Finite Group Databasebeta

← C151×#19728 #50324653

Subgroups — C151×#19728 #50324653

Order 38656.

690 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3231×C151C211yesmaximal, characteristic, complemented
2#3226×C151C211yesmaximal, characteristic
3#3210×C151C211yesmaximal, characteristic
4#3209×C151C211yesmaximal, characteristic, complemented
5#3182×C151C211yesmaximal, characteristic
6#3165×C151C211yesmaximal, characteristic, complemented
7#1723×C151C211yesmaximal, characteristic, complemented
8#1723×C151C211yesmaximal, characteristic, complemented
9#1722×C151C211yesmaximal, characteristic, complemented
10#1720×C151C211yesmaximal, characteristic, complemented
11#1718×C151C211yesmaximal, characteristic, complemented
12#1714×C151C211yesmaximal, characteristic, complemented
13#1713×C151C211yesmaximal, characteristic, complemented
14#1708×C151C211yesmaximal, characteristic, complemented
15#1453×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17#533×C151C2211yescharacteristic
18#532×C151C2211yescharacteristic
19C2×C4⋊Q8×C151C2211yescharacteristic
20#501×C151—22no—
21#500×C151C2211yescharacteristic
22#500×C151C2211yescharacteristic
23#500×C151C2211yescharacteristic
24#500×C151C2211yescharacteristic
25#500×C151C2211yescharacteristic
26#500×C151C2211yescharacteristic
27#498×C151C2211yescharacteristic
28#498×C151C2211yescharacteristic
29#498×C151C2211yescharacteristic
30#494×C151C2211yescharacteristic
31#494×C151C2211yescharacteristic
32#494×C151C2211yescharacteristic
33#492×C151C2211yescharacteristic
34#492×C151C2211yescharacteristic
35#487×C151C2211yescharacteristic
36#487×C151C2211yescharacteristic
37#487×C151C2211yescharacteristic
38#487×C151C2211yescharacteristic
39#487×C151C2211yescharacteristic
40#487×C151C2211yescharacteristic
41#486×C151C2211yescharacteristic
42#486×C151C2211yescharacteristic
43#486×C151C2211yescharacteristic
44#486×C151C2211yescharacteristic
45#485×C151—22no—
46#480×C151—22no—
47#479×C151—22no—
48#474×C151—22no—
49#468×C151—22no—
50#464×C151—22no—
51#462×C151—22no—
52#452×C151—22no—
53#451×C151—22no—
54#440×C151—22no—
55#431×C151C2211yescharacteristic
56#431×C151C2211yescharacteristic
57#428×C151—22no—
58C4×M16×C151C2211yescharacteristic
59#322×C151C2211yescharacteristic
60#322×C151C2211yescharacteristic
61#322×C151C2211yescharacteristic
62C82×C151C2211yescharacteristic
63C2×#41×C151—21no—
64C22×Q8×C151—21no—
65C2×Q16×C151—22no—
66C2×Q16×C151—22no—
67C2×Q16×C151—22no—
68C2×SD16×C151—22no—
69C2×SD16×C151—22no—
70C2×M16×C151D412yes—
71C4⋊Q8×C151—21no—
72C4⋊Q8×C151—21no—
73C4⋊Q8×C151—21no—
74C4⋊Q8×C151C2311yescharacteristic
75C4⋊Q8×C151C2311yescharacteristic
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78C4⋊Q8×C151C2311yescharacteristic
79C4⋊Q8×C151C2311yescharacteristic
80C4⋊Q8×C151C2311yescharacteristic
81#127×C151C2311yescharacteristic
82#125×C151—21no—
83#125×C151—21no—
84#124×C151—21no—
85C22⋊Q8×C151—21no—
86C22⋊Q8×C151—21no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—21no—
89#121×C151—21no—
90#121×C151—21no—
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×D4×C151—21no—
96C4×D4×C151—21no—
97#117×C151—21no—
98#117×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—21no—
101C2×C42×C151C2311yescharacteristic
102#107×C151—22no—
103#107×C151—22no—
104#107×C151—22no—
105#107×C151—22no—
106#107×C151—22no—
107#107×C151—22no—
108#106×C151—22no—
109#106×C151—22no—
110#106×C151—22no—
111C4⋊C8×C151D412yes—
112C4⋊C8×C151D412yes—
113#103×C151—22no—
114#103×C151—22no—
115#103×C151—22no—
116#103×C151—22no—
117#103×C151—22no—
118#103×C151—22no—
119#102×C151—22no—
120#102×C151—22no—
121#102×C151—22no—
122#102×C151—22no—
123C22⋊C8×C151D412yes—
124C22⋊C8×C151D412yes—
125#97×C151D412yes—
126C4×C8×C151C2311yescharacteristic
127C4×C8×C151C2311yescharacteristic
128C4×C8×C151C2311yescharacteristic
129C4×C8×C151C2311yescharacteristic
130C4×C8×C151C2311yescharacteristic
131C4×C8×C151C2311yescharacteristic
132#41×C151—82no—
133C2×Q8×C151—21no—
134C2×Q8×C151—21no—
135C2×Q8×C151—21no—
136C2×Q8×C151—21no—
137C2×Q8×C151—21no—
138C2×Q8×C151—21no—
139C2×Q8×C151—21no—
140C2×Q8×C151—41no—
141C2×Q8×C151—82no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151—21no—
145C2×D4×C151—41no—
146C22×C4×C151—41no—
147C22×C4×C151—41no—
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151Q16×C151—82no—
152Q16×C151—82no—
153Q16×C151—82no—
154SD16×C151—44no—
155SD16×C151—82no—
156M16×C151—24no—
157C2×C8×C151C2×D412yes—
158C2×C8×C151C2×D412yes—
159C2×C8×C151C2×D412yes—
160C2×C8×C151C2×D412yes—
161C2×C8×C151C2×D412yes—
162C2×C8×C151C2×D412yes—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—41no—
178C4⋊C4×C151—41no—
179C4⋊C4×C151—41no—
180C4⋊C4×C151—41no—
181C4⋊C4×C151—41no—
182C4⋊C4×C151—41no—
183C22⋊C4×C151—41no—
184C22⋊C4×C151—41no—
185C22⋊C4×C151—41no—
186C22⋊C4×C151—41no—
187C42×C151—41no—
188C42×C151—41no—
189C42×C151C2×D411yescharacteristic
190C42×C151C2×D411yescharacteristic
191C42×C151C2×D411yescharacteristic
192C42×C151C2411yescharacteristic
193C23×C151—41no—
194C23×C151#12711yescharacteristic
195Q8×C151—42no—
196Q8×C151—42no—
197Q8×C151—42no—
198Q8×C151—42no—
199Q8×C151—42no—
200Q8×C151—42no—
201Q8×C151—42no—
202Q8×C151—82no—
203D4×C151—42no—
204D4×C151—42no—
205D4×C151—42no—
206D4×C151—82no—
207C2×C4×C151—22no—
208C2×C4×C151—22no—
209C2×C4×C151—22no—
210C2×C4×C151—41no—
211C2×C4×C151—41no—
212C2×C4×C151—41no—
213C2×C4×C151—41no—
214C2×C4×C151—41no—
215C2×C4×C151—41no—
216C2×C4×C151—41no—
217C2×C4×C151—82no—
218C2×C4×C151—82no—
219C2×C4×C151#12711yescharacteristic
220C2×C4×C151#12711yescharacteristic
221C2×C4×C151#12711yescharacteristic
222C2×C4×C151C22×D411yescharacteristic
223C2×C4×C151C22×D411yescharacteristic
224C2×C4×C151C22×D411yescharacteristic
225C8×C151—22no—
226C8×C151—22no—
227C8×C151—22no—
228C8×C151—22no—
229C8×C151—22no—
230C8×C151#13714yes—
231C22×C151—21no—
232C22×C151—21no—
233C22×C151—21no—
234C22×C151—81no—
235C22×C151—81no—
236C22×C151—81no—
237C22×C151C2×#12711yescharacteristic
238C4×C151—21no—
239C4×C151—21no—
240C4×C151—21no—
241C4×C151—81no—
242C4×C151—81no—
243C4×C151—81no—
244C4×C151—81no—
245C4×C151—81no—
246C4×C151—81no—
247C4×C151—81no—
248C4×C151C2×#13712yes—
249C4×C151#57612yes—
250C4×C151#57812yes—
251C2×C151—41no—
252C2×C151—161no—
253C2×C151#315211yescharacteristic
254C2×C151#315511yescharacteristic
255C2×C151#315611yescharacteristic
256#19728C15111yesmaximal, characteristic, direct product factor, Sylow
257C151#1972811yescharacteristic, direct product factor, Sylow
258#3231C2×C15111yescharacteristic, complemented
259#3226C2×C15111yescharacteristic
260#3210C2×C15111yescharacteristic
261#3209C2×C15111yescharacteristic, complemented
262#3182C2×C15111yescharacteristic
263#3165C2×C15111yescharacteristic, complemented
264#1723C2×C15111yescharacteristic, complemented
265#1723C2×C15111yescharacteristic, complemented
266#1722C2×C15111yescharacteristic, complemented
267#1720C2×C15111yescharacteristic, complemented
268#1718C2×C15111yescharacteristic, complemented
269#1714C2×C15111yescharacteristic, complemented
270#1713C2×C15111yescharacteristic, complemented
271#1708C2×C15111yescharacteristic, complemented
272#1453C2×C15111yescharacteristic, complemented
273#533C22×C15111yescharacteristic
274#533C22×C15111yescharacteristic
275#532C22×C15111yescharacteristic
276C2×C4⋊Q8C22×C15111yescharacteristic
277#501—22no—
278#500C22×C15111yescharacteristic
279#500C22×C15111yescharacteristic
280#500C22×C15111yescharacteristic
281#500C22×C15111yescharacteristic
282#500C22×C15111yescharacteristic
283#500C22×C15111yescharacteristic
284#498C22×C15111yescharacteristic
285#498C22×C15111yescharacteristic
286#498C22×C15111yescharacteristic
287#494C22×C15111yescharacteristic
288#494C22×C15111yescharacteristic
289#494C22×C15111yescharacteristic
290#492C22×C15111yescharacteristic
291#492C22×C15111yescharacteristic
292#487C22×C15111yescharacteristic
293#487C22×C15111yescharacteristic
294#487C22×C15111yescharacteristic
295#487C22×C15111yescharacteristic
296#487C22×C15111yescharacteristic
297#487C22×C15111yescharacteristic
298#486C22×C15111yescharacteristic
299#486C22×C15111yescharacteristic
300#486C22×C15111yescharacteristic
301#486C22×C15111yescharacteristic
302#485—22no—
303#480—22no—
304#479—22no—
305#474—22no—
306#468—22no—
307#464—22no—
308#462—22no—
309#452—22no—
310#451—22no—
311#440—22no—
312#431C22×C15111yescharacteristic
313#431C22×C15111yescharacteristic
314#428—22no—
315C4×M16C22×C15111yescharacteristic
316#322C22×C15111yescharacteristic
317#322C22×C15111yescharacteristic
318#322C22×C15111yescharacteristic
319C82C22×C15111yescharacteristic
320C2×#41—21no—
321C22×Q8—21no—
322C2×Q16—22no—
323C2×Q16—22no—
324C2×Q16—22no—
325C2×SD16—22no—
326C2×SD16—22no—
327C2×M16D4×C15112yes—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4⋊Q8C23×C15111yescharacteristic
332C4⋊Q8C23×C15111yescharacteristic
333C4⋊Q8C23×C15111yescharacteristic
334C4⋊Q8C23×C15111yescharacteristic
335C4⋊Q8C23×C15111yescharacteristic
336C4⋊Q8C23×C15111yescharacteristic
337C4⋊Q8C23×C15111yescharacteristic
338#127C23×C15111yescharacteristic
339#125—21no—
340#125—21no—
341#124—21no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346#121—21no—
347#121—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×D4—21no—
353C4×D4—21no—
354#117—21no—
355#117—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C42C23×C15111yescharacteristic
359#107—22no—
360#107—22no—
361#107—22no—
362#107—22no—
363#107—22no—
364#107—22no—
365#106—22no—
366#106—22no—
367#106—22no—
368C4⋊C8D4×C15112yes—
369C4⋊C8D4×C15112yes—
370#103—22no—
371#103—22no—
372#103—22no—
373#103—22no—
374#103—22no—
375#103—22no—
376#102—22no—
377#102—22no—
378#102—22no—
379#102—22no—
380C22⋊C8D4×C15112yes—
381C22⋊C8D4×C15112yes—
382#97D4×C15112yes—
383C4×C8C23×C15111yescharacteristic
384C4×C8C23×C15111yescharacteristic
385C4×C8C23×C15111yescharacteristic
386C4×C8C23×C15111yescharacteristic
387C4×C8C23×C15111yescharacteristic
388C4×C8C23×C15111yescharacteristic
389#41—82no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—41no—
398C2×Q8—82no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4C2×D4×C15111yescharacteristic
406C22×C4C2×D4×C15111yescharacteristic
407C22×C4C2×D4×C15111yescharacteristic
408Q16—82no—
409Q16—82no—
410Q16—82no—
411SD16—44no—
412SD16—82no—
413M16—24no—
414C2×C8C2×D4×C15112yes—
415C2×C8C2×D4×C15112yes—
416C2×C8C2×D4×C15112yes—
417C2×C8C2×D4×C15112yes—
418C2×C8C2×D4×C15112yes—
419C2×C8C2×D4×C15112yes—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C42—41no—
445C42—41no—
446C42C2×D4×C15111yescharacteristic
447C42C2×D4×C15111yescharacteristic
448C42C2×D4×C15111yescharacteristic
449C42C24×C15111yescharacteristic
450C23—41no—
451C23#127×C15111yescharacteristic
452Q8—42no—
453Q8—42no—
454Q8—42no—
455Q8—42no—
456Q8—42no—
457Q8—42no—
458Q8—42no—
459Q8—82no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—82no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4#127×C15111yescharacteristic
477C2×C4#127×C15111yescharacteristic
478C2×C4#127×C15111yescharacteristic
479C2×C4C22×D4×C15111yescharacteristic
480C2×C4C22×D4×C15111yescharacteristic
481C2×C4C22×D4×C15111yescharacteristic
482C8—22no—
483C8—22no—
484C8—22no—
485C8—22no—
486C8—22no—
487C8#137×C15114yes—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22C2×#127×C15111yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—81no—
499C4—81no—
500C4—81no—
501C4—81no—
502C4—81no—
503C4—81no—
504C4—81no—
505C4C2×#137×C15112yes—
506C4#576×C15112yes—
507C4#578×C15112yes—
508C2—41no—
509C2—161no—
510C2#3152×C15111yescharacteristic
511C2#3155×C15111yescharacteristic
512C2#3156×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#127
commutator, Frattini, cosocleC42C24×C151
prime radical#532×C151C22
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
1. #3231×C151C2semidirect
4. #3209×C151C2semidirect
6. #3165×C151C2semidirect
7. #1723×C151C2semidirect
8. #1723×C151C2semidirect
9. #1722×C151C2semidirect
10. #1720×C151C2semidirect
11. #1718×C151C2semidirect
12. #1714×C151C2semidirect
13. #1713×C151C2semidirect
14. #1708×C151C2semidirect
15. #1453×C151C2semidirect
256. #19728C151direct (N × H)
257. C151#19728direct (N × H)
258. #3231C2×C151semidirect
261. #3209C2×C151semidirect
263. #3165C2×C151semidirect
264. #1723C2×C151semidirect
265. #1723C2×C151semidirect
266. #1722C2×C151semidirect
267. #1720C2×C151semidirect
268. #1718C2×C151semidirect
269. #1714C2×C151semidirect
270. #1713C2×C151semidirect
271. #1708C2×C151semidirect
272. #1453C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3231×C1512
#3226×C1512
#3210×C1512
#3209×C1512
#3182×C1512
#3165×C1512
#1723×C1512
#1722×C1512
#1720×C1512
#1718×C1512
#1714×C1512
#1713×C1512
#1708×C1512
#1453×C1512
#19728151