Finite Group Databasebeta

← C151×#24593 #50329518

Subgroups — C151×#24593 #50329518

Order 38656.

764 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C151C211yesmaximal, characteristic
2C2×#428×C151C211yesmaximal, characteristic
3#2503×C151C211yesmaximal, characteristic
4#2347×C151C211yesmaximal, characteristic
5#2085×C151C212yesmaximal, complemented
6#2068×C151C212yesmaximal, complemented
7#1949×C151C212yesmaximal, complemented
8#1927×C151C212yesmaximal, complemented
9#1894×C151C211yesmaximal, characteristic
10#1851×C151C211yesmaximal, characteristic
11#1824×C151C211yesmaximal, characteristic
12C22×M16×C151C2211yescharacteristic
13C2×C22⋊Q8×C151C2211yescharacteristic
14C2×#117×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16#485×C151—24no—
17#428×C151—24no—
18C2×#107×C151C2212yes—
19C2×#107×C151C2211yescharacteristic
20C2×#106×C151C2211yescharacteristic
21C2×#106×C151C2212yes—
22C2×C4⋊C8×C151C2212yes—
23C2×#103×C151C2212yes—
24C2×#103×C151C2211yescharacteristic
25C2×#103×C151C2211yescharacteristic
26C2×C22⋊C8×C151C2211yescharacteristic
27#400×C151—21no—
28#400×C151—21no—
29#391×C151C2212yes—
30#389×C151C2212yes—
31#388×C151—22no—
32#383×C151—21no—
33#382×C151C2212yes—
34#381×C151—22no—
35#380×C151C2211yescharacteristic
36C4×C4⋊C4×C151—21no—
37C4×C4⋊C4×C151C2212yes—
38C4×C22⋊C4×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151C2311yescharacteristic
44C23×C4×C151—21no—
45C23×C4×C151C2311yescharacteristic
46C2×M16×C151—22no—
47C2×M16×C151—24no—
48C22×C8×C151C2311yescharacteristic
49C22×C8×C151C2311yescharacteristic
50C22×C8×C151C2312yes—
51C22⋊Q8×C151—22no—
52C22⋊Q8×C151—22no—
53#117×C151—22no—
54#117×C151D414yes—
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151C2312yes—
61C2×C4⋊C4×C151C2311yescharacteristic
62C2×C4⋊C4×C151C2312yes—
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C4⋊C4×C151C2311yescharacteristic
65C2×C22⋊C4×C151—21no—
66C2×C22⋊C4×C151—21no—
67C2×C22⋊C4×C151—21no—
68C2×C22⋊C4×C151D412yes—
69C2×C42×C151—21no—
70C2×C42×C151—22no—
71C2×C42×C151C2312yes—
72#107×C151—24no—
73#107×C151—22no—
74#106×C151—24no—
75#106×C151—22no—
76C4⋊C8×C151—24no—
77#103×C151—24no—
78#103×C151—22no—
79#103×C151—22no—
80C22⋊C8×C151—22no—
81#95×C151—21no—
82#95×C151—22no—
83#95×C151—22no—
84#95×C151—22no—
85#95×C151—22no—
86#95×C151—22no—
87#95×C151—22no—
88#95×C151D411yescharacteristic
89#95×C151D411yescharacteristic
90C24×C151C2×D411yescharacteristic
91C2×Q8×C151—21no—
92C2×Q8×C151—22no—
93C2×Q8×C151—21no—
94C2×Q8×C151—22no—
95C22×C4×C151—22no—
96C22×C4×C151—22no—
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151—21no—
100C22×C4×C151—21no—
101C22×C4×C151—22no—
102C22×C4×C151—22no—
103C22×C4×C151—44no—
104C22×C4×C151—42no—
105C22×C4×C151C2×D412yes—
106C22×C4×C151C2×D412yes—
107C22×C4×C151C2×D411yescharacteristic
108C22×C4×C151C2×D412yes—
109C22×C4×C151#4112yes—
110C22×C4×C151C2411yescharacteristic
111M16×C151—28no—
112C2×C8×C151—22no—
113C2×C8×C151—22no—
114C2×C8×C151—21no—
115C2×C8×C151—21no—
116C2×C8×C151—22no—
117C2×C8×C151—22no—
118C2×C8×C151#4114yes—
119C4⋊C4×C151—21no—
120C4⋊C4×C151—21no—
121C4⋊C4×C151—22no—
122C4⋊C4×C151—21no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—22no—
125C4⋊C4×C151—21no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—44no—
128C4⋊C4×C151—42no—
129C4⋊C4×C151—42no—
130C4⋊C4×C151C2×D412yes—
131C4⋊C4×C151C2×D412yes—
132C22⋊C4×C151—24no—
133C22⋊C4×C151—42no—
134C22⋊C4×C151—42no—
135C22⋊C4×C151—81no—
136C42×C151—24no—
137C42×C151—22no—
138C42×C151—22no—
139C42×C151—82no—
140C23×C151—22no—
141C23×C151—22no—
142C23×C151—21no—
143C23×C151—21no—
144C23×C151#12112yes—
145C23×C151C22×D411yescharacteristic
146Q8×C151—41no—
147Q8×C151—41no—
148Q8×C151—42no—
149C2×C4×C151—22no—
150C2×C4×C151—22no—
151C2×C4×C151—22no—
152C2×C4×C151—24no—
153C2×C4×C151—22no—
154C2×C4×C151—22no—
155C2×C4×C151—22no—
156C2×C4×C151—22no—
157C2×C4×C151—22no—
158C2×C4×C151—22no—
159C2×C4×C151—22no—
160C2×C4×C151—22no—
161C2×C4×C151—42no—
162C2×C4×C151—41no—
163C2×C4×C151—41no—
164C2×C4×C151—41no—
165C2×C4×C151—41no—
166C2×C4×C151—42no—
167C2×C4×C151—42no—
168C2×C4×C151—42no—
169C2×C4×C151—42no—
170C2×C4×C151—44no—
171C2×C4×C151—42no—
172C2×C4×C151—41no—
173C2×C4×C151—41no—
174C2×C4×C151—84no—
175C2×C4×C151#12112yes—
176C2×C4×C151C22×D411yescharacteristic
177C2×C4×C151C2×#4112yes—
178C2×C4×C151C2×#4111yescharacteristic
179C2×C4×C1512−1+412yes—
180C8×C151—24no—
181C8×C151—41no—
182C8×C151—41no—
183C22×C151—22no—
184C22×C151—22no—
185C22×C151—22no—
186C22×C151—42no—
187C22×C151—42no—
188C22×C151C2×#12111yescharacteristic
189C22×C151#54712yes—
190C22×C151#57512yes—
191C22×C151#57711yescharacteristic
192C22×C151#57811yescharacteristic
193C4×C151—22no—
194C4×C151—42no—
195C4×C151—42no—
196C4×C151—42no—
197C4×C151—42no—
198C4×C151—82no—
199C4×C151—81no—
200C4×C151—82no—
201C4×C151—81no—
202C4×C151#52511yescharacteristic
203C4×C151#53611yescharacteristic
204C4×C151#55212yes—
205C2×C151—42no—
206C2×C151#241311yescharacteristic
207C2×C151#304011yescharacteristic
208C2×C151#304611yescharacteristic
209C2×C151#334912yes—
210C2×C151#335112yes—
211#24593C15111yesmaximal, characteristic, direct product factor, Sylow
212C151#2459311yescharacteristic, direct product factor, Sylow
213C2×#485C2×C15111yescharacteristic
214C2×#428C2×C15111yescharacteristic
215#2503C2×C15111yescharacteristic
216#2347C2×C15111yescharacteristic
217#2085C2×C15112yescomplemented
218#2068C2×C15112yescomplemented
219#1949C2×C15112yescomplemented
220#1927C2×C15112yescomplemented
221#1894C2×C15111yescharacteristic
222#1851C2×C15111yescharacteristic
223#1824C2×C15111yescharacteristic
224C22×M16C22×C15111yescharacteristic
225C2×C22⋊Q8C22×C15111yescharacteristic
226C2×#117C22×C15111yescharacteristic
227C22×C4⋊C4C22×C15111yescharacteristic
228#485—24no—
229#428—24no—
230C2×#107C22×C15111yescharacteristic
231C2×#107C22×C15112yes—
232C2×#106C22×C15111yescharacteristic
233C2×#106C22×C15112yes—
234C2×C4⋊C8C22×C15112yes—
235C2×#103C22×C15111yescharacteristic
236C2×#103C22×C15111yescharacteristic
237C2×#103C22×C15112yes—
238C2×C22⋊C8C22×C15111yescharacteristic
239#400—21no—
240#400—21no—
241#391C22×C15112yes—
242#389C22×C15112yes—
243#388—22no—
244#383—21no—
245#382C22×C15112yes—
246#381—22no—
247#380C22×C15111yescharacteristic
248C4×C4⋊C4—21no—
249C4×C4⋊C4C22×C15112yes—
250C4×C22⋊C4C22×C15111yescharacteristic
251#340C22×C15112yes—
252#340C22×C15112yes—
253#340C22×C15112yes—
254#336C22×C15112yes—
255C22×Q8C23×C15111yescharacteristic
256C23×C4—21no—
257C23×C4C23×C15111yescharacteristic
258C2×M16—22no—
259C2×M16—24no—
260C22×C8C23×C15111yescharacteristic
261C22×C8C23×C15111yescharacteristic
262C22×C8C23×C15112yes—
263C22⋊Q8—22no—
264C22⋊Q8—22no—
265#117—22no—
266#117D4×C15114yes—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4C23×C15112yes—
273C2×C4⋊C4C23×C15111yescharacteristic
274C2×C4⋊C4C23×C15112yes—
275C2×C4⋊C4C23×C15111yescharacteristic
276C2×C4⋊C4C23×C15111yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4D4×C15112yes—
281C2×C42—21no—
282C2×C42—22no—
283C2×C42C23×C15112yes—
284#107—24no—
285#107—22no—
286#106—24no—
287#106—22no—
288C4⋊C8—24no—
289#103—24no—
290#103—22no—
291#103—22no—
292C22⋊C8—22no—
293#95—21no—
294#95—22no—
295#95—22no—
296#95—22no—
297#95—22no—
298#95—22no—
299#95—22no—
300#95D4×C15111yescharacteristic
301#95D4×C15111yescharacteristic
302C24C2×D4×C15111yescharacteristic
303C2×Q8—21no—
304C2×Q8—22no—
305C2×Q8—21no—
306C2×Q8—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—44no—
316C22×C4—42no—
317C22×C4C2×D4×C15112yes—
318C22×C4C2×D4×C15112yes—
319C22×C4C2×D4×C15111yescharacteristic
320C22×C4C2×D4×C15112yes—
321C22×C4#41×C15112yes—
322C22×C4C24×C15111yescharacteristic
323M16—28no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8#41×C15114yes—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—21no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—44no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4C2×D4×C15112yes—
343C4⋊C4C2×D4×C15112yes—
344C22⋊C4—24no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C22⋊C4—81no—
348C42—24no—
349C42—22no—
350C42—22no—
351C42—82no—
352C23—22no—
353C23—22no—
354C23—21no—
355C23—21no—
356C23#121×C15112yes—
357C23C22×D4×C15111yescharacteristic
358Q8—41no—
359Q8—41no—
360Q8—42no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—24no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—84no—
387C2×C4#121×C15112yes—
388C2×C4C22×D4×C15111yescharacteristic
389C2×C4C2×#41×C15112yes—
390C2×C4C2×#41×C15111yescharacteristic
391C2×C42−1+4×C15112yes—
392C8—24no—
393C8—41no—
394C8—41no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—42no—
399C22—42no—
400C22C2×#121×C15111yescharacteristic
401C22#547×C15112yes—
402C22#575×C15112yes—
403C22#577×C15111yescharacteristic
404C22#578×C15111yescharacteristic
405C4—22no—
406C4—42no—
407C4—42no—
408C4—42no—
409C4—42no—
410C4—81no—
411C4—82no—
412C4—81no—
413C4—82no—
414C4#525×C15111yescharacteristic
415C4#536×C15111yescharacteristic
416C4#552×C15112yes—
417C2—42no—
418C2#2413×C15111yescharacteristic
419C2#3040×C15111yescharacteristic
420C2#3046×C15111yescharacteristic
421C2#3349×C15112yes—
422C2#3351×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
5. #2085×C151C2semidirect
6. #2068×C151C2semidirect
7. #1949×C151C2semidirect
8. #1927×C151C2semidirect
211. #24593C151direct (N × H)
212. C151#24593direct (N × H)
217. #2085C2×C151semidirect
218. #2068C2×C151semidirect
219. #1949C2×C151semidirect
220. #1927C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C1512
C2×#428×C1512
#2503×C1512
#2347×C1512
#2085×C1512
#2068×C1512
#1949×C1512
#1927×C1512
#1894×C1512
#1851×C1512
#1824×C1512
#24593151