Finite Group Databasebeta

← C151×#9688 #50314613

Subgroups — C151×#9688 #50314613

Order 38656.

482 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2861×C151C211yesmaximal, characteristic
2#1767×C151C211yesmaximal, characteristic, complemented
3#1745×C151C211yesmaximal, characteristic, complemented
4C2×#330×C151C212yesmaximal, complemented
5C2×#329×C151C212yesmaximal
6C2×#125×C151C2211yescharacteristic
7C2×#124×C151C2211yescharacteristic
8C2×C4⋊C8×C151—21no—
9C2×#97×C151C2212yes—
10C2×#97×C151C2212yes—
11#391×C151C411yescharacteristic
12#391×C151C411yescharacteristic
13#390×C151C411yescharacteristic
14#390×C151C411yescharacteristic
15#388×C151—21no—
16#388×C151—21no—
17#388×C151—21no—
18#388×C151—21no—
19C43×C151C2211yescharacteristic
20#336×C151—21no—
21#336×C151—21no—
22#336×C151—21no—
23#330×C151—24no—
24#329×C151—24no—
25C22×Q8×C151C2×C411yescharacteristic
26C22×D4×C151C2×C411yescharacteristic
27C22×C8×C151—22no—
28C22×C8×C151—22no—
29#125×C151—22no—
30#125×C151—22no—
31#124×C151—22no—
32#124×C151—22no—
33C2×C4⋊C4×C151—21no—
34C2×C4⋊C4×C151—21no—
35C2×C4⋊C4×C151C2×C411yescharacteristic
36C2×C4⋊C4×C151C2×C411yescharacteristic
37C2×C22⋊C4×C151—21no—
38C2×C22⋊C4×C151—21no—
39C2×C22⋊C4×C151—21no—
40C2×C22⋊C4×C151—21no—
41C2×C22⋊C4×C151—21no—
42C2×C22⋊C4×C151—21no—
43C2×C42×C151C2×C411yescharacteristic
44C2×C42×C151C2×C411yescharacteristic
45C2×C42×C151D411yescharacteristic
46C2×C42×C151D411yescharacteristic
47C2×C42×C151D411yescharacteristic
48C2×C42×C151D411yescharacteristic
49C2×C42×C151C2311yescharacteristic
50C4⋊C8×C151—24no—
51#97×C151—22no—
52#97×C151—22no—
53#97×C151—22no—
54#97×C151D414yes—
55#95×C151—21no—
56#95×C151—21no—
57#95×C151—21no—
58#95×C151—21no—
59C24×C151—21no—
60C2×Q8×C151—22no—
61C2×Q8×C151—41no—
62C2×Q8×C151—41no—
63C2×D4×C151—22no—
64C2×D4×C151—41no—
65C2×D4×C151—41no—
66C22×C4×C151—21no—
67C22×C4×C151—21no—
68C22×C4×C151—21no—
69C22×C4×C151C22⋊C411yescharacteristic
70C22×C4×C151C22⋊C411yescharacteristic
71C22×C4×C151C22⋊C411yescharacteristic
72C22×C4×C151C22⋊C411yescharacteristic
73C22×C4×C151C22×C411yescharacteristic
74C22×C4×C151C2×D411yescharacteristic
75C22×C4×C151C2×D411yescharacteristic
76C2×C8×C151—24no—
77C2×C8×C151—24no—
78C2×C8×C151—42no—
79C2×C8×C151—42no—
80C2×C8×C151—42no—
81C2×C8×C151—42no—
82C4⋊C4×C151—22no—
83C4⋊C4×C151—22no—
84C4⋊C4×C151—42no—
85C4⋊C4×C151—41no—
86C4⋊C4×C151—41no—
87C22⋊C4×C151—42no—
88C22⋊C4×C151—42no—
89C22⋊C4×C151—42no—
90C22⋊C4×C151—42no—
91C22⋊C4×C151—42no—
92C22⋊C4×C151—41no—
93C22⋊C4×C151—41no—
94C42×C151—22no—
95C42×C151—41no—
96C42×C151—41no—
97C42×C151—41no—
98C42×C151—41no—
99C42×C151—41no—
100C42×C151C2×D412yes—
101C42×C151#4112yes—
102C23×C151—41no—
103C23×C151—41no—
104C23×C151—41no—
105C23×C151—41no—
106C23×C151—41no—
107C23×C151—41no—
108C23×C151—41no—
109C23×C151C2×C22⋊C411yescharacteristic
110Q8×C151—82no—
111D4×C151—82no—
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—21no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—41no—
130C2×C4×C151—41no—
131C2×C4×C151—41no—
132C2×C4×C151—41no—
133C2×C4×C151—41no—
134C2×C4×C151—41no—
135C2×C4×C151—41no—
136C2×C4×C151—41no—
137C2×C4×C151—41no—
138C2×C4×C151#10412yes—
139C2×C4×C151C4×D412yes—
140C2×C4×C151#12112yes—
141C2×C4×C151#12411yescharacteristic
142C2×C4×C151#12711yescharacteristic
143C8×C151—44no—
144C8×C151—44no—
145C22×C151—81no—
146C22×C151—81no—
147C22×C151—81no—
148C22×C151—81no—
149C22×C151—81no—
150C22×C151—81no—
151C22×C151—81no—
152C22×C151#39011yescharacteristic
153C22×C151#41311yescharacteristic
154C22×C151#41311yescharacteristic
155C22×C151C2×#10411yescharacteristic
156C22×C151#42111yescharacteristic
157C22×C151#42111yescharacteristic
158C22×C151#42111yescharacteristic
159C4×C151—22no—
160C4×C151—22no—
161C4×C151—21no—
162C4×C151—21no—
163C4×C151—22no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151—41no—
167C4×C151—81no—
168C4×C151—81no—
169C4×C151—81no—
170C2×C151—161no—
171C2×C151#152911yescharacteristic
172C2×C151#153211yescharacteristic
173C2×C151#153511yescharacteristic
174C2×C151#153511yescharacteristic
175C2×C151#196311yescharacteristic
176C2×C151#196711yescharacteristic
177C2×C151#198011yescharacteristic
178#9688C15111yesmaximal, characteristic, direct product factor, Sylow
179C151#968811yescharacteristic, direct product factor, Sylow
180#2861C2×C15111yescharacteristic
181#1767C2×C15111yescharacteristic, complemented
182#1745C2×C15111yescharacteristic, complemented
183C2×#330C2×C15112yescomplemented
184C2×#329C2×C15112yes—
185C2×#125C22×C15111yescharacteristic
186C2×#124C22×C15111yescharacteristic
187C2×C4⋊C8—21no—
188C2×#97C22×C15112yes—
189C2×#97C22×C15112yes—
190#391C4×C15111yescharacteristic
191#391C4×C15111yescharacteristic
192#390C4×C15111yescharacteristic
193#390C4×C15111yescharacteristic
194#388—21no—
195#388—21no—
196#388—21no—
197#388—21no—
198C43C22×C15111yescharacteristic
199#336—21no—
200#336—21no—
201#336—21no—
202#330—24no—
203#329—24no—
204C22×Q8C2×C4×C15111yescharacteristic
205C22×D4C2×C4×C15111yescharacteristic
206C22×C8—22no—
207C22×C8—22no—
208#125—22no—
209#125—22no—
210#124—22no—
211#124—22no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C2×C4×C15111yescharacteristic
215C2×C4⋊C4C2×C4×C15111yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C42C2×C4×C15111yescharacteristic
223C2×C42C2×C4×C15111yescharacteristic
224C2×C42D4×C15111yescharacteristic
225C2×C42D4×C15111yescharacteristic
226C2×C42D4×C15111yescharacteristic
227C2×C42D4×C15111yescharacteristic
228C2×C42C23×C15111yescharacteristic
229C4⋊C8—24no—
230#97—22no—
231#97—22no—
232#97—22no—
233#97D4×C15114yes—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238C24—21no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×D4—22no—
243C2×D4—41no—
244C2×D4—41no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4C22⋊C4×C15111yescharacteristic
249C22×C4C22⋊C4×C15111yescharacteristic
250C22×C4C22⋊C4×C15111yescharacteristic
251C22×C4C22⋊C4×C15111yescharacteristic
252C22×C4C22×C4×C15111yescharacteristic
253C22×C4C2×D4×C15111yescharacteristic
254C22×C4C2×D4×C15111yescharacteristic
255C2×C8—24no—
256C2×C8—24no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C42—22no—
274C42—41no—
275C42—41no—
276C42—41no—
277C42—41no—
278C42—41no—
279C42C2×D4×C15112yes—
280C42#41×C15112yes—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23C2×C22⋊C4×C15111yescharacteristic
289Q8—82no—
290D4—82no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4#104×C15112yes—
318C2×C4C4×D4×C15112yes—
319C2×C4#121×C15112yes—
320C2×C4#124×C15111yescharacteristic
321C2×C4#127×C15111yescharacteristic
322C8—44no—
323C8—44no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22#390×C15111yescharacteristic
332C22#413×C15111yescharacteristic
333C22#413×C15111yescharacteristic
334C22C2×#104×C15111yescharacteristic
335C22#421×C15111yescharacteristic
336C22#421×C15111yescharacteristic
337C22#421×C15111yescharacteristic
338C4—22no—
339C4—22no—
340C4—21no—
341C4—21no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—81no—
349C2—161no—
350C2#1529×C15111yescharacteristic
351C2#1532×C15111yescharacteristic
352C2#1535×C15111yescharacteristic
353C2#1535×C15111yescharacteristic
354C2#1963×C15111yescharacteristic
355C2#1967×C15111yescharacteristic
356C2#1980×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C43×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1767×C151C2semidirect
3. #1745×C151C2semidirect
4. C2×#330×C151C2semidirect
178. #9688C151direct (N × H)
179. C151#9688direct (N × H)
181. #1767C2×C151semidirect
182. #1745C2×C151semidirect
183. C2×#330C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2861×C1512
#1767×C1512
#1745×C1512
C2×#330×C1512
C2×#329×C1512
#9688151