Finite Group Databasebeta

← C151×#18081 #50323006

Subgroups — C151×#18081 #50323006

Order 38656.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3172×C151C211yesmaximal, characteristic
2#2994×C151C211yesmaximal, characteristic
3#2986×C151C211yesmaximal, characteristic, complemented
4#1592×C151C211yesmaximal, characteristic, complemented
5#1591×C151C211yesmaximal, characteristic, complemented
6#1587×C151C211yesmaximal, characteristic, complemented
7#1585×C151C211yesmaximal, characteristic, complemented
8#1584×C151C211yesmaximal, characteristic, complemented
9#1583×C151C211yesmaximal, characteristic, complemented
10#1579×C151C211yesmaximal, characteristic, complemented
11C8×SD16×C151C211yesmaximal, characteristic, complemented
12#1565×C151C211yesmaximal, characteristic, complemented
13#1482×C151C211yesmaximal, characteristic
14#1481×C151C211yesmaximal, characteristic, complemented
15#1453×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17#529×C151C2211yescharacteristic
18#501×C151C411yescharacteristic
19#497×C151C411yescharacteristic
20#491×C151C411yescharacteristic
21#489×C151C411yescharacteristic
22#470×C151C411yescharacteristic
23#470×C151C411yescharacteristic
24#468×C151C411yescharacteristic
25#468×C151C411yescharacteristic
26#446×C151—21no—
27#446×C151C2211yescharacteristic
28#446×C151C2211yescharacteristic
29#446×C151C2211yescharacteristic
30C8×Q8×C151—21no—
31C8×Q8×C151C2211yescharacteristic
32C8×Q8×C151C2211yescharacteristic
33C8×Q8×C151C2211yescharacteristic
34C4×Q16×C151C2211yescharacteristic
35C4×Q16×C151C2211yescharacteristic
36C4×SD16×C151C2211yescharacteristic
37C4×SD16×C151C2211yescharacteristic
38#436×C151C2211yescharacteristic
39#435×C151—21no—
40C8×D4×C151—21no—
41C8×D4×C151C2211yescharacteristic
42#433×C151—21no—
43#433×C151—21no—
44#433×C151—21no—
45#431×C151C2211yescharacteristic
46#431×C151C2211yescharacteristic
47#431×C151C2211yescharacteristic
48#424×C151—21no—
49C2×C4⋊C8×C151C2211yescharacteristic
50C4×M16×C151C2211yescharacteristic
51#335×C151C2211yescharacteristic
52#335×C151C2211yescharacteristic
53#334×C151C2211yescharacteristic
54#334×C151C2211yescharacteristic
55Q8⋊C8×C151C2211yescharacteristic
56Q8⋊C8×C151C2211yescharacteristic
57Q8⋊C8×C151C2211yescharacteristic
58Q8⋊C8×C151C2211yescharacteristic
59Q8⋊C8×C151C2211yescharacteristic
60Q8⋊C8×C151C2211yescharacteristic
61D4⋊C8×C151C2211yescharacteristic
62D4⋊C8×C151C2211yescharacteristic
63#322×C151C2211yescharacteristic
64#322×C151C2211yescharacteristic
65#322×C151C2211yescharacteristic
66C82×C151C2211yescharacteristic
67C2×Q16×C151C2×C411yescharacteristic
68C2×Q16×C151C2×C411yescharacteristic
69C2×SD16×C151C2×C411yescharacteristic
70C2×SD16×C151C2×C411yescharacteristic
71C2×M16×C151—21no—
72C2×M16×C151C2×C411yescharacteristic
73C2×M16×C151C2×C411yescharacteristic
74C22×C8×C151—21no—
75C22×C8×C151—21no—
76C4⋊Q8×C151C2×C411yescharacteristic
77C4⋊Q8×C151C2×C411yescharacteristic
78#126×C151—21no—
79#125×C151—21no—
80#125×C151C2×C411yescharacteristic
81#124×C151C2×C411yescharacteristic
82#123×C151—21no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151C2×C411yescharacteristic
85C22⋊Q8×C151C2×C411yescharacteristic
86C22⋊Q8×C151C2×C411yescharacteristic
87#121×C151C2×C411yescharacteristic
88C4×Q8×C151—21no—
89C4×Q8×C151C2311yescharacteristic
90C4×Q8×C151C2311yescharacteristic
91C4×Q8×C151C2311yescharacteristic
92C4×D4×C151—21no—
93C4×D4×C151C2311yescharacteristic
94#117×C151—21no—
95#117×C151—21no—
96C2×C42×C151C2311yescharacteristic
97#107×C151C2×C411yescharacteristic
98#107×C151C2×C411yescharacteristic
99#106×C151C2×C411yescharacteristic
100#106×C151C2×C411yescharacteristic
101C4⋊C8×C151—21no—
102C4⋊C8×C151—21no—
103C4⋊C8×C151—21no—
104C4⋊C8×C151—21no—
105C4⋊C8×C151—21no—
106C4⋊C8×C151—21no—
107C4⋊C8×C151—21no—
108C4⋊C8×C151—21no—
109C4⋊C8×C151D411yescharacteristic
110C4⋊C8×C151D411yescharacteristic
111C4⋊C8×C151C2311yescharacteristic
112C4⋊C8×C151C2311yescharacteristic
113C4⋊C8×C151C2311yescharacteristic
114C4⋊C8×C151C2311yescharacteristic
115#103×C151C2×C411yescharacteristic
116#103×C151C2×C411yescharacteristic
117#103×C151C2×C411yescharacteristic
118#103×C151C2×C411yescharacteristic
119#103×C151C2×C411yescharacteristic
120#103×C151C2×C411yescharacteristic
121#102×C151C2×C411yescharacteristic
122#102×C151C2×C411yescharacteristic
123C22⋊C8×C151—21no—
124C22⋊C8×C151—21no—
125C22⋊C8×C151—21no—
126C22⋊C8×C151—21no—
127C22⋊C8×C151D411yescharacteristic
128C22⋊C8×C151D411yescharacteristic
129#97×C151—21no—
130#97×C151—21no—
131#97×C151—21no—
132#97×C151C2×C411yescharacteristic
133#97×C151C2×C411yescharacteristic
134C4×C8×C151—21no—
135C4×C8×C151—21no—
136C4×C8×C151—21no—
137C4×C8×C151—21no—
138C4×C8×C151C2311yescharacteristic
139C4×C8×C151C2311yescharacteristic
140C4×C8×C151C2311yescharacteristic
141C4×C8×C151C2311yescharacteristic
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144C2×Q8×C151—21no—
145C2×Q8×C151C22×C411yescharacteristic
146C2×Q8×C151C22×C411yescharacteristic
147C2×Q8×C151C22×C411yescharacteristic
148C2×D4×C151—21no—
149C2×D4×C151C22×C411yescharacteristic
150C22×C4×C151—21no—
151C22×C4×C151C22×C411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151#4111yescharacteristic
154Q16×C151—22no—
155Q16×C151—41no—
156SD16×C151—22no—
157SD16×C151—41no—
158M16×C151—22no—
159M16×C151—41no—
160M16×C151—81no—
161C2×C8×C151—21no—
162C2×C8×C151—21no—
163C2×C8×C151—21no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151—81no—
168C2×C8×C151—81no—
169C2×C8×C151C22×C411yescharacteristic
170C2×C8×C151C22×C411yescharacteristic
171C2×C8×C151C22×C411yescharacteristic
172C2×C8×C151C22×C411yescharacteristic
173C2×C8×C151C2×D411yescharacteristic
174C2×C8×C151C2×D411yescharacteristic
175C2×C8×C151C2×D411yescharacteristic
176C2×C8×C151C2×D411yescharacteristic
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151C22×C411yescharacteristic
189C4⋊C4×C151C22×C411yescharacteristic
190C4⋊C4×C151C22×C411yescharacteristic
191C4⋊C4×C151C22×C411yescharacteristic
192C22⋊C4×C151—21no—
193C22⋊C4×C151—21no—
194C22⋊C4×C151—21no—
195C22⋊C4×C151—21no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—21no—
199C42×C151—21no—
200C42×C151—21no—
201C42×C151—21no—
202C42×C151C22×C411yescharacteristic
203C42×C151C2×D411yescharacteristic
204C42×C151#4111yescharacteristic
205C42×C151C2411yescharacteristic
206C23×C151—21no—
207C23×C151C4×D411yescharacteristic
208Q8×C151—21no—
209Q8×C151—21no—
210Q8×C151—21no—
211Q8×C151—21no—
212Q8×C151—21no—
213Q8×C151—21no—
214Q8×C151—42no—
215D4×C151—21no—
216D4×C151—21no—
217D4×C151—42no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151C4×D411yescharacteristic
233C2×C4×C151C4×D411yescharacteristic
234C2×C4×C151C4×D411yescharacteristic
235C2×C4×C151C23×C411yescharacteristic
236C2×C4×C151C22×D411yescharacteristic
237C2×C4×C151C2×#4111yescharacteristic
238C8×C151—21no—
239C8×C151—21no—
240C8×C151—21no—
241C8×C151—21no—
242C8×C151—21no—
243C8×C151—21no—
244C8×C151—21no—
245C8×C151—41no—
246C8×C151—41no—
247C8×C151—41no—
248C8×C151—41no—
249C8×C151—41no—
250C8×C151—41no—
251C8×C151#13112yes—
252C22×C151—21no—
253C22×C151—21no—
254C22×C151—21no—
255C22×C151—41no—
256C22×C151—41no—
257C22×C151—41no—
258C22×C151C2×C4×D411yescharacteristic
259C4×C151—21no—
260C4×C151—21no—
261C4×C151—21no—
262C4×C151—21no—
263C4×C151—41no—
264C4×C151—41no—
265C4×C151—41no—
266C4×C151—41no—
267C4×C151—41no—
268C4×C151—41no—
269C4×C151—41no—
270C4×C151C2×#13111yescharacteristic
271C4×C151#56811yescharacteristic
272C4×C151#57711yescharacteristic
273C4×C151#57811yescharacteristic
274C2×C151—41no—
275C2×C151—81no—
276C2×C151#293511yescharacteristic
277C2×C151#294711yescharacteristic
278C2×C151#295511yescharacteristic
279#18081C15111yesmaximal, characteristic, direct product factor, Sylow
280C151#1808111yescharacteristic, direct product factor, Sylow
281#3172C2×C15111yescharacteristic
282#2994C2×C15111yescharacteristic
283#2986C2×C15111yescharacteristic, complemented
284#1592C2×C15111yescharacteristic, complemented
285#1591C2×C15111yescharacteristic, complemented
286#1587C2×C15111yescharacteristic, complemented
287#1585C2×C15111yescharacteristic, complemented
288#1584C2×C15111yescharacteristic, complemented
289#1583C2×C15111yescharacteristic, complemented
290#1579C2×C15111yescharacteristic, complemented
291C8×SD16C2×C15111yescharacteristic, complemented
292#1565C2×C15111yescharacteristic, complemented
293#1482C2×C15111yescharacteristic
294#1481C2×C15111yescharacteristic, complemented
295#1453C2×C15111yescharacteristic, complemented
296#533C22×C15111yescharacteristic
297#529C22×C15111yescharacteristic
298#501C4×C15111yescharacteristic
299#497C4×C15111yescharacteristic
300#491C4×C15111yescharacteristic
301#489C4×C15111yescharacteristic
302#470C4×C15111yescharacteristic
303#470C4×C15111yescharacteristic
304#468C4×C15111yescharacteristic
305#468C4×C15111yescharacteristic
306#446—21no—
307#446C22×C15111yescharacteristic
308#446C22×C15111yescharacteristic
309#446C22×C15111yescharacteristic
310C8×Q8—21no—
311C8×Q8C22×C15111yescharacteristic
312C8×Q8C22×C15111yescharacteristic
313C8×Q8C22×C15111yescharacteristic
314C4×Q16C22×C15111yescharacteristic
315C4×Q16C22×C15111yescharacteristic
316C4×SD16C22×C15111yescharacteristic
317C4×SD16C22×C15111yescharacteristic
318#436C22×C15111yescharacteristic
319#435—21no—
320C8×D4—21no—
321C8×D4C22×C15111yescharacteristic
322#433—21no—
323#433—21no—
324#433—21no—
325#431C22×C15111yescharacteristic
326#431C22×C15111yescharacteristic
327#431C22×C15111yescharacteristic
328#424—21no—
329C2×C4⋊C8C22×C15111yescharacteristic
330C4×M16C22×C15111yescharacteristic
331#335C22×C15111yescharacteristic
332#335C22×C15111yescharacteristic
333#334C22×C15111yescharacteristic
334#334C22×C15111yescharacteristic
335Q8⋊C8C22×C15111yescharacteristic
336Q8⋊C8C22×C15111yescharacteristic
337Q8⋊C8C22×C15111yescharacteristic
338Q8⋊C8C22×C15111yescharacteristic
339Q8⋊C8C22×C15111yescharacteristic
340Q8⋊C8C22×C15111yescharacteristic
341D4⋊C8C22×C15111yescharacteristic
342D4⋊C8C22×C15111yescharacteristic
343#322C22×C15111yescharacteristic
344#322C22×C15111yescharacteristic
345#322C22×C15111yescharacteristic
346C82C22×C15111yescharacteristic
347C2×Q16C2×C4×C15111yescharacteristic
348C2×Q16C2×C4×C15111yescharacteristic
349C2×SD16C2×C4×C15111yescharacteristic
350C2×SD16C2×C4×C15111yescharacteristic
351C2×M16—21no—
352C2×M16C2×C4×C15111yescharacteristic
353C2×M16C2×C4×C15111yescharacteristic
354C22×C8—21no—
355C22×C8—21no—
356C4⋊Q8C2×C4×C15111yescharacteristic
357C4⋊Q8C2×C4×C15111yescharacteristic
358#126—21no—
359#125—21no—
360#125C2×C4×C15111yescharacteristic
361#124C2×C4×C15111yescharacteristic
362#123—21no—
363C22⋊Q8—21no—
364C22⋊Q8C2×C4×C15111yescharacteristic
365C22⋊Q8C2×C4×C15111yescharacteristic
366C22⋊Q8C2×C4×C15111yescharacteristic
367#121C2×C4×C15111yescharacteristic
368C4×Q8—21no—
369C4×Q8C23×C15111yescharacteristic
370C4×Q8C23×C15111yescharacteristic
371C4×Q8C23×C15111yescharacteristic
372C4×D4—21no—
373C4×D4C23×C15111yescharacteristic
374#117—21no—
375#117—21no—
376C2×C42C23×C15111yescharacteristic
377#107C2×C4×C15111yescharacteristic
378#107C2×C4×C15111yescharacteristic
379#106C2×C4×C15111yescharacteristic
380#106C2×C4×C15111yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8D4×C15111yescharacteristic
390C4⋊C8D4×C15111yescharacteristic
391C4⋊C8C23×C15111yescharacteristic
392C4⋊C8C23×C15111yescharacteristic
393C4⋊C8C23×C15111yescharacteristic
394C4⋊C8C23×C15111yescharacteristic
395#103C2×C4×C15111yescharacteristic
396#103C2×C4×C15111yescharacteristic
397#103C2×C4×C15111yescharacteristic
398#103C2×C4×C15111yescharacteristic
399#103C2×C4×C15111yescharacteristic
400#103C2×C4×C15111yescharacteristic
401#102C2×C4×C15111yescharacteristic
402#102C2×C4×C15111yescharacteristic
403C22⋊C8—21no—
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8D4×C15111yescharacteristic
408C22⋊C8D4×C15111yescharacteristic
409#97—21no—
410#97—21no—
411#97—21no—
412#97C2×C4×C15111yescharacteristic
413#97C2×C4×C15111yescharacteristic
414C4×C8—21no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8C23×C15111yescharacteristic
419C4×C8C23×C15111yescharacteristic
420C4×C8C23×C15111yescharacteristic
421C4×C8C23×C15111yescharacteristic
422C4×C8C23×C15111yescharacteristic
423C4×C8C23×C15111yescharacteristic
424C2×Q8—21no—
425C2×Q8C22×C4×C15111yescharacteristic
426C2×Q8C22×C4×C15111yescharacteristic
427C2×Q8C22×C4×C15111yescharacteristic
428C2×D4—21no—
429C2×D4C22×C4×C15111yescharacteristic
430C22×C4—21no—
431C22×C4C22×C4×C15111yescharacteristic
432C22×C4C2×D4×C15111yescharacteristic
433C22×C4#41×C15111yescharacteristic
434Q16—22no—
435Q16—41no—
436SD16—22no—
437SD16—41no—
438M16—22no—
439M16—41no—
440M16—81no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—81no—
448C2×C8—81no—
449C2×C8C22×C4×C15111yescharacteristic
450C2×C8C22×C4×C15111yescharacteristic
451C2×C8C22×C4×C15111yescharacteristic
452C2×C8C22×C4×C15111yescharacteristic
453C2×C8C2×D4×C15111yescharacteristic
454C2×C8C2×D4×C15111yescharacteristic
455C2×C8C2×D4×C15111yescharacteristic
456C2×C8C2×D4×C15111yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4C22×C4×C15111yescharacteristic
469C4⋊C4C22×C4×C15111yescharacteristic
470C4⋊C4C22×C4×C15111yescharacteristic
471C4⋊C4C22×C4×C15111yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42C22×C4×C15111yescharacteristic
483C42C2×D4×C15111yescharacteristic
484C42#41×C15111yescharacteristic
485C42C24×C15111yescharacteristic
486C23—21no—
487C23C4×D4×C15111yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—42no—
495D4—21no—
496D4—21no—
497D4—42no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4C4×D4×C15111yescharacteristic
513C2×C4C4×D4×C15111yescharacteristic
514C2×C4C4×D4×C15111yescharacteristic
515C2×C4C23×C4×C15111yescharacteristic
516C2×C4C22×D4×C15111yescharacteristic
517C2×C4C2×#41×C15111yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8#131×C15112yes—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×C4×D4×C15111yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4C2×#131×C15111yescharacteristic
551C4#568×C15111yescharacteristic
552C4#577×C15111yescharacteristic
553C4#578×C15111yescharacteristic
554C2—41no—
555C2—81no—
556C2#2935×C15111yescharacteristic
557C2#2947×C15111yescharacteristic
558C2#2955×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC42C24×C151
socleC22×C151C2×C4×D4
prime radical#121×C151C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ #431×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2986×C151C2semidirect
4. #1592×C151C2semidirect
5. #1591×C151C2semidirect
6. #1587×C151C2semidirect
7. #1585×C151C2semidirect
8. #1584×C151C2semidirect
9. #1583×C151C2semidirect
10. #1579×C151C2semidirect
11. C8×SD16×C151C2semidirect
12. #1565×C151C2semidirect
14. #1481×C151C2semidirect
15. #1453×C151C2semidirect
279. #18081C151direct (N × H)
280. C151#18081direct (N × H)
283. #2986C2×C151semidirect
284. #1592C2×C151semidirect
285. #1591C2×C151semidirect
286. #1587C2×C151semidirect
287. #1585C2×C151semidirect
288. #1584C2×C151semidirect
289. #1583C2×C151semidirect
290. #1579C2×C151semidirect
291. C8×SD16C2×C151semidirect
292. #1565C2×C151semidirect
294. #1481C2×C151semidirect
295. #1453C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3172×C1512
#2994×C1512
#2986×C1512
#1592×C1512
#1591×C1512
#1587×C1512
#1585×C1512
#1584×C1512
#1583×C1512
#1579×C1512
C8×SD16×C1512
#1565×C1512
#1482×C1512
#1481×C1512
#1453×C1512
#18081151