Finite Group Databasebeta

← C151×#9351 #50314276

Subgroups — C151×#9351 #50314276

Order 38656.

416 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3080×C151C211yesmaximal, characteristic
2#2970×C151C211yesmaximal, characteristic
3#1528×C151C211yesmaximal, characteristic, complemented
4#1488×C151C211yesmaximal, characteristic
5#1470×C151C211yesmaximal, characteristic, complemented
6#1307×C151C211yesmaximal, characteristic, complemented
7#1299×C151C211yesmaximal, characteristic, complemented
8C2×#125×C151C2211yescharacteristic
9C4×#41×C151C2211yescharacteristic
10#479×C151—21no—
11#479×C151—21no—
12#478×C151—21no—
13#478×C151—21no—
14#446×C151—21no—
15#435×C151—22no—
16C8×D4×C151—21no—
17#432×C151—21no—
18#432×C151C2211yescharacteristic
19#432×C151C2211yescharacteristic
20#431×C151C2211yescharacteristic
21#428×C151C411yescharacteristic
22#428×C151C411yescharacteristic
23#423×C151C2211yescharacteristic
24#417×C151C411yescharacteristic
25#417×C151C411yescharacteristic
26C4×M16×C151C2211yescharacteristic
27C2×#97×C151—21no—
28#330×C151—21no—
29#330×C151—21no—
30Q8⋊C8×C151—21no—
31D4⋊C8×C151—21no—
32#324×C151—22no—
33C2×#41×C151C2×C411yescharacteristic
34C2×M16×C151—21no—
35C2×M16×C151C2×C411yescharacteristic
36C2×M16×C151C2×C411yescharacteristic
37C22×C8×C151—22no—
38#125×C151—21no—
39#125×C151—21no—
40#125×C151—21no—
41#125×C151—21no—
42C4×Q8×C151D411yescharacteristic
43C4×Q8×C151D411yescharacteristic
44C4×D4×C151—21no—
45C4×D4×C151—21no—
46C4×D4×C151D411yescharacteristic
47C4×D4×C151D411yescharacteristic
48#117×C151—21no—
49#117×C151C2×C411yescharacteristic
50C2×C4⋊C4×C151—21no—
51C2×C4⋊C4×C151—21no—
52C2×C4⋊C4×C151C2×C411yescharacteristic
53C2×C4⋊C4×C151C2×C411yescharacteristic
54C2×C42×C151—21no—
55C2×C42×C151C2311yescharacteristic
56#107×C151—21no—
57#107×C151—21no—
58#106×C151—21no—
59#106×C151—21no—
60C4⋊C8×C151—22no—
61C4⋊C8×C151—21no—
62C4⋊C8×C151—21no—
63C4⋊C8×C151—21no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66#103×C151—21no—
67#103×C151—21no—
68#102×C151—21no—
69#102×C151—21no—
70C22⋊C8×C151—22no—
71C22⋊C8×C151—21no—
72C22⋊C8×C151—21no—
73C22⋊C8×C151D412yes—
74#97×C151—22no—
75#97×C151—21no—
76#97×C151—21no—
77#97×C151D411yescharacteristic
78#97×C151D411yescharacteristic
79C4×C8×C151—21no—
80C4×C8×C151—21no—
81#41×C151—22no—
82#41×C151—41no—
83C2×Q8×C151C22⋊C411yescharacteristic
84C2×D4×C151—21no—
85C2×D4×C151C22⋊C411yescharacteristic
86C22×C4×C151—21no—
87C22×C4×C151—21no—
88C22×C4×C151—21no—
89C22×C4×C151—21no—
90C22×C4×C151—21no—
91C22×C4×C151C22×C411yescharacteristic
92C22×C4×C151C2×D411yescharacteristic
93C22×C4×C151#4111yescharacteristic
94M16×C151—42no—
95M16×C151—41no—
96M16×C151—41no—
97C2×C8×C151—21no—
98C2×C8×C151—21no—
99C2×C8×C151—21no—
100C2×C8×C151—21no—
101C2×C8×C151—22no—
102C2×C8×C151—44no—
103C2×C8×C151—41no—
104C2×C8×C151—41no—
105C4⋊C4×C151—21no—
106C4⋊C4×C151—21no—
107C4⋊C4×C151—21no—
108C4⋊C4×C151—21no—
109C4⋊C4×C151—21no—
110C4⋊C4×C151—21no—
111C4⋊C4×C151—41no—
112C4⋊C4×C151—41no—
113C4⋊C4×C151—41no—
114C4⋊C4×C151—41no—
115C4⋊C4×C151C22⋊C411yescharacteristic
116C4⋊C4×C151C22⋊C411yescharacteristic
117C22⋊C4×C151—21no—
118C22⋊C4×C151—21no—
119C22⋊C4×C151—21no—
120C42×C151—21no—
121C42×C151—21no—
122C42×C151—21no—
123C42×C151C2×D411yescharacteristic
124C42×C151C2×D411yescharacteristic
125C42×C151C2×D411yescharacteristic
126C42×C151#4111yescharacteristic
127C23×C151—21no—
128C23×C151C4×D411yescharacteristic
129Q8×C151—21no—
130Q8×C151—21no—
131D4×C151—21no—
132D4×C151—42no—
133D4×C151#10112yes—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—41no—
140C2×C4×C151—41no—
141C2×C4×C151—42no—
142C2×C4×C151—42no—
143C2×C4×C151—42no—
144C2×C4×C151—41no—
145C2×C4×C151—41no—
146C2×C4×C151—81no—
147C2×C4×C151—81no—
148C2×C4×C151C2×C22⋊C411yescharacteristic
149C2×C4×C151C4×D411yescharacteristic
150C2×C4×C151#12011yescharacteristic
151C2×C4×C151#12111yescharacteristic
152C2×C4×C151#12111yescharacteristic
153C2×C4×C151#12311yescharacteristic
154C8×C151—22no—
155C8×C151—42no—
156C8×C151—41no—
157C8×C151—41no—
158C8×C151—41no—
159C8×C151—81no—
160C8×C151—81no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—22no—
164C22×C151—21no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151#38611yescharacteristic
168C4×C151—21no—
169C4×C151—21no—
170C4×C151—21no—
171C4×C151—21no—
172C4×C151—21no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151—81no—
177C4×C151—81no—
178C4×C151C2×#10111yescharacteristic
179C4×C151#41311yescharacteristic
180C2×C151—41no—
181C2×C151—42no—
182C2×C151#188111yescharacteristic
183C2×C151#190111yescharacteristic
184C2×C151#190611yescharacteristic
185#9351C15111yesmaximal, characteristic, direct product factor, Sylow
186C151#935111yescharacteristic, direct product factor, Sylow
187#3080C2×C15111yescharacteristic
188#2970C2×C15111yescharacteristic
189#1528C2×C15111yescharacteristic, complemented
190#1488C2×C15111yescharacteristic
191#1470C2×C15111yescharacteristic, complemented
192#1307C2×C15111yescharacteristic, complemented
193#1299C2×C15111yescharacteristic, complemented
194C2×#125C22×C15111yescharacteristic
195C4×#41C22×C15111yescharacteristic
196#479—21no—
197#479—21no—
198#478—21no—
199#478—21no—
200#446—21no—
201#435—22no—
202C8×D4—21no—
203#432—21no—
204#432C22×C15111yescharacteristic
205#432C22×C15111yescharacteristic
206#431C22×C15111yescharacteristic
207#428C4×C15111yescharacteristic
208#428C4×C15111yescharacteristic
209#423C22×C15111yescharacteristic
210#417C4×C15111yescharacteristic
211#417C4×C15111yescharacteristic
212C4×M16C22×C15111yescharacteristic
213C2×#97—21no—
214#330—21no—
215#330—21no—
216Q8⋊C8—21no—
217D4⋊C8—21no—
218#324—22no—
219C2×#41C2×C4×C15111yescharacteristic
220C2×M16—21no—
221C2×M16C2×C4×C15111yescharacteristic
222C2×M16C2×C4×C15111yescharacteristic
223C22×C8—22no—
224#125—21no—
225#125—21no—
226#125—21no—
227#125—21no—
228C4×Q8D4×C15111yescharacteristic
229C4×Q8D4×C15111yescharacteristic
230C4×D4—21no—
231C4×D4—21no—
232C4×D4D4×C15111yescharacteristic
233C4×D4D4×C15111yescharacteristic
234#117—21no—
235#117C2×C4×C15111yescharacteristic
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4C2×C4×C15111yescharacteristic
239C2×C4⋊C4C2×C4×C15111yescharacteristic
240C2×C42—21no—
241C2×C42C23×C15111yescharacteristic
242#107—21no—
243#107—21no—
244#106—21no—
245#106—21no—
246C4⋊C8—22no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252#103—21no—
253#103—21no—
254#102—21no—
255#102—21no—
256C22⋊C8—22no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8D4×C15112yes—
260#97—22no—
261#97—21no—
262#97—21no—
263#97D4×C15111yescharacteristic
264#97D4×C15111yescharacteristic
265C4×C8—21no—
266C4×C8—21no—
267#41—22no—
268#41—41no—
269C2×Q8C22⋊C4×C15111yescharacteristic
270C2×D4—21no—
271C2×D4C22⋊C4×C15111yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4C22×C4×C15111yescharacteristic
278C22×C4C2×D4×C15111yescharacteristic
279C22×C4#41×C15111yescharacteristic
280M16—42no—
281M16—41no—
282M16—41no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—22no—
288C2×C8—44no—
289C2×C8—41no—
290C2×C8—41no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4C22⋊C4×C15111yescharacteristic
302C4⋊C4C22⋊C4×C15111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42C2×D4×C15111yescharacteristic
310C42C2×D4×C15111yescharacteristic
311C42C2×D4×C15111yescharacteristic
312C42#41×C15111yescharacteristic
313C23—21no—
314C23C4×D4×C15111yescharacteristic
315Q8—21no—
316Q8—21no—
317D4—21no—
318D4—42no—
319D4#101×C15112yes—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4C2×C22⋊C4×C15111yescharacteristic
335C2×C4C4×D4×C15111yescharacteristic
336C2×C4#120×C15111yescharacteristic
337C2×C4#121×C15111yescharacteristic
338C2×C4#121×C15111yescharacteristic
339C2×C4#123×C15111yescharacteristic
340C8—22no—
341C8—42no—
342C8—41no—
343C8—41no—
344C8—41no—
345C8—81no—
346C8—81no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22#386×C15111yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—81no—
363C4—81no—
364C4C2×#101×C15111yescharacteristic
365C4#413×C15111yescharacteristic
366C2—41no—
367C2—42no—
368C2#1881×C15111yescharacteristic
369C2#1901×C15111yescharacteristic
370C2#1906×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC2×#41×C151C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1528×C151C2semidirect
5. #1470×C151C2semidirect
6. #1307×C151C2semidirect
7. #1299×C151C2semidirect
185. #9351C151direct (N × H)
186. C151#9351direct (N × H)
189. #1528C2×C151semidirect
191. #1470C2×C151semidirect
192. #1307C2×C151semidirect
193. #1299C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3080×C1512
#2970×C1512
#1528×C1512
#1488×C1512
#1470×C1512
#1307×C1512
#1299×C1512
#9351151