Finite Group Databasebeta

← C151×#18652 #50323577

Subgroups — C151×#18652 #50323577

Order 38656.

938 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3503×C151C211yesmaximal, characteristic
2#3229×C151C211yesmaximal, characteristic, complemented
3C2×#498×C151C211yesmaximal, characteristic, complemented
4#3039×C151C211yesmaximal, characteristic
5#1653×C151C214yesmaximal, complemented
6#1651×C151C214yesmaximal, complemented
7#1549×C151C211yesmaximal, characteristic, complemented
8#1493×C151C211yesmaximal, characteristic, complemented
9#1476×C151C211yesmaximal, characteristic
10C2×#137×C151—21no—
11Q82×C151—21no—
12#557×C151C2212yes—
13#554×C151—21no—
14#554×C151—22no—
15D4×Q8×C151—22no—
16D4×Q8×C151C2212yes—
17#544×C151—22no—
18#544×C151—21no—
19#533×C151—21no—
20#533×C151C2211yescharacteristic
21C2×C4⋊Q8×C151—21no—
22C2×C4⋊Q8×C151C2211yescharacteristic
23C2×C4⋊Q8×C151C2211yescharacteristic
24#520×C151—21no—
25C4×#41×C151C2211yescharacteristic
26#498×C151—22no—
27#498×C151—21no—
28#498×C151C2214yes—
29#487×C151—21no—
30#483×C151—22no—
31#475×C151C2214yes—
32#462×C151—21no—
33#462×C151C2212yes—
34#461×C151—21no—
35#461×C151C2212yes—
36#431×C151C2211yescharacteristic
37C2×#106×C151—22no—
38#423×C151C2211yescharacteristic
39#419×C151—21no—
40C2×C4×C8×C151C2211yescharacteristic
41#332×C151C2214yes—
42Q8⋊C8×C151C2214yes—
43Q8⋊C8×C151C2212yes—
44D4⋊C8×C151C2212yes—
45C2×#41×C151D411yescharacteristic
46C22×Q8×C151—21no—
47C22×Q8×C151—22no—
48C22×Q8×C151—21no—
49#137×C151—44no—
50C2×Q16×C151—22no—
51C2×SD16×C151—22no—
52C2×M16×C151—21no—
53C22×C8×C151—21no—
54C4⋊Q8×C151—22no—
55C4⋊Q8×C151—22no—
56C4⋊Q8×C151—24no—
57C4⋊Q8×C151—22no—
58C4⋊Q8×C151—21no—
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151—21no—
61C4⋊Q8×C151—22no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151D412yes—
65C4⋊Q8×C151D411yescharacteristic
66C4⋊Q8×C151D411yescharacteristic
67C4⋊Q8×C151C2312yes—
68C4⋊Q8×C151C2312yes—
69#125×C151—22no—
70#125×C151—24no—
71#125×C151—22no—
72#125×C151—21no—
73C22⋊Q8×C151—22no—
74C22⋊Q8×C151—24no—
75C22⋊Q8×C151—24no—
76C22⋊Q8×C151—21no—
77C22⋊Q8×C151—22no—
78C22⋊Q8×C151—24no—
79C22⋊Q8×C151D412yes—
80C4×Q8×C151—22no—
81C4×Q8×C151—22no—
82C4×Q8×C151—21no—
83C4×Q8×C151—22no—
84C4×Q8×C151D411yescharacteristic
85C4×Q8×C151C2311yescharacteristic
86C4×Q8×C151C2312yes—
87C4×D4×C151—24no—
88C4×D4×C151—22no—
89C4×D4×C151—21no—
90C4×D4×C151—21no—
91C4×D4×C151D411yescharacteristic
92C4×D4×C151C2311yescharacteristic
93#117×C151—22no—
94#117×C151—21no—
95#117×C151—21no—
96#117×C151D411yescharacteristic
97C2×C4⋊C4×C151—22no—
98C2×C4⋊C4×C151—22no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151D412yes—
103C2×C42×C151—21no—
104C2×C42×C151C2311yescharacteristic
105#106×C151—28no—
106#106×C151—24no—
107C4⋊C8×C151—21no—
108C4⋊C8×C151C2312yes—
109C4⋊C8×C151C2312yes—
110#103×C151—22no—
111#103×C151—22no—
112#103×C151—24no—
113C22⋊C8×C151—21no—
114C4×C8×C151—21no—
115C4×C8×C151—21no—
116C4×C8×C151C2312yes—
117#41×C151—22no—
118#41×C151SD1614yes—
119C2×Q8×C151—24no—
120C2×Q8×C151—21no—
121C2×Q8×C151—22no—
122C2×Q8×C151—22no—
123C2×Q8×C151—22no—
124C2×Q8×C151—41no—
125C2×Q8×C151—42no—
126C2×Q8×C151—42no—
127C2×Q8×C151—82no—
128C2×Q8×C151—84no—
129C2×Q8×C151C2×D412yes—
130C2×Q8×C151C2×D411yescharacteristic
131C2×D4×C151—21no—
132C2×D4×C151C2×D411yescharacteristic
133C22×C4×C151—21no—
134C22×C4×C151—24no—
135C22×C4×C151—22no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—41no—
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142Q16×C151—44no—
143SD16×C151—44no—
144M16×C151—42no—
145C2×C8×C151—24no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—22no—
149C4⋊C4×C151—24no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—24no—
152C4⋊C4×C151—24no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—41no—
166C4⋊C4×C151—41no—
167C4⋊C4×C151C2×D411yescharacteristic
168C4⋊C4×C151C2×D411yescharacteristic
169C4⋊C4×C151C2×D414yes—
170C4⋊C4×C151C2×D412yes—
171C22⋊C4×C151—24no—
172C22⋊C4×C151—22no—
173C22⋊C4×C151—21no—
174C22⋊C4×C151—21no—
175C22⋊C4×C151—21no—
176C42×C151—24no—
177C42×C151—21no—
178C42×C151—21no—
179C42×C151—21no—
180C42×C151—22no—
181C42×C151C2×D411yescharacteristic
182C42×C151C2×D411yescharacteristic
183C42×C151C2×D411yescharacteristic
184C42×C151C2411yescharacteristic
185C23×C151—21no—
186C23×C151#12011yescharacteristic
187Q8×C151—21no—
188Q8×C151—24no—
189Q8×C151—44no—
190Q8×C151—42no—
191Q8×C151—42no—
192Q8×C151—42no—
193Q8×C151—82no—
194Q8×C151—84no—
195Q8×C151—82no—
196Q8×C151C2×SD1612yes—
197D4×C151—24no—
198D4×C151—21no—
199D4×C151C2×SD1612yes—
200C2×C4×C151—21no—
201C2×C4×C151—22no—
202C2×C4×C151—24no—
203C2×C4×C151—22no—
204C2×C4×C151—21no—
205C2×C4×C151—24no—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—21no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—82no—
213C2×C4×C151—84no—
214C2×C4×C151—82no—
215C2×C4×C151#12011yescharacteristic
216C2×C4×C151#12011yescharacteristic
217C2×C4×C151#12011yescharacteristic
218C2×C4×C151C2×SD1612yes—
219C2×C4×C151#13712yes—
220C2×C4×C151C22×D411yescharacteristic
221C2×C4×C151C22×D411yescharacteristic
222C2×C4×C151C22×D411yescharacteristic
223C8×C151—24no—
224C8×C151—42no—
225C8×C151—42no—
226C22×C151—21no—
227C22×C151—21no—
228C22×C151—22no—
229C22×C151—41no—
230C22×C151—41no—
231C22×C151#44812yes—
232C22×C151C2×#12011yescharacteristic
233C4×C151—22no—
234C4×C151—21no—
235C4×C151—21no—
236C4×C151—41no—
237C4×C151—42no—
238C4×C151—44no—
239C4×C151—41no—
240C4×C151—42no—
241C4×C151—82no—
242C4×C151#44812yes—
243C4×C151#45612yes—
244C4×C151C22×SD1611yescharacteristic
245C4×C151C2×#13711yescharacteristic
246C4×C151#57712yes—
247C2×C151—22no—
248C2×C151—42no—
249C2×C151C2×#44811yescharacteristic
250C2×C151#300911yescharacteristic
251C2×C151C2×#45611yescharacteristic
252#18652C15111yesmaximal, characteristic, direct product factor, Sylow
253C151#1865211yescharacteristic, direct product factor, Sylow
254#3503C2×C15111yescharacteristic
255#3229C2×C15111yescharacteristic, complemented
256C2×#498C2×C15111yescharacteristic, complemented
257#3039C2×C15111yescharacteristic
258#1653C2×C15114yescomplemented
259#1651C2×C15114yescomplemented
260#1549C2×C15111yescharacteristic, complemented
261#1493C2×C15111yescharacteristic, complemented
262#1476C2×C15111yescharacteristic
263C2×#137—21no—
264Q82—21no—
265#557C22×C15112yes—
266#554—21no—
267#554—22no—
268D4×Q8—22no—
269D4×Q8C22×C15112yes—
270#544—22no—
271#544—21no—
272#533—21no—
273#533C22×C15111yescharacteristic
274C2×C4⋊Q8—21no—
275C2×C4⋊Q8C22×C15111yescharacteristic
276C2×C4⋊Q8C22×C15111yescharacteristic
277#520—21no—
278C4×#41C22×C15111yescharacteristic
279#498—22no—
280#498—21no—
281#498C22×C15114yes—
282#487—21no—
283#483—22no—
284#475C22×C15114yes—
285#462—21no—
286#462C22×C15112yes—
287#461—21no—
288#461C22×C15112yes—
289#431C22×C15111yescharacteristic
290C2×#106—22no—
291#423C22×C15111yescharacteristic
292#419—21no—
293C2×C4×C8C22×C15111yescharacteristic
294#332C22×C15114yes—
295Q8⋊C8C22×C15114yes—
296Q8⋊C8C22×C15112yes—
297D4⋊C8C22×C15112yes—
298C2×#41D4×C15111yescharacteristic
299C22×Q8—22no—
300C22×Q8—21no—
301C22×Q8—21no—
302#137—44no—
303C2×Q16—22no—
304C2×SD16—22no—
305C2×M16—21no—
306C22×C8—21no—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8—24no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8D4×C15111yescharacteristic
318C4⋊Q8D4×C15112yes—
319C4⋊Q8D4×C15111yescharacteristic
320C4⋊Q8C23×C15112yes—
321C4⋊Q8C23×C15112yes—
322#125—22no—
323#125—24no—
324#125—22no—
325#125—21no—
326C22⋊Q8—22no—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329C22⋊Q8—21no—
330C22⋊Q8—22no—
331C22⋊Q8—24no—
332C22⋊Q8D4×C15112yes—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—21no—
337C4×Q8D4×C15111yescharacteristic
338C4×Q8C23×C15111yescharacteristic
339C4×Q8C23×C15112yes—
340C4×D4—24no—
341C4×D4—22no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4D4×C15111yescharacteristic
345C4×D4C23×C15111yescharacteristic
346#117—22no—
347#117—21no—
348#117—21no—
349#117D4×C15111yescharacteristic
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4D4×C15112yes—
356C2×C42—21no—
357C2×C42C23×C15111yescharacteristic
358#106—28no—
359#106—24no—
360C4⋊C8—21no—
361C4⋊C8C23×C15112yes—
362C4⋊C8C23×C15112yes—
363#103—24no—
364#103—22no—
365#103—22no—
366C22⋊C8—21no—
367C4×C8—21no—
368C4×C8—21no—
369C4×C8C23×C15112yes—
370#41—22no—
371#41SD16×C15114yes—
372C2×Q8—24no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—41no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×Q8—82no—
381C2×Q8—84no—
382C2×Q8C2×D4×C15112yes—
383C2×Q8C2×D4×C15111yescharacteristic
384C2×D4—21no—
385C2×D4C2×D4×C15111yescharacteristic
386C22×C4—21no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—41no—
392C22×C4C2×D4×C15111yescharacteristic
393C22×C4C2×D4×C15111yescharacteristic
394C22×C4C2×D4×C15111yescharacteristic
395Q16—44no—
396SD16—44no—
397M16—42no—
398C2×C8—24no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4C2×D4×C15111yescharacteristic
421C4⋊C4C2×D4×C15111yescharacteristic
422C4⋊C4C2×D4×C15114yes—
423C4⋊C4C2×D4×C15112yes—
424C22⋊C4—24no—
425C22⋊C4—22no—
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—21no—
429C42—24no—
430C42—21no—
431C42—21no—
432C42—21no—
433C42—22no—
434C42C2×D4×C15111yescharacteristic
435C42C2×D4×C15111yescharacteristic
436C42C2×D4×C15111yescharacteristic
437C42C24×C15111yescharacteristic
438C23—21no—
439C23#120×C15111yescharacteristic
440Q8—21no—
441Q8—24no—
442Q8—42no—
443Q8—44no—
444Q8—42no—
445Q8—42no—
446Q8—82no—
447Q8—84no—
448Q8—82no—
449Q8C2×SD16×C15112yes—
450D4—24no—
451D4—21no—
452D4C2×SD16×C15112yes—
453C2×C4—21no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—82no—
466C2×C4—84no—
467C2×C4—82no—
468C2×C4#120×C15111yescharacteristic
469C2×C4#120×C15111yescharacteristic
470C2×C4#120×C15111yescharacteristic
471C2×C4C2×SD16×C15112yes—
472C2×C4#137×C15112yes—
473C2×C4C22×D4×C15111yescharacteristic
474C2×C4C22×D4×C15111yescharacteristic
475C2×C4C22×D4×C15111yescharacteristic
476C8—24no—
477C8—42no—
478C8—42no—
479C22—21no—
480C22—21no—
481C22—22no—
482C22—41no—
483C22—41no—
484C22#448×C15112yes—
485C22C2×#120×C15111yescharacteristic
486C4—22no—
487C4—21no—
488C4—21no—
489C4—41no—
490C4—42no—
491C4—44no—
492C4—41no—
493C4—42no—
494C4—82no—
495C4#448×C15112yes—
496C4#456×C15112yes—
497C4C22×SD16×C15111yescharacteristic
498C4C2×#137×C15111yescharacteristic
499C4#577×C15112yes—
500C2—22no—
501C2—42no—
502C2C2×#448×C15111yescharacteristic
503C2#3009×C15111yescharacteristic
504C2C2×#456×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#41×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3229×C151C2semidirect
3. C2×#498×C151C2semidirect
5. #1653×C151C2semidirect
6. #1651×C151C2semidirect
7. #1549×C151C2semidirect
8. #1493×C151C2semidirect
252. #18652C151direct (N × H)
253. C151#18652direct (N × H)
255. #3229C2×C151semidirect
256. C2×#498C2×C151semidirect
258. #1653C2×C151semidirect
259. #1651C2×C151semidirect
260. #1549C2×C151semidirect
261. #1493C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3503×C1512
#3229×C1512
C2×#498×C1512
#3039×C1512
#1653×C1512
#1651×C1512
#1549×C1512
#1493×C1512
#1476×C1512
#18652151