Finite Group Databasebeta

← C151×#23747 #50328672

Subgroups — C151×#23747 #50328672

Order 38656.

858 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C151C211yesmaximal, characteristic
2#2285×C151C211yesmaximal, characteristic
3#2101×C151C214yesmaximal, complemented
4#2100×C151C212yesmaximal, complemented
5#2099×C151C212yesmaximal, complemented
6#1736×C151C212yesmaximal
7#1736×C151C212yesmaximal
8#1728×C151C211yesmaximal, characteristic
9C22×M16×C151C2212yes—
10C2×#117×C151C2212yes—
11C22×C4⋊C4×C151—21no—
12C22×C4⋊C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C42×C151C2211yescharacteristic
15#389×C151—21no—
16#389×C151—21no—
17#389×C151C2212yes—
18#389×C151C2212yes—
19#384×C151C2211yescharacteristic
20#384×C151C2211yescharacteristic
21#382×C151C2212yes—
22#380×C151—21no—
23#380×C151—21no—
24C4×C4⋊C4×C151—21no—
25C4×C4⋊C4×C151—21no—
26C2×#95×C151—21no—
27#340×C151C2214yes—
28#340×C151C2214yes—
29#340×C151C2214yes—
30#340×C151C2214yes—
31#336×C151C2212yes—
32#336×C151C2212yes—
33C23×C4×C151—21no—
34C23×C4×C151—21no—
35C23×C4×C151D411yescharacteristic
36C23×C4×C151D411yescharacteristic
37C23×C4×C151C2311yescharacteristic
38C2×M16×C151—24no—
39C2×M16×C151—24no—
40C2×M16×C151—24no—
41C22×C8×C151C2314yes—
42#117×C151—28no—
43C2×C4⋊C4×C151—21no—
44C2×C4⋊C4×C151—22no—
45C2×C4⋊C4×C151—24no—
46C2×C4⋊C4×C151—21no—
47C2×C4⋊C4×C151—21no—
48C2×C4⋊C4×C151—21no—
49C2×C4⋊C4×C151—21no—
50C2×C4⋊C4×C151—21no—
51C2×C4⋊C4×C151—22no—
52C2×C4⋊C4×C151—22no—
53C2×C4⋊C4×C151—44no—
54C2×C4⋊C4×C151Q814yes—
55C2×C4⋊C4×C151C2312yes—
56C2×C4⋊C4×C151C2312yes—
57C2×C4⋊C4×C151C2312yes—
58C2×C4⋊C4×C151C2312yes—
59C2×C22⋊C4×C151—22no—
60C2×C42×C151—24no—
61C2×C42×C151—22no—
62C2×C42×C151D411yescharacteristic
63C2×C42×C151D411yescharacteristic
64C2×C42×C151C2311yescharacteristic
65C2×C42×C151C2311yescharacteristic
66#95×C151—22no—
67#95×C151—22no—
68#95×C151—22no—
69#95×C151—22no—
70C24×C151C2×D411yescharacteristic
71C22×C4×C151—24no—
72C22×C4×C151—22no—
73C22×C4×C151—22no—
74C22×C4×C151—22no—
75C22×C4×C151—22no—
76C22×C4×C151—22no—
77C22×C4×C151—22no—
78C22×C4×C151—22no—
79C22×C4×C151—22no—
80C22×C4×C151—41no—
81C22×C4×C151—41no—
82C22×C4×C151—42no—
83C22×C4×C151—42no—
84C22×C4×C151—42no—
85C22×C4×C151—42no—
86C22×C4×C151—42no—
87C22×C4×C151C2×D411yescharacteristic
88C22×C4×C151C2×D411yescharacteristic
89C22×C4×C151C2×D411yescharacteristic
90C22×C4×C151C2×D411yescharacteristic
91C22×C4×C151C2×D411yescharacteristic
92C22×C4×C151C2×Q812yes—
93C22×C4×C151#4112yes—
94C22×C4×C151#4114yes—
95C22×C4×C151#4114yes—
96C22×C4×C151C2411yescharacteristic
97M16×C151—48no—
98C2×C8×C151—24no—
99C2×C8×C151—24no—
100C2×C8×C151—24no—
101C4⋊C4×C151—24no—
102C4⋊C4×C151—22no—
103C4⋊C4×C151—24no—
104C4⋊C4×C151—24no—
105C4⋊C4×C151—24no—
106C4⋊C4×C151—42no—
107C4⋊C4×C151—42no—
108C4⋊C4×C151—44no—
109C4⋊C4×C151—42no—
110C4⋊C4×C151—42no—
111C4⋊C4×C151—44no—
112C4⋊C4×C151—42no—
113C4⋊C4×C151C2×Q814yes—
114C22⋊C4×C151—44no—
115C42×C151—22no—
116C42×C151—22no—
117C42×C151—22no—
118C42×C151—22no—
119C42×C151—44no—
120C23×C151—21no—
121C23×C151—21no—
122C23×C151—21no—
123C23×C151—21no—
124C23×C151C22⋊Q812yes—
125C23×C151#12312yes—
126C23×C151#12412yes—
127C23×C151C22×D411yescharacteristic
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—24no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—44no—
140C2×C4×C151—44no—
141C2×C4×C151—48no—
142C2×C4×C151—42no—
143C2×C4×C151—42no—
144C2×C4×C151—42no—
145C2×C4×C151—42no—
146C2×C4×C151—42no—
147C2×C4×C151—42no—
148C2×C4×C151—42no—
149C2×C4×C151—42no—
150C2×C4×C151—42no—
151C2×C4×C151—42no—
152C2×C4×C151—42no—
153C2×C4×C151—84no—
154C2×C4×C151C22⋊Q812yes—
155C2×C4×C151#12312yes—
156C2×C4×C151#12412yes—
157C2×C4×C151#12518yes—
158C2×C4×C151#12618yes—
159C2×C4×C151AGL(1,ℤ/8)12yes—
160C2×C4×C151#13712yes—
161C2×C4×C151C22×Q811yescharacteristic
162C2×C4×C151C2×#4112yes—
163C2×C4×C151C2×#4112yes—
164C2×C4×C151C2×#4111yescharacteristic
165C8×C151—44no—
166C22×C151—22no—
167C22×C151—22no—
168C22×C151—22no—
169C22×C151—22no—
170C22×C151—22no—
171C22×C151—22no—
172C22×C151#40014yes—
173C22×C151C2×C22⋊Q811yescharacteristic
174C22×C151C2×#12311yescharacteristic
175C22×C151C2×#12411yescharacteristic
176C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
177C22×C151C2×#13711yescharacteristic
178C22×C151#57511yescharacteristic
179C22×C151#57511yescharacteristic
180C4×C151—22no—
181C4×C151—22no—
182C4×C151—44no—
183C4×C151—41no—
184C4×C151—41no—
185C4×C151—82no—
186C4×C151—82no—
187C4×C151—82no—
188C4×C151#40014yes—
189C4×C151C2×#12512yes—
190C4×C151C2×#12612yes—
191C2×C151—24no—
192C2×C151C2×#40011yescharacteristic
193C2×C151#307711yescharacteristic
194C2×C151#307811yescharacteristic
195C2×C151#309411yescharacteristic
196C2×C151#309511yescharacteristic
197C2×C151#314111yescharacteristic
198C2×C151#314211yescharacteristic
199#23747C15111yesmaximal, characteristic, direct product factor, Sylow
200C151#2374711yescharacteristic, direct product factor, Sylow
201C2×#389C2×C15111yescharacteristic
202#2285C2×C15111yescharacteristic
203#2101C2×C15114yescomplemented
204#2100C2×C15112yescomplemented
205#2099C2×C15112yescomplemented
206#1736C2×C15112yes—
207#1736C2×C15112yes—
208#1728C2×C15111yescharacteristic
209C22×M16C22×C15112yes—
210C2×#117C22×C15112yes—
211C22×C4⋊C4—21no—
212C22×C4⋊C4C22×C15111yescharacteristic
213C22×C4⋊C4C22×C15111yescharacteristic
214C22×C42C22×C15111yescharacteristic
215#389—21no—
216#389—21no—
217#389C22×C15112yes—
218#389C22×C15112yes—
219#384C22×C15111yescharacteristic
220#384C22×C15111yescharacteristic
221#382C22×C15112yes—
222#380—21no—
223#380—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C2×#95—21no—
227#340C22×C15114yes—
228#340C22×C15114yes—
229#340C22×C15114yes—
230#340C22×C15114yes—
231#336C22×C15112yes—
232#336C22×C15112yes—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4D4×C15111yescharacteristic
236C23×C4D4×C15111yescharacteristic
237C23×C4C23×C15111yescharacteristic
238C2×M16—24no—
239C2×M16—24no—
240C2×M16—24no—
241C22×C8C23×C15114yes—
242#117—28no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—44no—
254C2×C4⋊C4Q8×C15114yes—
255C2×C4⋊C4C23×C15112yes—
256C2×C4⋊C4C23×C15112yes—
257C2×C4⋊C4C23×C15112yes—
258C2×C4⋊C4C23×C15112yes—
259C2×C22⋊C4—22no—
260C2×C42—24no—
261C2×C42—22no—
262C2×C42D4×C15111yescharacteristic
263C2×C42D4×C15111yescharacteristic
264C2×C42C23×C15111yescharacteristic
265C2×C42C23×C15111yescharacteristic
266#95—22no—
267#95—22no—
268#95—22no—
269#95—22no—
270C24C2×D4×C15111yescharacteristic
271C22×C4—24no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4C2×D4×C15111yescharacteristic
288C22×C4C2×D4×C15111yescharacteristic
289C22×C4C2×D4×C15111yescharacteristic
290C22×C4C2×D4×C15111yescharacteristic
291C22×C4C2×D4×C15111yescharacteristic
292C22×C4C2×Q8×C15112yes—
293C22×C4#41×C15112yes—
294C22×C4#41×C15114yes—
295C22×C4#41×C15114yes—
296C22×C4C24×C15111yescharacteristic
297M16—48no—
298C2×C8—24no—
299C2×C8—24no—
300C2×C8—24no—
301C4⋊C4—24no—
302C4⋊C4—22no—
303C4⋊C4—24no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—44no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C4⋊C4—44no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4C2×Q8×C15114yes—
314C22⋊C4—44no—
315C42—22no—
316C42—22no—
317C42—22no—
318C42—22no—
319C42—44no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23C22⋊Q8×C15112yes—
325C23#123×C15112yes—
326C23#124×C15112yes—
327C23C22×D4×C15111yescharacteristic
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—24no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—48no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—84no—
354C2×C4C22⋊Q8×C15112yes—
355C2×C4#123×C15112yes—
356C2×C4#124×C15112yes—
357C2×C4#125×C15118yes—
358C2×C4#126×C15118yes—
359C2×C4AGL(1,ℤ/8)×C15112yes—
360C2×C4#137×C15112yes—
361C2×C4C22×Q8×C15111yescharacteristic
362C2×C4C2×#41×C15112yes—
363C2×C4C2×#41×C15112yes—
364C2×C4C2×#41×C15111yescharacteristic
365C8—44no—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22#400×C15114yes—
373C22C2×C22⋊Q8×C15111yescharacteristic
374C22C2×#123×C15111yescharacteristic
375C22C2×#124×C15111yescharacteristic
376C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
377C22C2×#137×C15111yescharacteristic
378C22#575×C15111yescharacteristic
379C22#575×C15111yescharacteristic
380C4—22no—
381C4—22no—
382C4—44no—
383C4—41no—
384C4—41no—
385C4—82no—
386C4—82no—
387C4—82no—
388C4#400×C15114yes—
389C4C2×#125×C15112yes—
390C4C2×#126×C15112yes—
391C2—24no—
392C2C2×#400×C15111yescharacteristic
393C2#3077×C15111yescharacteristic
394C2#3078×C15111yescharacteristic
395C2#3094×C15111yescharacteristic
396C2#3095×C15111yescharacteristic
397C2#3141×C15111yescharacteristic
398C2#3142×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2101×C151C2semidirect
4. #2100×C151C2semidirect
5. #2099×C151C2semidirect
199. #23747C151direct (N × H)
200. C151#23747direct (N × H)
203. #2101C2×C151semidirect
204. #2100C2×C151semidirect
205. #2099C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1512
#2285×C1512
#2101×C1512
#2100×C1512
#2099×C1512
#1736×C1512
#1728×C1512
#23747151