2×SD16×C15111yescharacteristic
273Q8—42no—
274Q8—42no—
275Q8—81no—
276Q8—81no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—82no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4#99×C15111yescharacteristic
293C2×C4#99×C15111yescharacteristic
294C2×C4#102×C15111yescharacteristic
295C2×C4#102×C15111yescharacteristic
296C2×C4#104×C15111yescharacteristic
297C2×C4#104×C15111yescharacteristic
298C2×C4C2×C22⋊C4×C15111yescharacteristic
299C2×C4C2×D8×C15111yescharacteristic
300C8—21no—
301C8—21no—
302C8—21no—
303C8—21no—
304C8—44no—
305C22—22no—
306C22—21no—
307C22—21no—
308C22—41no—
309C22—41no—
310C22—42no—
311C22—81no—
312C22#327×C15111yescharacteristic
313C22#327×C15111yescharacteristic
314C22C2×#102×C15111yescharacteristic
315C4—21no—
316C4—21no—
317C4—82no—
318C4—82no—
319C4#327×C15111yescharacteristic
320C4#327×C15111yescharacteristic
321C4C2×#99×C15111yescharacteristic
322C4C2×#104×C15111yescharacteristic
323C2—21no—
324C2—21no—
325C2—41no—
326C2—41no—
327C2#1342×C15112yesdirect product factor
328C2C2×#327×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#327
commutatorC2×C8C22×C4×C151
Frattini, cosocleC2×M16C23×C151
prime radicalC24×C151SD16
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C22×M16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1342×C151C2direct (N × H)
162. C2×C151#1342direct (N × H)
164. C2×#1342C151direct (N × H)
165. C151C2×#1342direct (N × H)
169. #1342C2×C151direct (N × H)
327. C2#1342×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#470×C1512
C2×#349×C1512
C2×#338×C1512
#1342×C1512
C2×#1342151