Finite Group Databasebeta

← C151×#24318 #50329243

Subgroups — C151×#24318 #50329243

Order 38656.

1014 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3501×C151C211yesmaximal, characteristic
2#3078×C151C212yesmaximal, complemented
3#2326×C151C211yesmaximal, characteristic
4#2060×C151C212yesmaximal, complemented
5#2028×C151C212yesmaximal, complemented
6#1995×C151C212yesmaximal, complemented
7#1885×C151C212yesmaximal
8#1856×C151C212yesmaximal
9#1800×C151C211yesmaximal, characteristic
10#554×C151—22no—
11#554×C151—24no—
12D4×Q8×C151—22no—
13#544×C151C2212yes—
14#543×C151—22no—
15#533×C151C2212yes—
16C2×#124×C151C2211yescharacteristic
17C2×C22⋊Q8×C151—22no—
18#518×C151C2212yes—
19C2×C4×Q8×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21#479×C151—24no—
22#477×C151—22no—
23#475×C151—22no—
24#428×C151C2214yes—
25#423×C151C2212yes—
26#419×C151C2214yes—
27C2×#100×C151C2212yes—
28#391×C151C2211yescharacteristic
29#390×C151C2211yescharacteristic
30#388×C151—22no—
31#385×C151—22no—
32#384×C151C2211yescharacteristic
33#376×C151C2211yescharacteristic
34#343×C151C2212yes—
35#339×C151C2214yes—
36#339×C151C2214yes—
37C22×Q8×C151—22no—
38C22×Q8×C151C2311yescharacteristic
39C22×D4×C151C2311yescharacteristic
40C23×C4×C151D412yes—
41C2×M16×C151C2314yes—
42C4⋊Q8×C151—24no—
43C4⋊Q8×C151D412yes—
44C4⋊Q8×C151D412yes—
45#125×C151—24no—
46#125×C151D414yes—
47#124×C151—22no—
48#124×C151Q814yescomplemented
49C22⋊Q8×C151—24no—
50C22⋊Q8×C151—24no—
51C22⋊Q8×C151—28no—
52C22⋊Q8×C151—28no—
53C22⋊Q8×C151—22no—
54C22⋊Q8×C151—24no—
55C22⋊Q8×C151—22no—
56C4×Q8×C151—22no—
57C4×Q8×C151—22no—
58C4×Q8×C151—22no—
59C4×Q8×C151—22no—
60C4×D4×C151—24no—
61C4×D4×C151—24no—
62C4×D4×C151—22no—
63C4×D4×C151—22no—
64#117×C151C2314yes—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151—24no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C22⋊C4×C151—22no—
72C2×C22⋊C4×C151—24no—
73C2×C22⋊C4×C151—22no—
74C2×C22⋊C4×C151D412yes—
75C2×C42×C151—21no—
76C2×C42×C151C2311yescharacteristic
77C2×C42×C151C2311yescharacteristic
78C2×C42×C151C2311yescharacteristic
79#107×C151—24no—
80#106×C151—24no—
81C4⋊C8×C151—22no—
82C4⋊C8×C151—22no—
83#103×C151—24no—
84#103×C151—24no—
85#100×C151—24no—
86#95×C151—21no—
87#95×C151—21no—
88#95×C151—22no—
89C24×C151C2×D412yes—
90C2×Q8×C151—24no—
91C2×Q8×C151—22no—
92C2×Q8×C151—22no—
93C2×Q8×C151—21no—
94C2×Q8×C151—22no—
95C2×Q8×C151—22no—
96C2×Q8×C151—84no—
97C2×Q8×C151C2×Q812yescomplemented
98C2×D4×C151—22no—
99C2×D4×C151—22no—
100C2×D4×C151C2×Q812yes—
101C2×D4×C151#4112yes—
102C22×C4×C151—21no—
103C22×C4×C151—21no—
104C22×C4×C151—24no—
105C22×C4×C151—24no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—21no—
109C22×C4×C151—21no—
110C22×C4×C151—82no—
111C22×C4×C151C2×D412yes—
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2×D411yescharacteristic
114C22×C4×C151C2411yescharacteristic
115M16×C151—24no—
116M16×C151—24no—
117C2×C8×C151—24no—
118C4⋊C4×C151—24no—
119C4⋊C4×C151—28no—
120C4⋊C4×C151—24no—
121C4⋊C4×C151—22no—
122C4⋊C4×C151—24no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—22no—
125C4⋊C4×C151—22no—
126C4⋊C4×C151—41no—
127C4⋊C4×C151—41no—
128C4⋊C4×C151—82no—
129C4⋊C4×C151C2×D414yes—
130C4⋊C4×C151C2×D414yes—
131C22⋊C4×C151—28no—
132C22⋊C4×C151—28no—
133C22⋊C4×C151—24no—
134C22⋊C4×C151—24no—
135C22⋊C4×C151—82no—
136C42×C151—24no—
137C42×C151—21no—
138C42×C151—22no—
139C42×C151—42no—
140C42×C151C2×D412yes—
141C42×C151C2×D412yes—
142C42×C151C2×Q812yescomplemented
143C23×C151—22no—
144C23×C151—22no—
145C23×C151—42no—
146C23×C151—42no—
147C23×C151C22⋊Q814yes—
148C23×C151C22×D411yescharacteristic
149Q8×C151—24no—
150Q8×C151—44no—
151Q8×C151—42no—
152Q8×C151—82no—
153Q8×C151—84no—
154D4×C151—24no—
155D4×C151—24no—
156C2×C4×C151—24no—
157C2×C4×C151—22no—
158C2×C4×C151—24no—
159C2×C4×C151—22no—
160C2×C4×C151—22no—
161C2×C4×C151—41no—
162C2×C4×C151—41no—
163C2×C4×C151—44no—
164C2×C4×C151—41no—
165C2×C4×C151—41no—
166C2×C4×C151—41no—
167C2×C4×C151—41no—
168C2×C4×C151—42no—
169C2×C4×C151—41no—
170C2×C4×C151—42no—
171C2×C4×C151—41no—
172C2×C4×C151—41no—
173C2×C4×C151—41no—
174C2×C4×C151—82no—
175C2×C4×C151—84no—
176C2×C4×C151—84no—
177C2×C4×C151#12011yescharacteristic
178C2×C4×C151#12012yes—
179C2×C4×C151#12011yescharacteristic
180C2×C4×C151C22×D412yes—
181C2×C4×C151C22×Q811yescharacteristic
182C2×C4×C151C2×#4111yescharacteristic
183C2×C4×C1512−1+412yes—
184C8×C151—44no—
185C22×C151—21no—
186C22×C151—21no—
187C22×C151—24no—
188C22×C151—44no—
189C22×C151—42no—
190C22×C151—42no—
191C22×C151—82no—
192C22×C151C2×#12011yescharacteristic
193C22×C151C2×C22⋊Q811yescharacteristic
194C22×C151#53611yescharacteristic
195C4×C151—21no—
196C4×C151—21no—
197C4×C151—22no—
198C4×C151—42no—
199C4×C151—42no—
200C4×C151—42no—
201C4×C151—44no—
202C4×C151—44no—
203C4×C151—81no—
204C4×C151—81no—
205C4×C151#54812yes—
206C4×C151D4×Q812yes—
207C2×C151—21no—
208C2×C151—21no—
209C2×C151—44no—
210C2×C151#240911yescharacteristic
211C2×C151#301911yescharacteristic
212C2×C151#302211yescharacteristic
213#24318C15111yesmaximal, characteristic, direct product factor, Sylow
214C151#2431811yescharacteristic, direct product factor, Sylow
215#3501C2×C15111yescharacteristic
216#3078C2×C15112yescomplemented
217#2326C2×C15111yescharacteristic
218#2060C2×C15112yescomplemented
219#2028C2×C15112yescomplemented
220#1995C2×C15112yescomplemented
221#1885C2×C15112yes—
222#1856C2×C15112yes—
223#1800C2×C15111yescharacteristic
224#554—22no—
225#554—24no—
226D4×Q8—22no—
227#544C22×C15112yes—
228#543—22no—
229#533C22×C15112yes—
230C2×#124C22×C15111yescharacteristic
231C2×C22⋊Q8—22no—
232#518C22×C15112yes—
233C2×C4×Q8C22×C15111yescharacteristic
234C2×C4×D4C22×C15111yescharacteristic
235#479—24no—
236#477—22no—
237#475—22no—
238#428C22×C15114yes—
239#423C22×C15112yes—
240#419C22×C15114yes—
241C2×#100C22×C15112yes—
242#391C22×C15111yescharacteristic
243#390C22×C15111yescharacteristic
244#388—22no—
245#385—22no—
246#384C22×C15111yescharacteristic
247#376C22×C15111yescharacteristic
248#343C22×C15112yes—
249#339C22×C15114yes—
250#339C22×C15114yes—
251C22×Q8—22no—
252C22×Q8C23×C15111yescharacteristic
253C22×D4C23×C15111yescharacteristic
254C23×C4D4×C15112yes—
255C2×M16C23×C15114yes—
256C4⋊Q8—24no—
257C4⋊Q8D4×C15112yes—
258C4⋊Q8D4×C15112yes—
259#125—24no—
260#125D4×C15114yes—
261#124—22no—
262#124Q8×C15114yescomplemented
263C22⋊Q8—24no—
264C22⋊Q8—24no—
265C22⋊Q8—28no—
266C22⋊Q8—28no—
267C22⋊Q8—22no—
268C22⋊Q8—24no—
269C22⋊Q8—22no—
270C4×Q8—22no—
271C4×Q8—22no—
272C4×Q8—22no—
273C4×Q8—22no—
274C4×D4—24no—
275C4×D4—24no—
276C4×D4—22no—
277C4×D4—22no—
278#117C23×C15114yes—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4C23×C15111yescharacteristic
284C2×C4⋊C4C23×C15111yescharacteristic
285C2×C22⋊C4—24no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4D4×C15112yes—
289C2×C42—21no—
290C2×C42C23×C15111yescharacteristic
291C2×C42C23×C15111yescharacteristic
292C2×C42C23×C15111yescharacteristic
293#107—24no—
294#106—24no—
295C4⋊C8—22no—
296C4⋊C8—22no—
297#103—24no—
298#103—24no—
299#100—24no—
300#95—21no—
301#95—21no—
302#95—22no—
303C24C2×D4×C15112yes—
304C2×Q8—24no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—21no—
308C2×Q8—22no—
309C2×Q8—22no—
310C2×Q8—84no—
311C2×Q8C2×Q8×C15112yescomplemented
312C2×D4—22no—
313C2×D4—22no—
314C2×D4C2×Q8×C15112yes—
315C2×D4#41×C15112yes—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—24no—
319C22×C4—24no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—82no—
325C22×C4C2×D4×C15112yes—
326C22×C4C2×D4×C15111yescharacteristic
327C22×C4C2×D4×C15111yescharacteristic
328C22×C4C24×C15111yescharacteristic
329M16—24no—
330M16—24no—
331C2×C8—24no—
332C4⋊C4—24no—
333C4⋊C4—28no—
334C4⋊C4—24no—
335C4⋊C4—22no—
336C4⋊C4—24no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—82no—
343C4⋊C4C2×D4×C15114yes—
344C4⋊C4C2×D4×C15114yes—
345C22⋊C4—28no—
346C22⋊C4—28no—
347C22⋊C4—24no—
348C22⋊C4—24no—
349C22⋊C4—82no—
350C42—24no—
351C42—21no—
352C42—22no—
353C42—42no—
354C42C2×D4×C15112yes—
355C42C2×D4×C15112yes—
356C42C2×Q8×C15112yescomplemented
357C23—22no—
358C23—22no—
359C23—42no—
360C23—42no—
361C23C22⋊Q8×C15114yes—
362C23C22×D4×C15111yescharacteristic
363Q8—24no—
364Q8—44no—
365Q8—42no—
366Q8—82no—
367Q8—84no—
368D4—24no—
369D4—24no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—44no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—82no—
389C2×C4—84no—
390C2×C4—84no—
391C2×C4#120×C15112yes—
392C2×C4#120×C15111yescharacteristic
393C2×C4#120×C15111yescharacteristic
394C2×C4C22×D4×C15112yes—
395C2×C4C22×Q8×C15111yescharacteristic
396C2×C4C2×#41×C15111yescharacteristic
397C2×C42−1+4×C15112yes—
398C8—44no—
399C22—21no—
400C22—21no—
401C22—24no—
402C22—44no—
403C22—42no—
404C22—42no—
405C22—82no—
406C22C2×#120×C15111yescharacteristic
407C22C2×C22⋊Q8×C15111yescharacteristic
408C22#536×C15111yescharacteristic
409C4—21no—
410C4—21no—
411C4—22no—
412C4—42no—
413C4—42no—
414C4—42no—
415C4—44no—
416C4—44no—
417C4—81no—
418C4—81no—
419C4#548×C15112yes—
420C4D4×Q8×C15112yes—
421C2—21no—
422C2—21no—
423C2—44no—
424C2#2409×C15111yescharacteristic
425C2#3019×C15111yescharacteristic
426C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3078×C151C2semidirect
4. #2060×C151C2semidirect
5. #2028×C151C2semidirect
6. #1995×C151C2semidirect
48. #124×C151Q8semidirect
97. C2×Q8×C151C2×Q8semidirect
142. C42×C151C2×Q8semidirect
213. #24318C151direct (N × H)
214. C151#24318direct (N × H)
216. #3078C2×C151semidirect
218. #2060C2×C151semidirect
219. #2028C2×C151semidirect
220. #1995C2×C151semidirect
262. #124Q8×C151semidirect
311. C2×Q8C2×Q8×C151semidirect
356. C42C2×Q8×C151semidirect

Maximal subgroups

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

subgroupindex
#3501×C1512
#3078×C1512
#2326×C1512
#2060×C1512
#2028×C1512
#1995×C1512
#1885×C1512
#1856×C1512
#1800×C1512
#24318151